: cb hle SS 7 CO ory ght R TG ARRAN MSc et : eee Fi at Many crm oun : He ANN “ . : ea ete : Sara eh NS, Sat hE Re alee POPU ener - oer’ Pfhaiety oF ty Hh Seth cBeatal wt Sale eh AW A rsh ie sone Ie eae WE Aus Meisaeinaohiaes Hy at ihetion re ee ad eee Fp NENT fe -feeiy Fp, Tete ae Sl ee € 8+ 4 2h- tet iy ARS o Fee ee ER HO Hert Bele erty EOP AS 08m Ate to OR ne « Pat nhe i RL Re Et eh Te As: Ay THE LONDON, EDINBURGH, ayp 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, Kyr. LL.D. F.RB.S. &e. AND | WILLIAM FRANCIS, Pu.D. F.LS. 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.” Jnez. Lies. Polit. lib.i. cap. 1. Not. Pp P VOL. IJI.— FIFTH SERIES. JANUARY—JUNE 1877. LONDON. TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London ; ' §0LD BY LONGMANS, GREEN, READER, AND DYER, KENT AND CO.; SIMPKIN, MARSHALL, AND CO.; AND WHITTAKER 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 queestionem, queestio investigationem, investigatio inventionem.”— Hugo de S. Vietore. —‘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 ccelo, Quo micet igne Iris, superos quis conciat orbes Tam yvario motu.” J. B. Pinelli ad Mazonim. CONTENTS OF VOL. III. (FIFTH SERIES). NUMBER XV.—JANUARY 1877. Dr. K. Heumann’s Contributions to the Theory of Luminous ELS EL ES 2 2 co Sie IRIE SREB Ie eRe oie ier cae Mr. W. Spottiswoode on a Large Induction-coil .......... Mr. A. Cayley on the Number of the Univalent Radicals oy eLuzrect 6 ee he en ae rar Baer era Prof. Wéhler on the Action of the Flame of Alcohol upon Seem eeHm ret ACHEUNAN oe. ceo je 2) 5) Sent ete’ s/'s sola ace siti delle 8 a ot ac ene Prof. J. Emerson-Reynolds’s Reports from the Grensel Labo- ratory of Trinity College, Dublin. No. 1—On Glucinum: is Atomic Weizht and Specific Heat .................. Lord Rayleigh on a permanent Deflection of the Galvanome- ter-needle under the influence of a rapid series of equal and _ epposite induced Curtemtsycip: eee = 12 se ec ete Captain Abney on the Alkaline ——_ o:*une Photo- EMP MEMMACS 5... ae ere eI ee se ee ee Mr. F. Field on Ludlamite, a new Cornish Mineral Notices respecting New Books :— Prof. M. E. Mascart’s Traité d’Electricité Statique Mr. B. T. Bosanquet’s Treatise on the Trisection of an Angle of thirty degrees, and of any other plane Angle. The Rey. G. T. Carruthers’s Earth supported by Vapour. Proceedings of the Royal Society :— Prof. T. Andrews on the Gaseous State of Matter .... Mr. R. J. Moss on the Condensation of Vapour of Mer- cury on Selenium in the Sprengel Vacuum ........ Sir John Conroy on the Absorption-Spectra of Iodine .. Proceedings of the Geological Society :— Mr. H. Hicks on the Pre-Cambrian (or Dimetian) Rocks OMS Lead Sires eee.) tapers Sone ALAR a Prof. 8. Calderon on the Fossil Vertebrates of Spain Messrs. W. Topley and G. A. Lebour on the Intrusive Character of the Whin Sill of Northumberland ...... On the Portative Force of Horse-shoe Magnets, by V.-S.-M. SMO OE AWiUNG CNR T. a ad os sees by ese Wie etn Experiments on the Sympathetic Resonance of Tuning-forks, by Robert Spice lv CONTENTS OF VOL. III.—-FIFTH SERIES. Note on the Correction of the Variations of Rate of Astro- nomic Pendulums proceeding from differences of Atmo- Spherie Pressure, by cA. Redier ... 20... . seen ee NUMBER XVI—FEBRUARY. Mr. S. W. Holman on a New Method of Studying the Rela- tion between the Viscosity and Temperature of Gases .. Mr. J. W. Draper on the Fixed Lines in the Ultra-red Invi- sible -Region( of the Spectrum ....%.. 2...) 24). oe Dr. K. Heumann’s Contributions to the Theory of Luminous Mlamess— Part 1s ee ee es eta ee Mr. R. Mallet on the Conversion of the Geyser-throats in Leeland into Volcante Vents’. 32. /..0.. > ace eee Dr. W. F. Hillebrand on the Specific Heats of Cerium, Lan- thanum, and Didymimm (22.625 ee see Dr. E. Bouty on the Magnetization of Steel by Currents .... Mr. N.S. Maskelyne on the Optical Characters of Ludlamite. Mr. T. Muir on a Theorem in Continuants.:.............. Mr. F. Guthrie on a Sensitive Mercury Barometer ........ Notices respecting New Books :— Dr. W. Fleming’s Vocabulary of Philosophy, Mental, Moral, az. Metaphysical: with quotations and refer- ences for the use of Students ............+s.es4e- Proceedings of the Royal Society :— Mr. W. Spottiswoode on Stratified Discharges.—II. Ob- servations with a Revolving Mirror................ Proceedings of the Geological Society :— Prof. T. McKenny Hughes on the Silurian Grits near Gorwen; North Wales...:% 0. ..23...4. 3: oo eee Mr. W. Morgan on Mineral Veins) 395 se eee The Rev. J. F. Blake and Mr. W. H. Hudleston on the Corallian Rocks of England... 2)... . 22 ence Note on Mr. Lodge’s Paper ‘On a Mechanical Illustration of Thermo-electric Phenomena,” by Prof. M. Avenarius .. On an Arrangement for Reproducing, with the aid of the Siren, the Experiment of Foucault (arrest of a Rotating Disk ander the Action of an Electromagnet), by M. Rone OUZE eats aripe ts wm escde wre Ss SRT ee Aecle ee tt tee ee Observations on a Property of the Retina, first noticed by Tait, by Ogden N. Rood, Professor of Physics i in Columbia College On some Effects of Heat upon Voltaic Circuits completed by an Electrolyte, by W. Hellesen, of Copenhagen.......... Page 80 CONTENTS OF VOL. III.—FIFTH SERIES, Vv NUMBER XVII.—MARCH. Prof. G. Wiedemann on the Laws of the Passage of Electricity SUARECESSOS co 5 oer Te reste ait s aise Vie hues Atle 161 Mr. G. H. Darwin on a suggested Explanation of the Obli- em@iny.ot Planets to their Orbits)... 2... ee ey ee 188 Dr. E. Bouty on the Magnetization of Steel by Currents .... 192 Prof. P. E. Chase on the Nebular Hypothesis ——V. Athereal NE EN eo es Pea lhe sable escaws ols 203 Mr. O. Heaviside on the Speed of Signalling through Hetero- memes Neleamaph Circuits... 2. 2 ee ee one eon noes 211 Captain Abney on Fixed Lines in the Ultra-red Region of the © A STTSTIGD o/6) SIG epg prneiga weep Ion ee ace ieee pera ne 222 Notices respecting New Books :— Prof. A. Cayley’s Elementary Treatise on Elliptic Func- PPE PEN Pt el oe ch gos eo ora ety cag teats s ates 223 Mr. B. Williamson’s Elementary Treatise on the Differ- ential Calculus, containing the Theory of Plane Curves, with numerous examples....... Tice ie Cece year 227 Proceedings of the Royal Society :— Prof. J. Thomson on the Origin of Windings of Rivers in Alluvial Plains, with Rewarks on the Flow of Water Rouge bends in, Pipes)... ) eee ak pee re oe 228 Mr. W. Crookes on Repulsion resulting from Radiation. ieifiuence of the Residual Gates. 6 25 e- ee a - Proceedings of the Geological Society :— =: - - Mr. H. F. Blanford on the Origin, Glacial or Volcanic, of ‘the Talchir Boulder-bed of India and the Karoo Boul- Memeo Sout ATTICA 8 je okey a ees ks eee! 235 Mr. J. A. Phillips on the Chemical and Mineralogical Changes which have taken place in certain Eruptive iockwsnor INortn Wales... 05.66. sc es he bene 235 On the Determination of the Polar Distance in Magnets, by "s,, LECSEDIOIE Gh. ieee ete IAM nein AGE gay en Plea oe a ie he inne a re a 236 Photographs of the Spectra of Venus and e Lyre, by Professor 221. LEDGE. arate epee ee a ee ir eres oar cr err 238 On the Spectra of Metals at the Base of Flames, by M. Gouy. 238 NUMBER XVIIT.—APRIL. Prof. C. Niven on the Theory of an Imperfectly Homogeneous — Aa rete SOI lay oe ese ig 8 SAPS nae, CH TY pu ee ae MS eee 241 Prof. G. C. Foster on the Polarization of Heat ............ 261 Mr. J. Ennis on the Physical and Mathematical Principles wimenow Ne pillar, EheCOry Renin wc. asses kB ss th lia eae ak 262 Mr. R. H. M. Bosanquet on the Theory of Sound......... 271 Prof. Challis on a Theory of the Action of the Cup-shaped Radiometer with both sides bright .................... 278 vil CONTENTS OF VOL. IlI.—FIFTH SERIES, Page Mir, We Pattison Mar on Galltum:.?2220¢ .anee ae eee 281 Prof. J. Emerson- Reynolds’s short Reports from the Chemical Laboratory of Trinity College, Dublin (Nos. 2 and 3) . 284 Prof. J. Trowbridge on Liquid Vortex-Ringsic Goan eee 290 Proceedings of the Royal Society : Prof. W. G. Adams and Mr. R. E. Day on the Action of dixehton Selenium 5 oo 2ce tee a chee) i he ee 295 Lord Rayleigh on the Application of the Principle of Reciprociby, bo “A COMShICS ie ere ee ee 300 Mr. J. G. Grenfell on Supersaturated Saline Solutions.. 304 Proceedings of the Geological Society : The Rey. J. F. Twisden on possible Displacements of the Earth’s Axis of Figure produced by elevations and depressionsion her suriace i, = o.06 58 311 Mr. F. G. H. Price on the Beds between the Gault and Upper Chalk, mear Folkestone. 2258.25. 0.00 soe 313 On Diffusion and the Question, Is Glass Impervious to Gases ? by Gz, Quincke of. cf cau fee eee ee ee 314 On) Cosmic Vulcanism, by Mo schermale 2.227. ee 316 Researches on Heat-Spectra, by P. Desains .............. 318 On the Polarized Light of the Rainbow, by Prof. J. Dechant. 319 On the Nature of Gas Molecules, by L. Boltzmann, of Graz.. 320 NUMBER XIX.—MAY. Dr. J. Kerr on Rotation of the Plane of Polarization by Re- fection trom the Pole olla; Mapnet.. 77a ae ee 321 Mr. R. H. M. Bosanquet on the Theoryof Sound.) o: \ ee 343 Mr. O. J. Lodge’s Reply to the Note of Professor M. Avenarius. 349 Mr. W. J. Lewis on Crystallographical Forms of Glaucodote. (Rlate WG y.attcetiek PU Mabey it oi. nee ume nee 354 Prof. A. Des Cloizeaux’s Supplementary Note to his Memoir onbumite 32h eae ee eas rece ee 357 M. E. Bertrand on the Law of Twinning and Hemihedrism of Leucophane:c gc. shew ce tee eee hee te ee ee 307 Mr. T. Muir on an Extension of a Theorem in Continuants, wibh an importantwapplicahon ei...) ne. he eee 360 Dr. K. Heumann’s Contributions to the Theory of Luminous Mlames.’ (Plate TD.) ) foe t hE Po ch eae ee on ee 366 Messrs J. A. Wanklyn and W. J. Cooper ona Method of de- termining the Amount of Proteine Compounts in Vege- table uUbSPANCES toc. fe ete ae eee een eek ee 382 Notices respecting New Books :— Mr. G. K. Gilbert on the Colorado-Plateau Region consi- dered as a Field for Geological Study...........:.. 386 Proceedings of the Royal Society :— Mr. J. Thomson's Experiments on Contact Electricity between Non-Conductors....¢.. 05. .: 020. + es ee 389 CONTENTS OF VOL. III.— FIFTH SERIES. vii Proceedings of the Geological Society :— Page Prof. R. Harkness and Dr. H. A. Nicholson on the Strata and their Fossil Contents between the Borrowdale Series of the North of England and the Coniston Flags .... 392 Mr. C. Callaway on anew Area of Upper Cambrian Rocks in South Shr opshire, with the Description of a new Rereribaewe 20s Siew seat Atl eho Pee atleta ee tasie 3 eRe sso a 393 Mr. J. D. Enys on Sandworn Stones from New Zealand. 394 Supplement to a Theory of the Cup-shaped Radiometer, by MONET LEM ne occ eS a ce Sve Mallat MRM CL Ne! oh an ety 395 Diathermaneity of Metals and of Paper, by M. Aymonnet .. 396 On the Reflection of Polarized Light, by M. Croullebois .... 397 Note on Molecular Volumes, by Prof. F. W. Clarke........ 398 NUMBER XX.—JUNE. Mr. W. M. Hicks on some Effects of Dissociation on the Phy- SieommheOMeTtcs OL Gases! 2). ois seine esse ow es 401 Mr. R. H. M. Bosanquet on the Theory of Sound.......... 418 Mr. J. R. Harrison’s Experimental Researches on the sup- posed Diathermancy of Rock-Salt. (Plate III.).......... 424 Prof. E. Edlund on the Thermal Phenomena of the Galvanic ‘Eile: and Electromotive Forées..103 3 4. sno esse ee ep 428 Mr. S. T. Preston on the Mode of the Propagation of Sound, and the Physical Condition determining its Velocity, on the Basis of the Kinetic Theory-or asess: Sonne. sees ok 441 Mr. W. J. Lewis’s Crystallographic Notes. (Plate 1V.) .... 453 Lord Rayleigh’s Acoustical Observations ................ 456 Notices respecting New Books :— Prof. W. C. Unwin’s Elements of Machine Design : an Introduction to the Principles which determine the Arrangement and Proportion of the Parts of Machines, and a Collection of Rules for Machine Design ...... 464 Proceedings of the Royal Society :— Mr. W. Crookes on the Theory of the Radiometer .... 467 Researches on the Metallic Reflection of Polarized Obscure Mentctvayie. by Wi Moutomee asc) dese. & aoe aman Ee ATT On the Diffusion of Vapours through Clay Cells, by Dr. J. LPULLION). SSG a Ae eae hah ns ge eae anne 480 NUMBER XXI.—SUPPLEMENT. Dr. R. Bornstein on the Influence of Light upon the Electrical esistance Ob Wetalsi ceo, 2 ee Et oe 481 Drees. Mallson Cumulative Resolution= 424.425.0512... .. 492 Prof. E. Edlund on the Thermal Phenomena of the Galvanic eile and Mlectromotive Morces.. ¢) 2. Wee. a oe 501 Vill CONTENTS OF VOL. III.—FIFTH SERIES. Page Mr. R. E. Baynes on the Steam and Hoar-frost Lines of : WW aber-Substamee 5 acs parece oi $ avene'st ps, ch ea eee eae ee 512 Mr. O. J. Lodge on a Modification of Mance’s Method of measuring Battery Resistance. (Plate V.). ............ 515 Mr ONS; Maskelyme.on Umdlamite . \o15. je cycien apie eae 525 Notices respecting New Books :— Mr. A. H. G. Hobson’s Amateur Mechanic’s Practical Handbook, describing the different Tools required in the Workshop, the Uses of them, and How to Use them; also Examples of different kinds of Work, with full De- scriptions and, ra wan pss easterlies cur tele ee ee 526 Mr. W. Whitaker’s Geology of the Eastern End of Essex. 527 Proceedings of the Royal Society: — Dr. W. Huggins on the Photographic Spectra of Stars.. 527 Mr. G. F. Fitzgerald on the Rotation of the Plane of Po- larization of Light by Reflection from the Pole of a Miaomet o..s 5 tse ste Sepia tina vafeuge aca a ha ah ee 529 Mr. H. Tomlinson on the Increase in Resistance to the Passage of an Electric Current produced on Wires by Stretching sl eer ete adele ore cen es ie 532 Mr. W. Spottiswoode on Stratified Discharges.—III. On a rapid Contact-breaker, and the Phenomena of the PLOW 0. LES s else canes eae sece ate Geos gi 539 ees of the Geological Society :— Prot. i. Hull on the Upper Limit of the essentially Nae Beds of the Carboniferous System, and the necessity for the establishment of a ‘Middle Carboni- ferous Group<.c sso ee ae ee eee 539 Mr, H. K. Jordan on Coal-pebbles and their Derivation. 541 On the Employment of a Silvered Glass as a Camera Lucida, by, Av Derquem:). Gos eile owe cles cine creas (ones ee 541 Note on the Sensation of Colour, by C. 8S. Peirce .......... 543 On Accidental Double Refraction, by J. Macé ............ 547 PLATES. J. Illustrative of Mr. W. J. Lewis’s Paper on n Crystallegraphical Forms of Glaucodote. II. Illustrative of Dr. K. Heumann’s Paper on the Theory of Luminous Flames. III. Illustrative of Mr. J. R. Harrison’s Paper on the Supposed Diather- maucy of Rock-Salt. IV. Illustrative of Mr. W. J. Lewis’s Paper on the Crystallography of Barium Nitrate. V. Illustrative of Mr. O. J. Lodge’s Paper on a Modifcation of Mance’s Method of measuring Battery Resistance. THE LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES. ] SAN UATE YV 1ST. I. Contributions to the Theory of Luminous Flames. By Dr. Kart Heumann™*. NTI lately Davy’s theory of luminous flames sufficed to explain all observed phenomena; but recently our knowledge has been enriched by a series of observations which cannot be well brought into accordance with generally ac- cepted notions. For example, the observation of Frankland that the flames of hydrogen and carbon monoxide become luminous when these gases are burned under pressure, is opposed to the former view that the luminosity of flame is caused by the presence of solid particles which become intensely heated. Knapp’s experiment, showing that the luminosity of a flame may be diminished, not only by admitting air, but also by a due admixture of nitrogen or carbon dioxide, can- not be explained on the supposition of an oxidation of the carbon previously suspended in the burning gas. For these and other reasons, Davy’s theory must either be altered or replaced by a new hypothesis. The latter course does not appear to me to be required. In the following contributions I shall endeavour rather to develop this theory than to over- throw it. The genius of Davy is made apparent when we find that the discovery of so many facts since his day has in no way overthrown his theory, but has only rendered a de- velopment of it necessary in order to bring it into keeping with an advancing science. * From Liebig’s Ann. der Chemie, vol. clxxxi. part 2, pp. 129-153, and vol. clxxxil. pp. 1-29. Translated by M. M. Pattison Muir, the Owens College, Manchester. Phil. Mag. 8. 5. Vol. 3. No..15. Jan. 1877. B 2 Dr. Karl Heumann’s Contributions to I have generally in my remarks adopted a chronological arrangement of the various researches, because it is only thus that the course of thought which I have followed can be logically represented. A systematic arrangement would, it is true, place the simpler before the more complex conditions ; but in the present case the latter, which occur chiefly in the case of luminous carbon-containing flames, are the more im- portant and have been more studied. The experience gained from the study of flames burning under complex conditions is tested and applied in the case of simpler flames, and so becomes a guide to the explanation of the conditions affecting luminous flames in general. Diminution and Restoration of Luminosity in Hydrocarbon- flames. In the greater number of researches which have hitherto been conducted upon the luminosity of flames, those flames have been principally examined the luminosity of which is to be ascribed to the presence of carbon, and methods of re- search in which the luminosity has been either increased or diminished have, for the most part, been adopted. Such methods are open to many objections, the principal of which (viz. the introduction of various agencies acting now in this way, now in the opposite, during the same ex- periment) has been too much overlooked. By reason of this oversight, researches, leading to diametrically opposed conclusions, have been published ; and since Davy’s theory is no longer of universal application, we have been left with- out any means of bringing the facts concerning luminous flames into harmony with one another. Frankland has broached the hypothesis that the luminosity of flame is not due to particles of suspended carbon, but is caused by the vapours of heavy hydrocarbons which radiate white light. Strong positive evidence in support of a view so much at variance with the generally accepted theory, could hardly be expected ; and Frankland has relied principally upon the fact that we are acquainted with many luminous flames in which we cannot suppose that solid matter is present. To the instances already known Frankland has added the interesting observation that hydrogen and carbon monoxide when burned in oxygen under a pressure of 10 to 20 at- mospheres, yield a luminous flame affording a continuous spectrum, and also that the faintly luminous flame of alcohol becomes as bright as that of a candle when the pressure is in- creased to 18 or 20 atmospheres*. These experiments are * Compare L, Cailletet, Compt. Rend. clxxx. 487. the Theory of Luminous Flames. a not so convincing as might at first sight appear, inasmuch as we know that the temperature of the flame is increased at high pressures*, and also that at the temperature of the electric spark many gases yield a continuous in place of a line spectrum. The power of gases as regards emission of light also varies considerably under these circumstances; and it does not ap- pear that we are absolutely necessitated, as Frankland has supposed, to ascribe the increase in luminosity to the increased density of the gas, although doubtless this circumstance is not without considerable influence. The inquiry as to the nature of hydrocarbon-flames is quite independent of the meaning which we may attach to these appearances ; and if Frankland puts forward the aboye-cited phenomena of combustion as analogies to guide him in views concerning carbon-flames, no very forcible argument can be really deduced from the examples, because, as W. Stein f has pointed out, it cannot be shown that the reaction in luminous carbonaceous flames must be an analogous one to that described above. Frankland’s declaration that the soot must be regarded as an accumulation of heavy hydrocarbons whose vapours are condensed on the cold body brought into the flame, may be regarded as almost confuted by Stein’s objection that in this case the soot must become gaseous at higher temperatures (which is not the case). New doubts arise concerning the prevailing theory when we consider that the admixture not alone of air, but also of nitrogen, carbon dioxide, or other completely indifferent gases, with coal-gas causes a great decrease in the luminosity of the flame of that gas. Hence we cannot trace the decrease in luminosity solely to the more energetic oxidation of carbon contained in the flame. The experiments of Steint and R. Blochmann§ allow us to supposé that, the particles of carbon being more widely separated by the admixed gases, the oxygen of the air is able to oxidize them to carbon monoxide more quickly than under the ordinary circumstances of combustion. To the theory of these authors, viz. that diminution of luminosity is a consequence of dilution, Wibel || opposes the view that the absorption of heat brought about by the admix- ture of an indifferent gas is the sole cause of decrease in * Ste.-Claire Deville, Compt. Rend. Ixvii. 1089, + J. pract. Chem. [2] viii. 401. t Ibid. § Lieb. Ann, elxyii. 355. || Deut. chem, Ges. Ber. vil. 226. Be 4 Dr. Karl Heumann’s Contributions to luminosity. Wibel was led to this view by considering the fact that a mixture of coal-gas and air, nitrogen, or carbon dioxide, which burned with a blue flame, became luminous and burned with a smoky flame when the tube from which the mixture issued was strongly heated. In this case the dilution must have been increased by the increase of tempera- ture ; nevertheless the flame became luminous. Jn order to convince one’s self of the justness of the conclu- sions which are drawn from this observation, it is necessary to examine somewhat closely the method adopted by Wibel in his investigation. He says, “A tube of platinum, 8 to 10 centims. in length, is attached to an ordinary Bunsen’s burner which is closed at the bottom; the gas to be burned is brought into the burner by means of a tube soldered to the lower part; when the flame of the burning .gas has been adjusted to the proper point, the indifferent gas is admitted until the flame is rendered non-luminous ; the platinum tube is then heated by means of two non-luminous Bunsen flames held horizontally on either side of the tube, so as to ensure that it be equally heated . ... The same appearance is noticed in the case of the ordinary Bunsen flame, rendered non-luminous by ad- mixed air, when the platinum tube is placed in the opening of the lamp and is heated.” The last mentioned experiment, as described by Wibel, must be controlled before one can justly identify the diminution of luminosity in the Bunsen burner with Knapp’s experiments upon diminution. Some time ago Barentin* showed that the amount of luminous gas which enters a given space is very different according as the gas is or is not ignited. Barentin believed that the explanation of the smaller amount of gas entering a burning lamp was to be found in the counter pressure exercised by the burning, and therefore expanding gas, upon the entering gas. Blochmannf showed that the diminished consumption of gas was to be traced solely to the increase of volume caused by the gas passing over the heated upper part of the burner. The fact that a mixture of gases issuing from a Bunsen lamp through a strongly heated tube burns with a luminous flame, may therefore be due to causes other than that put forward by Wibel, viz. rise in temperature of the flame ; for it is evidently an improbable supposition that the consumption of gas, and therefore also the quantity of air (or other gas) drawn into the burner, will be unaffected by the passage of the gas over a glowi ing tube ; and so also it cannot, & priort, be expected that the proportion between air and gas will re- * Poge. Ann. cvii. 183. t J. fiir Gastelennnna v. 355. | the Theory of Luminous Flames. 5 main the same when the mixture is passed over a hot as when it is passed over a cold tube. I was therefore compelled to alter the conditions of experi- ment in order to render void that particular effect of the hot tube which has just been described. If rise of temperature of the flame is the cause of increased luminosity, the effect must be the same if one heats, not the gaseous mixture, but only the indifferent gas. This experi- ment may be readily carried out with a Bunsen’s burner, through the two air-tubes of which are passed small platinum tubes about 7 centims. in length ; the outer openings of these tubes are narrowed so that a quantity of air just sufficient to bring about complete non-luminosity is allowed to enter. A thin-walled glass tube, the upper rim of which is covered with platinum, may, with advantage, take the place of the ordinary metal tube of the Bunsen’s lamp; the latter tends to cool the heated air to too great an extent. On lighting the gas issuing from the glass tube it burns with a non- luminous flame ; but on strongly heating the two platinum tubes by means of Bunsen’s burners (care being taken that the products of combustion do not enter the platinum tubes) the flame becomes luminous. It might be supposed that this fact is to be explained on the supposition that the volume of air passing over the plati- num tubes is unaltered by heating these tubes, but that the true quantity of air calculated for equal temperatures is much smaller when the tubes are hot, and that there is therefore a deficiency in the amount of oxygen required to completely burn the carbon, and so to maintain the flame in a non- luminous state. In order to show that this supposition is untenable, and that the increase in luminosity is to be ascribed solely to the rise in temperature of the flame, the experiment must be modified. Coal-gas and air, or carbon dioxide, are mixed in a gasometer in such proportions that, when conducted through a platinum tube about 10 centims. in length and 8 millims. in width, the mixture burns with a clear blue flame. If the platinum tube be heated to redness, the flame becomes nearly as luminous as that of ordinary coal-gas. On allowing the platinum tube to cool, the flame again becomes non-luminous. From this experiment the conclusion is evidently to be drawn that it is the added heat alone which has caused the ~ flame to become luminous, inasmuch as a diminished supply of air cannot in this case, as in the former, have influenced the result. It remains, however, to be investigated whether the gaseous 6 Dr. Karl Heumann’s Contributions to mixture, burning with a luminous flame in consequence of the application of heat, has or has not been altered so that its luminosity shall continue when it has been allowed to cool to the ordinary temperature. In other words, if the increase in luminosity is directly due to increase in temperature of the flame, and is not brought about by a chemical change in the gaseous mixture, then the flame which appeared luminous at the point of the strongly heated tube should again become non- luminous when the gaseous mixture is cooled, after having passed through the heated tube, and is then ignited. This experiment may be carried out by connecting two glass tubes by means of gypsum to the platinum tube, the outer glass tube being V-shaped and being surrounded by cold water. If the mixture of gases be passed through this ar- rangement, the platinum tube being strongly heated, and be ignited at the orifice of the glass V-tube, a non-luminous flame is noticed ; whereas if the V-tube be removed and the gases be ignited at the orifice of the platinum tube, the flame becomes luminous. More simply, the experiment may be carried out by burning the gaseous mixture as it issues from a platinum tube about 12 or 15 centims. in length: in heating this tube near to its orifice the flame becomes luminous; but on heating the tube at a point further back the luminosity of the original flame is not increased, because the heated gases are again cooled by passing over the outer part of the platinum tube. In employing a mixture of air and coal-gas under certain conditions, it is found, as Wibel has noticed, that “the gas aspirated from the opening of the burner reveals—by the amount of water and carbon dioxide which it contains, as also by its burning with a luminous flame under the ordinary conditions ’’—that a partial decomposition has taken place. - While Wibel noticed a not inconsiderable deposition of carbon when air and coal-gas were passed through a red-hot platinum tube, in my experiments, in which the air only was passed through a heated platinum tube, no such deposition was noticed in the glass tube, at the orifice of which the gases burned with a luminous flame for a considerable length of time. In Wibel’s case the deposition of carbon was doubtless due to a too great local heating of the platinum tube through which the gases were passed. Such an intense heating is not necessary in order to attain the aim of the experiment. From that experiment in which the flame of a gas, previously ren- dered non-luminous, was restored to luminosity by means of heat, Wibel draws very far-reaching conclusions. He rejects the deductions of previous experimenters; but in doing so he rushes too far to the opposite extreme. Tor example, he believes himself justified in concluding :— the Theory of Luminous Flames. 7 “1. Decrease in luminosity cannot be due to dilution of the gases, whether understood in Frankland or Blochmann’s meaning of the term, inasmuch asin the above mentioned re- searches such dilution was at any rate increased by heating, yet the flame became luminous.” “2. Decrease in luminosity, in Knapp’s experiments, as also in the case of the ordinary Bunsen’s flame, is much more to be traced to the cooling effect, on the interior of the flame, of the entering gas. By heating the latter the flame becomes luminous.” Wibel finds “a most noteworthy argument” in favour of these two points in the peculiar behaviour of the flame of coal-gas and oxygen. On the one hand, this flame becomes non-luminous only when the current of oxygen is rapid, and when the flame is cooled by metallic gauze ; on the other hand, by proper treat- ment the flame may be made a source of intense light. These circumstances show, according to Wibel, that neither dilution nor oxidation is a cause of decrease of luminosity. By similar reasoning it might be shown that Wibel’s theory is itself erroneous. Hvyeryday experience tells us that the blue flame of Bunsen’s burner, as well as that of the blowpipe, possesses a much higher temperature than the ordinary luminous flame ; but if Wibel be correct in saying that decrease of luminosity is a consequence of cooling only, then, logically, the tempe- rature of the luminous flame ought to be higher than that of the non-luminous flame. Those flames whose luminosity is decreased by means of air might perhaps not be classed with those in which a similar result is brought about by means of indifferent gas; but little would thus be gained, for the Bunsen’s flame behaves, so far as its power of becoming luminous is concerned, similarly to Knapp’s flame, the only distinctive point (the higher flame-temperature consequent upon the entrance of oxygen in the admitted air) not being proportionately altered by heating the tube of the burner, the flame nevertheless becoming luminous. But while, in the case of flames rendered non-luminous by indifferent gases, it might be supposed that the heat gained when the tube of the burner is warmed merely serves to re- place that lost by absorption into the entering inert gas (which heat had formerly caused luminosity), this supposition is con- tradicted by the already cited analogous case of decrease of luminosity by means of air, inasmuch as it cannot be supposed that there is a withdrawal of heat from the luminous material in the flame, the temperature of which is greatly increased. 8 Dr. Karl Heumann’s Contributions to In experiments upon decrease of luminosity caused by com- pletely indifferent gases free from oxygen there will, of course, be a considerable decrease in temperature, because a fixed sere of heat must be divided throughout a larger volume of gas. W. Stein*, however, has pointed out that in these cases a cause other than lowering of temperature is at work. He shows that a flame rendered non-luminous by means of nitro- gen yet possesses so high a temperature that it is able to decompose, with deposition of carbon, coal-gas conducted in a glass tube through it; he also observes that an inflammable gas, carbon monoxide, whose pyrometric effect is nearly as great as that of coal-gas, causes the flame of the latter gas to become non-luminous. In order to bring about the complete non-luminosity of 1 volume of coal-gas, there is required 1-6 volume in Bunsen’s burner, and 0°9 volume in Brénner’s burner, of carbon monoxide. In this case decrease in luminosity is not accompanied by a real decrease in the temperature of the flame; and we are obliged to allow that dilution of the burning gas plays an important part, and may of itself, independently of any ab- sorption of heat (which often takes place simultaneously) cause decrease in luminosity. Wibel’s experiment does not prove, as that author supposes it to do, that cooling of the interior of the flame is the sole cause of decreased luminosity, because the flame is simul- taneously altered in its composition, i.e. it is largely diluted by the entering gas. We find, then, some of those observers who have been already mentioned tracing decreased luminosity, brought about by admixed gases, solely to the diluting action of these gases ; we find Wibel, on the other hand, tracing this decrease solely to the cooling action of these gases; but it appears to me that the truth lies between these two conflicting views. It is difficult to devise experiments in which two or more causes tending to decrease luminosity are not simultaneously at work ; and yet every thing depends upon our being able sharply to distinguish between these various causes. It will only be possible to gain a clear knowledge of the processes going on in flames when we are able to separate these pro- cesses and to study each alone. It appeared to me necessary to devise an experiment in support of the well-known statement—the luminosity of a flame is diminished by cooling—which should admit of no other interpretation than this. By the following method I have been able to show that * J. pract. Chem. ix. 183, the Theory of Luminous Flames. 9 cooling a flame is of itself capable of bringing about decrease of luminosity, and that luminosity may be then restored by simply applying heat; the result cannot be called in question by supposing dilution or oxidation to have taken place. A luminous gas-flame, 5 to 4 centims. in length, proceeding from the point of a blowpipe or other narrow tube, is allowed to play horizontally upon a platinum basin suspended in a vertical position, so that the flame may broaden out and be- come blue. In this well-known experiment decrease of luminosity must not be traced solely to withdrawal of heat by means of the metal, inasmuch as the broadening out of the flame enables oxidation and dilution, as well as cooling, to influence the result. If the platinum basin be now heated, on the side opposite to that on which the flame impinges, by means of a Bunsen’s lamp held horizontally, the gas-flame becomes more and more luminous as the temperature of the basin increases, until it finally is restored to its original degree of luminosity. Of course the metal must be perfectly pure, and must not be touched with the fingers before the experiment; else the flame will be coloured yellow. It is here shown that luminosity of the flame, which had been diminished by the use of the platinum basin, is restored solely by raising the temperature. If the Bunsen lamp be removed, the flame quickly decreases in luminosity until it becomes blue. In this experiment, in which decrease of luminosity is brought about by lowering the temperature, the objection formerly fraised—vyiz. that the broadening out of the flame complicated the result—can no longer be maintained, inas- much as the small decrease of volume consequent upon the cooling would tend to produce an opposite result. It is there- fore experimentally proved that cooling a flame is itself sufficient to cause a decrease in the luminosity of that flame. Reasons have been already given which oblige us to ac- knowledge that dilution of a flame by admixed gases is of itself sufficient to cause decreased luminosity* (Bunsen’s flame, decreased luminosity by carbon dioxide); and inas- much as the admission of a cold gas into a flame must with- draw heat from that flame, it is concluded that the decrease in the luminosity of carbon-containing flames brought about by * Frankland has observed that decrease of luminosity of carbon-con- taining flames is a consequence of dilution by lowering of atmospheric ressure; and he has concluded that the decrease of luminosity is con- nected with the decrease of pressure. I have not cited this experiment in proof of the effect of dilution in decreasing luminosity, because lower- ing of temperature is associated with lowering of pressure, and this must have an intluence in decreasing the intensity of the light. | 10 Dr. Karl Heumann’s Contributions to admitting indifferent gases is due to dilution, and also to lower- ing of the temperature of the flame by these gases. The fact that a flame which has been rendered non-luminous by means of indifferent gases may be again rendered luminous by heating the tube of the burner, ia hope to explain by es- tablishing the following points. A flame formed of coal-gas and an indifferent gas or air, and burning blue, requires, in order to cause it to become luminous, a higher temperature than that which is possessed by the luminous undiluted flame. The flame of a Bunsen’s burner in which non-luminosity has been brought about by means of air is very hot, but becomes luminous when the temperature is much increased by heating the tube. These points in the behaviour of the flame of coal-gas and oxygen, which Wibel adduced in support of his theory, are explained by me as follows. Blochmann and Wibel both noticed that the luminous flame of a Bunsen’s lamp, fed with oxy gen by one opening while the other is closed, can be rendered non-luminous only by employing a rapid current of oxygen and a cooling surface of metallic gauze, simply because the temperature of the flame, when pure oxygen is employed, is very high. The absorption of heat caused by the entrance of cold oxygen, as also the absolute rise in temperature required by the gaseous mixture in order that it shall become luminous, are entirely, or almost. entirely, equalized by the intense heat produced by the combustion in pure oxygen. ‘Therefore the production of non-luminosity is so difficult; that non-lumino- sity should be brought about only by employing a rapid stream of oxygen and a cooling metallic surface is self-evident. It is known that a gas-flame may be caused to burn with great luminosity by the admission in proper quantity, and by a proper method, of pure oxygen. ‘This fact certainly depends upon the production of a very high flame-temperature unac- companied by such dilution as is noticed in the Bunsen’s or blowpipe flame when air is employed, and when the diluting gas is nitrogen. In this experiment it is found that the greatest luminosity occurs when a rapid stream of oxygen is introduced, but that too great a quantity of oxygen, as too small a quantity, tends to decrease luminosity. Inasmuch as a much higher temperature might be reached by increasing the quantity of oxygen beyond that at which the maximum of light is evolved, it seemed probable that the actual action of this excess of oxygen in decreasing luminosity was not to be traced solely to its cooling and diluting the burning gas, as is the case with altogether indifferent gases, but that a third cause, perhaps more energetic than either of those just men- tioned, was at work. the Theory of Luminous Flames. 11 This supposition led to a more exact examination of the changes brought about in the flame of coal-gas by an excess of oxygen. When a flame, burning at the orifice of a wide tube, is placed in an atmosphere of pure oxygen, a notable increase in luminosity takes place within the flame-mantle, which is itself, nevertheless, considerably decreased in size, while the outer non-luminous border of the flame is broadened out. In order to study this action more narrowly, I have found it ad- vantageous to make the flame very small by allowing the gas to issue from a narrow tube. If, for instance, a flame of coal- gas 4 to 5 centims. in length, issuing from a blowpipe-nozzle, be plunged into a reversed jar of oxygen, the appearance of the flame is greatly altered. The outer, scarcely visible, part of the flame increases enormously in size at the ex- pense of the inner and luminous part. A small luminous _ point alone represents what was formerly a broad luminous band; at the same time, the whole flame decreases propor- tionately from what it had been in air. This is to be ac- counted for by the absence of diluting nitrogen, a circum- stance which also causes the temperature of the flame to increase considerably. The decrease in luminosity can scarcely be traced to any other cause than the large quantity of pure oxygen, which, by diffusing inwards into the narrow flame, brings about an immediate oxidation of the contained carbon, which is, therefore, not necessitated to spread through the flame in a red-hot state in order to find oxygen sufficient for its combustion. | | If this supposition be true, it follows that decrease of lumi- nosity can only be brought about by combustion in oxygen in the case of those flames the light-giving constituent of which is capable of being conyerted by excess of oxygen into a feebly luminous gas, but that those flames the luminosity of which is due to some substance which cannot be transformed by oxygen into such a gas must continue to burn in oxygen, even when issuing from the smallest orifice, with brillianey— that, indeed, an increase in luminosity must be brought about under such conditions, because of the increased temperature of the flame. Direct experiment confirms these deductions, and therefore also the original supposition. Hydrogen saturated with vapour of chromium oxychloride (Cr,0,Cl,), and issuing from a blowpipe-nozzle, burns in oxygen with a dazzling white light: the luminosity is in this case due to the presence in the flame of chromium oxide. If the hydrogen be laden with the vapour of stannic chloride (SnCl,), it burns, under the same conditions, with a blue flame of much 12 Dr. Karl Heumann’s Contributions to greater brilliancy than when the combustion proceeds in ordinary air. The product of combustion is in this case also a solid, viz. stannic oxide. In order to prove that a similar appearance is noticeable in the case of luminous vapours, in so far as these are not oxi- dized to non-luminous gases by excess of oxygen, hydrogen was conducted through a vessel containing common salt and zine filings moistened with dilute hydrochloric acid (as in Bunsen’s well-known experiment). The gas issued from a blowpipe-nozzle and burned with an intensely yellow flame, the luminosity of which was not decreased, but rather the reverse, when the flame was plunged into a vessel containing oxygen. Inasmuch, therefore, as the decrease in luminosity which a small coal-gas flame suffers when burned in oxygen is due to the presence of an excess of the latter gas, the fact that this decrease does not take place to so marked a degree when the flame is burned in ordinary air is to be traced to the presence of inert nitrogen, which, by diluting the oxygen, diminishes the energy of the oxidation. ~ In order to prove the justness of this conclusion, the nitro- gen in a given volume of air was replaced by carbon dioxide ; 2.