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Ut i) va ‘ Pe eC I EL Pa acy Bel 6 eae aN i ey <4 sa 7 " TRIER LS i Ms ae ee Ae ka estas LH uae eee 4s Oe Oe so 4ee Oa PECL LE 4, 28 Ue -e we Rh Fy a A? : aoe ME: oe ‘awans eer WELLE ECR. ih ; } wh .* =" h Ww 4eels co « Ne if -eake mare 422444556 <# 4 , ts s) ae - Me Ke SEP y SY ak Lamy $0 ¢ haw cas CAA! ao) MAT AN es rate FE SeeseaeeeseeseeeeeeT LIBRARY OF CONGRESS. ¢ [SMITHSONIAN DEPOSIT. | - Chap. bh. .: ' Shelf 5 5 Ore —@ UNITED STATES OF aMpRICa.? G6S6666S6SS55S5555686)) rN ee J ; | . Daa? ee ie Ee Be fe ‘ % F A - : ¥ ‘ ; H, I F La \y , i ni 2) 4 H s 5 ; iN c 7 : Utah! r g , ic ¢ ae Py } ? ‘ aM i ~ , wt ; \ THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Kynr. LL.D. F.R.S. &e. AND WILLIAM FRANCIS, Pa.D. F.L.S. F.R.A.S. F.C.S. “Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not. VOL. XLIV.—FOURTH SERIES. JULY—DECEMBER 1872. | ye LONDON. TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the Uniwersity of London ; SOLD BY LONGMANS, GREEN, READER, AND DYER; KENT AND CO.; SIMPKIN, MARSHALL, AND CO.; AND WIIITTAKER AND CO.;—-AND BY ADAM AND CHARLES BLACK, AND THOMAS CLARK, EDINBURGH; SMITH AND SON, GLASGOW :— HODGES, FOSTER, AND CO, DUBLIN:——-PUTNAM, NEW YORK :—AND ASHER AND CO., BERLIN. “Meditationis est perscrutari occulta; contemplationis est admirari perspicua ..... Admiratio generat questionem, quzstio investigationem, - investigatio inventionem.”’—Hugo de S. Victore. —“Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas; Quid pariat nubes, veniant cur fulmina ceelo, Quo micet igne Iris, Superos quis conciat orbes Tam vario motu.” J. B. Pinelli ad Mazonium, CONTENTS OF VOL. XLIV. (FOURTH SERIES.) NUMBER CCXC.—JULY .1872. Page Mr. J. Croll on What determines Molecular Motion ?—the Fun- damental Problem of Nature ......-.. cess cece ee ceee 1 Dr. A. M. Mayer on a new Lantern-Galvanometer .....-. 25 Canon Moseley on the steady Flow of a Liquid. (With a Plate.) 30 Mr. S. Taylor on Variations of Pitch in Beats ....---+---- 56 The Hon. J. W. Strutt on Mr. Moon’s Views on Gaseous Pres- Re fol ak Wine lacs orale face Ga das le ye silo 64 Prof. A. Cayley on a Bicyclic Chuck ........6+-+ ees eer: 65 Notices respecting New Books :— The Right Rev. J. W. Colenso and the Rev. J. Hunter’s Introductory Algebra, containing the chief rules in the first part of Colenso’s Elements of Algebra simplified ; with additional illustrations &c. ....-+.-+e eee eee 67 Archdeacon Pratt’s Treatise on Attractions, Laplace's Functions, and the Figure of the Earth ........-..:. 68 Proceedings of the Royal Institution :— Mr. W. Spottiswoode on Optical Phenomena produced by Crystals submitted to Circularly Polarized Light .... 69 Proceedings of the Royal Society :— Dr. J. H. Gladstone and Mr. A. Trike on the Decompo- sition of Water by Zinc in conjunction with a more Ne- gative Metal .,.-c2:ceer- ee sceecr ester ees eager 73 On the Influence of Pressure on the Lines of the Spectrum, by MeO nilletctaee os (He waleescl du micsiosats seestints ltl Further Researches on the Reflection of Heat, by M.P. Desains. 77 On Electrical Pyrometry, by Lieut. Abney, R.E., F.R.A.S., F.C.S., Assistant Instructor in Telegraphy,S.M.E.,Chatham. 80 NUMBER CCXCI.—AUGUST. M. E. Edlund on the Nature of Electricity .......-...--++-- 8] Mr. R. Moon’s Reply to some Remarks of the Hon. J. W. Strutt on Gaseous Pressure ........ 0. se ee ee eeee creer Dr. J. W. Draper’s Researches in Actino-Chemistry.—Memoir First. On the Distribution of Heat in the Spectrum. (With 3, (UBUD) og = eee oe Sabla suatea elie ch Wal dua a) stcuewara ewe eal 104 10] 1V CONTENTS OF VOL. XLIV.—-FOURTH SERIE Page Prof. R. Clausius’s iataas Correction of one of Mr. Tait’s Remarks..... 17 Mr. R. W. Atkinson on 1 the Atomic Theory, i in “Reply to Dr. Wrght. por. 50 los bie coe eee asker eee ee 118 Mr. A. Tribe’s Remarks on the alleged amen me and unnecessariness of the Atomic Theory . BP 121 Prof. N. S. Shaler on Earthlight on the Moon .... oa. Cee Mr. W. R. Birt’s Contribution to our knowledge of Atmospheric IWAVES (503.888 s chara tetera alee Beets gw ee rr 125 Notices respecting New Books :— Mr. G. J. Symons’s British Rainfall, 187] |... 2a 138 Proceedings of the Royal Society :— Dr. J. H. Gladstone and Mr. A. Tribe on the Action of Oxygen on Copper Nitrate in a state of Tension .... 139 The Astronomer Royal on a supposed Periodicity in the ele- ments of ‘Terrestrial Magnetism, with a periodof 264. days. 141 Proceedings of the Geological Society :— M. D. M. d’Orueta on the Geology of the neighbourhood of Malaga —5 3... :asers- cot bse on be oe Be 146 Prof. A. C. Ramsay on the Bivereourses of England and Wales. . .. 146 Sir P. de ve Grey Egerton o on | Prognathodus Giintheri, a new Genus of Fossil Fish from the Lias of Lyme Regis, and on two specimens of Ischyodus, from the Lias of Lyme “Regis: 2 fait. ss oa oh ainsi se ds er 147 Prof. J. Nicol on how the Parallel Roads of Glen Roy were formed ... 3 eels MrCuJs A. Meyer o1 on the Wealden as a Fluvio-lacustrine Formation .... 148 Researches on theElectricJet in Rarefied Gases, and in n particular on its Mechanical Force, by MM. A. de la Rive and E. Sar- BASU tai 149 On the Electrical Condition of Gas- flames, by John Trowbridge, Assistant Professor of Physics: 2.6.4.0... +. 0 ee 153 On the Primary Spectrum of Iodine, by M. G. Salet........ 156 On a simple Apparatus for the production of Ozone with Elec- tricity of High Tension, by Professor Arthur W. Wright .. 156 On a singular appearance of Magnesium in the Chromosphere of the Sun, by M. Tacchini, in a letter addressed to M. Faye.. 159 NUMBER CCXCII.—SEPTEMBER. Mr. L. Schwendler on Differential Galvanometers ... 161 Mr. F: C. Webb on an Electrical Experiment with an Insulated POO OME PSN tN sa oe iia ia Ha US a os ean eee 170 M. E. Edlund on the Nature of Electricity ................ 174 Prof. Challis on the Se aul pes ashe of Attractive and BeemMlsive’ PORCES As 812 fa. a2 Sele alee tee ee teret seen loo CONTENTS OF VOL. XLIV.—FOURTH SERIES. Dr. H. Hudson on Wave-Theories of Light, Heat, and Elec- PE eo 8 oho oa ol NMR Ne) aio se haa aise « The Hon. J. W. Strutt on the Law of Gaseous Pressure . Bee Proceedings of the Royal Society :— Messrs. C. Tomlinson and G. van der Mensbrugghe on Supersaturated Saline Solutions.—Part III. On a re- lation between the Surface-tensionof Liquids and the Supersaturation of Saline Solutions .............. Proceedings of the Geological Society :— Dr. Oldham and Mr. R. Mallet on some of the Secondary Effects of the Earthquake of the 10th January, 1869, in MRE Mr cae tne eo cs CR Rar ee tote eal See ee ana On the Influence of Pressure in the Phenomena of Endosmose woexasmose. by MM. Geequerel ti8. 6.5 e468) Meld a las. a On the Action of Ozone upon Vulcanized Caoutchouc, by Prof. RMRSMEMERNNEONN RTE E 2 Eee ME ee wb e ee ea edeuse alin On the instantaneous Oxidation of Alcohol, by M. A. Houzeau. On some Effects of Slow Actions, produced in the course of a eeetaim number of years, by M:. Becquerel.............- fepigeorecotcssor Clausius, by P.G. Tait’). 0.0. .e eet cafes NUMBER CCXCIIT.—OCTOBER. MM. Jamin and Richard on the Cooling of Gases.......... Bis. TE. ees on an Improved form of Filter- moe ey With ablate,) *..:. a : M. H.F. Weber on the Specific Heat of Carbon 210.0. 6... Dr. A. M. Mayer on a precise Method of tracing the Progress and of determining the Boundary of a Wave of Conducted SBE. 0 6 oo jk Shue Peni AR Ale bead es are em ee ab sua Re a amas M. G. Quincke on Peer: and the Passage of Electricity through Liquids. . Mr. J. W. L. Glaisher on some new Pace in the early History SIMO atelMIe “PADlES hs: fc ees. Wigs viet dale ae ees = ee oe Mr. R. Moon on the Definition of Intensity in the Theories of Light and Sound .... as Mr. J. Dewar on the Chemical Efficiency of Sunlight ea en eit Proceedings of the Royal Society :— Dr. J. W. Mallet on the Gases occluded in Meteoric Iron from Augusta Co., Virginia .... Mr. G. Gore on some Properties of Anhydrous Liquefied PANTO VMN MP PA AS Reni feria dees AE LN Sadie Syscae hath ica Prof. G. G. Stokes on the Law of Extraordinary Refraction Mee LAS PAE Lr SI SR RA Nie Aue Sah Te Report on a Memoir by MM. F. Lucas and A. Cazin, on the Duration of the Electric Spark, by Edm. Becquerel ...... On a new Galvanic Pile, of Economic Construction, by M. Gaiffe. On ‘‘ Acoustical Experiments” &c., by Alfred M. Mayer .. 223 257 . 304 307 dll 316 320 320 v1 CONTENTS OF VOL. XLIV.—FOURTH SERIES. NUMBER CCXCIV.—NOVEMBER. Page Dr. A. M. Mayer on a Method of detecting the Phases of Vibra- tion in the Air surrounding a Sounding Body, and thereby measuring directly in the vibrating air the lengths of its Waves and exploring the form of its Wave-surface ...... 321 The Hon. J. Wi Strutt.on Bessel’s Wunctions _< 22-5. 22a 328 Dr. H. Morton on the Fluorescent Relations of certain solid Hydrocarbons found in Coal-tar and Petroleum Distillates.. 345 Dr. W. Marcet on the Nutrition of Muscular and Pulmonary Tissues in Health and when affected with disease from Prathisisnch Lesh saat hie te’ aes Be er 349 Prof. R. Clausius on the Connexion of the Second Propesition of the Mechanical Theory of Heat with Hamiiton’s Principle. 365 Mr. H. A. Smith on some Points in the Chemistry of Acid- mMawulacture 2 hits tee ek sed lo fh 370 Mr. R. H. M. Bosanquet on an Experimental Determination of the Relation between the ee and eae eae of Sounds of different Pitch . 2 oe) edhe CORO | Notices respecting New Books :— . Mr. R. A. Proctor’s The Orbs around us: a Series of familiar Essays on the Moon and Planets, Meteors and | Comets, the Sun, and coloured Pairs of Suns........ 388 Mr. C. Taylor’s Geometry of Conics.—Part I. ........ 390 Mr. W. C. Ley’s Laws of the Winds prevailing in West- ern Murope 7 ee oe eS ee eee 391 Proceedings of the Royal Society :— | The Hon. J. W. Strutt on the Reproduction of Diffraction- | gratings by means of Photography “2. 7.22222 o seme 392 , On the Anomalous Dispersion exhibited by certain Substances, | by Md L: Soret. eres et eb er 395 On the Measurement of the Intensity of Currents by means of the Eleetrometer, by M. Ei. Branly >. ...... 2: eee 396 On the Specific Heat of Hydrogenium, by James Dewar, F.R.S.E. 400 NUMBER CCXCV.—DECEMBER. Captain F. W. Hutton on the Phenomena of the Elevation and | subsidence of the Surface of the Earth: ...).2. 2575 seme 401 | Mr. G. K.Winter on the Relation which the internal Resistance of the Battery and the-Conductivity of the Wire bear to the ) maximum Magnetizing Force of an Electromagnet Coil.... 414 | M. F. Zollner on the Spectroscopic Reversion-Telescope. (With | BaP late. jer. Os. ae pee Ria ko Al oe da es See Oe 417 I Dr. J. W. Draper's Researches in Actino-Chemistry. —Memoir | Second. On the Distribution of Chemical Force in the Spec- INURL, jcncr cca a) foma0 «6 cialis 'e Gin g's wibllote « etetstal ine eters aie aaa 422 CONTENTS OF VOL. XLIV.—FOURTH SERIES. Vil Page Dr. W. Marcet on the Nutrition of Muscular and Pulmonary Tissues in Health and when affected with disease from Phthisis. 443 MM. Jamin and Richard on the Laws of Cooling .......... 457 Mr. J. Dewar on the Specific Heat of Carbon at a Pete i 3 461 Notices respecting New Books :— Mr. F. A. Ranken’s Strains in Trusses computed by means of diagrams ... ET POPSET Cape ee BAU BIB OTE cy Proceedings of the Royal Society :- — Mr. R. Mallet on Volcanic Energy: an attempt to deve- lope its true Origin and Cosmical Relations ........ 468 Sir B. C. Brodie on the Action of Electricity on Gases .. 470 Proceedings of the Geological Society :— Mr. R. Daintree on the Geology of the Colony of Queens- Pema tiee ko 474 On the Collision of Elastic Badics ana a Denchical aieation erieduration, by H.Schneebeli 4.02 3002. S es veak 3 476 On the Spectrum of the Aurora, by Edward I. Holden ...... 478 Continuation of the observations relative to the presence of Magnesium in the Chromosphere of the Sun, by M. Tacchini. 479 NUMBER CCXCVI.—SUPPLEMENT. M. H. Weber on the Heat-conducting power of Iron and Ger- mameomyer, (With). Plate.) cevariaut. vidauia th oh<.. 008 481 Mr. J. W. L. Glaisher on some early Logarithmic Tables.... 500 Peer. J. Willson Elective Attraction’ ....2. 00.0 Pes. 8 -. 906 Mr. A. S. Davis on Recurrent Vision . : WR Cetin te MOO M. Helmholtz on the Theory of Electrodynamics Proceedings of the Royal Society :— Mr. A. Schuster on the Spectrum of INItROSemia)iyslecn oh) Poor Proceedings of the Geological Society :— Mr. S. J. Whitnell on Atolls or Lagoon-islands ........ 541 Mr. J. R. Dakyns on the Glacial Phenomena of the York- SUAS LG) OWING I Ieee eeibreas ane veal Sarat eMC SN IE aad lax 54] Mr. D. Mackintosh on a Sea-coast Section of Pere in Cheshire. . 542 The Rev.W. Bleasdell on 1 Modern Glacial Action i in ‘Canada. 542 The Rev. O. Fisher on the Phosphatic Nodules of the Cre- taceous Rock of Cambridgeshire .... ot .. 948 On the Absorption of Ozone by ‘Water, by L. ‘Carus Beka Oa On the Heat of Expansion of Solid Bodies, iy aeeleaisiunihe s Atennen 544 Experiments on Collision with Balls of different Metals, by H. = NGS es EE ON see ae nL es 546 PLATES. I. Illustrative of Canon Moseley’s Paper onthe steady Flow of a Liquid. II. lustrative of Dr. J. W. Draper’s Paper on the Distribution of Heat in the Spectrum. III. Illustrative of Mr. T. E. Thorpe’s Paper on an Improved form of Filter-Pump. IV. Illustrative of M. F. Zollner’s Paper on the Spectroscopic Reversion- Telescope. V. Illustrative of M. H. Weber’s Paper on the Heat-conducting Power of Tron and German Silver. ERRATA. Page 352, line 25, instead of like a jelly in the fact read like a jelly from the fact. — 357, — 31, mstead of composition of fibrous mass read composi- tion of the fibrous mass. — 358, imstead of B'= B+A’ A 3 C'= B+aA A read B= B >< A ; A Bx A!’ ———— A — 359, in the Table, instead of calculated in 5°74 albumen read cal- culated for 5°74 albumen. — 362, line 5, instead of between the albuminous read between these theoretically albuminous. Phil. Mag. 8.4. Vol. 44. PUY. PVE) LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] fOULY 1872. I. What determines Molecular Motion ?2—the Fundamental Pro- blem of Nature. By James Crott, of the Geological Survey of Scotland*. {* is an opinion which is daily gaining ground that at some future time, perhaps not far distant, all the purely physical sciences will be brought under a few general laws and princi- ples. However wide and diversified physical phenomena may seem at first sight, and however great and radical the apparent distinction between the several sciences, yet to the eye of the thoughtful physicist, who sees deeper into the subject, they begin to appear as but the varied modifications of a few common principles. For example, Heat, Electricity, and Magnetism are in their ordinary phenomena very unlike each other ; yet modern investigation has shown that they are mutually convertible. Heat can be converted into Electricity, and Electricity into Mag- netism. Magnetism can be converted into Electricity, and Elec- tricity mto Heat. This indicates that these corresponding sciences are not radically distinct, that their phenomena have a common origin, that in each we have the same force manifested under different forms. To arrive at unity among the facts of nature has ever been, and ever will be, the aim of physical investigation. We try to induce a unity amongst the multifarious facts of the senses by bringing as many of them under a certain conception as will be rationally connected by it. But we soon find that we must -have a higher unity ; and we endeavour to reduce the number of * Communicated by the Author. Phil. Mag. 8S. 4. Vol. 44. No. 290. July 1872. B 2 Mr.J. Croll on What determines Molecular Motion 2— our conceptions by finding one of a higher order—and so on, ever trying to reach the highest unity, the most general conception possible. The point, however, which more immediately claims our spe- cial attention at present is this :—As the physical sciences pro- ceed in their generalization, they advance more and more towards Molecular Physics. We may illustrate our meaning by examples without number from any of the sciences. In Electricity, for example, all the ordinary questions—such as how a Leyden jar becomes charged, or how the electricities are supposed to be decomposed on a conductor, or by what means one body charged positively will act upon another body charged negatively—were formerly considered to be answered quite satisfactorily without making any reference whatever to the molecular condition of the bodies under the electric influence. But when we come to in- quire more deeply into what is meant by induction—what that peculiar condition is which constitutes the charged jar, and the nature of that hidden change which takes place on the conductor while what we call its electricities are being decomposed,—we begin to find that we are entering upon deep and difficult ques- tions regarding the hidden operations taking place among the molecules or the atoms of the electrified body. Electricity was formerly supposed to be a fluid substance altogether distinct from the body in which it manifested itself; and, of course, in- quiry was directed towards this hypothetical substance, and not to the molecular condition of the body. But the grounds for believing in the existence of this hypothetical fluid are fast dis- appearing ; and electricity is now generally believed to bea con- dition or motion of the molecules or the atoms of the electrified body itself. Similarly, heat at one time was considered to bea substance to which the name Caloric was applied. It is now, however, proved to be not a substance, but a particular mode of motion of the atoms of the heated body. The same is proved to be the case in regard to Light ; and Magnetism, which was for- merly explained by means of hypothetical fluids, is now believed to consist also in a particular molecular condition of the mag- netic body ; whilst Chemistry is fast becoming a question re- garding the dynamical actions of the atoms of the combining substances. In Physical Astronomy questions regarding the constitution of the sun, the fixed stars, and nebule are being determined by Molecular Physics; and even the direction and velocity of their motions are now resolved by the same method. Physical in- quiry in every direction is converging towards Molecular Phy- sics, is resolving itself into questions regarding the dynamical action of the ultimate particles of matter. the Kundamental Problem of Nature. 3 To determine (1) the constitution of the ultimate atoms and molecules of matter, what they really are, and (2) their beha- viour (the laws of their motions), are two great problems of Mo- lecular Physics towards which all physical investigation is tend- ing. These are the two important problems which first present themselves for solution; but neither of them, as we shall see, is the grand and fundamental problem. On a former occasion: I referred to some considerations bear- ing on the first of these two problems*. I shall now briefly refer to the second, which, in consequence of its more immediate relation to the ultimate question of scientific inquiry, is of much more importance than the first. The second problem, we have seen, refers not to the nature of the molecule, but toits motions. Now in regard to all physical change or motion, no matter what the nature of that change or motion may be, there are at the very outset two fundamental questions which suggest themselves:—(1) What produces the change—causes motion? (2) What determines or directs it ? In regard to the first question, there is no diversity of opinion. All agree that what produces change or causes motion is Force. The second question, however, viz. what determines or directs the motion, is not so easily answered. This question is not only the more difficult of the two, but also by far the more important. All physicists agree that what is called Physical Law is just the expression of the manner in which forces act in the produc- tion of their effects, or “ the paths along which they travel to their particular results,” as Mr. Lewes expresses itt. In the produc- tion of all physical phenomena we have therefore two distinct elements, viz. force, and the way or manner in which force acts —force, and the paths along which it travels, so to speak—or, in other words still, Force and the Laws of Force. One of the most important results of modern physical inquiry has been to show that the various phenomena of Light, Heat, Electricity, &c. are but different modifications in the action of the same forces. When the forces take one path, we have light ; taking another path, we have Heat; another produces Electricity, and so on. Now it will be observed that the funda- mental question is not, what is the particular force in action, or upon what does its exertion depend, but rather what is it that causes the force to act in the particular manner in which it does act? In other words, what determines the paths along which it acts? Physical phenomena are produced in general by the motion of the molecules or of the atoms of bodies; now the great question is not simply what produces the * Philosophical Magazine for December 1867. + Comte’s Philosophy of the Sciences. By G. H. Lewes. Section V. B2 4, Mr. J. Croll on What determines Molecular Motion 2— motion, but what produces the particular kind of motion? It is not what gives existence to the motion, but what determines its direction? This is evident, because the particular phenome- non, regarding which our inquiries are concerned, does not di- rectly depend upon the mere existence of the motion, but upon its special direction or determination. The same exertion of force which produces one phenomenon would probably produce any other phenomenon, were determination in the proper diree- tion given to it. It is the determination of the force which accounts for the particular phenomenon ; the mere ezertion of foree may be supposed to be the same in all phenomena. We are therefore led to the following proposition, viz. :— (1) The Production of Motion and the Determination of Motion are absolutely and essentially different. The radical and essential distinction between motion and the determination of motion could not possibly have escaped the observation of physicists; but the important bearing that this distinction has on physical inquiry has certainly been overlooked. In physics we have been accustomed to attribute every thing to force ; force, at least, has always been regarded as the all-im- portant jlencat This, however, is a mistake; for, as we shall see, far more depends upon the RPE? of force than upon its existence, and therefore, unless force be determined by force, the most important element in physical causation is a something differ- ent from force. And this holds equally true whether our inqui- ries relate to the inorganic or to the organic world. In the production of organic forms from the simplest up to the most special and complex in the vegetable and animal king- dom two things require to be accounted for, viz. (1) the motion of the matter of which they are composed, and (2) its disposition or arrangement with reference to time and space. The particles which are to compose the organism must not only move, but move with a particular determination in regard to time and space. Ifa molecule has to be placed in any particular place of an organism, it must move in the particular direction in space which will lead to that place, and stop at the particular moment of time when it reaches it. Motion is not only produced, but it is produced in a particular manner and under particular conditions or determinations in re- gard to time and space and other circumstances. In other words, not only must something produce the motion, but some- thing must determine it also. The causing of, or giving mere existence to the motion, I have called the Production of the motion. The causing of it to happen in the particular manner in which it does, rather than in some other manner, I have called the Fundamental Problem of Nature. 5 the Determination of the motion. It must-be evident to every one who will consider the matter that these two things are radically distmct. And they are not only radically distinct, but must be separately accounted for. ‘To account for the mere existence of motion, does not account for its happening in one way rather than in some other. It is quite true that the one cannot be produced without the other; we cannot deter- mine motion unless there is motion to be determined; we cannot determine that which has got no existence; neither, on the other hand, can we produce motion without at the same time giving it some particular determination in regard to time, place, or other circumstance. But, although the one cannot be pro- duced without the other, yet they are the result of different agen- cies ; and to assign a sufficient cause for the one does not in the least degree satisfy the mind as to the presence of the other. To account for the motion of a ball does not account for why it moves, say, east rather than west or in any other possible direc- tion. Dr. A. M. Mayer on a New Lantern-Galvanometer. 25 mined by the comparative anatomist, no biological researches, no microscopic investigations, no considerations regarding natu- ral selection or the survival of the fittest can solve the great problem of nature; for it lies in the background of all such in- vestigations. The problem is molecular. From the hugest plant and animal on the globe down to the smallest organic speck visible under the microscope, all have been built up mole- cule by molecule ; and the problem is, to explain this molecular process. If one plant or animal differs from another, or the parent from the child, it is because in the building-up process the determinations of molecular motion were different in the two cases; and the true and fundamental ground of the difference must be sought for in the cause of the determination of mole- cular motion. Here in this region the doctrine of natural selec- tion and the struggle for existence can afford no more light on the matter than the fortuitous concourse of atoms and the ato- mical philosophy of the ancients. This, I trust, will be rendered still more evident when we come to examine in detail the argu- ments advanced by modern evolutionists in support of their fundamental hypothesis, “that the whole world, living and not living, is the result of the mutual interaction, according to definite laws, of the forces possessed by the molecules of which the primitive nebulosity of the universe was composed.” II. On a new Lantern-Galvanometer. By AuFrep M. Mayer, Ph.D., Professor of Physics in the Stevens Institute of Tech- nology, Hoboken, N. J., U.S. America®. N the 21st of December, 1871, I delivered a lecture on Magnetism before the American Institute at the Academy of Music in the city of New York. It was necessary for the experimental discussion I then made of the earth’s magnetism to use a galvanometer so constructed that the deflections of its needle would be visible to a large audience; at the same time the astatic condition of this needle had to be so controlled that it could readily be altered during the progress of the lecture ; while, finally, the arrangement of the damping-magnets had to be such as allowed me instantly to bring the needle into the magnetic meridian when disturbed therefrom whenever I set in action the huge electromagnet used on that occasion. Indeed one of the principal uses to which this galvanometer was applied in the lecture was the exploration of the magnetic condition of the space surrounding this electromagnet. This I accomplished * From the American Journal of Science for June 1872. Communicated by the Author. 26 Dr. A. M. Mayer on a new Lantern-Galvanometer. by rotating around the line of ‘‘ the dip,” as an axis, wire coils at various distances and positions, and leading the induced mag- neto-electric currents through the galvanometer. The lantern-galvanometer, which | will now proceed to de- scribe, I devised on the 13th of last November; and as subse- quent work with it has convinced me of its value in the lecture- room, | have decided to give it this formal publication. Referring to the figure, M is a plane mirror inclined 45° to the vertical. In front of this are the back condensing-lenses of an oxyhydrogen lantern; while the front lens of the condenser is placed in a horizontal position at c, above the mirror. The back condensing-lenses are of such curvatures that when the calcium light is placed about two inches from the one nearest it, a nearly parallel beam issues from them to fall upon M, thence to be reflected to the upper condensing-lens at c*, on which rests a disk of glass on whose border is photographed a divided circle. In the centre of this disk is a short needle-poimt on which freely rotates a magnetic needle, Above the needle is the projecting lens L, the pencils from which are reflected in any desired direction by means of the plane mirror R, which revolves on a horizontal axis, and has also a motion in azimuth round the axis of the lenst. The horizontal condensing-lens is 5 inches in diameter ; and the magnetic needle is 4 inches long. With this arrangement I have obtained sharp and bright images of the graduated circle 16 feet in diameter. To deflect this needle by means of an electric current, I place as close to the condensing-lens as possible the two vertical wire spirals 8S, 8S, formed of ;|,-inch copper wire of square section so as to bring the convolutions as close together as possible. The turns of the spirals are separated with very thin vulcanite ribbon * This arrangement of lenses, which is due to President Morton, gives a bright and uniformly illuminated field free from coloration. In the Quarterly Journal of Science, October 1871, is a report of Professor Morton’s account of this invention [‘‘ the vertical lantern ”], de- livered before the American Institute, as follows :—“ The original idea and general plan of the instrument shown was, as the speaker stated, due to Professor J. P. Cooke, of Cambridge—his own work in connexion with it being confined to the devising of a convenient mechanical arrangement of parts, the improvement of the combination of condensing-lenses with the reflecting lenses | mirror? so as to secure a white and evenly illuminated field on the screen, and the discovery that an ordinary silvered mirror would serve for the final reflection as efficiently as a metal speculum or glass silvered by Foucault’s plan, which are so difficult to obtain and keep in order.” + In a college course of lectures it is sometimes convenient to reflect the image of circle and needle down on a white-covered table below the class. The galyanometer can then be placed on the lecture-table. Dr. A. M. Mayer on a new Lantern-Galvanometer. 27 coated with paraffine, and are wrapped on the faces of vulcanite disks. The spirals have an internal diameter of 4 inches and an external diameter of 10 inches; and each contains 49 feet of wire in 26 turns. The four terminals of the spirals are con- necting-screws, two of which serve to join the spirals so that a current will circulate in the same direction in both. The spirals are so placed that a line joining their centres will pass through the centre of the magnetic needle. The vertical lantern rests on a base 34 feet long, with guides on its sides, between which slide boards carrying two bar-mag- nets, A and B, 15 inches long and 1 inch in diameter, as shown in the figure. These magnets can not only approach to and re- — Ys [o} SSS, == yA Va (S) S/ 4 © | | M ‘ \ fy ee cede from the lantern, and thus alter their distances from the gal- vanometer-needle, but they can also rotate around their centres on vertical axes. The like poles of the magnets and of the needle point in the same direction ; and by sliding the magnets to or from the lantern-needle we render the latter more or less astatic. Also, mm case the needle should not hold to the meridian as you approach the magnets, it can be made to do so by rotating one or both of them in the horizontal plane; and thus also can be neu- | | 28 Dr. A. M. Mayer on a new Lantern-Galvanometer. tralized any exterior disturbance which may tend to deflect the needle from the magnetic meridian. The needle may be also rendered astatic in the usual way by suspending it by a silk fibre, and attaching to this needle a wire which passes through a hole in the condeuser and in the inclined mirror and carries beneath the latter another needle with poles reversed. In working with thermal currents we use a smaller needle and condenser, which allows the spirals to approach nearer ; but for thermal currents it is better to wind close round the needle a flat coil only one wire in breadth, and to use a suspended astatic system, of which the /ower needle is the stronger and is under the control of the damping-magnets*. The breadth of the coil used in this last device need not exceed 5), of an inch; and its image on the screen can answer for a rough zero-point. I will now give a few experiments in which this galvanometer has been employed ; and they will serve to show its usefulness. Experiment 1.—A cal of 25 feet diameter, containing forty turns of 300 feet of ;/)-inch wire, was placed with its plane at right angles to “ the: dip. *? Its terminals were connected with the galvanometer, whose needle was rendered astatic by means of the damping-magnets. I now quickly rotated the coil 180° round an axis at right angles to the direction of the dipping- needle. The galvanometer-needle was deflected about 12° by the magneto-electric current induced by the earth’s magnetism. Exp. 2.—I placed the coil used in Exp. 1 on a wooden wheel provided with a commutator, and rotated it round an axis at right angles to the dip. The galvanometer-needle went steadily up to a deflection of 85°, and was held there as long as the coil revolved. Exp. 3.—The two cores of the large electromagnet of the Stevens Institute of Technology were placed end to end, thus forming one iron bar 7 feet long and 6 inches in diameter. This was surrounded by its eight bobbins, containing in all 2000 feet of 1-inch copper wire; and through them was sent the electricity developed by the most advantageous combination of sixty plates of zinc and carbon, 10 x 8 inches. A coil of 20 inches diameter, formed of one turn of 35-inch wire, was rotated 180° round a vertical axis 34 feet from the end of the magnet. The needle was defected 3°. * The upper needle of this astatic combination swings in the interior of the coil which encloses both the needle and the condenser c; the lower needle swings under the inclined mirror M, and is attached to the upper needle by means of a stiff wire, which passes through holes in the condenser and in the inclined mirror. In another combination I have placed this lower needle above the coil, and have “ damped” it by means of a magnet placed above the reflector R. Dr. A. M. Mayer on a new Lantern-Galvanometer. 29 Exp. 4.—A coil of 20 inches diameter, having five turns of gij-inch wire, was rotated 180° round a vertical axis at a dis- tance of 34 feet from end of magnet. Deflection of needle was 30°. Exp. 5.—Same as Exp. 4, only coil had ten turns of wire in- stead of five. Galvanometer-needle deflected 50° to 60°. Exp. 6.—A coil of 20 inches diameter, formed of ten turns of 54-inch wire, was revolved 180° round a vertical axis 64 feet from end of magnet. Deflection of needle 22°. Exp. 7.—The coil used in Exp. 6 was placed 3 feet 8 inches above centre of axis of the magnet, and revolved 180° round a vertical axis; the needle was deflected 80°. Exp. 8.—A coil of 24 feet diameter, formed of forty turns of 300 feet of J-inch wire, was placed 28 feet distant from the centre of the magnet, and with its plane coinciding with the plane of © the magnet’s equator. On rotating it round a vertical axis the needle was deflected 20°. The following experiments will show the excellent proportions (arrived at by a long series of experiments) of the coil used in Exps. 1, 2, and 8, for the evolution and study of the electric currents induced by the earth’s magnetism. Exp. 9.—The coil used in Exps. 1, 2, and 8 was laid on a table, and its terminals connected with a galvanometer which is — used in connexion with Nobili’s thermo-electric pile. The needles of this instrument made one oscillation in nine seconds. I lifted the east side of the coil only six inches; the needle was deflected 10°. Lifting the same side nine inches, the needles went to 22°. I now placed the coil in a north and south vertical plane; and suddenly tilting its top six inches to the east or to the west, the needles went to 60°. Tilting the coil nine inches sent the needles with a blow against the stop at 90°. The advantages of the new galvanometer may be summed up in a few words. It gives on the screen a bright clear image of only the graduated circle and of the needle. It can readily be rendered more or less astatic to adapt it to the character of the electric currents worked with. -The direction of its needle is completely under the control of the damping-magnets; and, finally, it is of simple construction, and can be rapidly adjusted to the requirements of any special experiment. bee Gl III. On the steady Flow of a Liquid. By the late Henry Mosetry, M.A., D.C.L., Canon of Bristol, F.R.S., Corre- sponding Member of the Institute of France, &c. Edited by Watrter R. Browne, M.A., Fellow of Trinity College, Cam- bridge. [Continued from vol. xli. p. 362. | [ With a Plate. | Prefatory Note. Te following paper completes the series on the steady Flow of Liquids published in the Philosophical Magazine by the late Canon Moseley. He did not live to revise it for publication ; that task was, by his request, entrusted to me. The paper, however, was practically complete; and all that I have found necessary, beyond numbering the equations and su- perintending the publication, has been to make a very few ne- cessary additions and corrections, the more important of which are noticed where they occur. The circumstances, however, under which the paper was finished seem to me to demand, and will, I think, excuse some- _ thing beyond this brief explanation. It was the work on which Canon Moseley was engaged when seized with his last illness ; and during that illness it still occupied his thoughts. Some time after all hope of recovery had ceased, and when death had already come very near, there was a short rally of strength; and he then dictated to his daughter the last three paragraphs. No one can read these without being struck by their composure, their courtesy, and perfect clearness of thought; and no one would, I believe, suspect under what circumstances they were written down. Nevertheless that the mind, even in full view of death, should still move freely along the paths to which it is accustomed may be, although a striking, not a very rare pheno- menon., But that which as men of science we may well note is this :—that whereas it is often asserted and oftener assumed that a deep study of the laws of nature forbids the mind to acknow- ledge any thing beyond those laws, we here see one who in the very last hours of life could still pursue that difficult branch of earthly knowledge in which his high distinction had been won, and who could also turn directly from such pursuit to receive the ministrations of that religion and that church in which he had lived, and in which he was well content to die. General Conditions of the Uniform Flow of a Liquid in a closed Channel of any given geometrical form which it enters from a reservoir. By the uniform flow of a liquid is meant here (as before in Canon Moseley on the steady Flow of a Liquid. bl these papers) that state of steady motion to which it would attain in a channel of uniform section whose internal surface was everywhere of the same degree of roughness, and whose di- rection was straight and its shape constant. The liquid would under these circumstances flow in filaments parallel to one an- other and to the sides of the channel, having different velocities. By equation (2)*, U=U,+ U,+ Ust+ Uy, where U =work done per unit of time on the liquid which enters the pipe by the pressure of that in the reservoir. U,= work carried away per unit of time by the liquid which flows from the extremity of the pipe. U,= work expended on the various resistances which are op- posed to the descent of the liquid in the reservoir and to its passage from the reservoir through its aperture into the pipe. U,== work expended on the resistance of the internal surface of the pipe to the flow of the liquid along it. U,= internal work of the resistance of the films to the flowing of each film over the surface of the next in succession. Let a plane be imagined to intersect the liquid in a direction at right angles to that in which it flows, and let the point in the plane where the filament of maximum velocity intersects it be taken as the origin of the coordinates; also let # and y be the rectangular coordinates of the point in this plane where any other filament intersects it, being horizontal. Let v be the velocity of this filament. Its displacement in the unit of time over the filament immediately above it will then be represented by -() dy, the negative sign being taken because v diminishes as y increases. But the resistance opposed to the shearing by the horizontal face of the filament is w/Az ; » representing the unit of resistance, and / the length of the filament. Therefore the work done in the unit of time by the resistance of the lower of these two fila- ments to the motion of the upper is represented by dv In the same manner the work done by the resistance of the side surface of the filament to the motion of the next contiguous filament sidewise is represented by Pai Ay (z) fk * Phil, Mag. September 1871. 32 Canon Moseley on the steady Flow of a Liquad. The whole work of the resistance of this filament is represented therefore by 2 ee & dp ie = aa de and 7) being the partial differential coefficients of v with dx respect to x co y; or, passing to the limit, the work of the re- sistance of this filament is represented by dv dv Therefore the aggregate work U, of the resistances of all the fila- ments is represented by v=-(fu{(e ) 4 (Z) avay. If h represent the actual head of liquid in the reservoir, then, supposing the channel to be horizontal, (Ui wh \\ vde dy. The effect of the resistance whose work is U,, however, is prac- tically to diminish the head of liquid /. Let = represent, as before, this diminished head ; hens if we substitute — for A in the above equation, we may neglect U, in the preceding equation. If moreover we suppose the liquid after leaving the reservoir to descend through an inclined chan- nel whose length is /, we must substitute G +Isin#) for - for — ie -0= w(- +/ sin "ff dy. U,= half the vis viva of the discharge per unit of time = lpwrdedy\ , ws ={fa( g yr=a 4 fo po Hence, neglecting U,, we have by equation (2), . é ads i) (ode Hint a ae ee i { “iG ©) hae dy. . (46) Canon Moseley on the steady Flow of a Liquid. 33 Differentiating twice and dividing by dz dy, eS 54 fe el w(< +0sini)o= > Dy v +i ult (Z) . dU; Observing that Fee =0, and transposing, w (h ¢ + +(2 a= my Za ale + Lsin ie, Let EN? 2. Sagl aioe “(7 + Jsin i)= [E28 _ (2 UY _ 2,3. 22 4 (+ a) =e ve — 80, and 7) dx +(¢ =) de = ( ay? — 8?)\vdzx ; but * w=(F =) dy +( ~ ) ae 5 *, adding, dv dv w+ (7) dar = (a8 — Bode +(7) dy ; transposing, dv — (av? — B? vdr = (z) (dy — dz); d dv (a) Jay Pr (FB o Since the left-hand member of this equation is an exact differen- tial, the right-hand must be one alsoy: This condition is sa- tistied if — : is a function of (y—#); but it may be any eee * In the original MS. this expression has been inadvertently written (G,)@ a+ 2 ) dy. I have corrected this error as far as it goes; it does not affect the form of equation (48).—W. R. BRownE. + This is the well-known method of Lagrange. Phil. Mag. 8. 4. Vol. 44, No. 290. July 1872. D 34 Canon Moseley on the steady Flow of a Liquid. Let @ — B)0 = qd! (y—z) where d — #y-2) =, ¢ being any function of (y—z); Gey = 8-2) (ty ae); : (ae, 2 =by-2)-400) ae But ee 1 1 oe I a I (eo Bp ~~ Bev * 28? (ev—B) * 28? (@v+B)’ ee ie dv wate Vp av—B 1, av+ PB see 2+ gle, Saat 36a Te (:0) alee 8) agile, (; = @) op eae) a E ont 4) —$(0) .1- (5) = 1-¢) 5 MAT O25 10); @) i 41-( = £y} e262 {2+Gy—2)—9(0)} Canon Moseley on the steady Flow of a Liquid. 35 Substituting for a and @ their values, h 29i — + fs i) AG wih ae 1— 41 —2g (- + Jsin i) at Tavis AS EREAL Oe Y G5 | The conditions of equation (46) are satisfied by the above equation, whatever may be the form or value of the function o(y—zx). But these conditions are not the only ones to which the flow of the liquid is subjected. They do not include the form of the channel, or the degree of roughness or smoothness of its sides. The term Ug, in equation (46) represented these ; but it disappeared in the double differential, and has no place in equation (47), from which equation (48) is deduced. ‘he inde- terminateness of d(y—z) results from the neglect of this condi- tion; and the function is to be determined by taking it into account. let us suppose it to be so determined. Laguid Films. If in any cross section a curve be taken whose equation is e+ b(y—x)—$(0)=p, where p is constant, that curve will represent the intersection of it by a film. For, by equation (48), the velocity v of the liquid at every point in that curve will be the same. By varying the values of p, all the films of a given stream flowing uniformly may thus be determined. In closed channels of symmetrical forms and uniform roughness the velocities of such particles as flow nearly in contact with the sides approach probably to equality. A film nearly in contact with the sides has therefore nearly the form of the channel itself; and as the films are geometrically similar, it follows that approximately all the films, from the fila- ment of maximum velocity to the internal surface of the channel, take approximately the geometrical form of that surface. The degree of that approximation can only be determined by com- paring theoretical results founded upon it with the results of experiment. That is the object of what remains of this paper. a * To compare this equation with equation (10) (Phil. Mag. September 1871), we must make sint=0, y=1, 2gh=v?, — =i. We shall thus ob- l tain ee ee Sze Ts (i- ba pare) Ae ah V7 Assuming 2+¢(y—2)—(0)=r, this equation becomes identical with equation (10). D2 36 Canon Moseley on the steady Flow of a Liquid. The Velocity (at any point) of the Flow of a Liquid through a straight pipe of any shape. Let it be supposed that the liquid fills the pipe, and that it arranges itself in films geometrically similar to the internal sur- face of the pipe, the molecules in each film moving with the same velocity, but those in different films with different velocities. The sections of these films made by a plane perpendicular to the axis being geometrically similar, let straight lines be supposed to be similarly placed in them, one in each section, and let the length of any one of these lines be represented by vr. Let yf re- present the area of that section for which r=1, and 2, the perimeter of that section. The area of any other section will then be represented by rf, and its perimeter by 2ryy. Adopting the same nctation and reasoning in the same way as before (p. 186, Phil. Mag. Sept. 1871), u=af ‘wo(2prdr), U,= eee, F e 0 é dv U,=- ( 2 rly =) ars - fe = “. 2bwh (ohS uD Cae U,—2y/ ("y (rar . (49) 0 ! 0 20 dr Differentiating and considering U, constant, a fe, pili, =) 2ypwor = sr — Dy I (= _ Taking 29h=v?, and ue =Y, and reducing, l oe AF (g2-p2yp 2 —. : 20 ji at Vw " Ndr J (v?—0?)v (gh ’ a eeuy Leet ) _ Vw? dr} \v © 2\uv—v vv toy 2Qglu iz Vwh _ ee lp pb Integrating between the limits 0 andr, v \(v?—vn2 Vwir log, a :) =— ; ise ra 4 liad Canon Moseley on the steady Flow of a Liquid. o7 ae Vwir 7 ee Reel; ad... (50) Vo aye as vy? v2 ee ES (51) re ce 2vwir ° i y 1+4 (=) aber L \% Taking, as before, oe =ry, and neglecting, as before, the work 2 — accumulated in the liquid which escapes per unit of time (Phil. Mag. Sept. 1871, p. 193), DSO NTH uC, oulelicg its ie Nt uric at( (4) The discharge from a closed straight channel of any given geometric form in terms of the maximum velocity. Assuming R to be the value of r for that film which is in con- tact with the interior of the channel, and Q to represent the discharge per unit of time, and reasoning as before (Phil. Mag. Sept. 1871, p. 195), R R R Qa ={ (Qrdr)v= al ordr = ahr e—*y"rdr by equation (52), 0 0 0 ( <—*nir = os Bp bs ara _— Brat a irgp : My, iia gy Vy 1 -—Wyr ache ce (orre= a hg e—fyYRR— oi (e—¥yR_ ]) 0 Vy (Wy) 1 _ (Vy)? ; 1—(WyR+ Lenin} : ay VR —WRy l ie Qn= TWHyp it 6 ytle Eon Cons oy Bue (53) in which expression y is dependent on the work U, lost in the descerit of the water in the reservoir and in its passage into the pipe, and on the amount of work U, which it carries away with it on leaving the pipe, but is approximately constant for the same pipe and the same reservoir under different heads of water. Equation (53) may be put under another form. Let = actual section of the pipe,-y = actual perimeter. Then Q=R yp, y=2Ry,, EPEAT VF RP aa Sha ya EEE 38 Canon Moseley on the steady Flow of a Liquid. aa m to (53), ee a4 1- es ely +1)e TE hy aay This formula has this ete in its application to Messrs. Darcy and Bazin’s experiments, that the numerical values of ¥ and © have in every case been calculated by them. The discharge Q in terms of the head of water h, and the length of the pipe l. It may be shown, asin equation (4), that R 3 R Wi eal v?rdr = “Vo GRenelilya lime yi v0 g 0 since v= ,€~ “7”, or, as In equation (25), : a ae Oey a also Us=*2Rypl(u, +r, V?)V, or, neglecting mu, as small compared with A, V%, Us 2 Rao. whence we obtain, as in equation (26), vs o.. oe {39R—3yVR—1} + 4p ylRV2=wr/ 2ght R2; al i wi (29)2h?R2 Be oe 3yhR f agree —BYYR—]; + 4k 1 a Mid ee 2 (w)3(29)*h?RS sae — ("R38 VR—1) + 4nyr b° But. V ven? =, 21 Ug ee Vie tees aia Nn eames |) emcee * Editor’s Note.—The form of the expression ,+A,V* is discussed in a note at the end of this paper. Canon Moseley on the steady Flow of a Liquid. 39 *. by equation (53), 24V = pe cucoeety ly (w¥)®(2g) ehERS (AR — YVR — 1) (eek 7 Te sy VR — pray LP 2 UR 2Rs oe! (2g) et : eis yVR— LAER Go) (wey? {ee ae 36R Neglecting the first term in the denominator a reducing, ge (x = 23 gts Gia Ale 1)/ ARE Vs vrei? , y¥R_yVR—1 ee a =20691 x(¥)(“—* |) in )*U°RS, . (57 Q vi pa (sin 2) (57) The discharge of a rectangular pipe. Let 6 and c be respectively the breadth and depth of a rectan- gular pipe internally, and let the line similarly placed in each of the films which is represented by r be its breadth 5b. Then R=4; also the depth of that film whose breadth (r)= 1S 53 PHlxG, Wy=Wt+253 W145: aie b c Se eel As, wil comand a8) Wry Lae b+c If the line (r) similarly placed in each of the films had been its depth c instead of its breadth 5, then Aesiranll e+ * If R be exceedingly small, equ giwayys WRB a) (59) + Editor’s Note.—I have inserted ra in this expression ; it was omitted in the MS. 40 Canon Moseley on the steady Flow of a Liquid. By equation (58), 9° Qnfr a b wid 2(b +c)? Cr eet ee ber? € sls 2) i By equation ee Sey ‘ “eee | 60 ae a {i- Gat ee ay ee Substituting in like manner Be rf a , for R, Ww, and V in equation (55), : Ul _ 20°691(5 +-¢)3 ( ybe be chrom —1)(sin ‘27. . (61) Flow of water through a closed rectangular pipe placed in continua- tion of an open stream of greater section and fed by it. Two sets of experiments were made by MM. Darcy and Bazin * on the flowing of water through closed pipes with rectangular sec- tions, which they completely filled, the former in 1857 with a pipe having an internal section of 0°8 metre by 0°5 metre, a length of 70°3 metres, and an inclination of 0:0049 metre per metre, and the latter with one having an internal section of 0°48 metre by 0°3 metre, a length of 44°43 metres, and an inclination. of 0:0049 metre. Each of the pipes was fixed in the bed of an open stream 200 metres long, of uniform section and inclination. The water could be supplied from the Canal de Bourgogne, and * Recherches Hydrauliques, Paris, Imprimerie Royale, 1865, p. 162. Canon Moseley on the steady Flow of a Liquid. 41 was carried off by the river Auche. The pipe was formed of planks of poplar nailed lengthwise on wooden frames; their joints were carefully made water-tight ; and when the pipe was fixed, the space between it and the channel of the stream was filled with earth rammed down. As the water was entirely to fill the pipe, it was necessary that each end should be under water. A bar was for this purpose provided across the stream at the upper end of the pipe, so as to keep the level of the water above the mouth, and a dam was made across the stream 20 metres below the lower end of the pipe, high enough to keep the water also above the level of that end. The upper edge of this dam could be raised at will, so as to keep the lower end of the pipe (by which the efflux took place) immersed to any re- quired depth. It was by varying the height of this dam that the quantity of water which flowed through the pipe in a given time was made to vary. The end of the pipe by which the water entered it was 129 metres from the point where it was received from the canal into the open channel. Having flowed 129 metres freely along the open channel of greater section than the pipe, it could not but have acquired a greater amount of vis viva than that with which the water ultimately flowed from the pipe. Since — is the effective head of water, where f/ is the ver- tical feiehe of the top over the bottom of the pipe, and the effective height is increased by the barrage which brings the level of the water where it enters the pipe above the top of it, it follows that y is diminished by the barrage; and if there were no other causes operating on the other hand to increase y, it would necessarily be less than unity. These causes have been before discussed ; one of them is the accumulation during the de- scent of the water through the pipe of the work U, which it carries away with it. The other is the work U, expended in the hori- zontal pipe on the water in descending through the reservoir and in entering the pipe. But in this case the water descends through 130 metres of an open channel of much larger section than the pipe before it enters; and thus when it enters it has already acquired an amount per cubical unit at least equal to that with which it leaves it; moreover the difference between the aggre- gate vis viva of the water of the stream and that of the pipe cannot be expended wholly in causing it to boil up to the level of the barrage; part of it cannot but take effect in aiding the rush of water into the pipe, and thereby increasing the effective height, and thus, instead of increasing y, diminishing it. As to the work U,, that part of it which is due to the resistance to the descent of the liquid before it enters the pipe may obviously in 42 Canon Moseley on the steady Flow of a Liquid. this case be neglected, as may that which is due to the contrac- tion of the current in the act of entering the pipe, its section being so great as compared with its periphery. On the whole, then, y is to be expected to be, in this case of an inclined closed pipe fed by an open stream, less than in the case of a horizontal closed pipe fed froma reservoir; and it may be less than unity. This will appear from the two following Tables, which have reference to experiments made with the two rectangular pipes above described, in one of which the value of y is assumed to be 1:5, and in the other 1. Experiments, series 52, p. 170, closed rectangular pipe, breadth (6) =0°48 metre, depth (c)=°3. By ae (60), 2(-484-3)2 48 x “By eat G48 % -3y ee By? {1 ecrec, Med tig 8:45 | °, Qisaae 41 — (-184€y + 1) e184} 09. : v—sleo» 8°45 os . Q= 995 11-1 2769 e~ LNs Q=3°77 }1—-96805! x, Q = "1199722505... -2.. ». 2 ee Taste VIII. Experiments, Series No. 52, p. 170. Closed rectangular pipe, 0-48 metre broad, 0°3 metre deep. (March and April 1859.) Discharge per second in Velocity cubie metres, mee BE LSS Voe = NEAL tea EU/P ces ee By theory, By experi- y=15. ment. metre. m.c m. ¢. 1 0°465 0-0558 0-054 2 0-672 0-0806 0-078 3 0886 0°1065 0-100 4 1/103 0°1323 0:129 5 1-306 0°1567 0-155 6 1:634 0:1960 0-191 7 1-777 0-21382 0:203 8 1:966 0:2359 0:233 Canon Moseley on the steady Flow of a Liquid. 43 In the experiments of MM. Darcy and Bazin, Series 51, closed rectangular pipe, breadth (6) internally was 0°8 metre, and its depth (c) 0°5 metre. For this series of experiments therefore, by equation (60), Ee ie pee By jes ae : Sing xeaye SEHD JS, Ope iO? ; Q= =P f1- “(8077/4 Ney, 2... 62) Assuming y= ip Q=8-45 {1 —1:3077e— 3771 vp, Q=8°45(1—-96133)0,, Q=°32676r. Tase IX. Experiments, Series No. 51, p. 168. Rectangular pipe closed. Breadth 0°8 metre, depth 0°5 metre. (October and Novem- ber 1857.) Discharge per second in Se Velo city at cubic metres, La tes axis of pipe, j Vo. ; By theory, | By experi- ye ment. metres. m. C. m. ¢. Ly. 0-618 0:2019 0:203 2. 0:908 0:2967 0°307 3. 1-213 03964 0-411 A, 1505 0:4918 0-515 5. 1:826 0:5967 0-618 6. 1-961 06408 0-674 7. 2115 0-6912 0-721 8. 2:270 0-7418 0:777 Oren CHANNELS. The steady flow of a Liquid in an open channel of a constant section and uniform direction and inclination. If we imagine a plane to pass through the axis of either of the rectangular pipes above referred to and to be parallel to the Boron of the pipe, it will divide the water flowing through the 44, Canon Moseley on the steady Flow of a Liquid. pipe into two equal portions, acted upon by similar and equal forces, and subjected to similar and equal conditions of motion. If, therefore, we conceive the portion of the liquid above the plane to be removed, and the same pressures to be exerted on every point of the surface of the portion which remains as it exerted, it is clear that the motion of the latter will remain un- changed, as also the discharge of that portion, which, as the discharge of the whole was represented by Q, will be represented by $Q. But by the removal of the upper portion of the liquid, the pressure on the different points on the surface of that which remains will be changed; for whereas before it cannot but have been different at different distances from the axis, because the velocities at such different distances were different*, now they are the same, being everywhere equal to the pressure of the at- mosphere. As the pressure is everywhere less where the velocity is greater, it is evident that there will bea tendency in the liquid on the surface to flow from the sides of the channel towards the centre, and that thus the velocity of the surface-water at the centre will be diminished, and the water heaped up, drowning, as it were, the point of greatest velecity in the section. This disturbance of the motion of the liquid will not be limited to the surface ; there will result therefore a disturbance of the films of equal velocity. The experiments of MM. Darcy and Bazin afford evidence of this disturbance. In the first of the accompanying figures the films of equal velocity are shown in the pipe (sect. 0-8 metre by 0°5 metre) when closed and full, and in the second when open and half full. (Plate I. figs. 1 & 2.) Notwithstanding this new disturbance of the velocities of the different parts of the liquid, it is to be observed that the work of its weight over a given space remains the same; so that if there is no considerable change in the resistances, the discharge of the half of the now opened pipe may be expected to be the same as the discharge of that half was before. This was found by the experiments+ to be the case. The rectangular pipes above described, whose sections were respec- tively O°8 metre x 0°5 metre and 0°48 metre x 0-3 metre, had their tops removed, and water was made to flow through them so as just to half fillthem. The following were the results :— * Phil. Mag. November 1871, equation (20). + Recherches Hydrauliques, pp. 176 &c. Canon Moseley on the steady Flow of a Liquid. AS When the pipe was full and before | When the pipe was half full and its top was removed. after its top was removed. | Section of stream 0°5 x08 metre.| Section of stream 0:2458 x 0:8 met. Slope per metre 0-00427 metre. | Slope per metre 0-0043 metre. Discharge per sec. 0°618 m. c. Discharge per sec. 0'307 m. c. Section of stream 0°3X0-48metre.| Section of stream 0°1513 0-48 m. Slope per metre 0-:00627 metre. | Slope per metre 0-006 metre. Discharge per sec. 0:191 m. c. Discharge per sec. 0:093 m. c. Discharge from an open channel of any form. If, then, Q be taken to represent the discharge from an open rectangular channel half filled, 2Q will represent that from the same channel having its section doubled and being closed and filled. If, then, we take c, as before, to represent the depth of the stream, and 6 its breadth, and substitute 2Q for Q in equa- tion (60), and 2c for c, the resulting value of Q will be that of the discharge from an open rectangular channel. Moreover the reason for the discharge from an open rectan- gular channel being half that from a closed one of double the section applies equally to channels of all other forms, so that the fact of the half discharge being obtained from the open channel of half the section of the closed one may be assumed to be generally true. If therefore we substitute 2Q for Q in equa- tion (54), 2y for y, 20 for ©, we shall obtain a formula in which Q represents the discharge from an open channel of any given form, © representing the section of the stream, and the wetted periphery of the section of the channel. We thus obtain from equation (54) an equation for the discharge from an open rectangular channel. By equation (60), (6+ 2c)? 2ybe \, wee COPE. r {1 —(14+ € re bay ey ae Oo) By equation (61), Qybe - . (Ce acs ae —1) (sin) 2[6, 2y7r? (be) * 3 pre b¢ = SUR sel (Be ee —1)(sin yc, . (64) Pa (be)} as For the discharge from a uniform open channel of any given Ce en Se ce ee oot eee tee ae tins Dnemindie A EINE ES REE 46 Canon Moseley on the steady Flow of a Liquid. section, inclination, or degree of roughness or smoothness, ama 4 daa (pega mae 7 Q= shee! (i+ - jee pte ae) In the case of an open channel y=1. The value of y has been shown to be dependent on that of U, + U,*. If U,+U,=0, y=1. Now U, represents the work done by the head uf water to overcome the resistances to the motion of the water before it enters the pipe, and U, represents the work similarly done to accumulate in the mre the work with which it leaves the pipe ; if therefore we reason only of that portion of the liquid flowing through an open channel which is at a considerable distance from the point at which it is received into the channel, and which has acquired a uniform and steady state of motion, and if we mea- sure the head of water at any other point below it from this point as its commencement, it is clear that the work U, is all done by its weight before the liquid enters upon this portion, and also the work U,; so that the liquid enters upon this por- tion with no resistance of contraction any longer to be overcome, and no work further to be accumulated in it, but only with the resistances to motion in its channel and motion upon itself as it descends still to be overcome. In respect of that portion of its channel, therefore, U, + U,=0 and y=l1f. Comparison of Theoretical with Experimental Discharge in open Channels of different shapes. Assuming y= 1, equations (63) and (65) become _ (b+2c\? 2be ~ ase b Q=(") {1-( 1+ om Te a) ar (610) x? _ 2a =%41-(1 + ge inte ae Mean Seay =? 5( Je {1- ase ox} . (68) I propose now to test these formule a) comparing them with the important experiments made by MM. Darcy and Bazin on the motion of water in openchannels. They made several hun- dred of such experiments in fifty series on channels of different forms and inclinations and with streams of different depths. The results of the comparison with experiments taken from among these without selection are recorded in the following Tables. * Phil. Mag. November 1871, p. 351. + Editor’s note. —This 1s the case alluded to in the Philosophical Magazine for November 1871 as still remaining to be discussed. Canon Moseley on the steady Flow of a Liquid. 4.7 TaBLE X. Open rectangular channel; the sides and bottom covered with gravel-stone fixed in cement; sides of stones of gravel from 0-01 metre to 0-02 metre in diameter. Inclination of channel 0:0049 metre per metre; breadth of channel 1°832 metre. Darcy, Series 4, pp. 75, 77. * a) {1— @ eet Jena bay | Rass Depth of 20, 20 |Maximum QQ. Q. ‘number. | Stream, ( =) e—Y-| velocity, By By expe- | ; e. x V% theory. | riment. | metre. metres. m. ¢. m. ¢. | i 0°830 0-98953 0°847 0-1164 0-100 | 2. 0-1234 0-98156 1-246 0-2197 0:203 Et) sate 01651 0°96854 1:360 0°3357 0-307 | 4. 0:1917 095921 1-616 0:4606 0-411 ) 5... | 0-2226 0:94928 1:748 05636 0515 11 ee: 0:2499 0:93828 1:847 06776 0-618 7. | 02782 0:9060 1:964% | 0°7627 0721 8. | 03025 0:92317 2:032% | 0-8365 0°824 9. | 03240 0:91621 2:124% | 0:9224 0:927 _ 10. 03507 0:90760 2:205x | 1-0181 1-030 ner at, 0°3737 0:90031 2:323 1-1253 1°133 12. 0:3957 | 0:89287 2-352 1-194 1-236 Note.—The maximum velocities v9 marked with an asterisk were determined by floats, the others with the gauge-tube (tube- jaugeur). TaBLe XI. Open rectangular channel, the sides and bottom covered with gravel-stones from 0:03 metre to 0:04 metre in diameter fixed in cement. Inclination of channel 0:0049 metre per metre ; breadth of channel 1-861 metre. Darcy, Series 5, pp. 75, 76. Q= — 4 {1—(14 = ox boy, ey | Depth of oq | Maximum Q. Q. one me stream, (1 45 =) e— {| velocity, By _| By expe- | c. Das theory. | riment. metre. metres. m. Cc. m=: 8. 0°3436 0:90925 1-887 0:8961 | 0:°824 9. 0:3690 | — 0-90106 1-912 0:9305 | 0:927 asa O: 03946 0°89293 1:951 0:9988 | 1:030 ia FAD 04176 (88580 2-006 1-133 10716 12. 0°4448 0°87750 2:037 11405 | 1-236 EEE EE OO EO OO 48 Canon Moseley on the steady Flow of a Liquid. TasBLe XII. Open trapezoidal channel, differing but little from a rectangle, the width at the bottom being 1°8 metre, and the sides being inclined 1 in 10; constructed with rough building-stones laid in cement. Inclination 0: 037 metre per metre. The ma- sonry of the sides was more perfect than that of the bottom, the latter being somewhat worn. The bottom was covered with a slight deposit of mud which adhered to it. Darcy, Series 33, pp. 110, 111. =e 1+( 14 Je x bap Soe Depth of 99 | Maximum} Q. meee stream, ( <) é—X-| velocity, By pa se C. Diy. theory. metre. metres. m.c. At 0:1497 0:97176 3°49 0°7993 2. 0:2351 0:94429 4:55 1523 3. 0:2972 0:92329 | 5:4] 21861 4, 0°3553 0:90385 6:15 2°7936 Tasie XIII. Open Trapezoidal Channel. 20 XS 4 (a i =) zee =z rece Seo 1 Vo- 20, x ° Index Maxi- ee number. 2Q _22 | mum iy sense Se oe 1+> em x? ss B By city experi- Series.|Exp. D,. theory, eae ef metres.| m.c. m. ¢c. 21. 9. | 2°3038) 0°58469 0°88295 1:651 | 0°7611 | 0-927 21, | 12. | 2-4542) 0-6739 0:81718 1-805 | 1:1974 | 1-236 22. 1. | 1-168 | 0-1570 0:9889 1-420 | 0°1174 | 0-100 22. 2. | 1:2864| 0-2198 0-979038 1:785 | 0:21907) 0-203 22. 3. | 11-3893) 0-2740 0:96866 1:956 | 0:31082) 0-307 22. 4. | 1:4776) 03150 0:95967 2:114 | 041008) 0-411 22. 5. 1-5541) 03478 0:95187 2°390 | 0°4770 | 0°515 : Trapezoidal ; constructed) | | { | | \ ( Trapezoidal ; constructed} —_— nation of sides 45°. Q By expe- riment. Mises 0-749 1-489 2:247 2:996 Nature of channel. es with planks. Width at} i bottom 1 metre. Incli-| In-}| clination of channel] 0-0015. with planks. Width at} bottom 0:945 metre ;|_ one of the sides inclined} at 45°, the other vertical,| Inclination of bottom of| channel 0:0049 metre| per metre. | 49 quid. idy Flow of a L . Canon Moseley on the steo ee 66 *syur[g "qavde a.13aUi C).¢ a.10\. spre0q oy? yey, 3daoxa ‘oaoqe se ous aL ‘sede 9.490 10.0 pur aprm orj9U 120-0 ‘Uloq} ssooe paxy Spivoq YIM syuelg 66 66 66 66 *syurtd "P2USMID 5 $0.0 07:¢9.9 JozauNVIp { jaavig "P9}U9WI9d $9.0 0} 10.0 JojomeNIp {joavry ‘VER prey syorrg ‘(9and) yuawa9 sr a ae, NS pa eeecene —— “9ORJANS Jo ainyen IL¥-0 166E-0 | GF0-6 F6CG6- L006-0 008-0 £F00-0 ‘8 6 ¥E8-0 | SPOLL-0 | 096-6 T90€6- 66EE-0 £61-1 6700-0 8 ‘St 0€0-T EPEO-L | 906-6 SIII6- 61EE-0 [f6-1 98800-0 9 ‘Lt 9€6-1 FOSL-T | 090-6 L8188- GOGP-0 £961 6200-0 ‘L ‘of 819-0 6165-0 | 180-T 19988: SSOF-0 096-1 £100-0 AM ‘st 020-1 LOFO-L| LFL-G C(8e6- PESE-0 66-1 98300-0 9 vi ¥Z8-0 868-0 | 966-4 1S076- SVFE-0 196-1 6200-0 § ‘él 819-0 £69-0 | FEE-1 TISt6- OLTE-O 096-1 £100-0 Ue él T1¥-0 IFF-0 | 6966 6LI186- Eetl-0 686-[ 62800-0 6 LL I1L¥-0 veVv-0| F96-1 SELL6: L6EL-0 L86-T 6500-0 6 ‘OL €06-0 1cé-0 | 866-0 86EL6- PIVI-0 686-1 [100-0 & 6 £26-0 €106-0 | LF8-Z VG9S6- 9ZL61-0 66-1 ¥é800-0 6 8 819-0 GPS9-0 | 91-6 S196: 1981-0 66-1 6F00-0 9 ‘L 001-0 IST-0 | 908-0 GE066- 1620-0 66-1 8000-0 it 9 cell 8040-1 | 900-6 S8SR8- 9L1F-0 198-1 6700-0 Ul $ O6O-L | LELLO-T | 02-6 €£L06- L066-0 GE8-1 6F00-0 ‘Ol Ay 16f- SéL- L06-6 60056: OSlz-0 TT6-1 6700-0 iL & IéZ- 9602: 169-4 [696- E161-0 E181 6F00-0 L 6 2 Ul ‘OU | *Ssorjoul "91J9UI *2.10UL "19 UL “quam | *A10aTy 09 og-+ ; ‘ 4 Z ee *SITLIG -odxa Ag Ag Abe! 0% os Geer t) ee = ae wat pea Wodx i o “1Xt I 3s LO URSIN PPO Mey se negh UONVvUlpoUy |'Jaquinu xepuy _ {9 2 2 ozt9 9 oad +1 a) % )=0 993 \ 996 > Jer er? ‘spouueyyg wodg “ATX @TavVyy, Phil, Mag. S. 4, Vol. 44. No. 290, July 1872. E 50 Canon Moseley on the steady Flow of a Liquid. The Discharge when the Maximum Velocity is not given. The preceding Table serves to verify equation (63), in which the maximum velocity vg is supposed to be given by experiment, and the discharge Q determined from it. It affords no verifica- tion of equation (64), in which vg is not supposed to be given, but the discharge Q determined from the form and dimensions of the channel, the slope, and the nature of the surface. The dif- ficulty of the latter verification lies in the indeterminateness of the nature of the surface as represented by re. Verification of Formula.—It may nevertheless be verified by dividing by one another the discharges from the same channel corresponding to two different depths c, and c, of the stream as given by theory and by experiment ; re will be eliminated by this division from the formula representing this division. Let the discharges be represented by Q,, and Q,,; then, by equation (64), : | chet eves : Oe bBo Ae eee it Of ina G mig. 3 b+-2¢, Applying this formula to experiments 8 and 12, Series 2, 6=1°812, c,='2778, co='1102; b 7 5e1)'(2)' =-63585 Coe , ‘e b+ 2¢, 2bcy 2be OPE Ve a ee Se e eb 2c] b+ 2c, 1='10441; 2bez ) E+ 2c — i —1=:01898; .. by theory, a == 63535 x TOO) = 3-8334; by experiment, OQ. 2 1236 Q,, ~ B07 =4:02._ Similarly, by comparing experiments 12 and 8, Series 2 6==1°812, ¢,=:2778, c,=:2095,' we have by theory, - id Qe 7 = 1°4702 ; Canon Moseley on the steady Flow of a Liquid. 51 by experiment, ~ = 155. s = And comparing experiment 8 and 3, Series 2, _ 6=1:812,. 6) ="2005;) c= 719097; by theory, Q. ~—! =2°6081 ;gx Q.. by experiment, Q., 5 =2'68 Q.. Current-lines and Curreni-sur faces. In fig. 3, A B represents a line supposed to be drawn in a ho- rizontal plane through the point of maximum velocity at right angles to the current experimented on, MM. Darcy and Bazin’s Series 53, and represented in fig. 1. The divisions along it, through which are drawn lines parallel to the sides of the chan- nel, represent distances of 0°11 metre each; the figures repre- sent the velocities of the current at those several points as deter- mined by experiment. The velocity at each point is set off on the line passing through it in the direction of the current, twelve successive times ; and then the points so set off are supposed to be joined across the current so as to form a series of polygons, which, if the points of division in A B had been infinitely near to one another, would have been curves. If a line of small floating bodies, such as particles of camphor, be supposed at any instant to be dropped on the surface of the current along the line A B, then at the end of 1” these particles carried along by the water will have arranged themselves in the curve next to A B, and at the end of 2" in the curve next beyond that, and so on, until at the expiration of 12" they will form the curve acb. These current-lines are those in which particles of liquid starting at the same given instant from the same line mea- sured across the current will de at the end of the same given time. If instead of a powder being dropped upon the surface along the line A B, a wavelet had instantaneously been created along that line, that wavelet would have taken the form of the current-line, and the ripple would have been created which is seen in currents. It is not necessary that such a wave should be called into existence right across the current. If created by some obstruction in the side of the channel, it would still be absorbed into the portion of the current-lime nearest it and constitute an imperfect ripple. 52 Canon Moseley on the steady Flow of a Liquid. Fig. 4 represents a vertical section through the axis of the same current, the line D C being the depth of the current in the centre, and being divided as the central line (vertically) of fig. 1 is divided. Jines are drawn parallel to the surface through these points of division ; and the velocities at the corresponding depths, as shown in fig. 1, are set off twelve times along each of these parallellines. These points being jomed laterally, the cor- responding curves represent the positions into which the vertical filament of fluid, which coincides at any instant with DC, would be brought at the end of 1", 2", 3", &c. from the time of its starting. The point of maximum velocity, as shown in fig. 4, is not at the surface, but at 0-03 metre fromit. This explains the lip-like form of the curve as it approaches the surface. If we imagine a line of particles of camphor to be made instantaneously to fill the line D C, they will arrange themselves, after 1”, 2”, 3”, &c., in the corresponding lines of the figure. If instead of these par- ticles being made to fill a vertical line, they had been made to occupy a vertical cross plane through DC, they would, after these given periods of time, have arranged themselves succes- sively in curved surfaces, of which the current-lines of fig. 3 re- present the intersections with the surface of the current, and those of fig. 4: the intersections with a vertical plane through the axis. By equations (52) and (53) we obtain for the case of this channel Y= 124567 7092, Vo= 1°245e77 49, where v, 1s the velocity of the current measured across from the surface at a distance w from the centre; and v, is the velocity at a vertical depth y from the surface measured from the surface. Beneath the observed velocities in fig. 1 are given the theoretical ones as determined by these formule. If ¢' represent any number of seconds and each formula be multiplied by ¢, (¢v,) will represent an ordinate of a current-line of the surface of the liquid, corresponding to the abscissa 2, z" after it has left the position A B ; and (¢v,) will represent a similar ordinate of the current-line of the depth corresponding to the abscissa 7. Putting (¢v,) =z), and (tv,)=zZ,, we have Be (lees) emt en eed en aes which are the equations to the current-lines of the surface and the depth respectively. The Value of p. Tn the preceding investigation w is taken to represent the statical resistance per unit of surface to the motion of one film Canon Moseley on the steady Flow of a Liquid. 53 over the surface of another. As the motions of the films over one another are supposed uniform, the statical resistance must, in respect of each, equal the pressure to which the film is sub- jected in the direction of its motion and which causes it to move. But this last is in every case given in amount; the former is therefore also given in amount. It is this equivalent of » which comes in the place of uw, and which eliminates it from the in- quiry. Whence yu arises does not, therefore, come into question, but only the fact that it exists, and is of that amount without which the motion could not be uniform. I have now brought to an end the inquiries which I pro- posed to myself. I have investigated the conditions of the lateral propagation of motion in aliquid flowing from a reservoir through a circular pipe, whose particles move parallel to one another with a steady motion, to be represented by the equation (see equation 13) V=VpE—’,; where v, is the maximum velocity of water flowing from the axis of the pipe and y a quantity constant for the same pipe, what- ever the -head of water, but variable for different dimensions of the pipe and different conditions under which it receives the water from the reservoir. From this equation I have deduced the discharge from such a circular pipe per unit of time. It is given in terms of the maximum velocity in equation (17). The discharge being known in terms of the maximum velocity, it remained to determine the maximum velocity itself under the given conditions of the dis- charge. That is done by equation (29); while the absolute value of the velocity is determined by equation (28), and the discharge per 1" by equation (31); equations (39) and (40) de- termine the same thing with respect to inclined pipes. Incidental to these inquiries is that as to the work expended by water in flowing through a pipe, and the rise of temperature due to that expenditure of work. These are represented by equations (44) and (45). These are the subjects of my two former papers. In the pre- sent one I have investigated the general conditions of the lateral propagation of motion in a liquid whose particles move parallel to one another. It results from it that the particles move in films geometrically similar to one another. It was the obvious fact that when a liquid moves uniformly in a circular pipe which it completely fills, its particles necessarily form themselves into such films, which was the ground of the whole of my preceding investigations. That this principle, which is true of circular pipes is true of pipes of all other forms of section, enables me to 54 Canon Moseley on the steady Flow of a Liquid. apply the same method of investigation to them. The filament of maximum velocity is the common axis of all the films. Assu- ming the forms of the films to be given, equation (52) determines in terms of the maximum velocity thevelocity at any given distance from that axis ; equation (53) determines the discharge in terms of the maximum velocity. Equations (54a) and (546) deter- mine the maximum velocity itself, and equation (55) the dis- charge from a pipe of any given form and dimensions, the geo- metrical forms of whose films are also given, as they are in the. case of circular pipes. | Hitherto my inquiries have applied only to the case of closed channels supplied from a reservoir, and my results have been complicated by that arbitrary constant y which is dependent on the oblique direction of the liquid on passing from the reservoir into the channel. - In open channels this difficulty disappears, and y assumes in every case the value unity. The discharge from an open channel being half that from a closed channel of twice the dimensions, is determined at once from the formule I have given for the latter by the substitu- tion (mutatis mutandis) of unity for y. There remains, there- fore, only the determination of the relation which exists*between the forms of the films and the internal form of the channel. In the case of a closed circular channel this relation is one of iden- tity. In the case of channels of other forms it approaches it in - greater or less degrees of accuracy. I have tested this degree of accuracy in great numbers of the experiments of MM. Darcy and Bazin, in respect of open rectangular and trapezoidal chan- nels of great varieties of forms and dimensions and depths of water. ‘The results are stated in various Tables of the present paper, and compared with the results of experiment. It is on the faith of this comparison that I propose (in all those cases to which my comparison has extended) the following formula as representing sufficiently for all, practical purposes the discharge from a stream of given section in terms of its velocity at its mid surface—that is, its maximum velocity *. This formula is independent of the inclination of the stream, or the roughness or smoothness of the channel, both of which conditions are re- presented in the maximum velocity. And now I have to acknowledge my obligations to the admi- * Editor’s Note.—This formula is not actually specified in the panes There can, however, be no doubt that it is that given in equation (67), viz. 2 9 20 Ss Bee PRS ee g=X[1 C+). x | where Q=area of stream, x=wetted perimeter. Canon Moseley on the steady Flow of a Liquid. 55 rable experiments of MM. Darcy and Bazin. The labours of the late M. Darcy appear to me, as regards scientific precision, the admirable design of the instruments used in them, and the admirable industry with which they were carried on, among the greatest scientific labours of our age. I could not have arrived at my results without them ; but these are not founded upon them, but on the principles of mechanical philosophy. They have served me rather as the scaffolding on which my structure has been raised than as the foundation ; the scaffolding being withdrawn, the structure stands by itself. Note referred to in page 38*. I will venture to propose the following explanation of this formula. The resistance to the flow of the liquid which is next to that in contact with the surface of the pipe is supposed to be due to its ad- hesion to the liquid fixed to the surface of the pipe and to the impinging of its molecules on those of that liquid and on those of the pipe itself. The work per unit of time of that resistance is therefore equal to the work per unit of time of the shear of a flowing liquid film over a fixed one plus the work per unit of time necessary to replace that which is lost in the impact of the mole- cules of the moveable film on those of the fixed one. Let P=whole resistance per unit of surface to the motion of the one film over the other at rest. V=uniform velocity of the motion of the one film over the other. K=area of the surfaces of the films in contact. pf, =unit of shear, being that per unit of surface of contact of the films. PK =whole resistance of one film to the motion over it of the other. ' PKV=work per unit of time of that resistance. Ky,V= work per unit of time of shear. To determine the work lost per unit of time by the impact of the molecules of the moving film over that of the fixed one, let it be observed that this loss is proportional to the number of such impacts per unit of time and the work lost in each such impact, and that this last is measured by half the ws viva lost in each impact. But the number of impacts per unit of time is proportional to KV ; and the vis viva lost in the impact of one molecule on another at rest is proportional to the square of the * Editor’s Note-—This note, evidently made in connexion with the pre- sent paper, was found amongst Canon Moseley’s MSS. ; and it seemed fit- ting to publish it here. ; 56 Mr. S. Taylor on Variations of Pitch in Beats. velocity of the impinging molecule. This may be proved as follows. , By a well-known formula, if W, and W, be the weights of two imperfectly elastic impinging bodies, and V,, V, the velocities of their impact, and e the measure of their elasticity, and u, half the vis viva lost by W, in its impact, then __ (L+e)W,W.(V,+ Vo) BAG (WE Was s2W,V,+ (l1—e) WV, + (1+ ¢)WeVo}. | (See “‘ Mechanical Principles of Engineering and Architecture,” by the author of this paper, Art. 440.) If V;=0, or if one of the bodies be at rest, ale +e)W,W, | ‘5 “= 29(W, +W,)? f2W, + (1 —e)WIV; ; u, varies, therefore, in this case as Vi—that is, as the square of the velocity of the impinging body. Therefore the work lost per unit of time by the impact of the ‘molecules of the moving film on those of the fixed one is pro- portional to (KV)N? or to KV®. Let it = A, KV? ; “ PKV=Ky,V+A,KV%, and Ppa LV. On Variations of Pitchin Beats. By SEpury Tayuor, Esq., late Fellow of Trinity College, Cambridge*. ia HELMHOLTZ, as all readers of his great work, Die Lehre von den Tonempfindungen, are aware, has proved that discord in music invariably arises from certain phe- nomena called deats, which were well known to previous writers on Acoustics, though their extreme importance had not been re- -cognized. Beats occur whenever two musical sounds of slightly different pitch are simultaneously produced. Helmholtz describes their effect in the following words :—* The intensity of the sound becomes alternately strong and weak in regular succession.” Up to the second edition of the Tonempfindungen no variation save that of intensity wasmentioned. In the third edition, how- ever, the author states that a slight oscillation in pitch on the part of the beating sound is likewise perceptible, adding that this fact was communicated to him by M. Guéroult+. But, although * Communicated by the Author. t P. 259, References are to the third edition, Braunschweig, 1870. Mr. 8. Taylor on Variations of Pitch in Beats. 57 this additional element of variation in beats is thus recognized, dissonance is still, as in the earlier editions, represented as due to alternations of intensity only. The following paper is an attempt to show that the pitch-variations are important consti- tuents of dissonance, and ought, in a complete view of the sub- ject, to be taken into account. I am not aware whether M. Guéroult originated the observa- tion the result of which he laid before Professor Helmholtz, but may remark that in a paper read before the Cambridge Philo- sophical Society in 1857, by the late Professor De Morgan *, the existence of alternations of pitch in beats is distinctly asserted as a known fact which he had himself experimentally verified. It will be convenient to begin by laying down theoretically the conditions under which pitch-variation occurs, as the results thus to be obtained facilitate the experimental examination of the phenomenon. Let two simple tones of different intensities, but of nearly the same pitch, coexist. An assigned molecule of air will be si- multaneously solicited by two sets of sound-waves. Hach of these may be represented by a curve of sines, the times elapsed from a given epoch being denoted by distances measured along the axis of abscissee, and the contemporary displacements of the molecule by corresponding ordinates. The problem to be solved is the composition of the two series of vibrations. Two cases must be distinguished, according as the higher or lower of the two tones is the more powerful. We begin with the first of these. The waves acting on the molecule may have any degree of difference of phase. The two extreme cases, where they are in complete accordance and in complete opposition, are represented in figs. 1 and 2 respectively. The strong line in each is half a wave of the resultant curve. O is the origin at the undisturbed position of the molecule; O X the axis of abscisse; OA, OB * « On the Beats of Imperfect Consonances,” Trans. of Camb. Phil. Soc. vol. x. p. 137. 58 Mr. S. Taylor on Variations of Pitch in Beats. half wave-lengths of the constituents ; C the point in O X where the ordinates CD and CE are equal in length but opposite in hiss: eae Lo D aes =—~ direction, and where, accordingly, the resultant curve meets the axis. In fig. 1 OC is greater than O A and less than OB, while in fig. 2 OC is less than either OA or OB. But OC is im each case the half wave-length of the resultant tone, OA and OB those of the primary tones. Hence, when the two sets of waves are in complete accordance, and the intensity of the resultant tone therefore a maximum, its pitch will he between the two pri- maries. In the opposite case, where the intensity is a mimimum, the pitch of the resultant tone will be more acute than the higher of the primaries. Figs. 3 and 4 represent the state of things when the lower of the two original tones is the more powerful. Fig. 3. Here, when the intensity is a maximum, the pitch will be, as in the first case, intermediate between the primaries; when a mi- nimum, lower than the more grave of the primaries. Thus, in both the cases under consideration, each beat will be Mr. 8. Taylor on Variations of Pitch in Beats. of two different degrees of pitch at the moments when it is loudest and weakest respectively. In order to as- certain what happens at intermediate points of time, we have only to deter- mine the resultant curve for a suffi- cient number of wave-lengths. This is done in fig. 5, which is constructed for the interval of a semitone (16: 15), and represents completely the state of things from a maximum of intensity to the adjacent minimum. The higher tone is taken as the louder of the two. The wave-lengths here gradually di- minish as we advance from the maxi- mum to the minimum of intensity ; and, accordingly, the pitch of the va- rying tone rises continuously, passing through every gradation which sepa- rates its gravest value, at the maxi- mum of intensity, from its acutest value, at the minimum of intensity. After the latter moment the same in- terval is again traversed in the same manner, butin the opposite direction, the pitch falling continuously, until, at the next maximum of intensity, it once more reaches its lower limit. Thus in every beat there is a regular oscillation of pitch, as well as of inten- sity, each taking place between fixed limits. When, as in the case repre- sented by the figure, the more acute primary is the louder of the two, the variable tonesinks in pitch as its power strengthens, and rises in pitch as its power weakens. When the lower pri- mary is the louder the reverse is the case, as can be shown by a suitable figure. ‘The effects of these two kinds of beats may be indicated in musical notation thus, GE. EE irs: EG =act: EEE a-|te= t Fei i: ceameEs ‘2 QINSLy 2 = 60 Mr. 8, Taylor on Variations of Pitch in Beats. it being understood that the variations, both of pitch and inten- sity, are to be perfectly continuous between their limits, and, further, that the pitch-limits do not form an exact semitone. Our figures afford the means of obtaining an approximate algebraical expression for the number of vibrations executed per second by the varying tone when its intensity is either a maxi- mum or minimum, assuming its pitch at those moments to be instantaneously stationary. For this purpose we will assume that OA and OB are nearly equal, 7. e. the primaries only slightly different in pitch, and that, in determining the point C, the portions of the constituent curves about A and B may be regarded as approximately straight lines coincident with the tan- gents to the curves at those points. If, now, we take for the two displacements A, sin 277,¢ and A, sin 27nt, where n, and n, are the number of vibrations per second made by the primaries, and A,, A, the corresponding amplitudes, ¢ being, as usual, the time elapsed, we may put, for the position of maximum intensity (figs. 1 and 3.), OAS an Ohno ae Qn, DPS can CRD = oni 2Ng From the figures AC tan CAE=BC tan CBD; Fig. 1. (OC —OA) tan CAE= (OB—OC) tan CBD ; Fig. 3. (OA—OC) tan CAE= (OC —OB) tan CBD ; .*. in both cases OC (tan CAE+ tan CBD) =OA tan CAE+ OB tan CBD, 1. Ce OC(27n,A,+27n,A,) = on .277,A,+ = 27, A, 5 A,+A DOG = s22sl es 3 20C is the wave-length of the varying tone; its number of vibrations per second is therefore equal to ~~~ 200 mA, + Nga Mr. 8S. Taylor on Variations of Pitch in Beats. 61 To find the corresponding number for the mimimum position (figs. 2 and 4), it is only necessary to change the sign of one of the amplitudes; the result therefore is nA, Nah A,—Ag A, being supposed > Ag. The two principal cases are therefore the following :— I. Higher tone the louder, A,> Ag, 2, >No. For maximum intensity, number of vibrations per second MA, + Nghe bee A, (2 — M9) Bee Ag(n,— Mo) A, +A, a AEN MOA AG For minimum intensity, number of vibrations per second & my A,— NA, =n, + Ag(m =o) , A,—A, A,—A, II. Lower tone the louder, A,>A,, >. For maximum intensity, number of vibrations per second mA, +NgAo A, (2—7,) sy ola Ag(n, — Ng) A, +Ag A, +A, Os aR es For minimum intensity, number of vibrations per second =Ng+ — Meho—maAy As Sa Aj (2 —7%9) - A,—A, as Ag—Ay These equations, which embody the conclusions already ob- tained directly from the figures, are deduced by Helmholtz*, as particular cases, from a more general analytical investigation. It will be observed that when A,=Ag a discontinuity arises, . which indicates that the assumptions on which our equations were obtained are here no longer applicable. The case has not been considered by Helmholtz, but admits of easy direct treat- ment. The displacement of the molecule depends on the ex- pression sin 2an,¢ + sin 27n,f, or 2 sin (n, +7.) mt cos (nj —n,) 77. The second factor, cos (nj —7,)7#, 1s a slowly varying function of ¢ which determines the number of beats per second. The first factor vanishes whenever (n,+7,)7¢ is a multiple of a, 7. e. whenever ¢ isa multiple of This result is not, lke the 1 previous one, merely approximate, but rigorous. The successive BURP G22% 62 Mr. 8. Taylor on Variations of Pitch in Beats. wave-lengths will therefore be all equal, each having the value 2 my at Ne . . e e whatever, the number of vibrations per second remaining con- stant, and equal tom . Hence, in this case, there will be no variation of pitch In passing to the experimental verification of the above theo- retical conclusions, l may mention a confirmatory instance which is interesting from its undesigned character. Helmholtz has given* a copy of a curve representing the movement of a mem- brane resonating under the action of two beating organ-pipes, drawn by means of K6nig’s phonautograph. In this instru- ment a small steel pointer is connected with the membrane and ~ registers the vibrations of the latter on a rotating cylinder which has previously been covered with lampblack-coated paper. The figure is intended by Helmholtz to illustrate variations of mten- sity alone; nevertheless the roughest measurement suffices to show that the wave-lengths near the minimum of intensity are shorter than those near the maximum, and therefore that pitch- variations are also present. It isclear, by what has been shown in the present paper, that in the experiment thus recorded the more acute of the two organ sounds must have been likewise the louder. As another example of how easy it is to miss a phenomenon lying directly under our eyes, when we are not specially on the lcok-out for it, I may be allowed to relate a conversation with an organ- and pianoforte-tunist of much experience, Mr. Ling, of Cambridge. I asked him whether he had ever noticed changes of pitch in slow beats. He replied in the negative, and expressed a decided opinion that no such changes occurred. On trying the experiment, however, upon a pianoforte in my rooms, he at once perceived the variations in question, though remarking that he would not have accepted the fact save on the testimony of his own ears, so convinced was he that the alternations of intensity, to which he had hitherto exclusively attended, constituted the whole of the phenomenon. I had afterwards the advantage of Mr. Ling’s assistance in some experiments made on the organ in the chapel of Trinity College. A stopped diapason, Ap, having been flattened until — it gave slow beats with the neighbouring G, we found, in accord- ance with the result obtained above for sounds of equal intensity, that the pitch of the beating tone was perfectly steady. On combining, however, the same G with an Ab belonging toa softer stop on another manual, which had first been similarly *- Bagels Mr. S. Taylor on Variations of Pitch in Beats. 63 treated, we recognized the oscillations of pitch without difficulty. By arrangements of this kind the zntermediateness* of the beating sound between the primaries at its maximum of intensity, and its passage beyond their limits*, either of graveness or acuteness, at its minimum, were brought out very distinctly. Dissonance arises, as Helmholtz has proved, from the presence of beats too rapid to be separately recognized. Except when they are due to sounds of exactly equal intensities, they contain, as we have seen, oscillations of pitch. It remains to inquire whether alternations of this latter kind produce any appre- ciable effect on the character of the combination in which they occur. There seems some antecedent probability that they will do so. The essential character of a musical sound is steadi- ness of pitch. Here we have a sound which is never steady for a moment, and thus comes under the definition of a mere noise. ‘The unmusical nature of such a sound can hardly fail to make itself felt. We can, however, put the question to the test of experiment by producing rapid alternations of intensity, while the pitch is kept constant, and ascertaining whether the whole sensation we call dissonance can be thus excited. In order to do this, I employed the principle of interference, as ex- hibited by a single tuning-fork. It is known that a fork in- making one revolution about its own axis passes through four positions of maximum intensity separated by four positions of absolute silence. By twirling the handle of the fork between the fingers of both hands, I was able to command quick alternations of intensity unaccompanied by changes of pitch. As a further experiment, a resonance-box, with its fork screwed into it, was fastened into a lathe, and, the fork having been struck, set ro- tating, so that the open and closed ends of the box were alter- nately presented to the ear. The lathe was then urged to its fullest speed and a series of very rapid intensity-variations pro- duced. I owe the means of performing this experiment to an excellent amateur turner, Mr. J. Aspinall, of Crewe, who was kind enough to place his lathe and his own dexterity at my dis- posal for the purpose. The result of both the trials just de- scribed was, that the effect, though distinctly rough, lacked the peculiar sourness usually characteristic of a discordant interval. These observations seem to show that it 1s the pitch-variations which excite in our ears the special element of discord just men- tioned. In fact the conditions under which dissonance arises frequently themselves indicate that variations of intensity can have but an insignificant influence upon the total result. Thus the dissonance of two tuning-forks forming the interval of an * These facts were also experimentally ascertained by Helmholtz, p. 622. 64: The Hon. J. W. Strutt on Gaseous Pressure. imperfect octave is due to the beats of the combination-tone of the first order with the lower of the two fork-tones. The former sound is much weaker than the latter; the variations of inten- sity cannot, therefore, be considerable, though the sourness of effect is marked. A similar observation applies to the case of two simple tones forming the interval of an imperfect fifth, where the dissonance arises between combination-tones of the first and second orders, the latter being extremely weak compared with the former. Further, with composite sounds, such as those of most musical instruments, the dissonance of all intervals wider than a tone, or tone and a half, is due to the beats of over-tones of dif- ferent orders. These are, in general, correspondingly different in loudness ; and, accordingly, variations of pitch are developed at the expense of those of intensity. I should, in particular, attri- bute the slight imperfections by which the ordinary concords of the scale (fifth, fourth, thirds, &c.) are rendered less smooth than the unison or octave, mainly to the pitch-variations, since the difference in order, and consequently in strength, between the beating over-tones is here usually sufficient to render the in- | tensity-variations inconsiderable. V. On Mr. Moon’s views on Gaseous Pressure. By the Hon. J. W. Strut, M.A., late Fellow of Trinity College, Cambridge. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, WISH to make a few remarks on some views of Mr. R. Moon promulgated in your June Number and (more at length) in the Number for August 1868. It is a received opi- nion among physicists that, in the case of such motions of air as constitute sound, the differential pressure is proportional to the differential density. Mr. Moon, on the contrary, holds that density (and temperature) do not determine pressure, and brings forward a mathematical argument (which I shall consider pre- sently) to show that velocity also is a datum which it is necessary to know before pressure can be calculated. The first question that arises is, What is here meant by velocity? Ifit be absolute velocity which is intended, two repetitions of Boyle’s (not Ma- riotte’s) experiment with an interval between of twelve hours during which the earth’s diurnal motion at the place of obser- vation would be reversed, would suffice to settle the question. Perhaps Mr. Moon means the velocity relatively to the contain- ing vessel; but this does not alter the matter, because in the case chosen for illustration the cylinder may be moved in the direction of its length with any velocity, and leave the air behind Mr. A. Cayley on a Bicyclic Chuck. 65 it; for no account is taken of friction or viscosity. But apart from all this, is it not obvious that the physical condition of a small mass of air is independent of any velocity animating all its parts? Ifthe pressure changes, why not the other properties of air with it? With regard to Mr. Moon’s analytical argument, [I would remark that the question at issue is a purely physical one. Apart from their meanings, it would no doubt be difficult to establish the proportionality of the symbols p and p. But Mr. Moon’s reasoning is fallacious. In any particular case of motion in one dimension, p, v, and p are doubtless functions of 2 and ¢. Eli- minate # and ¢, says Mr. Moon, and you are left with p, a func- tion of v as wellasp. In this expression lurks an ambiguity. Mathematicians often say that one quantity is a function of a second, meaning that they may depend on one another, without exclusion of the particular case of mdependence. If Mr. Moon objects to this use of the word function, his inference that p is a function of v does not follow. His opponents, of course, main- tain that when you eliminate 2 and ¢, v will disappear with them; but they do not arrive at this conclusion, as Mr. Moon seems to suppose (Phil. Mag. vel. xxxvi. p. 117), as the result of a process similar to that adopted by him. Whether an assump- tion is gigantic or not depends on the grounds on which it is made; and I have never heard that Boyle’s law was regarded otherwise than as a clear result of experiment. It is a part of that result that the velocity of the containing vessel (which is shared by the gas) is not an element in the matter. If you begin by throwing overboard the relations between symbols which exist in virtue of their physical interpretation, you need not be surprised if an analytical process fails to force them back on you. I am, Gentlemen, Your obedient Servant, ~ Joun W. Srrvrt. RETAIN the former title; but I wish chiefly to describe the general plan of a curve-tracing apparatus. The arrange- ment may be considered as consisting of two chucks, X, Y, ca- pable of connexion in any manner, and of a pentagraph working from the underside of a bridge, the pencil P on the upper sur- face of chuck X, or, say, on the chuck-table X, and the pencil Q on the chuck-table Y, cach pencil being capable of attachment to the corresponding chuck-table. * Communicated by the Author. Phil. Mag. 8. 4. Vol. 44. No. 290. July 1872. 1 66 Mr. A. Cayley on a Bicyclic Chuck. Then, the chucks being connected and Q being attached to Y— moving X, this moves Y, which moves Q, which (through the i H é i 1 I pentagraph) moves P; that is, we have the chuck-table X and the pencil P both of them in motion, and P traces out on X a curve compounded of these two motions. eee In my own roughly constructed apparatus, X is a bicyclic (or an oval) chuck, Y a mere circular chuck rotating through an angle of about 40°; and a point M of the chuck-table X can be so connected as to be at a given distance from a point N of the chuck- table Y; the complete rotation of X thus gives to Y a recipro- cating circular motion. The connexion is made by an excentric working below the chuck-table X; viz. we have rigidly con- nected with the chuck X a cylindrical axis of about 3 inches radius and inch high, carrying rigidly connected therewith the chuck-table X ; and the excentric works round this axis (the centre of the axis being thus the point M), and its other extre- mity round an axis on the upper surface of chuck-table Y: the pencil Q can be connected (within limits) with any point of the chuck-table Y. The result is that, the chucks being disconnected, the fixed pencil P traces out on chuck-table X the curves determined by the construction of this (bicyclic or oval) chuck; but when the connexion is established, the complete rotation of X gives to Y a reciprocating circular motion, which Y communicates to Q, and Q to P; that is, the pencil P, instead of being fixed, has a reci- procating circular motion. I obtain hereby, among other forms, elegant three-looped curves. Notices respecting New Books. 67 Suppose the chucks disconnected and the chuck-table Y fixed; then by placing Q on a determinate point of Y, we thereby place P in the position to trace out (on the moving chuck-table X) a curve of determinate form. For instance, the bicyclic chuck X being adjusted in any given manner, it is easy to draw on the fixed chuck-table Y a locus which is such that, Q being placed at any point thereof, the curve traced out by P shall be cuspidal (the locus in question is, with a difference of position only, the locus of P such that the curve traced out by P shall be cus- pidal) ; and this being so, as Q is placed on the one or the other side of the locus, the curve traced out by P will have or will not have a node. The locus is of a high order—in the case in which I have drawn it, a closed self-intersectmg curve met by various lines in four real points. Moving Q along any such line, the curve traced out by P is successively A, C, N, C, A,O,N,C,A (A without a node, C cuspidal, N nodal). Similarly, if Q be moved along a line which meets the locus in only two real points, then the forms are A, C,N,C, A; and if the line does not meet the locus, then the form is A throughout. We thus by means of the locus obtain a curve of the required form. Again, supposing the chucks disconnected, and Q attached to Y: keeping Y fixed and moving X we obtain on chuck-table X a curve; moving Y through a small interval and again fixing it, we obtain a second curve, and so on; that is, we obtain on chuck-table X a series of curves each due to the construction of X, but in an arrangement due to the construction of Y. VIL. Notices respecting New Books. An Introductory Algebra, containing the chief rules in the first part of Colenso’s Elements of Algebra simplified ; with additional illustra- tions, and followed by a large Appendix of new examples arranged in the order of the rules. By the Right Rev. J. W. Coxenso, D.D., Lord Bishop of Natal, and the Rev. J. Hunter, M.A., for- merly Vice-Principal of the National Society’s Training College, Battersea. London: Longmans, Green, and Co. 1872. 18mo. Pp. 242. RE title-page, which we have given at full length, sufficiently describes the work. It contains the usual course of Elementary Algebra, including, however, indeterminate equations of the first | order connecting two unknown quantities, and excluding the Bino- mial Theorem. All elementary books on Algebra with which we are acquainted place the solution of simple equations early in the course; the present authors go a step further in this direction than most of their predecessors ; for no sooner has the learner been taken through addition and subtraction than they set him to work easy equations of the first degree of one unknown quantity, then to ex- press numerical relations in algebraical language ; and thus they lead ‘ i <4 ‘68 Notices respecting New Books. op him up to easy problems producing simple equations. For instance, such a question as the following occurs very early in the book :— « A and B began to play with equal sums; A won 30 shillings ; and then 7 times A’s money was equal to 13 times B’s: what had each at first?’’ But before letting the learner try such questions, he is set a number of exercises like the following :—If 2 stand for a num- ber of shillings, and if A has 13 shillings and B has 21 shillings, (1) what will A have after spending z shillings? (2) What will B have if he receive twice as many shillings as A has spent? (3) If A receives x shillings from B, how many will each have? and so on. ‘On the whole the book seems very well done; and the large number of examples which it contains will doubtless make it useful to learners, who are at first mainly concerned to acquire a sort of me- chanical ease in manipulating algebraical expressions. A Treatise on Attractions, Laplace’s Functions, and the Figure of the Earth. By Joun H. Pratt, M.A., F.R.S., Archdeacon of Cal- cutta. Fourth edition. London and New York: Macmillan and Co. 1871. Crown 8vo. Pp. 245. | The third edition of this book was the subject of a rather long notice in our pages (vol. xxxi. pp. 144-149) ; we shall therefore limit our notice of the present edition to making mention of the chief points in which it differs from its predecessor. ‘These are three in number :—(1) The chapter which treats of the Attraction of 'Table- lands, Mountains, &c. has been greatly enlarged. The author has introduced a discussion of certain formule for calculating the effect of variations in the density of the earth’s superficial mass, which formed the subject of a pamphlet written by him in 1868. (2) The chapter which treats of the Earth considered as a Fluid Mass has -been modified to bring it into accordance with the author’s recogni- tion of the fact that the variations of the force of Gravity on the Earth’s surface are not in themselves sufficient to prove that the earth was originally fluid. (8) In the section on the determination of the mean figure of the earth, supposing it to be spheroidal, the author gives at much greater length than in the earlier edition his views of the best method of deducing the mean value of the Axes of the Earth from the principal measured long arcs, viz. the Anglo- Gallic Arc, the Russian Arc, and the Indian Arc. The substance of this addition appeared in our pages (vol. xxxiil. p. 10). Besides these there are several. minor alterations, the result of the whole being to increase the volume by 83 pages. The preface is dated Calcutta, November 8, 1871, not long before the author’s death ; this date, compared with that of the second edition of the author’s Treatise on the Mathematical Principles of Mechanical Philosophy; (October 5, 1841), shows that his life in India extended over more than thirty years; and when we remember that his scientific pursuits were entirely additional to his professional duties, that they were pursued under the disadvantage of the climate of Calcutta, involved laborious calculations, and were continued up to the end of his life, we cannot but regard the composition of the yolume before us as a striking instance of devotion to science. poo | VIII. Proceedings of Learned Societies. ROYAL INSTITUTION OF GREAT BRITAIN. May 3, ON Optical Phenomena produced by Crystals submitted 1872. to Circularly Polarized Light. By William Spottis- woode, Esq., LL.D., M.A., Treas. R.S. “and R.L. On a former occasion * I exhibited some phenomena depending upon circular, or as it was then also called, successive polarizaon, and in particular I adopted and explained a method for producing circularly polarized light devised by Sir Charles Wheatstone. [ propose on the present occasion to pursue the subject into some of its ulterior consequences. In terms of the wave theory, light is said to be circularly polarized when the vibrations are circular, as distin- guished from plane polarization (when they are rectilinear), And further, it is known from mechanical principles that a circular vibra- tion may always be produced by the combination of two rectilinear vibrations, the amplitudes or extents of which are equal, and whereof one is in advance or in rear of the other by one or by any odd number of quarter wave-lengths. In the former of these cases the circular motion will take place in one direction, say right-handed ; in the latter in the opposite, say left-handed. The contrivance used for producing circular polarization this evening is known by the name of a ‘‘quarter-undulation plate,” and caalsists of a plate of mica split to such a thickness that one of the two rays into which plane-polarized light is divided on entering it is retarded by an odd number of quarter wave-lengths behind the other. The optical phenomena produced by crystals when submitted to polarized light are usually divided into two classes, viz.:— (1) those arising from the use of parallel light, and consisting of broad sheets of colour; and (2) those due to convergent light, and consisting of the rings and brushes, the general character of which is well known. _I propose to take a few specimens from each class, and to examine the modifications which the known phenomena undergo when the light is both polarized and analyzed circularly, 7. e. when one quarter-undulation plate is interposed between the polarizer (Nicol’s prism) and the crystal to be examined, and the second between the crystal and the analyzer (Nicol’s prism). In the first place, it is known that if a plate of selenite be placed in an ordinary apparatus when the polarizer and analyzer are either parallel or crossed, there are four positions at 90° apart in which the plate will produce colour—and further, that if the analyzer be turned through 90° the same result will be obtained, except that the colour will be complementary to that first seen. The intensity of the light at any given point is then given by the formula cos’s— sin 27 sin 2(¢—s) sin” " where 7 and s are the angles made with the original plane of polar- * Phil, Mag. for May 1871, p. 398, 70 Royal Institution :—Mr. W, Spottiswoode on Optical ization by the principal sections of the crystal and of the analyzer respectively, and 6 is the retardation. If, however, the two quarter-undulation plates (say the plates A and B) be introduced, the light undergoes the following processes :— First, it is plane-polarized by the polarizer; secondly, the plate A’ being placed so that its axis is inclined at + 45° to the original plane of polarization, the light undergoes right- or left-handed circular polarization, and in that condition falls upon the crystal; thirdly, in their passage through the crystal C the rays are each divided into two, whose vibrations are at right angles to one another, and whereof one is retarded in proportion to the thickness of C; fourthly, the plate B being placed so that its axis is parallel or perpendicular to that of A, each of these sets of rays is circularly polarized, one set right-handed and the other left-handed ; fifthly, these two oppositely circularly polarized sets of rays combine, according to known me- chanical laws, on emerging from B into plane rays, in which the planes of polarization of the different colours of the spectrum are turned through different angles. Hence, finally, by turning the analyzer round we shall cross these various planes in turn and successively extinguish the different colours, leaving the comple- mentary colours visible. The system of plates A, C, B consequently acts in this respect like quartz. It is, however, to be observed that if the plate B be turned from one of the two proposed positions to the other, the directions of motion in the two emergent circularly polarized rays, and consequently the planes of polarization of the different colours, will be reversed; in other words, with the plate B in One position we shall imitate a right-handed, with the plate B in° the other a left-handed quartz. The intensity of the light at any point is then given by the formula | sin®’ for one position, 20 cos a the other. Again if, the plates A B retaining either of the positions before indicated, the crystal C be turned round in its own plane, then, _ since the light emerging from A and B is circularly polarized, it has lost all trace of direction with reference to the positions of the polarizer and analyzer, and consequently no change of tint will be observed. The same is abundantly clear from the formula written above, because the only term it contains depends upon the retar- dation within the crystal C. This experiment was made by Airy. If the plates A and B have their axes directed 45° on either side of the axis of C, and the three plates be turned round as one piece, the colour will remain unchanged; while, if the analyzer be turned, we have the colours shown in the regular order. If the plates A and B have their axes directed at 45° on the same side of the axis of C, and the pieces be turned round bodily as before, the colours change in the same order as above, and ge through their cycle once in every Phenomena of Crystals and Circularly Polarized Light. 