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T'h4sX1t-l'4.
SCIENCEXEMESB.
l^
^m
ILLUSTBATED GIFT BOOKS.
lEEDICAL ANATOMT. ByPBANCi8SiB8ON,M.D.,F.R.0.P., F.B.S. Imperial folio. 21 Coloured Plates. Cloth, £2 28.; balf-morocco, £2 lOs.
S1TB6ICAL ASATOMT. A series of Dissections, illastrating the Principal Regions of the Human Body. By Joseph Maclise, F.B.C.S. 8ec<md EdUum, Folio. 52 Plates. Cloth, £3 128.; half-morocco, £4 48.
OB DISLOCATIOBS AND FBACTUEES. By Joseph Macijse, F.B.C.S. This Work is uniform with "Surgical Anatomy." Folio. 36 Plates. Cloth, £2 108. ; half-morocco, £2 178.
PATHOLOOT OF THE HTTMAH ETE. By John Dalbymplb, P.R.C.S., F.R.S. Imperial 4to. 36 Coloured Plates. Half -bound morocco, gilt tops, £9 158.
POBTEAITS OF DISEASES OF THE SKIN. By Es^sHrs WiMON, P.R.C.S., P.R.S. Folio. 48 Coloured Plates, life size. Half-morocco, £13.
THE THAH ATOPHIBIA OF INDIA ; being a Description of the Venomous Snakes of the Indian Peninsula ; with ar Account of the Influence of their Poison on Life, and a Series of Experiments. By J. Faybeb, M.D., P.R.C.S., C.S.I. FoUo. 31 Plates (28 Coloured), £7 78.
J. & A. CHURCHILL, New Bublinoton Stbeet.
J
Tfi£ £LEIENTS
OF
NATUEAL PHILOSOPHY.
THE ELEMEBIS OF
NATURAL PHILOSOPHY;
STUDY OF THE PHYSICAL SCIENCES.
CHAMESJSOOKE, M.A., KHS., PR.M.S,
GOLDlllG BIED, M.A., M.D., E.B.S,, F.I.S.
LONDON: JOHN onUBCHILL AND SONS, NEW BUBLINOTON STKBET.
Thv^^'^'^^n'^
PREFACE.
Love before the pnblicatioD of the last edition of tliis work in 1860, the light of physical truth had dawned on the Author's mind, but it was yet in the dim and hazy distance ; but seven years of further study and thought have served only to raise that light high above the horizon of uncertainty. A change of views was indicated in the last edition, by a substitution of the titles of " Physics of Matter" and " Physics of Motion" for the two sec- tions of the work, in place of the physics oi ponderahU and of in^pondercible. matter ; but as the above distinction of sections is illogical, and purely arbitrary, it has been altogether omitted. The numberless facts that have in the interval been observed and recorded, have tended only to confirm the opinion that the various physical agents are not forms of matter, but modes of motion; and that the unnatural quality of imponderability, or exemption from the universal law of gravitation, need no longer he reckoned amongst the physical attributes of any kind of matter : these views will be found more fully developed in the Introduction.
The ideas of the late Author were mainly those current in his day, and they were embodied or implied in the language in which the physical facts were expressed and explained. But as most of these views have been completely changed, an entire change of diction became necessary ; and of the original treatise, the bare facts, common, more or less, to all elementary treatises on Physics, alone remain : it would therefore have been unreasonable to retain the much- respected name of Grolding Bird, as author of the present treatise, which contains numerous facts and principles that were imknown at the date of his decease. This edition is the third that has passed through the present Author's hands, each of which has received considerable modification and extension, but neither to nearly so great an extent as the present : which somewhat resem-
VI PREJfACB.
blcs the fowling-piece in the old story, that had first a new lock, then a new stock, and lastly, a new barrel ; after which process of renovation, it is needless to say that not much of the original prodaction remained.
Amongst many other important topics, the magnetic properties of iron in relation to marine architecture, the determination of electrical constants, submarine telegraphy, the relations existing between electric energy and the fnnctaons of muscles and nerves, spectrum analysis, and the nature and properties of heat, have each received a lai^ge development since the last edition was published, and it is sincerely hoped that neither in these, nor in any other department of physical science, has any important branch of the subject remained entirely unnoticed.
Again the Author earnestly requests of his readers a communi- cation of any observed errors or deficiencies: several minor additions and improvements, occurring in the present edition, are due to the kindly-expressed views and wants of careful and intelligent readers.
10, FmaoT Sqttabk, Mag, 1807.
TABLE OF CONTENTS.
INTEODTJCTION, Page xxi.
CHAPTER I. ; Page 1.
KLBVENTASr LAWS AND PBOPBHTIBS OP UATTBR — IKTEBNAL OS
UOLKCT7LAR FOBCE8.
If.B, — The numhtrt re/tr to paragrapkt, not to pages.
Dnittbilitj of matter ... 1
PnmertiM of matter ts
lIolMiilar forces 9,10
Att6iK»7prt>pertin of matter 12—19 I^efinite aggregation of mole-
ealet
Forms of crrttalB
Primary ana secondary forms Law of symmetry in crystals ... Remarkable deriatkms Twin crystals
... ao— 22 i Dimorphoos snbstances
23,24
2o 28 29 27 28
CHAPTEE 11. ; Page 18.
PIOPBBTIBS OF MASSES OF UATTBB — BXTBBHAL P0BCE8.
DtfAision of gases ... ... 47
Ansell's fire-damp indicator ... 48
Transpiration of gases 48
DilTUsion of liquids W
FricUon of sar&ees 62—65
Friction of cordage 56
Friction rollers 67
Gravitation 68-82
Weight 83,64
|
AUnettTe forces |
... 30,31 |
|
Coheiion |
82 |
|
Cohcsioa figmres of oils |
33 |
|
Adhesion |
... 84,35 |
|
Oi(ii»aiy attraction ... |
... 86—40 |
|
capillary repulsion ... |
41 |
|
Gaieoas adhesion |
43 |
Apparent attraction and repulsion 43 E&<loiaiose and exosmose ...44—46
CHAPTER IIL; Page 38.
STATICS— OB THR MBCHAKICAL BELATIONB OF BODIES AT BEST.
8tstioi *nd dynamica distin-
gvidMd 65
BqnUibrium of pressures ... 68 Pnoores repreiented bj Unes or noobcrs 67,68
Composition and resolution Kesoltant of pressures... Parallel pressures Moment of a pressure ... Equilibrium ot moments
69
70—74
75,76
77 78—90
▼Ill
TABLE OF C0KTEKT8.
Theory of couples 81—83
StiuUcal problems 84
Centreofgravitj 86,86
Centre of gravity of a line ... 87 Centre of gravity of a sorfkoe ... 88, 89 Centre of gravity found by sus- pension ... ... ... 00
Centre of gravity in a body of
variable density 92
Equilibrium 93,94
Stability 96
Path of the centre of gravity 96—100
Equilibrium ol a cone 101
Construction of an arch . . . 102 EquUibrated arch ... 103—106 Equilibrium of the arch in prac- tice 106—108
CHAPTEB IV. J Page 69.
THE MECHANICAL POWERS, OB 8IUFLE MACHINES.
Exchange of time for power ... 109
The lever 110-113
The balance 114
Balance of precision 116
Weighing with fklso bslances... 116 Method of double-weighmg ... 117 Power of the lever ... 118,119
The steelyard 120
Varieties of levers ... 121—125 Principle of virtual velocities ... 126 Principle applied to the lever... 127 Roberval's balance ... .. 128
Weighing machine 129
The gcnou; lever press ... 180 The wheel and axle lai
The pulley 132,133
Systems of pulleys ... 134—136 Conditions of equilibrium ... 137
Diflbrential pulleys 138
Chinese capstan 138
Rigidity or cordage 139
The inclined plane 140
Conditions of eqnilibrixmi ... 141 These determined by experiment 142
The screw 143
Differential screw 144
The wedge 146,146
The eccentric cam 147
Animal mechanism j examples of levers 14S— 160
CHAPTEB v.; Page 63.
rBINCIPLES OF MECHANISM.
Ol^ect and definitions ... 163—169 Elementary combinations ... 160
Constant velocity-ratio 161
Velocity-ratio in link-work ... 162 Velocity-ratio in contact motions 163
Amount of sliding 164
Boiling contact 166—169
Form of surfaces ... 170,171
Frictional gearing 172
Varieties of toothed wheels 173—179 Forms of teeth of wheels 180—187
Teeth and staves 188
Necessaiy number of teeth 189—192 Addendum, clearing ... 193—196 Practical forms of teeth 197—201
Endless screw 202—206
Uultiple gearing ... 206,207
Wrapping connectors ... 208,209
Forms of pulleys ... 210—216
Parallel link-work ... 217, 218
Link-work in general ... 219—223
Combinations in trains. . . 226-231
Calculating machines 232
Difference engine 233
Principle of its action 234
Varyhig velocity-ratio hi wheel- work 236—240
Varying velodty-raUo in contact
|
motion |
• ■• |
241—243 |
|
Parallel cones ... |
• •• |
244 |
|
Fusee |
• • • |
246 |
|
Expanding pull^ Hooke's joint ... |
• •• |
246 247—260 |
|
Hangle-wheels ... |
• »• |
261,262 |
|
Mangle-rack |
• •• |
263 |
|
Cams |
«■ a |
264 |
|
Swash-plate |
• • • |
266 |
|
Escapements ... |
■ •• |
266-268 |
|
Propelments |
• •• |
269 |
|
Reciprocating linkwork |
260—264 |
|
|
Ratchet and click |
• •• |
266—267 |
|
Silent dick |
• •■ |
268 |
TABLE OF OOMTXIITS*
IX
CHAFTEB YT. ; Page 143.
]>r«AiaC8 — THB BEULTIONS OF BODIES IN UOTIOV.
of motion [asure of Telodtj Beiative reloci^... Aeodexstin^ force Man<tfabodj ... Yolome of a oody Momentain
The eooeossion foxe ... Pint law of motion Sesood law of motion ... ParalleloffTam of vdodtiea Third law of motion ... Ccdliai<» and impact ...
Elasticity
CoUiaion of indaatic bodies Collision of elaetio bodies Inetdence and reflection SSbcta of impact
Gravitation
Morin'a apporatoa Attwood'a machine Yalne of the force of gravi^ Motion of prqjectiles ...
Parabolic patb
Tdodty of projection ... Greatest eleration
Hmcofflirht
HorizontaTraoge
OUIqaeranffe
AUb in a resisting medlnm Prindple of the rme ...
The Mini^ ball
Fli^bt of a rocket dotation and translation
.. 270
271
272
273
274
.. 276
276, 277
278,281
280
282
283
284,285
286,287
289.290
291,282
283—296
296
297
298—300
301
303
304—306
307
I.. 908
I.. tnW
310 311 312 813 814 315 316 317 818,319
Centrifugal foroe ... 820—4124 Formation of Saturn's ring ... 826 Motion on inclined planes 828; 327
Motion on a corre S2S
Motion of a pendulam 829
Oscillation in a cycloid 830
Time of oscillation ... 831,332 Length of a pendalmn . . . 383, 834 Application to terrestrial phy- sics 836—837
Conical pendulam • 388
D'Alembert's principle 839
Conservation of vis Tiva 840, 841
Unit of work 34S
Accumulated energy ... 818—846
Moment of inertia 846
Centre of oadllation ... 847—849
Kater's pendulum 350
Centre of pereussion ... 861—363 Compeniated pendulums 864—866 Botation of plane of oscillation 867, 368 Rotation of a rigid body 86&-868
Examples of rotation 864
Thegyraaeope 366—367
PrecMsiou and nutation ... 368 Vibratory motion ... 869, 370
Pro^TdSsive undulations ... 371 Stationary undulations ... 872
Nodal points 373
Vibrations of rods . . . 87^ 376 Transverse and longltucUnal vi- brations 876
Longitudinal vibrations of arow
of particles 877
Vibrations isochronous 378
CHAPTEB TIL; Page 208.
BTDBOSTAT1C8 — THE FB0PEBTIE8 OF FLUIDS AT BEST.
Properties of floida 879
Their elastidty 880
Oorsted's piexometer 881
C<mipression of fluids 882
Johnson's pressure-gauge ... 383 Socikce of liquids horizontal 884, 885
Spirit level 386
Level sur&ce in communicating
vessels ... ... ••> ... 09/
Hydrostatic level 388
Artesian well 389
Level of liferent fluids ... 390
Level of the sea 891
Pressure on the base of a vessel 892 HydrosUtie'* paradox" ... 893
Bramah's ^ress 394
Hydranlicjack and punch ... 896 Vessel of greatest strength ... 396
Upward pressure 897
Lateral pressure ... 898—400
Centre of pressure 401
Besultant pressure ... 402,408
Equilibrium of floatiDg bodies 404,406 Metacentre 406
TABLE OF CONTENTS.
StabOiiy of flotation ... 407,406
Equilibriam of immenod body 409 Principle of Archimedes 410, 411
Specific ffravity 412
Means or determining it 413—417
HTdrometer 418
Kicholaon's hydrometer ... 419
Hare's hydrometer 420
8tereometer 421
Temperaturo-rarrection of spe^
dfic grsTitics 428
Specific gravity of gases ... 423
luiamples 424
Table of specific graTlties ... 426
CHAPTEE VIIL ; Page 232.
HTDBODYNAMICS— THE PROrSBTIES OF FLUIDS TN MOTION.
Laws of sponting fluids 426, 427
Vena ooutracta 428
M. Lacontoure's results ... 429
Barker's mill 430
Velocity in channels 431
Springs and fountains 432
Geysers hi Iceland 433 '
Friction of li<)uids 434
Action of conical tubes ... 435
Lifting pump 436
Forcing pump 437
Stomach pump 439
California pump 439
Fire engine 440
Hydraulioram 441
Centrifhgal pump 442
Appold'spump 443
Chain ana bucket pump ... 441
Bope pump 445
The syphon 44A
Tantalus' cup 447
Hiero's fountain 448
Persian wheel, &C. 449
Water wheels 450
Turbine 451
Paddle wheels 452
Screw-propeller 453
Windmill sail 464
Steam-engine 456
Watt's steam-engine 466
Non-condensing en^ne ... 457 Stationary, locomotive, and ma- rine engines 458
Water-engines 469
Steam-hammer 400
Gyrometric governor 461
Undulation of fluids 462,463
Reflection of undulations . . .464, 466 Interference of undulations ... 466 Inflection of undulations ... 467
Lateral accumulation 468
Undulations of elastic fluids 469—471
Theory of Tides 472,473
Sprinv and neap tides 474
Establishment of a port ... 476 Double tides 476
CHAPTEB IX.; Page 268.
FNEUHATIC8 — THE PROPERTIES OF ELASTIC FLUIDS.
Composition of the atmosphere 477
Finite extent of the atmosphere 478
Elasticity of the atmosphere . . . 479 Weight and pressure of the
atmosphere 480—482
Water barometer 483
Mercurial barometer ... ... 484
Syphon barometer 485
Standard barometer 486
Correction for temperature ... 487
Correction for capillarity ... 488
Conical barometer 469
Horary variations 490
Mean diurnal height 491
Annual variation ... ... 492
Geographical variation ... 403
Height at difi'erent altitudes ... 404
Self-registering barometer ... 496
Vedy's aneroid barometer ... 496
Bourdon's aneroid barometer... 497
Bojrle'slaw 406—600
Weight of the atmosphere ... 601
Preesure-gaoge 602
Exhausting syringe 603
Air-pump 604
Smeotons air-pump 606
Cuthbert's and Grove's air-pump 606
Barometex^gauge 607
S}'phon-gauge 606
Condenser 600
Air-gun 610
Pneumatie experiments ... 611
TABLE OF 0OKTEHT8.
Xt
of tbe fttmofiphere. . .
Vareef ■ sppantoa
Hdgbt of aoifonn atraoc^here ^'^ of denritiw of dry air and
Presrare of mixed gasM Prassore of airandvaponr ., Fl^irieal propertieB of yapoor Pmrare of fapoar
612 613 514
616 616 617 618 619
Premxre of steam 620
Lateral pressore of gaaee . . .621, 622
Pressure of wind 623
Anemometers 624
Self-registering anemometers 626
Forecasts of weather 626
Pneumatic lerer 627
Compressed air engine 628
Lenoir's gas engine 629
CHAPTER X. ; Page 204.
acoustics; THB PBODOCTIOIT, TRANSMISSIOIV, AITD PBBCBPTIOll
OF SOUND.
Natvie of soond Isoehronooa Tibrations Inftrior numerical limit GoDdoctiDg medium essentia] Inteosity of soand
690 631 632 633 634—536 ...537,633 ofHelmhoItz ... 639 ion of sound ... 640
CoDcarrence of sounds ... 641
Velocity of sound in air 642-^644
Tdocsfcf of soond in varioos
txidiea 645>-648
InterfereDce of sound 649, 650
Pboaographfl 661,562
Opdcal aeoostie fisfures ... 663 Bxamidas of interference ...664^ 656 riiiisur of sound through hete-
Yogeaaoua media 666, 657
Ooatinnitj of direction 658, 669
Beflectioo of sound 660,662
EdkO ... ... ... ... 661
Be&adiOD of sound 563
Acoustic lens 664
Inflection of sound 666
Siren .•• ... ... ... 666
Timbre, or quality of tone . . . 667
Musical notes 668
Length of sound-waves 569, 670
Yariations of pitch 571
Normal diapason 672
Scheibler's tonometer 673
Musical intenrals 674
Harmonic sounds 676
Vibrations of chords 576, 677
Vibrations of rods 578
Vibrations of air in tubes 679—681 Modes of exciting them ... 682
Vibrations of plates 583, 684
Vibrations of membranes ... 586 Strehlke's experiments ... 586
Trevelyan's experiments ... 5S7
Vocal sounds 688
Vowel sounds 689
Forced Tibntions 690
CHAPTEB XL; Page 839.
XAORBTISIC.— DIAMAGNETISIC.
On^gin of magnetism 691
Magnetic field 692
P^iles of A magnet ... 698,594 Magnetic inductioii ... 695,596 Magnetism a molecular pro- perty 697—600
Hie mariner's compaae 601, 602
Devlatioo of the compass ... 608
Soorees of deviation 604
Varieties of deviation 606
HorixontAl and rertical induo-
tkni ... ... 606
Hedii^ error •.• 007
Tonstrlal polaiity 609
Declination 609,610
Inclination— dipping needle ... 611
Aclinic lines
Kraflt'slawofthedip
Secular change of dip
Solar diurnal variation of decli- nation 616,616
Lnnar-diumal change of deoU- nation ... ... ... ...
Annual change of force
Horizontal and vertical compo- nents of total force
lyisturbance variations
Periodicity of variations
612 613 614
617 618
619 620 621
zu
TABLE OF CX>HTBKTB.
HMDiofobMiTAtioii ... 622,623
Antomatio registration ... 624
Magnetie storms 626
Eanh-ourrents 626
Local changes of intensity ... 627
VagDetism a <(Jrec<»o« force ... 628
Consecutive poles 629
Manetio metals 680
Moaes of excitation 831
Single tooch 632
DoiU)letonch 633
Jaoobi's method 634
Gompoimd magnets 636
Magnetic capacity 638
Temperatore-change of force... 687
Magnetic metals 688
Law of magnetic attraction ... 639
Artificial magnets 640
Diamagnetism 641— -644
Diamagnetic bodies ... 646—648
Dinmagnetic fluids 649
Effects of msgneUsm ... 660,661
Influence of molecular aggre- gation on magnetism 662, 668
CHAPTER XIL; Page 366.
FBAKKLnriC ELECTRICITT.
Excitation of electricity ... 664 Attraction and repulsion ... 666 Positive snd negative electri-
city 66B
Conduction of electricity 667, 658
Insulation of electricity ... 669 Concurrence of opposite forms 660
Electroscopes 661—662
Baddiffb's electroscope 663
Coulomb's electrometer ... 664
Peltier's electrometer 666
Thomson's electrometer ... 666 Excitation of various bodies 667—669
Pyro-electric minerals 670
ETolution of light ... ... 671
Superficial distribution ... 672
Electrostatic laws 673
Potential depends on surfhce 674^ 675 Electric induction ... 676—678 Kind of electricity tested ... 679 Spedflc inductive capadtr ... 680 IvadaVs theory of induction. . . 681 Examplos of induction ... 682—684 Electrophorus ... 686—688
Theory of points and knobs ... 689 Earliest electric machines ... 690
Cylinder machine 691
Plate machine ... 692
Mode of using a machine ^ 693
Formstion oioxone 694
Development of potential ... 695
Action of amalgam 696
Ebonite plate 697
Hydro-electrio machine 696—700
Holt^ induction machine 701, 792
Brush and star 703
Sparks in Interropted oondoctor 704
Lane's discharger 706
Induction in a racuum 706^ 707
Heat accompanies a spark 706, 709
Henley's electrometer 710
Electrical toys ^ 711
Convective currents of air ... 712 Dynamic energy manifested ... 718 Spark evolves coloured light ... 714
Forms of discharge 716
Potential constrained 716
Induction on glass plates 717—719
Lerdenjar 720,721
Jomted discharger ... ... 723
Charge by induction 723
Leyden battery 724^726
Residual charge 726
Velocity of electricity 727
Charge not in the coating ... 728
Universal discharger 729
Eflbcts of discharge ... 730^781
Identity of electricity 732
Heat evolved l^ discharge ... 783 Light evolved bv discharge ... 784 Fiffures of Leuchtenberg ... 786
DifiVision of potential 736
Unitjar 737
Condenser 788—740
Multiple inductor 741
Applications of condenser ... 743 Lateral induction ... 743, 744
Unipolar bodies 746
Gradations of oondnctiTity ... 746 Potential of the atmosphere 747—763 Potential of clouds ... 764—766 Lightning conductors . . . 767, 768
cuiguiiies ... ... ... /Ov
St Elmo's lights— Aoiota ... 760
TABLS OP OOHTKVTB.
••• XIU
CHAPTEB XnL; Page 424.
YOLTAIO ELEGTSICITT.
Amrent flrrfUtion hj contact ofmetila ... ... ••• 761
Sflbet doe to ebemieal aotlon. . . 762 Beetric and ehamifal aotioii re- lated 763
ElaetrlcaeTiet of elements ... 761 Toltaie aetlon of zinc and copper 76 >
Comae of tbe current 766
Conent dneio diemieal action 767—770
Saiee^a battery 771,772
Two flnids emplojed 773
Oaoieirs cell 774
Bkctrotype ... .*« ... 776 G rove's cdl •.. «■* ... 776
Booaen'seell 777
Scbonbeln'e cell 778
MOTnoothoell 779
Sobcrts's batteij 780
Leeson'g battery 781
PlsHnnm^potaasiiim comUna- tion ... ... ... ••• 782
ZfaM-csrbon battery excited by
anlpbate of mercury 783
Modes of prodadngcarrenti 784—787
YolU'spile 78d»789
Pahrermaehei's cbsin-piila ... 790
Blrin^feUow'B battery 791
Marie Dayy'i pile 792
Crailuhanrs Dattexy 798
Snlell's battevy ... 79^795
Grovels battecy 796
Obm's theory 797
SadoedoDsfttmit ... 798^799
b's bridge 800
Form fVeqaently naed 801
Unitofresistaooe 808
Resistanoe coils 803
Kneostat ... ..■ ... ... 80a
Condnctivity of metals 805
Kleotrio light 806—809
Serrin's electric lamp 810
Slratiaed discharnre 811
Inflaenoeofresistanoe... ... 812
Insolation by a vacunm ... 813 Inflaence of magnetism ... 814
Ignition of wire 816
Oalranio Icuife and canteiy ... 816 Cold produced by a current ... 817 Dry piles ... ... ... ... 818
Grove's gas battenr ... 819,820
Water decomposed ... 821,823
Ozone formed 828
Ozone generator 834
Definite electrolyiie ... 825—827
Voltameter 838
Secondary currents 828
Contrary energy... of th<
830 CondacCiTity ot the fluid !.'! 831 Electrolysis by one element 832—834
Beoquerel's battery 835
Seduction of metals ... 836—839 Reduction of ammonium 840,841 Electrolysis by a fl^nklinio cur- rent 842,843
Apparent anomalies ... 844—846 Bednctlon of salts ... 847,848
Franlilinio and voltaic currents compared 840
CHAPTEB XIY.; Page 478.