é. a cylinder was filled over water with 1 volume of oxygen and 4 volumes of carbon dioxide ; and, after carefully mixing the gases, a coal-gas flame, burning at the orifice of a small brass tube, was brought into the mixture. The flame conti- nued to burn with a degree of luminosity equal to that which it exhibited in ordinary air; it follows, therefore, that the fact of dilution alone influences the result, the nature of the diluting gas being unimportant. Hvery indifferent gas, including the products of combustion themselves, must exert a similar influence. When an ordinary flame, issuing from a fine orifice, is burned in oxygen, the luminosity decreases for the reason formerly assigned; but as soon as the products of combustion (water and carbon dioxide) accumulate sufliciently to dilute the oxygen considerably, the luminosity begins to increase. The flame which had been re- duced to a luminous point becomes enlarged until it presents an appearance similar to that exhibited by it when burning in ordinary air; this happens at the moment when the oxygen in the vessel is diluted by the products of combustion to the same proportionate extent as it is diluted by nitrogen in the atmosphere. If the combustion be continued beyond this point, the lumi- nosity again decreases—not as was noticed in the former case, by a great decrease in the size of the flame-mantle, but by the Theory of Luminous Flames. 13 general weakening of the light until complete non-luminosity is attained. The flame then increases in size, and finally goes out. ' This kind of non-luminosity exhibits a great resemblance to that noticed when the burning material is diluted by mixing with it indifferent gases, such as carbon dioxide and nitrogen; the causes of non-luminosity are indeed in both eases identical. Inasmuch as every ordinary flame (with the exception of the flames of explosive substances) requires for its existence two combustibles, the chemical union of which brings about the glowing of the gases, it follows that it is a matter of indifference which of the combustible materials is diluted by indifferent gases—the coal-gas for example in Knapp’s experiments, or the oxygen of the atmosphere. And in fact it may be shown that a gas burning with luminosity in ordinary air, burns with a blue flame when plunged into a mixture of 5 volumes of air with 2 volumes of carbon dioxide. This experiment is the converse of Knapp’s; and, as in that case, decrease of luminosity is due to dilution, and cooling of the flame. Instead of diluting the air with carbon dioxide previously to the experiment, the products of combustion may be allowed themselves to bring about this dilution, the gas being burned in an inverted globe: it is then noticed that the flame quickly becomes less luminous and then burns blue, at the same time increasing in size. The flame remains non-luminous and yet large, but again becomes luminous if transferred at the proper moment to the atmosphere ; otherwise it goes out. This experiment on decreased luminosity is perfectly ana- logous to that described in the case of a flame burning in oxygen; only in this instance nitrogen was absent, and the products of combustion were the sole diluents of the oxygen. ! When a small gas-flame is plunged into an inclosed volume of oxygen there is noticed, then, 1. Decrease in luminosity of the flame, accompanied by increase in the size of the flame, the light from which is very small ; 2. Increase in luminosity commences, and proceeds until the flame exhibits an appearance similar to that which it possesses in ordinary air, because the energetic oxidizing action of the pure oxygen upon the glowing matter in the flame is moderated by the diluting products of combustion ; 3. A general decrease in luminosity ensues, but now by a lowering of the intensity of light of the whole flame, brought about by the increasing dilution of the oxygen by the pro- 14 Dr. Karl Heumann’s Contributions to ducts of combustion, and also by lowering of the temperature of the flame. These two causes gradually increase, until the flame, which continually increases in size, becomes blue, then invisible, and finally, being cooled below the point of ignition, goes out. Besides cooling and dilution of the carbon-containing flame, a third cause has been shown to influence the decrease of luminosity—viz. the energetic destruction of the luminous material, 2. e. theyoxidation of carbon to feebly luminous gases (carbon monoxide and dioxide). Generalizing the results of the experiments upon the means by which flames which have become non-luminous may be again restored to luminosity, we find: 1. That hydrocarbon flames which have lost their luminosity by withdrawal of heat again become luminous by the addition of heat. 2. That flames rendered non-luminous by dilution with air or indifferent gases become luminous by raising their tempe- ratures. 3. That flames rendered non-luminous by excess of oxygen, which brings about energetic oxidation of the carbon, are again rendered luminous by diluting the oxygen with indifferent ases. : It would be very interesting to observe whether flames rendered non-luminous by admixture of indifferent gases may be again rendered luminous by heating the tube of the burner, the combustion being carried out under such pressures as would cause the molecules of the burning gases to maintain their original proximity to one another, notwithstanding the ad- mixture of nitrogen or carbon dioxide. I have not myself the necessary apparatus at hand ; but I would direct the attention of any chemist who is interested in these experiments upon lumi- nous flames to the subject. It would also be well to note whether the decrease in luminosity suffered by a small gas-flame when burned in oxygen is maintained when the oxygen is diluted to one fifth or further. If, in the case of previous observers, the point of dispute was whether cooling or dilution were the cause of decreased luminosity in carbon-containing flames when the combustible material was mixed with air or indifferent gas, to me it appears that there are at least three causes, each of which is capable of decreasing the luminosity of these flames, viz. withdrawal of heat, dilution, and oxidation of the luminous material. In most cases two or all of these causes are at work :—in the Theory of Luminous Flames. 15 non-luminosity brought about by nitrogen and carbon dioxide, especially dilution and heat-absorption; in the widening out of the flame caused by a cold surface, absorption of heat and more rapid oxidation of carbon; and in non-luminosity caused by air, each of the three causes is at work. In the latter case the presence of the oxygen of the ad- mitted air tends to cause a rise in the temperature and a diminution in the size of the flame, circumstances which are opposed to the absorption of heat and dilution of the flame. The flame of the Bunsen’s burner appears to be the final product of a whole series of causes acting some in one direc- tion, some in another; and it is not to be wondered at that observers of luminous flames have arrived at such diverse and contradictory conclusions, inasmuch as they have made the study of this flame their principal object, overlooking the great complexity of the conditions affecting it, instead of preceding such a study by an investigation of more simple instances of combustion. Effect of Withdrawal of Heat upon Flames. On account of the simpler conditions affecting so-called non-luminous flames I have considered these first, omitting all mention of changes in the intensity of light, until a study of the effect of the withdrawal of heat shall have given us some exact knowledge concerning this cause of decreased luminosity. Distance between Flame and Burner. In a paper of Blochmann’s* the fact is noticed that a gas- flame does not touch the rim of the burner, nor a candle-flame the wick. Blochmann says:—‘ If a gas-flame be closely ex- amined it is seen not to rest immediately upon the opening of the burner. In the case of a highly luminous flame the luminous portion presents too great a contrast to enable one to notice this fact with certainty ; but by decreasing the quan- tity of gas the space between burner and flame becomes more apparent in proportion as the intensity of the light diminishes. The small semicircular non-luminous flame issuing from a bat’s-wing burner when the supply of gas is small, may be arranged so that the space between the burner and the flame shall appear as great as the height of the flame itself.” This small intermediate space may be proportionately in- creased by mixing an indifferent gas, such as nitrogen or carbon dioxide, with the coal-gas before the latter is ignited. Blochmann also noticed that the intermediate space was in- creased by burning the diluted coal-gas under diminished * Liebig’s Annalen, clxviii. 346. * 16 Dr. Karl Heumann’s Contributions to pressure ; and he concluded that the cause of this increase was to be traced to the presence of the diluting gas. He supposed that there is a ‘momentary combustion taking place in the lowest part of every flame ;”’ this can only be when the issuing gas is mixed with a due proportion of air ; therefore Blochmann supposed that the explanation of the increased distance between flame and burner, which is observed to take place when coal-gas is diluted with an inert gas, was to be found in the following statement:—“ The greatly diluted gas issuing from the burner at once becomes mixed with air. In order to maintain the constancy of the flame this mixture must contain a fixed quan- tity of combustible gas. But that this quantity may be main- tained, in the case of a diluted gas, at the same point as if the diluting gas were absent, a much larger volume of the issuing gas must become mixed with the air; that is, the space between flame and burner must be increased.” The following facts are, I think, opposed to Blochmann’s somewhat strained explanation. Where a cold object touches the flame, a dividing space, similar to that noticed between flame and burner, is always observed. The colder the object and the more diluted the burning gas, the greater is the observed space. If a flame be diluted with a considerable excess of carbon dioxide, for example, a-piece of thick metallic wire brought into this flame causes a clear space around itself, which increases in proportion to the amount of carbon dioxide present. This experiment is best carried out in a darkened room: it is always difficult to distinguish the limits of the very slightly luminous flame, even if a dark background be employed. These facts point to the conclusion that withdrawal of heat from the flame by means of the upper part of the burner is the cause of the observed vacant space, and that to the same cause (withdrawal of heat) is to be assigned the ewtinction of the flame in the neighbourhood of a cold object. The explanation of the increase in the distances between flame and burner, or cold object, brought about by the presence of diluting indif- ferent gases, is to be found in the fact that the presence of such gases lowers the flame-temperature, by causing a partition of the quantity of heat needed to maintain a given quantity of the coal-gas in a state of combustion throughout a’ greatly increased volume of gas. If the temperature of the flame be already low, the further decrease occasioned by the introduc- tion of a cold body, although small in actual amount, is sufh- cient to cool a considerable extent of gas beneath the ignition- temperature: the flame is therefore extinguished in this cold space. If this be the true explanation of the production of the the Theory of Luminous Flames. 17 observed vacant space, it follows that heating the object placed in the flame should cause a decrease in the extent of this space. The following experiments prove that this actually takes place. A cold iron wire held in a non-luminous flame which has been diluted with an excess of indifferent gas, causes extinction of the flame throughout a considerable space around itself; but as the wire becomes hotter, this space gradually decreases in extent, until when the wire is raised to a red heat (either by the heat of the flame or by an extraneous source of heat), the flame is observed to rest upon the wire without any interve- ning space. Again, a mixture of coal-gas and carbon dioxide may be burned at the orifice of a platinum tube, so that a non- luminous flame, separated from the upper rim of the tube by a vacant space, is produced. If the platinum tube be now heated by means of a Bunsen’s lamp near its orifice, the non- luminous flame spreads down throughout the formerly appa- rently empty space until it touches the platinum tube. _ These experiments not only confirm the explanation already given, but they also completely exclude the possibility of any such cause as that suggested by Blochmann taking part, even to a subordinate extent, in the production of the space observed between the flame andthe burner. For the experiments prove that a flame, even when largely diluted with indifferent gases, burns in contact with a heated burner; whereas an effect such as Blochmann imagined, tending to produce separation be- tween flame and burner, although it might possibly be decreased, yet certainly could not be removed by heating the burner. I therefore look on the following conclusion as perfectly just:—The fact that a gas-flame does not touch the ring of the burner, nor a candle-flame the wick—further, that a flame does not actually impinge upon a cold body placed within it, is caused by the withdrawal of heat from the glowing gas. The flame is cooled below its ignition-temperature ; it ceases to glow and becomes invisible: the flame in the neighbourhood of a cold body is extinguished. The experiment just described, which proved that a greatly diluted gas may be caused to burn in contact with the metallic burner when the latter is heated, leads us to inquire whether the action of the upper part of the burner in causing a separa- tion between itself and the burning gas is not aided by the cold gas issuing from the centre of the burner, or, indeed, whether this cold gas is not of itself sufficient, under certain conditions, to produce the observed effect. The temperature of the lower part of the flame is certainly not so high as that of the middle portions; and the cause of Eieiage S00 Ola ds Now la. Jan. 1877. C 18 Dr. Karl Heumann’s Contributions to this fact might be sought for in the presence of unburned and comparatively cold gas, which afterwards becomes heated at the expense of the lowest flame-mantle. It has been already shown that the distance between the flame and any object in contact with it is increased so soon as the temperature of the flame is decreased by the admission of indifferent gas. The cold unburned gas in the ordinary flame plays the same part, in reference to the lowest part of the flame, as the indif- ferent gas in the above-cited example did towards the burning gas in general. That the action of this cold gas in increasing the space between flame and burner is not, however, very great, is evident from the fact that, in an ordinary burner the vacant space alluded to is no greater, or not much greater, than that noticed between the flame and a metallic rod held in the upper part of the burning gas. The foregoing observations are only applicable in the case of flames which burn under moderate pressures, as the flames of our ordinary lighting apparatuses—gas-burners, oil and petroleum lamps, candles, &c. If abnormal pressures are em- ployed, the phenomena presented by the flames are greatly altered: in place of a space measuring scarcely 2 millims. from burner to flame, there is noticed a distance of very varying magnitude, generally to be measured in decimetres, the pro- duction of which is to be ascribed to quite other causes than those operative in ordinary flames. An experiment has long been known in which spirit of wine is confined in a strong brass vessel furnished with an exit-tube and stopeock, and is then boiled until, when the stopcock is opened, the spirit rises towards the ceiling of the room: on bringing a flame near the exit-tube, the spirit burns with a luminous flame only near the ceiling, the stream of issuing liquid appearing non-luminous. By boiling spirit of wine in a copper vessel, and causing the vapour to issue through a glass tube drawn to a fine opening about 3 millims. in width, a long flame is obtained the base of which is separated by a distance of 10 or 12 centims. from the orifice of the glass tube. This distance is diminished by warm- ing the exit-tube, or by holding a small rod in the issuing vapour and thereby decreasing its velocity. A small drop of alcohol soon gathers at the opening of the glass tube ; if this be ignited by bringing a source of heat near it, or by causing the flame of the burning vapour to rush back by means of a rod held in the vapour, a small flame is produced which mo- mentarily diminishes the distance between flame and burner ; but so soon as the little drop of alcohel is burned, the original distance is again assumed. According to a recent investiga- the Theory of Luminous Flames. 19 tion of F’. Benevides*, the flame of strongly compressed coal- gas allowed to issue into the air, is separated by a space of several centimetres from the orifice of the tube whence it issues. If the pressure amount to two atmospheres, and the tube be 45 centims. in length and 4 to 9 centims. in width, the distance between the orifice of the tube and the flame amounts to about 4 centims. Benevides found the tempera- ture of the dark space to be very low, which is only what one would expect. The same author noticed that a flame brought near to the dark space was carried along by the stream of gas. This he regarded as proof of the dilution of the gas with air, caused by the surrounding atmosphere being carried along with the gas-stream which issued from the exit-tube with considerable velocity. If a wire be placed in the flame and be moved backwards through the dark space, the flame also moves back- wards towards the burner, but returns to its original position immediately the wire is removed. Benevides looks on these facts as justifying the conclusion that the formation of the dark space is due to the mechanical action of the issuing gas, whereby the air is driven aside for a certain distance from the orifice of the exit-tube ; in this space the requisite amount of oxygen is therefore not obtainable by the gas, which consequently remains unburned. If the exit- tube be very narrow and the velocity of the issuing gas be great, the pushing back of the air may become so intense as to render combustion impossible ; the flame is therefore extin- guished. . I cannot profess to be satisfied with these explanations. I cannot yet understand how the existence of the flame becomes impossible on the ground that the oxygen is driven back by the gas, and at the same time that the flame is extinguished through want of oxygen. Such a condition is found in the interior of every ordinary flame, not in the flame of compressed coal-gas only, and is recognized as the cause of the low tem- perature of the interior of a flame, and of the fact that the flame forms a hollow cone of glowing gas. This driving away of air occurs throughout a proportionately small space only, and on the outer margin of this space the chemical combina- tions constituting combustion take place. These facts are so elementary that it would have been superfluous to men- tion them, were it not that Benevides has constructed a theory without taking them into consideration. From the following passage one would derive a singular idea of the nature of flame; for if the phrase “l’action mécanique du gaz * Ann. de Chim. et a Phys. | 4] xxviii. 358. 2 20 Dr. Karl Heumann’s Contributions to sur la flamme’”’ &c. be not taken in a figurative sense, Bene- vides appears to regard the flame as a separate substance which is carried along by the stream of gas:—“ Lorsque l’on intro- duit un solide, par exemple un fil métallique, on oppose une résistance au mouvement du gaz, dont la vitesse diminue et par conséquent, l’action mécanique du gaz sur la flamme qui tend A la projeter 4 distance diminue aussi, d’ot il résulte que Yespace obscur diminue, et le jet lumineux se rapproche du chalumeau.”’ In opposition to this theory it must also be remembered that extinction of the flame could not be caused by the gas- stream driving back the air, because combustion would always be possible at the line of contact between gas and air. Out- ward and inward diffusion would continuously tend to increase the magnitude of the space where combustion was possible. It is therefore quite impossible that the space noticed by Bene- vides between the burner and the flame of compressed coal- gas could be caused by the absence of oxygen, the oxygen having been driven away by the stream of issuing gas. By this removal of oxygen the inner cold portion of the flame would be increased in size; and the flame itself would be Jengthened by the increased velocity of the gas-stream ; but extinction could not be brought about at the outer limits of the flame-mantle, as was noticed by Benevides. The mechanical action of a rapid stream of gas upon the air would also only cause an increase in the size of the flame, but no removal of that flame from the burner. I believe that one cause of this removal is to be found in the absorption of heat occasioned by. the gas issuing with so considerable a velocity, but that a second cause is also at work, viz. the relation be- tween velocity of the gas-stream and velocity of propagation of combustion—a circumstance which Benevides overlooked in his theory, although he had apparently noticed it in his expe- riments. The cooling action exercised upon the lowest portion of the flame by the quick inrush of gas may be divided into two parts. The temperature of the cylindrical flame-layer formed nearest to the burner is lowered by the coal-gas in the same manner, although to a smaller degree (on account of the low conductivity of gas for heat), as when a metallic rod is held in the flame. The innermost portion of the burning layer, consisting of coal-gas and air which has diffused inwards, may by this means be cooled to such an extent as to be extinguished; in other words, the ignited layer may be carried further from the point where the gas issues, and an unburned mixture of gas and air may take its place. the Theory of Luminous Flames. 21 But besides this cooling action exercised by the gas itself, the temperature of the flame suffers diminution by means of the action of the cold air surrounding the stream of gas. The air which the issuing gas carries along with it not only tends to withdraw heat from the outer portions of the flame, but penetrates also into the flame-mantle, the temperature of which it therefore diminishes. Such withdrawal of heat by means of the cold gas, and by means of admixed air, takes place in every flame, even when burned under small pressure; but the action of these two causes, especially of the latter, increases as the velocity of the gas-stream increases ; and if this be great and the gas be also under high pressure, the flame may be so cooled in the neigh- bourhood of the burner as to be extinguished, and a mixture of air and unburned gas may be formed and carried forward on the surface of the issuing gas-stream. In this case the existence of a flame will become possible only at a consider- able distance from the burner, where the velocity of the gas has diminished, and where therefore the ignited gas is not so greatly cooled. By increasing greatly the velocity of the gas and by dimi- nishing the orifice through which the gas issues, it may be possible to prevent the stream of gas from becoming ignited at all—as, for instance, it is possible to extinguish the flame of a gas issuing from a burner with a small velocity, the stopcock being partially closed, by fully opening the stopcock and so increasing the rush of gas. The explanation of this extinction of the flame is to be found in the fact that the space between burner and flame is increased by cooling the gas, and that in this space an excess of air finds its way into the gas-stream, which, as it increases its distance from the burner, becomes more and more diluted with air, until at last the mixture cannot be caused to ignite. If the orifice be smali this state of affairs is attained the sooner, because under such conditions the diameter of the stream of gas is small, and the gas therefore quickly becomes diluted with air. IJf the explanation which has been given of the fact that a rapid stream of gas burns only at some distance from the orifice whence it issues be true, it follows that the distance between burner and flame must be decreased by raising the temperature of the gas previously to its leaving the burner. I have been able to prove that this is the case by making use of the flame of alcohol-vapour already described. A thin platinum tube, the length of one’s finger, was attached to the glass exit-tube at which the alcohol vapour was burned. The alcohol was boiled, so that a space of 2 or 3 centims. in- tervened between tke flame and the orifice of the tube. The 99 Dr. Karl Heumann’s Contributions to platinum tube was then heated by means of a Bunsen’s burner held not too near to the issuing vapour, whereupon the dis- tance between flame and burner gradually diminished until the two were in contact. On removing the Bunsen’s lamp the original distance was quickly regained. If the stream of gas be very rapid, the experiment carried out as just described does not succeed, because the temperature of the vapour in the tube is not sufficiently raised. I do not doubt that, in the experiment described by Benevides, the dis- tance between flame and burner would be greatly diminished, if not actually removed, by passing the compressed gas through a long tube maintained at a full red heat before igniting it. Although the explanation which I have given of the fact that a space is noticed between flame and burner in the case of quickly moving gases has taken into account all the points which have been observed, and although I have not found any facts opposed to this explanation, yet I must confess that I am scarcely altogether satisfied with it. Thus the fact that the approach of a small flame to the orifice whence the burn- ing gas issues causes a diminution in the size of the observed space, is not to be set down so much to the decreased with- drawal of heat by the issuing cold gas (as was the case in the experiment with the heated platinum tube*), but much more to the carrying over of the combustion to the heated part. I cannot look upon the cooling actions described above as alone sufficient to cause all the observed circumstances. The second explanation already given of the cause of the observed space in the case of compressed gases takes into account the relation existing between the velocity of the gaseous stream and the velocity of propagation of combustion. In order to gain a clear idea of the action of this factor, let us suppose that the flame of a compressed gas issuing from a tube is separated by a distance of several centimetres from the orifice of the tube. The question suggests itself, Why does not the flame make its way backwards towards the burner? or, in other words, Why is not the combustion propagated back- wards throughout the line of contact of gas and air towards the burner ? The gaseous stream is evidently surrounded by a zone con- sisting of a combustible mixture of air and gas molecules (I use this expression on account of its shortness). As soon as the temperature of a pair of molecules in one part of the zone is raised to the ignition-point by means of a flame brought near, chemical action occurs (combustion), and so much heat is thereby evolved as suffices to raise the temperature of the * Supra, p. 17. the Theory of Luminous flames. 23 neighbouring pair of molecules likewise to the ignition-point. This action is propagated throughout the mass, and continues so far and so long as the combustible mixture extends. Such a process takes place in the combustion of all sub- stances, whether solids, liquids, or gases; and to this propa- gation of combustion is due the continuity of all flames. Now, inasmuch as the gas existing between flame and burner in the cases noticed clearly consists of such a combustible mixture (which may be proved in the case of alcohol vapour by bringing a small flame to the orifice of the tube), it follows that the heat given out by the last pair of molecules actually undergoing combustion must act, in the manner described, upon the pair next them, and so on throughout the gaseous mixture; yet this does not appear to be the case. I say does not appear to be the case, because we are too lable to look on the flame as something having an existence of its own (see Benevides), and not to regard it as a part of the gaseous stream, which 1s visible to us for a short distance. If we may forget for a moment the true nature of the gas, we might compare the burning stream to a rod placed ina fire, which glows in the central parts, the ends emitting no rays of light. In a magnesium lamp the metallic wire is kept in motion by means of clockwork: the position of the flame is thus maintained constant. If the wire is pushed out too quickly or too slowly, the flame is advanced or withdrawn; and a constant position is only maintained by moving out the wire at that rate at which the flame would recede were the wire immovable. This recession of the flame is conditioned by the propaga- tion of the ignition; it becomes more rapid the higher the temperature of combustion and the lower the temperature of ignition of the combustible body. Thus a stick of phosphorus ignited at one end, and placed in a horizontal position, burns almost at once throughout its entire surface ; a longer period elapses before the ignition of a wick impregnated with petro- leum is propagated throughout the length of that wick ; and if rape-oil be used instead of petroleum, the rate of propagation of ignition is yet slower. Besides the difference between ignition- and combustion- temperature, two other points must be noted as conditioning the velocity of propagation of ignition: these are, the specific heat and the conductivity for heat of the burning body*. So far as these are concerned, the withdrawal of heat from the issuing gas and admixed air is a circumstance which may * The magnitude of the surface and the diameter are of eis but these may be eliminated by parallel trials. 24 Dr. Karl Heumann’s Contributions to be eliminated and which may be looked on as immaterial. But even without this, parallel experiments might lead to the discovery of interesting relations existing between the veloci- ties of ignition and the combustion-temperatures of different combustible bodies. For solid bodies (magnesium for instance) the velocity of propagation of ignition is equal to the velocity with which a wire of the substance must be moved forwards in order that the position of the flame may remain constant. The time re- quired for the flame to travel to the end of a wire of known length might also be determined. Hasily combustible liquids might: be placed in a hollow, and the time which expired between the ignition of one end of the liquid and the arrival of the flame at the other end noted. Liquids which burn only when absorbed by wick, might be so absorbed by wicks of known length, and the time required for the flame to travel throughout the length of the wick placed horizontally might be determined. By the aid of such experiments a comparative quantitative expression for the liability to ignition of various combustibles might be gained. For gases, the velocity with which the gas must issue in order to maintain a constant distance between burner and flame might be determined; or the distance might be measured, the velocity of issue being maintained constant. In order to do away with the changing velocity of different gases for the same distance from the burner (depending on the nature of the gas itself), it would be better to measure that velocity which is just sufficient to remove the flame from the burner. I am here reminded of Bunsen’s method for determining the velocity of ignition in the mixed gases evolved in the electrolysis of water*. The explosive mixture was burned at a small orifice of known area, the velocity with which the gas issued being gradually diminished by reducing the pres- sure until the flame passed backwards through the opening and ignited the mass of the gaseous mixture. This point must be reached when the velocity of the issuing gas is an infinitely little less than that with which the ignition is propagated forwards. Bunsen calculated the velocity of propagation of ignition, C, from the formula C= where V denotes the volume of wat gas issuing in ¢ seconds, and d the diameter of the opening. In the case of the mixed gases from the electrolysis of water C was found to be equal to 34 millims. per second, while for * Poge. Ann. cxxxi. 165. the Theory of Luminous Flames. 25 an explosive mixture of carbonic oxide and oxygen C was equal to less than 1 millim. per second. These numbers cannot be made use of in the determination of the rate of propagation of ignition of a gas burning in air, inasmuch as in this case the admixed nitrogen and the ab- normal conditions under which the combustible gas is mixed with air greatly diminish the rate of propagation. In order to render clear the relations existing between the rates of issue and of propagation of ignition in the case of rapid gas-streams, the following considerations will be serviceable. A burning gas obeys the law that the position of the base of the flame remains fixed when the rate of propagation of ignition is equal and opposite to the rate of issue of the gaseous stream. ‘The latter is greatest close to the orifice of the burner, and decreases as this point is receded from, because of the opposition offered by the surrounding air. At all points where the velocity of the gas is greater than the velo- city of propagation of ignition, the flame cannot exist of . itself, because each gas-molecule will be carried to a point further than that to which the ignition is transmitted in the same time. If, on the other hand, the rate of propagation of ignition is greater than the rate at which the gas-stream moves, the base of the flame will be driven back against the burner and will remain stationary at that point where the two velocities are exactly equal. If a burning body be brought into the stream of gas, issuing under high pressure, at a considerable distance from the burner, the flame which is produced moves back against the stream of gas until it reaches the point defined above, where it re- mains stationary; if, however, the gas be ignited at the opening of the burner, the flame is carried along with the stream until the same point is reached. If the velocity of the gas-stream be increased, the flame moves further from the burner; if the velocity be diminished, the flame approaches the burner; and the flame rests quietly upon the burner only when the two velocities are equal, or when the velocity of propaga- _ tion of ignition is greater than that of the issuing gas. The last-named condition holds in our ordinary luminous flames, the small distance generally noticed between flame and burner, or wick, resulting from the cooling action of the surroundings of the flame. The phenomena just described may be noticed in the flame of alcohol vapour issuing from an orifice with considerable velocity, as already described. If air be blown through benzol and a light be then brought to the mixture, a flame is produced which moves backwards or forwards as 26 Dr. Karl Heumann’s Contributions to the velocity of the gaseous mixture is increased or diminished. The same phenomenon may be well shown by passing carbon dioxide through ether contained in a vessel surrounded with warm water, and igniting the issuing mixture. ‘The distance between flame and burner may, in this experiment, be altered either by altering the velocity of the stream of carbon dioxide, or by warming or cooling the vessel containing the ether. Or the mixed gases may be caused to issue from a small balloon furnished with an exit-tube and stopcock: by slightly altering the pressure by means of the hand, the flame may be caused to move backwards or forwards; or it may be main- tained in aconstant position. If the exit-tube be of platinum, the flame may be caused to rest upon the orifice of this tube by heating the tube with a Bunsen’s burner. Such flames then behave in a manner exactly analogous with that observed in the case of rapid streams of gas; and the explanations already given of the observed distance between flame and burner can be predicated of these flames, although diluted with carbon dioxide &c.; for the decrease in velocity of the gas is compensated for by the increase in the proportion of indifferent gases. The temperature of the flame is therefore low, and the withdrawal of heat by the indifferent gases con- siderable. The second explanation given of the distance between flame and burner, depending upon the different velocities of the gaseous stream and of the propagation of ignition, holds good in the case of these flames. One might be disposed to raise the objection that in these experiments the gaseous mixture was not strongly compressed, and therefore did not issue with any great velocity. But it has been shown that the greater distance between flame and burner is a function of the difference of velocities of the gaseous stream and the propagation of ignition ; and in the foregoing cases the latter must be very small, because the temperature of the flame is very low, and the molecules of carbon dioxide interspersed between the molecules of the com- bustible gas must carry away heat from the latter. In these flames, for the reasons just stated, the rate of propagation of ignition is small and is easily exceeded by the velocity of a comparatively slowly moving gas-stream, whence results the great distance between flame and burner. This explanation is rendered more probable by considering that experiment in which the distance spoken of was diminished by warming the ether through which carbon dioxide was passed. Inasmuch as the volume of diluting gas was here propor- tionally diminished, the temperature of the flame was in- creased ; the rate of propagation of ignition was also increased, the Theory of Luminous Flames. 