71 90° of rotation ; and if the analyzer be turned in the same direction, the colours change, but in the reverse order. The explanation of this is to be found in the fact that when the plates A and B are crossed, the retardation due by A is compensated by that due to B; so that the only effective retardation is that due to the crystal C. But upon this depends the rotation of the plane of polarization; if, therefore, the polarizer and analyzer remain fixed, the colour will remain unaltered. When the plates A and B have their axes parallel there is no compensation, and the colour will consequently change. This experiment was made by Fresnel. ‘The mathematical expres- sions for the intensity of the light in the two cases respectively are cos” (i+i+5) and cos'(j-i-5), where 7 is the angle made by the principal sections of A with that of the polarizer, and 7 that of the principal section of B with that of the analyzer. The first expression is obviously unchanged when the angle between the polarizer and analyzer, viz. stits ig unchanged. It’should be added that the rotation of the plane of polarization, and consequently also the sequence of tints, does not follow exactly the same law in the above cases as in quartz. We now come to the case of convergent light—that is, to the phenomena of crystal rings; and let us examine the effects produced by the same arrangement as before, viz. two quarter-undulation plates A, B, one in front and one behind the crystal C. To quote from Mr. Airy :—‘‘ The first thing that strikes us in this combi- nation is that there is nothing, except in the crystal, that has any respect to sides. For the only incident light is circularly polarized ; the only light allowed to emerge is circularly polarized. ‘The ap- pearance therefore of the coloured rings &c. must be such as conveys no trace of any plane of polarization, and must not vary as the crystal is turned round. In the common exhibition of the coloured rings the principal trace of the planes of polarization is in the un- coloured brushes. In uniaxial crystals they form an eight-rayed star, composed of two square crosses, inclined at any angle equal to that between the planes of polarization, every ray of which sepa- rates complementary rings. In biaxial crystals they compose two pairs of rectangular hyperbolas, the angle between whose asymptotes is the same as that between the planes of polarization, and whose branches divide complementary rings. ‘The two crosses or two sets of hyperbolas unite when the planes of polarization are parallel or perpendicular. But in the case under consideration the rings exhi- bited by crystals will not be traversed by any brushes. Uniaxial crystals will exhibit circular rings without a cross; and_ biaxial crystals will exhibit complete lemniscates, without any interruption from curved brushes.”’ And it is further to be noticed, as the formula given above indicates, that the centres of the rings will be bright or dark according as the analyzer stands at 0° or 90°. (2 Royal Instttuiion. To pursue this matter further. Suppose that, the arrangements remaining otherwise as before, the analyzer be turned round; then in any position intermediate to 0° and 90° the rings will be con- tracted and extended in opposite quadrants, until at 45° they are divided by two diagonals, on each side of which the colours are complementary. Beyond 45° the rings begin to coalesce, until at 90° the four quadrants coincide again. During this movement the centre has changed from bright to dark. If the motion of the analyzer be reversed, the quadrants which before contracted, now expand, and vice versd. Again, if the crystal (say positive) be re- placed by another (say negative), the effect on the quadrants of the rings will be reversed. ‘This method of examination therefore affords a test of the character, positive or negative, of a crystal. A similar process applies to biaxial crystals; but in this case the diagonals interrupting the rings are replaced by a pair of rectangular hyperbolas, on either side of which the rings expand or contract ; and the effect is reversed either by reversing the -motion of the analyzer, or by replacing a positive by a negative crystal, or vice versd. The experiment may then be made in biaxial crystals by turning the analyzer slightly to the right or to the left,.and observing whether the rings advance towards, or recede from, one another in the centre of the field. In particular, if, polarizer and analyzer being parallel, the plate A have its axis in a N.E. direction to a person looking through the analyzer, the plate B its axis in a N.W, direction, and the crystal be so placed that the line joining the optic axes be N.S., then on turning the analyzer to the right the rings will advance to one another if the crystal be negative, and recede if it be positive. The mathematical expression for the intensity of the. light at any point P is in this case 5(1+ sin 27 cos 6+ sin 26 cos 2; sin 8), where 6 is the angle between the principal section of C through P and the principal section of B, and 7 the angle between the principal sections of Bandthe analyzer. This shows that when the polarizer and analyzer are parallel or crossed at O° or 90°, and consequently 7 =45° or 135°, the expression is independent of 6 (i. e. the intensity is the same throughout circles about the centre), but that when the polarizer and analyzer are crossed we have an expression of the form 3(1+ sin 20 sin 6), the sign of the second term depending upon the direction in which the analyzer has been turned, and also upon the sign of 6—that is, upon the character (positive or negative) of the crystal. The dispersion of the planes of polarization effected by the passage of plane-polarized light through a plate of quartz cut perpendicular to the axis may be rendered visible by interposing such a plate of quartz between the polarizer and a uniaxial or biaxial crystal when the analyzer is at 90°, 7. e. when dark brushes are formed. In this case the brushes cease to be black and are tinged throughout with colour. The analyzer, however, must be turned back or forward, according as the quartz be right-handed or left-handed, in order that Royal Society. 73 it may cross in succession the planes of polarization of the different coloured rays, and so produce the most vivid effects. ‘The dispersion of the brushes by a plate of quartz, however, may be studied by em- ploying an additional polarizer and quartz plate between the source of light and the whole system previously used. By turning this polarizer round we extinguish each ray of the spectrum in turn and tint the whole field with the complementary colour. ‘The brushes will then appear to revolve about their centres as the tints vary continuously from one end of the spectrum to the other. If the polarizer be turned still further round, the tints which had changed continuosly from red to violet, or vice versd, change suddenly from violet to red, or vice versd, and the brushes jump suddenly back to their origina] position. This last optical arrangement may be employed to examine the more important phenomena of the dispersion of the optic axes produced, not by a quartz plate between the usual polarizer and erystal, but by certain biaxial crystals themselves. ROYAL SOCIETY. [Continued from vol. xliii. p. 542. ] March 14, 1872.—The Earl of Rosse, D.C.L., Vice-President, in the Chair. The following communication was read :— “The Decomposition of Water by Zinc in conjunction with a more Negative Metal.” By J. H. Gladstone, Ph.D., F.R.S., and Alfred Tribe, F.C.S. Pure zinc is incapable of decomposing pure water, even at100° C., but at a considerably higher temperature it is known to combine with itsoxygen. Davy exposed pure water for two days to the action of a pile of silver and zinc plates, separated only by pasteboard, with- out obtaining any hydrogen; Buff, however, has shown that a very minute trace of gas can be formed at the ordinary temperature by a pair of zinc and platinum plates. | During a series of experiments, of which we have already published ait instalment, it occurred to us to ascertain whether by bringing the two metals closer together, and so increasing the electrical tension of the liquid, we could effect the same combination of zine with oxygen at the ordinary temperature which takes place without the second metal at a very high temperature. Thin sheets of zinc and copper were hammered together and placed in a bottle filled with distilled water. Small bubbles of gas were formed. The experiment, however, was tried in a more perfect form. Some zinc-foil was allowed to remain in a somewhat dilute solution of copper sulphate until its surface was well covered with spongy copper. The metals were thoroughly washed with distilled water, and then they were immersed in a bottle of distilled water with a delivery-tube. Minute bubbles of gas quickly made their appearance, which proved to be hydrogen, and zinc-oxide was formed, Two experiments were made quantita- 74 Royal Society :—Messrs. J. H. Gladstone and A. Tribe on tively, the gas being collected and measured at the end of 24 or 48 hours. The quantity of gas in cubic centimetres is given in the third and fourth columns of the subjoined Table, corrected for temperature and pressure. ‘The mean temperature in the second column is simply the mean of the maximum and minimum during the period. In ex- periment A, 33:4 grms. of zinc-foil were employed, being 2°6 metres long and 0:05 wide. The coils were kept apart by muslin. In experiment B there was used | metre of similar foil crumpled up. Day. ee Exper. A. Exper. B. Day. ca Exper. A. Exper. B Cale Oe Cx C. Gve: C..C; A fe) 117-1 49°6 18. 6:7°| 20:0 76 2. 12:2 | 938 379 19,2051 Gel 1) ie} 57 (2) ou 117 | 738 276 21. 4-4 | 20:0 66 ah 11:1 | 66:2 24-7 22. 50 | 15:3 4:8 5, 6. 100 | 49°3( x2) 175 (x2) || Interval. t S50) lel 14:9 44. 10:0 | 205 5:5 8. 105 | 40:9 158 45,46. | 10:5 | 22:5( x2) 6°5 (x2) 9. 10:0 | 40:9 14:8 nde Lido) 227 65 10. 78 | 338 10:3. 48. Ill | 241 8-1 ne ONG) : : Ar r to acquire that augmeutation, and therefore at y is inferior to that which corresponds to the distance 7. This diminution, all cir- cumstances being equal, is a function of the wre velocity h. The repulsion at y may therefore be expressed by — cy i ), where the value of f(A) is less than 1. If, on the contrary, m recedes from m! with the same constant velocity A, passing in the time At through the distance y—z! (fig. 2) =Av, the repulsion at the moment when m arrives at y must be greater than that which = 2. as corresponds to the distance 7, pro- — vided the repulsion cannot be di- 1 ee minished with the velocity of the ar increase of the distance. Therefore the repulsion may in this case be expressed by a B(2 , where F(A) is greater than 1. If in the first case, in which the distance between the molecules is diminished, the velocity be considered negative, it must be po- sitive in the second. Concerning the functions f() and F(A) we know nothing beforehand, except that the former must be less, and the latter greater than 1, and that both approach 1 as h diminishes. But as the causes which retard or accelerate the development of the repulsion at the time of the approach, must have the same effect upon its disappearance when the molecules recede from each other, it is probable that the two functions have the same form, or that the development of the repulsion follows the same law as its disappearance—and that both can be ex- pressed by the same function of the velocity, if we take care to put the latter negative in one case and positive in the other. We have thus, for the repulsion between two ether molecules, ! the expression = E(—2) if the molecules sate” each other with a constant velocity h, and the expression “3 meh if the M. E. Edlund on the Nature of Electricity. 91 distance between them increases, the function F being such that it becomes =1 for h=O, is <1 for a negative value, and >1 for a positive value of A. These expressions may conveniently be written in the form | mnt mn +4(-) and —z 1+ ¢(+A)), the function (A) being such that it becomes =O when A=O, has a negative value when / is negative, and a positive value when / is positive. What has just been said applies exclusively to the case in which the velocity is constant. We will now suppose that m approaches m’, and makes the same way Ar im the same time Ag as before, but with diminishing velocity, so that the velocity is greater when m is nearer z (fig. 1) than when it has arrived at y. Although m makes the same way during the same space of time, = has the same value in this as in the former case, the repulsion at the point y can no longer be the same. The molecule m has moved more rapidly in the vicinity of x than when nearer to y, and has therefore remained longer where the repelling force is stronger than where it is weaker. The result must evidently be that the repulsion at y will be stronger than if the velocity had been constant. The repulsion, then, 4 ae but also on 2 If we now pass to the limit, we thus find that the repulsion does not depend merely on the velocity, but again on the variation of the velocity, dh di? the latter dependence augmenting, in the present case, the and consequently depends not only on quantity of the repulsion-force. If the molecule m increase its distance from m! while its velo- city augments, but m such a way that the determined path Ar is traversed in the fixed time Af, the repulsion in this case, as in the preceding, will be greater than if the velocity were constant. Here also the molecule will remain longer at the points where the repulsion-force is greater, than at those where it is less. It is therefore necessary to add to the expression representing the amount of the repulsion under constant velocity a term depen- dent on the variation of the velocity. The electric molecule moves in its course with a constant ve- locity ; as was said above, variations in the intensity of the cur- rent exert no influence in this respect. If, therefore, a molecule approaches or recedes from another which is on the straight line in which the movement takes place, there can be no variation in 92 M. E. Edlund on the Nature of Electricity. the relative velocity. The circumstances, on the contrary, are different if one of the molecules is on one side of the direction of the other. Suppose two molecules, m and m’, the first of which is in motion on the line ad (fig. 3), and the other, m/, at rest. The distance 7 between the mo- lecules is then equal to VW z?+p?; and Fig. 3. their relative velocity (that is, the ve- @ m' y locity on the line of junction) “ee dr xdx 22 P dt ae dt “9 : ; em Walaa é Therefore the relative velocity dimi- ee nishes as m approaches the point 0, where it is =0. When, on the contrary, the distance between the molecules increases, their relative velocity increases simulta- neously. The variations of the relative velocity are obtained by differentiating the last expression, which gives da eee ee d@ rd2@ - di®’ or if we introduce the cosine of the angle in the place of > and hin place of — ue we obtain dt P 2 2 =e (1 — cos? 0). The variation of the relative velocity, therefore, is proportional to the square of the velocity of the molecule in the circuit; it presents its maximum at the point o (fig. 3), and diminishes as the molecule moves away from it. By corresponding substitu- tions we obtain for the expression of the relative velocity dr 7= cos Oh. If the molecule m moves with a constant velocity on ‘the line ab (fig. 3), in which case the relative velocity varies in relation to the fixed molecule m!, the repulsion between the two molecules for a determined distance r is, according to what precedes, greater than if the relative velocity were constant. This is so, whether m recedes from, or whether it approaches the point o. To the expression denoting the repulsion between the two mole- cules when their relative velocity is constant we must therefore add a term constituting a function of the variation of the velocity. We will designate this function by (= [1 — cos? @)). We know beforehand, with respect to this function 1, that it must M. FE. Edlund on the Nature of Electricity. 93 be =0 when cos @=1, since in this case the molecule m moves in the line of junction between m and m’, and consequently the relative velocity of the two molecules is constant. We know moreover that the value of the function Wy is always positive, whether the molecule m approaches or recedes from m!. It may, besides, be remarked that the value of the fonction may depend not only on the amount of the variation, Fe (1— cos? @), but also on the distance r between the molecules, and consequently r may enter under the sign of the function at the same time that the same variable enters into the expression of the quantity of the variation. The complete expression of the repulsion between two mole- cules of zether » and m’, the latter of which is fixed, and the former, m, moves with a constant velocity / in a line forming the acute angle @ with their line of junction, will therefore be :— When m approaches m/’, — MT 1 + 6(—A. 00s 0) +4([1— cos? aE When m recedes from m’, Se oa (+A. cos 6) +4 (— -[1 — cos? 6]. (2) What has a been said we shall first apply to the case of two molecules m and m' moving with equal and constant velocity in the same direction in parallel lines (see fig. 3). According to the principles established by W. Weber*, we shall admit that the effect of the reciprocal action between two molecules is entirely communicated to the circuits in which they move. The motions only of the circuits can be observed in the reciprocal action of two currents; and the empirical formule founded on the observations relate to those motions. Now, in order to find the variation produced in the distance between two circuit-elements by the reciprocal action of the ether molecules, one of the elements may be regarded as fixed, and the other alone as free. Wesuppose, in the present case, that the element in which m! moves is free, and that which belongs to m is im- moveable. If in the whole mass of ether the molecule m! were alone in motion, it could not be admitted, in the same manner as if it were at rest, that the repulsions exerted upon it by the whole of the surrounding ether annul each other; on the con- trary, those repulsions might have a resultant Snot =O. The repulsion exerted on the moving molecule m! by all the sur- rounding ether with the exception of m should therefore be ob- __ mn! * Abhandlungen iiber elektrodynamische Maasbestimmungen, p. 309. 94 M. E. Edlund on the Nature of Electricity. tained by deducting from S the repulsion which takes place between m and m'—or, what comes to the same thing, by adding to S the latter repulsion taken with the opposite sign. The question now is, what is the motion impressed on the circuit- element in which m! moves by the molecule m being put in motion ? In the same way as for electrostatic phenomena, we have to take into consideration the four following circumstances :— 1, the direct reciprocal action of the two molecules; 2, the dif- ference between the action exerted upon m! by the whole of the surrounding ether when m is supposed at rest and the action exerted upon the same molecule m! by all the ether with the ea- ception of m; 3, the action of m upon the space occupied by m' ; and, 4, the action upon the same space of all the surrounding ether with the exception of m. The difference mentioned at no. 2 is evidently equal to the repulsion, taken with the oppo- site sign, between m, supposed immoveable, and the molecule m’; and the action indicated at no. 4 is identical with the repulsion, taken with the opposite sign, between the molecule m regarded as immoveable and the space in question. If weadd the actions upon m’!, foreseen in the first two cases, and if we subtract the corresponding sum of the last two, we obtain, in accordance with Archimedes’s principle, the action upon m! sought, or upon the ~ circuit-element in which m! moves. In order to understand more clearly the accuracy of the above process, let us state the problem thus :—To find the motion pro- duced in the molecule m’, or in the circuit-element in which m! is found, by the molecule m being put in motion. Now the motion sought depends evidently on the modification induced in the repulsion between m! and m by the circumstance that the latter has been put in motion. The expression of the motion of the circuit-element of m!' is therefore obtained by subtracting from the repulsion between the molecules m! and m (the latter being regarded as in motion) the repulsion between the same molecules when m is considered to be at rest. The remainder thus obtained is in reality the sum of the first two cases above stated. The effects of repulsion to which the last two cases relate are obtained in an analogous manner. It is now easy to find the algebraic expression of the reciprocal action of two ele- ments of a current. If the two molecules m and m! move in - parallel lines in the same direction, as, for example, towards 5 and 0', their reciprocal distance will undergo no modification, provided they move with the same velocity. Their direct action upon each other will thus be the same as if they were both at rest. We have, therefore, for the action belonging to case 1 :— mm ye , i Oe * M. E. Edlund on the Nature of Electricity. 95 As m! recedes from m if the latter is at rest, we have for case 2 :— + MTL + 6( +h. 0086) +¥(= [1 — cos? 6} )]. For case 3, in which m approaches the space occupied by m’, we obtain :— I 2 = mit o(—h. cos @) + (= [1 — cos? 6) | : In the last place, we have for No. 4:— mm! EOI « 3 r Subtracting now the sum of the last two expressions from the sum of the first two, we obtain the definitive result ;— = me [ $+ 2.c0s0) + $(—h.cos6) +20h(— [1 — cos? @1)]. (3) This result is the theoretic expression of the reciprocal influ- ence of two current-elements which move in the same direction in parallel lines. By making, in formula (3), cos @=0 (that is to say, by sup- posing the line of junction between the two current-elements to form a right angle with the lines of direction of the currents), the function ¢ will become, as we have seen, =O. We shall therefore have for this case :— mm! h? a .24(=). SO ea Now, according to the preceding reasoning, the value of the function »f is always positive. It hence follows that in this po- sition the current-elements attract each other—a fact already demonstrated by experiment. We will now compare the theoretic result with experiment, in order to determine the functions ¢ and ». Ampere, as is known, has determined experimentally the mu- tual action of two current-elements; and W. Weber has proved by very accurate experiments the correctness of the results ob- tained by the French physicist. or the case in which the cir- cuit-elements are parallel, 7 being their distance, and @ the angle made by one of them with their line of junction, Ampére’s for- mula is iy aa (1— 5 cos? @ \ds a, USM Mh aa ik ahaa 9, in which z and 7’ denote the intensities of the two currents, ds and ds! the two circuit-elements, and ka constant. As long as this expression is positive, there is attraction between the circuit- a 96 M. E. Edlund on the Nature of Electricity. elements along their line of junction. If the two currents fol- low the same direction, and consequently have the same sign, the elements attract each other as long as the term 5 cos? 6< 1. But if they go in opposite directions and therefore have contrary signs, repulsion takes place as far as that limit. If, now, w and bie denote the quantities of electricity in the unit of length of the io circuits, we shall have wh=i and wh=7', h denoting the velocity of the current. Now pds and plds’ correspond to “what in the theoretic formula were denoted by m and m'. Ampeére’s formula may therefore be written 4 OUP (1— 5 eos? O Nine «= eee} Making cos @=0, we obtain, by comparison with formula (4), QW (=) ee whence we derive, on replacing h? by h?(1 — cos? 8) :— Qp i [1—cos? 6] )=Hi2(1— cos?@). . (7) Making, in formula (3), cos@=1, the value of the function vr becomes =0. In this case the two current-elements are in one and the same line, by which their relative velocity becomes constant and =O. Formula (3) thus becomes = Gh+6(—)]. - ns Putting, in the same way, cos @=1 in the empiric formula (6), and comparing it with formula (8), we obtain b(+h) +$(—A) =—akk’, from which, substituting A cos @ for h, we get d(+h.cos 0)+6(—h. cos 6) = —$kh?. cos? @. . (9) Introducing now into the theoretic formula (8) the found values of the function w and the sum ¢(+4/.cos@) +6(—A.cos@), we obtain kmm!h? Bische ) a 2 G- 3 0O8 ox. which is identical with the formula derived directly from the ob- servations. Formula (9) determines the sum of the two functions @. This sum is always negative. Of course we cannot immediately con- clude from this the form of the function itself, since a term may have vanished in the addition. We know, from the preceding, that @(—A) must always be negative, but, per contra, p( +h) always M. KE. Edlund on the Nature of Electricity. 97 positive. This is only possible by one means alone, viz. that the function @ contains, besides the term into which the square of the relative velocity enters, a term into which an odd power of that velocity enters, and that the value of the latter term is greater than that of the former. We will now suppose the odd power to be the first—which is the only correct supposition, as will be seen when we consider two parallel currents in opposite directions. This gives us b(—h.cos 6) = —ah.cos9—1kh? cos? 8, }(+h . COs 0) = +ah.cos O—1kh? cos? 0, in which a is a constant. We have therefore obtained the same result as if we had imagined the function ¢ developed in a series according to ascending powers of the relative velocity, and re- tained only the first two terms of that series. We now pass to the case in which the molecules m and m! move in opposite directions in parallel circuits. We suppose that the molecule m’ moves towards the point a’, while m advances towards the point b (fig. 3). It is evident that in this case the relative velocity of m and m! must be twice as great as if one of the molecules were to rest while the other moved with the same velocity h as before. 2h, then, must be written in the place of h; and the same applies equally to the variation of the velocity. It makes no difference whether the molecules are approaching or receding from one another. Hmploying formule (1), (7), and (10), we obtain in this way, for the direct action between two molecules in motion (case 1) :— Pea) mm! a [1—2ah cos 0—1.. Akh? cos? +4. 4kh?(1 — cos? @) |. For the action to which no. 2 refers (viz. the repulsion, taken with the contrary sign, between the molecules m! and m, the former considered in motion, and the other in the state of repose) we obtain ! + Ty [1—ahcos O— $41? cos? 0 + $ h1°(1 — cos? 6)]. We get, for the action foreseen in no. 3, Mt +1 _ ah cos 0-~1KA® cos? 0 +. bkh2(1 — cos? 6)) - —~z [Lah cos —1kh? cos* 6+ $kh?(1 — cos? 8) | ; and for no, 4, min! 72 Phil. Mag. 8. 4. Vol. 44. No, 291. Aug. 1872. H 98 M. E. Edlund on the Nature of Electricity. Subtracting now the sum of the last two numbers from that of the first two, we obtain as the expression of the action which two current-elements exert upon one another when they move in opposite directions in parallel circuits :— kmm! h? ANT [t= zen |, $e a) which is found to be in full accordance with Ampére’s empiric formula. - x What has just been said refers to the supposition that the ve- locity # is the same in both circuits. It is easy, however, to prove that the above demonstration applies equally to the case in which the velocity is greater in one circuit than in the other. Let us suppose that the velocity in the circuit a’ U! (fig. 8) is H, while that in the circuit ab is equal to h, that h' NW RISING. SLOPE. N.W = b b STRONG WIND. ANTERIOR TROUGH. On the 19th of April, 1872, the weather-charts show a stream of air along the eastern coast of Great Britain, direction N.N.W., curvilig over the eastern counties of England and crossing the channel as a N.E. wind. The isobars or lines of equal pressure show the highest barometers in Ireland, and the lowest in the south of France. The gradations of pressure can be arranged 1 in a Table in accordance with the following enunciation, Mr. W. R. Birt on Atmospheric Waves. 127 The barometric heights and corresponding winds, as shown on the charts for each day, may be resolved into two sets, the intersecting angles approaching more or less to right angles; and these heights and winds may be exhibited in Tables showing the decrease or in- crease of pressure from regions of high to low barometers, and the reverse. Diurnal isobars, which are simply lines of equal pressure re- sulting from existing natural arrangements, do not exhibit any meteorological entity. To find such natural arrangements it is necessary to resolve the isobars and wind-curves into their baro- metric and anemonal elements. TasiE I.—Distribution of Pressure and Wind over the North- west of Europe on April 19, 1872. Crest of S.W. wave Bree _ bably near Valencia. First or highest zone below the crest. S.W. wave. Barom. Direction. Force. Walencias <2: 380:ls ELN.E. A, Conanna: (ice -e1 29°77 N.E. 6 Second zone below the crest. S.W. wave. Roche’s Point . . 80°03 N.N.E. A, Third zone below the crest. S.W. wave. Greencastle . . 80°09 NINO W.. 2 Belle sw i 29798 N.E. 5 Iiatilitee 6 pe 2UOF i. 3 Fourth zone below the crest. S.W. wave. ‘Holyhead . . . 80°03 N.N.E. 5 Pembroke . ... 80°03 N.E. 3 Piymontiie,.° +. 2 29°96 E.N.E. 3 ieOrient 2. 2. 29°87 N.E. A, Riocwetort.-. .. 4; 29877 E. 5 Fifth zone below the crest. S.W. wave. Ardrossan . « «. 30°08 N.W. g Liverpool . . . 30°03 N.N.E. 3 Portsmouth . . 29:92 N.H. 3 Sizth zone below the crest. S.W. wave. Merthe 3. 2 8? £3005 N.E. Hondom..- 5) 2? 4 29°90: N.N.E. 3 3 Dover . . 57 29°36 N.N.E. A, Cape Gris Ned = 29232 N.E. Z arts ei 2O"82 N.N.E. 2 ~Charlevilie. 5). 2980 E.N.E. 3 livonsy 2 eee O69 N 1 A, Toulom °° 6). 329568 N.E. 128 Mr. W. R. Birt on Atmospheric Waves. Seventh zone below the crest. S.W. wave. Barom. Direction. Force. Thurso ne eet fo ee Os N. 3 Wick Seren 30:08 N. 3 Nairn he te 0-07 N.E. 3 Aberdeen 6. 3 29°97 N.N.W. 6 Shields: >. 2° 7 29°98 N.E. 5 Scarborough . . 29:93 N. 5 Marnrout inverts see D26r, N.N.W. 4 Brussels . . . 29°79 N.N.W. = 4 Eighth zone below the crest. S.W. wave. Eleldery gene) «ee oso ?S8. 2 The regular decrements of pressure in each zone are in accord- ance with the anterior slope of a N.W. wave, the crest of which was not far from Valencia, Greencastle, and Nairn. Tapie II.—Distribution of Pressure and Wind over the North- west of Kurope on April 20, 1872, exhibiting a diminution of pressure and consequent production of the posterior slope of a S.W. wave. Zone on 8.W. next above trough of S.W. wave. Barom. Direction. Force. Valencia . . 29:59—0°59 ~~ XN. IL 7/ Corunna . . 29°67—0°10 N, +9 Trough of S.W. wave. Roche’s Point. 29°46—0°57 *N.N.E. 4, Biarritz . . 29'40—0°27 Calm. First zone above trough. 8.W. wave, posterior slope. Scilly . . . 29°64—0°34 *8.8.W. —38 bh Ortent).4). 29:63 0:19.) Sane —2 Rochefort . . 29°54—-0°23 . N.E, 5 Second zone above trough. S.W. wave, posterior slope. Greencastle . 29°53—0°56 *H +5 Pembroke . . 29°62—0-41 *S, 3 Plymouth . . 29°67—0:29 = E.S.H. 1 Third zone above trough. S.W. wave, posterior slope. Holyhead . . 2962-041 *S.S.E. -38 * The winds marked (*) thus are cyclonic. Mr. W. R. Birt on Atmospheric Waves. 129 Fourth zone above trough. 8.W. wave, posterior slope. Barom. Direction. Force. Ardrossan. . 29°66—0°42 E.S.FE. +5 Liverpool . . 29:69—0°34 S.E. ae Portsmouth . 29°71—O°21 N.E. 3 Fifth zone above trough. S.W. wave, posterior slope. Thurso. . . 29°79-—-0:24 E.N.E. —2 Wick . . . 29:81—0°22 E.S.E. 3 Narn . .«. 29°76—0:31 E. +2 Aberdeen . . 29°77—0:20 N.N.W. —2 fein... 29°73 —0'S2 S.E. 3 Shields. . .. 29°73—0°25 S. —2 Scarborough . 29°74—0°19 SSE. —1 Yarmouth. . 29°75—0°12 N.E. A London . . 29:73—0°18 E.N.E. 3 Dover . . . 29°71—0°12 E.N.E. A, Cape Gris Nez. 29°72—0°10 KE. Brussels . . 29°72—0:07 N.E. 3 Pans. 2 2 29°65 —0'17 N.N.E. 2 Charleville . 29°66—0°14 N.E. 3 Lyons . . . 29°55—0°14 Ne +3 Toulon. . . 29°44—0°19 E.N.E. +7 The column of barometric differences shows the rise or fall of the mercury since the preceding day, while the + and — signs in the column of force indicate an increase or decrease of strength as compared with that of the preceding day. While a general fall of the barometer was recorded at every station, it was greatest in Ireland and least in Belgium—a result obtained in my former researches. ‘This fall could not have re- sulted from the progression of the waves; for we find the pro- eression of both well marked, the crest of the N.W. wave extend- ing along the English Channel and that of the 8.W. wave along the eastern shores of Great Britain; yet along each crest the barometer had falien. The fall must have resulted from an — irregular change in the elasticity of the air, which commenced most probably near the western shores of Ireland, where the di- minution was greatest. In this locality it assumed the form of a cyclone, not of very great force, but still well marked sc far as the circulation of the wind was concerned. The cyclonic winds are distinguished in the Table by an asterisk (*). There are one or two note-worthy features in the Table, particularly the approach to an equality of pressure in that part of the fifth zone extending from Thurso to Brussels, in which portion we have the highest pressure (29°81) at Wick with a fall of 0°22 since the Phil. Mag.8. 4. Vol. 44, No. 291. Aug. 1872. K 130 Mr. W. R. Birt on Atmospheric Waves. 19th, and the lowest (29°71) at Dover with a fall of 0:12. The fall at Brussels was 0°07 only, the barometer standing at 29°72. Another note-worthy feature is the synchronous preser- vation of the wave-form with the general decrease of pressure, a feature of great importance as Bearitis on the principles of storm- prevision. Tasxe [II.—Distribution of Pressure and Wind over the North- west of Europe on April 21, 1872. During the twenty-four hours, from 8 a.m. of the 20th to 8 A.M. of the 2Ist, the relations of the crests and troughs of both the 8.W. and N.W. waves were reversed; the localities of high barometers on the 20th were those of low barometers on the 21st, except at the N.W. stations. First zone on N.E, above trough of 8.W. wave, posterior slope. Barom. Direction. Force. Brussels . . 29°22—0°50 a] Oe Trough of S.W. wave. Miurso.. -* .. +29-800702 N.N.E. +4 Wack »52 28. o29:824.0-0k E.N.E. 423 Nairn: y+. 9. (29278. 0:02 EN... ae Aberdeen . . 29:70—0:07 N.E. +7 Metths f 9S) 2° 29-67 0-06 > > NUE +6 Shields :-~ .. 29°58—0:15 E.N.E. +5 Scarborough . 29:51—0:23 aie +6 Yarmouth . . 29:39—0:36 E.N.E. +8 fiondon. ~~. 29-21 — 052 ERNE eee Dover 2° 29°16—0°55 *H:N.E. +5 Cape Gris Nez. 29°15 —0°57 *K, +8 Paris . ©. 8 29:16—0°49 *S_E. +4 Charleville. . 29°26—0:40 *S_E. 3 Diyens se") 57 29-55— O22 S. Toulon 29% S" 29°47 COs S. —5 First zone on 8.W. above trough of S.W. wave, anterior slope. _ Ardrossan . . 29°70+40:04 E.N.E. +7 Liverpool . . 2953—0:16 N.N-E: 333 Portsmouth . 29:21—0-50 ENE eee Second zone on 8.W. above trough of 8.W. wave, anterior slope. Holyhead . . 29°51—0-11 N.N: Es eees * The winds marked thus (*) are eyclonie. Mr. W. R. Birt on Atmospheric Waves. 131 Third zone on 8.W. above trough of S.W. wave, anterior slope. Barom. Direction. Force. Greencastle . 29°70+0:17 N.E. +6 Pembroke . . 29°43—0°19 N.E. +6 SLL ee Ye DES OR N.E. +6 Plymouth . . 29:31 —0°36 By ae V’Orient . . 29°21—0°47 E.N.E. +4 Rochefort . . 29°26—0°28 5 Fourth zone on S.W. from trough of 8.W. wave, anterior slope. Roche’s Point. 29°52+0:06 N.E. +5 Biarritz . . 29°37—0:03 S. 5 Fifth zone on 8.W. from trough of S.W. wave, anterior slope. Valencia . . 29°60+0:°01 N.N.E. rf Corunna . . 29:'40—0:27 Ss.W. —6 In casting the eye over the differences of fall along the line of trough, it will be seen that the greatest diminution of pressure occurred at London, Dover, and Cape Gris Nez; and on com- paring the heights of the barometer at these stations (29°21 to 29°15) with the lowest point in the cyclone of the 20th in the S. of Ireland (29-46), it will be seen that not only did the cy- - clonic depression travel from the S. of Ireland to the N.W. of France, but the diminution of elasticity increased as it pro- gressed ; so that the decrease of nearly 0°60 in the S. of Ireland from a pressure of about 30°00 between April 19 and 20 ap- peared in the neighbourhood of Dover on the 21st, reducing the. pressure there by about the same amount from about 29°71 or 29°72 the readings of the 20th. Changes of elasticity of this nature modify, but do not destroy the wave-forms, which ordi- narily continue to travel in their normal directions. The hne from Valencia to Christiansund (barometer from 29°60 to 29°86) represented the crest of a slope of which the trough extended along the English Channel. This trough in- tersected the trough from Thurso to Paris at the stations Dover and Cape Gris Nez; and near this point of intersection a semi- cyclone was established. The winds of this semicyclone are marked with an asterisk (*). The anterior slope between the crest, extending from Valencia to Christiansund and the trough along the English Channel, did not pass onward towards the 8.K., but was apparently broken up over the British Isles by a still further reduction of pressure. It. is the study of this phenomenon of decreasing (or its opposite of mcreasing) pressure, irrespective of the transference of masses of air either of augmented or diminished elasticity from one lo- 182 Mr. W. R. Birt on Atmospheric Waves. cality to another in certain given directions, that should engage the closest attention of the meteorologist as being at the root of all our atmospheric movements, and intimately connected with the origin of cyclones and atmospheric waves. The constant relation existing between the direction of the wind and regions of high and low pressures so well expressed by the crests, troughs, and slopes of atmospheric waves, is but a stepping-stone to a still higher generalization which may be arrived at when, in addition to the heights of the barometer and the direction and force of wind, the temperatures at each station shall be discussed with them. The elasticity of the air at any given moment isa resultant of its temperature modified by the presence of aqueous vapour; and for arriving at such higher generalization these weather-elements, temperature and moisture, should be examined daily during a specified period. Taste [V.—Distribution of Pressure and Wind over the North- west of Europe on April 22, 1872. First or lowest zone next above posterior trough. S.W. wave. Barom. Direction. Force. Biarritz . . 29°36—0:01 S.-W 5 Rochefort . . 29°30+0-04 S.W. 5 TV’Orient . . 29:18—0:08 WS Wiese Sally . . . 2887—0°43 W.N.W. —4 Roche’s Point. 29°06—0°46 N.N.E. +6 Valencia . . 29°25—0°35 N.N.E. +8 This zone cuts the point of greatest depression (Scilly, 28-87), which was probably in the trough of both waves. The S.W. winds existed on the S.E. of this point, and the N.E. winds on the N.W., with increasing pressures in each direction. Second zone above the posterior trough. S.W. wave. Plymouth . . 2897—0°34 oASs —-4t Pembroke . . 29°01—0°-42 N.N.E. 6 The trough of the N.W. wave between these stations ; wind at Plymouth changed from E. to S. Third zone above the posterior trough. S.W. wave. Portsmouth . 29°15—0-06 S.S.W. —5 Holyhead . . 29°14—0°37 K. —3 Greencastle . 29'-40—0°30 E.N.E. 6 Trough of N.W. wave between Portsmouth and Holyhead. The E. wind at Holyhead was cyclonic around the area of least pressure. The anterior slope of the advancing wave was charae- terized by the greatest wind-force. Mr. W. R. Birt on Atmospheric Waves. 133 Fourth zone above posterior trough. S.W. wave. Barow. Direction. Force. Toulon . . 29°63+0°16 SV. = yous... 29°61 0-28 S.E. 2 Charleville . 29°34+0°08 H.S.h. --6 Pas. 29°31+0°15 S.E. = Cape Gris Nez. 29°24+4 0:09 S. —38 Dover. . 29:22 +0:06 S.W. —4 London . . 29:°20—0°01 S. —4 Waverpool 7). 29:22 —0-51 IDS de hee Ardrossan. . 29°36—0°34 H..N.E. 7 Trough of N.W. wave between London and Liverpool. The S.E. winds in France were those of the posterior slope of the S.W. wave. The E.S.E. wind at Liverpool was part of the cy- clonic stream of air drawing round the area of least pressure. The apparent stationary character of the barometer at London would indicate that the trough of the 21st remained in the neighbourhood during the elapsed twenty-four hours; but it is uncertain. This shows that the telegrams to the Meteorological Office should be forwarded at shorter intervals. Fifth zone above the posterior trough. S.W. wave. essels 20). 29:32-+ 0°10 S.E. +6 Yarmouth . . 29°27—0:12 S.8.H. —4 Scarborough . 29°25—0°26 S. —2 Shields. . . 29°28—0°30 E.N.E. +6 Leith . . . 29°42—0°25 N.E. +8 Aberdeen . . 29°51—0°19 N.E. +9 Naim . . . 29:60—0:18 EK. +6 Wick . . . 29°68—0°14 E.N.E. —4 Thurso. . . 29°67—0'14 N.E. = +5 Trough of N.W. wave between Yarmouth and Scarborough. The winds at Brussels, Yarmouth, and Scarborough appear to have been those of the S.W. wave, while all to the N.W. of Scarborough were those of the anterior slope of the succeeding N.W. wave. Sixth zone above the posterior trough. S.W. wave. Goxhaven-", .° +. 29°33 W. yy xn, ee GD N.E. A Skudesnaes .-. . 29°56" N.N.E. 4 Christiansund. . . 29°80 Calm. This Table, in conjunction with the weather-maps, brings out with great distinctness the contemporaneity of no less than four independent (?) atmospheric arrangements. First, circular zones of pressure around the lowest point, extending from 28°9 to | : 134: Mr. W. R. Birt on Atmospheric Waves. 29-3, accompanied by an approach to a cyclonic movement of wind; second, a stream of N.K. winds reaching the force of a gale in the E. of Scotland; third, a stream of 8.W. winds over the N.W. of France drawn over the central parts of England into the vortical movement around the point of lowest pressure ; | fourth, the posterior slope of a 8.W. wave extending from Va- lencia to Cuxhaven. ‘These arrangements appear in a great measure to have been brought into existence by the diminution of pressure in the west of Ireland. Taste V.—Distribution of Pressure and Wind over the North- west of Kurope on April 23, 1872. First zone on S.W. of anterior slope above trough of S.W. wave. Barom. Direction. Force. Biarritz . . 29°55+0°19 : — 4 Rochefort . . 29'49+40-°19 S.W. 5 L’Orient . . 29°23-+0°15 SW. +8 Scilly yet CoOL Oy W.S.W. +6 | Roche’s Point. 29:00—0:06 N.N.E. —5 | Valencia . . 29:14—O°11 N.E. —5 | Trough of N.W. wave between Scilly and Roche’s Point. Trough of S.W. wave. Plymouth . . 29°09+40°12 Se +5 Pembroke . . 28:99—0-:02 S.S.H. +8 Trough of N.W. wave N.W. of, but near Pembroke; the baro- meter having fallen by the progression of the S.W. trough, the two troughs imtersected near Pembroke. First zone above trough, posterior slope. S.W. wave. Portsmouth . 29°29+0°14 S.S.W. +6 Holyhead . . 29-14 EK. 3 | Greencastle . 29°25—0:15 N.N.E. +8 Trough of N.W. wave between Portsmouth and Holyhead. Second zone above trough, posterior slope. S.W. wave. Toulow. 9.4) 29°74+40:11 S.S.W. 4, nyons!7 20; weser2 9 :6ll S.E. Charleville. . 29°55+0:21 S.W. 6 Paris . . . 29:50+0°19 S. 2 Cape Gris Nez 29°3940°15 S.S.W. +5 Dover wie. 22° 29:336-- 0:16 S.W. A lLondomi7 2 os Ole S A; Liverpool . . 29244002 ESE. +3 Ardrossan. . 29°28—0:08 E.N.E. = —4 Trough of N.W. wave between London and Liverpool. Mr. W. R. Birt on Atmospheric Waves. 135 Third zone above trough, posterior slope. S.W. wave. Barom. Direction. Force. Brussels . . 29°50+0°:18 —4, Marmouth..--.+ 29738-0514 S.S.E. A Scarborough . 29°32+0:07 S.S.—. +3 Shields =. . 29832004". —3 beth... S629 O11 Aberdeen . . 29°89—0°12 Naim . . . 29:°39—0°21 Wiek ... . 29°46—0:22 Thurso . . 29:'46—0°21 —2 Trough of N.W. wave between Scarborough and Shields. Lowest Barometer at Leith. be ed bo i Fourth zone above trough, posterior slope. S.W. wave. Helder. . . 29°43 . 3 Fifth zone above trough, posterior slope. S.W. wave. Cuxhaven. . 29°54+40°21 S.E. 2 Oxo ¥ 17.5. 8 29-56-+ 0:04 N.E. A, Skudesnaes . 29°52—0:°04° E.N.E. —2 Christiansund. 29°52—0:28 TaN Ee +2 Trough of N.W. wave S.H. of Oxé. A very important point to investigate in such inquiries as these, has reference to changes of elasticity in large bodies of air, such as occurred on the 20th and again on the 22nd per- fectly independent of any progressive movement. ‘Table V. shows that the distribution of pressure and wind was much the “same as on the 22nd, but that during the twenty-four hours elapsed from 8 a.m. of the 22nd to 8 a.m. of the 28rd the trough of the S.W. wave had advanced but a very short distance towards the N.E. from its locality on the 22nd—also that the trough of the N.W. wave occupied nearly the same locality as it did on the 22nd, having rather receded towards the N.W. than otherwise. The most svcmarlable feature is that the ante- rior slope of the should-be advancing N.W. wave suffered a diminution of “Se which resulted in a fallof the barometer at all stations N.W. of a line joming Cape Clear and a point between Ox6 and Skudesnaes, which is exactly the reverse of the phenomena presented by the anterior slope of an atmo- spheric wave. This fall was accompanied by a diminution of wind-force. At all stations S.H. of the line mentioned on the posterior slope of the shouwld-be receding N.W. wave, a rising ba- rometer oceurred, with, at some stations, an increase of wind- 136 Mr. W. R. Birt on Atmospheric Waves. jorce, again the reverse of the usual phenomena of a wave pro- eressing towards the S.E. While, therefore, we had on the 23rd the area divided into two regions of rising and falling barometers, differing from the normal conditions, the wave-form was maintained in all its integrity. The reversal of the phenomena is very im- portant (see figs. 1 & 2). TasiE VI.—Distribution of Pressure and Wind over the North- west of Europe on April 24, 1872. First zone on 8.W. of anterior slope above trough of S.W. wave. Barom. Direction. Force. Corunna=. 9 2 29°77 S.W. 6 Valencia 2. ~ 2973142017 W. —4 Trough of S.W. wave. Biarritz . . 29°81-4-0°26 S. —3 Roche’s Point. 29°29+0:29 W.S.W. ~3 First zone above trough, posterior slope. S.W. wave. Rochefort . . 29°73+40°24 WwW; 5 Orient . . 29°61+0°33 Ww. —5 Scilly “. . > '29:40-F0:36 W.S.W. —5 Second zone above trough, posterior slope. S.W. wave. Plymouth . . 29:42+0°33 S.S.W. —2 Pembroke . . 29°3440°35 SW. —3 Holyhead . . 29°3040°16 S.S.E. +4 Greencastle . 29°25 iDsnile eee Third zone above trough, posterior slope. S.W. wave. Portsmouth . 29°53+0:°24 S.W. 6 Liverpool . . 29°42+40°18 S.S.E. 3 Ardrossan. . 29°35+0:07 S.S.E. —3 Fourth zone above trough, posterior slope. S.W. wave. Toulon. . . 29°84+40°:10 SS.W. —1 Lyons Charleville . 29°74+0°19 S.W. 6 Paris ~; 29°72 +0°22 S 2 Cape Gris Nez 29594020 SW. 5 Dover’. 2 29758 O20 S.W. +5 hondon™ 3°" 2'"2952 4020 S.S.W. —38 Mr. W. R. Birt on Atmospheric Waves. 137 Fifth zone above trough, posterior slope. S.W. wave. Barom. Direction. Force. Brussels . . 29°68+0°18 SW. —3 Yarmouth. . 29544016 S.S.E. —3 Scarborough . 29°45+4+0:13 S.W. 3 Shields . . 29°42+40°10 S.S.W. 3 ethyo.. = .. 29:40 0:09 Ki. —3 Sixth zone above trough, posterior slope. S.W. wave. Helder oe 29:6) -- O18 S.W. pa) Aberdeen . . 29°44+0°05 S.E. 3 Nairn . . . 29°43+0:°04 E.S.EH. y Wace’... . .29°50350:04 S.E. A Thurso. . . 29°47+0°01 E.S.E. 2 Seventh zone above trough, posterior slope. S.W. wave. Cuxhaven-. . 29:67-40:13 S. 3 Oxorehs Ns 29°07 OF E.N.E. A Skudesnaes . 29°62-+0°10 S.E. + 4 Christiansund. 29:61+0:09 Calm This Table is one of the most interesting of the series; it ex- hibits a general rise of the barometer over the entire area, and the establishment of the posterior slope of the N.W. wave, the direction of the trough of which has been specified in Tables Ifl., 1V., and V. It would appear at first sight that the wave had progressed towards the N.W.; but it is likely that this ap- pearance arose from the irregularity of increase of elasticity being greatest along the English Channel. It is, however, noteworthy that with the extension of the trough towards the N.W., or in other words, of zones of decreasing pressure from the crest towards the N.W., the winds in the N.W. should be those of the S.W. wave, the zones of which are given in the Table. Space prevents the further discussion of the barometric curves and sections, which are capable of yielding a valuable har- vest of results; but as the Tables contain the heights of the ba- rometer and their differences for each day, the reader can easily construct them for himself; indeed this course is recommended - for the elucidation of the preceding Tables. In the year 1843 the late Sir John Herschel, writing on the subject of barometric fluctuations, said “it would be no*small — meteorological discovery if by the study of the characters and progress of barometrical fluctuations we could either make out ~ any law of the greater ones which would enable us even roughly to predict them, or any peculiarity in their physiognomy by which we could recognize them in their earlier stages, as by this we 138 Notices respecting New Books. might possibly be led to the prediction of great storms.” Although up to this time no such law has been RECOGNIZED by our leading meteorologists, it may be permissible to inquire if the steps which have hitherto been taken, such as are exhibited in the preceding Tables, and capable of being rendered still more in- telligible by curves and sections, have not developed these prin- ciples, viz. that the vast bodies of air, possessing regular grada- tions of pressure analogous to wave-forms associated with cer- tain definite winds which always accompany these gradations of pressure, move in certain directions, viz. from N.W. to 8.H., and from 8.W. to N.H., and also if such regular motions are not of the nature of “laws” different from Buys Ballot’s law. The present paper shows that other forces of a still higher character than wave-motion come into operation, producing changes of elasticity the laws of which require to be investigated. This work is a laborious one, but without it little progress will be made in meteorology. The study of atmospheric waves must conduce to a clearer conception of the changes giving rise to the production of new or the modification of existing waves. XVIII. Notices respecting New Books. British Rainfall, 1871. By G. J. Symons. London: Stanford, Charing Cross. pee annual, which has made its appearance recently, contains the usual amount of information on the rainfall during the past year in the British Isles, accompanied with a few most interesting notices of rainfall on the Continent and in India. We-notice it especially on account of some important experiments on rainfall at different ele- vations, particularly at Aldershot Camp, by Colour-Serjeant Arnold, who found that at heights of 6 feet and <0 feet respectively gauges with the receiving apertures tilted at an angle of 45° and kept to the wind by powerful vanes, collected as nearly as possible the same amount of rain; while gauges at 6 feet and 25 feet of elevation with the receiving apertures placed horizontally callected d'fferent amounts, the greatest quantity being found in the lowest gauge. A collateral phenomenon, although not mentioned in the volume, may yet be gathered from the Tables inserted: it is that during four years (1868 to 1871) at Rotherham a gauge placed horizontally 5 feet above the ground gathered 71 per cent. of the rain gathered in a rotating gauge (angle 45°) at the same elevation, the quantity gathered at Aldershot in the horizontal gauge as compared with the tilted gauge at an elevation of 6 feet being 70 per cent. These re- sults at two stations, extending over four and three years respectively, show that we have much to learn as regards rainfall, especially in relation to the standard quantity; for if gauges separated from each other by a vertical space of 24 feet gather the same quantity, our Royal Society. 1389 results must be influenced by the smaller quantity gathered in our horizontal gauges in proportion to the differences. We hope Mr. Symons will give especial attention to this subject. We hear much now-a-days of the need for Government aid to science; and yet our Government establishments have not detected these anomalies! XIX. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 75. ] April 11, 1872.—The Har! of Rosse, D.C.L., Vice-President, in the - Chair. TV following communication was read :— “The Action of Oxygen on Copper Nitrate in a state of Ten- sion.” By J. H. Gladstone, Ph.D., F.R.S., and Alfred Tribe, F.C.S. In our experiments on the action between copper and nitrate of silver in solution, we frequently noticed that the tips of the silver crystals became red, as though coated with a thin layer of metallic copper. This apparent deposition of a positive on a more negative metal of course raised our curiosity, and led us to look closely into the circumstances under which it occurred. We found that it took place only when the nitrate of silver was exhausted, and only on those silver crystals which remained in metallic connexion with the copper. We found, too, that the cupreous coating formed most readily where air had the freest access, and, in fact, that it would not form at all in vessels from which oxygen was excluded, nor on those white crystals which were far below the surface of the liquid, though they might be in immediate contact with the copper plate. When an inverted jar was filled with nitrate-of-copper solu- tion and silver crystals resting on branches of copper, and the liquid was displaced by oxygen gas, it was found that the tips of the crystals became red, and the solution gradually filled the jar again by the ab- sorption of the gas. In the same way the oxygen was absorbed from air, or from its mixtures with hydrogen or carbonic anhydride. This action was further studied by employing plates of the two metals instead of copper covered with silver crystals. When the two plates, connected by a wire, were partially immersed in an ordinary aqueous solution of copper nitrate, it was found that a slight yel- lowish deposit made its appearance speedily all over the silver plate, and went on increasing for a day or two, while at the air-line there was a thicker deposit, which gradually grew and extended itself a little below the surface. This deposit changed from yellowish to red, and under the microscope presented a distinctly crystalline appear- ance, Thinking that this slight crust all over the silver plate was due to air dissolved in the solution itself, we took advantage of the re- 140 Royal Society :— action to prepare copper nitrate absolutely free from dissolved oxygen. An ordinary solution of the salt mixed with some silver nitrate was placed in a narrow cylinder, with a long piece of copper-foil arranged somewhat spirally, so as to retain the deposited silver on its surface, and allowed to rest for twenty-four hours. The solution thus obtained was exposed to the action of the conjoined copper and silver plates ; but even after some hours there was no dimming of the lustre of the silver plate, except at the air-line, which was sharply defined. The same solution, shaken for some time in the air, produced a yellowish deposit on the white metal in three minutes. The colour and general appearance of this crust, together with its formation only where oxygen can be absorbed, showed that it was not metallic copper, but the suboxide. This was further proved by the action of dilute sulphuric acid, which resolves it at once into red metallic copper and copper sulphate. There is also another curious reaction, which can only be properly observed under a micro- scope. When treated with a solution of silver nitrate, this cupreous deposit does rot give the ordinary crystals of the white metal; in fact it is only slowly acted upon ; but presently there shoot forth thin threads of silver, which run through the liquid, often twisting at sharp angles, while the yellowish crystals change to black. This also was found to be a property of the suboxide cf copper. This deposition of oxide on the silver is accompanied by a corre- sponding solution of copper from the other plate. Thus, in an ex- periment made with nitrate-of-copper solution that had been exposed to air, and which was allowed to continue for four days, there was found :— Gain of silver plate 0:016 grm. Loss of copper plate 0°015 grm. The copper necessary for the production cf 0-016 grm. of suboxide would be a little above 0:014 grm. The wire connecting the two plates in this experiment is capable of deflecting a galvanometer. The current takes place through the fluid from copper to silver—that is, in the same direction as if the copper had been dissolved by an acid and hydrogen evolved on the silver plate. If the two plates have their sides parallel, the suboxide is deposited not merely on that side of the silver plate which faces the copper, but after about a minute on the other side also, showing that in this, as in other cases, the lines of force curve round. It became interesting to consider what started this electric current. The original observations convinced us that it was not due te the action of oxygen on the copper; but, to make the matter more certain, bright copper and silver plates in conjunction were immersed, the “copper ina pure, z. e. deoxygenized, solution of nitrate of copper, the silver in an oxygenized solution: the two liquids communicated through the diaphragm of a divided cell. In half an hour the silver plate was covered with a reddish film, while not a trace of tarnish On a supposed Periodicity in Terrestrial Magnetism. 141 was perceptible on the copper. On continuing this experiment for three hours, it was found that the copper plate lost 0°003 grm., and the silver plate was increased by 0:004 grm. Oncleaning the plates, and reversing their position, the copper was covered with a film of oxide, while the silver remained free from cupreous deposit. We believe therefore that, through the simultaneous action of the two metals, the dissolved salt is put into such a state of tension that oxygen brings about a chemical change which otherwise would be impossible, and that this change is initiated in close proximity to the more negative metal. Though we have examined only this particular reaction, we have satisfied ourselves that it is not an isolated fact. ach of the ele- ments concerned may be replaced by others: thus the sulphate may be substituted for the nitrate of copper, or platinum may. be used instead of silver; chlorine may take the place of oxygen, with the production of the subchloyide instead of the suboxide; and zinc may be employed as the positive metal, with zinc chloride as the salt in solution, in which case copper may be taken as the negative metal, and on its surface will form a deposit of oxide of zinc. April 25.—George Biddell Airy, C.B., President, in the Chair. The following communication was read :— ‘“Onta supposed Periodicity i in the elements of Terrestrial Mag- netism, with a period of 263 days.” By George Biddell Airy, Astro- nomer Royal. In a paper published in the ‘ Proceedings of the Imperial Aca- demy of Sciences of Vienna,’ vol. lxiv., Dr. Karl Hornstein has exhi- bited the results of a series of observations which appeared to show that the earth’s magnetism undergoes a periodical change in suc- cessive prods of 264 days, which might with great plausibility be referred to the rotation of the sun. It appeared to me that the deductions from the magnetic obser- vations made at the Royal Observatory of Greenwich, and which are printed annually in the ‘Greenwich Observations,’ or in the detached copies of ‘ Results of Magnetical and Meteorological Ob- servations made at the Royal Observatory of Greenwich,’ wouid afford good materials for testing the accuracy of this law, as appli- cable to aseries of years. The mean results of the measured hourly ordinates of the terrestrial magnetic elements are given for every day ; and it is certain that there has been no change of adjustments of the declination and horizontal-force instruments in the course of each year. For the horizontal-force instrument the temperature of the room has been maintained in a generally equable state, and in later years it has been remarkably uniform. It is easy to see that an error of a single day, or of a large fraction of a day, in the beginning of each period, is of no importance, pro- vided that the errors are not permitted to accumulate. It was allow- able, therefore, to take successive periods of 26, 26, 27, 26, 26, 27, &c. days; aud in instances when a single day was omitted, or even 142 Royal Society :—The Astronomer Royal on a supposed two days, no sensible error would be introduced by interpolating be- tween the numbers for the days immediately preceding and following the omitted days. The years selected for this examination were 1850, 1851, 1852, 1868, 1869, 1870; and the beginning of the first period in each year after the first was thus found :—Fourteen periods of 264 days each amount to 3682 days. For convenience, after completion of the an- nual winter adjustments, the first period in 1850 was made to com- mence on January 17; therefore the first period in 1851 was com- menced on January 21, and that in 1852 on January 25. Similariy, the first periods in 1868, 1869, 1870 commenced on January 1, 4, and 8 respectively ; and the beginnings in the three later years are not uncounected with those in the three earlier years: for, from 1852, January 25, to 1868, January 1, are 5820 days, and 221 periods of 26} days each are 58192 days ; but as the years are widely sepa- rated, and a small error of period would produce a large discordance, it Has appeared best to exhibit the results of the two three-years’ groups separately. Some periods, in which there were unusually large interruptions, or which were partly occupied with experiments, were omitted entirely. The following is a complete list of periods omitted :—In 1850, that beginning with December 24 for horizontal force ; in 1851, that be- ginning with March 14 for western declination, and those beginning with March 14, June 28, July 24, for horizontal force; in 1852, those beginning with February 20, May 9, December 6, for both elements ; ; in 1868, those beginning with Febr uary 23 for declination, and Ja- nuary 1, January 27; February 23, and December 8 for horizontal force ; in 1869, those beginning with October 21 and December 12 for both elements; and in 1870, those beginning with June 15 and December 16 for declination, and that beginning with December 16 for horizontal force. Interpolations of three days occur only in the following instances :—1850, (dec.) Feb. 4-6, (h. f.) Feb. 9-11, July 23-25; 1851, (dec.) Feb. 18-20, Oct. 20-22, (h. f.) June 9-11; 1852, (dec.) Feb. 7-9; 1868, (dec.) Feb. 15-17, (h. f.) none; 1869, (dec.) June 6-8, (h. f.) June 6-8; 1870, (dec.) Sept. 24-26, (h. f.) Sept. 24-26. The mean values of each element for each progressive day in every period of the several years, uncorrected for the proportional part of secular change through the 26 days, and omitting the imper- _ fect 27th day, are as follows :— * neil baie 19-GG | G9-GG | SECS | 81-6 | 16-2 | 60-ES | 86-2 | EL:GG | GZ-EE | ST-ES | 62-9 | LE-E¢ | GZ-E¢ 69-7. |69-7 |09-7 |69-7 |FS-F |1¢7 |F8.P |68-F | LVF |€¢-7 | 18-7 |69-0 | 8L-P VEEL | 6-61 | GO-ET | TL-€T | SO-€T | SL-6T | L9-GL | 99-21 | LL-2T | GL-31 | GL-21 |66-C1 | £8-CT OGL | 16-91 | 06-91 | G6-LT | TO-LT | 68-L1 | IL-LT | 81-LT | 88-LT | 69-11 | 66-91 |80-LT | 9T-LT 69-81 | SS-8T | 6F-8T | 9€-8T | 69-81 | 79-81 | SP-8T | TI-8I | LT-ST | 8€-8T | S&-8T | LE-8T | 6L-8T LL-&6 LV-E% 60-86 VG-6 GEES 16-66 ST-€6 60-6 VS-G6 CLG 90-&@ 66-&@ 8-46 OS | 18G | L6G | LOS | 6S | T86 | T6Z | OLZ | LOS | ELS | F8e | ZOE | 664 | ‘69ST 6FG | SZ | BLE | G9G | GZS | 8S | G9S | SLE | 066 | LOS | 662 | 8S | 8% | ‘89ST S8e | 01h | VOY | 988") Tee |-OSE | SPE | 6IE | BPE | Gee | Ges | Lee | Ise | ‘s¢est 86¢ | G9G | SEG | 8c | OSS | GGG | O€&S | HHS | 19G | BEG | GFE | Lee | Zee | ‘TEST 806 | OSG | G&G | 086 | G6G | 6G | 6SG | 8LZ | G9Z | 69S | SHS |} 892 | OIE | OGST 9&€-§S LG-ES TG-SG | GF-EG | PSE | G9-ES | GO-FG | LZ-SG | S1-E¢ | ¢¢-E¢ 60-€¢ 86-ES | IF-¢ | “OL8T PLD (0G |60- |09-F {8L-b |OP-F (66-7 |96-F |88-F |OL-G |91-¢ |PE-E |E¢.¢ | 698T OG-GT | 69-61 | LF-GT | LG-1 | LT-E1 | L3-€T | GP-ET | 60-E1 | 06-21 | GEL | §8-GT | QI-ET | SET | “S98T G6-9T | 68-91 | 98-9T | O8-LT | 6F-LT | 9E-LT | 99-LT | OL-LT | LY-LT | €6-LT | LG-81 | 88-LT | €6-LT | “Sest 66-61 | G3-61 | 8P-8T | GE-8T | GE-8I | 06-21 | 16-21 | €0-8T | G6-LT | 81-81 | 96-81 | 23-81 | S6-LT | “ISST 6LEG 9S-&6 6&-&6 V9-&6 &L-G6 00-6 10-86 SL-&6 £0-&@ £6-£6 96-46 16:6 G9-€6 | “OLST ‘COLST UI o6L {69ST ‘89ST UI 00% £ ZEST ‘TEST ‘OG8T Ul 92g SuIgIIUIO) UOTYeUTPOG 96 GG VG 86 66 IZ 06 61 81 LT oT SIGs aT PCO» HKG 8 L 9 g 7 g z Tea | ' ‘ported yous jo Avp oatssousorg: —The Astronomer Royal on a supposed 144 Royal Society 48] UE opeut SuOTeArTasqoO 0} PozTUT] SBM NONWVSISIAUT 8 ULOISUIOTT “AZ ‘aqquqord arom sdep 9% Jo Aypenbaur oy) srspuas osayy JO UOIVA9}[B OU yn £ dBAv] 00} o1e ZORT “ORT portad oy} ur pasn sosuvyo avpnoas oy) yey poyoodsns oq youlpe yysium yy *skup 497 oy} ur Jvorporsad Ayenbour ue jo vept ayy jtoddns 03 Suryy Aue ‘saarno ur payaoload sv 10 syexaumu UI UIATS $B LOY} ‘suBOUL 1aq}0 oY} UT yARULOA JOU opy mg ‘Aup yIPT oy} ynoqe OSBIIOUL UB JqIYXs 07 twodde Y/R] Ul soL0f [eUOZTIOY OF UBaLE oY} “ATQeyIeUIOI o10W 1148 ‘pue QL8T Ul uoeurpop 10f uo ou, CO | ED Wel Cay ee Sse Clin | tee |) UOT) Editi | re) EP ane) kp el ead Gee ll aa |) aah ey ek a ten eee EP NT EE PSS, oie ce PE A ee Ton ks tt tte A ell a tg) Geeta) a |) aan rar 4 et ‘(puodos oY} UL OOPPT. puv ‘savod Jo oFuva yay oy} Ur OOLTI. SUA) OdTOKT [RIUOZLAOTT 1 ane CLP |00-F |98-8 |80-F |20-F7 {16-8 | 16.¢ OLS | 66-8 | 88-8 | FOF | 00-F | 868 | 29-8 | 222 68-6 | GLE | €0-F | 66-6 | 8tF | 68-8 | PLE | G68 | SLE C6-E | OL? , a 6601 | G6-OL | 90-01 | ST-OT | 91-01 | PZ-0L | 0-01 | 98.6 81-6 | 96-6 | 18-6 | 66-6 | 16-6 | 10-01 | ST-OT | 8.6 | 16.6 11-6 | 69:6 | 01-6 | P16 | 8¢.6 | 98.6 | 98.6 | O16 8:6 , “GS8T 1 / / 1 7 0 ” / D ! / ! / 0 1 | / ! ’ / ! / / / i / OSST ‘(puooos OY} UL .0g puL ‘savok Jo oFuLA ysay oY UT OT oZs SuyprU0) UOMVUIpa(y U10}S9 AA. nt ae a a a ee ee oe 96 | & | VG | &@ GG | 1 | 06 | 61 | 8T | LT | 9T | ST | at | I | él | II | Or | 6 | 8 | L | 9 | ¢ | Vv | & | (a | I |‘savod — ae az = = = Se = a = a : ~ jo ‘ported youve Jo Kup oaissoasoarg oduvy —S}[NSo1 SUIMOT[OF OY} DAVY] 941 ‘VOI0J [BIUOZ “Hoy Ut sdup 9% OJ ETOOO.-— JO oywA OY} 4B PU “HoOreUIPap UIO\S0M ut skup 9% 40} ZO.,Q-+ JO ova 04} 4% “UONDaII00 AvNoas Jo syaed [euorjrodord oy} Surdjdde pue “9/81-gogt pus zeg{—0ce] savok Jo sdnoxs oy} ag Ajoyervdas sroquinu osayy Jo suvou oyy Suryey, 145 SMe in Terrestrial Magnet city 1 Period | LL-&I | 66-81 GET | SF-9T €G-21 | 2-81 8G-IT | 22-21 10-81 | 69-21 GL-ZI | S881 6L-Z | $9.11 62-FT | SL-21 / / eee eee 9% | & G8.2T | S2-€T B1-ST | 90-91 BPG | 89-21 G0-IT | 00-11 88-IT | 6F-2I GE-8T | ST-€I GZ.0L | FS-1T GET | 9F-ZI Uy / 1% | €@ SL-GI 66-ST 89-61 01-6 6-1 | 62-1 OF-ST | 93-91 ELFI | 82-1 CE.O1 | S201 90-81 | F881 L&ET | 89-FT LLIL | 18-11 ELF | ¥0-F1 Ul I 0 | 61 89-61 8F-E1 66-81 69-01 LT dLOJOIIY} &&-ST OL-F1 86-FI 10-11 FSET | S&-61 | S6-ET LO-§T | 6F-F1 €0-FT | 81-FT GO-0T | 60-1T GS-61 | LE-ST SV-EL | SPF vO-IT | ST-ST C¢-GL | F8-61 jj / GT la €¢-P1 60-ST 18-FI CL-ET 8I-€1 | G8-ET 66-61 18-61 I 9G-FT | 9L-E1 OL-€1 | £0-F1 GO-FI | 82-81 98.GT | LF-ST 19.61 | &F-81 LPG | 91-FT GIT | $3.11 9-21 | 68-TT / f} ie || 0 *portod yoro jo Lep oaissoasoag or 6o-6 “UOTJVULPapP U1oj}SoMm JO aouRYo [BUANIp [v}0], ‘pound ay bt 98-11 T9-TT c9-6T €G-C1 ae [8-61 Soe leer | ‘O28Tl pe oa a $661) eae | | FE-ST | €6-FT.|10-91 | OLST | | | | | my. lee.1 | 19-11 (9h-11 | ‘69st | & | Is CO | 68-11 | 89-01 |6%1T |"898T | re Se | | = | SG-EL | Ee | oO Lae Ce COFI Zz 96-01 | § ae i } eB =H PLEL 10-€1 (9t-ct / | / | / aS | Oo i ~ ee, ae 5 ee | — el ae "savok | ) Se 13 BA igi i Siu ba tal vio! 13:45) 5.03414 Bn Is |) ae 12 ees Mle dnOea es Pith DAD aa 13. ae 13 Fue ral ites sy al Wig ia tees 3 | 336 13 | erty eee. LE Sh Ns (eae ee - | ba ee 13° 3a i) ees 1s ten ee pao) 258 13:5 | “Saree wal fou ere Iss lipagaaae ae Peete 13° (| 354) ie eae W. 90 sane 14 AS! ASO celecct 12. |E.270 ...... 12 Ns ee 15 There is, then, at the south pcle a marked depression; it is the contrary at the north pole. Hence it is natural to ask, Does the greatest activity at the surface of the sun correspond to the greatest rumber of protuberances, or to the greatest extension of the mag- nesium-regions with the exaggerated flames of the chromesphere? This is a question which I cannot yet answer.—Comptes Kendus de l’ dead. des Sciences, July 1, 1872. 5.4 Vol. 4 PUI Phil Mag. Spectrum. G E or Dispersion E 2 D BC -E Spectrunv D Cc B Diffraction JV a ye ees Mintern Bros. lith . ) = * . ‘ \ ; ; . 5 - Ai j - « . . e . > ¥ . = A . . 7 | ° ‘ - . . ee = xe x ‘ - 4 % Catt ' THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] SEPTEMBER 1872. XXI. On Differential Galvanometers. By Lovis ScuwenpueEr, Lsq.* : Jena is one very interesting question connected with the construction of these instruments which, as far as I know, has not yet been answered, and which is of sufficient practical importance to form the subject of an investigation. This question may best be put as follows :— A certain battery of given electromotive force and given. internal resistance has to supply the two coils of any differential galvano- meter with a current; what must be the resistance of either cout in order to obtain the most delicate reading when measuring a given resistance 2+ The solution of this problem in its most general form would naturally be extremely intricate, and could not be effected with- out tedious calculation ; but there is one special case where it is comparatively easy to determine the law which connects the re- sistance of the coils with the external resistances to be compared, in order to have the greatest sensitiveness of the instrument. Suppose, for instance, that the two coils of a differential gal- vanometer have equal resistances and equal magnetic momenta, and further, that the battery which supplies the two coils with current has an internal resistance sufficiently small to allow of its being neglected against the resistances to be compared. Then, on account of the battery resistance being so small, it * From the Journal of the Asiatic Society of Bengal, vol. xli. part 2, 1872. Communicated by the Author. t+ Inthe Philosophical Magazine of May 1866 and January 1867 I solved a similar question, viz. the proper resistance of the galvanometer to be employed when testing by Wheatstone’s balance ; and the result of that investigation has led me to examine the present question. Phil. Mag. 8. 4. Vol. 44, No. 292. Sept. 1872. M 164 Mr. Louis Schwendler on Differential Galvanometers. The magnetic moment of the coil g, when a current G passes through it, may be designated by Y; and the magnetic moment of the coil g', when a current G! passes through it, may be called Y’. Both these magnetic momenta are taken with respect to the same needle, or system of needles; and we may suppose that neither Y nor Y’ alters perceptibly when the needle, or system of needles, slightly alters its position towards the coils, which are supposed to be fixed. (This condition will be fulfilled as closely as possible near balance, when the needle is approximately always in the same position with respect to the coils; and it is only for such a case that the following investigation is of any practical interest.) According to the principle of the differential galvanometer, we have rior NaN where a represents the deflection of the needle before balance is arrived at, and which may be positive, zero, or negative, depend- ing on the relative strength of the currents which at the time are acting through the coils, on the relative position of the needle towards the coils, and on the shape and size of the latter. Approximately we have further, Yo =m, U,G; Yam UG", U and U! being the number of convolutions in the coils g and g’ respectively, and m, m! representing the magnetic momenta of an average convolution (one of mean size and mean distance from the needle) in the coils g and g' respectively, when a cur- rent of unit strength passes through them. Further, as the space of each coil to be filled with wire of constant conductivity is given, we have U =n r/ gs Ws / 9, as can be easily proved. n and n! are quantities independent of g and g! so long as it may be allowed to neglect the thickness’ of the insulating cover- ing of the wire against its diameter, which for brevity’s sake we will suppose to be the case. With this reservation » and w! de- pend entirely on the size of the coils and on the manner of coiling. Substituting these values, we get a ocmns/9G—m'n'/o'G', .. .. = which general expression for the deflection we may write in two Mr. Louis Schwendler on Differential Galvanometers. 165 different forms—either Bi _ mil Vg oy a cxmnv 9 (6 aa Vat } mat He) AES or nt mn Vil fe ') ; a om! fg! Find oe GOs Frey which means that any deflections observed may of course be con- sidered due to either coil. In the first form (equation I.) it is ely pa considered due to the coil g when a current G— —— VE os flows through it ; in the latter form (equation I’.) itis considered / due to the coil g' when a current it 7a G—G' flows throughit. Now, considering that the same Thatteny K has to supply the current to both the coils, we have #2 gt! ‘ G=h" and 1 wgtw G'=E N where N= (g+w)(g! +u! Jt f(gtwt+g'+u’). Thus, substituting in (I.) and (I’.), we get either A vy UI Fis Vg! ie O Oh iit pet, alle Oe a eam (9 shes Fig+w)), ate baleowi(ls) or A! : w!) Le, Vg ae oa a a mln! E VEC g ert We (gtw));. (U) and either A or A’ i the factor which at balance becomes zero. mn! ./¢ The coefficient — g means, therefore, nothing else than what is generally called the constant of the differential galvano- meter, i. e. the number by which the total resistance in one branch of the differential galvanometer has to be multiplied in order to obtain the total resistance in the other branch, when balance is established. This constant o the differential cole nometer is a given Ween of g and g!, the resistance of the coils; and as g and g/ are to be determined, by being variable, it cannot be considered a constant in this investigation. But the 166 Mr. Louis Schwendler on Differential Galvanometers. In! factor aa 8 entirely independent of any of the resistances, it represents what may appropriately be called the ‘‘ mechanical arrangement” of the differential galvanometer, and may be de- signated by p. It must be borne in mind that p represents an absolute number, which theoretically may be any thing with the exception of O anda. Ifp had a value equal to either of these two limits, the instrument would be a simple galvanometer with a shunt, and not a differential galvanometer. The deflection a may now be written more simply as follows :— A a a ae oc KYI(y + 0 =p Lc ae Ken A or A! vg git+u! Vg Vg! (e) ! ee ! ! ! ak N (es Wwe — (g+w) )=K Ne AT) K and K! being independent of g and g', and also of w and w’. N is a known function of all the resistances in the differential circuit. A and A’ are similar functions of g and yg’, w and w’, and which both become zero at balance. For the further investigation only one of the two possible ex- pressions of a will be used, viz. equation (I.). Sok nA Differentiating this expression with respect to w', the external resistance belonging to the coil 9’, we get da_yxS vg _ ARV a du! N N? ; where alii ” ae or the variation of the deflection a, when w’! varies, 1s bu=K{ Vo add: | Bc =Kd¢ddu! Now it is clear that the a is most sensitively con- structed when, for the slightest variation.in w’, the variation in @ : AR is greatest. This will be the case if the factor o= ahh shee is as great as possible, This factor dis a known mate of the / Mr, Louis Schwendler on Differential Galvanometers. 167 resistances in the circuit ; and as w and w! are given, @ can only be made a maximum with respect to g and g’; the resistances of the two coils. Thus our physical problem is reduced to the following mathe- matical one :— A function ¢ containing two variables is to be made a maxi- mum, while the two variables are connected with each other by the relation VA ! A=y'+w'— Ty Ot) A being a constant with respect to g and g! and becoming zero at balance. Solving this question (relative maxima), we get (w—g) (w'+ 9) +fwtutg'—9) _ 2l(y+wtyf) (I.) plg—w)g 2Vg9V9'—p (g-+w)>” * To some of the readers a more detailed working out of the mathema- tical problem may perhaps be welcome; and as this will also prove to be an easy control over the equations (II.) and (II’.), I will give it here in a somewhat condensed form. We had KK VI, Oe ear hae eee, Sa) al (I) where K represents a constant, 7. e. a quantity independent of any of the resistances in the differential circuit (fig. 3), while A=g'+w'—p vg! (g+w), z. e. a resistance which at halance becomes =0; and further, N=(g+w)g't+w')tfgtwutg'+w'). Differentiating a with respect to w', and remembering that s =1, and sub- w stituting ae =R, we have Ww’ da V9g_,RV9 OF =K4 NI AK dw' af N Ww I? “, ja=K { I — U8 Sw’; Wek : £24, Wa *, da=Kodw’. Thus the variation of a is always directly proportional to @,a known fune- tion of g and g’; and to make da for any dw! as large as possible, we have to make d a maximum with respect tog and g’, while g and g' are connected by the following equation : A=g'+wu!— vg (Grr w]e Kecamemes serie ey (Te : g Pig 7 (1.) p being a constant with respect to g and g’, as also is A. We have therefore to deal here with a relative maximum ; andin accord- ance with well-known rules we have to form the following partial differ- 168 Mr. Louis Schwendler on Differential Galvanometers. which equation, with the other, Vo! gj +u' aD va (g--v)—A—0; ieee gives all that is required to determine g and g!; and the values thus obtained would be those which would make the reading ential coefficients :— dN N—29 — dpe {” g dg slo sh, ij aa ay Gee dies R ay I TO: dN dA Wig = dp 1 dg! if ways: dg' N? N? ; dN 2 __ Mg (dR _ w KR N2 dg' N dA __w—gp Nee dA _ 2VgN9'—plg+w) dg! 20 9/9 At or near balance, when A is =0 or very small, the terms AS and AS’ in the respective differential coetficients are to be neglected, because neither S nor 8’ becomes infinite for any finite values of g and g’. Thus we have approximately, dN dA N-—29 — — dg 2 gN Mi ys” dN dA vo Rv gS d d dg’ gh =— {et ye J =-ce'40). Further, we will substitute da, dg oe dikes dg' es thus we have the following differential equation :— (P— Q)dg—(P'+-Q')dg'+d(adg+ Bag’) =0, Mr. Louis Schwendler on Differential Galvanometers. 169 most delicate near balance, when the variation takes place in w', 7. e. the external resistance belonging to the coil g/. If, instead of differentiating the expression for a with respect to w! by using the expression (I.), we had done so with respect to w by using the expression (I'.), we should have obtained in a similar way the following relation between g and g’, ee wg) + wre tg) etwas) bas / |) J (gt—y! DA Va mea ae ) ging 7p eee (II'.) which equation, connected with the other, Tew! a Vg tw=A'=0, . aa Nt) gives all that is necessary to determine g and 9’, being those values which would make the reading at or near balance most A being the undetermined factor. From this equation we have P-—-Q +rAe=0 — (P'+Q')+8=0; and or, A eliminated, pr a o B but we have always Oe cee thus we have as final equation, ety Mie Pane (Ou: or, the value for P, P’, «, and & substituted, we have dN 2dN N—2g9 —— adel g ee dg’ PI G—%) 2NgN7—pG+w) further substituting NT G aI te +h on =g+twtf, and reducing as much as possible, we have (ww +9) +flwtw'tg'-9)_ U9+wth) ayy plg—w)gy 279 9'—p(g+w) which is the equation (II.) as given above. In quite a similar manner equation (II’.) can be found; it must only be remembered that it is more simple to use expression (I’.) for the purpose than (1.). | | | | | — 170 Mr. F. C. Webb on an Electrical Experiment sensitive when a variation in w, the external resistance belonging to coil g, takes place. Now it is clear that equations (II.) and (I1’.) are not necessarily identical, as long as p does not fulfil certain conditions, and therefore the first set of equations (II.) and (1) may give entirely different values for g and g' from those obtained from the second set (IL'.) and (I.), which means that a simultaneous maximum sen- sitiveness with respect to an alteration of the external resistance w or w’ in either of the two differential branches, is not always pos- sible. The following very important and interesting question, therefore, remains to be solved. What general condition must be fulfilled in the construction of any differential galvanometer in order to make a simultaneous maxt- mum sensitiveness possible, with respect to an alteration of external resistance in either of the differential branches ? [To be continued. | XXIT. On an Electrical Experiment with an Insulated Room. By F. C. Wess, M. Inst. C_.E* | OME ten years ago, in a series of articles m ‘The Hlectri- cian,’ afterwards published in book-form, I submitted some new views on the explanation of the action which takes place in various well-known electrical phenomena. I endea- voured to prove by reasoning that the ordinary explanations given of the discharge of a charged conductor by communica- tion with the sround were erroneous ; and I suggested an ex- periment with an insulated room as ‘a means of proving the fallacy of these ordinary explanations of discharge &c. This experiment I performed in May 1869 at Keyham Dockyard ; and I think the results are worth placing on record. To make the bearing of the experiment intelligible, however, it is necessary to recapitulate a little of what I have before urged. It is generally stated mm books on electricity, that, when an electrical machine has its rubber to earth, on the action of the machine the prime conductor becomes charged positively and the equal quantity of negative electricity which is generated is lost in the earth—and that when the prime conductor is then placed in contact with earth, its discharge is merely the conse- quence of its sharing its electricity with the earth, the propor- tion remaining on the conductor being, in virtue of the almost infinite size of the earth as compared with the conductor, almost infinitely small and consequently quite inappreciable. I will not weary your readers by quoting, but will merely alee them to:—Professor Daniell’s ‘Chemical Philosophy,’ p. 241; * Communicated by the Author. with an Insulated Room. 171 Lardner and Walker, p. 248; De la Rive, vol. 1. p. 3; Ganot, translated by Atkinson, p. 536. When, therefore, the ordinary experiment of charging the prime conductor is performed in an insulated room, according to the theories which I deny, the negative electricity being unable to share itself with the earth, some differences in the effects produced should be attamed. The negative electricity, for instance, if it tends to flow to the earth, should influence an electrometer placed in contact and exterior to the room. Again, if the room is connected to the earth during the charging of the prime conductor and is afterwards insulated, the prime conductor, if touched to the room, ought not to be discharged, since it can only share its electricity with the room instead of with the almost indefinitely large surface of the earth. Now [ argue that when electricity is produced, at any rate by an artificial means, the negative and positive are not only always produced in equal quantities, but remain each as much in abey- ance as the other, and that complete discharge always consists in the recombination of equal quantities of opposite electricity. Thus when a conductor is charged, say, positively from a plate- machine having the rubber connected to the earth, the negative electricity has no tendency to flow to and distribute itself equally over the earth, but distributes itself principally on the nearest _ conducting- surfaces to the positively charged surface ; and when the surface to which the negative pole is attached entirely bounds the dielectric which separates it from the positively charged surface, the negative electricity is entirely distributed on that surface, none flowing to any other part of the earth. When these are joined by a conductor, discharge occurs through the recom- bination of the exactly equal quantities of electricity previously produced. The experiment to which I allude was performed in H. M. Dockyard, Keyham, where I was engaged in repairing a part of the Persian-gulf cable which had been thrown overboard from the ship ‘Calcutta, and recovered and landed under my su- perintendence. The insulated room was erected in the large glass-covered quadrangle of the dockyard. I intended to make a series of experiments, carefully recording every step. After a few preliminary experiments, however, of which unfortunately no record was kept, our regular work had to be suddenly pushed on; and before any series of experiments could be made and re- corded, the whole apparatus had to be removed. Thus I am only able to write from memory; but Mr. Herbert Taylor (one of Mr. Latimer Clark’s assistants, and a well-known electrician) was associated with me at the time and performed the expe- riments with me. I have submitted this article to him, and he indorses it as a correct statement of what occurred, i ee eee ORE ag ine ne 9 ea rn ae inl ee 172 Mr. F.C. Webb on an Electrical Experiment The room was about 8 feet by 9 and about 8 feet high. The floor was of wood, and the sides of wooden framework covered with calico and with pieces of tinfoil pasted about it to make it a good conductor. It had a door and two windows of wire gauze. A small table was placed in it, and a frictional electrical machine was placed on this. The room was suspended by four double parts of half-inch-round gutta-percha band to a wooden frame, the floor being about 4 feet from the ground. The gutta percha was covered with paraffin ; and the whole room was tested for insulation with five hundred Daniell’s elements with a delicate astatic Thomson’s reflecting-galvanometer, and gave no perceptible loss. A Peltier electrometer was placed on the ground outside; and a wire from the brass knob of this was connected to the gauze of the window. ‘The table was con- nected with the tinfoil that was pasted about the surfaces of the room, so that when the rubber or prime conductor was con- nected to the table it was in connexion with the sides of the room. Thus arranged, the machine acted to all appearance exactly the same as in an uninsulated room. When the rubber was connected to the table, on turning the glass disk the prime conductor was charged so as to give off sparks the same as when the room-was uninsulated; and the conductor was completely discharged when touched to the insulated room. Not the slightest effect was produced on the electrometer, even when sparks were flashing from the prime conductor to the wire gauze of the win- dows to which the wire from the electrometer was attached. Connecting the room to the earth made no difference. A sphere about a foot in diameter was then charged when the room was insulated, and then handed out by an insulating handle, when the electrometer immediately diverged to about 50°, showing that the outer surface of the room had become negative. On taking the sphere back into the room, the electrometer fell to zero. _ These results agree exactly with what I have suggested would occur under such circumstances in my treatise on Hlectrical Accumulation published in 1862; andit is impossible to recon- cile these results with the explanation of the action that takes place in charging and discharging as given and republished in most works. Take, for instance, the following from Noad’s Student’?s Text-book :— Thus, in order to get any develop- ment of electricity, there must be either with the rubber or with the prime conductor, electrical communication with the earth as the great natural reservoir of electricity.” (P. 29.) This is about the same language as that used by Lardner, De la Rive, Daniell, Gavarret, and later by Deschenelle. According to the views I have advocated, the accumulation on the prime conductor depends on the resistance of what I have termed the inductive circuit, which in the case of charging the with an Insulated Room. 173 prime conductor with the rubber connected to surrounding ob- jects, consists simply of the resistance of the dielectric sepa- rating the prime conductor from the surrounding objects, and is therefore the same whether the room is connected to earth or not. More complete views on this subject will be found in what I have written before, both in my ‘ Electrical Accumu- lation? and in a paper “ on Inductive Circuits, or the Application of Ohm’s Law to Problems of Electrostatics,’ in the Philoso- phical Magazine for May 1868. Dr. Ferguson, in his ‘ Electricity,’ seems to have a tendency to discard the older explanations ; but at times his explanations ap- pear to me incomplete, so that it is impossible to form an opinion as to what his theory is as regards the actions that take place. The following paragraph, however, appears to me remarkable, as it seems to show a tendency towards the theory which I have advocated :— | “We have hitherto taken no notice of the —E that, for in- stance, is said to be lost in the ground when glass is charged positively. Now it may be lost, and the —E induced by the glass on surrounding conductors may be new —H induced by it. But it is also possible, nay, even probable*, that this —K is none other than the — said to be lost. If this be the case, the ground acts as much on the glass as the glass on the ground ; and the action 7s precisely the same as in a galvanic circuit, when the polarization proceeds in opposite ways in two opposite direc- rections, the action of the one strengthening the action of the other.” Here we have stated as probable what I have urged ten years ago, and which I think I have now demonstrated by experiment. Dr. Ferguson adds, “ However, it makes no practical differ- ence ; and it is simpler to suppose the insulated body to be the one centre of force.” With this last paragraph I cannot agree, as it will be found that, by considering problems of electrostatics by means of the theory of inductive circuits, many can be solved which cannot be explained by an allusion to the earth as a com- mon reservoir. ‘I'he experiment with the insulated room is only one of them. I maintain that no electricity is ever lost in the ground or drawn from the ground as areservoir. All electricity generated, if we consider it as a quantity, is produced in equal quantities, and can only be neutralized by an equal quantity of electricity of the opposite name. Thus when the sphere in the insulated-room experiment was charged positively from the prime conductor, an equal quantity of negative went to the room. When the sphere was taken out of the room, this negative went to the outside of the room at * The italics are mine.—F. C. W. 174 M. E. Edlund on the Nature of Electricity. the same time that the external conductors to the room became polarized, so that there remained on external objects a charge of negative opposing the positive on the sphere, and a charge of positive opposing the negative on the external surface of the room. By connecting the sphere to the earth, the sphere’s charge and its opposing charge on surrounding objects neutralize each other, leaving the room negative to a positive charge in the earth, which, when touched together, neutralize each other. Or if the sphere is touched to the room, the positive of the sphere neutralizes the negative on the room, the negative and positive charges in surrounding objects at the same time recombining also. Or when the sphere was taken back into the room, the negative returned to the inside of the room, the positive and negative which were induced on external conductors by the sphere and room when the sphere was external to the room recombining. Ii is to be regretted that circumstances prevented me, as I have stated, from performing a regular series of experiments with the insulated room ; nevertheless, as the experiment re- quires space and apparatus not always attainable, I have thought that the experiments, even so far as they went, are worthy of record, even if they do not carry the conviction which my argu- ments have for so long failed to establish amongst the authors of our text-books on electricity. XXII. On the Nature of Hiectricity. By M. E. Epiunp. [Concluded from p. 100.] Part [I. 5 fe the first part of this memoir we have endeavoured to show that both electrostatic and electrodynamic phenomena can be explained with the aid of the luminiferous ether. The same basis of demonstration will serve to explain to us some of the other principal properties of the galvanic current. 4. Phenomena of galvanic induction.—A molecule m! is at rest if it is equally repelled on all sides by the surrounding ether. Suppose now that, from any cause whatever, = ether has been compressed towar ds a pone a in the vicinity ‘of m!; the repulsion exerted on this side upon m’ will Se be greater than on the others. In consequence, the molecule m', not being able to keep intact its state of equilibrium, will inevitably seek to move away from the point a. It will be the same with all the mole- cules within the sphere of action of the compressed ether. The consequence will be a rarefaction of the ether in the vicinity of a. The ether at a greater distance from a, the density of which has therefore undergone no sensible modification, seeks now to bring M. E. Edlund on the Nature of Electricity. 175 back towards that point the ether which is in the vicinity of a. As soon as the rarefaction about a has reached a certain limit, the molecules enter a new state of equilibrium, which they pre- serve as long as the increase of density at a continues. If now the increase suddenly ceases, the molecules about a resume their primitive equilibrium, and in this case travel, although in the opposite direction, the same path as when the density was in- creasing. A corresponding modification must be effected in the state of equilibrium of the surrounding molecules if the ether at a be rarefied instead of compressed ; but in this case the direction of the motion of the molecules is the reverse of what it was in the preceding: they approach a at the commencement of the rare- faction, and recede therefrom when it ceases; and the amount of displacement is the same in the approach asin the recession. It is moreover evident that the modification of the state of equili- brium of a molecule, or the amount of its displacement, does not depend exclusively on the modification of the repulsion of the ether which surrounds it to a certain distance, but depends also on the facility with which it moves—or, in other terms, on the resistance to conduction as well as on the action of the nearest molecules. We have admitted, in the first part of this memoir, that the action of one molecule upon another varies inversely as the square of the distance. As we also indicated, this rule only applies where the molecules are at a sufficient distance from each other. If the molecules be in contact, or ata molecular distance from one another, the law of repulsion will perhaps be different —a circumstance which in no way affects the present consi- deration. It is obvious that the ether molecules about a will change their position of equilibrium if, from any cause whatever, the repulsion exerted upon them by the ether of a be modified with- out becoming denser or rarer. Now the ether of a being set in motion will produce a modification of this kind. If, then, that ether be set in motion, the molecules of the surrounding ether will be displaced, and will remain in their new positions as long as the «ther of a continues its motion without change. The instant the motion ceases, the molecules return to their original positions of equilibrium. Such, in our opinion, is the cause of galvanic induction. When a galvanic current commences in the vicinity of a closed circuit, the positions of equilibrium of the ether molecules are changed, not only in the closed circuit, but also in the insulating medium encompassing it; and the induction-current is simply the passage of the molecules from the first position of equilibrium to the second. The new state of equilibrium of the ether in the closed 176 M. E. Edlund on the Nature of Electricity. circuit is not determined exclusively by the direct action exerted by the inducing current upon it, but also by the modification of the state of equilibrium in the ether of the surrounding insulating medium. As soon as the inducing current ceases, the ether molecules return to their primitive position of equilibrium, and consequently we have in the closed circuit an induced current equal in intensity, but opposite in direction, to the former. When an inducing current 1s brought near or removed from a closed circuit, the effect is evidently the same as when a current commences or ceases in a circuit at rest. Although no induced current properly so called is observed in the insulating medium, since the great resistance to conduction impedes the origination of such a current, we have nevertheless no reason to suppose that the ether molecules therein remain in a state of perfect repose: the positions of equilibrium are modified there also, since expe- riment has demonstrated that no substance can be considered absolutely nonconducting. If two molecules cf ether, mand m’, are at rest at the distance r one from the other—according to what has been said before, ! . . . mim ; their mutual repulsion is — a For the unit of measure of sether masses we have obviously taken here the mass of ether which is capable of giving to another mass of equal amount the acceleration 1 in the time J], the distance between the masses being 1. If, on the contrary, m’ only is at rest while m moves with the constant velocity / in a direction making the angle 0 with the line of junction between the two molecules, we have, for the case in which m approaches m! (in which we designate the acute angle by @), I 1,2 \ — TP [1+4(—heos at4(= [1— cos? 61) | as the expression of the repulsion according to equation (1) of the first part of this memoir. For the case in which m recedes from m!, and designating the obtuse angle by @, we obtain the same formula, except only that h cos @ (which is equal to the projection of the velocity along the Jine of junction) has the opposite sign. From equations (7) and (10) we have :— h? ) k ) 2 ¥(~ [1 — cos 6] = 5h (1— cos 6), and d(—hcos 8) = —ah cos 0— fie cos? 6. Introducing these values of W and ¢ into the above expression M. E. Edlund on the Nature of Llectricity. 177 of the repulsion between two molecules of which only one is in motion, we obtain :— I ~ [ 1—ab cos 0+ : h? ae 5 cos? 6) -pleaentl2) If m is receding from m’, the angle @ is obtuse and the second term becomes positive. Formula (12) expresses the direct repulsion between m and m/, the first being in motion and the second at rest. Now the molecule m is also repelled by all the rest of the mass of ether which surrounds it. At the first instant, before the molecules have been able to change their positions of equilibrium, the re- sultant of the repulsions exerted upon m by the rest of the sur- rounding ether will be equal to the repulsion between m (con- sidered at rest) and m’, but will have an opposite direction. This comes out evidently from the fact that the resultant of the repulsions exerted upon m! by al/ the surrounding mass of ether was =O when the molecule m was still at rest. We obtain, then, the sum of the forces which, at the first instant that m is put in motion, act upon the molecule m/, if we subtract from the repul- sion expressed by formula (12) the repulsion between m and m! when the former is at rest. It follows from this that at the first instant the molecule m! is repelled along the line of junction be- tween m and m! with a force which is expressed by ! ~- [ah cos 0 —518(1—5 cos? 8) |. shy er-erpipnaad suit lie) If this expression be negative, the molecule m! will tend to remove itself from m in the direction of their line of junction ; if, on the contrary, it be positive, an approach will be effected along the same line. If m recedes from m', the angle @ is - greater than a right angle, and consequently the first term is negative; if, on the contrary, an approach takes place, that term is positive. If, then, » designate the quantity of ether in motion in the unit of length of the conductor in which m moves, and ds be the element of that conductor, m will be equal to wds. Now ph is equal to the intensity 2 of the current. In an analogous manner m! may be replaced by pds’. We thus obtain instead of for- mula (13) ;— olf wone0— #4(1— 8 cont) Je es acos 0 5f(1 5 008 6) ASUS wie CLL) Formula (14) is the expression of the force with which an element of the inducing current whose intensity is 2 tends af the first instant to move, in the induced circuit, the quantity of eether yds! along the line of junction between the two elements. Phil, Mag. 8. 4, Vol. 44. No. 292. Sept. 1872. N 178 M. E. Edlund on the Nature of Electricity. This is the maximum value of the force; after the first moment, it diminishes continually until, at last, it becomes =0 when the molecules have reached their new positions of equilibrium. Formula (14) can be divided into two parts, viz. + Ecos 4 ds ds', and awh (1— ® cos? 0) ds ds!. If in the second part we denote by 7 the intensity of current indicated by wh, that part of the formula becomes ae i = COs” 6) ds re Or? Now this expression indicates half of the electrodynamic repul- sion between two circuit-elements ds and ds’ when —_ are parallel and respectively traversed by the currents 2 and 7’. In the theoretic deduction of the electrodynamic formule, we have assumed that the repulsion between two molecules of ether is communicated without dimmution even to the elements of the circuit in which they are moving. Of course this hypothesis applies only to the part of the repulsion-force between the mo- lecules which remains in the electrodynamic formule, and not to the part which vanishes (of itself) in the formation of those formule. It consequently applied to the terms in the expres- sion of the repulsion which are multiplied by 4, and not to that . containing the constant a. But if we maintain this hypothesis for the terms multiplied by & in the expression of the repulsion between two ether molecules, the theoretic deduction gives a result perfectly accordant with Ampére’s empiric formula. But the communication of the part in question of the repul- sive force entirely to the cireuit-elements in which the molecules move, presupposes necessarily that that part cannot communi- cate any proper motion to the molecules themselves in their re- spective circuits; for, if it did, a portion of the repulsion would be expended in generating that motion and in producing the heat resulting from the resistance opposed by the circuit. In this case, then, the whole of the repulsion could not pass to the circuit-elements. Still the molecules of «ther may possibly receive some motion from the repulsion mentioned, but too slight to permit a difference between theory and experiment to be observed in electrodynamic phenomena. Be it as it may in this respect, we coe as a necessary consequence of the hypo- thesis we have made in the deduction of the electrodynamic phe- nomena, that the terms in formula (14) which are multiplied by the constant & exert only an insignificant influence on the dis- placement of the «ther particles in the induced circuit, and that consequently their importance for the mduction is very little. M. E. Edlund on the Nature of Electricity. 179 But evidently, that this may be so, kh (or the velocity of the eether in the inducing circuit multiplied by the constant &) must have a very small numerical value. With regard to the velocity h, experiments have not, as we have seen, led to an accordant result. Fizeau and Gounelle found that the velocity rose in a copper wire to 180 millions, and in an iron wire to 100 millions of metres in a second. Walker estimated the velocity in an iron wire at 50 millions only, and Gould at less than 26 millions in a wire of the same metal. The experiments made on a copper telegraph-wire between Greenwich and Edinburgh gave a little more than 12 millions of metres per second; and only 44 mil- hons was obtained on the telegraphic line which connects Green- wich with Brussels. The small velocity on this last line, which was also of copper, may be partly explained by a great length of it being submarine. It must further be remarked that, from the manner in which the experiments were made, the numbers cited express the velocity with which the first quantity of wether propagates itself, at the commencement of the current, from one pole to the other. The ratio of this velocity to the velocity when the current continues with constant intensity has not yet been determined by experiment. Of the velocity of the ether ina wire under the conditions of an ordinary induction experiment we know almost nothing more than that it is very great. The constant & enters as a factor in Ampére’s formula for electrodynamic phenomena; and its value has been determined experimentally by W. Weber and Kohlrausch*. Taking as unit that above given for the measure of the ether, we have from the experiments of those two physicists, in round numbers :— 1 : —= = 440 millions of metres per second. he Loe Admitting for the velocity 4 a value within the limits of the results of the above-mentioned experiments, a very small value is obtained for the product kh. Now the constant a of the first term of formula (14) should also have only a triflimg numerical value. it follows evidently, from the considerations set forth in these pages, that ah must be lessthan]. If, then, we admit for example the value of 2 found by Walker, or 30 millions of metres On this sup- per second, the value of a will be < 30 willons’ II 12,900 millions’ and conse= position, the product A malne p= quently a may be 400 times = This shows that, far from con- x Poge. es xeix. p. 10. 180 M. E. Edlund on the Nature of Electricity. tradicting, experiment much rather confirms the result arrived at theoretically—namely, that the terms in formula (14) multiplied b kh ie ment alone can decide if this is permitted in reality. The action upon the ether of the circuit-element- ds', ex- pressed by formula (14), is exerted along the line of junction between ds and ds’. But asthe ether of ds! can only move along this element, we must, in order to have the measure of the mo- tion produced in the ether of ds, muitiply that expression by the cosine of the angle formed by the acting force with the cir- cuit-element. Calling this angle 6’, we must multiply by cos 6". By electromotive force of induction is meant the accelerative force exerted by the inducing wire upon the ether contained in unit of length of the induced wire. ‘The value of this we obtain by dividing the expression (14) by p’; and thus we get as ex- pression of the induction of a current-element upon an element of the induced circuit during the first mstant :— may be neglected in comparison with the first. Experi- — E cos 0— a a cee 6) cos 0! ds dale a( ra) r 2 2 ; The induced circuit must always be closed that an induction- current may be possible. In the integration of the formula (15) 5 200s Olds ds!) vanishes, whatever be the form of the induced circuit, provided it is closed. ‘This is easily proved by the following reasoning. Imagine two spherical surfaces with the element ds for centre, the one having the radius 7, and the other the radius r+dr. Now, if a part of the induced circuit, be upon either of these concentric surfaces, evidently the above-mentioned term must vanish for that part of the circuit. Eyerywhere, in this case, cos 7 is =0, since the radius of a sphere always makes a right angle with the lines drawn from the terminal point of the radius upon the surface of the sphere. The elements of the induced circuit which fall between the two concentric surfaces must be in pairs, since the circuit is closed. A current, then, in the in- duced circuit will pass as often from the outer to the inner sut- face as from this to the former. The cosine of the angle 6’, which any one of the elements included between the surfaces with respect to ds!, the term independent of cos 0 (viz. forms with the corresponding radius, is equal to sa and the number of these cosines bearing a positive sign is equal to that of the cosines with a negative sign. It hence follows that, for all the elements whieh fall between the two surfaces, the product M. E. Edlund on the Nature of Electricity. 181 of = ds — ds! will be equal to zero. Now, as this is true for 272 ds any value of 7, it must in like manner be true for the whole cir- cuit. We can therefore, in the place of formula (15), employ in the integration the formula + mG cos + = khcos*6) eos Oh dsids!. 7a" (1G) Now this formula expresses the induction of the first instant only, before the molecules both of the wire and of the surround- ing medium have been able to quit their primitive positions of equilibrium. But the induction continues until the new posi- tions of equilibrium are reached, when the inductive force be- comes zero. The force of induction undergces a continual diminution from the commencement to the end of the duration of the induction; and formula (15) only gives the maximum value during the first instant. The result should be, that at the commencement of their existence induction-currents appear very strong and then diminish in intensity—a fact which has been proved by experiment*. If, then, we wish to calculate the amount of an induction-current in given circumstances, we must take into account not only the maximum value of the induction at the first instant Az¢, but also the sum of all the inductions during the whole of the time of induction. If for the sake of brevity we designate the maximum value of the induction exerted by a current-element upon an element of the induced circuit by A¢ Ar when the distance between the elements is 7, we can express the induction which takes place during the im- mediately following instant by A¢pAr, when p is less than unity. In this way the sum of all the inductions will be At l+p+p,+py+..-+0)Ar, in which each consecutive term of the series is less than the preceding. This can be expressed more briefly by At FAr, where F denotes the sum of the series. For another element of the induced current, of which the distance from the inducing element is 7,, we obtain in the same way AZF,Ar,. Now, if F were always equal to F, (that is, if the sum of the series were constant), the sum of the inductions would be proportional to the maximum value, whatever might be the variations in the force 2 of the cur- rent and in the distance 7 between the elements, and we could at once calculate from formula (16) the relative magnitude of the induction-current. The fact that F is independent of 2 cannot * See Lemstrém, K. Vet.-Akademiens Hand. ny foljd. vol. vin. (1869); Blaserna, Giornale di Scienze Naturali ed Economiche, vol. vi. (Palermo, 1870). 182 M. H. Edlund on the Nature of Electricity. be doubted ; but the same cannot be said with respect to r. The force of induction at a given moment upon the mass of ether jvds' of the induced circuit is proportional to the difference be- tween the repulsion exerted upon pds’ by the element of the inducing current (in which the mass of ether wds moves with the velocity 4) and the repulsion upon the same mass of all the rest of the ether. The first of these repulsions diminishes (as is evident from the preceding reasoning) inversely as the square of the distance between the elements ds and ds’. Now, if this were also the case with the latter, viz. the repulsion exerted upon pds! by all the rest of the mass of ether, F would evidently be independent of r; for we could express, for a given instant, by = the repulsion proceeding from the element ds of the inducing current, and that of all the remaining mass of ether by“ expres- sions in which aand 4 would be constants. The force of induction for that moment would then become 5 (a—b), which may be written pAr, p being aconstant. As long as the ether molecules are in their normal primitive positions of equilibrium, the repul- sion exerted upon pds! by all the surrounding mass of ether 'ds ds! with the exception of uds is = are 2 : , and therefore indeed diminishes inversely as the square of the distance. But this can no longer be the case after the molecules are displaced and the mass of ether about y/ds! has undergone a distribution different from its normal condition; for the repulsion exerted upon pids! by the surrounding ether is of course not independent of the distribution of the ether. F must necessarily depend on 7; and hence we shall write F(r) instead of F, We have therefore obtained the following formula to. express the magnitude of the induction-current :— + = ) (« cos 04° kh cos? é) cos O's as; ee or, if we neglect the last term, a +> cos 8 cos OG! dsdsio° 1 eee - We now suppose that the inducing current is closed, and that its form is such that it can be divided by a plane into two sym- metric halves. Then each element a on one side of the plane has a symmetrically corresponding element a! on the other side. We suppose further that the induced circuit is closed and sym- metric about the same plane; so that to each element 8 on the M. E. Edlund on the Nature of Electricity. 183 former side corresponds a symmetric element 0! on the other. It thence follows that the distance between a and 0! must be as great as that between a! and 8, that the cosine of the angle be- tween the element @ and the line of junction ab’ must be equal to the cosine of that between a! and a’d, but that the cosines will have opposite signs, since the directions of the elements on the two sides of the plane are determined by the direction of a cur- rent which traverses the circuit. In the same way, the cosines of the angles formed by the above-mentioned lines of junction and the elements 2 and J! of the induced circuit will be of equal magnitude but have contrary signs. Thus, in the induction of the element a upon L' and of a! upon 4, the two cosines of 0 will be equal to each other in magnitude, but will have contrary signs, which is also the case with the two cosines of 6’. It hence results that the part of the induction which corresponds to the term in formula (17) into which cos? 0 enters will be =O for the two symmetric elements combined. It will be the same with all the other symmetric elements. Consequently, if the two cir- euits, inducing and induced, be each cut symmetrically by one and the same plane, the integral of the term into which cos? 0 enters will be equal to zero. In this case, then, the integrals of the formule (17) and (18) will be perfectly equal. We will now compare the theoretic result with the results of experiment. We suppose that the circuits of both the inducing and the induced current are circular, that the radius of the first is R, and that of the second is R,, that the planes of the two circles are parallel, and that the line joiming the two centres makes a right angle with those planes. In this case the two circuits are placed symmetrically about the same plane, and the induction-formula (18) is applicable. Imagining then the inducing circle situated in the plane of zy of a system of rectangular coordinates of which the origin is at the centre of the circle, the induced circle 1s ata certain distance z from this plane. The distance 7 from an ele- ment ds, of which the coordinates are v=Oand y= —R, an ele- ment situated in the inducing circle, to an element ds’ with the ° coordinates 2%, y,, 2), situated in the induced circle, is then equal to +,/a?+(y,+R)?