ELECTRO-DTKAMICB.
ActhmofaenrrentoD a magnet 850^ 851 1
Ampere's law 862
Law of amount of action ... 853
jBvenor ... ... ... ... 864
Galvanometer 856
Astatic needle 856
SquUfbrlnm of needle 857!
Bensltfve galvanometer ... 858 Tlkomson's reflecting galvano- meter ... ... ... '•• 8)9
nomaon's marine galvanometer 860
Gaogain's tangent galvanometer 861 MagaetiamolAeo&diiGtor 862,863
Mutual action of ourrenta ... 864 Roget's galvanic spiral ... 866
Rotation of a magnet round a
conductor 866
Rotation of a conductor round a
magnet ... ... 867,868
Vibrating conductor 869
Spur wheel 870
M agnetic effects of a current 871, 872
Dels Rive's ring • 873
Rotation ofDe la Rive's ring 874
Electro-d>namic cylinder 875, 876 Ktoctro-magnets ... 877* 87B
XI?
TABLB OF COKTBKTS.
Botation of magnets ... 879,880
Botation of one condootor
round another ... 881,883
Theory of Ampere ... 883,884
Electro-dynamio engines ... 886 Induced, or secondary cur- rents ... ... ... 886 — 880
Self-indaction in a coil. . . 880, 891 Elongation of a bar by magne- tisation 892
Shock from seoondazy coil ^ 893
Currents in a revolving disc ... 894 Electro-magnetic machines 896—807
Inductorium 896—908
Faraday's original experiment 904 Magneto-electrio machines 906 — 907 Siemens and Halske's magneto- electric machines 906
Wilde's magneto-electrio ma- chines 911
Induced rotation ... 912,913
Induction on varioiu metals ... 914
CHAFTES XY. ; Page 614
ELECTRO-TELEGBAPHY.
Ronalds' telegraph 916
Needle-telegraph 916
Communicator of needle-tele- graph ... ... ... ... 917
Alarum-bell 918
Wheat8tone*s rotating disc tele- graph ... ... ... ... 919
Wheatstone's magneto-telegn^>h 920 The first magneto-telegraph ... 921 Siemens' magneto-telegraph ... 922 Wheatstone's private tele- graph 923—926
Morse key 926
Horse telegraph 927
If orse alphabet 928
Horse printing telegraph ... 929
Belay ... ... ••• ... 980
Siemens' polarised relay ... 931 Bain's eieotro-chemical tele- graph ... ... ... ••• 932
Wheatstone's printing telegraph 933 Wheatstone's automatic tele- graph ... ... ... 084
Buewell's copying telegraph... 936
Conditions of long circoits ... 936
Submarine tel^raphy ... 937
Siemens and Ualske's cable ... 938
Hooper's core 939
F. Jenkin's diiforential gearing 940
Electrical teste 941
Resistances of metals and alloys 942 Resistances of copper, ftc., at
various temperatures ... 943
Insulation teste 944
Induction teste 945
Teste for fkulte in a cable 946, 947
Teste for fkulte in land Unes ... 948
Tests of resistance of a battery 949
Electro-magnetic loom 950
Electric docks 951
Bain's electric clock 962
Shepherd's electric clock ... 963
Froment and Hardy's clock ... 966
Synchronous docks , 956
Wheatetone's chronbsoope ... 967
Chronofrraphs 968,060
Greenwich time-bell Electric regcdator
060 961
CHAPTEB XVL; Page 646.
THEBKO-ELECTRICITT.
Origin of thermo-dectridty ... 962 iniermo-series of metals ... 968 Current from one metal un- equally heated ... ... 964
Cmnent shown by attraction... 966 Thermo-dectric rotation 966,967
Thermopiles 968,969
Pdtier's hygrometer
Beoonerd's and Marcus* thermo-
Conversion of thermic and dy- namic onergy
ThermoHsnrrente of low poten- tial
w.— * ... ... ... ...
Thermo-dectric oombinatioDS
970 Eleotro-thennio eflBMta...
971 972
m
974 976
TABLE OP COMTEHTS.
XY
CKAPTEB XVIL; Page 662.
OBOANIO ELEGTBIdTT.
SItetrielbhes 976
ToTpeik) 977
GymDotot 978
Fvadaj'B experiments on gjvch
notofl 979
Direettooof emrrent in gymnotna MO
Silanis 961
Electric imectfl 982
GahraBii's discovery 983
Yolta't experiments 984
Aldlni'f experiments ... ... 985
LawofVaUi 968
Kenro-electric theory ... 987,988
Vncealsr currents 989
Matteofid's fVotr-bftttery ... 990
Mstteood'a ftog rheosoope ... 991
Pigeon-battery 992
Dlieetion of currents 993
Proper corrent in frogs ... 994
BeseanhesofDaBois-BeynKmd 996
BeaeaRhesordianveaa ... 996
Fh^ological effects of a onrrent 997 Evidence in favoor of the dy- namic theory 996
PhvBiological effects not dne to
direction of current . . . 999, 1000 Muscular and nerre currents subside with functional acti- vity 1001
Eckbard's experimimts ... 1002 Rate of transmission in nerves 1003 Time of - transmitting impres- sions 1004^1006
Electricity firom friction ... 1006 Electricity firom chemical
changes 1007—1009
Liebig's theory lOlO
Indications of potential 1011,1012
Piles of organic tissue 1013
Electricity in animal ftmo-
tions 1014—1016
Vegetable electricity 1017
CHAPTER XVIIL; Page 676.
LIGHT — CATOPTRICS AHD DIOPTBIC8.
Naftnre of light ... ... •••
Undnlatory hypothesis Means of transmission Natare of wave-motion Analogies of sound and light ...
Telodty of light
Lizminoail7 1024^
Law of intensity
Fhotocnetry ... •*•
Cokored rays 1028,
Modifications of light
Direction of rays
Law of illumination
BeAeetaon of light ... 10S3— Bcflection from a plane Image defined ... ... ...
Baecwaion of images
Eefleetlon from a concave mir- ror-focus 1039 — '.
BcAectlon firom a oonvez mirror
Caustie carves
Image in concave mirror Image in convex mirror
SpheriMl aberration
Least circle ci aberration ObUqiae reflection— focal lines CSrele of least confiiaion
:oi8
019 .020 1021 022 .023 026 .026 .027 i020 .090 031 032 066 086 .087 038
.041 042 .043 044 .046 .046 .047 048 .049
Curve of sorfiMe of mirrors 1060, 1051 Fouoault's gloss speculum ... 1052
Method of silvering 1063
Refraction— law of sines ... 1054 Mutual direction of ravs ... 1065 Movable diagram of refraction 1066
Index of refraction 1057
Relative refraction 1058
Velocity varied in refraction ... 1069 Intemu reflection — limiting
angle of refiraction 1000
Irregular refraction 1061
Newton's experiment 1062
Direction of refracted rays ... 1063
Prism 1084
Refiraction at a spherical sur*
ilMiO 1065,1006
Caustic bvreflm^ion 1067
Forms of lenses 1068
Fochs of a sphere ... 1069, 1070 Refiraction through a lens ... 1071
Focus of lenses 1072
F06US of concave lenses 1073—1076 Focal length of combinations 1076 Images formed by lenses 1077, 1078 Magnifying power ... 1079^1080
Spherical i
ition in lenaes 1061
ZTi
TABLE OF CONTEVTB.
CHAPTEB XIX.; Page 611,
UQHT — CIIJU>MATIC8.
Prismttlc deeompoeitioii Goloon in solar Bpectnun Beflraottre indices of coloured rays Kecompodtion of colourless
MM^Mmw ••■ ■■■ ••• ■••
Leiwth and Telocity of waves
of ooloared light
LaTender band of Herschd ...
Simple oolonrs
Primary ooloors
Superposed spectra ... ...
Ccnnposition of colours
Gornam's colour-top
Absorption by transmission ... Absorpti<m by reflection
Mean rays ofspectrum
Prismatic dispersion
Dispersive powers
Irrationalitr of spectrum
Fraunhdfers lines
Absorption bands
Indices of fixed lines
Temperature-ebaDge of index ...
Lonjgmapofspec^m
Variation of light in upectrum Tariation of heat in spectrum Variation of chemical action 1106, Spectrum-analysis
082 083 084
066
086 067 068 089 090 091 092 093 094 096 096 097 098 099 100 101 102 103 104 106 107 108
Cttsium, Rubidium, and Thal- lium discoTered
Spectra of gases
Character of Ifaies in spectrum
Inferred nature of solar photo- sphere ... ... ... ...
Spectrum of a temporary star
Fluorescence
Spectrum of invisible rays
Laws of fluorescence ...
Ingesta detected
Phosphoresceuce
1108 1109 1110
nil
1113 1118, 1114 1116 1116 1117 1118 Chromatic aberration of a lens 1 1 19
Mode of correction 1120
Interference of waves 1121
Analogy in sound 1122
Experiments on interference 1128,1124
Difflraction 1126
Explanation of diffhustion ... 1126 Experiments ou diffraction 1127—1131 Colours of thin plates ... 1132
Complementary colours ... 1133 Kewton's chromatic table ... 1134 Rings in.bomogeneous light 1136, 1136
ThinplHtesofair 1137
DiffWiction by small particles 1138 Barton's buttons— Moberfs lines 1118 Theory of the rainbow ... 1140
CHAPTEB XX. ; Page 648.
OPTICAL IKBTRUMEMT8.
The concave mirror ... ...
Newton's telescope
Chregory's telescope
Cassegr^u's telescope
Browning's equatorial telescope Speculum and plane mirror of tdescope ••• ...
Camera ebscora
Megascope
Prismatic lens
Solar microscope
Magic lantern
Camera ludda ... •.• ...
Mirror of Soemmering
Stanhope and Coddington lenses
Shnple microscopes
'Wollastou's doublet
Compound microscope
Achramatio microscope
Compound olyectives
Roar a<yustinigol4eetive
1141 Ne([ative eye-pieoe • 1160
1142 Positive eye-inece 1160
1143 Modes of obtaining Ugh power 1161
1144 Wenham's binocular microscope 1162 1146 Modem compound microsoope 1163
Magnifying powers 1164
1146 Adjustment of illumination
1147 necessary 1166
1148 Dark-ground illumination ... 1166
1149 Glllitrs condenser 1167
1160 Oblique illumination 1167
1161 Amid prism 1168
1162 Kelracting telescope 1169
1163 Erecting telescope 1170
1164 Galiho's telescope 1171
1164 Opera gUuses 1172
1166 ' Spectroscope 1173
1166 i Rigid spectroscope 1174
1167 I Straight spectroscope 1176
1168 I Speciro-Rucroacope 1176
1160 I Fahrenheit's heliostat 1177
TABLB OP 00HTBST8.
mi
flnbsrmann's helkMtei 1178
StnifCture of the eje 1179
BefravtioD of the hamoan ... 1180
Their action on light 1181
Xjei of the higher orders liniilar
iaatructure 1182
Fonaation of images 1183
The two imagee corohlned ... 1184
Sllbet of hlno<ailar Tiflioa ... 1185
Ailaptation of the ^e 1186
M jopie vt«ioo 1186
Pnabjopie Tiaion 1187
Astigmatiam 1188
Duration of ImpreMioDt on the
retina 1189
Spectral coloars ... 1190—1193
Coloor-biindnees 1194
Binocular Tiition 1196
Itefleeting stereofcope 1195
Refiractiug stereoeoope ... 1199
Pieudoaoope 1197
Ophthalmoscope 1198
Larrngoaoope 1198
Kodofloope 1199
GHAPTEB XXL; Page 688.
POLABIZED UGHT.
Dooble refraedon, ordinary and
extraord nary rays
Principal aection in oystali ...
Optic axia
Uniaxial ciyatala
Hnjgena' law of ▼dodties . . .
Lawofrefractioo
Biaxial crystals
Beriation of both rajs
ftrahi prodneea doable refraction
Form oT wave-ftront
Plane of polarization
Modes of polarixlog
jneol'8 prism ... ••• ...
DoaUe-image prism
Folariayon by agate
Polarisation by tonrmaline ... Pdariation hy hcrapathite ... Biof s polarisoope latcsstty of polarised light Identity of polarized Hsrht Actum of a Dandle of plates Piitlal poiarixation ... Bktwater's law of tangents . . . Polarisation by internal reflection Polarixation of coloured rays ... Polarisation of day-light Wbeat«toae'a polar cloclc Iaws of Arago and Fresnal ... Ttau of vdenite plates Oomplnncntary tints .., Biafs <^ intorterenoe .. BiagB in calcite
1200
1-aOI
1202
1203
1204
1206
1206
1207
1206
12Q0
... 1210
... 1211
... 1212
... 1213
... 1214
... 1215
... 1216
1217, 1218
... 1219
... 1220
... 1221
1222,1223
... 1224
1226
1226
1227
1228
12z9
1230
1231—1234
1236,1237
Interferenoe of positiTe and
negstive crystals 1238
Rings with homogeneous light 1239 Rings in biaxial crystals 1240-1243 Rings in nitre. Ac. ... 1244^ 1246 lirewBter's mode of analysis ... 1246 Rings in aiiaunealed glass 1247^1260
Leconnt's polariscope 1261
Depolarization by organic sob*
stances 1262—1265
Circular polarization 1266
Resultant waves ... 1267, 1268
Fremel's rhomb 1269
Actiun of quarts 1260
TioU produced 1261
Rotation of rays ... 1262,1263
Tints always mixed 1264
Boution by msgnedo energy 1266, 1266
Blot's apparatus 1267
Rotating power of Tarious
bodies 1268—1271
1272 1272a 1273 1274 1275 1276 1277
1278 1279 128(k
Opposite rotating powers Jellett's saccharometer Influence of temperature
Influence of solution
Elliptic polarization
Change of rinrs in ealdte
Angle of polarization
Polarization by suocesai?e re- flections
Table of elliptical constants ... Dichroiam
CHAPTEB XXIL; Page 720.
CHBHICAL. AOnOH OF UOHT — PHOTOORAPHT.
Chamieal action of light ... 1281 CUoride ot siWer decomposed 1282 Xassaremeni of tolsr acwoa... 1283
Amount dependent on state of atmosphere ... ... ... 1284
Action of colooredn^ ... 1285
zrili
TABLB OF OORTKim.
1286
Opposing inflaence of t»ts • . . Influenoe of rays ttt mfferent
places 1287
Action of lupra-cpectnl njt . . . 128S
Photography 1289
CopvtnjT by raperposition ... 1280
Posltivea and negatirca ... 1291
Pint attempt! 1292
The camera 1293
Achromatic lens 1294
Orthoacopio lens 1295
Panoramic lens 1296
Camera frame 1297
Dagaerreolype 1298—1300
Processes on paper 1301
Selection of paper 1302
Application of chemicals ... 1303
Solution of silver 1304
Argentotype 1305
PotitiTe pictures 1306
Developing a^nts 1307
Calotype 1306
Modification of calotype ... 1309
Means of incressing sensibility 1310
Channing's process 1311
Paper for photographic registration 1312
Waxed paper process 1313
Albuminiied paper 1314
Perrotype* 1816
Cyanotype 1316,1317
Amphitype 1318
Chromotype 1319
Anthotype 1320
Action of heat 1321
Potiitive printing 1322
Collodion processes 1323
Preparation of plate 1324
Development 1325
Protection by varnish 1326
Collodion positives 1327
Black varnish for ooUodion
positives 1828
Dry collodion process 1329
Albuminized glass 1330
Reproduction of colours ... 1331 Image in microscope photo- graphed 1332
Micro* photographs 1383
Stereoscopic slides 1334
Celestial photography 1835
Carbon-printing 1336
Photo-lithography 1837
Photo-glyphy 1338
Photo-galvaiiography 1839
Photo-sculpture 1840
Necessity of cleanliness ... 1841
CHAPTEB XXIIL; Page 766.
THBBIIIC8.
Theories of heat 1342
Proximate sources of heat . . . 18-13
Dynamic theory of heat ... 1344
Dynamic equivalent of heat ... 1345 Relations ot heat and work 1346,1347
point of absolute cold 1848
Sensations of heat and cold ... 1349
DilaUtion by heat 1850
Dilatation of glass, water, and
mercury 1351
Dilatation of gases 1352
Bxoeptions to general law ... 1358
Air-thermometer 1354
Air and mercurial oompared ... 1356
Differential thermometer ... 1856
Mercurial thermometer ... 1857
Scales of division of thermometer 1858
Compound bar thermometer ... 1359
JohxMon's deep-sea thermometer 1360 Maximnm and minimum
thermometer 1861
Merourial maximum thermometer 1862
Casella's minimum tiiermometer 1863
Actinometer 1864
Aoenrate graduation 1865
Index errors 1368
Thermograph 1367
Appold's regulator 1368
Wedgwood's pyrometer ... 1869
Dani ell's pyrometer 1370
Bvstrdm's hydro-pyrometer ... 1371
Thermic unit 1372
Conduction of heat 1373
Law of propagation 1874
Influence of stmcture on
conductivity 1876
Influence of temperature ... 1876 Influence of molecular aggre- gation 1877
Liquids bad oonducton ... 1378
Gases still worse conductors ... 1379
Application to clothing ... 1380
Senvation of heat 1381
Convection of heat ... 1882,1883
Hot-wster apparatus 1384
Law of convection by gaaes ... 1886
Trade winds and Gulf-stream 1386
Isothermal lines 1387
Specific heat 1388
Calorimeters 1389
Calorimeter of Regnanlt ... 1380
Calorimeter of Prof. U. Kopp 1891
Specific heat of various bodies 1892 Influence of temperature on
specific heat 1308
Specific heat of gaaei 1894
TABLB OF COXTBMT8.
Z1X
Atomieheat 1906
Iaw of spedfie eapadty In gnaes 1396
Latent heat 1397, 130H
Amoants of latent heat ... 1399 Absorption of heat in liqneflus-
tkmnrsolida 1400
ErolutiooofheatonioUdlfleation 1401
Abaorption by vapours ... 1402
Distillation 1403
'*Dr7"ateam 1404
Latent heat of steam 1405
Latent heat of Tapoun ... 1406
Temperafcareoffaiiion 1407
Infliuncie of preuure on the
melting-point 1406
Influence of mixture of elements 1409
Kegelation 1410
Temperature of ebullition de- pend* on prenure ... 1411,1412 BelatioD of boiling-point to
eompoeition 1413
Presence of matter necessary. . . 1414 Spheroidal state of liquids 1415, 1 416
Bonti(^y's experiments ... 1417
Vaporizition of fluids 1418
Pall of temperature in fluids ... 1419
I eo-inaking machines 1420
Cryophorus 1431
Aqueous vapour at common
temperatures 1421
Deir-point 1438
Daniell's hygrometer 1434
iveguault's hygrometer ... 1425
Mason's hygrometer 1426
Psychromeler 1126
Evaporation in animals ... 1427 IMrect transition fh>m solid to
gaseous state 1428
Condensation of gases 1429
Heat of combination 1430
Water decomposed by heat ... 1431
Terrestrial heat 1432
CHAPTEB XXIV. ; Page 801.
BADIAMT HEAT.
Pereeption of radiant heat ... Heat reflected to a fucua 1434^
Theorj uf exchangee
Identity of njiture of light and
Bate of cooling by radiation ... Bate of oooHnff by convection. .. Proportiuns of heat reflected ...
Forbes' thermopile
Befraction uf heat
CooTen^iice by a rock-«alt lens Beftaetion by prism of rock-
■BvW -•• *•• •■• ■••
Tramcolcncv and transparency contras'eu
Hrat-spectmm of electric lamp
Calorei>cett>-e
BurfiMe-radiatlon
Bate of cooling depends partly ooaarfluM «
Terrestrial ntdiation
Heaos uf comparing radiation
Xoaer's fig*ires
Thenp<igraphy
Badiatioii and absorption paral- klpiopv-riies
Influence of pulverization
Influence of chemical constitu- tion
Ba^acinir power little influ- enced bvcommlnatiun
QHaiii/^urbeat
Means of cumpariaon
Abaorption oj transparent BOnia «•• ••• •••
1433 1495 1436
1437 1433 1439 1410 1441 1442 14&3
1444
1445 1416 1447 1446
1440 14S0 1451 1462 1453
1454 1455
1456
1457 1458 1459
1460
Quality of transcalency ... 1461
Comparison of results 1462
Physical change of heat-beam 1443 Hypo^pectral rays nut luminous 1464 Bock-salt UoHt permeable to its
own radiations
lYansoalency of fluids
Internal absorption
Quality of radiaut heat
I ronscalency of gases
TranM^alency of gases at dUTe-
rent densities 1470, 1471
Radiation and absorption paral- lel in gases
Absorption at different pressures TrA'isparency and transcalency
not comparable
Absorption by vapours
A bsorptions compared
Absorption by aromatic vapours
Radiation from nsea
Internal nuiiaiion
Absorption by aqueous rapour Absorption at various tempera-
•111 68 ••* •■• ..a aaa
Radiation flrom flames
I'olartsation of heat
Polariz.iiion by plates of mica... Polarization by reftacliou
ttimugh rock-salt
Polarization of solar heat
Uepolarisation of heat
Circular polarizntioii of heat 1480,1400 CirouUr polarization by Fres-
nel's rhomb 1401
1465 1466 1467 1463 1160
1472 1473
1474 1475 1476 1477 1478 1479 14d0
1481 1432 14!»
1484
1496 1486 1488
62
INTRODUCTION,
OV TUB VATURS OF SNBMQT, AND TBS OOSRBLATlOir ABB TBAB8MUTATJ0N8 OF ITS VARIOUS PBTSICAL FORXA
As the teniiB '' force** and ''energy,** with their qualifying adjuncts, '* actual'* and "potential/* will, in the following treatise, be defi- nitely employed, it may be as well, in liminet to define the terms themselves. The term energy means simply the power of doing work ; force means the power of prodncing energy. These terms have been frequently confounded together ; thos we are accustomed to speak indifferently of the force of the powder, and the " force*'^ of the shot. But this is one of those confusions of terms, that is very likely to lead to a confusion of ideas: strictly speaking, the powder has force, the shot only energy* Again, the force of the powder is only potenHal^ or capable of being called into activity, while it remains yet unignited ; but on the moment of ignition, its force becomes aetttal. Again, while the raised steam-hammer reposes tranquilly on its soft cushion of steam, the force of gravity in the one is counteracted by elastic force in the other, and the energy of the hammer is potential only ; but when the cushion is withdrawn, that energy soon becomes destructively actual. The term " actual" is not constantly employed, but may always be im- plied in the abeence of the qualifying adjunct, " potential :*'^ and moreover, the term, potential, is frequently employed elliptically for potential energy, thus we speak of the potential of an electric charge, or of a voltaic current.
while speaking of the relations of force and enei^, it may be well to notice, in reference to the sequel of this work, a radical and misleading error that has found its way into some elementary treatises on Physics, that of including time as an element of an unit of worlc, or d^amic unit, or foot-pound, as It is commonly estimated in this country. The Author has noticed the foot-pound defined as the force required to raise one pound through the height of one foot tti one second. Now the insertion of the last clause of the definition is worse than useless : it is mischievous, because it is misleading ; — ^the definition shoola
XXll IHTSODUCTIOV.
involve the amount of work only, which is wholly irrespective of the length of time occupied in doing it.