27 and therefore became equal to the velocity of the issuing gas at a point nearer to the burner than that at which these two velocities were previously equalized. The diminution in the distance between flame and burner which was observed to take place in every case when the burner was heated, or when a wire was introduced between the flame and burner, must now be commented upon in the light of the second explanation already detailed. It is easy to understand why the distance in question should be dimi- nished by heating the burner. This distance depends upon the difference between the velocities of the gas and of the propagation of ignition ; and the latter is itself a function of the difference between the ignition and combustion temperatures. The combustion-temperature is high because of the gas being heated previously to ignition ; the gas has been already heated nearly to its ignition-temperature. These two circum- stances necessarily cause a considerable increase in the rate of propagation of ignition; the velocity of ignition becomes greater than the velocity of the issuing gas; and the distance between flame and burner is therefore diminished or entirely removed. The diminution in this distance which is brought about by holding a metallic wire between the flame and the burner, and moving the wire towards the latter, may be thus explained:—The flame-mantle is produced immediately behind the wire because the latter serves to shelter the flame from the cooling influence of the quickly rushing stream of gas. The heat so produced is communicated to the nearest portion of non-ignited gas, and the flame is thus caused to travel backwards towards the burner. The familiar phenomenon of the flame of a petroleum-lamp burning above the slit in the piece of thin metal which sur- rounds the wick, is explicable on similar grounds. The flame is so cooled by the metal, at a small distance from the wick, as to be extinguished ; but the lower part of the petroleum- gas still continues to burn. A mixture of unburned petro- leum-vapour and products of combustion of this vapour, therefore passes upwards through the slit. This mixture may be ignited by properly regulating the screw which raises the wick ; but the flame only appears at the distance of a few centimetres above the metallic cap. The velocity of ignition is very small, inasmuch as the combustible matter consists of heavy, easily condensable vapours, which are moreover greatly diluted by the products of combustion of the lower part of the gas, viz. by carbon dioxide and water, substances having high specific heats. The distance between the metallic cap 28 Dr. Karl Heumann’s Contributions to and the upper flame may be still further increased by cooling the combustible vapours. The following experiment is in- structive :— A glass tube, 8 to 10 millims. wide and about 10 centims. long, is fastened vertically in the middle of the slit in the metallic cap surrounding the wick of a lighted petroleam-lamp. By raising the wick a thick white vapour may be made to issue from the upper orifice of the glass tube. If this vapour be ignited, a small flame is produced, which plays above the smoke at a distance of perhaps 10 centims. from the tube. The products of combustion present above this flame are in- visible, because the combustion is complete and the water which is produced is dissipated by the heat evolved. If the column of visible vapour between the tube and the small flame be carefully observed, it is seen to be rendered transparent by the action of the heat radiated from the lower flame, and finally to become ignited. In this way the fact may be explained that the small flame does not rest directly upon the visible column of vapour, but is separated from it by a transparent space 1 or 2 millims. in extent. If the glass tube in this experiment be replaced by one made of platinum, and if this be heated, the small flame may be caused to approach and finally to rest upon the orifice of the platinum tube. The column of smoke which is seen to issue from a petro- leum-lamp burning without the glass cylinder, is caused by the cooling action of the metallic cap which surrounds the wick. The flame-mantle impinges upon this metallic cap, is thereby held back, and so is rendered unfit for propagating the ignition upwards. The lower flame, being fed by air entering from below, continues to burn, and produces new gases and vapours from the oil-saturated wick, performing, therefore, a part similar to that of the retort-fires in the manufacture of coal-gas. As the metallic cap gets heated, the cooling action which it exercises upon the stream of ascending vapours diminishes, and the distance separating the upper flame from the lower is decreased. If the metallic cap be heated by a Bunsen’s lamp, this distance becomes very small, and entirely disappears when the cap begins to glow. If a cap already heated to redness be placed upon a lighted and properly adjusted lamp, the flame does not become separated at all. Hveryday experience tells us that placing a glass cylinder upon the lamp causes the two flames to unite. The diminished supply of air brings about an elongation and curtailment in the dimensions of the flame, whereby it no longer touches the the Theory of Luminous Flames. 29 sides of the metallic cap; at the same time the flame-tempe- rature is increased, and the motion of the heated particles of gas is accelerated. These circumstances act in opposition to the cooling effect of the metallic cap. These experiments may be interpreted as pointing to the withdrawal of heat from the sides of the stream of gas and air as the cause of the space noticed between flame and burner ; but it has been shown that this action is but small, and that the superior velocity of the stream of gas over that of the propagation of ignition is the principal cause of the observed effect. Whether this be the sole cause cannot be determined until further experiments have been carried out. The most important points established in the foregoing part of this paper may be summarized thus :-— 1. The fact that a gas-flame does not rest upon the burner nor a candle-flame upon the wick, as also the fact that a flame never directly touches a cold body held within it, is to be explained by the cooling action exercised upon the gas by its surroundings. The combustible gases are cooled throughout a definite space below their ignition-temperature ; the flame is there- fore extinguished. This conclusion is opposed to that of Blochmann. 2. The very considerable distance noticed between the burner and the flame of a gas issuing under high pressure, or mixed with a large volume of an indifferent gas, cannot be accounted for on the grounds put forward by Benevides. The production of such a distance is much rather to be traced to the cooling action of the stream of gas and of the outer air, and perhaps more especially to the fact that the velocity of the stream of gas in the neighbourhood of the burner is greater than the velocity of propagation of ignition within the gas. | 3. In order that other circumstances conditioning the effect may be removed, the velocity of propagation of ignition must be equal to that of the gas-stream at the point, situated some distance from the burner, where the flame begins. Determinations of the velocity of ignition should be made under these conditions for different gases; and since this magnitude is a function of the difference between ignition and combustion temperatures, conclusions may be drawn from such experiments regarding the relations existing between these points”*. * Since going to press, | have noticed an interesting paper by E. Mallard [Annales des Mines, 1875, ii, 355], in which the velocity of 30 Mr. W. Spottiswoode on a large Induction-coil. 4, The velocity of propagation of ignition may be easily determined for solid and liquid combustible bodies; and the numbers so obtained may be regarded as comparative quanti- tative expressions for the liability to ignition of these sub- stances. II. Description of .a Large Induction-coil. By Wiutam Sporriswoone, 1.2.8. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, LTHOUGH I have not as yet many experimental results sufficiently complete for communication to your Maga- zine, I still think that the construction of an induction-coil capable of giving a spark 42 inches in length is an instrumental feat deserving of record in the annals of science. I therefore venture to submit the particulars of this coil, recently com- pleted for me by Mr. Apps, of 433 Strand, to whose skill and perseverance the success of the undertaking is due. The general appearance of the instrument is represented in the following figure, by which it is seen that the coil is sup- ported by two massive pillars of wood sheathed with gutta- percha, and filled in towards their upper extremities with paraffine wax. JBesides these two main supports, a third, capable of being raised or lowered by means of a screw, 1s placed in the centre, in order to prevent any bending of the great superincumbent mass. The whole stands on amahogany frame resting on castors. The coil is furnished with two primaries, either of which may be used at pleasure. Hither may be replaced by the other by two men in the course of a few minutes. The one to be used for long sparks, and indeed for most experiments, has a core consisting of a bundle of iron wires each *032 inch thick, and forming together a solid cylinder 44 inches in length and 3°5625 inches in diameter. Its weight is 67 lbs. The copper wire used in this primary is 660 yards in length, ‘096 inch in diameter, has a conductivity of 93 per cent., and offers a total resistance of 2°3ohms. It contains 1344 turns wound singly in 6 layers, has a total length of 42 inches, ignition of explosive mixtures of hydrocarbons and air is measured by Bunsen’s method. The maximum velocity for marsh-gas and air was 0.524 millim., the minimum 0-041 millim. per second. The numbers for coal-gas and air were—maximum 1:01 millim. and minimum 0:097 millim. per second. The velocities are in these instanees very slow; and the experiments show that they are still further reduced by an excess of either constituent of the mixture. Mr. W. Spottisw oode a large Induction ‘cs Milly i HM ] ! \ SATA nT EAR ' ti iia =, AN cr . P 3 l | i I \ ——————— ; a [eer ereRReT SET TOTTTTTO r gi LL ee fil; : by lite Mt = 7 = , iil be uA 32 Mr. W. Spottiswoode on a large Induction-coil. with an internal diameter of 3°75 inches and an external of 4:75 inches. The total weight of this wire is 55 lbs. The other primary, which is intended to be used with bat- teries of greater surface, e.g. for the production of short thick sparks, or for spectroscopic purposes, has a core of iron wires 032 inch thick, forming a solid cylinder 44 inches long and 3°8125 in diameter. The weight of this core is 92 lbs. The copper wire is similar to that in the primary first de- scribed ; but it consists of 504 yards wound in double strand forming three pairs of layers whose resistances are ‘181, °211, -231 ohms respectively. Its length is 42 inches, its external diameter 5°5, and its internal 4 inches. Its weight is 84 lbs. By a somewhat novel arrangement, these three layers may be used either in series as a wire of ‘192 inch thickness, or coupled together in threes as one of *576 inch thickness. It should, however, be added that, owing to the enormous strength of current which this is capable of carrying, and to the highly insulated secondary coil being possibly overcharged so as to fuse the wire, this larger primary is best adapted for * use with secondary condensers of large surface, for spectrum- analysis, and for experiments with vacuum-tubes in which it is desirable to produce a great volume of light of high inten- sity as well as of long duration at a single discharge. The alternate discharges and flaming sparks can also be best pro- duced by this primary. It has been used for high-tension sparks to 34 inches in air, the battery being 10 cells of Grove’s with platinum plates 61 x 3 inches. Great facilities for the use of ditferent sets of batteries are afforded by the division of this primary into three separate circuits, to be used together or separately; and by a suitable arrangement of automatic contact-breakers, the primary currents may be made to follow in a certain order as to time, duration, and strength, with etiects which, when observed in the revolving mirror, will doubtless lead to important results in the study of strize in vacuum-tubes. We now come to the secondary, which consists of no less than 280 miles of wire, forming a cylinder 37:5 inches in Jength, 20 inches inexternal, and 9°5 inches in internal diameter. Its conductivity is 94 per cent. ; and its total resistance is equal to 110200 ohms. ‘The whole is wound in four sections, the diameter of the wire used for the two central sections being 0095 inch, and those of the two external being :0115 inch and :0110 inch respectively. The object of the increased thickness towards the extremities of the coil was to provide for the accumulated charge which that portion of the wire has to carry. Mr. W. Spottiswoode on a large Induction-coil. 33 Each of these sections was wound in flat disks ; and the average number of layers in each disk is about 200, varying, however, with the different sizes of wire, &. The total number of turns in the secondary is 341,850. The great length of the wire necessary can be easily under- stood from the fact that near the exterior diameter of the coil a single turn exceeds 5 ft. in length. The spark, it is believed, is due to the number of turns of wire, rather than to its length, suitable insulation being preserved throughout the entire length. In order to ensure success, the layers were carefully tested separately and then in sets, and the results noted for comparison. In this way it was hoped that step by step safe progress would be made. As an extreme test, as many as 70 cells of Grove’s have been used, with no damage whatever to the insulation. The condenser required for this coil proves to be much smaller than might at first have been expected. After a variety of experiments, it appeared that the most suitable size ~ is that usually employed, by the same maker, with a 10-inch- spark coil—viz. 126 sheets of tinfoil 18 x 8°25 inches in sur- face, separated by two thicknesses of varnished paper, the two thicknesses measuring ‘Ollinch. The whole contains 252 sheets of paper 19 x 9 inches in surface. I hope, at some future opportunity, to make further experiments with other condensers. Using the smaller primary, this coil gave, with 5 quart cells of Grove, a spark of 28 inches, with 10 similar cells one of 35 inches, and with 30 such cells one of 37°5 inches and sub- sequently one of 42inches. As these sparks were obtained without difficulty, it appears not improbable that, if the insu- lation of the ends of the secondary were carried further than at present, a still longer spark might be obtained. But special adaptations would be required for such an experiment, the spark of 42 inches already so much exceeding the length of the secondary coil. When the discharging points are placed about an inch apart, a flowing discharge is obtained both at making and at breaking the primary circuit. The sound which accompanies this discharge implies that it is intermittent, the time- and current-spaces of which have not as yet been determined. With a 28-inch spark, produced by 5 quart cells, a block of flint glass 3 inches in thickness was in some instances pierced, in others both pierced and fractured, the fractured pieces being invariably flint glass. If we may estimate from this result, the 42-inch spark would be capable of piercing a block 6 inches in thickness. hile Mogasao. Vol. 3. No. 15. Jan. 1877. D 84 On the Number of the Univalent Radicals C, Hon+1- When used for vacuum-tubes this coil gives illumination of extreme brilliancy and very long duration: with 20 to 30 cells and a slow-working mercury break, giving, say, 80 sparks per minute, the strie last long enough for their forward and backward motion to be perceived directly by the unassisted eye. The appearance of the striz when observed in a re- volving mirror (as described in the Proceedings of the Royal Society, vol. xxv. p. 73) was unprecedentedly vivid, and this even when only two or three cells were employed. Ill, On the Number o the Univalent Radicals C,, Hon41. By A. Cayiey, Esq.* HAVE just remarked that the determination is contained in my paper “On the Analytical Fornis called Trees ”’ &c., British-Association Report, 1875 ; in fact, in the form Ci, Hen+1 there is one carbon atom distinguished from the others by its being combined with (instead of 4, only) 3 other atoms ; viz. these are 3 carbon atoms, 2 carbon atoms and 1 hydrogen atom, or else 1 carbon atom and 2 hydrogen atoms (CH;, methyl, is an exception ; but here the number is =1). The number of carbon atoms thus combined with the first- mentioned atom is the number of main branches, which is thus =3,2,or 1; hence we have, number of radicals C,, Ho»41 is = No. of carbon root-trees C, with one main branch, + No. of a5 - with two main branches, + No. of RS o with three main branches; and the three terms for the values n=1 to 13 are given in Table VII. (pp. 296, 297) of the paper referred to. Thus'n=5 (an extract from the Table) is Index 2, or | Index ¢, or num- Altitude. number of ber of main © | 22 knots. branches. 0 1 D) a 4 5 1 il 2 Jee Wl: yy 2 1 3 3 1 fF 4 1 1 Total: 1 4 3 1 io} and the number of the radicals C;H,; (isomeric amyls) is * Communicated by the Author. Action of the Flame of Alcohol upon Palladium. 35 44+3+1 =8 (or, what is the same thing, it is 9—1, the corner-total less the number immediately above it). The tree forms corresponding to the numbers 1, 2,1; 2,1; 1 in the body of the Table are the trees 2 to 9 in the figure, p. 258. The numbers of the radicals C,, Hop+1, as obtained from the Table in the manner just explained, are:— Number of radicals C, Hon). ~ ~ 2 it 1 | Ethyl. 3 1 1 | Propyl. 4 4. 4 | Butyls. 5 Qeso—— sh 8 | Amyls. 6 18 — | 17 | Hexyls. a 42 — 3 39 | Heptyls. 8 96 — 7 89 | Octyls. 9 229 a= 18 211 | Nonyls. 10 | 549 — 42 D07 | Decyls. 11 | 1846 —108 1238 | Undecyls. 12 | 33826 —269 3057 | Dodecyls. 13 | 8329 —691 7638 | Tridecyls. The question next in order, that of the determination of the number of the bivalent radicals C, H.,, might be solved with- out much difficulty. Cambridge, November 20, 1876, IV. Note on the Action of the Flame of Alcohol upon the Metal Palladium. By Professor WouLER, Por. Mem. B.S. &c.* N the year 1824 I published f the observation that palla- dium, both in the spongy form and in that of foil, pos- sesses the property of becoming gradually covered with a thick coating of carbon when held in the flame of a spirit-lamp. A small piece of palladium sponge thus heated swells up to many times its own volume, cauliflower-like bunches of carbon being deposited on the surface of the metal. The same phenomenon is observed if the metal be allowed to glow in a coal-gas flame. When the adhering porous mass of carbon is allowed to burn away, a fine skeleton of palladium remains behind ; and this is the case even if the carbon has been deposited upon a piece * Translated by Professor Roscoe from the Gottinger Nachrichten, No. 20, 1876. : + Pogg. Ann. vol. iil. p. 71. D2 36 Prof. Wohler on the Action of the Flame of foil, which is then found to have been penetrated through and through with carbon and rendered quite brittle. At the time of that publication I believed that a peculiar affinity must be supposed to exist between palladium and carbon; but the remarkable discovery by Graham of the occlusion of hydrogen by palladium makes it probable that the above phenomenon is rather connected with this power of the metal to absorb many hundred times its volume of hydrogen. The behaviour of palladium to olefiant gas appeared likely to throw light upon this question. More than 6 grams of chemically pure spongy palladium, which, as experiment had shown, was. capable of absorbing many hundred times its volume of hydrogen, was placed in a tube, and a slow current of ethylene led for some hours over the metal heated to 100°. Neither at this temperature nor at other higher temperatures below a red heat did any action take place; no gas was ab- sorbed, no blackening of the metal could be observed. Only when the glass tube in which the metal was placed was heated to redness was carbon deposited with evolution of hydrogen. But the point at which the decomposition of ethylene began — in presence of the metal was found to be lower than that neces- sary to bring about decomposition of the gas in the absence of palladium. Marsh-gas was also found to be without any action on palladium. From the above experiment, it appears that palladium is un- able to absorb ethylene or the gases of the alcohol-flame, but that it is able to bring about the deposition of carbon from such gases at a temperature lower than that at which ethylene by itself undergoes decomposition. Possibly this action may be explained by the supposition that a combination of hydrogen goes on contemporaneously with the deposition of carbon, but that at the same time a rapid dissociation of the hydrogen compound occurs—much in the same way as we may explain the remarkable physical changes which take place in copper when heated in ammonia- gas by a temporary combination of the nitrogen. A circum- stance which favours this explanation is, that the bright palla- dium-foil, after it has been exposed to the action of the alcohol- or ethylene-flame, has altogether lost its brilliancy as well as its malleability. The fact that when palladium is fused with carbon it does not take up any of this element, is a sufficient proof that the phenomenon in question is not caused by the affinity of the metal for carbon ; and this fact was proved in 1857 by Dr. Th. Wood, who at my suggestion made an examination on the relations of palladium to carbon compounds. His experi- ments were afterwards carried out in Professor Bunsen’s of Alcohol upon the Metal Palladium. a7 laboratory *; but he was unable to obtain satisfactory results so far as the main question is concerned. The apparatus shown in the figure serves as a simple and effective means of exhibiting the absorption of hydrogen by palladium. a is a tall glass cylinder filled with water; 0 is a divided tube of at least 100 cubic centims. capacity ; ¢ is a very narrow gas-delivery tube, one end of which passes under the open end of the divided tube; dis a tube for the palladium, bent so that it can be placed in a vessel of boiling water ; ¢ is a chloride-of-calcium tube for drying the hydrogen ; /f a glass stopcock leading to a gas-holder. After a few grams of palladium sponge have been placed in the tube d, whilst the one end of the tube remains open a cur- ‘rent of hydrogen gas is passed for some time over the metal placed in the boiling water. In the mean time the tube 6 is filled with water, and the cylinder as well as the tube c. After the lapse of about half an hour the tube d is taken out of the hot water and allowed to cool, the current of gas still passing through. Then the stopcock f is closed, the drawn-out end of the tube d connected with the gas-delivery tube c and the screw-tap loosed. The palladium is now heated ; and the occluded gas is quickly set free and passes into the graduated tube b. As the metal cools, the gas is again absorbed; and at last all the hydrogen disappears and the tube b becomes, as before, full of water. An apparatus of this kind, fitted with glass stopcocks, may therefore serve for exhibiting the experiment any wished-for _* Th. Wood, ‘The Action of Palladium on Carbon:’ Gottingen, 1859, 38 Prof. J. Emerson-Reynolds on Glucinum : number of times. If the palladium sponge, when saturated with hydrogen, be brought into the air, it becomes red hot. Palladium which has become of a bluish-green tint from igni- tion in the air, becomes hot when plunged into hydrogen and assumes the original grey colour of the metal. V. Reports from the Chemical Laboratory of Trinity Col- lege, Dublin. By J. Emerson-Reynowps, MD., IR.LA., Professor of Chemistry, University of Dublin*. No. 1.—On Glucinum: its Atomic Weight and Specific Heat. MONGST the few rare elements found in Ireland is the metal glucinum or beryllium, which occurs in the well- known alumino-glucinic silicate, beryl or “emerald.” This mineral is found in comparative abundance, though in a rough state, in the granites of Donegal, and is somewhat less freely distributed through the granites of the Mourne Mountains in the county of Down. As the “‘atomic weight” of glucinum has not yet been definitely fixed by the determination of the specific heat of the metal, it seemed desirable that we in Ireland should make the necessary crucial experiments. Hence, about seven years ago, | commenced to collect the crude Irish beryls or “emeralds,”’ and ultimately succeeded in obtaining 3 kilo- grammes of the dressed mineral, from which I prepared nearly 350 grammes of the pure glucinic oxide. I have to thank my friend Mr. William Harte, C.E., the excellent County Surveyor of Donegal, for the valuable assist- ance he kindly afforded me in collecting much of the mineral from which the glucinic oxide was prepared. The satisfactory nature of the results ofa set of preliminary experiments with the material at my disposal must be my apology for laying a short communication upon the subject before the Academy at a very early stage of the investigation. Some glucinic oxide was converted into the anhydrous chlo- ride by the action of chlorine upon it at a full red heat in presence of finely divided carbon; and the metal was subse- quently procured by the action of metallic sodium on the pure sublimed glucinic chloride. The reduction was eftected b heating a suitable mixture in a platinum vessel; but the tem- perature was not allowed to rise sufficiently to liquefy the mass ; and on removal of the material from the crucible, those por- tions which had been in contact with the platinum were rejected. The resulting mixture of sodic chloride and reduced glucinum * Communicated by the Author, having been read before the Royal Trish Academy, April 10, 1876. its Atomic Weight and Specific Heat. 39 was then fused under common salt in a lime crucible; this precaution was taken in order to avoid contact with siliceous compounds. Considerable loss occurred in this operation ; but I succeeded in obtaining a small coherent mass of metallic glucinum, which latter was found to agree in characters with the metal described by Debray*, though that distinguished chemist effected the reduction of his metal in a different manner. If we admit, with Awdejew and with Debray, the number 4-6 to be the equivalent of glucinum (H=1), the question remains whether the atomic weight, so called, is a multiple of the equivalent by 2 or 3. If, as some assert, the atomic weight is 4°6 x 3=13°8, the only known oxide of glucinum must resemble alumina. If, on the other hand, the atomic weight is 4°6 x 2=9°2, glucina must be an oxide like that of zinc or of magnesium. Hach view has received the support of a group of chemists of the highest eminence ; but, owing to peculiar difficulties surround- ing the case, an appeal to chemical criteria has hitherto been insufficient to decide between the two conflicting opinions—a determination of the specific heat of the metal, or of the vapour-density of one of its compounds of simple constitution, being necessary for the final settlement of the question. Of these methods I chose the former; and having made several determinations of the capacity for heat of metallic glucinum, I have the gratification to state that the data obtained lead to the conclusion that the atomic weight of glucinum is double the equivalent weight. Glucinum is therefore a diatomic metal with an atomic weight of 9°2—though, I may add, this num- ber may be slightly affected by a new determination of the equivalent, in which I am engaged. The method pursued in making the necessary determina- tions upon which to found the conclusion just stated was devised for the purpose of this inquiry ; and as it is essentially different from any with which I am acquainted, I may be per- mitted to indicate very briefly the plan adopted after a good deal of preliminary investigationf . * Annales de Chimie et de Physique, troisiéme série, tom. xliv. p, 5 (1855), +. The preparation of pure metallic glucinum in quantities exceeding two or three grammes is difficult and costly. For this amongst other reasons I determined to employ Bunsen’s admirable and theoretically perfect ice- calorimeter in the estimation of the specific heat of the metal, as small quantities of material only are required. It proved, however, to be impos-. sible, owing to various engagements, to prepare the glucinum in a state of sufficient purity until the season had passed when Bunsen’s ice-calorimeter can be conveniently used. I had therefore to devise a calorimetric me- thod which could be employed during the warm weather, and which could. 40 Prof. J. Emerson-Reynolds on Glucinum: The well-known law of Dulong and Petit, as modified by Cannizaro, asserts that the atoms of elementary matter have the same capacity for heat, when we compare them in the solid state. The outstanding exceptions to this important law are few; and even these appear to have been cleared away in some degree by the recent researches of Weber on the specific heats of silicon, boron, and carbon. ~The principle, however, is ad- mittedly sufficiently general in its application to enable us to found upon it a plan for the determination of the atomic weight, so called, of a particular element ; for it is evident that if we employ as a standard a metal whose atomic weight and specific heat are both accurately known—-silver for example (=100) —the weight of another solid element which contains the same quantity of heat at 100° C. as 108 parts of pure silver at 100° C. is the atomic weight of the element. In seeking to com- pare glucinum with pure metallic silver in this way, I suc- ceeded in arranging an experimental method which not only enabled me to attain the object I had in view, but also to de- monstrate the truth of the law just referred to. The apparatus — required is easily constructed, and consists of a spirit-thermo- meter with a cylindrical ‘bulb ”’ in which a test-tube is sealed, after the manner of Bunsen’s ice-calorimeter. This part of the apparatus can be conveniently made from a small chloride- afford trustworthy results with small weights of material. I have given in the text an outline of this method; but the details of its application to the determination of atomic and molecular heat will form the subject of another communication. | its Atomic Weight and Specific Heat. 4} of-caleium drying-tower, as shown in the diagram. Although the larger “bulb”’ of the thermometer is full of spirit, the lower one and the stem are full of mercury, and connected with a fine capillary tube carefully graduated in millimetres, and calibrated. The arrangement constitutes an exceedingly delicate spirit-thermometer, with a mercury index. When it is desired to compare a solid element with silver, in order to fix the atomic weight, it is necessary to make a preliminary experiment with the standard metal. Tor this purpose one cubic centimetre of distilled water is placed in the test-tube, which is immersed in the bulb of the thermometer ; and when the temperature has been equalized, and the thread of mercury has reached a suitable position in the stem, a piece of pure silver weighing 108 centigrammes, and heated to 100° C. in steam, is rapidly dropped into the cubic centimetre of water, and the expansion caused in a given time carefully noted*. According to the law above stated, a centigramme atom, if I may use the term, of any other metal than silver, ought to cause exactly the same expansion when the experi- ment is made with it under precisely the same conditions; and these conditions are very easily realized. J have ascertained that such is the case; and the approximate equality in “ atomic heat ” of many of the metals has thus been easily demonstrated. The comparison of glucinum with silver was made on this plan; and it was found that the weight of glucinum which contains nearly the same quantity of heat at 100° C. as 108 centigrammes of silver at the same temperature is not 4°6 or 4-6 x 3, but 4°6 x 2, or 9°2 centigrammes. The “atomic heat”’ of silver, or the product of the specific heat (=°05701 according to Regnault) into the atomic weight (=108), is 6-157. Using this number as the standard for reference, the experimental number found for the atomic heat of the specimen of glucinum operated with is 5°91. Thus :— Atomic heat of silver . . =6°157 Atomic heat of glucinum . =5°910 The difference is less than the known difference between the atomic heat of silver and that of aluminum ; but I am inclined to think that the lower number found for the glucinum used is due to the presence of a little platinum in the specimen of metal. Owing to the high atomic weight of platinum ( =197-1) as compared with that of glucinum (9:2), the presence of even a small quantity of the former metal must very sensibly affect the determination of the atomic heat of glucinum. I hope * The apparatus is carefully protected from the influence of air-currents during an experiment. 42 On Glucinum: its Atomie Weight and Specific Heat. soon to be in a position to continue these experiments with the pure metal. It will, however, appear from the following considerations that we may fairly regard the above determination of the atomic heat of glucinum as being of such value as to enable us, even at an early stage of the inquiry, to use it as a physical eontrol, and to fix the atomic weight of the metal, subject of course to the probably small change in the numerical expression which may prove to be necessary as the investigation proceeds. If we assume the atomic weight of glucinum to be 9°2, and employ the value I have obtained for the atomic heat, 2. e. 5°91, we can calculate the specific heat of the metal by means of the formula H Sart) oer when § represents the specific heat, H the atomic heat, and A the atomic weight of an element. The specific heat of gluci- num thus calculated is -642. If now we substitute for H a constant, which in this case is the product of the well-ascertained atomic weight of silver* into its equally well-determined specific heat, AS=6°157, the expression becomes 6157 Se> aes EY Se aes and with its aid we can calculate the specific heat of any solid element, if its atomic weight is known or assumed. I have thus calculated the specific heat of glucinum on the assumption (a) that its atomic weight is 9:2, (b) that its atomic weight is 4°6, and (c) that it is 13°8. The results are compared in the following Table with the specific heat obtained by calculation from the actual determi- nation of the atomic heat of the metal:— Specific heat of glucinum calculated (1) from the result of determination of atomic heat. A= 912. eee aes shy) HOAe. Specific heat of glucinum calculated by (2). When A= 9:72 . ., , 669 When A= 46 . . 1'338 When A=138 . . -446. I am therefore justified in concluding that the atomic weight of glucinum is nearly if not exactly 9-2. * We might obviously take any other product; but that of silver is here preferred because the atomic heat of that metal has been employed as the standard for reference. ie aul VI. On a permanent Deflection of the Galvanometer-needle under the influence of a rapid series of equal and opposite in- duced Currents. By Lorp RayueicH, 2.8. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, Poe publication, in your December Number, of a memoir by Mr. Chrystal on Bi- and Unilateral Galvanometer Deflection recalled to my mind some observations of a like character made some years ago by myself. I have lately suc- ceeded in finding the manuscript of a communication with the above title read (literally) before the British Association at Norwich in 1868, which contains a short account of these observations. As the subject has acquired an additional inter- est in consequence of the investigations of Dr. Schuster and Mr. Chrystal, I shall be glad if you can find room for my paper, which has not been printed in full hitherto. I am, Gentlemen, Your obedient Servant, Terling Place, Witham, RAYLEIGH, December 11, 1876. The following paper contains a short account of some ex- periments which led to rather unexpected results, of which I can find no notice in the methodical treatises on Hlectricity, although they might seem to be in the way of any experi- menter on induced currents. The arrangement of the first experiment was nearly the same as that described by Faraday in his original memoir on induction. Two thick copper wires were coiled together—the circuit of one being completed by the battery and make-and-break apparatus, and that of the other by an ordinary astatic galvanometer of moderate sensi- tiveness. The make-and-break arrangement was a very rude one of my own construction, acting either by the dipping of needles into mercury, or by the intermittent contact of a spring with a toothed wheel. When the handle of the instrument is turned, there are generated in the second circuit, as is well known, a series of instantaneous currents which are alternately opposite in sign but whose magnitudes are equal, although that corresponding to the break of the battery-circuit is the most condensed. When, then, the instrument is worked with such rapidity that the interval between the currents is very small in comparison with the time of free oscillation of the needle, the latter might be expected to be sensibly unaffected. But so far was this from being the case, that although the swing of Ad Lord Rayleigh on a permanent Deflection the needle produced by a single impulse was only a few degrees, yet under the influence of the series of equal and opposite cur- rents it remained steady at 60 or 70, and that on either side of the zero-point, which had in fact become a position of un- stable equilibrium. Since it took place indifferently in either direction, the deflection cannot be ascribed to an inequality in the alternate currents, giving on the whole a balance in one direction such as, according to the experiments of Henry d’Abria, might arise from imperfect contacts in the second circuit. The first explanation which suggested itself to me was that, while no doubt the currents of the two series were strictly equal (numerically), the resulting impulses, or rather impul- sive couples, acting on the needle might be slightly different owing to the change of the latter’s position in reference to the coil in the small vibration which the series of currents must produce, however quickly they may follow one another, which would give.one set an advantage over the other. Those cur- rents would prevail which tend to increase the deviation of the needle ; for they would have, as it were, the greatest purchase on it. To make this perfectly clear, suppose either the galva- nometer to be turned round, or the direction of the magnetic force altered by permanent magnets, so that the position of equilibrium of the needle is now no longer zero, but say 20°, and then let the series of induced currents pass. There might appear at first sight to be two cases, according as the first cur- rent tends to diminish or increase the already existing devia- tion; but the result is the same in both, and I will take for the sake of illustration that in which the needle is first sent towards zero. When the second instantaneous current passes, it finds the needle nearer zero, and therefore acts upon it with greater force than did the first ; and this process continues, so that if for the moment we imagine the needle to vibrate about 20°, there is an outstanding force tending to increase the deviation. As this is unbalanced, the equilibrium at 20° cannot be main- tained, and the needle must move further from zero: instead of equilibrium, perhaps, I should say resultant equilibrium ; for the rapid vibration of the needle just now referred to of course goes on in any case. J worked out the mathematical theory of this action fully for a tangent-galvanometer ; and for the case, to which experiment is not limited, of an equal interval between consecutive instantaneous currents of opposite sorts. The most conspicuous result (which might, however, have been anticipated) was that the effect is independent of the rapidity with which the make-and-break apparatus works. As this was not at all what I had inferred from the experiment, I began to of the Galvanometer-needle. 45 doubt whether I had hit upon the true cause of the pheno- menon ; and on more close examination of the mathematical result, it appeared that the needle could not remain perma- nently deflected from its position of equilibrium at zero, unless each instantaneous current was powerful enough to swing it right round when acting on it alone, although an already ex- isting deviation would be always increased. I have already mentioned that the phenomenon was observed when the swing for a single current was only a few degrees, so that there is no doubt of the inadequacy of the foregoing explanation. The real cause is, I believe, to be found in a deficiency in the hardness of the steel needles, rendering them to some extent capable of temporary magnetism when placed in a field of force. If this temporary magnetism alone be considered, the two sets of instantaneous currents conspire in their effects instead of opposing each other ; for if a soft-iron needle be freely suspended in a uniform field of magnetic force, it has, as is known, four positions of equilibrium, of which those two are stable which would be positions of equilibrium (one stable and one unstable) for a magnetized steel bar. If while the needle is in equilibrium the direction of the magnetic force is reversed, no disturbance takes place, because the magnetism of the needle is at the same time reversed also. If such a needle be suspended in the coil of a galvanometer, the force with which a current acts upon it is independent of the direction and varies as the square of the current; or when there is a rapid series of varying but periodic currents, the deflecting force varies as the integral of the square of the current, and as the sine of twice the deviation from zero. The deflecting force would, according to this, be for a given position of the needle with reference to the coil (or deviation) proportional to the heating-power of the discontinuous current ; but it must be remembered that the case is an ideal one, as no iron is per- fectly soft or capable of at once assuming the magnetism due to the field of force in which it is placed. A remarkable illus- tration of this will be mentioned a little later. In order to test the correctness of these views, I removed . the steel needles from the galvanometer and replaced them b a single soft-iron needle, with which it was found that all the phenomena observed before were reproduced. Being anxious to submit the arrangement to a more severe test, I placed the galvanometer in a third circuit, so that it should be acted on by the currents induced by the induced currents of the second circuit,as in Henry’s experiments. The effect was very marked, though for this it was necessary that the galvanometer should be turned round so that the position of equilibrium should be 46 Captain Abney on the Alkaline Development about 20° or 25°; in a tangent-galvanometer the most favour- able position would be at 45°. ‘Throughout these experiments the effect always increased with the velocity of the contact- . breaker up to a certain point, about 100 per second, and then declined. The general increase is in accordance with the ex- planation here advanced, while the falling off might be owing to an imperfect action of the make-and-break machine when a certain velocity is reached. Jam more inclined, however, to attribute it to a want of theoretical softness in the iron, which prevents it from taking the full magnetism when the alterna- tion of currents is too rapid. In support of this opinion I adduce one more experiment. Returning to the first arrange- ment, in which the galvanometer was placed in the second eircuit, I arranged a third circuit in the neighbourhood of the second or galvanometer circuit, whose ends could be joined or kept apart *. In the second case, of course, no effect is produced by the third circuit ; but what will be the result of completing it? It is known that while the magnitude of each instantaneous current in the galvanometer circuit is unaffected, the duration of them is increased by the induction. This dilution, so to speak, of the induced currents diminishes their heating-power, which depends on the integral of the square of the current while it lasts, and would, if the iron were perfectly soft, dimi- nish the deflecting force on the galvanometer-needle ; but it was found, on the contrary, considerably to increase it. In fact, the induced currents are too condensed to produce their full action, passing away before the needle is properly mag- netized. It is too soon to say whether any use can be made of these results ; but it is possible that such a soft-iron galvanometer might be available for measuring the currents produced by the new magneto-electric machines when the consecutive waves are opposite. VII. On the Alkaline Development of the Photographic Image. By Captain Aspyey, A.L., FRS.F INCE alkaline solutions have been introduced for the development of the photographic image, there has been a certain amount of ambiguity regarding their action. It has * There were two similar coils, each containing two wires A,, A,, B,, B,. The battery-circuit included A, and the interrupter. The second circuit consisted of the wires A,, B, and the galvanometer. B, gave the third circuit, which was closed or open, according as the ends of B, were in connexion or not.