+ 22, or, what comes to the same, to +4/ R2+ R24 2Ry, + 22, The tangent of the element ds is parallel to the axis of the 2’s; and if we assume that the inducing current passes in the positive direction of the axis, ,cos9=— and consequently changes sign with x, If the ele- r ment ds' of the induced current be reckoned in the direction 184 M. E. Edlund on the Nature of Electricity. opposite to that of the inducing current, cos 6’ will be sek 1 which also changes sign with x,;. Introducing these values of 7, of cos @, and cos @ into the induction-formula (18), we obtain ai RE (raz ste Ry It follows from this that the induction of the element ds is the same in both the halves into which the imduced circuit is divided by the plane of yz, and that the induced currents go in the direction inverse to that of the inducing current on the same side. But it is evident that each element of the inducing circle has the same mducing action as the element ds above considered. Therefore the total induction of the inducing circle upon an ele- ment of the induced circle will be 9 Dy PEN aN 27 Rai ¥ (7) x} + ) ds!. Now ds = "7 Re and 2?=R?—7?. If we introduce these 1 1 values and that of 7, and (after taking the integral between the limits y;= +R and y,= —R) multiply the latter by 2, we obtain as expression of the total induction, after replacing y, by Ryu and consequently dy, by R,du:— BS F(r) V1 —u2du _, (Rit B+ 2RR w+ 2?) * Felici has experimentally demonstrated the following prin- ciple. Let two circular current-circuits A and B, of equa! radius R, be placed parallel at the distance z the one from the other, so that the line uniting their centres makes a right angle with the planes of the circuits ; two other circular circuits C and D, each having the radius R,, are placed in the same manner, but at + 47R?R2ai (19) ee t= a distance z, from each other such that -=> If now through 1 ‘each of the circles A and C an inducing current of the same in- tensity be passed, the induced current of B will be to that of D as the radius BR is to the radius R,. With the aid of this principle the function F(r) can be deter- mined. If, in the above imtegral formula, R be made =R, and iM) =n 6 VOR? + 2R2u +2, in which D is a constant, we obtain u=+1 fas 2dh + 4rrabiR ( i vJu=—l (24+2u+4,) M. E. Edlund on the Nature of Electricity. 185 As what is under the sign of integration is independent of R, if — remain constant, the induction-current will be proportional R to R, in accordance with Felici’s experiments. In this way we obtain, instead of formula (18), the following expression of the induction between two elements :— +003 CheosiMalstds Mais Have. ol(20) In order to ascertain if the results obtained by formula (19), after the determination of the function F(r) in the way above indicated, agree with experiment, Dr. Sundell, Aggregate Pro- fessor at the University of Helsingfors, devoted himself to a great number of experiments at the physical laboratory of the Stockholm Royal Academy of Sciences. Such an inquiry was necessary to enable us rigorously to control the results obtained by theory ; for previously we had only a very limited number of experiments applicable to the object we are here pursuing. We take the liberty of communicating one series of those experi- ments, referring the reader to Dr. Sundell’s memoir itself for further details*. The radius R of the induction-coil was equal to 21°7 centims. ; the radius R, of the induced coil was 7:1 centims. The distance between the planes of the two circles is indicated in centims. under the letter z. Deflections of the Magnetometer. é Observed. Calculated. Difference. Meena iol 76°09 aie. oo.) MFO wide iis. 16 4 ORF DOmaeets Sie l27 40, pay in) VLSI etsy ai sho OO 15 Camo Jeued sin GOA) wit pala az Oul 20 Patan caso Gulkessu sme.c tp OOOn ise sche Oed 20 rex PinasAOi8) a. nein AOGegudus, Be 20-2 30 RR Yeitielh COO OMS HOA OOTONe bios) aa. a= Ro AO seated city yal sO 6. isis, ty) sali Sel ore: Gols, ae tase The agreement between the calculations, on the one hand, and Dr. Sundell’s experiments, on the other, is fully satisfactory in every respect. if the inducing circle is in the plane of zy with the centre at the origin, and the induced circle in the plane of yz, but has its centre neither on the axis of z nor on the axis of y, integration causes the term of the induction-formula (17) containing cos @ to vanish, wlile the other term, which contains cos 6’, alone remains. Such an arrangement of the induction-circuits is consequently suitable for mvestigating whether that term has or has not an appreciable inductive force. By means of this pro- * (Efversigt af Vet.-Akad, Forh, February 1872. 186 M. E, Edlund on the Nature of Electricity. cedure Dr. Sundell has made some experiments, which have given no certain appreciable results ; and this likewise cor- roborates the theoretic deduction explained above. The true law of indaction between two elements is therefore expressed by the above-given formula (20). In virtue of the principles on which our present theoretic imvestigations are founded, it is evident that the formula in question applies also to the case in which mduction takes place with a current of constant intensity, resulting from the distance between the in- ducing element ds and the induced element ds’ dimmishing from infinity to 7 . 5. Distribution of the free ether at rest upon the conducting wire between the two poles of a batiery—W hen a conducting wire with considerable resistance connects the poles of a ealvanic battery, there is produced, as we know, free electricity at the surface ofthe wire. The ee electricity exhibits its maximum tension in the vicinity of the positive pole. With increasing distance from this the positive electricity diminishes ; and if the resistance of the wire is the same im every part of its length, there exists in the centre an indifferent point, beyond which “the second half of the wire shows itself negativ ely electric, with a tension which increases towards the negative pole. When the resistance of the wire is greater towards one extremity than towards the other, the indifferent point is nearer the same ex- tremity as the greatest resistance. The difference between the electrical tensions at two points in the wire, divided by their mean resistance to conduction, is everywhere constant. This position of equilibrium of*free electricity appears difficult to explain ; for it seems that the negative and positive electricities ought to clear the indifferent pomt and combine. Nor in this respect has any explanation been hitherto given satisfactory and free from all arbitrary hypothesis. The theory now presented offers, as of itself, that explanation :—When a galvanic current commences, the molecules of the surrounding mass of ether abandon the positions of equilibrium which they have hitherto occupied, and pass into new positions ; hence there results an induced current in a neighbouring closed conductor. The molecules which are in a “nonconducting body near are also driven from their positions of equilibrium, and take new ones, although the absence ef conductivity prevents the rise of an induction-current properly so called. ‘The molecules remain in their new positions of equilbriam as long as the active cause (the galvanic current) continues with constant force. The law of the action of an element of the inducing current upon an element of the induced current is expressed by the formule given above. But it is evident that it must be altogether the same M. E. Edlund on the Nature of Electricity. 137 with two elements ds and ds’ in one and the same closed circuit. The galvanic current, then, tends from the commencement to produce a current in a direction opposite to its own. The electromotive force of the pile obstructs this motion. The ether of the conducting wire which unites the two poles is carried by the force of induction to the positive pole, and there collects until its tension is sufficient to overcome the re- sistance opposed by the electromotive force or to surmount the inductive force. It is perfectly evident that the density of the ether must diminish as the distance from the positive pole in- creases. The quantity of ether contamed in the wire being constant, when that ether is conducted towards the positive pole there must result a deficit of «ther at the negative pole ; and this deficit will be equal to the excess at the positive pole. A direct consequence of the preceding considerations is that the algebraic difference between the excess and the deficit must be proportional to the intensity of the current. 6. The Chemical and other related phenomena.—The limits of this memoir do not permit us to give here a complete exposition in detail of the application of the above-mentioned theory to the action of the galvanic current. We can only trace the starting- points of the explanation of the chemical phenomena. We will first call attention to the fact that the theory of induction given in the preceding pages has placed at our disposal a new force in permanent activity as long as the current continues. This force, the magnitude of which is determined by formula (16), tends to carry a molecule of ether, previously at rest, im a direction opposite to that of the current itself. Suppose now the current traversing an electrolytic liquid constituting a chemical combination of two elements p and q, and that, ac- - cording to the ordinary idea adopted by Berzelius and other chemists, p is electropositive, and g electronegative—that is to say (according to our view), that p has an excess and ¢ a deficit of ether. It follows that the molecule p is carried by the current towards the positive pole with a greater force than the molecule g. As this action is effected in every part of the liquid, the latter molecule will even, in pursuance of the Archi- medean principle, endeavour to arrive at the negative pole. If now the force with which the molecules tend in this way to move in epposite directions be greater than their chemical affinity, decomposition will result, and we shall have an excess of the molecules p at the positive pole, and of the molecules g at the - negative pole. In the first part of this memoir we expressed the opinion that the material particles of a liquid can be mechanically carried along with the current, and that in this fact may be seen the 188 M. E. Edlund on the Nature of Electricity. chief cause of the phenomena studied by Wiedemann. But regard must also be had to the current-force expressed by for- mula (16), in virtue of which force the current tends to cause the ether molecules at rest to move in a direction opposite to its own. Now, if these molecules are intimately united with material particles, these latter must be carried along in the same direction. It is possible, therefore, to obtain for the particles in a liquid traversed by a galvanic current a motion in the one direction as well as in the other, since the direction depends upon which force presents the greatest intensity. We think that the phenomena of this category studied by Quincke* may be explained in this way, without having recourse to the action of the free electricity which is found at the surface of the liquid. The circumstance that particles from the negative pole of a voltaic arc are carried to the positive pole, although in consider- ably less quantity than that of the particles which are detached by the current and impelled in the opposite direction, it must also be possible to attribute to the inductive force of the current, understood according to the theory here given. 7. Rotation of the plane of polarization of light under the action of the current.—In order to explain this phenomenon, it has generally been supposed that the material molecules of the transparent body in which the rotation is effected undergo a direct action from the galvanic current, and that this action produces the rotation of the plane of polarization. OC. Neumann, on the contrary, considers that the rotation results from the action exerted upon the ether molecules by Ampére’s molecular currents, which are due to the action of the galvanic current. H[e endeavours to demonstrate that the phenomena in question can be explained by the hypothesis that those molecular currents act upon the ether molecules as if these were electric. The preceding statement upon the nature of electricity shows that, of the two opinions, Neumann’s approaches nearest to the truth. The ether of the transparent body round which the galvanic current passes cannot, under the action of the current, be in the normal state. The ether molecules have changed their posi- tions of equilibrium; and molecular currents of ether are esta- blished, or, if they previously existed, have received a determined direction under the infiuence of the galvanic current. Neumann’s opinion relative to the direct action of the molecular currents upon the molecules of ether is no longer an hypethesis requiring confirmation, but a ¢ruth, if it be true that the phenomena of electricity take place im the ether. Certainly, however, in this explanation we must also have regard to the change in the positions of equilibrium of the «ther particles. * Pogg. Ann. vol. cxiil. p. 513. Foksot a] XXIV. On the Hydrodynamical Theory of Attractive and Repul- sive Forces. By Professor Cuauuis, M.A., LL.D., F.R.S.* T the commencement of the “ New Discussion of the Hy- drodynamical Theory of Magnetism” contained in the Number of the Philosophical Magazine for June, I have enun- ciated the following principles:—(1) That all the active forces in nature are different modes of pressure under different circum- stances of a universal elastic ether, which may be mathematically treated as a continuous substance pressing always proportionally to its density. (2) That all visible and tangible bodies consist of inert spherical atoms of constant magnitudes, held, when un- disturbed, in positions of equilibrium by attractive and repulsive forces, acting according to laws which are referable both to the active pressure of the ether and the passive resistance of the atoms to such pressure due to the constancy of their form and magni- tude. In conformity with these principles the xther at rest is assumed in that theory to be everywhere of the same density ; and I have, besides, supposed the atoms to be so small that even in dense bodies the space they occupy is very small compared with the intervening spaces. These physical principles (which are applied in the above-cited article in the theoretical explanation of a large number of facts both of galvanism and magnetism) will be seen to be partly hy- pothetical and partly inferential. All that relates to the qualities of the ether and the atoms is hypothetical; but what is asserted respecting the dependence of the laws of the physical forces on modes of pressure of the ether must rest on deductions by ma- thematical reasoning from the hypotheses, and can be established by nothing but such reasoning. To account by this deductive process for the modus operandi of forces to which facts of obser- vation are attributed, has been the object of various articles which from time to time I have communicated to the Philosophical Magazine. After giving reconsideration to these theories, and in particular the Hydrodynamical Theory of Magnetism in the June Number, it occurred to me that they might be much elu- cidated by separately exhibiting the principles and processes of the mathematical reasoning which connects the different forces with hydrodynamical pressure ; and accordingly to do this is the purpose of the present communication. It is to be understood that the following discussion has reference to reasoning founded on hypotheses, irrespectively of their being true or false, and that I do not ask any one to accept the hypotheses, but only to give consideration to the mathematical reasoning by which the consequences that result from them are ascertained. It may, * Communicated by the Author. 190 Prof. Challis on the Hydrodynamical Theory of however, be said that if the reasoning be such as cannot be called in question, it may possibly suffice to determine, by the consequences to which it leads, whether or not the hypotheses are true. 1. As it is proposed to account for the physical forces and the laws of their operation by hydrodynamical pressure, it will first of all be necessary to discuss the principles and rules of the ap- plication of mathematics in hydrodynamics. A perfect fluid (and such, by hypothesis, the ether is) may be defined to be one the elementary parts of which possess the properties (1) of beng susceptible of movements which continually change their relative positions, (2) of being separable one from another without as- signable force by the insertion of an indefinitely thin solid parti- tion, (3) of pressing against each other and against any solid substance with which they arein contact. In order that the mo- tions of the fluid and its pressures may be capable of mathema- tical treatment, the following axioms must be conceded :—first, that the directions of the motion in any elementary portion of the fluid are always and everywhere normals to a surface which is geometrically continuous through either a finite or an infi- nitely small extent; secondly, that the motions are consistent with the principle of constancy of mass; thirdly, that the pres- sures of the fluid, together with the action of extraneous forces, are governed by D’Alembert’s Principle. These three axioms being granted, mathematical reasoning founded upon them leads to general differential equations, from the integrals of which may be determined by appropriate treatment the motion and pressure of the fluid under given circumstances. 2. The first axiom has reference to the principle of geome- trical continuity, to which, it is clear, the motions of the fluid must be subject. Calling, for the sake of shortness, the surface to which the directions of the motion are normal ‘* a surface of displacement,” it 1s regarded as an axiom that for each element there isin successive instants such a surface. It is, however, to be considered that a surface of displacement of finite extent may consist of an unlimited number of parts the equations of which are expressed by different functions, but that neither the tan- gent-planes of two contiguous parts at a given instant, nor the tangent-planes of the surfaces of displacement of a given particle in sunee cane instants, can make a finite angie with each other. These conditions of continuity, which are dynamical rather than geometrical, exclude changes per saltum of the directioris of mo- tion with respect both to space and time, forasmuch as such changes could only be effected by infinite forces. 3. Let, therefore, u, v, w be the velocities, resolved in the di- rections of the axes of coordinates, at the point of a surface of Attractive and Repulsive Forces. 191 displacement the coordinates of which at the time? are 2, y, 2 Then, passing from that point to any other indefinitely near on the same surface, the coordinates of which are #+dz, y+dy, 2+dz, the equation u v Ww —-dx+ —-dy+ —dz=0 wi eit, AE Pe will express generally that the motion at cach point is in the igs direction of a normal to the surface, 1S being a factor which makes the left-hand side of this equation a complete differential. Hence, representing that differential by (dr), according to the above- stated axiom we shall have, as well as (dr) =0, also 6(dyr) =0, the symbol 6 having reference to change of the surface of dis- placement of the given element by change of the time and of its position. On account of the independence of the symbols a operation 6 and d, that equation is equivalent to (d.dyr) = But ne TP te HE bet HF ay 4 OF be and because the variation with ed to time has reference to the change of position of the given element, eL=Uop, oys=vol, oe =wol. Hence (aby) =(a. | + Tout eet w|8t) = 0. Consequently the differential, with respect to space, of the quan- tity within the brackets [ ] is zero, and by integration any +e Ewa Re te Be Ga) 4. The reasoning thus far has already been given under the head of Proposition VI. in an article “On the Principles of Hy- drodynamics” in the Philosophical Magazine for January 1851, and more recently in pp. 174 and 175 of the ‘ Principles of Mathematics and Physics.’ It is reproduced here for the pur- pose of drawing an important inference which I had previously overlooked. Before doing so, however, it will be proper to enun- ciate for future use the following general rule respecting the ap- plication of analysis to physical questions. When the funda- mental principles of any department of applied mathematics have been expressed in the form of differential equations, the solutions of the equations are coextensive with the physical con- sequences of the principles ; so that there is no such consequence which the solved equations do not embrace, and no positive 192 Prof. Challis on the Hydrodynamical Theory of analytical result of the solutions which does not correspond to a physical reality. This rule is applied in the following infe- rences from the general equation (a). 5. That equation is plainly equivalent te (= i )= x(¢); whence by integration yr=y,(#)+C, y,(¢) being an arbitrary function of the time, and C an arbitrary quantity independent of ¢. The argument in art. 17 of the communication in the June Number, being conducted so that y(¢).is included in the function vy, dy gives + )=0, and by integration w~=C, an arbitrary quantity not containing ¢. The present argument shows that the func- tion ~w has in fact this character if y(t) be assumed to be zero, but that it may also vary in an arbitrary manner with the time. Now, according to the foregoing rule, this result must be taken into account as well as the other, both being significant; and the inference to be drawn is that, consistently “with the principle of geometrical continuity, there may be ¢wo classes of motions, for one of which the functions y have constant values and the surfaces of displacement have fixed positions in space, and for the other these functions vary with the time, and the surfaces of displacement are continually shifting their positions. Generally, the former is the class of steady motions, and the other that of unsteady or vibratory motions. It should be observed that the actuality of such motions cannot be demonstrated without taking account of the other general equations, and that the foregoing reasoning only shows that their existence would be compatible with the principle of geometrical continuity. 6. To proceed in logical order, it would next be required to investigate mathematically the general differential equation d.pu d.pv. d.pw =m =a ia) Ee . aa . * * . 1 errs dy "az °, (0) which is derived from the principle of constancy of mass, and the three dynamical equations, dp (du dp 5.5% filp af dw pdx 5s eT a) oie (a) Eo 1—(F) ©) which are given by D’Alembert’s Principle; but these investi- gations are so well known that they need not be introdweed here. N.B. The expression udxv+vdy+wdz occurs so freauently that in future it will be designated by [udz]. 7. The reasoning thus far would be the same whether we sup- posed [udz] to be an exact differential, or to become such by Attractive and Repulsive Forces. 193 means of the factor = As there is an analytical distinction be- tween these two cases, according to the before-cited rule there must exist, consistently with the principle of geometrical conti- nuity, a corresponding difference in the actual circumstances of the motion. It is possible to point out such difference by em- ploying the following argument. In case [udx] be an exact differential, the equation [ede] = O is the differential equation of a surface the curvature of which is generally finite, and conti- nuous through at least an indefinitely small extent. Hence it follows, since the normals converge to two focal lines, that the form of the element to which the coordinates x, y, z apply at the time ¢ is undergoing change. The same is the case with respect to any other element, the continual change of form. of identical portions of matter being a general characteristic of a fluid mass in motion. But it is also possible that a mass of fluid may under certain circumstances move in such manner that each ele- ment continues to be of the same form throughout the motion— for instance, if the fluid rotate avout a fixed axis, and the velocity be a function of the distance from the axis. For by the prin- ciple of easy divisibility the fluid may in that case be conceived to be divided into indefinitely thin cylindrical shells, having as their common axis the axis of the motion, the velocity of rota- tion of any shell being at the same time a function of the dis- tance from the axis. Also on the same principle each shell might have, in addition, a motion of translation parallel to the axis, the form of every element of the shell still remaining constant. 8. In articles 18 to 25 of the communication in the June Number I have shown that for the above-mentioned cases of con- -stancy of form of the elements in motion, [udz] is integrable by a factor, and that this analytical circumstance not only proves that such motions are compatible with the principle of geome- trical continuity, but also distinguishes them from all other mo- tions. I have also in the same articles determined the condi- tions under which these motions satisfy the general equations (b) and (c), whence it appears that they must be s¢eady motions. I consider it therefore unnecessary to introduce these investiga- tions here, and shall only remark further on this part of the subject, that the cases of motion for which [udx]| is integrable by a factor are appliedin the hydrodynamical theory of galvanic currents along slender wires. (See arts. 26-40 in the Theory of Galvanism and Magnetism, contained in the June Number.) I proceed now to the discussion of the classes of motion for which [wd] is integrable per se. Phil, Mag. 8. 4. Vol. 44. No, 292. Sept. 1872. O 194 Prof. Challis on the Hydrodynamical Theory of 9. Resuming the aaa e and putting it under the form there will be two cases for consideration: first, that for which is independent of ¢, in which case [wd] may, from what is said in the preceding paragraph, either be an exact differential, or be integrable by a factor; and secondly, that in which wW varies with the time and [wda] is necessarily an exact differential. 10. Taking the case in which y does not contain ¢, we have ay =0, so that (diy)=(t)dt. In order that this result may be consistent with the condition that wp is independent of ¢, we must have y(¢t)=C, an arbitrary constant ; and then, since di may be considered constant, it will follow that (dy), which is the change of yr in passing at a given instant from any point toa contiguous point, is an arbitrary infinitesimal quantity. Being of arbitrary value we may suppose it to vanish, or that (dr)=0. Since this is the differential equation of a surface of displacement, the pre- ceding argument has shown that such a surface can exist, con- sistently with the principle of geometrical continuity, in every case of steady motion, whether [uda] be an exact differential or be integrable by a factor. 11. It will be now proper. to state that in the proposed hydro- dynamical theory of the physical forces, certain of these forces are referable to pressure of the ether in steady motion, while the remainder are accounted for by pressure accompanying its un- steady or vibratory motions. Two classes of forces, known ex- perimentaily, are found to correspond to two kinds of motion of a fiuid which haye been ascertained by the aid of mathematics. The forces which correspond to steady motions of the ether will be first considered. 12. The way in which the particular cases of steady motion for which [udz] is integrable by a factor account for the conduc- tion of galvanic currents along slender wires has already been sufficiently referred to in art. 8 of this communication, and need not be discussed here. 13. The forces which, according to the theory, are asctibable to pressures of the ether in the cases of steady motion for which [udz | is an exact differential, are magnetic, galvanic, and electric attractions and repulsions. Itis assumed to be a necessary con- dition of the existence and maintenance of the appropriate steady motions, that a gradation of atomic density should exist in the interiors of the attracting or repelling substances. In arts. 4 to 9 of the Theory of Magnetism in the June Number I have pro- Attractive and Repulsive Forces. 195 posed a mathematical theory of the generation of steady streams under that condition. 14, Respecting the origination of the gradations of atomic den-. sity, 1t will suffice for my present purpose to say that in galvanism the producing cause appears to be chemical action between dis- similar substances in contact; in magnetism the act of magneti- zing may be supposed to generate a gradation of atomic density which is afterwards maintained, with more or less persistence, by the intrinsic atomic and molecular forces of the magnetized body; and in frictional electricity the friction seems to superin- duce an abnormal state of equilibrium of the atoms of an ex- tremely thin superficial stratum of the electrified substance, together with an interior gradation of its atomic density, depend- ing, as to degree and permanence, on the capacity of its intrinsic atomic and molecular forces to retain the superficial atoms in the abnormal positions. 15. Now, in whatever way steady streams are generated, ac- cording to hydrodynamics they will be accompanied by variations of the density and velocity of the fluid from point to point of space, while the density and velocity at any given point and the direction of the velocity will be constant. Hence it evidently follows that a small spherical atom, immersed in the ether under these circumstances, will be differently pressed at different points owing both to the motion and to the variation of density of the fluid, and consequently that the atom will in general be acted upon by an accelerative force. The exact mode of this action is now to be investigated. The following mathematical reasoning employed for this purpose is almost exactly the same as that I have given in the solution of Example VIII. in p. 3138 of the ‘ Principles of Mathematics and Physics.’ But as that reasoning is not directly referred to in the Theory of Magnetism in the June Number, and [ have reason to think that on account of this omission some difficulty may be felt in following the arguments, I propose to reproduce it here. 16. The investigation being restricted to motion for which {uda] is an exact differential, the equations (b) and (c) give, by the usual process, . V? a? Nap. log p+ oa a tit) =0;3 avd as the motion is steady, se which is equal to = ds, va- nishes. Since also the fluidis by hypothesis of unlimited extent, there will be distant points at which V=O and the density p is that which the fluid has in its undisturbed state. Calling this 02 196 Prof. Challis on the Hydrodynamical Theory of density po, we shall have a? Nap. log p9+f(¢)=0. Consequently v2 Pp = Poe 2”, ° e e e e e ° (d) which is an exact equation, applying to the fluid at every point of space it occupies, provided it is acted upon by no extraneous force. It will be seen that I have not here substituted the con- stant a! for a, as in art. 8 of the Theory of Magnetism, the reason being that, according to the hydrodynamical principles which I have long maintained, the substitution is not required when the motion is steady. 17. Respecting the above expression for p, it is to be ob- served that it not only applies to the whole of the fluid in steady motion, but applies also whether the steady motion be simple or be compounded of two or more steady motions. For, according to hydrodynamics, such motions may coexist, and the resultant is consequently steady motion. (See ‘ Principles of Mathematics and Physics,’ pp. 242 & 243.) As V will always be very small compared with a, instead of equation (d) we may use 7 v2 Pisaho ds a2) 18. Lect us conceive, at first, the spherical atom to be fixed, and to be acted upon by a stream of the eether in steady motion. Then if the lines of motion were parallel, the distribution of density on the surface of the sphere, due to the sphere’s reaction, would be symmetrical with respect to a plane through its centre perpendicular to the direction of the stream. (for proofs of this proposition I may refer to an article in the Philosophical Maga- zine for November 1859 (p. 823), and to the argument con- cluded in p. 802 of the ‘ Principles of Mathematics &c.’) Con- sidering that the atom is of extremely small dimensions, and consequently that the lines of motion in the very slender portion of fluid incident upon it must originally be very nearly parallel, it may be admitted that the above-mentioned symmetrical dis- tribution of density will not be sensibly affected by their con- vergency or divergency. Thus, so far as regards any modification of the pressure arising from the reaction of the atom, we may suppose that no accelerative action upon the atom is thereby pro- duced. There remains only the accelerative force resulting from that variation of pressure from point to point of the spherical surface, which is due exclusively to the steady motion, and would be sensibly the same at the same points if the motion were not interfered with by the reaction of the atom. 19. Suppose now that trajectory to the surfaces of equal pres sure to be drawn the direction of which passes through the Attractive and Repulsive Forces. 197 centre of the sphere, and let s be any length along this line reckoned from a given point on it as origin. The sphere being by hypothesis extremely small, it may be assumed, in accordance with what is argued above, that for all points of any transverse circular area the centre of which is on the trajectory, and the radius not less than the radiusof thesphere, with sufficient approximation p=f(s). Let s, be the value of s corresponding to the sphere’s centre, and let @ be the angle which any radius of the sphere makes with the trajectory, so reckoned that for a point of the surface s=s,—O cos @, 6 being the radius. Then for any such point p=f(s,—6 cos 0) =f(s,} —b cos Of"(s,) very nearly, the remaining terms being omitted because the variation of p through the small extent of the sphere’s diameter maybe assumed, with sufficient approximation, to be uniform. Accordingly the whole pressure on the sphere estimated in the positive direction of s is 2m | a°pb? sin 0 cos 0 d0, from 0=0 to =m. This integral, on substituting the above value of p, will be found to be ous f'(s). Hence, A being the density : the sphere, the accelerative force is == f(s). If p, and V, be the density and velocity corre- sponding to the centre of the sphere, pPi=f(5)) = Po (a ras Hy and f'(s;) = — = Ao i Hence, by substituting for f/(s,), the expression for the accelera- tive force becomes This result proves that the accelerative action on the fixed sphere has a constant ratio to the acceleration of the fluid where the sphere is situated, and is in the same direction. The direction is therefore positwe or negative according as p decreases or in- creases, or according as V, increases or fae eases as Ss creases. 20. If the sphere, mmistend of being fixed, moved uniformly in a given direction, the accelerative action of the fluid upon it in any position would still have the same constant ratio to the ac- celeration of the fluid in the same position. For if the uniform motion be impressed in the contrary direction both on the fluid and the sphere, the latter will be reduced to rest, and the rela- 198 Prof. Challis on the Hydrodynamical Theory of tive action will not be altered; and as under these circumstances a uniform stream is incident on the sphere at rest, from what has already been said in art. 18, no change in the accelerative action of the steady stream on the sphere is thereby produced. 21. If, however, the sphere be free to move in obedience to the pressure of a steady stream, it will in general be continually accelerated, and the acceleration will give rise to resistance due to the inertia of the surrounding fluid, which will in turn be impelled by the acceleration of the sphere. The amount of this retardation may be calculated just as in Poisson’s solution of the resistance of the air to a ball-pendulum. Hence it follows, if 2 | > be the actual acceleration of the sphere, that the retarding 2 force is — £. = (Principles &e. p. 266), and consequently RA. di? that DiS; Pp NilV, 4. fo CS dia OA nis, 2k Y de Therefore d?s, eee wae V dV, dis = Ap. eds, It thus appears that, whether the atom be fixed or moveable, its acceleration by the pressure of the fluid in steady motion has a constant ratio to the acceleration of the fluid where the atom is situated. It may be observed that the acceleration is inde- pendent of the magnitude of the atom. 22. This result furnishes a general rule for ascertaining the mode and the direction of the motive action of magnetic and galvanic currents. It is required for that purpose to deduce from the given circumstances under which the steady motion, whether simple or composite, is produced, the values of p and V expressed. as functions of coordinates, and also the courses of the trajectories to the surfaces of equal pressure. When by means of these deductions the accelerative force of the fluid is determimed at each point as to magnitude and direction, in virtue of the foregoing equation both the magnitude and direction of the ac- celerative action on any atom are also determined. In illustra- tion of this conclusion it may be added that by the above-men- tioned trajectories the theory accounts for the lines of magnetic force, the courses of which are exhibited by the distribution and arrangement of iron filings submitted to the attraction ofa mag- netized bar. it may now be stated that the many theoretical explanations of magnetic and galvanic phenomena given in the article in the June Number all depend on principles the consequences of Attractive and Repulsive Forces. 199 which, as deduced mathematically, have thus far been discussed ; and I hope that this supplementary treatment of the d@ priori arguments may serve to make the explanations more intelligible and more worthy of acceptance. I proceed to the dynamical action of the unsteady motions of the ether. 23. This part of the inquiry is distinguished from that which precedes by the circumstance that at each point the velocity and its direction both vary with the time, or, if not both, that the ve- locity varies. (In the ‘Principles of Mathematics,’ p. 218, an instance of composite vibratory motion occurs in which the di- rection of the motion is constant.) Hence in the subsequent application of the general equation (a) it is assumed that the motion is not steady, and that consequently [udz] is always and everywhere an exact differential (see art. 7). Accordingly, as may vary with ¢, we may now suppose the arbitrary function v(¢) in that equation to be included in Yr; and then putting re- spectively “e = for wu, v, w, we have dr? a +t) = ER lets 1 ON ere (Cc) An important inference is next to be drawn from this equation antecedently to making use of the other general equations. I have already given the reasoning proper for this purpose under Proposition VII. in the Philosophical Magazine for March 1851, and in pp. 186-188 of the before-cited volume. It is repeated here with certain modifications, which, I think, will have the effect of exhibiting more completely the logic of the argument. 24. Since A(dvr)= [ude], and by hypothesis the right-hand side of this equality is an exact differential, it follows that A 1s a function of yr and ¢. Conceive a line to be drawn at a given instant in the directions of the motions of the particles through which it passes, and let 2, y, z be the coordinates of a point the distance of which measured at the given instant along that line from a given point of the same is s, Then, V being the velocity at the point wyz, (ay) _ ayy da, dyp dy , chp de ds dx ds~ dy ds dz ds ale yi ON dy w ide Wy da VV Sondepianl = (uw? +0? + w?) = 200. Prof. Challis on the Hydrodynamical Theory of But by the equation (e), db V? a+ “dt a new dr 3 Hence, substituting A ea for V, Is Introducing now the condition that A is a function of and f, this equation must admit of an integral of the form W=/(s, 2), in which s is, by definition, the length of a trajectory of surfaces of displacement. Now we may suppose that at the time 7 one extremity of the trajectory is on a certain given surface, and the other on the undetermined surface which passes through the point whose coordinates at the time Zz are z, y, z. Accordingly the above value of ~% may be taken to be general as to space for the time 7, so that its variation with respect to space gives for any position :— 25. Since (vr) is the variation of the function 4 in passing at the given time from the poimt zyz to any contiguous point, we may Inguire, as in the Calculus of Variations, under what conditions that function may have a maximum or minimum ~ s * d. t . . value. Let, therefore, (6v-)=0. Then, since = , which is $ py V equal to = or >> may be supposed not to vanish, the sole con- BY dition is that (6és)=0. This result signifies that in the ease of maximum or minimum, contiguous trajectories, intercepted be- tween two surfaces of displacement separated by an arbitrary interval, are of the same length. But this cannot be the ease unless the trajectories are straight lines and the motion conse- quently rectilmear. We have thus been led to an indication of rectilinear motion by arguing solely from the general equation (e), which was derived from the principle of geometrical conti- nuity. It is to be observed that this inference has been drawn antecedently to any supposition as to the mode of putting the fluid in motion, and that it rests on the abstract assumption that there is a certain form of the function w& which gives it a maxi- mum or minimum value. Hence, if it be urged that the indi- cated rectilinear motion is such as might take place if the velo- city were a function of the distance from a centre or from a fixed plane, the reply is that this interpretation is inadmissible be- Attractive and Repulsive Forces. 201 cause these rectilinear motions are produced under arbitrary conditions. Besides, it does not appear that for such motions vr has the character of a maximum or minimum. The validity of the foregoing argument is confirmed by the fact, which I think I have on previous occasions sufficiently certified, that the two cases of rectilinear motion just mentioned cannot be mathe- matically treated with success till the circumstances and laws of the rectilinear motion now under consideration have been as- certained. 26. It is further to be noticed that, as the indication of recti- linear motion was arrived at by empioying one general equation without reference to the other two, the result is not of general application, and we are not compelled to infer from it that the motion is always and everywhere rectilinear. Yet, according to the rule already laid down, the indication must be significant, and cannot without error be left out of consideration on proceed- ing to draw inferences from the other two equations. Accord- ingly I propose the following course of reasoning. As the motion is not exclusively rectilinear, let it be supposed to take place in part along a straight line which relatively to the density and the rest of the motion is an azis. This hypothesis may be analytically expressed by first supposing the axis of the motion to coincide with the axis of z, and then assuming that (dy) ==(d. fo) =udz +vdy + waz, f being a function of 2 and y only, and ¢ a function of z and ¢ only. The complete exhibition of the present argument would require to be given next an investigation of the consequences to which this supposition leads when the second and third general equations are taken into account. As this investigation is too long for msertion here, I can only refer to it as given in the Phi- losophical Magazine for August 1862, and in fuller detail in the proofs of Propositions XI. to XVII. contained in pages 201-240 of the volume I have so frequently cited already. The researches in this portion of my work, which are of a peculiar and novel character, lead to certain results which, according to my views, are indispensable for the progress of analytical physics. This remark will receive illustration from the use I now proceed to make of these results. 27. The mathematical consequences that are deduced from the above hypothesis relative to the composition of the differen- tial (dr), after taking into account the second and third gencral equations, are found to involve no contradictions, are definite and unique as regards both the motion and the density of the fluid, and account at once for certain observed facts which are due to essential properties of the fluid apart from arbitrary con- ditions, such as the fact of uniform propagation, and that of co- 202 Prof. Challis on the Hydrodynamical Theory of existence of small vibrations. In the course of the reasoning it is shown (p. 202) that, corresponding to motion along a recti- linear axis, the function fp has a maximum value, which is con- firmatory of the antecedent argument in art. 25. As the inves- tigation conducts to motions of a definite kind prior to any sup- position as to the mode of disturbing the fluid, these motions may be called spontaneous, to di stinewish them from those that result from arbitrary disturbances. The chief characteristic of these spontaneous motions is that they are vibratory, and that the directions of the vibrations are partly parallel and partly transverse to the axes of motion. Moreover the investigation shows, to whatever order of terms it be carried, that the vibra- tory motion, whether direct or transverse, is such that the move- ment of a particle in any direction is just equal to its movement in the opposite direction, so that there is no permanent motion of translation. This agrees with the principle stated in art. 10 of the Hydrodynamical Theory of Magnetism, according to which there can on the whole be no transfer of fluid across an unlimited plane having any position in a mass of fluid of unli- mited extent. As in steady motions this necessary condition is satisfied by movements in complete circuits (see art. 10 above cited), so in unsteady motions it is satisfied by vibrations such as those above described; and hence it seems possible to per- celve an @ priori reason for the spontaneity of these vibrations. 28. In my researches on the Undulatory Theory of Light, I have shown that those phenomena which depend only on properties of the medium in which the light is generated, as especially the characteristics of a polarized ray, are readily explained by the laws of the spontaneous vibrations. Also by the coexistence and combination of such vibrations we may account for a beam of light of very small transverse section being transmitted to an unlimited distance without undergoing lateral dispersion, and for the limited lateral divergence of rays in phenomena of diffrac- tion. But the phenomena which depend besides on the consti- tution of visible and tangible substances are referred by the theory to mutual action between the vibrations of the ether and the atomsof the substance. Im this respect light isto be ranked with the physical forces, and its dynamical action is equally to be ascribed to pressure of the ether. In treating mathemati- cally of this action, I have supposed the etherial waves to be composite in such manner that the transverse vibrations are neutralized. This supposition requires that a*, the exponent of the elastic force of the medium, should be changed into another constant a’?, as is done, for a different reason, in the usual mode of treating hydredynamical questions. Excepting what relates to this difference, the reasoning I employ in the dynamics of the Attractive and Repulsive Forces. 203 vibrations of an elastic fluid agrees, do the first order of small quantities, with that which is commonly adopted. For instance, I solve the problem of the resistance of the air to the vibrations of a ball-pendulum exactly as Poisson has done. Also the re- verse problem of the acceleration of a ball by vibrations of the air, which is more to my present purpose, I have solved to the same approximation in an analogous manner. From the solu- tion of the latter problem it appears that, so far as is indicated by the first approximation, etherial waves produce vibratory motions of the atoms without permanent motion of translation. The impression of such vibrations on the atoms of nerves of the eye may be considered to be the proximate cause of the sensation of hght. 29. In order, therefore, to determine whether the etherial vibrations are capable of giving to atoms a permanent motion of translation, which is a question of essential importance in the proposed theory of the physical forces, it 1s necessary to proceed to the second approximation. The obvious way of doing this would seem to be to start from the first approximation, and then make use of it, according to the usual rules, in advancing to the second. But this course is liable to the objection that it does not differ, except in having a! in the place of a, from that which would be proper if it were unnecessary to take account of the effect of the spontaneous movements. Having, in fact, succeeded in overcoming the mathematical difficulty of effecting a second approximation by this means, I have ascertained that the solution contains terms of indefinite increase, whence it must be con- cluded that the logic of the process is somewhere at fault. The failure may, I think, be accounted for as follows. In the first approximation the effect of spontaneous motion is included by assuming that the actual vibrations result from an unlimited number of the spontaneous vibrations so combined as to neu- tralize the transverse vibrations ; and this assumption is allowable for a first approximation on the principle of the coexistence of small motions. But this principle does not extend beyond the first approximation ; and consequently, on proceeding to the second, additional steps are required for including the influence of the spontaneous movements. 30. Both in this Magazine and in my work on the Mathema- tical Principles of Physics, 1 have in various ways attempted to solve to the second approximation the problem of the motion of a small sphere acted upon by the vibrations of an elastic fluid. But I must confess that, owing to the difficulty of including the effect of the spontaneous vibrations, my efforts have been only partially successful. The arguments employed for this purpose in pp. 439-455 and in pp. 490-498 of the above-mentioned 204 Prof. Challis on the Hydrodynamical Theory of work involve two unknown constants H, and H,, for which no analytical expressions are obtained, and their values are conse- guently left undetermined. On this account the theories which attribute the forces of heat, molecular attraction, and gravity to action on the atoms by pressure of the ether in vibration are incomplete. Recently, however, a different course of reasoning has occurred to me, which, although it does not directly meet the difficulties of the second approximation, seems to give an intel- heible account of the way in which vibrations of an elastic fluid are capable of producing an accelerated motion of translation of a small sphere. This new process I shall now endeavour to explain. 31. Supposing at first the smatl sphere to be fixed, let a series of plane-undulations be incident upon it in a given direction. Then, if a line of abscissee (2) be drawn in that direction through the centre of the sphere, it is evident that the whole of the mo- tion and condensation will be symmetrical with respect to this line as an axis, and that the condensation (c) on the surface of the sphere will be a function of z and ¢. We may therefore make the general assumption that c=o,f(z, t), and take a, to be the condensation at the time ¢ in the plane perpendicular to the axis through the centre of the sphere, so far as it is unaf- fected by the disturbance of the motion by the reaction of the sphere. (I have reason from previous researches to say that throughout this plane, and therefore where it cuts the surface of the sphere, the condensation has that same value o,.) The un- duiations are supposed to be incident in the positive direction of 2. 32. Now there are three circumstances which determine the distribution of condensation on the surface of the sphere: first, the reaction of the sphere against the incident vibrations causes a certain amount of condensation, which is so much the smaller as the sphere is smaller, and for spheres the diameters of which are very small compared with dis extremely small; secondly, after taking account of the condensation produced by this reaction, the proper condensation of the incident undulations is not zm- mediately disturbed, and is therefore, ceteris paribus, the same at the surface of the sphere that it would have been at the same points if the sphere had not been there; but, thirdly, the distri- bution of the condensation is modified by the circumstance that the undulations are composed of spontaneous direct and trans- yerse vibrations, in consequence of which, when they are dis- turbed by incidence on the sphere, /ateral action is brought into play. The kind of effect thence resulting may be conceived of as follows. I1f undulations of very small breadth were incident on a very large sphere, the condensations which reach the further Attractive and Repulsive Forces. | 205 half of the surface would be much diminished by reason of their limited lateral divergence on being transmitted beyond the first half. In extreme cases a portion of the fluid in contact with the second hemispherical surface might be altogether undisturbed. On the other hand, if waves of large breadth were incident ona small sphere, the condensations might become by lateral diver- gence greater on the second half surface than on the first, because the conditions of the motion would approximate to those of spontaneous motions along an axis, in which the condensation corresponding to a given velocity is greater than in plane- com- posite waves in the ratio of a’ to a®. Accordingly, so far as the action of the spontaneous vibrations takes effect, the condensa- tion on the surface might either decrease or increase as x is greater; but in the actual physical circumstances of the ether and the atoms the gradation must always be extremely small ; otherwise, by reason of the vast elastic force of the ether, the acceleration of the atom would exceed the amount which expe- riment and observation appear to indicate. 33. This being understood, let @ be the angle which any radius makes with the part of the axis on the negative side of the sphere’s centre, so that, if w, be the abscissa of the centre, x=2,—bceos0, b being the radius of the sphere. Also let p= a"’p=a'1+oc). Then we have with sufficient approximation G—G, jf, 1)—7o,/(v,—0 cos 0, t) =o, f(z, 1) —o f(a, t)b cos 0, because, from what is said above, the value of f'(x, ¢) must be very small and very nearly constant. Consequently the whole pressure on the sphere estimated in the positive direction is {2aal?ob sin 0cos @d0, from 0=0 to =m. On substituting the above value of o this integral will be found to be 3/2 ens C, fia and consequently, if A he the ratio of the density of the sphere to that of the ether, the accelerative force = — agi 71 fi (oa which is positive if f'(z, ¢) is 1 is, if the condensa- tion decreases as x is greater. 34. With respect to the composition of the function f, so far as it depends on the second of the causes of distribution of con- densation on the surface of the sphere mentioned in art. 82, it will contain only periodic terms, because the action of this cause is periodic. In fact it may be shown, just as in art. 19, that 206 Prof. Challis on the Hydrodynamical Theory of the acceleration of the sphere by the proper condensation of the undulation has a constant ratio to the acceleration of the fluid where the sphere is situated. Now, since the fluid is just as much accelerated in the condensed as in the rarefied parts of the wave, the positive and negative velocities bemg exactly equal (art. 27), it follows that the sphere, not being of variable den- sity like the fluid, is acted upon by greater accelerative forces when in the condensed part of a wave than when it is in the rarefied part. Since, however, for each part the posztive accele- rative forces are exactly equal to the negative, there is no residual accelerative action in either direction, and therefore no tendency to produce permanent translation. 35. I have ascertained by previous researches that the con- densation due to the reaction of the sphere is, to the first ap- proximation, so distributed that at each instant there is as much condensation on one half of the surface as rarefaction on the other half, and that they are similarly distributed about the axis. Also the variation of condensation ‘at any given point of the surface follows the law of the incident undulations, so that the resulting accelerative action on the atom is periodic. When, however, it is considered that the reaction due to the incidence of the con- densed portion of a wave must be greater than that due to the rarefied portion, quantities of the second order being taken into account, it will be seen that the accelerative action in the one case is not exactly compensated for by that in the other, and that there may be a residual action tending to produce permanent transfer. The effect will be extremely small on account of the very small condensations produced by the reaction, and may be considered to be taken into account by the process about to be applied to the distribution of density due to the third cause. 06. The law of distribution due to the third cause is inde- pendent of the time, being determined by the relative magni- tudes of b and X, the breadth of the undulations, or it may be by Xonly. Hence, omitting periodic terms contained in f! (2, 2), which do not apply in the present research, and assuming, for reasons already given, that this function is equal to an unknown constant H, we obtain d’x, — a?’o A Seah Paucar At another epoch, and for a different value of the condensation, we might have dn! ao! — iia oan me : for although the epoch be different, dt may be assumed to be Attractive and Repulsive Forces. 207 - the same. Consequently GG ON ae i ee iy ROL ss For taking the next step in the argument reference is to be made to a law already admitted (art. 27), according to which the vi- brations of an unlimited elastic fluid must be such that for every acceleration and movement of a particle in a given direction there must be an equal acceleration and movement of the same in the opposite direction. Let therefore o, and o/ be conden- sations corresponding to movements so related. ‘Then we shall have (o,+ oa) . ado; di aualtdo} ~ (l+o)dx~ (l+o/)dx Consequently deo, i ola) x8 0 (+o )de “ Afe)ar or d.(o,+¢/)+d.o0/=0. Hence, by integration, o,+0/+e,0/=0, no arbitrary constant being added, because plainly o, and o/ must vanish together. This result shows that o, and o/ must be one positive and the other negative. Let o/ be negative, so that it belongs to the rarefied portion of a wave. Then, since o/=— mee apart from sign o/ is less than o; which belongs i to the condensed portion; as plainly should bethe case. Also, from the above equation, 2) Maa a fiz a, +0, =—00,= J =o/? nearl l+o, ea rad y: Therefore GQ (Git Oy) ae gel Oe iia ee This equation gives the residual acceleration of the atom when the actions upon it at any two corresponding positions in the condensed and rarefied portions of an undulation are taken into account simultaneously ; whence it may be inferred that the total condensations and rarefactions accompanying every com- plete vibration of the fluid backwards and forwards produce on the whole an acceleration of the sphere in the direction of the propagation of the waves if H be negative, and in the opposite direction if that quantity be positive. These effects correspond respectively to repulsive and attractive forces. 2 Oo)". 208 Prof. Challis on the Hydrodynamical Theory of The value of o, at any time ¢ at a given position being ex- I ae + 2) we shall have us (Ana't t= 5 (1—eos("5" +20)), 12 showing that together with a periodic part the force — O, pressed by the function p sin( 2 has a constant part, which is proper for giving to the sphere a constantly accelerated motion. 37. If the sphere, instead of being fixed, were free to move in obedience to the accelerative force, the acceleration of its motion would give rise to resistance from the inertia of the medium ; but it might be shown, just as in the case of acceleration of a sphere by fluid in steady motion, that the only effect would be to diminish the acceleration in a certain constant ratio. 38. If the series of incident waves be propagated from a centre, ~“, as is known, varies inversely as the distance from the centre, and therefore y* and the accelerative force would vary inversely as the square of the distance, in agreement with the law of gravity. Since it is known by experience that gravity accele- rates all atoms equally, in applying the foregoing formula to account for the laws of gravity, it must be supposed either that all atoms are of the same size, or that, for vibrations proper for producing the observed effects of gravitation, the factor H is in- dependent of the magnitudes of the atoms. The latter suppo- sition is, I think, more likely to be true than the other. 39. If the value of o, be expressed by the sum of any number 27a t ‘3 r of terms such as pu sin ( +c), we should have 2 op= 34 | + periodic terms ; from which it follows that the whole acceleration is the sum of the accelerations due to the separate terms. In the proofs of Propositions XV. to XVII. contained in pp. 225-239 of the ‘Principles of Mathematics,’ I have demonstrated that those condensations in different sets of vibrations which correspond to non-periodic terms of the second order may coexist ; so that the results obtained by extending the investigation to cases of the propagation of different sets in different directions in space ac- count generally for the coexistence of all attractive and repulsive forces which are referable to vibrations of the ether. 40. The phenomena of light indicate the existence of an un- limited number of coexistent eetherial vibrations for which 2» has every gradation of value within certain limits, and make it pro- Attractive and Repulsive Forces. 209 bable that beyond these limits others exist not recognizable by the power of vision. According to the hydrodynamical views I maintain, the special form of the simple vibration and the values of X result spontaneously from a disturbance without being de- termined by the particular character of the disturbance (see arts. 13-15 in the Theory of Magnetism, June Number). Of all orders of vibrations those may be presumed to have the least values of X which emanate from individual atoms, and are due to the aggregate of reactions at their surfaces consequent upon the incidence of vibrations from a]l surrounding quarters. According to a foregoing argument (art. 32), it may be assumed that, for undulations of this order incident on an atom, H will be a negative quantity, and consequently that any given atom is always repulsive towards surroundmg atoms. ‘This is the theory of the force I call atomic repulsion, which I consider to be the same as the repulsion of heat. 41. The vibrations emanating from a vast number of atoms constituting a molecule may be conceived to produce by their com- position vibrations of another order, in which the characters of the component vibrations are obliterated and the values of A are much larger. If we may suppose that for vibrations of this order H has a positive value, we shall be able to account for a molecular attraction acting so as to control at the boundaries of substances the atomic repulsion, and thus have the effect of maintaining the atoms, both superficial and interior, in positions of equilibrium. Assuming that H may have both a negative and a positive value, we might infer that for certain values of that quantity either vanishes or is very small. Possibly these may be the values for light-undulations, which seem to possess vibratory rather than translatory power. The whole theory, however, of attractive and repulsive forces, regarded as due to vibrations of the ether, is incomplete for want of an @ priori de- termination of the composition and value of the quantity H. 42. The composite class of vibrations to which the theory ascribes molecular attraction must, by the mere effect of separa- tion caused by propagation to a great distance, be resolved into the component primitive vibrations, which will again act repul- sively, and require to be controlled by another order of attrac- tion-vibrations, and so on till we come to the attraction-vibra tions of gravity. Moreover, as it is impossible to account for the stability of the general system of stars, or of systems of stars which constitute resolved nebule, if the individuals simply attract each other by the force of gravity, it seems reasonable to suppose that the gravity-vibrations may in like manner be re- solved by propagation to vast distances into repulsive-compo- nents. In this manner neighbouring stars would be mutually Phil, Mag. 8. 4. Vol. 44, No. 292. Sept. 1872. le 210 Dr. H. Hudson on Wave-Theories of repellent, while the whole stellar system might be kept together by a still higher order of attraction-vibrations resulting from composition of the vibrations from all the individual stars. This theory would receive confirmation if observation should eventu- ally decide that the proper motions of stars are vibratory. I have now adverted to the more essential parts of the theories of all the physical forces, and have endeavoured to account for their modes of action by mathematical arguments founded on the hypothesis that all the forces and their laws are ascribable to pressures of the ether. The extent and comparative facility of the applications of the deductions from this hypothesis im ac- counting for observed facts and laws seem to justify the conclu- sion that it is (to adopt an expression employed by Whewell in his ‘ Inductive Sciences’) “ the appropriate idea” of Physics. Cambridge, July 24, 1872. XXV. On Wave-Theories of Light, Heat, and Hlectricity. By Henry Hunson, M@.D., MRAZ HE withering infivence which the authority of a great name exercises over the views of men of science is perhaps no- where so strongly marked as in the theory of optics. If the genius of Fresnel had not arisen to develope the views of our own Young (to whom we owe not only the idea of “ transversal vibrations” but also the grand conception of the “ interference of light ’’), the emission-theory of the illustrious Newton might have continued much longer to check the progress of true science. Although the undulatory y theory may he said now to be com- peel triumphant, it must still be admitted that there remain certain phenomena which require explanation, and I have long thought that there is ene very weak point in the physical con- ceptions upon which the wave-theory has been founded. Huyghens (in order to explain the phenomena of double re- fraction) assumed the existence of a second vibrating medium, consisting of the ether and molecules of matter conjointly ; and Young as well as other eminent philosophers have adopted this view. This assumption is, I believe, erroneous. We know that waves of sound in our atmosphere are 10,000 times as long as the waves of light, and their velocity of propagation about 850,000 times less; and even when air has been raised to a temperature at which waves of red light are propagated from matter, the velocity of sound-waves is only increased to about i Communicated by the Author, having been read im Section A. of the British Association, at their Meeting at Liverpool (1870). es Light, Heat, and Electricity. 211 double what it was at zero Centigrade. ven their velocity through glass is 55,000 times less than the speed of etherial undulations, and the extreme slowness of change of temperature in the ‘conduction of heat” (as contrasted with the rapidity with which the vibrations of the ether exhaust themselves, be- coming insensible almost instantaneously when the action of the exciting cause ceases) marks distinctly the essential difference between molecular and etherial vibrations. It appears to me, therefore, a very crude hypothesis to imagine a combination of eetherio-molecular vibrations as accounting for the very minute difference in the retardation of doubly refracted rays in crystals. Among the known facts which remain unexplained by Fres- nel’s theory the following are prominent :— Ist. That no interference can take place between two rays originally polarized in perpendicular planes, even when they have been brought into the same plane of polarization. 2nd. The rings from thin plates (observed by Arago) when viewed through Iceland spar with its principal section parallel oR perpendicular to the plane of incidence—the result being that the light of both the transmitted and the reflected rings is wholly polarized in the plane of incidence, the colours being comple- mentary and their intensities perfectly equal. drd. That, in common light, in order to explain the pheno- mena of interference, it is necessary to admit a sudden transition ( per saltum) from one system of waves to another, in which the vibrations are altogether different and have no apparent con- nexion. Ath. The case of double refraction in crystals of quartz ap- pears to afford another example of the inadequacy of the theory of a system of waves propagated through a single elastic medium, Inasmuch as it presents a total breach of continuity in the transi- tion from the velocity of the one ray to that of the other. 5th. The phenomena of “absorption,” which will, I believe, — be ultimately explained through the principle of interference. We know, from the aberration of the light of the fixed stars, that “the ether” encompassing our earth does not participate in its motion ; and therefore it is only the “ uxcuss”’ of ether, associated with the molecules cr atoms of matter, which is carried along with it in-its motion through space; and we can have no doubt with respect to the sameness of the density and elasticity of the ether throughout space, inasmuch as the velocity of the propagation of light (which depends on them) is the same what- ever be its origin. How, then, can we explain such theoretical difficulties as I have alluded to? I believe it will be necessary to consider what we term the ether as consisting of two media, each possessed of Pe saamneupacnemcatens sunk REGEN NN Sonam 212 Dr. H. Hudson on Wave-Theories of equal and enormous self-repulsion or elasticity and both existing in equal quantities throughout space, whose vibrations take place in perpendicular planes, the two media being mutually indiffer- ent, neither attracting nor repelling. Common light, therefore, will consist of waves (equal in every respect and undistinguishable by our organs of vision) in each medium, the vibrations being in a plane perpendicular to the direction of the wave’s progress. But the reflected ray in the one medium will, I conceive, present the qualities of the refracted ray in the other; and it is manifestly impossible, no matter how perfectly similar they may appear to be, that any interference can take place between waves thus propagated independently in different media. By this slight modification of the physical conception on which the wave-theory is founded I believe every difficulty will be re- moved, and the cause of the equal quantities of polarized light obtained by reflection and refraction is obvious. I think we have a proof of the existence of two distinct media in the ether in the fact that the “ordinary ” and “extraordinary” rays (when produced by two similar plates of the same crystal in rectangular positions) will interfere, whereas the two rays of the same denomination (even when brought into the same plane) are incapable of interference. The reason is obvious if the two or- dinary rays (thus produced) are in different media, while the ordinary ray from one plate and the extraordinary ray from the other are in the same medium. As a further test of the hypo- thesis, I beg to suggest an attempt, experimentally, to make the “ordinary refracted” ray (through Iceland spar) show any indi- cations of interference with the apparently similarly polarized ray obtained by total reflection. As I have already said, I believe they are produced by vibrations in different media, and must uniformly increase the illumination (instead of producing dark- ness or fringes), no matter how either ray may be retarded in its path. With regard to calorific waves, I believe that they are due to those vibrations of the ether which take place in the direction of the wave’s progress, and, as such, are totally distinct from lu- miniferous undulations. In reference to luminiferous (or transversal) vibrations, Fres- nel has shown that, “in such a medium as the ether, the force which resists the approach of two strata is much greater than that which opposes their sliding on one another.” Poisson in his researches (1830) points out that, according to his theory, there will be two waves, the vibrations in one being “in the direction of propagation and attended with dilatations proportional to the absolute velocity of the molecules” (this I therefore look upon Laight, Heat, and Electricity. 213 as the “calorific wave”), “the vibrations of the second wave being transversal and unaccompanied by any change of density in the medium.” The latter is therefore my “ luminiferous wave.” Again, according to Cauchy’s investigations, “a ray entering any medinm will be subdivided into three rays, and, when the elasticity of the ether in this medium is the same in all direc- tions, the three will havea common direction and two of them a common velocity, being thus reduced to two, viz. a single ray and a double ray—the vibrations of the former [my calorific ray] being in the direction of propagation of the wave, and those of the double ray transversal,’ constituting (on my view) common or unpolarized light. It may be observed also that Fresnel’s theory admits that the vibrations of polarized light may be either parallel or perpendi- cular to the plane of polarization; but, finding that the vibra- tions of the “ordinary ray” (by double refraction) are perpen- dicular to the principal plane of the crystal, which is the plane of its polarization also, he drew the conclusion that the vibrations of all polarized light must be perpendicular to the plane of pola- rization. On the other hand, Cauchy’s researches led him to the conclusion that the vibrations of a polarized ray are in the plane of its polarization. ‘This apparent difference in the results of these two eminent analysts may, I should hope, be reconciled (on my view) by supposing that Cauchy’s investigations refer to the “ordinary ray” polarized by reflection ; for its vibrations I consider to be in the plane of its polarization. If I am right, therefore, [ think we shall have obtained a most satisfactory general accordance between the able researches of the three great French mathematicians. Although the disturbance of the ether associated with the molecules of a body, by a luminiferous wave, is very trifling, I believe nevertheless that it 1s to this cause we must look for the explanation of the phenomena of phosphorescence and also of fluorescence. Molecular vibrations being, as we know, compa- ratively very sluggish, are required to maintain the contiuance of the etherial (phosphorescent) vibrations, which must other- wise be expected to subside almost instantaneously (on the withdrawal of the exciting cause) if not sustained by the reaction of the associated molecules, in like manner as heat-waves (in the conduction of temperature) are maintained after the source of the heat has been withdrawn. With regard to the nature of calorific waves, long before I had arrived at any definite views I felt compelled to reject the idea of their consisting in molecular motion, for the following rea- sons :—Ist. Because they are propagated through space, where 214: Dr. H. Hudson on Wave-Theories of every indication is opposed to the existence of matter in the or- dinary sense. 2nd. To suppose an etherial wave impinging on a body to act primarily on its material molecules (instead of upon the associated ether) appears to me a most gratuitous and un- likely assumption. 3rd. In the case of free transmission of light or heat-waves through any substance without producing (so far as we can perceive) the slightest disturbance of the molecules of the body (evidenced by phesphorescence or increase of tempera- ture), I find it impossible to admit Tyndall’s conclusion, viz. “that free transmission indicates discord and absorption con- cord.” If the vibrations of an impinging etherial wave mterfere with those of the ether (associated in the molecules), there must be disturbance of the latter, which will, no doubt, cause disturbance of the molecules also, and hence, on my view, “ phosphorescence or increase of temperature.” 4th. The existence of very intense light without any appreciable heat (as in moonlight concentrated by lenses or mirrors), as also of great heat from perfectly dark matter, compelled me to dis- card the idea that light and heat could only differ in refran- gibility or wave-length. The fact also that a compound beam of light and heat can be so easily deprived of either of its con- stituents by transmission through different substances, as well as the different march of the luminiferous and calorific rays (of the same refrangibility) in respect to their intensities, all pomted to the same conclusion, viz. “that both sets of waves could not be ascribed to the same function of the etherial vibrations ;” and from this consideration arose the idea that calorific waves are probably due to eetherial vibrations in the direetion of the wave’s progress. A theory, however, may be plausible (as I hope this will appear) and yet require proof, which the theory itself, if true, ought to supply. I have already dicated an experimental test in reference to two media, and beg now to suggest that Foucault’s experiment of the revolving muror (with lenses of rock-salt and a thermopile) may be applied to ascertain the velocity of calorific waves. ‘The resistance to wave-progress where the vibrations are normal must be considerably greater than in the case of transversal vibrations ; and, as a consequence, the progress of the calorific wave ought to be considerably slower than that of the luminiferous wave. I may add that the “conduction of heat ” im crystals is, so far as I am aware, better in the direction of their planes of cleavage (as in bismuth) than in any other direction, and, with wood, in the direction of the fibre, facts which appear to me in favour of my views, that calorific vibrations are in the direction of wave- progress ; the molecules gliding more easily and attaining greater Laght, Heat, and Electricity. 215 amplitude of vibration in the interstices of the planes of cleavage, in which direction we must necessarily conclude that the etherial waves (which act on the molecules) must also have their vi- brations. I have classed fluorescence with phosphorescence:—1st, because none of the fluorescent rays are transmitted; and 2nd, because they are not polarized even when the light which produced them was polarized. Now I find it difficult to admit the mere change of refrangibility of the incident rays; but to believe them to be also depolarized is, in my mind, impossible. So far as I am aware, the alleged “ polarization of heat” is the only serious objection to my views; if calorific waves be normal (uot transverse) there can be no polarization. Melloni has shown that Forbes’s experimental proofs cannot be accepted ; and I have never been satisfied with Melloni’s own experiments. The velocity of heat-waves is, I believe, the point which must decide the question; but I conceive it to be possible that the conside- ration of those waves whose vibrations are intermediate between the direction of progress and its perpendicular may account for some small indications of heat polarization, as such waves un- doubtedly would partake in some degree of the qualities of both luminiferous and calerific undulations. Having thus discarded molecular vibrations as causing “ calo- rific waves,” in order to satisfy the experimental researches of Rumford, Davy, Joule, Tyndall, and other philosophers we have only to substitute “temperature” im the place of heat; for, to my thinking, temperature is simply an accident of matter, and represents the state of motion of its molecules under the influence of their associated ether. I look, therefore, on ‘‘ temperature of space’ as a pure myth; and I believe a zero of temperature to be an utter impossibility; for, in a world constituted like our universe, absolute rest is unattainable, and equally absurd with “perpetual motion.” I believe that the dark lines in the solar spectrum are due to the interference of waves of like refrangibility, which differ in their periods by an odd number of semiundulations, and consider the same explanation applicable to certain phenomena of heat which have generally been referred to the theory of exchanges. According as the quality of the radiation (as regards velocity of vibration) approaches more nearly to that of the ether assc- elated with the molecules of matter through which we transmit the rays, the greater will be the tendency, I conceive, to an in- crease of interference. ‘Thus, for instance, the most transparent glass loses almost entirely its power of transmitting light when its temperature is so raised that it becomes “ self-lumimous ;” and even below ared heat its transparency is greatly diminished. 216 Dr. H. Hudson on Wave-Theortes of In this case it is obvious we cannot have recourse to a “ theory of exchanges ;”’ and yet the explanation of the phenomena must, I conceive, on the undulatory theory be similar for both light and heat. I may add that a diminution of the index of refrac- tion produced by increasing the temperature of a medium (as shown experimentally by Gladstone, Dale, and Landolt) appears an obvious consequence of the views here indicated. Whether we consider the case of sound, light, or heat, there can be no doubt that ‘intensity 7’ depends on the amplitude of vibration, and quality (viz. pitch in music, and colour or refran- gibility in light and heat) depends on the number of vibrations in a given time. Increased temperature thus represents greater amplitude of the vibrations of the molecules of matter as con- radistinguished from those of their associated ether, which, ee er, we must consider as generally synchronizing with the former, although their number per second must be enormously greater. When we consider molecular motions separately, we can scarcely doubt that the momenta of the molecules (V x W) of two bodies at the same temperature are equal; that is to say, the “velocity of vibration”? (in chemical language “the capacity for heat’) varies znversely as the molecular weight—a deduction which is in accordance with experiment. A curious consequence appears to flow from these views when we compare the same substance at the same temperature in dif- ferent states of aggregation. ‘Thus water and ice at zero Centi- grade have the same molecular momentum. But the specitic heat of ice is only one half that of water (viz. as 0°5050: 1), therefore the molecule of ice should be to that of water as 2:1 (to maintain their equal momenta). Again, in comparing water and steam (at the boiling-point), their specific heats (as 1 : 0-4805 per Regnault) appear in like manner to indicate a ratio of 2: 1, whence it would in fact follow that the molecular weight of water is only one half of the molecular weight of either ice or steam! Thus if the molecular weight of Steam be taken as 9 (in accordance with hydrogen’s s gaseous unit), then the mea of water can only be 4°5, and the atomic weights of hydroge and of oxygen cannot exceed 0°25 and 4 respectively ; so that ie gaseous molecule of both hydrogen and oxygen must consist of at least 4 atoms each ! With regard to electrical phenomena, it appears to be abun- dantly proved by Faraday that the two electricities exist in equal quantities associated with the atoms or molecules of matter, and the amount is so great that the electricity evolved from 13 grain of water (decomposed) is adequate to charge 500 acres of cloud surface; they are each self-repellent, and are both attracted by Light, Heat, and Electricity. 217 matter, from which they can be separated and a portion trans- ferred at pleasure from one surface to another without losing their distinctive properties. I believe, therefore, that they must be admitted to have a real existence, and cannot be regarded as mere motion or as properties of matter. Assuming this, it ap- pears to me that Wheatstone’s experiment with the revolving mirror leaves no doubt that electricity consists of two self-repel- lent fluids, and can no longer be considered merely the excess or deficiency of a single fluid. In addition to the above properties, it 1s generally assumed that there is a mutual attraction between the two fluids; but a careful consideration of the phenomena has led me to the conclu- sion that this opinion is erroneous, and that they are mutually in- different. An experiment of Mohr’s appears to me strongly in favour of this view ; viz. when an electrized body was placed at 1 centim. from one end of an insulated cylinder (65 centims. long), the neulrai point was found to be at only 1 centim. from this extre- mity of the cylinder. If attraction existed between the two electricities, we should expect a large accumulation of the oppo- site fluid at the end of the cylinder nearest to the charged body, while the actual result appears plainly to indicate MERELY a re- pulsion of the electricity of the same denomination with that of the charged body. The facility with which the two fluids are separated even by the slightest friction, and their not instantly disappearing again (as separate entities) when eliminated, first excited a suspicion on this point, which has grown up into a firm belief that all the statical phenomena supposed to establish mutual attraction can be accounted for by the attraction of each for matter and the self-repulsion of each fluid. Assuming, therefore, this to be the constitution of the two electricities, and feeling bound to admit no more causes than are necessary to account for phenomena, I have arrived at the conclusion that “‘the two electricities,” in equal quantities, each possessing self-repulsion (and mutually indif- ferent to each other), possess those qualities which are, in my mind, essential to a thorough explanation of theundulatory theory, and constitute by their diffusion throughout space that “ ether” whose existence is generally admitted as proved by the pheno- mena of optics—the luminiferous vibrations of the two fluids taking place in perpendicular planes, and always transverse to the direction in which the hght is propagated. On this hypothesis the cause of the intimate connexion be- tween the state of the sun’s photosphere and magnetic storms, as well as other terrestrial electromagnetic phenomena, becomes obyious ; and, as regards affections of molecules, I recognize in ee ee ———E—E—E—EeEeoeeeeee 218 On Wave-Theories of Light, Heat, and Electricity. their associated ether the principle of elasticity, or of that re- pulsive force which equilibrates the attractions of molecules or atoms inter se. With regard to Boscovich’s theory of alternations of attraction and repulsion between particles themselves at minute distances, I reject it as irreconcilable with the phenomena, inasmuch as at any temperature a body resists either compression or extension ; so that its actual state must result from an equilibrium of two opposing forces, viz., on the one hand, the mutual attraction of the molecules (which even with gases must be allowed to exist at whatever distance, inasmuch as gravity has no known limit, and the attraction which our earth exercises over gases at their extreme rarefaction is an undoubted fact), and, on the other hand, the self-repulsion of the zther associated with the molecules, which may thus (in chemical philosophy) take the place of the “caloric ” of former times. In accordance with these views, electricity should be looked on in future (in chemical theories) as causing decomposition by se- parating combined molecules, and thus allowing the action of various forces of attraction to play their allotted parts in the changes which take place. The views of the illustrious Faraday on this subject appear to have varied much from time to time: although he admits that chemical combination alone never eliminated electricity, and that “decomposition ”” was an essential in voltaic arrangements, still, on the whole, his leaning appears to have been to the views of Davy, “that electricity was the cause (not the opponent) of che- mical affinity”? (Researches, 858-861). With respect to electrical phenomena, it appears to me that there are ‘‘ waves of translation” as well as waves of vibration, the former being always productive of the latter, and the prin- cipal agents, as such, in dynamic electricity. The “parallelism ” of the quality of conductivity m bodies (for temperature and for electricity) corroborates the view I have taken of the intimate connexion of the motions of molecules with those of their asso- ciated ether—the former sluggish and persistent, the latter amazingly rapid and evanescent, while both present the same relative velocities in passing through the same substance*. In conelusion I would submit that many erroneous theories appear to have arisen from regarding the ultimate particles of a body as spheres. They might be spheroids or ellipsoids; or more probably they may have the simplest forms of those crystals which they build up by their mutual aggregation; but taking into account the polar forces which come into play at insensible * Dessaignes first observed that “bad conductors ofelectricity are re co rendered phosphorescent, Bnet conductors rarely, if ever.’ The Hon. J. W. Strutt on the Law of Gaseous Pressure. 219 distances, the sphere appears to me the most improbable of all forms. The law of attraction (as = I conceive to exist at all dis- tances (subject to a polar force which becomes insensible at mi- nute distances) ; and with regardto chemical equivalents or atomic weights, whether they are due to an unchangeable difference of mass (in the sense of gravitation) of the ultimate particles, or are essentially different forces of what chemists have termed “ affinity,’ we must not forget that they in truth only repre- sent “the mean force of attraction exerted between OUR EARTH (as a whole) and the combining quantities of those different substances,” XXVI. On the Law of Gaseous Pressure. By the Hon. J. W. Strutt, M.A., late Fellow of Trinity College, Cambridge. | ie reply to Mr. Moon, I will consider first the objections which he offers to the received theory. In the Philo- sophical Magazine for July 1868, four particular cases of the problem in one dimension are considered, in each of which the law p “p is supposed to lead to error. The first is reprinted in the August Number. A cylinder contains air which is at rest, but whose density varies discontinuously in crossing a certain section. Such diffi- culty as the problem presents appears to me to be purely of a mathematical character, arising out of the discontinuity. In any case of fluid motion the possibility of a difference of pressure at two points, P and Q, finitely distant, depends on the inertia of the intervening air and its consequent resistance to accele- ration. If, as in ordinary cases, the acceleration be finite, the difference of pressure will tend to zero as P and Q approach one another, without limit, because this is true of the inertia. But the conclusion no longer follows if there be an infinite accelera- tion. The reaction of an infinitely small mass to an infinite ac- celeration may be as finite as that of a finite mass to a finite acceleration. Now the layer of air situated at the boundary is subject to an infinite acceleration, and therefore, no matter how thin it may be taken, its resistance to acceleration cannot be left out of account. That the pressures which act on its two faces are unequal is, therefore, not in contradiction to any true principle. Mr. Moon’s other arguments depend also, as I believe, on logical fallacies in the treatment of infinitesimals. The second supposes the case of “a vertical cylinder closed at its lower end, * Communicated by the Author. 220 The Hon. J. W. Strutt on the Law of Gaseous Pressure. and having an air-tight piston capable of moving freely in the upper part of it. Below the piston the cylinder is filled with air, which is kept in equilibrium by means of a weight, W, rest- ing on the piston, above which there isavacuum.” If asecond weight, W, be placed on the piston, we know, that the equili- brium will be destroyed ; but, according to Mr. Moon, if the received law of pressure were true, such ought not to be the case. Kven Mr. Moon must admit that it is remarkable that so apparently reasonable a law should lead to such an absurd con- clusion. Of course, it is easy enough to deduce the opposite result from the same premises. Ifthe piston do not descend, it must be supported by a pressure which is confessedly in- adequate. So far as I understand it, Mr. Moon’s argument may be ex- pressed thus :—The lamina of air beneath the piston will not begin to move until the pressure exercised on it by the piston (equal to its own pressure on the piston) has changed. And the pressure of the lamina (by hypothesis) cannot change until there has been a relative displacement of its parts, which requires that the motion should have already begun. It would appear, there- fore, that the downward motion of the lamina (and piston) can- not begin. Precisely the same argument may be used to prove that a body cannot begin to fall under the influence of gravity ; for a body cannot leave its initial position without acquiring velocity, and (by the law of energy) cannot possess a velocity without having already fallen. An argument of this kind is destitute of validity ; and its conclusion may or may not be true. In the case of gravity, where v* as, we all know that falling from rest is possible; but if the law of motion be that v simply varies as s, it is true, as may easily be shown, that a body once at rest cannot begin to move. In order to arrive at a safe con- clusion by the method followed by Mr. Moon, a much closer consideration of the order of the infinitesimals concerned is in- dispensable. A nearly similar objection would apply to Mr. Moon’s treatment of cases 3 and 4:*, A remark of a more general character may be made, which in most people’s judgment would be sufficient to dispose of the question. Mr. Moon proves a little too much ; his arguments, if valid at all, would establish that the received view is not merely false, but self-contradictory. Thus in case 2, starting from iden- tically the same premises, we prove by two different lines of rea- * Mr. Moon assumes, if I rightly understand him, that if a state of things once exist, and it can be shown that, whenever it does exist, the rate of departure from it vanishes, then the state is necessarily permanent. On this principle it would follow that a curve once meeting the axis of z, aa ae meeting without also touching it, necessarily coincides wholly with it. The Hon. J. W. Strutt on the Law of Gaseous Pressure. 221 soning (1) that the weight W will fall, and (2) that it will not fall. The same may be said of the other arguments. Now, whether air obey Boyle’s law or not, surely an ideal fluid may be imagined which shall do so without any inherent contradic- tion. However interesting Mr. Moon’s problems may be as logical paradoxes, they convey no information on the physical question which is under discussion. In his restatement of the analytical arguments by which it is proved that p is a function of v, Mr. Moon has made some alterations the effect of which is to obviate the objection that I urged in the July Number. “‘ Tf we have three relations, p=fi(2t), p=f,(#), v=f, (20), where the forms of f,, f,, /5 are utterly unknown to us, the pre- sumption is that p=funct. (p,v). This is the rule, to which there may possibly be exceptions ; but those who rely on the ex- ceptions must prove them to exist.” On this I have two remarks to make. In the first place, I had understood (as it now appears mistakenly) that the argu- ment was put forward to prove that p was necessarily a function of v. Understanding may instead of must, the reasoning is be- yond cavil. But the objection is only transferred to the pre- mises ; for, of course, I entirely deny that the forms of fi, f,, f, are utterly unknown to us. On the contrary, I assert that Ff, «f,; and even Mr. Moon admits that we have this @ priori knowledge of the forms of the functions in the case of relative equilibrium. I quite agree with Mr. Moon that the attempt to extract Boyle’s law from the sole eonditions that p, p, v are fune- tions of z and ¢ subject to dv 1 dp ED (A)* must necessarily fail; but this is only because some of the re- quisite conditions have been omitted. The reason why I reject his expressions for the pressure, velocity, and density is simply that, though they satisfy the conditions he prescribes, they do not satisfy the conditions that I prescribe. If Mr. Moon has really obtained the most general values con- sistent with (A) (a point on which I am scarcely competent to judge), they necessarily include all the results of the received theory. Only so far would they have any application to gaseous dynamics, though from a purely analytical point of view their value may be very great. * Another equation should properly be added, d e dv dt 1s ae a ee ee et ai i ee en a 222 The Hon. J. W. Strutt on the Law of Gaseous Pressure. In the second place, I wish to observe that even if Mr. Moon were right in rejecting Boyle’s law when there is relative mo- tion, it would still be without physical significance to express p as a function of v. That this might be done in any particular case of motion in one dimension is admitted ; but the statement, though true, would express, as it stands, no physicallaw. What the pressure at any point of a fluid in motion may be under pre- scribed circumstances is (as I said before) a purely physical question; and we are agreed, I believe, that the magnitude of the actual velocity at the pot, whether measured absolutely or relatively to other parts of the fluid at a distance, has nothing to do with it. Under these circumstances the expression of p asa function of v in a particular case, though it may be correct, is not instructive. Perhaps an illustration will render my meaning clearer. In the actual course of events the length of Mr. Moon’s hair and the length of mine are both functions of the time. Eli- minate the time and the length of our hairs are expressed as functions one of another; but no physical connexion is thereby proved. Again, in the motion of the earth round the sun, the force of attraction exercised upon it is (according to received views) proportional to 7~?; but inasmuch as 7 is a function of 0 (the angular coordinate), or of the time ¢, the force of gravity may without error be expressed in terms of @ and ¢—either sepa- rately, or jointly in an indefinite number of ways. Yet no one, I imagine, would say that the law of gravity could properly be so stated. It is therefore desirable that Mr. Moon should state what he conceives to be the real physical law of pressure, true at all times and places. It is perhaps abstractedly possible that besides p the differen- tials of p and v with respect to space may be elements on which the pressure depends. (That the velocity itself is not an element in the matter is, I believe, admitted by Mr. Moon, and is at any rate a direct result of experiment.) Indeed any theory of gases which professes to be more than a first approximation, must give an account of the tangential force which acts between two por- tions of the gas separated by an ideal plane, whenever the first differentials taken normally of the tangential velocities of the gas in the neighbourhood of the plane are finite. Of course nothing of this kind can happen when the motion is in one dimension merely. I do not know what Mr. Moon may think of the kinetic theory of gases ; but it has certainly great and increasing claims to be considered at least a truthful representation of the facts. The dependence of pressure on the density (and temperature) only, is one of the simplest consequences of its fundamental assumptions. ‘Royal Society. 225 In the absence of any other even plausible theory, and in view of the fact that all its legitimate consequences are in perfect har- mony with observation whenever they can be brought to the test, the received law of pressure is, I maintain, the only rea- sonable one. XXVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 145.] May 16, 1872.—Francis Galton, M.A., Vice-President, in the Chair. HE following communication was read :— “On Supersaturated Saline Solutions.—Part III. On a relation between the Surface-tension of Liquids and the Supersaturation of Saline Solutions.” By Charles Tomlinson, F.R.S., and G. van der Mensbrugghe. It was stated by one of us in Part II.* that when a drop of a liquid is deposited on the surface of a supersaturated saline solution, it will do one of three things—(1) mingle with the solution without any nuclear action, (2) spread out into a film with powerful nuclear action, or (3) assume the form of a lens, without any separation of salt. It was further stated that when a liquid forms a film or alens, it does so according to the general proposition, that if a drop of a liquid B, with the surface-tension 6, be placed on the surface of another liquid A, with the surface-tension a, the drop will spread into a film, if a>6+¢ (c being the tension of the common surface of the liquids A and B); but if, on the contrary, a<6+c, the drop will remain in the form of a lens. Hence, if B spread on A, A will not spread on the surface of B. When the liquids A and B mingle in all proportions, chas no value. The spreading of the drop may also be interfered with by the superficial viscosity of the solution, or the greater or less difficulty in displacing the superficial molecules. It was also stated that if a greasy smear be made upon the clean interior surface of a flask above the solution, and the flask be in- clined so as to bring a portion of the solution against such smear, the liquid does one of two things: (1) it breaks up into well-defined globules, which roll over the smear without loss of tension, in which case the smear has no nuclear action; or (2) as soon as the solution reaches the smear its edge flattens and becomes ragged, in which case the smear is nuclear and the salt separates. A glass rod drawn through the hand becomes covered with a smear or film; or the same rod, by exposure to the air, contracts a film by the condensation of floating vapour, or a deposit of film- forming dust, and so is brought into the nuclear condition. It was further stated that when a lens of oil is resting on the sur- face of a solution, the flask may be rapidly rotated ov briskly shaken, * Philosophical Transactions for 1871, p. 52. i =e eee eee: 224 Royal Society :—Mr. Tomlinson and Van der Mensbrugghe so as to break up the oil-lens into a multitude of minute globules, giving the solution the appearance of an emulsion—and that by repose the solution regains much of its transparency, without any separation of salt—but that if, while the flask is being turned round, a sudden jerk be given to it, so as to flatten some of the globules against the side, the solution instantly becomes solid. The powerful action of films in putting an end to the state of su- persaturation being thus established, it occurred to one of us, who had already succeeded in explaining a number of obscure phenomena on the principle of surface-tension*, that that force, properly handled, would suffice to account for most, if not all, the varied phenomena of supersaturation. Accerding to this view, whatever tends greatly to lower the surface-tension of a supersaturated saline solution, causes a separation of salt, and at once puts an end to the condition of su- persaturation. In order to test this view, a large number of experiments have bee performed by one of us during the last six months, consisting of repetitions of former experiments or of new ones suggested by one or both of us. All these experiments have been performed in the open air at Highgate, near London, the object being to avoid all possible miscarriage from the effects of floating dust in the air of a room. It had been suggested that some of the former results as to the action of films might have been vitiated from this source; and although this does not appear to have been the case, yet it is with much satis- faction that the experimenter refers to the greater facility and cer- tainty with which experiments of this kind are conducted im the open air, as compared with those made in a room. In the open air a gentle wind would sometimes .blow over the mouths of the flasks, sufficient to produce a low musical note, without any nuclear action, unless a speck of soot or a small insect were carried into the solu- tion; but in general, in order to prevent evaporation, the flasks were kept covered with watch glasses or small beakers, except when per- forming an experiment. The salt used in the following experiments was sulphate of soda, in large crystals, not effloresced, one of three strengths being adopted as circumstances required, which will be indicated when necessary —namely, 1 part of salt to 1 of water, 2 parts of salt to 1 of water, aud 3 parts of salt to 1 of water. Every solution was first madein a large flask, and filtered boiling into eight or ten small flasks, which were reboiled, covered with watch glasses or beakers, and carried on a tray into the open air. The same experiment was repeated on a number of these solutions of the same strength. The points to which this experimental inquiry tended are included in the four following propositions :— I. That a supersaturated saline solution contained in a catharized flask will remain liguid so long as its free surface, or the surface in * “Sur la Tension superficielle des Liquides,” par G. Van der Mensbrugghe, Répétiteur 4 Université de Gand. Mémoires couronnés par Acad. Royale de Belgique, tome xxxivy. 1869. Seealso Phil, Mag. for Dec. 1869 and Jan. 1870. on Supersaturated Saline Solutions. 225 contact with the sides of the flask, does not undergo in one or many points a notable diminution of surface-tension. If. That if we deposit on the surface of a supersaturated saline solution a drop of a liquid of feeble tension, it spreads, and crystal- lization takes place immediately or after a short time. Til. That while a liquid of feeble tension produces crystallization after a time more or less short, a liquid of considerable contractile force (such as pure water) not acting chemically on the solution, may be brought into contact with it without producing change of state. IV. That as a liquid of feeble tension produces crystallization, so a solid covered more or less with a film of such liquid produces change of state, either at once or after a short time. But before any conclusions could be drawn from the results of experiments as to the relation between the surface-tension of liquids and the state of supersaturation in saline solutions, it was necessary to measure the surface-tension of the solutions of Glauber’s salt operated on. Accordingly the following data were determined, first, for a solution containing 1 part of salt to 1 of water, and, secondly, for a solution containing 2 parts of salt to 1 of water. The dia- meter of the capillary tube was 1°598 millim.* Specific gravity of the solution 1 salt to 1 water at 17° C.= 1-198. The capillary height 11 millims. The specific gravity of the other solution = 1°289. The capillary height 8°7 millims. r.h.d 2 é is the tension, A the height, d the density, and 7 the radius of the tube), for the superficial tensions of the solutions in question, not a greater value than from 4 to 5:2. If the states of supersaturation of saline solutions depend on the maintenance of surface-tension, according to the first proposition, any force or substance that produces a notable diminution of such tension will cause the state of supersaturation to cease. Such a force is heat, while such substances as camphor, benzoic acid, &c. have a marked effect in lowering the superficial tension of water, and in doing so undergo those remarkable gyrations which are so well known. | And first with respect to heat, applied not so as to affect the whole solution, but locally, so as to raise the temperature at one part or point of the surface, while the other parts remained at the tem- perature of the atmosphere. Hezperiment \. Four flasks, each about half full of a supersaturated solution of Glauber’s salt (2 salt to 1 water), were expesed to a tem- perature of 32° F. for an hour. A red-hot poker was then passed down the neck of each flask, and in two of them the hot metal was brought into contact with the surface of the solution so as to raise a volume of vapour. There was no separation of salt in any one case. Experiment 2. A solution containing a considerable mass of the * The tube was calibrated by Dr. E. J. Mills, F.C.S. &e. Phil. Mag.8. 4, Vol. 44, No. 292. Sept. 1872. Q These data give, according to the formula ¢= (in which 226 Royal Society :—Mr. Tomlinson and Van der Mensbrugghe seven-atom salt at the bottom of the flask was moved over the flame of a spirit lamp in a line from the bottom of the flask to the neck, so as to heat one part only of the flask. The only effect was to convert a portion of the surface of the seven-atom salt into the anhydrous ; but there was no crystallization. After some hours the anhydrous portion had again taken up its water of crystallization. Experiment 3. A solution of 2 salt to 1 water that had been in the open air SEL twenty-four hours was uncovered, and water nearly boiling was dropped upon it. A slight cloudiness came over the solution, but there was no crystallization. Next day avery weak solution of Glauber’s salt nearly boiling was dropped upon the surface, with no nuclear action. Eaperiment 4. An eight-ounce globular flask had the globe filled with a solution of 2 salt to lwater. Solutions of two different strengths, namely | salt to 1 water, and 3 salt to 1 water, at a nearly boiling temperature, were dropped upon it, but with no nuclear action. Eaperiment 5. A solution of 1 salt to 1 water had filtered into it a nearly boiling solution of 3 salt to 1 water. The drops descended to the bottom of the flask in beautiful rolling rings, but there was no nuclear action. Experiment 6. The neck of a fiask was inclined over the flame of a spirit-lamp, so as to boil the upper part of the solution, while the lower part remained cold. Water was driven off in vapour, so as to leave a crust of salt in the neck. This, when the flask was left to itself, gradually absorbed moisture and trickled down, and was also washed down into the solution; but there was no nuclear action either from this or from the heat. These experiments on the action of heat lead to the conclusion that, however much it may diminish the superficial tension of the solutions, it does not apparently disturb the state of supersaturation. This result may be explained by reference to the feeble tension of the solution (=4), and to the fact that heat locally applied does not greatly diminish it. Moreover heat tends to oppose crystallization by increasing the solubility. Numerous experiments were tried as to the action of newly sub- limed camphor and benzoic acid on the solutions. The flasks con- taining these bodies floating on the solutions were plugged with cotton- wool and kept for some months, during which time they were re- peatedly shaken; but there was no separation of salt. The camphor and benzoic acid formed weak solutions with the supersaturated solutions ; but the tension of camphorated water being = 4°5, and that of an aqueous solution of benzoic acid falling within the limits 4 and 5:2, the difference in tension is too small to produce a rupture of equilibrium. The same remark applies to a solution of scap and of bicarbonate of soda, which had no nuclear action. Action of Vapours.—It has been shown by recent researches that the presence of vapours in the air of a room, even in minute quan- tity, has a marked influence in lowering the tension of water and other liquids, so as to account for the discordant values of various careful measurements of the capillary heights of such liquids. As to on Supersaturated Saline Solutions. 227 the nuclear action of the vapours of certain volatile liquids upon su- persaturated saline solutions, many observations had been made by one of us, leading to the conclusion that such vapours are strongly nuclear when they become condensed into the form of films on the surface of the solutions, as when the latter is of a lower temperature than the former. In order to ascertain whether vapours as such (that is, without forming films) have any nuclear action, the following experiments were contrived. The vapour was presented to the surface of the solution by means of a bit of sponge tied to the end ofa glass rod, wetted with the volatile liquid and carefully passed down the neck of each flask, so as to avoid touching the side, and bringing the sponge close upon the surface, avoiding also touching that*. The sponge was held over the solution several minutes, then carefully with- drawn and the flasks covered, leaving the interior charged with va- pour. The liquids used were ether, absolute alcohol, chloroform, bisulphide of carbon, wood-spirit, and benzole. The solutions were of all three strengths, and the temperature from 40° to 47°F. After many hours, and even days, the flasks had a strong odour of the vapours in question; but there was no separation of salt. Vapour of camphor was also tried in the following manner :— Experiment 7. A quantity of camphor was placed in a small retort, the beak of which, made chemically clean by being heated in the flame of a spirit- lamp, was passed into a flask containing a solution of 2 parts salt to 1 of water. The camphor in the belly of the retort was then boiled so as to produce a powerful jet of vapour upon the surface of the solution. The camphor condensed upon such surface in the form of a fine white powder without any nuclear action. In this case a portion of the vapour of camphor or of the powder would dissolve in the solution without producing in it a notable diminution of surface-tension. The same remark applies to the other vapours, to the action of solid camphor and benzoic acid, of heat, &c. So also, as stated in Part II., glycerine mingles with the solution without any nuclear action. Now the surface-tension of glycerine =4°2; so thatit can have no effect in lowering the surface-tension of a solution=4, and does not sufficiently lower the tension of a solution = 5:2 to produce a rupture of equilibrium. It was also stated that bisulphide of carbon f=3°3 to 3°5, and chloroform =2°98 to 3:12, formed lenses on the surface of the solu- tion, and that on gently agitating the flask they fell to the bottom, where they remained permanently without any nuclear action. Creo- sote (=3) behaves in the same manner. Now, in any one of these cases, the tension ¢-+c must be greater than 4:5, and hence there can be no separation of the salt. We now pass on to consider the second proposition—namely, that if on the surface of a supersaturated saline solution there be depo- * Tn a few cases the wet sponge did touch the solution for an instant, so as to take up a small portion, which immediately crystallized upon the sponge; but the crystallization thus produced not being in contact with the solution, the latter retained its liquid state. . } a, ee 228 Royal Society :—Mr. Tomlinson and Van der Mensbrugghe sited a drop of a liquid of feeble tension, the drop spreads and erys- tallization is determined. Now it is shown in Part IT. that drops of ether, of alcohol, and of similar volatile liquids, as well as of certain oils, both volatile and fixed, spread over the surface of the solutions and act as powerful nucle}. On the surface-tension theory, a liquid such as ether, of which the tension=1°88, or aleohol =2°5, or wood- naphtha = 2°11, or oil of lavender = 2-9, must spread on the surface ofa supersaturated solution of Glauber’s salt of which the surface- tension is as high as from 4 to 5:2. This is true in a large number of cases that have been observed ; and so far the phenomena are consistent with the theory; but there are cases in which liquids of low tension, such as oil of turpentine=2-2 to 2-4, and some varieties of castor-oil=2°5, do not form films, but well-shaped lenses, and Temain as such during many hours, and even days. Quincke seems to have met with cases of this sort in his elaborate inquiry on the capillary phenomena of the common surface of two liquids*; and he endeavours to account for these exceptions to the general law by the statement that if a lens-shaped drop of a liquid 2 (of low tension) remain on the free surface of a liquid 1 (of much higher tension) without spreading itself out, then it is certain that in most, and pro- bable that in all cases the free surface of liquid 1 is rendered impure by a thin layer of a foreign liquid 3. Now in experiments on super- saturated saline solutions the flasks, the filtering-apparatus, and the solutions must be, as already explained by one of us, chemically clean; so that in boiling and filtering a solution into clean flasks in which it is boiled up again, covered over, and left to cool in the open air of the country, it is difficult to imagine the existence of such a film as M. Quincke refers to. Moreover, did such a film exist, the solution in cocling would probably become solid under its action. Indeed this sometimes happens in the case of flasks that have been already used in experiments on the nuclear action of oils; for, however carefully they are cleansed, it may happen that one or two out ofa dozen may not be quite clean, so that, in the cooling of a boiling solution, a film detached from the walls of the flask may spread over the surface with nuclear action. In order, if possible, to prevent the formation of such a film, the following experiment was made :-— Experiment 8. A solution of 1 part of Glauber’s salt to 1 of water, with the addition of a bit of caustic potash, was boiled and filtered into four clean flasks. When cold, a drop of eastor-cil was deposited upon the surface of each of the solutions. It flattened at first, but soon recovered the lenticular form. There was no nuclear action during an hour. On gently shaking the flasks, the oil was diffused through the solution without nuclear action. in an experiment described in Part II. fragments of stearine were scraped into a solution with immediate nuclear action. In such a case, the stearine furnished the film-forming material that produced the solidification of the sclution. The solution was boiled with the stearine In it; and in cooling the stearine formed into solid disks Without nuclear action, although the flask was frequently shaken. * Poggendorif’s Annalen, vol. cxxxix. See also Phil. Mag. for April 1871. re . on Supersaturated Saline Solutions. 