The inevitable tendency of the comparison of innumerable carefully observed and recorded facts, revealed by modem phy- sicists, is to satisfy and convince the reflecting mind of the unity and universality of force, and thence to guide the mental vision (unless it be obscured and distorted by the false pride of human reason) to the unity of that Almighty power by whose arm uni- versal force is wielded.
It is a difficult thing to dislodge -ideas from the deeply-worn grooves, in which they have long and perhaps smoothly run ; hut the writer cannot doubt that ere long all the physical phenomena, that are amenable in all their endless variety to our senses, will he acknowledged to be the results or effects of various but inter- changeable modifications of energy. And there can be probably as little doubt, that the universal medium of communication be- tween mind and matter, the means by which the impressions of external things are one and all rendered cognizable to the senses, is wave-moivon^ excit«d in the molecules of palpable matter.
With regard to the functions of the eye and ear, the application of this law 18 not less evident, than universally acknowledged, pro- Tided electricity and magnetism be admitted (as they must be) into the category of wave-motions.
The sense of touch or feeling is awakened only by actual con- tact or impact, or by the closed-allied wave-motions of heat and electricity, %.«., by dynamic, thermic, or electric energy ; and the amount of sensuous impression is progressive from the lightest touch to the actual teanng asunder of the nerve filaments by saw- teeth (for the edge of the keenest razor is nothing more than a saw), and the mode of excitation may, in this case, be roughly ■ymbolized by the action of a bow on a stretched chord. But in physiological as in physical dynamics (279) time fr^uently enters in as an important element, for relatively considerable time is occupied by the transit of electric motion alon^ the nerves (1003), this transference being probably in analogy with that of thermio motion by conduction, whereas electric induction is probably more in analogy with thermic radiation. Thus also in a rapid stroke of a keen cutting instrument, or in the rapid motion of a bullet through the living tissues, the impression on the nerves may be too sudden for transmission : just as the damage to a sheet of glass by a rifle shot is confined to the point of impact, while the glass is shivered into a thousand pieces by the far less energetic impact of a stone, or a brickbat.
Again, the sense of itching or tingling is excited by the frec^uent repetition of very slight impulses either of dynamic, thermic, or electric energy ; and the intensity of the sensation (when intense more intolerable than even actual pain) is proportioned not to the mnargy of each impresdon, but to their^/refueiMy. The excesaivo
IVTBODUCTTIOir. ZZlll
tingliiig of the 8o-caIled " foot asleep" at the moment of the resto- ration of onimpeded fluid motion through the capillary vessels is notorious.
llie dependence on wave-molion of the closely allied senses of taste ana smell may be not less readily indicated. Very cold sabstances are notoriously tasted and smelt with difficulty, and the sensibility of the terminal loops of the olfactory and gusta- tory neryes is considerably impaired by cold : for example, odours are less perceptible on a very cold day, when the olfactory sur- faces are chilled by respiration; and the sense of taste is noto- riously impaired when the gustatory surfaces of the mouth are chilled by ice. Thus it appears that the sensuous impressions of smell and taste are influenced quantitatively by temperature, %.e,, by the amount of thermic energy. But as to qualitative influence nothing is known with certainty : the minute anatomy of the heat spectrum is a much more ioscrutMble subject than that of the speo- tnun of light ; but for all that is known to the contrary, the odours of the rose and the violet may be due to relatively red and violet rays of the heat-spectrum impingiug upon " resonant'* or recipro- cating vapours, which are capable of taking up and imparting to the sentient nerve-fibres their own peculiar periods of wave- motion. It may perchance be, moreover, that to the naturally acute and hiehly cultivated olfactory sensibility of a Rimmel, the " Harmony oT Perfumes" is as much a reality, as the harmony of ooloiirs to the eye of the painter, or the harmony of sweet sounds to the musician's ear : these several faculties being alike acute perceptions of vibratory cougruencies. It may then with much probability be assumed, that the universal means of exciting sensuous impressions is wave-motion.
The universality of wave-motion as the connecting link between mind and matter, having been thus premised, the nature of the motion resulting from each recognised form of energy becomes an interesting subject of investigation. In the waves of sound the direction of the disolacement of each vibrating particle is demon- strabW lon^tudinal, or coincident with the direction of the wave (Ch. X.). In the waves of light and heat that displacement is in- ferentiaUy proved to be transverse by the phenomena of refraction, diffraction, interference, and polarization (Ch. XIX. and XXI.)i which are wholly inexplicable on any other hypothesis. It will appear in the sequel tnat there exist valid grounds for assuming etectricit)r, and conseouently magnetism, to be forms or modes of wave-motion, and furtner that at all events the magnetic wave is a spiral, the path of each disturbed particle being probably a cin^e in a plane to which the direction of the wave is a normal.
The principle of the "conservation of energy" implies that when once actual energy has been developed in matter it cannot be annihilated, it can only be transferred in some form to other matter. So imivenal is the troth and practical application of this
ZZIV iKTBODUCnOV.
principle of conserratioii that it may almost be taken as an axiom, that it is no more within the narrowly bounded power of man to create or annihilate /orce or energy, than it is to create or annihi- late matter itself: energy mny be yariously transmuted and directed, and matter may be variously combined and modified in form and physical properties, bnt that is all. This principle has been so ably advocated by Mr. Grove in his "Correlation of Physical Forces," and by others elsewhere, and will be found so repeatedly illustrated in the following pages, that it will snfBce here to mention a few examples that nave more recently been presented to notice. The writer has clearly shown the inter- change of thermic and dynamic energy at the point of junction of the bars of a thermoelectric element of antimony and bismuth (972), and he has also pointed out (997) that the dynamic nature of electric enei^gy is not less clearly indicated by tiie long known fact that an ordinary voltaic current always commences with a rush, as it were, the instant that the circuit is closed. The dyna- mical cause of this is clearly pointed out by an experiment due to the genius.of Prof Wheatstone. If a tuning-fork, tne tail of which is inserted longitudinally into a wooden handle, like a file or chisel, be made to vibrate, and the end of the handle rested obliquely on a table, the resonance of the table will instantly be heard, but on moving the diapason parallel to itself in any direction on the table, the resonance ceases, from the perpetual interference of the suc- cessive planes of vibration with each other. But now comes the illustration : — On arresting the motion of translation the resonance immediately recommences, but with a rush or momentary increase of sound : this most unquestionably arise from the resistance offered by the inertia of the molecules of wood to the commencement of wave motion ; and the parallel phenomenon in electricity may un- doubtedly be similarly accounted for. And the momentary reflex current (the terminal extra current of Faraday), which is well kno^n to take place at the instant of opening the circuit, is equally susceptible of a dynamic interpretation ; it is the analogue of the wave reflected from the fixed end of a stretched chord, after having been imparted by the hand to the free end.
The dynamic nature of electric energy is clearly indicated by the dynamo-electric* machine of Holtz (701), in which dynamic is directly converted into electric energy, and by the cognate machines of Wilde (911), Wheatstone.f Siemen8,t and Ladd,t in
* The Author hM elsewhere appUed (p. 660. «o<«) a definite and inteUiipble meanrng to the oooBtraotion of these oompoond terms, which moat be oonetantly employed in reUtioo to the conTeraioos of energy ; this may be •ooompliahed by uking the llret section of the tenn to mean the acHno eoMe, the aeoood, the ruuUin§ efeet} thns • dynsmo-eleolrio machine wiU he O'te in whieh dynamic eoergy la emploved to produce an electric onrreot^ and an elfotro-dynamio engine, one in which a correat is employed to evolve dynamic energy.
t Prooeedings of the Boyal Society, Feb. 1867. | lb. Msrah, 1867.
nmoDncnoy. xxv
ftU of whicli alike there is an interTening coiiTenion of dynaimo into ma^etic energy. The enormoos amount of current-energy erolTed in Mr. Wilde's machine, when the power of a steam-engpne 18 employed to rotate the armatures, may he jud^d of by the fact that a long piece of platinum wire 0*2 inch in thickness was seen to be disintegrated and partially fused. It is difficult to conceive that in these instances dynamic energy can be converted into magnetic " fluid,*' and that again into thermic energy : the con- veniion of motion into matter, and the subsequent reconversion of matter into motion, is obviously impossible.
Some further consideration of the effects of electric energy may serve to indicate the probable nature of the wave-motion. The facts of electric and magnetic polarity imply and necessitate a polaritjT or directionality in the motion itself, which has no analogue in the wares of sound, light, or heat. This requirement is fully met by the hypothesis of a circular spiral wave, analogous to that of a pencil of circularly polarized light, the motion of which 18 direct or positive if viewed from one end, and retro- grade or negative if from the other; and this suffices to explain the well-known polarity of electric and magnetic induction.
Thns far the spiral hypothesis is merely inferential| but in ro« gaid to magnetic wave-motion some strong presumptive evidence may be aduuced. it appears from the experiments of Mr. Joule, made more than twenty years ago, that if a suspended mass of copper be, by twisting the suspension, made to rotate between the poles of an unexcited electro-magnet, the rotation of the mass is anestod the instant the magnet is excited ; and furthermore, if the mass be forcibly rotated, heat is developed in it. And it has been since ascertained that if two cylindrical magnets be so placed that their axes lie in the same straight line, and their contrary poles are opposed to each other, then if a cylinder of copper be made to rotate on its own axis, coinciding with the common axis of the ma^ets, no heat will be evolved by its rotation.
Now these phenomena must alike be the necessary conse- quences of the assumed dynamical theory ; for if the copper mole- cules be thrown into sniral-wave motion, then the motion of all the distorbed particles wiA be one of revolution in planes to which the lines of magnetic force are normals: and the inertia, or energy, of rotation (as it has been variously termed), ».«., the resistance offered hv each revolving particle to any change in the direction of its plane of revolution (as exemplified by the gyrascope), will resist the rotation of the mass in any direction perpendicular to that of the axes of molecular revolution, and arrest its motion. And con- versely^ if the mass be forcibly rotated in the above direction, or in any other direction at right angles to the lines of roaenetio force, heat will be freely developed, doubtless bv internal friction arising from the ]>erpetnal displacement of the planes of molecular isn^ution. But in the second case, the axis of rotation of the
XXTl TNTRODDOTIOH.
mass coincides in direction with those of the axes of molecular revoluiioni hence there is no displacement of the molecular orbits, and consequent!/ no internal friction, and ver/ little if any heat is generated.
The rotatory character of the magnetic wave is further con- firmed by the known fact that if a plane polarized beam pass through a transparent solid in the direction of the lines of force of a powerful electro-magnet, the plane of polarization will be rotated the instant that the magnet is excited. The truth of a theory can be established only by the Terification of its necessary consequences; and it may not be too much to assume that in the present case the evidence already adduced by the writer is, in the entire absence of all contradictory evidence, strongly presumptive of the reality of the hypothesis.
It has been authoritatively stated that ordinary electric and magnetic waves cannot both be assumed to be spirals, because each of these forms of energy notoriously evolves the other in a direction perpendicular to its course ; and the question is not without grave dynamical difficulties, but they may perhaps not be insuperable. It may possibly be that from some unknown con- straining condition or property inherent in magnetic bodies, a spiral wave, on being constrained into a spiral course, may lose its original spirality, and become a secondary spiral, having mole- cular motion in a direction perpendicular to that of the primary spiral.
The relation between the various modes of motion, their physical results, and the sensuous perception of those results, having thus been inferred, the question next arises as to the nature of the media by which the several modes of motion are transmitted. It is unquestionable that sound-waves are transmissible by all kinds of matter, but can any valid reason be assigned in favour of the still prevalent opinion that other modes of wave-motion are in- capable of transmission by ordinary matter? — ^this incapacitpr being implied in the adoption of the self-contradictory hypothesis of an imaginary medium, not cogniasable by any known means of per- ception. It is a remarkable fact that in all the superseded crude notions of physical causation, each phase of physical energy has been presented in the garb either of impalpable, imponderable (in fact imm<Uerial) matter itself, or of the vibrations thereof; and each of these hypotheses has been successively subjected to some violent supplementary hypothesis, in order adequately to meet the reonirements of advancing knowledge.
To begin with chemical action: — ^What are now universally recognised as simple metals were once supposed to consist of some earthy matter (their oxides) combined with "Phlogiston,'* — the material principle of brilliancy. But, unfortunately for the theory, it was soon found that the metals, on parting with their share of
DrrsoDUcnoir. xzvn
phlogiston (t.e., beoomine oxidated), not only did not lo»e anj, Dot actually acxptired weij^ht ; tbereforo phlogiston was assumed to be not only impondsrahlt^ but Ayper-imptinderable — t.e., en- doiwed with the property of absolute leyity, or negative weight !
In the next place, the Newtonian theory of light assumod light to consist of molecules (of course imponderM^ emanating from the source of light, and impinging on the perceptive organs of Tiaion. But this hypothesiB would not fit the phenomena of dif- fraction (1125) and interference (1121), and to suit these physical facts, the molecules must either be thrown into periodical *' fits^* of transmission or reflection, or the ray must be a row of eg^-shaped molecaies perpetually making isoperiodic somersaults, and plun^> ing into a medium if they come on their heads, or bounding off, if they^ fall sideways against it. Then again, heat was supposed to oonsiat of material pacticies emanating from the source of heat; and aa a ball of ice placed in one focus of a concave mirror was found to lower the temperature of a thermometer placed in the conjugate focus, there were assumed to be particles of coU, aa well as of htal : it is needless to add how completely the theory of exchanges (1392) accounts for the latter fact. At length these wild speculations were superseded, and light and heat were admitted into the category of wave-motion ; but electricity and magnetism were still supposed to be either single or dual forms of " fluid" matter: and
"Svca etism molll dora tanmtur sqoi i"
these "fluids" are probably still running in the deep channels they have wpm in some philosophic minds.
But the principle of admittiag imponderability into the cate- gory of legitimate physical hypothestes had become tacitly ac- oeptod ; and the conclusion was at once jumped at by the authors of the undulatory theory that the wave-motions of light and heat take place in an imperceptible, imponderable, highly elastic fluid medium, pervading all space, andaUmcUtert denominated "ether :" and this theory, with all its inconsistencies and inconsequences, is still probably entertained by many physicists.
That some highly elastic and attenuated medium pervades infi- nite space, as the means of transmission of the energies of light and heat uom the centre of each solar system to its oependent satel- lites, is a necessary consequence of the dynamic theory: its ex- istence is, in fact, demonstrated by the periodic retardation of Eocke s Comet. Bat the remainder of the hypothesis, namely, that all palpable matter is pervaded by ether, tor the purpose of transmitting light- and heat-waves is by no means equally neces- sary, or even tenable ; for not a shadow of evidence of the inade- qoAoy of aU matter to transmit these motions has e ver been produced,
xzriii nrrBODUcTiov.
and in default of sncli evidence, the contrary hypothesis is at least eqnallj tenuMe : and this interstitial-ether theory (in common with all preceding physical theories involving imponderability) is hnr- dened with grave inconsistencies. In the first place the well-known phenomena of single anddouble refraction and p<>lariasation, whether of light or heat, necessitate the Romewhat viiJent hypothesis that the elasticity of (he supposed transmitting mediam, etner, is not, as it is in all cognizable fluids, a fixed and definite (jualitv capable of numerical estimation, but an ever- varying quality, depending quantitatively on the elasticity of adjacent matter, and in the case of double refraction, actually varying in tioo or in three directions, within the same svbttance : it would be not more re* pugnant to reason to assume that the elasticity of a gas is one thing in a glass bottle, and another in one of braes; or that the specific gravity of silver is a function of the moon's age, or the melting point of gold dependent on the- sun's zenith distance. Secondly, the fundamental ideas of inertia, energy, and *'work'' are inseparably associated with gravitation, and a contradiction of terms seems to be implied, in ascribing either inertia or energy, t.e., the capability of doing work, to an imponderable particle, which is consequently destitute of attraction for any other particle in the universe.
The known enormous velocity, probably not less than 250,000 miles in a second, at which electricity travels through a cop- per conductor is complete evidence that ordinary matter is capable of transmitting aomeihing (whether matter or motion it signifies nothing for the present argument) at a considerably greater velocity than the waves of light and neat, why bhuuld not appropriate kinds of matter be assumed cspable of transmitting these also? and if so, the need of the interstitial presence of ether ceases altogether ; and it may with great advantage be excluded from the domains of ponderable palpable matter, by the very mild hypothesis that it is not miedble with air, any more than oil or ptupahU ether with water, but that it floata above the boundaiy surface of our atmosphere: this hypothesis is not repugnant to reason, nor adverse to physical experience. On this supposition it is no longer needed to impute to ether imponderability, t.€., an exemption from the otherwise universal law of gravitation ; it will then be imperceptible, only because it exists beyond the reach of observation : and thus imponderability will cease to he reckoned amongst the physical attributes of matter. Moreover, as there are no means of limiting the poeeihle amount of molecular dis- placement in a medium so attenuated as ether must be, an amount of energy is conceivable sufficient to impart effective motion to indefinitely denser matter ; and thus, witnout doing any violence to the fundamental principles of dynamics, this denizen of infinite apace may be assumed competent to ito divine mission of impart*
nTBODDcnoir* zxix
ing to material worlds thow essentials to corporeal existence,— the very mainsprings of organic lire, — light and heat.
The question then natuitttly aris'^s — what becomes of the waves of heat and light, when they reach the confines of tiie atmo- sphere?— and is ordinary matter sufficient and effectual for their transmission ? Thin question can be answered only from analogy, which appears to infer an affirmative.
That sound-waves are transmitted by air, and not by interstitial ether, is unquestionable; and if air be capable of transmitting S6,000 vibrations in one second, it will probably be difficult to aasigu any valid reason why the same medium is incapable of tnmsmitting the far more rapid waves of heat and light ; and if capable, then where lies the necessity for assuming the presence of another medium? Again, the refraction of sound, as demon- strated by the experiments of Hujech and Sondhaus (563, 564), is in exact accordance with the laws hitherto assigneil to the refrac- tion of light and heat. And it appears that the velocity of sound in solids and liquids is much greater than in air (545) ; in water it is nearly 5000 feet, and in iron nearly 17,000 feet in one second : is there, then, any known fact whatever that tends to assign a fimit to the powihU velocity of transmission of wave-motion through these and other material media? — ^if not, then the pre- sence of ether, as generally assumed, cannot be deemed essential to the transmission of light and heat ; and if not essential, why should the interititiaXrWier hypothesis be any longer entertained ?
'* If eo Deat intenit, nisi dignot tindioe nodus Indderit.'*
Moreover, Prof. Tyndall, to whom the progress of Dynamical Physics is indebted for many laborious and important researches, has observed that in various kinds of wood there is a remarkable hannony between their respective condnctivitiesfor sound and heat in three mutually perpendicular directions, namely, longitudinal, transverse-radial, and trms verse-tangential (546) : now although there is certainly no direct analogy between the conduction of heat, and the radiation of light and heat, beyond that of their coounon dynamic origin, a much closer analogy may nevertheless be traced through the phenomena of pho.«phorescence, fluorescence, and caloreseence. It appears to oe highly probable that the "caloresoence'' of a plate of platinizeuplatinum, the phospho- nscence by heat of the minerals Fluor and Apatite, and ordinary incandescence are analogous phenomena; differing only in the temperatare (t.e., the amonnt of thermic energy) at which heat- notion, impressed on the molecules of different substances, is im- parted as nght-rootion to the surrounding medium. And some phenomena of phosphorescence present further evidence of the in- tiointe relations existing between light, heat, and electricity : it
XZX IXTBODDOTXOV.
haB been observed that Flaor mtij be rendered phosphorescent by a very moderate application of heat ; but that it will not again
Eoosnhoresce under similar circumHtances, until an electric spark as Deen repeatedly passed over its surface. But perhaps the closest analogy between the radiation of light and the conduction of heat may be traced in the observations of M. De Scnarmont, who has found that, in plates of ciystals cut in a direction coin- ciding with that of the optic axis, the relative conduction of heat, in directions parallel and perpendicular to the optic axis, is governed by precisely the same laws as those of optical elasticity, which determine the relations of the ordinary and extraordinary polarized rays : and moreover that in plates cut perpendicularly to the optic axis, thermic conductivity is, like optical elasticity, equal in all directions. It may also be remarked that the con- Terse permeabilities to light and heat of a crystal of alum, and one of dark smoky quartz, or a smoked plate of rock-salt, present striking examples of the existing yet unknown diflemnces of physical constitution, which are met with in the variiius kinds of matter, and which involve special capabilities of transmitting, or of arresting and diffusing, particular kinds of energy.
The correlation of the various lornis of energy and their trans- mutations have been so well collated by Mr. Grove, and so fre- quently referred to in the preceding and subsequent pa^es, that repetition here w*ou1d be wearisome ; it will suffice to refer to the before-mentioned enormous magneto-electric engine dehigued for the illumination of lighthouses, and constructed also by Mr. Wilde of Manchester (91 1). Acting like those of Messrs. Wheat- stone, Siemens, and Ladd, on a principle of reduplication, or self- reaction, it is a grand instance uf the transmutation of energy ; and it may here be cited as a good example of a series of succes- sive conversions.
In long bygone ages the energies of solar light and heat were occupied in the development of woody linsue, and this became gra- dually converted into coal, perhaps without much gain or loss of energy. The dynamic energy arising from the collision of the molecules of carbcm with those of atmospheric oxygen, in the act of combustion, f.e., combination, is yielded up as thermic energy to the boiler of a st-eam-engine, and generates steam, the elastic force of which, through the medium of the engine, drives round the annatnres of the electro-magnetit. Dynamic becomes now con\*erted into magnetic, and this again into electric energy, and an in- terrupted current of intense power is produced. This being trans- mitted between carbon electrodes, an immense amount of light and heat is produced by molecular friction at the point of great resistance to the passage of the current, and these are prodnced at the expense of electric energy, as proved by the loss of current ; here, theo, we have the final transmutation of electric into thennic
ISTBODUCTIOV. ZXZl
•Did pbotic* energy: the latter being so intense as to have thrown a shaditw a:rro88 the brightest sanbeam, and to produce an amoant of illomiDiition unattainable by any other known means. This entire series of transmutations ma^ be viewed as a complicated process of erolving stored up saudhine in an intensified form, for occa- sionaJ use.