— Note added Dec. 1876. + Communicated by the Author. of the Photographic Image. 47 usually been assumed that their sole function is to reduce to the metallic state the particles of silver bromide which have been acted upon by light. - The alkaline developer consists of pyrogallic acid or other oxygen-absorber, an alkali such as ammonium hydrate, and a restrainer such as potassium bromide. These are generally mixed together and applied to the film on which has been im- pressed an invisible image in the camera. Those parts acted upon by light darken under the influence of the solution; whilst, if the surface be in a proper condition and the proportion of the restrainer to the alkali be well balanced, the portions un- acted upon by light remain unchanged. ‘The image thus formed is soluble in nitric acid; and further tests show it to be metallic silver. In order to discover the part which the alka- line developer played to cause this reduction, a large series of experiments have been conducted in the laboratory of which I have charge; and the results appear sufficiently interesting to be published. Bulbs were made of the shape shown in the accompa- nying figure. In A was placed, fa whilst carefully excluded from all Mi light, thoroughly washed silver bromide and pyrogallic acid. In B was placed a solution of potas- sium hydroxide or other alkali ex- cept ammonium hydrate. If ammo- nium hydrate were required,the bulb B was made double ; in the first was placed ammonium nitrate and in the other potassium hydroxide, calcu- — lated so that the ammonium salt should always be in excess when the potassium was brought into contactwith it. The tube C was attached to a Sprengel pump; and when the apparatus was exhausted, C was sealed, and the whole of the alkali caused to enter A. After from 2 to 60 hours the bulbs were broken, and the solids and liquid kept for analysis, As far as can be judged, the silver bromide was instantaneously attacked by the alkaline pyrogallate. (There is no action due to pyro- gallic acid on the silver bromide without the presence of an alkali, as was proved by keeping them in contact for weeks and noting their appearance.) After a large number of experi- ments, it was found that the amount of silver bromide capable of reduction was primarily dependent on the amount of pyro- gallic acid present, and in a secondary degree on the amount of alkali present. Thus 1 equivalent of pyrogallic acid can 48 Captain Abney on the Alkaline Development reduce 4 equivalents of silver bromide to the metallic state if sufficient alkali be present to combine with the bromine libe- rated. The solution, after evaporation to dryness, was found insoluble in benzole or ether &c., and only partially solublé in alcohol. A part of that dissolved was further found to be the bromide of the alkali; and the excess of alkali not in combination with carbonic acid was also found in the solution. The amount of carbonic acid was found to be considerable, equal to 1 equivalent of pyrogallic acid. (It seems unneces- sary to give the analysis of the organic residue. Apparently the compound formed is totally different from that obtained by Stenhouse* when investigating the action of bromine on alka- line pyrogallate.) From the above experiment, it will be noted that the reduction of the silver is independent of the absorption of external oxygen, and that only a definite amount of silver can be reduced by a given amount of pyrogallic acid. When, in addition to the alkali, a large excess of soluble bro- mide was added to the bulb B, the same results were obtained, though the reduction of the silver bromide seemed to take rather longer time to effect. The following is an example of the quantities employed in these experiments :— In bulb A was placed . . 3800 grains of AgBr and 10 grains of C, H, O3; In the bulb Bwasplaced . 300 grains of KHO dissolved in the least possible quantity of water. The amount of Ag found to be reduced was 33°86 grains ; and the amount of K Br found in solution was 36°97 grains. Layers of thoroughly exposed and unexposed silver bromide were next treated with a rather weaker solution of the alkaline developer; and when the restraining soluble bromide was omitted, the reduction to the metallic state took place in each layer almost equably. When the soluble bromide was present in equivalent quantities with the alkali, the reduction took place first in the layer that had been exposed to light, and spread gradually into the other layer. From this we may gather that the exposed silver bromide is more readily reduced than that unexposed, and that the solution of soluble bromide and the alkali acts less vigorously than the alkali alone. Another point to investigate was as to the means by which the density in an alkaline-developed image was produced ; for it could not be supposed that merely those atoms of silver bro- mide which had been reduced to the state of subbromide would be attacked, since the subbromide of silver is essentially a coloured compound and can be distinguished even in small * Journal of the Chemical Society, January 1875, of the Photographic Image. 49 quantities. A plate prepared with silver iodide was flowed over with tannin and dilute albumen, and dried. It was then exposed in the camera, and after exposure half of it coated with an emulsion formed in collodion by silver bromide. Now a pho- tographic image impressed on silver iodide is not amenable to alkaline development unless the solutions be excessively strong. An alkaline developer made as below was therefore employed :— 1. Pyrogallicacid . . 16-grains. Nie rel tiie) ie csi lh OZ: 2. Potassium bromide . 20 grains. Wivatens hee ed o's hes I o7z3 3. Liquorammonie (‘880) 4 oz. Watery ee te a 0 OL, or Potassium hydroxide. 15 grains. Nets yt a ae wy, fib 02: One part of Nos. 1 and 3 were added to every three parts of No. 2. As might have been expected, but a trace of an image was seen on applying the developing solutions to the uncoated iodized plate (and this trace was subsequently proved to be due to the sensitive albumen salt); but where the emulsion had been used, an image gradually appeared, not very strong, but still perfectly visible and of printing density. Silver bromiodide plates were treated in the same way: in this case there was a feeble image on the part uncoated with bromide emulsion; but on that part coated with emulsion the image appeared on the bottom surface of the emulsion film, and gradually worked its way up till reduced silver was obtained on the top surface, where the light had most strongly acted on the exposed film. The recoated half-plate, on fixing with potassium cyanide, gave a perfectly bright image, clear and dense, whilst on the other half it remained feeble. With bromide plates in which only a feeble image could. be obtained, the same procedure gave the requisite density; and this fact is likely to be of practical value. It was next proposed to ascertain in which film the de- veloped image was really situated—whether in the exposed or the unexposed film. The double films, which had been treated as described, were taken from the glass plate by applying a damped piece of gelatinized paper to the surface; and after detachment, a similar piece of paper was applied to the surface which had been next the glass. When very nearly dry, the two pieces of paper were pulled apart; one film was found attached to one and the other to the other. Conside:able difficulty was found in this operation, and only about 20 per Phil. Mag. 8.5. Vol. 3. No. 15. Jan. 1877. iD) 50 Captain Abney on the Alkaline Development cent. of the whole were properly manipulated, through our not being always able to hit on the exact amount of desiccation. In examining these films differences were observable. In some cases the image was found to le almost entirely in the exposed film, whilst in others a strong image was obtained in the unexposed film. The difference was eventually found to depend on the alkali used in the developer, and on the porosity of the collodion in which the emulsion was formed. When ammonium. hydrate was employed and a porous emulsion, the image was on the exposed film; whilst if potassium hy- droxide were employed, a vigorous image was in the top un- exposed film. This can be explained through the solubility of silver bromide in ammonium hydrate. ‘The silver bromide would be first dissolved by the ammonium, and then during the course of reduction be carried down to the reduced silver beneath it. Since silver bromide is insoluble in potassium hydroxide, the haloid would be reduced in situ. Having determined this point, it was next endeavoured to ascertain if the photographic image impressed by light on the bottom surface caused a sympathetic action in the unexposed emulsion film. Plates were prepared as before, one half being coated with emulsion after exposure, and put aside for some days. The films were then separated as described, and to each the developer was applied separately. With one or two exceptions, no wage was obtained on the unexposed jilm. The reason of an image (always imperfect) being obtained in some cases was traced to the adhesion to it of the thin layer of albumen, with which the exposed film was coated; for when the albumen was applied after exposure, no image was de- veioped. The foregoing experiments clearly show that the photo- graphic image has no power of transferring itself, or of creating a sympathetic action in an unexposed film previous to development, and that therefore the increase of density and formation of a secondary image must be due to other action than chemical. If further proof be required, it is only necessary to expose a dry plate, and develop it in the ordinary manner, and after drying to coat it with an emulsion, and develop again. It will be found that where the metallic silver of the first’ image. is beneath it, there the top film develops and gives a coun- terpart of it. The metal exercises an attraction for the silver on the point of being reduced from the bromide in a similar way that it does when a silver tree is built up, or when a developed image is intensified by the application of pyrogallic acid and silver nitrate. There seems to be a of the Photographic Image. D1 further action, however, which must be taken into account. It has already been shown that silver subbromide is more easily reduced to the metallic state than is the bromide. In these last experiments I have found that there is great dif- ficulty in starting the development in the unexposed bromide film if the layer of albumen be too thick, but that when once started it proceeds more rapidly. This can be accounted for on the supposition that the attracting particles of silver were too far distant from the emulsion film to exercise their attrac- tive power. But it seems, from other experiments which are still in pro- gress, that the atom of reduced silver immediately combines with the nearest molecule of silver bromide and forms subbro- mide, which is reduced to the metallic state, and its two atoms of silver combine with two other molecules of silver bromide, and so on, the image being gradually built up in this manner. Workers accustomed to alkaline development must have no- ticed that the feeble image first formed in the film grows in intensity rapidly up to a certain point and then flags: the reason of this is apparent if we consider the above reaction to take place, and the subsequent exhaustion of available silver bromide which can be acted upon. One more experiment must be noted. Ifthe film of albumen or gum &e. between the two films be very thick, a reversed action will take place, which can be explained by the fact that the strength of the developing agent is exhausted in producing the image on the exposed parts of the under film, whilst on the other portions the silver bromide most readily attackable is in the upper film. I have already indicated that this application of a film of silver bromide after exposure, either before or after development, might prove useful when employing plates which only yield a thin image when developed in the usual manner: other applications will suggest themselves. I have also previously pointed out* that intensity may be given to an image by alkaline development if a silver compound soluble in the alkali be gradually added to the developer. This new method, how- ever, seems the preferable one to adopt. * Photographic News, March 27, 1874. Hi 2 igh ie VIII. On Ludlamite, a new Cornish Mineral. By Freperick Frevp, £.A.S.* UDLAMITE is found associated with quartz, chalybite, Vivianite, iron pyrites, and mispickel. In the gangue of some specimens galena, blende, and fluor have also been noticed. Hardness 3:4. Specific gravity 3:12. Colour clear green, from pale to dark, transparent and brilliant. Streak very pale green, approaching white; powder greyish white. Before the blowpipe on charcoal, tinges the flame slightly green, and yields a semifused blackish residue. In closed tubes yields water on heating, decrepitating vio- lently, breaking up into brilliant crystalline plates of an intense bluish-green colour by transmitted light. Soluble in dilute hydrochloric and sulphuric acids; oxidized and dissolved by nitric acid. Perfectly insoluble in glacial acetic acid. De- composed immediately by boiling with solution of potassium or sodium hydrate into ferrous oxide and phosphate of the alkali metal. Consists entirely, when pure, of ferrous oxide, phosphoric acid, and water. Ovxidizes slightly, like Vivianite, by long exposure to air, with the formation of ferroso-ferric phosphate. The crystals contain generally minute particles of chalybite, which are very difficult to separate, also specks of iron pyrites. Lisiimation of Water.—As the mineral, when heated in air, is more or less oxidized, and that very readily, it was evidently neccssary to prevent oxidation. The crushed crystals were pressed between folds of warm bibulous paper to remove any small amount of mechanical water, wrapped in thin platinum- foil, and heated to low redness in an atmosphere of carbonic acid. 0-214 orm. lost 0:086=16°82 per cent. 0-192 A 0:083=17:18 i 0.230 Fe 0°039 =16°95 Mean of analyses ... 16°98 per cent. H, O. Estimation of Iron—tThe iron was estimated by a standard solution of potassium permanganate. When the crystals are pure, there is no difference in the quantity of the test-solution employed, whether before or after the addition of a deoxidizing reagent to the solution of the mineral in dilute hydrochloric acid, showing the absence of the higher iron oxides. * Communicated by the Crystallological Society, having been read December 15, 1876, : i a : On Ludlamite, a new Cornish Mineral. 53 Mineral. Per cent. Per cent. FeO. 0°196 gave 40°80 iron =952°45 0184 ,, 41:24 ,, =53-02 0:243 ,, Ale1d ,, =52°85 O20 ye 40 Gam yi 52°64 Mean! Of irONhiscscsvere: ioe 41:03 Mean of ferrous oxide ....s.0. SST KGy Estimation of Phosphoric Acid.—The phosphoric acid was estimated as magnesium pyrophosphate. Mineral. Mor iP, Oras Pencentbn0., 0:214 gave 0-101 = 30:13 OS Gan OMT so 30709 Mean of analyses ...... 30°11. This gives a formula closely corresponding to fHeO. 1 2E 0. oO, OF, which requires the following numbers:— Calculated. Found. PweOe x wack 53°05 52°76 PAU Ose iss 29:88 30°11 DEEL Operas 17:05 16°98 99°98 99°85 That different specimens of the mineral vary somewhat in their composition there can be little doubt. Owing to the kindness of Mr. Ludlam and Mr, Talling, I had sufficient for many other analyses, not published here; and in one or two * Ludlamite is doubtless a basic ferrous phosphate ; and its relation to Vivianite or normal ferrous phosphate may with much probability be re- presented by the following formule :— O Oe PO O| Be PO 0} Be 5 Fe im Fe PO : Also in general it will be seen from the nature of the apparatus 7 a Setemac 1 Lt aby’ the temperatures at which V, and V,. are transpired. Hence m _ Hide PimP2 1+ad, 6) Tap, pl aera a 6 From equation (5) it will be seen that, in order to deter- mine with this apparatus the ratio 7:7), between the coefh- cients of viscosity in the two tubes when the temperatures of these are 5, and 6, respectively, we have only to know the ratio ie RAr where 6, and 6, represent respectively of the dimensions as expressed by , and to measure 1, Pe, * Pogg. Ann. oe pp. 199, 353. 2 84 Mr. 8S. W. Holman on the Relation between and p; by reading three mercury columns. Also we can obtain ee RH from readings of the gauges when 6,=6,, a value of 1 which needs only to be corrected for expansion of the glass to be used directly in equation (5). The whole process is thus reduced to the simple matter of reading columns of mercury, no measurements of volumes of gas being necessary. The nature of the correction of R and X for temperature appears by putting into the above formule, in which these values are supposed to be for 0° C., the coefficients of expansion of the glass = A; we thus get from (5), m Ri(1+A6,)*,.(1+ Ad.) pi—p, 1+.a8, M2 Ri + Adz) 4A +A8) p2—p? 14d; _ RL +A6)2 pimp; 144d, 6) R4(14+A6,)°"A, p2—p? 1+ad; ° ~ Lest, however, an error might occur in the last reduction from a difference between the coefficient of expansion of the bore of a capillary tube and of its lineal expansion, I have care- fully measured both, and find that the coefficient for the bore is 0:0000075, while for the linear expansion I find 0:0000080 per degree Centigrade, a difference too slight to affect the re- sults in my use of it; I have thought it best to use the value 0:0000075, as it entered in the fourth power, while the other entered only in the first power. The tubes used have also been calibrated to ensure the selection of those of uniform bore; and their dimensions have been accurately measured by mercury and a micrometer-screw. The dimensions of the two tubes used in the experiments to be described were, for tube No. L, X=1272°3 millims., R=0°1098 millim.; for tube No. IL., A=1274:1 millims., R=0-1115 millim. To make an experiment with this apparatus, it is merely necessary to start the jet of water and allow the exhaustion to proceed until the mercury columns in F and E have come completely to rest. Readings are then taken of the heights of these columns, by means of a cathetometer, from a steel scale placed beside the gauges. The reading of the barometer cor- rected for instrumental error gives the pressure at A. All these are reduced to the freezing-point; and Hand F are cor- rected for capillarity by the Tables of Delcros. The tempera- ture of the baths is also taken by thermometers in various po- sitions in the troughs. This must be kept constant throughout the experiment; and I have therefore principally used the tem- peratures of melting ice and boiling water. In the experi- the Viscosity and Temperature of Gases. 85 ments of which the following Table gives the results, advantage has been taken of the four methods of checking the results of one experiment by another, by reversing the direction of flow of the air through the tubes, and heating alternately, in each case, first one and then the other trough. In the Table, the first column gives the number of the experiment; column second the direction of flow of the air (which entered at the tube whose numberis first given, and passed out from the other); columns three, four, and five give the pressures at A, B, and D respectively ; columns six and seven show the temperatures, in Centigrade degrees, of the baths around tubes I. and LI. Rirs Rr, respectively ; column eight shows the values of the ratio at different temperatures ; column nine the values of be CGO 7) 2 m at the higher to 7 at the lower temperature; column ten shows the values of the exponent w in the equationn=7”. This is the quantity which it was the object of the experiments to obtain. Direc- TR ON te] PN Oe ae. ||. «Dis Foxe De Aree eens RA Th ae S55 millim.'milim,/millim,} , x 1, | III. | 759-9} 525:2) 16:3 | 17:0 | 17-0 | 0-912 2 > 5 549°3 | 17-1 | 17-0 | 47: ... | 1083 | 0:799 4 0 759°8 | 525°6| 18-0 | 15°] | 15-t | 0-916 5. a A 534-4 | 18-9 si » | 0-921 6. 69 765°7 | 550°9| 18-6 | 17:8 | 17-8 | 0-934 7 he Ee 490-7 | 17:7 | 17-5 | 99-0 ... | 1212) 0:776 8 ks i 491-2} 17-6 | 17:5 | 99°5 .. | 1206) 0°755 9. + is 490:0| 17:3 | 17:5 | 99°8 ..- | 1:215 | 0-780 1]. 45 755°2 | 467-8 | 20°4 0-0 |100-0 we | 1272) 0-771 12. Bs 468-4) 19-4 9 ” oe | 1267) 0757 13. . 467-9 | 19°6 3 * .. | 1271] 0-768 14, x rf 467-7 | 19°3 9 9 ... | 1273) 0:773 16. a 5 544-2 | 20-7 00 | OO | 0-927 17. | L-Il.| 756°7| 525-3) 23-4 i 0-923 18. a » | 0948) 215 0-0 100-0 . | 1277) 0°782 19. = 761-4) 529-1} 16-1 {100-0 (100-0 | 0-933 20. 5 762°0| 5380°2|; 167 | ,, 53 0937 21. i 763°1| 452-2) 185 (100-0 | 0-0 »» | 1:259) 0-738 | In the calculation of the ratio = of this Table, the value of Rin, Rory and 17, after correcting for temperature. The agreement of these two values within O°l per cent. is a test of the accuracy of the method, as the two experiments were made on different 2 used was the mean of that obtaimed from experiments 16 86 Prof. J. W. Draper on the Fived Lines in the days, and the direction of the current was reversed. It will be seen that the value of this quantity increases slightly with the temperature, as we should expect from the slight difference in size of the two tubes used. The values of « will be seen to agree quite closely, with the exception of experiments 2 and 21. A comparison of these results with those of Meyer, Max- well, Puluj, or von Obermayer will show the superior accuracy of this method. Such a comparison can be most easily made by means of a graphical construction. Let »=crt® be the general form of the equation ; then log n= log e+ log, which is of the form of the equation to a straight line referred to rectangular axes, and making an angle whose tangent is # with the axis of X, the value of log c being the intercept on the axis of Y. Therefore, if we plot the various values of log n as ordinates, and of log 7(7),= —273° C.) as abscisse, we shall obtain points lying along a straight line, from whose tangent with X the value of « may be determined. An in- spection of the lines thus obtained from the data of various experimenters furnishes the most ready means of comparing the accuracy of their results. By such an examination it will be seen that, while Meyer obtained values of « from 2=2°3 to e2=0°21, and Puluj from z=0°65 to e=0°47, the above Table shows variations from #=0°799 to «=0°738 only in these preliminary experiments. As a result, then, of these experiments, it would appear that the viscosity of air increases proportionally to the 0:77 power, nearly, of the absolute temperature between 0° and 100° C. But more determinations at temperatures between these limits are necessary to prove the law of this variation. XII. On the Fived Lines in the Ultra-red Invisible Region of the Spectrum. By JOHN WiuLu1AM DRAPER. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, DESIRE ito call the attention of those experimenters who are at present occupied in investigating the less-refran- gible end of the spectrum, to a paper illustrated by an en- oraving in the Philosophical Magazine for May 1843. From this it will be seen that in the preceding year I had made photographs, not only of the Fraunhofer lines, but also of many others at both ends of the spectrum, and in exploring the less-refrangible region had found three great lines far Ultra-red Invisible Region of the Spectrum. 87 beyond the line A, and had designated them as a, B,y. Of the existence of a fourth, still lower down, I had obtained imperfect evidence. Three years subsequently these lines were rediscovered by MM. Foucault and Fizeau, who used the photographic method previously discovered by me. In 1871 they were again detected by M. Lamansky by the aid of a thermo- multipher. I formerly supposed that the experiments of Sir John Herschel, made with paper blackened on one side and washed with aleohol on the other, indicated the existence of these lines ; but a more attentive consideration of the apparatus he employed has led me to change that opinion. He did not use a slit, but the direct image of the sun, which with the optical train he had was more than a quarter of an inch in diameter. Under such circumstances it was impossible that either these or any other lines could be seen. The result he obtained was a succession of circular patches or spots—solar images—commencing above the yellow, and continuing into the ultra-red. More recently Captain Abney has experimented in the same direction, using collodion containing various colouring or other material supposed to promote the photographic action of the less-refrangible rays ; and in a very recent Number of Poggendorff’s Annalen (No. 10, 1876), MM. H. C. Vogel and O. Lohse have published similar experiments. It is this last paper that leads me to make the present remarks ; for those physicists seem not to be aware that what they are attempting now was accomplished in America thirty-five years ago. I think, from some expressions that Captain Abney has used in one of his papers, that he entertains a very low estimate of the photographs so produced; he depreciates the process by which they were obtained very much. Sir John Herschel, than whom no one was a more competent judge of a fine photograph, says of one of these that I sent him (Philosophical Magazine, February 1843), “I should hardly be doing justice to the beauty of the specimen itself as a joint work of nature and art were I to forbear acknowledging its arrival, and offering a few remarks on it..... The spectrum itself is extremely remarkable and beautiful..... Want of habitude in the manipulation of the daguerreotype process, and by no means want of sun, prevented my obtaining any thing like so fine.an impression.” If Captain Abney will for once excuse an inventor for praising his own invention, [ who have seen very many photographs, and know the difference between a good and an imperfect one, will assure him that 88 Fixed Lines in the Ultra-red Region of the Spectrum. these spectrum-impressions were superb. If he will only try the process, he will never give himself any concern about collodion spectra again. [ have attempted ineffectually to draw attention to this process. There is, in my opinion, no fact more striking among the chemical effects of light, none that promises, from its inv vestigation, more impor tant seemliis There are two modes by which this process can be carried into effect. Ist. Submit a silvered plate to the vapour of iodine until it has acquired a yellow tarnish; or, better (since the plate will become thirty times more sensitive), submit it to iodine, bromine, and again to iodine, until the same tint of tarnish has been obtained. _Now expose it to a pure spectrum in a room to which a feeble daylight is admitted. On developing by the vapour of mercury, a photogr aph will be obtained of the visible spectrum from end to end, and extensive regions beyond the violet and the red respectively. In all the part above the blue the day- light and the sunlight have acted in unison, in all that below the blue they have antagonized, and the plate remains unacted upon, except where the Fraunhofer lines occur, and where, therefore, there has been no sunlight. Then the daylight has depicted those lines in white, while the more refrangible are black. 2nd. Prepare a plate as before. Expose it to a feeble day- light or lamp-light, until, if developed with mercury, it would whiten all over. But instead of developing it, now let it re- ceive a pure spectrum. ‘Then develop, and the result will be the same as in the preceding case. So it is not necessary that the daylight and the sun- light should act simultaneously ; they may act successively —an important fact in settling the nature of their anta- gonism. To produce a perfect result, the two (the daylight and the sunlight) must be exactly balanced. If the daylight should preponderate, the protection is only in the extreme red; as it is diminished the protection extends higher and higher; and the exact equipoise being attained, it reaches the confines of the blue. All the Fraunhofer lines in the less-refrangible portion of the spectrum come out in white; all those in the more refrangible are dark. In my early experiments I could not obtain D, HE, F; but my son, Henry Draper, operating under this rule, has since photographed them all. Of all photographic facts. this antagonizing action is the most extraordinary. I still work at its elucidation, though in Contributions to the Theory of Luminous Flames. 98 a very desultory manner. I earnestly commend it to the attention of those interested in an examination of the chemical action of radiations, as one of the most important and pro- mising topics. JOHN W. Draper. University, New York, December 13, 1876. XIV. Contributions to the Theory of Luminous Flames.— Part Il. By Dr. Kari Heumann*. Influence of Withdrawal of Heat from, and Addition of Heat to Luminous Flames. See the phenomenon of a small distance existing between flame and burner, or flame and a cold substance placed therein, is most apparent in the case of non-luminous flames, or of those flames which have been diluted by indifferent gases, nevertheless this appearance is also noticeable in the ease of luminous flames. In the latter flames the eye is some- what overpowered by the light, and hence has difficulty in ob- serving the vacant space; the recognition of this space is made easier by placing a screen in such a position as to cover the luminous part of the flame as completely as possible. Mention has already been made of the fact that a flame loses luminosity by being pressed down or widened out by the in- troduction of a cold substance; and by properly regulating the experiment, it has been shown that the withdrawal of heat is of itself sufficient to account for the observed diminution in luminosity. By combining the results so obtained with those which we have gained concerning the distance between flame and burner, or flame and cold object placed therein, we are led to deductions of great practical interest. Ifa cold metallic wire be placed in a luminous gas- or candle- flame, the flame is totally extinguished in the immediate neigh- bourhood of the wire, and the luminosity of the flame is dimi- nished throughout a very considerable area. In this experiment the low conductivity for heat of gases comes into play, aided by the great freedom of motion and dif- _ fusibility of the particles, whereby highly heated particles are continually brought into fresh contact with the cold wire. The cooling action of the wire is therefore the greater, and extends throughout a larger space, the lower the temperature of the-wire itself. The wire is therefore also more potent in * Translated from Liebig’s Annalen, vol. elxxxiii. part 1, pp. 102-141, by M. M. Pattison Muir, the Owens College, Manchester, 90 Dr. Karl Heumann’s Contributions to this respect immediately it is introduced into the flame ; as its own temperature increases, it loses its power of cooling the surrounding particles of heated gas. A thick wire also will evidently cause a diminution of luminosity for a longer period than a thin wire. It is generally a matter of indifference in what part of the flame the cooling body is placed; hence the burner itself may play a not unimportant part in cooling the burning gas in its neighbourhood, and so in aiding in the production of the dark zone of flame which is noticed just over the orifice of the burner. 3 Before studying the action of the burner in detail, however, it will be well that we should inquire more narrowly into the cooling action exercised by a cold object brought into the flame upon the luminosity of that flame. Ifa luminous gas-flame be slightly pressed down by means of a porcelain basin, the luminosity of the flame is somewhat diminished, and the basin is covered with a deposit of soot. If, however, the basin be at the beginning of the experiment deeply depressed within the flame, the luminosity is at once decreased ; but there is no deposit of soot on the basin. I have already shown that the decrease of luminosity is to be traced in this experiment to the cooling action of the cold object placed in the flame. If, as may easily be done, an equal area of the porcelain basin be brought into the flame in each case, the cooling action of this cold surface will be approxi- mately the same in each™ ; nevertheless when the basin is brought into the upper part of the flame it is covered with soot, while no such deposition occurs when the basin is brought into the lower part of the flame. The following experiments will throw light upon these phe- nomena. A porcelain rod was brought into the lower part of a gas- flame burning at a round orifice 8 millims. in width ; the flame throughout a considerable area became blue. (By cutting off the still luminous portion of the flame by means of a shade, the action of the porcelain rod is rendered more apparent.) No scot was deposited on the porcelain. The same rod was held in the upper part of the luminous flame: it was gradually covered with a tolerably thick deposit of soot; at the same time diminution in the luminosity of the flame was noticed. In order to explain these facts, I put forward the following * Rather more heat will be withdrawn from the upper hot flame, on account of the greater difference of temperature between it and the basin, than from the lower part of the flame, in equal time-intervals. the Theory of Luminous Flames. ah: hypothesis (I shall endeavour to bring together further proof of this hypothesis in the succeeding parts of the present paper):— Carbon-containing sources of light may burn with luminous flames, i. e. with separation of carbon in the flame, or with non- luminous flames, i. e. without separation of carbon*. The maintenance of a certain (high) temperature, dependent wpon the nature of the combustible substance, is an essential condition of luminosity; a flame whose temperature has been lowered by any means is no longer able to bring about the required separa- tion of carbon. Combustible matter, when diluted with imdif- ferent gases, requires to be maintained at a higher temperature in order that it may burn with a luminous flame than when it is undiluted with such gases. Chemistry furnishes us with many reactions analogous to the last-mentioned circumstance: thus dilute solutions gene- rally undergo decomposition or throw down precipitates only when strongly heated, &c. The various parts of a luminous flame are possessed of very varying temperatures ; a cold object brought into different parts of the flame, and withdrawing nearly equal amounts of heat from each, will cool the upper hot parts only slightly below that point at which deposition of carbon takes place ; this process will therefore continue all around the cold object. In sucha case as this, separation of carbon will also be taking place at a point in the flame lower than that where the cold object is situated ; hence these little particles of separated carbon will rise upwards, and some of them will be deposited on the cold object. But if this object be placed in the lower and cooler part of the flame, the temperature of this part of the flame will be decreased beyond that point at which carbon is separated ; hence the object will not be covered with a layer of soot: and, from the conditions of the experiment, there can be no separation of carbon in parts of the flame underneath the point where the cold object is now placed. Bearing these points in mind, we shall be able to trace the phenomena noticed in the first part of the experiment with the porcelain rod to two circumstances :— | 1. Deposition of carbon was noticed upon the rod when held in the upper part of the flame, because the cooling action of the porcelain was not sufficient to reduce the temperature of this part of the flame below the point at which carbon is separated. * IT strenuously uphold the old idea that the luminosity of carbon-con- taining flames is to be traced to the presence of separated carbon. In a future paper I will bring forward new proofs of the truth of this idea. 92 Dr. Karl Heumann’s Contributions to 2. The particles of carbon separated in the lower uncooled parts of the flame rose upwards, and were deposited upon the porcelain rod. The decrease in luminosity, unaccompanied by deposition of carbon, which was noticed when the -rod was much de- pressed in the flame, is to be traced to the fact that the tem- perature necessary for separation of carbon could not be attained in this part of the flame, which previous to the expe- riment was already cooler than the upper part. These considerations teach us that, in order to obtain a large deposit of carbon (as in the manufacture of lampblack c.), the cooling of the flame should not be carried too far, while at the same time the maintenance of a very high temperature or the presence of much air should be avoided. Further, we learn that, in order to obtain deposition of carbon, it is not ne- cessary to cool the flame, imasmuch as the maintenance of a high temperature is a necessary condition of the separation of carbon. The object brought into the flame may be compared to a redoubt which intercepts the balls shot forth. The cool- ing action exercised is productive of carbon-deposition only so far as it prevents the oxidation both of the particles of carbon suspended in the flame and of those caught by the ex- tended surface. Flence it follows that the surface of a giowing body immersed in the luminous flame must become covered with soot. The carbon which is separated in a smokeless luminous flame is burned partly in the outer, partly in the inner por- tions of the flame: it is evident, however, that this burn- ing will take place to a less extent where the flame is en- closed by the solid body placed within it than where it is surrounded by air. Hven in the former part of the flame, however, the supply of air is not altogether shut off; hence a part of the soot which has been deposited, and which is at a high temperature, will be burned. Deposition of soot is therefore generally somewhat less upon a hot than upon a cooler surface ; nevertheless it may happen that a very cold substance is scarcely, if at all, covered with soot. In performing the following experiment, which exhibits the fact that a hot surface may have carbon deposited upon it, care must be taken not to bring the surface covered with car- bon into the air until it cools; else the soot will almost imme- diately be burned. . e=0°003839, so Orlies a=0-:00112, se O27 14e in this equation, we obtain for the specific heat of pure didy- mium the value 0:04563. * Abhandl. d. Schwedischen Akad. vol. 11. No. 6. Phil. Mag. 8. 5. Vol. 3. No. 16. Feb. 1877. if 114 Dr. W. F. Hillebrand on the Specific Heats Assuming that didymium oxide has the formula DiO, we obtain from analysis II. for the atomic weight of didymium the value 96°52*, and for its atomic heat 4°40, which differs so considerably from the atomic heat of the other elements as to render the formula DiO completely invalid. If, on the other hand, we adopt the formula Di, O3, the weight of the didymium atom becomes one and a half times that of the above number, namely 144:78, and its atomic heat becomes 6°60, a number which agrees most satisfactorily with Dulong and Petit’s law. The oxide of didymium is accordingly, without doubt, a sesquioxide. B. Specific Heat of Lanthanum. The following data have served for the determination of Gy:— Exp. I. Exp. IT. Vv =0°60. 1:00 G, =0'1721 0-2154 Gin —= (Ue SJL 16828 Sy 75) 2D Sin = 6049 4-049 t =40° 40° P =0°756 0°758 By substituting these elements in formula (2), we obtain Hrommiixp. eye G,=0-000438, From Exp. Il. . G,=0:00071. The following are the elements for the determination of the specific heat:— | Weight of Weleauet Weight of |1 sal tem-| Duration lanthanum, ) ® . lair in glass _ | of the ex- in grms pean envelope. | Perature. criment germs. aang, pe. periment. Gm. Ge. Gi. ts M,—M, Exp. I. ...