229 In this case the boiling solution had saponified or otherwise removed the film-forming matter, or, in other words, had made the stearine chemically clean. There is also a difficulty in the case of oil of turpentine, asin the following experiment :— Haperiment 9. A drop of an old but clear and bright oil of tur- pentine was deposited on the surface of a solution containing 2 parts of salt to 1 of water. The drop flashed out into a film, and the solution immediately became solid. The turpentine was now distilled, and a drop of the distillate was deposited on a similar solution, when it formed a well-shaped lens with no nuclear action, although the flasks were left out during several days. | Now the tension of the old oil first used is =2°2; and had the effect of distillation been greatly to exalt the tension, the experiment would have been intelligible according to the theory ; but on mea- suring it the tension was found to be only 2:4. A somewhat similar case is given in Part II., in which an old oil of bitter almonds was strongly nuclear, while the same oil freshly distilled had no such action, but became converted into benzoic acid, still without any separation of salt. After some days, to prove that the solution was still supersaturated, it was touched with an unclean wire and it immediately became solid. Still, however, there are such a large number of cases in which oils and other liquids spread upon the surface of the solutions with nuclear action as to justify the labour bestowed upon the theory by one of us during the last six months. Many of these cases are stated in Part IT. ; but a few of them may be repeated here for the sake of comparing the action of such liquids upon solutions of different strengths, which was not done before. If we take a number of oils, the tension of which varies from about 2°5 to 3°5, a drop of any one of them, according to the theory, ought to spread on the surface of a solution where ¢=5-2, and not in all cases spread on the solution of which t=4. Lzperiment 10. Twelve flasks, containing a solution of | part salt to 1 of water were prepared, and a drop of each of the following oils formed films with immediate crystallization of the solutions, viz. pale seal-oil, sperm-oil, cotton-seed oil, and niger-oil. A drop of linseed-oil formed a lens; but this soon becoming ragged, crystals diverged from it. A drop of castor-oil formed a lens with no nuclear action. Experiment 11. Three of the above solidified solutions were heated over a lamp, boiled, and covered over. ‘The oil collected on the sur- face in innumerable small disks. Next morning one of the solutions was found crystallized, and the other two became solid on gently agitating the flasks. In this case as the solutions cooled down or were gently agitated the disks spread out into films with nuclear action. Euperiment 12. A solution of 3 parts salt to 1 of water was filtered into twelve flasks, when a drop of each of the following oils deposited on the surfaces of the solutions became lenticular without 230 Royal Society :—Mr. Tomlinson and Van der Mensbrugghe any separation of salt, viz. pale seal-oil, olive-oil, rape, castor-oil, eroton-oil, niger, sperm, and cotton-seed oil. So far this result is in accordance with the theory. Experiment 13. A solution of the same strength as in the last experiment was employed, when a drop of seal-oil, sperm, cotton- seed, and niger spread out into films with powerful nuclear action. Linseed- and castor-oil formed lenses with no such action. Now it must be remarked that on the day when Exp. 12 was made the weather was dull, damp, and cloudy, and during the time of Exp. 13 the weather was bright and clear. Some years ago it was a matter of frequent observation to one of us, that the formation of co- hesion-figures on the surface of water was much more rapid and de- -cisive, with altogether finer and sharper results, in bright weather as compared with dull, damp, wet, or foggy weather. The same remark applies to the motions of camphor on water, and to those curious phenomena known as “camphor-currents”’ and “ camphor- pulsations’’*. In the production of ali these phenomena, as has been shown by one of us}, surface-tension plays a most important part; and such tension is lowered in dull foggy weather probably by the condensation of the vapour of volatile matters contained in the atmosphere. A drop of a liquid under such conditions may not spread on the surface of water or of mercury, the latter being espe- cially liable to such influences; whereas on a bright day such sur- faces are particularly active, and experiments succeed which some hours or days before failed to produce the results expected. Then, again, as pointed out by one of us in Part II., the viseosity of the surface, or of the drop of liquid placed upon it, may greatly interfere with the operation of the law by which a liquid B spreads upon the surface A. A supersaturated saline solution has a consi- derable viscosity of surface, which it retains for many hours after it has cooled down. In the course of about twenty-four hours the more watery particles come up to the surface and the tension im- proves; so that the same surface which may have sufficient tensile force to cause a drop of oil to spread upon it, might some hours earlier have retained it in the lenticular formt. . There are also certain modifications to which oils &c. are subject in consequence of the presence of ozone and other matters in the air, which may somewhat disturb the results expected to be obtained front the action of surface-tension. It was stated in Part II. that when an oil &c. assumes the len- ticular form, the solution may be agitated so as to break up the lens * Phil. Mag. for Dec. 1869. - Tt Sur la Tension superficielle des Liquides, par G. Van der Mensbrugghe. ~ Some of the distinguished physicists who are now engaged in studying the phenomena of surface-tension refer to the embarrassing effects of surface-vis- cosity. Thus Herr Liidtge remarks that a solution of soap (¢=2°8 to 3) does uot spread upon a solution of Panama-wood (f=5'7) ; and it has been shown by one of us that the viscosity of the surface expiains why a solution of soap does not spread on a solution ofsaponine or of albumen; and, on the other hand, the liquid drop being viscous, there is no extension, or only a feeble one, since the slight difference in tension is equilibrated by the resistance of the viscous liquid. on Supersaturated Saline Solutions. 231 into a multitude of globules, and give the solution the appearance of an emulsion. In such a case the tensions of the two liquids are of nearly the same value ; if not, the agitation often produces crystalli- zation ; but even in the former case it was stated that a sudden jerk will sometimes produce immediate solidification of the solution. Now, taking the tension of the solution at 5:2, and that of oil of olives at 3:7, and the tension at the surface of separation of the solution and the oil-lens at about 2, then the sum 3°7-+2 is equal to the tension of the solution, and the spreading on the surface ought to be impos- sible, unless fine clear weather, absolutely clean vessels and solutions, and the absence of surface-viscosity concur to increase the surface- tension of the solution. At the surface of separation of the solution and of the glass, spreading may be possible in the case of certain oils without these concurring circumstances. Suppose a drop or a mi- nute globule of oil to be brought into direct contact with the wet solid side of the solution, as by the jerk above referred to, the film of solution is displaced and the oil can wet the solid side. It may hap- pen that the tension ¢ of the solution at the wall of the flask is greater than the sum of the tension ¢ of the surface of separation of the so- lution and of the oil plus the tension of the oil in contact with the solid side; that being the case, the instant solidification consequent on the jerk is accounted for. It will be seen, then, that when the drop of oil &c. remains as a lens on the surface, there is a diminution of tension at the surface of the solution in contact with the oil; but in such a case the tension is not sufficiently lowered at one point to render molecular equili- brium impossible at this point and so break up the whole system of supersaturation. But if the solution be agitated, so as to bring into contact with the surface of the glass a portion of the drop, there will still be diminution of tension at the surface of the solution in contact with the solid, and now the diminution is sufficient to pro- duce crystallization. ‘Thus it appears that oils may act differently according as they alter the tension of the liquid freely exposed to the air, or the tension of the liquid in contact with the glass, which is not of the same value. With respect to Proposition IIT. there is no difficulty. A liquid of considerable contractile force, such as pure water, produces no separation of salt in a solution of less contractile force. This explains a number of cases described in a note by one of us submitted-to the Society in July last*, in which solutions exposed for hours together to heavy rain did not crystallize, unless the rain brought down a speck of soot or some unclean body that lowered the surface-tension of the solution. Indeed we know of no liquid of superior tensile force to that of the solution, and not acting chemically upon it, that has any influence in producing crystallization. Proposition IV. also agrees with the phenomena. A glass rod or other solid, more or less smeared with a film of a liquid of low tension, when brought into contact with the solution determines crys- tallization by lowering the surface-tension. Such, then, is the func- * Proc. Roy. Soc. vol. xx. p. 41. 232 Geological Society. tion of a nucleus with respect to supersaturated saline solutions. If the solid be made chemically clean, it may be plunged into the solu- tion without altering its tension, and hence there is no separation of salt. And here it may be remarked that such a case is possible as that a crystal of the salt itself may be brought into contact with the solution without disturbing its tension, and hence be mactive. It has never been pretended that a crysial of the salt is not a good nu- cleus for a supersaturated solution of its own kind; all that has been stated by one of us is that, under special conditions, such a rystal may be lowered into the solution without acting as a nucleus. GEOLOGICAL SOCIETY. | Continued from p. 149. | April 10, 1872.— His Grace the Duke of Argyll, K.T., F.B.S., President, in the Chair. The following communication was read :— « Notice of some of the Secondary Effects of the Earthquake of the 10th January, 1869, in Cachar.” Communicated by Dr. Oldham, of Calcutta, with remarks by Robert Mallet, Esq., C.E., FRA. , This earthquake was a severe one, being strongly felt in Calentia, distant from the meizoseismic area-about 200 miles, and far into the plain of Bengal. The effects were examined on the spot a few weeks after the shock by Dr. Oldham, who anticipates being able to fix the position and depth of the centre of impulse by following the same methods as those first employed by Mr. Mallet with respect to the great Neapolitan earthquake of 1857. These results have not yet been received; but Dr. Oldham has forwarded an extremely interesting letter on the circumstances of production of very large earth-fissures, and of the welling up of water from these, derived from the water-bearing ooze-bed, upon which reposed the deep clay-beds in which the fissures were formed. Dr. Oldham rightly views all these fissures, which were all nearly parallel to and not far distant from the steep river-banks, as ‘secondary effects,” and not due to fractures produced by the direct passage of the wave of shock. He also shows that the welling up or overiiowing of the water in the fissures was a secondary effect also, and negatives the notion entertained on the spot of mud-yol- canoes &c. having originated at those fissures. The chief aim of Mr. Mallet’s remarks was to point out the importance to geologists of mghtly comprehending the dynamics of production of these phenomena, and to show that the older notions of geologists as to earthquake-fissures are untenable. He explained clearly, aided by diagrams, the train of forces by which the elastic wave of shock, on passing cut of the deep clay-beds where these have a free side forming the steep river-banks, dislodges certain por- tions and throws them off towards that free side—and that this is bet a case of the general law in accordance with which such elastic Intelligence and Miscellaneous Articles. 238 waves behave towards more or less incoherent deposits reposing on inclined or on leyel beds, under various conditions. Mr. Mallet also explained the dynamic conditions under which the water from water-bearing beds, such as that of ooze beneath the Cachar clay-beds, becomes elevated in the fissures formed, and gave approximate expressions for the minimum height to which the water can rise in relation to the velocity of the elastic wave particle. The paper concluded with some explanatory remarks upon the continual noises, like the irregular fire of distant artillery, heard long after the shock had passed, and when the country had become perfectly quiescent. The noble collection of photographs which were made by Dr. Oldham, and forwarded to Mr. Mallet, illustrative of the physical features of the huge earth-fissures and other effects of this earth- quake, were exhibited to the Fellows present, and are well worthy of attentive study. XXVIII. Intelligence and Miscellaneous Articles. ON THE INFLUENCE OF PRESSURE IN THE PHENOMENA OF EN- DOSMOSE AND EXOSMOSE. BY M. BECQUEREL. eee various causes to which the phenomena of endosmose, exos- mose, diffusion, and dialysis are due have been the object of the important researches of Dutrochet, Graham, Liebig, and other physi- cists and chemists, who have determined the part that each of them contributes in the production of the phenomena observed ; but they have not taken into consideration all the conditions which intervene in that production, especially the following :—(1) the pressure which acts as soon as endosmose has raised the level of one of the liquids above that of the other, whence results a filtration, through the se- parating film, of the most pressed liquid towards that which is less so, the effects of which appear to be subject to very simple laws, as we shall see; (2) the formation of an insoluble compound by the reaction of the two liquids upon each other when this takes place, a case which had not yet been examined; (3) the action of the electrocapillary currents resulting from the same reaction, which I have already brought before the Academy in several memoirs. I commence by giving a very succinct analysis of the researches of Dutrochet and Graham, as well as of those of Magnus and Liebig, on endosmose, in order the better to establish the relation of the effects which they observed to those about to be considered, relative to the influence of pressure on the filtration which takes place through a capillary film—an influence which makes itself perceptible in the phenomena of endosmose and exosmose, as well as in the effects resulting from the circulation of liquids in the tissues of living bodies, especially of the blood in the arteries and veins. Two apparatus were set up to exert pressures up to 2500 millims. of water or another liquid, and were provided with a cathetometer which permitted the determination of the height of the liquid columns 234 Intelligence and Miscellaneous Articles. with great accuracy. For diaphragm I took successively parch- ment paper, bladder, and a porous vessel of unglazed porcelain. The results obtained show that the ratios between the quantities of liquid which pass through and the mean pressures are constant ; that is, whatever be the liquid, the quantity which passes through in a given time Is proportional to the mean pressure, alcohol not excepted. I have found that, during the filtration, the outside of the porous vessel becomes covered with bubbles proceeding from the air con- tained in the water and in the diaphragm, which is disengaged in passing through the latter in consequence of the capillary affinity exerted by it upon the liquid. These bubbles, more or less obstructing the pores, render the filtration irregular—an inconvenience which is in great part got rid of by working with distilled water from which the air is expelled by boiling. But this is not the only error to be avoided; the inequality of calibre in different parts of the length of the tube is another for which allowance must be made. These two causes are sufficient to account for the differences which have been observed. The following coefficients were found to express the ratios between the mean pressures and the quantities of liquid filtered through a porous porcelain diaphragm in half an hour with the same filtering surface :— diydtochlone atids. 2.52.55 s aah ess 2: 0°187 Distilled waters. .i) P4534 S32 2 0°165 | increased by their AMMONa! 154 2c nee Veeke eee oe 0139 { volume of water. Chloride of calcium in solution at 35° 0°055. The experiments were made at temperatures varying from 15° to 20°. Itis to be remarked that, when experimenting with bladder, after a certain number of hours the cells are distended and the coefficients progressively increase until they become double; with vessels of porous porcelain nothing of the kind happens; the course of the flow is regular. Other solutions were also submitted to experiment; but in this abstract I shall only mention the results obtained with a solution of sulphate of soda and another of sulphate of lime, both concentrated and deprived of air, and giving rise by their reaction to an insoluble crystallized precipitate. «I have shown, in a previous memoir, that when a solution of nitrate of lime is introduced into a tube closed at the lower end with parchment paper, and the tube dips into a test-glass containing a solution of sulphate of soda, we soon see form on the surface of the diaphragm in contact with the sulphate solution, and also in that solution, a very great number of fistular stalactites of crystallized sulphate of lime, which little by little lengthen until they reach the bottom of the test-glass, where the substance spreads out. I then worked in the opposite direction: I poured into the tube containing the liquid exerting the pressure a solution of sulphate of soda, and the nitrate-of-lime solution into the test-glass, in order to Intelligence and Miscellaneous Articles. 235 force the sulphate through the diaphragm; I did not succeed in doing so. In seven hours the column was lowered one sixth; but, what is remarkable, the stalactites were not formed; merely a not very thick and pretty compact layer of crystals of sulphate of lime was deposited on the surface in contact with the sulphate solution. The pressure therefore hindered the formation of the stalactites and the passage of the sulphate solution into that of the nitrate. Some filtration-experiments were also made with defibrinated blood under 150 millims. pressure of mercury, equal to that of the blood in the arteries; the filtrate consisted of serum only. It is to be presumed that in the arteries, under the pressure of 150 millims. to which the blood is subject, there must be an infil- tration of serosity through the walls of the arteries in quantities proportional to the variations of the pressure. It has been said above, that the flow through the organic membrane distended the cells ; under the empire of life nothing like this should take place, at least in the normal state; equilibrium in the constitution of the vessels must be constantly maintained. ; We have now some conception of the possible origin of exosmose: it is due partly to diffusion, and partly to the filtration resulting from the pressure of the column of liquid resulting from endosmose. I conceive that it was hardly sensible in the experiments of Graham, who operated with large surfaces affording but little elevation to the liquid columns resulting from the endosmose. Dutrochet was right in saying that exosmose transports more of salts than endosmose, as exosmose results partly from pressure, which causes the liquid to filter through with the salt which it holds in solution.—Comptes Rendus de l Acad. des Sciences, July 8, 1872, pp. 50-52. ON THE ACTION OF OZONE UPON VULCANIZED CAOUTCHOUC. BY PROF. ARTHUR W. WRIGHT. In using the Holtz’s electro-machine, in the summer season it is often very difficult to make it retain any considerable charge, or even to keep up its action for more than a few minutes. ‘The ebonite insulators are found to have lost in a large degree their insulating power, and to have become conductors to such an extent that con- siderable sparks may be drawn from them at points several inches distant from the metal parts supported by them, thus dissipating the greater portion of the charge. ‘This is the usual condition of things when the machine, after much use, has stood for some weeks in the warmer portion of the year unused. ‘The surface of the ebonite becomes hygroscopic, condensing upon itself a large amount of moisture, the accumulated liquid being sometimes so abundant as to trickle down in drops. Having noticed on one occasion that this liquid had an acid taste, I was led to examine it more closely; and the ordinary tests very speedily showed it to be sulphuric acid. Its presence was a suffi- cient explanation of the defective insulation. Similar deposits of moisture were found upon the ebonite jackets of two induction-coils some time after they had been used. i Foe ee ee ee ee ee Cae ee ee a eR le ee oe © a Ad ay Ee oe en el ei —— ra ET ee Ee ee a ee ee ee ee 236 Intelligence and Miscellaneous Articles. As nothing containing sulphur had been used about the apparatus, the acid was evidently derived from the ebonite itself. The first thought was that the material had been heated in the process of vulcanization sufficiently to oxidize the sulphur; but as the sulphu- rous oxide, if thus formed, would be dissipated by the heat, this could hardly be regarded as the source of the sulphuric acid, especially as the latter did not appear until after the apparatus had been used. It is well known that vulcanized caoutchouc is affected by ozone, and that the ordinary rubber tubes through which it is passed are attacked and quickly perforated by it. It seemed most probable, then, that the acid was the result of the action of the ozone upon the insulators; and experiments were made which entirely confirmed this supposition. To the exit-tube of the ozonizing apparatus described in the Phil. Mag. for August(p. 156) was attached one end of a vulcanized rubber tube a few inches long, the other end being slipped upon the glass tube of a small wash-bottle containing some thirty or forty cubic cen- timetres of water. Air was slowly driven through the apparatus, and, having been strongly ozonized by the action of the electricity, bub- bled up through the water. This was continued for an hour anda half. At the end of this time common air was passed through the appara- tus to displace the ozone left in it, the tubes were removed, and the bottle closed with a glass stopper. On opening the bottle some time afterward, there was an unmistakable odour of sulphurous oxide, and the water reddened blue litmus paper very quickly and strongly. A strip of litmus paper, hung in the bottle so as not to touch the water, was completely reddened in a short time; and this happened even after several days had elapsed from the time of the experiment. The water tested with chloride of barium gave a considerable crys- talline precipitate, leaving no doubt of the presence of sulphuric acid. A small. slip was cut from a thin plate of ebonite, cleaned and dried, and placed in a small bottle, into which ozone was driven as before. In a short time it was bedewed with moisture having an acid taste, and exhibiting the same properties as that found upon the insulators of the machine. In order to determine whether the sulphur itself could be directly oxidized by ozone, a quantity of fine flowers of sulphur was gently rubbed into a loose lock of dry cotton, so as to diffuse it as much as possible. The cotton was placed in a dry wash-bottle, and connected | by means of a glass tube with a second wash-bottle containing a little water, all the connecting tubes being of glass. Ozone was passed through the bottles for an hour anda half; but at the end of this time not the slightest evidence of any action upon the sulphur could be detected. ‘This was what might have been expected; for as the air often contains a small percentage of ozone, sulphur exposed to it would undergo slow alteration, with loss of weight; and it does not appear that any thing of the kind has ever been observed. It is evident that while the ebonite is undergoing decomposition by the ozone, the oxygen combines with the issuing sulphur to form ‘sulphurous oxide, which with the atmospheric moisture produces Intelligence and Miscellaneous Articles. 237 sulphurous acid, this in turn being converted into sulphuric acid by the further action of the ozone. ‘The absorption of moisture from the atmosphere by the sulphuric acid produces the dew-like deposits observed. ‘ The deleterious effect upon the insulators can be remedied by neutralizing the acid with some substance which will not form a hygroscopic compound or essentially lessen the insulating power of the ebonite. I have used oxide and carbonate of magnesium with very good effect. A little of either of these substances in fine pow- der is sprinkled upon a soft cloth or piece of chamois leather and rubbed over the insulators. The excess is removed with a wet cloth, and the surface, after drying, cleaned and polished by rubbing with a soft woollen cloth very slightly moistened with carbonic disulphide. As the ebonite is attacked by the latter substance, care should be observed, in employing it, to use only so much as is needed to faci- litate the polishing process without injuring the surface. The ebonite may be somewhat discoloured by these operations; but the colour can be restored by rubving with a little oil, or will return of itself after a time. Probably a better method may be found; but this gives very good results. On one occasion, early last autumn, when the electro- machine had not been used for some months, the sparks obtained on charging it and using small condensers were only about one quarter of an inch in length, and the action of the apparatus was very feeble. The insulators were quite damp with the accumulated moisture. When this had been removed by the process described, sparks eight or nine inches in length were obtained at once, and the machine worked with nearly its usual energy.—Silliman’s American Journal for July 1872. 3 ON THE INSTANTANEOUS OXIDATION OF ALCOHOL, BY M. A. HOUZEAU. Here is a simple example of the direct conversion of alcohol into acetic acid and aldehyde, without the cooperation of any other agent than oxygen modified by electricity. if, into a bottle of half a litre capacity filled with concentrated moist ozone obtained by means of one of my single- or double-acting ozonizers, about 10 cubic centims. of absolute or hydrated alcohol be poured, a strong agitation of the bottle for a few seconds is suffi- cient to cause the neutral and almost inodorous alcohol to manifest a strong acid reaction with litmus paper, due to the acetic acid formed*, and exhales an odour of aldehyde, the presence of which is demonstrated by the reducing action of the liquor upon an ammoniacal salt of silver. But the most curious fact of the experi- ment is the simultaneous formation of relatively considerable quan- tities of oxygenated water; a few cubic centims. of the alcoholic liquor turn the mixture of chromic acid and ether deep blue. * After the action of ozone, alcohol saturated with lime-water and eva- porated to dryness leaves a residuum which liberates acctic acid on contact with diluted sulphuric acid. = 238 Intelligence and Miscellaneous Articles. On operating in like manner with ordinary oxygen (that is, before the gas has undergone the obscure electrification), nothing similar is observed. Even after twenty-four hours of contact the alcohol remained neutral, inodorous, and without action upon either the salt of silver or chromic acid. Ether, in the same circumstances, undergoes from concentrated ozone an analogous and still more rapid oxidation, attended by the production of oxygenated water. If we compare these effects of oxidation with the similar effects upon alcohol of contact with oxidizing bodies such as chromic acid, a mixture of sulphuric acid and bichromate of potass, &c., one cannot but recognize the profound analogy which seems to exist between free ozone and oxygen as it exists in its combinations; indeed it was this very analogy which led me long ago to suppose that ozone might be only the primitive state of oxygen. However this may be, these experiments demonstrate that con- centrated ozone (which can now be easily produced with my ozonizing tubes) is an oxidizing agent at the same time simple and energetic, the employment of which may be useful in researches of organic chemistry. When we endeavour to calculate the real quantity of ozone con- tained in odoriferous oxygen from the products of the oxidation of alcohol, and compare the result with that furnished by the oxidation of either iodide of potassium or metallic silver, the numbers arrived at differ remarkably from one another, and silver gives the smallest product. Hence at present we ought not to accept without reserve the numbers expressing that quantity of ozone. In concluding I cannot too strongly advise chemists who make use of concentrated ozone to do so with the utmost caution ; breathed, even in very small quantity, it suddenly occasions inflammation of the mucous membranes, which I have known to bring on spitting of blood. —Comptes Rendus de Acad. des Sciences, July 15, 1872, pp. 142, 148. ON SOME EFFECTS OF SLOW ACTIONS, PRODUCED IN THE COURSE OF A CERTAIN NUMBER OF YEARS. BY M. BECQUEREL. I have already called the attention of the Academy to the effects © which constitute the subject of this memoir; but I have thought it necessary to resume the question in order to develope it further, and then to show the influence of time in the effects produced. I used, in these researches, either a cracked tube filled with a metallic solution and dipping in an alkaline solution in which a metallic oxide was dissolved, or a porous diaphragm of unglazed por- celain instead of the tube, or a glass vessel hermetically sealed, con- taining an acid or alkaline solution in which was immersed a mineral substance. With an electrocapillary apparatus, a solution of gold and another of plumbate of potash gave, in the space of two years, on the one hand minium in the crystallized condition, similar to that obtained in the dry way, and, on the other, metallic gold. Intelligence and Miscellaneous Articles. 239 Among the products obtained in consequence of slow actions in a vessel hermetically sealed during twenty years, and which have their analogues in nature,-I will mention the following :— (1) Some crystals of arragonite, formed upon a piece of gypsum shaped like a spearhead, 1 decim. in length and | centim. in thick- ness, digested in a solution of bicarbonate of potash contained in a vessel hermetically sealed; the sulphate of lime almost entirely dis- appeared, and there remained a thick coating of crystals of arragonite. (2) Operating with a solution of subcarbonate produced rhombo- hedric crystals of carbonate of lime. (3) A similar piece of gypsum, kept during the same time in con- tact with a solution of arseniate of ammonia, gave crystals of arseniate of lime, perhaps as fine as the natural ones. (4) With a solution of aluminate of potass and gypsum, I obtained crystallized double sulphate of lime and potass, which is no other than glauberite in which soda has been replaced by potass. (5) Pieces of galena, immersed during twenty years in a solution of bicarbonate of potass, gave well-characterized crystals of carbonate of lead belonging to the system of the right prism with rhombic base. (6) With pieces of limestone immersed in a solution of plumbate of potass, I obtained hydrated carbonate of lead in crystalline scales with a nacreous aspect. (7) Malachite (bibasic carbonate of copper) I had already obtained by the reaction of a solution of nitrate of copper upon limestone to change it into subnitrate, which was then digested with bicarbonate of soda to form a double carbonate, which was decomposed with a fresh solution of nitrate of copper. Working thus I obtained a crust of more or less thickness adhering to the surface cf the lime- stone. I studied this formation again, modifying the process. The limestone was in slabs of 1 centim. thickness; and the operation took place in vacuo, in order that the solutions might penetrate the interior of the slabs and the gases formed there escape. By working with a solution not much concentrated, it was ascertained that the first two transformations sufficed for obtaining a slab of malachite sensibly free from lime and nitric acid, having the same grain as the limestone; the epigeny, therefore, was complete. The grains are in the crystalline state. Under high pressures the same result may probably be obtained with rather compact limestone. The effects of the slow actions we have here considered, and which sometimes produce epigeny (that is, replacement of substances by other substances without changing either the form of the body or those of its constituent parts), I explain as follows :— When, for example, porous limestone is digested in a concentrated solution of nitrate of copper, there results from the reaction which takes place a disengagement of carbonic acid gas and a production of nitrate of lime, which remains in solution, and of insoluble sub- nitrate of copper, which takes the place of the grains of limestone thus transformed into subnitrate, as the subnitrate is forced to occupy the place of the grains of limestone by the carbonic acid gas and the solution of nitrate of lime filling the pores. The gas and the solu- 240 Intelligence and Miscellaneous Articles. tion of nitrate of lime can only issue completely from the pores by placing the transformed limestone in the vacuum of the air-pump in contact with the water and renewing it from time to time. When the subnitrate is placed in contact with a solution of bicar- bonate of soda to change it into malachite, nitrate of soda remains for a long time in the pores, which in time effloresces upon the sur- face of the malachite, so great is the molecular attraction exerted by the walls of the pores upon this compound. I do not speak of the electrochemical effects which may intervene in the actions of which we have spoken, because I have already described them. The analyses of the substances above mentioned were made by M. Guéraut, a distinguished pupil from the Laboratory for Advanced Studies, under the direction of our confrére M. Fremy, at the Mu- seum of Natural History, whom the Minister of Public Instruction kindly placed at my disposal to aid me in my experiments.—Comptes Rendus de ? Acad. des Sciences, July 8, 1872, pp. 52-54. REPLY TO PROFESSOR CLAUSIUS. BY P. G. TAIT. Professor Clausius has so long, and so repeatedly, claimed as his own the correct proof of the Second Law of Thermodynamics, that no one can be astonished to find him unwilling to allow that his claims are unfounded. But I must protest against his making accusations of deliberate suppression (dbsichtlichkeit) &c. and repeating them in the indirect and offensive form of a statement that he did not apply them to Sir W. Thomson. There has been nothing in the language I have employed, even had it been tenfold more pointed, which is not admissible in fair and temperate discussion. I have made no charges (though strongly tempted to do so by Professor Clausius’s first letter), I have simply examined historical facts and given what appears to me to be the natural and inevitable conclusion from them. But, after having taken every precaution to insure accuracy, to be first accused of deliberate suppression, and then to be told that the tone of my far too mild reply renders it impossible for Professor Clausius to continue the discussion, is a trifle too much. In common with all the scientific friends I have consulted, I am unable to perceive that Professor Clausius has “‘ refuted’ any one of my former remarks, or that he is likely to be able to refute any of the others—though he says it can be easily done. Let Professor Clausius attempt the refutation, if he thinks proper to do so: but in future it is to be hoped he will leave offensive and unjust charges unmade. As I consider that my last letter contains all that it is necessary for the present to say for my own view of the matter, I shall continue to maintain and to promulgate the opinions therein expressed, until convinced by argument, not by personalities, that they are incorrect or insufficient. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES. ] OCTOBER 1872. XXIX. On the Cooling of Gases. By MM. Jamin and RicHarp*. ULONG and Petit, in their celebrated work on the laws of cooling, studied first the effect of a vacuum. They found that the velocity of cooling of a thermometer in the centre is expressed by the formula v=ma‘(a'—1). a is an invariable quantity, m a coefficient proportional to the surface and the emissive power of the thermometer, ¢+ @ and 6 the temperatures of the thermometer and the enclosure. No objection can be made to this law, which has moreover been confirmed by the admirable researches of De la Provostaye and Desains. The second part of the work, which is devoted to the study of gases, is not so unexceptionable. Dulong and Petit, remarking that in this case the diminution of temperature is more rapid, assume :—(1) that the radiation persists without alteration, just as if it took place in vacuo; °(2) that the augmentation of the observed effect represents the cooling-power of the gas. They then measure the total velocity of cooling, V, from which they subtract » (that which would take place in vacuo for the same values of 0 and #), and find that the remainder v’ satisfies the relation Dee It is sensibly equal to 0:5; and mis a coefficient which de- * Translated from the Comptes Rendus de l’Académie des Sciences, vol. Ixxv. pp. 105-113. Phil, Mag. S, 4, Vol. 44, No, 298. Oct, 1872, R 242 MM. Jamin and Richard on the Cooling of Gases. pends only on the gas—very small for carbonic acid, greater for air, and very considerable for hydrogen. It is assumed that v! measures the effect of the gas. In reasoning thus, Dulong and Petit make a pure hypothesis, and probably commit an error. It is always possible to repre- sent the total velocity V by the sum v+v'; but it is not proved that v expresses the radiation as it exists in the gas, and v’ the cooling due to the gas itself. On the contrary, it is probable that the radiation is less than v, since the gas is imperfectly diathermanous, as Tyndall has proved, and consequently that the effect attributable to the gas must be augmented by so much. Besides, Dulong and Petit appear to have taken no account of the kind of action exerted by the gas; at least they do not attempt to explain it. They present that action as a fact; they assume that the gas remains at the temperature of the enclosure, that the presence of the thermometer changes neither its tem- perature nor its pressure. The apparatus they employ would not permit the ascertaining of this change, if it took place. Thus they overlooked the true conditions of the problem. In truth, the gas is warmed, and its pressure increases. Let us take a glass balloon immersed in water, furnished with a sen- sitive manometer, and traversed along one of its diameters by a fine and resisting platinum wire. As scon as it is heated by an electric current, we shall see the manometer rise progressively and the temperature of the gas increase. One of us, in a pre- vious study, even ascertained that the heating was much greater in proportion as the pressure and volume were less. This observation explains to us, in the first place, the pertur- bations discovered by MM. de la Provostaye and Desains in the case of yery small enclosures and feeble pressures. The gas being then very much heated, its temperature can no longer be confounded with @ (that of the enclosure) and the excess ¢ measured by the difference between the degree of the thermometer and @. ‘The real excess is smaller; the factor ¢¢ must be dimi- nished, either by replacing ¢ by its true value and diminishing d, or by attributing to d decreasing values variable with the pressure H. But this fact has a still greater importance in that it clearly reveals the part played by the gas during the cooling. It is heated by contact with the thermometer, and transmits the heat to the exterior covering, which absorbs it. At the first instant it receives more than it gives up; and the manometer rises pro- gressively with a decreasing velocity, then remains stationary when the heat taken up by the thermometer is equal to that which it yields to the enclosure. The gas, therefore, acts as a conducting mass, being heated on one side, cooled on the other, : 4 % i! 4 J rf t 2 v ‘ ; MM. Jamin and Richard on the Cooling of Gases. 248 serving as a vehicle for the heat, and being in unstable equili- brium between the gain and the loss. But-its mode of conductivity is quite special. Let us in thought divide the gaseous mass into two concentric equal parts by an impermeable partition placed between the thermometer and the enclosure. We can imagine the interior mass alone being heated 27, taking an excess of pressure 2h. If we open the partition, the pressure and the temperature will fall + and h in this mass, but will rise as much in the part exterior to the partition ; both will then have the same pressure and the same heating. This reasonmg may be repeated by multiplying the partitions; and on passing afterwards to continuity, we find that the heat is transmitted from the thermometer as far as the en- closing boundary with and by the transmission of the pressures, and that the temperature is the same at every point. But a thermometer placed at one point will not give this temperature ; for it will receive and absorb the heat radiated through the gas, of which it will receive sc much less as it is nearer one side of the vessel. _ It will be remarked that, the transmission of the pressure being instantaneous, it will be the same with the propagation of the heat from the ‘centre to the exterior—and that if different gases become heated or cooled more or less rapidly, this can only: depend on the greater or less rapidity with which they take heat: from a heated solid surface or give it up to the wall of the vessel: which contains them. In short, gases have an instantaneous: internal conductivity, and place themselves in equilibrium of temperature and pressure. These conclusions, however, sup- pose that they are diathermanous. The part played by gases being so well defined, it will be con- ceived how their cooling-power can be deduced. Let us replace Dulong’s thermometer by a wire heated by means of an electric current to an excess of temperature ¢. It will lose during each unit of time a quantity of heat equal to — Peo and give it up to the gas. This will take excesses of temperature and pressure d@ and h, and eee to its envelope the quantity of heat pe Te When the stationary condition is attained, this gain and this loss will be equal, and we shall have —Pe7 =pe— Abe cist eae nck Dip lS) On the other hand, the heat given up by the gas to the en- closure is proportional to the surface of contact s, to a factor which will be special for each gas, and to a function of H and 244. MM. Jamin and Richard on the Cooling of Gases. of h; we shall therefore have dbo pe-7, =sKf(H, 4). L: Ss) “Se If, then, we knew /(H, 4)—that is to say, if we knew the law according to which the velocity of cooling of a heated gas dx at ould be calculated b f equation (1), and » 7, could be caleu ated by means of equation (1), and we could measure directly and without hypothesis the cooling-power of the gas. The two questions are connected and equally inter- esting. We shall therefore divide this memoir into two parts, and, Ist, study the cooling of heated gases within an enclosure ; 2ndly, measure the heat given up to these same gases by a heated solid placed in their midst. Part I. Laws of the Cooling of Gases. The apparatus consists of a large balloon of glass, 32 centims. in diameter. It is immersed in a vat at @ degrees filled with water which is continually agitated by a current of air, and con- nected with a mercurial manometer, which, observed by means of a cathetometer, gives the initial pressure H. The balloon is accompanied by a bottle, which shares its temperature; the two communicate by a three-way cock, through which a vacuum can be produced in both or a gas introduced at the same pres- sure. When this is done, the communication is closed, and a second is opened through a differential water-manometer, one of the two branches of which communicates with the bottle, the other with the balloon. The heights are equal when the tempe- ratures are the same; but if we heat the gas in the balloon, it assumes an excess of pressure 2, which the manometer measures with great delicacy, since it contains water, whatever the initial pressure H. 7 The balloon is traversed along one of its horizontal diameters by a platinum spiral of great resistance; thisis a focus, of neg- ligible mass, which developes, by means of an electric current, a known quantity of heat, of which one part traverses the enclo- sure by radiation, while the other heats the gas. The wire is heated to redness; and when the manometer has attained its stationary condition, the circuit is broken. The spiral is extin- guished immediately; at the end of ten seconds it is entirely cooled; and from that moment / diminishes regularly with de- creasing rapidity. Then, while an assistant counts the time aloud, at the end of every five seconds the observer reads the value of A, which is written down by a third person. Use readily familiarizes this kind of observation; and more precision varies MM. Jamin and Richard on the Cooling of Gases. 245 is attainable than could be supposed. One then constructs the curves of the values of 2, taking the times for abscisse. They differ from one another; and it is immediately seen that the cooling is as much more rapid as the pressure H is less. These curves express the phenomenon graphically ; we must now find the equation. We thought at first that, the excess of pressure / being very small, Newton’s law h=Me-“ could be applied. Indeed it differs very little from experience, which it represents well enough for a time not very great; but it cannot embrace the whole of the observations. We made the compari- son by three operations. First we took, upon the curve, abscissz in arithmetical progression: the successive ordinates were to be in a constant ratio; they were not found to be exactly so. Then we drew tangents which should satisfy the condition dh irs =ah loge; that is to say, - ought to represent the ordinates of a straight line of which f would be the abscissa; but we ascertained that the line thus constructed had a parabolic form. The third and best process is the following. Newton’s law gives log h= log m—az loge, which is the equation of a straight line forming with the axis of #2 an angle whose tangent is —aloge. In reality the line is curved ; Newton’s law must therefore be rejected. We then thought to express by Dulong’s formula the heat which a gas yields to its envelope, which regulates that which the gas takes from the central thermometer, and which would be a UP a esigga’ ees GRA Se cee at SOEs) dz or else, replacing d6@ by its value as a function of h, which is ee ah 2 enh fe Ae Mea Ge dae yale? e e e e ° e (4) or else, finally, taking the logarithms of both sides, log (- = logm+d' log h—(d'—c)log H. . (5) by Under this form equation (5) has been completely verified ; it signifies :— fe al (1) That, for any constant values of the pressure H, log (— =| represents the ordinates of a first system of straight lines, all parallel, whose abscisse are lug /, and which make with the axis 246 MM. Jamin and Richard on the Cooling of Gases. of the abscissz an angle the tangent of which is equal to the expo- nent d’; (2) That, for any constant values of the excess of pressure h, the values of log { — se are represented by the ordinates of a second system of parallel straight lines whose abscissz are log H, and which make with the axis of the abscissee an angle the tan- gent of which is equal to the exponent d’—c’. We will indicate how the verifications were made, taking hy- drogen for example. Under pressures successively equal to 823°7 millims., 689°7 millims, ..., the value of h was observed every five seconds (as was said befor e); then, on one and the same sheet of ruled paper, the values of h were construc ected, the time being taken for ab- scissa—which gave as mnany curves as there were series of ob- servations; and upon these curves the points having equal ordinates h 200, 190,..., were marked by horizontal lines. These values of / are entered in the first column of the opposite Table. The tangents were drawn to these several points, and the value of - obtained for each curve. They are placed in the columns marked A. (1) The and the same value of H and to different excesses of pressure ; and if, taking log / for abscissee, we construct the line whose or- dh . 7B each column A correspond to one i dinates are log(— =), it is found to be exactly a right line. On repeating the same construction the same result is found for each of the pressures H. Moreover all these right lines are parallel, and differ only by the ordinate at the origin; they make with the axis of the abscissee an angle the tangent of which is =1:2. The exponent d' is therefore equal to this number. : adh’ The columns No.1 contain the values of — Fe derived from the several right lines opposite the observed numbers of series A. The agreement is very satisfactory. dh (2) The observed values of — a in any of the horizontal lines answer to equal values of the excess of pressure f and to different dh initial pressures H. The logarithms of — Jp te constructed by taking for abscisse the values of log H; and as many outlines are obtaized as there are horizontal lmes in the Table. We find that they represent a second system of right lines, all parallel, d on the Cooling of Gases. 247 1 d Richar min an MM. 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FBP= Tl ee ee eee Se ee = Pe EB A at hale RES grag am a a 7 Ei ST Sa RS IN Ov 8-E 6-§ Ué 0-€ &E Gs 0-G GG LV 6-€ 0-7 £°9 G9 €-9 1G 6-7 O-G LL GL GL 1-9 6G 8-G 68 8-8 6-8 LZ 6-9 EL GOL) GOL | L010 | &8 0-8 v8 Ee Sele Gils || eGo L6 &-6 Sél | Gél | GEL | GOL | GOL | 0-01 GPL | GFL | £hL | PIE | Sth | GIT VSL | 8ST | O9L | €6T | Vel | 9-é1 OoONG| BO Vasile GG cackelieOoc L O21 | 88l | 6:61 | &Fl | Gr) OT 61 | 606 | G06 | 9-ST | O-9L | 6-S1 9-06 | GIS) 616 | 9-91 | ELE | F-91 C66 | &E6 | £16 | &8l | &8E | €-81 8-SI | G-6L | €-8T 0:06 | 6:06 | 9-6 (GON | TON "PaArS "6 ON | “ON “PpoAros AO) -4O “poqupnoeg ‘Vv "pozepno[ea ‘Vv an xp YP UP ; ‘StUTTU 4.689= 1 LG LG 9-€ 9-€ a VV VG £9 £-9 G9 EL 66 v8 G8 L-6 1-6 0-0T | 1-01 O-[L | T-Il GIL | &él Lél| €&€l 6-E1 | GFT €-E1 | €-S1 VOL | €-91 I-41 | &-8t 6-21 | £81 ‘ON | "1 ‘ON *poqepnoyeg “p YP OF | [acca [22799 cecenrayy jreee*gg P2506 eee COTS | eeiacee aay | [ROCHA | ger OPE } [eine ne Sree gy [22 ae SBCA Yo) | [ee° 9G 7 serene 1g GY Wg 19 > Dk 6 19 SOS GN *POAIOS a SUD) “Vv “SUUTTTIU /-868= ‘uasorpATy oF Rg oe ie 248 MM. Jamin and Richard on the Cooling of Gases. making with the axis of the abscisse an angle whose tangent Is — 0°66, which signifies that the exponent d'—c' is =0°66, or ee dh that c’=0°54. The columns No. 2 indicate the values of — oe derived from the right lines of the second system, opposite the observed values; and it can be seen that they are equal to them. This happy method has therefore permitted us to verify sepa- rately the law relating to the two variables H and f, and to determine the two exponents c’ and d'. The coefficient m 1s deduced from formula (38) : _ dh H?-" = es pea m As many values are found as there have been observations ; and the complete equality of all the results is a wholesale verification of the formula found. ! n Value of m= = a Hydrogen (pressure 689°7 millims.). h. n'. h. a DOO. ae teeta 120 - « eae HOO” ee ere ees 110. A) sae 18083 Deere 70 100°. Mik 2 as AO ia ses aes ees 00>... ‘+s. ) seo MOOI at oe One SO. 3s oi aes POU es Or 70. 3.) oe AOS ee Pee OS 60° i Ss ae TSOP ea sce OF Mean . 92°69 Formula (38) gives, for the velocity of diminution of pressure of heated hydrogen, ga ea wees ene. ene ae b= 2°69), ne Such is the final formula, which sums up all the observations. There only remained the extension of it to other gases, which we did for carbonic acid and air, the following being the numbers found :— Carbonic acid. Air. Hydrogen. Mean. / Se at nO Woe unk els eee a do ss 0-54. 054 Ges 0:54 7 ape mer B8 1 118 1°20 1°16 ! 5 ' ; Mr. T. E. Thorpe on an Improved form of Filter-Pump. 249 To recapitulate :— (1) The velocity of cooling of gases = is expressed by Dulong’s formula _ ah nlHe36e. (2) The exponents c’ and ad! are the same for all gases, and sensibly equal to those found by Dulong for solid bodies. (3) n’ is different according to the gas; in our experiments it has constantly the same ratio as in Dulong’s. (4) The quantity of heat lost in the unit of time is poe’ SK Hen, Soir iaelemikiee see Meru) or, reducing, — Fh _Kt te peage, dx The coefficient n’ is therefore ar as the radius of the bal- loon, proportional to (1+ a@) and to a factor K characteristic of each gas. XXX. On an Improved form of Filter-Pump. By T. EH. Tuorer, F.RS.EL* [| With a Plate. ] ie the Berichte der Deutschen Chemischen Gesellschaft (No. 7 1872), Dr. Mendelejeff is reported to have described a new form of ae -pump devised by M. Jogno, of Moscow, which is so exceedingly simple and efficacious that it will doubtless be univer- sally set up in laboratories. The disposition of the apparatus will be readily understood from the annexed figure (Plate III.), which represents it in the modified form about to be described. It con- sists of atube A A about 1 metre in length and from 8 to 10 mil- limetres in diameter, to the side of which is affixed a side tube B about 5 centims. in length. The upper end of the vertical tube A is cut slantwise in the manner represented in the enlarged figure (fig. 2), and is connected by means of a strong but sufficiently elastic caoutchouc tube with the stopcock C in connexion with the water-supply. In the original apparatus a Bunsen valve was fitted into the side tube; that is, the caoutchoue tube DD was stopped at the upper end witha short piece of glass rod and cut along its length near the end by a smart blow from a chisel. * Communicated by the Author, having been read before the British Association at Brighton, 1872. 250 Mr. T. E. Thorpe on an Improved form of Filter-Pump. The edges of the slit were thus left sharp ; and on applying any outward pressure to the tube they readily adhered, making a perfectly air-tight conjunction. The valve was then pushed within the tube B, which was narrowed at the end so as to retain the caoutchouc tube perfectly air-tight. The other end of the caoutchouc tube DD was connected with the vessel to be eva- cuated. On allowing the water from the main to flow through the vertical tube, the caoutchouc tube commences to pulsate rapidly as it falls over the upper edge of the tube A, and periodi- cally closes the opening. The Bunsen valve in consequence intermittently opens and shuts, and rapid suction is set up; and it is thus easy to obtain a vacuum equivalent to 0:7 metre of mercury. The working of the apparatus is obviously akin to that of the hydraulic ram; so easily and efficaciously does it exhaust, that it will doubtless take the place of the Bunsen filter- pump. It has the great advantage of portability over the older form, since it may be so constructed that it can be transported to any position in the laboratory: it obviates the necessity of a fall of upwards of 30 feet, and therefore requires no alteration in the existing arrangements of pipes and fittings; and, lastly, its cost need not exceed a few shillings. - There are a few disadvantages connected with the use of the Hosa valve above described, Owing to the gradual dimi- nution of its elasticity by long-continued working, its efficacy diminishes after a time; it not only then fails to bring about rapid exhaustion, but so soon as the conjunction of its edges ceases to be perfect, it allows the water to flow back into the eaoutchouc tube. To obviate these inconveniences another form of valve was devised. A hollow metal cone shaped like a funnel is soldered air-tight into the end of the side tube B (fig. 2). This cone is pierced near its apex with a number of holes, and into it is fitted a piece of unvulcanized sheet caoutchouc shaped like a filter. This is retained in its place bya small screw passing through the sheet caoutchouc and into the apex of the cone. By its elasticity the india-rubber sheet presses firmly against the sides of the cone and effectually prevents the entrance of air or water from the tube A; but the slightest pressure from within B is suf- ficient to disturb the adhesion, and to allow of the ready trans- raission of air through the holes in the cone. This valve is ofa more durable and permanent character than the original form, and permits of a more rapid exhaustion. in the modified form of the instrument a manometer M is fixed to B: this allows the degree of exhaustion to be immediately ascertained from the position of the mercury along the graduated scale. The rapidity of the pulsations in the caoutchoue tube WW may be regulated by the moveable arm T, which by means of a screw can be clamped Dr. H. F. Weber on the Specific Heat of Carbon. 251 in any desired position. The screw S serves to regulate the ra- pidity of the exhaustion, or, in cases of simple aspiration, the amount of air passing through the holes in the cone. S! isa clamping arrangement, by which the vacuum within the pump can be maintained without disturbing the screw S if it should be necessary suddenly to disconnect the caoutchouc tube D from the vessel to be exhausted. This brief account of the slight but serviceable modifications in the original instrument of M. Jogno is made with the object of introducing an exceedingly valuable piece of laboratory appa- ratus to a more extended notice than it has hitherto met with in this country. XXXI. On the Specific Heat of Carbon. By H. F. Waser, Assistant in the Physical Laboratory of Geh.-R. Helmholtz.* To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, Berlin, 25th Aug. 1872. i yesterday’s Number of the ‘Atheneum,’ 24th August, p. 238, I find the following :-— ‘ BrittsH AssocraATION. Section B. Chemical Science. “ Mr. Dewar made a communication ‘ On the Specific Heat of Bodies at high temperatures, with particular reference to that of Carbon,’ which he showed, from the results of a very carefully conducted series of experiments, mcreased in a very rapid man- ner with the increment of temperature. His observations were made at the temperature of boiling zinc, and of the oxyhydrogen blowpipe &c.” This property of carbon, however, I had previously discovered, and laid a detailed memoir on the subject before the Physical and Chemical Society of Berlin. An abstract of that memoir was published in the Berichte der deutschen chemischen Gesellschaft in April of this year. The latter seems to have escaped the notice of the Chemical Section of the British Association. As from this it appears that the Berichte are not so widely cireu- lated m England as we in Germany think, I request you to print the enclosed brief memoir and this letter in the next Number of your valued Journal. Your most obedient, Dr. Frizprich WEBER. In 1819 Dulong and Petit deduced, from the investigation of * Translated from a separate copy communicated by the Author, from the Berichte der deutschen chem. Geselisch. zu Berlin, having been read by the Author at the Meeting on the 24th of March, and at the Physical Society on the 21st of March, 1872. : > 252 Dr. H. F. Weber on the Specific Heat of Carbon. twelve metals, the law that the product of atomic weight and specific heat, the so-called atomic heat, has the same value for all elements, about 6:3. In numerous trials, carried on from 1840 to 1862, M. Regnault tested the universal validity of this law of Dulong and Petit. The result was, that for most solid elements it is approximately true; only the specific heats must be deter- mined at temperatures sufficiently below the melting-points of the elements in question. For 82 solid elements the mean of the atomic heats obtained was 6°3, with extremes of 6°76 for sodium and 5:7 for sulphur; phosphorus and silicium have con- siderably smaller atomic heats, namely 5°39 and 5:04, while erytallized boron has only 2°67, and crystallized carbon even as little as 1°76. Accordingly boron and carbon stand far outside the sphere of the validity of Dulong and Petit’s law. This remarkable exceptional position of carbon induced Reg- nault to determine comprehensively the specific heats of its various allotropic modifications. In his second memoir on specific heat (1841) he showed that the different allotropic modifications of carbon possess quite different specific heats, and that not one of them fulfils the law of Dulong and Petit. That is to say, the following were the specific heats obtained :—for Animal Charcoal . . . 0°2608 Wood charcoal . . . O:2415 = Cokteyi ei. Wise, Worst io Ore Olea Gas-C0aliei pie a) te ey. 020386 Native graphite... |...) 0;2019 urmaceserapnitey: 2). O,Lo70 Dramond’e i.e. es LOMAS A second series of experiments, made in 1862, gave the values :— 0:1987 02020 > for three different pieces of Canadian graphite. OgN) 01988 for Siberian graphite. 0:2000 for pure gas-coal. Almost simultaneously with Regnault, De la Rive and Marcet investigated the specific heat of carbon by the cooling method. They found for charcoal from oil of turpentine 0°1801, for pure sugar charcoal 0:140—0°159, and for diamond 0°119 as the valucs of the specific heat; but they are too great, from two causes: first, the specific heat of copper, which served for comparison, was set 4 per cent. too high; and secondly, the values given by the cooling method, for all substances which are not good con- ductors of heat, are always too great. The difference between the results obtained by Regnault and by Dela Rive and Marcet i “4 a Dr. H. F. Weber on the Specific Heat of Carbon. 253 thus becomes extraordinarily great—so great that it is impossible to account for it by the different methods used for the determi- nation, by errors of observation, impurity of the substances, &c. Kopp, in his comprehensive investigation of the specific heat of solid bodies (1865), subjected that of carbon to a new deter- mination. By means of the mixing method somewhat modified by him, he obtained for the specific heat of Gaseous. OTS Wativeveraphite “~~. °, 0-174 Furnace graphite . . 0°165, values from 9 to 16 per cent. less than those found by Regnault. These considerably smaller values determine M. Kopp to the as- sumption that carbon in all its modifications has only one and the same specific heat, that of the diamond, 0°1469, and conse- quently that carbon forms an indisputable exception to the law of Dulong and Petit. - In the numbers found by him for gas-coal and graphite, rather greater than 0°1469, he sees the influence of condensed gases and vapours; and Regnault’s still higher numbers he accounts for by the heat of moistening which ensues when the heated porous substance is immersed in the water of the calorimeter. In order to test this latter assumption of M. Kopp, a new and eareful determination of the specific heat of carbon was recently (1868) undertaken by Willner and Bettendorf, in the memoir entitled “‘ Experiments on the Specific Heat of Allotropic Modi- fications.” ‘Their procedure was in substance that of M. Kopp; only it was carried out with greater accuracy, and the heat of moistening was excluded. The specific heats obtained were :— for gas-coal . . . . 0:2040 pilative staphiter, a.) 02900 » furnace graphite. . 0O-1961 3 diamond = 70% esis HO81488 But these values almost exactly agree with those found by M. Regnault. Hence Willner and Bettendorf conclude that “in- deed essentially different specific heats belong to the different forms of carbon; and the heat of moistening of the porous forms does not, as Kopp assumes, cause their specific heat to appear too great.” A slight error, however, has slipped into the calculation of the above values, through the following circumstance. The sub- stance under examination (1-5 grms.) was heated in a glass with water (1-5 grms.) to about 70°, and cooled in the calorimeter to about 20°. In the calculation it was assumed that the specific heat of this water was constant and equal to 1; but the mean specific heat of water between 20° and 70° is 1:004. The effect 254 Dr. H. F. Weber on the Specific Heat of Carbon. of this apparently small variation is that the values found for gas-coal and graphite must be diminished by 14 or 2 per cent.* The amount of this correction for the diamond cannot be calcu- lated from the data given in the memoir mentioned, because they appear to be vitiated by numerous misprints; most pro- bably, however, it is of the same order as the above; and con- sequently the very good accordance mentioned between the values found by MM. Wiillner and Bettendorf and by M. Regnault vanishes. In order to afford a readier view, the results of the four series of experiments just mentioned are placed together in the follow- ing Table :— Wood Native | Furnace |,,. Temperature- sOBservers, charcoal. Gas-coal. graphite. | graphite. Te interval. Regnault......... 02415 | 020386 | 0:2019 | 0:1970 | 0:1469 8° to 98° De la Rive and § x ° ° Aha: I WE eee cerry oa Pb aceehee ag | jeeteece 01146 | 38°to 14 KOR acces) becoming independent of n, except as toits phase. This might have been anticipated from (1). : The roots of the equations J,(z)=0, J',(z)=0 are all real. When z is very great, they approximate respectively to ne oe ae earn rae se 4m+2n+1 eM rae mney) aay var * Series (4) was employed by Hansen im his calculations of Bessel’s functions. Hansen’s Tables will be found in Lommel, Studien iiber die Bessell’schen Funktionen, Leipzig. Mr. J. W. L. Glaisher (to whom I am indebted for the loan of Lommel) informs me that the B.A. Committee on Mathematical Tables, of which he is the Secretary, are about to turn their attention to the completion of the existing Tables of Bessel’s functions. Convenient expressions for the caleulation of Jn, and the roots of the equa- tion Jn=0, for n=0, and (virtually) n=1, are given in Professor Stokes’s paper referred to below. 330 The Hon. J. W. Strutt on Bessel’s Functions. where m is an integer; but the smaller roots deviate greatly from these values. If +p denote the roots of J,(z)=0 (exclusive of zero), | O=srepy shat (a whence, from bi 34 ES a TH 2.4. (2n+ 2) (2n+ 4) 26 — 2.4.6. 2n+2)Qn4+4)Qn+6) 1°" . 2 2 = log {1-5} + log {1-5 h4 eee < P; D3 Expanding both sides in rising powers of z, we find, on equating coefficients, Bs toil am i 4(n+1) 1 Si p* ~~ 16(n+1)2(n+2) cs For example, if n=0, and, if n=1, ar har a WT In a similar manner, if +g denote the roots of J’,(z)=0 (n not being zero), linea > Gg ~ dn(n-+ 1) &e. Ifi.n=0, Sais Ce > @ 8 It should be noticed that a well-known enero is included as a particular case. Ifn=4, Ji wsinz, and Se == = Since we know that the roots are of the form + mz, we infer that 1 1 s 1 Tm 6 Very simple relations exist between the functions of neigh- bouring orders. As I shall have occasion to refer to them, I The Hon. J. W. Strutt on Bessel’s Functions. 3315 state them here. They may easily be proved from the ascend- ing series. 2J! Stes Get ees | 2 ps | a ge Rie ceed —In=IntIntas f ( whence may also be derived A ee ee ae The simpler forms approximated to, as z increases relatively to n, should be noticed. One of the important applications of Bessel’s functions is to the investigation of aérial vibrations in cylindrical spaces, the motion being perpendicular to the axis of the cylinder. The general differential equation governing the small vibrations is dh Pb os d*$y = a Tee sr) + + + (10) where ¢ is the velocity-potential ee to exist). If we transform to polar coordinates in the plane zy, there results d*h _ «(ss ldd , 1 d*¢ d*p\ de AES re ee If now the motion be independent of z, and of such a period that 20 ih (11) =x, we have (omitting the time factor) ab Vad «il aid me 5 Fee 72 gee t® OO ee Ole) Suppose that we are considering the motion that can proceed within a rigid cylinder of radius r=1. Whatever it may be, it can be divided into simple vibrations of various periods, each satisfying an equation like (12). Again, @ in (12) can by Fourier’s theorem be expanded in a series proceeding by sines and cosines of multiples of @. Considering the term containing cos (n@+«), substituting in (12) and dropping the factor con- taining 0, we find GhatPee-H)po soo which, on division by «*, appears in the form (1). The general integral of (13) may be written o@=AJ,(«r) +B (another function of r), but the function multiplied by B becomes infinite when 7 va- nishes. In point of fact the function in question does not, pro- 332 The Hon. J. W. Strutt on Bessel’s Functions. perly speaking, satisfy equation (10) in passing through r=0. The solution of (12) may therefore be written d= > >I,(Kr) cos (nO+2a), the one summation relating to « and the other ton. We have dp dr It appears that only such values are admissible for « as make J',.(«)=0. Reflecting now that iitially @ may have any value within the circle r=1, we infer that any function of r may be expanded from r=0 to r=1 in a series of the form A,J,,(«,7) + Aod,, (Kar) +... Ky, Ko,.+» being roots of J’,(«) =O. A similar argument would apply if « were a root of J,(«)=0. A rigorous analytical proof of the possibility of these expansions would probably be difficult. The values of the coefficient we shall see how to determine pre- sently. Let us consider the functions @ =e ~ cosnO J,(xr), t do! =e **cos nO 3 ,(«'r) They satisfy Laplace’s equation. When z=0 they become o=cosné.J,,(«r), pd’ =cos nO J,(«'r), respectively, and they vanish when z=o. IfS denote the space bounded by z=0, z=o0, and the cylinder r=7, we have, by Green’s theorem, \{ox tf Se =({#? ds. Over the plane end z=0, dg! = cosné J,(xr), Anak oe «! cos nO 5 ,(«’7) ; now to satisfy the boundary condition, that —- =O when v=1. (14) over the cylindrical surface, ! h=e—* cosnO J, (xr), = Ke—" cos nO J!, (Kr); whence dq! 27 ( r (\» ae dS : ) rd@dr cos? n@ . x'. J,,(«r)J,(«'r) Y 0 ay ( a0 az OFF 68? 08 . 1e'S, (0r) J'p (xr) 0 ame! (" rite (ice) Tair gery oe: PUT RT ALON e 0 K+K The Hon. J. W. Strutt on Bessel’s Functions. 303 Therefore, by Green’s theorem, ox) ( ial Vitec doen) e/ 9 as I (er) I'a(e'7) — aI 'n(er) Falter) =O. . (15) K+K | Thus, if « and «! are different, and such that Jn(«) J',(«!) —1J',(«)In(e')=0, . « » (16) we have 1 ( ral (er). Omens Henn et 2/9 ; The equation (16) may be satisfied in several ways. First, we may have J,,(«), J,(x’) equal to zero, so that x, «/ are roots of J,(z)=0; or «, «’ may be roots of j! n(z)=0; or lastly, they may be roots of the more general equation Meo Gia NI (2) S08 eee se Hag lS) which has an application in the theory of heat. In any of these cases (17) holds good. If «'=«, (15), as it stands, becomes identical. We must take «’=«+6«, and seek the limiting form as 6« tends to vanish. Thus 2 ("rr [J,,(«r) |? i thi! (xr) I n(« + d«)r— («+ 6x) I, (ar)I'n(e + dx)r} KOK = ~ 4 «r[S'a(«r)]?—In(er) [J (er) + «rJ",, (Kr) | t ‘ Accordingly 9 ( Pens ere = (Ite) |e te) [ale F = Ja(e) | But by (1), = limit of Ie) + © ale) = — (1 5) Sales so that 2( rdr[Ja(er)}*= [J!n(«)]? {i *\ [Jn(m)]?, . (19) (19) holds good for any value of « ; but in special cases it assumes 334. The Hon. J. W. Strutt on Bessel’s Functions. a simpler form. If « bea root of J,(z)=0, we have 1 2 { rdr (J 4(er)]2=[J'a(@) P= Ingle]? « (20) 0 in virtue of (9). If «-he a root of J',(z)=0, aml n2) 2 ‘rdér[Fa(e)P=(1— EO = Jal"). 2D ; ¢ In particular, if n=O, 2 ra (ver) |e [a (a). More generally, if « be a root of (18), 2( rdr[J,(«r) y= {at = (Wen ~ *) Leal? = {14 (en) FOO ee Results corresponding to equations (17) and (22) are given by Fourier (Theorie de la Chaleur, Chap. VI.) for the special case of n=0. The extension to the general value of 2 (I am not sure that he contemplates fractional values) is due to Lom- mel; but he drops generality in another direction by confining himself to the case where « satisfies J,(«)=0. Huis results are accordingly equivalent to (17) and (20). So far as I am aware, the general equations (17), (18), (22) are new. It should be noticed that the same method is applicable to the hollow cylinder bounded by r=r,, r=7q, provided that instead of J, the complete integral of (1) is used. In general the form will be AJ, +BJ_,, where A and B are arbitrary constants ; but if x be integral, J, must be replaced by a more complicated function denoted by Y, (see Lommel). The complete primitive may be used, because the space through which Green’s theorem is to be applied does not include the axis 7=0; it must be used in order to get a general solution, because there will now be two boundary conditions to be satisfied. If f,,(«r) be the complete integral, and «, x’ are subject to the ane M fal (ar) +N fa(Kr, et Mokfy! («79) + Nadal my = with similar equations for «’, the equivalent of (17) stands ( “f(er)f,(lr)rdr= ery always provided that « and «’ are different. The arbitrary con- stants contained in the expression of f, allow of an indefinite The Hon. J. W. Strutt on Bessel’s Functions. 335. number of values of « satisfying the pair of boundary conditions written above, whatever may be the values of M,, M., N,, No for any assigned radii r, and7,. In certain cases it may happen that either A or B vanishes, and that only one of the component functions is required. It is scarcely necessary to say that, from the more general case of a hollow cylinder, the formule appro- priate to a complete cylinder may be derived by simply putting r,=—0. In the formation of equation (14) we have tacitly assumed that, after a complete circuit from 0=0 to 0=27, the functions ¢, d' recur. But if n be fractional, this will not be true; and in applying Green’s theorem, we must take account of the fact by including the surface-integrals over the planes 0=0, 0=2r, which now no longer destroy one another. However the addi- tional integrals are, as is easily seen, symmetrical in & and x’, and therefore disappear from equation (15). Accordingly the results remain precisely as before. Previously to applying (17) and (22) to the expansion of an arbitrary function of 7 in a series of Bessel’s functions of order n, a certain restriction should be noticed. The necessity of it will appear from the consideration that if r is indefinitely small, J,(«r) contains no lower power of r than rn, showing that the arbitrary function must possess the same peculiarity. This cir- cumstance, however, does not interfere with the generality of the expansion of an arbitrary continuous function of two variables within the circle r=1. Let the function be expressed by rect- angular coordinates 2 and y, and expand it by Taylor’s theorem in rising powers of those variables. On substitution of polar coordinates, any power of r, say 7”, will be accompanied by powers of sin@ and cos@ not higher than the nth; or, when these again are expressed by sines and cosines of multiple arcs, the coefficient of @ will not arise above n. It follows that when a continuous function is expanded by Fourier’s theorem in the manner supposed, the coefficient of cos (n+), considered as a function of r, will contain no lower power than 7”. Suppose now that f(r), subject to the above restriction, is ex- panded in the form fC) = ZAI shee Ga is ite 2 (aa) where «, 1s a root of (18). If we multiply both sides by J,(Xpr).r, and integrate with respect to r from r=O0 tor=1, we have by (17) and (19), | 2) vars Gin (kar) Zara CAa@iells = 4,4 (ele)]? +(1— LT } 336° The Hon. J. W. Strutt on Bessel’s Functions. whence Ay =2h ‘nar (e2)+ Tol P+(1— 5) Bl, 24) In particular, if « be a root of J,(«)=0, 1 ,=2) rdrf(r)J,(«r)~-[J", («) ]?; : : or if « be a root of J',(«)=0, the same integral must be divided by (1-5). M2 vork—deicidiater An application of these formulz will be found below. If f(r) does not fulfil the above specified condition, but remains finite when r=0, we may, following Lommel, write GG Ss Ga Cae, 1 2( e' 0 as before. The application to the problem of vibration in two dimensions is very easy. The particular solution of (12) is p= cos (xat+e).J,(xr).cos(nO+a), . . (25) « being determined from (18) or one of its special forms accord- ing to the circumstances of the case. The most interesting in the application to acoustics is when the cylinder r=1 is rigid, so that J',(«)=0. The lower values of « (calculated from Han- sen’s Tables by means of the relations allowing J, to be expressed in terms of J, and J,) are given in the following Table :— whence ret'f(r)J,,(ar)dr = Al ‘2rd [Jn(«r) ]?, Order of Harmonie. 0. 1. 2. | 3. 0 3°832 1:841 3°054 1 7015 5°332 6°705 2 10°174 8°336 9°965 3 13°324 11°706 4 5 16°471 14°864 19°616 18°016 Number of internal circular nodes When « is very great the roots are given by (6), the series being the same for the alternate functions. The trouble of the calculation of the earlier roots increases rapidly with n. When n 1s great, it would appear probable from physical considerations that the first root varies as n; but I have not succeeded in put- The Hon. J. W. Strutt on Bessel’s Functions. 337 ting the functions under any simple form when n is very great. Both the ascending and descending series fail in such a case if z is comparable with n. Light is thrown on the question by a consideration of the differential equation (1) itself. The ascend- ing series is founded on the supposition that the coefficient mul- 2, tiplying y, really oe can be approximately represented 2 by — “; if the term 1 be absolutely neglected, the solution is 22 y we”. On the other hand, the descending series has its foundation ina substitution of 4 for n, when the exact solution becomes y “Ji(z) oz? sin z. When, however, x is great and z comparable with it, neither 2 n term in 1— —, over a large range of z, can be treated as rela- Zz tively unimportant. For aconsiderable range in the neighbour- hood of n the differential equation approximates to dy _ldy_, domed fk: of which the solution would be y=A+B log z. The question is worthy of the attention of analysts; for Bessel’s functions with large values of n (1000 or more) would have phy- sical applications, for instance, to the problem of the rainbow. In virtue of the integral formule, a combination of the partial solutions (25) can be iound to correspond to any initial values dp of @ and a The problem becomes only a little more complicated if we suppose the cylinder closed at z=O and z=/, and discard the restriction that the motion shall be independent of z. The par- ticular solution is 2) 2 b= cos («at + €) cos (» 7) cos (nO + a) J, { (2 —p? = r} » (26) p being an integer. For a rigid cylinder of radius unity we have a2 ze where K denotes the values corresponding to p=0, being those given in the Table. To every value of K corresponds a series of values of «, found by ascribing to p in succession the values Phil. Mag.8. 4. Vol. 44, No. 294. Nov. 1872. Z Ke= p? HK: doh uve nnul nen) 338 The Hon. J. W. Strutt on Bessel’s Functions. 1, 2, 3,... The purely axial vibrations correspond to a zere value of K. A similar analysis would apply on Euler and ha- grange’s hypothesis if the ends or the side of the cylinder were open, though in the latter case the result would be no approxi- mation to the truth. At the plane ends we may legitimately take as an approximation 6=0, provided that the radius of the cylinder bears but a small ratio to the wave-length of the vibration under consideration. (See a paper “On Resonance,” Phil. Frans.° 1371} In the problem, partially considered by Fourier (Théorie Ana- lytique de la Chaleur, Chap. V1.), of a cylinder of uniformly con- ducting material heated arbitrarily and then allowed to cool by radiation, the cosine factor containing the time would be replaced by an exponential, the coefficient of ¢ being negative, and (18) would have to be used as boundary condition, but otherwise there would be little change. Hitherto we have had to do with integral values of nm only ; but if instead of the complete cylinder we take the sector cut off by 6=0, 0=8, fractional values will be introduced. ‘The ele- mentary solution for the acoustical problem in two dimensions then becomes d= cos (xat+e)cosnO.J,(kr), . . . (28) where n= (m= integer) x = Dae « rs Hence, as might have been foreseen, if 6 be an aliquot part of 7 (or 7 itself), the complete solution requires only integral values of n; but otherwise functions of fractional orders must be intro- duced. An interesting example is when B=2z7, corresponding to a cylinder with a rigid partition from the centre to the cir- cumference. When m is even, 2 becomes integral, and we have motions which might take place without the partition, and there- fore presenting nothing peculiar for consideration; but if m is odd, z assumes the form (integer +4), in which case, as we have seen, J, 1s expressible in finite terms. Thus ifm=1,n=4, and b= cos (Kat + €) cos of 1(Kr) & cos(Kat + e) Coss . («r)—? sin xr. (80) The admissible values of « are those which render tan « equal te 2x. The first value of « is 1:1655, giving a much lower tone than any of which the complete cylinder is capable. If instead of (14) we were to take b =e~*cosnOJ, (7), } 3] g'=e-* cos m9 (7), 1) The Hon. J. W. Strutt on Bessel’s Functions. 339 we should find by an application of Green’s theorem to the space bounded by z=0, z= w, r=r, 6=0, 0=a:— r {Fu TnI Sn} = (21) Tue In (32) In a similar manner, by use of ee ine Mee Oil (OR. g' =r” cos m0, another useful formula may be arrived at. But it is perhaps simpler to proceed from the differential equation (1) itself. r 2 { dr ym} 13 A ail, a (1— ee I } —(! e Now [raes", +J',) =( reds \— ne mf" J! dr 0 0 a Ty — mM 4 Jn— mom ‘Dh, ar \ 0 Thus (“msy, dr = mr" J, — 7 HS! + (0? —m?) ("; maar. (oA) Yar 2/9 —a formula of reduction, by means of which, if m be even, the integral on the left may be evaluated. If m=n, we have { itd, er rts by (9), 0 a formula given by Lommel, p. 20. iin, { POS (r)dr=mr" Sor) —r" tS (r) — nt "vn Jo(r)dr. (35) 0 ty) Thus rard,(r) = —rJ"y(r) =rJ(r), { Pdr3 o(r) = 27759 —7? J!) + 4rd", did = (474 —82r*) J+ (—7? + 1673 — 641) J! &e. If risa root of J')(r) =0, the three integrals become simply 0, 2r2Jg(r), 47? (7?—8)J_(r). Z2 340 The Hon. J. W. Strutt on Bessel’s Functions. In the theory of the vibrations of a gas, or the flow of heat within a sphere, the notation of Bessel’s functions may advanta- geously be introduced. The expansion in Spherical Harmonies replaces the series of Fourier, and instead of (13) the equation satisfied by the coefficient of 8, becomes d*h _ 2db ats n(n +1) 2 Wy? oo eee O+ep=0, 2 29 tee) which may be also written d?(r it 1 UP) 4 (a mi ee \e= =). , Equation (13), however, may be 4 into the form d2(r¥) Ane gee ee +(e—-= TS rig=05 5 : (38) from which we see that, since the solution of (38) (subject to the condition at r=0) is O—w), ene rap =Tred , (Kr), the solution of (87) under a like condition must be rp =r2d 143 (KP) == Una g(KT) Sng os, ws Sgeeen if the angular factor be restored. J,4: 1s, as we have seen, ex- pressible in finite terms; but it is not easy thence to derive the approximate form when 7 is small. As itis, the known theorems about Bessel’s functions allow us to expand (39) at once in an ascending series. For the problem of vibrations in a rigid or or sphere, we require the roots of ie (5 er mij iL. dr Ini) 2g (k). . |. An investigation of this problem will be found in the Mathema- tical Society’s ‘ Proceedings’ for 1872. For the conduction question, we have a linear relation between om and a when r=1, say, dd Ht eae M'f+N aR =0. Hence from (89), when r=], (M!—4N J ,42(e) + Ned a(k), . 2. « (AD) which comes under the form (18). The Hon. J. W. Strutt on Bessel’s Functions. ol The compounding of particular solutions like (89) to repre- sent given arbitrary values of ¢ and aa (or, m the heat pro- blem, of & merely) presents no difficulty after what precedes. Fourier himself has given the complete solution for the case of n=O, when Jnii(z) x Eb a ; but I am not aware that the pro- = w2 blem has been considered before in its generality. The problem appended forms a good example of the applica- tion of Bessel’s functions to a special case, in which a numerical result is required; it was not invented for the purpose, but pre- sented itself in the course of an acoustical investigation two or three years ago. At the time I was not able to give a solution. A rigid cylinder contains incompressible fluid which has been once at rest, and is set in motion in such a manner that at a certain section (perpendicular to the axis) the velocity parallel to the axis is expressed by-1 + wr?, where ris the distance of any point from the centre of the section. It is required to determine the motion and the energy thereof. Taking the axis of the cylinder for that of z, and z=0 for the plane section, while y=1 is the equation of the cylinder, we have the following conditions to which the potential @ is subject :— (1) that when r=1, = =O for all positive 2; (2) that when z=0, ol + pr?, from r=0 to r=1. The rate of total flow across z=0 is { aardr(l + pr?) =7(1 +p). 0 Let ¢@p correspond to this distributed uniformly, so that d Po=1+ hu and go=(1+4u)z. For the remaining part of @ we have db ras = mr? —3). Assume for ¢, b= a, eS .( pr), where p is a root of the equation J!o( p) =0. Hach term in the expression for ¢, satisfies Laplace’s equation and the condition laid down for the cylindrical boundary, while it vanishes when z becomes infinitely great. 342 The Hon. J. W. Strutt on Bessel’s Functions. The first value of p is zero ; but we have already included the corresponding terms in ¢,. ‘The next values are 3°8318 13°324 70152 16°471 1071735 19-616, approximating to the form iL asd 2 a * (m+ +)m—'15198 Tegal When 2=0, d = = — pay Io( pr) ; 30 that the condition to be satisfied from r=O to r=] is — Zpd, Jg( pr) =h(r?—-3). Multiplying both sides by Jp( pr) and integrating from 0 to I, every term but one on the left vanishes, and we have by the theorem I P45 o(p) « I" (p) =2f rdrJ o( pr) (7? —4) 5 e/@ or, since from (1) Mo(P) + Jo(p) =9, 2 i \ — pa, [Fol 2)? 2a ‘rary pr) 023). 0 Now, on the right-hand side, I &: ia { Ope = ae = = { “der $a3" (ar) + Sto(ar)} 9 6 = — [ pJ'g( p)] =0. * See a paper by Professor Stokes in the Cambridge Transactions, vol. ix., “On the Numerical Calculation of Definite Integrals and Infinite a Series.” In example III. the ote ( xdaJ,(x) is considered under the A Z : ] el notation v. Now, since J”,-+ = J‘) +J,=0, it follows that a i) ada) (x)= —23',(x)=adi(zx) ; 0 so that the roots of the equation y=0, given by Stokes, are none other than the roots of J’)(7)=0, or Ji(~)=0. The Hon. J. W. Strutt on Bessel’s Functions. Again, by the formula of reduction, { rd, (a — mine de, (ris an) ae en 0 + (n? —m?*) ( (psa Ail F 2/90 putting n=0, m=2, we find {rs o(r)dr = 2773 9(r7) —733"0(7) —a{ rdrJ (7) 0 20 or, taking p as the upper limit of integration, "PJo(r) dr = 2p°J9(p) 0 Thus ; 3 1 Q 2 7drJ(pr) = | . 2p*To(p) =~ Io(p)- 0 Ve p Accordingly, to deter oe Ap, we have whence Aw : 16p:? a i — ; pS oP) EP ope The complete value of 1s bine o= (Sea) —4yz——— Ta i pie Jo(p i) db dz(= if we r=1, we find 1 L+ pal ttt sus; at ah) + 4p — 3 52") == 1 + pr. p5o(p) so that d gn, i = 3 in accordance with what we have proved already. The energy of the om =3\\(=(@) ih dy dz, =| 2ardrg when z=/=00, — if amr dr ap when z=0, e/0 dz by Green’s theorem. 344. The Hon. J. W. Strutt on Bessel’s Functions. The first integral =w/(1 +4,)?. In forming the second, we must remember that if p, and p, are two different values of p, 1 ( 2ardrJ y( pyr) J 9( por) =9- vo Thus 1 ( atric. when z=0 a dz : J,( pr) |? I = — 16p? ( oe SEES elie = —l6p*r7t—- “d. PUOM pee asim Accordingly 2 Kinetic Energy =7/(1+4y)*+167p*2 = or 2 Kinetic Energy _ / +16 yp? = er [Rate of Total Flow]? = 7(1+4p)2~ p® By calculation I find for the approximate value of ee > Bo = "0012822. i In the application to the investigation which was the origin of the problem here considered, 160012822 v 8 lttet se (+3)? *3e (1+4p) has to be made a minimum by variation of p. The minimum value comes out a='8281. In the paper “ On Resonance” (Phil. Trans. 1871) I had deter- mined a="8282 by the consideration of a motion within the cylinder satisfying the same boundary conditions as in the pre- sent problem, but not having a velocity-potential. The close agreement of the results furnishes a confirmation of the methods used on that occasion. ine XLI. Fluorescent Relations of certain solid Hydrocarbons found in Coal-tar and Petroleum Distillates. By Henry Morton, Ph.D., President of the Stevens Institute of Technology*. a the course of a general research on the fluorescent spectra, I have encountered certain facts in reference to anthracene and one of its associated bodies, and also with regard to a new solid hydrocarbon or mixture of hydrocarbons first observed and separated by me from certain petroleum distillates, which seem to merit a special notice. Tt will, I think, avoid confusion first to discuss the substances first named, and afterwards point out the relations and proper- ties of the second class of bodies. Proceeding, then, to the consideration of anthracene, I will describe The Materials used.—These consisted of :—1. Crude anthra- cene from L. C. Marquart, of Bonn. This is a dark olive-green pulverulent mass with fragments of a lighter green scattered in it. 2. Crude anthracene from the works of Page, Kidder, and . Fletcher, Bull’s Ferry, New Jersey, U.S. This was kindly fur- nished by Mr. J. C. F. Chever, Chemical Superintendent, and was in three forms: (a) fused, as a dark olive-green, hard, crys- talline mass; (5) washed and pressed, much like that from Marquart, but of a lighter colour; (c) in powder, darker and less free from tarry matter than the foregoing. 3. Chemically pure anthracene, supplied by Mr. Schering, of Berlin, a light yellow-brown crystalline powder. 4. A purer form, obtained by washing the preceding with cold alcohol, or by distilling 1, or 2 (a), or 2 (6) ina current of air, as indicated in the ac- companying cut (fig. 1), and Fig. 1. then washing with cold alco- ibe’ we hol. 5. A yet purer form, | D My obtained as above by distil- IES lation with great care and i / ie vw oot repeated crystallization from Ag SY a hot alcohol as recommended —-24 by Kopp (see Moniteur i | Scientifique Quesneville, Aug. \ 1872, p.535). 6th. Abso- | el aa lutely chemically pure an- ——== Asia |B. <: thracene, obtained by expo- sure of the hot solution to sunlight and subsequent recrystal- lization. Method of observing the Fluorescent Spectrum.—This is essen- tially that described by Stokes as his first method (see Phil. * Communicated by the Author. ey 346 Dr. H. Morton on the Fiuorescent Relations of certain Trans. 1852, Part II. p. 469), and also used by Becquerel (see La Lumiére, vol. i. p. 535, and Comptes Rendus, vol. Ixxv. p- 297), as also by Hagenbach. Figure 2 hardly needs any explanation, except that A Fig. 2. is a porte-lumiére with a lens at B, and a small tank of ammo- nio-cupric sulphate in front, Ca revolving stand to hold objects, and D a spectroscope. Observations on the Fluorescent Spectrum.—All the forms of an- thracene except the last show, when observed as above, the same spectrum, which seems to me also Nh to correspond as nearly as one : would expect with the drawing given by Becquerel (in Za Lanmere) of a hydrocarbon having the colour of the uranium salts and ob- tained from Fritzsche, who first investigated what we now call anthracene. This spectrum is shown in fig. 3. Fig. 3. 3 ’ eae C4. fh TTT TT [ seat Need D E Spectrum of Impure Anthracene referred to Bunsen’s Scale.— The anthracene described above as the sixth variety, however, shows a fainter fluorescence and gives a continuous spectrum. It yields, however, with the various solvents and chemical tests, abundant evidence that it is not para-anthracene, but simply a perfectly pure condition of anthracene itself. It would thus appear that some part of the brilhant blue fluo- rescence ascribed to anthracene may have been due, as was beyond doubt the spectrum figured by Becquerel and also the one measured by Hagenbach, to an adherent impurity. Cause of Fluorescence and of the Banded Spectrum of Commer- cial Anthracene.—A series of experiments make it clear that the yellow body persistently adhering to anthracene and soluble in ether, benzole, and carbon-bisulphide, as described by Fritzsche under the name chrysogen, was the substance in question. It is most abundant, and free from interfering substances, in the fourth sort of anthracene ; for it seems to be practically inso- luble in alcohol, the brown or yellow matter take up by that fluid beg quite a different substance. Hydrocarbons found in Coal-tar and Petroleum Distillates. 347 Fluorescent Spectrum of Solution.—When impure anthracene in the fourth condition 1s dissolved in benzole, it gives a bright- vellow solution fluorescing strongly with a light which appears green and yields, on analysis, a spectrum which closely resembles that of the solid, having, however, all its bands displaced towards the more refrangible end. This is shown in fig. 4. Fig. 4. Spectrum of Chrysogen in Solution.—But I ought to say that in this, and also the preceding spectrum, the band at 6:1 of the scale here and 4:7 in the other, is represented in the engraving as too strong and broad, being in fact fainter and narrower than the other bands. This displacement of fluorescent bands by solution finds a pa- rallel in the case of a substance first observed by me in some petroleum-residues many months since (see ‘Proceedings of Franklin Institute,’ vol. xii. p. 296). This gives a fluorescent spectrum having a close relation to that of chrysogen, and, like it, showing a displacement upwards by solutions differing with the solvent. Hagenbach, in his last paper, which has just reached me in due course of post (see Poggendorfl’s Annalen, 1872), announces that he has just observed a displacement of maxima in the fluo- rescent spectrum of some solutions by a change in the solvent. Absorption-spectrum of Chrysogen.—When the same impure anthracene (4), if spread thinly on paper or mixed with pa- raffine, is spread on glass, or is fused between slips of mica, and is then viewed by transmitted blue hght in the manner shown in fig. 5, we obtain a marked absorption-spectram which A is the port-lumiére with a diaphragm at B, C is a tank containing a so- lution of ammonio-sulphate of copper, D an adjustable table carrying the solid or solution to be examined, and E a Browning one-prism Spectroscope. 348 On the Fluorescent Relations of certain Hydrocarbons. is very characteristic and may be recognized in all but the white forms (5 and 6). This spectrum consists of a dark band about and above the Fraunhofer-line F, of another not quite so well defined and broader between F and G, and lastly a band about G, which continues into the absolute absorption commencing at 14 of scale (see fig. 6). This absorption-spectrum has its bands displaced upwards by solution in the same manner as the fluorescent one; and the same is true of the new body obtained from petroleum above de- scribed*. This absorption (figs. 6 and 7) is undoubtedly due to chrysogen ; for, among other facts, it rapidly disappears from a solution on exposure to sunlight. To see it clearly, the brown matter soluble in alcohol should be removed; for this exerts a general absorption of the entire spectrum above 10 of scale. Mazima and Minima. When a pure spectrum is thrown on a screen coated with either of these hydrocarbons, or on a tank filled with their solutions, a series of maxima and minima are observed corresponding exactly with the absorption-spectra of the same substances, a maximum of fluorescence coinciding with a band of absorption. Sucha condition as this was entirely to be expected, and was observed by Stokes in solution of leaf-green (Phil. Trans. 1852, Pt. IT. p. 491), in canary-glass, and in nitrate of uranium (Ib. pp. 497 and 517). Hagenbach has likewise re- marked the same thing in many instances; but the complete- ness of this relation, changing with the change due to solution, makes these examples specially interesting. I would also here remark that the analogy between anthra- * I have observed also a displacement downwards of the absorption- bands of oxalate of uranium by solution. On the Nutrition of Musculur and Pulmonary Tissues. 349 cene and this new body which I have found in petroleum residues does not cease here. If this latter is exposed in hot solution in benzole to strong sunlight for many hours, it deposits, on cooling, needle-like crystals which are almost colourless, and give a spectrum by fluorescence which corresponds very closely with that of the so- lution of the same body mentioned already. Its bands, how- ever, are far less strongly marked than those of the unsolarized material; and | have little doubt that, as with impure anthra- cene, they are due, not tothe mass of the material, but toa trace of a coloured substance which is not, lke chrysogen, entirely decomposed by sunlight, but only so far modified as to occasion the above changes. To avoid circumlocution in speaking of these bodies in future, I would propose to call the white material petrolescene, from its source, fluorescence, and general analogy to anthracene and the colouring-matter which is the source of the brillant fluores- cence by which my attention was first drawn to the body thallene, from the two brilliant green lines which are the most prominent characteristics of its spectrum. I should mention that petrolescene is distinguished from an- thracene by its high boiling- and melting-point (about 700° F.), by its very sparing solubility in boiling alcohol and benzine, and by its crystallizing in spirules and not in scales. Thallene differs from chrysogen in its spectra of fluorescence and absorption, and in its action under the influence of sunlight. My friend Dr. Geo. F. Barker, to whom I am indebted for references to some original papers and aid in procuring a supply of material, has kindly undertaken the chemical examination of these bodies ; and in connexion with him [| hope soon to report more fully on the subject. I wish here also to acknowledge my obligation to Mr. W. H. Geyer, my assistant, and to Messrs. P. P. Poimier and A. H. G. Sorge, students in the Institute, for various assistance in carrying on the observations. XLII. On the Nutrition of Muscular and Pulmonary Tissues in Health and when affected with disease from Phthisis. By Wiriram Marcet, M.D., F.R.S.* Part 1. On the Nuirition of Muscular Tissue in Health. ate object of the present memoir is to give a description and an explanatory statement of the investigation I have undertaken into the phenomena of the nutrition of animal tis- * Communicated by the Author. 350 Dr. W. Marcet on the Nutrition of sues, these inquiries relating more particularly to the nutrition of muscles and lungs in health and when affected with phthisis : and I must begin by acknowledging the valuable assistance of Messrs. H. Bassett, F. A. Manning, and M. J. Salter in the ana- lytical portion of the inquiry; I am much indebted to these gentlemen for the care they have bestowed on the work. The subject is treated by methods of investigation which may be considered new; it is therefore necessary that I should enter into their details, so as to make the mode of reasoning, the analytical process adopted, and the results obtained equally and thoroughly clear to the reader. By this means only can I hope to forestall objections and establish the correctness of my work. I must beg leave to begin with a few introductory remarks relating to liquid diffusion, a subject which has been so admira- bly treated by Graham. If we suppose a solution of common salt, on which a fiat piece of cork is floated, and if a stream of water be poured carefully upon the cork, the water will not mix immediately with the solution of salt, but form an upper layer in the receiver, while the solution will occupy the inferior layer. Supposing no cause whatever to agitate the fluids, that they be neither shaken nor subjected to any current of air, they will, however, undergo a tolerably rapid process of mixing, the solution of salt moving into the water, or, in other words, distributing itself throughout the water. This phenomenon is called Liguid diffusion. The rate at which diffusion takes place varies according to the substance in the solution ; hence it is said that different solutions have different rates of diffusibility. Chloride of sodium may be regarded as yielding aqueous solutions possessed of this property in avery high degree ; while white of egg or blood allow of the distribution of their albumen through water at a very slow rate indeed. Now, supposing that a jelly be prepared, by dissolving isin- glass in a weak solution of chloride of sodium (in a strong solution the jelly may not set). Ifdistilled water be poured over this jelly, the salt will by degrees find its way out of the jelly into the water, and will continue doing so until it be distributed equally through- out the jelly and the water. Should the water and the jelly occupy the same bulk, we shall find, after a certain number of hours, the same amount of chloride of sodium in the jelly and the water. Should the volume of the water be twice that of the jelly, a cer- tain bulk of the water, after complete diffusion, will only contain half the amount of salt present in an equal bulk of the jelly, and soon. On the other hand, if a solution of common salt in water be poured over a jelly of gelatine, after a time the salt will be found distributed throughout the water and Jelly propor- Muscular end Pulmonary Tissues. 35] tionally to their respective volumes. Should a jelly be prepared consisting of a mixture of a solution of isinglass and white of ego, it will exhibit, with reference to the albumen it contains, diffusible properties entirely at variance with those observed in the case of the mixture of jelly and salt. When water is poured over this albuminous jelly, the albumen will not diffuse out, or its diffusion will be extremely slow; hence a jelly con- taining albumen has such a thorough hold upon it that this sub- stance can no longer be extracted from the jelly; no amount of trituration or pounding or washing will separate the albumen; this simple want of diffusibility caused the albumen to become firmly united with, or fixed by, the isinglass jelly. Graham has observed that, as a rule, substances possessed of the property of crystallizmg (such as common salt or sugar) yielded solutions much more diffusible than those of substances which were not possessed of the power of crystallizing, such as gelatine; hence he has classed substances into crystalloids and colloids. How can we explain these phenomena, unless it be admitted that there existed a degree of attraction or adhesion between the albumen and the jelly greater than that occurring between the salt and the jelly—so that in the one case the albumen was fixed in the jelly, while in the other the salt moved freely out of it? Substituting the simpler cases of pure white of egg and a solution of common salt in water, the different degrees of diffusibility exhi- bited in these two instances will admit of a similar explanation, the water retaining the albumen in one case, and letting out the salt in the other. If this view be taken of the cause of the various degrees of diffusibility of different solutions, it must be acknowledged that there exists a certain attraction between substances and the water which holds them in solution; and this attraction varies in its degree according to the substance. I propose, for want of a better denomination, to call this by the name of colloid attraction, and to say that the albumen in white of egg is held to the water by “colloid attraction.” I[ therefore retain the names colloid and crystalloid given by Graham—colloids not being possessed of the power of crystal- lizing, and being sparingly diffusible, while crystalloids are erystallizable substances, yielding readily diffusible solutions. Crystalloid solutions never gelatinize ; colloid solutions either gelatinize or solidify into a thick, gummy, adhesive substance, which dries into a residue exhibiting, frequently, somewhat the appearance of a varnish. This colloid attraction, which keeps water and isinglass united together in a jelly, is also apparently concerned in the formation and physical existence of animal tissues. Muscular 352 Dr. W. Marcet on the Nutrition of tissue 1s formed of fibres running parallel with each other in the form of bundles, which are not in mutual contact, but separated from those in their immediate vicinity by connective tissue. These fibres consist physically of animal matter and water, held together by a peculiar power which cannot be considered due to a chemical property, but appears to exhibit the character of colloid attraction. The present view rests on the following considerations :— 1st.. That muscles have a soft pliable consistence, and are dry to the touch as a jelly would be. 2nd. That Kiihne, of Heidelberg, has obtained from muscular tissue a real jelly he has called myoszne. 3rd. That muscular tissue contains a proportion of water which does not appear to vary in health. Ath. That chloride of sodium, in a certain proportion, inter- feres with the setting of gelatine; and muscular tissue is nearly free from this substance, while blood (which remains liquid) contains it in a comparatively large quantity. And it is worth noticing that when blood loses its chloride of sodium by dialysis (diffusion) it becomes considerably thickened. 5th. That after removing by diffusion (dialysis) certain diffu- sible substances which muscles contain in the small proportion of about 25 per 1000, there remains a mass differing, it is true, from a jelly, inasmuch as it yields a solution of colloid substances by trituration in water, but like a jelly in the fact that the re- moval of these colloid substances leaves a material consisting of substances in a semisolid condition, which are fixed by the water present ; no amount of trituration or pounding or squeezing in water will alter the composition of this soft solid mass, which, if it were not for its tenacity and fibrous consistence, would possess in many respects the characters of a jelly, holding certain pro- portions of albumen and other equally colloid substances. The fact of there being a fixed proportion of water in muscular tissue is remarkable. The consistence of a jelly depends on the amount of water it contains; a solution of gelatine in too large a bulk of water will not set at all, while the less water this solution contains the more solid the jelly will be. Now it is but fair to assume that muscles must have a certain fixed consistence for the normal performance of their functions ; and if their consistence depends on the proportion of water present, as in the case of a jelly, muscles must contain a fixed proportion of water, which they really do. Kiihne has succeeded in extracting from the muscles of frogs immediately after death a substance which sets into a firm coagulum. ‘ “Tf a frog be opened, a 1-per-cent. solution of chloride of Muscular and Pulmonary Tissues. 358 sodium driven through the blood-vessels until all the blood is removed, the muscles then rapidly chopped up and subjected to firm pressure, a liquid will be obtained which in a short time sets into a firm coagulum.”—Myologische Untersuchungen (ex- tracted from Watts’s Dictionary of Chemistry). Therefore juice of flesh has a tendency to coagulation, as would a solution of gelatine ; this tendency must be possessed by those substances in juice of flesh which are soluble and colloid, and therefore, as I shall show, destined to the nutrition of flesh, or to become transformed into muscular tissue. I conclude that there is a strong ground for the belief that the elementary physical constitution of muscle is that of a jelly— with this difference, that it is organized so as to possess due tenacity for the performance of its functions; but the water, al- bumen, and other constituents hold apparently the same rela- tion to each other as water would to gelatine in a jelly*. Bone may be considered as consisting eriginally of a jelly of a colloid material and water, the water being subsequently re- placed by phosphate and carbonate of lime and magnesia, which are united with the colloid material much in the same way as the water had been originally united to this same material. The existence of a colloid constituent of bone very much resem- bling gelatine is easily demonstrated by the well-known expe- riment of immersing a bone in dilute hydrochloric acid, when the earthy matters are removed, water taking their place and entering into a colloid union with the gelatinous matrix, the union bemg apparently similar to that which had existed before between the earthy matters and the colloid material. The connexion between water and gelatine in a jelly obviously takes place between two colloid bodies, although water may under certain circumstances, as under the influence of cold, assume the crystalloid condition ; and moreover we find that, in the formation of bone, phosphate and carbonate of lime and magnesia exist in an amorphous or non-crystalline state; I therefore consider these earthy sub- stances as existing in a colloid condition in osseous tissue. Animal tissues, although in some respects resembling a jelly, vary, of course, essentially from this colloid material because of their having a definite structure. Virchow has discovered with the microscope that there exists in muscular and other tissues a complex system of minute channels, the object of which is ap- parently to allow of the transmission of the nutritive material to the different parts of the tissues. Indeed it is very difficult, not to say impossible, to account for the distribution of the col- loid material destined to nourish tissues after it has left the blood, * Nerves and vessels form such a very minute proportion of muscle that I have overlooked them in the present inquiry. Phil. Mag. 8. 4. Vol. 44. No. 294, Nov. 1872. 2A 354 Dr. W. Marcet on the Nutrition of unless the presence of these channels be admitted. That such a nutritive material really exists must be acknowledged, as (Quain’s ‘Elements of Anatomy,’ vol. 1.) ‘the capillaries des- tined for the proper tissue of the muscle form among the fibres a fine network with narrow oblong meshes, which are stretched — out in the direction of the fibres....none of the capillary vessels enter the sarcolemma or proper sheath of the fibre.” There must consequently be a material intermediate between blood and tissue, reaching every particle of the tissue to be nourished ; and with this object in view, there must exist proper means for the thorough distribution of this material. I have shown (Bibl. Universelle, Feb. 1865), by a very simple obser- vation of a physical nature, and without the use of a microscope, that a system of channels ramifies through muscular tissue, containing the material destined to the nutrition of flesh. On considering the physical condition of flesh, it occurred to me that there would be no difficulty in determining whether muscular tissue is strictly a colloid mass like a jelly or not, by merely immersing a piece of muscle or raw meat in water. Should it be a solid colloid body, no albumen could be expected to diffuse out of the meat into the water; on the other hand, if it was a porous mass, and should these pores or minute channels contain albumen, some of the substance would necessarily pass out of the meat into the water by a process of porous distribution, as would take place if a sponge containing white of egg were immersed or hung up in water. It is an observation nearly of daily occurrence that raw meat steeped in cold water yields albumen. 200 grammes of ox-fiesh wereminced and extracted with 125 cub. centims. of distilled water, the phosphoric acid and albumen being subsequently determined in the extract. On the other hand, a piece of raw beef weighing 200 grammes was immersed for 26 hours in 125 cub. centims. of distilled water, when the phosphoric acid and albumen were also determined in the fluids; the result of the analysis showed that the amount of albumen which had passed out of the meat in the water was less than half of that which had been obtained by extraction ; while there was separated by diffusion more than half the proportion of phosphoric acid contained in the extract. The numerical results were as follows :— In 100 cub. centims. fAuid In 100 cub. in which the flesh had centims. extract. been immersed, Phosphoric Acid : ~ 0233 0:169 Albumen ; ‘ » 2°925 1:067 This experiment shows that flesh is permeated in every direction throughout its mass with a multitude of minute channels charged Muscular and Pulmonary Tissues. 