Having sufficiently considered the physical, it now remains to Rview the moral aspect of the large questionH that have been raised in the preceding pages. The Author cannot but feel that in thus seeking to simplify by generalization the conception of the powers of nature, and to unify their source, he may in some minds, misguided by the pride of human reason, unwittingly encourage the pantheistic tendencies of the present age ; than which nothing can possibly be further removed from his desire, or design. Where, it may be asked, is the faintest shade of difference between modern pantheism and the nature-worship of the oldest times, save that the mode of culture may have been humanized by civilization? in both alike reason and the objects of sense are deified, the thing created is set up on the Creator's throne, and the light of reve- lation, with it« priceless coiiseqnenceM, being invisible lo the mere carnal eye of sense, is practically extinguished. Ihe author vottid rather remonstrate openly with those who, conscious it maT be of great intellectual power, have unfortunately been led to Ignore ail things divine, tnat are not cognizable by unaided reason, and to aucn he would say, in the emphatic words of the peat Tishbite of old, *' How loug halt ye between two opinions ? if the Lord be God, follow Him ; but if Baal, then follow him :" and he would earnestly entreat them to reflect that between the two alternatives there can be no compromise.
The grand mysteries of Crention must of course be ignored by all those who have closed their eyes against all things not visible m the light of unaided reason ; and accordingly it has not long siooe been asked before a large and intelligent audience, Whence came ihe fir^t elephant? *'did he fall from the sky (i.e., from the interplanetary space) ? did he rise moulded out of a mass of amoruhoDS earth or rock ? did he appear out of the cleft of a tree? ' — to which, responding in the same key, the writer answers so : — ^nor yet from the endless transmutations either of a sign-post, or a galinwM-tree ;-r>nor even from the adaptive efforts of countless generations of huge boar-pigs, inheriting from their primseval ancestor a weakness for the green tufts that grow on tall and leaf- less tropical stems; — ^nol — that wonderful mechanism of inter- Iscing niujvcular fibres, by which a boneless appendage can acquire abno*«t the rigidity of an outstretched arm, and the prehensile sensibi'ity of opposed digits, could only have come, and must have coiue direct, from the hand of an all-beneficent Creator.
* ThA Greek roots are generallj adopted in all similar words.
zzzii iHTBODucnoir.
It may by some be thonght that tbeae remarks are ^xtra vires in a treatise on Phjsics, but the Anthor cannot ignore the apostolic injunction — " Whether ye eat or drink, or whatsoever ye dOj do all to the gloiy of God ;*' and he feels that when such language has been publicly proclaimed, he would fail in his Christian duty if he failed to give equal publicity to his earnest and indignant protest.
ERRATA.
N.B. — It will be foand oonvenient to make these corrections before reading the work.
|
Line, |
Error. |
OMTtoAon* |
|
|
S3 |
i,note |
log Pi -log Pj |
p f «.tan^ |
|
w |
n |
log,I>i-log,P, |
|
|
205 |
26 |
andiB |
and in the first column is |
|
SIS |
126 |
casting |
forging |
|
268 |
23 |
manytinieB |
much |
|
289 |
16 |
M. Clement Desormes hai |
MM. Clement and Desormes hare |
|
310 |
10 |
of the hypothetical me- |
} dele |
|
dium ether |
|||
|
312 |
86 |
% |
|
|
313 |
8 in table |
s |
0» |
|
346 |
1, note |
6A.lf. |
Sajc |
|
887 |
1 |
potential electricity |
electric potential |
|
308 632 |
176 16 |
TnieBuued |
(713) unTmcanlaed |
|
M |
146 |
600 |
flOOO |
|
WW |
126 |
800 |
8000 |
|
Ss |
Pig. 636 |
B» 10 coils |
B, 11 coils |
NATUEAL PHILOSOPHY.
1. Au. TBrietieB tnd drmi of nuttter ue nmiUrly composed, bring mule ap of an iDdefinile Dumber of extremelT, and mdeed inooDceiTtLblj, minute indcatmctible porticlei, irbich, from their not admitting of Further mecluQical oinBion, &re lenned atotnt* Soma philoaophen baie, bowaier, conceiied that no tma atom czi»ts, and that all matter ia capable of undetgoine diiinon to mfinitv. a atatement capable of being aatiibctori^ prored in r^snC to space, by the ooiuideration of matbemarical lines and HontB. Tbns, let ^ b, c d, -. .
be lines drawn parallel to ^' '
cBchotber^drawuieabliqtw I line r o, aod ^m r on the I indefinite right Lne, c n, I take anv number o! equal I paitt,aerabed,&c. Ymm I B draw lines connecting ihis I point to<i,i,e,(i,&c.,C''tUDg | lbs oblique line r a ; ihen,
aa the munber of poinle a, h, c, &c., on the line t; i> ni» be infinite, H bllows Uiat the line r o ma; be infinitel; dirided by lines cod- Decting such points with ».
Acgnmenta of this kind ongbt, however, to be regarded as qipficable onl; to mathematical lines and point*, wliich, the former being witLont breadth, and the latter withont magnitode.f
* A, ud ■ri^rm, Hbido.
t Endid, Book L itb. 1, 1.
n bo ref^rded but ■« mental conceptions, md not plijsicnl
2. The nltimmte particles or alomi [I] of matter poawss the
three funUiaZ cbnrnoterB a( impenetnAtliiy, txtetuion, Hodjiirure.
Of thsMi properties, the first flows directly frotu the definition of
sn at^nn, as it is obrious that nothin;; cnn be to impenetrable aa
that which ia incapable of farther division. When anj solid 'bod;
is immersed in a fluid, some portion of ihe latter is displaced,
sndllinB, on a snperficial ticw, might ba supposed lobe penetrated
bj the immersed body; it nil], however, be found that no real
penetration occnrs, as a quantity of fluid becomes displaced, equal
in hoik to the solid immersed. (Ch. VII.) On forcing a nail or a,
ki.ifeinto a piece of wood, Iheultimate physical atoms of the latter
are not penetrated, the instromentbeinK merely
«*. »■ insinnaied into the interstices eiisti 05 between
the indivisible molecules. Again, air and all
them, are really as impenetrable as solids, allhough their particles arc tapable of mucli ^ater condensation bj nieclianica) means. If a glsBB receiver, *, be inverted over a lighted taper Ried on a cork floating en the surface of water, it can bo pushed to the bottom of the containing vessel, and the taper will thus con- , tinue to bnm under water so long ss sufficient 'b present to support combustion; a
3. The aeccnd chnraclcr, or erttniion, is also a necessary conse- quence of the delinilion of nn atom alrcndj ^ven, as that which possesses a pliysical existence must necessarily occupy a portion of space, and puiiiicss sides nod rurfnccii in relation to other atonis. "nie citpnsion iif bodies is oipTeased by the ibi-ee dimeneions of leDgth. breadth, and thiitness.
4. The third character, yti/ure or ^rm, is nl<>o essential to tlic existence of an atom, as nulhiug c;in bo conceiII^d aa phybicallv existing, unless it possesiies some determinate aliajie, althoush this ]iroperly is tiot tnmcient of itself to prove the material eiislonce ufan o^'cct ; for in sha^on-s and in spectral illusions, produced by various optical means, wo have cxbRiples of ligure or form wiiliout
5. Of the actual form or sixe of atoms, nolhinf; p'wiiive is knon-H, it is. however, probable that Ihov are sphorlcnl : hut In their difnenalont Ecarcely an app'oiimaliun can be oblnincd by
MIKUTEXB98 OF ATOMV. 3
nnj meiuiB we are jet acquainted with. An ounce of gnid can b^ drawn into wire several miles in length (12), and jet no flaw, of evidence of separation between its atoms can be diflcoyered by the closest microscopic examination. Cbemistir affords ns eyidence of the ezcessiye minuteness of atoms, for when seyeral metals, as nickel, cobalt, or iron, are reduced from their oxides at the lowest possible temperature bj means of a current of hydrogen gas, the fitate of diyiMon of the reduced metal is almost inconcciyablt*. Each particle of metal slowlj evolving its ox jgen, forms a powder which maj be considered as composed of ultimate atoms. These are in everj case less than the one-hundred-millionth of an inch in diameter, so that bj a simple calculation it maj be proved that a cubic inch of them would, if extended on a level surrace so that they maj touch, but not overlap each other, cover an area of 218,166 square feet, or more than five acres of ground.
6. AnoUier illustration of the extreme minuteness of atoms is met with in the thin films of soap bubbles. These present fine iridescent coloured bands, and at the npper part ot each, it is demonstrated that the thickness of the film, just before it burets, cannot exceed the four-millionth of an inch ; and jet even this thin lajer is not composed of a single stratum of atoms ; as it must consist at least of the atom of soap and ono of water ; the former compoeed of soda, stearic, or margaric, and oleic acids, in the simplest view that cm be taken of its composition, and the latter made up of at least a molecule of oxjgen and one of hydrogen.
We may likewise appeal to organic life for evidence of the un- limited divisibilitj of matter, in the extreme minuteness of definite structures that have been revealed bj the microscope, exhibiting the wonders of creation not less manifested in the most minute, than in the most stupendous works of which our senses are cogni- sant. Animalcules exist, so minute that mjriads can swim in a drop of water, and jet everj individnal possesses organs of diges- tion, circulation, and reproduction. The polishing-slate from Bilin in Bohemia, composed almost entirelj of the siliceous shells of infusoria, has been calculated to contain 41,000,000,000 in one cubic inch, which weighs 220 grains; consequentlj each shell, possessing nevertheless, the most exquisite beauty of structure, would weigh little more than the two nundred-millionth part of a grain.
7. The minute molecules composing masses of matter maj be, and often are, chemicallj compound, althongfa phjsicallj simple ; thus a piece of marble maj be divided into its ultimate molecules, each CQouisting of carbonate of lime, and here physical analjsis stops ; but bj chemical analysis we can separate each of these atoms into carbonic acid and lime, the former being asrain chemicallj divisible into carbon and oxygen, and the latter into calcium and oxygen. In physics, therefore, a molecule is reganled as simpio
B 2
4 GBHEBAL PB0PEBTIE8 OF MATTER.
when it cannot be farther diyided without separating its chemical elements.
8. The indestroctibility of matter must be regarded as one of its inherent properties. It is no more within the limited scope of human agency to destroy any of the ultimate material elements, than it is to create^ or even to commute them, as the alchemists of old vainly attempted. The tenns "destruction by fire,'* " destructive distillation," must be understood in a limited sense,as referring only to the previously existing form of matter, and not to the matter itself. The stick of charcoal is consumed, and leaves no vinbiU trace of its existence but a minute quantity of white ash : it is not however destroyed, an invisible gas has been gene> rated by the union of the carbon with the oxygen of the atmo- sphera, which manifests its existence by its power of extinguishing alike (and for the same reasons) die flame of a candle, and the vital spark of organic life.
Many fluids, water for example, will readily evaporate ; but its particles are merely suspended invisibly in the atmosphere. This mav be rendered evident by their precipitation on any suitable cola surface, as on that of a glass vessel filled with iced- water.
Tbe history of the earth's crust informs us that these wonderful transformations of matter have been progressively in operation during vast periods of time, of the extent of which the human mind can form no conception. £ven the humble "earth-worm that we tread on" plays an important part in the scheme of creation in continually reclaiming to a hi^ner grade of organiza- tion the organisable materials of the soil in which it lives and moves and Las its being.
9. Atoms and molecules are held together by means of a force denominated aUraction^ the finnness of their union being modified bv the presence of an opposing force, termed reptdtion; and upon the preponderance of one of these forces over the other, depends all the physical properties of matter, known as hardneu^ Boftnen^ JUiiaity, &c. ^ Tne intensihr of this molecular attraction varies considerably in different bodies, which thus acquire very varying degrees of coherence.
If the mutual attraction of atoms be so considerable as to prevent a rigid body beine readily inserted between them, the mass is said to be hard; but if so feeble as to permit their easy separation, the resulting mass is soft; and &fiuui or a acueous body results, when the intensity of the mutual attraction between the atoms is so far counterbalanced, as to allow any substance to be moved between them without experiencing any considerable resistance. The hardness of many bodies is mucn influenced by external con- ditions ; thus most metals may be considerably hardened by ham- mering or rolling ; and the hardness <^ steel, resulting from sudden cooling, when at a red heat, is a familiar example. On the con- traiy, an alloy of one part of tin and four of copper is said to be
-n
DBH8ITT OF MATTES.
5
ductile when cooled enddeDlf , and Inittle when cooled slowly. Thne the varions states in which matter exists, as soUdj viteouSf Uqvidt or oasetnu, merely dej^nd upon the yaiying intensity of the moleciuar forces of attraction ana repnlsion. The property of emitting a sonnd on percussion is ascribed to the hardness ofbodies ; hat this property may be shown to be possessed hy hoth fluids and gaseous ixxiies. The water-hammer, a glass tube containing water, nt»n which the air has been nearly exhausted hy boiling the water in the tube, and then hermetically sealing it, emits a loud sound, prodnced hy the concussion of the water against the elass. The crack of a whip, or the peal of thunder, auke show the* effect of the concussion of the particles of air against each other, when they ha^ been separated by .anything passing between them with a -velocity greater than that with which air would rush into a yacnum. These seyeral states of matter are readily conyertible into each other by yarious mechanical means, and by alterations of temperature : thus, water at 32** F., and mercury at — 40** F., or 72* lower, are solids, the one being transparent, the other opaaue ; and at about — 90* F. carbonic acid may be obtained in the form of snow. At ordinaty temperatures the former are liquids, and the latter, gaseous : whilst at 212* F. water, and 670* F. mercury, become yapours or gases, both being transparent ; these seyeral changes depending merely on the neater separation of their atoms efiected by the repulsiye power of heat. The original yolume of &e fluid becomes amazingly increased by this separation of the oonsfiitnent molecules. The following table shows at a glance their enormous increase of yolume by yaporization, under ordinary atmoapherio pressure.
1 cubic foot of water expands into 1689*0 cubic feet of yapour. alcohol . . . 493'5 ether .... 21218 turpentine . . . 192*15
10. The most elastic gases can, h^ the application of sufficient pressure, be compelled to asmme a yisible form ; becoming liquids if the pressure be great enough to bring their constituent atoms sufficiently near to each other.
it
n n
n
It It ti
ti it tt
|
GSMt. |
Tamperatore. |
|
|
Sulphurous acid Chlorine . . . Carbonic acid . Nitrous acid . . |
2 4 86 60 |
45* Fahr. 60 „ 32 „ 45 „ |
11. The density of matter in any of its three states is measured
6 GENERAL PROPEETIES OF MATT&B.
hy the quantity contained in a given bulk, and is expressed hy its specific gravity or relative weight, as compared with some body, taken as a standard ; thus, if a given bulk of water consists of 1,000 atoms of matter, an equal bulk of platinum Avill contain about 23,000, if each atom has the same weight ; of copper nearly 9,000, of iron 8,000, and of glass about 3,000 ; these several num- bers being proportional to the specific weight or gravity (Ch. Yll.) of the respective substances.
Masses of matter moreover possess several properties which may be considered as accessorv, all depending upon the different de- grees of intensity with which the physical atoms are mutually tie- 1 together. Among the more important of these may be ranked DivmbiUti/, I^lexibilitVf TetiacUyi BritUeness, £lcwticUyf &c.
12. Divisibility or iJxtenaion of Maasea, — This character may be considered as well illustrating the extreme, and almost incon- ceivable, minuteness of phvsical atoms ; depending upon the im- mense, although finite number of parts into which a mass may be divided. Thus, an imperceptibly small portion of strychnia will render a whole pint of water bitter, and a single grain of the ammoniacal hyposulphite of silver will render intensely sweet 32,000 grains of water. One grain of iodide of potassium dis- solved in 480,000 of water, when mixed with a little starch, will tint every drop of the fluid blue on the addition of a solution of chlorine. In all these cases, we have at once evidence of the extreme minuteness of atoms furnished by the divisibility of the masses of strychnia, silver, and iodine by means of solution. Excellent illustrations of the same property are met with in many ])rocesses of art ; a sinde pound oi wool will furnish a piece of yarn 100 miles in length. Gold ander the hammer is reduced to such state of tenuity, that 360,000 of the leaves produced would, if piled on each other, only equal the thickness of an inch. Even this is far exceeded in the art of the wire-drawer, who, in the most economical mode of preparing gilded silver wiiy, extends two ounces of gold over a length of 1,351,900 feet, or rather more than 768 miles. The exquisitelv delicate wires of platinum made by the ingenious process of Dr. Wollnston, afford a remarkable instance of the extension of matter, no less than of the almost inconceivable minuteness of the component atcms. The finest of these wires is but the three-millionth of an inch in diameter, and 140 of them placed together would just equal in thickness a single fibre of silk. This extreme degree of tenuitv was attained by enclosing a platinum 'wire in a silver tube, tnen drawing both together, and lastly, dissolving awav the silver coaling by an acid.
13. Flexihility. — When any substance is capable of being bent in anv given manner within moderate limits, hj the application of sufficient force, it is said to he flexible. For a body to possess this property it is necessary that the distance between its contiguous ])articles should be capable of being slightly augmented, without removing them beyond the sphere of their mutual attraction. The
TLEXIIUUTT.
property of flexilnlitj maj be illnstrated by tbe followiDg simple
aj^paratas : — ^Let ▲ b be a piece of whalebone, haviiig a number of
viies CD, d vff &c., passed
througb equidistant bolea : let ^« >•
two series of balls c, c', &c., i>, ]/, &c., be fixed to tbe ends of tbe wires, and let a third series, b, e', &c., loose on the wires, rest on tbe piece of whalebone. If tbe rod be bent, as p o, the row of particles rs- presented by the balls c will oaTe receded from each other, and the particles d have become more closely approxi- mated, while the distance be- tween the particles b is not perceptibly altered. That such a change in the relative distance of the atoms really occurs, is rendered evident by merely inspecting the fignre of a thick wooden plank which has been allowed to become curved by _, .
its own weight. Let a b, c d, ^*
represent the section of such a p!ank supported at ita extre- mities c, D, it win be seen at QQce that the surfaces a b and CD represent two concentric
cm^es, of which a b is the smaller, consequently the atoms nearest the Borface ab must be more closely approximated than those seaieat c d. The atoms lying in some line intermediate between A B and c D, undergo no change, the line b p, therefore, in which these lie, constitutes what is called the neutral €ucia of the body, and this portion mij^ht be excavated and removed ■without mate- rially diminishing the strength of the plank, provided a sufficient amoant of substance be left, to prevent the collapse of the surfaces ABandcD. ^
14. On this principle, hollow cylinders of different materials are employed instead of solid ones, when used as mechanical supports. Inoeed, if all opposing causes in the shape of flaws, bad workman- ship, &c., are absent, such hollow cylinders not only have the advantage of lightness and economy of material, but are found in practioe to be actuaUy stronger than solid ones of equal weight. Tredgold found that when the inner semi-diameter of the hollow c^inder is to the outer as 7 to 10, it will possess double the strength of a solid cylinder of the same weight
Similariy in the construction of ca6t>iron girders, for supporting the floors of buildings, it is found that the greatest strength is obta^ied by making the transverse action lu some degree to
8 MOLECULAR OB IMTBRHAL FORCES.
resemble the itiverted letter Xi ^^® reBistance to oompressfon and extension being equally sustained by the upi>er and lower lamins respectively, the areas of the sections of which are as 1 : 6, while the yertical lamina serves to maintain the equidistant position of the former. Wroufht-iron is, however, now almost universally used for girders, ana as in this form of the metal, its powers of resisting extension and compression are much more nearly e^ual, the upper and lower laminn are usually made of equal dimensions^ the giraer, if small, being rolled between grooved rollers, like the railway rails ; or if larfi:e, being formed of strips of boiler plate and angle-pieces riveted together.
15. Tenacity. — This character is dependent u^n the intensity of attractive force existing between atoms bemg sufficient to oppose their ready separation, to such an extent as to cause the rupture or fracture of the whole mass. Consequently, all flexible, ductilOi and malleable bodies are tenacious ; althougn many sub- stances possess the latter property without the former. The tenacity of matter is well shown in the remarkable malleability of copper ; for from a flat plate of this metal the skilful workman forms a hollow vessel without any joint or seam by the use of his hammer alone ; and by well-directed and repeated blows, the vessel he has formed, however much differing in ngure from tne original plate, is everywhere of nearly the same thickness. Tenacity varies extremely in different substiuices : metals afford the best examples of it ; dius, a piece of steel wire of g^ven diameter is capable of suj^porting witnout fracture 39,000 feet, or seven miles and a half, of its own length.^ Wires of different metals of the same diameter require different weights to overcome the mutual attraction of their component atoms, as shown in the following table; the figures representing the number of pounds avoirdupois required to break wires of the metals enumerated, each being ono-tenth of an inch in diameter: —
|
M«tals. |
POQDdfl. |
Metals. |
Pooiidi |
|
Bismuth . |
. 20-1 |
Silver . . |
18713 |
|
Lead . . |
. 27-7 |
Platinum . |
274-31 |
|
Tin . . |
. 34-7 |
Copper . . |
302-26 |
|
Zino . . |
. 109-8 |
Iron . . . |
54925 |
|
Gold . . |
. 16007 |
Cables constructed of fine iron wires of from tt ^^ rir ^^^^ in diameter, are stated to possess the enormous tenacity of 60 tons in each souare inch. It is this wonderful tenacity which renders wires of this metal so applicable to the construction of light sus- pension bridges. The followinp^ table shows the tenacity possessed by different bodies calculated m tons weight.*
* MoMley'i *< lUnstntiona of MediMiifl%" p. 886.
TEVACJTT.
9
Teaaoiif in tona^ p«r iqaireiiiolu
Wrongbt iitm, in vire ^ to^ inch in diameter 60 — 91
„ in wire ^ inch diameter . . 36 — 43
in Iwn (English) 25i
„ in bars nammered 30
„ in chains of six-inch links . . . 21 ( — 25
Cast iron 6 — 9J
Steel, cast 44
„ Damascus 31 ■ 44
Ccnpper, cast 8^
wire 274
Silver, cast 8
„ wire 17
Gold, cast 9
„ wife 14
Flatinom 17
The tenacity of the fibres used in the mannfactnre of different &brica, has been found bj M. Labillaidi6re to be very different ; he has ascertained the tensile stoeugth of fibres of equal sectional area of silk, New Zealand flax, hemp, and common flaz^ to be nearly proportional to the numbers 17, 12, 8, and 6, respectively.
16. Tredgold has shown that many solids witt bear an enormous amount of pressure before they yield sufficiently to allow any ^r- maaent alteration in their shape. The fieures in the following table represent the weight in pounds required to effect a change in the figiue of a one-inch cube of the solids submitted to experiment.
Malleable inm. . 17,8001bs.
Cast iron . . . 15,300 „
Brass 6,700 „
Zinc 5,700 „
Tin 3,880 „
Lead 1,500 „
KedFir . . . . 4,2901be.
Oak 3,960,,
White Fir . . . 3,630,,
Ash 3,540,,
Ehn 3,240,,
From a comparison of these tables it will be observed that the relative powers o£ resisting compression and extension differ consi- derably m different substances : thus while the tenacity of iron is to that of sine as 5 : 1, the resistance to compression is nearly as 3:1; hence the position of the neotral axis will differ in different mat^ials, and titerefbre likewise the sectional form of a beam of greatest strength in proportion to its weifcht, a point of great im- portance in the arts of constructioo. This may be further illus- tnted by the preceding ^paratus (13), in which the mutual recessioD of the particles o may be in any required ratio to the sppraximation or the particles d, by varying their relative distances Ami; *
10 UOLECULAJl OK 2KTBRXAL FORCES.
Connt Rumford found that a cylindrical roll of paper, with the folds glued together, and presenting a sectional area of one square inch, would support a weight of 30,000 pounds.