| 0-8911 01721 0:00043 99°°76 49". Exp. I....| 1-6828 02154 000071 99°°69 950’. Scale- Scale- Retraction variation variation jof mercury in} Reduced before after scale- retraction. experiment. | experiment. | divisions. Zo vat fT ro . Mo My aps a Exp. I. 0:105 0-11 104°5 109°77 IDrgeh IOUS Se 0:058 0-08 1746 178-05 oO, ; of Cerium, Lanthanum, and Didymium. 115 Hence we have for the specific heat of lanthanum:— Hrom Expo lee 2 es 6004582 From Exp. Il... . . 0°04692 Meanmre ea" ty 6o7 The metallic lanthanum employed in these experiments was likewise not quite pure. It was obtained from chloride of lan- thanum after the larger globules of lanthanum had been sepa- rated, and in which the traces of didymium originally present had become concentrated, since lanthanum is more easily sepa- rated by the current than didymium. 0°8911 grm. of the same specimen which had been employed in the foregoing ex- periments, when oxidized with nitric acid, gave 1:0516 grm. of oxide of lanthanum, which, on solution in hydrochloric acid, evaporation, and re-solution, left 0-054 grm. of silica. All the oxides were precipitated from the liquid by means of ammonia and filtered off; the filtrate, after evaporation and ignition, gave in addition a few milligrams of oxide of lan- thanum. By digesting the hydrates with oxalic acid an inso- luble white residue of the oxalates of lanthanum and didymium was obtained, which, after ignition, together with the above- mentioned small residue, gave 1:0276 grm. of oxide of lan- thanum containing didymium, and, on the other hand, a solution which, after evaporation and ignition, left a residue consisting of 00156 grm. of ferric oxide, 0:0026 grm. of alu- mina, and 0-0004 orm. of oxide of lanthanum. The amount of oxide of didymium associated with the lan- thanum oxide was determined by means of the photometric spectral method originally applied by Professor Bunsen. For this purpose a solution was prepared which, in V, cubic centimetres, contained g; grm. of pure sulphate of didymium free from lanthanum. ‘The 1:0276 grin. of oxide of lanthanum which was to be tested for the amount of didymium which it contained, was then dissolved in sulphuric acid, and gradually mixed wlth so much water that both solutions, tested before the spectroscope in equally thick layers, showed the didymium bands of equal intensity. When this point was attained the volume V of the liquid was read off. From these data we ob- tain the amount of didymium g by means of the equation Yn=5 Va Gia: The experiment gave , V,=25°7 cubic centims. V =23°5 “ Ji =0°0520. 12 116 Dr. W. EF. Hillebrand on the Specific Heats The 1-018 grm. of oxide of lanthanum contained accordingly 0:0476 of oxide of didymium. The oxide obtained by the solution of the metal in nitric acid consisted therefore, in 100 parts, of Oxide of lanthanum = 93°23 Oxide of didymium = 4°52 Oxide of iron . = 1°49 Silica = (51 Alumina = ()°25 100:00 Since it follows, from the oxidation experiment above de- tailed, that 100 parts of oxide correspond to 84°737 parts of im- pure metallic lanthanum, which, after subtraction of the metallic impurities calculated from the analysis, contain 79°431 of pure lanthanum, corresponding to 93:229 pure oxide of lan- thanum, we have for the percentage composition of the pure oxide as directly found :— Manthanum. 4 ane eee 10 Oxi oem io gota) cet 0 100°00 This composition is almost identical with that deduced from Cleve’s* analysis of the lanthanum sulphate (made with great care for the special purpose of determining the atomic weight of lanthanum), on the assumption that the quantity of oxygen in the oxide is one third of that contained in the sulphuric acid necessary for saturation :— Wanthannim ieee tee eo ase9 Oxycon say casas laa 100°00 The sample employed for the determination of the specific heat was found by analysis to have the following composition :— anthanumia ea en enn eosiee Didyma Ge. 7.05 Sis a AsOU aN: Lv epee eats? fs ees Silicon ae hit eens Ahuminiumlre see) Oak 100-00 By means of formula (3) the specific heat of pure lanthanum is found to be 0:04485. Assuming, with Cleve, that the weight of the atom of lan- %* Abhandlung. d. Schwedischen Akad. vol. ii. No. 6. of Cerium, Lanthanum, and Didymium. thanum is 139, corresponding to the formula La, O3, this number gives the atomic heat as 6°23; if we adopt the for- mula LaQ, the atomic heat is 4°15, which does not agree with the law of Dulong and Petit. The oxide of lanthanum must therefore likewise be regarded as a sesquioxide. C. Specific Heat of Cerium. The smaller globules of cerium were employed in this as in the former experiments, and for the same reason. The value of the constant G, is obtained from the following elements :— Wo SSI: G, =) GUE G,, = 2°0935, It amounts to Sg =2°5, 8, = 5'7128, Ae P =0°759. G,=0:00089. The experiments with the ice-calorimeter gave:— ave Weight of | Weight of | Weight of Initial tem-|Duration of cerium, in | glass enve- |air in glass the experi- 1 1 perature. grms. ope. envelope. ment. Gre Gy. Gi. le M,—M,. Exp. I. 2°0935 0‘1601 0:00089 99°:70 60' Exp. II....) 2°0935 0:1601 0:00089 94°-93 60' Scale- Scale- Retraction variation variation jof mercury in| Reduced before after scale- retraction. experiment. | experiment. | divisions. £0, one. =O, Ty wo a yO) xp: Ly... 0-060 0:067 184-6 187°31 Exp. II....| — 9-040 — 0-026 188-0 186°42 _ Hence we have for the specific heat of certum:— From Exp. I. . From Exp. Il. . Mean . 0:04613 0:04554 0:04583 117 118 Specific Heats of Cerium, Lanthanum, and Didymium. In order to determine the composition of the metal under investigation, 0°7946 grm. of it was dissolved in nitric acid and the resulting nitrate ignited ; the residual oxide of cerium weighed 0°9768 grm. By treatment with concentrated sul- phuric acid and repeated evaporation with sulphurous acid 1:6303 anhydrous cerous sulphate was obtained, which, on solution, left a residue, consisting of 0°0031 grm. of silica and 0:0127 ferric oxide, which was found to be free from oxide of cerium and alumina. The amount of didymium was determined by spectral ana- lysis as above described; it was estimated at 0°0352 grm. The cerous sulphate, when converted into cerous chloride and tested in the electric spark before the spectroscope, exhibited only a few very weak lines of the lanthanum spectrum. The ceric oxide obtained by the oxidation of the metal contained in _ 100 parts:— Oxide of cerium . = 94-98 Oxide of didymium . = 3:40 Oxide of iron = 1°30 Silica = 0°32 100-00 Since 0°9768 germ. of this impure ceric oxide was obtained from 0°7946 grm. of the impure cerium metal, 100 grms. of the above oxide must contain 81°347 orms. of the impure metal. By subtracting the amount of the metals contained in the impurities, we have, out of 94°98 grms. of pure ceric oxide, 77-362 grms. of pure cerium metal. The composition of the ignited oxide obtained after treat- ment of the pure metal with nitric acid as directly found is therefore @eritinr ss | ter al eee eon Oxygenie ks ener Nee o 100-00 According to very careful experiments upon chemically pure cerous sulphate, which were performed in Professor Bunsen’s laboratory some time ago by C. Wolf, this salt contains Cerous oxide §..-<. . «| =07:294 Sulphumesacidis: #2). 7 —=42°706 100-000 On the purely hypothetical assumption that in this salt the quantity of oxygen is one third of that contained in the sul- phuric acid needed for combination, it follows that the compo- sition of the highest oxide of cerium is Dr. KE. Bouty on the Magnetization of Steel by Currents. 119 Cenium) (Mies er eue OG Oxygen) PA WMPeMe ak ea Oe 100-00 closely agreeing with that above determined. The foregoing analysis gives for the composition of the speci- men employed in the determination of the specific heat:— Cannume ghia: Ghai, 2 of oro Dickanatamar 91/53 ei) t..e e ar 00 irony eee als tp ell? iliconi. Ph) Joba spacial 7 ORL 100-00 from which we find, by formula (3), the following value for the specific heat of pure cerium, 0:04479. If we assume the formula of the lowest oxide of cerium to be CeO, then the atomic weight of the metal becomes 92, and its atomic heat 4:12. If, on the other hand, we regard cerous oxide as a sesquioxide, we find the atomic weight 138, and the atomic heat 6°18, which agrees in a most satisfactory manner with the atomic heat of the other metals. We must therefore adopt the following formule as representing the composition of the oxides of cerium:— Ce, Os, Ce On. XVII. On the Magnetization of Steel by Currents. By i. Bouty, Docteur és Sciences*. Introduction. PG MAGNET may be regarded as a combination of a great number of elementary magnets, differing from one another in the directions of their axes and the amounts of their magnetic moments. The actual distribution of these magnetic elements (of which we owe the notion to the experi- ment of the broken magnet) remains inaccessible to experi- ment, at least as long as the integrity of the magnet. under investigation is preserved; but in most cases some restric- tions are imposed beforehand on the problem which simplify it much. In the first place, we demonstrate that for true magnetiza- * Translated from a separate impression, communicated by the Author, from the Annales de? Ecole Normale Supérieure, année 1876, pp. 123-154, 120 Dr. E. Bouty on the Magnetization of Steel by Currents. tion* a fictitious superficial distribution of polar (austral and boreal) magnetism may be substituted, which replaces it in respect of all the actions exerted by the magnet exteriorly to its mass. This is the distribution usually studied since Coulomb; and the knowledge of it is sufficient as long as the magnet is not disunited. In the second place, when the practical case of a bar magnetized regularly is considered, it is observed that the — magnetic distribution of the bar is limited to two regions, equal in quantity and of opposite signs, occupying the two extremities. We may suppose each of these masses condensed in its centre of gravity ; and the bar will then be replaced by two magnetic poles of which the masses are m and —m, and the distance of the one from the other a quantity Xf. Lastly, in regard to the actions at infinite distance one magnet differs from another by one element only, which 1s designated under the name of magnetic moment, and of which the rational measure, in the case of a regular bar, is the pro- duct mr of the quantity of magnetism of each pole by their distance. Such is the term of this analysis. | The methods to which recourse is had for the experimental study of magnets are of two kinds: the one sort, utilizing action at contact or at minute distance, are employed for determining the magnetic distribution; their employment is tedious and laborious, and their application subject to special theoretical difficulties. The others, founded upon action at very great distances, furnish in a manner as simple as it is accurate the measurement of the magnetic moment. I purpose in this investigation to apply these latter methods to the study of the distribution. Biot has already set the example of this kind of research, by combining in a mathe- matical formula (subsequently connected by Green with the * See, in the Journal de Physique, tome ii. p. 297, my article “ Sur les distributions fictives d’électricité et de magnétisme,” Xe. + Physically we may, with M. Jamin, consider a bar as a bundle of indefinitely thin magnets having their poles at their extremities. This bundle, embraced by the mean section of the bar as by a ring, expands on the two sides its oppositely named poles, which form the superficial distribution. This synthesis amounts to replacing the unknown distri- bution of the magnetic elements by the equivalent solenoidal distribution (see Thomson’s memoirs), and is perfectly legitimate from the mathema- tical point of view. It has the advantage of addressing the imagination, and of giving a precise physical meaning to all the quantities met with in the analytical study of magnets. Thus the power m of the pole of a bar measures the number of files (rows) of magnetic elements comprised in it; and the distance A is the mean leneth of the files, reckoned in the direction of the axis: it may be called the reduced or magnetic length of the bar. Dr. E. Bouty on the Magnetization of Steel by Currents. 121 theory of the coercive force *) the laws of the distribution in a series of saturated cylindrical bars with the magnetic mo- ments of the bars. The portion of my memoir which relates to large bars is only a wider development of Biot’s method ; that relative to long and thin needles is more original, and its purpose is to determine independently of any hypothesis the two factors m and X of the magnetic moment. Given that we possess a series of magnetized needles in which the quantity of magnetism m is the same, as well as the distance : from one pole to the nearer extremity. This will be the case when the needles are obtained, by breaking, from the middle of one and the same strongly hardened needle f; and we shall see in the sequel that it is a very general one. Then let y be the magnetic moment of a needle of which the length is x; we have WTO CIRO 1S erie ehnaadet elle acted stoic alle) and, theoretically, two measurements, made upon needles of different lengths, will be sufficient for determining the two quantities m and d. This, I believe, is the first time that determinations have been published relative to the situation of the poles in needles magnetized by currents. As regards the quantities of magnetism, their investigation. has been the object of the researches of a great number of physicists, of which I have elsewhere f cited the principal and most recent. The appli- cation of the methods employed requires great delicacy, and supposes the possession of considerable homogeneous masses of the metal under investigation—a condition very difficult to fulfil. Moreover these masses must take the form of ellipsoids§ or of rings|| for the magnetization they receive to be the same in all their points; then the quotient of their magnetic moment by their volume gives the quantity of magnetism pw referred to the unit of volume. * Annales de Ecole Normale Supérieure, 2° série, t. iii. p. 34. + Ibid. pp. 36, 43. fectbid! pal: § Poisson has demonstrated (Mémoires de l Académie des Sciences, t. vii.) that, in an ellipsoid submitted to the action of a constant magnetic force acting in the direction of its major axis, the magnetization is iden- tical in all the points of the mass, and equal to the value which it has at the centre of an infinitely long cylindrical needle submitted to the same force. Quintus Icilius employed ellipsoids. || Stoletow and Rowland made use of rings. The magnetization is the same in all the points by reason of symmetry ; but, a closed solenoid being without action upon any exterior point, they were obliged, in order to accomplish their measurements, to produce induced currents accompany- ing the magnetization or demagnetization of the metallic ring. 122 Dr. E. Bouty on the Magnetization of Steel by Currents I have effected only relative measurements of «4; but the physicists who have studied the question have found its values so variable from one steel or soft iron to another, and even for one and the same sample, in physical circumstances ap- parently so closely similar, that there is but little interest in realizing absolute measurements as long as the laws which govern this variability are not entirely known to us. The greater part of these researches were effected at the Lycée of Rheims; they were finished in the laboratory of M. Jamin. Permit me here to return thanks to that able master for the kindness with which he has welcomed me and for the counsels which he has not ceased to lavish upon me. I. The Permanent Magnetization of thin Needles tempered hard. The quantity of magnetism acquired temporarily or per- manently by a steel needle submitted to the action of a cur- rent depends on the intensity of the magnetizing force em- ployed. Itis important first of all to define the latter with precision. ; In order to magnetize it, the needle is placed in the axis of a helix very long relatively to the needle, and sufficientl wide. Under these conditions the action exerted by the current is the same at all the points of the needle, and pro- portional to the intensity of the current and to a coefficient which depends on the number and width of the turns ; but if we limit ourselves to employing always the same helix and to relative measurements, we can take the measure of the in- tensity of the current for that of the action exerted upon the needle—that is to say, of the magnetizing force. The relative measurement of the intensity of the currents was performed by means of a sort of tangent-compass of very simple construction. A small helix AB (fig. 1), excited by Fig... the current is adjusted so that its axis, sensibly perpendicular to the magnetic meridian, passes through the centre o of a small magnetized needle ab, furnished with a mirror and suspended by a cocoon-fibre. The tangent of the deflection produced is proportional to the current-intensity*. Great * Suppose the needle a6 and the helix A B indefinitely small in com- parison with the distance Ao=r. The helix can be replaced by a magnet of which the moment M is approximately equal to the product Sz of the sum of the surfaces embraced by each turn separately multiplied by the Dr. EH. Bouty on the Magnetization of Steel by Currents. 123 care must be taken, in order to eliminate all action extraneous to the helix, to recurve the two electrodes which convey the current to it the one upon the other, and very close, so that their action upon an exterior point shall be very sensibly nil. - A commutator permits the reversal of the current in the helix, and thus the elimination, by a second measurement of the deflection in the opposite direction, of the error resulting from the imperfection of the adjustment. With respect to the measurements of magnetic moments, they were usually effected by the method which I have pre- viously described for very small magnetized needles *. I have investigated, in the first place, the permanent magnetism of thin needles tempered very hard. These needles have a length at least equal to, and generally above, fifty times their diameter. It is easy to verify that the moments y acquired permanently by these needles submitted to the sanie magnetizing force are represented by the formula y=m(a—da) ; and consequently the method indicated in the Introduction is applicable to such a series of needlest. It would therefore suffice to measure the corresponding values of « and y for a great number of needles of the same diameter and different lengths, and to make all the observations cooperate for the determination of m and d. But here the method presents an inconvenience: it is in fact very difficult to communicate to a great number of needles a truly identical degree of hardening; and if this _ condition is not realized, one of the two determinations, that intensity of the current. If now a be the deflection of the needle a 6, p its magnetic moment, we have, after Gauss, 2Mp_ 28z. ten a= 3 pps If the lengths of ad and A Bare no longer negligible in comparison with 7, the coefficient of ¢ is much more complicated, but tan a remains - proportional toz. , * Annales del Ecole Normale, 2° série, t. iii. p. 12. This method, ab- solutely faultless in the case of very small needles, sometimes becomes a little faulty when one wishes to measure the moment of very long ones very feebly magnetized. This is in consequence of its not being per- missible in the latter case to suppose no reciprocal influence between the directing bar and the needle. But this cause of error, when present, is betrayed by the non-accordance of measures | and 3; and the correspond- ing determinations are rejected. + Equation (1) represents a right line, on the condition that x and y be regarded as current coordinates. The simplest way of proving the applicability of this formula consists in verifying that the characteristic points of the various needles really fall in a straight line. 124 Dr. HE. Bouty on the Magnetization of Steel by Currents. of d, becomes almost illusory. Relying, however, upon a result of experiment which I have already indicated else- where *, we may determine m and d by means of only one needle. When a regular magnetized needle, tempered hard, is broken, the different fragments taken from its middle portion, and of sufficient length, have magnetic moments represented by | Uf sin (a SOV a ee ee The quantity 6 is independent of the intensity of the magneti- zation ; and it is almost evident a priori that the quantity m is the same as in the mother needle. Besides, we demonstrate it experimentally ; remarking that equations (1) and (2), in which z and y are considered as current coordinates, represent two straight lines, we have only to trace these by a sufficient number of observations, and prove that they are parallel— that is, that the two quantities m are equal. 3 This being admitted, let us determine the length and the magnetic moment, « and y, of a needle, then reduce it by ablation of the two ends to a suitable length, and determine again the magnetic moment 7 and the corresponding length x’. The distance 9 of the pole of a rupture-needle from its extremity is known beforehand, and is equal, for example, to 2°75 millims. for a needle of 0°55 millim. diameter. Hqua- tions (1) and (2) therefore completely determine m and d by means of one needle only. Let us add that we can further shorten the primitive fragment by successive breakings, and obtain as many points as we please, in order to determine better the straight line (2)—that is, the value of m. The quantity of magnetism will thus be ascertained to a very great nicety f. * Annales de UV Ecole Normale, 2° série, t. iii. p. 43. + Let BC and A D (fig. 2) be the straight lines represented by equa- Fig. 2. tions (1) and (2). The problem of the determination of d comes geo- metrically to the following—through a given point C to draw CB Dr. E. Bouty on the Magnetization of Steel by Currents. 125 The determination of d is, to be sure, less precise, since it rests upon a single observation, that which refers to the mother needle, and, besides, d is always a rather small quantity ; still, by multiplying observations and taking the means, satisfactory results can be arrived at. Quantities of Magnetism.—The following results refer to needles of 0:553 millim. diameter; the numbers of both columns are expressed in arbitrary units :— Intensity of the current. Quantity of magnetism. SN oe\aiejajsisiss'e:e otssicin's hardly sensible. Ds) eiPenitienss «ae 6 od esis wo sic.cicie 0-12 ec cae stare ction ooielas sicia a Oro Ral es SRNR Cpe naeace 109 14” Meaceoas tose s o Geboodode 2°11 MES stoi ceicie ste < sisis)asle/cie'dse o> 2°89 IIS SsneBeencne SoebdounSbCbO 3°39 IK BB eer Sdocecoscnsesepesse 5°65 PRONE Tas etna clcis vores aisle'are\o\s'ee gc 9 JURE POM sa secliescicssaesiodcties 17-90 NOM MR eee msiss cess cetentice 23°00 Ape cts cccenies occas sivas « 24-00 O10) MeSBECSaanCaR SHES Op EDBDEE 25°90 SOR staidcevciias'e manos (oars 28°90 In order to represent better the course of the function m, a curve can be constructed by taking the intensities for abscisse, and the corresponding values of m for ordinates. At first con- cave towards the positive ordinates, the curve then presents an inflection-point corresponding to the abscissa 22 nearly, and approaches asymptotically a parallel to the axis of the abscissze. These characters are identical with those of the curves which, according to Rowland and Stoletow, represent the magnetizing function of iron or steel*. The general features are every- where the same; and the resemblance is especially striking when, opposite the preceding curve, we draw that found by Rowland for Bessemer steel f. It is nevertheless expedient to examine if there is for tem- pered steel a true magnetizing-function—that is, if the quo- parallel to a given straight line AD. The line A D is perfectly known; as to the point C, its position on the ordinate CP admits an error, in excess or defect, Cc, whence results for D an error, negative or positive, equal to Bd. * This is the quantity of magnetism p referred to unit volume and re- garded as a function of the intensity of the magnetizing force. + Here is the Table which has served for tracing this curve; it is de- duced from the original memoir published, in August 1873, in the ‘Phi- 126 Dr. E. Bouty on the Magnetization of Steel by Currents. tient of the quantity m by the square of the diameter preserves, for one and the same value of the current-intensity, a constant value. The difficulty of ascertaining this resides in the in- equality of the hardening communicated to needles of different diameters placed in the same external conditions—for instance, on immersing them in water when they exhibit the same bright red *. On the other hand, if we compare the phenomena of the steeping of steel with those of the steeping of iron, we are led to attribute to the steeped steel a certain degree of heteroge- nelty from the surface to the centre; and if it really existed, one could no longer talk of a magnetizing function of steeped steel. Therefore, upon the advice of M. Jamin, I tried dissol- ving in an acidf the superficial layer of steeped needles, so as — to reduce them to less diameters, and afterwards magnetizing the needles thus obtained. In this way I proved, not without some surprise, the existence of a perfectly determinate mag- netizing-function. The steeped steel of my thin needles is, then, very sensibly homogeneous}; and the experiment in question permits us to state precisely what should be under- stood by the rather vague expression identical temper when applied to needles of different diameters. The following Table is intended to prove the existence, in the present case, of a magnetizing-function ; it relates to the magnetism acquired permanently by needles thinned with acid from an initial dia- meter equal to 1:178 millim. ; losophical Magazine; the numbers of both columns are expressed -in absolute units :— Intensities. Quantities. Intensities. Quantities. OABOCE ese okie 18 PAM AD) Oe aR Sayers 26880 ORAS ST sens Bee 80 Spa ge aera ne 34200 O;O2 BiG. eee eee. 255 SrOolb gepate wie ok 40320 QSOS eres eat 127 APA OOF IN. sis 52940 AQ ee een 2526 OOO s SLE 61920 1:880 5108 DlsAdls ., ass eR 91530 Wea a insted 8% 6482 2069) nahin 96940 PeSOO Be coe ios a 13510 OSiO0! ty eee 100770 * In this case it is the thickest needles which are the most hardened; they approach more slowly than thin needles the maximum of magnetism of which they are susceptible. Nevertheless, as I have demonstrated (Ann. de? cole Normale, 2° sé. t. 111. p. 40), this maximum verifies the law of the diameters. + Boiling chlorhydric acid, or aqua regia. + The outermost layer, toa depth of 0:05 millim. at the most, possessed perhaps different properties; but to decide this question requires new experiments. | Dr. E. Bouty on the Magnetization of Steel by Currents. 127 Tnitial diameter 1:178 millim. Diameter. Current. Mean. Jmm-988,| O™™-948,) O™-854.| OE™-762. 19°55 | 01800 | 01722 | 0-1202 | _...... 01631 27:91 | 0:3709 | 0:3764 | 0:3350 | 0°3783 | 0:3663 36-25 | 06298 | 0:°6424 | 06078 | 06821 | 06424 45:50 | 08697 | 08863 | 09078 | 0°8712 | 08881 To avoid the errors which might result from an inaccurate valuation of the diameter*, this Table contains, opposite to each value of the current-intensity, the fraction of the extreme quantity of magnetism attained by each group of needles. These numbers should be equal in one horizontal line, if there really exists a magnetizing-function. Here are, besides, the values of the quotients w= — M D. —D?’ millim. millim. 1:088 | 0:1346 0:948 0:1291 0-854 0°1095 0°762 071125 Wiean ste oes. a ele The rotating velocity of Venus, relatively to its orbital ve- locity, has been accelerated in the ratio of its mean rupturing- radius to Harth’s mean perihelion. For log p=2°191493; log (2p? = 207°583) = 2°366824 = 08 2382°715; 224-7 d. = Zo2lo—29 We 3m O's. a. Sh 6 (15) The rotating velocity of (evans eee ane to its orbital velocity, has been accelerated in the ratio of its initial rupturing- radius to Sun’s aggregating-radius. For log (p= & sec. aph.) =1°990608; log (2p? 219°0894) = 1: 041619 = log 87°422 ; 87/0.d 87-490 = 240 Simi ol (16) Jupiter’s secular aphelion (5°5193) is a mean proportional between Earth’s mean distance and Neptune’s secular aphelion (30°4696).' See (27) tor QO)! 9 eas oa The secular perihelion of Uranus (17°688) is at the centre of the supra-asteroidal belt. For Neptune’s secular aphelion (30°47) + Jupiter’s secular ee e seu) = od O00) 30°396—2=17:678. —.. : Se: (18) The secular perihelion of Catena or its iat of nebular rupture, is also a mean proportional between Saturn’s secular aphelion (10°343) and Neptune’s mean aphelion (30°336). (19) The centres of the outer and inner planetary belts are so related that the mean distance of Uranus (19:184) and Harth’s rupturing-locus (sec. per.="932) are at apsides of a major axis Prof. P. BH. Chase on Athereal Nodes. 207 which would be traversed by light-undulations in the time of planetary revolution at Sun’s surface. For 19°184+°932= 20°116; 688°3 x 27—214°86 = 20°128. Seni cat saver eeu eO) The major axis of the November meteoric orbit is also nearly equivalent to the major axis of these primeval light-undula- tions. or the meteoric period =33:25 yrs.; 2x 33:253= 20°68. Be Sal od AE eaten OO amhai ie G2iT ) When Sun’s surface of dissociation was at the extremity of Harth’s mean radius vector, the locus of complete aggregation, or the vertex of the stellar-solar paraboloid*, was at Mercury’s present perihelion (-3187). For l+=w='3184. . . (22) The orbital velocity varies as the 4 power of the gravitating velocity (3). The orbital velocity at the mean aphelion of the intra-asteroidal belt is equivalent to the mean velocity of the centripetal gravitating impulses beyond the belt. For log (sec. aph. ¥ xsec. aph. g)®= 215437; log mean aph. ¢ = ee a eee a ei re aah Py te al Mehl ar (238) The mean velocity of the centripetal gravitating impulses in the principal nucleal belt is also equivalent to the mean- aphelion intra-asteroidal velocity. For log (sec. aph. h x mean YJ )?=:216362. (24) There is therefore an equivalence between the mean exterior and the mean nucleal gravitating impulses beyond the Telluric belt. For log (sec. per. ¥ x sec. aph. ¢)?='855866 ; log (sec. aplemaoamean per 7 )'=-350450.,. 0. .. « ies, (25) The orbital velocity varies as the $ power of the rotating velocity of a varying nebula. The mean orbital velocity due to nebular action in the Neptuno-Uranian belt is equivalent to the rotating velocity at the locus of nebular rupture in the principal nucleal belt. For log (mean per. ¥ x mean 6)? = saad log sec, por. = 683982. 2 si) a os 226) The initial rupturing-position of the centre of planetary mass (17) is determined by the mean influence of the intra- asteroidal centre (6), the supra-asteroidal centre (18), and the nebular centre of planetary inertia. For log (mean @ x sec. per. 6 x mean h )3="742338; log sec. per 4 = °741881. (27) The same position is also a mean proportional between the centre of the supra-asteroidal and the outer limit of the intra- * It was inadvertently stated in the article on “ Correlations,” that there are nine absciss:s between Neptune and # Centauri. There are nine in my original paraboloid ; but if the vertex is taken at the locus of complete solar aggregation, there are eighteen. 208 Prof. P. E. Chase on Athereal Nodes. asteroidal belt. For log es ee 6» sec. aph. ¢)? = 7s 5 (Ce ae ers cs) The See enti AcGhes of the Bone of planetary mass is at the centre of the initial planetary system. For sec. aph. ¥(30° OR eu 6 oe oe 2x sec. per. 4 (4386). ... Be es (29) The initial ogists of mean alae ferns is detent by the mean positions of the rupturing-loci of the two principal two-planet belts. For log C x tae "999583 ; log mean aph. n=1-000003. 6: a Le ee The atmospheric Minit (4) of the ‘aifhibuataroidall belt is de- termined by positions of Sun, Jupiter, and Neptune. For ee ooo = 3:429079 ; Soe vr é+Or)= 3°429048. Th Gi The senouplions limit of the nail puson of the infra- asteroidal centre is determined by positions of Sun, Jupiter, and Saturn. For log (sec. per. 4% X sec. per. h 3+@Or)= 3147264; log (sec. aph.@+ Or)? =3'147491,. . . . (32) The atmospheric limit of the initial tendency to infra- asteroidal rupture is determined by positions of Sun, Jupiter, and Harth. For log (mean per. 4 x ®)?=2°680698 ; log (see. aphe.S.—-On)? = 208001)... 5 ee ee eee The atmospheric limit at the inner locus of infra-asteroidal rupture is the nucleal rupturing-limit of Mars relatively to Harth. For log (sec. per. § +O r)3=2-420721 = log 1:226 @ - Yr, wec,;. (sec. per. 6 — ©)t#= 1225, os eee The atmospheric limit at the central locus of infra-asteroidal rupture is at Jupiter's mean aphelion. For log (see. per. 6+ ©r)?=3:068927; log(mean aph. 1 + @r)=3-066743. (35) The atmospheric limit at the rupturing-locus of Mars is near the rupturing-limit of Saturn. For log (sec. per. g+@r)? =3°266367; logsec.per. kh +Or = 3:273391 ; 3°273391 — 3°266367 =:007024= log 1:0163. This indicates a similarity of contraction at the centre ( » and at the outer limit of the eG a yh see. cae ae 940244; log sec. per. hi O23 Gaga tire (51) The mean oachone limit of ‘s te anus tole ifort to Jupiter’s rupturing-locus, is at Neptune’s mean aphelion. For log (8 + sec. per. 4)*= 1:480913; log mean aph. YP = DPA BT OGL 4 AY eo, oft pet HG Se RE ani eae ee The same limit (52), referred to Jupiter's mean perihelion, is at Neptune’s mean locus. For log is — mean ee Yo RA SO oy meatal ce eae = (90) The same limit, referred to Jupiter’s mean » position, is at Neptune’s rupturing-locus. or log ie oy = 1°471828; los see: per. ¥) — lay t2oo, ayo. (54) The important influence of Barth’ s ae at a centre of early nucleal condensation is also shown by the simplicity of relations between Harth’s radius vector and the secular epicy- clical undulations of the supra-asteroidal planets. Harth and Sun are convertible points of suspension for a linear pendulum equivalent to the secular excursion of Uranus. For 3 = 38°365=:0782 ; the maximum eccentricity of Uranus is 0780. See (20), (21). . SENDS ES EM 29 a The excursion of Saturn is ‘nearly equivalent to the atmo- spheric limit of a nucleus which has Harth’s thermal radius (1:4232s=1-601). For 1:601+19-078=-0839 ; the maximum eccentricity of Saturn is°0843. . .. v2 ey The excursion of Jupiter is equivalent to the mean radius of rotating inertia at Harth’s orbit (V-4='6325). For -6325 10-406 = 06078, pee Ss maximum bee being GOS Olt Astle Ss SG de eae (57) The excursion of niaannae is in thie inverse ratio of its own coefficient (#), and in the direct ratio of the coefficient of Uranus ({), in the abscissas of the solar aggregating-parabo- loid. .. For 4£—-60:074= 0146; N ene: Ss maximum eccentri- city.is "0149. eae: Pt Bae (58) On the Speed of Signalling through Telegraph Circuits. 211 The following Table shows the closeness of approximation, (theoretical — observed) ~ observed in each of the foregoing vihg isons:— — 0039 16. —-0028 * Gis 00380 | | 31. ool | 45. —-0009 2, 0197 17. 0001 32. —-0005 | 46. —-0070 3. —-0158 18. —-0006 | 33. 0002 | 47. —-0043 | 4. 0109 19. ‘0019 | 34. 0008 | 48. —-0291 | 5. —0014 20. -0006 | 35: 0050 | 49. —-0016 6. 0001 21. —-0224 | 36. -0U06 | 50. -0093 | 7. 0033 22, —-0013 | 37. 0000 | 51. —-0023 | 8. 0074 23. —-0012 | 38. 0000 | 52, — 0025 | 9 0000 24. -Y0l0 | 39. .-0000 | 53. —-0014 | | ie -o7u* | 25. -volo | 40, -0009 | 54, —-0013 ll. —-0023* | 26> -vu0l 41. —-0045 55 ‘0030 12. -G169% | 27. -OOLL | 42. —-g018 | 56. ---0050 | 13. 0238" 28. -0039 | 43 —-0088 | 57. —-0008 | 14. 0319" 29, -vol9 | 44. —-0078 | 58 0014 | | 15, -0052* | 30. —-oo10 | | XXVIII. On the Speed of Signalling thr a Heterogeneous Telegraph Cirewts. By OLIvER HEAVISIDET. W HEN the first trials of speed of working were made on the Anglo-Danish cable, then recently laid (September 1868), it was. found that a considerably higher speed could be reached in one direction than in the other. The “ line ’’ portion of the circuit consisted of a land-line on the English side of 240 ohms resistance, then a cable of 2500 ohms resistance and capa- city 120 microfarads, and a land-line on the Danish side of 1250 ohms—all approximate. The circuit was completed through a battery of 150 ohms at one end and a Wheatstone’s receiver of 750 ohms at the other, the circuit being worked on the earth-to-earth principle, 7. e. without condensers. But although the battery and receiver at each end were the same, or near rly so, the maximum speed obtained with W heatstone’s transmitter, making mechanically exact signals, was 40 per cent. higher from England to Denmark than from Denmark to England}. This unexpected result was abundantly confirmed by the sub- sequent experience of every-day practice, which proved the existence of a difference in working-speed in opposite direc- tions varying from 20 to 40 per cent. at different times, mainly according to the state of insulation of the land-lines. * According to Herschel. t+ Communicated by the Author. } It may be interesting to state the actual speeds obtained on this cir- cuit with different instruments. Morse, 60 to 75 letters per minute; -Wheatstone’s transmitter and receiver, 90 to 140 letters per minute; Wheatstone’s transmitter and Thomson's recorder, 300 to 360 letters i minute: in all cases without condensers. EZ 212 . Mr. O. Heaviside on the Speed of Signalling -Later on the same instruments were introduced between London and Amsterdam, on a circuit consisting of a land-line of 130 miles on the English side, then a cable of 120 miles, and on the Dutch side a land-line of 20 miles (Culley, Journ. Soc. Tel. Eng. vol.i.). In this case the maximum speed ob- tained was 50 per cent. higher from Amsterdam to London than vice versd. Again, on the London-Dublin circuit, con- sisting of cable 66 miles and land-lines 266 and. 10 miles, the longer line being on the English side, the speed from Dublin to London was double that obtained in the reverse direction, viz. 80 and 40 words per minute respectively. Similarly be- ween London and Belfast. 7 In all these cases it is to be observed that the station nearest the cable receives the most slowly, and that the greater the inequality of resistance of the land-lines, the greater is the dif- ference in the working-speeds. This seems to point directly to the conclusion that the uncentrica] position of the cable in the cireuit actually causes the retardation to be greater in one direction than inthe other. The fact that the cable receives a much larger charge of electricity when the battery is connected to the end of the shorter than to the end of the longer land- line might, on a cursory examination, seem to corroborate this conclusion. But when the light of theory is thrown upon this view of the matter it.is at once found to be untenable. -. It is easily shown that if condensers be distributed in any arbitrary manner along a line which is to earth at each end, dividing it into sections having any resistances, and the con- densers be all initially discharged, the introduction of an elec- tromotive force in the first section will cause the current to rise in the last section, in the same manner as the same electromo- tive force in the last section will cause the .current to rise in the first section, Furthermore, it may be shown that if leaks be introduced on the line in any arbitrary manner, the same property will hold good. (The differential equation of the current, which is linear and of the same degree as the number of condensers, is the same for the first and last sections; and the conditions to determine the arbitrary constants are the same.) Now every telegraph-line, however irregular it may be in its resistance, capacity, and insulation in different places, may be considered as such a system of condensers and leaks, infinite in number if necessary ; whence it follows that on any line there is absolutely no difference in the retardation in either direction, meaning by retardation the time required for an electromotive force at one end to cause the current at the other end to reach any stated fraction of its maximum. Therefore, to account for the facts, which cannot be gainsaid, we must through Heterogeneous Telegraph Circuits. 213 look outside the line and fix our attention on the sending- and receiving-apparatus. The actual cause or causes must, how- ever, be of such a nature that they only come into operation when the capacity, or the leakage, is unsymmetrically situated in the circuit. No perceptible difference in working-speed was observed on the Anglo-Danish circuit when the corre- spondence was maintained between the two ends of the cable itself. Now, since in all the cases described Wheatstone’s transmitter was employed, it is natural to inquire whether the difference is due to any peculiarity in the method of making the signals with that instrument. If so, then we need not expect any difference to exist when simple reversals are made. But, in fact, it exists even then. An instance bearing this out was described by Mr. Varley before the Submarine-Cable Committee (Sub. Report, p. 156). Experimenting with his “wave-bisector ’’ on the underground lines between London and Liverpool, Mr. Varley found that the introduction of re- sistance at the battery-end of the line lowered the speed to a greater extent than its introduction at the receiving-end, where indeed it made little difference. Here the speed was inversely as the retardation, since the wave-bisector made simple rever- sals. Mr. Varley attributed the difference to the leakage ; but this is in direct contradiction to the theoretical result, that neither leakage nor irregularity in distribution of capacity can, acting alone, cause any difference. Also the difference existed on the Anglo-Danish circuit when simple reversals were made with the transmitter, but apparently to a smaller extent. It was quite perceptible (10 or 20 per cent.) with key-sending, using a common reversing key—though the exact amount of the difference could then not be exactly esti- mated, since operators differ nearly as much in their hand- signalling as in their hand-writing. Although, therefore, in the case of Wheatstone’s transmitter the difference in working- speed may be, and I believe is, mainly due to a peculiarity of that instrument, yet when plain reversals are sent, there must actually be a difference in the retardation in opposite direc- tions ; and this I believe is due to the fact, which comes out on closer inspection, that it is not the same circuit which is being worked when the direction of working is reversed. Let the line consist of a cable of resistance c, having land- lines of resistances a and 6 attached to its ends, and let the battery and receiver resistances be f and g respectively. Then. ~ fig. 1 shows the arrangement when A sends ‘to B.