355 with the material destined to its nutrition, to which the albumen belonged. It might be objected that a small quantity of blood was possibly left in the tissue after slaughtering, which would account for the presence of albumen in the water in which the meat was steeped ; but meat from slaughtered animals is perfectly free from blood. On triturating minced ox-flesh with salt water I could not find any blood-corpuscles by subjecting various por- tions of the mass to microscopical examination, while on adding one or two drops of serum containing some blood-corpuscles to a few ounces of the pulpy mass, and agitating the whole together, the blood-corpuscles could be detected most readily. In the tissue of the heart of the ox, however, I usually found small quantities of blood, and had to give up determining the albumen in extracts of that organ because of the results being too high on that account. On these occasions I had no diffi- culty in detecting the presence of blood. Returning to my subject, I hope to have succeeded in showing that muscular tissue consists of a solid material permeated by channels containing an albuminous fluid, and that the consti- tuents of the solid material are bound together by a force similar to that which connects gelatine and water in a jelly. On the Mode of Nutrition of Tissues. A tissue consists of a solid portion containing a fluid nutritive material within its mass. It must appear obvious at the outset that if the solid portion is colloid, the material for its for- mation must also be colloid; indeed it is well known that albu- men, a thoroughly colloid substance, takes a considerable share in the process of nutrition. I shall show that the phosphoric acid, together with the smail quantity of potash (and, we may assume, also the magnesia), which enter into the composition of the nutritive material are also colloid; muscular tissue contains, however, nearly 25 per 1000 of crystalloid material, consisting of potash and magnesia salts, and very small proportions of chlo- rine and soda, together with crystalloid organic nitrogenized sub- stances, such as kreatine and kreatinine. It occurred to me that the formation of these crystalloid substances was due to the pro- cess of waste—a view which derived some support (before it was thoroughly investigated) from the fact that the urinary secretion consists of diffusible substances; the transformation of colloids into diffusible crystalloids appeared moreover at the outset a convenient method for a process of elimination ; and also, blood being much more colloid thau tissues, could hardly be considered the source of the crystalloid substances they contain. The nitrogenized crystalloids in tissues would result entirely, according to this view, from a transformation of assimilated albu- 2A2 356 Dr. W. Marcet on the Nutrition of men with a view to its ultimate elimination. The investigation upon which I now beg to enter, extending over a period of about five years, proved the correctness of this theory. A tissue is con- stantly undergoing change. Very soon alter it attains its highest stage of development, or its state of maturity, it dies, and is decomposed into crystalloids. Dr. Beale (‘ Life Tlieories’ &ec.) believes that as soon as what he calls the bioplasm is transformed into the insoluble matrix of a cell, it dies, then disappears, and is replaced by other cells*. We may therefore regard tissues as formed of three different materials :—(1) the nutritive ma- terial which has Jeft the blood and is on its way to become assi- milated ; (2) the fully developed or ripe tissue ; (3) the material resulting from the waste of tissues, which is on its way out as effete matter. After much time and consideration had been devoted to the available means of separating from each other these three diffe- rent materials and effecting their analysis, | adopted the follow- ing process, which answered the purpose most satisfactorily. If, say, 200 grammes of flesh be minced thoroughly and mixed with 500 cub. centims. of water into a homogeneous pulpy mass, there will be obtained, after strainimg through calico or muslin, about 500 cub. centims. of extract (including that wetting the calico), while about 154 cub. centims. of solution will remain in the fibrous mass left in the calico. This solution is estimated by drying the weighed fibrous mass, the loss of weight so obtained representing the volume of the extract without any material error. The total extract will there- fore be equal to 654 cub. centims., and will contain: lst. The whole of the colloid material on its way to form flesh ; 2nd. The whole of the crystalloid material resulting from the waste of the tissue and on its way out of flesh ; 3rd. Probably a small portion of colloid material in progress of assimilation, which is squeezed out by the process of extraction. The fibrous portion in the muslin, imagined dry and free from extract, will represent a mass weighing rather less than 46 grms., and consisting of colloid material assimilated and insoluble in water plus a small portion of colloid material in process of assi- * Beale states :—“ Every tissue may be divided anatomically into ele- mentary parts [sic]. Each elementary part consists of the living matter or bioplasm and the lifeless formed matter (cell-wall, envelope, tissue, inter- celiular substance, periplastic matter) produced at the moment of the death of the particles of the first.” Beale, therefore, apparently considers as dead organized particles what I have called ripe or mature tissue, which, however, is on the point of becoming dead and lifeless. It appears to me mature because it is in this state only that it can perform 1 its functions. Muscular and Pulmonary Tissues. 357 milation. This partly assimilated colloid material has the same composition as that of the insoluble fibres; indeed I shall be able to show that the whole of the colloid material destined to become assimilated has the same composition as the fully deve- loped and insoluble tissue; so that the passage from fluid to solid is a mere morphological change. I must now state how the composition of the above three different classes of materials was determined, these materials con- stituting :— Ist. The fibrous insoluble mass ; 2nd. The colloid fluid, destined to form the insoluble mass ; drd. The crystalloid solution, destined to remove from flesh the effete material it contains. A few words will suffice, I trust, to make the method of ana- lysis quite clear. Having prepared the extract of 200 grammes of flesh with 500 cub. centims. of water as stated above, the albumen, phosphoric acid, and potash, with the soda and chlorine, it contained were determined. On the other hand, the fibrous mass in the muslin, after the estimation of its water, was sub- mitted to analysis for the determination of the same substances (with the exception of chlorine), and also of its nitrogen, which was done by combustion with soda-lime. The water (estimated by desiccation) represented the bulk of the extract left after straining the fibrous mass; and the composition of this portion of the extract (retained in the fibres) was calcu- lated from that which had been found for the solution separated from the flesh by extraction. Now, by subtracting respec- tively the numbers obtained for the constituents of the por- tion of the extract retained in the fibrous mass from those found for the constituents of this fibrous residue, it is obvious that the result represented the composition of fibrous mass free from extract. The composition of the colloid material in solu- tion destined to nourish the tissue was calculated from that of the insoluble fibrous mass (insoluble fibrous mass considered free from extract), assuming that the relation the constituents held to each other in both cases was the same—an assumption which I shall show to be correct. The proportion of albumen assimilated, calculated from the nitrogen found in the insoluble fibres, and of soluble albumen in the total colloid solution, were taken as starting-points for the calculation. Finally, the composition of the crystalloid material was cal- culated by adding together the numbers representing the pro- portions of the constituents of the insoluble fibres and nutritive colloid solution, and subtracting the result from the ¢otal quantity of each constituent respectively found in 200 grammes of flesh. A simple way of explaining this will be as follows. Let the 358 Dr. W. Marcet on the Nutrition of albumen, phosphoric acid, and potash be represented respec- tively :—in the insoluble fibrous mass by da eles bp gk Ce in the soluble colloid material by ON babe Oe in the total flesh by A" BM, Cr; in the crystalloid material by AM BM CM, B’ and C’ are calculated as follows :— A: B=A’: B Ae C=A!: CF B+A’ faz B= ae C +A!’ pals c— A The crystalloid material has also to be calculated, Al being =A”—(A+A), Bl = pics (B are B’) ; Ge =C0”—(C+C’). The colloid material was calculated, as previously stated, on the assumption that it possessed the same relative composition as the insoluble fibrous mass; and I must now show the truth of this theory. It will be necessary to begin by establishing the fact of the colloid nature of the solution. The proof that this material is colloid is derived from the consideration that aloumen, its main constituent, is possessed of strictly colloid properties. Moreover, juice of flesh contains, as I have observed by submit- ting it to dialysis, a certain quantity of phosphoric acid and pot- ash which, even after 24 hours does not pass through the dia- phragm of the dialyzer, and may therefore be considered as colloid. With reference to the composition of the colloid solu- tion, it is difficult to obtain accurate quantitative determina- tions of colloid phosphoric acid and colloid potash by dialysis ; still, by submitting to this process for 24 hours minced flesh made into a pulp with water, the proportions of albumen, col- loid phosphoric acid, and colloid potash were found in the fol- lowing analysis very much the same as those obtained for the Muscular and Pulmonary Tissues. 359 albumen, phosphoric acid, and potash in the insoluble fibrous portion of the tissue. The numerical results. were :— Total colloid constituents of 200 grammes of ox-flesh prepared by dialysis. Mean composi- tion of the ma- Proportion ture tissue cal- cale. in 5°74 | culated in 5-74 Albumen kdsteanined as pee) 38°06 | albumen. albumen. Phosphoric acid.. .. 0375 0-056 0051 HMEASIE, ace ens we tas cece retccsosses ts 0-132 | 0-020 0-017 In this analysis the colloid substances contained in solution in juice of flesh plus these same substances as constituents of the insoluble fibrous mass, bore to each other respectively very nearly the same relation as the constituents of the mature or insoluble tissue. Other experiments undertaken by dialyzing extracts of muscular tissue yielded similar results; it happened, however, occasionally that they differed—obviously on account of the method of analysis, by means of a dialyzer not being in- variably reliable. It follows that the material destined to become transformed into the insoluble portion of flesh, or ripe tissue, undergoes a mere morphological change, one molecule of the ripe tissue as it wastes away being replaced by one molecule of the nutritive material having precisely the same composition. I shall not take into account my earliest analyses, amounting to fourteen in number, which are incomplete in several respects. Moreover the methods of analysis then adopted were not near so correct as those with which the subsequent inquiry was con- ducted. I have to report seven analyses of muscular tissue. For the first four, the flesh was taken from the muscles of the neck of as many oxen immediately or but very few hours after slaughtering. For the last three analyses, the muscular tissue was obtained at the Consumption Hospital (Brompton) from human subjects after death from phthisis, before decomposition had set in. The composition of these last three samples varied but slightly from that of the other four ; and the result respect- ing the phosphoric acid and potash effete was precisely the same. I shall at present consider only the first four analyses. 360 Dr. W. Marcet on the Nutrition of Table showing the Constituents of Muscular Tissue in 200 grms. Class No. |. Composition of the material forming the mature and insoluble Tissue. ih IL. IIL. IV. sy I In In 200 Beopoee 200 | Prop or-| In 200 Propor- In 200 Propor-| 200 grms. grms. | tion a tion, | &™™s: tion, | 8™™S: tion, | °X-flesh. ox-flesh. x-flesh. ie flesh. X- flesh. ae 31-16 |100 | 27-216 100 ie 100 {27:3 100 | 28-070 material Phosphoric || 9.189) 0-606] 0-239 0-88! 0:3 | 1:13] 0-276] 1-01] 0-251 acid... Potash ...... 0-054; 0:173] 0-017, 0:06} 0:244) 0:94] 0:03 | 0-11] 0-086 IMaenesia. 2..|"s 0-55 |liseosssslicceeee: | senses 0423; 1:6 | 0509) 1:86 Class No. 2. Composition of the material destined to become Flesh, entirely Colloid. Albuminous | ‘ Berit a - material f | 6°62 |L00 | 5:67 100 | 52651100 | 5-428)100 | 5-745 eee 0:04 | 0-604] 0-050' 0-882] 0-060) 1-13] 0-055' 1-01] 0-050 Pots o @ 0-011} 0-166] 0-003 0-053} 0-048] 0-91] 0-006) 0-11] 0-017 IVE NE STA per al cent | dee se a | to oe sslomal aeons 9-009 17 | 0:049; 0-18 Class No. 3. Composition of the effete material on its way out of Flesh, entirely Crystalloid. Albuminous] | 4. | Pa gl oe ; nant onial | 3°64 |100 3-622'100 3°622)100 3:913 |100 3°70 Phosphoric | | 9.595] 1634) 0-62 | 17-12] 0-518] 14:8 [0521 | 1381] 0563 Potash ......| 0-762! 20-93 0-803 22-17] 0°723) 19-96)0-759 | 19-69] 0°764 Magnesia Alves oles. bedpapere rer 0:025| 0:69)0°0955| 2-44 In 100 Found. Mean 2KO PO’, — — found. Theory. Phosphoric acid . 43°38 43:7 41:7 40:4 42-4 43°0 Potash ©4774." S652 56'S" 58:3” 59-6 57 57°0 I shall now beg to offer a few remarks on the mature fibrous and insoluble material, and on the effete crystalloid constituents of flesh. I, The insoluble fibrous material. It is this part of muscular tissue which may be considered as giving muscles their tenacity and contracting power. It is Muscular and Pulmonary Tissues. 361 formed of molecules disposed according to a certain definite structure, and consisting of albumen, phosphoric acid, potash, and magnesia, which, however, do not exhibit fixed proportions, but vary within certain limits. These materials are constantly undergoing destruction, and may be considered as dying very shortly after they are ripe. The regularity with which the nutrition of this mature por- tion of flesh takes place is strikingly shown by the fact that the soluble and coagulable albumen in a given weight of tissue always bears the same proportion to that of the albumen assi- milated in the insoluble fibrous mass. The absolute quantity of albumen assimilated in a given weight of muscle varies, pro- bably in a great measure on account of the different proportions of fat muscle contains; but the relation of this assimilated albumen to the soluble and coagulable albumen remains very nearly the same in every case, as shown in the following Table :— Found in 200 grammes of ox-flesh. In 100. Albumen insoluble. Albumen. | Albumen | aipumen. insoluble. Analysis I. 31°16 ............ 6°62 82:48 17°51 . Me gio WG, Becea gute 5°67 82:76 17:24 a DN 266. cncsescctsss 5:265 83:48 16°52 . LEN suet cea el el 5:428 83:40 16-60 Rea ral ed Fes ahd 08 eal. calc aen ae as 83°04 16:97 From which results the fact, that for every molecule of albumen assimilated or converted into insoluble muscular tissue, an equal quantity of albumen is withdrawn from blood into the tissue. This mean proportion of soluble to insoluble (or assimilated) albumen is as 16°97 to 83°14, or 1 to 4:9, which means that there is 4°9, say 5 times as much assimilated albumen in flesh as in its nutritive fluid. II. The effete material on its way out of flesh entirely crystalloid. This includes perhaps the most interesting results from my inquiries. I shall first beg to draw attention to what I have called the effete albuminous material, and compare it with the corre- sponding constituent of the fluid destined to nourish flesh. What I have considered as the albuinimous material of the third class is crystalloid, having assumed the form of kreatine, kreati- nine, &c. It was determined by evaporating to dryness the fil- trate and washings from the coagulated albumen of a known bulk of the extract. A small quantity of sulphate of lime was 362 Dr. W. Marcet on the Nutrition of added to the fluid during the evaporation, so that there was no difficulty in taking up the residue for the combustion with soda-lime ; 15°7 parts of nitrogen corresponded to 100 of albu- men. Notwithstanding the variety of substances into which albumen is thus transformed, we find a relation between the albuminous materials of both classes which does not vary between wide limits. Thus :— | Mibumen. 0) Material tom | coagulable albumen : | and colloid, | erystalloid, Relation. | 2nd class. 3rd class. 6°62 | 3-64 1:82:1 5-67 | 3-622 157:1 5265 | 3-622 1-45:1 | 5428 3-913 1:30:1 | Meaa.: | 2.0 5046 | 3699 | 1-56:1 Hence the nutritive fluid of flesh contains a mean of rather over one half more albumen than is present in the solution of the effete material. Now it is obvious that if a muscle should retain a certain composition, which it does within certain limits, it must draw upon the blood in proportion to its waste. There- fore for every 3°699 grammes of albumen (in the crystalloid form) on its way out, 200 grammes of flesh must draw 3°699 grammes of albumen colloid and coagulable from the blood. But we find 200 grammes of muscular tissue to contain a mean of 5°746 grammes of colloid coagulable albumen; and as the albumen must regulate the supply of the other substances muscular tissue requires for its nutrition, it follows that about one third of the whole of the nutritive material present in flesh is in store, not being required for immediate use. Therefore if the blood, from want of food, were incapable of nourishing flesh, yet the muscle would apparently continue for a certain time deriving food from the material accumulated within the tissue. This appears to be a provision of nature to allow of muscular exercise during prolonged fasting. Of course this view must be considered a mere deduction open to future investi- gation. The relation of phosphoric acid and potash to albumen in the third class varies in the different analyses, the former be- tween 13°31 and 17°12 per cent. (of the albumen), and the latter between 19°80 and 22°17 per cent.; but it is highly in- teresting to observe that these two substances, relatively to each other, are present in muscle as effete material precisely in the proportion of 43 of phosphoric acid to 57 of potash, correspond- Muscular and Pulmonary Tissues. 363 ing to pyrophosphate of potash, which may be originally the neutral tribasic phosphate of potash subsequently decomposed by incineration. It will be observed that these four analyses all yield a similar result, which will be found confirmed by the composition of the human muscles subjected to analysis*. This result is the discovery of the existence of phosphoric acid and potash in the effete material exactly in the right proportion for the formation of pyrophosphate of potash. I believe this is the first time the composition of an inor- ganic chemical compound has thus been determined by bringing together, theoretically, its constituents in an animal tissue. The formation of this substance is very remarkable; it shows be- yond a doubt that blood yields (besides albumen, phosphoric acid, and small quantities of potash and magnesia to be transformed into flesh) a large proportion of potash the only object of which is the removal of the phosphoric acid of the ripe muscular tissue. Potash may also be concerned in the oxidation of the albumi- nous portion of the tissue into crystalloid compounds ; and I may remind the reader that Dr. H. A. Parkes has shown that potash taken into the body favours oxidation, causing an in- creased elimination of urea and sulphuric acid. The proportions of the constituents of flesh I have introduced under class No. 3 are originally derived from the composition of the extract, from which are subtracted respectively the propor- tions of the colloid substances present. These colloid consti- tuents are calculated from the composition of the insoluble fibrous portion of the tissue and the proportion of the soluble albumen ; so that any error in any one of the determinations of albumen, phosphoric acid, or potash would suflice to vitiate the whole of the result. Absence of Soda and Chlorine from ripe Muscular Tissue, or the insoluble portion of flesh. The proportions of chlorine and soda contained in juice of flesh are very small; in eleven analyses of the extracts from the flesh of as many different animals, the proportions of chlorine in 200 grammes varied from 0:094 to0-212. These results may be considered correct, notwithstanding their being represented * The proportions of phosphoric acid and potash effete in human mus- cular tissue after death from phthisis were as follows in three analyses :— Analysis I. II. III. Mean. Phosphoric acid ...... 43°2 42-9 42-7 42:9 ROLASIE dare'e) ssa oi sie e)el he 5O:S oF Dis) eof] 364 On the Nutrition of Muscuiar and Pulmonary Tissues. by such low numbers. They were obtained by the dialysis of a certain bulk of the extract, and determined volumetrically im portions of the fluid outside the dialyzer, being finally calculated for the whole bulk of the fluid in and out of the dialyzer. The proportion of soda present varied in six analyses from 0°155 to 0°333 gramme in 200 grammes of flesh submitted to analysis, being about twice as much as the chlorine would require to be made into chloride of sodium. Some of the soda is there-. fore eliminated in combination with one or more of the organic acids resulting from the decomposition of the organic portion of flesh. My present object, however, is mainly to show that chlorine and soda take no part in the actual formation of flesh. With this object in view, 300 grammes of sheep’s flesh were minced and extracted with 750 cub. centims. of water, as usual. The fibrous mass and dry extract were incinerated slowly with pure lime, and the ash was mixed with water, in which the chlorine was determined volumetrically. The extract retained in the fibrous mass yielded (by calculation) 0:032 gramme of chlorine, and the fibrous portion 0:035 gramme of chlorine—the difference amounting to 0:003, or 0-001 gramme per 100 grammes of flesh, which is insignificant and proves the absence of chlorine in the ripe or insoluble tissue. The experiment relating to the soda was undertaken by mincing 200 grammes of ox-flesh, adding water to the mass, and dialyzing the whole for twenty-four hours. The soda was then determined in the diffusate ; and the amount of diffusible soda retained in the colloid portion was calculated from the volumes of the fluids in and out of the dialyzer. This was subtracted from the soda found in the total colloid mass—the difference amount- ing to only 0-004 gramme, or 0°002 gramme per 100 grammes of flesh, which is insignificant; and I conclude that the ripe or in- soluble muscular tissue contains no soda. The object of the pre- sence of chloride of sodium in flesh appears to me to be con- nected with the distribution of water throughout the tissue. This would be a subject interesting to investigate, and likely to yield important results. On the Constitution and Nutrition of the Muscular Tissue of Fish. My inquiry on the nutrition of the muscular tissue of fish is limited to an analysis of salmon’s flesh, which has yielded the following results :— On the Second Proposition of the Mechanical Theory of Heat. 365 Composition of Salmon’s Flesh, in 200 grms. Composition of | Composition of | Composition of insoluble tissue. | nutritive material. | effete material. Albunien! 2.700...: 25°16 12-470 4°360 Phosphoric acid... 0-171 0:085 0°945 OLAS Ra. i S8eeca 0:065 0-032 0:828 Soda, total found | _....... _ eeeees 0-058 Effete, in 100 parts. Theory. Phosphoric acid . . 53:3 43 PRotashs ye 5 Oe e466 57 In the present case the proportion of albumen of the nutritive material is no less than twice as large as in ox-flesh; and about two thirds of the amount of this substance present was in excess of that required for immediate use. The necessity of this large store of nutritive material in salmon’s flesh may be accounted for by a consideration of the rapid growth of the fish, amounting in a few months to several pounds during their migration to the sea. (I could not ascertain where the fish was taken.) The high proportion of phosphoric acid and potash in the effete state is a remarkable circumstance, considering that salmon is constantly subjected to loss of substance from liquid diffusion ; but this is explained by the fact that phosphoric acid and potash in salmon, in the effete condition, are not present in the exact proportion to make a crystalloid potash salt; there is an excess of phosphoric acid present ; and therefore these sub- stances are less crystalloid and consequently less diffusible than in the higher class of animals. [To be continued. | XLIII. On the Connexion of the Second Proposition of the Me- chanical Theory of Heat with Hamilton’s Principle. By R. -Cravsivs*. | SES by a memoir of mine published not long previ- ouslyt, M. Szily has instituted an interesting consideration of the second proposition of the mechanical theory of heat {, in which he arrives at this result—that the equation which expresses that proposition can be deduced as an immediate consequence from Hamilton’s principle. * Translated from a separate copy, communicated by the Author, from Poggendorff’s Annalen, vol. exlvi. p. 585. + Sitzungsbericht der Niederrhein. Gesellschaft fiir Natur- und Heilkunde, 1870; Phil. Mag. Sept. 1871, p. 161. ~ Phil. Mag. May 1872, p. 339. 366 Prof. Clausius on the Connexion of the Second Proposition That the second proposition of the mechanical theory of heat is connected with the principle of least action was also stated by me, and, as I subsequently learned, also still earlier by Boltz- mann*, This connexion becomes, as M. Szily quite correctly insists, still more striking when the amplified expression given by Hamilton of the principle of least action is employed. But for this purpose Hamilton’s equation must not be taken in the form in which it is usually cited in the text-books of me- chanics and is found, for example, in Jacobi’s ‘ Lectures on Dy- namics,’ p. 58: viz., for a system of material points in motion under the influence of forces which have a force-function or ergal, let the vis viva be denoted by T and the ergal by U, m the sense that the sum T+ U is constant; then the usually cited form of Hamilton’s equation is S(T U)dt0.. 6 6. In order that this equation may be correct, the variation sig- nified by 6 must be so understood that in variating we neglect the alteration of the time—although in reality the altered motion to which the variation refers is different from the original motion not merely in respect of the coordinates and velocities, but also of the time in which it happens. : If, on the contrary, we understand the variation-symbol 6 in the sense usual in other cases, as signifying the entire alteration of the variated quantity, the equation must read :— 6 | (T—U)dt+(T+U)8{ dt=0, or, if we denote by 2 the duration of time to which the integra- tion refers, and for the sum T+ U (the energy of the system) introduce the symbol E, | (@—U)dr+ BBi=0. 0 The same equation can, as is readily seen, be also brought into the following still more simple form :— 25 { "rai =i8n, i) «o:cillenet ci 0 This is the form of Hamilton’s equation made use of by Szily, and which expresses the principle of least action with variable energy. It agrees with Boltzmann’s equation (28a) in the above-cited memoir, if we understand under the quantity which he denotes by e not merely the vis viva supplied, but, in accord- * Sitzungsberichte der Wiener Akademie, vol. liii. of the Mechanical Theory of Heat with Hamilton’s Principle. 367 ance with his later explanation, the augmentation of vis viva and work, soas to attribute to it the same signification as to the va- riation dE in equation (2) above. Szily derives, in the simplest manner possible, from equation (2) another equation, which he regards as synonymous with the second proposition of the mechanical theory of heat. In relation to this I cannot help saying that his development appears to me too simple, because in it important difficulties remain unnoticed and unsolved. Of that mechanical equation which I produced and employed in my memoir mentioned at the commencement he speaks as if it were contained in Hamilton’s equation. But that is not pos- sible; for my equation possesses a more general applicability than Hamilton’s. The latter, namely, presupposes as a neces- sary condition that with the altered motion the ergal is to be expressed by the same function of the space-coordinates as with the original motion ; while my equation remains valid even when the function of coordinates which represents the ergal undergoes an alteration. As the simplest case of this kind, we may assume that the function contains, besides the coordinates, also a quan- tity which with each motion remains constant. Hamilton’s then presupposes that this quantity with the altered motion has the same value as with the original motion, while mine permits an alteration of the value of this quantity. -I have already, in a memoir® relative to Boltzmann’s, ex- plained this difference between the two equations, and have there shown more particularly how far Hamilton’s equation would be incorrect for the case in which the ergal undergoes an alteration independent of the alteration of the coordinates. The erroneous supposition that my equation can be derived from Hamilton’s appears to me to have arisen from this, that M. Szily has not quite correctly understood my notation. For the more convenient elucidation of the matter, we will here confine ourselves to the consideration of a single moveable point. Given, then, a material point of mass m, which with the original motion describes a closed path or moves between two given points. Let it likewise with the altered motion describe a closed path or move between two points, which latter may either be identical with those previously given, or, when that is not the case, fulfil the condition that the quantity dy dt has the same value at the final point of the motion as at the dz * Pogg. Ann. vol. exliv. p. 268. 868 Prof. Clausius on the Connexion of the Second Proposition initial point*. If we then retain the letters 7 and E for the du- ration of the motion and the energy respectively, and denote by v the velocity of the point, and if we further, with variable quan- tities, indicate their mean value by putting a horizontal stroke over them, we can give to Hamilton’s equation as quoted under (2) the following form :— S(mv%)=i8E.. . . . . . « (Qa) In first forming my equation I wrote it thus :— sU= 5 Su? + mo*dlog i. . 2 But I did not there employ the letter U as a universally valid symbol for the ergal, but said explicitly that it only denoted the ergal for the original motion. In asubsequent memoir{, in order to show the difference very clearly, | wrote the equation in the following form :— be+ at oe be= 5 8? + mv*8 log i; . (3a) and I added, “‘ The sum dU dU dU cannot at once be regarded as the variation of the ergal, and hence, if the signification of U be extended so that it shall re- present the ergal not only for the original, but also for the altered motion, cannot at once be denoted by 6U.” If we assume for example the above-mentioned ease, that the function U contains, besides the coordinates, also a quantity ¢ which is constant with each motion, but may change its value from one motion to another, then the above sum does not con- tain that alteration of the ergal which is occasioned by the alte- * Ifthe latter condition be not fulfilled, the difference dz dy dz ) —(< dy dz, (i a dt oy + dt ez), dt Pe dt out az) (the indices 0 and 1 signifying the initial and final values of the quantity) must occur in the following equations. For our considerations, however, the simpler form of the equations suffices, which corresponds to the as- sumption that the difference is =0. + Sitzungsber. der Niederrhein. Ges. fiir Natur- und Heilkunde, 1870, p- 174; and Phil. Mag. September 1871, p. 167. + “On the Application of a Mechanical Equation advanced by me te the Motion of a Material Point round a fixed Centre of Attraction, and of two Material Points about each other,” Phil. Mag. November 1871, p. 321; Nachrichten der Géttinger Gesellschaft der Wissenschaften, 1871, p. 248; Math. Ann. von Clebsch u. Neumann, vol. iv. p. 232. of the Mechanical Theory of Heat with Hamilton’s Principle. 369 ration of c. We can therefore in this case write instead of (3a) :— se ie Oe 241+ m%logi, . . . (3) by. which the aia 2 ee of the quantity which stands on the left-hand side of my equation comes out still more distinctly. In order that we may conveniently compare together the three mutually related equations with which we have to do in the newer considerations on the mechanical theory of heat, in refer- ence to their applicability, it will probably be advisable to sum- marily recapitulate the differences which prevail between them. The equation which expresses the principle of least action in its original form, and which in our notation is O(me i= One eas. tie ee oth (4) presupposes that the ergal is represented by an invariable func- tion of the coordinates, and also that the energy has an invari- able value. Inthe Hamilton’s equation (2a) an invariable func- tion is likewise presupposed, but the energy may vary. Lastly, in my equation both an alteration of the energy and also of the function representing the ergal are admissible. The latter generalization was absolutely necessary for the ap- plication to the theory of heat, because, with the changes of state of a body which there come into consideration, occur variations of the effective forces which are independent of the space-coor- dinates and cannot be represented by an ergal of invariable form. Besides this, other difficulties are met with in the cases to be considered in the science of heat, which render the immediate appplication of the Hamilton’s equation (2) inadmissible. Hquation (2) presupposes that all the material points in the system under consideration take for their motion one common time 2, which with the change of motion changes in like manner for all the points. But if we conceive a body as a system of a great many moving material poiuts, and make even the simplified assumption that all the points move in closed paths, yet we are not at liberty to presuppose that they all describe their paths in the same time, and that with a change of state of the body all the times of revolution change in like manner. Consequently, to take into account this circumstance, special considerations are necessary. The difficulties become still greater when we drop the assump- tion that all the points move in closed paths, and admit that their motions are quite irregular. In M. Szily’s analysis, however, not one of these difficulties is mentioned. Bonn, May 1872. Phil. Mag. 8. 4. Vol. 44. No. 294. Nov. 1872. 2B f \arosg XLIV. On some Points in the Chemistry of Acid-manufacture. By H. A. Smira, Junior Assistant in the Laboratory of Owens College, Manchester*. Section I. On the presence of Arsenic in Alkali-manufacture. PRESEN CE of Arsenic—The great drawback in the ma- nufacture of sulphuric acid from pyrites is most undoubt- edly the presence of arsenic. Its removal, even if it can be done completely, is a work of difficulty and expense, as in our methods for purification we must take into account the various uses to which the acid is to be put. It is my intention in the present part of my paper to trace this impurity (arsenic) from the original pyrites, through the various operations with which the acid made from it is connected, to the last stages of alkali-manufacture ; and to show also that, not content with throwing the injurious gases of sulphurous and hydrochloric acids into the air, alkali- works must bear the blame of polluting the atmosphere with the still more dangerous substance—arsenious acid. Although the amount escaping from a single work is comparatively small, yet, when we consider the number of works using pyrites in the for- mation of sulphuric acid, we must confess that in the end it mounts up to something very considerable. General amounts in various pyrites.—There are two things to be looked to in choosing an ore for sulphuric acid-manufacture. Ist. Its breaking property, if I might so call it,—that is, its power of breaking into small lumps without leaving what are technically called “ smalls.” 2ndly. Its freedom from arsenic. If we compare the amount of arsenic in published analyses of various kinds of pyrites, we shall be astonished at the difference between these and the amounts of arsenic found in the acid ma- nufactured from the same ores. From ores containing from 0-21 to 0-31 per cent. arsenic we have acid containing from 1 to 1°5 per cent. arsenic, showing that some mistake has been made in the analyses. Taking, for instance, the analyses of various pyrites given in Richardson and Watts’s ‘Chemical Technology,’ I find that the largest mean percentage of arsenic present varies from 0°31 to 0-33 per cent. arsenic, whilst some are mentioned as containing merely a “trace,” and others as being perfectly pure. These results, however, are never corroborated when these ores are being worked on a manufacturing scale. Being obliged, in my capacity as chemist in an alkali-work, to turn my attention to this subject, I determined to make an extended series of analyses of such specimens of pyrites as were * Communicated by the Author. On some Points in the Chemistry of Acid-manufacture. 871 likely to suit our purpose, and accordingly drew up a Table of results of analyses which differed to a very great degree from those generally given. In the following Table I. I give in Part I. the amounts of arsenic in the various ores given in Richardson and Watts’s ‘Chemical Technology ;? and in Part II. my own analyses are given at full length. The differences are very great ; still [ remain satisfied of the truth of my own results when I consider that the increase in the different specimens obtained by laboratory analysis was an index to the increase obtained as the result of manufacture. TaBLeE I, Part I. . Arsenic per cent. Name of pyrites. Nica STLIGS 2 scekSbedeeas adc ane aae Aen ee 0:21 to 0:31 ESE tf. S'S clo aislsiiciels Bale ontcle ds si.e trace Ne aR AI aya F 55 ojala sate sinlcberan sie osteo trace BPMN Rite solo ac « caja seis. iejecierissie'sieios «= none TEL cisdadidg As tilsae ela Als aae inane mnre sae 0:33 TIDES 2. 2 de oe eee 0°32 ee REM oo cose chan ole Vals wd sis njatiosorwie’s trace ST LITSE .2secce eae ee trace MCMURDO cee sk cece cccccseutecscde ss Part II. Arsenic per cent. Mean. Spanish :— Tharsis’...1°542, 1:620, 1:644, 1-790, 1-526, 1-700, 1°552, 1-661, TGSG ZO Ge Noe Meee ere eee ree 1°6517 Mason’s...1°-744, 1°810, 1-891, 1:770, 1-661, 1:692, 1:71], 1°754, MSGON ALOE ae shin ca Bayne eee beeaseeck Sete oman 1°7453 Belgian...... 1:000, 0-664, 1:621, 0°743, 1-002, 0-624, 0-972, 0:924 | 0:9437 Westphalian 1°886, 1:794, 1-802, 1-936, 1:899, 1-900, 1-921, 1-889 | 1:8783 Norwegian :-— Hard ... 1-440, 1-916, 1-638, 1-621, 1-648, 1-611, 1:692, 1-631 | 1:-6490 Solte.. +. << 1-794, 1:731, 1:664, 1:632, 1-700, 1°621, 1°816, 1°709 | 1°7085 Here the Belgian pyrites contains the smallest amount of im- purity; but this had the fault, on bemg broken, of crumbling very much and leaving a large amount of “smalls.” The next in order of purity is the hard Norwegian. This was a good breaking and burning ore, firm, compact, and easily raised toa red heat in the kilns; so it was found preferable to burn this ore, even with the increased amount of impurity, rather than use the Belgian containing a small amount, but which carried along with it the great inconvenience of making “ smalls,” 2B2 372 Mr. H. A. Smith on some Points in the Deposit in flue leading from kilns to lead chamber.—This flue when cleaned out presented a strange appearance. Its length was about 20 feet, and, with the exception of about 10 feet from the “kiln” end, was thickly coated (and even partially filled) with a shining deposit, which on examination proved to be a mass of sulphur in a perfectly viscous state, containing (as a mean of four analyses) 46360 per cent. arsenic trioxide. When lighted it burned with the ordinary blue atitphay flame, and on inserting a piece of cold porcelain in the vapour, gave a deposit of sulphur along with a considerable amount of arsenious acid. (See Table II.) Sulphuric Acid.—Passing along the flue into the chamber, I find the sulphuric acid containing a large amount of arsenic. As an average of twelve analyses, 1-051 per cent. arsenious trioxide is the result; so that in passing through the flue above men- tioned it must have lost a large proportion of that originally pre- sent in the pyrites. (See Table II.) It is from the sulphuric acid itself that the arsenic should be removed, as this acid is the groundwork of the whole following alkali-manufacture. Deposit on bottom of lead chamber.—On the bottom of the lead chamber and sometimes on the sides, a grey siliceous mass is found, interspersed here and there with clusters of delicate regular erystals, the transparent elongated prisms of arsenic acid. The transformation from the arsenious acid we find in the flue to the arsenic acid of these crystals, has evidently been completed along with the oxidation of the sulphurous acid. In this deposit the percentage of arsenic trioxide varied from 1:81! to 1:9 per cent., the rest consisting of sulphate of lead and silica. (See Table IT.) Hydrochloric Acid—When the sulphuric acid made from py- rites is mixed with common salt in the reverberatory furnace for the formation of sodium sulphate, the arsenious acid present in the acid is converted into the terchloride of arsenic, and escapes along with the hydrochloric acid to the condensing-towers. This conversion is very nearly complete, as the amount of arsenic pre- sent in the sodium sulphate is very small. Jn the hydrochloric acid a mean of eight analyses gives 0°69 per cent. arsenic trioxide, the amounts varying from 0°589 to 0911 per cent. (See TableII.) Sulphate of Soda.—The amount present in this is very small. As mentioned above, the conversion from the teroxide to the ter- chloride of arsenic is wonderfully complete, the percentage in the sodium sulphate being only 0°029 per cent. (See Table IT.) This still shows us how careful we ought to be in obtaining pure sulphate of soda for medicinal purposes. Deposit in flue leading from salt-cake furnace to condensing- towers.—This flue, about 20 feet long, leads for the most part in the open air, from the salt-cake furnace to the condensing-towers. 373 Cremistry of Acid-manufacture. a a ee ee ee eg a ie eh Sey ie ee es pre ey or SE ate fa Tee ——-S=— —rhDh—h ir COLO | aVPr-0 eeeoen Alii Pos aa eee Lo9-1 eonree 098-95) 190-1 | 666-0 cong | 6F9-1 | ce ‘182 IN eeeecoo eeoecee eeovee 008-0 veecee esceee eesrece 198-0 669-1 ‘TI @1avy, eeceece 166-0 (19-1 ‘qua. Jed (aprxom}) otuasry GPP-0 G9F-0 6E0-0 666-0 Gé8-T 009-9F O6I-1 PSP-0 129-1 —_ | uoltyvoyund sayy 106-0 |°'°7‘ssaooid s,puoyy —: mydjns pa1aa0day —— |" epos Jo ayeuoqued 119.0 fo a4SBM-Bpog 900-0 vesccesee Bpos jo ayeyding 112-0 [0° ploe® Olof yoorpAyy 198-1 667-9F Gll-T 696-0 OFF-1 Liorgete soit Jaquieyo peo| ee m0}30q uo yIsodaq teeeseres OQUIBYD Prot 0} suyry-soqdd woul Zurpes] ong ut ysodaq eoeceesececuece proe olunyding sevese Buruang 199 Vv see | Burund a.10joq —: (ue3 -OMION paey) sayadg *yuaso1d st o1uasae Yor Ul SsavuRysqus 374 Mr. H. A. Smith on some Points in the The part from which the deposit was taken was about 15 feet from the furnace. At first sight the deposit seemed to be com- posed merely of common salt and a little sodium sulphate ; but on examination with a hand-microscope, small octahedral crystals of As? 0? were distinctly seen. Tas_e III. Tons. | | Ton As. 100 | Hard Norwegian pyrites (Table I.) contain, before burning | 1-649 9 “ “5 “- “ after burning | 0-465 tons. 100 | Hard Norwegian pyrites make 140-875 H* SO#, containing | 1-481 140-875 | Sulphuric acid make ......... 104-9 HCl Ee 0-724 a | at + 20412 Na?SO* _,, 0-059 In this Table the amounts are given in a manner more useful to manufacturers. On analysis this deposit gave (as a mean of nine analyses) 43°4 per cent. arsenic trioxide. This flue had been in constant use for some years. (See Table IV.) Tare LV. Flue from Salt-cake Furnace to Towers. Deposit. No. of analysis. | Arsenic trioxide. per cent. 1 44-664 2 42-936 3 45°333 A. 39-982 5. 46-449 6. 44-398 7 40-441 8 38-977 9 47°732 390-912 Mean accereseo: 43°4346 Coke in condensing-towers.—Although not expecting to find any arsenic in this, thinking that the water in the towers would completely decompose the chloride of arsenic which escaped from the reverberatory furnace, I made an analysis for it. For every analysis 10 lbs. of coke were employed, and digested first with pure distilled water and afterwards with perfectly pure hydro- chloric acid. Arsenic was very easily detected in this solution. As an average of three analyses, I find 2°8 per cent. arsenic tri- Chemistry of Acid-manufacture. 375 oxide, the variation being from 2°6 per cent. to 3°2 per cent. As? O08. It is difficult to imagine how this arsenic has been re- tained in the coke, as it would have been expected that the decomposition of the terchloride by the water in the towers would have been complete. (See Table V.) TaBLe V. Coke from Condensing-towers. No. of analysis. Arsenic trioxide. 2641 me ee ee | ee Air in flue from condensing-towers to chimney.—Not only is the decomposition of the arsenic terchloride not completed in the towers, but a considerable amount of arsenic (in what condition I am not aware) escapes from the flue leading from the conden- sing-towers to the chimney of the works. The amount of air passing through this flue was 31,722 cubic feet per hour; and for each analysis 500 cubic feet were taken. The method em- ployed for collecting the arsenic (trioxide ?) contained in the air passing through this and the next mentioned flue was as fol- lows :—The air was aspirated through three bottles containing respectively H?O, HCl, and AgNO®. The gas was allowed to bubble very slowly through the solutions ; the bottles containing them were capable of holding 40 ounces, and were about half filled. It was found in most cases (it might almost be said in all) that the AgNO solution was unnecessary, the H? O and the HC] absorbing all the arsenic which was in the air drawn through. As an average of twelve analyses, the following results were obtained :— As? O° As’ 03 As? 0? per 1000 cubic feet. per hour. per day. 0-158 grain. 5°012 grains. 120°282 grains. This amount may appear small; but when we consider that the 120 grains per day are from the chimney of ene works only, the question becomes rather a serious one when we take into account the number of manufactories employed daily in throwing this amount into the air even within a short distance of Man- chester. (See Table VI.) 376 Mr. H A. Smith on some Points in the Tene VI. Flue leading from Condensing-towers to Chimney. Amount of air taken for each analysis = 500 cubic feet. Amount of air passing = 31,722 cubic feet per hour. As? 0? per 1000 No. of analysis. Amount per hour. |Amount per day. cubic feet. grain. grains. grains. 1. 0-068 2°157 51-768 2. — — —_— 3. 0-082 2-601 62-424 4, 0-072 2°284 04°816 8 0-102 3235 77-640 6. 0-064 2-030 48-720 7. 0-198 6-280 150-720 8. 0-248 7867 188°808 9. 0-186 5-900 141-600 10. 0-232 7359 176-616 11. 0°262 8-311 199-464 12. 0-382 12-117 290-808 1-896 60-141 1443-384 Mean *35s0¢5 63 0°158 5012 120-282 Closely connected with this is the specimen of Air taken 10 feet from bottom of chimney.—The same amount of air was taken for each analysis in this case as in the former, namely 500 cubic feet, the mean of nine analyses in this case being As? 0% per 1000 cubic feet. 0-086 grain, or nearly 7 gr. per 1000 cubic feet. Surely such a state of things ought to be prohibited. The arsenious acid thrown into the atmo- sphere must in some places be very large. Of its danger there can be no doubt. But the great problem will be how to prevent its escape. Itis owing to no carelessness on the part of the manu- facturers ; and it is one of those things that in our present state of knowledge it is scarcely profitable to remove. On whom must the blame rest ? SS * Chemistry of Acid-manufacture. 377 Tasie VII. Specimens of Air taken 10 feet from the bottom of Chimney. Amount of air taken for each analysis = 500 cubic feet. As” 03 per 1000 cubic feet. es ee No. of analysis. I hope to speak in another part of this paper on some of the methods employed for the removal of this “ nuisance ;”’ in the mean time I must proceed to speak of the remaining substances of alkali-manufacture. The last examined was the sodium sul- phate; the next to undergo analysis was the Sodium Carbonate-—This, up to the present time, has been found perfectly free from arsenical impurity; fifteen samples from twelve different works were submitted to analysis, and none was discovered. Soda-waste.—In this the amount is comparatively trifling, giving as an average of six analyses 0°442 arsenic trioxide. (See Table IT.) Recovered Sulphur. Monda’s process, before and after purification. —lIn specimens of sulphur recovered by Mond’s process I have sometimes found great differences, the amounts varying some- times from 0°442 to 0-901 per cent. arsenic trioxide; but its presence to this extent is only found in the unpurified samples. In those which have. undergone purification none whatever is found, the average of four analyses of the unpurified sulphur being 0-7 per cent. I think the foregoing analyses allow a simple and direct de- duction to be drawn; and that is, if the arsenic is to be removed at all, every thing points to the sulphuric-acid stage as that in which the removal ought to take place. Sulphuric acid is the -corner-stone of alkali-manufacture ; cleanse it, and the whole is clean. 378 Mr. H. A. Smith on some Points in the Section II. Methods of removal. Two precautions have to be taken into account in the methods employed for the removal of arsenic from sulphuric acid. Ist. The substance or agent which is used in the purifying process must have no deleterious effect on any article in the manufacture of which the acid is required. 2ndly. We must prevent our works, as far as in us lies, from becoming a nuisance to our neighbours. : The item of expense is naturally a matter of course. The following purifying agents have been carefully tried, with the following results. Sulphuretted Hydrogen in a gaseous state.—This is, I believe, in use in many cases, but, as far as I can make out, with very variable results. For my own part I found it infringed the second requisite of a purifier, inasmuch as it became a “nuisance,” and, which was much more serious, was too expensive. The plan employed in this case was a very simple one. A large flat leaden pan was employed covered with a wooden top, and having access to a chimney by means of a long flue. About 20 feet from the pan this flue was led through a fire, which, decomposing the escaping sulphuretted hydrogen, not only prevented a great escape to the atmosphere, but allowed the deposited sulphur to be recovered. Whether from defective draught, or from the unsuitability of the process to the required purpose, this plan did not answer ; whilst the use of acid to liberate the gas, together with the dif- ficulty in regulating the supply, made the expense of working too great. Instead of using separate acid to liberate the sulphuretted hydrogen, I tried to use that which was to undergo purification, by the addition first of Sulphide of Iron.—This plan is, of course, only admissible in -certain cases. For acid employed in wire-working, galvanizing, or similar work, purification by the simple addition of ground sulphide of iron is quite safe, and completely answers the pur- pose required ; whereas that containing arsenic cannot be used, its action having a deleterious effect upon the iron. Acid purified by this means, however, cannot be used in bleaching, dyeing, or printing; so that its field of usefulness is extremely limited; still, as a purifying agent, it was all that was required. Sodium Sulphide.—As this was a substance capable of being used in most cases, more care was expended on it than on either of the former. The sulphide of sodium employed was made from black ash, and, although contaminated with a little lime, answered the purpose completely. The method of application was as follows :— Chemistry of Acid-manufacture. 379 A known amount of sulphuric acid containing a determined percentage of arsenic trioxide was run into a large leaden pan, and a calculated amount of sodium sulphide added. At the bottom of this pan a layer of coke, which had previously been well di- gested with hydrochloric acid to free it from iron and other impurities, was placed, through which the acid, being run upon it, filtered, thus freeing it from the precipitated tersulphide, whilst it wasrun out from the pan by a tap at the bottom. The precipitate was removed from this filter every night; but the coke was allowed to remain for along time, two or three months sometimes elapsing before removal. The escaping sulphuretted hydrogen was conveyed away by a process similar to that em- ployed in the sulphuretted-hydrogen method. - The results obtained by this method were very satisfactory, and the expense was extremely moderate—one hundred gallons of sulphuric acid giving only a very minute trace of arsenic after being subjected to this process. The deduction I naturally draw from the results of the above methods of purification is, that sulphuretted hydrogen can pre- cipitate the last traces of arsenic in the acid it is required to purify. The only difficulty lies in the method to be employed, and the means of getting rid of the escaping sulphuretted hy- drogen which has been allowed to be present in excess. It is necessary to state that the above method of decomposition of that gas did not fully answer the purpose required. Sodium Chloride.—The next plan tried was purification by the addition of common salt to theacid. It was thus supposed that, according to the general rule, the arsenious acid would be con- verted into the terchloride of arsenic and escape as such. This, however, was found unsuitable, for many reasons. In the first place, the decomposition of the salt is not perfect, a considerable amount remaining in the acid as sodium chloride. Next, its action upon the ordinary brown vitriol (as it runs from the chamber) was found not to be so perfect as upon that under- going refining, so that it was necessary to add the salt to the glass retorts after they had been in action for some time. This, of course, entails great inconvenience. The necessity for open- ing the retort after the acid has been for some time in a state of ebullition is at once very disagreeable and very dangerous, whilst the sudden and powerful (partial) action upon the salt makes it an attempt not to be incautiously determined upon. If, on the other hand, the salt is introduced into the retort before the acid hes commenced boiling, it collects in considerable amount at the bottom, and thus causes the mortality among the retorts to become a matter of some consideration, as well as making it a dangerous occupation for the man whose business it is to watch 380 Ox some Points in the Chemistry of Acid-manufacture. them, as the bursting of such a retort over a fire carries with it great danger. This plan then was thrown aside. Although it could compete with any in cheapness, yet it carried too many inconveniences with it to become practicable. The following numbers may perhaps be interesting :— Sulphuric Acid. Sulphuric Acid. As? O? per cent. As’ O3 per cent. (before purification). (after purification). 1131 contained 0°34 1°303 5 0:48 0-991 re 0°63 The above figures show that the decomposition was not per- fect enough for the plan to be made use of on a manufacturing scale. I had found it to answer perfectly in my laboratory ex- periments, and so hoped that, when extended to the working scale, it would be equally successful. Hydrochloric Acid.—A stream of hydrochloric acid gas was passed into the acid required to be purified, supposing the decom- position in this case would be similar to the above. This, how- ever, was open to the same objections as the former, with the additional one that the expense entailed by the process is too great for any practical purpose. In looking over the foregoing processes, one or two natural conclusions force themselves upon me. The process which, as far as I can yet see, we must rely upon for the purification of our acid is that which depends upon the use of sulphuretted hydrogen. Precipitation is much surer, and, indeed, more per- fect, than decomposition. The latter is dependent upon too many conditions. The heat, the compieteness of decomposition of the salt, the rapidity with which the liberated bubbles of hydrochloric acid gas pass through the acid, all exercise a great influence upon the success of the process. Whilst sufficiency of gas is the only requisite in the former case, the latter depends upon too many causes, too many conditions. Certainty in this case must be striven for before rapidity: once gain the former, and we may be sure of the latter following in its own good time. Besides, in the present condition of the law of the country in such mat- ters, sulphuretted hydrogen is a much safer gas to throw into the atmosphere than hydrochloric acid ! I have thus given my own experience of the best methods of the purification of sulphuric acid, gathered during a pretty con- tinued search after some sure and practicable method both in respect of efficiency and economy. I have chosen to do this rather than gather together the experiences of others—partly because these experiences are comparatively few and far between, Energy and Apparent Intensity of Sounds of different Pitch. 381 and partly because this matter has been looked upon by manu- facturers as being of a merely secondary nature. But I was led to inquire into it in a more serious manner from the fact of having seen much acid returned to the manufacturers as being unfit for use owing to the presence (supposed !) of iron, while all the disturbance arose from the presence of this extremely diffi- cult-to-be-got-rid-of substance, arsenic. In several instances also which have come to my notice in the cases of manufacturers of ammonium sulphate, many hundred pounds’ worth of mate- rial has been lost through the use of acid containing this im- purity, while the unfortunate makers were vainly searching for their old enemy, iron. The importance of examination for the presence of arsenic can scarcely be too strongly urged upon the manufacturers of such materials. In conclusion let me say that, as far as my own ex- perience goes, the use of sodium sulphide answers the purpose to a more perfect degree than any other process. Of course many improvements can be made upon the method of application given above; yet, for a rough but satisfactory method, I have found it sufficiently accurate. XLV. On an Experimental Determination of the Relation between the Energy and Apparent Intensity of Sounds of different Pitch. By RK. H. M. Bosanauet, M.A., F.C.S., F.R.A.S., Fellow of St. John’s College, Oxford. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, i eae comparison of the intensities of sounds of different pitch has always been considered to present considerable diffi- culty ; and the theoretical suggestions which have been made as to the measure of intensity have not been regarded as con- clusive. The problem, however, is solved empirically every day ; and the comparison of the intensity of sounds not differing widely in pitch presents no great difficulty. The tones of every keyed instrument are so proportioned in power that in all parts of the range the effect may be as uniform as possible; and in the case of the organ, in which the power of each pipe is fixed once for all by the voicer, we have in each stop a graduated series of tones, the power of which has been adjusted to the production of a uniform effect, by the exercise of a skill more easy to admire than to imitate. Strictly speaking, the effort of an organ-voicer is to make the more acute tones so far prominent above the lower ones, that the higher may be clearly heard through the lower. ‘hat the 382 Mr. R. H. M. Bosanquet on the Relation between the effect sought is really a predominance of the upper notes, appears as well from the statement of the voicers as from some of the means employed to produce the desired effect. Thus one organ- builder uses two pipes instead of one throughout his trebles ; others employ a heavier wind in the treble; so that we must allow that in organ-stops the intensity of the treble is required slightly to exceed that of the bass. But, allowing for a variation of this nature (namely, a slight excess in the intensity of the treble over that of the bass), it seems reasonable to assume that the apparent intensity of the different notes of a well-voiced organ-stop is the same. The work consumed in an organ-pipe in a given time is mea- sured by the amount of wind it draws from the bellows in that time. There is a statement in Topfer’s work on the organ (1842, reprinted 1862, Korner, Erfurt and Leipzig), that when a stop is scaled according to his measures, and properly voiced, the wind-consumption of the pipes is proportional to their lengths, or to the wave-lengths: this law is stated without reasons or measures; so that some verification was essential ; but before passing. to the verification I will notice the immediate conse- quences of the law, if true. The quantities of wind consumed by the pipes in a given time are measures of the work done by the weights on the bellows. We have to assume that in similar pipes the work converted into sound is a constant proportion of the whole work supplied ; for undoubtedly loss takes place in the pipes. Subject to this, we derive from Topfer’s law the statement that the work con- verted into sound by the pipes of an organ-stop in a given time is proportional to the wave-length of the tone, or the periodic time. Admitting, then, that the notes of an organ-stop are fair repre- sentatives of a series of tones of different pitch and equal appa- rent intensity, we have more generally :—Tones of different pitch have equal apparent intensity when the work consumed by them in a given time is proportional to the wave-length or periodic time; or if W is the work consumed in a unit of time, the in- tensity is measured by the fraction = where 7 is the periodic time—assuming that the intensity in notes of the same pitch is proportional to W, which will not be denied. For the purpose of obtaining some verification of Topfer’s law, I employed the new open diapason on the great organ of the instrument in St. John’s Chapel, Oxford; it draws wind enough to observe conveniently as far up as about the top of the treble staff, and is tolerably uniform in tone. Some difficulty \ Energy and Apparent Intensity of Sounds of different Pitch. 383 was found in following out Topfer’s method of observation with accuracy, until the minutiz which follow were attended to. The object is to observe the time of descent of the bellows under dif- ferent circumstances. A pendulum of bullet and string was employed to observe the time, by counting the oscillations ; the eye was thus occupied. The points of full and empty were de- termined by the feel of the bellows-handle, as follows :—The excess-valve is placed between the bellows and one of the feeders ; so that, when the bellows is overfull, the pressure of the wind comes on the feeder, and destroys the equilibrium of the handle, causing a downward pressure, which is sustained by the hand. At the moment of closing of the excess-valve this pressure dis- appears, and thus the moment of departure of the observation is distinctly announced. A similar sudden change of pressure in- dicates the emptying of the bellows and close of the observation. Until this method was adopted it was impossible to obtain the accuracy required; but with it the accuracy was great, so that, if the same element was observed repeatedly, the number came almost always the same. As a preliminary experiment, J observed some time ago the wind-consumption of the five C pipes; the results were as follows :-— 2 Peer epee W_49-3, Goa Tr T Be ss OF 59 641 40-0 Gate. 92 69 4.06 50:7 +1°4 Ce 95 79 191 47:7 —1°6 eles. 100 9] 99 49°5 +0°2 aes). 96 9] 57 57 The first column contains the name of the key depressed. a is the number of oscillations of the pendulum counted during de- scent of bellows with stop closed. 6 is the number of oscillations during descent of bellows, pipe sounding. : and : are conse- quently the fractions of the content of the bellows consumed in one ae 1 Ve. oscillation in the two cases, and 57a 8 the fraction of the con- tent of the bellows consumed by the pipe alone in one oscillation of the pendulum ; and this I have taken as the measure of the work W converted into sound during one oscillation of the pendulum. =) where 7 is referred to the periodic time of cl as unity, is the next column; it should be constant according to Tépfer’s law, and is the measure of intensity according to what precedes. The number for c is seen to depart widely from the result of 384 Mr. R. H. M. Bosanquet on the Relation between the the three middle observations, which agree closely. This is easily explained, and the rejection of the observation for our purposes justified as follows: —The largest bass pipesof the manual in an organ have almost unavoidably a deficient supply of wind. In consequence of the heaviness of the touch caused by large valves, the valves and, therefore, the wind admitted by them are hmited in size and quantity respectively ; and as this limited amount of wind has to be distributed amongst a number of large pipes, each has to put up with less than a full supply ; and it is well known that the power of the bass invariably suffers more or less in consequence of this difficulty. The number for c!” is rejected because the quantity to be ob- served is in that case too small, with reference to the method of observation, for accurate results. So far as the above “light observations went, they appeared, then, to corroborate Topf .’s law. But with the view of ascertaining more exactly how f:. the uniformity sought for prevails, I subse- quently observed the wind-consumption of each pipe from tenor C (cg) to treble C (c") inclusive. Several months had elapsed and the organ been tuned, which must account for the difference in the relative behaviour of the C pipes on the two occasions. The results are as follows :— C, 143 11 201 50-2 (+63 (a 73 ext | 153 123 159 42-1 es —1°8 — 08 d, 159 125 171 48-0 et 44+] | + 51 e) | 159 | 128 152 452 joo Weeds 4+ 23 e, 149 127 115 36-4 | Sle | —75 — 65 ty 158 132 124 41-4 —25) _. | — 15 Sot | 159 137 101 35-7 ( 6:2) eee % 152 130 11 41-6 Osa he 13 ap 148 129 99°5 39:3 o | —2-6 i 36 a, 160 134 121 50-9 = 490 + 86 bp | 166 | 126 | 191 =| +48 4+ 38 \ 4-4 \ 54 : —26 (8 ; e | +50 + 68 83 [hs | | or [hee 8] 22 | Seaham Fi Fe [oes | as ! 162 150 49-4 37:0 (—94| | ; —10-2 a'p 170 154 61-2 48-6 x 6 | 4+22/s);e | 4+ 14 a’ 168 152 62-7 527 = J +63 + 55 bb 164 152 48:1 42-8 l —3-6 — 44 b' 162 149 53-8 508 |Ble eae + 36 c" 171 158 46-9 46-9 +05 \— 03 Energy and Apparent Intensity of Sounds of different Pitch. 385 The error of the method of observation may be entirely dis- regarded ; the deviations from uniformity are to be taken as resulting from irregularities in the proceedings of the voicer. Collecting the results, we have :— Ww WwW a ra Coto 43°9+1°37 Sge-¢ 41:9+ 1°60 c¢-f'Z 48:0+1:01 it an. ye 4441-57 Cee 47240982 The probable errors of these arithmetic means are appended. From the near equality of these in the results of the two se- parate octaves, we infer that the estimation by the ear of equal intensities of tone has about the same accuracy whatever the pitch may be. This discussion establishes almost beyond a doubt the exist- ence of the Jaw of Topfer as a basis; but the results are affected by irregularities of a more continuous nature than are to be ex- pected in ordinary cases. The upper half of the tenor octave, for instance, furnishes the mean 41°9, which deviates widely from all the rest. Jf, however, we call to mind the nature of the estimation of intensities (which takes place for the most part by comparison of adjoining notes), we see that an error once committed is liable to perpetuate itself; and therefore precisely this description of continuous irregularity is to be expected. If we admit the existence of an error of this kind in the upper half of the tenor octave, and if we admit that, according to the practice of voicers, some increase in strength is looked for on entering the octave above middle c, we completely account for the discrepancies in the results. The 6.) (which is omitted in the above discussion) has a wind- consumption quite disproportionate to all the rest; the tone of the pipe indicates a difference in the voicing: a mouth cut up a good deal higher than usual would account for both effects; a pipe with a high mouth takes much more wind to reach the upper lip properly. On the whole, the law of Topfer is not supported by this discussion as an accurate expression of the properties of the organ-stop examined; but the very deviations from this law which occur in the above figures support the proposition that coc! 42°9+1-0005 = is a measure of the apparent intensity of the tone. If 1 be the apparent intensity of a tone of periodic time 7, we have seen that it is eee by m8 if, then, w be the constant proportion of W (say —) which reaches a thin plate Phil. Mag. 8. 4. Vol. 44. No. 294. Nov. 1872. 2C 386 Mr. R. H. M. Bosanquet on the Relation between the of air at the orifice of the ear in a unit of time, we may put yee 2 Here a certain proportion of the energy expended traverses, at right angles we suppose, a small plate of air whose mass we will assume constant and equal to unity. Then the air is subjected to a forced vibration, which may be represented by x=a sin nt in the simplest case; and the energy of this vibra- ahi an QT a? tion is measured by a where nt=27; that is to say, waar measures the energy communicated to the plate of air in a quarter of a vibration. It is clear that if we take the expression for the velocity where nt = 277, we cannot avoid having the square of the periodic time in the denommator of the vis viva. In a recent paper in the Philosophical Magazine, Mr. Moon has omitted this element. See the determination of the energy of a vibrating string, Donkin’s ‘Acoustics,’ p. 127, which is to some extent analogous to the present case, except in the difference of the vibrating body. If the plate were moving freely, the energy gained as kinetic in the first quarter oscillation would be transformed into the form of potential in the second ; but here we have no potential energy in the plate of air, the movement at every instant depend- ing on what is transmitted from the source of energy. Thusall the elements of work in both directions proceed from the source, and must be reckoned in estimating its action on the air: this observation occurs in Mr. Moon’s paper. The work passed through the plate of air in a whole oscilla- tion is then Qar2y2 2 7 Hence the following proposition :—In notes whose oscillations are similar, 7. e. have the amplitudes proportional to the wave- lengths or periodic times, the work transmitted by one oscilla- tion of each note is the same. 1 bgcauadih Sa cis tae ; : Since there are — oscillations in a unit of time, T shel 87r7a? 3 Substituting this for w im the expression for the intensity, we have (a eee ah ease whence proceed the following propositions :— In notes of different pitch the apparent intensity varies as the Energy and Anparent Intensity of Sounds of different Pitch. 387 square of the amplitude, and inversely as the fourth power of the wave-length or periodic time. In series of notes of equal apparent intensity, but of different pitch, the amplitudes vary as the squares of the wave-lengths or periodic times. In some works which allude to this subject, a confusion exists between the energy of a vibrating instrument, as a string, and the intensity of the tone produced thereby. It is necessary to remember that the energy of the instrument has nothing to do with the tone heard, as it is only that portion of the energy which is lost to the instrument by being communicated to the air that causes the spread of the tone. Thus the energy of a string set in vibration is gradually exhausted by communication to the air, and the energy of the string does not represent the apparent intensity of the tone at any instant, but the total energy expended during the duration of the tone until it dies away. Again, in an organ-pipe there is reason to believe that the energy actually stored up in the vibrations of an organ-pipe in steady motion is considerable ; in fact it goes on storing until the com- munication of energy to the outer air equals the accession con- stantly received from the source of power. Thus the energy of vibration within the pipe may be much greater than that which, so to speak, flows through it. We have neglected in the fore- going the energy of the pipe itself, and confined our attention to that supplied to it, which in steady motion is necessarily equal to that parted with to the surrounding air. The result is then different from that propounded heretofore; for the energy of a pipe or strmg necessarily contains the integral of the motion throughout the vibrating mass, a quantity with which the energy which passes out has nothing todo. As another illustration, the energy of a tuning-fork sharply struck is considerable; that of the vibrations excited in the air around is in comparison eva- nescent. When the impulse in this case is constantly renewed in Helmholtz’s machine by the electromagnetic apparatus there applied, and the tone taken over by a resonator into the sur- rounding air, we have another example of what has been de- scribed in the case of the organ-pipe: the store of energy of the fork is quite independent of the flow of energy from the electro- magnet into the resonator; and in estimating the apparent in- tensity of the tone, the latter alone is to be regarded. In answer to the note on the second page of Mr. Moon’s paper, as to the law of the intensity in optics, it is enough to observe that the law of Malus, connecting the intensities of the ordinary and extraordinary rays in doubly refracting crystals, affords an experimental confirmation of the law of the squares of the amplitudes, for waves of the same period. 202 [ 388 ] XLVI. Notices respecting New Books. The Orbs around us: a Series of familiar Essays on the Moon and Planets, Meteors and Comets, the Sun, and coloured Pairs of Suns. By Kicuarp A. Proctor, B.A. (Camb.) London: Longmans, Green, and Co. 1872. HERE are two classes of scientific authors—one consisting of men who chronicle the results of their researches obtained by the aid of observation or experiment, the other of men who, gathering up these results, present them to the public in a pleasing and attractive form. In each of these classes we find men who are justly entitled to be regarded as “ the leaders of scientific thought,” and from the general character of the now numerous works that have issued from the pen of Mr. Proctor, the position of ‘‘ leader of popular astronomic thought’’ may be unhesitatingly accorded to him. The work before us contains a series of essays originally published in ‘St. Paul’s,’ ‘Fraser’s,’ and the ‘ Cornhill’ Magazines, on spec- trum-analysis, the habitability of the planets Venus, Mars, and Jupiter, meteor and meteor-systems, comets and their tails, the sun’s corona, and the colours of double stars. Most of the subjects are treated ina lucid and familiar style, particularly that of spectrum- analysis, under the title of ‘‘The Gamut of Light,” and alse that of ‘‘ Meteor Systems.” Musical readers who possess an acquaint- ance with the science of sound will have no difficulty in following our author in his exposition of the phenomena of the spectrum, ‘‘ The Gamut of Light;’’ and his exposition of the connexion between meteor-systems and comets will at once commend itself to the thoughtful reader who can appreciate the difficulty that must have been experienced by the eminent mathematicians who worked out the orbits, and who showed the close connexion between the two great meteor-systems now known to belong to the solar system, and the two comets with which they are intimately associated. Occa- sionally our author departs from his more popular style, indulging in one somewhat more abstruse, particularly in the enunciation of theories which he has originated ; and we find in several instances a spice of the fanciful, bordering on the sensational, as in such titles as ‘‘ the planet of love,” “‘ the planet of war,” and a ‘“‘ minia- ture sun,’’—also in the very frequent use of the word “ startling,” as if the sober realities of science were so far removed from the general track of ordinary thought that the unravelling of the symmetrically woven web of natural knowledge should be accom- panied by sensations different from that of a deep feeling of admira- tion at the power given to man to read, mark, learn, inwardly digest, and understand the great book of Nature spread open before him. Viewing the book as the production of a recognized leader of popular astronomic thought, we have marked a few passages in which we apprehend the author has fallen short of his high vocation. Speaking of the attempt to secure clearness of illustration with strict scientific exactness, he says, ‘‘ Scientific exactness can come afterwards,” &c. In one or two instances the author has followed his own rule (as we conceive) detrimentally. He tells us that Dr. Notices respecting New Books. 389 Huggins has proved that Sirius is receding from us at the rate of several hundred miles per second. Now Dr. Huggins has done nothing of the sort; his earliest determination of the motion of Sirius before Mr. Proctor wrote his essay was twenty-five miles per second ; he has since found reason to reduce the velocity to eighteen, or at most twenty-two miles per second. Another instance is, that the equatorial belts of Jupiter and Saturn are in no sense comparable withthe zone of calms or doldrums—in their being persistent, whereas our zone of calms travels far north of the equator in summer, and far to the south in winter. We were not aware, until thus enlightened by Mr. Proctor, that a zone about 6° broad, its mean position being north of the equator with its northern edge somewhere near the parallel of 8°, was removed far from this position; perhaps his readers would have been really more enlightened had the two limits of 15° N. and 5° S. been given; and we think that in both the cases alluded to “‘ clearness of illustration ’’ would not have been sacrificed by giving these quantities with scientific exactness. On the subject of ‘‘ other habitable worlds,” much as has been written, we cannot possibly obtain any definite knowledge, beyond that of ascertaining by observation the conditions of habitability of “the orbs around us.’” One, and only one, has yielded us any definite information on this head. It is now seven years since Professor Phillips constructed a map of Mars, and showed, from the osciilations of the snow-zones of the planet, that its climatic rela- tions are similar to those of the earth—in other words, that it is a suitable residence for beings of a similar constitution to the human race. One or two quotations from Phillips occur in Mr. Proctor’s description of Mars ; but the map is passed over unnoticed, although we have a map constructed by our author from drawings by the late Mr. Dawes. A comparison of the two is very suggestive. In the essay entitled ‘‘The Rosse Telescope set to New Work,” we find large reflecting telescopes described as inadequate to present objects in a perfectly distinct manner, their value consisting in their light- grasping powers. The new work of the Parsonstown reflector is that of testing its heat-grasping powers ; and in this it has been suc- cessful in furnishing us with a measurable amount of heat derived (or rather reflected) from the moon; and this result our author cha- racterizes as ‘‘Lord Rosse’s discovery.’ It appears that Mr. Proctor must have forgotten, or he would certainly have referred to, Professor Piazzi Smyth’s work in this direction, recorded on pages 212, 213 of the account of his celebrated astronomer’s experiments. It is, however, quite possible that this particular passage escaped his attention ; but what are we to think of the following? In his essay on shooting-stars, alluding to the theory of meteors being propelled from the moon, he speaks of the inadequacy of the force of propul- sion to give them their observed velocities, ‘‘ even,”’ he says, ‘‘ if it were proved (which is far from being the case) that any active volcanoes now exist in the moon.” This was published in the * Cornhill Magazine’ for November 1867. We have now before us the Number of ‘ Temple Bar,’ published only three months earlier, viz.in August 1867 ; and in it we find an article headed, “ A Lunar 390 Notices respecting New Books. Voleano in Eruption, by Richard A. Proctor, B.A., F.R.A.S., author of ‘ Saturn and its System, &c.,” in which the author is at some pains to establish the then supposed change on the moon’s surface, in the celebrated case of the Crater Linné. We can hardly be mistaken in the authorship of this paper; for the probabilities are immense against two men bearing the same name and writing on the same subject. Now what does the Mr. Proctor of ‘ Temple Bar’ say of this supposed change? We would quote the passage at length did space permit. Suffice it to observe that he speaks of an actual change having taken place, which he explains by a mass of matter having been poured into the crater from below, overflowing its barrier, and covering the steep sides of the former ring, and commences his concluding paragraph with these words: “ For the first time, then, after so many years of patient labour, we have undoubted evidence of change upon the moon’s surface.” His closing words are, ‘‘ The most sceptical must accept the combined evidence on this interesting point as absolutely decisive.’ This looks very like a proven case on the part of the author. There are a few other records of some importance which appear to have escaped Mr. Proctor’s attention. Our space will not allow further notice than merely to refer to the unique view of Venus in the last century, when the surface of the planet appeared to be in- dented with spots similar to those on the moon. In Mr. Proctor’s remarks on Jupiter as ‘a miniature sun,” our author calls attention to the absence of any thing in the meteorology of the earth at all comparable with the mutual disturbances of the Sun and Jupiter by each other, synchronous with the ‘‘ Sun-spot period.” ‘This, it appears, was somewhat premature. Professor Meldrum, from a study of the frequency of the cyclones of the indian Ocean, has succeeded in establishing a periodicity of these phenomena synchronous with the ‘“‘Sun-spot period.”” We are now, therefore, not warranted in concluding that the meteorology of Jupiter alone suffers disturbances originating in the sun; for Professor Meldrum’s discovery establishes that our earth sympa- thizes with both. Setting aside the instances to which we have alluded as indicating a want of sufficient care by the author in the composition of his pleasing and lucid articles, we consider the book well calculated for its ofice—that of spreading a knowledge of astronomy among ordinary readers ; and in taking leave of it, we may remark that we have derived much pleasure from its perusal, and hope the author will take an early opportunity of placing before his readers, in his usual familiar style, the omissions we have mentioned. The Geometry of Conics.—Part I. By C. Taytor, M.4A., Fellow of St. John’s College, Cambridge. Cambridge: Deighton, Bell, and Co. London: Bell and Daldy. 1872. (8vo, pp. 88.) We do not find that the author any where states what will be con- tained in the other part or parts of this work, except incidentally that orthogonal Projections and the sections of the Right Cone will be ‘discussed in sequel.” This first part contains a complete ac- Notices respecting New Books. 391 count of the chief properties of the Parabola, Ellipse, and Hyperbola considered as distinct curves. Under the head of the Ellipse, how- ever, the author has distinguished those properties which belong to the Conics in common. He states that the work is the “ result of an attempt to reduce the chaos of Geometrical Conics to order,” and that he has ‘‘ endeavoured to reconstruct it on a uniform plan, taking as a standard, whereby to regulate the sequence of the proofs, the principle that Chord properties should take precedence of Tan- gent properties.” Accordingly each curve is discussed in two chap- ters, the former treating of its chord properties, the latter of its tan- gent properties. HH. g.in the case of the parabola two simple proofs are given of the proposition that the locus of the middle points of any system of parallel chords is a straight line parallel to the axis; and that the bisecting line meets the directrix on the straight line through the focus perpendicular to the chords. From this the relation QV* =4SP.PV is easily proved. Before passing to the tangent proper- ties the author mentions, with brevity and clearness, several ways in which a chord may be made to assume a position of tangency. One marked peculiarity of the book is the detailed treatment of the rect- angular hyperbola—a curve which stands to the hyperbola in the same relation as the circle stands to the ellipse; its numerous pro- perties are deduced with great simplicity. The book, as a whole, is not easy to describe: it consists, as all such books must consist, of proofs of a number of well-known properties of the Conic Sections ; its merit lies in the arrangement of the propositions and the way in which they are proved; but this merit can hardly be duly appreciated unless the book be compared page by page with one of the older treatises on the same subject. It is designed for the use of rather a high class of students, and will meet their wants admirably, both in regard to the text and the numerous examples and exercises with which it is furnished. The Laws of the Winds prevailing in Western Europe.—Part I. By W. Cxiement Ley. London: E. Stanford. 1872. In this work, which is an admirable companion to the Weather Maps of the Meteorological Office, Mr. Ley has treated a subject of no little difficulty and complexity with great clearness and perspicuity. Those of our readers who daily consult the Weather Maps are doubt- less familiar with the “‘ baric depressions’ which are every now and then specified as travelling eastward. ‘These meteorological pheno- mena the author has specially examined, the data being the ‘daily weather reports”’ from numerous stations in Western Europe, and finds that they are associated invariably with extensive areas of pre- cipitation of aqueous vapour, in the central portions of which ascend- ing columns of air are induced, and to which an indraught is esta- blished. This indraught by the rotation of the earth is so modified as to produce circulatory currents or winds of a cyclonic character, moving in a direction contrary to that of the hands of a watch. This circulatory movement brings successively over a tract of country two oppositely conditioned winds, the south-westerly in advance of the baric minimum, or lowest barometer, laden with aqueous vapour from 392 Royal Society :—The Hon. J. W. Strutt on the the Atlantic, and the north-easterly and north-westerly, very much drier, which succeed the passage of the minimum. By the precipi- tation of the vapour of the south-westerly winds a new area of pre- cipitation is formed to the eastward of the initial area, accompanied byits baric minimum; and thus an apparent travelling of the minimum and its accompanying baric depression is induced, the direction varying with the season ; it is also greatly modified by the general dis- tribution of land and water. ‘These are the principal features of the work before us, which we strongly recommend to meteorologists as indicating a course of study which in our opinion must contribute to the advancement of Meteorology. While the Meteorological Com- mittee of the Royal Society specifies in the maps issued under its auspices the ‘‘baric depressions”’ which pass over Ireland, Great Britain, and the north-west of Europe, and so far brings an important meteorological phenomenon into view, we think that an extension of Mr. Ley’s work by the Office—in classifying for each month in the year the paths of these depressions, and showing to a greater extent than he has done their relations to season and also to the configuration of land and water—would greatly contribute to the improvement of the data on which storm-signals are ordered to be hoisted, and would result in a greater percentage of the justified orders than obtain at present. — XLVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 316.] June 20, 1872.—Sir James Paget, Bart., D.C.L., Vice-President, in the Chair. _ following communication was read :— “Preliminary Note on the Reproduction of Diffraction-gratings by means of Photography.” By the Hon. J. W. Strutt, M.A. During the last autumn and winter I was much engaged with experiments on the reproduction of gratings by means of photo- graphy, and met with a considerable degree of success. A severe illness has prevented my pursuing the subject for some months, and my results are in consequence still far from complete; but as I may not be able immediately to resume my experiments, I think it desi- rable to lay this preliminary note before the Royal Society, reserving the details and some theoretical work connected with the subject for another opportunity. It is some years since the idea first occurred to me of taking ad- vantage of the minute delineating power of photography to reproduce with facility the work of so much time and trouble. I thought of con- structing a grating on a comparatively large scale, and afterwards reducing by the leus and camera to the required fineness. [ am now rather inclined to think that nothing would be gained by this course, that the construction of a grating of a given number of lines and with a given accuracy would not be greatly facilitated by enlar- ging the scale, and that itis doubtful whether photographic or other lenses are capable of the work that would be required of them. Reproduction of Diffraction- gratings by means of Photography. 393 However this may be, the method that I adopted is better in every respect, except perhaps one. Having provided myself with a grating by Nobert, with 3000 lines ruled over a square inch, I printed from it on sensitive dry plates in the same way as transparencies for the lantern are usually printed from negatives. In order to give myself the best chance of success, I took as a source of light the image of the sun formed by a lens placed in the shutter of a dark room. I hoped in this way that, even if there should be a small interval between the lines of the grating and the sensitive surface, still a shadow of the lines would be thrown across it. Results of great promise were at once obtained, and after a little practice I found it possible to produce copies comparing not un- favourably with the original. A source of uncertainty lay in the imperfect flatness of the glass on which the sensitive film was pre- pared, though care was taken to choose the flattest pieces of patent plate. The remedy is, of course, to use worked glass, which is re- quired in any case if the magnifying-power of a telescope is to be made available. Almost any of the dry processes known to photographers may be used. I have tried plain albumen, albumen on plain collodion, and Taupenot plates. The requirements of the case differ materially from those of ordinary photography, sensitiveness being no object, and hardness rather than softness desirable in the results. After partial development, I have found a treatment with iodine, in order to clear the transparent parts, very useful. In proceeding with the intensi- fying, the deposit falls wholly on the parts that are to be opaque. It is more essential that the transparent parts should be quite clear than the dark parts should be very opaque. The performance ofthese gratings is very satisfactory. In ex- amining the solar spectrum, I have not been able to detect any de- cided inferiority in the defining-power of the copies. With them, as with the original, the nickel line between the D’s is easily seen in the third spectrum. I work in a dark room, setting up the grating at a distance from the slit fastened in the shutter, and using no col- limator. The telescope is made up of a single lens of about thirty inches focus for object-glass, and an ordinary eyepiece held inde- pendently. I believe this arrangement to be more efficient than a common spectroscope, with collimator and telescope all on one stand ; at any rate, the magnifying-power is considerably greater, and it seems to be well borne. I have also experimented on the reproduction of gratings by a very different kind of photography. It will be remembered that a mixture of gelatine with bichromate of potash is sensitive tothe action of light, becoming insoluble, even in hot water, after exposure. In ordinary carbon printing the colouring-matter is mixed with the ge- latine and the print developed with warm water, having been first transferred so as to expose to the action of the water what was during the operation of the light the hind surface. In my experiments the colouring-matter was omitted, and the bichromated gelatine poured on the glass like collodion and then allowed to dry in the dark. A few minutes’ exposure to the direct rays of the sun then sufficed to 394 Royal Society. — produce such a modification under the lines of the gratings that, on treatment with warm water, a copy of the original was produced capable of giving brilliant spectra. In these gelatine-gratings all parts are alike transparent, so that the cause of the peculiar effect must lie in an alternate elevation and depression of the surface. That this is the case may be proved by pressing soft sealing-wax on the grating, when an impression appears on the wax, giving it an effect like that of mother of pearl. It is known that the effect of water on a gela- tine print is to make the protected parts project in consequence of their greater absorption, but it might have been expected that on drying the whole would have come flat again. It is difficult to say exactly what does happen; and I am not even sure whether the part protected by the scratch on the original is raised or sunk. Gelatine can scarcely be actually dissolved away, because the uppermost layer must have become insoluble under the influence of the light. I do not at present see my way to working by transfer, as in ordinary car- bon printing. I have not yet been able to reduce the production of these gela- tine-gratings to a certainty, but can hardly doubt the possibility of doing so. One or two of considerable perfection have been made, capable of showing the nickel line between the D’s, and giving spectra of greater brightness than the common photographs. Not only so, but the gelatine copy surpasses even the original in respect of brightness. The reason is that, on account of the breadening of the shadow of the scratch, a more favourable ratio is established between the breadths of the alternate parts. Theory shows that with gratings composed of alternate transparent and opaque parts the utmost fraction of the original light that can be concentrated in one spectrum is only about =4,, and that this hap- pens in the first spectrum when the dark and bright parts are equal. But if stead of an opaque bar stopping the light, a transparent bar capable of retarding the light by half an undulation can be substi- tuted, there would be a fourfold increase in the light of the first spectrum. I accordingly anticipate that the gelatine-gratings are hkely to prove ultimately the best, if the conditions of their production can be sufficiently mastered. With regard to the application of the photographs, I need not say much at present ; it is evident that the use of gratings would become more general if the cost were reduced in the proportion, say, of 20 to 1, more particularly if there were no accompanying inferiority of per- formance. The specimens sent with this paper are both capable of showing the nickel line and give fairly bright spectra, but they must nut be supposed to be the limit of what is possible. From their appearance under the microscope I see no reason to doubt that lines 6000 to the inch can be copied by the same method, a point which I hope shortly to put to the test of experiment. | 395 ] XLVIII. Intelligence and Miscellaneous Articles. ON THE ANOMALOUS DISPERSION EXHIBITED BY CERTAIN SUBSTANCES. BY M. J. L. SORET. M CHRISTIASEN and M. Kundt have recently published some ® very remarkable experiments upon the anomalous dispersion that certain substances, such as the aniline colours, permanganate of potash, and others, exhibit when examined in concentrated solutions, A prism formed of these fluids between two plates of glass shows a spectrum wherein the sequence of the colours differs from that of ordinary substances, blue and violet being less refracted than red. When performed in this manner the experiment presents a certain difficulty, inasmuch as the fluids are of a very deep colour, and the light can therefore pass through but a very limited thickness thereof, so that the pencil can only be allowed to traverse the fluids quite close to the edge of the prism. The importance of the phenomenon in question will not have escaped the notice of any physicist ; and I therefore conceive it may prove of some interest to specify a consequence thereof that may be rendered evident by an experiment which can be repeated without difficulty. It consists in the inversion of the spectrum. This is effected by putting the solution under examination into a hollow prism of about 30°, and placing this prism in a cell with sides of parallel glass, which is filled with the fluid used for forming the solution of the substance with anomalous dispersion experimented upon. One can then observe the inverted spectrum in a less con- centrated, and consequently more transparent solution, than when the prism remains in air. I will cite a few instances. Fuchsine, or Magenta.—Take a spectroscope, and having removed the ordinary prism, replace it by a hollow prism filled with a con- centrated solution of fuchsine. If one employs an intense pencil of light falling very near the edge of the prism, one succeeds in getting a sight of the inverted spectrum without having recourse to the cell spoken of above—that is to say, when the prism is left in air. With a solution of fuchsine that is only moderately concentrated the spectrum is normai, or, in other words, the red is less refracted than the violet. With a solution of intermediate strength, the spec- trum becomes reduced almost to a single bright red-coloured band; in this case the inverted dispersion due to the fuchsine is almost exactly balanced by the opposite dispersion brought about by the alcohol employed as the solvent; we have deflection without dispersion. If we now remove the prism filled with this latter solution into the cell containing alcohol, the general deflection of the rays is nearly entirely annulled, while the anomalous dispersion of the fuchsine remains ; the deflection of the red exceeds that of the violet. It is no longer required to employ so intense a light, or to let it fall close to the edge of the prism. On measuring the angle of deflection for the solution in question, I found, when the prism was in air, that it amounted, for the red band, to about 11° 30’, but when put into alcohol there was scarcely 396 Intelligence and Miscellaneous Articles. any deflection of the violet, while that of the red was 15/, and that of the orange-yellow 23’. With a far less concentrated solution of fuchsine the deflection of the violet was also nearly imperceptible, while that of the red was 6! and of the orange-yellow 16’. Hence, for the violet rays, solutions of fuchsine have almost the same refractive index as alcohol, but for the red rays a higher one. Aniline violet.—With an aqueous solution of this substance, and with the prism situated in air, I obtained a normal spectrum, wherein all the colours were visible ; the deflection of the red was 10° 24’, and that of the violet 10° 43’. On placing the prism in the cell filled with water, the spectrum became reduced to two bands (one blue, and one of a carmine red), which overlapped when the slit of the spec- troscope was not extremely narrow. When sunlight was made use of, there was, in addition, a trace of green towards the end of the spectrum at the side of the blue band. The deflection of the blue amounted to 1’, that of the red to 4’. Permanganate of Potash.—When filled with a solution of per- manganate of potash, the prism, in air, gave a normal spectrum, wherein the deflection of the red was 10° 33’, and that of the violet 10° 53’. When placed in water, the prism gave, for violet, a deflec- tion of 6!, for red of 9’, and for yellow of 12’. From these numbers we perceive how the addition of substances having anomalous dispersion lessens the dispersive power of the solvent without materially affecting its mean refractive index. If one goes on increasing the strength of the solution, the dispersive power becomes at first zero, and then negative. The experiment with the prism surrounded with the solvent is of higher interest with the substances last named than in the case of fuchsine, inasmuch as aniline violet and permanganate of potash must be used in extremely concentrated solutions if they are to exhibit an inverted spectrum with the prism in air. In this case the observation is far more difficult to make than with fuchsine. . The papers of Messrs. Christiasen and Kundt, referred to above, are to be found in Poggendorff’s Annalen, vol. cxliii. p. 250, vol. exlii. p. 163, and vol. exliii. pp. 149 & 259. Vol. exliv. p. 128, vol. exlv. pp. 67 & 164, vol. cxlvi. p. 154 contain further papers on the same subject.—Poggendorft’s Annalen, vol. cxliii. p. 325. ON THE MEASUREMENT OF THE INTENSITY OF CURRENTS BY MEANS OF THE ELECTROMETER. BY M. E. BRANLY. When a wire is traversed by a voltaic current, its different sec- tions present different charges of static electricity. A and B being two points in the conductor, a@ the electric potential in A, 6 the po- tential in B, the difference a—é4 is proportional to the intensity of the current. This is expressed by Ohm’s formula his pee Yh C is a constant ; 7 represents the resistance of the part AB. If the wire is cylindric and homogeneous, the electrical density at each Inielligence and Miscellaneous Articles. 397 point (quantity of electricity on the unit of surface) is proportional to the potential. The proportionality between the difference of potential and the intensity is easy to verify by means of the mirror-electrometer which I described in a communication on the 19th of February last. One of the pairs of sectors of the electrometer takes the same potential as A, and a quantity of electricity proportional to that potential; the other pair takes the same potential as B. Between the poles of a pile, liquid or metallic resistances were in- terposed; Pouillet’s tangent-compass gave the intensities for the strong currents, Weber’s for the feeble ones. The electrometer measured the differences of potential or tension* corresponding to the extremities of various coils of known lengths of telegraphic wire. The results which follow are referred to a kilometre of wire, equivalent to 100 metres of Pouillet’s unit (a column of mercury of 1 metre length and 1] millim. section). The difference between the two poles of a Daniell’s element, open, is represented by 100. Electrometer. Compass. Ratio of one Weber’s. Ratio be- : deflection “114? ee eee eween two Defiections. bath a fol. Pouillet’s. I Cente rots ian Ge lowing. wire. "| tangents. ° 146 43 42 (tan =0-956) 72) CoS es padi Oa Sa ie RR eC oe IE met Ae E RARER 2-18 67°6 23 15 (tan =0°429) MGS Ome re eee) Marlette Sb rapes) wuictad dela coins latices de 1677 40°34 14 18 (tan =0-255) TRUE. ce Mite hai manera lacie 1G teh de li Meal ac ei de 1-50 28 9 39 (tan =0°17) 63°67 DZ GO {ipo nrth ay Sa iiintelany Pk a bain gee tee 3 SE SMM EMER oh AD ye LUINS Bhi shang premenanes 21-22 eS) iets Lh i NEC, ae MEO ea ee her oe og 2°358 ROO MMM Ne aye Se ale oe 9 86-4 2:414 2°383 1-64 36°25 The current being produced by eight fresh Daniell’s elements, the number given by the electrometer shows in each case the total re- sistance of the circuit expressed in kilometres. It was ©? in the 146 first measurement, a in the second Ff. * This word “tension” is generally employed in the case in which the expression “‘ potential ”’ will be adopted. 1 I suppose here that the electromotive force of a Daniell’s element does not change when the current passes. JDirect experiments have shown me that it is, except one per cent., the same when the circuit is open and when it is closed with as little external resistance as possible. 398 Intelligence and Miscellaneous Articles. If from time to time we make a comparative measurement at once with an electrometer and a tangent-compass in the preceding con- ditions, the numbers given by the compass, multiplied by a coeffi- cient, will show the difference between the tensions corresponding to the extremities of 1 kilometre of wire; we shall thus have the exact value of the total resistance of the circuit, if the elements em- ployed are fresh. That value will only be approached if the electro- motive force of the pile has diminished. The use of the electrometer for the determination of the intensities of currents is known; the results obtained at different periods are comparable if we are careful to measure at the same time the differ- ence of the tensions at the two poles of a Daniell’s element. The Daniell’s element gives constant differences between its two poles when it is constituted in the following fashion :—a vessel con- taining a plate of amalgamated zinc and a saturated solution of sul- phate of zinc; a second vessel with a saturated solution of sulphate of copper and a plate of copper: a U-tube containing sulphate of zinc, and closed at its extremities with gold-beater’s skin, puts the two vessels in communication. a—b r of intensity will be that for which the difference of the potentials at the two extremities of the unit of resistance is equal to the unit of electric potential. The unit of potential is the potential of a sphere, charged with the unit of electricity *, whose radius is equal to the unit of length. If we take for the unit of intensity the intensity of the current which produces at the two extremities of 1 kilometre of telegraphic wire a difference of tension equal to one hundredth of that which exists between the two poles of a Daniell, the intensities of the cur- rents in the above-reported experiments will be 146, 67°6, 40°34, &c. But, in order to give more generality to the definition of the unit of intensity, it is expedient to value in electrostatic units the poten- tial at one of the poles of a Daniell’s element when the other pole is connected with the earth. If the pole of the pile is putin communication by a long wire with a sphere of radius 1, this sphere takes the same potential as the pole of the pile, and the quantity of electricity on its surface expresses the potential of the pole. The measurement was made with a torsion-balance, which was constructed as follows. A moveable gilt ball was fixed at the extre- mity of a rod of gum lac which was supported by a torsion-thread ; this last was in metallic communication with the ball. A fixed ball, of the same diameter as the other, was borne by a stick of gum lac; and a fine thread connected it externally with the prolongation of the torsion-thread. The centres of the two balls were at first placed at a certain distance (about 3 centims.) without there being any torsion. In the formula 2=C » let C=1; the current having the unit * The unit of electricity is the quantity which, acting upon an equal quantity placed at the unit of distance, viz. 1 millimetre, produces a repul- sive force of 1 milligramme. Intelligence and Miscellaneous Articles. 399 A mirror in the prolongation of the torsion-thread permitted the measurement of the displacements of the moveable ball, and, at the same time, of the torsion of the thread. The two balls were at first connected with each other and with the earth; afterwards they were charged permanently by the nega- tive pole of a pile of Daniell’s elements, the positive pole being led to the earth. Here are the details of an experiment, the units adopted being the millimetre and the milligramme :-— Position of equilibrium of the moveable ball (the not 83 balls connected together and with the earth) The two balls communicating with the negative pole 1785 of a pile:of 65 Daniell’s elements ....0.2.0...¢. The communication with the earth reestablished. ... 82°75 178°5 —82°87 =95'63. The equation vl cos 5 =n gives the quantity qg of electricity which is found on each ae d is the distance between the two balls. To find its value, a tele- scope placed at a measured distance permitted the angle to be mea- sured under which the centres of the two balls were seen; d=32°6 millims. when the two balls communicate with the negative pole of the pile. I, length of the gum-lac spindle, 70 millims., reckoned from the point of suspension from the torsion-thread to the centre of the ball. n represents the force necessary to twist the thread an arc equal to the radius. ‘This quantity is obtained by causing the thread to oscillate after replacing the stick of gum lac by a metallic spindle of known weight and length. The thread of the balance was 30 cen- tims. long; »=5°47; with the units employed it required a force of 5°47 milligrammes, applied at the distance of 1 millim., to twist the thread an arc equal to the radius. @ is the angle of torsion. ‘The rule being divided into millimetres 99°63 | and placed at 3°13 metres from the mirror, = 37130" a, the distance-angle ; a a =e 2018 COS = — 0) ie 3 72 We obtain g?=2°77, g=1'76. This is the quantity of electricity which was found upon each of the two balls. The potential will be = r, the radius of one of the balls, 8°3 millims. ; 4 =0°0255. 4 therefore represents the density of the electricity distributed upon the sphere, taking for unit of surface in measuring the density the surface of the sphere which has the unit of length for its radius. In this case a sphere of 1 millim. radius, communicating with the negative pole of the pile of 65 elements, is charged with a quantity of electricity which produces upon an equal mass concentrated at the 400 Intelligence and Miscellaneous Articles. distance of 1 millim. a repulsive force of 0°0255 milligr. Witha single Daniell’s element, the density on the sphere of 1 millim., put in communication with the pole, would be only the sixty-fifth part of this, or 0:00039. This number 0:00039 measures in electrostatic units the difference of potential at the two poles of a Daniell’s element constituted as indicated above. To assure myself that the balance worked properly, I ascertained, by connecting the two balls with different series of Daniell’s ele- ments, that the results found were proportional to the number of the elements—Comptes Rendus de Acad. des Sciences, Aug. 12, 1872, p-. 431-435. od NOTE ON THE SPECIFIC HEAT OF HYDROGENIUM. BY JAMES DEWAR. The real specific heat of a substance, according to Clausius, ought not to vary with the physical state; and his calculation of the theoretical true specific heats of compound gases assumes this con- stant, in the case of the elementary bodies, to be identical in the free and combined state. Kopp’s value of the atomic heat of combined oxygen is considerably in excess of that of the element, being 4 as compared with 2°48, whereas hydrogen is taken as 2°3, nearly agreeing with 2°4, that of the free element. As Kopp’s numbers rest on the assumption of the atomic heat of a compound being equal to the sum of the individual atomic heats of the elements con- tained in it, and as the data are few from which the value of hydrogen has been determined, we cannot regard the mere coinci- dence referred to as satisfactorily proving the constancy in the combined condition. The results obtained by Kopp from calcula- tion agree often remarkably well with experiment; and this is a strong point in their favour. It would be useful to determine the specific heat of either of the above elements in a condition ap- proaching chemical union—that is, in the enormously condensed state in which oxygen occurs in platinum black and hydrogen in palladium. We know from Graham’s beautiful researches, the result of the absorption of hydrogen by palladium is to produce a substance having all the characters of an alloy ; and the specific heat of an alloy has been proved by Regnault to equal the sum of the constituents. It is not my intention at present to describe with any detail the experiments already made in this direction ; suffice it to say that, by means of a specially constructed calorimeter, the specific heat of hydrogen in palladium is found to be 3°1 per atom weight, nearly identical with that of gaseous hydrogen. The details of the experi- ments, and some other physical constants of hydrogenium, will shortly be given in a special paper. TA LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] DECEMBER 1872. XLIX. On the Phenomena of the Elevation and Subsidence of the Surface of the Earth. By Captain F. W. Hurton, F.G.S., of the Geological Survey of New Zealand*. @ was in 1834 that the late Mr. C. Babbage read to the Geo- logical Society a paper on the Temple of Jupiter Serapis (Proc. Geol. Soc. vol. 1. p. 72), im which he proposed to ac- count for the elevation and subsidence of land by the theory of the change of isothermal surfaces within the earth. Two years later, and without any knowledge of Mr. Babbage’s paper, the late Sir J. Herschel also arrived at very similar conclusions (Proc. Geol. Soc. vol. 11. p. 548); and in a later communication (Proc. Geol. Soc. vol. 11. p. 596) he says that he thinks that Mitscherlich or Laplace had suggested the same theory before ; but from that time until the present no attempt has been made to follow the lead given by these distinguished philosophers, and to work out in detail the theory they started. It has, however, always appeared to me that, of all the various theories put for- ward to account for the elevation of land, the Herschel-Babbage theory is the only one founded upon universally acknowledged factst from which results can be deduced by means of well- established laws, the accuracy of which results can be tested by observation, and the theory either proved or disproved by their * Communicated by the Author. 7 In his lecture on Voleanoes and Earthquakes, Sir J. Herschel has quite destroyed the plausibility of his theory by saying (Lectures on Sci- entific Subjects, p. 11) that all he wants is a sea of liquid fire below him. He does not want it; and few geologists would be inclined to let him have it. Phil. Mag. 8. 4, Vol. 44. No. 295. Dec. 1872. 