The tenacity of metals is greatly influenced bj their tempera- ture. At a certain elevation of temperature the readily fusible metals entirely lose this property, and assume the consistence of putty. This peculiar st^te is made use of in the arts, as in the formation of a plumber*s joint ; and lead pipe is mafle by the metal in this condition being forced through a round hole in an iron plate, with a concentric plug placed in the aperture.
17. £rUtleness,^TLh\H is obviously the converse of the last pro- perty of matter ; it points out that condition of a substance, in wliich the attraction between its molecules, althoughperhaps very intense, is mnch limited in its sphere of action. Hardness and brittlencHs are not incompatible qualities, but, on the contrary, Irequcutly coexist ; thus a piece of glass, notwithstanding its pro- verbial brittleness, will scratch a surface of polished steel. If, however, glass be spun into fine threads, or blown into thin laminie, it exhibits a high aegrec of flexibility as well as elasticity. The opposite properties of hanluess and brittleness, or ductility and tenacity, are frequently manifested by the same substance under different conditions of molecular arrangement ; thus cast-iron and hardened steel are brittle, while bar-iron and soil steel are amongst the toughest substltnces in nature.
18. JSlasticity. — A body is said to be elastic when, after being bent in anv direction, it spontaneoualv tends to recover its former shape on the force which had altered its figure being removed ; all elastic bodies must be so constituted as to allow a certain number of their atoms to be brought, at least momentarily, nearer each other than they previously were. If the body be a metallic rod, then, on being bent in the curved form a b D o. Fig. 4, it will have a tendency to resume its primitive rectilinear form on the removal of the coercing force, in consequence of the exertion of two forces, \iz., attraction between the partially-separated atoms on the out- side, and repulsion between the closely-approximated atoms on the inside of the curve. In this case, the cnange of form which brought into action the elasticity of the body is very obviouB, from the ourve produced by its flexure ; sometimes this change of figure, even in the most highly elastic bodies, is not evident to the eye, from its short duration ; still such change does demonstrably take place. Thus a ball of ivory is elastic, and this property causes it to rebound from the floor when forcibly thrown upon it, its figure, on impact, becoming altered and compressed ; as may be shown by causing onn ivory ball to impinge forcibly on another, smeared with some dark unctuous matter, as printing ink; the surface marked by the impact will be much larger thau if the balls were merely brought gently into contact with each other, thus showing that a mutual compression of the substanco of the balls hati taken
MOLECULAR AGOBEOATION. 11
place (Inring the impact. Two balls of caoutchouc, which poMtesa a mnch greater degree of compreaaibility, will produce this effect io a mai« marked degree.
19. A body is said to be perfectly elastic, when the force with which it tenda to recover its original form, or as it is called, the force of rtHitviion^ w exactly equal to the compressing force. No kind of solid matter is perfectly elastic, bat many are elastic io a high deeree, the forces of compression and restitution being nearly ^qual. Different elastic bodies vary extremely in the extent to wiiich lliey will yield without rupture ; thus caoutchouc, and espe- cially the vulcemized variety, may be stretched to five or six times its original length, and will afterwards very nearly regain its ftinuer shape, nnleas the tenuion has been maintained for some time. Threads, and thin laminss of glass, and tempered steel springs are highly ehuitic ; unannealed iron, brass, and copper, are also elastic, but in a less degree than the former. Fluids, and especially gases, are the only forms of matter that exhibit the property of perfect elasticity : the latter, on account of their phy- sical constitution, will permit their atoms to be very considerably appcoximatod, by the application of sufficient force ; again sepa- rating instant jineousiy, and even with violence, on the removal of pressnre : the air-g^n, and condensed air-fountain are examples of this property in atmospheric air.
20. AIthriu|^h the scope of an elementary treatise forbids a de- tailed discussion of many important branches of phjrsical research, the sulject of molecular attraction would be incomplete without some notice of those remarkable conditions of pohmty in molecular aj!gregation, that ^ve rise to the formation of crystals. The term cry9tal originally implied transparency, bnt, in its more extended sense, it is applied to any portion of matter that has spontaneously assumed a definite geometrical form, bounded by four or more plane surfaces ; four planes being the least number that can enclose a fipace. Crystals that have been ibrmed by the agency of natural causes are tenned natural crystals, while tho^e that result arti- ficially from fnsion, solution, or any kind of chemical action, are called arf(^ScuzZ crystals.
21. The varieties of crrstalh'ne form depend on the different directions in which the forces of molecular aggregation act most pnweriiilly in different kinds of matter, and also on the relative mtensity of those forces. Some direct evidence of definite direc- tions of greatest molecular attraction may be derived from the fact, that many crystals will yield to any applied foix;c and break or hph't only in plane surfaces having a constant direction ; this pro- perty is callea cleavage. If a natiual crystal of Calcite, commonly Known as Iceland tpar^ or of the lead-ore called Galena, be broken into fragments, the surfaces of each fragment will have the same relative position as those of the entire crystal, or portion of a crys- tal, from which they were derived ; and if these migments be tri-
13
tanited in > morUr to an impalpable powder, and examined bj a micToacope, it will be foaiid tnateach particle is boundsd by plaiMi having the same mutual iDclinationB.
22. The lUreotiona of greatait molecnlar action CMDot in all cijitali be di«coTered hj cleavage ; bnt in all caaei, three lines of direction ma; be taken, pasting throngh the Bame point, bnt not lyinff in the (ame plane, which will bear some known relation to the direotioni of the molecnlar forces, or to the obterred inrfacei of Uie ctjita] ; ^eee three lines are called the Axe* of the crplal.
28. All the obeerved hnai ofetTstaU maj be referred te oite of nx AMentiall; diffenet ■jatems c^ crTstallixation, each of which may be defined by die relative podtion andmsffnitudeof the axes. The relative lengths of the axes, which define the formof a crystal, •re called voroiMlsrs.
S4. In tnree sjatenu the ciystallographic axes ore all perpen. dicolar to each other.
I. If the axes are all equal, the crjstal formed beloDKS to the QtUe system, of which common Salt, Alum, and Floor Spar are examples. Ctystals belonging to the cubic ^item are chiirac- terised by an appearance of symmetiy in whatever direction they
tig. i. rsf. t.
Silicate ofNickel are examples. Ciyslak of this class ftw^aentiy
it tin mppearmnce of > iqiiare pyramid. When Tiawed in the .... ion at tbe mieqnal aiia, ttieu oatline U Brmmetrioal with regaid to the foitr ndei or eoniera of > aqnAre, bat when riewed In tbe directioii of either of the two equal axes, the ontline ii ijmme- trioLimlj with regard lo the opporite lidei of a rectansle : this taaj be imdentood bj a reference to the flgntet, in wbiob tbe nn- aqnal axes are TertkkL
IIL If th« axes are nnequal'in ail three directiona, Ihe renilting fcrmatioa lepreaenta the iVitniatie B.vatem, of which tbe Snlpbatea of Folaab aitd Zinc, and Rochelie Salt are eiamplee: the latter salt, LoweTBT, fracjiKiitlj crjstalliEeB in half prianiB, ahowinE one of the irrwdariliea that occssionally occur in tbe (onoation of CTjstala. The fonns belonging to this ajslein freonently present a ijnunetrical bz«ng&«baped ontline, when view^ in the direc- tion of tbe «xi* of tbe priam, which is Tertioal in tbe entire ci7>taL FIg.t.
[isles to each other in a
_, .__ , but in a vertica! plana,
ptiing tbrongh either of the other two, tbe OUtjue s^tem is eumpTified. Proto-snlpbate of Iron, Carbonate of Soda, and Tar- taric Acid, with nameroos other natural and artificial ciratals beknig to thia sjBtem. Ciystals of thia claee can be divided into two mnmetrical halves only by tbe plane in whioii the obliqae axis bee : thia paaaea through the edge at which tbe planes Mand n' meet, and tbrongh a diagonal of the plane p. T. If tbe three axea are eqoal and equally inclined to each other,
Prttt-tM2fiat§ i^Itoi.
14
nil. 13 but not at right anglM, the B\omhoktdral
iyilera reiulta. Tha crjutala nf thJH tjpo ubiibUj pntMnt a trianeular or bexaguiial STmmetrical ouclino, irben viewed in tho direction of the niia of the Rhombohsdran, wliich IB UBiMlly drawn verticallj, u in ibc following figure; but it muBt be obaeireJ ihat thiH niia in Hat One nr tlio crjstallo- graphic aiee, Calcite, and Quartz ar Rock Crriitiil, aa [t ia commnnly turmed, are fa- miliar examples of ihis clau. of the forcf^iag conditionx Hfe fulfilled, Uie O the AnoTthic Bj-Btem ; which although com- pnsing an alrncul endlesB lariet; of fnuiblo relntialia, hw verv few knnwn reproaeiitalivBH ID nature ; in which fact we rccogtiiae the universal tendency to STmmetrical and har- moiiiauB arrangnnient, thai Ih met with in all llic wonderful wurka of creation.
biulpbnt« of Cop^r, and Aiiuite (Fig. 13), are ffiod iliualr«iionB of ihiii gjateni ; Ihe cry bUIb belonging tuwIiichSirBcliiirBcteriioil Aiifiit. \jy a total want nf syiumolry.
Bft. Tlie position of the rariouB planes or faca at which the surface of a cryBtal !-> compoaed, is aometiiues determined lijtbeir relation to the facea of a paralleb^pipcd of the limpluBt form IliHt exbibils the characterigLicH of the eyBti^m to which it belongs. Thin ia called the prinurtf form ; and the planea by which its edges and angles an modified nro culled ttamdary planes. In tho pivreding figures the primary planes are marked by capital letters, and the secondary by italics.
Jr. 14 26. 'He law of aymmelry, which prevBita
to a remarkable eiteut amonff cryatala, re- quires that all simiUr edges and angles of the primary form should be similarly modilied ; hence in a Urge number of inatunccs, tbo ayni- nietrical arrangement of the aecundary pluneii will point out the Byslemto which thecrystiil ahoukl be referred.
27. In some crystals a deviation from the law ofs.vmmeti^ is obiicrved in the exiatencu nf only batf tlie comphto number of planeii, ticher the altemata or tho oppojiCe plnnen beinp Duiitted, aa in Fig. 14 : lUse are callcl ItejaihedTol fmma. In some of these tbere ii a correapondenco between the unajmmetricHl fiinn. and other phTeical ibnractora; as in aitKiQ nbich cithertbe right or Ihu kit huDil
CTALS. 15
plines are omitted, as in tlie itnneied Heart, In tlieas an effect is pmdoced on n ray of l!f;ht trBnsmitt«d Inmugb > horizoutal slice flf the crjitsJ, which will ba Bubsequentlj explained aa righv or Wa-banded circular polsritation. (Cb. XXUL)
In Ihe cubic sjstem two ilintinct cliasea nf bemihednl fnnns ara freoDentlj met witb. One oT tbeae, the heniiheitral ictlA paraBei face*, reiults from the alternate deficKnc; of o:
■hich the complete form 120 (that of wbich the indicia are 1, 3. 0,1 ia represented in a (Fig. 15) while the corresponding hemihedral form is b; in which of tbe pnirg of similar ptaneii a, b, in a, the plaaci a odIj are developed.
The bemihedml form mth obliqut fane* ariwa from the defi- ciency of one of each pair of immiu pUnes, of Ibis the simplciit fxaaipk ii the tetTohedrori, which resuiis from the depoailioD of hucceMiTe lajera of molecules oa tbe alternate faces of the octa- hedron (Fig. 61 ; this is represented in a (fi^. IC); The tetmhe- dron ii unall/ dnwD in Ihe poaition b, in which position its retatioD to the oclAhednm is less apparent.
anorthic si hemihednl formi of the obliqiH ; but no utiiiwtoi^ nnlt appear* U foUaw from this att«mptad genenluatioD.
In PfTO^lectrie cr;»t»l», or thaw wbioh ezhilnt electrical pola- rity wben beated^ aa the TourmaliDe, a want of ajmmetrj between the two eitremlties ot the cryital ia nsuallj obaerred,
38. In many crjatiUine subttancei a remarkable, bat not un- ■ymmetrica], deviatioa Irom the nnialfbrtn ii oocanonallj obeerred. An; crjatal may be dirided into two equal and nmilar portione bj a plane passing throagh ita centre, sad parallel to one of ita faces, aa in Fig. IT, or (ai it i< in aome cases man ccmTtnienllj considered) perpendionlar to one of ita edges ; but the two halves are in a rSTenodjiaaliaQ u regarda each other. If, however, the aucoearire depoaition of particlea shoold take plaoe on opposite aides of thia median plane in Ihe tame dirMtion, the crrstal npre- sented in the seoond figure woold result, io place of tbe fonner; the letters 01^,0, Ac, showing the felatiooi of tbe planes in tha two fignrea. Crystsb of this kind are ealled twin oijttals or macles. The/ have also been called Henutroptt, beoanse the same resolt would be obtained if an ordinair ciystat were cut in half, and one portion tamed half ronnd on the other, a* maj bo easil; shown bj a model representbg these figures.
«».iT.
'odiilinct
forms not referable (0 the same class: tbns Calcite, which is rhombobedral, is chemically identical with Arragonite, which is
Eriamatic; and natural crTatabofSulphar,as well as those obtaioed T anbiimation, and bv the slow araporatioD of a solution of Sal- pilar in bisulphide of Carboo, are pnraatic ; bnl those formed in the cooling of ^nlphor heated considerably ebave the point of tonon. HM occasionally, though rarely, those fonnedio the above- named sehition, bebng to tbe oblique system. Substances poa- sessiog tiiis property of aaanming two different fbrms are called dunorphout. Some substances also are trimoT^hovt, or oocorring in three different forma; thus Titanic acid in the mineral spedea Butile and Analase is pyramidal, bat the inclinations of tbe laces are very different, while in Brookile it is prismatic By moat recent aathors, the podtioD of any face of a crystal is
h
POemON OF A FACE DEFIITED. 17
detennined, without reference to a hypothetical primaiy form, by the relative distances from the origin (the point at which all the axes intersect each other) of the points at which the given plane intersects the axes: these distances are generally either in&nite, in which case the plane is parallel to an axis, or very simple sub- mnltiplea of the parameters (23) of the crystal : these submul- tiples are called tne indices of the face in question.
In the language of analytical geometry a face of a crystal is defined by the equation
A + B + c ^'
in which A, B, C, are the parameters of the species, ajidp^ q, r, the indices of the plane.*
* For ftirther i2if<»ination on tlda sabjeot the reader is referred to the Art. CrfBtallofraphy, in the " Encjdopsdi* Meiropolitanm," and to a reprodac- tianof Pfaiilipars "Mineralogy," Vj the late Mr. H. J. Brooke and Prof. W. H. Miller.
18
CHAPTER II.
PHOPESTIES OF MAflSEB OF If ATTEB : — EXTERNAL FOBOSS.
30. ATTSAcnYE forces are capable of acting not only between atoms but also between masses, and form a very important sabject of consideration. The Molecular attraction of aggregation, which ties atom to atom, has been already alluded to. iVe have next to examine those forces which act between masses of matter ; these may be divided into two sections, the first comprehending attrac- tions at insensible distances, including cohesion and ecmjUarUy; the second, attractions at sensible, and eyen at unlimited distances, including gratfitation.
31. iAJl attractive forces, whether exerted between atoms or masses, diminish in intensity as the centres of attraction of the attracting molecules or masses recede from each other, snd gene- rally obey one law of the attractive force being invertdy as the equares of the distances between the attracting bodies. Attraction is always mutual, and exerted by one body on another, cceteris paribuSf in the ratio of their masses. As an example of the general law of attraction, let us suppose that two bodies, A and b, mutually attract each other when at a certain distance with a force equal to 1, at double that distance this force will be ^ instead of k of that when at a distance of 1, because the square of 2 is 4 ; at four times the distance the force will be diminished to ^, and BO on.
ATTRACTION AT INSENSIBLE DISTANCES.
Cohesion and Adhesion.
32. Wheneyer two smooth and clean flat surfaces of ax\j sub- stance are pressed together, a considerable resistance is expenenced in attempting to separate them ; this is owing to an attractive force called cohesion^ so termed from its causing bodies to cohere, or stick together. As an example of this force, if two clean surfaces of iron, at a white heat, be forcibly pressed, or hammered together, the cohesion is so perfect that they are subsequently inseparable : — this is the ordinary process of welding ; and some other metals are capable of being similarly united more or less perfectly. The mode of preparing black-lead for pencils, devised oy the lat« Mr. Brockedon, is another good example of the utilization of the force of cohesion. The plumbago is ground and finely levigated, all
nit being csrcfall; ramOTftd ; Iha powdsr ii than labjected to njdnuilic premira, by which it i« to e(Hnp1el«lj oonnlidated a* (o be eqiul, or erea laperior, in hanlDflaa to the nataral runnaltoa. Two freshlT-cat Bomce* of lead or caontchono will, on being preaKd together, cohere w tightlj that it ii acanxlj poarible to aepaiste them : uid availing luinaelf of thia fact, ths chemist pi«- pam tabes of the latter valaable anbatance, applicable to numeiuiu important parposei id bia maDipalaCioDa.
33. Cohaion fyara. — Soma caiioDB obMrration* ham been made bj Hr. Tomhnsati* oo the Tariet; of figurea produced, when dropa 01 diSerent kinds of oil are drepprid on the surface of water. To tbeaa the name of cohenon-fignr^a has been applied, aa their difirencei most depend on the different dogreee of coheaion exiit- ing between the reapedive particles. These figures appear to bi very constant for the same kind of ail, bnt to dISer connderablj ii
connderablj in taken as a teat of the purity of the oi
diKient kinds ; so mnch ao indeed, that the figure may ■ ■ "leoil. Oli'
M. Attraction takes place not nnlj between two portions of the aame tind of matter, but also between the a4)acent surface! of 4iifereDt substances, as between those of s soliil and a liquid ; this Tanety of attractJTe force has tieen termed adJiaiim.
It fnnn one arm of a balance, a plate of copper, c, be anspendecl, and carefully counterpoised by weigbta in the scale auspen^ed from the oppoeite end of the beam, a very alight additional weight will cause either the plate or the acale Co prepondenite ; place a basin full of water, B, nnder the plate, c, in mch a manner that the latter may jnat touch the surface nf the water in b ; on placing weights in a, a very considerable reaistsnce is experienced to the aeparation
• "Jaon^DTtlHSacMrrof Aru," 1M4, p.HS.
20
EZTEfiHAL F0BCE8.
of c from the fluid surface, owing to this adhesive attraction. With a circular plate of smooth copper, presenting an area of 6*75 inches,
Fig. 19,
|
4f^ |
l£ — |
~ |
<? n |
|
\ 1 111 |
1! |
ii ill |
ii 1 |
the weight required to overcome the attraction of the metallic surface for the water exceeded 1000 grains.
35. The intensity of this force, although constant, cceteris pari- bus, for the same solids and liquids, varies considerably in dinerent kinds of solids or liquids ; the following table represents the com-
Sarative intensity of the adhesive attraction exercised between ifferent metallic surfaces and mercury, according to the researches of Guyton and Quetelet»
|
HetaJ didn |
Force of adheaion in grain*.* |
Biakof metal. |
ComparatiTe force of adbeaion.t |
|
Gold . . . Silver . . . Tin. . . . Lead . . . Bismuth . . Zino . . . Copper . . Antmiony Iron . . . Cobalt . . . |
446 429 418 817 872 204 140 126 115 8 |
Gold . . Silver . Tin . . Lead . . Bismuth . Platina . Zinc . . Copper . Iron . . |
23-63 22-74 2215 2104 19-71 14-98 10-81 7-52 610 |
Gay-Lussac suspended a circular disk of glass, 4*6 inches in dia- meter, over surfaces of water, alcohol, and oil of turpentine. He
* Onyton-Marreau, in Kaatner*! ''Ezperimentalpfaysik." Heidelberg, 1810. t Quetelet, ** Foaitiona de Vhjuque," p. 104. BnxzeUca, 1834.
CAPILLAB7 ATTSACnOH.
21
fiMiiid die force required to separate the diak from the floids to Tarj isoasiderabl J, as shown in the following table : —
AdhMire force
Flnid.
Water Alcohol
If
Spaelfio gr»Ti^. ^ ^^^^
. 1000 414-7
. 0-8196 477-4
. 0-8695 6061
. 0-9415 669-8
0-8695 623-6
.B
Oil of turpentine ,
The force which causes the disks in these experiments to adhere to the fluid is identical with that which causes fluids to ascend in capillary tubes (37). The disk attracts an infinitely thin layer of the fluid on which it rests, and it is the molecular attraction of the mass of fluid for this thin layer adhering to the plate, which causes the resistance opposed to raising it from the surface of the liquid submitted to experiment
CapOiarity,*
36. If a plate or rod of any substance be plunged into a fluid capable of moistening it, as a plate of glass in water ; the surface of the fluid, ab, fig. 20, instead
of remaining perfectly horizontal, ^' ^*
will rise to a nigher level at the
eodes of the plate, as shown by the
dotted lines, as if the water were
attracted bj the glass. If the glass
plate be slightly greased prior to
immersion, or be plunged into a
fluid incapable of moistening it,
as mercunr, then a depression
instead of elevation will take
flace on either side of the plate, f a plate of glass, e, Fig. 21, be plunged into mercury, c d, this ap- parent repulsion will take place; and appears to be owing less to any peculiar property of the fluid metai, than to the presence of a minute film of moisture adhering to tiie immersed solid, and pre- venting the actual contact of the mercury with the glass.
37. These phenomena are best witnessed by immersing glass tubes of small diameter in water tinted with archil or ioi ; the fluid will rapidly rise, attaining the greatest elevation in the
• For an saalytiettl iiiTMtigation of this Bubieot the reader is referred to J.Da«Milz,"11i(eori0Metb£ii»tiqaedelaCapflUri^^^ Paris, 1886.
Fig, tl.
O-
^
7"
>D
miMt RkpillHrf InbM. Thna it will rise mDch higher in Jl tbnn ia B, in > than in o, &c. Tbis mnde of ftttroo- tion, eTiclently * modificBtion of ibo last-described pheaomena, ia ^, ji_ termed capillority tnm its beint most ob-
vious in tabes of capillsrj orhaiiOike bores. He. height attaitjed by fluids ia tfaei^e tnbflH is constaot, and incT^aeea ioTerselj as tbe disnieten of the tuhea ; it bears do evident ratio to the density or speciBo gra- I vitj of the fluid emploji-d in the oxpvri- ' ment : for Moschenbriick* found that, in Inhes of equal diameter, fluids rose to the comparative heights shown in lh« IblJowing table : —
Nun* of flaid. ElrrMioiu
SulphDric acid ■ ■ ; I '30
Sulphuric ether, eoDtaining alcohol . . I'40
AnhydroQ* aloohol 1-80
H^rochloric acid ....
Niti
207 2-53 3'40
Uil of turpentine ■ .
Distilled water . . . SolutiDn of ammonia . Solution of carbonate of . H. Gay-Luasac hu ascertained tliat water, altobol, and m\ of turpentine, ascend in tubes of tiie diameter of -05 inch to the fol- luwiDg elevations : —
PtuM. Speclfla gnvftf. SlvratiBo.
Water 1*000
. 081 98
Atcuhol . . .