***Further,: suppose for simplicity, and to avoid analytical calculations, that the cable’s resistance is small compared with the total” resistance of the circuit. -Then we may obtain tolerably accti=* 214 Mr. O. Heaviside on the Speed of Signalling rate results by considering the cable’s capacity as collected at its centre. Then, by the ‘theory of the condenser, when A < ap- Fig. 1. a Cc 6 g 5 plies his battery to the line, the current rises at B according to the formula C= Sl) where C is the current, E the electromotive force, R the total resistance between A and B, ¢ the time, and T= ; eto +b+9), where S is the cable’s capacity. Thus the magnitude of T determines the slowness of the rise of the current, and we may therefore call it the retardation. (In the time T. the eurrent reaches about 63 per cent. of its maximum.) Now when B sends to A, fand g change places, producing the arrangement shown in fig. 2. If C’ is the current B produces at A, Fig. 2 Vd a c b A eat oe an Oe ee % he 1D ha Ni ies shea C= Rl e 7’), where a S /e ¢ ) / oe — — i Comparing the values of T and T’, we shall find that if a=5, ie as aleo 1k if ge ta but if ag. Or, in plain English, the retardation is the same in both directions if the land-lines have equal resistances, whatever may be the resistances of the bat- tery and receiver ; it is also the same in both directions if the battery and receiver have equal resistances, whatever may be the resistances of the Jand-lines ; but if the resistances of the land-lines are unequal, the retardation is greatest when the station nearest the cable is receiving, if at the same time the through fF. leterogeneous Telegraph Circuits. — 915 battery is less than the receiver resistance, and least in the contrary case. Now if the battery is always in circuit, as in making signals with a reversing key, the effect of any arbitrary signals may be calculated by the same formula, and the maxi- mum working-speed (always provided it be within the reach of the apparatus) will be least when the station nearest the cable receives, if the battery is less than the receiver resistance, and greatest in the contrary case. Generally, the more cen- trally the capacity is situated the greater the retardation. The influence of leakage or faults may be readily determined in a similar manner, since the retardation is proportional to the resistance through which the charge in the cable discharges to earth. In all cases the retardation is reduced by a fault, and the more so the nearer the fault is to the centre of capa- city. Ifa fault be introduced on the long land-line 0, the dif- ference of the retardation in opposite directions is the same as before as regards direction, while its percentage amount is in- creased. The influence of the natural leakage of the land- lines is the same, since nearly all the loss will, under ordinary circumstances, take place on the long land-line. But if a fault be introduced on the short land-line, the percentage dif- ference is reduced instead of being increased, and its direction may even be reversed. : We have thus found that on any circuit consisting of a cable with land-lines of unequal resistance at its ends, a difference in the retardation in opposite directions is necessarily intro- duced when the battery and receiver have not the same resist- ance. Suppose, in figs. 1 and 2, f=1, a=10, c=10, b=100, g=10; then the retardation from A to B is to the retardation from B to A as 184: 265, 2. e. 44 per cent. greater from B to A than from A to B; and the natural leakage of the land- lines increases this difference. But with Wheatstone’s trans- mitter the observed difference is greater than can be thus accounted for, and exists even when there is no inequality in resistance of the battery and receiver. This is due to a pecu- liarity in the method of making the signals with that instru-. ment, which is at the same time the cause of two other ano- malies, viz.:—reduction of working-speed by leakage, although the retardation is thereby reduced ; and increase of working- speed by the addition of resistance, although the retardation is thereby increased. To understand this, it is necessary to examine the way the sending-end of the line is operated upon. The point & in fig. 1, or k’ in fig, 2, is always connected with the positive or negative pole of the battery, or it is insulated. Currents of equal duration follow each other, alternately + and —, separated either by no interval, or by intervals equal 216 Mr. O. Heaviside on the Speed of Signalling to twice, four, or six times the time of a eurrent*. The arma- ture of the receiver is adjusted neutral, so as to remain on the side any current sends it to, until an opposite current reverses its position. Lines of two lengths are thus made:—a “ dot” by first a + current immediately followed by a — current to terminate it, thus + —; and a “dash” of three times the length by first a + current, then an interval of insulation for twice as long, and lastly a — current to terminate it, thus +00—. Ata speed much below the limiting speed the sent signals are reproduced at the receiving-end without sensible alteration ; but as the speed of working is increased and the currents have not time to reach their full strength, irregulari- ties show themselves, which increase rapidly as the length of each contact is reduced, until at length a limiting speed is reached at which some of the signals miss fire altogether. Consider the suceession of signals @ LID) ae Nd We Tig Ren 7 +—+—+—+-—0000+ — +00— + —0000 (illustrating a typical failure), consisting of a series of dots, followed, after an interval of insulation, by a dot, a dash, and a dot. Ifthe receiver is adjusted so as to record the dots a, 6, c, d perfectly, the signals g and 9 will fail. g will fail because the — current e¢ has time to die away during the interval of no sent current 0000, thus making the succeeding + current f too strong; and 7 will fail because the + current h has time to die away during the interval of no sent current 00, thus making the — current i toostrong. In the first case the dot is continued on to the dash, in the second the dot is lost. Thus, although generally, to get the greatest possible working- speed, the retardation should be as small as possible, yet in this system of contacts of equal duration to make lines of unequal length, it is important that some of the currents, viz. those com- mencing dashes or spaces, should not die away too quickly. They are prevented from doing so, in a great measure, by the insulation of the line at the sending-end during the intervals of no sent current, which, by closing up the path at one end for the charge to escape, prolongs the current at the other. (The compensation currents, sent by an improved form of trans- mitter, have for their object to still further lengthen out the currents.) Now it will be seen from the figures that when A insulates the line at 4, fig. 1, the charge of the cable discharges through the resistance a tb+9, and that when B_ insulates at k’, fig. 2, it discharges through the smaller resistance * Mr. Culley’s ‘ Handbook ’ contains a full description of the apparatus. through Heterogeneous Telegraph Circuits. 217 c 2 the latter case, and, by reason of the before-mentioned pecu- liarities, the station A nearest the cable receives more slowly than B. The explanation of the reduction of speed by leakage is similar. The leakage lessens the retardation and conse- quently quickens the signals. Ifevery signal were quickened in the same proportion, as would happen were the circuit always complete, it is evident that the speed of working must be increased ; but it is easily seen that the decrease in the re- tardation caused by the loss is proportionally much less when the circuit is complete than when the line is insulated at the sending-end, thus increasing the irregularity in the re- ceived signals due to the unequal intervals between the sent signals, and consequently lowering the working-speed. Again, the addition of resistance at the receiving-end, as at A in fig. 2, when B sends to A, may increase the work- ing-speed. Now, since the addition of resistance obviously increases the retardation, nothing could result save a de- crease of speed if the retardation of every signal were in- creased in the same ratio. But this is not the case; for the retardation is increased in a greater ratio when the line is in- sulated at the sending-end than when the circuit is complete —exactly the opposite to what occurs with leakage: then the working-speed was lowered; now it is increased. (This rea- soning will not, of course, apply to other systems of transmis- sion.) On the other hand, the speed is lowered by inserting resistance at the sending-end, B, fig. 2; for the retardation is unaltered with line insulated, and increased with complete circuit. +a+g. Therefore the current dies away more quickly in To ascertain the exact amount of retardation produced by resistance at either or both ends of a submarine cable, each case must be calculated separately, because the form of the eurve of arrival of the current is altered, the law of the squares only holding good when exactly similar systems are compared. A B c D Let BC be a cable of length J, resistance & per unit of length, capacity c per unit of length ; and let AB and CD be resistances equal to mkl and nkl respectively, connected to the cable at Band C, and to earth at A and D. Let v be the potential of the conductor of the cable at distance x from B at the time ¢. Then, according to Sir W. Thomson’s theory, v must satisfy d2u 1 dv ede 218 Mr. O. Heaviside on the Speed of Signalling between z=0O and «=l. The general solution is yp a2t . v=SAsin ee vf bere, oene Laie where T=cki?, if v vanishes for t=0o. Three sets of con- stants, A, a, and 6, have to be determined from the terminal conditions for z and t. In AB and CD the current follows Ohm’s law. Therefore . v 1 dv a a ae when 2=0, and v 1 dv ——= «ss SSS — a ae hap ee for all values of t. Therefore, by (1), sin b=ma_cosb, or tanb—ma=0, and 3 sin (a+b)=—nacos (a+b), or tan (a+b)+na=0. Hence, eliminating 0, tana= Kens he mna*—1 from which the a’s can be found when m and n are given. The 6’s are already known in terms of the a’s, and the A’s can be found by integration if the potential of every part of the conductor of the cable is given for t=0. Let it be that pro- duced by an electromotive force EH in A B, 7. e. v=. JOM ame 5 ((1+m+n)’ then, by integration, a 14+ ma? © 14n7a? and finally, the potential at time ¢ is wy 1 tee2h 1410? i=1 C; re (sin + ma’ cos) - ene 1+ ——,.+--— >; : i ie ee nar from which the arrival-curves of the current may be found by making 2=/, In the diagram six cases are shown. The “ - ~~ “> ~} > -S i) S. S 5 S "> NS nH 5 © = &§ ) > > ied Se) Ss laa ny ee > > S =~ ~ ; Current. 220 Mr, O. Heaviside on the Speed of Signalling abscissas represent time, from t=0 to t=40a, the unit being ck? a=T0-3 log. 10. The ordinates represent the arrived current, the maximum strength being in all cases =100. 1. m=0, n=0. Let N be the percentage amount of received current at lees t, then N 2 iY i272 —~ = le = > ecosame sik. T 100 2. m=O; n=4 tana+ 5 =0, N Rg ZCOSsia np ewe Woes Ome : 3. m=0, n=1. tana+a=0, a2t N ene, 100 =1-4 cosa+ seca 4 m=(0, n=2. | tana+2a=0, N Gieosiae, 2 ee) ——————¢€ 100 2+ cosa 9: m=0, n=0. N COs tr aE ck 100 m14 2558) Tegner Be 6: m=1, n=l. tan a= ra share, Noses 100 35a" Curve (1) is the arrival-curve when no resistance is inserted at either end ; curve (2) when a resistance equal to one half the cable’s resistance is inserted at either end ; curve (3) when a resistance equal to the cable’s is inserted at either end ; and curve (4) when twice the cable’s resistance is inserted at either end. (5) shows the curve of arrival of the potential at the insulated end of a cable when the other end is raised to a con- through Heterogeneous Telegraph Circuits. 221 stant potential ; (6) shows the arrival-curve when a resistance equal to the cable’s is inserted at each end. It will be observed from an inspection of the curves, that, when resistance is added at one end of a cable only, the effect in increasing the retardation is very great when the added resistance is small, but as more and more resistance is added there is not much further effect. The limit is reached in curve (5). But the insertion of resistance-at both ends has a much greater retarding influence, which increases without limit. Compare (4) with (6): in (4) we have twice the cable’s resistance at one end and none at the other ; in (6) the same resistance is equally divided at each end, and the retar- dation is very greatly increased. With respect to the change in the form of the arrival-curyes, it will be seen that, when resistance is inserted, the first part of the arrived current is proportionally less retarded than the later parts. Thus, comparing (1) with (6), when there is no resistance inserted the current reaches 5 per cent. of its maxi- mum in 2°45, whereas (6) takes 6a, or 2°4 times as long ; to reach 10 per cent. (6) takes 3°3 times as long as (1); to reach 40 per cent. it takes 3°7 times as long, and to reach 70 per cent. 4°5 times as long. Curves (1), (7), and (8) show the effect of different distri- butions of the same amount of capacity in a line of given resistance. (8) shows the arrival-curve when the capacity is all collected at the centre of the line as a single condenser, (7) when the capacity is uniformly distributed over the middle third of the line, and (1) when it is uniformly distributed over the whole length. The more the capacity is spread, the longer is the time taken for the current to reach a sensible strength, whereas the current rises rapidly the moment contact is made when the capacity is collected at one place. Curve (7) is the same as (6) with the abscissas of the latter reduced in the ratio 3:1; and curve (8) is the limiting form of the arrival-curve when very great equal resistances are inserted at both ends of the cable, the abscissas being reduced in the same proportion as the resistance of the circuit is increased. Its equation is N ~s TO ae r, Behe? XXIX. On Fived Lines in the Ultra-red Region of the Spectrum. By Captain ABNEY, f.F., PRS. ‘0 the Editors of the Philosophical Magazine and Journal. GENTLEMEN, : ie the February Number of the Philosophical Magazine there is a communication from Dr. Draper in which refer- ence is made to myself. May I ask that you will insert a few remarks on the points in which I am interested ? May I premise by saying that I am excessively sorry if any paper of mine has caused Dr. Draper to think that I have de- preciated his method of photographing the least-refracted end of the spectrum. Jam very familiar with the method he has indicated in his paper, and have employed it with marked suc- cess. The object with which my experiments were undertaken was to find some method by which the lines in the red and ultra-red end of the spectrum could be photographed, in a manner known as wnreversed ; that is, that a black iine in the spectrum should, after being photographed by the coilodion process on glass, show as a transparent line in the picture when viewed by transmitted light. It is fairly easy to obtain a picture in which they appear opaque compared with the ad- joining portions of the developed image; but it has hitherto proved much more difficult to obtain them as indicated above. In this attempt I have been fairly successful, and in some negatives have obtained transparent lines far below those already photographed. It may interest Dr. Draper to know that last autumn I studied, with most encouraging results, the “ antagonism ”’ which seems to exist between various portions of the spectrum when they are used to excite a photographically sensitive plate. This research I hope to continue when the sun appears a little more frequently than it has during the last four months. I trust I may be allowed to differ from Dr. Draper regard- ing the advisability of abandoning the researches previously alluded to. It seems to me that a method of obtaining a nega- tive picture of the least-refrangible portion of the spectrum will — be valuable in more ways than one. Yours faithfully, W. vE W. ABNEY. - _— —_ [ 223 ] XXX. Notices especting New Books. An Elementary Treatise on Elliptic Functions. By Antuur Cay- LEY, Sadlerian Professor of Pure Mathematics in the University of Cambridge. Cambridge: Deighton, Bell, and Co. London: Bell and Sons. 1876. 8vo. Pp. 384. N most works on the Calculus the subject of Elliptic Integrals is either altogether excluded or treated inadequately; and not merely is this the case with works that are in fact elementary, but even in the elaborate treatise of the late Professor De Morgan the subject is dismissed in two paragraphs, which are in substance as follows :—‘‘ Important as Elliptic Integrals are in certain classes of probiems, and numerous as have been the properties of them, which have been investigated, it cannot yet be said that either these problems or methods lie so close to the grand route on which the students’ elementary course should be marked out as to require a detailed treatise on them to be inserted here.” He then goes on to state :—-that an Integral is called Elliptic when it can be put into | Rd: the form | 7 where R is a rational function of xv, and X a rational and integral function of the fourth degree ; that itis capable of being shown that the actual calculation of all such Integrals is attainable when Tables of the following integrals (called elliptic integrals of the first, second, and third kind respectively) have been constructed, viz. Pade EG) es g phx {° ue ait ERE 9)’ cs V (1—? sin’¢)d¢, dp i 1 o sin?@ 1 (1—k’sin?¢)’ in which & (the modulus) is less than unity, and ¢ (the amplitude) does not exceed $7; and that extensive Tables of the first two kinds © have been given by Legendre, with methods of approximating to integrals of the third kind (pp. 656, 657). In fact Legendre worked at the subject, systematizing and supplementing the work of his predecessors and making the actual numerical calculations, for about forty years. His results, in their final form, were published in 1825-26. They were scarcely out when the subject was treated from an entirely new point of view by Jacobi, whose Pundamenta Nova was published in 1829, being preceded and followed by memoirs from 1828 to 1858, and by Abel, whose memoirs appeared from 1826 to 1829. It will be seen from this statement that the student who wishes to make out the subject will not gain much help from the ordinary textbooks ; and indeed not much has been written (we believe) on the subject in English, beyond the works referred to in the note to the above-quoted passage in De Morgan’s ‘ Differential Calculus.’ An Elementary Treatise on Elliptic Integrals was therefore much 224 Notices respecting New Books. needed; and students have reason to be thankful that the task of writing such a book has been undertaken by one in every way so competent as Professor Cayley. His Treatise “is founded upon Legendre’s Traité des Fonctions Elliptiques, and upon Jacobi’s Fundamenta Nova and memoirs by him in Crelle’s Journal;” he has made ‘‘ comparatively very little use of the investigations of Abel or of those of later authors.” A good deal has, however, been done in treating “various points which require to be more fully discussed ” than they have been by Jacobi, and particularly the theory of the Elliptic functions themselves, and not included in the Fundamenta Nova the “ theory of the partial differential equation satisfied by the functions ©, H, and deduced therefrom the partial differential equa- tions satisfied by the numerators and denominators in the theories of the multiphcation and transformation of the elliptic functions.” The Treatise is expressly designed for the use of students, and great care has been taken to prevent them from being lost in the wilderness of symbols to which the author introduces them. Thus the first chapter is taken up with a general outline of the subject, and the student is directed to peruse the chapter, not dwelling on it, but returning to it as he finds occasion, the object being that he may always have certain landmarks in view, and be the more able to keep in mind the mutual relations of the parts of the subject. With the same object, introductory articles of the nature of outlines are prefixed to most of the chapters. The student is also directed to confine his attention in the first instance to five specified chap- ters, viz. 2, 3, 4, 12,13. We will mention briefly the contents of these chapters, both for the purpose of giving some notion of the treatment which the subject receives at Professor Cayley’s hands, and as showing what he regards as a sort of first course of the subject. | The reduction of (“ to one of the three kinds of Elliptic In- tegrals is treated in chapter 12. That this can always be done the author shows both by Legendre’s method of supposing X to be decomposed into two quadratic factors, and by a method of his own based on a linear transformation of the undecomposed quartic func- tion (X). In chapter 2 he establishes the well-known fundamental relation, viz. if F() denotes an elliptic integral of the first kind with amplitude g, and if wy and p are the amplitudes of two other elliptic functions of the first kind such that Fg)+FQ)=F(z), then cos p= cos ¢ cos W— sin ¢ sin Py / (1—K’ sin? p). Of this equation (the addition equation) seven distinct proofs are given. It is plain that this equation enables us to determine the amplitude of the function which is the sum (or difference) of any two functions of given amplitude, and hence the amplitude of the function which is twice a function of given amplitude, and then of one which is n times a given function, Indeed it would be possible to lay down a method of calculating the numerical value of a function Notices respecting New Books. 295 of given modulus for an assigned amplitude by deductions from this equation. When F(,) or w is regarded as a function of its ampli- tude, it is found very convenient to call sin ¢ the sine of the ampli- tude of uw, and to contract these words into the notation snw; and similarly cosg and /(1—k’ sin’) are denoted by enw and dnw: e. g. the addition equation given above would be written en(w+v)=cnucnu—snwusnvdn(u+v). There is no difficulty in deducing an enormous number of relations between these functions, such as sn(w+v)(1—k’* sn? ucn?v)=snuenvdnv+snvecnudnu. lt will be seen that this formula closely resembles the formula for the sine of the sum of two angles, which indeed it becomes if k=0. The fourth chapter contains the development of the relations be- tween the functions of the amplitudes and those of the sums, differ- ences, and multiples of the functions. The third chapter contains :—the solution of a number of elemen- tary questions, particularly those relating to the curves whose ares represent the integrals; the discussion of ‘“ the march” of the func- tions, or their graphic representation ; some of the properties of the complete functions (viz. the integrals when ¢=37), suchas the theorem enunciated by the equation ie EF +H Y—FER=f7; methods of obtaining series for the complete functions when & is either small or nearly equal to unity; and the properties of the “‘Gudermannian,” 7. ¢. the amplitude of the function F(~) when k is unity. It has been already mentioned that a method of calculating F(d) numerically might be based on the addition equation. Practically speaking, however, the calculation is more conveniently effected by transforming the integral with a given amplitude and modulus into another with a different amplitude and modulus, and repeating the process of transformation until an integral is found of assigned am- plitude with a modulus not differing sensibly from zero. Chapter 5 is devoted to showing how this can be done, by means of Landen’s theorem, for functions of the first and second kind. The chapter contains the original proof of Landen’s theorem in an altered notation. A proof of the same theorem is also given in chapter 2, as a deduction from one of Jacobi’s proofs of the addition equation, viz. that depending on two circles. It may just be no- ticed that this first course gives a view of the subject about equiva- lent to that attained by Legendre shortly after he had begun his labours, though many points are here worked out systematically and in a new notation (particularly all that relates to the functions snwu é&ec.); and some points are new, such as the proof of the double ‘periodicity of these functions, the properties of the Guderman- nian, &c. These chapters occupy about a third part of the volume, and will not offer any serious difficulty to the student, though he will have “to dwell upon them sufficiently to become accustomed to the nota- tion, much of which will be new to him. The difficulty increases Phit. Mag. 8.5. Vol. 3. No. 17. March 1877. Q 226 Notices respecting New Books. considerably when the properties of the third class of integrals are considered, and those of the © functions (in terms of which the elliptic functions can be expressed) as wellas the general theory of the transformation of the elliptic functions, of which Landen’s theorem is in fact a particular case. Professor Cayley has taken a great deal of pains to clear up the difficulties to be met with at the entrance of the subject. But when all has been done, the elliptic functions will probably appear to most students at first sight somewhat intangible entities. It is perhaps with a view to this circumstance that the following para- graph was written, which we venture to extract as an admirable specimen of elementary exposition :—“ In further illustration” of the elliptic functions sn wu, env, dn wu, ‘suppose that the theory of the circular functions sine, cosine was unknown, and that we had de- fined Fw to be the function dx 2/0 Vv (1 atte Then taking the variables w and y to be connected by the differen- tial equation dx dy Ja—a)* Vy) and supposing that z is the value of y answering to «=0, we have Fv+Fy=Fz. But the differential equation admits of algebraic integration: and determining in each case the constant by the condition that for «x=0, y shall be =z, the algebraic integral may be expressed in two forms, wr (L—y?)+yV7 (1-2?) =Z, ry — V—2)/ I—y)= V(1-2); so that either of these equations represents the above-mentioned transcendental integral; and thus we have a circular theory pre- cisely analogous to the elliptic theory in its original form. But here the function Fw is the inverse function sin—! a, and the last- mentioned two equations are the equivalents of the equation sin—! @-p'sin—=) y= sin—" Zz, whence writing sin-!v=u, sm—! y=v, and therefore x= sin w, y=sin v, z=sin (w+v); and also assuming »/ (1—sin?w)=cosu, and therefore /(1— sin? v)=cosv,and Vf (1 — sin®(w+v))= cos(u+v), the equations in question become sin(w+v)= sinwcosv+ sinv cos u, cos (w+v)= cos u cos v— sin wu sin v, and it is clearly convenient to use these functions sin, ecs in place of F, denoting as above sm—! ..... The circular theory aw ° SIT4V5O we ‘ gives rise to a numerical transcendent 7, viz. a7 5 Tv Tv us 0 Sm cos 5 =(() 3 being the smallest po- sitive value of the argument for which the two functions have these such a quantity that sin —— i values ; and in developing the theory from the integral le a a Notices respecting New Books. 227 * would be the complete function defined from the equation wil 1 da a7) Va=a) Moreover the circular functions are periodic, having for their com- mon period four times this quantity, =27; viz. we have (w+ 27) = rote Us bo! sin cos us 2 instance the complete function K; viz. K is areal positive quantity defined by the equation T 2 dg K=) >=’ { V/(1—k? sin? @) where K is of course not a mere numerical transcendent, but a function of k: Kis such that we have sn K=1, cn K=O, dn K=k’ eco (lk)... ... , and it ultimately appears that the sn, cn, and dn of w+4K are the same as the sn, cn, and dn of w respec- tively ; or the functions have a real period 4K.” (pp. 10, 11, 12). Our limits do not allow of our extracting the whole article ; but we may just add that, as well as the analogies between the circular and elliptic functions, attention is drawn to the transformation theory, and the second period 4( + 7 —1.K’')in the elliptic func- tions, which have no analogues in the circular theory. Corresponding to 5 we have in the elliptic functions in the first An Elementary Treatise on the Differential Calculus, containing the Theory of Plane Curves, with numerous examples. By BENJAMIN Wriiamson, M.A., Fellow and Tutor, Trinity College, Dublin, Third Edition, revised and enlarged. London: Longmans, Green, and Co. 1877. (Crown 8vo. Pp. 416.) We have already noticed the first and second editions of this ex- cellent work, and have now to notice the third. As might be expected, the work in its present form is not substantially different from what it was when it first appeared. In fact, a considerable part of the second and third editions agree page for page; so that the amount of difference may be pretty accurately inferred from the fact that the former edition contains 367, the latter 416 pages. The alterations are made in two ways :—/irst, by small additions and occasional omissions here and there; secondly, by the insertion of a few articles of considerable length, Of the first kind we may notice such changes as these :—the insertion of the proof of a con- dition that Pdw+Qdy may be an exact differential (p. 143); the recasting and extension of the article on the curve 7r™=a™ cos m0 (p. 227); the additional examples of algebraical maxima and minima (p. 163); the additions to and omissions from the examples on Partial Differential Coefficients (pp. 1387-40), and so on. Of the second kind may be mentioned :—two long extracts from M. Navier’s Lecons d Analyse on the principles of the Differential Calculus (pp. 7-10), and on the Failure of Taylor’s Theorem Q 2 : 228 Royal Society:—Prof. J. Thomson on the Origin (pp. 405, 406); a large addition to the articles on Infinitesimals (pp. 40- 43) ; and a new article on the direction of the normal in Vectorial Coordinates (pp. 230-233). The additions of most import- ance, however, are two—an appendix containing a brief geome- trical discussion of the chief properties of the Cartesian Oval (pp. 411-416), and the account of Rolling Curves or Roulettes. In the second edition the subject fills about ten pages at the end of the chapter on tracing Curves; in the present edition these ten pages are expanded into a separate chapter (XIX.) of twenty nine pages, which gives a fairly complete view of the questions suggested by cycloids and analogous curves, such as might be looked for in a work which protessedly treats of the Theory of Plane Curves, together with sume kinematical applications. On the whole it is plain that these additions are not suchas to change very materially the general character of the work; they serve, however, to render it somewhat more complete, and to make it still more worthy of the attention of every student of geometry. AXA. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 153. | May 4, 1876.—Capt. F. J. O. Evans, R.N., C.B., Vice-President, in the Chair. HE following communication was read :— “*Qn the Origin of Windings of Rivers in Alluvial Plains, with Remarks on the Flow of Water round Bends in Pipes.” By Pro- fessor James Thomson, LL.D., F.R.S.E. In respect to the origin of the windings of rivers flowing through alluvial plains, people have usually taken the rough notion that when there is a bend in any way commenced, the water just rushes out against the outer bank of the river at the bend, and so washes that bank away, and allows deposition to occur on the inner bank, and thus makes the sinuositv increase. But in this they overlook the hydraulic principle, nov yenerally KuOwn, that a suream n Howi ing along a straight channel and thence into a curve must flow with a diminished velocity along the outer bank, and an increased velocity along the inner bank, if we regard the flow as that of a perfect fluid. In view of this principle, the question arose to me some years ago:—Why does not the inner bank wear away more than of Windings of Rivers in Alluvial Plains. 229 the outer one? We know by general experience and observation that in fact the outer one does wear away, and that deposits are often made along the inner one. How does this arise ? The expianation occurred to me m the year 15/2, mainly as follows :—For any lines of particles taken across the stream at different places, as A,B, A,B,, &c. in fig. 2, and which may be designated in general as AB, if the line be level, the water-pressure must be increasing from A to B, on account of the centrifugal force of the particles compesing that line or bar of water; or, what comes to the same thing, the water-surface of the river will have a transverse inclination rising from A to B. The water in any stream-line C D E* at or near the surface, or in any case not close to the bottom, and flowing nearly along the inner bank, will not accelerate itself in entering on the bend, except in con- sequence of its having a fall of free level in passing along that stream- lineT. But the layer of water along the bottom, being by friction much retarded, bas much less centrifugal force in any bar of its particles extending across the river; and consequently it will flow sidewise along the bottom towards the inner bank, and will, part of it at least, rise up between the stream-line and the inner bank, and will protect the bank from the rapid scour of that stream- -line and of other adjacent parts of the rapidly flowing current; and as the sand and mud in motion at the bottom are carried in that bottom layer, they will be in some degree brought in to that inner bank, and may have atendency to be deposited there. * This, although here conveniently spoken of as a stream-line, is not to be supposed as haying really a steady flow. It may be conceived of as an average stream-line in a place where the flow is disturbed with eddies or by the sur- rounding water commingling with it. + It must be here explained that by the free /evel for any particle is to be under- stood the level of the atmospheric end of a column, or of any bar, straight or curved, of particles of statical water, having one end situated at the level of the particle, and haying at that end the same pressure as the particle has, and hay- ing the other end consisting of a level surface of water freely exposed to the atmosphere, or elso having otherwise atmospheric pressure there ; or, briefly, we may say that the free level for any particle of water is the level of the atmo- spheric end of its pressure column, or of an equivalent ideal pressure-column, EEE eeeeeoereooeoreeeee —- 230 Royal Society :-— On the other hand, along the outer bank there will be a general tendency to descent of surface-water which will have a high velo- city, not having been much impeded by friction ; and this will wear away the bank and carry the worn substance ina great degree down to the bottom, where, as explained before, there will be a general prevailing tendency towards the inner bank. Now, further, it seems that even from the very beginning of the curve forward there will thus be a considerable protection-to the inner bank. Because a surface stream-line C D, or one not close to the bottom, flowing along the bank which in the bend becomes the inner bank, will tend to depart from the inner bank at D, the com- mencement of the bend, and to go forward along D E, or by some such course, leaving the space G between it and the bank to be supplied by slower-moving water which has been moving along the bottom of the river perhaps by some such oblique path as the dotted line F G. It is further to be observed that ordinarily or very frequently there will be detritus travelling down stream along the bottem and seeking for resting-places, because the cases here specially under consideration are only such as occur in alluvial plains; and in regions of that kind there is ordinarily *, on the average, more de- position than erosion. This consideration explains that we need not have to seek for the material for deposition on the inner bank in the material worn away from the outer bank of the seme bend of the river. The material worn from the outer bank may have to travel a long distance down stream before finding an imner bank of a bend on which to deposit itself. And now it seems very clear that in the gravel, sand, and mud carried down stream along the bottom of the river to the place where the bend commences, there is an ample supply of detritus for deposition on the inner bank of the river even at the earliest points in the curve which will offer any resting-place. It is especially worthy of notice that the oblique flow along the bottom towards the inner bank begins even up stream from the bend, as already explained, and as shown by the dotted line FG in fig. 3. The transverse movement comprised in this * That is to say, except when by geological changes the causes which have been producing the alluvial plain have become extinct, and erosion by the river has come to predominate over deposition. Mr. W. Crookes on Repulsion resulting from Radiation. 231 oblique flow is instigated by the abatement of pressure, or lower- ing of free level, in the water along the inner bank produced by centrifugal force in the way already explained. It may now be remarked that the considerations which have in the present paper been adduced in respect to the mode of flow of water round a bend of a river, by bringing under notice, conjointly, the lowering of free level of the water at and near the inner bank, and the raising of free level of the water at and near the outer bank relatively to the free level of the water at middle of the stream, and the effect of retardation of velocity in the layer flowing along the bed of the channel in diminishing the centrifugal force in the layer retarded, and so causing that retarded water, and also fric- tionally retarded water, even in a straight channel of approach to the bend, to flow obliquely towards the inner bank, tend very mate- rially to elucidate the subject of the mode of fiow of water round bends in pipes, and the manner in which bends cause augmentation of frictional resistance in pipes, a subject in regard to which I believe no good exposition has hitherto been published in any printed books or papers; but about which various views, mostly crude and mis- leading, have been published from time to time, and are now often repeated, but which, almost entirely, ought to be at once rejected. June 15.—Dr. J. Dalton Hooker, C.B., President, in the Chair. The following communication was read :— “On Repulsion resulting from Radiation. Influence of the Resi- dual Gas.”