2D 402 Captain F. W. Hutton on the Phenomena of the means. I propose, therefore, to discuss, in as much detail as the length of a paper will allow, the bearings of this theory, and hope to show that it is adequate to account for all, or nearly all, the phenomena observed on the globe. It will not be necessary to inquire into the much-disputed question as to the state of the interior of the earth; for whether it be solid or fluid is immaterial to the theory, provided that at no considerable depth the temperature is above the melting- point of ordinary rocks under the pressure of the atmosphere. This is universally admitted, and is proved by the small mean density of the globe and the rapid rate of increase of tempera- ture as we descend into it. If, therefore, at some distance below the surface the rocks are heated above their melting-point, it follows that the particles composing them must be in a state of repulsion, and only kept in their position by pressure; and if that pressure is lessened at one point, the rocks will expand and the diminution of pressure will be distributed through the super- heated mass until it becomes again equalized throughout. In like manner, it necessarily follows that if the pressure be in- creased at any point, that increase of pressure will also be dis- tributed until the whole attains equilibrium once more. As we know that the interior heat of the earth increases at the rate of 1° F. for about 50 feet* in depth, it follows that this state of superheating will commence at a depth of about 23 miles from the surface, while above this the cohesive force will be greater than the repulsion caused by heat, and the rocks therefore will be more or less rigid, thus forming a rigid crust round a super- heated or expansible interior. If, now, we suppose the interior portion to be removed, it is evident, from what we know of the strength of the materials forming the crust, that this outer por- tion could not support itself, but would be crushed by the enor- | mous lateral thrust of the arch and would fall in. From these considerations it follows that the surface of the earth is main- tained in its position by three forces—viz. (1) its own weight, (2) the support of the interior mass, and (8) the lateral thrust of the various portions against one another ; and so long as these forces are in equilibrium, the surface will remain immoveable ; but if one or other of them is sufficiently changed in intensity to overcome the rigidity of the crust, movement will follow; and movement in one place necessarily involves corresponding movements in other places, as already explained. If, for ex- ample, from some extraneous cause elevation takes place in a certain district, the pressure on the underlying rocks will be * The rate of increase is known to vary in different districts: but we may feel sure that it increases faster than the mean of our observations; for all borings tend to cool the rocks whose temperature we are observing. Elevation and Subsidence of the Surface of the Earth. 408 lessened; but this reduction of pressure will spread beyond the elevated district, and will subvert the equilibrium in all surround- ing areas, which will necessarily subside, and equilibrium will only be restored when the mass of the subsided portion is equal to the mass of the elevated portion. Subsidence must therefore be a necessary consequence of elevation, and vice versd, unless the increase or relief of pressure is general all over the surface of the globe. A general increase of pressure is impossible, as it implies an increase in the total heat of the interior of the earth. A general decrease of pressure is doubtless brought about by the radiation of heat from the earth imto space; but this decrease must have been, at any rate since tertiary times, so small that it is totally madequate to account for the great changes that have since then taken place*. The late Mr. W. Hopkins and others have also shown that the results that we should expect to follow from a general decrease of the internal pressure do not at all accord with the phenomena we find to exist on the surface of the globe, especially in the general direc- tion of the depressions, in the occurrence of many minor oscilla- tions in the same place, and in the thickest or heaviest deposits having been elevated instead of depressed. Where, then, are we to look for the agencies that are at work to disturb this equili- brium, and so give rise to the movements which we know to have taken place repeatedly over many parts of the earth’s surface ? There are two, and only twot, agents constantly at work to produce this effect ; these are denudation and deposition. The former, as I shall presently show, has comparatively little effect ; for it necessarily brings into play another force, which counter- acts, or more than counteracts, the diminution of pressure caused by the removal of matter; and it is to deposition that we must look as the principal cause of all the changes that have taken place on the surface of the globe. This, as I have already stated, has been pointed out by Mr. Babbage and Sir J. Herschel ; but it still remains to show its adequacy. We learn from the laws of the conduction of heat that points of equal temperature in the ‘interior of the earth must be arranged in more or less spherical * Mr. Lesley has deduced that the earth ought to have shrunk 2 per cent. linearly to account for the observed geological phenomena. Upon this Mr. P. Pierce remarks (see ‘ Nature,’ Feb. 16, 1871) that this involves a cooling of not less than 2000° C., which would melt the rocks that are supposed to have shrunk. + Terrestrial magnetism may also have some effect; but it must be very small, as the magnetic intensity in London is only about one 6000th part of that of a single Daniell cell; and as the directions of this force are not constant, the effects that it is capable of producing will be still further reduced. 2D 2 404 Captain F. W. Hutton on the Phenomena of the surfaces called isogeothermal surfaces, and that at great depths these isogeothermal surfaces “ will be spherical; but as they ap- proach the surface, they will by degrees conform themselves to the solid portion” (Herschel, Proc. Geol. Soc. vol. u. p. 548) and to the mean temperature of its surface. Any change, there- fore, in the temperature or outline of the surface must necessa- rily cause them to move; so that if a surface of rock be covered by deposits 100 feet in thickness, and the new surface have the same mean temperature as that formerly belonging to the old surface, all the isogeothermals below that area will move out- wards 100 feet; and if we assume that the internal tempera- ture increases 1° F. for 50 feet of depth, the old surface will have its temperature raised 2° F. The same result would of course follow if, instead of being covered up, the old surface had its mean temperature raised by 2° F. by a warm current passing over it. If its temperature were lowered 2° F., or if 100 feet of rock were denuded off, the effects would be just the reverse; the isogeothermals would recede 100 feet, and all the region below would be 2° colder. The effects of this increase or decrease of temperature would be to increase or decrease the volume of the rocks. : From experiments made by Colonel Totten (Lyell’s Pr. of Geol. vol. ii. p. 235) and Mr. Adie (Trans. Roy. Soc. of Edinb. vol. xin. p- 354), it appears that rocks expand from ‘0000045 to ‘0000095 with an accession of temperature of 1° F. If, now, the heated rock consisted of loose, incoherent particles which could move among themselves, the increase in volume would, owing to lateral re- sistance, all take place upward ; and if we suppose the rate of expansion to be the maximum just given, we find that we should have an elevation of ‘00034 inch for every foot in depth raised 1° F. in temperature*. This effect is so small that it would be quite imperceptible for all thicknesses of deposit and increase of temperature that we are warranted in assuming. If, however, the particles of which the rock was composed were rigidly fixed together, the case would be very different; the expansion in height would still take place upward; but those in length and breadth could not be so diverted, and they would give rise to an irresistible pressure, which could only be relieved by the rock rising up in one or more anticlinal ridges. Now sands and clays are always deposited in the incoherent state first mentioned ; but deposits of carbonate of lime are indurated almost immedi- * It must be remembered that in this case the lateral thrust would not have to support the arch entirely. As soon as sufficient lateral thrust was developed to overcome the rigidity of the crust, movement would com- ‘mence, and the remainder of the force necessary for supporting the arch would be borne by the expansible underlying rocks. Elevation and Subsidence of the Surface of the Earth. 405 ately after deposition, and therefore the expansion which must necessarily follow the formation of thick deposits would throw it into anticlinal ridges. The same would occur with incoherent rocks when they were covered up with limestone—with this dif- ference, however, that the amount of lateral pressure developed would be limited by the weight of the superincumbent deposits. The deposition of limestone, therefore, relieves the pressure, while the deposition of sand and clay increases it. The following Table exhibits approximately the height, in ee of the anticlinals caused by an accession of heat to rocks forming the surface of a sphere with a radius of 3956 miles, the rock being supposed to expand in length ‘000005 for each degree of temperature. The upper line shows the thickness, in feet, of the deposit necessary to raise the temperature the number of degrees indicated in the second line from the top. The left-hand column shows the breadth of the anticlinal in miles. Thick.| 500 ft.| 1000 | 1500 | 2000 | 2500 | 5000 | 10,000) 15,000) 20,000) 25,000 Temp.| 10°. | 20°. | 30°. | 40°. | 50°. | 100°.) 200°.| 300°.| 400°. | 500°. | ee | | | Dist. miles. | feet. | feet. | feet. | feet. | feet. | feet. | feet. | feet. | feet. | feet. 100 | 1140 | 1950 | 2550 | 8100 | 8700 | 5,650} 8,700 |10,900 |12,700 |14,600 200 | 1200 | 2600 | 3700 | 4650 | 5500 | 9,200 14,700 |19,300 |22,700 |25,100 300 | 1450 | 2850 | 4250 | 5300 | 6350 |11,400 |19,100 |25,400 |33,100 |36,800 400 | 1530 | 3000 | 4350 | 5800 | 7050 |12,860 |21,650 |30,160 |37,470 |43,400 500 | 1550 | 3050 | 4500 | 5900 | 7220 |13,200 |24,200 |33,400 {41,550 49,300 1000 | 1570 | 3080 | 4650 | 6150 | 7700 {14,500 |28,600 |41,700 [53,750 |65,400 2000 | 1900 | 3200 | 4700 | 6250 | 7800 {15,400 |30,700 |45,600 |57,300 |74,400 It appears from this Table that deposits no thicker than we know some formations to be, spread over areas of moderate extent, are capable, under favourable circumstances, of producing higher mountains than any we know at present ; but it will be noticed that this operation will only take place on an extensive scale if the rate of heating from below is slower than the rate of deposition from above; for if such were not the case, the elevation would follow so quickly after the formation of the lime- stone that no very thick deposit could be formed before the bed was raised to the sea-level. If, however, deposition took place more rapidly than the conduction of the heat outward, large deposits would be formed, which would be below the normal temperature due to their depth from the surface; and these therefore would continue to expand, and therefore to rise, until their normal temperature was attained; and the greater the difference between the rates of deposition and conduction, the greater would be their ultimate height. It is therefore ne- -cessary to examine this point. 406 Captain F.W. Hutton on the Phenomena of the Baron Fourier has calculated that the earth decreases in temperature 1° F. in 3,000,000 years. Now a hollow shell one mile thick surrounding the earth is to the rest as 1 : 1316; if, therefore, this shell collected all the heat radiated outward, it would be raised in temperature 1316° F. in 3,000,000 years. If, now, we suppose the total amount of this heat to be spread out through a shell of rock in such a manner that it decreased outward =),° F. for every foot until it was zero on the outside, a simple calculation will show that this shell would have to be 26,364 feet in thickness; so that if the earth were enclosed in a shell of this thickness, the internal heat would reach the surface in 3,000,000 years ; consequently it would have travelled out- ward at the rate of ‘1 inch per year. Sir W. Thomson (Proc. Roy. Soc. of Edinb. 1864, p. 200, and 1865, p. 512), basing his calculations on the experiments on the conductivity of rocks made by Forbes, Glaisher, Angstrom, and Peclet, concludes that the earth decreases in temperature 1° C. in 2,000,000 years, or 2°°7 F. in 8,000,000, which gives an outward conduction of *27 inch per year. These experiments, however, were made on dry rocks, while newly formed deposits would be saturated with water ; and if we suppose that the thermal capacity of mud and sand saturated with water is the same as that of water, his cal- culations will have to be reduced by one half, which would make the outward conduction ‘135 inch per year. Peclet’s experi- ments show that the conductivity of marbie is only two fifths of the average taken by Sir W. Thomson ; so that in limestone the conduction outwards might only be -1 inch per year. These calculations, therefore, although founded on but few experiments, agree so closely with the results arrived at by Baron Fourier, that we may place considerable confidence in their accuracy ; and if we assume that the internal heat is conducted outward through limestone at the rate of ‘1 inch per year, and through wet sand and mud at the rate of :13 inch per year, we shall pro- bably be not very far from the truth. Prot. Dana (Manual of Geology, p. 386) estimates that lime- stone grows at the rate of -125 inch per year, and sedimentary rocks from five to ten times as fast, or from ‘62 to 1°25 inch per year. The Mississippi delta has been estimated to increase in thickness ‘17 inch per year, and that of the Ganges ‘26 inch per year. The mean of these estimates is ‘6 per year; and if we assume that in a formation one third consists of limestone, the average rate for the whole would be °4 inch per annum; so that the rate of deposition would be more than three times as fast as the rate of heating. From this it follows that when the internal temperature in- creased three times as fast as it does now, or at the rate of =° F. Elevation and Subsidence of the Surface of the Earth. 407 for each foot, no land would rise from this cause above the sea- level ; for as the temperature would then increase as fast as the deposition, as soon as the latter stopped the former would stop also. This, according to Sir W. Thomson’s calculations (“ On the Secular Cooling of the Earth,” Trans. Roy. Soc. Edin. 1862), would have happened about 11,500,000 years after the cooling of the crust, or some 88,500,000 years ago; and from that time to the present, elevations must have been on an increasing scale. If also the interior heat travels outward at from ‘13 tol inch per year, it would take from 46,200 to 60,000 years to advance 500 feet, which is equal to an increase of temperature of 10° F. Now from the Table we find that an increase of temperature of 10° F. implies an elevation of 1140 feet if the heated area was 100 miles in diameter, or of 1900 feet if its diameter was 2000 miles; so that in the first case an elevation of 1140 feet would have taken place in from 46,200 to 60,000 years, or at the rate of from 1-9 to 2:44 feet per century, while in the latter case the elevation would have been 1900 feet in the same time, or at the rate of from 3°17 to 4°11 feet per century. We may therefore conelude that elevation from this cause proceeds at a rate of from 2 to 4 feet per century. Professor Geikie and Mr. Croll have shown that subaérial denudation is a very slow process, requiring from 700 to 12,000 years to remove a foot in thickness, so that at pre- sent it will hardly affect the elevation; but as the earth cools, the radiation and conduction outwards will be slower, and consequently elevation will be slower also; and a time will come when it will not exceed the rate of denudation, and when consequently no land can be formed, and the earth will again relapse into a quiescent globe surrounded by water*. If we take the least estimate of denudation, or 1 foot in 12,000 years, as that which will be nearest to the truth when the land is nearly all flat, it follows that the elevation, if it just keeps pace with the denudation, will have to be only <4, of its present rate, or ibe interval of temperature must increase only at the rate of Teaop U- perfoot. This, according to Sir W. Thomson’s theory, will not take place until about 13 billions of years have passed ; consequently the earth is as yet only in its infancy between birth and the repose of old age. Before proceeding any further with these speculations, it will, I think, be advisable to give an illustration of this theory taken from nature. In his celebrated paper on the structure of the Wealden * Unless indeed the oxidation of the interior had before this time ab- sorbed the water and the oxygen from the air, thus leaving a bald earth surrounded by a thin atmosphere of nitrogen, which is not likely. 408 Captain F. W. Hutton on the Phenomena of the district (Trans. Geol. Soc. Ser. 2, vol. vii.), Mr. W. Hopkins showed that if a district is elevated by the upward pressure of an underlying fluid mass, tension will be produced in the rocks, which will cause the formation of two systems of fissures—one parallel to the major axis of the area undergoing elevation, the other at right angles to its periphery ; and he takes the Wealden district as an example agreeing in all respects with his deduc- tions, thus proving that the Weald anticlinal has been formed in this manner. Now, without for a mément questioning the effects which Mr. Hopkins has shown must necessarily follow from such an upward pressure, it is quite allowable to inquire whether he has been happy im selecting the Wealden area as an illustration, and whether the Herschel-Babbage theory will not give a far better explanation of the phenomena. In his able description of the district, Mr. Hopkins represents the chalk escarpment which surrounds it, and which is supposed to be parallel with the periphery of the elevating fluid, as being traversed by transverse faults or fissures which have originated the valleys in which the rivers now flow that drain the area of the Weald, these fissures being those of his second system. He also describes longitudinal minor anticlinal axes, or “lines of elevation,” as he calls them, parallel to the major axis of the ele- vated district ; and these, curiously enough, he considers as an- swering to his first system of fissures. Mr. Hopkins candidly acknowledges that one only of the transverse fissures of his se- cond system, that between Battle and Hastings, rests on posi- tive evidence, all the others are only supposed to exist owing to the direction of the valleys. I need hardly say that at the pre- sent time, with our greater knowledge of surface-geology, this evidence is quite worthless; and I feel sure that Mr. Hopkins would not now bring it forward in support of a theory. On the other hand, the longitudinal “lines of elevation ” are observed facts ; but they are nearly all anticlinal and synclinal folds, and indicate compression and not tension. The evidence, therefore, goes to show that this area has not undergone tension, and that therefore it has not been raised by the upward pressure of an underlying fluid mass. If, now, we attempt an explanation of the structure of this district by means of the Herschel-Babbage theory, we have for our data a thickness of 2100 feet for the Cretaceous for- mation, and 1300 for the Wealden formation, making a total thickness of 8400 feet. The Wealden beds on the anticlinal reach a height of some 800 feet above the sea-level; and to this we must add the thickness of the removed deposits, thus making the original height about 8600 feet above the sea. At - London the chalk is about 500 feet below the sea-level; so that Elevation and Subsidence of the Surface of the Earth. 409 the total rise of the arch was about 4100 feet, while its breadth from London to some point in the English Channel may be taken at 100 miles. If now we turn to the Table, we find, by interpolation, that a thickness of 3400 feet implies a rise in temperature of 68°, which, acting over a breadth of 100 miles, would cause an elevation of about 4650 feet. Anample margin is therefore allowed for the check to the upward movement of the isogeothermals caused by denudation after emerging from the sea. The lower beds being more highly heated than the upper chalk, would expand more and give rise to those minor folds, or “lines of elevation,” described by Mr. Hopkins. Another illustration may be desirable. During the early eocene period an extensive ocean existed from Spain and Morocco eastward through Switzerland, North Africa, Turkey, Asia Minor, Persia, and Northern India to China; and in this ocean the num- mulitic limestone, some 8000 feet thick, was deposited. Here, therefore, if there is any truth in the theory that thick and ex- tensive limestone deposits cause elevation, we ought to find marked evidence of it; and accordingly in the Atlas, Pyrenees, Alps, Apennines, Carpathians, Persian mountains, and Hima- laya, all of which have been elevated since the nummulitic lime- stone was deposited, we see effects produced commensurate in their grandeur with the extent and thickness of theformation. For if the deposition of the nummulitic limestone and the overlying deposits was not the cause of the elevation of these mountain- ranges, we have to seek for some other cause acting over exactly the same area at the same or nearly the same time, and yet, if each chain had its own independent origin, acting in different directions. It certainly seems to me far more reasonable to view them simply as wrinkles in the limestone caused by its expan- sion; for it must be remembered that by this theory mountain- chains would be formed at those places where the deposits were thickest, so that they might take various directions although all formed at the same time. It is also remarkable that the highest mountains, although situated in various parts of the world, have all risen to about the same height (8000 feet) above the snow- line. This, although difficult to account for in any other way, is readily explained by supposing that the cold of the upper regions has stopped their growth by preventing the further out- ward movement of the isogeothermals. In this way perhaps we may account for the Himalaya being higher than the Alps, with- out having to suppose that the nummulitic forniation was thicker in India than in Switzerland. I have already pointed out that an alteration in the mean temperature of the surface will produce the same effects as the deposition or removal of matter; and in this way many of the 410 Captain F. W. Hutton on the Phenomena of the movements of the surface can be accounted for. For example, the Gulf-stream carryig a high temperature into northern lati- tudes may be the cause of the recent elevation of Sweden, while the cold arctic current sweeping down through Davis’s Straits may be the cause of the depression of Greenland*; for on a spherical surface contraction would cause depression by decrea- sing the lateral thrust and throwing more weight on to the un- derlying superheated rocks. Again, if, as explained by Mr. Croll, the earth should enter upon a cold period, all land of a higher mean temperature than 32° would have a tendency to sink, while that previously covered by snow or ice would not be affected, thus helping to increase the cold. The submergence of a large part of North Wales during the glacial period, and its subsequent reemergence, may perhaps have been owing to the cold of the period itself, followed by a return to its original temperature. A difference in temperature of about 10° would be sufficient to effect this. South Sweden was also depressed when the cold was most severe, and has since been raised more than 200 feet. I will now proceed to consider the second cause of oscillations, viz. the alteration of pressure by the denudation and deposition of rocks. In this case, unfortunately, I cannot make even ap- proximate calculations as to the weight of deposits necessary to cause movement, in consequence of our ignorance of the rigidity of the outer crust of the earth. We certainly know that this rigidity is sufficient to overcome the attraction of the moon ; but as this force acts only for very short periods in the same direc- tion, the inertia of the rocks will help to supplement the rigidity ; so that I do not see how even a minimum quantity can be ob- tained for it. Every geologist, however, knows many facts proving that all thick formations have been deposited durmg subsidence; and the fossils in these formations often prove that the subsidence has been about equal in rate to the deposition, and also that in most (if not all) cases high land has been not very far off. Now it is highly improbable that the rate of depo- sition and subsidence should coincide so often unless one was caused by the other; and as we know from a@ priori reasoning the great probability there is of an increase of pressure causing subsidence, we may, I think, safely assume that such is the ease. What, then, would be the effects resulting from this cause? Where denudation was going on, the mass of land would be les- sened; but, as already stated, the rate of denudation is much slower than the conduction of heat through rocks, consequently the isogeothermals would recede as fast as the denudation went * The climate of Greenland is known to have decreased in temperature during the last 900 years. See ‘The Land of Desolation,’ by I. J. Hayes, M.D. London, 1871. : he Elevation and Subsidence of the Surface of the Earth. 411 on, and the contraction of the rocks from this cause would more than counterbalance the relief of pressure, and subsidence in- stead of elevation would be the result. Where deposition was going on, the isogeothermals would be rising; but as deposition is more rapid than the outward conduction of heat, the under- lying rocks would not be able to uplift the incumbent mass, which being loose sand and mud would render no assistance, and the area would sink. The underlying rocks, therefore, as well as the lower parts of the new formation, would be undergoing compression from forced subsidence, and at the same time ex- pansion from an increase of heat, and foldings and contortions would be the consequence. If, now, we assume, what the facts tend to show, that subsi- dence equals deposition, we can calculate the amount of com- pression the underlying rocks will undergo from subsidence, and - the amount of their expansion from the increase of heat due to the thickness of the new deposits, the two together being the amount of squeezing available for contortions. The following Table gives approximately the sum of these two in decimal parts of a mile for areas of 100, 200, and 300 miles breadth. The upper line gives the thickness of the formation in feet, which is supposed to be equal to the depth of the subsidence :— Miles. 1000 5000 | 10,000 | 15,000 | 20,000 25,000 | feet. feet. feet. feet. feet. feet. 100 “014 "095 23 415 200 028 15 33 5 oF ( 1 300 "04 21 42 675 9 1:5 From this Table we can deduce the following, which will be sufficiently accurate for practical purposes in testing the theory :— Thickness of beds, in feet... Amount of compression...... 1000 | 5000 | 10,000) 15,000; 20,000) 25,000 pees reer 7000 1 ——— 1 1000 400 500 zoo | 200 These results may be thought to be much too small to account for the great contortions and foldings that we see in mountainous districts ; but it must be remembered that these districts have been elevated and depressed many times, as proved by the uncon- formities among the strata, and that the contortions now observed will be the sum total of all tliese movements. In the section given by Professor A. Ramsay of North Wales, from Snowdon to Aran Mowddwy (Mem. Geol. Surv. of Great Britain, vol. ii.), I find that, after making due allowance for faults and dykes, the compression of the rocks has been 54... But even in this section, ad; BG" itis admirable as it is, the data are not sufficient for comparing the 412 . Captain F. W. Hutton on the Phenomena of the observed facts with theoretical deductions; for in order to do this we must know the thickness of all the formations that have ever overlain the district, and the number and amount of the oscillations they have undergone; and even then there might be various causes, such as alterations in temperature, which would affect the result. I have now explained the Herschel-Babbage theory in its simplest form; but in nature this simplicity would seldom or never exist. Complications would arise (1) from changes in phy- sical geography causing changes in the surface-temperature, according to the theory of Sir C. Lyell, (2) from the movements of the isogeothermals being often oblique, (3) from the different degrees of fusibility of rocks, (4) their different conducting- power and (5) rates of expansion, and (6) their varying degrees of porosity, and also (7) from new fluctuations of temperature commencing before the old ones had terminated. The two great motive powers, alteration in volume and increase of weight, would also sometimes combine, and at other times interfere with one another like cross waves on the surface of the sea, and would thus give rise to the great irregularities that we see in nature. I will now shortly consider from the stand-point given by this theory some of the principal geological phenomena that have not yet been mentioned. Volcanoes require an upward pressure of the superheated rocks and sufficient tension in the upper rigid crust to form fissures ; they ought therefore to be situated on land rising from the up- ward pressure derived from adjacent subsiding areas, which are sinking either from an increase of pressure or from a decrease in temperature. This can certainly be shown to be the case with the volcanoes of South America, the Pacific*, Indian Archi- pelago, and Iceland; but it is not so easy to account for Hi and Vesuvius. Faults can only be formed when the rocks are anidedenae tension, as it is mechanically impossible that compression should force up a wedge of rock; for it would crush or bend before it would move. After a district has been folded by compression the rocks would not, on tension following, go back into their former position, but fissures would be formed through them, and those wedge-like masses that have their point turned downwards would descend by their own weight; or if the land be stretched by pressure from below, those with their points turned upwards will be driven upwards. Cleavage.—Mr. Sharpe has remarked (Quart. Journ. Geol. Soc. vol. i. p. 104) that “there are reasons for thinking that * Coral islands would not cause elevation, as they are not connected with one another. Elevation and Subsidence of the Surface of the Earth. 4138 pressure could not have been the sole agent in the operation ; for the cleavage did not take place on the first upheaval of the dis- trict, when, the crust not having yet given way, the pressure might be supposed the greatest, but only after the beds had assumed their present position and the various anticlinal axes had been formed.” The Herschel-Babbage theory, however, entirely gets over this difficulty ; for the pressure would not be so great during the upheaval caused by limestone, as afterwards when the refrigeration and contraction consequent on denudation had come into play; for the extra weight thus thrown on to the underlying superheated rocks would give rise to an upward pressure which would force dykes into the overlying beds, and give rise to a cleavage that would either obliterate former ones, or intensify them where the planes of the two coincided. Conclusion.—If the surface of the earth were level and the sea spread evenly over it, the depth of this universal ocean would be at least two miles; and as we cannot suppose that in a sphere slowly cooling from an incandescent state any gases or other vo- latile substances would have been retained in the interior so as to produce eructations on the surface, the question naturally arises, what could first have caused the subversion of the equili- brium that has ultimately led to such stupendous changes? There can only, I think, be one answer to this question, viz. the origin of life on the globe. This life, by abstracting the carbo- nate of lime from solution in the sea* and depositing it on the bottom first disturbed the equilibrium, and prepared the way for the countless multitude of forms that now crowd over the surface of the globe+. When the earth was entirely enveloped by the ocean, the trade-winds would cause surface-currents flow- ing in N.E. and S8.E., and undercurrents flowing in N.W. and S.W. directions ; and if we suppose life to have originated at any one spot these currents would spread the organisms in these directions, and the first deposits, and consequently the strike of the first-elevated rocks, would have these directions also. The direction of the first land, by affecting the distribution of future deposits, would probably exert an influence even up to * Bischof (Chemical Geology, vol. i. p. 37) and Sterry Hunt (American Journal of Science [2] vol. xxxix. p. 184) both agree that the primeval ocean probably contained carbonate of lime in solution. + It follows from this that it is to the ocean that we must look for the nearest representatives of primordial life. The freshwater monads and bacteria are probably quite complicated beings compared with the first- formed organisms. It may he that the organic matter distributed through the ocean at great depths, and which is so small as to be invisible to our most powerful microscopes, and only capable of being recognized by che- mical reagents, 1s composed of living organisms intermediate in structure between the Rhizopoda and the first living germs. 414 Mr. G. K. Winter on the Maximum Magnetizing the present time, but getting more and more irregular; and I need hardly say how well this agrees. with the observed facts both of the present disposition of mountain-chains, and the strike of the oldset known Laurentian rocks. Summary.—Mountain-chains may be divided into two classes— the one characterized by folds and contortions associated with metamorphic rocks (such as the Alps), the other by slightly inclined beds associated with volcanic rocks (such as the Andes). The former class of mountains are owing to heavy masses of clay and sand having caused subsidence and contortion, and then having been subsequently elevated by the superposition of a thick bed of limestone. The latter class are owing to the depressions caused by deposition necessitating an equal uprising m other places. Many intermediate varieties also occur, which are owing partly to one cause and partly to the other. Such is a sketch of the Herschel-Babbage theory ; to elaborate it in detail would . require a far greater knowledge of the geology of the world than I possess. But although it may be shown that it is not in itself sufficient to account for all observed phenomena, yet I hope that some good will arise to science by sifting out by its means from our heterogeneous mass of facts all those that it will ex- plain, and thus limiting the residual phenomena in a way that will be most likely to lead ultimately to a complete solution of the question. L. On the Relation which the internal Resistance of the Battery and the Conductivity of the Wire bear to the maximum Magne- tizing Force of an Electromagnet Coil. By G. K. Wintsr, F.R.A.S., Telegraph Engineer, Madras Railway*. ey Poggendorff’s Annalen for November 1865, and in the i Philosophical Magazine for December of the same year, is published an investigation by Dr. Menzzer on the relation of the weight of a magnetizing spiral to the magnetizing force. In this paper the author shows that, ceteris paribus, the mag- netizing powers of two coils, arranged to give the maximum force with a given battery, are as the square roots of their re- spective weights. In this investigation the average length of a convolution is supposed to be constant; and as the iron rod 1o be magnetized is, I presume, supposed to remain the same, the length of the helix will also be a constant. It is difficult to conceive, under these circumstances, how the law can be ap- plied, except within narrow limits—since, the size of the coil being constant, the weight of the wire must be a constant too, * Communicated by the Author. Force of an Electromagnet Coil. 415 if we except a slight variation due to the different proportion of the space occupied by the insulating material according to the size of the wire. e In looking into this subject a short time since, I found two other relations regarding electromagnet spirals or coils, equally simple in their nature to that we have noticed, but not subject to a similar anomaly. I believe these relations are new; and they are certainly interesting, if not of any very great practical value. For the sake of clearness and brevity, it will be advisable to give here two definitions of terms it is proposed to make use of. 1. The minimum resistance of a battery 1s the resistance it would have if all the positive and all the negative poles were respectively joined together so as to form one element of large surface. : 2. The reduced resistance of a given wire is the resistance of a wire of uniform gauge, equal in volume and specific conducti- vity to that of the given wire, and one metre in length. Let r = the minimum resistance of the battery to be employed, n = the number of elements to be joined in series, e = the electromotive force of one element, R= the reduced resistance of the wire forming the magneti- zing coil, 1 = the length of the wire, C = the strength of the current, k = the conductivity of the wire, M= the maximum magnetizing force of a given combination ; then ne = re RE ° F heehee e (1) The condition of maximum effect is rn? = Ri? Therefore a r l=n R ; ® 5 (2) and ne e nO hamiea a (3) The size of the frame on which the wire is wound being con- ‘stant, the number of convolutions will, of course, be proportional 416 On the Magnetizing Force of an Electromagnet Coil. to the length of the wire; we may therefore say The maximum magnetizing force, therefore, varies directly as the electromotive force of one element of the battery, and in- versely as the square root of the product of the reduced resist- ance of the coil-wire into the minimum battery resistance. The volume of the wire used in the coil being constant, its reduced resistance will vary inversely as its conductivity, or — Re Then Rep earelnamptinasee: . ite dea Day r Supposing the dimensions of the helix to remain constant, and the combination to be always arranged to give the maximum effect, we learn from this equation :— Ist. That, the battery remaining the same, the magnetizing force will vary directly as the square root of the conductivity of the wire. 2ndly. That, the conductivity of the wire remaining constant, the magnetizing force will vary inversely as the square root of the minimum battery resistance ; or since, if the battery consist of a number of cells, equal in all respects, the mintmum battery resist- ance will be inversely as the number of cells employed, the magne- tizing force will vary directly as the square root of that number. It must be remembered that we are dealing, in the above re- lations, with the magnetizing powers of the helices, and not with the amount of magnetism developed by them; this magnetism, however, according to the laws of Lenz and Jacobi, varies as the magnetizing force within wide limits—that is, so long as we are not approaching too near to the maximum magnetic force the iron is capable of receiving. While we are upon this subject, it might perhaps be well to point.out a very useful application of equation (5) in my paper published in the Philosophical Magazine for February 1870, page 113. We have frequently to wind a coil of given size with wire, and at the same time it is necessary that the coil should have some given resistance; the question arises, what must be the size of the wire? A slight modification of the equation above men- tioned will enable us to answer this question without difficulty. M. F. Zollner on the Spectroscopic Reversion-Telescope. 417 The equation is as follows:— "0000002 im ~ ar(r+s)2e” in which = the specific conductivity of the wire, that of pure copper at O° C. being unity, J = the average length of a convolution in inches, m = area in square inches of a semisection of the coil (that is, the sectional area of the space to be filled with wire), s = thickness, in inches, of the msulating covering, G = the resistance of the coil, in ohms, ry = the radius of the wire, in inches, a = a constant depending on the method of coiling the wire, but generally =4. Let y = 0000001 ; d = the diameter required, in inches. Then a encyln G— DFG PEL ue anita Ts haem (6) 2 o_ yim meres) 9Gc ae Vin wise ay ry ie Peres semen (7/3) As s is generally very small, we may write this equation a yim __ § pag) Ti wos arrinjoiailaseec oho) =) eo) LI. On the Spectroscopic Reversion- Telescope. By ¥. ZOuuNER*. [ With a Plate. | A YEAR since, I had the honour to communicate to the Royal Society of Saxony the successful application of my reversion- spectroscope to the observation of the rotation of the sun}. In endeavouring to introduce the extraordinarily delicate principle and .. * Translated from a separate copy, communicated by the Author, from the Berichte der K. Sachs. Ges. der Wiss. July 1, 1872. + See Phil. Mag. S. 4. vol. xlin. p. 47. Phil. Mag. 8. 4. Vol. 44. No, 295. Dec. 1872. 24h 418 M. F. Zéllner on the Spectroscopic Reversion- Telescope. which underlies this instrument, viz. the principle of the rever- sion of spectra, to general use in the determination of the posi- tions of the lines in spectral analysis, I have striven to remove the circumstances which permit to the reversion-spectroscope, constructed three years since*, only a limited applicability. The principal of these circumstances were the following :—first, that it was absolutely necessary to employ prisms with direct vision; and secondly, that the relative displacement of the two spectra could only be effected by means of the displacement of the halves of the object-glass of the telescope. In both these ways was the applicability of the principle confined to a certain very limited portion of the spectrum. The generally immove- able attachment of the illuminating object (the slit) to the ob- serving-telescope, however, has enabled us to effect the reversal of either the entire or divided spectrum simply by means of a reversing-prism with total reflection. By this the relative dis- placement of the two spectra is at the same time connected with the variations of the angle of the plane of reflection to the optic axis of the collimator ; so that the mobility of the two halves of the objective parallel to the plane of division is no longer necessary. The alterations of angle of the face of the total-reflection prism can be effected in two ways—either by micrometric motion of the prism alone, or by moving the observing-telescope in combi- nation with the prism. It would in general be advantageous to combine the two motions,—the first, mzcrometric, for differential determinations, the second for determinations of position of all the lines of the spectrum with the aid of an index and a graduated arc. The reflecting prism can have two different positions in the observing-telescope, viz. either with the object-glass or the eye- piece. ‘The advantages, corresponding to the particular purpose, ob- tained by the use of the one or the other construction I have discussed /. c. You will permit me now to lay before you a perfectly finished specimen of a spectroscopic telescope with a reversion-objective, and at the same time some measurements which have been ob- tained with a reversion-eyepiece in another telescope, executed by M. Merz from data supplied by me. The telescope with reversion-objective is represented in fig. 1 (Plate IV.), one third of the natural size. The telescope A contains at B the objective-halves moveable perpendicularly to the plane of division. By this motion we can either cause one of the spectra to overlap the other, or make * Berichte der K. Siichs. Ges. der Wiss. Feb. 6, 1869. Phil. Mag. — November 1869, p. 360. M. F. Zollner on the Spectroscopic Reversion-Telescope. 419 them appear distinctly side by side like a vernier and scale. For this purpose we have only to move the arms of the objective more or less from one another, and not, as before, to shift them micrometrically parallel to the plane of division after the manner of the heliometer. The reflection-prism is placed in the receiver H, and is move- able in front of the halves of the objective by means of the screw F. The screw G permits the telescope to be moved round the axis K, and thereby effects, as remarked above, the relative dis. placement of the two spectra. The magnitude of this angular motion can be read off on a graduated are H with the aid of the lens L. At I the rays from the system of prisms enter the telescope. By means of the screw-thread M the instrument can be com- bined with any spectral apparatus; and for the purpose of ad- justing the refracting edges of the dispersing and reflecting prism (EK), it can be turned upon its longitudinal axis by means of the annular appendage I. The Merz spectroscope contains two direct-vision prism-systems, which can be used either singly or combined. As in the usual arrangement of that kind of spectroscope the collimator is at all times immoveably fixed to the prism-piece, the strong dispersion of the prisms used limits the observation to a proportionally small portion of the spectrum. I therefore proposed to M. Merz to remedy this inconvenience by making the collimator-telescope in like manner moveable and its position controllable by an index and graduated are. This alteration, which I had previously had applied to the spectroscopes manufactured here, answered the purpose completely. It is obvious that then the graduated are on the collimator served not to measure, but merely to mark the best position of the collimator for a certain part of the spectrum. The magnitude of the dispersion and the clearness of the images produced by the spectroscope made for me and recently sent to me from Munich are so considerable that, between the two sodium lines in the solar spectrum, besides the nickel line, there is seen distinctly a finer and more refrangible line, and that, too, when the sun is at his greatest altitude. This instrument is converted into a reversion-spectroscope by merely substituting for its eyepiece-cover one containing a small reflection-prism which covers exactly half of the aperture. The reflecting face stands parallel to the optic axis of the instrument, and thus, being at the same time parallel to the refracting edges of the dispersion-prisms, effects a partial inversion of the spec- trum. When the instrument with such a reversion-eyepiece is directed to a candle-flame impregnated with sodium, two par- tially overlappmg spectra are seen, which move in opposite di- 22 420 M. F. Zollner on the Spectroscopic Reversion- Telescope. rections when the observing-telescope is moved by the microme- tric screw, and afford an extraordinarily accurate observation of the coicidence of homologous lines. In order to effect this partial overlapping of the two spectra in observations of the dark lines of the solar spectrum, it is necessary to cause divergent rays likewise to fall upon the slit. Hence, if the spectroscope is not combined with a telescope (in which case coincidence of the plane of the slit with the optical image of the sun satisfies the above-mentioned condition), a small lens of short focal distance fixed in front of the sht imparts to the rays the requisite property. Fig. 2 represents the impression made by the two sodium lines when the most powerful eyepiece in the described spectro- scope is employed; n is the nickel line, and x the above-men- tioned fainter line. In order to give an idea of the great accuracy attainable in the determination of the positions of lines by the employment of the reversiou-prism, I take the liberty to add a number of measure- ments of the distance of the sodium lines and of the others found between them. The numbers given are parts of the circumfe- rence of the screw; on which it is to be remarked that for these measurements the thread was not sufficiently fine, as the tenth part of the values given had to beestimated. The letters placed together at the head of each column denote the lines which were brought to coincidence in the measurements. | Series 1. | Series 2. aa,..| bb,. \bb,—aa,. | 3(bb,—aa,). | aa,. | any. | aa. | aby. 957 | 316) 59 | 2-05 26-0 | 27-4 | 28-0 | 29-0 25-7 | 317] 6-0 3-00 26-0 | 27-5 | 28-0 | 29-1 25:3 | 37 | 5:9 2-95 96-0 | 27-6 | 28:1 | 29-0 25-9 | 318] 59 2-95 261 | 27-6 | 28:1 | 29-1 25-9 | 318] 59 2-95 261 | 27-6 | 281 | 29-1 260 | 318] 5:8 2-90 96-2 | 27-5 | 281 | 29-1 25-9 | 31:8 | 5-9 2-95 962 | 27-6 | 28-2 | 29-0 25:3 | 3191 61 3-05 262 | 27-7 | 281 | 29-1 26-0 | 31:9 | 5-9 2-95 26-1 | 27-5 | 282 | 29-1 25:9] 319| 60 3-00 26-2 | 27-5 | 281 | 29:0 | |Mean 2:965-40-009) 26:11 | 27-55| 28-10| 29-06 It will be seen that the delicacy of the measurements 1s extra- ordinarily great, and well justifies the hope that, with the speedy improvement of spectroscopic instruments, my endeavours to demonstrate the rotation of the earth from the displacement of the lines in the solar spectrum will before very long be successful, in like manner as the rotation of the sun has been already shown M. F. Zoéllner on the Spectroscopic Reversion-Telescope. 421 satisfactorily by Vogel’s observations*. For at the rising of the sun a point in the equator moves toward it with a velocity of about 1, of a geographical mile+, and at sunset with about the same velocity from it, so that in the course of twenty-four hours the point undergoes, in consequence of the rotation, a variation of about +1, of a mile in the velocity of its motion relative to the sun. But this quantity would alter the position of the sodium lines z=} of their distance, and hence, with the aid of the rever- sion-prism, amount to 545 of the ascertained distance. Now, since the mean value derived above from ten observations shows a probable error of only 345 of the said distance, it is evident from this how near we have already approached to the successful solution of the problem. How great an importance these ob- servations may acquire in regard to ascertaining both the velocity of light and, through the connexion of this with the constant of aberration, the parallax of the sun, cannot a priori be estimated, depending entirely on the progressive improvement of spectro- scopic instruments. Relative to the facility of the general application of the rever- sion principle in spectrometric investigations, I take leave, in conclusion, to state that I have succeeded, by a combination of two reflection-prisms immediately behind the eyepiece-cover, im constructing a reversion eyepiece which perfectly fulfils the con- dition of exact superposition of the two spectra. The reflecting hypotenuse surfaces of the prisms are simply placed perpendi- cular to each other, one of them being parallel to the width, and the other parallel to the length of the spectrum. One half of the eyepiece-aperture is supplied with light from the first, the other with light from the second prism; so that the first prism effects the reversion of the spectrum, while the other, with cor- responding inclination of the plane of reflection, accomplishes the juxtaposition of the, as regards the order of the colours, un- changed spectrum. The action of this eyepiece is surprising : for example, when combined with a Brownimg’s miniature spec- troscope it is at once converted ito a measuring-apparatus which, by micrometric motion of the reversion-prism, permits the determination of the positions of the lines by coincidence with all the delicacy desirable in so compendious an instrument. As soon as a sufficient number of measurements have been accomplished according to this method upon star-spectra, I will take leave to communicate to the Royal Society the results of my observations. * Conf. Ber. d. K. Sachs. Ges. July 1, 1871; Phil. Mag.S. 4. vol. xliii. p- 47; and ‘ Beobachtungen angestellt auf der Sternwarte des Kammerhern von Bilow zu Bothkamp von Dr. H. C. Vogel, Astronom der Sternwarte.’ Leipzig (Engelmann), 1872. 7 1 German = 4 English geographicai miles. [ 422 ] LII. Researches in Actino-Chemistry.—Memoir Second. On the Distribution of Chemical Force in the Spectrum. By Joun WiiiraM Draper, M.D., LL.D., President of the Faculties of Science and Medicine in the University of New York*. ITH scarcely an exception, the most recent works on the chemical action of radiations and spectrum-analysis de- scribe a tripartite arrangement of the spectrum, illustrated by an engraving of three curves, exhibiting the supposed relations of the calorific, the luminous, and the chemical spectra. This view, which by a mass of evidence may be shown to be erroneous, is exerting a very prejudicial effect on the progress of actino- chemistry. : I propose now to present certain facts which may aid in cor- recting this error. For this purpose it is necessary to show that chemical effects (decompositions and combustions) may take place in any part of the spectrum. The points to be established may be thus distinctly stated :— 1st. That so far from chemical influences being restricted to the more refrangible rays, every part of the spectrum, visible and invisible, can give rise to chemical changes, or modify the molecular arrangement of bodies. 2nd. That the ray effective in producing chemical or molecular changes in any special substance is determined by the absorp- tive property of that substance. I may here remark that both these propositions were main- tained by me many years ago; an example of the first will be found in the Philosophical Magazine (Dec. 1842), and of the second in a paper in the same journal, “On some Analogies between the Phenomena of the Chemical Rays and those of Radiant Heat” (Sept. 1841). The opinion commonly held respecting the distribution of chemical force in the spectrum is mainly founded on the be- haviour of some of the compounds of silver. These darken when exposed to the more refrangible rays, and, unless correct methods of examination be resorted to, seem to be unaffected by the less refrangible. Hence it has been supposed that in the higher parts of the spectrum a special principle prevails, to which the designation of “actinic rays” is often applied—an inappropriate iteration. In these pages I use the derivatives of axris, not in this restricted sense, but as expressive of radiations — of every kind. This is their proper signification. Every part of the spectrum, no matter what its refrangibility may be, can produce chemical changes; and therefore there is no special localization of force in any limited region, Out of a * Communicated by the Author. — On the Distribution of Chemical Force in the Spectrum. 423 large body of evidence that might be adduced, I select a few prominent instances. Ist. Case of the Compounds of Silver. Silver is the basis of the most important photographic sensi- tive substances. Its iodide, bromide, and chloride, darkening with rapidity under the influence of the more refrangible rays, have mainly been the cause of the misconception above alluded to respecting the tripartite constitution of the spectrum. It is necessary, therefore, to determine what are really the habitudes of these substances. (1) If a spectrum be received on iodide of silver, formed on the metallic tablet of the Daguerreotype, and carefully screened from all access of extraneous light, both before and during the exposure, on developing with mercury vapour an impression is evolved in all the more refrangible regions. This stain corre- sponds in character and position to the blackening effect which, under like circumstances, would be found on any common sen- sitive silver paper. It is this which has given rise to the opinion that the so-called actinic rays exist only in the upper part of the spectrum. If, however, the action of the light be long con- tinued, a white stain makes its appearance over al] the less re- frangible regions. It has a point of maximum, to which [ shall again presently refer. (2) But if the metallic tablet, during its exposure to the spectrum, be also receiving diffused light of little mtensity, as the light of day or of a lamp, it will be found on developing that the impression obtained differs strikingly from the pre- ceding. Every ray that the prism can transmit, from below the extreme red to beyond the extreme violet, has been active The ultra-red heat-lines «, 8, y are present. It must be borne in mind that the impression of these lines is a proof of proper spectrum-action, and distinguishes it from that of diffused hght arising either from the atmosphere or from the imperfect trans- parency of the prism—a valuable indication. The resulting photograph shows two well-marked regions or phases of action. On its general surface, which, having condensed the mercury vapour, has the aspect of the high lights of the Daguerreotype, and forms, as it were, the basis for the spectrum picture, there is in the region of the more refrangible rays a bluish or olive- coloured impression, the counterpart of the result described in the foregoing paragraph. But in the region of the less refran- gible rays no mercurial deposit has occurred, the place of those rays being depicted in metallic silver, dark, and answering to the shadows of the Daguerreotype. This protected portion, which stands out in bold relief from the white background, 424, Dr. J. W. Draper on the Distribution of reaches from a little below G to beyond the extreme red, and en- closes the heat-lines above named. They are in the form of white streaks. Though I speak of them as single lines, they are in reality groups, or perhaps bands. The general appearance of the photograph at once suggests that the less refrangible rays can arrest the action of the day- light, and protect the silver iodide from change. A close exa- mination shows that there are three points, the extreme red, the centre of the yellow, and the extreme violet, which appa- rently can hold the daylight in check. There are also two in- tervening ones, in which the actions conspire. The point of maximum protection corresponds to the point of maximum action referred to above in paragraph (1). (3) If the metallic tablet, previously to its exposure to the spectrum, be submitted for a few moments to a weak light, so that were it developed it would at this stage whiten all over, the action of the spectrum upon it will be the same as in the last case (2). But this change in the mode of the experiment leads to a very important conclusion. The less refrangible rays can reverse or undo the change, in whatever it may consist, that light has already impressed on the iodide of silver. Now, bearing in mind these facts, that the photographic action of diffused light on this icdide is mainly due to the more re- frangible rays it contains, we are brought by these experiments to the following conclusions :— lst. Every ray in the spectrum acts on the silver iodide. 2nd. The more refrangible rays apparently promote the action of the daylight on that substance ; the less refrangible apparently arrest it. . 3rd. For the display of this arresting or antagonizing effect, it is not necessary that the less and more refrangible rays should be acting semultaneously. An interval may elapse, and they may act successively. Hence the effect is not due to the contempo- raneous interference of waves of different periods of vibration with one another; the material particles of the changing sub- stance of the silver iodide are involved. I abstain for the moment from giving further details of these spectrum impressions. That has been very completely done by Herschel, in the case of one I sent him many years ago. His examination of it, illustrated by a lithograph, may be found in the Philosophical Magazine (Feb. 1843). I shall have to return to the subject of the behaviour of silver iodide in pre- sence of radiations on a subsequent page of this memoir. The main point at present established is this :—that the silver iodide, under proper treatment, is affected by every ray that a flint-glass prism can transmit; and therefore it is altogether Chemical Force in the Spectrum. 425 erroneous to suppose that chemical force is restricted to the more refrangible portions of the spectrum. 2nd. Case of Bitumens and Resins. These substances are of special interest in the history of pho- tography, since, in the hands of Niepce, they were probably the first on which impressions in the camera were obtained and fixed. Their use has been abandoned in consequence, as it seems to me, of an incorrect opinion of their want of sensitive- ness. Properly used they are scarcely inferior to chloride of silver. The theory of their use is very simple. Alcohol, ether, and various volatile oils respectively dissolve certain portions of these substances. If such a solution be spread in a thin film upon glass, as in the collodion operation, and parts of the surface be then exposed to light, the portions so exposed become insoluble in the same menstruum; they may therefore be developed by its use. Practically, care has to be taken to moderate the sol- vent action, and to check it at the proper time. The former is accomplished by dilution with some other appropriate liquid ; the latter, by the affusion of a stream of water. The substance I have used is West-Indian bitumen dissolved in benzine, and developed by a mixture of benzine and alcohol. The bitumen solution being poured on a glass plate in a dark © room, and drained off as in the operation of collodion, leaves a film sufficiently thin to be indescent. This is exposed to the spectrum for five minutes, and then developed. The beginning of the impression is below the line A, its ter- mination beyond H. Every ray in the spectrum acts; the proof is continuous, except where the Fraunhofer lines fall. A better illustration that the chemical action of the spectrum is not restricted to the higher rays, but is possessed by all, could hardly be adduced. ord. Case of Carbonic Acid. The decomposition of carbonic acid by plants under the in- fluence of sunshine is undoubtedly the most important of all actino-chemical facts. ‘The existence of the vegetable world, and, indeed, it may be said, the existence of all living things, depends upon it. | I first effected this decomposition in the solar spectrum, as may be found in a memoir in the Philosophical Magazine (Sept. 1843). The results ascertamed by me at that time from the direct-spectrum experiment, that the decomposition of car- bonie acid is effected by the less, not by the more refrangible rays, have been confirmed by all recent experimenters, who 426 Dr. J. W. Draper on the Distribution of differ only as regards the exact position of the maximum. In the discussions that have arisen, this decomposition has often incorrectly been referred to the green parts of plants. Plants which have been caused to germinate and grow to a certain stage in darkness are etiolated; yet these, when brought into the sunlight, decompose carbonic acid, and then turn green. The chlorophyl thus produced is the effect of the decomposition, not its cause. Facts derived from the visible absorptive action of chlorophyl do not necessarily apply to the decomposition of carbonic acid. The curve of the production of chlorophyl, the curve of the destruction of chlorophyl, the curve of the visible absorption of chlorophyl, and the curve of the decomposition of carbonic acid are not all necessarily coincident. ‘To con- found them together, as is too frequently done, is to be led to incorrect conclusions. Two different methods may be resorted to for determining the rays which accomplish the decomposition of carbonic acid. Ist. The place of maximum evolution of oxygen gas in the spectrum may be determined. 2nd. The place in which young etiolated plants turn green. I resorted to both these methods, and obtained from them the same results. The rays which decompose carbonic acid are the same which turn etiolated plants green. ‘They may be desig- nated as the yellow, with the orange on one side and a portion of the green on the other. Though the form of experimenta- tion does not admit a close reference to the fixed lines, I think we are justified in supposing that the point of maximum action is in the yellow. It must be borne in mind that the rapidly increasing concentration of the rays occasioned by the peculiarity of prismatic dispersion towards the red end, will give a decep- tive preponderance in that direction. Without entering further into this discussion, it is sufficient for my present purpose to understand that the decomposition in question is accomplished by rays between the fixed lines B and F. The two absorptive media, potassium bichromate and cupro- ammonium sulphate, so often and so usefully employed in actino-chemical researches, corroborate this conclusion. Plants cannot decompose carbonic acid, nor can they turn green, 1n rays that have passed through a solution of the latter salt. They accomplish both these results in rays that have passed through the former. The decomposition of carbonic acid, and the production of chlorophyl, by the less refrangible rays of the spectrum, afford thus a striking illustration that chemical changes may be brought about by other than the so-called chemical rays. Chemical Force in the Spectrum. 427 Ath. Case of the Colours of Flowers. The production and destruction of vegetable colours by the agency of light has, of course, long been a matter of common observation. Little, however, has been done in the special ex- amination of the facts, and that little, for the most part, by Herschel. We have only to examine his memoir in the Philosophical Transactions (Part II. 1842) to be satisfied that nearly every radiation can produce effects. Thus the yellow stain imparted by the Corchorus japonica to paper is whitened by the green, blue, indigo, and violet rays. The rose-red of the Ten-weeks Stock is, in like manner, changed by the yellow, orange, and red. The rich blue tint of the Viola odorata, turned green by sodium carbonate, is bleached by the same group of rays. The green (chlorophyl) of the Elder leaf is changed by the extreme red. | It is needless to extend this list of examples. ‘The foregoing establish the principle that every part of the spectrum displays activity, some vegetable colours being affected by some, others by other rays. It is, however, desirable that the general principle at which Herschel arrived, viz. that the /uminous rays are chiefly effective, should be more closely examined. Some important physiological explanations turn on that principle. These so- called luminous rays are such as can impress the retina, which, like organic colours, is a carbon compound. There are strong reasons for inferring that carbon is affected mainly by rays the waye-lengths of which are between those of the extreme red and extreme violet, the maximum being in the yellow. It is, however, to a former experimenter, Grothuss, that we owe the discovery of the law under which these decompositions of the colours of flowers take place. This law in repeated in- stances was verified by Herschel, and more recently by myself. It may be thus expressed :—“ The rays which are effective in the destruction of any given vegetable colour, are those which by their union produce a tint complementary to the colour de- stroyed.” Even the partial establishment of this law, already accomplished, is sufficient to prove that chemical effects are not limited to the more refrangible places of the spectrum, but can be occasioned by any ray. 5th. Case of the union of Chiorine and Hydrogen. In the Philosophical Magazine (December 1843) may be found the description of an actinometer invented by me, depend- ing for its indications on the combination of chlorine and _ hy- drogen, those gases having been evolved in equal volumes from 428 Dr. J. W. Draper on the Distribution of hydrochloric acid by a small voltaic battery. This instrument, modified to suit their purposes, was used by Professors Bunsen and Roscoe in their photometrical researches. Many of my ex- periments were repeated by them (Transactions of the Royal Society, 1856, 1857). In Table III. of my memoir above referred to, it is shown that this mixture is affected by every ray of the spectrum, but by different ones with very different energy. The maximum is in the indigo, the action there being more than 700 times as powerful as in the extreme red. 6th. Case of the bending of the Stems of Plants in the Spectrum. It is a matter of common observation that plants tend to grow towards the light. Dr. Gardner, however, was the first to examine the details of this phenomenon in the spectrum ; his memoir is in the Philosophical Magazine (Jan. 1844). When seeds are made to germinate aud grow for a few days in darkness, they develope vertical stems some inches in length. These, on being placed so as to receive the spectrum, soon ex- hibit a bending motion. The stems in other parts of the spec- trum turn towards the indigo; those in the indigo bend to the approaching ray. Removed into darkness, they recover their upright position. These movements are the most striking of all actinic phenomena; I have often witnessed them with ad- miration. Dr. Gardner’s experiments were repeated and confirmed by M. Dutrochet, who, in a report to the French Academy of Sciences (Comptes Rendus, No. 26, June 1844), added a number | of facts respecting the bending of roots from the light, which he found to be occasioned by all the coloured rays of the spectrum. In Dr. Gardner’s paper there are also some interesting facts respecting the bleaching or decolorization of chlorophyl by light. He used an ethereal solution of that substance. “The first action of light is perceived in the mean red rays; and it attains a maximum incomparably greater at that point than elsewhere. The next part affected is in the indigo; and accompanying it there is an action from + 10°5 to + 36:0 of the same scale (Herschel’s), beginning abruptly in Fraunhofer’s blue. So striking is this whole result, that some of my earlier spectra contained a perfectly neutral space from —5'0 to +10°5, in which the chlorophyl was in no way changed, whilst the solar picture in the red was sharp and of a dazzling white. The maximum in the ae was also bleached, producing a linear spectrum as follows, ——— 9s ——-»{___., in which the orange, yellow, and green rays are eae These, it will be remem- a aa] Chemical Force in the Spectrum. 429 bered, are active in forming chlorophyl. Upon longer exposure the subordinate action along the yellow &c. occurs, but not until the other portions are perfectly bleached. “Tn Sir J. Herschel’s experiments there remained a salmon- colour after the discharge of the green. ‘This is not seen when chlorophy] is used, and is due to a colouring-matter in the leaf, soluble in water, but not soluble in ether.”’ I have quoted these results in detail, because they illus- trate in a striking manner the law that vegetable colours are de- stroyed by rays complementary to those that have produced them, and furnish proof that rays of every refrangibility may be che- mically active. At this point I abstain from adding other instances showing that chemical changes are brought about in every part of the spectrum. ‘The list of cases here presented might be indefinitely extended if these did not suffice. But how is it possible to restrict the chemical force of the spectrum to the region of the more refrangible rays, in face of the fact that compounds of silver, such as the iodide, which have been heretofore mainly relied upon to support that view, and in fact originated it, are now proved to be affected by every ray, from the invisible ultra- red to the invisible ultra-violet ? how, when it is proved that the decomposition of carbonic acid, by far the most general and most important of the chemical actions of hght, is brought about, not by the more refrangible, but by the yellow rays? The delicate colours of flowers, which vary indefinitely in their tints, originate under the influence of rays of many different refrangibilities, and are bleached or destroyed by spectrum-coiours complementary to their own, and therefore varying indefinitely in their refrangibi- hty. Towards the indigo ray the stems of plants incline; from the red their roots turn away. There is not a wave of light that does not leave its impress on bitumens and resins—some un- dulations promoting their oxidation, some their deoxidation. These actions are not limited to decomposition ; they extend to combination. Every ray in the spectrum brings on the union of chlorine and hydrogen. The conclusion to which these facts point is, then, that it is erroneous to restrict the chemical force of the spectrum to the more refrangible, or, indeed, to any special region. There is not a ray, visible or invisible, that cannot produce a special chemical effect. The diagram so generally used to illustate the calorific, luminous, and chemical parts of the spectrum serves only to mislead. Whilst thus we find that chemical action may take place throughout the entire length of the spectrum, the remarks that have been made in the previous memoir (Phil. Mag. August 4.30 Dr. J. W. Draper on the Distribution of 1872), respecting the difference of calorific distribution in dispersion and diffraction, apply likewise to the chemical force. To be satisfied of this, it is only necessary to compare photogra- phic impressions given by a prism and by a grating. I published engravings of such diffraction-photographs in 1844. They are referred to in the Philosophical Magazine (June 1845). As they were obtained on silver plates made sensitive by iodine, bromine, and chlorine, they do not extend to the line F. I had found that certain practical advantages arise from the use of a reflected instead of a transmitted spectrum. The ruled elass was therefore silvered upon its ruled face with the amalgam, copying the surface perfectly. Of the series of spectra, I used the first. The fixed lines were beautifully represented in the photographs. They were, however, so numerous and so delicate that I did not attempt to do more than to mark the prominent ones. These were, [ believe, the first diffraction-photographs that had ever been obtained. The wave-lengths assigned were according to Fraunhofer’s scale, which represent parts of a Paris inch. The length of the photographic impression given by the prism I was then using, from the line H to the ultra-violet end of the spectrum, was about three times that from H to G; but in the spectrum by the grating, though the exposure was in one in- stance continued for a whole hour, the impression beyond H was not more than 14 times that toG. In more moderate exposures, the last fixed line in the photograph was about as far from H on one side as G was on the other. This, therefore, showed very clearly the difference of distribution in the diffraction and dis- persion spectra. On THE CHEMICAL ACTION OF RADIATIONS ON SUBSTANCES. Having offered the foregoing evidence in support of the first proposition considered in this memoir, which was to the effect “That, so far from chemical influences being restricted to the more refrangible rays, every part of the spectrum, visible and in- visible, can give rise to chemical changes, or modify the mole- cular arrangement of bodies,” I now pass to the second, which is “That the ray effective in producing chemical or molecular changes in any special substance 1s determined by the absorptive property of that substance.” This involves the conception of selective absorption, as I have formerly shown (Phil. Mag. Sept. 1841). A ray which pro- duces a maximum effect in one substance may have no effect on another. Thus the rays which change chlorophy! are not those which change silver iodide. Chemical Force in the Spectrum. 431 In the examination of this subject I shall select two well- known instances, presenting the fewest elements and the sim- plest conditions. They are (1) the decomposition of silver iodide, the basis of so many photographic preparations; (2) the pro- duction of hydrochloric acid by the union of its two contituents, chlorine and hydrogen, a mixture of these gases being exceed- ingly sensitive to light. Ist. Of the decomposition of Silver Iodide. There are two forms in which the silver iodide has been used for photographic purposes :—(1) when prepared by the action of the vapour of iodine on metallic silver, as in the Daguerreotype tablet; (2) when nitrate of silver is decomposed by iodide of potassium or other metallic iodide. These preparations differ strikingly in their actinic behaviour, the former furnishing by far the most interesting series of facts. When a polished surface of silver is exposed at common tem- peratures to the vapour of iodine, it speedily tarnishes, a film of silver iodide forming. ‘This passes through several well- marked tints as the exposure continues and the thickness in- creases. They may be thus enumerated, in the order of their occurrence :—(1) lemon-yellow, (2) golden yellow, (3) red, (4) blue, (5) lavender, (6) metallic, (7) deep yellow, (8) red, (9) green. All these films are sensitive. Under the influence of radia- tions they exhibit two phases of modification :—(1) an invisible modification, which, however, can be made apparent or developed, as Daguerre discovered, by exposure to the vapour of mercury— the iodide turning white by the condensation of mercury upon it wherever it has been exposed to the hght, but remaining unacted upon in parts that have been in shadow; (2) a visible modification, which arises under a longer exposure, the iodide passing through various shades of olive and blue, and eventually becoming dark grey. But though all the variously tinted films of silver iodide are impressionable, they differ greatly in relative sensitiveness when compared with each other. This may be very satisfactorily shown by producing on one silver tablet bands of all the above- named colours—an effect readily accomplished by suitably un- screening successive portions of the tablet during the process of iodizing, and then exposing all at the same time to a common radiation. It will be found, on developing with mercury vapour, that the bands of a yellow colour have been the most sensitive, those of a metallic aspect have been scarcely acted on, and those of other tints intermediately. It is to be particularly remarked that the second yellow, numbered 7 in the above series, is equally sensitive as the first yellow, numbered 2. 432 Dr. J. W. Draper on the Distribution of From this it appears that the sensitiveness of this form of iodide depends not merely on its chemical constitution, but also on its optical properties. The explanation of this different sensitiveness in different films of iodide becomes obvious when we cause a tablet, prepared as just described, with tmted bands to reflect the radiations falling on it to another tablet iodized to a yellow colour and placed in a camera. After due exposure and development of both with mercury, it will be found that the image of the first tablet, formed on the second, consists of bands of different shades of whiteness. The yellow parts of the first tablet have scarcely affected the second, but its metallic and blue parts have acted very powerfully. On comparing the first plate and its image on the second together, it will be perceived that the parts that have been affected on the one are unaffected on the other. It may therefore be inferred that the yellow films are sensitive because they absorb the incident radiation, and the metallic and blue are insensitive because they reflect it. The effect, in whatever it may consist, which occurs during the invisible modification is not durable; it gradually passes away. If tablets that have received impressions be kept for a time before developing, the images upon them gradually dis- appear. On these tablets there is no lateral propagation of effect, nothing answering to conduction. On examining the operation of a radiation continuously applied to one of these sensitive films, it will be discovered that a certain time elapses (that is, a certain amount of the radiation is consumed) before there is any perceptible effect. When that is accomplished, the radiation affects the film to a degree propor- tional to its quantity, until a second stage is reached. There is then another pause, followed by the second stage, in which visible modification or chemical decomposition setsin. The film begins to darken; it passes through successive tints, brown, red, olive, blue, and eventually becomes dark grey. I have described in some of the foregoimg paragraphs the action of the spectrum on silver iodide, as presented on the tablet of the Daguerreotype, showing the difference in the im- pressions obtained, Ist, when extraneous light has been exclu- ded; 2nd, when it has been permitted simultaneously or pre- viously to act. In the latter case, in all that region of the spectrum from the more refrangible extremity to somewhat beneath the line G, the usual darkening effect, manifested by silver compounds, is observed ; but below this, and to the extreme less refrangible rays, with certain variations of intensity, the action of the ex- ee ee ee ee Chemical Force in the Spectrum. 4.33 traneous and simultaneously acting light is checked, and the effect of previously acting light is destroyed. It happened that in 1842 I obtained two very fine specimens of the latter spectra: one of these I sent to Sir J. Herschel; the other is still in my possession. In the Philosophical Magazine (February 1843) Herschel gave a detailed description of these spectrum-impressions. He was disposed to refer the appearance they present to the phe- nomena of their films, but at the same time pointed out the difficulties in the way of that explanation. He also sent me three proofs he had obtained on ordinary sensitive paper, darkened by exposure to light, then washed with a solution of iodide of potassium, and placed in the spec- trum. He described them as follows :— (1) “ Blackened paper, from which excess of nitrate of silver has not been abstracted, under the influence of an iodic salt. Produced by a November sun. N.B. View it also transpa- rently against the light.” (2) “ Blackened paper, under the influence of an iodic salt, when no excess of mtrate of silver exists in the paper.” (3) ‘Action of spectrum under iodic influence when very little nitrate of silver remains in excess in the paper. To be viewed also transparently.” These paper photographs I still preserve. They are as per- fect as when first made. The different coloured spaces of the spectrum are marked upon them with pencil. The appearances they respectively present are as follows :— (1) is bleached by the more refrangible rays, and blackened deeply from the yellow to the ultra-red. (2) is bleached from the ultra-invisible red to the ultra-violet. A maximum occurs abruptly about the blue. (3) has the same upper spectrum as the others, a bleached dot in the centre of the yellow, and a darkened space in the extreme red. The action has reached from the ultra-red to the ultra-violet. In Herschel’s opmion, these effects in the less refrangible region are connected with the drying of the paper. It is well known that paper in a damp condition is more sensitive than such as is dry. But obviously this condition does not obtain in the case of the Daguerreotype operation, which is essentially a dry process. In 1846 MM. Foucault and Fizeau, having repeated the ex- periment originally made by me, presented a communication to the French Academy of Sciences, to the effect that when a silver tablet which has been sensitized by exposure to iodine and bro- mine, and then impressed by light, is exposed to the spectrum, Phil. Mag. 8S. 4. Vol. 44. No. 295. Dec. 1872. 2k 43.4: Dr. J. W. Draper on the Distribution of the effect is greatly increased in all the region above the line ©, and is neutralized in all that below C. They remarked the di- stinctness with which the atmospheric line A comes out, and saw the ultra-spectrum heat-rays a, 2, y, described by me some years previously. | The interpretation given by them is, that the more refran- gible rays promote the previous action of light, the less neutral- ize it. The curve representing the chemical intensities of the different rays would cross the axis of abscisse about the boundary of the red and orange; below that point, to the ultra-red, the ordinates would have negative values; above it, to the ultra- violet, those values would be positive (Comptes Rendus, No. 14, vol. xxiti.) Hereupon M. Becquerel communicated to the same Academy a criticism on this interpretation, the opinion maintained by him -bemg that, while the more refrangible rays excite sensitive sur- faces, the less refrangible, far from neutralizing, continue the action so begun. To the former he gave the designation “ rayons excitateurs ;”’ to the latter, “rayons continuateurs ” (Comptes Rendus, No. 17, vol. xxii.). In 1847 Mr. Claudet communicated a paper to the Royal Society, subsequently published in the Philosophical Magazine (February 1848), on this subject. His attention had been drawn to it by observing that the red image of the sun, during a dense fog, had destroyed the effect previously produced on a sensitive silver surface, and that this destruction could be occasioned at pleasure by the use of red and yellow screens. A surface which had been impressed by daylight, and the impression then obli- terated by less refrangible rays, had recovered its primitive con- dition. It was ready to be impressed again by daylight; and again the resulting effect might be destroyed. Claudet found that this excitation and neutralization might be repeated many times, the chemical constitution of the film remaining unchanged to the last. ; These facts seem to be inconsistent with Herschel’s opinion, that positive and negative pictures may succeed each other by the continued action of aradiation, on the principle of Newton’s rings. On a collodion surface such negative neutralizing or reversing actions cannot be obtained by the less refrangible rays. The spectrum-impression, developed m the usual manner by an iron salt, presents a sudden maximum about the line G, and con- tinues thence to the highest limit of the spectrum. In the other direction it extends below F. From E to the ultra-red not a trace of action can be detected. The lines a, 6, y cannot be obtained on collodion. There is therefore a difference be- Chemical Force in the Spectrum. 435 tween its behaviour under exposure to light, and that of a Daguerreotype tablet. The reversals that are obtained on collodion by the use of haloid compounds are altogether different from the reversals on the thin films of a silver tablet. They are produced by the more refrangible rays. On exposing a collodion surface prepared in the usual manner to daylight long enough to stain it completely, then washing off the free nitrate, and in succession dipping the plate into a weak solution of iodide of potassium, exposing it to the spectrum, washing, again dipping it into the nitrate bath, and finally developing, a reverse action is obtained. The daylight is per- fectly neutralized, but not after the manner of a Daguerreotype. In the region about G, the place of maximum action in collo- dion, the impression of the light is totally removed by an expo- sure of five seconds. In twelve seconds the protected space is much larger; in thirty seconds it has spread from F to H. It is, however, to be particularly remarked that the less refran- gible rays show no action. The results are substantially the same when, instead of i0- dide of potassium, chloride of sodium, corrosive sublimate, bro- mide of potassium, or fluoride of potassium is used. In all these the reversing action is from F to H, and has its maximum somewhere about G; that is, the reversing action coincides with the direct action ; there is no protection in the lower por- tion of the spectrum, as in the Daguerreotype. The effect is altogether due to the change of composition of the sensitive film. Ordinarily it contains free nitrate; now it contains free iodide, chloride, &c. The silver compounds in collodion absorb the radiations fall- ing on them which are capable of producing a photographie effect. Yet, sensitive as it 1s, collodion is very far from having its maximum sensitiveness, as is shown by the following experi- ment, which is of no small interest to photographers. I took five dry collodion plates, prepared by what is known as the tannin process, and, having made a pile of them, caused the rays of a gas-flame to pass through them all at the same time. On developing, it was found that the first plate was strongly im- pressed, and the second (which had been behind it) apparently quite as much; even the fifth was considerably stained. From this it follows that the collodion film, as ordinarily used, absorbs only a fractional portion of the rays that can affect it. Could it be made to absorb the whole, its sensitiveness would be corre- spondingly increased. A ray that has suffered complete absorption can bring about no further change; partial absorption, arising from inadequate 22 436° Dr. J. W. Draper on the Distribution of thickness, may leave the ray possessed of a portion of its power. There must be a correspondence between the intensity of the incident ray and the thickness of the absorbing medium to produce a maximum effect. Though the silver iodide is affected by radiations of every re- frangibility, it is decomposed (so that a subiodide results) only by those of which the wave-length is less than 5000; if in presence of metallic silver (as on the Daguerreotype tablet), the iodine disengaged unites with the free silver beneath. The rays of high refrangibility occasion in it chemical decomposition, those of less refrangibility physical modification. In the Jan- guage of the older theories of actino-chemistry, this substance may be said to exert a selective absorption. In thisit illustrates the general principle, that it depends on the nature of the pon- derable material presented to radiations, which of them shall be absorbed. 2nd. Of the union of Chlorine and Hydrogen. An interesting experiment, iliustrating the fact that chlorine gas absorbs the radiations which bring about its combination with hydrogen, may be made by covering a test-tube contain- ing an explosive mixture of equal volumes of those gases with a large jar filled with chlorine. This arrangement may be exposed in the open daylight without risk of exploding the mix- ture; but if the experiment be made with a covering jar con- taining atmospheric air instead of chlorine, the gases immediately unite, and commonly with an explosion. I placed a mixture of equal volumes of chlorine and hydrogen in a vessel made of plate glass, the edges of the pieces being cemented together. This vessel was so arranged on a small porcelain trough containing a saturated solution of common salt that it could be used as a gas-jar. The radiations of a lamp were caused to pass through it so as to be submitted to the selec- tive absorption of the mixture. They were then received on a chlorhydrogen actinometer. Successive experiments were then made (1) with the radia- tions of a lamp after passing through the absorption-vessel, (2) with the same radiations after the vessel had been removed. Two facts were now apparent: Ist, the mixture of chlorine and hydrogen in the absorption-vessel began to unite under the influence of the rays of the lamp; 2nd, the rays which had passed through that mixture had lost very much of their che- mical force. It was not totally extinct; but the actinometer showed that it had undergone a very great diminution. From this it follows that, on its passage through a mixture of chlorine and hydrogen, the radiation had suffered absorption, Chemical Force in the Spectrum. 437 and, as respects the mixture under trial, had become deactinized ; simultaneously the mixture itself had been affected, its con- stituent gases uniting; and thus it appears that the radiation had undergone a change in producing a change in the ponderable matter. The following modification of this experiment shows the part played by the chlorine and hydrogen respectively when they are in the act of uniting :— (a) The glass absorption-vessel above described was filled with atmospheric air, and the chemical force of the radiation passing from the lamp through it was determined. It was measured by the time required to cause the index of the actinometer to de- scend through one division: this was 12 seconds. (6) The absorption-vessel was now half filled with chlorine, obtained from hydrochloric acid and peroxide of manganese. The chemical force of the ray, after passing through it, was deter- mined as before. It was now represented by 254 seconds. (c) To the chlorine an equal quantity of hydrogen was added, the absorption-vessel being consequently full of the mixture. The radiation was now passing through a stratum of chlorine diluted with hydrogen; and the point to be determined was whether it had undergone the same or a greater or less loss than in the preceding case, since the chlorine was now uniting with the hydrogen. On measuring the force it was found to be represented by 19 seconds. (d) Lastly, the first (a) of these measures was repeated, with the view of ascertaining whether the intensity of the lamp had changed. It gave 12 seconds, as before. From these observations it may be concluded that the addition of hydrogen to chlorine does not increase its absorptive power. Moreover it is obvious that the action of the radiation is expended primarily on the chlorine, giving it a disposition to unite with the hydrogen, and that the functions discharged by the chlorine and by the hydrogen respectively are altogether different. The ray itself also undergoes a change; it suffers absorption, and loss of a part of its vis viva. As to the ray which is thus absorbed. In 1835 I found that a radiation which has passed through a solution of potassium bichromate could not accomplish the union of chlorine and hy- drogen, but one which has passed through ammonio-sulphate of copper could do it energetically. .This indicates that the effective rays are among the more refrangible. On exposing these gases in the spectrum, the maximum action takes place in the indigo rays (Phil. Mag. December 1843). Recently (1871) some suggestions have been made by M. Budde respecting the action of light upon chlorine. 438 Dr. J. W. Draper on the Distribution of Admitting the correctness of the theorem that the molecules of most elementary gases consist of two atoms, he conceives that the effect of light on chlorine is to tend to divide or actually to divide its molecules into isolated atoms. These atoms, if the gas be kept in the dark, may reunite into molecules. The chlorine molecule cannot unite with hydrogen; the chlorine atom can ; hence insolation brings on combination. But if the chlorine be unmixed, there will, as a consequence of insolation, be a certain proportion of uncombined atoms; and from this, together with Avogadro’s theorem, is drawn the con- clusion that this gas, through insolation, increases in specific volume. Moreover, as the reunion of the chlorme atoms probably pro- duces heat, rays of high refrangibility will cause chlorine to ex- pand; but it will contract to its original volume when no longer under the influence of light. In corroboration of this conclusion, Budde found that a diffe- rential thermometer filled with chlorine showed a certain expansion when placed in the red or yellow rays ; but it gave an expansion six or seven times as great when im the violet rays. With carbonic acid and ether no such effect took place. It should not be forgotten, however, in considering the bearing of these experiments, that chlorine, merely because it is yellowish green, will absorb rays of a complementary (that is, of an indigo and violet) colour, and become heated thereby. It has next to be determined whether the points of maximum action (that is, the points of maximum absorption) correspond to the rays of emission of either or both these gases, as they appa- rently ought to do under Angstrém’s law: “A gas, when lumi- nous, remits rays of light of the same refrangibility as those which it has the power to absorb.” Of the four rays characteristic of hydrogen, there is one the wave-length of which is 4840. It is in the indigo space. Pliicker gives for chlorine a ray nearly answering to this. Its wave-length is 4338; and also another, 4346, the latter being one of the best-marked of the chlorine lines. There are therefore rays in the indigo which are absorbed both by hydrogen and by chlorine. The place of these rays in the spectrum corresponds to that in which the gases unite, the place of maximum action for their mixture. But the absorptive action of chlorine is not limited to a few isolated lines. That gas removes a very large portion of the spectrum. Subsequent experiments must determine whether each of these lines of absorption is also a line of maximum che- mical action. The chlorhydrogen actinometer, referred to in previous para- « Chemical Force in the Spectrum. 4:39 graphs as depending for its indications on the union of chlorine and hydrogen, furnishes the means of ascertaining many facts respecting the combination of those substances, since it gives accurate quantitative measures. By referrmg to my papers in the Philosophical Magazine (Dec. 1843, July 1844, Nov. 1845, Nov. 1857), it will be found that chlorine and hydrogen do not unite in the dark at any ordi- nary temperature or in any length of time; but if exposed to a feeble radiation, such as that of a lamp, they are strongly affected. The phenomena present two phases:—lIst. For a brief period there is no recognizable chemical effect, a preliminary actiniza- tion or (as Professors Bunsen and Roscoe subsequently termed it) photochemical induction taking place; it is manifested by an expansion and contraction of the mixture. 2nd. The com- bination of the gases begins, it steadily increases, and soon ac- quires uniformity. In obtaining measures by the use of these gases, we must therefore wait until this preliminary actinization is complete. That accomplished, the hydrochloric acid arising from the union of the gases is absorbed so quickly that the movements of the index liquid over the graduated scale give trustworthy indications. As regards the duration of the effect produced on the gases by this preliminary actinization, I found that it continued some time—several hours (Phil. | Mae. July 1844). Professors Bunsen and Roscoe, however, in their memoir read before the Royal Society, state that it is quite transient (Trans. Roy. Soc. 1856). This preliminary actinization completed, the quantity of hy- drochloric acid produced measures the quantity of the acting radiation. This I proved by using a gas-flame of standard height, and a measuring-lens consisting ‘of a double convex, 5 inches in diameter, sectors of which eonldabe wacuvaued by the rotation of pasteboard screens upon its centre, the quantity of hydrochloric acid produced in a given time being proportional to the area of the sector uncovered. The same was also proved by using a standard fiame, and exposing the gases during different periods of time. The quantity of hydrochloric acid produced is propor- tional to the time. The following experiment illustrates the phenomena arising during the actinization of a mixture of chlorime and hydrogen, and substantiates several of the foregoing statements. The diverging rays of a lamp were made parallel by a suitable combination of convex lenses. In the resulting beam a chlor- hydrogen actinometer was placed, there being in front of it a metallic screen so arranged that it could be easily removed or replaced, and thus permit the rays of the lamp to fall on the actinometer or intercept them. Se. “he al : 4.40 Dr. J. W. Draper on the Distribution of... On removing the screen and allowing the rays to fall on the sensitive mixture in the actinometer, an expansion amounting to half a degree was observed. In sixty seconds this expansion ceased. The volume of the mixture now remained stationary, no ap- parent change going onin it. At length, after the close of 270 seconds, it was beginning to contract, and hydrochloric acid to form. At the end of 45 seconds more a contraction of half a degree had occurred ; the volume of the mixture was therefore now the same as when the experiment began, this half degree of contrac- tion compensating for the half degree of expansion. The rate of contraction of the gaseous mixture (that is, the rate at which its constituents were uniting) was then ascertained. From these observations it appeared that when chlorine and hydrogen unite under the influence of a radiation, there are four distinct periods of action :— 1st. For a brief period the mixture expands. 2nd. For a much longer period it then remains stationary in volume, though still absorbing rays. drd. Contraction, arising from the production of hydrochloric acid, begins; at first it goes on slowly, then more and more rapidly. 4th. After that contraction is fully*established, it proceeds with uniformity, equal quantities of hydrochloric acid being pro- duced in equal times by the action of equal quantities of the rays. The prominent phenomena exhibited by a mixture of chlorine and hydrogen are a preliminary absorption and a subsequent definite action. It may be remarked, since a similar preliminary absorption occurs in the case of other sensitive substances, that there is in practical photography an advantage, both as respects time and correctness in light and shadow, gained by submitting a sensitive surface to a brief exposure in a dim light, so as to pass it through its preliminary stage. The expansion referred to as taking place during the first of these periods may be advantageously observed when the disturb- ing radiation is very intense. It is well seen when a Leyden jar is discharged in the vicinity of the actinometer. Though this light lasts but a very small fraction of a second, it produces an instantaneous expansion, followed by an instantaneous con- traction. Not unfrequently the gases unite with an explosion ; I have had several of these instruments destroyed in that manner. It might be supposed that this instantaneous expansion 1s due to a heat-disturbance, arising from the absorption of rays a San re Chemical Force in the Spectrum. 441 that are not engaged in producing the chemical effect. But this mterpretation seems to be incompatible with the instan- taneously following contraction. Though it is admissible that heat should be instantaneously disengaged by the preliminary actinization, it is difficult to conceive how it can so instanta- neously disappear. When the radiation is withdrawn and the hydrochloric acid absorbed, there is no after-combining. The action is perfectly definite. For a given amount of chemical action an equivalent quantity of the radiation is absorbed. The instances I have cited in this discussion of the mode of action of radiations are one of decomposition in the case of silver iodide, and one of combination in the case of hydrochloric acid. I might have introduced another, the dissociation of ferric oxalate, which I have closely studied; but it would have made the memoir of undue length. From the facts herein considered, the following deductions may be drawn :— When a radiation impinges on a material substance, it im- parts to that substance more or less of its vis viva, and there- fore undergoes a change itself. The substance also is disturbed. Its physical and chemical properties determine the resulting phenomena. lst. If the substance is black and undecomposable, the ra- diation establishes vibrations among the molecules it encounters. We interpret these vibrations as radiant heat. The molecules of the medium do not lose the vis viva they have acquired at once, since they are of greater density than the ether. Each becomes a centre of agitation; and heat-radiation and conduc- tion in all directions are the result. The undulations thus set up are commonly of longer waves; and as the movements gra- dually decline the shorter waves are the first to be extinguished, the longer ones the last. This, therefore, is in accordance with what I found to be the case in the gradual warming of a solid body, in which the long waves pertain to a low temperature, the short ones arising as the temperature ascends (Phil. Mag. May 1847). In some cases, however, instead of the disturbing undulation giving rise to longer waves, it produces shorter ones, as is shown when a platinum wire is put into a hydrogen flame, or by Tyn- dall’s experiment, in which invisible undulations below the red give rise to the ignition of platinum. 2nd. If the substance is coloured and undecomposable, it will extinguish rays complementary to its own tint. Its tem- perature will rise correspondingly. 442 On the Distribution of Chemical Force in the Spectrum. 3rd. If the substance is decomposable, those portions of the radiation presented to it which are of a complementary tint will be extinguished. The force thus disappearing will not be expended in establishing vibrations in the arresting parti- cles, but in breaking down-the union of those which have ar- rested them from associated particles. No vibrations, there- fore, are originated, no heat is produced, there is no lateral con- duction. In actinic decompositions the effects may be conveniently divided into two phases :—Ist, physical; 2nd, chemical. The physical phuse precedes the chemical. It consists in a preliminary disturbance of the group of molecules about to be decomposed. Up to a certain point the dislocation taking place may be retraced or reduced, and things brought back to their original condition. But that point once gained, decomposition ensues, and the result is permanent. I may perhaps illustrate this by a familiar example. If a sheet of paper be held before a fire, its surface will gradually warm ; and if the exposure be not too long or the fire too hot, on removing it the paper will gradually cool, recovering its former condition without any permanent change. One could conceive that the laws of absorption and radiation might not only be studied but again and again illustrated by the exposure and removal of such a sheet. But a certain point of tempera- ture or exposure gained, the paper scorches—that 1s, undergoes chemical change; and then there is no restoration, no recovery of its original condition. Hence it may be said of such a sheet of paper that it exhi- bits two phases, in the first of which a return to the original condition is possible ; in the second such a return is impossible, because of the supervening of a chemical change. An investigation of the effects produced by a ray presents, then, these two separate and distinct phases—the physical and the chemical. GENERAL CONCLUSIONS. The facts presented in the former and the present memoir suggest the following conclusions :-— 1st. That the concentration of heat heretofore observed in the less-refrangible portion of the prismatic spectrum, arises from the special action of the prism, and would not be perceived in a diffraction-spectrum. 2nd. From the long-observed and unquestionable fact that there is in the prismatic spectrum a gradual diminution in the heat-measures, from a maximum below the red to a minimum On the Nutrition of Muscular and Pulmonary Tissues. 44d m the violet, coupled with the fact now presented by me, that the heat of the upper half of the spectrum is equal to that of the lower half, it follows that the true distribution of heat throughout the spaces of the spectrum is equal. In con- sequence of the equal velocity of ether-waves, they will, on com- plete extinction by a receiving surface, generate equal quantities of heat, no matter what their length may be, provided that their extinction take place without producing any chemical effect. ord. That it is incorrect to restrict to the upper portion of the spectrum the property of producing chemical changes. Such changes may be produced by waves of any refrangibility. 4th. That every chemical effect observed in the spectrum is in consequence of the absorption of specific radiations, the ab- sorbed or acting radiation being determined by the properties of the substance undergoing change. oth. That the figure so generally employed in works on actino-chemistry to ‘indicate the distribution of heat, hight, and actinism in the spectrum, serves only to mislead. Tis nen curve is determined by the action of the prism, not by the pro- perties of calorific radiations ; its actinic curve does not repre- sent any special peculiarities of the spectrum, but the habitudes of certain compounds of silver. LIII. On the Nutrition of Muscular and Pulmonary Tissues in Health and when affected with disease from Phthisis. By Wiii1am Marcer, M.D., F.R.S. [Concluded from p. 365.] Parr II. On the Constitution and Nutrition of Pulmonary Tissue in Health. I HAD been prepared to find that the mode of nutrition of muscular tissue equally applied to pulmonary tissue ; but the result of the inquiry showed that there is a difference between the two processes. The investigation was carried on in the same way as in the case of muscular tissue. Three samples of pulmonary tissue from three different oxen, submitted to analysis, gave the following results :— ; 444: Dr. W. Marcet on the Nutrition of Class I. Composition of Pulmonary Tissue proper or insoluble in water (mature tissue). Analysis I. Analysis II. Analysis III. Mean. On 200 | propor-| On 200 Propor- On 200 Propor-| 07 200 Propor- erms. | «tiom | S'S 1 tion. | StMS. |S tionk Wea eee tissue. tissue. tissue. tissue. Albuminous material'21°442 |100 18°204 |100 20:04 |100 19-895 |100 Phosphoric acid ....| 0°543| 2°53} 0-432; 2°37} 0-467] 2°32) 0-481) 2:41 PO tas Wee sweet cree 0-061, 0:28) 0-043) 0-23) 0-050; 0:25) 0-051) 0:25 Class II. Composition of Nutritive Material, entirely colloid. ANNOY 25 oco4ds500 /12-93* 100 13°9 . |}00 12-257 | 100 l13-029 100 Phosphoric acid...... 0:327| 2°53 | 0:33 2°38 | 0:°285} 2°32) 0-314] 2:41 Rotashymcasoceosccest 0:037| 0:28) 0033} 0:24; 0:°030| 0:24) 0-083] 0°25 Class III. Composition of Effete Material, entirely crystalloid. 100 1-406 |100 3°69 | 0°058| 4:11 26°64 | 0:451 | 32°66 Albuminoid material] 127 [100 | 1-27 100 | 1-678 Phosphoric acid...... 0-060) 4:72 Raa 3:93 | 0-063 Posh ee 0-475 | 87-40 0-431 33-94 | 0-447 | Proportion of Phosphoric acid and Potash in Effete Material. Analysis I. Analysis II. | Analysis ITI. | Mean. Found.| In 100.| Found. | In 100. | Found | In 100. Phosphoric acid ............ 0-060] 11-21] 0-050! 10-40| 0-063) 12:35! 11-32 OAS Hts oe achlassioe's aocesbion 0:475| 88:79, 0431 89°60, 0:447 | 87:65 | 88-68 Amount of Water, Fat, Soda, and Chlorine in 200 grms. of Pulmonary Tissue. Analysis I. {Analysis II.) Analysis IIT. | Analysis TV. Sheep. Sheep. Sheep. Lamb. Mean. Water...... 157-24 157:56 157°84 160-14 158-2 Batiste. as undetermined 3°56 4:10 5:18 4°28 In 200 grms. Ox-lungs. Analysis I. | Analysis II. | Analysis IIT. Mean. Soda ie. verses eee 0°453 0°657 0-450 0-520 Chlorine. 0.6.0.6. 463 undetermined 0-415 0:439 * There may have been a mere trace of blood in the pulmonary tissue analyzed, but so little that it cannot have interfered practically with the estimation of the albumen, or with the results in other respects. Muscular and Pulmonary Tissues. 445 L By referring to the analyses of muscular tissue, it will be seen that there is a marked difference between the composition of flesh and that of pulmonary tissue, the mature tissue of the lungs containing less albumen and much more phosphoric acid than the mature muscular tissue. The effete material of the lungs is very different from that of muscles, the proportion of albumi- noid material and potash it contains being much smaller, and that of the phosphoric acid is about ten times less. In order to establish clearly the difference existing between the composition of muscle and lung, I have constructed the fol-. lowing Table, which shows the mean results of the analyses, in such a way that a mere glance is required to form an idea of the relative composition of these two different tissues. Mean composition of Muscle and Lung, in 200 grms. | | Mature tissue. Nutritive materia].| Effete material. i Muscle. | Lung. | Muscle.; Lung. | Muscle.; Lung. Albuminous mat!. |} 28-070 | 19°895 5°745 Phosphoric acid...) 0°251 0-481 0:051 POU AS es isiacs osteo 0-086 0:051 0:017 13-029 3°70 - 1-406 0-314 0:563 0:058 0:033 0:764 0451 In Effete Material. Found in 100. Theory. Muscle. | Lung. Pieperc ast | 18) Tapas of winh| (224 | 1038 The most interesting fact brought out in this inquiry refers to the proportion found to exist between the phosphoric acid and potash effete in muscles and pulmonary tissue—as, while in the former their proportion is precisely that of pyrophosphate of potash, no such result is obtained in the case of the lungs, where the proportions of these substances exhibit no chemical relation. This circumstance would appear at first sight to clash with my theory that phosphoric acid and potash must be transformed into crystalloid chemical compounds, with a view to their elimination by a physical process of diffusion ; but a close consideration of the circumstances bearing on the case will show that the pre- sent discrepancy 1s very satisfactorily accounted for. I explained, im a communication to the ‘Lancet’ for February 2, 1867, how the evolution of carbonic acid from the lungs during respiration was due to the diffusion of the gas from the blood through the moist substance of the pulmonary vesicles, the same theory being given 7 4.46 Dr. W. Marcet on the Nutrition of subsequently by Bert (Legons sur la Physiologie comparée de la Respiration, par Paul Bert, 1870). By passing through the sub- stance of the lung-tissue, carbonic acid must combine with what- ever free potash and soda it may contain, and consequently transform most of the potash into crystalloid carbonate of potash; .. the potash is therefore removed as phosphate and carbonate, bué.— mostly as carbonate ; while in the case of muscular tissue, the potash is entirely eliminated as phosphate. Now, does the colloid condition of phosphoric acid and potash found in animal tissues exist in soil, or only in plants? This is a very interesting question, open to investigation. One thing is certain—that the liquid excreta of animals and other liquid manures are, as a rule, crystalloids. Plants take up the material they require in quantities which have no relation with equivalent proportions, thereby forming colloids; thus, if soil should con- tain phosphate of soda and soluble potash salts, plants will take up phosphoric acid and potash in quantities utterly at variance with their equivalent weights, leaving behind nearly the whole of the soda as carbonate and chloride. But I have also reason to believe that crystalloid mixtures are transformed, to some extent, into colloids in the earth. On the Colloid Condition of Plants. As a rule, the mineral constituents of plants are very much the same as those of animal tissues; they mostly consist of phosphoric acid, potash, and magnesia, and are very poor in chloride of sodium. Now phosphoric acid and potash are found in a great measure in the colloid state in vegetable as well as in animal tissues. The vegetables I have examined are wheat or wheaten flour, potato, and rice, selecting those mostly used as food for man. It is remarkable that, although the total amount of phosphoric acid and potash they contain varies, still we find, after dialyzing for twenty-four hours a mixture of these materials with water, the same or nearly the same relation to exist between the colloid and total phosphoric acid and the colloid and total potash respectively in each of them. The analysis was conducted in the following way. 100 grammes, say, of wheaten flour, were mixed with enough dis- tilled water for the whole to be nearly liquid; and this was placed in a dialyzer which was floated for twenty-four hours over a bulk of water equal to eight or ten times that of the contents of the dialyzer. After that lapse of time the volumes of the con- tents of the dialyzer and of the solution outside were determined. The material in the dialyzer was then dried and incinerated, and the ash was analyzed for the determination ef the phosphoric acid and potash. On the other hand, a certain quantity of the 4 Muscular and Pulmonary Tissues. 