Oil of turpentini
0-9415
0-37 0-33 0^9
comea ipto play equally between two
fluids, aa in the case of lubes. If two
platea of glass, i, B, touching at
o, and aeparated at b at a very
small angle, be plnneed into a
trough D, filled with coloured
the fiuid will, aHer a i^hort
. rise between the platea,
attaining the greatest elevation
where the edges of the g!
scribing II ectangular hyperbola. The utmoe • "DiM.P)>7Sla.Bip«lmaBt,L.B.."in«.
CAFtLLABT ATTlUOnOV.
23
Fig.U.
aittmed by the fluid in this arrangement is one-half of that which vodld haTO taken place in tubes having their diameters equal to the distance between the plates, and is always inversely as t lis distance. And the distance between the plates at any given point is, by similar triangles, proportional to toe distance of the point from the vertical edge, c ; hence the elevation of the fluid at any point multiplied by the distance of the point fi^)m the ver(ic<vl edge, c, is a constant quantity, which is a property of the rectan- gular hyperbola.
39. Ita drop of water be placed in the wide end of a conical glass tube, as at B, it will rapidly move towards the smaller end, a. The drop on being placed in the tube, becomes bounded by two concave sni&ees, of which that nearest the apex of the tube is the most curved ; the drop, therefore, moves towaids the apex in consequence of the attraction of the sides of
tbe cone for th^ water ; bein^, according to Laplace, inversely as the radius of the curve termmating the fluid coramn.
Let A B D, Fig. 25, be a compound tube, consisting of a flue tube, bavmg a capillary bore, inserted into a wider one. ^ Let the latter be immersea in water, the fluid will rise to a certain elevation, l. Then let the whole tube be filled with water, and again immerse it, the fluid will fall to a certain point in the finer tube, as to m, sod there remain suspended as perfectly as if the whole tube had been of the same diameter as the part a b. On ndfiing the tube gradually until the point u reaches B, the fluid will again sink rapidly until it again attains its former elevation, L. In tnis experiment a Iai)|;e quantity of fluid is supported partly b v capillary attraction in the small tube, and partly by tne co- hesion of its particles in the large one ; and as the elevation at m is found to be the same, whether the lower part of the tube be larae or small, it follows that the portion of fluid which, oy its gravity, opposes JTirther elevation at m, is a column of which the height n that of M above the surface, and its area the section of the tube at u. The convene of this will subse- quently (see Hydrostatics) be found to be true with regard to the pressure of a fluid on the base of a vessel contain- ingit.
It is a remarkable fact, that capillary attraction is capable of eppoeiog the evaporation of fluids under its influence. Fine tubes 01 glass, containing as much water as they could under the influ- ence of this force retain, have actually been suspended for months together in the summer's sun, without losing by evaporation any appreciable portion of their contents. It is, however, questionable
^.26.
24 EXTEBKAL FORCES.
whether this result is not partly due to the extreme minatenees of the evaporatiog surface.
40. By means of capillary attraction, oil is raised in the wicks of lamps, water ir. bibulous paper, cotton threads, or any porous substance immersed therein; m fact, all phenomena, in which fluids insinuate themselves into the pores of solids, are referable to this force.
41. If, instead of using water in the experiments just detailed, a fluid incapable of moistening the surfaces of the solids immersed be employed, the converse of the phenomena is observed, repulsion taking place instead of attraction. Thus tubes or plates of glass immersed in mercurv in their ordinary state, cause a depression instead of elevation (36) ; or, if water be used, and the tubes are greased or rubbed over with resin, or still better, lycopodium, the same thing occurs. In tubes thus circumstanced, the depressed surface of the fluid always presents a convex, instead of concave surface. This repulsion at some distance is well observed by nibbing the hana over with lycopodium, and immersine it in water ; on withdrawing it, it will be found to be perfectly dry, not a drop of water adhenng to it.
The following table shows the amount of this capillary repul- sion observed when glass tubes are immersed in mercury, luler care has been taken by boiling the li(^uid metal in the tubes to expel all air and moisture adhering to their surfaces, which, accord- ing to Baniell, diminishes the capillary depression one-half. The amount of the depression of the mercury is always in the inverse ratio of the diameter of the tube.
Diameter. I>epre8Bion.
0-60 in. . . 0002 in.
0'60 „ . . 0*003 „
0-46 „ . . 0 005 „
0-40 „ . . 0-007 „
Diamet«r. Depreadon.
0-30 in. . . 0-014 in.
0-25 „ . . 0-020 „
0-20 „ . . 0029 „
0-15 „ . . 0044 „
0-10 „ . . 0070 „
0-35 „ . . 0-010 „
42. Adhesive attraction (34) is exerted not only between liquids and solids, but is equally active between the latter and invisible gases. Thin films of air adhere by virtue of their attractive force to the surfaces of most solids, and become very obvious in glass tubes when mercury is poured into them ; the fluid metal, instead of closely and equally adhering to the inner surface of the tube, will be separated from it in several places by interposed bubbles of air, which adhere with the utmost obstinacy to the glass. This curious form of attraction is well shown in porous bodies, as cork, pumice-stone, charcoal, &c. When a fragment of either of these 18 immersed in water, and placed under the receiver of an air* pump, the escape of torrents of bubbles of air on exhausting the receiver is very evident. The term tibsorption is generally applied to this power of porous bodies in attracting gaseSj and is
EHDOfiUOSS AKD EZ0BM06E.
25
remarluMT intense in the cftfie of fresbly-bomt charooaL Thus one cubic mch of this subatance will reaoily absorb^
90 cab, in. of ammonia. 86 „ hydrochloric acid. 55 „ hydrosulpburic acid. 35 ,« carbonic acid.
n
9*2 cub. in. of oxygen. 7*5 „ nitrogen. 17 „ hydrogen.
1}
All hodies in the state of powder possess this property of absorbing air, which becomes obvious when they are immersed in water. Toleiably coarse iron-filings will thus actually float in water, if carefully sifted on its surface, being buoyed up by the adhering air, which appears like little gbbules of polished silTor in the water.
43. A class of phenomena referable to eaptUariiy is the appa- rent attraction and repulsion of small bodies floating on water, when placed at small distances from each other. If one of the bodies only be composed of a substance capable of being moistened by water, mutual repulsion will occur. But if both are incapable of being moistened, as two balls of wax, mutual attraction ensues. If the balls a, b. Fig. 26, be of wax, or cork, rubbed over with lyoo- podium or resin, the water is repelled, and two depressions in which the balls lie are producea. If thev are then placed suf- ficiently near each other, the repulsion of the opposed surfaces of the balls exerted on the water at c will ^^ 26.
lender its surface concave, and the balls^ by the lateral pressure of the water beyond, will be pushed together, and appear to attract each other. In the second case, if the ball d be of clean moistened cork and e of wax, the reverse takes place, the water being raised by attractive force on all sides of the first, and repelled by e. There- ibre, on the balls being placed in con- tact, they appear to repel each other in consequence of d attracting the fluid, which is repelled by e, the Tatter being incapable of being moistened by the water. If both bodies are wetted by the fluid in which they float, as two clean cork balls, r, G, in water, they will be drawn together by the united effects of the cohesion of the particles of fluid, and their adhesion to the Rufaces of the balls ; and when in contact, the fluid will rise higher between the balls, than at any other part of their surfaces.
44. Closely allied to capillarity are the phenomena of endomioae and exosfnosCf discovered by Dutrochet. Whenever two liquids of di&ivnt densities, capable of being mixed with each other, are separated by a ii!iembranous or porous partition, two currents be-
come esUblirheil, ona & currant or fluid proceeding from witbia to without (exoBinaBe, JE Bid iiafiit, impulse), uid anolLer in the contrar; direction (cndoB- moM, Iviov and uir/iic). If a gUu tube cloied at one end witb a piece of bladder, ±, be paitl; filled with a I tolution of sugar, aalt, &c., and immened In a teasel partly filled with pure water, the fluid will rapidl* rise ID the tuba b, the water having entered tbronK" jl the bladder b/ endosmoae, and, adding to tbe I contents of the tnbe, cause tbe fluid to be elevated
much above its former level. If. now, the conditions be revereed, Bvrup being placed in c, and water in B, exosmoee will occur, b; which the tobe b will become nearlj emptied. Ab a general rale, liable, howerer, to Mveiil eicoptioos, it appears that fluids of tea tpe- dfic gravity have a tendency (o pass througb membranes and B bodies, to mix with those of greater density (provided thef .-iscibla), and consequently to dilute them.* Tbe general rule may probably be thus more correctly ex- pressed, that the fluid, between which and the porous paitilian the greatest amount of capillary attraction eiiBts, will usually pass through and mix with the other fluid.
i6. These phenomena admit of a very simple explanation, (banded on tbe capillary attraction or repulsion- exerted by the porous diaphragm npon the fluide expoeed to ita influvnce. In the case of a piece of bladder, this is readily moislened by water, but not bjr alcohol. Let the tube b be partly filled with alcohol and then immenied in water, Tbe first action in this coae ia the ~ ID of the membrane to the water, whilst it repels the alco- hol. A portion of water permeates the bladder, ia immediately mixed with the alcohol, and is do longer attracted by tbe bladder. A fresh portion then enters, and this continucB mitil the al(»hal is considerably diliit«d.
Ths moBt conTcnient form of apparatus for demonatrating endoamosa or eioamoae is a amall rnnnel-sbsped flaaa vessel, tbe month of which ia about two inchcB in diameter, and fur- niahed with a rim, over which a piece of thin bladder may be aecorely tied. Int« the neck of this a piece nf barometer tube about 18 inches long, and O'l in internal diameter ia ground. By this means tbe veaael may be readi^ filled and emptied, and the area of tbe acting sarface Ib bo large compared witb tbe section of the tuba, that the fluid will nae two or three inches in the tube in s quarter of an hour.
Tbe endoamose or influx of fluid is always attended by an > "IIaaT.l(MtMnih.iBrrKiido«ao«*,"lU,pwH.Dilncbat. Fuda, 1898.
mdfttinn of > ceitki'n porticni of the liquid confinod by the poron» diaphragm, Thii ihiit bo illmrtrslBd bypUcing in the tube ■ aolation ^ sulphate of iron, unci immening it in water. In * short time the lolution will ri«e in the tube from Ihe FDtnoce of water ; and if then a few dropi of tincture of galls be added to the water is the external lessel, the purple colour which ia produced will saliafactorilj prove that a portion of Ihe solutioD of iron has really ainded through the membrane.
The onuotic foireof dillerant saline solutions difiers considerablv; tbns a ■olulion of chloride of almniDUEn is, according to Mr. QTshain, 45 times more eneigetic than one of chloride of sodiam.
46. If the capillary action of the two ffnids on the diaphragm ia nearly equal, the endoBmose and eioamoee will be rery feeble ; bat will take place with considsrablo actirity in the direction of a gal- Tank current transmitted throuzh the flaids. This fact maj be ludjly ahown thua : take four pieces of glass tabe (hat will suc- ceniTcly pass within each olher, close the oaler one with a piece of cvtk, through which the poaitiTe electrode of a Tollaic battery may be paaaed, and tie a piece of Chin mem-
hnne oTer the ends of the olher three. 'V- ^
If a satmsted solution of gallic acid be placed in the Srst and fourth tube, and a weak solntionorprotoaulphate of iron* in the aBcond and third, and the tabes be | placed one within (hs other, and a current pissed throDgh the whole, by dipping the iiegatiTB electrode in the flnid con- tained in the inner tube, the formation oTgallate of iron in the second and fourth lobM will immediately indicate the pas- sage of gallic acid in one case, and of prcto-enlphale of iron in the other case,
aoooTding to the direction of the current. "*
This fact ia important in Physiology in +
indicating the probable manner in which the nerToos syitem influences the tarioos animal Beoratians.
47. Analogous phenomena are also eihiblled hj gases or seri- (bnn fiuida. If, fur instance, a glass Teasel full of airliaTs a piece of thin bladder tied firmly OTer its mouth, and he then placed in ajar of bydroEen, the gas will permeate the membrane and enter l>w Teasel. The contents ofthe latter areconseqaently increased; the snrface of Ihe bladder becomes comex, and if safGciently thin will erentaalty burst. It has been demonstrated by Hr: Graham, who has moat elaborately examined these phenomena, that gaaea difler in tlieir tendency to difluse Ihemselves through membrane* or poroua diaphragnu. This tenilencj diminishes with
*(IT. ofnlBeuid, and 7or8 (r. arprDtaaalphaleotima, each in 1) «.
le of density ot the gtn, boing inTeraely proportional lo root of tbis deDBitj. It maj b« rBmarked. tlat the
ipplies lo tbe relative Telocity with which diSerent giweB will be discharved from bd orlGce into a Tacnum : cLia fact seeme to comiborale the brpotheaii of Dallon, that any one gu acta aa a Tacnnm ia relation to another.
hydrogcD, oxygen, and nitrogen will b« aa fallowe : —
Oi;g«n . . Dene. 1105 . . Diff. 0'94S
Nitrogen . . „ (C972 . . „ 1014
Hydrogen. . „ 0-069 . , „ 3*807
If a long tahe be closed with a p)a^ of dry plaat«r of Paris,
inverted in a cup of <rater, and filled witb hydrogen |
will BO rapidly permeate the planter, ' ""
1 a plnp of dry plaat«r of Paris, filled!^ witb h;rdra»n jrag, the gas «r, to diffusa itMlfin toe air, as to
46. AnieS't -Fin Vamp Indicator. — The diffiuive power of gasDB baa been ingenioaaly ntiliaed in the Kg. to. conBtmction of this apparatiis. An inflated
film of caoutclioaB, a, snrrounded by a hand of linen, to prevent ita expanding transvenely, ia Qxed on a stand, r, no that the upper aurface rests aeainBt a lever, b. Thtg lever bolds a BCftpe-wiieBl, c, which is driven round by a cord attached to a weight, d, in tbe hollow stem. The two palleta of a cratch, to which the clapper of the bell, e, is attached, work agunst the wheel, t. If this appatatus be placed in an atmosphere containing a dangerous percentage of coal-gaa, the gas will ra[udly permeate the film, and distend- ing it longitadinally will press npon the krer, and release the oacapement, and thus set the bell ringing, to give tbe reqaiaite alam). Tbe lever, b, may also be employed to complete a voltaic circuit, and thus b; saitabla means a signal may be conveyed from the bottom of a mbe to the mouth of the shan, or elsewhere.
An analogous contrivance is tbat of makinfc the bottom of the c»ae of an aneroid barometer to consist of a disk of parous eaiih- •nwore, similar to that of which the porous cells of a voltaic batteiy are made. With tbis the diffuaion is so energetic, that the indication of the presence of gas is almoet instantaneonsL It is to be hoped tbat these and similar coatrivancna may be inatm. mental in migrating the fearful loss of human life tbat constantly occurs amidst the perilous occupation of the miner.
D1FFT7810S OF LIQUIDS. 29
49. The following results also Bave been obtained* with regtird to the transpiration of gases throagh capillaiy tubes: — 1. The resistance of a capillary tube of uniform bore to the passage of any gas is directlj proportional to the length of the tube. 2. The Telocity of the passage of equal Tolumes of air of the same tern-
Serature but of different densities, is directly proportional to the ensity. 3. Tllat rarefaction by heat has precisely the same effect as loss of density bj dimimshed pressure^ in diminishing the Telocity of the transpiration of equal Tolumes of air. And finally, that transpiration is promoted by density, and equally whether the increased density is due to compression, to cold, or to the addition of an element in combination ; thus the velocity of oxygen is in- creased b^ combining it Trith carbon Tnthout change of yolume, as in carbonic acid gas.
50. The tendency of gases thus to diffuse themselves among each other, is a property participated in by liquids. This is, how- ever, not vrithout exception, as some, like oil and water, are not miscible vrith each other; and others, as ether and water, are miscible but in small proportions. In most cases of miscible fluids, an actual penetration of the mass of one fluid by j^^, 31, the atoms of the other seems to occur ; and the mixture consequently occupies less bulk than the fluids did when separate. Thus, if two glass bulbs. A, B, Fig. 31, filled, one with water and the other with alcohol or sulphuric acid, be connected by means of a tube, c, passing water- tight from one to the other, the fluids will mix, and when the mutual diffusion or mixture is complete. Trill no longer fin both bulbs. On allowing the apparatus te rest for a few minutes in a vertical position, a space unfilled by ^^ fluid Tsill be observed in the bulb, a, in consequence of /^v the mixture having been accompanied by a diminution in ^^^ volome. If 100 parts of alcohol be added to 100 of ^^ water, the mixture will measure but 196 parts ; the same bulks of sulphuric acid and water will, after mixture, measure only 135 parts.
51. It appears from the observations of Mr. Graham,f that neutral salts and various other substances in solntion have a diffiisive tendency, similar to that of gases. The results were obtained by^ immersing wide-mouthed bottles, containiog any pro- posed solutions, in glass vessels of distilled water; great care being taken to avoid any mere mechanical mixture of the contents of the bottle, and the surrounding fluid, by agitation. It was found that, with most substances, when the quantity in solution varied finom 1 to 5 per cent., the Quantities diffiised in the same time ^usually a period of eight oays), were proportion^ to the quantities in solution, the temperature remaining constant ; also. Shot the diffusibility increased Trith increase of temperature. It appeared also, that, of the whole quantity rather more than one-
• Graham on the Motion of Gmss; ** Phfl. Trans." 1849, Part n. t On tlie I>iiRiai(m of Idqnids ; *• Phil. Trama." I860, Part I.
80
BXTEBKAL FOBCEB.
fourth was diffused dnrio^ the fint two days, the qnftiitities dif- fused during each remaining period of two dajs being yery nearly- equal. The following table exhibits the relative quantities of rarioas substances diffused at a temperature of 60'5' F. daring eight days, from solutions containing 20 parts to 100 of water: —
Sulphuric acid . . . 69'32 Chloride of sodium . . 68*68 Nitrate of soda . . . 51*56 Sulphate of magnesia . 27*42 Treacle 32*25
Glucose . . , . . 26*94 Cane sugar (crystals) . 26*74 Gum arabic . . ... 13*24 Albumen . . . .' . 3*08
Salts of different bases may be separated by difiusion, for the quantities of the carbonates of soda and potash diffused in the same time from a solution containing equal parts by weight, were found to be as the numbers 35 and 65, very nearly ; and while the quantity of magnesia in the salts obtained from sea-water was 6 per cent., the proportion in the salts diffuRed was only 4 per cent. In some instances the difiusive power appears to be sufficiently energetic to effect the decomposition of tnple salts, such as alum, and the ammonio-sulphate of copper.
52. Friction is the resistance to motion which any portion of matter offers to another portion in contact with it; and beinf? analogous to adhesion, may be most appropriately considered in this chapter. Friction is of two kinds, one of which opposes the commencement of motion of one body in contact with another, but ceases to act when the body is actually in motion, the other con- tinually resists and retards the motion. To these forces the terms »t(ttical and dynamiecd friction have been applied : but, to avoid any error from the'confusion of terms. Dr. Whewell has proposed to designate the former atiction^ a simple and intelligible term, retain- ing firiction to express the latter force. We may therefore desi^ate these retarding forces by their initial letters, J?* and /Sf respectively.
Between two plane surfieu^es, either of the same or of different
materials, F is proportional to the pressure P by which the two surfaces are held together, or,
in other words, p is a constant quantity : but at the same time .r'is independent of the extent of the surfaces in contact. This may be shown by the apparatus represented by Fig. 32, m which a weight, a, placed in a scale attached to a strinz passing over a pulley, b, is employed to drag a mass, c, along the horizontu surface of a table, de. The mass c, whether of wood, iron, or other material, is in the shape of a rectangular parallclopiped, .the breadth of which is B or 4
Fig. 32.
nuonoH or smrACES. 81
tiiDM tke height, and baTing one of the broad sides hollowed ont BO as to leave only two narrow margins. K a is jtui iuffident to keep c in motion, it will be fonnd to have the same effect, whether c rests on the broad or narrow side, or on the two maigins, here represented uppermost. ^ Also, if one or more weights, each equal to c, be placed on it, in either jiosition, a proportionai increase of the weignt, a, will be foand eqaivalent to tae increased friction.
63. The retarding force represented by S increases from the mstant when both sor&ces are qniescent, and attains its mazimnm e&ct in the course of a few minutes. It may be yery readily coanteracted by jarring the surface of the table slightly, but re- peatedly, by the hand, during the time of the preceding experiment.
When the weight, a, has been determined ezperimentallv, and the body, c, then allowed to remain qniescent for a short time, it will be found to require a considerable increase of weight, in some instances eyen greater in amount .than c itself, in oraer to start the body, c, from its position of rest* The added weight will re- present the resistance, 8.
Sh^B been found by experiment not to be independent of the extent of sur&oes in contact, or proportional to the nressure, and therefore not to follow the same laws as JFl No dennite law has hitherto been assigned to this Quantity.
54. Between hard surfaces, P is found to be an uniform retard- ing force ; but between soft surfaces, as those of felt or leather, it increases with the yelocity of motion.
i^is fonnd to be diminished by coating the surfaces in contact with any unctuous Rubstance. S may or ma^ not be diminished by the same means. It appears from the experiments of M. Morin, that if a complete stratum of the unguent be interposed, F is the same for all substances. This result is manifest, as in this cafie' the retarding force is the cohesion of tbe unguent., and not the friction of tne opposed surfaces. Finely powdered plumbago, either dr^, for sumces of wood, or inixed with pease for those of metal, is found to have tbe greatest effect in diminishing friction.
In many instances ^is dimi- _.
Dished by polishing the surfaces *^'
in contact ; 8 is generally in- creased by the same means.
56. The yalue of ^ may like- wise be determined by the fol- lowing method. One edge of the tiulace, A B, under experiment, is raised from the horizontal plane until the body, c, placed on it^ will just slide down, and the angle of eleyation deter- mined by a graduated arc, d e, •i in the annexed diagram.
ir this angle be celled f, then ten ^ {the trigonometricel tan- gent of the mgle) ia called the coefficient of friction, and the angle itself bu been called the iliijin^ angie, or limiting angle of railtanet, becaoite, If two jilane surfaces of any kind of material rast againgt each otber, it is evident that no nmount of preaauro will caute the surfacss to alids over each other, if they •re inclined at an angle leaa than p to a plane perpendicular lo the line of preaaure. The limiting angle of reaiatance ia important ia the arts of conatruction, aa, lor instance, in delemiining th« neceasar; direction of the joints of archea, and of the alopea of
The value of f having been thua determined, the value off +:S ma; be aimilarly determiiied bj allowing the bodies to remain for a abort time at rest, and then gradual!; raiaing the plane, until
Friction between cjlindrical .aarfacea is found to follow the aame law, bnt S ia said not to eiist between cylindeia. This, however, has been found not to be the caae, if a hollow and a solid cylinder are very accuratelr fitted to each otber, as ia the caae in Whit- worth's cyhndrical gaagea.
56. If a cord pasiing over the anrfac« of a wboci or cylinder is emplojed lo soatuQ a weight, bb in the capstan, or to coroinnni- cate motion, as in tbe driving parts of machiner;, the amoont of friction dependa oa the angle of contact between the cord and auTface on which it reals, and ia independent of the radiiia of tbe surface ; it ia alao greater when the cord testa in an angolar groove, than when resting on a curved auriocc, or on tbe aurface of the cjlinder, aa may be thua abown : — l^ake three caat-iron vlieels, one of two or three inchee, A, and another a foot or more in diameter, b, with similar angular groovea, and a third, c, of any oonveoient diameter, withsplunrim; take, alao, apiece of hempen cord, vitb two equal weights, Fif-U. II, K, attached lo each end of it.