—(Preliminary Notice.) By William Crookes, F.R.S. &c. I have recently been engaged in experiments which are likely te throw much light on some obscure poimts in the theory of the repulsion resulting from radiation. In these I have been mate- rlally assisted by Professor Stokes, both in original suggestions and in the mathematical formule necessary for the reduction of the results. Being prevented by other work from completing the experiments sufficiently to bring them before the Royal Society prior to the close of the session, I have thought that it might be of interest were I to publish a short abstract of the princ pal results I have obtained, reserving the details until they are ready to be brought forward in a more complete form. In the early days of this research, when it was found that no movement took place until the vacuum was so good as to be almost beyond the powers of an ordinary air-pump to produce, and that as the vacuum got more and more nearly absolute, so the force increased in power, it was justifiable to assume that the action would still take place when the minute trace of residual gas which theoretical reasoning proved to be present was removed. The first and most obvious explanation therefore was that the repulsive force was directly due to radiation. Further con- sideration, however, showed that the very best vacuum which I had succeeded in producing might contain enough matter to offer considerable resistance to motion. JI have already pointed out that in some experiments, where the rarefaction was pushed to a very high point, the torsion-beam appeared to be swinging in a 252 Royal Society :— viscous fluid (194); and this at once led me to think that the re- pulsion caused by radiation was indirectly due to a difference of thermometric heat between the black and white surfaces of the moving body (195), and that it might be due to a secondary action on the residual gas. On April 5, 1876, f exhibited at the Soirée of the Royal Society an instrument which proved the presence of residual gas in a radiometer which had been exhausted to a very high point of sen-. sitiveness. A small! piece of pith was suspended to one end of a cocoon fibre, the other end being attached to a fragment of steel. An external magnet held the steel to the inner side of the glass globe, the pith then hanging down like a pendulum, about a mil- limetre from the rotating vanes of the radiometer. By placing a candle at different distances off, any desired velocity, up to several hundreds per minute, could be imparted to the fly of the radiometer. Scarcely any movement of the pendulum was produced when the rotation was very rapid; but on removing the candle, and letting the rotation die out, at one particular velocity the pendulum set up a considerable movement. Professor Stokes suggested (and, in fact, tried the experiment at the time) that the distance of the candle should be so adjusted that the permanent rate of rotation. should be the critical one for synchronism corresponding to the rate at which one arm of the fly passed for each complete oscil- lation. In this way the pendulum was kept for some time swinging with regularity through a large are. This instrument proved that, at a rarefaction so high that the. residual gas was a non- -conductor of an induction-curr ent, there was enough matter present to produce motion, and therefore to offer resistance to motion. That this residual gas was something more. than an accidental accompaniment of the phenomena was rendered - probable by the observations of Dr. Schuster, as well as by my own. experiments on the movement of the floating glass case of a radio- meter when the arms are fixed by a magnet*. | My first endeavour was to get some experimental means of dis- criminating between the viscosity of the minute quantity of re- sidual gas and the other retarding forces, such as the friction of. the needle-point on the glass cup when working with a radiometer, or the torsion of the glass fibre when a torsion-apparatus was used. A glass bulb is blown on the end of a glass tube, to the upper. part of which a glass stopper is accurately fitted by grinding. To. the lower part of the stopper a fine glass fibre is cemented, and to the end of this is attached a thin oblong plate of pith, which hangs suspended in the centre of the globe; a mirror is attached to the pith bar, which enables its movement to be observed on a graduated scale. The stopper is well lubricated with the burnt india-rubber which I have already found so useful in similar. cases (207). The instrument is held upright by clamps, and is. connected to the pump by a long spiral tube. The stopper is fixed. rigidly in respect to space, and an arrangement is made by which. the bulb can be rotated through a small angle. The pith plate, * Proc. Roy. Soc. vol. xxiv. p. 409. Mr. W. Crookes on Repulsion resulting from Radiation. 233 with mirror, being suspended from the stopper, the rotation of the bulb can only cause a motion of the pith through the inter- vention of the enclosed air. Were there no viscosity of the air, the pith would not move; but if there be viscosity, the pith will turn in the same direction as the bulb, though not to the same extent, and, after stopping the vessel, will oscillate backwards and for- wards in decreasing arcs, presently setting in its old position rela- tively to space. It was suggested by Prof. Stokes that it would be desirable to register not merely the amplitude of the first swing, but the readings of the first five swings or so. This would afford a good. value of the logarithmic decrement (the decrement per swing of the logarithm of the amplitude of the ares), which is the constant most desirable to know. The logarithmic decrement will involve the viscosity of the glass fibre; but glass is so nearly perfectly elastic, and the fibre so very thin, that this will be practically in- sensible. According to Professor Clerk Maxwell, the viscosity of a gas should be independent of its density; and the experiments with this apparatus have shown that this is practically correct, as the logarithmic decrement of the arc of the oscillation (a constant” which may be taken as defining the viscosity of the gas) only slightly diminishes up to as high an exhaustion as I can con-- veniently attain—higher, indeed, than is necessary to produce re- pulsion by radiation. I next endeavoured to measure, simultaneously with the loga- rithmic decrement of the arc of oscillation, the repulsive force: produced by a candle at high degrees of exhaustion. The motion produced by the rotation ef the bulb alone has the advantage of exhibiting palpably to the eye that there is a viscosity between the’ suspended body and the vessel; but once having ascertained that, and admitting that the logarithmic decrement of the are of os- cillation (when no candle is shining on the plate) is a measure. of the viscosity, there is no further necessity to complicate the apparatus by having the ground and lubricated stopper. A move-: ment of the whole vessel bodily through a small are is equally effective for getting this logarithmic decrement; and the absence of the stopper enables me to have the whole apparatus sealed up in glass, and I can therefore experiment at higher rarefactions than would be possible when a lubricated stopper is present. The apparatus, which is too complicated to describe without a drawing, has attached to it:—a,aSprengel pump; 6, an arrange- ment for producing a chemical vacuum; c, a lamp with scale, on which to observe the luminous index reflected from the mirror ; d, a standard candle at a fixed distance; and e, a small vacuum- tube, with the internal ends of the platinum wires close together.. I can therefore take observations of :-— 1. The logarithmic decrement of the are of oscillation when under no infiuence of radiation ; 2. The successive swings and final deflection when a candle shines on one end of the blackened bar ; | 234 Royal Society. 3. The appearance of the induction-spark between the platinum wires, 1 measures the viscosity ; 2 enables me to calculate the force of radiation of the candle; and 3 enables me to form an idea of the progress of the vacuum according as the interior of the tube becomes uniformly luminous, striated, luminous at the poles only, or black and non-conducting. The apparatus is also arranged so that I can try similar experi- ments with any vapour or gas. The following are some of the most important results which this apparatus has as yet yielded. Up to an exhaustion at which the gauge and barometer are sensibly level, there is not much variation in the viscosity of the internal gas (dry atmospheric air). Upon now continuing to exhaust, the force of radiation commences to be apparent, the viscosity remaining about the same. The viscosity next commences to diminish, the force of radiation increasing. After long-con- tinued exhaustion the force of radiation approaches a maximum ; but the viscosity measured by the logarithmic decrement begins to fall off, the decrease being rather sudden after it has once com- menced. Lastly, some time after the logarithmic decrement has com- menced to fall off, and when it is about one fourth of what it was at the commencement, the force of radiation diminishes. At the highest exhaustion I have yet been able to work at, the loga- rithmic decrement is about one twentieth of its original amount, and the force of repulsion has sunk to a little less than one half of the maximum. The attenuation has now become so excessive that we are no longer at liberty to treat the number of gaseous molecules present in the apparatus as practically infinite; and, according to Professor Clerk Maxwell's theory, the mean length of path of the molecules between their collisions is no longer very small compared with the dimensions of the apparatus. The degree of exhaustion at which an induction-current will not pass is far below the extreme exhaustions at which the loga- rithmic decrement falls rapidly. The force of radiation does not act suddenly, but takes an ap- preciable time to attain its maximum—thus proving, as Prof. Stokes has pointed out, that the force is not due to radiation di- rectly but indirectly. In a radiometer exhausted to a very high degree of sensitive- ness, the viscosity of the residual gas is almost as great as if it were at the atmospheric pressure. With other gases than air the phenomena are diiferent in degree, althongh similar in kind—aqueous vapour, for instance, retarding the force of repulsion to a great extent, and carbonic acid acting in a similar though less degree. The evidence afforded by the experiments of which this is a brief abstract is to my mind so strong as almost to amount to con- viction that the repulsion resulting from radiation is due to an action of thermometric heat between the surface of the moving Geological Society. 235 body and the case of the instrument, through the intervention of the residual gas. This explanation of its action is in accordance with recent speculations as to the ultimate constitution of matter and the dynamical_theory of gases. GEOLOGICAL SOCIETY. {Continued from p. 156. ] January 24th, 1877.—Prof. P. Martin Duncan, M.B., F.RS., President, in the Chair. The following papers were read :— 1. ‘* Note on the Question of the Glacial or Volcanic Origin of the Talchir Boulder-bed of India and the Karoo Boulder-bed of South Africa.” By H. F. Blanford, Esq., F.G.S. The author, referring to a doubt expressed by the President in a paper on Australian Tertiary Corals as to the glacial origin of the Talchir Boulder-bed, indicated that the hypothesis of its formation by the action of local glaciers under present climatal conditions would require the elevation of the whole region to the extent of 14,000 or 15,000 feet, and the assumption that the denudation of this great mountain mass was so moderate that large tracts of the ancient surface are still preserved at levels now only a few hun- dred feet above the sea. This the author regarded as very im- probable. He assumed that the President, rejecting the evidence adduced by various writers in favour of the glacial origin of the Talchir and Karoo Boulder-beds, was inclined to fall back upon the notion of their being of volcanic origin, and quoted a letter from Mr. King, who had described the Talchir rocks of Kamdram as trap- pean, in which that gentleman stated that the rocks so interpreted by him prove to be dark green and brownish mudstone. He cited further evidence of like nature, and concluded that the ascription of a volcanic origin to these boulder-beds was probably in all cases due to similar misinterpretations. 2. “On British Cretaceous Patelloid Gasteropoda.” By John Starkie Gardner, Esq., F.G.S. 3. “ Observations onremains of the Mammoth and other Mammals from Northern Spain.” By A. Leith Adams, Esq., M.B.,F.R.S., F.GS. February 7th, 1877.—Prof. P. Martin Duncan, M.B., F.R.S., President, in the Chair. The following paper was read :— 1. “On the Chemical and Mineralogical Changes which have taken place in certain Eruptive Rocks of North Wales.” By John Arthur Phillips, Esq., F.G.S. In this paper the author described the felspathic rock of Pen- maenmawr, which has been erupted through Silurian strata, and rises to a height of 1553 feet above the level of the sea. The rock, which is composed of crystalline felspar with minute crystals of some hornblendic mineral, is fine-grained and greenish grey, divided into beds by joints dipping north at an angle of about 45°, and again divided by double jointings, sometimes so developed as to 236 Intelligence and Miscellaneous Articles. render the rock distinctly columnar. At the eastern end of the mountain the stone is so close in texture as often almost to resemble chert. In the next two quarries westward the rock is coarser, and its jointing less regular. In the most westerly quarry the stone is generally fresher in appearance, closer in grain, and greener in colour. All these stones are probably modifications of the same original rock. From the chemical analysis of the rocks the author concludes that, supposing them all to have had originally the same composition as the unaltered rock in the most westerly quarry, that at the extreme east of the mountain has lost about 3 per cent. of silica, and the others have. received respectively an increase of 1°35 and 0:77 per cent. of silica. ‘The altered rocks contain an abun- dance of quartz granules, due probably to the crystallization of pro- gressively dissociated silica, as the specimens of rock in which these granules occur do not contain a larger proportion of silica than those in which its presence can hardly be detected under the microscope. ‘The proportion of alkalies in the different specimens does not materially vary. Overlying the second quarry at the east end of the mountain is an ash bed of reddish brown colour, containing more than 10 per cent. of protoxide of manganese and nearly 20 per cent. of peroxide of iron, and showing a great diminution in the percentage of silica when compared with the associated crystalline rock. The author further described the characters of the uralite-por- phyry of the Mawddach valley near Dolgelly, which is of a greyish- green colour, spotted with black, and consists of a granular base enclosing patches and crystals of uralite, the outlines of which are sometimes sharp and well defined, but generally rounded and merging into the general base. eo XXXII. Intelligence and Miscellaneous Articles. ON THE DETERMINATION OF THE POLAR DISTANCE IN MAGNETS. BY R. BENOIT. (Be IIe Cie had the notion of making use of the equation of equili- brium of a magnetized bar placed in given conditions (into which equation its polar distance enters), in order to determine the pre- cise place occupied by each of the poles*. The following method is both more direct and more general than that which he employed. Let AB, A'B’ be two magnetized bars placed horizontally one above the other so that their centres O, O' are in the same vertical line. ‘The first is fixed; the second can turn freely about the axis OO'. As long as the distance separating them is sufficient, the resultants of the reciprocal actions of their magnetic elements pass very evidently through the poles A, B, A’, B’. Now these actions give rise (1) to symmetrical vertical forces destroyed by the weight and the resistance of the suspending wire, and (2) to a horizontal couple which tends to cause the movable magnet to rotate, and of which the expression is easily found. Let m, m’ denote the quantities of free magnetism which we may — * Comptes Rendus de [Académie des Sctences, Feb. 5, 18€5. Intelligence and Miscellaneous Articles. 237 suppose condensed at the respective poles of the two magnets, 27 the polar distance of the fixed magnet, 2/' the polar distance of the movable magnet, d the distance (O, O’) of the centres of the two magnets, and ¢ the angle made by A'B’ with the vertical plane con- taining AB; the moment of the horizontal couple is represented by the formula M=2mm'll' sin f(a? +? +1?+ 211 cos d)-3+ (7 +040? — 211’ cos 6) - =]. The movable bar, submitted simultaneously to the influence of the earth and to that of the fixed bar, generally takes a new position of equilibrium, and makes an angle g with the magnetic meridian. ‘Phe moment of the earth-couple, 2m'l’H sin g, is then equal and contrary to M. This being admitted, let us suppose AB rotated about the axis OO’ until its direction is perpendicular to that of A’B’; 6 will then be equal to BE and consequently we shall have, for any position of equilibrium, Hsin ¢=2mU(24+24 1'2)—8, whence 8 sin o(P+P+41?)-2= 2S The conditions of this experiment are easily realized by an arrangement similar to that of the sine-compass: we need only to replace the movable multiplier of the latter instrument by a support ‘to hold the fixed magnet, and upon which it can be fixed at differ- ent heights. If the magnet AB be transferred to another distance d’, » be- comes ¢’, and we have i . : em sing (d?+P?+41?)2= Ee These two formule give ee See a eee Oe SRG A a , sin’ 9’ — sin? p To obtain a second equation between /? and J”, the interposition of a third bar having 20” for its polar distance will be sufficient. Operating upon bars 1 and 2 we shall have ; CLi@—A; in like manner bars 1 and 3 will give P+U2=B; and lastly, bars 2 and 3, 724 7206, ° From these three equations J, l’, 1’ will be obtained. _ The following experiments, carried out merely for the purpose _of verification, and with apparatus which permitted only moderate precision in the measurements, nevertheless conducted to very con- cordant results when the means of the observations were taken. They were made upon four needles of tempered steel, magnetized to saturation, 1:3 millim. in diameter, and the lengths of which were 18, 16, 14, and 12 centims. 238 Intelligence and Miscellaneous Articles. For want of space I cannot give here the details of the observa- tions, but only the result of the calculations—that is to say, the values of 1, l', U' for the three needles, combining the series of ob- servations successively in threes :— Series AL By Dey oA eG. 2B. Ch Rl Dias millim. millim. millim. wmillim. Bat. cele ipa ce (fori 78:3 fish sgt LIES eases hes 70:0 69°38 oar 69°8 wes ONAL Se ai wets 61:6 wens Gilie7 61:9 Moulage ola) 496 49:9 49:6 I may remark that, once the polar distances are determined, the : ; .- 2ml same experiments will furnish the value of the ratio yp? Recessary in order to measure the intensity of terrestrial magnetism by Gauss’s method.—Comptes Rendus de 0 Académie des Sciences, Jan. 8, 1877, tome Ixxxix, pp. 76-78. PHOTOGRAPHS OF THE SPECTRA OF VENUS AND @ LYRAL. NOTE BY PROF. HENRY DRAPER, M.D. Since the spring of 1872 I have been making photographs of the spectra of the stars, planets, and Moon, and particularly, among the stars, of a Lyre and a Aquile, with my 28-inch reflector and 12-inch refractor. In the photograph of a Lyre, bands or broad lines are visible in the violet and ultra-violet region unlike any thing in the solar spectrum. The research is difficult and consumes time, because long exposures are necessary to impress the sensitive plate, and the atmosphere is rarely in the best condition. The image of a star or planet must be kept motionless for from ten to twenty minutes; and hence the driving-clock of the telescope is severely taxed. During last summer I obtained good results, and in October took photographs of the spectrum of Venus which show a large number of lines. JI am now studying these pictures, and have sub- mitted them to the inspection of several of my scientific friends, among others Professors Barker, Langley, Morton, and Silliman. There seems to be in the case of Venus a weakening of the spec- trum toward H and above that line, of the same character as that I have photographically observed to take place in the spectrum of the Sun near sunset.—Silliman’s American Journal, February 1877. ON THE SPECTRA OF METALS AT THE BASE OF FLAMES. BY M. GOUY. It is known that a flame produced by a mixture of coal-gas mil air, in proportions suitable for burning without the help of the ex- ternal air, has for its base an inner cone, at the surface of which the combustion commences. This surface is brilliant, of a blue or green colour, and gives the spectrum of carbon. The experiments which I am about to relate show that this same surface gives a very different spectrum from that of the flame of which it forms the base when the combustible mixture holds in suspension saline powders. Intelligence and Miscellaneous Articles. 239 The saline solutions are pulverized by a jet of compressed air ; the air, charged with powder, enters a regulator, into which the gas also comes, and whence a mixture issues of constant composi- tion. This mixture passes into a vertical tube of 19 millims, diameter, capped with iron-wire gauze, above which it burns with a conical flame 6-8 centims. in height. The height of the inner cone varies from 3 or 4 centims. to zero; and the flame can be rendered oxidizing or reducing. By means of a lens the image of the flame is thrown upon the slit of the spectroscope. ‘Two spectra are then seen, the one above the other. The lower spectrum is produced by the light of the blue surface; and all the lines of which it is composed remain at exactly the same height. The other is produced by the flame proper ; and the lines belonging to it encroach upon the lower spectrum, by reason of the shape of the flame. When the apparatus is employed void of powder, the lower spectrum shows brightly the carbon-lines. If we pulverize a solu- tion of chloride of lithium, the following is observed :—The upper spectrum shows a very bright red line anda feeble line in the orange. The first of these appears of equal brightness throughout ; the other becomes much brighter just at the point where it pene- trates into the lower spectrum. Moreover the lower spectrum shows distinctly a blue line (y of the electrical spectrum), which terminates at the same height as the carbon-lines and is absent from the upper spectrum. _ These characters will be again found with other metals :— Sulphate of Thallium.—rThis gives its characteristic green line, which is clearly strengthened on penetrating into the lower spectrum. Chloride of Calerwn.—The upper spectrum is deprived of the line proper to the undecomposed chloride. The blue line is a little strengthened on entering the second spectrum. Chloride of Strontium.—The upper spectrum offers nothing pe- culiar ; the lower shows three faint blue lines, which belong to the electric spectrum of strontium. Chloride of Bariwm.—The lines and bands of the upper spectrum are reinforced on penetrating into the other, especially the bright green line. Chloride of Mag gnesium. —The upper spectrum shows traces of the lines a and y of the electric spectrum ; the latteris more visible when the flame is oxidizing. The spectrum gives the line @ very bright, and close by the green line of carbon. This line is triple in the electric spectrum ; I have only been able to distinguish two of the components, the third being doubtless confused with the carbon line. Of these two components the brightest is as bright as the latter ; and as it is very near it, one can verify that they have the same height. ‘The line y is not reinforced in the lower spectrum. Chloride of Iron.—The flame is pretty luminous, greenish yellow. The upper spectrum consists of bands and numerous fine lines upon a continuous ground; the lower one shows three groups of suffi- ciently visible lines, corresponding to the groups 6 and ¢ of the electric spectrum between the green and the blue, and y in the violet. 240 Intelligence and Miscellaneous Articles. Chloride of Cobalt.—The flame very much resembles the pre- ceding. The upper spectrum is continuous, and fairly bright; the lower shows three faint lines in the violet and the extreme violet (y, 6, and n of the electric spectrum). Chloride of Zinc-—Nothing more than a feeble continuous lumi- nosity in the upper spectrum ; the lower shows pretty clearly the violet line @ of the electric spectrum. Chloride of Cadmium.—Nothing in the upper spectrum ; the other presents a feeble violet line, 6 of the electric spectrum. Nitrate of Manganese.—There is nothing particular in the upper spectrum ; the lower shows a group of three feeble violet lines, of the electric spectrum. Nitrate of Copper.—The upper spectrum shows several bands ; one of them, in the red, is notably reinforced in the lower spectrum. Nitrate of Lead.—Nothing in the upper spectrum; the other presents a very distinct line in the extreme violet, a of the electric spectrum. Nitrate of Silver—Nothing in the upper spectrum ; the other shows two well-marked lines, « and 6 of the electric spectrum. Chloride of Platinum.—tThe flame is of a bluish whiteness ; its illumination is equal to that of a wax taper. The upper spectrum shows a continuous bright luminosity, with some feeble bands and lines. The lower does not resemble the electric spectrum ; it is formed of a fine series of sufficiently brilliant bands, less bright on the side towards the red, their other edge being clean ; a few fainter lines are also seen. Of the other metals, some have not been submitted to experi- ‘ment, and others have not given any clear results. The spectra above described were observed with flames in sone -degree reducing. On charging the flame with gas the interior cone lengthens, and its spectrum becomes less bright without changing its nature. With a large excess of air the cone changes its form, dividing into violet points, sometimes very tall. At this moment the lines of carbon have disappeared, save that in the violet; they are replaced by a continuous ground, on which the metallic lines, enfeebled, detach themselves. The fiame properly so called is almost invisible, and shows scarcely a trace of the sodium-line ; but it becomes visible and coloured green when it contains copper. In brief, we have seen that the base of the flame gives, over a very small elevation, a spectrum which approaches the electric spectrum of the same metal; I purpose to extend these researches to other flames. T will remark in conclusion, that in the usual spectral analyses a mixture of both spectra (of the cone and the flame) is seen; therefore the relative intensity of the lines must change according to the part of the flame which is viewed, as Lecog de Boisbaudran has observed for the chloride of manganese *. This investigation was made in the laboratory of M. Desains, at the Sorbonne.—Comptes Rendus de Académie des Sciences, Jan. 29, 1877, tome lxxxiv. pp. 231-234. | * Spectres Lumineux, p. 122. From this work we have borrowed the letters assigned to the lines. : THE LONDON, EDINBURGH, ayn DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES. ] SIE 1B TOTO AMEE XXXII. On the Theory of an Imperfectly Homogeneous Elastic Solid. By Professor C. NIvEN, Queen’s College, Cork*. i ee present paper attempts to deal with the theory of a solid composed of elastic material, homogeneous on a large scale but not homogeneous when considered in detail. It may be likened, to use Sir W. Thomson’s comparison, to a wall built of rubble, which appears homogeneous enough when looked at from a sufficiently great distance. Inside such a substance the stress across a small plane area will not be a simple force, but may, under certain circumstances, consist of a force anda couple. In fact the investigation was suggested by the theories of the bending and twisting of wires and of the bending of thin plates, in which the stress is thus specified. On forming the equations which determine the small mo- tions of the solid, I found that it was possible to frame a mathematical illustration of the phenomenon of the circular polarization of light in quartz and other substances—and that if we admit that the substance transmits in every direction two wayes consisting of transversal vibrations, these waves must necessarily be elliptic and oppositely polarized, according to Professor Stokes’s definition. In certain directions the ellipses become circles. The results are thus far the same as those obtained by Clebsch in his geometrical development of Cauchy’s theory; but the method of solving the equations of motion is quite different, and the physical foundations of the two theories have nothing in common. It is unnecessary, there- * Communicated by the Author. Phil. Mag. 8.5. Vol. 8. No. 18. April 1877. R 242 Prof. C. Niven on the Theory of an fore, to dwell upon Cauchy’s or more recent theories, which, though more complete, possess some of its general features. One result of the present investigations, which is a little startling, is, that part of the energy of the substance resides at its surtace. It may be that a more complete investigation might show that this part of the energy must necessarily vanish ; but I have preferred to leave for the present untouched the question as to whether any or what physical interpretation might be given of these terms. The coefficients which produce circular polarization contain as a factor a quantity of the order of the molecular distance ; and, conversely, the phenomena of the rotation of the plane of polarization in quartz may be applied to form a rough estimate of this distance. The result is not very widely different from that which Sir W. Thomson and others have deduced from other considerations. 2. In dealing with the bending of a wire the mathematical element chosen is a length ds of the wire bounded by two cross sections ; and the stress which acts on the element across one of these sections consists of a force and a couple, and not, as in the case of the element-area in the interior of a homo- geneous elastic solid, of a force only. In the case of a lamina, the stress acting across any small element of a normal sec- tion consists also of a force and a couple. These couples, which, as already observed, do not present themselves in specifying the stress inside a homogeneous elastic solid, arise from the unequal contractions and expansions of the sub- stance at different points of the normal section of the plate, or cross section of the wire. Moreover the mathematical ma- chinery used is of a coarser type than that employed in dealing with a homogeneous solid—coarser in one dimension in the case of the plate, and in two dimensions for the wire. Now if the constitution of a solid itself be such that, though sensibly ho- mogeneous on a large scale, it is really heterogeneous when examined more closely, the forces across two neighbouring indefinitely small parallel areas may not be parallel and pro- portional to the areas. If, therefore, the mathematical element were chosen large enough to eliminate all trace of this coarse- ness of structure, the actions on the faces of the element might not result each in a definite force but in a force and a couple— what Dr. Ball calls a “wrench,” or even in stress of a more complex type. Sir W. Thomson has pointed out in ‘ Nature’ (vol. i. p. 551) that this discontinuity is what is established in Cauchy’s theory of the dispersion of light; and he has even used Cauchy’s results to obtain a numerical estimate of the intermolecular spaces of matter. Imperfectly Homogeneous Elastic Solid. 243 Mathematical theories of an apparently continuous substance are sometimes based upon finer molecular theories. The dis- tribution, however, of the molecules and of their properties ‘presents so many irregularities and discontinuities, that it is impossible to trace the changes which take place in each indi- vidual, and we are thus obliged to confine ourselves to taking the average of a large number of them; and it is this average with which we are concerned in explaining the sensible pro- perties of matter. In this way the dynamical theory of gases has been constructed; and the earlier theories of elasticity rested on a similar foundation. Green’s theory of elasticity, on the other hand, is based on the general consideration that, whatever be the nature of the forces acting in the interior of a solid, the energy required to produce the change of form of an element-volume depends only on the deformations which it experiences. These may be expressed in the following man- ner. If u,v, w be the displacements of a point (2, y, 2), u+Au, v+ Av, w+ Aw those of an adjacent point (v7+h, y+k, z+1), then du .-du | {du Au=h— hag tia, Ge. provided we neglect squares and products of h, k,l. These terms may be analyzed (after Helmholtz) as follows:—Putting du dv ; dw dv a AO aa dw dv du dw dy du ; 2a,= — aos ede 8 de de de ay’ we shall have Au — A ete tkK+ Hl—a3k+ aol, Av =FA+Bk+ Di—a,l +a;)h, ee) Aw=HA+ Dk+Cl—a,h+ a,k. The terms depending on a, a2, @3 represent a rotation of the parts of the medium near (2, y, z) round lines parallel to the axes ; and when the motions of the solid are exceedingly small compared with the length of a wave in it, the remaining terms express a pure strain of the substance in the neighbourhood _ of (a, y, z). The energy contained in the element is a function gras ee, Dt TF: This theory, which compares the mathematical element with a homogeneously strained solid, assumes that the element may be taken so small that the enclosed solid may be treated as homogeneously strained, and that the whole distortion of the R 2 244 Prof. C. Niven on the Theory of an solid may be represented by supposing the elements of this strain and rotation to vary continuously from point to point. If, however, the solid be not perfectly homogeneous in detail, though it may be so on a large scale, it will be necessary to take the element-volume great enough to eliminate the effect of the irregular variation of the different particles of the solid within the element itself. In order to understand how this may be represented, let us first suppose that A, B, C, D, H, F, @1, By, @3; vary regularly and continuously within the element; then, if these symbols refer to some definite point P(a, y, z)in its interior, say its centre of gravity, the value of a, at some other point P, (w+h, y+k, +1) will be denoted by da, Snap Pie dy a! dz do 1 da, But even if we admit that these quantities may vary gradually, though not necessarily regularly, we may suppose that the value of a, at P, differs from its value at P by linear func- tions of the differential coefficients of itself and of the remain- ing elements of the distortion, and that the coefficients are quantities of the order of the magnitude (m) which measures the extent through which the coarseness of structure is sensible —that is to say, the molecular distance. Thus the circum- stances of the strain of the element-volume will require for their complete specification the nine quantities above men- tioned, and also their twenty-seven differential coefficients with regard to x, y, 2. 3. Now the known cogrediency of a, a2, a3, with the dis- placements u, v, w, enables us to analyze their differential coefficients into the two groups:— da, da, da, dw, da; dw, . day. dz” dy ; da, da, da, daw, dw, day, (3) dy dy dz” dz dz lay The first group are cogredient with strains, and will be denoted by a, b, c, d, e, f; they represent three uniform twists of the element about three rectangular axes. The second group are cogredient with displacements, and will be denoted by 2a,, 2o'5, 2@’3. With respect to the differential coefficients of A, B,... F, I have not attempted to analyze them further; but this is of no consequence, as they will give rise to terms in our equations which will be subjected in the sequel toa special treatment. It may be useful to make here the remark that the theory just given is equivalent to supposing that, instead 2 da, da, da? * dy? * Imperfectly Homogeneous Elastic Solid. 245 of the expression originally given for Aw, we use the second approximation, ad d d IL sea d aNe Au=( ee poied =) Al ee ] ese i) ? ; ee oe dy at we ire ay dy ne dz) “ But, to pass on, the state of strain of the element depends now upon the following groups of magnitudes:— GAL Bs C.D is, Bi: au Bi, BW, B35 GUT. na, Onc d yey 75 CIV.) a), a2, a3; (v.) aA ak d¥ da’ dy?" dz We may now follow Green, and assume that the energy in the element-volume can depend only on these five groups. It must, however, be independent of group II.; for if any term contained a, the energy in the substance might be increased or diminished by giving it a rotation as a whole round the axis of z—a result contrary to experience. It must also be remembered that the constituents of the last three groups bring with them coefficients involving as a factor the intermolecular distance 1; and this will cause the coefficients of these terms to be very small compared with those which arise from the combination of group I. with itself. Designating, therefore, as of class (I., III.) those terms which arise from the combination of groups I. and III., we need only consider the classes (1.,I.), (1., 11I.), C., TV.), (.., V.) and neglect the classes (III., [IV.), (IIL, V.), (1V., V.), the terms of which would involve, in the case of transmission of a plane 2 wave of length X, the factor (=) . We shall thus obtain a first approximation to the theory of a hetero-homogeneous solid. Specification of the Internal Stress. 4, In the case of a perfectly homogeneous elastic solid, the stresses upon the faces of a rectangular element which inter- sect at a solid angle are resolvable, in the first place, into nine forces, Sry Sry; --- Sez, Wherein S,, is the force per unit area on the face perpendicular to the axis of wu acting in the direc- tion of the axis of v, and reckoned as tractions exerted by the surrounding substances. And in order that the angular acce- lerations of the element may be all finite, it is necessary that 246 Prof. C. Niven on the Theory of an — the tangential stresses be equal in pairs, so that SS. Se=Si. Seco ee But in the case of an imperfectly homogeneous solid this specification is no longer sufficient; the stress will involve other elements, depending on the form of the expression for the energy of the solid due to distortion. If, for example, the energy contains terms of classes (I., III. ys (1., LV.) 5 ire enough to introduce nine couples ae the ‘aoa Tipe aia ae where L,,, 1s the couple per unit area on the face of the ele- ment perpendicular to the axis of u, the axis of the couple having the direction of the axis of v; and we must also sup- pose that the tangential stresses are no longer connected by the relations (4). If we suppose the energy “to contain terms of the class (1., V.), we have also to introduce force of a different type. We shall return to this point; but in the mean time it may be proved that, in order that the angular accelerations of the element may not be infinite, we must F have three new rela- tions connecting the stress-forces and couples, as follows. The symbols L,,.... Ly, referring to the couples on indefinitely small areas placed at the centre of the element, we may sup- pose that two faces perpendicular to the axis of 2 are acted on by couples whose axes are in this direction, of amounts equal to | ee + — ey So) dydz, — (i Lae a) dy dz, the resultant of which is the couple Tine | 7 dx dy dz. In the same way the couples on the other faces will result in two couples, whose axes are in the direction of the axis of a, of amounts Liye dy Des da dy dz. da dy de, = We may similarly find the resultant couples in the directions of the axes of y and z. But the stress-forces acting on the faces give rise to the three couples (S,-—S.,)de dy dz, (Szr—Syz)dax dy dz, (Sry—Syz)dx dy dz. Hence the condition for finite angular acceleration requires that Imperfectly Homogeneous Elastic Solid. 247 dig) diy (ally | koe yx ay Segal 10) ie ay GET ALES if yy Ee dL, dx dy dz Aine dLy, dz, da dy rl dz + Sz2—S2z=0, tet (5) + Say—Sy2= 0. | The existence of these internal stress-couples was indicated by Professor Stokes in his review of MacCullagh’s theory of double refraction (Rep. Brit. Assoc. 1862). 5. The laws of resolution of these internal forces and couples may be readily investigated by considering the equilibrium of an elementary tetrahedron, three adjacent edges of which are dz, dy,dz. If X, Y, Z be the three forces, and L, M, N the three couples which act on the oblique face per unit area of the same, we shall have X= Bye + MB yo + 2Szey Vee Pes ens 7 7=. L=(lL,.+ mLye + rLze, M=lLy+.-., oe 1, m, n being the direction-cosines of the normal to the cues face. These expressions satisfy the condition that the work done by the external forces on the oblique face (dy) during any indefinitely small arbitrary twist (du, dv, dw, da,, da, da) shall be dd(X8u t+ Vdu+ Z8w+ Lde,+MSe,+Nbda,); . . (7) and, indeed, the values of X, Y,... N might have been found from this condition by the application of the principle of vir- tual velocities. 6. We shall now prove that, if the energy contain terms be- longing to either of the classes (I., III.) or (1., IV.), the cor- responding part of the stress will consist of a force and couple satisfying equations (5). Let us consider any portion of the solid, and let it receive infinitesimal arbitrary displacements _ throughout its interior and over its boundary, and let 6W be the work done by the forces arising from the action of the sur- rounding matter, and 6H the increase of energy stored up in the solid; the increase of ae energy 6« will be (\\Gee eB ut Teor aaa re au) dx dy dz, the density being taken as unity ie simplicity, and impressed forces neglected for the same reason. by the principle of the conservation of energy we have OWES OH Oe.) 3. eee (8) 248 Prof. C. Niven on the Theory of an and if 6H be now separated by integration into surface-terms and a term of the form Vy (Pu + Oia Renee dy dz, we may find at once both the components of the stress over the boundary and the equations of motion. If we consider the term in HE due to A di *, the result may be most conveniently exhibited thus :—Let is be any element of the surface, /mn the direction-cosines of the normal at that point, and let Vs iy denote integrations over the surface and throughout the enclosed solid respectively ; then / 3. ipods alge — ( Ambo, + = . lou +4 gp nov — 1nd) TR "ay ay a Cm » hae dA :) +\(- indy dy de ae The corresponding parts of the stresses are da, Q dA. Q 1 dA se 8. ——, Sy=—45— Me cs Bios ahs dy’ ae the others being zero. | These evidently satisfy equations (5); and the same thing may be proved true for each of the terms arising from multi- plying A, B,... I by differential coefficients of a, a, 5. Theory of an Isotropic Solid. 7. We shall now find the form of the energy when the sub- stance is isotropic. This is done by considering what inva- riants arise by combining the different groups w ith group I. (1) Group I. gives of “itself the two invar iants, A+B+C, D?+H?+F’—BC-—CA—AB. (2) Group III. gives the invariant a+6+c, which, how- ever, is identically zero. Class (1., ITI.) contains the invariant Aa+Bb+Cc+2Dd+2He+2kf (3) There is no invariant in class (1., [V.), and none in class (1.,V.); fora’,...are cogredient with vyz, and , a are cogredient with a”... Gwy. The. energy corresponding to the element-volume is there- fore equal to {A(A + B+C)?+e(D? + H? + F*— BC—CA— AB) +v(Aat Bb+...2H/)\dedy de. . (a) Imperfectly Homogeneous Hlastic Solid. 249 We might now find, by the method of last article, the values of the stress-components and the equations of motion of the solid. If this were done, it would be found that the substance transmits in every direction two circular waves oppositely po- larized, and would therefore give rise to rotatory polarization. We need not st: ry to discuss these calculations, as the results are included under the general theory of an eolotropic solid, to which I now proceed. Theory of an Holotropic Solid. 