447 flour was carefully incinerated, and the phosphoric acid and potash were determined in the ash. A correction had to be introduced in the analysis by diffusion, owing to the colloid mass still holding a proportion of diffusible phosphoric acid and potash, depending on the relation existing between the volumes of fluid in and out of the dialyzer. Thus, if the volume of the outside solution was eight times that of the contents of the dia- lyzer, one eighth of the phosphoric acid found outside the dia- lyzer would have to be subtracted from the phosphoric acid found in the dialyzer in order to obtain the correct proportion of col- loid phosphoric acid. The following Table shows the result of these analyses :— Phosphoric Acid and Potash, total and colloid, in Flour, Potato, and Rice, in 100 grms. Total phosphoric acid. | Colloid phosphoric acid. onal Colloid potash. GN eles nies so. 0:3142 0°2062 found 0:1797 0:0557 found Potato No. J. ... O-0911 0:0581 # 05801 0:2175__,, Potato No. Il. ... 0-111 0:0698 ss, 0678 0-265 .,; | _ Fae 0-2020, 0:1144 __,, 0:0856 0:2825. ,, Proportions. Total. Colloid. Total. Colloid. ; corrected ; corrected Tour 1 to 0-60 ee ae i 1 to 0-21 { SEL Beis PeNOe lax. ..... 4°47 4-437 4:437 4°548 Phosphoric acid 0:037 0-033 0-021 0:030 Botashtt))..... 0-008 0:009 0-006 0-007 Composition of Effete Material, entirely Crystalloid. Albuminoid ... 2°7 2°7 2:7 2°7 Phosphoric acid 0-318 0352 0°327 0°332 BGAN Her tse. . :e 0-418 0:469 0-439 0-442 * The following analysis of human muscular tissue after death from Phil. Mag. 8. 4. Vol. 44. No. 295. Dee. 1872. 2G 450 Dr. W. Marcet on the Nutrition of Table B. (continued). Effete Phosphoric Acid and Potash as Pyrophosphate. Analysis I. Analysis II. Analysis III. Mean. | Theory. Found. | In 100. | Found. | In 100.| Found. | In 100. Phosphoric acid} 0-318} 43-2 | 0-352] 42:9 | 0:327!| 42-7 | 42:9 | 43-0 | Potash ......... 0:418| 56°8 | 0-469) 57-1 0:439 | 57-3 57:1 | 570 In this Table the result found for the albumen of the fibrous tissue in analysis No. I. was introduced in Analyses II. and III. The albumen of the nutritive material in analyses Ii. and III. is the mean of all my determinations of albumen in the extracts. These analyses show that, although the solid constituents of flesh be deficient, still they exist in the same relative proportion, or nearly so, as in healthy muscle—the phosphoric acid and pot- ash of the effete material bearing to each other precisely the same relation as they do in pyrophosphate of potash, namely 48 to 57, the exact numbers found being 42°9 to 57-1. It follows that in consumption there is no actual change in the relative proportion of the solid substances concerned in the nutrition of flesh. It is remarkable, however, that the flesh of tubercular subjects should be found to contain more water, chlorine, and soda* than muscular tissue does in health. The proportion of chlorine and soda in healthy muscular tissue and muscle from consumptive subjects is shown in the following Table :— consumption, which was accidentally omitted in my manuscript, confirms strikingly the results obtained in Table B :— In 200 grammes. Fibr. proper. Nutritive. Effete. Albuminous...... 20752 4°437 DSF Phosphoric acid .. 0°176 - 0°038 0°346 | Potash sade pe + 0:075 0-016 0°462 Found. Theory ———_———,_ (Pyrophosph. of potash), erm. per cent. per cent. Effete Phosphoric acid .. 0°346 42°5 43 Potash). sioner. - 0°462 572 57 This is the eighth analysis of flesh which bears out my theory. * Chlorine and soda cannot, apparently, be assimilated. Muscular and Pulmonary Tissues. 451 Chlorine and Soda in different samples of Muscular Tissue in Health and after death from Consumption. In healthy muscular tissue, in | In muscular tissue from consump- 200 grms. tive subjects, in 200 grms. Analyses. Chlorine. Soda Analyses. | Chlorine. Soda. i Oxefleshi|) SO296 oo sc... Tan (262 Il. ap O2hGor | &2 22... Le. 0-341 Ree tt, O84 | PLR. Ill. ...| 0-291 pes, O1G26 i cit: IV. ...| 0-401 Ve 4 OSes V... 0-466 Mee O212 |e VI. ...| 0-430 VIL. ke undeter. | 0279 WITS 0:387 VIII. Pa 0-210 0-333 | VIII 0-390 IX. 5 0-094 UAE TS nana Mart the See eas 0:385 X. As 0°176 0-289 IX. ...| undeter.| 402 XI. i 0-117 0:172 Dd. 0-335 0-434 XII. Human 0°183 0°155 — _—_— SSS —_— Mean 0-369 0:407 Mean | ¢..c:. 0°167 0:237* This Table shows that muscular tissue in consumption con- tains rather more than twice as much chlorine and consider- ably more soda than it does in health; and from what has been stated above, it follows that muscular tissue in phthisis yields more water, and is moreover wetter than healthy flesh, the proportion of water being 154 for 200 of flesh in heaith, and 166°5 after death from consumption. Now chlorine and soda do not enter into the composition of the completely assimilated mus- cular tissue ; they form part, however, of the constituents of muscles ; and it will be interesting to consider how their increased proportion in the muscles of consumptive patients can be ac- counted for. The various constituents of flesh, in health, in- cluding the water, may be considered to be supplied from the blood in the form of molecules, each of them containing certain proportions of these constituents, which may vary in quantity within certain limits. The water, however, is subject to very slight variations, its proportion of 77 per cent. being very tole- rably constant. This water binds together in the colloid form the other material which enters into the composition of flesh, so that the constituents of healthy muscle are not wet from the pre- * These chlorine determinations were made by dialyzing for twenty-four hours a known proportion of the watery extract of a given weight of flesh. A portion of the fluid outside the dialyzer was then evaporated to dryness, and the residue was incinerated, the chlorine being determined volumetri- cally in the solution of the ash. It was finally calculated for the total vo- lume of the fluid (in and out of the dialyzer). This may be considered as giving very correct results, twenty-four hours being long enough for chlo- rine to diffuse out of a dialyzer proportionally to volumes. Chlorides may be safely considered as never being colloid. 2G2 452 Dr. W. Marcet on the Nutrition of sence of the water, which acts a part not unlike that it would take in the formation of a jelly. In consumption it appears that the proportion of water in every flesh-molecule the blood yields is too high, and moreover that the constituents of these molecules are not bound together by water as they should be; at the same time the chloride of sodium of the blood begins to diffuse into the tissues by a physical process which had been kept in abeyance during the maintenance of health, passing through the capillary vessels into the flesh, just as it would have done through the diaphragm of a dialyzer into water; hence it is that in consumption, the physical force of matter is gradually overcoming that force which belongs exclu- sively to life, the nature of which is still a mystery; and the slow ebb of life in phthisis is a gradual return to a purely physical condition. On Pulmonary Tissue and its Nutrition in Phthisis. My inquiries into the chemical changes pulmonary tissue un- dergoes in phthisis has led to some very interesting results. In health the lungs consist of a tissue, which, from its struc- ture, allows readily of expansion and contraction; this tissue becomes thoroughly permeated with air during respiration, the oxygen of which diffuses through the substance of the lungs and the pulmonary capillary vessels into the blood, the carbonic acid being eliminated from the blood by a similar process. This gaseous diffusion can only take place so long as the soft and deli- cate walls of the capillary vessels and pulmonary air-vesicles remain physically unaltered; if they should become hardened or changed in any other way, the diffusion of the gases through their substance must be interfered with or entirely checked. Now in the most common form of phthisis, as shown by Dr. Sanderson, the process begins by a new growth of the inter- stitial tissue of the pulmonary honeycomb, having its seat in the very walls of the blood-vessel. Even at an early stage, the effect of this is not only to diminish the circulation of blood in the affected part, but to render the pulmonary capillaries more and more unfit for the exchange of gases, by diffusion, between the blood and the inspired air. Eventually the air- cells or alveoli in their turn become filled up with a solid ma- terial, losing completely their fitness for respiration. Then the tissue softens and breaks down, apparently from the loss of the colloid state of the consolidated pulmonary tissue. It is this last stage which is usually observed after death ; and the pulmo- nary tissue I have submitted to analysis was mostly in that con- dition, The method of analysis I adopted was precisely the same as that which had been applied to flesh and healthy pul- monary tissue, spec Bn 5 Sa de Muscular and Pulmonary Tissues. 453 Constitution and Composition of Human Pulmonary Tissue (consolidated and softening) in Consumption, in 200 gris. Composition of the Tissue insoluble in water. Mean. : j ; On 100 Analysis I. Analysis II. Analysis III. Mean. cipaaeen Albumen ......... 17°20 14:32 15:63 15°72 | 100 Phosphoric acid 0-292 0:288 0-286 0:289 1:84 502s 0-031 0-025 0-026 0:027 0:17 Composition of the material considered nutritive. Albumen ......... 763 6:98 6:57 7:06 | 100 Phosphoric acid 0-129 0-140 0:120 0-130 1:84 LCS) en 0-014 0-012 0-011 0-012 0°17 Composition of the material considered effete, entirely Crystalloid. Albuminoid ...... 2-04 2-066 3°059 2-388 | 100 Phosphoric acid 0-220 0-230 0-377 0-276} 11°55 OLAS. 85.63.00 0-272 0-268 0365 0:302| 12-65 In 200 grammes of Tissue. VS ere 2 ae ee 164-00 167-00 164:00 165-00 CED UR See ce sis 50's 20 oi 4-17 33] 4:25 3°91 Se 0:582 0°580 0-471 0-544 Chiorines <2... :. 0°450 0-470 0:437 0°452 Effete Phosphoric Acid and Potash. Theory. Found. | In 100.| Found. | In 100. | Found. | In 100. ies uae In 100. ee ee Phosphoric acid | 0°220| 44:7 | 0:230| 46°8 | 0:377)| 50°8 | 47-7 43 OHASING (52:60 2052 0-272 | 55°3 | 0-268 |.53°2 | 0°365 | 49-2 | 52°3 57 In analysis No. I. the soft semifluid portions of tissue were separated as much as possible, and the harder portions only submitted to analysis. Inthe other two analyses no such selection was made. The principal and most striking results obtained from the analysis of pulmonary tissue, consolidated and softening, are :— lst. A considerable reduction in the amount of albumen, phosphoric acid, and potash, both in the insoluble tissue, and in the nutritive material, compared with the amount of these substances in healthy pulmonary tissue, while the proportion of these substances effete and crystalloid in the diseased tissue 1s considerably increased. This shows a diminished rate of nutrition, 454 Dr. W. Marcet on the Nutrition of while there is an increase of material to be eliminated, appa- rently from a deficient action of that process which under normal circumstances causes its removal. 2nd. That the state of semifluidity in which tubercular lungs are usually found after death, is attended with but a triflmg in- crease in the quantity of water beyond the proportion lungs contain in health—water in the normal tissue amounting to 79°1 per cent., and in the diseased to a mean of 82°5 per cent. At first sight this softening appears to be unacountable; but on a closer consideration the fact admits of an explanation. It may be conceived that in the earlier stage of phthisis the adenoid (tubercular) cells are held together by a colloid attrac- tion, but that after a time, and under certain influences which lower the vital power, this colloid attraction becomes lessened and softening takes place. 3rd. The relative proportions of effete phosphoric acid and potash in the three analyses are very remarkable, as they are found to be quite different from what they are in health. In the normal condition, pulmonary tissue contains effete phosphoric acid and potash in the proportion of 11°32 to 88°68, there being a great deal more potash than is necessary for the formation of a pyro- phosphate ; and I explained how the removal of the potash could be satisfactorily accounted for, by assuming that it was trans- formed into a carbonate by the carbonic acid formed during the process of respiration. Now as respiration cannot possibly take place in tuberculosis where the pulmonary structure is altered, if my view is correct we shall expect to find in the effete material of tubercular lungs the proportion between the phosphoric acid and potash materially changed; indeed, as these substances must be removed by a process of physical diffusion, we shall conclude that their relative proportions must be such as to form a crystalloid body. ‘The mean relation obtained was, Phosphoric Acid . ; ; 47°7, Potash : : 4 ; 52°38, which approximates the formation of a pyrophosphate of potash, requiring Phosphoric Acid . : - 43, Potash : ° - AT. I have therefore to point out the singular fact that consolidated and softening lungs in phthisis undergo a process of nutrition which appears to be closely allied to that of muscular tissue. Conclusions. The conclusions I have arrived at from the inquiry which forms the subject of the present paper may be summed up as follows :— Muscular and Pulmonary Tissues. 455 lst. That there is a safe ground for the belief that the elemen- tary physical constitution of muscle, and of other animal tissues, is similar to that of a jelly—with this difference, that it is an organized jelly whose fibrinous or cellular form gives it due tena- city for the performance of its functions; but its water, albumen, and other constituents appear to hold the same physical relation to each other as would water to gelatine in jelly. 2nd. That all tissues are formed of three different classes of substances, namely :—those which constitute the ripe tissue, or the portion of the tissue insoluble in water; next, those constitu- ting the nutritive material of the tissue, which are soluble in water and colloid ; and, finally, those of which the effete material is formed ; they are soluble in water, crystalloid, and diffusible. Srd. That the nutritive material and ripe tissue have the same chemical composition, so that the mature tissue is merely an organized form of the nutritive material, the change being purely morphological. Ath. That in muscular Sees the whole of the phosphoric acid is eliminated under the form of a neutral tribasic phosphate of pot- ash. Liebig has shown by chemical tests, in his admirable work on the Chemistry of Food, that this compound really exists in flesh ; but the result of my inquiry is that the whole of the phosphoric acid and potash are eliminated in the proper proportions to form exactly either a neutral tribasic phosphate or a pyrophosphate of potash ; while at the same time there exist in flesh certain quantities of phosphoric acid and potash which are not in the proportion of a phosphate, and take part in the actual formation of the mature tissue. This is, I believe, the first time it has been shown with mathematical accuracy by a physiological mode of reasoning, if I may so express it, how substances are brought together and combine in obedience to those laws which regulate and maintain the phenomena of life. 5th. That the albuminous constituents of muscular tissue appear to be eliminated, in the process of waste, under the form of kreatine, kreatinine, and other crystalloid substances. 6th. That blood yields to flesh considerably more potash than is required for the formation of muscular tissue, the excess being necessary for the elimination of the phosphoric acid by converting it into a crystalloid phosphate. 7th. That the nutrition of pulmonary tissue differs from that of muscles, from the parenchyma or substance of the lungs con- taining a much larger proportion of nutritive material and much less waste, showing apparently that the tissue of the lungs under- goes a more rapid nutrition than that of the muscles. 8th. That while in muscles the phosphoric acid and potash are eliminated in the form of a crystalloid phosphate, in pulmo- 456 On the Nutrition of Muscular and Pulmonary Tissues. nary tissue there is every reason to believe that the potash is eliminated in a very great measure as a crystalloid carbonate, due to the action of the carbonic acid emitted from the blood during its circulation through the lungs. The effete material in muscles contains phosphoric acid and potash in the proportion of 43 to 57, and in lungs in the proportion of 11°32 to 88°68. 9th. That wheaten flour, potato, and rice contain certain proportions of colloid phosphoric acid and colloid potash, which exist in the three kinds of vegetables very nearly in the ratio of one part of total phosphoric acid to 0:55 part of colloid phos- phoric acid, and one part of total potash to 0°24 part of colloid potash—thus establishing the remarkable fact that, at all events in the three above kinds of vegetable food, although the propor- tion of phosphoric acid and potash respectively differ, still the proportion of total to colloid phosphoric acid and potash in each of them remains very nearly the same. 10th. That in phthisis a given weight of muscular tissue con- tains less nutritive material than it does in health, less mature or insoluble tissue, rather more water, and a much higher pro- portion of chlorine and soda. 11th. That, in phthisis, the phosphoric acid and potash effete in muscular tissue are present exactly in the right proportion for the formation of a pyrophosphate, as occurred in healthy flesh. This shows that the process of waste of muscles in phthisis takes place precisely as it did while in the state of health, and con- firms the result relative to the composition of the effete ma- terial of muscular tissue, eight analyses of flesh yielding phos- phoric acid and potash effete in the proportion of a pyrophosphate. 12th. That the emaciation in phthisis appears due mainly to the blood not being in the proper condition to supply nutritive material to muscular tissue. The damp or wet state peculiar to muscles after death from phthisis appears to show that the colloid state of flesh in that disease is somewhat deficient. 13th. That the tubercular or adenoid formation in pulmonary tissue actually undergoes nutrition, and is consequently a growth, the phosphoric acid and potash being apparently eliminated, as in the case of flesh, under the form of a crystalloid phosphate. The nutrition of the abnormal growth accounts for the absence of any smell of decomposition, which is nearly invariably observed at the post-mortem examination when performed shortly after death from consumption. 14th. The process of softenmg of the tubercular substance appears due to a loss of colloid power; it can hardly be owing to an increase in the proportion of water, as there is but very little more water in softening tubercular lungs than in healthy lungs—the proportion being, for 200 grammes of tissue, 158 in MM. Jamin and Richard on the Laws of Cooling. 457 healthy lungs to 165 in pulmonary tubercular growth, partly softening, partly consolidated. 15th. That there is apparently no increase of fat in tubercular pulmonary tissue, there being a mean of 4°28 of fat in 200 grammes of healthy lungs, and 3°91 in a similar weight of the diseased tissue; but as there isa little more water in the diseased than healthy lungs, it follows that a given weight of tubercular matter from the lungs apparently contains, proportionally to its dry residue, a little more fat than healthy pulmonary tissue under a similar circumstance. 16th. That in nature soluble matter is undergoing a per- petual transformation—taking place, in rotation, from the crys- talloid into the colloid condition, and from the colloid into the erystalloid condition. Animal secretions and the products of decomposition of animal and vegetable tissues are crystalloid, admitting of their ready distribution through land and water by a physical process of diffusion. These crystalloid substances are transformed into colloids by plants and used in that form as food for animals ; and both plants and animals yield them back again in their original crystalloid condition. Chloride of sodium alone appears to be an exception to this rule. LIV. On the Laws of Cooling. By MM. Jamin and Ricuarp*, Part II. Cooling Power of Gasest+. T the meeting of the 15th July last we announced to the Academy that a gas heated to 0+66 in an enclosure the walls of which are at @° cools regularly, and loses during each unit of time a quantity of heat expressed by the law which Du- long and Petit found for solid bodies, and which is g=SKH°S6", S expressing the surface of the enclosure, and K a coefficient depending on the gas. We shall now inquire what is the heat which a gaseous mass takes away, by its contact, from a heated solid placed in its centre. The apparatus remains the same. Itisa large balloon of glass immersed in a trough filled with water continually agi- tated by a current of air, and kept ata sensibly constant tempe- rature 9. The initial pressure H is given by a mercury mano- meter, and the increments of pressure / by a water manometer. * Translated from the Comptes Rendus de l Académie des Sciences, 1872, No. 8, pp. 453-458. + For Part I. see the Philosophical Magazine, October 1872, p. 244. 458 MM. Jamin and Richard on the Laws of Cooling. The heated body is no longer a thermometer, but a platinum wire traversed by an electric current ; it does not gradually cool, but, on the contrary, remains at a constant temperature and emits an invariable quantity of heat. Of this the gas takes a portion, is heated, and its pressure augmented to a limit 2. When the stationary condition is reached, the heat g’ taken by the gas from the wire is equal to that which it yields to the sides of the enclosure, or =qg. As the latter is known, the former can be found, viz. the velocity of cooling of the wire as a function of its excess ¢ of temperature and of the pressure H of the gas. I. To arrive at this it is necessary first to measure the excess of temperature ¢ of the wire. Now we know that the electrical resistance of platinum increases with the temperature. Nume- rous experiments, which will shortly be published, on this sub- ject have been performed in my laboratory by M. R. Benoit : they have shown that, by a valuable exception, the resistance of this metal increases proportionally to the temperature as far as the volatilization of sulphur, and probably beyond; so that the resistances 7 and 7! (at 8 and at f+) are r=r(1+py0), r=r[l+u(t+4)]; consequently —r=rppt. The augmentation of the resistance of the platinum wire is there- fore proportional to its excess of temperature ¢, which will be known in degrees Centigrade when we have determined 7, and p. We shall see that this determination is unnecessary, that we need only express ¢ by the values of 7/—r, which are propor- tional to it—which merely amounts to changing the thermome- tric scale. To measure the increment of resistance 7! —7, the electric cur- rent is divided into two branches, both of which pass first through copper wires of large section, of little resistance, and equal, wound the same number of times round a differential compass, but in opposite directions. ‘The first branch is then continued by the balloon-wire 7’, and the second by a rheostat with a mer- cury cursor (constructed after the pattern devised by Pouillet), and by a second wire identical with the wire in the balloon, but immersed in water at @ and retaining its resistance r. When the current passes, the needle is deflected; we bring it back to zero by adding a length of rheostat which compensates and mea- sures the increment of resistance 7/—r, and consequently the excess of temperature ¢. II. While the current is circulating in the wire and giving it an excess of temperature 7’—r, the pressure of the gas rises to a limit H+A. If we change the intensity of the current, 7/—r MM. Jamin and Richard on the Laws of Cooling. 459 and f# vary at the same time. They both vary equally if we change the initial pressure H. We may make abstraction of the current (which is here only a means for producing the heat), and say that 7’—r is a function of H and of h which it is the question to determine. For this purpose several series of observations were made under different initial pressures H (for example 814 millims., 788 millims.,...73°9 millims.); and in each case the number of elements of the pile was varied from 5 to 20, which gave as many pairs of values of 2 and r!—r as there were observations. Taking one of these series (for example, that upon hydrogen under the pressure of 788°4 millims.), and constructing the series of points which have for abscissz log h, and for ordinates log (r'—r), the tracing shows immediately that all these points arrange themselves in a very regular straight line which makes with the axis of the abscisse an angle whose tangent is 1:02; its equation is log (r' =r) =log A+ 1-02 log hay 2s 4) 2) If we now pass from this series to those corresponding to other pressures, from 814°5 millims. to 73°9 millims., we find in each case a right line parallel to the preceding; they all make with the axis of the abscisse an angle whose tangent is 1:02. These results are recorded in the following Table, which gives a summary of a portion of the experiments we have made upon hydrogen. The accordance between calculation and experiment _ is rigorously maintained. Cooling of the wire in hydrogen. (d=1:17; c=0°37; n=0-000267.) H = 788-4. H=656-2. H=587-7. H=543-2., | Obs.|Cale. Obs.|Cale. Obs.|Cale. Obs.|Cale. 222 |1920/1865] 217 1847/1862 196 {1921/1921} 180 |1941)1908) 192 2344 2389 161 |1352|1060} 156 18461341) 127 |1244'1229) 122 |1271)1271) 138 |1729)1704 100 | 817; 817,102, ©81) 869} 74) 683) 693) 70| 685) 710] 93 |11382)11384 33 256) 260] 32 255 261) 29) 225) 263) 27 | 244 263 49 | 610) 590 H=481°3. H=407°'3. H=31s5-2. H = 182°3. H=73°9. 176 |2408 2363] 164 |2509|2538) 140 126172617! 99 |293112962 59 |3588 3805 133 |1794 1774] 122 |1859|1873] 104 1952/1934] 72 |2108|2145| 42/2729 2718 91 {1171/1197} 80/1225/1220| 70 |1294/12811 49 11528/1447| 29 1852 50/ 631] 640] 44, 673) 661] 40] 718) 718} 29) 825) 832) 111224 1852 ” 460 MM. Jamin and Richard on the Laws of Cooling. It is now proved that the coefficient of log A is independent of the pressure; but as the various right lines differ by their ordi- nate at the origin, log A must be a function of H, a function we will now seek. If, for that purpose, we give to log f any constant value what- ever, for example 2-000, and take from the various right lines the corresponding value of log (7’/—r) for the pressure H to which each line corresponds, we get log A= log (r/—r)— 1:02 x 2:000. We next construct these values of log A, taking H for abscissa, and obtain as many points as there were values of H. Now these points arrange themselves again in a very well-drawn right line which makes with the axis of the abscissz an angle whose tangent is 0°88. Its equation is log A= log k—0°88 log H. The following numbers show the agreement of the observations and the calculation :— ! r'—r. H. -—_————_| Observed. Calculated. SibAshyanert aie 2 819 819 GOoAna 6) Sue. 847 847 65672 ant rales 954: 971 DST -sc see LOZA 1084 HAG ete. mies oh 20S 1163 ASVSO =. eee, ko Sok: AQ On 2 sgh 4 5 Oe 1498 SWoe ae face, LOLO 1868 tooo fe et OO 2954 COO” ca hs) we OA 6637 Supposing now that H and A are both variable, on substitu- ting for A in equation (2) its value we have log (r'—r) = log k—0°88 log H+ 1:02 logh, . (8) fyi-92 Hoss k is a constant determined by the whole of the measurements. On making the same observations for air and carbonic acid, we arrived at the same formula, or rl—r=k —r=k es H® The following are the values of a and B :— Carbonic acid. Air. Hydrogen. a 0:79 0:88 1:02 B —0°6] — 0-80 —0°88 On the Specific Heat of Carbon at High Temperatures. 461 Ill. We now, by a perfectly natural deduction, arrive at the law of cooling. Indeed, since the gas when it has attained its stationary temperature 0+d@ takes from the wire a quantity of heat g' equal to that which it yields to the outer wall, it is only necessary to make g and g' equal. Now the quantity ¢ is known: according to our previous memoir it is equal to tie) H?-¢ 3 or, taking logarithms, logg=log Bk'+d'logh—(d'—c)logH. . . (4) But we have just found by experiment log (r!—r) =logk+alogh—Blog H. . (3) Eliminating / between these two equations, we shall have g as a function of 7!—r and of H—that is, the law of cooling. This elimination conducts to an equation of the form log g=logn+dlog (r’—r)+clogH, . . . (5) and, passing again to numbers, Gt pe ee Fae SAP Oa TR ONT G) which is precisely the law of Dulong and Petit, found again by an entirely different process. These are the values of the con- stants :— Carbonic acid. Air. Hydrogen. ee. O92 2°07 26:70 Oi aisha 0-44: — 0°42 Che TS. Re nem Waa 1:28 1°30 The exponents differ little from those found by Dulong and Petit. We shall not now insist on this point, as we believe that they are variable; we purpose to return to it in an early com- munication. LV. On the Specific Heat of Carbon at High Temperatures. By James Dewar, F.R.S.E., Lecturer on Chemistry, Edinburgh. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, Edinburgh, October 25, 1872. HE following paper contains a few details of some of the experiments on which I founded the communication to the British Association at Brighton, on the Specific Heat of Car- bon at High Temperatures, that has seemingly caused some un- necessary annoyance to Dr. H. F. Weber, of Berlin. So far as I am aware, very few observations have been made in this direction since Pouillet’s well-known research on the Spe- cific Heat of Platinum. It was with the object of fillmg up this 462 Mr. J. Dewar on the Specific Heat of gap that I thought of makinga series of experiments, employing the boiling-points of sulphur, cadmium, and zine as fixed points. The experiments on carbon were made before I became ac- guainted with Dr. Weber’s paper, and were in reality undertaken as part of a communication made to the Royal Society of Edin- burgh on the Ist of April, 1872, entitled, “On recent Estimates of Solar Temperature.” An abstract of Dr. Weber’s excellent paper appeared in the ‘Chemical Journal’ for the month of July ; and I am surprised he should have overlooked this fact before charging the entire Chemical Section of the British Association with a startling amount of ignorance regarding the progress of scientific research in Germany. Yours respectfully, James Dewar. As carbon, of all known elementary bodies, is the most refrac- tory, it would be a matter of some interest at the present time to arrive at some approximate knowledge regarding its boiling- point. If this could be defined within reasonable limits, it would be a strong argument against those enormously high tem- peratures recently attributed to the sun by Secchi and Waterston. In order to acquire some idea of the highest temperatures pro- duced by chemical action, suppose we calculate the hypothetical maximum temperatures that could be produced during the for- mation of some of the stable oxides—that is, neglecting dissocia- tion and any increase in the specific heat of the product at high temperatures. On this supposition it is easy to show that silicon would give in oxidizing 19,500° C., aluminium 15,000° C., and magnesium about 14,600° C. As these are the highest results that can be obtained, we may conclude that direct chemical energy could not produce a temperature above 15,000° C. in the case of the formation of binary compounds ; and as more complicated groupings are generally less stable at high temperatures, we may regard this point asa maximum. [Ii is worthy of remark that the above products form a large portion of the earth’s crust; and the observation of Despretz, that magnesia, when exposed to the temperature of the electric arc, only became partially fused, and did not, like all the other substances experimented on, vola- tilize, strongly supports the stability of this oxide at very high temperatures. Andrews showed many years ago that, in the case of a metal forming two oxides in the same physical condition, the number of heat-units generated in passing from the metal to the first oxide was nearly identical with those obtained in the combustion of the first oxide itself; in other words, the thermal energy is Carbon at High Temperatures. 463 proportional to the number of oxygen atoms combined. The two metals experimented on by Andrews were copper and tin ; but recently Thomson has shown the same law 1s applicable to the oxides of nitrogen, and even to the oxides of manganese. The numbers obtained, starting from the first oxide in the latter series, diminish by a constant quantity. The author has communicated some preliminary experiments to the British Association which induce him to believe the same law is applicable in the negative direction, viz. to the oxides of chlorine. We are therefore justified in concluding that the two oxides of carbon ought either to have the same thermal value, or the first one may evolve 15,000 or 16,000 units more per oxygen atom than the second. Taking into consideration the general chemical analogies existing between the oxides of tin and the oxides of carbon, we may in the first instance suppose the thermal value identical. It is to be observed that the fact of carbonic oxide being an incondensible gas, and carbonic acid a condensible one, does not interfere with the applicability of An- drews’s law, as the total latent heat of vaporization of each sub- stance would be nearly identical. This is confirmed by noting that the following total latent heats of elements and compounds do not differ much, although their physical properties are very different :— COX solidele ss ictyd uxt LOl00 Oe IG HIG esis aiar ees) eo G00 NAO lignids jai. wii sree 4400 OSes ud feds dobsdeirn OOOO DG cha edi key kia vole ee OOO. Last ses iaat ae ae eas 7 OD OO BL ne dae darcarnenuse bee OO) As a fair mean we may accept 4000 units as the absorption value per atom for real latent heat of vaporization ; and as the latent heat of fluidity in the case of non-metallic bodies is very small, we may suppose it included in the above value. Taking now the thermal values of the oxides of carbon, we have C; OF 26) 6196000 CO; OF.) 2 5 > =68;000 therefore C Ort ns oe 8.000 The difference, therefore, between CO, O—C, O =40,000 units, which must be regarded as the total number of heat-units required to raise 12 grammes of carbon into the gaseous state. If we de- duct from this number 4000 units for liquefication and evapori- 464: Mr. J. Dewar on the Specific Heat of zation, we have 36,000 units left to be expended in raising the carbon to its boiling-point. Despretz has shown that carbon does not liquefy in the ordinary sense, but passes at once into the form of vapour, so that we may consider it solid up to its point of vaporization. It now only remains to ascertain the rate at which the specific heat of carbon varies with the temperature ; and it will be shown in the sequel that the mean specific heat between 0° and 2000° C. is 0°42. The amount of heat required to raise the 12 grammes of carbon 1° C. is therefore 0°42 x 12=5-04; and the approxi- mate boiling-point is thus 86,000—5°0=7200° C. If we give the first oxide 16,000 units in excess of the second, the boiling- point would then only reach 10,000° C.; and it would be diffi- cult to make it any higher by more favourable suppositions based on analogy. The first series of experiments on the mean specific heat of carbon at high temperatures were made between 1040° C. and 20° C. For this purpose a large plumbago crucible, holding about 30 lbs. of zinc, was heated up to the boiling-point by means of a smith’s forge and kept continuously boiling by means of a regulated blast. Into this bath wrought-iron tubes about half an inch in diameter were inserted, with ground iron stoppers for the purpose of holding the pieces of carbon. The part of the tubes above the surface of the zinc have each a short screw turned on the outside in order to attach a plate of sheet iron 8 inches in diameter with rapidity before the tube is removed. The object of the plate is to prevent any particle of zinc adhering to the tube being thrown, in the sudden transference along with the carbon, into the calorimeter, and to prevent radiation. The tubes remain in the bath about twenty minutes; the plate of iron is then screwed on ; the’smith catches the iron tube near the surface of the zinc with a pair of tongs while the iron stopper is removed ; and the carbon 1s instantly transferred to the calori- meter. The pieces of carbon are not broken or disintegrated by the action of the water ; nor is there any steam generated. After the experiments they were dried and weighed. The experiments have always been made with the purest French gas-retort car- bon, selecting pieces as free as possible from ash. The calori- meter was carefully surrounded with three cylindrical rings, of which the two outer ones were filled with water in order to keep the temperature of the interior constant. The following Table contains the experimental results of a few observations executed in the above manner :— Carbon at High Temperatures. 465 Taste I. Mean Specific Heat of Carbon to Boiling-point of Zinc (1040°C.). Calorimeter and water equivalent to 514°5 grm. units. Weight of Initial Final | Increase : tempera-| tempera-jof tempe- Specific heat. carbon. : ture. ture. rature. ee es LE | 4-91 17-88 | 2050 | 3-62 | 0-314 II. | 4-04 1616 | 1867 | 251 | 0-312 Ti. | 4-20 | 13-62 | 1625 | 2-63 | 0-314 Iv.| 5-292 | 13-92 | 1720 | 328 | 0311 V. 5°332 14-22 17°56 3°34 0-315 Wi. 4-890 13°40 16°46 3°06 0-314 VII. 2-0z1 17-08 18°37 1-29 0-338 VIII. 4°190 15°80 18:45 2°65 0-318 PX. 5°760 15°75 19-30 3°55 0-310—Graphite. X. 2-940 16°34 18-42 2:08 0-356 —Cocoa-nut charcoal. XI. 0:3864| 14:22 14°83 0-61 0-366—Diamonds (black). The mean specific heat of gas-carbon between 1040° C. and 20° C. may be taken as 0°32. In order to try and find the specific heat of carbon at the highest temperature we can in any way define with accuracy, a series of tentative experiments were made with different forms of crucible to ascertain the shape best adapted for observation with the oxy- hydrogen blowpipe. After a number of trials, a cubical block of lime, 2 inches in the side, pierced with two channels one fourth of an inch wide at right angles to each other through the middle of the mass, was found the most convenient form of apparatus. The directions of the channels were inclined so as to meet in the centre of the cube; and in general only one of them passed com- pletely through the mass. The carbon was placed at the junc- ture of the two channels; and two powerful oxyhydrogen blow- pipes had the apices of their cones meeting at this point. After the interior was ata white heat, the carbon was inserted and kept as long as possible. The mass of lime was then lifted and the piece of carbon dropped into the calorimeter. Bunsen’s elegant experiments on the temperature of combus- tion of hydrogen and oxygen under a pressure of ten atmospheres define the limit as 2800° C.; but in the ordinary oxyhydrogen flame the temperature does not reach 2500° C., according to the observations of Deville and Debray. On several occasions platinum was fused in the lime cube and thrown into the calorimeter. From several concordant observa- tions the temperature in no case was found to exceed 2100° C.* * By transferring fused platinum the following results were obtained :— 6°75 grms. gave in one experiment 697 grm. units, and 6°7 grms. of metal gave im a second observation 672 grm. units. The latent heat of platinum was taken as 12 grm. units, and the mean specific heat as 0:042. Phil. Mag. S. 4. Vol. 44. No. 295. Dec. 1872. 2 466 On the Specific Heat of Carbon at High Temperatures. The following Table contains some of the results obtained m working with this form of apparatus :— TasBie II. Mean Specific Heat of Carbon up to temperature of Oxyhy- drogen Blowpipe (2000°). Calorimeter and water equivalent to 523-4 gramme units. Increase of Weight of | Initial tem-| Final tem- | Increase of | temperature, | | carbon. perature. | perature. | temperature.| per gramme weight. ie) 50) io) 52) ie 0:747 17:54 15°59 1-05 1-49 i: 0°792 IAs) 18°47 119 1:50 Til. 0-741 17°38 18-44 1-06 1-43 IV. 0°3915 17°52 18:12 0:60 1:53 Vv 0-14 17:92 18-15 0:23 1:64 Calculating from the highest result obtained at a temperature of 2000° C., the mean specific heat of carbon is about 0°42. The true specific heat at 2000° must be at least 0°5; so that at this temperature carbon would agree with the law of Dulong and Petit, In general the rate at which the specific heat varies in the case of the metals may be represented by a straight line ; and the increment seems to be directly related to the rate of variation of the coefficient of expansion. Now in the case of diamond, graphite, and gas-carbon 4 are as the numbers 4°32 :3°03:3°3, according to Fizeau; and as he has further shown that diamond has a minimum volume at —42°3 C., and that below this temperature it expands as the temperature falls, we may anticipate some marked alteration in the specific heat at very low temperatures, which Dr. Weber proposes to in- vestigate. Of the three varieties of carbon, graphite is certainly the most stable at very high temperatures. Gas-retort carbon, after being used as poles in a powerful electric are, is in part transformed into graphite ; and the diamond exposed to the tem- perature of the voltaic are passes also into graphite. Unless graphite or carbon can pass into the form of diamond under cer- tain conditions of pressure at comparatively low temperatures, or is of vegetable origin, it is difficult to conceive how diamond could occur if this earth ever had a temperature as high as that of the voltaic are. Starting from absolute zero, carbon as graphite most probably increases regularly in specific heat, whereas diamond probably diminishes until we reach —42°°3C., and then increases regularly until it exceeds that of graphite, which it continues to do until they agree at very high tempera- tures. The excess of heat taken in by the diamond accumulates Notices respecting New Books. 467 until it is sufficient to produce a change of state, so that it is not taken in at one particular temperature, as occurs in the case of allotropic phosphorus, but throughout a long range. If we could define the point where the change referred to takes place, we might, by keeping carbon near this temperature, change it partially into diamond. But all these questions must remain without any decisive answer until we know with certainty the heat of combustion of graphite and diamond. LVI. Notices respecting New Books. The Strains in Trusses computed by means of diagrams: with twenty examples drawn to scale. By Francis A. Ranken, M.2., C.L., Lecturer at the Hartley Institution, Southampton, formerly Assistant Eingineer on the Cambrian Railways, &c. London: Longmans, Green, and Co. 1872. (Pp. 64, 8vo.) — object of this work is to illustrate, by a variety of examples, the solution of the following problem :—Given that a number of points in one plane are joined two and two by straight lines in such a way as to form a rigid system, and that forces act in the same plane at these points in such a way as to hold the system in equili- brium, to determine the forces transmitted along the lines, and whether they tend to stretch or compress them severally. It is scarcely necessary to add that this is the question presented for solu- tion when trussed roofs are designed and all considerations of trans- verse strain are put on one side. ‘The book consists mainly of ex- amples; and the solutions are effected entirely by means of the tri- angle and polygon of forces, without calculation, merely by means of a construction made with scale and compasses. The general ques- tion is one which lends itself very readily to the method of solution adopted; and though in some cases, where the truss is of a compli- cated form, the diagram giving the solution is intricate, yet the result is obtained by very simple means, and does away with the need of a most laborious though not otherwise difficult calculation. The number of cases actually solved is very considerable ; in fact all the ordinary forms of trusses are discussed, and the diagrams which yield the solution drawn carefully to scale. The book will doubtless prove useful to students of Engineering, and might be studied with advantage by all who are going through a course of Theoretical Mechanics. While fully recognizing the great care that has been bestowed upon the diagrams, we may perhaps add that it would have been of service to beginners if Mr. Ranken had shown (say in one diagram) all the forces which actu- ally keep each joint in equilibrium. ‘To bave done this throughout the book would have made the diagrams unnecessarily complicated ; but it might have been done, for instance, in the diagram on p. 18, and would have helped the student to understand the action of the forces in this and other cases. When several forces are shown, a beginner is very apt to think that they are all he is concerned with. 2H 2 [ 468 ] LVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 394.] June 20, 1872.—Sir James Paget, Bart., D.C.L., Vice-President, in the Chair. HE following communications were read :— “Volcanic Energy: an attempt to develope its true Origin and Cosmical Relations.”” By Robert Mallet, F.R.S. The author passes in brief review the principal theories which in modern times have been proposed to account for volcanic activity. The chemical theory, which owed its partial acceptance chiefly to the fame of Davy, may be dismissed, as all known facts tend to show that the chemical energies of the materials of our globe were almost wholly exhausted prior to the consolidation of its surface. The mechanical theory, which finds in a nucleus still in a state of liquid fusion a store of heat and of lava &c., is only tenable on the admission of a very thin solid crust ; and even through a crust but 30 miles thick it is difficult to see how surface-water is to gain access to the fused nucleus; yet without water there can be no volcano. More recent investigation on the part of mathematicians has been supposed to prove that the earth’s crust is not thin. Attaching little value to the calculations as to this based on precession, the author yet concludes, on other grounds, that the solid crust is pro- bably of great thickness, and that, although there is evidence of a nucleus much hotter than the crust, there is no certainty that any part of it remains liquid; but if so, it is in any case too deep to render it conceivable that surface-water should make its way down to it. The results of geological speculation and of physico-mathe- matical reasoning thus oppose each other; so that some source of volcanic heat closer to the surface remains to be sought. The hypothesis to supply this, proposed by Hopkins and adopted by some, viz. of isolated subterranean lakes of liquid matter in fusion at no great depth from the surface remaining fused for ages, sur- rounded by colder and solid rock, and with (by hypothesis) access of surface-water, the author views as feeble and unsustainable. A source, then, for volcanic heat remains still to be found; and if found under conditions admitting to it water, especially of the sea, all known phenomena of volcanic action on our earth’s surface are explicable. The author points out various relations and points of connexion between volcanic phenomena, seismic phenomena, and the lines of mountain elevation, which sufficiently indicate that they are all due to the play of one set of cosmical forces, though different in degree of energy, which has been constantly decaying with time. He traces the ways in which the contraction of our globe has been met, from the period of its original fluidity to the present state :— first by deformation of the spheroid, forming generally the ocean- basins and the land; afterwards by the foldings over and elevations of the thickened crust into mountain-ranges &c.; and lastly by the Royal Society. 469 mechanism which he points out as giving rise to volcanic action. The theory of mountain-elevation proposed by C. Prévost was the only true one,—that which ascribes this to tangential pressures pro- pagated through a solid crust of sufficient thickness to transmit them, those pressures being produced by the relative rate of contraction of the nucleus and of the crust: the former being at the higher temperature, and having a higher coefficient of contraction for equal loss of heat, tends to shrink away from beneath the crust, leaving the latter partially unsupported. This, which during a much more rapid rate of cooling from higher temperature of the whole globe and from a thinner crust gave “rise in former epochs to mountain- elevation, in the present state of things gives rise to volcanic heat. By the application of a theorem of Lagrange, the author proves that the earth’s solid crust, however great may be its thickness, and even if of materials far more cohesive and rigid than those of which we must suppose it to consist, must, if even to a very small extent left unsupported by the shrinking away of the nucleus, crush up in places by its own gravity and by the attraction of the nucleus, This is actually going on; and in this partial crushing, at places or depths dependent on the ‘material and on conditions pointed out, the author discovers the true cause of volcanic heat. As the solid crust sinks together to follow down after the shrinking nucleus, the work expended in mutual crushing and dislocation of its parts is transformed into heat, by which, at the places where the crushing Soe ntly takes place, the material of the rock so crushed and of that adjacent to it are heated even to fusion. The access of water to such points determines volcanic eruption. Volcanic heat, therefore, is one result of the secular cooling of a terraqueous globe subject to gravitation, and needs no strange or gratuitous hypothesis as to its origin. In order to test the validity of this view by contact with known facts, the author gives in detail two important series of experiments completed by him :—the one on the actual amount of heat capable of beg developed by the crushing of sixteen different species of rocks, chosen so as to. be representative of the whole series of known rock formations from Oolites down to the hardest crystalline rocks; the other, on the coefficients of total contraction between fusion and solidification, at existing mean temperature of the atmo- sphere, of basic and acid slags analogous to melted rocks. The latter experiments were conducted on a very large scale; and the author points out the great errors of preceding experimenters, Bischoff and others, as to these coefficients. By the aid of these experimental data, he is enabled to test the theory produced when compared with such facts as we possess as to the rate of present cooling of our globe, and the total annual amount of volcanic action taking place uponits surface and within its crust. He shows, by estimates which allow an ample margin to the best data we possess as‘to the total annual vulcanicity of all sorts of our globe at present, that less than one fourth of the total heat at 470 Royal Society :— present annually lost by our globe is upon his theory sufficient to account for it ; so that the secular cooling, small as it is, now going on is a sufficient primum mobile, leaving the greater portion still to be dissipated by radiation. The author then brings his views iato contact with various known facts of vulcanology and seismology, showing their accordance. He also shows that to the heat developed by partial tangential thrusts within the solid crust are due those perturbations of hypogeal increment of temperature which Hopkins has shown eannot be referred to a cooling nucleus and to differences of conductivity alone. He further shows that this view of the origin of volcanic heat is independent of any particular thickness being assigned to the earth’s solid crust, or to whether there is at present a liquid fused nucleus, all that is necessary being a hotter nucleus than crust, so that the rate of contraction is greater for the former than the latter. The author then points out that, as the same play of tan- gential pressures has elevated the mountain-chains in past epochs, the nature of the forces employed sets a limit to the height of mountain possible of the materials of our globe. That voleanic action due to the same class of forces was more energetic in past time, and is not a uniform but a decaying energy now. Lastly, he brings his views into relation with vulcanicity pro- duced in like manner in other planets, or in our own satellite, and shows that it supplies an adequate solution of the singular and so far unexplained fact that the elevations upon our moon’s surface, and the evidences of former volcanic activity, are upon a scale so vast when compared with those upon our globe. Finally, he submits that if his view will account for all the known facts, leaving none inexplicable, and presenting no irreconcilable conditions or necessary deductions, then it should be accepted as a true picture of nature. “Qn the Action of Electricity on Gases.” By Sir B. C. Brodie, Bart., F.R.S., Hon. D.C.L. Oxon. This memoir, which is intended to be the first of three commu- nications as to the action of electricity on gases, is devoted to the consideration of the changes produced by the action of electricity on oxygen gas as estimated by the changes thus effected in its chemical properties. The memoir is divided into four sections. Section I. contains an account of the methods employed for gene- rating, collecting, and preserving the electrized gas, and also of the measuring-apparatus employed for estimating the changes in the volume of the electrized gas effected in the various experiments subsequently described. The gas, carefully dried, was submitted to the action of electricity by causing a current of the gas to pass through the induction-tube of Siemens, the interior of which was filled with water or (where a low temperature was desired) with a saline solution. The tube was placed in a glass cylinder containing water or a refrigerating- =——" 2 : Sir B. C. Brodie on the Action of Electricity on Gases. 471 mixture. The interior and exterior of the tube were respectively connected with the terminals of a powerful Ruhmkorff’s coil. The electrized gas, after its passage through the induction-tube, was collected, in a gas-holder of peculiar construction, over concentrated sulphuric acid. It may be thus preserved for several hours without sensible variation in its properties. The principle employed for the measurement of the gas in which it was desired to estimate the changes in volume produced by the ex- periment, was the principle of pipette-measurement which has been so successfully employed by chemists for the measurement of liquids. In this way a considerable volume (say from 250 to 300 cub. centims.) may be measured with facility and precision. sin n= —(Z)—Z,) which is convergent for all values of « between 0 and J. of Iron and German Silver. 485 convenient to deduce from equations (2) the difference of tempe- rature of two points in the bar, one of which has the distance x=], and the other the distance #=4/; for in this special case all terms in which n is divisible by 2 and 3 vanish from the series which occur in both expressions ; and these hereby take a form so convergent that even the second term becomes vanishingly small in comparison with the first as soon as the time @ has reached a certain value. When, therefore, a commencement is made with the observations first at the expiration of a certain time @ reckoned forward from the beginning of each period, only the first term of that series need be taken into consideration. Let D,,, denote the difference of temperature, in an even period, between two points whose distances from the end are r=4/ and x=l, and let D.,,, denote the same value in an odd period ; then, from equations (2), we find :— D =(2"!_v)(A—B) +0" (A+B) | 2. ¢ _ 8rrk\/3 Uo—% e—Pe pl? 1+e7#t i (4) Dae (“54 —U)(A—B)— 5s (A+B) Stk/3 Yom" no ple, Mee oP esi Here 4p? p= = k+h. Raper ane he (5) Cn has: k h h A h po CV Ene ape VE) CA Raat k The first two terms in the above expressions (4) are constant quantities ; the same holds for the factor of e-?°; consequently the expressions of D», and Ds, +, have the form D, = M eg Dou+i= —M'+Ne ores a oe (6) 436 M. H. Weber on the Heat-conducting Power If, then, for a series of different values of @ in the same period we obtain by observation the temperature-differences D,, or D541 belonging to these times, from these we get a series of equations from which M and N or M! and N’ can be eliminated ; and therewith the quantity P is given. According to (5) a second equation is hereby obtained between A and k, which, in conjunction with equation (3), leads to the knowledge of hf and &, and therewith also to that of H and K*. Description of the Apparatus. The arrangements made use of in order to fulfil rigorously the conditions presupposed in the theory were the following. The heating and cooling of the ends of the bar were effected by alter- nately conducting over the ends steam of about one atmosphere tension and water at a certain temperature. The bringing of steam or water took place through the four cocks, A, B, C, D (Plate V. fig. 1). The cocks A and B served for bringing the steam. Hach of them had three small pipes attached, e, §, y, which brought and carried away the steam. From two boilers, in which the steam was generated, it was conducted through pipes to the pipes a, whence, according to the position of the cocks, it either entered through y into the pipes 6, and through these was conducted over the ends of the bar MN, or passed through the pipes @ into other pipes, through which it issued into the air. Thus, during the observations, two mdependent currents of steam were continuously kept up ; and by the arrange- ment described steam could at any moment, by a suitable posi- tion of the cock-plugs, be conducted to the ends of the bar. Fig 2 is a horizontal section of the cocks A and B. The line p gives one, and the dotted line g the other normal position of the plug. C and D are usually single-bored cocks: when they are in one normal position, the pipes e and 6 are in communication ; when, on the contrary, they are in the second normal position, the pipes e are shut off. The pipes e were connected with the municipal waterworks. The small receivers (figs. 3 and 4), finally, into which the ends of the bar were soldered, were ma- nufactured of very thin sheet brass. On the inside of the upper * If not satisfied with the first term of the above-mentioned series, we might also take the second term into consideration. For this we have 10072 ——k+h }0 40kmV 3 _ Uo th gil fs a Te ee MOOnos) wae LOGE Ae ra po e+ aa je ea |e which would have to be added to the above expression for Do, with plus, anid to the expression for Do, +1 with minus signs. Its value, however, in the following observations does not amount to the millionth part of that of the first term. of Iron and German Silver. 437 pipes & a scoop-like piece of sheet brass was soldered for the pur- pose of diverting the entering water to the end-surface of the bar. During the experiments the ends & were connected with the pipes 6, and the ends A with pipes which carried off the steam or water, by means of caoutchouc tubing. It follows from the theory above given that the most favour- able circumstances for the determination of K occur when the ends M and N of the rod have simultaneously different tempe- ratures—M being heated and N cooled during the first period, M cooled and N heated during the following period, or vice versd. In order to regulate with facility the supply of the water and steam according to this arrangement, the levers which turned the plugs of the watercocks C and D, on the one hand, and those of the steamcocks A and B, on the other, were connected by a bar; so that by the motion of the two bars the four plugs could be put into their right positions. All the cocks were pro- vided with stops, and consequently could only turn within their normal positions. With such an arrangement, it is easy to see how the four cocks could be regulated at a distance. It was only necessary to fasten cords to the ends of the connecting bars, two of which were stretched by weights, whereby the plugs took one of their normal positions; and when the cords at the other ends were pulled, the plugs were turned so as to take their second position. In order to give the cocks a firm support, each two of them (A and D, and C and B) were let into a piece of wood, by which all sae non of heat to the bar was avoided. Instead of four cocks, two four-way cocks might have sufficed, as used by Angstrom in his researches. But then such a cock would have been traversed at the same time by steam and by water; and, on the one hand, steam would have been condensed, while, on the other, the temperature of the water would have been raised. By the above arrangement this imconvenience was avoided. The temperature of the water was measured by a ther- mometer inserted in the water-pipe. In order to observe the distribution of temperature in the bar, in the first place a thin iron wire and a thin German-silver wire were soldered in the middle of it, L, opposite to each other. The ends of these two wires were soldered to two copper wires which led to a galvanometer, and formed with the copper wires points as shown in fig. 5. Between the points was the bulb of a sen- sitive thermometer. The thermometer and wires were retained in this position by a suitable keeper made of wood. If now the middle of the bar and the points (which are in the surrounding air) have different temperatures, a thermo-current ensues, the intensity of which may be supposed proportional to the ditference between the temperature of the middle of the bar and that of the 488 M. H. Weber on the Heat-conducting Power points. In the places H and I, at the distances 1/ and 4/ from the end of the bar, two German-silver wires were soldered to the iron bar, two iron wires to the German-silver one; and their ends, at about 6 inches from the bar, were soldered to two copper wires which led to the same galvanometer as the wires before mentioned. In front of the galvanometer was a regulator such that now the conduction to the middle of the bar, and now the conduction to the places H and I could be connected with the galvanometer. Each of the thermo-currents circulating in the two conductions could be passed in opposite directions through the galvanometer ; and, finally, it was also possible to shut off the galvanometer and to determine the stationary position of the needle at any moment. If the conduction to H and I was con- nected with the galvanometer, the intensity of the thermo-current circulating in this circuit was evidently proportional to the dif- ference between the temperatures of H and I. The bar and the cocks were in a room by themselves, the galvanometer and the two steam-boilers were in two adjoining rooms. The pipes for steam and water were carried through the dividing wall, and wrapped tightly round with strips of cloth and tow. In this manner any considerable alteration of temperature of the air surrounding the bar during the experiments was avoided. The Galvanometer and its Employment. The galvanometer made use of in the experiments was con- structed according to the rules for attaining the maximum of sensitiveness*, The length of the needle was 100 millims.; and the multiplier had a resistance of 0°59064 x jo nu at a second temperature of 10° C. When the galvanometer was shut off, the arresting-power was so great that the needle returned from deflections of 12° to the position of rest after two oscillations. Hence the logarithmic decrement 2% could not be determined immediately from the diminution of the are of oscillation, but had to be deduced from a series of observations in which different known resistances were inserted. For it the following value was found :— DV = 42458. The time of an oscillation with the circuit open was 4/466. Now, for all galvanometers constructed according to the direc- tions above mentioned, the torsion-moment can be determined which is exerted by the multiplier upon the needle deflected to an angle @ from the plane of the meridian when a current of the intensity I flows through the multiplier. For, denoting this * Pogg. Ann. vol. exxxvil. p. 121. of Iron und German Silver. 489 moment, which 1s called the galvanometer-function, by f(®), it can be shown that I ($) =f (O)cos (1 +4 sin ¢?+56 sin d4+csin g°+ ...), where a, b, c,... are constants. The smaller the angle ¢, the more rapidly convergent is this series; and in observations in which ¢ remains always small, we may content ourselves with the first two terms, so that we have Fo) —7 (Oycos O(a sino?) t. . | If we connect the galvanometer with the conduction to the middle of the bar, the thermo-current (whose intensity may be 2) deflects the needle from the plane of the meridian to an angle ¢; and for this new position of rest the following equation holds :— af(p) =Tm sin ¢, m being the magnetic moment, T the horizontal component of the earth’s magnetism. With the aid of equation (7) we find from this :— fe lms a atan (8) iO) 1+asin 6? Tee On ERA BO But, on the other hand, the intensity of the thermo-current is also proportional to the difference between the temperatures of the middle of the bar and the points A (fig. 5), the latter of which have the temperature of the surrounding air. Hence, if we denote by W the resistance of the whole circuit, by V,, and U (as before) the temperature of the middle of the bar and the surrounding air, then . a(V,—U = olay e e e e ° e (9) where « denotes the electromotive force which corresponds to a temperature-difference of 1° C. From (8) and (9), therefore, if * The quantity f(0) is the torsion-moment exerted upon the needle in the plane of the meridian by the multiplier when it is traversed by the unit of current. In the previously mentioned memoir (Pogg. Ann. vol. exxxvii. p- 134) it is denoted by D. There it was found that Oj=osssa_@ /W, ee VL /* in which L denotes the length of the needle, k the specific resistance, and. W the total resistance of the galvanometer-wire. For the above-mentioned gal- vanometer it was found from direct observations that f(0)=48-09 .m; while, illimetr according to the formula given, f(0)=47°41 . mif k=219274 a = Probably the value of k on which the calculation is based is somewhat too great. 490) M. H. Weber on the Heat-conducting Power for shortness we put WTmn = "Pn? te)”. Sher) Chea dete 10 | of 0) ae we obtain V,-l=ke re l+asin ¢? Accordingly, when the quantities R and a are known, and ¢ and U observed, the temperature of the middle is thereby given. The quantity a had been determined after the method given by Poggendorff*. As the above galvanometer (constructed by myself) had perfectly regular coils, and care had been taken to secure a good centring of the multiplier, the values of a, calcu- lated from various angles of torsion of the multiplier, exhibited a satisfactory accordance. For example, a set of such observa- tions gave for a@:— | —0°6328 —0°6259 — 0°6265 —0°6316 —0°6274 Mean . . —0°6288 A second set gave similar results. For the following obser- vations the value a= —0-63 is perfectly sufficient. The quantity R depends on the resist- ance W of the circuit, and therewith upon the temperature of the galvanometer-wire. An alteiation of this temperature could have been easily reckoned according to the known law of the va- riation of the resistance with the temperature; but as the tem- perature of the wire cannot be accurately determined, it was preferred to determine R specially before each series of obser- vations. At the beginning of each series of experiments, before the ends of the bar were exposed to a heating or cooling, the temperature of the bar was that of the surrounding air. To control this, the conduction to the middle was inserted, so that the needle showed no deflection. A vessel with heated oil was now approached from beneath to the points and the thermometer between them (fig. 5) until they were in the centre of the oil. The vessel contaiming the oil was suspended free in a cylindrical vessel of wood of 1 inch thickness (fig. 6), upon which was a wooden lid with a circular aperture. Through this the points and thermo- * Pogg. Ann. vol. lvii. p. 324. of Iron and German Silver. 491 meter were introduced into the oil, and then the aperture was closed with cotton wool. In this way an extreme retardation of the cooling of the oil was attained (in 45 minutes it amounted, on the average, to about 5° C.), and the temperature of oil, points, and thermometer could at any moment be taken as equal. A second thermometer was suspended by the side of the bar, giving the temperature of the surrounding air, and consequently that of the bar. During the experiments the temperature of the air remained nearly constant. The two thermometers were read off with the aid of a telescope. It is now easy, from simulta- neous observation of the temperatures of the oil and the bar, and of the accompanying deflection of the needle, to deduce, according to equation (11), the value of R. For this a single simultaneous observation would indeed have sufficed; yet, for control, several such observations were always made. The de- termination of R in the first series of experiments with the iron rod may serve as an example. ; Tempera- ae uae pe the ture of the Difference R Calculated iéedle m middle of ! 3 b difference. ; ou the rod. io} i {o) 1 (e) fe) fo) 5 19°3 29 16 C. 4°85 C. 24-31 259°5 24-32 C. 422-2 | 2370, | 4-80, 19-90 259-4 | 19-92 ,, 3245 | 2032, | 478, 15-54 260-3. | 15°50 ,, From this we obtain the mean value R=259°7. tan d Nh pa Ol Se i) ae ee gee % 1— 0°63 sind? (12) The numbers in the sixth column are obtained by calculating the differences of temperature from the observed angles ¢. In those experiments in which the ends of the iron rod were alter- nately heated and cooled, the points A (fig. 5) possessed the lower, the middle of the rod the higher temperature, and, ac- cordingly, the current was in the opposite direction to that in the above experiments. With the aid of the regulator, however, it was easy to make the deflection of the needle follow the same direction. Besides, no particular stress need be laid upon the deflection being in the same direction, since before the experi- ments the turns of the multipher-coil were placed parallel to the plane of the magnetic meridian, and the deflections, when a con- stant current passed through the multiplier in either direction, were equally great on both sides of the position of rest. 492 M. H. Weber on the Heat-conducting Power In order to determine the quantity p in accordance with equa- tions (6), when the rod had assumed the state of periodic limits the conduction to H and I was connected with the galvanometer. A motion of the needle then commenced, variable with the time @. The forces on which this motion depends are (1) the horizontal component of the earth’s magnetism, (2) the deadening force, (3) the force exerted by the thermo-current upon the needle. The torsion-moment which the first two forces exert upon the needle with a deflection ¢ are 2 ee, | AONE a w at’ T being the horizontal component of the earth’s magnetism, m the magnetic moment of the needle, and w the resistance of the circuit. In order to determine also the torsion-moment of the third force, we must consider that the intensity of the thermo- current is a quantity which varies with the time, whereby an induction of the current upon itself is occasioned, and the con- sequence is a diminution of the intensity. For, let 2 be the in- tensity of the thermo-current which is actually passing through the circuit at the time @, 2, the intensity which would be ob- served if the current remained constant, then is ah apa 947i, deze, Sah a6 Wagga lugs a where y is a constant depending on the resistance and the form of the circuit. According to equations (6), however, in an even period __ a(M—Ne-?*) any grt an oe in an odd period re 2 ae re cma — = From this it follows that the intensity 7 actually present in the circuit at the time @ can be represented by an expression of the form en a(A+ Be-?*) SS Ww where A and B are constants. Hence the torsion-moment of the third force becomes a gi *) (4), and we obtain for the equation a motion of the needle of the galvanometer, if « denotes the moment of inertia of the needle of Iron and German Silver. 493 and the suspension :— d? ra Tn . A + Be-?? ost Pas = + dele ppunst BA ) Fb) =0. It is only for small angles . that the integration of this equation can be effected in a definitive form. Presupposing small angles, it is transformed into aS , [flO]? db | Tm KW a(A + Be-??) de? Kw dO K ors KW yO=0; from which by integration we obtain aif (0) 0) af(O) Be-?? 25 wTm : ewe, =Lf(O))?_ | Tm i Cf0)]*4 +Ce ? = "sin 4 (C— oa / HYCO ie a C and C’ here denote two integration constants. From this we perceive that the motion of the needle is composed of two mo- tions superposed the one upon the other—first, of that which the needle would have if no thermo-current were present, and then of that which it would have if the periodic part were omitted. If now we construct a galvanometer with great deadening force, so that the needle approximates to the aperiodic state, as was done in the present case, and make the time of an oscillation ¢ of the needle and the resistance external to the galvanometer small, then the logarithmic decrement X= 4 =—~—- bh , t will have a great value, and the periodic part in the ae of the needle will after the lapse of a very short time be vanishingly small. Consequently, if at the commencement of each period we let a certain time elapse before we begin the observation of the deflec- tions @ corresponding to the different times 6—which, besides, is necessary in order that we may employ the simplified expres- sions of D,, and Dz,+1, equations (6),—the periodic part may be omitted, and we obtain for ¢ simply an expression of the form p=P'+Qe", where P! and Q! are constants. If these observations are made with mirror and scale, it 1s more convenient to introduce the arcs of double the angles of deflection instead of the deflections g@ themselves. Let r be the distance of the mirror from the scale, s the arc corresponding to the angle ¢, then s=2rd, and we have SS Ph Qe Py is Wh eh 9s sig 4S) 49 4. M. H. Weber on the Heat-conducting Power —where P and Q denote the same constants as before, multiplied by 27. The angles s were not, indeed, observed directly on the scale, but their tangents; these, however, can easily be referred to the corresponding arcs by a well-known reduction. Let ¢ denote the observed number of scale-divisions, corre- sponding to the angle ¢, and let r be expressed in parts of the scale, then the corresponding arc S=O— 35 In the same way, from a series of observed values of o corre- sponding to certain times 6, p can be found. For the logarithmic decrement when the conduction to the points H and [I of the rod was connected with the galvanometer, there was obtained A=3 704 with a time of an oscillation t=6"-904, whence it follows that at the end of 15 seconds the periodic part of the motion of the needle had already vanished, even when the deflections were the greatest. The sensitiveness, however, of the galvanometer was such that the deflections were too great. This inconvenience can be remedied in two ways—either by increas- ing the resistance of the circuit, or by strengthening the hori- zontal component of the earth’s magnetism by placing a suitable magnet in the meridian-plane. But in the former case the deadening is diminished in equal proportion, which is unfavour- able for the observations; in the latter case the deadening re- mains unaltered, and the sensitiveness can be regulated as we choose. ‘The latter, therefore, was the procedure adopted in the following observations. Observations. After the preliminary observations for the determination of the quantity R, the ends of the rod to be investigated were, at equal intervals of time T, alternately heated and cooled. At the end of about three quarters of an hour the extreme periodic con- dition commenced, being recognized by the temperature ef the middle of the rod no longer increasing. Before the first series of observations, and between each two of the succeeding ones, the temperature U of the vicinity, the temperature uw, of the water, the position of rest of the needle, and the scale-division corresponding to the temperature V,, of the middle of the rod were read off. The temperature of the steam was ascertained from the state of the barometer. It now appeared that the dif- of Iron and German Silver. 495 ference between the temperature of the middle of the rod and that of the surrounding air was not perfectly constant, as it should have been according to the theory, but that variations oecurred which might have for their consequence deviations of half a degree from the mean value. It may be that the cause of this is to be sought in the non-aecordance of the bases of the theory with what takes place in reality, orin the place where the middle wires were soldered to the rod not coinciding exactly with its centre. But in this case there would necessarily have been a certain regularity in the variations, which, however, was not observed. It is therefore probable that they were occasioned by air-currents, which, notwithstanding all precautions, could not be entirely avoided. Each series of observations consisted of an even number of readings So, S;,+ ++ San—1, which were made in regular intervals of time 6=15", the first of which fell on 6>-=45". In order from these observations to calculate the value of p according to equa- tion (13), it appears the simplest to form the differences (sy—s;), (Ss; —Sq), (sy—S3),... and to divide these by one another. A little consideration, however, shows that herein the unavoidable errors of observation must have a very important influence on the result. The following treatment leads to more accurate results. If we first form the differences (So—Sn)> (S$) —Sn4i)>°+ + (Sn-1—San—1)5 we obtain a series of equations of the form Somsn. = Ql Mol—e P), $1 — Sn41= Q (e—P%0 — en) e— PF, So Sn42= Q(e7?%— e-#9n) e~ 78, If we take the logarithms on both sides and denote log(sy—s,), log (s,—Sp41),+-- by mo, m,,... and for abbreviation put log Q(e-% —e~P*n) =a”, loge P=y, there result equations of the form My =2, mM,=2+yY, m,=x+2y, ia from which, by the method of least squares, x and y, and with them p and Q, were found. With the aid of these values we 496 M. H. Weber on the Heat-conducting Power can, for control, calculate the constant P corresponding to each s, which must come out equal for each of the values. All the following observations were calculated in this way. The fundamental units of measurement employed are millimetre, miligramme, and second; and accordingly the heat-unit is that amount of heat which is capable of raising the temperature of 1 milligramme of water from 0° C. to 1° C. I. Iron rod (annealed). Leneth .°. £=230-35-millims. D=7-760 7 Diameter... = 7:°5168 millims. C=0°1125 Distance of the mirror from the scale r=2927 millims. = 2952°4 parts of the scale. The density and the specific heat were specially determined, the latter according to the method proposed by Neumann. The temperature-formula has been already given (equation 12). An even period. o° z Differ- 6 C. a3 $. ca ence 12s | ae | 2 0 45 —440 32 —436°8| —441°5| 447 7298 1 0 —215 0-4 = 24-6 i — Jiao) pO 724-4 15 — 32 0-0 =32-0) —1 3061) 1-4 723-7 30 +117 0-1 +1169} +116°9 0-0 72571 45 +235 0-5 +2345 | +235:5/ —1:0 7241 2 ~0 +331 1:4 +3296) +3831:1| —15 723-6 15 +410 2-6 +407:4| +4080} —0°6 724:5 30 +475 4-] +4709| +4695) +1°1 726-2 45 +526 5°6 +520-4| +5197) +07 725°'8 3. 0 +567 70 +560-0| +559:7| +03 725-4 15 +601 8:3 +592-7| +5920; +07 725°8 30 +627 9-4 +6176| +618:0| —04 7247 45 +648 10-4 +6376) +6389} —1: 7238 4 0 +667 11:3 +655°7 | +655°7 0:0 725°1 15 | +681 | 121 | +668-9| +669-2| —0-3 | 724-8 30 | +693 | 12:7 | 4680-3) +6801] +402 | 725°3 Mean...| 725°1 Further, the height of the barometer, reduced to 0° C., was 75897 millims. u,=99:96 C. U = 5:37 C. uj= 472 C. Vn=33'14 C. K=15-07 heat-units. H=0-00267 heat-unit. In like man- ner in the following periods we obtained the values :— of Iron and German Silver. Even periods, 209 46 U = 5:47 K=15:09 Uj= 471 Vin = 90°22 H= 0:00266 we s000 Uy ="5'54 K=15:°29 Tee 7 Vn=o0o 16 H= 0:00271 u,=99°96 U = 5:59 K=15:°10 Ug= 4°52 Vin = 09°32 H= 0:00264 u,—90 96 U = 5:69 K=15:16 Up== 4°52 V 222 00'49 H= 0:00262 Odd periods. u,= 99°96 U = 5:97 K=14°39 Upg= 4°52 Vin 03°03 H= 0:00261 299-20 U = 6:00 K=14:°40 Up= 4°52 Vi —oo.0l H= 0:0026]) u,= 99:96 U = 6:04 K=14°68 Ug= 4°54 Vin = 3299 H= 0:00267 i — 0 96 U = 6:10 K=14:°76 Ug== 4°62 V n= 02'86 H= 0:00273 If we take the mean of the values of K and H given by the even periods, and likewise of those derived from the odd periods, we obtain :— KS15: 14: K = 14°56, H=0:00266; H=0:00266. The difference which appears here between the values result- ing from the even periods and those resulting from the odd ones is to be accounted for by a want of absolute coincidence of the soldering-places with the points z=1/ and #=4/; for a small deviation of the first-mentioned place may have a consi- derable influence. ‘The mean of the whole is :— K = 14:85, H=0-00266, As both K and H are variable with the temperature, we must, in order as far as possible to apply calculation to the variability, refer these values to the mean temperature of the rod. Deno- ting this by A, we find 1 t T A= 5 ( da { (Voi a Viv yee Phil, Mag. 8. 4. No. 296, Suppl. Vol. 44. 2K 498 M. H. Weber on the Heat-conducting Power With the aid of equations (2), if for abbreviation we put oe _), ie pl b=e aV Ee we accordingly obtain uet+u,—2U a—b IX — 1) en . . a HP a+6 KQ If we introduce into this expression the mean values of up, w,, U, H, K, the result is a ee A=389°%23 C. Consequently, if one surface of an infinitely large iron plate of one millimetre thickness be kept at the temperature of 39° C., and the other at 38° C., through one square millimetre area 14°85 heat-units will pass in a second from one surface to the other*. If, further, a body consists of iron the surface of which has the same constitution as our iron red, and if this body be constantly kept at the temperature of 39° C. while the temperature of the surrounding air is 388° C., from every square millimetre surface -0°00266 thermal unit will be given up to the air in one second. The surface of the iron rod had not the highest polish. In order to try whether the quality of the surface exerted a percep- tible influence on the value of K, the previous experiments were repeated with the same iron rod after its surface had been evenly coated with scot from a gas-flame. The thickness of the coat- ing was such that the metallic surface was just perceptible through it. Here the duration of the pericds amounted to 10 minutes, in order to make the observations in even and odd pe- riods alternately, not consecutively as before. Il. Lron rod coated with soot. Even periods. K=14-80 H=0-00333 Odd periods. K=14-65 H=0-00319 K=14-50 H=0-00322 Mean values. K=14°79 H =0:00328 We consequently obtain approximately the same value for K, which seems to indicate that, in this method of determining the heat-conducting power, the heat given up to the environs does * By multiplying the above by 0-6 we obtain the thermal conducting- power in the units used by Angstrom. of Iron and German Silver. 499 not exercise any prominent influence. That, notwithstanding the great exposing-power of soot, the quantity H does not assume a greater value is to be attributed to the bad conducti- vity of soot for heat. III. Drawn German-silver rod (annealed). Length . . /=230°4 C=0:0944 Wiameter 9. — 7-622 millims: “D=3 621 C and D were, as before, determined specially. Odd periods. K=8:404 H=0-00318 K=8:405 H=0-00316 Even periods. K=7°'832 H=0:00291 K=7°-791 H =0:00291 K=7:°317 H=0-00295 Mean value from the even periods. K=7°8138 H =0-00292 Mean value from the odd periods. K = 8°404 H=0:00317 Mean of the whole. K=8:108 H =0-00304: These latter values refer to the mean temperature A of the German-silver rod, N= S17 25°C, The determination of the mean temperature to which the values of K and H were referred can only be regarded as a rough approximation. A step would be taken towards greater accuracy if, in constructing the general equations for the propagation of heat, K and H were introduced as functions of the temperature, putting K=K,(1+e/), H=H,(14+ ¢). In fact, presupposing this, the stationary condition mm a rod whose ends are kept at constant temperatures can be determined generally*.. The solu- tion consists in an integration which can be effected in a defini- tive form for a rod unlimited in one direction. Great difficulties, however, oppose an experimental use of this solution for the de- termination of «, 8, Ky, and Ho. A knowledge of the dependence of K and H on the tempera- ture would also be desirable, in order to test the conjecture of * Poisson has given an approximate solution of this problem (Théorie mathématique de la Chaleur, p. 255). 2K 2 500 Mr. J. W. L. Glaisher’s Supplementary Remarks Wiedemann and Franz*, that the heat-conducting power of metals is directly proportional to their electric conductivity, or inversely as their specific resistance. If w denotes the specific resistance of a metal, C a constant, the heat-conducting power K=—: Ww Lenz+ has found this law verified when K and w refer to the same temperature. In a determination of K in the thermal millimetres second for one and the same iron rod, I obtained for the constant C C= 2458 x 104, in which the values of K and w referred to the temperature 44°°3 C. units above chosen, and of w in absolute measure LX. Supplementary Remarks on some early Logarithmic Tables. By J. W. L. Guaisuer, B.A., F.R.A.S., Fellow of Trinity College, Cambridge t. tie the October Number of the Philosophical Magazine I stated that Decker’s work left no doubt “that to him must be assigned the credit of having been the first foreigner who pub- lished Briggian logarithms, an honour which has always been hitherto assigned to Vlacq.”? This sentence requires some mo- dification, or at all events explanation, as Vlacq was not the only claimant for the honour in question. His rival was Denis Hen- rion, who published at Paris in 1626 a Traicté des Logarithmes, containing Briggs’s logarithms of numbers from 1 to 20,000 to ten decimals, and Gunter’s logarithmic sines and tangents. Hen- rion’s work has been so rarely met with by the bibliographers that it has become little more than a tradition. It is scarcely ever mentioned by German writers; and all De Morgan could collect is contained in the following extract :—“‘ (1626) Henrion’s ‘Logarithms,’ Paris. (Dodson, followed by Hutton.) Lalande knew nothing of this work, nor Delambre. All we can learn is from Dechales, who states that Henrion wrote on the propor- tional compasses in (1623), reprinted in (1681), and on the rule of proportion (which we take to be Gunter’s scale) in (1626) ; and that the last work contains logarithms of numbers up to 2000.” | * Pogg. Ann. vol. Ixxxix. p. 531.- bh Se de ? Académie Impériale des Sciences de St. Pétersbourg, vol. xiv. p. 54. { Communicated by the Author. on some early Logarithmic Tables. 501 There is, however, a copy in the British Museum, acquired in 1854; and as it bears the name of H.C. Schumacher, Copenhagen, 1816, it no doubt belonged to the celebrated astronomer. The preface is not dated; and there is no “privilége” or date* of com- pletion of printing (or perhaps the last page is torn out) ; so that there exists no means of deciding whether the priority of pub- lication belongs to Decker or Henrion. It struck me as not unlikely that there really was perhaps no “ privilége,” as the “ privilége ” to Henrion’s Cosmographie, 2nd edit., Paris, 1626, includes “toutes ses ceuvres,” and is dated Sept. 7, 1624, the “achevé d’imprimer” being April 1626; but the LZ’ Usage du Mecrométre, 1630, by the same author, has the “ privilége ” as usual. In the preface to his Traicté des Logarithmes Henrion makes no reference to Wingate’s publication at Paris the pre- vious year; he states that he had calculated some logarithms himself when the appearance of Briggs’s Arithmetica rendered the further progress of his work unnecessary. Lalande men- tions five books of Henrion; and I have met with three or four others; so that he must have been a somewhat prolific mathe- matical writer for the time: he describes himself on his title- pages as “ demeurant en l’isle du Palais.” Of Decker’s Eerste Deel vande Nieuwe Telkonst I have found another copy in the library of Trinity College, Cambridge, and have therefore been enabled to examine it at leisure. In the preface Decker remarks that, when he was professor of geometry and arithmetic, he noticed the great fear and dislike evinced towards the arts that involved long calculations, and, being very anxious to find a remedy for this, he carefully studied every new mathematical work on its appearance, and amongst others Na- pier’s Canonis Logarithmorum Mirifici Descriptio. This book (which Vlacq translated for him, as he was ignorant of Latin) pleased him exceedingly; but he saw that it was unsuitable for the general public. Soon after, Vlacq called his attention to and trauslated for him Napier’s Rabdologiat, which completely realized his desires. ‘The announcement contained in it about the other method of logarithms (viz. the adoption of the decimal base) led him to procure from England Briggs’s Arithmetica and Gunter’s Table of smes and tangents. ‘These pleased him so much and * Even if a copy with a “ privilége ” were produced, it would not afford a very satisfactory decision. Decker and Henrion may very well divide the honour. + Nothing shows better the fear with which arithmetical calculations were regarded than the eagerness with which the Rabdologia was welcomed. I have seen an Italian translation by Locatello, Verona, 1623, and an edi- tion by Ursinus, 1623 (not 1723 as given by Rogg), as well as references to two or three others (in booksellers’ lists), besides subsequent English editions. 902 Mr. J.W.L. Glaisher’s Supplementary Remarks were so unknown in Holland, that he determined to publish them all in Dutch, “incited thereto by the accomplished Adriaen Vlack, with the promise that he would not spare help nor labour till the completion of the work.” Decker then explains the ar- rangement of his work, viz. that it is to consist of two parts, of which the first (that under notice) contains the Rabdologia and. some developments of his own on commercial arithmetic; he. then gives a few details about the translation, and some advice about the construction of the instruments required in the Rab- dologia. After this follows a semi-apology for the use of Greek letters in the diagram of the Board in the Local Arithmetic, which he extenuates by pointing out that any other marks would do as well; and the preface concludes with an exhortation to the reader to wait with patience till the Tweede Deel is ready. ~ Decker’s own interest-tables are decimal, and Stevinus’s tract La Disme is appended in Dutch (De Thiende*). Apart from the mention of Vlacq and the interest attaching to Decker as one of the first who appreciated the invention of logarithms, his book is of value in reference to the spread of decimal arithmetic. On the whole he seems to have been an intelligent and useful worker, and one who merited more than he has received. I may mention that I have examined all the books published on logarithms during the twenty years following the first an- nouncement by Napier in 1614 that are to be found in the h- braries in the British Museum, the Royal Society, the Cambridge University, the Greenwich Observatory, and other institutions, and have thus been enabled to form from inspection a nearly complete bibliography of the works on the subject that appeared during this period. There are only five or six books or editions that I have not yet succeeded in seeing; so that the formation of a perfect bibliography for the time in question will probably be not nearly so difficult a matter as one would @ priori suppose. The Oxford libraries ought to be rich in books on the subjectt, as Briggs was Professor there, and the Bodleian possesses most of his manuscripts. ‘There are also several valuable mathema- tical libraries at present under arrangement, which will be pro- bably accessible for research within a reasonable time; so that the mathematical historian or bibliographer in England will soon be placed in a much improved position with regard to sources of information. * Whether this famous tract first appeared in French or Dutch I do not know. De Morgan speaks of a French edition, La Disme, 1585; and I have a Dutch edition of the same date (De Thiende, Leyden, 1585) before me as [ write. + On referring to the Catalogue of the Bodleian Library (1843), I find the collection of early logarithmic Tables there is by no means remarkably good. on some early Logarithmic Tables. 503 I have therefore hopes of being able to make my list nearly complete. A good deal of research and trouble has been devoted to the subject by the German bibliographers ; but, for want of the direct evidence derived from inspection of the books (the ma- jority being English, and no doubt even less common in Ger- many than here), they have been frequently led into error by the maccurate descriptions given in the second-hand sources whence they have been obliged to derive their information. There is no account which is not very inaccurate in its details. I will only refer here to one error that is universal. Hutton says that on Briggs’s return to London in 1617 “he printed the first thou- sand logarithms to eight places of figures, besides the index, under the title of Logarithmorum Chilias Prima.” This is the first publication of Briggian logarithms, and is therefore of historical importance; but no one seems to have seen the book itself; and Hutton’s statement has been quoted by every subsequent writer without verification. There is, however, a copy in the British Museum; and the Table contains the logarithms of the first thousand numbers to fourteen decimals. The whole forms a small octavo tract of sixteen pages, and has neither author’s name, place, nor date*. There is a brief preface, con- taining the often quoted remark that at is to be hoped that Na- pler’s posthumous work will explain why the logarithms are dif- ferent from those in the Canon Mirificus; and it concludes with the motto “In tenui, sed non tenuis fructusve laborve.”? Dodson does not mention this tract. Ward, in his ‘ Lives of the Pro- fessors of Gresham College,’ 1740, incorrectly says that it was printed in 1617, as appears by the titlepage. Wutton’s account is inaccurate as noted above; and De Morgan never saw the book and gives no account, while the foreign bibliographers rarely mention it. There has also been some difficulty about the date ; the facts are :—that Sir Henry Bourchier wrote on Dec. 6, 1617, to Dr. Ushert, “Our kind friend, Mr. Briggs, hath lately published a supplement to the most excellent Tables of logarithms, which I presume he has sent to you ;” but as Na- pier’s posthumous works are spoken of m the preface, while his death did not take place till April 3, 1618, it has been supposed that some incomplete copies may have been circulated in 1617, but that the real date of publication was 1618. Ward notices the difficulty; and Hutton regarded 1618 as the true date; Rogg also assigns 1618. Nearly all the writers before Hutton either knew nothing about the book, or confounded it with * No doubt one reason why the tract has been seen by so few is that in the Museum Catalogue, instead of being entered under “ Briggs,” 1617, it appears only under “ Logarithms,” with the date “[1695 as + Quoted by Ward, ‘ Lives of the Gresham Professors,’ p. 122. 504 Mr. J. W. L. Glaisher’s Supplementary Remarks Wright’s English translation of the Canon Mirificus in 1616. The statement, however, given on the authority of Mr. Mark Napier (in his ‘Memoirs of John Napier of Merchiston, 1834), that Napier died on April 4, 1617, explains the matter, and shows that the publication did take place in 1617. The other facts also agree: in 1614 Napier published the Canon Mi- rificus ; Briggs visited him at Merchiston in 1615 and 1616, and intended to pay a third visit in the summer of 1617 to show him his work. Dodson says that Briggs’s logar- ithms were published with Gunter’s Canon Triangulorum in 1620; and in the only copy of Briggs (or Gunter) that I have been able to see, the two are bound up together. It is not un- likely that Gunter did issue Briggs’s Chilias with his Canon ; and if so, the copies were most likely originally printed in 1617, and were not reprints. Henrion mentions that he received Briggs’s Chilias with Gunter’s Canon; but as both the Latin and English editions of the latter appear in the Bodleian Cata- logue, it is not worth while discussing a question so easy to set at rest. With reference to the relations between Napier and Briggs, with regard to the invention of decimal logarithms, it seems, after reading the facts, hard to believe that they could have formed matter for controversy. The statements of Napier and Briggs both agree in al] particulars; and the warmest friendship subsisted between them. Napier at his death left his manuscripts to Briggs ; and all the writings of the latter show the greatest reverence for him. Hutton, though stating the facts correctly, has unfortunately imputed to Napier want of candour, a charge which the evidence he adduces in no way justifies. Mr. Mark Napier, in his ‘“‘ Memoirs,” referred to above, has successfully refuted this imputation, but he has fallen into the opposite extreme of extra- vagantly eulogizing Napier and depreciating Briggs; he attri- butes Hutton’s assertions to national jealousy! Mr. Napier’s book, though published nearly forty years ago, has not been much referred to; and it is scarcely to be expected that many will care to pick out from a quarto volume of 534 pages of dif- fuse writing the slight additional matter it contains. Hutton’s history of logarithms is generally accurate and truthful; and it is a matter of regret that he should have systematically inter- preted Briggs’s remarks in a manner clearly contrary to their true meaning, and the more so as there unquestionably existed between the inventor of logarithms and his friend an attachment almost unique in science. Hutton’s account has now remained the standard work of reference for nearly a century, and his views have been adopted in a more or less modified form by De- lambre and Montucla; so that it will be long before the simple on some early Logarithmic Tables. 505 facts will become generally known apart from Hutton’s gloss*. One copy of the Canon Mirificus of 1614 that I have seen, viz. that in the Greenwich Observatory Library, is without the final Admonitio, in which Napier apologizes for any errors that may have crept into the Tables on the ground of his health and the work having been done all by himself, &c.; and there is no pos- sibility of its having been torn out, as in other copies it is printed on the back of the last page of the Tablest. Mr. Mark Napier mentions in a note that he has seen such a copy; but in the text he assumes Briggs to have had one with the Admonitio. There are signs that Hutton had not seen this Admonitio. I have col- lected together the few statements in Napier, Briggs, &c. that bear upon the invention of decimal logarithms, but refrain from publishing them till I have completed the bibhography of the period, so as incidentally to reproduce as few errors as possible ; but the most important quotations on the matter are to be found in Hutton. It is scarcely necessary to mention that in the note on p. 296 of * Since this was written, Mr. Sang, of Edinburgh, has circulated some specimen pages of his proposed nine-figure logarithmic Table, in which he states that ‘‘ John Nepair, the illustrious inventor of logarithms, having computed trigonometrical Tables according to that particular system which bears his name, perceived and announced the far greater advantages to be derived from the Denary system. He carefully explained the process to ve followed, and delegated the actual calculation to his friend Henry Briggs, of the University of Oxford.” This certainly conveys an incorrect impression. Briggs’s own words on the title-page of the Arithmetica, 1624 (I quote the English translation of 1631), are:—‘‘ These numbers were first invented by the most excellent John Neper, Baron of Marchiston ; and the same were transformed and the foundation and use of them illus- trated with his approbation [ex ejusdem sententia] by Henry Briggs.” Elsewhere Briggs states that when he suggested the advantage of decimal logarithms to Napier, the latter told him he had already thought of them, and pointed out a slight improvement (viz. that the characteristics of num- bers greater than unity should be positive, instead of negative as Briggs pro- posed). Briggs was a distinguished mathematician and not a mere computor. Decimal logarithms doubtless occurred to Napier and Briggs independ- ent'y ; but it was the latter who developed the idea and formed the Tables ; and that he would have done so even it he had never visited or corresponded with Napier, there is good reason to believe. The statement that Napier *‘ carefully explained the process to be fcllowed,”’ is supported by no evi- dence. That Napier did give Briggs assistance is likely enough ; and the probability is increased by the fact that Briggs’s method of calculation differs very little from that explained in Napier’s Constructio; but such as- sistance must have been given privately, if at all, as Briggs’s Chilias appeared in 1617, and Napier’s Constructio not till 1619; Briggs also was quite mathematician enough to have been able to investigate the method of com- puting logarithms for himself after reading the Descriptio. I may men- tion that Briggs, though Professor at Oxford towards the close of his life, was educated at Cambridge. + Of four other copies of the Canon Mirificus of 1614 that I have seen, three have the Admonitio, and the other has the last page torn out. 506 Dr. E. J. Mills on Elective Attraction. my former paper, 1820 is amisprint for 1620. With reference to the remark of Norwood about Vlacq’s work, quoted in the note on p. 801, I may add that I have since seen the first edi- tion, 1631, and the third, 1656, in both of which the passage in question occurs in the “‘ advertisement to the Reader.” It has occurred to me that Norwood’s remark was intended to apply rather to the prefixed Trigonometry &c. than to the Tables; and if this is the case, there is some justification for it. Trinity College, Cambridge. October 17, 1872. LXI. Researches on Elective Attraction. By Kpmunpv J. Mitts, D.Sc.* ** Jamne vides igitur magni primordia rerum Referre, in quali sint ordine queeque locata, Et commista quibus dent motus accipiantque.” Lucretius. pee following experiments had their origin in an attempt to prepare nitrylic chloride by the action of phosphorie oxy- chloride on plumbie nitrate. The reaction between these two bodies takes place, according to the common statement}, m ac- cordance with the fcllowing symbolic expression :— 3 Pb (NO®)?+ 2 POCI? = Pb? (PO*)? + 6 NO? Cl. Among other modes of verifying this equation, the examina- tion of the residue left behind when excess of the oxychloride is heated with the nitrate and then distilled off in a current of dry air was resorted to as the most simple and obvious. The results were found not to agree with the equation; and after three nitrates had been tried, a law of chemical attraction became evi- dent, rendering the reaction worthy of pursuit for its own sake, although as a practical source of nitrylic chloride it had failed entirely. The nature and mode of establishment of this law constitute the subject of the present memoir. When a nitrate is treated with phosphoric oxychloride as already described, the residue contains a chloride and a phos- phate,—the latter being probably always phosphorylic phosphate (PO . PO*) or phosphoric pentoxide. The ratio between these products is sensibly constant, and will be designated by a special symbol, in accordance with the following understanding :— weight of chlorine Cl weight of chlorine : 4#= Weight of phosphoric oxide weight of phosphoric oxide. P2085 * Communicated by the Author. + Compare Watts’s ‘ Dictionary of Chemistry,’ vol. iv. p. 77. 406. Dr. E. J. Mills on Elective Attraction. 507 The nitrates to which this particular method of determining chemical activity applies must, as necessary conditions, be capable of perfect desiccation and actually amenable to the influence of the oxychloride. It was also advisable to exclude the nitrates derived from ammonia, amines, and amides, inasmuch as the employment of these would have rendered indispensable a pre- liminary inquiry into the phosphamides—bodies whose formule are for the most part at present unknown, but which would almost certainly occur, and have to be quantitatively determined in a mixture already sufficiently complex. Omitting baric nitrate, upon which, when it is dry, phosphoric oxychloride is without action, there appears, then, reason to believe that « can be satisfactorily valued in eight instances only. Apparatus.—The preparation of a supply of air free from every trace of moisture is a well-known difficulty which has seldom been very satisfactorily overcome. For the purpose of these experiments an apparatus was eventually constructed which was found to answer every requirement. Seven glass vessels were filled to about one third of their capacity with pumice free from chlorine and supersaturated with oil of vitriol, and were connected with caoutcheuc tubing both to each other and a gas-holder contaiming air. A wash-bottle containing oil of vitriol was added to these, to serve as a timne-indicator; and the arrangement terminated with a long tube containing phosphoric followed by baric oxide. The volume of the air contained in this apparatus was at least four times as great as was required in any individual experiment. By closing it at both ends for twenty-four hours, the whole of the internal moisture would be removed ; and on admitting asmall stream from the gas-holder, it seemed highly probable that dry air only would leave the ap- paratus, even during the course of an entire operation. The next portion consisted of a narrow inverted U-tube, which was followed by the ‘ reaction-tube,” wherein the chemical pro- cess was actually carried out. The latter, which had the shape of an ordinary “ Liebig’s drying-tube ” (the body of which held about 7 cubic centims.), was used also for weighing the neces- sary materials, during which operation it was closed with a glass stopper and a caoutchouc fastening ; in the process its body was immersed in an oil-of-vitriol bath, the heat of which could be regulated at pleasure. By means of a perforated cork, an in- clined condensing-tube, about a foot long, was next attached. This was narrowed at the further extremity, so as to enter a small receiver, from which a tubulus, in its turn, carried the gaseous products of the reaction into a vessel containing lime. Materials.—Details respecting individual nitrates will be alluded to more especially hereafter. However carefully pre- 508 Dr. E. J. Mills on Elective Attraction. pared, even with hydric nitrate distilled without ebullition, they were all found to contain iron, a circumstance which points to the existence of a ferric oxide volatile with the vapours of that nitrate. Hence it was necessary that they should all be fused, dissolved, filtered, and evaporated to dryness. When ordinary “pure nitric acid”? was employed in their preparation, some sulphate was invariably found, doubtless owing to the known fact that hydric nitrate in large excess prevents the precipitation of baric sulphate, thereby rendering the impurity less easy of detection. The phosphoric oxychloride was prepared, according to Gerhardt’s recommendation, by the action of hydric oxalate, dried at 90°, on phosphoric chloride. By carrying out the pro- cess in a large flask having a long neck closed with a watch- glass, and adding oxalate in slight excess, a highly satisfactory yield was produced. The oxychloride had next to be purified from hydric chloride (with which it was saturated) by three dis- tillations ; on again distilling and collecting the last fourth of the distillate apart, a pure product was generally attained. This was secured in stoppered bottles holding each about 30 cubic centims., which were preserved under a desiccator containing lime and oil of vitriol; when about 24 cubic centims. had been removed from any particular bottle, it was judged expedient to reject the remainder, on account of the accumulated error due to repeated contact with common air. A chlorine determination was made in each portion to be actually employed, the adoption or rejection of which was decided on the basis of the evidence thus procured. The product was colourless and did not fume in the air. In the first experiments, not only the nitrate, but the oxy- chloride was weighed. It was soon evident, however, that the eye can easily form an adequate estimate of the sufficiency of such an excess of oxychloride as was here required; and as, owing to the occasional commencement of action in the tube at the ordinary temperature, the weighing could not be generally performed with accuracy, it was afterwards dispensed with altogether. ‘The amount of oxychloride taken was always more than enough to cover the nitrate. The course of the actual performance of the reaction will be apparent from the details above given. The followimg experi- ments, however, to which all that succeed bear a substantial re- semblance, are inserted asa proof of the efficiency of the general arrangements. (1) 1-93800 grm. plumbic chloride mixed with 5:1351 grms. phosphoric oxychloride and gradually heated to 127°5 in the dry air-current for 17 hour, increased in weight by 0027 grm. =00°19 per cent. Dr. BE. J. Mills on Elective Attraction. 509 (2) 0°7086 grm. sodic chloride with 4°5103 grms. phosphoric oxychloride, heated as before to 120°°5, gave an increase of ‘0007 grm.=00-09 per cent. (3) 08274 grm. potassic chloride and 3°5664 grms. oxychlo- ride, heated for 1 hour to 127°°5, increased by ‘0016 grm.= 00°19 per cent. (4) 1:9680 grm. phosphoric pentoxide was gradually heated in the air-current to 148° during one hour, and increased ‘0002 grm.="O1 per cent. ; and this, after mixture with a considerable quantity of two combined preparations of oxychloride and slow heating for ? hour to 145°1in the air-current, increased by ‘0114 grm.=00°59 per cent. (5) 1°3018 grm. baric nitrate, heated with an unweighed excess of oxychloride to 123° during 1+ hour, acquired ‘0006 grm.=00°05 per cent. The residue contained an infinitesimal trace of chlorine. I now proceed to the description of individual reactions. Argentic Nitrate. The ordinary commercial salt not unfrequently contains copper and some sulphate derived from the incompletely puri- fied hydric nitrate employed in its preparation. The salt actually used in these experiments was made by precipitating argentic chloride from the commercial nitrate, washing repeatedly with hot aqueous sodic acetate, and reducing the chloride by fusion with a mixture of sodic carbonate and chloride. The silver so obtained was dissolved in specially prepared commercial hydric nitrate containing but little sulphate; and the solution, after evaporation to dryness, was fused and crystallized from alcohol. In this way all the ferric nitrate was decomposed and removed simultaneously with the argentic sulphate. Desiccation and crystallization from water completed the purifying process. This nitrate, as was the case with each of its successors, was first reduced to a powder of moderate fineness; it was then dried at 180° and allowed to remain for some time to cool over oil of vitriol. When brought into contact with the oxychloride, there was a slight increase of temperature; and chemical action was indicated by the now dead-white appearance of the nitrate, the orange coloration of the oxychloride, and the evolution of minute bubbles of gas. At about 40° the action was evidently a maxi- mum, and a tawny gas of rapidly deepening colour came off freely, smelling of aqua regia, and capable of reddening and afterwards bleaching litmus. At this time also numerous light flakes were observed floating in the oxychloride. At about 71° ‘the reaction had apparently terminated; no more coloured gas was expelled, and the liquid resumed its ordinary appearance. 510 Dr. E. J. Mills on Elective Attraction. Between 100° and 110° the latter distilled over almost entirely. If the temperature were raised much beyond this point, it was noticed that,at some part of the interval 118°-125°,a little orange- coloured gas would be eliminated. The bare occurrence of this secondary reaction could not always be avoided. A short time after the last drop of the distillate had volatilized under the con- tinued influence of the heated air-current, the bath was removed and the apparatus was cooled, washed externally, dried, detached, closed up, and weighed. The average duration of the operation was 12 hour. The “ residue” had a pale orange colour. When cold water was added to it, a varying amount of heat was evolved, it being observed that this evolution was greatest when the consumption of nitrate had been greatest, and when conse- quently the effect of the action of water on the phosphoric pent- oxide was least masked by conversion into work of solution. The addition of water, moreover, immediately changed the orange tint of the residue into a white ; and the aqueous wash- ings always reddened litmus powerfully*. The analytical treatment of the residues presented no features of special interest T. Ee II. Argentic nitrate | | 9.o5¢¢ 2-1746 employed ...... Residue obtained..| 2°8098| 2-1800 Temperature ......| 125° 121° | Composition of the residue, viz. :— Argentic nitratet, 64°02 40°77 Argentic chloride! 31-78 | 49-77 Phosphoric oxide) 4°30 9°47 10010 100-01 Hence the values } | of a are respec- 7°32 5:21 GIVELY oc Joost III. 10519 | 1-0589 122° 25°96 61-91 12-93 100-80 | EV: Ww Vi WI. 2°76833 | 2°0152| 1:8878| 2-4959 2:7345 | 2°0182| 1:°8631) 2-4529 120° 115° 115° 118° | 57°87 54°78 53°57 47-13 | 36-44 38°03 40°31 46-09 6°60 8:23 7-02 8°49 100-91 |101-:04 |100-90 101-71 5°47 4°58 5°69 3°38 The mean of these numbers is 5°48; probable error 0-21. * This latter remark holds true for all the nitrates alluded to sub- sequently. + The composition of the residue is expressed in percentages throughout this paper, except in the case of lithic nitrate. This has been done partly for the sake of uniformity, partly for showing sensible aberrations in cer- tain reactions; it need not be remarked that the experimental error in ana- lyses of this kind falls considerably within the common departure of the totals from 100. { Calculated from the original nitrate on the basis of the ehleride found. Dr. E. J. Mills on Elective Attraction. 511 Plumbic Nitrate. A specimen of plumbic nitrate obtained by three crystalliza- tions of a commercial sample (the mother-liquor being rejected at each operation) was found to be sufficiently pure. By evapo- ration with hydric sulphate it appeared to contain 62°61 per cent. lead, theory requiring 62°55 per cent. On account of the tena- city with which this salt retains a small percentage of water, even at 100°, it was powdered finely and heated in an air-bath to 180°-185° during an interval varying from eighteen to forty- two hours. The reaction-tube generally received its supply of nitrate at the latter temperature, after which it was closed im- mediately and cooled. On bringing the oxychloride and nitrate together, some slight commencement of action was usually perceptible in the cold. At 60° the liquid became turbid and acquired an orange colour ; at 82° a gas was evolved closely resembling chlorine in smell and appearance, but of too light a colour to contain much nitric peroxide. At 100°, however, the tint of the gas had become a deep orange; and at 115° some phosphoric oxychloride emerged from the apparatus, having hitherto been retained, doubtless, by the nitrate, just as water 1s retained, above its puint of ebullition. Hence it was necessary to heat the residue to a higher degree than was required in the case of the silver-salt—an operation which, it was found, could be carried out with safety below 162°. Above this temperature a secondary and different reaction is speedily accomplished. The average time employed in one ex- periment was about 1? hour. The residue had a faint yellow tint, and did not, for the most part, become heated in contact with cold water. But it was several times observed that, when the water reached the exit end of the body of the reaction-tube, considerable heat was produced—an evident indication that the phosphoric oxide had wholly, or almost wholly, collected in that spot. For analysis, the contents of the tube were transferred to a beaker, and heated for twelve hours with aqueous and hydric nitrate. The argentic chloride so formed was weighed in the usual manner, aud calculated as plumbic chloride; the filtrate from it, after addition of ammonia until a precipitate began to form, was treated with ammonic hydrosulphide; and after pro- longed repose, the final filtrate was precipitated with magnesia mixture. The experiments exhibit a varying discrepancy, owing, as is probable, to the action of that portion of the oxychloride which was expelled at 115°, and which, being no longer in excess of the 512 Dr. E. J. Mills on Elective Attraction. nitrate, nor confined to its due distilling-point (below 110°), would be likely to affect a converse transformation. I. II. III. IV. V. Plumbic nitrate employed...