"- Jjet the cord be placed in the
grooves *, b, aucceaeively, and " It will be found that in both
cases the same weight, r, is necBBsary, when attached to one of the weights, n, to just drag up the otber s ; but that asmaller weight, f, will suffice, ' if the cord be laid on the plun rim, c. When the weights are ^ freely suspeuded, it is mani- fest that the oord will be in contact with the groove through theeileut of a semicircle, or 180°. If tbe cord be now carried from tbe wheel, a, horlion tally over a pulley, a, it will bo in contact with the wheel through a quadrant.
a&lYlTATIOV. 88
or 90* ool J. It win now be foand that ■ wiU juH move with a weight, F, Buch that, ifD+jraKs in the latter instanoe, then i>+P=K*B would giTe the ralne of f in the former. Thoa, if in the case of the strinf in contact with a quadrant of the circle, d and B being each llb^ f (including the scale) were also lib., then woold Ks2 ; and when the string is in contact with the whole semicircle, d and b remaining the same, k' woald be 4, and the weight, F (including the scale), would be Slbs.
Ctmaeqnentlj, in the capstan, the amount of friction depends on the number of coils of the rone ; this amount for each sucoesrive coil is, in fact, in geometrical progression, and between a wet hempen rope, and a cylinder of oak, the common ratio is 8 Tery neanj : thus, if the rope were held on with a force of 1 cwt. the weights sustained by 1, 2, and 3 coils respectiyely would be about 8 cwt, Si tons, and 25i tons.*
57. In the working of machinery friction gives rise to a oon- siderable expenditure of motive power, as well as wear and tear of material : but as there is no friction between surfaces that roll on each other without any sliding, this source of loss may be in a great measure obviated by the introduction of what are termed fnetionrToUerf gt frictionrwheeU. The axis of a fly-wheel, or other heavy rotating piece of a machine, is sometimes made to rest on the drcomference m a wheel at least ten or twelve times the diameter of the axis, eiiher before or after passing through the bearing collar : or if there be no considerable pressure on the circumference of the wheel, the axis may rest in me obtuse angle formed by the cir- cumferences of two wheels, placed near each other, and overlap- ping each other about one-third of their diameter ; in which case no bearing-collar or axle-box is required. The axes of the friction- wheels must of course sustain a certain amount of friction, but it will be small compared with the friction saved, on account of the slowness of their motion.
▲TTBJLCnOirB AT 8BKS1BLB DIBTAHCBB.
Qraviiation,
68. When a heavy substance is permitted to fall from the hand, every one knows that it rapidly reaches the floor ; and doee not rise towards the oeiHng, nor move laterally towards the walls of the room. A stone being mere inanimate matter, and consequently absolutely inert, this phenomenon cannot depend upon anj iamaU tendency to reach the lower part of the room, as one of the enmitial
* If Ian ^ be the ooeffldent of fHctioii between the rope and Bovlhea in ooBtaot with it. mod 9 the angle of oontaot ; alio Px, the weight rastslnedby Pi end the lirieiioa jointly, then
Pj=P,f*-*"* or logPi— k)gP,=«.ttti^.
8ee ICoeeley's " Meehanieal Prineiplei of Bngineering and Arobiteetve" for farther infonoatJon on this sal^iect.
34
ETRBHAL VOBOB.
^.35.
properties of matter ia its utter incapaciW to change ita porition. CoDseqQently, the rimple phenomenon of the falling of any hodj towards the earth mnst anse from the exertion of an attractive in- flnenoe or force emanating from the latter, and to this the name of OravUatian is applied, m consequence of its caasing that efiect which we recognise hy the term weiaht : the weight of any sub- stance being merely a measure of toe attraction of the earth for it. This form of attraction is exerted not only at comparatively small, bnt at all distances, however vast : thus, this force acts as effectually on the planet Herschel at the distance of 1,800,000,000 miles, as on the falling apple, in which Newton is said to have first recognised its existence. If a mass of lead be suspended by a string it will, when left iiee to move, point towards the centre
of the earth; now the same thing occurs in India, in America, and at our antipodes ; a fact proving at once that the lead does not obev a nahaxU im%deney tofaU; tor the plum- mets, A, B, point in opposite directions, aa alao do c, d, ac- cording as they are situated at the opposite poles or at east and weat ; all pointing towards the centre, e, of the earth.
59. Gravitation, in common with other attractive forces, obeya most strictly the ffeneral law already announced (31), its intensity being inversely as the square of the distance of the gravitating boay. Thus our moon, which is placed at a distance of sixty of the earth's semi-diameters from its centre, is attracted according to this kw with a force of 60 x 60=3600 times less than bodies are on the surface of our globe. The force of gravitation must always be considered as acting from the centre of g^vity of any body from
which it emanates. Fig. 96.
From this circumntance it is theoretically impossible for two plumb-lines freely sus- pended to hang perfectly parallel. Let A and B be two lines, each having a leaden ball suspended to it ; they will point towards the centre, c, of the earth, and of coarse, instead of being perfectly parallel, will form an angle with each other, which at small distances is so slight that it may be almost neglected
_ in reality, althougn it can never entirely vanish. In small distances, even to the
tK^^m^-:stmm^mmB^^Kmtrwr'^^mmr
ORAVrTATIOH. 35
extent of some hundreds of feet, the lines of gravity indicated br two plnmb-Iines may, on account of the magnitude of the semi- diameter of the earth, be regarded as parallel ; but when these lines are some miles apart, their convergence must be calculated accord- ing to the curvature of the earths surface; this will amount to about one minute in a FSg, 87.
geographical mile, and consequently to one degree m sixty miles.
LetABCDirbea section of the earth at the meridian of Paris, and ▲ a; its axis of rotation. Paris will be situated at c. and a pltunb>line freely suspended there will point in the direction of b o c. Dunkirk will be d St an angular distance of 2*^ 11' 6" from Paris, and its plumb-line will coincide with P D e. Barcelona will be at b, at an angular distance of 7" 28' 29' from Paris, and a plamb-Hne there will coincide with the line o B e, forming an angle of 9* 39' 35" with a omilar plummet at Dunkirk.*
60. The intensity of the attraction of gravitation varies, not onh- with the mutual distances of the attracting bodies, but also vitn the quantity of matter contained in them. In this wav the great centre of our universe, the sun, from its enormous bulk, its mass being greater than that of all the planets taken together, \b capable of attracting even the most remote, as Uranus and Nep- t^me, although placed at the enormous distance of hundreds of millions of miles. This force being mtUuaUu exerted between bodies, they idways move to meet each other : hence when a book or a stone falb towards the earth, the latter rises to meet it: this motion is of course almost infinitely small, because the attraction of these bodies for the earth being in the ratio of their masses, the enormous preponderance in favour of the earth would prevent its movinjT an appreciable distance to meet the stone, whilst it wonld be sufacient to enable our globe to attract the latter at a distance of several millions of miles. As a necessary consequence of this mntoal attraction of masses, elevated builuinss and mountains might be expected to gravitate towards each other, an effect pre- vented by the superior attraction of the earth which tends to keep them on their bases, and by the attractions at insensible distances which firmly bind their integral portions together. For whenever graritatton and cohesive or capillary attraction are opposed, the tatter within the limits to which they are confined are most ener- getic, instanced in the ascent of fluids in capillary tubes (37), above their level, aud in opposition to the gravitative attraction of the earth. Still, lateral attraction is exerted, for Dr. Maskelyne, in a
• PoaiUet, " moments de Physique." d2
86 KXTSBITAL FOBCK.
set of ezperimentB peifonned in 1772 near the moantain Shehallian in Scotland, found that a plummet was really drawn from the per- pendicular by the attraction of the mountain to the extent of 54". The same thing took place in the researches of the French astro- nomers, whilst engaged in America in determining the measure of the meridian ; nuinerous sources of fallacy arising from &e lateral grayitation of their instruments towards the surrounding moun- tains, opposing themseWes to the correctness of their results. The lateral attraction of Chimbora9o, the loftiest of the Andes, although much diminished by the existence of an enormous vol- oanic cavity in its centre, was found by M. Bonguer to deflect a plumb-line 7' or 8" from the perpendicular. The mutual attraction of bodies free to moye is beautifully illustrated in the celebrated Cavendish experiment,* which has lately been repeated by the late Mr. Francis Bailv.t In this noble experiment the attrac- tion of a large mass of lead for a given mass of light matter waa rigidly determined, and thus by comparing the attraction of the mass of lead for the light body with that of the earth, the meaa density of the latter was determined to be 6*6747 times that of water.
61. The ascent of vapours and balloons into the air, like that of light bodies, as corks, m water, is produced by the attraction of gravitation. For this attraction being greater in proportion to the quantity of matter, the denser bodies, as the atmospheric air or water, are drawn forcibly downwards ; and those containing a less quantity of matter in a given bulk, as the balloon in the former
case, and cork or wood in the latter, are forced •^'^^ to rise by the denser fluid bodies sinking
beneath them.
Let the vessel ▲ be filled with water, and a solid body, as b, be placed in it ; both the fluid and the bod^ b will be attracted by the earth. If B be heavier than an equal bulk of water, it will be more attracted by the earth than the fluid it displaces, and will sink : but if it be
less heavy than an equal bulk of water, the
fluid will obey the preponderating fravitative attraction of the earth, and b will oe forced to nse to the surface. Thus the floating of light bodies in fluids of every de- scription, is a direct and legitimate consequence of the law of gravitation.
62. The spheroidal form of our earth, and of the planets of oar system, appears also to result from this law. For as attraction is equal at equal distances, and virtually emanates from the centres of the masses, we may conclude, that the earth, when in a fluid or semi-fluid state, must necessarily have assumed the spherical form ;
• ••rUL Trans." 17B8,p. 409. t ** Mem. Astrononioal Boo." vol xiv.
OBAYTTATIOV. 87
becaofle no^figore bas every part of the line bounding its penpbery eqnidistuit* ttom the oenfane, except a circle : which would have been the exact figure of a meridian section of the earth, if the cen- trifi^^ force arising from its rapid rotation had not interfered, by opposing gravitation in the equatorial regions.
63. As weight is an acquired property of matter, and prodaced by an attractive force r58) emanating from the centre of our earth, hot dinunishing as tne distance from that point increases; it follows that a mass of matter would not appear so heavy on the top of a lofty mountain as on the earth's surface, because it will be there further removed from the centre of the earth. And ao cordingly it is found that a mass of lead weighing 1000 pounds at the level of the sea, loses two pounds of its weignt on being ele> vated four miles above the surface : and if carried to the surtace of the moon, and thus removed 240,000 miles from the earth, the attraction of the latter for it would not exceed five ounces.
For this reason, bodies weigh heavier near the poles than at the equator, on account of the former being nearer the centre of the earth than the latter ; and if it were possible to place any body in a cavity at the centre of the earth, it would be equally attracted on aU sides, and consequently remain suspended w space, like the fabled coffin of Mahomet.
64. It may here be mentioned, although the scope of this treatise precludes a rigorous demonstration of the fact, that be- neath the earth's surface the force of gravity varies, not inversely as the square, but directly as the distance from the centre, and con- B<H]aently ceases to exist at the centre. This is owing to the fact that at any given point the superincambent spheroidal shell exerts no attraction, in consequence of the attractions of all its compo- nent particles being mutually balanced.
88
CHAPTER ni.
BTATIGBy OB THS HBCHAHIGAL BBLATIONB OF BODIES AT BB8T.
65. The science of mechanicB treats of the effects of physical force on matter. If a force is counteracted or opposed in such a manner that no motion ensues, the idea of , its existence is best conveyed by the term pressure. Thus, if a weight be placed on the extended hand, and sustained by it, we are conscious of the existence of the force of gravity by the pressure on the hand, and the muscular effort necessary to counteract that force : or if the hand be placed between a heavy weight and a table, we then re- cognise tne existence of gravitation oy the pressure alone : bnt, when the hand is passive, the table appears to press against the under surface of it, just as much as the weight does on the upper surface ; and if the hand be removed, the doumward pressure of the weight is sustained by the upward pressure of the table.
We may hence perceive the propriety of dividing mechanics into two distinct hranches :
I. 8taiic8f which treata of the relations that must exist between two or more pressures applied to a point or body, in order that no motion may ensue ; and
IL Dynamics^ which treats of the relation between forces, which, when acting on a point or mass, put it in motion ; and of the nature and direction of the motion produced.
The former division, Statics, mil form the subject of the present chapter.
66. When two equal pressures act in precisely opposite direc- tions, as in the case oi the weight and table above mentioned, thev are said to be in equilibrium : and the effect of the j)re8sure is toe same at whatever point in the line of its direction it is ap- nlied : thus the weight on the table might be supported by a string from the ceiling, in which case the upward pressure of the table would be transferred to the hook from which the weight is spa- pended ; or it might be sustained by a vertical rigid rod, bv which the pressure would bo transferred to the floor, or to the earth beneath it, and the transferred pressure would be precisely the same in amount, neglecting the weight of the rod and string respectively.
67. In order to enable us to estimate the amount of pressures, it is necessary to employ some unit or standard of comparison ; we cannot, for example, compare 1 hour with 12., or either with one cubic foot. In this country, the unit of pressure is the weight of
SESULTijrr OP pbesbubbb apfusd to a poikt.
39
Fig. 39.
23*815 cdbio inchea of distilled water, weighed in air at the tem- pentnre of 62** F^ the height of the harometer being 30 inches; this weight is called 1 ponnd iroj, which is divided into 5760 grains, and 7000 grains make one pound (lb.) avoirdopoiB. ^
68. When two or more piessnreB are represented by lines or munbers, it is meant that they bear the same proportion to each other that the lines or nnmberB do ; and lines taken in the direc- tion of any pressores, and proportional to them in lencth, are said to represent them in magnitude and direction. If tne piessnres cannot be represented by finite numbers, as» for example, the side acd diagpnai of a square, tbey are said to be tnoommenmraibie,
69. When a system of pressures is in equilibriont, any nunber of them maybe removed and replaced by a single pressure, called the resultant of those it replaces ; of this the pressures replsced are oaUed the eomponents, and the act of replacing them, eonqxmtion.
Similaiiy any single pressure may be removed and replaced by sny nmnber of pressures, which would jointly produce the same effect; the pressore replaced is said to be reeohiedf and the act of replacing it is called nadhUum.
70. The resultant of two pressures ap- plied to the same noint is represented m magnitude and direction by the dia- gonal of the parallelogram, of which the s4i*oettt sides represent the pressures in magnitude ana direction, llie truth of Uiis proposition may be thus shown by experiment. In the annexed figure, A and B are two pulleys running on pins in a vertical board ; o and i>, two weights suspended by a string passing over them ; from any point, I, of the strmg another weight, p, less than the suni of o and n, is suspended ; b o, b h, s c, are three wooden rods jointed together at I, and Ko and kh are two similar rods jointed to a clamp sliding on BK, and connected by sliding clamps wiUi bg and Bfl. The rods are all marked in inches measured fiom the paints of connec- tion. Let us suppose the weights, a x>, p, to be 3, 4, 5 oa. reneo- tively ; then take b o, b h, any lenjg^ths proportional to 8 and i, as 6 sad 8 inches, and xnake kh, k o equal to b o, b h, respeotiv^y ; then BOKH is a parallelogram. Kow let the slidinj; piece, k, oe moved im or down until the anfle o bh coincides with the angle ABi^ which the string assumea when the weights were left free. It wUl be found that the dia^nal of the parallelogram b k is in a vertical position, and that its length is ten inches ; it therefore besrs the same numerical ratio to the weight p, that the sides b o, b B, do to the weights, c, n, respectively. Now the weight p would evidently be supported by an equal pressure acting vertically up-
wards &t the point ■, which will be Tepraeetited hj s i, u 0 und n
r«preMiita in magnitude and dirsc- tion the leenltant of two preHure& which are themselTeB repreeeDtH in magnitude and directian by the
±xat aidea, ta, an. If, then, required to 6nd tbe reniltant
be obtained bj completing tha parallelognun a b, of which the dia-
Ithe diagooal * n is the resnituit of A B And 1 0 : then complsU the panllslogram d k, and 4 F is the resDltaBt of 1 D and A ■, that is, of A B, A c, and A B, and so on. Faan the comtniclioa it ii clearlf immaterial whether a b, a c^ A B, &c., ai« all in the same pUne or not.
72. It ibllowB from the preceding pnipoaition that a'point will ho kept Bt rest, if acted on b/ three preuures, which are repi«Beiit«d in magnitode aad direction b; the three aidea of a triande taken m order, ij. is the aame direction, a> Aa ob, b a, in the anneied diagiBm (ilg. 4S]. For if we complete the parallelogram ■ d, tbs sideOD is equBlacd parallel to b a, and will therefore represent the
ot the joint eSect of o b and 0 D, which is represented bjr c A (70), it will therefore connter- act the nniled eflecta of cb and B A, and, if acting with them, will keep the point oiaclion at rest If the aides of a triangle are retpeo-
I tions of three preasnrea which keep
a point at i«tt, thej will repreaeat
the preasnrea in magnitnde, for if tbe three sides of one triaogla
are rsspectivelv peipendicnlBr to the thiM side* of another, the
triangles are amiitar to each other.
78. Bj an eiteasion of rimilu' reasoning, it may be ihown that a pdnt will be kept at rest bj anj nninDer of prsssares rspre>
MDted in Du^itDd« uid du«ction b^ the aim of ft pnlj'cr h U inunstenkl whether thi niiltw of the polygon Bra hi u fbmt or not. Tha tmth of this ni>7 be thus ihomi bj sxnri- ^V* ^■
nwnt. On * nrtickl bmrd draw >nT polygpn, u i D, of vhich the ■idea are in any ■smmied nome- rical proportion, aa 3, 6, 8, ID, and 7 inchea reepecdvelj; insert a pin at linj point, o, and place a tr it; attach polleyB ilhatH&eapaadng
.. ._.» the point OEoaj
be pnaHel to the nqwctiv* ridee of the paljgan, and in the aaoM dinctiai ftom o, aa the lidee taitm M order (bdicated b; the
AB,DitOBC,OCtOCD,OdtaDB,
ud 0 a to K A. Let aa manj atricgi be hooked on to the ring at 0, ukI TeighCa attached to them, ptoportional to tha aidee to
the.T VB mpectirelf ouallel, aa S, 6, 6, 10, and 7 ooncea, he ivnun^ from o, a rlghla
weigh^ aa one ounce lor initance, tbe ring «
The mn maj dov he ivnun^ from o, atid the "itifi'
But il either (rf the wei^hta be incraawd or diminiBhod by •mall weight, ai
with nlScient
ima peaitioa, that ia, provided the polleje more
jitae. Let the angle a of the polygvo be not in the aame plane ae Ibee otbera, a, o, d, then draw
. ._p „_ JOD, i%. 44,
andjon d^bb; then the pres- J
me B A i« eqninlent to b ■, ■ a
pi); and ad is eqmTalmt to A ■, id; tharafoie ba, ad, which
are together eqniTalent to b K, B A, A ^ ■ D, are eqniTalaot to B ■,
■ D, bacaaae ABandiA neatriJize each other.
14 'Die method bj which coal ia raited Dot of the hold of the cdlien ia a practical illaitmtion of the reenltant of «e*eral prea- nrei in difiereat pUnea. Sereral email ropea are attached to the end of a laiger one, which paaaea orer a pulley placed overhead, ud ie then carried down to the coal-basket. Each email rope ii beU b; one ohui, and all jumping down nmoltaneonaly from a ttiKd step, the loaded baeket ie laiaed by a jerk ; hence the term " ooal-whipper.''
75. Hie raenhant of two eqnal praeeorea acdng in parallel
a
tt
42 9TAT1GB.
directions, is a pressure equal to their snm, acting at the middle point between them : thas, when the two sides m a balance are equally loaded, the pressure of the beam on its support is its own weight together with the sum of the weights in the scales. This proposition, the truth of which is almost self-eTident, may be thus illnstrated by experiment. Take a small rod, ▲ b, similarly shaped J. ^ at both ends, and to its mid-
^' die point c, attach a string,
which, passing over a pulley,
D, supports a weight, k, which
=f====^="s«^^o just sustains the rod. If
1 D now two equal weights be
2' suspended from the eztremi-
Qf ties of the equal arms, and a
weight, F, equal to their sum, be attached to s, the whole will remain in eouuibrium : for the equal weights, ▲, b, being suspended from equal arms, cannot have any tendency to preponderate on one side more than on the other ; and the two weights, ▲, b, will have jnst the same e£R3ct in sup- porting F, as they would have if suspended from c, the middle _ point between them.
^' *•• 76. We may hence de-
duoe experimentaUy the -resultant of two unequal parallel pressures, and the point of its application. Let ▲ B be a balanoed bar tumine on a pin passing through the centre o, the upper edge of which is straight, and in a line with the centre of motion ; and let the edge be notched at equal distances (of one inch, for example) finom the cen- tre, as indicated by the figures; also let egual weights (as of one ounce each) be suspended Irom the odd diTisions i, •, &c. t, t, &c. It is clear that each pair of weights, i, t: s, t, &c., being equal and equidistant from the centre, will balance each other, and the whole will remain in equilibrium. If now the weights suspended from the points 6 and 7 be both suspended from 6, the middle point between them, their weights will have the same effect on the oar as before (75), and the equilibrium will not be disturbed. Similarly the weights at t and t may be suspended from t with tiie same recnilt, and the pairs of weiguts i and t, t and r, may be successively collected at the same point, without disturbing the equilibrium. We shall dow find that we have a ^ight, 6, acting at a distance, 2, from the point of support balancing a weight, 2,
irmrn
Mctii^ at k dittaDce, 6; but
And benee ■we nuj inler gcnerkUj th»t >n j two panllel pre vam vilJ balance each other, when tbej ve luTenelj prupoitioiul to ibeir dulancea from the pmiit of giijipoit.
77. The nwmcnt of on; prewnre ■■ it* teadeDc; to more i bodj to which it ii applied round any given ceotre, aai is meMur«d by the prodnct of the prestuTe, ftnd x parpeadicattu' line dnwn from the centre of motion to the line o{ directioii of the pTMsnie. It ■ppnmiB, fnm the preceding propoeitioa, that wbeo two premuM an in eqmlibriiim, iheir momenta roond the cealre of motion, nr wuDt of rapport, ve eqiul ; uid they «re alao in opponte direction*, for each of the weights ainglj wonld turn tbo rod in adiraalioti tmitztaj to the other.
78. And if any amnber of preaurea in th> eame plane, tending to prodoce motion roond a
given point, are in e^oili-
brinm, then iho ram of the monMnta which act in one Erection ii eqoal to the ram of tboae acting in Ibe con- ttij directiou, •« ma; be ■hown by the following ei- periment :— * a ii a circle <rf wood tnming tm a jriii in iti centre o; c„ c„ ftc.. an an; point* on it» inr- &ee to which atringi are attached ; tbeae pening over the poUers F|, Ff, Ac., rai- tain the weight* w,, w„ fto. If the board be allowed
te End ite own poeition of eqnilibrinm, and perpandicoJari o D ha drawn from the centre o to the lines l-o, or po produced, aa the caaa maj he, wb abaU find that the giun of the prodoola of the weiriila and correapondiug porpendicnlara, o d, which tend to tnra the board one waj, U equal to the aura of the limilHr product of ttia TO^ita acting the oontrarj way. In ^e above fignre the hiwaL^ ""™ '^^^ we^hla i« marked by arrowi, and wa
CUT to applj a ij^tem of parallfll preBsures to a rigid bodj, >nd to find eipeniuenbUlj the position of the reBiillaiit. For this par-
Applj & wrieB of weights r,. P^ Ac, the itringi of thoM which « intend to act upwards, passing Terticallj OTer pulleji. We ahau find that there u some poiot at which a siDgte presBUTe majr bo applied, which will maintain the rod in its honiontal poaitioD, nnless the sum of the weights actins upwards sbonld equal the ■nm of those acting downwaida, in which case the lod will be ma- tained without furUier rapport. But if them sunn of the weights ■IS not equal, the resnhant will act in the diivctiou of the greater sum, and the single premire, to counteract it, must conwqnentlj be in the oontraiy direction, and it will be eqoal in amoont to the difference of the above sums of weights. In the example here given, the weights p„ p„ ^- *>■ Ty are 8, 3, and 6 oonoea
reapectiTelj, and are sus- pended at diatanoei of 1, I 12, and 17 inches from th« end a; and the weights F„ F„ are 2 and 5 onnces, acting upwards, at dia- tsnces of 3 and 14 inchea from A. W« shall find that the whole sjitem will be Bnstained hj a support placed under the diiision o, distant B inches from a, and the dis- tances of op„ op- tc„ will be 7, 6, 4, fl, and 9 inches respectJTely: and the sum of the poiilive momenls round the point □, or those which tend to turn the tjstem tht sans looy a* the Aondi of a dodc nuws, wiU be equal to the son of the negative moments, or those which tend to turn the sTStam the eoMraty maj, for
(p^!x6 + W8x4 + (p^6>c9-(p,)8x7+(pJ6x6. Btit the snm oT the weights acting downwards is
(p,)8 + (pJ8 + Cp.)B-17; and the sum of thoM acting upwards is
(FjS + (p,>fi-7, and conaeqnentlj the difierence of these >unu is
17—7 = 10; that is, the resnltant oftbe sjrstem of pressures is a presinreof 10 acting downwaida at o; and if we attach a wei^tof lOoancM to
■qmLiBum o
I, Thsic is k puticalu cms of tbe i eqtialit7 of oppoaite monieiits, tl»t lequireB notice, on accooot of it* prac- , ticBl importiuice. If equal weighU, r, be raapeiided from anj tbrse poinU, i A, B, c, Bqniilistaiit Ktim each other ind fiinn the oentre of tha moveable boaid, thej ir!ll be in eqnilibriom in anj pod- Let the diagram lepretent anj pom- titm, joio B c, and bisect it in i> ; join A D, and producs it to meet the Terbcal Koe throngh b in ■ ; aim produce the vertical throngh c to meet as in p; then, because a b c ia an equilateral trian^. A B is peipendicalai' to a o, and
fHiri Ihrnnrii n; also A o ia twice o d. Bnt bjniiaiUrtiiaDglaa, V i>— D B, and therefore
and tlis momenta ronnd o in oppoeite directjooa are eqaaL
TUa eiplaina the advantage of emplojing three pmnpa, the piltooi of which are attached to a three-throw crank, m all kioda <if pnioMng machineiy, in which the crank-aiia ii driven round hj •a anifonii foree, becaurn the Bom of the momeuta of ^ acting nutancea ia the aama for all poeitiona of the crank.
■ If wfl eall tha npwird piuaum po^ttre, md ttia dcwnwmrd Dflgative^ " " ~B-hS-S+B-8— JO,
-B+I-HO-S+S-B^Ol tl«tia,iatlieiHaor wndHbriBm, tha olgtirmlaal mm of th» pnmatf = 0, fiat eonditiaii nwj be eipnwMl fama]^ by
-P,.O|ii-(-P»Op,-hP^Op,-Pt.0l.,+Pj.0l>,=0, (fat ^ tb* o^itntaiJ HiHi cf tlie mmaiti roDBd O ^0, wUsli i> aiFrtaaaa br
HP.O,)-0. niH ma Ibe nnoil «iiidltlinHofM|idUbriiiaiofa>iiv*r*t«ia of panUel H—IIW ■iillin iiimiililliiiilj ir iinjlii iilmiiiiiil Mill lliii liiiiaiiiiialliiii ■■d aiiiiUwi, M eppliai] lo Uaa, mtnij busb npodte dliMiiiliHia i llaM Moc eouldarcd niaiiliTe, irtuoli aie diavn is ■ duwtion oDntrar to tbu pliiiTi ■iiMwiilie til ni nndtJTn Prom left to rifht, np«fd>» aad lowerda a. m naaallj emiiiinl ■• th* poiltiv* XnaUoat g ud lh>m rifbt to lift, Aoinaard^ tad UneUr baa lu, tht BafUJn.
81. Tlura ii a p*rticnbr cms of panllel prnmres in which no
reiultoDt can b« obtained, that it, when tb« ajatem of prenorea
maj be radncfd to two equal preuuraa acting ia opponte direo-
_. tiona, but not at tbe rame point, which
'•"^ majbelbmelnciJalad;— Lelp, p^ba
■ an; two preaiuren acting at the pomta I Pi-Pf '" '''B same direction, and let I p, xon, ^ rjXO^,; then o istbepoint I to which the ntBulunt mult be applied, I and a pressure p, -f r, applied at o in I a direction conlmrjr to p„ and F,
■ will produce equilibrium (TG). Sun I Fi " "Pi = ■•. " <??!
add to each of theie qoaotltieB f, x op,, then i;xop, + e,xopi = r,xop, + r,Kop,,
or ^r,*f^'>Fl = f,''P>Pt■.
that ii, p, ii the pirint about wbicb the momenta of p, + p, and p, are equal, and at which, conaeqaontl;, their reaultant mutt be ap- plied : also, IB the 87Btem ia in equihbnuin, the remltant must be equal in magnitude to p„ and mnat act in a contrary direetion to p., that ia, in the direction of Pi + p^ We may, therefbre, remark, that if two unequal parallel preamrea act at any two points in ap- posite dlrectjona, ihotr resultant ia a preaanre e<|ual to their difier- ence, Rcting net at an; point between the giren pointa, but at wroe p int of the line joining them, produced in the direction of tb« gireater preasure. But when p, ia diminiihed in vaiae, r, -l- p, and p. become more nearly equal to each other, and at the aame time iha point p, becomea more remote, becauae the product P, X op, remaiua conatantly equal to (he aame quantilr P, x op^ _ .. and when f, becomea indeSnitely amall, and Op,
indefinitely large, the preasures at o and p, ap.
[ proach equalitv. We may henca conclude that ' - equal pi '" ' -• ■ -
I that is to say, there ia no point at which their
ol parallel prenures acting in oppoail
Itant,
I' ■■ .
B joint action can be Juatcounleracted by aaingle
I preaauic. Two auch preaeures as f, p, acting
■ Ht the points AB(Fig.51],arecalledaeoiit)^;
I A c, toe perpendicnjar diatance between their
I liaea of direction, the arm of tht onipb; and
™ p x * c, the moment of the eoupU. 82. As the IKO pressures cnnslituting a coaple are equal and in
-^ — - -_ - * familiarly illna-
ODlrifugol drill (Fig. 62), in which a rotatory impulse
ia oiimmDnicAted to the weight a, by forcibly unwinding the strings &om the alem, a ; also spinning a lop, and trundling a mop,
Bat the b«(t practical flliiitra- rf ooA or wcxJd, kept ir - "
. _ ._. ._, ■ loantuD jet ptajing against o
of it, bat witbont anj ebange of place, so loag aa the fore* of lbs jat TeiDaiDB perfectly onifonn (Fig. 68). In this oaae, the fwce of the jet acting opvaidi agwiut tlu loHhae of the kail b exact]; eqnal to the fbrae of gntn^ ar'' — ■" ' — '
rft.a.
t
S3. It may be tlated geaerallj, that aaj namber of prenmreB tctinf; in any direction, al the tame petal, maj atwaTS be reduced to a nngle leanltant, which vil1= 0, in caae of eqmlibriimi ; but if acting at diftrenl points, tbsj maj be reduced to a nngle RfilUnt, and a rSBollant couple, either or both of which ina/ = U. Ad eipenmebtal demonBtratioD of this wnnld, hovever, ho too fomplieated to be raadily intelligible, and a mathematjoal proof ii incompatible with the objects of this trsaliK.
84. Han; problenu relating to the coDdltiooa of eqailibrinm of bodice, Tanouil; connected and supported, are of laat importance in the arts of ooDBtmctioD ; and occaaiuDally verv curioui and unex- pected reBaitBareobtained. Thus, for instance, U we insh to obtain tlie but poaition in which any number of beams can be piactHi, n s« to form a roof of a given epan, that it may be uniformly Btrong in fitrj part, we have only to join loosely together an equal iDmber of rods of unifurm . weight and proportional length, and mapend their two free amis y^ ^^
fjoto two pointe at a pre- pmioDal distance in the I ume bonzonta! line, when I it wit] be foand that the I form which b;^ their own I wei^t Ihey will spontane- I ontly •nume, caTled thr I finicolar polj^on, is, when iavetted, lbt> strangeit fonn di which the beaioB can be placed
49 STATICB.
order to nipiMrt k weiglit nnifbmily digtributed orar tbem.
Agun, the rorm of the gracefiil calen&r; curve, that whicb, u its ^, ((, name impIieB, a chain umnies
when framj' auspcDded from two points, is an impartatit problem, as being the bans of the con- atmction of sospensicD bridges ; bnt for the foil inveetigation of this Bobject OUT readers must be refeired to the standard treatisea
86. Tbecentreof gravity of anybody, or mass of matter, is that ptnnt about which the bodf will be balanced in all positioDB. This point eridently coincidee with the centre of parallel preseares (79), erery particle of the body being considered as a poiot sepa- rately act«d on by grsvity. And as this is the point of apphca- tioa of the resultant, that is, of a single pressnre Eaving the same eSect 88 the individual pressures co^jomtly, it followe that the veisht of the body would in ell cases have preciael; the same Blalical effect, if it were all collected or concentrated at the centre of gravity.
j^^ gg_ SS. To End the centre ef gra-
Ivitv of any body, let it be con- sidered as a syetem or aaaemblage of material points, and of theee taE« any two, f,, p.; also lake any point o, draw o p, horimntal, and there- fore at right Angles to the verticals throogh p, aod r,; let o, be the centre of ^vitv of p, aod p, and o, g, a vertical throagb o,, then (76) 'i^Pi9i = ''t'^PiSi't
biitj',y, = oji, — oP|, andp,y, =op,— o j„ therefore "■j xoy,-P,xoj), = p,xoj.,-p,xoff„ or ?,>toy,+p,Koj,-p,jcop,-hP,xoft,
«■ ('•. + '-,)'>ft = Pi'<op, + p,xop„ , (a).
by an cxtBEBion of precisely similar r« ^ ^
other point p^ and finding s, then «, and p, and k find that
" p, + p, + p, +4c. '
liot OffU the diatance of a ftnia o^, a rerlical tbniugh o ; va3 tha ^■tatioe of a from op may he dslenaiaed in a limilar mKoner; and kence the position of o, the centre of graritj of the ijitem, tD*7 be foond. When the point; r,, p„ &c,, are not all in the eame plane, we find the diatance of a from a horizontal plane, then finm any vertical plane, and then from another Tertical plane, perpen- dicular to the other two, h^ which means the poeitioa of the point e in apace may be detennmed.
On refemne to the eqmition nurted (a) we may obserre that one dde of the eqnatioa eipreaaea the niamenC round o of the whole ayttem collected at a, and the other side the sum of the momenta of all the aeparat« particles round the aame point ; hence we lee tbat, in this inatonce, the statical effect of the whole sjstem, ciJkcted at its centre of giavi^, ia equal to the aggregate eOecta ol the Bcreral porta of the ayatem.
87. The centre of graritj of a material straight line aa, for example, a atraight noiforrQ rod of any heavy matter, must evi- dently be ita middle point; for, aa in Fig. 48, it may be conceired to be dirided into any even nnmber of equal portiona, each pair of wbicli, being equidistant from the centre, will balance each other.
88. The centre of gmrity of any material plane aurface, oa, for in- (tanoe.slamiriaof metal, of nni- v,. ... form denmty and inconaiderabie . thickness, may be readSy deter- J mined geometrically, if we can | find two)inet,eachofwbii:ii will I divide the fignre into two equal I halrea, for the centre of gravity I win bo the point of interaec" - of theae two lines. Thns, if take the parallelc^ism, a c (Fig. 57), and bisect ih« aides in the points B, F, B, K, and Join a H, f k, tben □, tbe point of inl«r- section of eh and Ft, will be the centre of gravity of (ha parallologram. For the parallalogram may be divided into narrow portioDn by lines, h e, b, e^, parallel to one of its sidea, n c ; each of these narrow nortiona may be considered aa rods, of each of which the middle point will be tbe centre of gravity. Bat the middle points of all the roda are in the line fk, and therefore the centre of gravity of the whole must he in tbat line; and for n'milar reosona the centre of gravity must be in the liaa K H, and therefore at the ptniit a.
m from which to tba langug* of Ui» diffemti
in the trianglB 1 B c, the Bides AC, CB, te biMctetl in d, b, uid lines drawn
I right lines, the centre of gniTitj msf be Tonnd hj dividing it into triutglea, and finding the centre of gnvitj of each. Tfana,UtABCDEbethefignra in qnestion, divide it into the trianglea A B c, A o D, and a D l, lind the centre of gravity of each in the manner already described (88). Let a, S, e, be the ceatres. Then join a b, and divide this line at d, in suuh a manner that the part j_ p, (Jftwill bear the mme ratio ton 4 as the
* _ triangle a b c does lo the triangle a B c.
■ The paint d vill thus be the centre of I gravitj of thi> figure A d c d. In like I maonerpoin ft.with <; by the line c«<f I and divide this at e, in such a manner I that ce vill bear the eame propoTtiati to I ed, that the quodrilatenJ figure a B o d, I does to the triangle A l> ■ ; then e will I be the centre of gravity of the whde
In a circle the centra of gravity is in its geometric centre; and in an oval, at that point where its trana- terae and longitudinal diametere intersect.
M. If a body be freely eaapended by any point, it will remun at rent when a perpendicular line let fall fnim that point paosea through its centre of t^ravity. becaaae the upward preuure which gupporte the body most be in the same vertical line as the resultant of its Ac a^regate grvvity. This law afiorda a ready mode of determining the centre of gravity of any bodyby experiment. For let A C a D, Fig. 60, lie an irregnlarly.Bhaped body, OS a board, &«ely aiuipenaed at a, a plumb-line, abb, hanging on the same support. The attraction or the earth will cauHO the line a n to hang pcrpendicnlariy downwards, and, acting ouacbd, will "■ -TB of gravity to fall
BqtUUBUDH.
o of letl in another directioD, itill bsvins the centre of ennt; ia Ihe conn« of the rgrticaJ line described b; the plumb-line : let this line be a ■>, then the point o, where A D anit ct D intermct each other, correepondi vitb the ceDli« of graTJtj of the figure a b b d.
91. The centre of ^ritjiibj no menni Ko- «. neceaurily placed within Ihe mosa of the ■
faodj itself; in a nag for example, aa i b, I thia point will be the centre, c, and cod- I ■eqnentl; in the space midway fima eTei^ I portioD of the solid. ■
92. If a body be not of nnifonn dendt;, I the centre of gruTitj ia not sitoaCed in ihe I places abore described. In a hom^^neona | circnUi Spin it correaponda. as above stated, with the Reometno cei in difierent pula, it becomei eccen- tric. Let 4 B c Kg. 6S, be^ an in- clined plane and ■ bmij of cylindrical
bnt in one of unei|ual dunalty
figure i> s a, be placed upon ; be composed of matter of eqnal den- iitv, o will be the centre of grarity, and being attracted hy the earth m the direction na, falling below the point aapported b j the plane, the bodj will necesaarilj roll down. Bat if the portion a of the figure
le composed of i leuC the n
, __ .. C the remaining portion
bring [rf* tight wood, as alder, then a bulk of the latter weighing 800 grains, will correspond in iiie to a mass of the former weighing 11,360 graios: these nnmbcrs being in the ratio of the reapectiTo specific gravities, or densitiea. of the two bodiea. The attraction of the earth will now act Tecy differantly on the cinmlar figure n, for the centre of gravity will do longer be at the geometric centre, bnt at a point nearer o, as at a. OraritatioD will act on t in the direction » t, cansing it to asanme tike loweet point, Ihe noint s will obev Ihia attraction, and the aicolar figure d will roll ap the inclined plane ^ remaining at rest when a line let fall from the centre of grUTity B passes through the point lopported by the ^lane.
93. A body reating on its boae cannot remain in a state of permanent eqnilibriDm, nnless a perpendicular line, passing through the centre of giaTitj, &11s within the base. Thus in the figme a B, f^g. 63, s represents the centre of grsiity, and a line
falling ftom that point pM«™ through the b«o, wh^h » mpported bTtlwt.ble: the figura tlierefore 8Und« wfelj. But pUce on it» wmmit wither piec«, o n, tha oeutre of giavty T ' ^,»?f** *J o ud u a perpeodiculir hne dr.wn from that point falli bejond ' tha supported base, the body necesisnly
Fit. in. falls. And the same effect w!ll_ be pro-
duced, if B portion of the material, as r, ba removed near the base. Hence the dangsr of loading waggons too high, and of building walla, if necesaaril; inclined, too loftv ; the leaiun^ tocera of Pi»» and BoSogna, may, accident a^rt, stand for ever, as long as perpendicular lines drawn from their centrea of grarity Ml vithin the bases of the buildioga. Thii is indeed the case with both these re- markable structures, for the tower of Pisa ii S15 feet higb, and has an incli- nation of ia-4 feet from Iha perpendicalar ; and that of Bologna, with an elevation of 134 feet, baa an inclination of but 92 feet.
91 A body, not acted upon by any external fbrcea except gravitation, will be in » state of tqiiiJibrium when ita centre of iravity ia aupported. But the equilibnum may ba of cither of three diffbrent kinds, vii., ttabU, umtabU, or lAdiffertnt. A body ia «id lo he in a aUte of stable equilibrium, whenever its cenlra of Rravity occupies a loiwr pooLion than it would do il Ihe Iwdy were moved a little in either direoUon; for as the toUl weip;ht would act in the same mwmer if collected at ita centre of gijvity, that point would tend to descend if the body were moved, that is, lo return to ita fonner position. And the amount of this tendency to return, or the itabauy of the body, is measured by the amount of a$ctnt of the centre of grtvity correapondipg to a given move- ment of the body. . - L ,1 IS Let J. B, Pig. G*, he the base on which the preceding fignre rests, am) a its centre of gravity ; then if Fig.t*. the body be tilled over towards A or B, the
I centre of gravity will describe the circular ansae or UD, of which a is the loweat point. Take the angle O i C ■— O B t>, ihrongh o draw the vertical line o B, and draw c E and D F horizontal, then o ■, a r, will represent the relative elevationt of the centre of gravity when the body ia moved round the points ± b, respec- tively : hence we see that the stalnlity of tbe body will be much greater towanb A than towards B, or, in other words, it will be more difBcult to ovenum tha body in tbe fonner direction than in the Utter.
Hence tlie atilit; of eitendiiig the baie of a bnildiDg bj iiie4nB of bottreneB, eapecisU; vhen the walla ore luliject lo the lateral (hraat of a roof of wide ipan, aa in catbedraU ami otIieT loft; edifieeB kavinff the iDterior apace entirely open.
9&. The Blabilitj of a ntapencled bod?, ami conaeijaently the re- aiitanca it oppoaea to diatorbaace of itseqailibrium, increaaeB with the distance of its cenire of gravity belov tht poiat of aopport. Hence in the coaBtnictionof very delicate baiancea, it ia necesaary for the centre of graTity to be but joat below the point of anpport, otherwise ao great a force would be required lo disturb the equili- bfinm of the beam aa to render its indicationa in the eatimation of unall weighta nearly naeleaa.
96. The eqailibriuin of a body is unstable, when the centre of graiity occupies a higher position than it would do if the body were displaced in any direction. In thia ease, the body will, if inoTed a little, recede still further from its poaition of reat, since the centre of gravity will then, by the auppoailion, descend. Thia if the condition of equilibriam of all bodies balanced, or supporled on a lingle point ; and the art of balancing any heavy body con- sists in repeatedly shining the point of support, ao as to keep it CtnitiDoally under the centra of gravity.
97. If when a body is moved, the centre of gravity neither rises Dor fklls, bat moiea in a horizontal line, that body is in the cod- dhioti of indifferent equiiibriuni, and when disturbed from its poaition, it has no tendency either to ad- Rn, m. vaoce or recede. The equilibrium of a sphere or cylinder, resting on a horizontal phne, is of thia kind, for it ia manifest thai tn theae bodies the centra of gravity will atWBya move horizontally, since all radii of s circle sie equal.
98. Whenever the path of the centre o< eratity of a moving body is a curved line, Uier« wilt be a poaition of stable squili- brinm at the lowest point of the curve, where the convexity in downwards, an4 one <£ unstable eqnilibnum at the highest, where the convexity is upwards. Tons, if any body, AB, of which s is the centre of gnnty, is raapended fram o, and capable of moving round that pant, the path of o will be a circle of which* o is the centre; there will be a position of stable equilibnum at a, the lowest point of the circle, and one of onstable cqailibrinm at o', the highest poiut.
99. This point may thus be further illustrated : — Take an oval board, thick enough to stand edgewise, with a hole in the centra Inge enongb to admit a pencil, and let this be railed along a ■trkieht e<^, A b, ll£. 66, resting on a sheet of paper ; a pencil pawiK throDgh the Eok will trace the corie, c d, the path of the
centre of gravity. When tha grsftter oxia ii honHmtal, u at b, » .. Iho oentra of gTsntTvill oc-
. cupjr tbe lowert point of Uie I curre, auiI tUe oquilibrium ii ■table ; when the aune axis U vertical, aa at v, tbe centre I of gravity it bigheat, and the equilibriiim it unalable.
100. Stable eqnilibiiniii in one direction tdkj, nnder I certain conditions, coexist I with nnstable eqnilibriam in another. For example, in the preceding figure, there are points of inflexion between the J. „ bigheat and loweat ptunta of Aa
curve, OD, or pointi at which the cnriB changpB Ironi conveiitj to ODD- :a*i^, or vice vtrt&; lets be a point It which the oval reita on a a, when ts centre ia at a point of inflection, and draw a line through the centra and the point o. If now a be railed above n tiDtil the line through o ia vertical, the oval will then be aup- ported in thia poaition.
In thia caie the path of the centre of gnvitj IB horiaontal juat at the point of equilibrium, a ; it uceoda towards o, and the equilibrium ii therefore itable in that direc- tion, hat \» nnatable towarda l>, in which direction the patb deacenda.
Kg.w. Again, if we plaoe the oral
I board on a amall horiiotital ojlinder, in. Fig. 68, with it« greater biib parnllel to the axi* of tbe cylinder, tbe equilibrinm will be atabla towarda a or