| {2°7727 | 3°9558 | 2°7015 | 3°4883 | 3:1795 Residue obtained ............ 2:7945 | 4:0138 | 2°7472 | 35477 | 3-2260 Memiperaturesasscesocceescts 3: 125° 137° 131°°5 130° 130° Composition of the residue, viz. :— Plumbic chloride ......... 10°76 10:69 12°65 8-1] 11:07 Phosphoric oxide ......... 2-02 167 2-63 1:98 2-20 Plumbic nitrate .........00 80-41 87-29 83:38 88-67 85°37 99:19 | 99-05 98°66 98°76 98°64 eee tee Se SS ee EEE SS eS ee eee The values of ware ........- 5°44 6:17 4-9} 4°18 5°14 The mean is 5°17; probable error 0°19. Were the equation 3Pb (NO®)2-+ 2 POCI?= Pb? /PO4)?+ 6NO2 Cl true, under the experimental conditions, the residue would con- tain no chlorine, it would be neutral to wet litmus, and, in any case, would weigh less than the original nitrate (for a total attack, 0°8534 of the nitrate). The above results, however, agree with neither of these suppositions. Thallous Nitrate. The thallous nitrate employed was free from sulphate and thallic salt; 1:2045 grm. of it yielded 1:1858 grm. sulphate = 94°30 per cent. (theoretically 94°72 per ceut.). For experi- ment it was dried for several hours at 156° and cooled in the desiccator. Phosphoric oxychloride hardly acted on thallous nitrate in the cold; but at 45° a yellow coloration was observed, which became red at 71°-75°, with turbidity. At 75°-80° the maximum change occurred, and a gas, having the unmistakable colour of nitric peroxide, was given off freely. Soon afterwards the reac- tion ceased. It was noticed, however, that on raising the tem- perature to 116°-118°:5, a very small quantity of a greenish gas was evolved, apparently chlorine. Each operation occupied rather more than an hour. The residue had a very pale yellow tint with a white border, and on the addition of water disengaged heat. Its aqueous solution gave a brown precipitate with am- monia. The course of analysis differed in no respect from that pursued in the case of the lead salt. Dr. E. J. Mills on Elective Attraction. 513 I Li, Thallous nitrate taken ............... 1:8993 2:14381 RCSTGHEN ee oe Rte oe oa 2-0870 2:4041 SPEMIPETAGUEE: sccccseecducens cgsaavies ee 118°-5 116°°5 Composition of the residue,viz. :— Bhallie dichloride jo2.5 ..c04acasi0ses 37°77 42-01 Phosphoric Gxide.7. 02.2. s. and iti Pate Ae, 5 (Qi ones es the expression for the energy of elective attraction in terms of specific heat. Comparing the coefficients («, a!) for any two nitrates, the following relations are obtained :— tt __ im Ses. Boe m >! as Where m=m! and v=w', we have the simple expression The following instances may be adduced in verification of the latter case :— GAMCHSSIC SURO) 1:17 by the methed of ratios ‘a (sodic nitrate) y ? —— =1'17 by specific heat ; ejithallous witrale) 2a Gotha ha ane nana # (argentic nitrate) _ 1483 0942 In the case of the other nitrates, which require the previous formula, I find the verification to be equally satisfactory. If the reader should desire to perform the calculation, he will observe that »=38 for plumbic nitrate, and x=4 for the other nitrates ; >s=25-00. (6) The experimental values of « lie between the limits in- = 1-538 by specific heat. Dr, E. J. Mills on Elective Attraction. 525 dicated by the following equations, the bracketed portions indi- cating potential (probably not actual) substances :— a=6:0 6MNO?+2POCP=6 MCl-+ P? 0° +3[N? 0°], a=15 6MNO?48POCF=6MC1+44P? 0°+6[NOCI]. By taking the first equation a times and the second 6 times, the elective coefficients may be reconciled with the whole num- bers required by common chemical equations. The value of M in the silver group, when «=6:0, would be 125°5, and for «=1°5 an analogue of lithium would have the symbolic value 4 nearly. (7) That the intensity of elective attraction is proportional to symbolic value, is written explicitly upon every page of the history of chemistry. I shall merely draw attention to a few out of hundreds of examples that might be adduced to cor- roborate the correctness of the law, and the fact that chemists have long unconsciously been guided by its results. When argentic nitrate is added to a dilute aqueous solution of potassic iodide, bromide, and chloride (these salts having been mixed in any proportion), argentic iodide, bromide, and chloride are successively precipitated, that is, in the order of their symbolic values. Argentic chloride may be wholly con- verted into bromide by digestion with aqueous potassic bromide ; and argentic bromide is completely transformable into iodide by aqueous potassic iodide. ‘These comparisons are extremely fair of their kind. The comparison of hot free chlorine with iodine weakened by combination with silver is of course not a fair com- parison. In the formation of salts, baryta has the preference over strontia, and strontia over lime. In the fractional separation of the volatile members of the fatty series C, Ho, O2 by Liebig’s process, the law is strictly ob- served, excepting inthe case where n=2, which is an intelligible anomaly. Heintz’s method of separating the non-volatile mem- bers of the same series by means of magnesia exhibits the same order. In a mixture of the hydrocarbons C, Hon_¢, benzol is the last to be chlorinated or nitrated. Warington has shown the superiority of ferric over aluminic oxide as an absorber of alkalies in soils. In cases of jaundice, taurocholic acid is destroyed in the sys- tem before glycocholic acid. It was the aim of the distinguished Bergman to unite all che- mical substances in a series according to the principle of elective attraction. A great part of his life was passed in experimenting qualitatively with a view to that purpose; and he left on record 526 Mr. A. S. Davis on Recurrent Vision. an earnest desire that numerical elective coefficients might one day be obtained. I submit to chemists the method of ratios as one out of several means of accomplishing that end. The work which Bergman commenced, and which has been now so long intermitted, may honourably occupy and well be concluded in our own time. It will have its results in a registration of actual or dynamic equivalents, and in the reform of a symbolic system which is every day becoming more disparate from experiment. My best thanks are due to Sir C. Taylor, Bart., for the use of his laboratory. LXII. On Recurrent Vision. By A. 8. Davis, M_A* Sees following curious phenomenon has not, I believe, been noticed before. If the end of a piece of charcoal be made red-hot in a flame and then waved about in the dark so as to describe an ellipse or circle a few inches in diameter, a blue image of the burning end is seen following the charcoal ata short distance behind it. The space between the charcoal and its blue image is as dark as the surrounding space. The phe- nomenon is much better seen if the charcoal be made bright by being blown upon. ‘The interval of time at which the sensation of blue light succeeds the primary sensation at any point of the retina is about a fifth of a second. This may be ascertained by noticing that when the charcoal is moved round im a circle at the rate of about 100 revolutions per minute, the blue image follows the primary image at a distance of about one third of the circumference of the circle. In seeking for an explanation of this phenomenon, it appeared probable that it was related to another phenomenon lately ob- served by Professor C. A. Young, and named by him “ recurrent vision?’ +. The phenomenon observed by Professor Young is as fol- lows :—When the objects in a room are lighted up by a spark from a powerful electric machine (care being taken to screen the eye from the direct light of the spark), it is observed that the illumination is not single, but that the objects appear to be lighted up two or three times in rapid succession. Professor Young found that the interval between two successive illumi- nations is about the fifth of a second. He also ascertained that the phenomenon is a subjective one. He does not, however, appear to have noticed whether the colour of the recurrent image ‘differs from the actual colour of the object. * Communicated by the Author. + See American Journal of Science and Art for April 1872; and Phil. Mag. for May 1872. oa - Mr. A. S. Davis on Recurrent Vision. 527 It appeared to me probable, from the experiment with the burn- ing charcoal, that there would be such a difference of colour; and the experiments I am-about to describe prove that there is. Not having a powerful electrical machine at hand, I con- trived the following apparatus for producing an instantaneous illumination, and thus exhibiting the phenomenon of recurrent vision. In a board about 35 feet long and a foot wide, at about a foot from one end of it a rectangular hole was cut 3 inches in the direction of the length of the board and 5 inches in the direction of its breadth. Upon this board another, smaller board was made to slide and act as a shutter tothe hole. In this shutter a hole was made similar to the hole in the large board, so that when the shutter was partially drawn up the two holes coincided. A strong elastic band was attached to the board and the shutter in such a manner that, when the shutter was raised, the band acted upon it to pull it down, i in the same way as that in which a bowstring acts upon anarrow. A thick rug was nailed round the edges of the board ; and when this was thrown over the head, a dark space was formed which could be momentarily illuminated by drawing up the shutter and letting it spring back. The following experiments were made :— I. The hole in the board being turned towards the objects in a room and the shutter being drawn up and let go, a recurrent image of the objects was seen; but the illumination was in general too feeble and the impression too momentary for the eye to judge of the colours of the objects. When, however, a bright coloured object was placed in a strong light, the colour of the recurrent image was seen to be different from the actual colour of the object. By gaslight or feeble daylight the recurrent image appeared twice if the object was white, or nearly white. The recurrent colour of a white object is of a blue tint. II. Various coloured glasses were placed before the aperture, and the board was turned towards the sky. With a deep-blue glass the recurrent image was a greenish ellow. With a green glass and with a yellow glass it was a reddish blue. With a single red glass, which gave an orange- red light, it was a red-blue. With two red glasses superposed, which produced a pure red light, no recurrent image was seen, however bright the light. In the case of the blue, green, and yellow slasses the effect was much better seen when the intensity of the light was mode- rated by placing against the hole, along with the glass, one or two sheets of white paper; the recurrent image was stronger compared with the primary image, and the interval of compara- tive darkness between the two images was more clearly perceived, 528 Mr. A. 8. Davis on Reeurrent Vision. when this was done. With the red glass, on the other hand, the recurrent image was only seen when the light was strong. III. When, instead of producing a momentary illumination, the shutter was raised so that the two holes coincided, and after being held for a short time was let go, the image of the hole became for an instant before disappearing of the same colour as its recurrent image; but in this case there was no interval of darkness before the change of colour took place. We may con- clude from this experiment that the induced excitation, which, when the illumination is momentary, gives rise to a recurrent image, lasts as long as the light which produces it, beginning and ending a fifth of a second after it; but being much feebler, it is only seen after the primary light has disappeared. IV. The shutter being removed, a large piece of black card- board with a hole in the canvale of ae about half an inch in dia- meter, was moved quickly about before the hole in the board. A recurrent image of the hole followed the primary image in the same way as in the experiment with the burning charcoal. When the coloured glasses were placed before the hole, the colours of the recurrent images were the same as in the previous experi- ments with the same glasses. L The complementary colours of the coloured glasses were ascer- tained by fixing small pieces of white cardboard against them and holding them up to the light. The white cardboard took by contrast the complementary colour of the glass against which it was fixed. In this way it was found that the complementar y colour of the blue glass was yellow, of the green glass a blue- red, of the yellow a blue, and of the red a blue-green. It thus appears that, with the exception of the red glass, the recurrent colour does not differ much from the complementary colour. The recurrent image given by white light is, as I have already remarked, of a blue tinge. It follows that the less saturated any colour is the bluer will be its recurrent colour; for a colour which is not saturated may be regarded as a mixture of white light and a saturated colour. This explains the fact that, though the recurrent colour of a deep-blue glass is a greenish yellow, yet the recurrent colour of a blue object sufficiently light-tinted to give a recurrent image is of a blue tinge. In fact all light-co- loured objects give a recurrent image of a more or less blue tinge; for they all differ but little from white, ‘A recurrent image of an object may also be pr oduced without any apparatus whatever. To do this, place the right hand over the eyes so that the palm of the hand covers the right eye and the fingers the left eye. If the middle finger be then raised for a moment so as to admit hght for as short a time as possible into the eye, a recurrent image of any light-coloured object held Mr. A. 8. Davis on Recurrent Vision. - i 529- against a dark baekground may be seen. The effect is much better seen by twilight or gaslight than in full daylight. The phenomenon, however, is by no means so well observed by this method as by means of a board and shutter, owing probably to the illumination of the retina not being sufficiently instan- taneous. Professor Young, in explanation of the phenomenon noticed by him, suggests the idea that a nerve-current from the eye to the brain may, on reaching the brain, suffer partial reflection back to the eye, and thence again to the brain, and thus give rise to a second sensation. It being now, however, ascer- tained that the colour of the recurrent image is entirely different from the colour of the light which produces it, this explanation appears no longer tenable. If we admit the truth of Dr. Thomas Young’s theory of colour- sensation (namely, that the sensation of light is produced by the excitation of three different kinds of nerves,—an excitation pro- duced in one kind giving rise to the sensation of blue light, in another to that of green light, and in a third to that of red light), the above experiments appear to lead to the conclusion that when any one of the three kinds of nerves is excited at any part of the retina, an excitation 1s induced in those nerves of the other kinds which have their extremities in the same part of the retina. A slight difference between the recurrent and the com- plementary colour might arise from the mutual action between two kinds of nerves, differing in intensity for different kinds of nerves. Thus the fact that the recurrent colour given by blue light is rather greener than the complementary colour of the same light, may arise from an excitation in the blue-light nerves inducing a stronger excitation in the green-light nerves than in the red-light nerves. The great difference in the case of orange-red tight be- tween the recurrent colour, which is red-blue, and the comple- mentary colour, which is sea-green,1s, I believe, explained thus. It was noticed that pure red produces no recurrent image. Hence, when orange-red light, which consists chiefly of red and partly of green light, is used, only the green component gives rise to a recurrent image. Hence the colour of the recurrent image should be the same as that obtained with the green glass. It is, however, rather redder; and this, I think, arises thus: when a red glass is used the light must be intense in order that any recurrent image may be seen; and when the light is intense it continues for a short time after the shutter 1s closed, giving rise to what is known as a persistent image. This persistent image 1s superimposed upon the recurrent image and reddens it. With any other colour, the persistent image, if there is any, is Phil. Mag. 8. 4. No. 296, Suppl. Vol. 44. 2M 530 M. Helmholtz on the Theory of Electrodynamics. so much feebler than the recurrent image that it produces no alteration in its tint. In conclusion I would remark upon the apparent analogy between the phenomenon of recurrent vision and that of in- duced currents in electricity. A nerve-current in one kind of nerves appears to induce nerve-currents in the other kinds in a manner analogous to that by which a current of electricity in one conducting wire induces currents in parallel conducting wires. Leeds Grammar School. November 9, 1872. LXIII. On the Theory of Electrodynamics. By M.Hetmuoutz*, HE theory of electrodynamic actions, besides its immediate value for the understanding of this important and prolific branch of physics, is more universally interesting in its relation to the fundamental principles of general mechanics. All the other known actions at a distance can be easily and completely reduced to attractive and repulsive forces of points of masses, while the intensity of these forces depends only on the reciprocal distances of the points and not on their motion. Moreover the hitherto known actions between molecules can either be entirely referred to such forces, or at least are so similar in their whole manner of appearance to the effects produced by gravity that we find no difficulty in imagining them the effects of forees similar in character. But the electrodynamic forces constitute an ex- ception. They form a class of distant actions produced only by the state of motion of the efficient agent, the electricity,—a state of motion which makes itself perceptible as such by a whole series of phenomena—by development of heat in solid conduc- tors, chemical decomposition in liquid conductors, &c. The real laws of the manner of appearance of these forces are, in the main, well known, and have been reduced by F. E. Neumann, Sen., to a comparatively simple expression, which, however, gives not the action of mass-poimt upon mass-point, but of one linear element of a current upon the other. I have myself given to Neumann’s expression of the potential a more general form f, in which it embraces also the differing expressions resulting from the theories of W. Weber and Maxwell for the potential of each two current-elements. For closed currents all these expressions give the same results ; on the contrary, for open ones, the actions of which have, indeed, at present been little investigated, they * Translated from the Monatsbericht der Kon. Preuss. Akad. d. Wis- senschaften zu Berlin for April 1872. ¥ Journal fir reine und angewandte Mathematik, vol. 1xxii. M. Helmholtz on the Theory of Electrodynamics. 581 exhibit differences. The plan of my memoir was principally to seek out those differences which it might be possible to discover by prac- ticable experiments. It must here be remarked that the various potential-expressions which I formed differ from one another only by a constant (in my memoir, denoted by k). We obtain Neu- mann’s expression if we put k= +1, Maxwell’sif k=0, W. We- ber’sifk=—1. The investigation showed that the expressions with & negative led to impossible consequences—namely, to an unstable equilibrium of the electricity in conductors, which, once disturbed, might give rise to infinitely great current-intensities and unlimited charges. On the other hand, the expressions with & positive, or with k=0, gave stable equilibrium, and, even for open currents, only such differences as, with our present ex- perimental means, can hardly be detected; so that what is yet doubtful in the mathematical conception of the law, viz. the value of the constant 4, appears to have no effect in the applica- tion of it to experiment. These expressions for the potential of each two current-ele- ments, however, are manifestly not elementary expressions of the last acting forces; for they lead, if we imagine each current- element as a solid body, to at least two forces for each, or to a force and a pair of forces; and the quantity and partly the di- rection of these forces depend not merely on the situation of the elements, but also on the velocity of the electric currents. The phenomena of induction are only indirectly derived from the electrodynamic potential, through the interposition of the law of the conservation of energy. Among the further-penetrating hypotheses which seek to ascertain the elementary forces that lie at the base of electrody- namic phenomena, two especially must be mentioned. Mr. Clerk-Maxwell drops the assumption of action ata distance, and assumes that all magnetic, electrostatic, and electrodynamic actions are translated to a distance by the propagation of mole- cular motions and forces in an elastic medium which fills space. As the theory finally gives for this medium the capability of executing oscillations which are perfectly similar to those of light and have also the velocity of propagation of light, this medium must be identified with the luminiferous ether. It is true that, for the reciprocal action of neighbouring volume-elements of this medium, he assumes laws considerably different from those of the elastic bodies known to us; but he has shown that a kind of reciprocal action, such as he attributes to the ether, can indeed be produced by a mechanical combination of solid elastic bodies. For this purpose a system of cells with elastic walls and cylin- drical cavities must be taken, in which elastic balls can rotate and be flattened out by the centrifugal force. In the walls of 2M2 532 M. Helmholtz on the Theory of Electrodynamics. the cells there must be other balls, of invariable volume, as fric- tion rollers. These would rotate freely; but their centres of gravity, im insulating media, would merely be displaced by elastic yielding of the cell-wall; in conducting media, on the contrary, at every displacement they must suffer a resistance similar to friction in a viscous liquid. ‘The transference of motion between these balls would be effected only through the adhesion of their surfaces to one another. Displacement of the last- mentioned balls gives dielectric polarization of the medium ; streaming of the same, an electric current; rotation of the elastic balls corresponds to the magnetizing of the medium, the axis of rotation being the direction of the magnetic force. Now, although the idea of such a molecular structure of the space-filling ether may be repugnant to our imagination as too artificial, yet the hypothesis of Maxwell appears to me very im- portant on this account—because it proves that there is nothing in electrodynamic phenomena to compel us to attribute them to an entirely anomalous sort of natural forces, to forces depending not merely on the situation of the masses in question, but also on their motion. Indeed, out of the assumption of those reac- tions of the volume-elements of the zther upon each other which Mr. Maxwell has assumed, a complete and mathematically very elegant theory of all electric phenomena (magnetic, electro- dynamic, and induction) can be developed; and the same theory also gives an account of the phenomena of light. On the other hand, M. Weber’s theory derives the explana- tion of electrodynamic actions from distant forces of a peculiar kind, acting between the points of the electrical masses, and de- pending simultaneously on the distances and the relative motions and accelerations of each pair of points. It gives comparatively simple explanations of electrodynamic attractions and of the induction-effects in linear conductors; and its analytic deduc- tions accord perfectly, for all the phenomena to be observed in closed linear currents, with the consequences of the potential- law derived by F. EK. Neumann from the phenomena. On this account, Weber’s theory (which preceded Maxwell’s) was very favourably received, especially by the German physicists. It had, and moreover retains, decidedly the merit of every acute and original thought which endeavours to strike out new paths in science when the old ones appear to lead into an inextri- cable thicket. I hardly need here remark that the value of such an attempt, if it was sufficient for the state of knowledge at the time, is not diminished when, after twenty-five years’ progress of science, the impossibility is shown of carrying it out. Even then such an attempt has not been fruitless. A reconnaissance of unknown ground lying beside the road hitherto kept, if car- [| "2.1 ee M. Helmholtz on the Theory of Electrodynamics. 538 ried out carefully and intelligently, retains its value even if it should only teach that no way exists except the high road. It was through Weber’s hypothesis that a question of the highest significance for the principles of natural science was for the first time tested in the problems of facts, viz. whether ele- mentary forces, incapable of further analysis, must be assumed dependent not merely on the position, but also on the motion of the acting points. In my work ‘ On the Conservation of Force,’ I had stated that forces which depend only on the distance and the velocities, and therefore only on the coordinates of the points, and on their first differential quotient, must necessarily infringe the universal natural law of the conservation of energy, which law proves everywhere true also in electrodynamic phenomena. At that time, however, I had not considered this still more com- plicated case set up by the Weberian law, in which the forces depend on the coordinates and on the first and second differen- tial quotients ; and this case is certainly compatible with a some- what extended form of the law of the conservation of energy. If we, as has always hitherto been done, name vis viva or actual energy the sum of the moved inert masses multiplied each by half the square of its velocity, then, in the usual form of the law, ‘the quantity which I have called quantity of tension-force, and the English physicists potential energy, is a function of the coor- dinates of the moved points only ; and the law of the conserva- tion of energy affirms that the sum of the actual and potential energy remains constant in every motion of a mass-system not influenced from without. If, however, under the action of external forces a self-repeating eyclical process takes place, at the end of which all the points of the system have exactly the same position, and the whole the same vis viva, as at the beginning, the sum of the work received from without and the work given out must be equal to zero, so that by no repetition of the process can work be permanently gained or destroyed. Ifthe former were the case, there would be possible a perpetually continuous gain of work without a pro- gressive alteration of the mass-system, and a perpetuum mobile might be constructed. Weber’s extension of the law of energy makes also the value of the potential energy a function not merely of the position, but also of the velocities of the mass-points. Under this assumption also, by no cyclical process which brings back not merely all the masses of the system to their initial positions, but also each one to its initial velocity, can more work be given out than is re- ceived from without, because those quantities of actual and po- tential energy which constitute the measure of the work are the same at the end of every such cyclical process as at the beginning. 584 M. Helmholtz on the Theory of Electrodynamics. - ~ Under these circumstances, however, the values of the forces must necessarily contain second differential quotients of the co-. ordinates, because the sum of the force-components correspond- ing to the individual points and axes of coordinates, each mul- tiplied by the corresponding component of the velocity, must be equal to the differential quotient of the potential energy, taken according to the time; and the latter, under the condition pre- supposed, necessarily contains also the second differential quo- tients of the coordinates according to the time. In relation to complete cyclical processes, M. W. Weber* has proved that his assumption concerning the value of the electric forces admits no production of work without a corresponding expenditure of forces capable of producing it. In another place, applications which I endeavoured to make of the differential equations deduced by Kirchhoff from Weber’s assumption had led me to the discovery that they corresponded toa state of unstable equilibrium of the electricity in conductors, and that, according to them, currents might be developed which would lead to infinite current-imtensities and infinite electric densities. Replies by MM. W. Weber and C. Neumann have induced me to resume and generalize these investigations, the results of which 1 will here briefiy lay before the Academy. If we have any number, however great, of mass-points, the inert mass of which may be denoted by yp, and all or some of which contain quanta of electricity, which, measured according to electrostatic measure, may be denoted by e,—if, further, 7m is the distance between the points n and m, and gq, the resulting velocity of the point 2, Sn, the angle which it makes with the direction of the line r,,,, prolonged beyond n, then the value (1) of the electrostatic potential P25 Cn» =. lnm (2) of the electrodynamic potential je 2 ae Ea In « Yq «£08 (Sam) « £05(Sm) Vnm We put, further, the quantity eee i em } Pa= oy, py |= cos (Sra) ’ mam * < Electrodynamische Maassbestimmungen, insbesondere tber das Princip der Erhaltung der Energie,” Adh. d. math.-phys. Classe der Konigl. Sdchsischen Ges. der Wissenschaften, 1871. The value of the potential was given by the same author in Pogg. Ann. 1848, vol. Ixxiii. p. 229. 1 The investigation will be published entire in the Journal fir reine und angewandte Mathematik. M. Helmholtz on the Theory of Electrodynamics. 585 and let V denote the potential energy of the remaining forces which act upon the inert masses; then the equation which, in Weber’s sense, expresses the conservation of the force becomes LS [(u,—Pye,)@2] + P+ V—Q= const. The sum here occurring, which occupies the place of the vis viva, and which shall be denoted by L, differs from the ordinary form of this expression by the necessarily positive squares of g, being not merely multiplied by the necessarily positive inert masses Hm, but, instead of the latter, the differences (u,—énp,) entering as coefficients of the squares. These differences, however, may become negative, since p» can at all events be reduced to what even Weber and C. Neumann regarded as an extraordi+ narily little inert mass of the electrical quantum e,, while the quantity »,, a function formed after the manner of potential functions, may proceed from as great electrical masses as we please. If, now, eng > pp, the point e, would possess a quasi ne- gative mass. Acceleration of its motion would correspond to a diminution of the vis viva. If the vis viva L consisted of a num- ber of positive and negative terms of this kind, it might con- serve an unchanged final value while its negative and its positive terms alike augmented ad infinitum. These relations are represented most simply when only one of the masses ~ is supposed to be in motion, and the rest spread over and adherent to a spherical surface surrounding the mass (perhaps the surface of an insulator). Then p and P become constants independent of the position of the point w in the sphere; further, Q=0; and the equation reduces itself to 4 (u—ep)g?+ V=const. If, now, the quantum of the electricity on the sphere is great enough, so that ep >, then g? and V must increase and diminish together. If w moves in a direction opposite to the force repre- sented by V, V augments and the velocity g must increase. If, on the contrary, 4 moves in the direction of the force, the velocity di- minishes. If w movesin a prescribed path against a force which constantly resists it (for example, against friction), its velocity must increase continually and ad infinitum, with which produc- tion of heat ad infinitum would be connected. If in its course the mass impinges again and again continually against a greater inert elastic mass, it will drive this onward, and at each impact increase its own velocity, so as to make the next collision more forcible. This would evidently give a perpetuum mobile. It may here be remarked that, if the linear dimensions of the spherical electric Jayer be increased n-fold, but the density be preserved unaltered, the quantity p will be augmented to x times 5386 M. Helmholtz on the Theory of Electrodynamics. as much ; so that we can make it as great as we please, in spite of continually increasing distance of the acting mass. We have here, therefore, by no means to do with actions at molecular distances, but with distant actions of the Weberian forces. The case I previously indicated, in which the mass ym attains infinite velocity, rests on the fact that this must always happen as often as, under the action of an accelerating force, it arrives at any place where the coefficient (~—ype) representing the mass becomes =O, because the mass zero receives infinite acceleration from a finite force. Besides, in the present memoir, I have shown that neither is it necessarily at molecular distances that this takes place, nor does it require an infinite initial velocity, if only sufficiently large electrical masses are chosen, and if upon the whole path of the two masses an exterior force acts which impels them towards each other and is powerful enough to over- come their electrostatic repulsion. The objections raised by W. Weber against one of the physi- cally impossible consequences which, in my earlier memoir, are deduced from his theory are thus removed. In his most recent electrodynamic researches, M. C. Neu- mann has expressed his concurrence in Weber’s objections, and, for his own part, has endeavoured to remove from the theory the deficiencies pointed out by me, in that he has imtroduced an alteration into Weber’s expression for very small distances. From what has just been said it is evident that such an altera- tion cannot obviate the physical impossibilities mentioned. Also, for electric currents, no introduction of molecular pro- cesses, motions, or forces can get rid of the unstable equili- brium, because when the dimensions are increased n-fold and the electric densities unchanged the work-equivalent of the mole- cular processes increases only as n°, but that of the potentials as n* or n°, according to whether they proceed from surfaces or spaces; so that the latter, if they represent a quantity of work which is smaller than in the resting equilibrium of elec- tricity, always obtain the preponderance with a sufficient aug- mentation. When everywhere equal quanta of positive and negative electricity move in opposite directions, the quantities Pn vanish, but the electrodynamic potential (—Q) may become less than zero. That sucha distribution of electric densities and currents may occur has been shown in my eazlier memoir, quite independently of the differential equations which regulate the course of the currents. Given a current-distribution which represents a less quantity of work than that of electric equilibrium, such a flow can only by the application of exterior work be brought to rest, and must otherwise, by withdrawal of work, such as takes place Royal Society. 537 by the development of heat in conductors, be augmented ad in- jinitum. In this manner an example makes clear how important it is that the analytical expression of the vis viva should contain only positive terms; and that this condition is not fulfilled by the action at a distanee of Weber’s law is here exhibited as the last cause of the physically impossible consequences to-which it leads. These, at all events, cannot be removed without very bold new auxiliary hypotheses, which must not only vary the actions at molecular, but also those at greater distances. In conclusion I have, in the present memoir, endeavoured to clear up the doubts expressed by M. J. Bertrand* respect- ing the structure of the differential equations of the motion of electricity. LXIV. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 473.] June 20, 1872.—Sir James Paget, Bart., D.C.L., Vice-President, in the Chair. (THE following communication was read :— «On the Spectrum of Nitrogen.”’ By Arthur Schuster, Stu- dent at the Physical Laboratory of Owens College. 1. Introductory.—The formation of the different spectra which one gas is said to exhibit, when examined under different conditions, still remains one of the most obscure points of spectrum analysis. In 1864, when Plucker and Hittorf published their researches ‘“*On the Spectra of Ignited Gases and Vapours, with especial regard to the different Spectra of the same elementary gaseous substance’’}, they drew attention to the close resemblance in character of the band- spectra which certain metals yield at a comparatively low tempe- rature to the band-spectrum of nitrogen and sulphur. Roscoe and Clifton, in their paper ‘On the effect of increased Temperature upon the nature of the Light emitted by the Vapour of certain Metals or Metallic Compounds”’ f, rendered it probable that the band-spectra of the metals belonged really to the oxides. ‘The two spectra of nitrogen were not, however, examined from that point of view, but, on the contrary, they were made the starting-point of new investiga- tions by Willner, who came to the conclusion,that certain gases may give even more than two different spectra. Angstrém§, expressing his doubts about the trustworthiness of Wiillner’s experiments, says in a note: “As regards the spectra which are usually attributed to nitrogen, I mention here, as a general fact, that it is my conviction that the fluted bands which are so characteristic of the oxides of metals are never found in spectra of elementary gases.” I propose to show, in the present communication, (1) that pure * Comptes Rendus de l’ Acad. des Sciences, vol. Ixxiil. p. 968. t Philosophical Transactions, vol. cly. p. 1. ¢ Chemical News, vol. y. p. 233, § Comptes Rendus, Aug. 1871, 538. Royal Society :— nitrogen gives only one spectrum; (2) that this is the lme-spec- trum; (3) that the fluted spectrum of the first order is due to oxides of nitrogen, formed under the influence of the electric spark. 2. Lirst experiment.—The first experiment which I made with. respect to the spectrum of nitrogen, was a repetition of an experi-. ment of Secchi, who found that in different sections of the same tube three different spectra of nitrogen might be obtained. A vacuum-tube was made exactly according to Secchi’s description, filled with nitrogen and exhausted. To my astonishment the tube showed, even in its widest parts, only a spectrum of lmes. No accu- rate measurements were taken at the time, but the spectrum was no doubt that of the second order described by Pliicker. Suddenly, and while I was looking through the spectroscope, the spectrum changed, and the well-known finted bands appeared. The first spectrum could now easily be obtained by introducing a Leyden jar in the. circuit. The spark very soon ceased to pass, and it was then found. that the tube was leaking. 3. The behaviour of this tube at once suggested the idea that the presence of air was necessary for the formation of the fluted spec- trum. It is well known that the oxides of nitrogen are formed on passing the electric spark through air, and the resemblance which this spectrum bears to the spectra of the oxides of metals rendered this view probable. In order to test it, a series of experiments were made, showing that,-— | ~ (a) Whenever the fluted spectrum appeared, it could be shown that traces of oxygen were present ; (b) Whenever there.was a certainty of no oxygen being present, the spectrum of the second order appeared under all pressures and in all temperatures. In order to free the nitrogen from every trace of oxygen, I adopted, at Dr. Stewart’s suggestion, the plan of heating a small piece of sodium placed in the vacuum-tube. This proved in each case per- _ fectly satisfactory ; for when every trace of oxygen had thus been absorbed, the line-spectrum alone was invariably obtained*. 4. Wave-length of the two spectra.—There is no possibility of confounding the two spectra. ‘The fluted spectrum is well known by its beautifully shaded violet bands; but in order to exclude any possibility of error, their position was read off on the reflecting scale of the spectroscope ; the measurements were reduced to wave-lengths, and the following numbers obtained for the least refrangible end of the bands in tenth metres +:— Fluted Spectrum. (Ae RE Te 5129 4436 4981 4390 4649 4318 4556 4237 * The formation of the fluted spectrum does not imply that all the nitrogen in the tube has been oxidized ; it has been remarked by different observers, and espe- cially noticed by Plicker, that when the spark passes through a mixture of two gases, the spectrum of one only is often seen. t A-tenth metre, according to "Angstrém, means a metre divided by 10, — Mr. A. Schuster on the Spectrum of Nitrogen. 539 - As the measurements were taken merely for the sake of reference, they do not lay claim to great accuracy. The true spectrum of nitrogen is easily recognized by a very bright green line followed at a small “distance towards the more refrangible parts by a green band ; it also contains some violet bands, which are not shaded. The position of the principal lines was read off; their wave-lengths, as determined by Dr. Marshall Watts from the measure- ments made by Plucker, are as follows:— Line-spectrum. 6243 5767 4214 ae 6176 5666 4199 6087 5164 (thegreenline) 4184 Bawa 6051 4894 diva ‘ 5908 4644 5. Description of apparatus.—The tubes generally used had two pockets, A and B, into which small pieces of metallic sodium were introduced by means of the tubes C and D. The tube C was con- nected with the receiver containing the mitrogen, whilst the tube D was connected with the air-pump. The nitrogen was generally pre- pared by the combustion of phosphorus in air. After'a few hours’ standing, when all the phosphoric acid formed had been absorbed, the gas became quite clear and was ready for use. This mode of pre- paration, it is true, does not give the nitrogen very pure ; but as my object was to get the nitrogen free from oxygen, and this was easily obtained by means of the absorption by sodium, the method was found sufficient. Other modes of preparing the nitrogen were tried, such as passing air over red-hot copper or the decomposition of ammonia by chlorine, but the same results were invariably obtained. The air-pump used was that of Carré’s freezing-machine, with which pressures down to 2 millims. could be easily obtained. When the pressure was measured, a J-shaped tube was employed, one side of which was connected with the Geissler’s tube, the other with the pump, while the mercury was drawn up in the longer part of the tube ; its height was read off and compared with a barometer. I now pass to the description of the experiments. 6. Method of experimenting.—When the air in the vacuum-tube had been exhausted, the communication with the receiver containing the nitrogen was opened, and the gas was allowed to pass through it for some time while the pump was being worked. ‘The tubing con- necting the tube with the receiver was then clamped air- tight, and the tube was exhausted. 540 Royal Society. The electric spark in passing through it exhibited a violet colour, and gave the spectrum of fluted bands : 5129 4436 4981 4390 4649 4318 4556 4237 The sodium was next heated until it presented a clean metallic surface. The light which the tube now emitted was bluish white, and much fainter than before; and the whole appearance of the spectrum had changed to that of the second order with its characteristic green line. It was, however, found that the pressure in the tube had slightly increased, owing most likely to the vapour of the sodium present ; and on bringing the mercury to its former level, the spec- trum became brighter, but remained the same in character. New nitrogen was then led into the tube, and after exhaustion the old fluted spectrum again appeared; this was, however, at once changed into that of lines by heating the sodium. This process was repeated several times in succession, but invariably with the same result. I have in my possession two tubes sealed off under 2 millims. pressure, one without sodium, showing the fluted bands, the other containing sodium, showing the spectrum of lines. Two other tubes, sealed off under 15 millims. pressure, show the same thing. I have repeatedly convinced myself that, from the highest pressure under which the spark of the induction-coil passes to the lowest pressure which I could obtain with an ordinary air-pump, pure nitrogen invariably gave one and the same line-spectrum. Once, when I intended to seal a tube off under higher pressures, it was found that the sodium was not sufficient to absorb all the oxygen present, so that a sort of mixture of the two spectra was seen. Such a mixture was often observed by Plicker and Wiillner at the point where one spectrum changed into the other; it is characterized by the green line of nitrogen and the fluted violet bands at the same time. » The tube showing the mixture at 15 millims. pressure was gradu- ally exhausted, but the spectrum remained exactly the same. If the formation of the two spectra depends merely upon the pressure or temperature to which the gas is subjected, how can a mixture of the two spectra, indicating a state of transition, exist under so entirely different pressures and different temperature? In order to ascertain whether nitrogen even carefully prepared contains oxygen, a drop of a solution of iodide of potassium and starch was introduced into the tube ; after the spark had passed for a few seconds only, the liquid was coloured blue—showing either the formation of oxides of nitrogen or of ozone, but at any rate the presence of oxygen. 7. Spectrum of oxides of nitrogen.—I tried to obtain the spectra of the different oxides of nitrogen; they all give the same fluted spectrum, and I could get no information as to which particular oxide the fluted spectrum is due: thisis, however, easily understood if we remember that it is just as difficult to prepare the oxides of nitrogen Geological Society. 541 free from oxygen as pure nitrogen itself; so that the oxide giving the spectrum in question will always be formed. I have, however, con- vinced myself that the absorption-bands of nitrous acid gas are not coincident with the bright bands of the spectrum ; and it is probable that the spectrum is due to nitric oxide, this being the most stable of all the oxides of nitrogen. I may add that one of the tubes containing the sodium and show- ing the lines one day cracked, and then at once showed the violet bands. This fact will not be easily explained by the assumption that the fluted spectrum belongs toa lower pressure and lower temperature than the spectrum of lines. I propose to subject the different spectra of the remaining gases to a careful examination. The above experiments were made in the Physical Laboratory of Owens College, Manchester ; and I have to thank Professors Balfour Stewart and Roscoe for many valuable suggestions. | GEOLOGICAL SOCIETY. [Continued from p. 476. ] May 8, 1872.—Joseph Prestwich, Esq., F.R.S., in the Chair. The following communications were read :— 1. “ Notes on Atolls or Lagoon-islands.” By 8. J. Whitnell, Esq. The author commenced by indicating certain facts which lead him to think that the areas of atolls are not at present sinking, and referred to one instance (that of Funafuti or Ellice Island) in which he thought there were signs of a slight upward movement. He noticed the occurrence of a furrowed appearance, or a series of ridges or mounds, in some islands, each of which he regarded as produced by a single gale. He also described a freshwater lagoon, about three miles in diameter, as occurring in the island of Quiros. 2. “On the Glacial Phenomena of the Yorkshire Uplands.” By J. R. Dakyns, Esq. The author stated that in Derbyshire and Yorkshire, south of the Aire, there is no glacial drift on the eastern slope of the Pennine chain, except where it is broken through by the valleys of the Wye and of the Aire and Calder, The basin of the Aire and the country northward are thickly covered with drift, which contains no rocks foreign to the basin, and thus points to formation by local action. The author ascribed this to the glaciation of the country in part by glaciers, and in part by a general ice-sheet. Evidence of the latter he finds in the fact that drift occurs only on one side of the valleys— namely, on the lee-side of the hills with respect to the source of the drift materials. Traces of the action of glaciers are:—the great amount of scratched and rounded pebbles in the mounds of drift, which in- creases in proportion to the distance from their source ; the presence of great piles of drift at the junctions of valleys, as if by the shedding of the lateral moraines of two glaciers ; and the existence of mounds of pebbles and of an alluvial deposit wherever a rock-basin crosses a 542 Geological Society. valley. The Kamés or Eskers, which are frequent in the valleys, he ascribed to the deposition of moraines in the sea instead of on land. 3. “On a Sea-coast Section of Boulder-clay in Cheshire.” By D. Mackintosh, Esq., F.G.S. The principal object of the author was to draw attention to the fact of the occurrence of numerous sea-shells in a lower boulder- clay at Dawpool as thoroughly glacial in its appearance, structure, ’ and composition as any clay to be met with along the shores of the Irish Sea, and differing in no essential respect from the Pinel, which runs up the slopes and valleys of the Lake District. He pointed out a number of very important distinctions between the Lower and Upper Boulder-clays of Cheshire, referring especially to the light grey or blue facings of the fractures of the latter. He gave a list of a number of large boulders, greenstone and Criffell granite predo- minating, though among the smaller stones Silurian grit was most prevalent. The author likewise explained the mode of striation of the stones found in the clay, and the positions they occupied in re- ference to their flattened surfaces. The paper was illustrated by samples of the two clays, a number of shells in various states of preservation, and about forty specimens (most of them named and their parentage assigned) of Silurian grit and argillite, greenstone, several varieties of felstone and porphyry, felspathic breccia, Criffell and Eskdale granites, and granites of un- known parentage, Wastdale or Ennesdale syenite, quartz, Carboni- ferous Limestone, chalk-flints (?), local gypsum, sandstone, &e. In a letter, Mr. Searles V. Wood, Jun., stated that he regarded the Boulder-clay containing the shells as later than the newest of the East-Anglian beds, and the Upper clay as probably equivalent to the Hessle clay. The fragmentary shells sent had been determined by Mr. J. Gwyn Jeffreys, who found’ eleven species represented among them, and stated that they agreed with the shells from Moel-Tryfaen and Mac- clesfield. He remarked especially on the occurrence of Astarte borealis, a species now extinct in the British area. 4, “On Modern Glacial Action in Canada” (second article). By the Rev. William Bleasdell, M.A. In this paper the author communicated some facts illustrative of the action of ice in Canada, in continuation of a former paper. Fid- lar’s Island, in the rapids of the river Trent (flowing into the head of Lake Ontario), has been removed within the last eighteen months. Patrick’s Island, a mile lower down, is also rapidly dis- appearing. Salmon Island, in the Bay of Quinte, between Amherst Island and the mainland, which had an area of about an acre fifty years ago, has disappeared, leaving a shoal with about 4 feet of water over it; and three neighbouring islets, known as the Brothers, are in course of removal. The removal of these islands is due to the action of drift-ice. The author also referred to the formation of ground-ice in the Canadian rivers. Rey. O. Fisher on the Origin of Phosphatic Nodules. 548 May 22, 1872.—Prof. Morris, V.P., in the Chair. The following communication was read :— ‘On the Phosphatic Nodules of the Cretaceous Rock of Cam- bridgeshire.” By the Rey. O. Fisher, M.A., F.G.S. This paper contained an attempt to explain the origin of the phosphatic nodules which lie in a thin bed at the base of the Chalk in Cambridgeshire and are largely extracted, by washing the stratum, for the purpose of making superphosphate of hme. Two hundred and seventy tons per acre, at the rate of fifty shillings a ton, represents the valuable yield of the deposit, which is followed to the depth of about 18 feet. The nodules and other fossils of the bed are chiefly derivative, forming a concentrated accumulation from a deposit belonging to the Lower Cretaceous period. Some of the fossils, however, are believed to be indigenous to the deposit. Plicatule are attached to all the derivative fossils and nodules; and the sharp broken surfaces of the latter, with Plicatule on them, show that they were mineralized before they were deposited in their present gisement. The green grains of chlorite have been drifted into patches. Certain calcareous organisms are preserved ; but many genera of mollusks only occur as casts in phosphate of lime. The deposition of the phosphatic matter has been determined by animal substances. ‘There are two chief varieties of the ‘ ordinary” no- dules. The first are amorphous, or else finger-shaped; the second formed lke a long cake rolled, partially or wholly, upon a stick. The surface of these two kinds of nodules is coriaceous and wrinkled ; and they usually show marks of attachment to some foreign body. Certain species, clearly zoophytes, are converted into phosphatic nodules; and when sections are made of these, they are found to show under the microscope structures and spicula allied to those of Aleyonaria. Slices of the common nodules show similar spicula, and occasionally reticular structure. When casts in plaster are made from Alcyonium digitatum, and coloured to resemble the nodules, the similarity in general form and structure of surface is very striking. The phosphate was probably segregated by the animal matter from its solution in water charged with carbonic acid, which is a known solvent of the phosphate; an analysis of the matrix has proved that phosphate of lime is appreciably present in it. The author doubted the derivation of the nodules from the denuda- tion of the subjacent Gault, and exhibited a collection of these to show that they were distineuished by more stunted growth. The deposit was on the whole considered to represent the thin band with similar fossils at the base of the Chloritic Marl, as seen in the west of England, in which district it is underlain by the true arenaceous Greensand. The absence of the true Greensand was attributed to the intervention of the old paleeozoic axis of the London area; and it was finally suggested that a similar axis might stretch from Leicestershire to Harwich, causing the change in character of the Lower Cretaceous beds between Cambridgeshire and Norfolk. [ 544 ] LXY. Intelligence and Miscellaneous Articles. ON THE ABSORPTION OF OZONE BY WATER. BY L. CARUS*., ZONE has generally been considered insoluble in water. Mean- while M. Soret has announced its absorption by that liquid; yet hitherto nothing positive is known on the subject. It is easy to ascertain that water into which ozonized air or oxygen has been made to pass exhibits all its reactions: it decom- poses iodide of potassium, decolours indigo and the sunflower, colours blue the tincture of guaiacum, transforms the protoxides of thallium, manganese, and lead into peroxides; by its action on silver one sometimes even succeeds in determining the formation of the peroxide of that metal. The author has, besides, proved that this water contains neither oxygenated water nor nitrous acid, either free or combined with ammonia, the presence of which might haye explained at least a part of these reactions. The power of absorption of ozone in water cannot be determined with precision, because we can only operate on mixtures in which that gas is only in a very small and never very constant proportion. In his experiments, the author produced ozone by Soret’s method —that is to say, by electrolysis of sulphuric acid spread out and kept at the temperature of zero C. In these conditions the proportion of ozone in the gas, determined by the decomposition of iodide of potas- sium, was found in two trials to be 0°93 and 1°21 volume per cent., supposing this gas to havea density equal to # of that of oxygen. The gas was caused to pass during from two to three hours into water kept between 2° and 4°; it was then submitted to analysis, and was found to contain per litre, in three experiments :— 0-0109 gramme of ozone, or 5°11 cub. centims. 0°0094 = pa 4-24 = 0:0083 - 3 3:86 p The author likewise analyzed the ozonized water supplied by the works of MM. Krebs, Kroll & Co., of Berlin, for medical uses. He found in it from 4:06 to 4°45 cubic centims. of ozone per litre; it, too, contained neither oxygenated water, nor nitrous or nitric acid.— Bibl. Univ., Arch. des Sciences, vol. xliv. p. 348. ON THE HEAT OF EXPANSION OF SOLID BODIES. BY H. BUFFY. The augmentation of yolume undergone by a solid body by heating is most analogous to the extension produced by the traction of a weight. Moreover one is naturally induced to seek the quantity ~ of the pressure, or of the force of extension, exerted by heat upon the unit of surface. ‘The solution of this question can be found, if we have, besides the coefficient of expansion of a body, its coefficient of traction, both referred to the unit of volume. Now the coefficient of traction of a certain number of bodies in the direction of their length is known; but the extensibility and com- * Berichte der deutschen chemischen Gesellschaft, 1872, p. 520. + Pogg. Ann. vol. exly. p. 626, lead Intelligence and Miscellaneous Articles. 545 pressibility of the unit of volume have hitherto been but little studied. It is true, however, that Wertheim has demonstrated, or at least has shown it to be very probable, that for homogeneous bodies the coefficients of cubic extension or compression are the same as those of linear extension or compression. He has, moreover, shown that this opinion was confirmed by M. Regnault’s experiments on the compressibility of copper, of brass, and of glass. Probability is also in favour of the accuracy of Wertheim’s law. For if the two coefficients of extensibility, linear and cubic, were not the same, this ought also to be the case with the two coefiicients of elasticity ; and it would follow that the velocity of propagation of sound is not the same in a rod anda ball, both of the same substance and perfectly homogeneous in all directions. It being, then, admitted that the two coefficients of extensibility are equal, the coefficient of cubic extensibility of iron, for example, referred to the millimetre as unit of length, isa =0°0000481. That is to say, a cube of iron of 1 cub. centim., drawn normal to its six faces by a force of extension of 1 kilom. per square millimetre, has its volume increased (:0000481 cubic centimetre. The coefficient of cubic dilatation of iron between O° and 100° is, for 1° C., 8=0:0000350. Gold? ie one 0:0001791 0:0000466 18°035 0°0324 1-899 Platinum .... 0°0000628 0-0000265 21:166 9°0324 0°920 Wieade es. eae ae 0°-0005634 0°0000854 11°165 0:°0314 5-800 Glass. 0°0001451 0:0000262 27446 - 0-17 703 es Water at 16°... 0°0045854 0°0001600 0:999 1:0000 3810 The numbers under 2d give the quantity of heat become latent, expressed in ten-thousandths of the total heat absorbed. his por- tion is only a very small aliquot part of the total heat absorbed—and that not only for solid bodies, but also for water. We can thus ex- plain to ourselves why all endeavours to raise the temperature of a solid body by compression have hitherto been vain. Wealso under- stand why the latent heat of extension exerts so little influence on the specific heat of the atoms of solid bodies.— Bibliotheque Universelle, Archives des Sciences Piys. et Nat. vol. xliv. pp. 341-8344. EXPERIMENTS ON COLLISION WITH BALLS OF DIFFERENT METALS. BY H. SCHNEEBELI*, In a previous communication on the collision of elastic bodies ¢ I have investigated the conditions of collision in one and the same substance placed i in different conditions. The substance employed was steel as hard as glass. which is elastic to the highest degree. I determined qualitatively in what proportion the duration of the impact depended on the mass, the ney and the height of fall of the striking body. * Pogg. Ann. vol. exly. p. 328. Tt See Phil. Mag., Dec. 1872, p. 4/6. Intelligence and Miscellaneous Articles. 547 In the present note I communicate the results I have obtained for collision with balls of different metals. The method of experimenting was the same as that which I described in my previons memoir. The weight of each of the balls was the same ; and they fell from the same height upon the flat and well-polished face, as hard as glass, of a solid cylinder of steel. The balls not all having the same radius, it would be necessary to make a correction in order to render the conditions equal, since the duration of the impact depends on the curvature of the surface. From the results which have been stated elsewhere, it follows that this cor- rection would be very small (lead and zinc, 23 per cent.), and that in all cases it may be neglected by the side of the other causes of error presented by these metals when the limit of elasticity is exceeded. In fact, even with very small heights of fall, such as those which I employed (about 10 millims.), the softest metals undergo a slight permanent deformation, which complicates the result. To render the experiments comparable with each other, I always caused the balls to strike with a fresh portion of their surface. I commenced by investigating the influence which might be exerted upon the deflection of the magnetized needle by the thermo- electric current produced by the contact of heterogeneous metals at different temperatures. When the ball was put in prolonged con- tact with the surface of collision connected, like it, with a galva- nometer, a slight difference of temperature (such as that resulting from the heating of the hand) sufficed to give the needle an oscillation of 100°. But when the ball only remained on the surface of contact during the shock, there was no perceptible current, even when it rebounded as many as ten times in succession on the plane surface of the steel. Nevertheless, in order to demonstrate clearly that no thermo- electric current affected the experiments, the ball was heated to about 200° before making it strike. Even in this case there was nothing perceptible at the galvanometer, although the shocks suc- ceeded each other rapidly. The experiments with the heated silver ball were repeated after the insertion of a hydroelectric element in the circuit: it is evident that the duration of the collision was then augmented by the heating of the ball; but the greater deflection of the needle must not in this case be attributed to a thermoelectric current, but, as we shall see, toa diminution of the elasticity in con- sequence of the rise of temperature. For these experiments, balls first cast and then turned were employed, of the following metals: — Coefficient of Ball, elasticity, E. DICE ater rts piexatcsper 19600 Woppen Mates eae a 10500 x UNINC Pe Oe ere TOL OO raSsme eee eee nee Oo LO Po UATE i enemy redehs ts eterna) LCL) MME yn neues aie a AOU Meade We he eee ee OO 548 Intelligence and Miscellaneous Articles. I transcribe here only two of the very numerous series of experi- ments I have made, reminding the reader that all the balls fell from the same height upon the plane surface of steel. Deviation at the Galvanometer. Ball. lst series. 2nd series. DECI eee OPS) 84°2 COPPer aie cierin 94:2 115:0 DING he Sate gest aes 111°0 130°0 PASS eres wae se 110°5 A SUIVel wate cen casi: 12 130 ita eae rice ur ure 164 194 ready Sorensen 270 320 The first series were performed on the 11th, and the second on the 22nd of January. As general result we may deduce from these two series that the duration of collision increases when the coefficient of elasticity dimi- nishes. A closer connexion appears between the duration of collision and the coefficient of elasticity when we form the product of that du- ration and the square root of the coefficient of elasticity of each ball. In this way we obtain the following Table :— Series l. Series IT. Paleo ea a a VE. a, aNRB.|} Corr. a. aNKE.| Corr. Steelugece ne 140 "725 | 1OL-5|+ 0-5) -842) 117-9/+ 21 Copper ...... 102 ‘942 | 96-1]4 5:9} 1150) 117:3)/4 2-7 DATO Oh ee 933) 1110) 103:6)— 6 3012s alee Brass ........- 92-4 |1:105 | 102-1 }+ O1/ 1:27 | 117-4|/4+ 26 Silver 3.25). 84-5 | 1-12 94-6|+ 7-4] 1:30 | 110:0}+10 Anat oes aoe 63 164 | 103 |— 1 1:94} 122, te 2 MCACE eS hi as 42 |\2-70 1.118 J 3-204) eee eat Mean... 102-0 | Mean... 120-0 From this Table we are justified in concluding that, when a series of elastic bodies strike the same elastic surface, the durations of the impacts are inversely proportional to the square roots of their coeffi- cients of elasticity. All the metals operated on conform to this law with sufficient ap- proximation, except the ball of silver and that of lead. With respect to the latter, this ought not to surprise us ; for the elasticity of lead is so slight that even with our small heights of fall the limit of elasti- city is considerably exceeded. As to the silver ball, we must suppose that its coefficient of elasticity is sensibly greater than that of the substance on which the measurement of the coefficient has been made. ‘This supposition is by no means inadmissible when we con- sider the very notable divergences on this point between the results of different observers.— Bibliotheque Universelle, Archives des Sciences Phys. et Nat. vol. xliv. pp. 335-338. INDEX tro VOL. XLIV. ABNEY (Lieut.) on electrical pyro- metry, 80. Acid-manufacture, on some points in the chemistry of, 370. Acoustical experiments, note on some, pore Actino-chemistry, researches in, 104, 422. Airy (G. B.) on a supposed periodi- city m the elements of terrestrial magnetism, |41. Alcohol, on the instantaneous oxida- tion of, 237. Ammonia, on some properties of an- hydrous liquefied, 315. thracene, on the spectrum of, 346. Arsenic, on the presence of, in alkali- manufacture, 370. Atkinson (R. W.) on the atomic theory, 118. Atmospheric waves, on, 125. Atomic theory, on the, 118, 121. Attractive and repulsive forces, on the hydrodynamical theory of, 189. Aurora, on the spectrum of the, 478. Becquerel (M.) on the influence of pressure in the phenomena of en- dosmose and exosmose, 233; on some effects of slow actions, 238 ; on the duration of the electric spark, 316. -Bessel’s functions, notes on, 328. Bicyclic chuck, on a, 665. Birt (W. R.) on atmospheric waves, 125. Books, new :—Colenso and Hunter’s Introductory Algebra, 67; Pratt’s Treatise on Attractions, Laplace’s Functions, and the Figure of the Earth, 68; Symons’s British Rain- fall, 1871, 138; Proctor’s The Orbs around us, 388; Taylor’s Geometry of Conics, 390; Ley’s Laws of the Winds, 391; Ranken’s Strains in Trusses, 467. Bosanquet (R. H. M.) on the deter- mination of the relation between the energy and apparent intensity of sounds of different pitch, 381. Branly (E.) on the measurement of the intensity of currents by the electrometer, 396. Brodie (Sir B. C.) on the action of electricity on gases, 470. Buff (Prof. H.) on the heat of expan- sion of solid bodies, 544. Cailletet (L.) on the influence of pressure on the lines of the spec- trum, 76. Caoutchoue, on the action of ozone upon vulcanized, 235. Carbon, on the specific heat of, 251, 461. Carus (L.) on the absorption of ozone by water, 544. Cayley (Prof. A.) ona bicyclic chuck, 65 Cazin (A.) on the duration of the elec- tric spark, 316. Challis (Prof.) on the hydrodynamical theory of attractive and repulsive forces, 189. Chrysogen, on the absorption-spec- trum of, 347. Clausius (Prof. R.) on the mechanical theory of heat, 117; on the con- nexion of the second proposition of the mechanical theory of heat with Hamilton’s principle, 365. Cooling, on the laws of, 241, 457. Croll (J.) on the determining causes of molecular motion, 1. Crystals, on optical phenomena pro- duced by, submitted to circularly polarized light, 69. Currents, on the measurement of the 590 intensity of, by the electrometer, 396. Davis (A. 8.) on recurrent vision, 526. De la Rive (A.) on the electric jet in rarefied gases, 149. Desains (P.) on the reflection of heat, ite ; Dewar (J.) on the chemical effici- ency of sunlight, 307; on the spe- cific heat of hydrogenium, 400 ; on the specific heat of carbon at high temperatures, 461. Diffraction-gratings, on the reproduc- tion of, by photography, 392. Dispersion, on the anomalous, exhi- bited by certain substances, 395. Draper (Dr. J. W.) on the distribu- tion of heat in the spectrum, 104, 422; on the gases occluded in me- teoric iron, 31l. Earth, on the phenomena of the ele- vation and subsidence of the, 401. Edlund (E.) on the nature of electri- city, 81, 174. Elastic bodies, on the collision of, 476, 546. Elective attraction, researches on, 506. Electric jet in rarefied gases, on the, and on its mechanical force, 149. spark, on the duration of the, 316. Electrical experiment with an insu- lated room, on an, 170. pyrometry, on, 80. Electricity, on the nature of, 81,174; on wave-theories of, 210; on the action of, on gases, 4/0. Electrodynamics, on the theory of, 530. Electromagnet coil, on the maximum magnetizing force of an, 414. Electrometer, on the measurement of the intensity of currents by the, 396. Endosmose, on the influence of pres- sure m the phenomena of, 233. Exosmose, on the influence of pres- sure in the phenomena of, 233. Filter-pump, on an improved form of, 249. Fisher (Rev. O.) on the origin of the phosphatic nodules of the Chalk of Cambridgeshire, 543. Flames, on the electrical condition of gas-, 153. Forces, on the hydrodynamical theory of attractive and repulsive, 189. INDEX. Fuchsine, on the anomalous disper- sion exhibited by, 395. Gaiffe (M.) on a new galvanic pile, 320. Galvanic induction, on the pheno- mena of, 174. pile, on a new, 320. Galvanometer, on a new lantern-, 25. Galvanometers, differential, on, 161]. Gaseous pressure, on Mr. Moon’s views on, 64, 101, 219. Gases, on the cooling of, 241, 457; occluded in meteoric iron, on the, 311; on the action of electricity on, 479. Gas-flames, on the electrical condi- tion of, 153. Geological Society, proceedings of the, 146, 252, 474, 541. German silver, on the heat-conduct- ing power of, 481. Gladstone (Dr. J. H.) on the decom- position of water by zine, 73; on the action of oxygen on copper nitrate in a state of tension, 139. Glaisher (J. W. L.) on some new facts in the early history of logarithmic tables, 291, 500. Gore (G.) on some properties of liquefied anhydrous ammonia, 315. Heat, on the reflection of, 77; on the distribution of, in the spectrum, 104; on the mechanical theory of, 117, 240, 365; light, and electri- city, on wave-theories of, 210; on a method of tracing the progress and of determining the boundary of a wave of conducted, 257; of ex- pansion of solid bodies, on the, 544. Helmboltz (Prof.) on the theory of electrodynamics, 530. Holden (Lieut. E. I.) on the spec- trum of the aurora, 478. Houzeau (A.) on the imstantaneous oxidation of alcvhol, 237. Hudson (Dr. H.) on wave-theories of light, heat, and electricity, 210. Hutton (Capt. F. W.) on the pheno- mena of the elevation and subsi- dence of the surface of the earth, 401. Hydrocarbons, on the fluorescent re- latious of certain solid, 345. Hydrogenium, on the specific heat of, 400. INDEX. 551 Iceland spar, on the law of extraor- dinary refraction in, 316. Todine,onthe primary spectrum of, 156. Tron, on the heat-conducting power of, 481. Jamin (M.) on the cooling of gases, 241, 457. Lantern-galvanometer, on a new, 20. Life, on the theories of, 14. Light, on optical phenomena _pro- duced by crystals submitted to cir- eularly polarized, 69; heat, and electricity, on wave-theories of, 210; on the definition of intensity in the theory of, 304. Liquid, on the steady flow of a, 30. Logarithmic tables, on some new facts in the early history of, 291, 500. Lucas (F.) on the duration of the electric spark, 316. Magnesium, on a singular appearance of, in the chromosphere of the sun, 159, 479. Magnetism, terrestrial, on a supposed periodicity in the elements of, 141. Mallet (R.) on the origin and cosmical relations of volcanic energy, 468. Marcet (Dr. W.) on the nutrition of muscular and pulmonary tissues, 349, 443. Mayer (Prof. A. M.) on 2 new lantern- galvanometer, 25; on a method of tracing the progress and of deter- mining the boundary of a wave of conducted heat, 257 ; on acoustical experiments, 320; on a method of detecting the phases of vibration in the air surrounding a sounding body, 321. Mensbrugghe (G. van der) on super- saturated saline solutions, 229. Metals, experiments on collision with balls of different, 545. Meteoric iron from Virginia, on the gases occluded in, 311. Milis (Dr. &. J.) on elective attrac- tion, 506. Molecular motion, on the determin- ing causes of, |. Moon, on earthlight on the, 123. Moon (R.) on gaseous pressure, 101; on the definition of intensity in the theories of light and sound, 304. Morton (Prof. H.) on the fluorescent relations of certain solid hydrocar- bons, 345. Moseley (Canon) on the steady flow of a liquid, 30. Muscular tissue, on the constitution and nutrition of, in phthisis, 448. Natural selection, observations on the theory of, 19. Nitrogen, on the spectrum of, 537. Oxygen, on the action of, on copper nitrate in a state of tension, 139; on the action of electricity on, 470. Ozone, on a simple apparatus for the production of, 156; on the action of, upon vulcanized caoutchouc, 235; on the unit of, 473; on the absorption of, by water, 544. Phosphatic nodules of the Cretace- ous rock of Cambridgeshire, on the, 543. Photography, on the reproduction of diffraction-gratings by means of, 392) Phthisis, on the nutrition of muscular and pulmonary tissues when affected with disease from, 448. Pitch, on variations of, in beats, 56. Plants, on the colloid condition of, 446. Pulmonary tissue, on the constitution and nutrition of, 443. Pyrometry, on electrical, 80. Richard (M.) on the cooling of gases, 241, 457. Royal Institution, proceedings of the, 69. Royal Society, proceedings of the, Folds 223, tol lea 92) 468" oars Salet (G.) on the primary spectrum of iodine, 156. Saline solutions, on supersaturated, WLS). Sarrasin (E.) on the electric jet in rarefied gases, 149. Sehneebeh (H.) on the collision of elastic bodies, 476, 546. Schuster (A.) on the spectrum of ni- trogen, 537. . Schwendler (4.) on differential galva- nowmeters, LOL. Shaler (Prof. N. 8.) on earthlight on , the moon, 123. Smith (1. A.) on some points in the chemistry of acid-manuiacture, 370. Soret (J. L.) on the anomalous dis- persion exhibited by certain sub- stances, 395. Sound, on the definition of intensity in the theories of light and, 304. 092 Sounding body, on a method of de- tecting the phases of vibration im the air surrounding a, 321. Sounds of different pitch, on the re- lation between the energy and ap- parent intensity of, 381. Spectroscopic reversion-telescope, un the, 417. Spectrum, on the influence of pres- sure on the lines of the, 76; on the distribution of heat in the, 104; on the distribution of chemical foree in the, 422. Spottiswoode (Dr. W.) on optical phenomena produced by crystals submitted to circularly polarized light, 69. Stokes (Prof.) on the law of extraordi- nary refraction in Iceland spar, 316. Strutt (the Hon. J. W.) on Mr. Moon’s views on gaseous pressure, 64, 101; on the law of gaseous pressure, 219; on Bessel’s func- tions, 328; on the reproduction of diffraction-gratings by photo- graphy, 392. Sun, on a singular appearance of magnesium in the chromosphere of the, 159, 479. Sunlight, on the chemical efficiency of, 307. Tacchini (M.) on a singular appear- ance of magnesium in the chromo- sphere of the sun, 159, 479. Tait (Prof.) on the dynamical theory of heat, 240. Taylor (S.) on variations of pitch in beats, 56. INDEX. Thorpe (T. E.) on an improved form of filter-pump, 249. Tissues, on the nutrition of muscular and pulmonary, 349, 443. Tomlmson (C.) on supersaturated saline solutions, 223. Tribe (A.) on the decomposition of water by zinc, 73; on the atomic theory, 121; on the action of oxy- gen on copper nitrate in a state of tension, 139. Trowbridge (Prof. J.) on the electrical condition of gas-flames, 153. Vision, on recurrent, 526. Voleanic energy, on the origin and cosmical relations of, 468. Water, on the decomposition of, by zinc in conjunction with a more negative metal, 73. Webb (F. C.) on an electrical experi- ment with an insulated room, 170. 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Price % THREE THOUSAND GUINEAS. y person wishing to become practically acquainted with the interesting and important of MINERALOGY and GEOLOGY will find this a good opportunity to obtain an five and valuable Geological Museum scientifically arranged, the specimens having llected with care and at great expense during the last thirty years. entary Geological Collections at 2, 5, 10, 20, 50, to 100 guineas each, and uisite to assist those commencing the study of this interesting branch of Science, wledge of which affords so much pleasure to the traveller in all parts of the world. . collection for Five Guineas, to illustrate the recent works on Geology, by Ansted, and, Lyell, Mantell, Murchison, Page, Phillips, and others, contains 200 specimens. lain Mahogany Cabinet, with five trays, comprising the following specimens, viz. : RALS which are either the components of Rocks, or occasionally imbedded in Quartz, Agate, Chalcedony, Jasper, Garnet, Zeolite, Hornblende, Augite, Asbestos, par, Mica, Talc, Tourmaline, Spinel, Zircon, Corundum, Lapis Lazuli, Calcite, Fluor, lite, Barytes, Strontianite, Salt, Sulphur, Plumbago, Bitumen, &c. Ative Murats, or Meratiirerovs Minerats; these are found in masses or beds, in 8, and occasionally in the beds of rivers. Specimens of the following Metallic Ores are n the Oabinet :—TIron, Manganese, Lead, Tin, Zinc, Copper, Antimony, Silver, Gold, inum, Mercury, Titanium, &c. KS: Granite, Gneiss, Mica-slate, Clay-slate, Porphyry, Serpentine, Sandstones, Lime- asalt, Lavas, &c. . £oz01¢ Fossrus from the Cambrian, Silurian, Devonian, Carboniferous, and Permian OnDARY Fossits from the Rhatic, Lias, Oolite, Wealden, and Cretaceous Groups. TARY Fossizs from the Plastic Clay, London Clay, Crag, &c. € more expensive collections some of the specimens are rare, and all more select, LES TENNANT, Mineralogist (by appointment) to Her Majesty, 149 Strand, London, W.C. August 1872. CONTENTS or N° 291.— Fourth Series. X. On the Nature of Electricity. By M. E. Eptunp...... page 81 XI. Reply to some Remarks of the Hon. J. W. Strutt on Gaseous Pressure. By Rosert Moon, M.A., Honorary Fellow of Queen’s Gollege, Cambridge 22% 2... 0.25. os. cae. 2s en 2 ter 101 XII. Researches in Actino-Chemistry.—Memoir First. On the Distribution of Heat in the Spectrum. By Joan Witiiam Draper, M.D., LL.D., President of the Faculties of Science and of Medicine in the University of New York. (Witha Plate.). .............. 104 XIII. A necessary Correction of one of Mr. Tait’s Remarks. By R. Cuavsivs ..... datGerecn ss Tes XIV. The Atoinics Theory in SRG to ie Wren ae R. W. ArRinson; F.Ci6.0 5 2 oe oe wine Ua ale 118 XV. Remarks on the alleged ambiguity, insufficiency, and unne- cessariness of the Atomic Theory. By Atrrep TRIBE .......... 121 XVI. Earthlight on the Moon. By N.S. Suater, Professor of Paleontology, Harvard University .. Sega as D2 XVII. A Contribution to our Raagledee of "Anoop Wares By W. R. Birt, F.R.A.S., F.M.S.. : 125 XVIII. Notices respecting New Dok oprah Rane ‘187 ‘ By Gc Je OV MONS 9 foe eka nie ae eit cele ae 4 wae iae $ oniee tee LOS XIX. Proceedings of Learned Societies :— Roya Society :—Dr. J. H. Guanstone and Mr. A. Tripe on the Action of Oxygen on Copper Nitrate in a state of Tension; The Astronomer Royat ona supposed Periodicity in the ele- ments of ‘Terrestrial Magnetism, with a period of 261 days. 139-145 GEOLOGICAL SOCIETY ........ 0% 8 b\s's, 5.076 oes ee 146-149 XX. Intelligence and Miscellaneous Articles :-— Researches on the Electric Jet in Rarefied Gases, and in particular on its Mechanical Force, by MM. A. de la Rive and E. Sar- PASM © sack co 8 cave wie ela 8 Wis lane Ge hoe On ee . 149 On the Electrical Condition of Gas-flames, by John Trowbridge, Assistant Professor of Physics °.:.. 3... {0-226 a .aeeeeene 1538 On the Primary Spectrum of Iodine, by M. G. Salet ...... Be, NEG On a simple Apparatus for the production of Ozone with Elec- tricity of High Tension, by Professor Arthur W. 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SEPTEMBER 1872. _ LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Sold by Longmans, Green, Reader and Dyer; Kent and -Co.; Simpkin, Marshall and Co. ; and Whittaker and Co. ;—and by A. and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam, Printers and Publishers to the University of London. 1 New York :—and Asher and Co., Berlin. ROYAL SCHOOL OF MINES. DEPARTMENT OF SCIENCE AND ART. During the Twenty-second Session, 1872-73, which will commence on the lst of October, the followmg COURSES of LECTURES and PRACTICAL DEMONSTRATIONS will be given :— . Chemistry. By E. Frankland, Ph.D., F.R.S. . Metallurgy. By John Percy, M.D., F.R.S. - Natural History. By T. H. Huxley, LL.D., F.R.S. natalesy: | By Warington W. Smyth, M.A., F.R.S., Chairman. . Geology. By A. C. Ramsay, LL.D., F.B.S. . Applied Mechanics. By T. M. Goodeve, M.A. . Physies. By Frederick Guthrie, Ph.D., F.R.S. . Mechanical Drawing. By the Rev. J. H. 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It is admirably adapted for a ' Museum, nearly all nown and well-determined species being adequately represented in “it, besides being accompanied with a carefully compiled descriptive Catalogue of 175 pages, containing in nearly every instance the history and locality of each specimen. Many years have been occupied in its formation, and it imeludes very many examples almost unique either for size of crystals or perfection of form. Price THREE THOUSAND POUNDS. FIRST-CLASS GHOLOGICAL COLLECTION. FOR SALE.—_TWO CABINETS, each measuring 9 feet 3 inches long, 2 feet 4 inches “wide, and 3 feet 10 inches high; each containing 45 drawers, with a Glass Case on the top of each Cabinet, 4 feet 11 inches high, and 15 inches from back to front. One Cabinet is filled with 2600 Minerals and Rocks, the other with 3400 Fossils, British and Foreign, ' stratigraphically arranged. _ The Collection is carefully named and consists of six thousand specimens, many very choice, and selected principally from the Duke of Buckingham’s (Stowe sale), Marchioness of Hastings, Sir John St. Aubyn’s, Drs. Buckland, Bowerbank, Mantell, and other cele- “brated collections. The first Gold Nugget received from Australia is in the Collection : also a fine series of Diamonds, illustrating crystalline form and colour, from India, Brazil, South Africa, and Australia. Price THREE THOUSAND GUINEAS. _ Any person wishing to become practically acquainted with the interesting and important study of MINERALOGY and GEOLOGY will find this a good opportunity to obtain an instructive and valuable Geological Museum scientifically arranged, the specimens having ‘been collected with care and at great expense during the last thirty years. + Practical Instruction in Mineralogy applied to Geology and the Arts ' is given by Professor Tennant, F.G.S., at his residence, 149 Strand, London, W.C. The Course commences with a description of the Physical and Chemical characters of ' Minerals in general, and includes a minute description of all the substances entering into | the composition of Rocks, and of those Minerals which are also used in the Arts; illus- trated by an extensive collection of characteristic specimens, and diagrams of the principal crystalline forms, &c. The Students are accompanied by the Professor to the Museum of Practical Geology, the British Museum, and other public institutions, and also on excursions into the country. ——— Two Courses of Lectures on Mineralogy will be given at KING’S COLLEGE, LONDON, by PROFESSOR TENNANT, to which the Public are admitted on paying | the College jFees. One Course is given on Wednesday and Friday Mornings, from 9 to 10 o'clock, commencing Wednesday, October 9th, and terminating at Haster 1873. The other Course is given on Thursday Evenings, from 8 to 9, commencing October 10th. The Lectures are illustrated by a very extensive Collection of Specimens. A Catalogue of 2000 of the most common Fossils found in the British Isles, being a list of those in the private collection of J. Tennant, F.G.S. Price 2s. All the recent Works relating to Mineralogy, Geology, Conchology, and Chemistry; also Geological Maps, Models, Diagrams, Hammers, Blowpipes, Magnifying-Glasses, Platinum Spoons, Electrometer and Magnetic Needle, Glass-top Boxes, Microscopic Objects, Forceps, Acid Bottles, &c., can be supplied to the Student in these branches of Science. Elementary Geological Collections at 2, 5, 10, 20, 50, to 100 guineas each, and | every requisite to assist those commencing the study of this interesting branch of Science, a knowledge of which affords so much pleasure to the traveller in all parts of the world. JAMES TENNANT, Mineralogist (by appointment) to Her Majesty, 149 Strand, London, W.C. September 1872. CON'TENTS oF N° 292.— Fourth Series. XXI. On Differential Galvanometers. By Louis ScHwENDLER, TSG. oe Sa oss wide oe amie et intel Sepale lala tla ee se stntethe page XXII. On an Electrical Experiment with an Insulated Room. By F.C. Wess; M. Inst. G.E: 2c oo. os. ot eee XXIII. On the Nature of Electricity. By M. E. Eptunp...... XXIV. On the Hydrodynamical Theory of Attractive and Repul- sive Forces. By Professor Cuauuis, M.A., LL.D., F.R.S... XXV. On Wave-Theories of Light, Heat, and Electricity. By Henry Huvson, M:D.,. MR IAS: os... see eee XXVI. On the Law of Gaseous Pressure. By the Hon. J. Ww. Srrutt, M.A., late Fellow of Trinity College, Cambridge ........ XXVII. Proceedings of Learned Societies :— Royat Socrery :—Messrs. C. Tomuinson and G. VAN DER MeEnsBruGGHE on Supersaturated Saline Solutions.—Part III. On a relation between the Surface-tension of Liquids and the Supersaturation' of Saline Solutions ....2.. 222 ees GxoxoeicaL Society :—Dr. Orpuam and Mr. R. Mauer on some of the Secondary Effects of the Earthquake of the 10th January, 1869, in Cachar....... 2.2... 2206 oe XXVIII. Intelligence and Miscellaneous Articles :— On the Influence of Pressure in the Phenomena of Endosmose and Exosmose, by M. Becquerel........... i855 On the Action of Ozone upon Vulcanized Caoutchouc, by Prof. _ Arthur W. Wright .. ost 3 6S le te ee/o wien 2 ou On the instantaneous Oxidation of Alcohol, by M. Hees 237 On some Effects of Slow Actions, produced in the course of a certain number of years, by M. Becquerel.......... Pram es Reply to Professor Clausius, by P.G. Tait 2... 2.2.32. eee 240 *.* It is requested that all Communications for this Work may be addressed, post-paid, to the Care of Messrs. Taylor and Francis, Printig Office, Red Lion Court, Fleet Street, London. Tol. 44. OCTOBER 1872. No. 293. SS See Published the First Day of every Month.—Price 2s. 6d. THE LONDON, EDINBURGH, anp DUBLIN |PHILOSOPHICAL MAGAZINE, a AND | JOURNAL OF SCIENCE Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘Journal, and Thomson's ‘ Annals of Philosophy. ee eee CONDUCTED BY } SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. i SIR WILLIAM THOMSON, Knr. LL.D. F.R.S. &c. sl AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S. FCS. 2 FOURTH SERIES. : Ne 298,—OCTOBER, 1872. WITH A PLATE, — Illustrative of Mr. T. E. Tuorrx’s Paper on an Improved form of Filter- Pump. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. | Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co.; and Whittaker and Co. ;—and by A. and ©. Black, and ‘Thomas Clark, Edin- burgh ; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin: :—Putnam New York :—and Asher and Co., Berlin. Second Edition, with Supplement, greatly enlarged, with 12 Maps and Plates, 1 vol. 8yo, 21s. DAUBENY ON VOLCANOS. A description of Active and Extinct Voleanos, of Earthquakes, and of Thermal . Springs. With remarks on their Causes, Products, and influence on the condi- tion of the Globe. By PROFESSOR CHARLES DAUBENY, M.D., F.R.S., &c. TAYLoR and Francis, Red Lion Court, Fleet Street, E.C. Just published, price 1s., post free 1s. 5d. ROYAL COLLEGE OF SURGEONS OF ENGLAND. The CALENDAR for 1872, containing the Charters, Bye-laws, Regula- tions, Lists of Fellows, Members, and Licentiates in Midwifery and Dental Sur- gery, together with much useful information respecting the College. TAayYLor and Francis, Red Lion Court, Fleet Street, E.C. BELVILLE’S MANUALS. Third Edition. Price ls. A MANUAL OF THE BAROMETER. Containing an Explanation of the Construction and Method of using the Mer- curial Barometer, with appropriate Tables for Corrections for Temperature, and Rules for obtaining the Dew-point and the Heights of Mountams; also, a De- scription of the Aneroid Barometer. . By JOHN HENRY BELVILLE, of the Royal Observatory, Greenwich. By the same Author. Price ls. A MANUAL OF THE THERMOMETER. Containing its History and Use as a Meteorological Instrument; to which is added an Essay on the Vapour-point and Terrestrial Radiation ; also, a General Outline of the Climate of the Eastern parts of England. TayYLor and Francis, Red Lion Court, Fleet Street, E.C. The Annals and Magazine of Natural History. Including Zoology, Botany, and Geology.—Monthly, price 2s. 6d. Complete sets (in Numbers) may be obtained at the following prices :— The First Sertes, in 20 volumes, from 1838 to 1847. Price £6. The Second Series, in 20 volumes, from 1848 to 1857. ,, £9. The Third Serves, from 1858 to 1862, Vols. I. to X. sp tee ‘5 = 1863 to 1867, Vols. XI. to XX. ,, £6. TaAYLor and Francis, Red Lion Court, Fleet Street, H.C. _ In 1 vol. 8vo, with Three Plates, price 15s. cloth. EXPERIMENTAL RESEARCHES IN CHEMISTRY AND PHYSICS. By MICHAEL FARADAY, D.C.L., F.R.S., - Fullerian Professor of Chemistry in the Royal Institution of Great Britain. “Tn conclusion, we ean only repeat the assertion with which we commenced this article. This is a book which ought to be in the library of every scientific man. ’—ILaterary Gazeite. ; TayLor and Francis, Red Lion Court, Fleet Street, E.C. |ADVERTISEMENTS continued on 3rd page of Cover. ¥ O50 “ e. . aon MR. TENNANT, $49 STRAND, LONDON, W.C., is commissioned to sell some valuable and choice Collectionsjof Minerals &c. The rich and extensive Collection of Minerals now at Godstone, Surrey, and formerly Ooksnest, comprising upwards of 7000 Specimens (in 170 Drawers), accompanied by following printed Catalogue :—Description d’une Collection de Minéraux formée par - Henri Heuland, et appartenant 4 M. Ch. Hampden Turner, de Rooksnest, dans le pté de Surrey, en Angleterre. Par A. Lévy, &. In 3 vols. 8vo, with an Atlas, 4to, 3 Plates (1857). Il. A LARGE AND FINE COLLECTION OF MINERALS — belonging to a private Gentleman residing thirty miles from London. he Collection contains 3800 specimens, and is carefully named and arranged like that British Museum, after the system of Gustave Rose. It is admirably adapted for a im, nearly all known and well-determined species being adequately represented in ides being accompanied with a carefuily compiled descriptive Catalogue of 175 containing in nearly every instance the history and locality of each specimen. years have been occupied in its formation, and it includes very many examples most unique either for size of crystals or perfection of form. Price THREE THCUSAND POUNDS. FIRST-CLASS GEOLOGICAL COLLECTION. R SARB-TWO CABINETS, each measuring 9 feet 3 inches long, 2 feet 4 inches and 3 feet 10-Seebes high; each containing 45 drawers, with a Glass Case on the each Cabinet, 4 feet inches high, and 15 inches from back to front. One Cabinet ed with 2600 Minerals a*% Rocks, the other with 3400 Fossils, British and Foreign, aphically arranged. ¥ Collection is carefully named and consists of six thousand specimens, many very ce, and selected principally from the Duke of Buckingham’s (Stowe sale), Marchioness stings, Sir John St. Aubyn’s, Drs. Buckland, Bowerbank, Mantell, and other cele- collections. The first Gold Nugget received from Australia is in the Collection : fie series of Diamonds, illustrating crystalline form and colour, from India, Brazil, th Africa, and Australia. Price THREE THOUSAND GUINEAS. “Any person wishing to become practically acquainted with the interesting and important y of MINERALOGY and GEOLOGY will find this a good opportunity to obtain an tive and valuable Geological Museum scientifically arranged, the specimens having a collected with care and at great expense during the last thirty years. Twe Courses of Lectures on Geological Mineralogy will be given at KING’S ILLEGH, LONDON, by PROFESSOR THNNANT, to which the Public are admitted paying the College Fees. One Course is given on Wednesday and Friday Mornings, m 9 to 10 o’clock, commencing Wednesday, October 9th, and terminating at Easter 3. The other Course is given on Thursday Evenings, from 8 to 9, commencing ober 10th. The Lectures are illustrated by a very extensive Collection of Specimens. Practical Instruction in woe and Geology is given by Professor | Tennant, F.G.S., at his residence, 149 Strand, London, W.C. Catalogue of 2000 of the most common Fossils found in the British Isles, being a list those in the private collection of J. Texnant, F.G.S. Price 2s. All the recent Works relating to Mineralogy, Geology, Conchology, and Chemistry; also ogical Maps, Models, Diagrams, Hammers, Blowpipes, Magnifying-Glasses, Platinum 1s, Hlectrometer and Magnetic Needle, Glass-top Boxes, Microscopic Objects, Forceps, Bottles, &c., can be supplied to the Student in these branches of Science. Elementary Geological Collections at 2, 5, 10, 20, 50, to 100 guineas each, and very requisite to assist those commencing the study of this interesting branch of Science, ‘a knowledge of which affords so much pleasure to the Traveller in all parts of the World. | JAMES TENNANT, Mineralogist (by appointment) to Her Majesty, io 149 Strand, London, W.C. October 1872. ae 1A = iy CONTENTS oF N° 298.—Fourth Series. XXIX. On the Cooling of Gases. By MM. Jamin and Ri- CHARD (5.8 ses cos os ain os vs 0 e's. ss Js oes ~0 w, 6 6) eneg ee XXX. On an Improved form of Filter-Pump. By T. E. Tuorre, Boke. (( Witha Plate.) °. estes ook ose eee «tai Ob oe paen 248 XXXI. On the Specific Heat of Carbon. By H. F. Weser, Assist- ant in the Physical Laboratory of Geh. -R. Helmholtz ............ 251 XXXII. On a precise Method pf tracing the Progress and of deter- mining the Boundary of a Wave of. Conducted Heat. By AurrEp M. Maver, Ph.D., Professor of Physics in the Stevens Institute of Tech- nology, Hoboken, N. J., U.S. America . PE es Ee 5. 25% XXXIII. On Electrolysis, and the Passige of Blecesiaiy through Liquids. By G. QuincKE......... a's Heme Rates cence eeceeees 261 XXXIV. Notice respecting some new Facts iygthe early History of Logarithmic Tables. By J. W. L. Guatsusr, B-a., F.R.A.S., Fellow of Trinity College, Cambridge................ 08... | ee 291 XXXV. On the Definition of Intensity in the Theories of Light and Sound. By Rosert Moon, M.A., Honorary Fellow of Queen’s — College, Cambridge. 2205.5 So teee le eda ccs ew. se caer 304 XXXVI. On the Chemical Efficiency of Sunlight. By Jamzs - Diwan, WSq,. Hees frac oo. hee eee cca wules eee 307 XXXVII. Proceedings of Learned Societies :— Royar Socrery:—Dr. J. W. Mautzr on the Gases occluded in Méteoric Iron from Augusta Co., Virginia; Mr. G. Gorz on some Properties of Anhydrous Liquefied Ammonia; Mr. G. G. Stokes on the Law of Extraordinary Refraction in Iceland ~* Spares. ss eas Wee Lee re Sie es oc ule ds oo eet eee XXXVIII. Intelligence and Miscellaneous Articles :— Report on a Memoir by MM. F. Lucas and A. Cazin, on the Duration of the Electric Spark, by Edm. Becquerel ....... . 8l6aq On a new Galvanic Pile, of Economic Construction, by M. Gaiffe. 320 — On ‘‘ Acoustical oe ges ” &e., by Alfred M. Mayer. seeees 320 ¥ iniage *,* Tt is requested that all . Gt iimeane for this Work may ne addressed, post-paid, to ‘the Care of Messrs. Taylor and Francis, Printing Office, Red : | Lion Court, Fleet Street, London. Pudlished the First Day e every Month.—Price 2s. 6d. I a LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘ Journal,’ and Thomson’s ‘ Annals of Philosophy.’ CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.CS. SIR WILLIAM THOMSON, Knr. LL.D. F.R.S. &e. AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S. FCS. FOURTH SERIES. Ne 294._NOVEMBER 1872. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co. ; and Whittaker and Co. ;—and by A. ‘and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin: :—Putnam, New York :—and Asher and Co., Berlin. NEW WORK BY MR. PROCTOR. Just published, in crown 8vo, price 7s. 6d. cloth, THE ORBS AROUND US: A Series of Familiar Essays on the Moon and Planets, Meteors and Comets, the Sun, and Coloured Pairs of Suns. By RICHARD A. PROCTOR, B.A. (Camb.), Honorary Secretary of the Royal Astronomical Society ; Author of ‘ The Sun,’ ‘ Other Worlds than Ours,’ &e. London: LoneGMans, GREEN, and Co., Paternoster Row. In One Volume, 8vo, price 15s. cloth, A BUDGET OF PARADOXES. By AUGUSTUS DE MORGAN, F.R.A:S. and C.P.S. of Trinity College, Cambridge. Reprinted, with the Author’s additions, from the ‘ Atheneum’ Journal. London: LonGMANS, GREEN, and Co., Paternoster Row. On the 15th of November next will be published No. I. of THE TELEGRAPHIC JOURNAL, and MONTHLY ILLUSTRATED REVIEW OF ELECTRICAL SCIENCE. The arrangement of this Journal will be as follows :—Leading Articles on Sub- jects of Immediate Interest and Importance—Original Papers—Abstracts of Pro- ceedings of Scientific Societies—Reviews of Scientific Books—Abstracts of all Foreign Memoirs upon Electrical Science—Share Lists and City Notes—A Stu- dent’s Column—A List of Letters Patent. The Journal will also be a Medium of Intercourse between Telegraphists, a Channel through which Operators can declare their wants, and a Guide to the Investor and those interested in the Commercial Progress of the Science. As a Review of Electrical Science, the Telegraphic Journal will contain Articles of value to the Electrotyper, Electroplater, and Amateur Experimentalist. Price 6d., or post free, 6s, per annum. London: Henry GILLMAN, Boy Court, Ludgate Hill, E.C. THE LONDON, EDINBURGH, AND DUBLIN Philosophical Magazine and Journal of Science. A Journal devoted to Physics, Astronomy, Mechanics, Chemistry, Mineralogy, and the allied Sciences. Monthly, price 2s. 6d. Complete sets (in Numbers) may be obtained at the following prices :— A few sets of the First Series, from 1798 to 1826 (wanting a few plates), in 6& volumes. Price £10. The Second Series, from 1827 to 1832, in 11 volumes. Price £2 4s, The Third Series, in 87 volumes, from 1882 to 1850. oy aos TayLor and Francis, Red Lion Court, Fleet Street, H.C. ‘The Annals and Magazine of Natural History. Including Zoology, Botany, and Geology.—Monthly, price 2s. 6d. Complete sets (in Numbers) may be obtained at the following prices :— The Furst Serves, in 20 volumes, from 1838 to 1847. Price £6. The Second Serves, in 20 volumes, from 1848 to 1857. ,, £9. The Third Series, from 1858 to 1862, Vols. I. to X. » £9. & Fe 1863 to 1867, Vols. XI. to XX. ,, £6. TayLor and Francis, Red Lion Court, Fleet Street, E.C. [ADVERTISEMENTS continued on 3rd page of Cover. MR. TENNANT, 149 STRAND, LONDON, W.C., is commissioned to sell some valuable and choice Collections of Minerals &c. I. The rich and extensive Collection of Minerals now at Godstone, Surrey, and formerly at Rooksnest, comprising upwards of 7000 Specimens (in 170 Drawers), accompanied by the following printed Catalogue :—Description d’une Collection de Minéraux formée par M. Henri Heuland, et appartenant 4 M. Ch. Hampden Turner, de Rooksnest, dans le ’ compté de Surrey, en Angleterre. Par A. Lévy, &c. In 3 vols. 8vo, with an Atlas, 4to, of 83 Plates (£837). Il. A LARGE AND FINE COLLECTION OF MINERALS belonging to a private Gentleman residing thirty miles from London. The Collection contains 3800 specimens, and is carefully named and arranged like that at the British Museum, after the system of Gustave Rose. It is admirably adapted for a Museum, nearly all known and well-determined species being adequately represented in it, besides being accompanied with a carefully compiled descriptive Catalogue of 175 pages, containing in nearly ‘very instance the history and locality of each specimen. Many years have been occtivied in its formation, and it imcludes very many examples almost unique either for size of crystals or perfection of form. Price THREE THOUSAND POUNDS. FIRST-CLASS GEOLOGICAL COLLECTION. FOR SALE.—_TWO CABINETS, each measuring 9 feet 3 inches long, 2 feet 4 inches wide, and 3 feet 10 inches high; each containing 45 drawers, with a Glass Case on the top of each Cabinet, 4 feet 11 inches high, and 15 inches from back to front. One Cabinet is filled with 2600 Minerals and Rocks, the other with 3400 Fossils, British and Foreign, stratigraphically arranged. The Collection is carefully named and consists of six thousand specimens, many very choice, and selected principally from the Duke of Buckingham’s (Stowe sale), Marchioness of Hastings, Sir John St. Aubyn’s, Drs. Buckland, Bowerbank, Mantell, and other cele- brated collections. The first Gold Nugget received from Australia is in the Collection : also a fine series of Diamonds, illustrating crystalline form and colour, from India, Brazil, South Africa, and Australia. Price THREE THOUSAND GUINEAS. Any person wishing to become practically acquainted with the interesting and important study of MINERALOGY and GEOLOGY will find this a good opportunity to obtain an instructive and valuable Geological Museum scientifically arranged, the specimens having been collected with care and at great expense during the last thirty years. ~ Two Courses of Lectures on Geological Mineralogy will be given at KING’S COLLEGE, LONDON, by PROFESSOR TENNANT, to which the Public are admitted on paying the College Fees. One Course is given on Wednesday and Friday Mornings; from 9 to 10 o’clock, commencing Wednesday, October 9th, and terminating at Easter 1873. The other Course is given on Thursday Evenings, from 8 to 9, commencing October 10th. The Lectures are illustrated by a very extensive Collection of Specimens. - Practical Instruction in Mineralogy and Geology is given by Professor Tennant, F.G.S., at his residence, 149 Strand, London, W.C. A Catalogue of 2000 of the most common Fossils found in the British Isles, being a list of those in the private collection of J. Tennant, F.G.8. Price 2s. All the recent Works relating to Mineralogy, Geology, Conchology, and Chemistry; also Geological Maps, Models, Diagrams, Hammers, Blowpipes, Magnifying-Glasses, Platinum Spoons, Hlectrometer and Magnetic Needle, Glass-top Boxes, Microscopic Objects, Forceps, Acid Bottles, &., can be supplied to the Student in these branches of Science. Elementary Geological Collections at 2, 5, 10, 20, 50, to 100 guineas each, and every requisite to assist those commencing the study of this interesting branch of Science, a knowledge of which affords so much pleasure to the Traveller in all parts of the World. JAMES TENNANT, Mineralogist (by appointment) to Her Majesty, 149 Strand, London, W.C. November 1872. CONTENTS or N° 294.—Fourth Series. AXXIX. On a Method of detecting the Phases of Vibration in the Air surrounding a Sounding Body, and thereby measuring directly in the vibrating air the lengths of its Waves and exploring the form of its Wave-surface. By Atrrep M. Mayer, Ph.D. &c., Professor of Physics in the Stevens Institute of Technology, Hoboken, Nis United States Bee Behe cong tag ewe w Vee oS Stee es ate Fee Egse 321 _XL. Notes on Bessel’s Functions. By the Hon. J. W. Srrurt, late Fellow of Trimty College, Cambridze <2... 2. - eee 328 XLI. Fluorescent Relations of certain solid dee found in Coal-tar and Petroleum Distillates. By HENRY Morton, Ph.D., President of the Stevens Institute of Technology; Us ps ae ae 345 XLII. On the Nutrition of Muscular and Pulmonary Tissues in 3 Health and when affected with Ewe from Phthisis. By Wittiam 5 Marcet, M.D., PRS. 2. Sacro ae oye + + ee 349 XLIII. On the Connexion of the Second Proposition of the Me- chanical Theory of Heat with Hamilton’s Principle. By R.Cuaustus. 365 XLIV. On some Points in the Chemistry of Acid-manufacture. By H. A. Suirn, Junior Assistant in the Laboratory of Owens Col- ice, Manehester oes 20 Seg ee eee er 370 XLV. Gn an Experimental Determination of the Relation between the Energy and Apparent Intensity of Sounds of different Pitch. By R.H. M. Bosanauet, M.A., F.C.S., F.R.A.S., Fellow of St. John’s College, Soxfort os ce Bu ae Pee 2 sik con = re XLVI. Notices respecting New Books :—The Orbs around us: a Series of familiar Essays on the Moon and Planets, Meteors and Comets, the Sun, and coloured Pairs of Suns. By Ruicuarp A. Proctor, B.A. (Camb.).—The Geometry of Conics.—Part I. By C. Taytor, M.A., &c.—The Laws cf the Winds prevailing in Western Europe.—Part &:.By W. Crumment Ley. 228 225.0 ee 388-392 XLVII. Proceedings of Learned Societies :— Roya Socrety :—The Hon J. W. Strutt on the Reproduction of Diffraction-gratings by means of Photography .......... 392 XLVHI. Intelligence and Miscellaneous Articles:— On the Anomalous Dispersion exhibited by certain ee ! by M. J, L: Soret «2 :: = 395 On the Measurement of the Intensity of Currents by means of 4 the Electrometer, by M. E. Branly .. -. -g@2se22 See eee 896 On the Specific Heat of Hydrogenium, by James pew R.S.E. 400 a *.* It is eae that all Communications for this Work may be sieewea: 3 post-paid, to the Care of Messrs. Taylor and Francis, Printing Office, Red Lion Court, Fleet Street, London. te 2 = = os ol. 44. DECEMBER 1872. No, 295. Published the First Day of every Month.—Price 2s. 6d. THE LONDON, EDINBURGH, anp DUBLIN” 2 PHILOSOPHICAL MAGAZINE, q AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosophical Magazine Nicholson’s ‘ Journal, and Thomson’s ‘ Annals of Philosophy.’ CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.CS. » SIR WILLIAM THOMSON, Knr. LL.D. F.RS. &e.* AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S. F.C.S. FOURTH SERIES. N° 295.—_DECEMBER, 1872. | WITH A PLATE, 7 Tilustrative of M. F. Zouiner’s Paper on the Specfaipecapic Reversion- Telescope. With this, the regular Number for December 1872, is published, and should be delivered to Subscribers, the Suprtumunt (No. 296) to Vol. XLIV., containing papers by M. H. Weser, Mr. J. W. L. - GuaisHeR, Dr. KE. J. Mitzs, Mr. A. S. Davis, M. Hetmuoxzz, together with Proceedings of the Royal Society, Geological Society, Intelligence and Miscellaneous Articles, and the Title-page, Table of Contents, and Index to Vol. XLIV. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREEP, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co.; and Whittaker and Co. ;—and by A. ‘and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin:—Putnam, New York :—and Asher and Co., Berlin. Errata in No. 294. Page 352, line 25, instead of like a jelly in the fact read like a jelly from the fact. — 357, — 31, instead of composition of fibrous mass read composition of the fibrous mass. — 358, instead of Z Rie a ye wee read BxA' B= ; A c= BXA! A — 359, in the Table, instead of calculated in 5°74 albumen read caleulated for 5°74 albumen. — 362, line 5, instead of between the albuminous read between these theo- retically alouminous. Second Edition, greatly bhieeo in 8vo, price 12s. CAUSALITY ; OR, THE PHILOSOPHY OF LAW INVESTIGATED. By the Rev. GEORGE JAMIESON, B.D., of Old Machar. London: LoNGMANS, GREEN, and Co., Paternoster Row. J. ROWSELL, BOOKSELLER, 9 KING WILLIAM STREET, CHARING CROSS. An extensive and valuable Collection of Books on Natural History, Botany, Conchology, Entomology, Ornithology, Geology, &c., including the Libraries of Dr. Hollingsworth, Dr. Day, late of Aberdeen, W. H. Benson, and others, con- taining a splendid collection of the Highest Class Works. 2220 Articles. Sent free; enclose stamp. Libraries purchased. Price 6d., post free 7d., TAYLOR’S CALENDAR OF MEETINGS OF THE SCIENTIFIC BODIES OF LONDON FOR 1872—73. TayYLor and FrAncis, Red Lion Court, Fleet Street, E.C. Second Edition, with Supplement, greatly enlarged, with 12 Maps and Plates, 1 vol. 8vo, 21s. DAUBENY ON VOLCANOS. A description of Active and Extinct Volcanos, of Earthquakes, and of Thermal Springs. With remarks on their Causes, Products, and Influence on the condi- tion of the Globe. By PROFESSOR CHARLES DAUBENY, M.D., F.R.S., &e. TAYLoR and Francis, Red Lion Court, Fleet Street, E.C. \ADVERTISEMENTS continued on 3rd page of Cover. Saari, INSTEPUTION OF GREAT BRITAIN, ALBEMARLE STREET, PICCADILLY, W. LECTURE ARRANGEMENTS FOR 1872-73. - Subscribers of Two Guineas are admitted to all the Courses. A Single Course, - One Guinea, or, Half-a-Guinea. Lecturé Hour, THREE 0’CLOCK.) CHRISTMAS LECTURES (adapted to a Juvenile Auditory). Professor Opiine, M.A., F.R.S.—Six Lectures, ‘On Air and Gas,’ on Decem- ber 28 (Seturday), Decanbes 31,1872; January QA e7. ONG7 3. BEFORE EASTER, 1873. Professor RuTHERrorp, M.D., F.R.S.E.—Twelve Lectures, ‘ On the Forces and Motions of the Body,’ on Tuesdays, January 14 to April |. ee Se F.R.S.—Three Lectures, ‘ On Oxidation,’ on Thursdays, January 16, Dr. H. E. ArMstRONG, F.C.S.—Four Lectures, ‘On the Artificial Formation ’of Organic Substances,’ on Thursdays, February 6 to February Qe: A. VERNON Harcourt, Esq., F.R.S.—Five Lectures, ‘On the Chemistry ae Coal and its Products,’ on Thursdays, March 6 to April 3. Epwarp A. 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When proposed, they are admitted to all the Lectures, to the Friday Evening Meetings, and to the Li- brary and Reading Rooms; and their Families are admitted to the Lectures at a reduced charge. Payment :—First year, Ten Guineas; afterwards, Five Guineas a year; or a composition of Sixty Guineas. Prospectuses (when prepared) may be had in the Hall. oo a Se mop r ; bee CONTENTS or N° 295 Fourth Series. - XLIX. On the Phenomena of the Elevation and Subsidence of the © Surface of the Earth. By Captain F.W. Hurton, F.G.S., of the Geo- logical Survey of New Zealand (000.0235 eee ies ooo sineeraee page 401 L. On the Relation which the internal Resistance of the Battery and the Conductivity of the Wire bear to the maximum Magnetizing Force of an Electromagnet Coil. By G. K. bidet F.R.A.S., Telegraph Engineer, Madras Railway... .°...0 2 9. og) ss). oa os 414 LI. On the ee ge Wee By F. Zouuner. CWithia Plate)> 00.5 sae ow eter ( 5 Se ee eee seks 417 LII. Researches in AGHHCuOR AE try. —Memoir Second. On the Distribution of Chemical Force in the Spectrum. By Joann W1iLLIam Draper, M.D., LL.D., President of the Faculties of Science and Me- dicine in the University of New York. .....<-. .» 5. cps oie LHI. On the Nutrition of Muscular and Palinoueey Tissues in Health and when affected with disease from Phthisis. By Witu1am Mazcet, M.D., F.R.S. ees PP eee LIV. On the Laws of ‘Gaoing: By MM. see ata Ridges 457 LV. On the Specific Heat of Carbon at High Temperatures. By James Dewar, F.R.S.E., Lecturer on Chemistry, Edinburgh ...... 461 LVI. Notices respecting New Books:—The Strains in’ Trusses computed by means of diagrams: with twenty examples drawn to scale. By Francis.A. Rangen, M.A.,OC.E. ....0..02. 28 ee LVII. Proceedings of Learned Societies :— | Roya Society:—Mr. R. Mater on Volcanic Energy: an attempt to develope its true Origin and Cosmical Relations; Sir B. C. Broprz on the Action of Electricity on Gases. 468-473 4 Grotoeicat Socrery :—Mr. R. Datnrrez on the Geol of the Colony .of Queensland: / 2.9.5). S23 seweeee ey) ey | LVIII. Intelligence and Miscellaneous Articles :— ee: - | On the Collision of Elastic Bodies, anda = valuation of | its duration, by H. aes ; eS *,* It is requested that all Communications for this Worl nayshe addres ed, post-paid, to the Care of Messrs. el and ait ie ae od Lion Court, Fleet Street, London. 3 % SUPPLEMENTARY NUMBER. Vol. 44. No. 296. Published the First Day of every Month.—Price 2s. 6d. LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. THE | Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘ Journal,’ and Thomson's ‘ Annals of Philosophy.’ | | | CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Kynr. LL.D. F.R.S. &e. AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.AS. FCS. FOURTH SERIES. N° 296._SUPPLEMENT. DECEMBER 1872. WITH A PLATE, Illustrative of M. H. WxezBer’s Paper on the Heat-conducting Power of Iron and German Silver, This SuprLement to Vol. XLIV. is published with the regular Number for December, and should be delivered with it to Subscribers. ——_—_ LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co.; and Whittaker and Co. ;—and by A. and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam, New York :—and Asher and Co., Berlin. LO OO A CRA tte cn te ee ii et ee Se ebaealicteaa sie SUPPLEMENTARY NUMBER. CONTENTS. LIX. On the Heat-conducting Power of Iron and German Silver. — By H. Weer of Brunswick. (With a Plate.) .............. page 481 LX. Supplementary Remarks on some early Logarithmic Tables. By J. W. L. Guaisuer, B.A., F.R.A.S., Fellow of Trinity College, é Gambridge 2.0... ee eee cet rene eee oe eee LXI. Researches on Elective Attraction. By Epmunp J. Mitts, . Se re es ce rr 506 © LXII. On Recurrent Vision. By A. S. Davis, M.A........... 526 j LXIII. On the Theory of Electrodynamics. By M, Hetmuonrz. 530 LXIV. Proceedings of Learned Societies :— Royat Society :—Mr. A. Scuuster on the Spectrum of Ni- 4 Hraronr et). caste te" Dietserth res.) en 537 GroLoeicaL Society :—Mr. §. J. Wuitnett on Atolls or La- goon-islands; Mr. J. R. Daxyns on the Glacial Phenomena of the Yorkshire Uplands ; Mr. D. MacxrinrosH on a Sea- coast Section of Boulder-clay in Cheshire ; The Rev. Wittiam BuieaspeLyt on Modern Glacial Action in Canada; The Rev. QO. Fisuer on the Phosphatic Nodules of the Cretaceous Rock of Canthaidgeshive 2c 05..c) ees ot 541-548 LXV. Intelligence and Miscellaneous Articles :— ; ‘ ; On the Absorption of Ozone by Water, by L. Carus.......... 544 | On the Heat of Expansion of Solid Bodies, by H. Buff ...... 544, | Experiments on Collision with Balls of different Metals, by He ; mchneebeli ope ee evs eed eee tes on oe ee «546 With Title-page, Contents, &c. das *,* It is requested that all Communications for this Work may be addresse post-paid, to the Care of Messrs. Taylor ape Francis, Printing Office, ia Lion Court, Fleet Street, Tend. ov val 4 "6 8155 SMITHSONIAN INSTITUTION LIBRARIES “I 3 9088 01202 4105 . ] f ‘ = : , i = 4 4 s ,. 5 oe ‘ Hy 5 hk Ye ‘ ‘ a r oS q 4 » ‘ 2 yen $ ‘ B. A ; : + s ‘ WAG