8. To the terms which occur in the ordinary theory of a homogeneous substance we have now to add the terms of classes ce Ti), Gd, LV.) (2, V.).. This part of the enersy apparently contains 6 x 27=162 coefhiicients. But it must be noted that there are nine relations connecting the members of group VY. with the differential coefficients of ,, a, #3, and that these differential coefticients are also connected by the relation da, da, das daw dy Tae as The number of independent constants is thus reduced to 102. I shall now endeavour to ascertain whether these terms afford any illustration of rotatory polarization in crystals, as they do in isotropic substances. It must be admitted that, in the pre- sent state of science, theories of double refraction based on the study of the vibrations of elastic bodies are rather of the nature of dynamical illustrations than real explanations. Still, even if they serve no more useful end, they may help us to picture to ourselves the geometrical laws of the phenomena. Green has given two theories of double refraction, one of which was based upon the hypothesis that the elastic substance was pri- mitively free from strain, and transmitted in every direction two plane waves whose vibrations were strictly in the front of the wave. In his second theory he introduces an initial state of stress, and by properly determining these stresses obtains the same geometrical construction for the wave-velocities as before, but with the direction of vibration now at right angles to that in the former theory. I shall make use of the first theory, and apply the same hypothesis of two strictly trans- versal waves to the new terms now introduced. It is clear, however, that the results will not be affected by adopting the second form of Green’s theory. The following method of introducing the condition that the substance shall always transmit two strictly transversal waves is substantially the same as that given by Lamé in his repro- 250 Prof. C. Niven on the Theory of an duction of Green’s theor y; and is somewhat more easily applied than his process or Green’s. Let the small motions of a solid be given by the pees au dv dt? =A(5 + dy rac pee); di =fe( Zp. +342, );-- then, if there be two transversal waves in every direction, the OH Gk aie GD , eo Te ae (= =P == Aye =| must be of the form a a = Na 0 For let us consider, first of all, an ordinary homogeneous solid, for which f,, fo, 73 are quadratic functions of = = = Wemaysatisfy the equations by putting w,v, w= (up, 0, Wp) sin &, expression for where = = (le +my +nz— Vt), obtaining the three following equations, Uys Voy Wy» V=fiy fo, fa- (E, mM, NV Uo, Voy Wo)- | But if V?(u,l+v,m+w,n), derived from these, do not con- tain u,/+v,m+ wn as a factor, we shall have two equations of the form u,l+vum+u,n=0, ul’ +v,m'+wu,n'=0, giving a single value for the ratios u,:v):W,, and by consequence a single value of V’, contrary to the hypothesis. The equations of motion of the solid take the form, as Lamé has shown, du 21, ,da3 | ara = 20% ten —2e¢; ak d’v ds de, 10 de 2 Al — 2a ( \ ) EW Oa, hoy) de me a a — 2b? Fa J wherein a, 0;, ¢, are the three principal wave-velocities. In the case where /,, fo,,/3 contain third as well as second powers of ag the necessary condition is clearly fulfilled by supposing the principle stated to apply to both sets of terms; and it may be readily shown that this is the only conclusion which will satisfy it. Reduction of terms of Class (1., 1I1.). 9. The part of the energy arising from this source will be Imperfectly Homogeneous Elastic Solid. 251 of the form ii yu» where J=KyAat K,,Ab+ ... + Keoki, K,, ... Kgg being constants. The variation of J, oJ = Ky, (Ada+adA) + . and each of the terms of this sum may De eee treated by the method given in art. 6, and applied to find the corre- sponding parts of the stress- components and of the equations do of motion, and thence the value of TE’ But we may avoid much labour in finding = Z if we observe that the variation of da can contribute nothing towards it. For f,Ada=21A—2[, 8a, 2 and we may put dv dw ieee aae which is equal to ddv ddw dz dy Thus, on integrating by parts again, we see that {Asa con- tains, besides sur a ae the volume-integral aA OPIN 4h (ee. dads 7 o” di a dx dy dz. Hence it appears that the part which this a conte to 24 2 =i is —K,, * , and the part contributed ne aes ‘Taken together they contribute nothing to fe The same thing is true for the terms due to 6d, 6c, dd, de, df. Writing, therefore, for A, B,...F their values, we find that a dou ddw dév {ar=( (Kya +. cts Kya(S— dy + Ge. + ee .). yy Integrating by parts, and forming the equations in a Sie we obtain the following equation in ae de GOES Va? TE = qe Weuet Bab +... + Kaci} 2 d eg ee eee? Sebi cla Kocoft. 252 Prof. C. Niven on the Theory of an Now, according to the test given above, the right-hand member of this equation ought to contain differential coefh- cients of @ only; but inasmuch as u,v, w appear only as con- da, da, da tained in w,, 72, #3,and as i t+ a +— ay y that the right-hand member contains differential coefficients of da, daw, . dw; de * dy + ie values, we have oy KGa: pO Waa oo +k ee =(, it is obvious only. Writing, therefore, for a, b,.../f their dx dat a “y eters “@ fg gdm ies 4 Gey b + aq Kn? Get ee Sets + Kee da * dy ae Pit, des do) =(Kit5 be SP G04 +2K, dx a Ax a dy Oe A comparison of the coefficients of like terms on both sides of this equation readily furnishes the following relations among the coefficients of J, O=K,,= Ky,= Ky.= Kop=Ky,=K 3, 5 Ky,=Kg=—Ky, Kyg=Kes=—Ky;, Ky;= K5,= —Kye 5 2K, = KGa i ZIKGs + Ker = 2KGs + K;;, 2K,=2Ky.=2K9, + Keg =2K33+ Ky, BK = 21K — 2Ke + Ker 2K >» ok KGa. Ky= Ky= Ky=Ky— Ky, K;= Ky= Ky3=K.— K;;, Ky= Ka= Ke=Ke3—Koq. Substituting these relations in J, we obtain J=(K,A+K,B+K,0+K,D+ K,H+K,F)(at+b+ce) > —1K,(Be+Cb—2Dd)—43K,;(Ca+ Ac—2Ee) | —4Kg(Ab + Ba—2Ff) r(i2) 2G ie Ag ey ok, (Eat Dp Ree | — K;,(De+ Ed—C/f—Fc). But this equation may be greatly simplified; for, in the first place, a+b+¢=0, and, moreover, Be + Cb—2Dd,..., De+ Ed—Cf—Fe are ae, edient with Xe, Ae OY ene X= yC— zn, ea ne =an—yé, sil where A... lane cogr edient with «?...2 wy, and @ ....f with: &* ..: En. Bat Xe Ne "7, ave themselves . cogredient with lines, being the compo- Imperfectly Homogeneous Elastic Solid. ya a nents of the vector pr oduct of (x, y,2) (2,7, €); hence X”... XY are cogredient with 2... wy, and consequently the coefficients = y,...K;, are also cogredient with w”...zy. It is possible, eet fore: so to choose the axes of coundineter that the last three terms shall vanish; and the expression of J will then re- duce to J =—a(Be+ Cbh—2Dd)—B(Ca+ Ac—2He) —y(Ab+ Ba—2Ff). (13) Suppose, then, that the axes are so chosen, and let us de- termine the values of the accelerations ee 5-,--- due to J, com- mencing with the variation of the coefficient of y ; we have to put therein | A= Bao, va3($ 49") dx’ dy Wie Olay) _ Ath Bai ee *—*“da — dady, dude °~ dydz dady fe du dw “e CEO CO Madd di?) dian dye On substituting these values and integrating properly, we finally obtain for 6(Ab+ Ba—2Ff) a series of surface-terms with the a CA aa da dp ab Al 1ee(i dix rae we a awe) 4 an Li gGe dB GUN GAS GFA’ dx dy * de dy da* a or) t - (4) oh Buo( = But _ GA dB du 1a du , dv _ 13 Hace” Gada dye! te dz) dx dB_dF _ dv -4+5-($ <= Ces on, A Ord Gu \ay hj dao/miad Substituting these, and inserting for a, b, f their proper values, expression (14) may be reduced to Cai Oe =! Ge. fom. Oe 2) +f fo rs i dy” +88 Gas Te tes oe Ss) (S a yi. a5) We may now take together all the three terms of J in ( 13), ~vhen we shall clearly obtain for the three accelerations 9’ay, 254 Prof. C. Niven on the Theory of an 0a, O’ar3, where ya ll :) (S L =, (4+ = 16 0 =a( + ae is det de) * 1 \ ae + yp Ge The acceleration in any other definite direction is obviously 0’a', where aw! is the component rotation in that direction. Consequently the component accelerations along the original axes are 0a), 0°m, 0'o3, where ad ai a pune a $e oes ax? tae Re ioe tat asd dy? e d Chae) some quadratic function of — ae a ie Adding these terms to the equations (10), the equations of motion of the solid now become du 21 ae q qe en 1 dz oA +0? 1) ee. di “ dx ei dz + O°, ( Tw» da, ads 5 ail = 2a oy. — 20? +0Q°a a I shall return to the solution of ue in art. (12), and in the mean time proceed to the discussion of the Terms of Class (1., IV.). 10. There isno reason a priori why the group @,, 7,,a, should not appear in the expression for the energy of the solid; for they correspond to a real strain of it. This species of strain may be easily analyzed geometrically, and has some interest- ing properties, especially in an isotropic homogeneous solid. Let us pass, however, to the expression for the energy depend- ing on these terms, w ‘hich must be of the form ( {oN A+NiB+ ...+ NF) +o,(NnA+ ... + Nock) +o(NnAt ... Neale The value of as which corresponds to it is clearly d ah d (Naga te #Nu a +(Nado tag iane qea)™ Bee .) a a © dx dy Imperfectly Homogeneous Elastic Solid. 259 But since da ds dw 14 2 4 teal Hach age: this must be (to admit of two transversal waves) of the form d ae d ee dz, da. ) = SSE Rae | (inet POC Trs PRO Jpe ty SS (Mig tM g, pe aes Ge ate dy 2 Ge us whence the following series of relations :— O= Ny. =Ny3= Nus= No = No3= Nos = Na =Nge= Noe, Ni = Ny = Nog= N35, No= Noo=Nig= Nou, Na=Ni5= Noy = N33: and the energy takes the form Ne {N,(Ao, + Pa,+Ha;)+N.(Fa' + Ba, + Da,) +N3(Ho' + Da,+Ca,)}. (19) Now A...F are cogredient with 2’...«y, and a, a,, a, with &,7,¢; thus the coefficients of N,, No, N3 are cogredient with w(Ex+ny+ &), yeatny + &), (Exe +ny + &)—that is to say, with lines. The energy in an element of volume appears, therefore, of the nature of the component of a force along a line, like the potential of a small magnet in a magnetic field. It may be shown, however, that the energy given by (19) resides wholly at the surface of the body. In tact, let N=MB3—NB,, b=nB—lo3, v=la,—may, and let o*=a?+a@2+a2; then the total energy of the solid arising from terms of this class is ‘ {N,(AA+ Fut Hy + 31a’) + No FA+ But Dvt+ 3 ma’) +N;(EX+ Dut Cr+ gna’)t. (20) Such terms therefore, if they existed, could not affect the in- ternal motions of the solid. Derms of Class (1, Vi): 11. We now come to the terms formed by the combination ” of groups ., V. Some of these are already complete inte- A ise ! grals, such as ae the integral of which throughout the solid =4( mA? Moreover it can be shown that, in every case, any term of the class (1., V.) may be resolved into a series of such surface-terms coupled with terms of classes (1., UT.), ., 1V.). The proof of this proposition will be given 256 Prof. C. Niven on the Theory of an for two of these terms; and we may observe that it follows from this that the interior parts of these terms may be sup- posed to have been already combined with those belonging directly to classes (I., IIL), (1., IV.). The existence, there- fore, of the terms of the class at present under consideration in no way affects the internal movements of the solid, though it does affect the specification of the stress to which the solid is everywhere subject. Jor in addition to the forces and couples which have been already considered in art. 6, we must also imagine stress whose proximate effect is a variation in the state of strain of the parts of the solid adjacent to the plane at which it acts. I proceed now to prove the proposition men- tioned in this article by taking two terms of the class, viz. — and { A . It is unnecessary to trouble the reader V with the Foley of a reduction ; and I shall therefore merely state that the former of these integrals is equal to hen do, da» das { (—pr +ADm-+ a n) +f Ga —I ae +D =), and the latter to af (—EFI+ AEm+AFn)+ 2( Ce oon 13 _ pF), dx dx Hach of the other terms of this class may be treated in the same manner; and we may therefore consider the proposition stated above to be established, and proceed to the consideration of the equations (18). Solution of the Equations of Motion. 12. Before proceeding to the general equations (18) it will be convenient to consider, first of all, equations (10). By differentiation we obtain from these latter the following:— Tom He 9 ds, Ge © oe dx’ da IW? ds de biV am ay Wome tre ds dae Ws ap where 7 v= d? LP & La? dy? dz’ od, p,dR2 | oda ae du O dy ae lz Imperfectly Homogeneous Elastic Solid. 257 Now equations (10) may be satisfied by w, v, w =U, Up) Wo + 81NG, where €= = (la+my+nz—Vt). If we find by differentia- tion @1, ®, ee it is easily seen that they form a vector at right angles to uw, v) w), and tolmn. If therefore its com- ponents be U,, Vo, W,- cos &, we shall have lU,tmV,+2W,=0, ) (V*—at)U)= —4,, | (V?—b1)V = —m,, actntes = (2a) | ai Yc) W = 73, where ,=alU,+ mV, -emW,. The two values of V are therefore a reciprocals of the semiaxes of the section of a?2?+bl*y?+c Cy whence _ Wiz —_ 2 e rol} If L be the length of solid necessary to produce a eomplete rotation of the plane of polarization, mip Oh ys AoC 2 T wae Sir W. Thomson has shown that the phenomenon of the dispersion of light enables us to form an estimate of the inter- molecular distances. But the phenomena of rotatory polari- zation afford a vastly more delicate test of differences of wave- velocity. In quartz, for example, whose rotatory effect is about 24° per millimetre, the rotation of the plane of polariza- tion reveals a difference of velocities amounting to less than the 20,000th part of either. We may therefore hope to find in these data some evidence regarding the distance m through- out which the want of homogeneity of structure is sensible. The magnitude c., used in the last equation, and introduced in art. 9, is obviously of the form m.@, where J is a quantity of the same dimensions as c?, and may, for aught we know, be of the same order of magnitude. The last equation may there- fore be written wherein we may replace pw by its value fa\ 4 es r Ty) es » Ty ra ar — Eo) (ae 1 1 But for the mean yellow rays of quartz, %)»=o 55 millim., L=15, i=%; hence a a) i a7 (ck og? a result apparently in harmony with Sir W. Thomson’s con- clusions. he2ei 4 XXXIV. Note on the Polarization of Heat. By G. Carry Fostrr, /.£.S.* VHE following determinations of the amounts of heat trans- mitted by two Nicol’s prisms, whose principal sections make different ang the Physical Laboratory of University College, London, by Mr. M. J. Jackson. Although the results amount to nothing more than an additional verification of a relation that is already thoroughly established, I venture to put them on record, not only because such verifications are satisfactory in themselves, but also because the apparatus required for conveniently re- peating experiments of this kind is not always at hand. The source of heat was a rather powerful paraftin-oil lamp (supplied by White, of Glasgow, for use with a Thomson’s quadrant electrometer). The rays from the lamp were con- centrated by a lens of 7°35 centims. diameter and about 22 cen- tims. focal length, placed so as to produce a real image of the lamp-flame within the silvered reflecting cone of the thermo- pile. Immediately behind the lens (on the side next the lamp) a double screen of polished sheet brass was placed, whereby the radiation could be cut off or allowed to pass at will. On the other side of the lens came two Nicol’s prisms, each about 20 centims. long, and giving a clear circular field about 6°7 centims. in diameter. ‘The prisms are protected at the ends by disks of thin glass, which were left on during the experi- ments. It is to the possession of these fine prisms, made for me by Mr. C. D. Ahrens, that the possibility of making the experiments with so much ease was due. The thermopile, which was about 95 centims, distant from the lens, was protected from stray radiation by a double hood of tin-plate. The galvanometer was a reflecting instrument of low resist- ance, on Sir William Thomson’s principle, made by my assist- ant, Mr. Grant. By means of a commutator inserted between the thermopile and the galvanomeier, two opposite deflections were obtained for each position of the prisms. In the follow- ing Table, the column headed 6, gives the means of the deflec- tions to right and left when the angle, 0, between the prin- cipal sections of the prisms was measured in one direction ; and the column headed 6,, the corresponding deflections when this angle was measured in the opposite direction. The num- bers denote divisions of the galvanometer-scale. * Communicated by the Physical Society of London, having been read to the Society on March 3, 1877. oles with each other, were recently made in ~ 262 Mr. J. Ennis on the Physical and Mathematical - Deflections Angle between : 3 3! principal sec- | Se ee ea 3. ,. ieee cos? 9° | (calculated). 0 32:25 | 31:5 | 319 31-9 311 15 29°75 29:25 29-5 31:6 29-0 30 22°75 23°5 23°1 30°8 23:3 45 14°75 14°75 14°75 29°5 15°5 60 7:75 775 775 31:0 78 75 2-25 2-0 2°1 au le 2-1 90 0°5 0:25 O24 ebieeert 0-0 Mean .. 31-1 The numbers in the last column of the Table are calculated by the formula 6/=31:1 cos’ 6. It will be seen that the ob- served mean values (6) never differ from the corresponding calculated values (6’) by a whole division of the scale, which represents about as high a degree of accuracy as can be ex- pected from the method of observation employed, it being impossible to read with certainty to any thing less than half a division: where quarter divisions occur in the Table, they result from taking the means of positive and negative deflec- tions. XXXV. Physical and Mathematical Principles of the Nebular Theory. By Jacos Ennis, A.M.* ee chief objections against the derivation of the stars from a former gaseous diffusion of matter have been these two :—first, that no cause can be discovered for the beginning of rotation in the primitive gaseous condition; and secondly, that this rotation, even if begun, could not become rapid enough to produce a centrifugal equal to the centripetal force, and thus to separate equatorial rings which may break and condense into revolving stars. Both these objections I will now remove. First. The force of gravity, by its interaction between nebu- lous masses, must necessarily begin rotation—NSir Isaac New- ton says that “if matter were evenly diffused through a finite space and endowed with innate gravity, it would fall down in the middle of that space and form one great spherical mass ; but if matter were diffused through infinite space, some of it would collect into one mass and some into another, so as to form an infinite number of great masses. In this manner the sun and stars might be formed, if the matter were of a lucid nature.”’ This is sound reason, an unavoidable conclusion. Therefore, * Communicated by the Author. # Principles of the Nebular Theory. 263 given a gaseous diffusion of all matter through all space, and a slow contraction from whatever cause, then there must result an infinite number of separate nebulous masses; and like the clouds in our atmosphere, they must be irregular in shape, different in size, and at unsymmetrical distances apart. Then, by the action of gravity, those which were near must have fallen into each other, until the resulting masses became so far apart as to be beyond each other’s sensible gravitation. But when one nebula fell into another it could never fall in the direction of the centre of gravity, because it must have been at the same time under the gravitating influence of other neighbouring nebule drawing it from a direct line and causing it to strike obliquely. If we strike a suspended ball in the direction of the centre, it will fly straight onward ; but strike it obliquely, and it will spin round. In like manner, from the oblique falls of the nebulze every resulting mass would rotate. A small nebula striking a large one very obliquely would cause a rotation only on the surface. Moreover clouds have high prominences, long projecting arms, and extended out- liers ; all these in falling to the level of rotundity would also be under the influence of other neighbouring nebule; and therefore they would fall obliquely and cause surface-currents. These surface-currents, by the composition of forces, would unite in one current; and this one resulting surface-current would be the rotation of the globe. But all surface-currents would be retarded by friction on the next interior layers ; still the momentum of rotation would not be lost. What was lost by the exterior would be gained by the interior, until the resulting mass rotated, however slowly. —_ Secondly. However slowly rotation might begin, the force of gravity would hasten its velocity until on the equatorial zone the centrifugal would equal the centripetal force—In consequence of the contraction of the nebulous globe, and of a very slow rotation, a particle at A (fig. 1) would move in the direction from A to C. It would there- Fig. 1, fore move in the direction of an inclined plane, and gra- vity would increase its velo- city downwards, All the other particles on the surface represented by dots on the outer circle would also move down in the inclined plane directions toward the centre; and all would be hastened alike by the same force of gravity. There would be no actual inclined planes, for a 264 Mr. J. Ennis on the Physical and Mathematical every particle would float on the level surface ; still the motions of all the particles would be in the direction of an inclined plane, and subject to calculation as inclined- Fie. 2 plane motions. In fig. 2, a ball rolling down nh the incline from A to C must gain the same a velocity as if it fell from A to B through the Lobe same height. And in fig. 1 the same truth sal uke gee C is illustrated by its triangle ABC. If the outer circle represent the surface of our solar nebula when expanded to the orbit of Neptune, and the inner when expanded to Uranus, then the velocity of rotation gained in contracting from the outer to the inner must be the same as the velocity gained by a fall directly toward the centre from orbit to orbit ; that is, the particle at A moving by rotation and contraction to C would acquire the same velocity as if it fell from A to B,— friction always excepted. Because action and reaction are equal and in opposite direc- tions, it follows in our terrestrial inclined planes that, as the ball rolls downward and forward, the plane must move upward and backward with the same momentum. But this upward and backward motion cannot occur in the nebula. This may be illustrated by the movements of comets. A comet in its aphelion at A (fig. 3) must gain the same velocity in moving to C as if it fell in a direct Fic. 3. line to B, equally near to the A sun at S; the distance BS =10/S} and ¢b) Si=:C.Sitéke: Also when the comet arrives abe Cr er cand Ciiamre= spectively, it must have the same velocity as if it fell to the points B’, BY”, B”, and B’” in a direct line, equally near the sun in the focus 8. At every step the sun, in- versely in proportion to its mass, moves in the direction opposite to that ef the comet. But if there were many comets equally large and distant, and moving in the same plane and direction all around the sun, then they would counteract one another’s influence on the sun, and the sun would not be moved, The particles on the surfaee of the nebula, re- Principles of the Nebular Theory. 265 presented by dots on our outer circle (fig. 1) all around, may be regarded as so many comets approaching the sun at the centre 8, and they must counteract one another’s influence in the same manner. While they move forward and downward more and more rapidly, they produce no upward or backward motion. Moreover they do not, like a rolling ball, press on an inclined surface, but on the level equatorial zone. Having shown that the particles on the surface of a con- tracting and rotating nebula must move like a comet approach- ing the sun with a velocity always accelerated by the force of gravity, let us now attend to the method by which this velo- eity of rotation may be calculated. Hvidently the velocity of rotation gained in contracting from the outer to the inner circle (fig. 1) must be the same as the velocity gained by a fall from one circle to the other in a direct line toward the centre. As eravity, the force causing both tie fall and the rotation, varies its power inversely as the squares of the distances, therefore a mass which would be attracted with a power or weight of 409,000,000 pounds at the sun’s surface wouid be attracted with only 9020 pounds at the earth’s orbit, with only 10 pounds at the orbit of Neptune, and with only the tenth part of an ounce at forty times the distance of Neptune. We need not inquire how far the ancient nebulz extended in order to find the beginnings of their falls toward their centres, because the force of gravity was so feeble on their surfaces that we may reject its precise amount, and assume as tanta- mount all the velocity which could be acquired by a fall from infinite distance toward their centres. If the velocity acquired by a fall from infinite distance to. the outer circle be repre- sented by a, and the same to the inner circle be represented by 0, then the velocity acquired by a fall from the outer to the inner circle would be b—a. ‘The velocity (V) of these falls from infinite distance may be computed by the following for- . mula, V=/2gr. Here r stands for the radius of the nebula (of our sun, for instance, when ina nebulous condition), and g stands for the velocity per second acquired by a fall during one second on the surface of the nebula. This velocity on the surface of our nebulous sun may be found from that on our earth’s surface, which is 32°16 feet per second, by comparing the mass and radius of our nebulous sun with the mass and radius of our earth. By using this formula, it appears that the velocity of a fall from the orbit of Neptune to that of Uranus becomes a mile and a quarter per second, deci- mally 1:244. This, added to the actual velocity of Nep- tune, 3°491, gives a velecity for Uranus of 4°735 miles per second. But the actual velocity of Uranus is 4°369, showing 266 Mr. J. Ennis on the Physical and Mathematical an excess of ‘366. Thus it appears that the force of gravity is enough, and a little more than enough, when acting on a nebulous mass, to cause a rotation with sufficient velocity to make the centrifugal equal to the centripetal force, and there- fore to separate nebulous rings from the equatorial zone.— Qe Ee D. But what became of the excess (*366) of the velocity due to the force of gravity? Plainly that proportion of the force was expended by the friction of the rotating exterior layer on the unrotating interior. As I have already shown, the rotation of some of the ancient nebulze began on the exterior ; and there- fore the exterior layer must necessarily have been retarded by friction on the interior layers. By calculation I have found that this retardation of the velocity due to gravity, all the way from Neptune to Uranus, amounted to 1 per cent. in a radial dis- tance of contraction of 125,000,000 miles; that is, down an inclined plane 125,000,000 miles in height (not in length) the velocity due to gravity was retarded 1 per cent. ‘This retar- dation became more and more as the unrotating centre of the nebula was approached. The following Table gives the num- ber of miles, not in diameter, but in radial contraction, from planet to planet, necessary to cause a retardation of 1 per cent. in the velocity due to the force of gravity as the sole moving power in the case. From Neptune to Uranus ...... 125,000,000 miles. a Wirants| to Saturn cesses: 80,000,000 __,, 5, Saturn to Jupiter ......... 38,000,000 _,, sy) epiterto; Mars: .e.ss cess 13,000,000 _ ,, oy me Lamsecon Martine ac ciccccass 5,783,000 _,, 5, Warth. to Venus: sc scccesccss 4,554,000 _,, » Venus to Mercury......... 4,459,000 _,, This retardation was very small; and the figures show a wonderfully close agreement between the theory and the facts. These facts are vastly multiplied when we take the asteroids into account, as I have done. As we might anticipate a priori, this retardation becomes much larger toward the unrotating centre of the solar nebula, Interior to Mercury it was enormous. At the orbit of Mer- cury the equatorial surface of the solar nebula rotated with a velocity of 110,000 miles per hour. But it became so greatly retarded by friction on the dense unrotating core, that now the rotation of the solar equator is only 4500 miles per hour. This explains why no planetary ring could be abandoned by centrifugal force interior to Mercury. It also explains why the equatorial region of the sun now makes a rotation in two Principles of the Nebular Theory. 267 or three days shorter time than the polar regions. Those polar regions, being near the axis of rotation, must always have sympathized more with the unrotating interior, because they had less distance to fall to the axis to acquire velocity by their falls. The present excess of equatorial velocity must be regarded as a relic of the past, just as fossil remains in the earth’s crust tell of the state of things in times long ago. It follows from these principles that the atmosphere of the sun sheuld rotate more rapidly than even its liquid equatorial zone ; and this has just been discovered to be true by Young. The solar atmosphere must have an inconceivably great mo- mentum ; and it cannot easily be stopped by friction on the flaming liquid interior. According to Harkness, “ one cubic mile of our atmospheric air weighs 5,621,000 tons.” If the solar atmosphere holds the same proportion in mass that ours does to the earth, then its height, according to Trowbridge, must be 606,000 miles. We know of no reason why the pro- cess of contraction in the sun should have ceased. And this contraction must add velocity to the solar atmosphere, and daily aid it to overcome friction, and to keep its speed in ad- vance of the underlying liquid body of the sun. 3 Having shown how rotation must begin in the vast primi- tive nebulz which formed sidereal systems, I now proceed to point out how rotation must begin in the nebule which resulted from broken rings, and condensed into individual suns and planets and satellites. Let C (fig. 4) be the centre of a Fig. 4. nebula, and A B D an abandoned ring, or fragment of a ring, moving with the arrow. The exterior (e) of the ring, or of the globe in which it has con- ~ densed, possesses a greater linear ve- locity than its interior at n. There- fore, in contracting, the exterior at ¢ will have a greater velocity than the centre, and will fall before it, and the interior at 7 will have a lesser velocity than the centre and will fall behind it. From these two facts, as seen by the arrows moving from e and n, the be- ginning of a rotation is plainly a necessity. In the sun we now behold the most unquiet and agitated of all known places, caused, as I have tried to prove, by chemical action. This agitation must have raged with ‘extreme violence in the nebule, and must have caused various irregularities in the sizes and densities of the planets, in their distances apart, and inclinations of their axes. 268 Mr. J. Ennis on the Physical and Mathematical The harmony between gravity as the only projectile force, and the velocities of all the planets and asteroids, is further confirmed by the satellites. By taking into account the masses of the planets in our five planetary systems, I found that in all cases the force of gravity was strong enough to produce in the planetary nebulze a velocity of rotation such that the cen- trifugal equalled the centripetal force, and therefore equatorial ‘rings were necessarily abandoned to form satellites. By cal- culation I found that in the cases of Mar s, Venus, and Mercury their nebular expansions were not far enough, and their force of gravity was not strong enough, to produce a rotation that could abandon equatorial rings. Our earth, from want of mass and want of nebular expansion, came very near to having no satellite, no friendly, softly shining moon. Having compared the power of gravity as the only projec- tile force with the actual velocities of the planets, asteroids, and satellites, we may advance an important step and prove the general abstract proposition, that, in all greatly expanded nebule, after rotation has once begun, and during a slow con- traction, the force of gravity is sufficient to cause a velocity such that the centrifugal must equai the centripetal forece—in other words, that the falls toward their centres from infinite space will be more rapid than the velocities required in their planets when formed. This demonstration is aided by the following diagram (fig. 5). The notation is the same as that in the formula V=,/2¢7, already given. Fig. 5 Let ABE be the orbit of ee pp a planet. HB an are passed ‘through by a planet in 1 : second. Then ED=BF ee =distance fallen toward the eB a \ sun im ivsecond =2.9. Avi en ae = twice the distance of a planet = 2r. BE (very nearly are BE) = the vale city of planet in orbit = v. HA Bil; , Phil) Mag. [IV.j vol. xx. p. 86. + Pogg. Ann. ne clvil. p. 353. 276 Mr. R. H. M. Bosanquet on the Theory of Sound. two to rotation; for by the hypothesis that the body is a solid of revolution, perfectly hard and smooth, vis viva of rotation about the axis of revolution is excluded. The Clausius equation then takes the form which gives The ratio of the specific heats for air, as deduced from the value of sound, cannot, as we have seen, be assigned with great accuracy from a comparison of experimental data ; ; all we can say is that the value of the velocity of sound, deduced from ratio 1:40, differs from our mean value by an amount i insigni- ficant compared with the difference of the mean value from the results of the various experimenters. (Mean yalue =331°35 metres, value due to 140=331°2 metres.) If, then, Kundt and Warburg’s result is worth any thing at all, it is clear that the explanation of the ratio of specific heats in air and allied gases may be placed on a perfectly analogous footing. The relation is so obvious that it is impossible to suppose that it has not occurred before to the eminent men who have dealt with the subject. I will notice the points of objection that occur to me; there may be others of a more conclusive character. Jt has been frequently assumed that if two or more atoms are built up into a molecule, they must be connected in such a manner that they can oscillate with respect to their common centre of gravity. Hvery degree of freedom in such oscilla- tions should, it appears, retain the same vis viva as a degree of freedom of the motion of the molecule itself*. Under these circumstances, if we supposed two spherical atoms joined by elastic forces, the system would have more than five degrees of freedom. If we ask, why must we suppose the two atoms joined by elastic forces and not rigidly? we are told that it is the vibra- tions of the atoms that do the work we see in the spectroscope lines. But these lines occur in the vapour of mercury, for which our explanation fails to suggest any collocation of atoms more than one in the molecule. Why not, then, admit that the lines are produced by something within the atom which we * Boltzmann, Ber. d. Wien, Akad. vol. 1xiii. Mr. R. H. M. Bosanquet on the Theory of Sound. 277 cannot at present account for, just as we cannot decompose it chemically *? I suppose, however, that the principal objection would have been that the experimental data were not consistent with the hypothesis. In answer it seems to be enough to look at the Table at the beginning of this note ; we can say without hesi- tation that, giving due weight to Regnault’s experiments, it is impossible to conclude with any certainty whether the true value of the ratio of specific heats lies above or below 1:40. At the same time, since there must be internal work done in the atoms in some way that we do not comprehend, though it is probably very small, we may regard such a value as Reg- nault’s (1°3945)as compatible with a possible explanation, since with such a value the total vis viva is slightly greater than that due to the 5 degrees of freedom. The admission of the number 1:40 as a working constant involves relations between the mechanical equivalent of heat and the specific heat of air at constant pressure. The following numbers indicate the nature of the relation, the ratio of specific heats of air being taken at 1:40:— Mechanical Specific heat at constant equivalent. pressure. 431 2377 (Regnault)f 429 2389 (Wiedemann) 424 (Joule) 2416 Regnault’s own computation of the mechanical equivalent gives 436°1. : A comment of Professor Foster on recent determinations in the Supplement to Watts’s ‘ Dictionary of Chemistry (1872, p- 687), after noticing the general accordance of modern results in values higher than Joule’s original number (424), proceeds:—“ Joule’s new result (429°3) is the lowest of three values obtained in distinct sets of observations; but it is adopted by him as the result of the investigation, in conse- quence of more complete precautions to ensure accuracy having been taken in the set of experiments from which it was deduced * There is nothing to prevent us from forming the conception of very small amounts of énergy existing in some way or other within an atom (regarding this as already complex in a manner which we do not under- stand), though we are unable to give any accurate account of the way in which the movement is originated or maintained. + Regnault’s determinations varied from ‘23536 to ‘25890, Wiede- mann’s from ‘2374 to ‘2414 (Poge. Ann. vol. clvii. p. 21). This last limit comes very near the number required by Joule’s value of the equivalent, 278 Prof. Challis on the Action of the Cup-shaped than in the othertwo. These, however, were closely accordant with each other, and would lead to 481°5 as the value of the mechanical equivalent.” In view of this comment, the above values cannot be regarded as beyond admissible limits. We may conclude, then, that the values 1:40 for ratio of specific heats, and 831°2 metres or 1087 feet for the velocity of sound, are a fair repre- sentation of experimental results—and that they give rise to no discordances in their connexion with other data and theories, which are of an amount to call for rectification on the evidence at present before us. P.S.—Since the above was written, and after my forth- coming little work, in which the matter is similarly treated, has gone to the printers, I read in the number of Poggendorff just received (1877, No. 1, p. 175) a short note from Boltz- mann, being an abstract from a paper in the Vienna Berichte, in which he shortly announces the above result and his adhe- sion to it. It is stated that the experimental values of sound are discussed in the original paper; so that the substance of my communication is anticipated. I have, however, thought that it may still not be entirely without interest. XXXVIT. A Theory of the Action of the Cup-shaped Radio- meter with both sides bright. By Professor CHALLIS, J/.A., elle se Sy Japa Se UT of the many experiments relating to the radiometers described by Mr. Crookes in his communication con- tained in No. 175 of the ‘ Proceedings of the Royal Society,’ I have selected for theoretical consideration No. 1035, in p- 318, because this experiment exhibits a novel and. signifi- cant phase of the action of the instrument. It is evident that in this instance the radiometer is caused to rotate simply be- cause the vanes are convex on one side and concave on the other, the conditions as to the incidence of light or heat being exactly the same for both; and accordingly a theory of the motion must explain how the effect is produced solely by the difference of the two sides as to form. Such an explanation will, I think, be found to be given by the following theory, which rests on the same principles as those applied in the ex- planation of the phenomena of the radiometer in two prece- * Communicated by the Author, Radiometer with both sides bright. 279 ding communications contained in the Numbers of the ‘ Phi- losophical Magazine’ for May and November 1876, and at the same time departs in no respect from the principles of the general hydrodynamical theory of the physical forces which I have now for a long time upheld. _ Considering, first, the case of the radiometer with the vanes blackened on one side, I assume that the radiant light or heat which is incident on the vanes, being thereby converted into heat of temperature, causes the atoms in a thin superficial stratum to be displaced from their neutral positions, and in greater degree on the blackened side than on the other, on account of the greater accession of temperature on that side. It is true that the intrinsic molecular forces of the vanes will tend continually to make the atoms return to their neutral positions ; but since at the same time the disturbing force is continually in action, the result of the antagonistic forces, so long as the disturbance is operative, will be a persistent ab- normal condition of the superficial stratum. This is a real change of condition of the vanes, by whatever name it be called. It seems to me that it would be best described by the term thermo-electric. But it is of chief importance to remark, that every such superficial disturbance, however caused, gives rise to a steady circulating etherial current, in which the pressure varies so as to be always less the greater the velocity, and that consequently atoms immersed in such a eurrent will be dynamically acted upon by reason of the vari- ation of pressure. In the present instance the course of the current is from the blackened to the opposite surface, because, on account of the greater expansion of the vane on the warmer side, the channel for the current diminishes and the velocity increases towards the bright side, and accordingly the dyna- mical action is the same as if the vane were pushed on the blackened side. [I have so fully discussed the above-cited hydrodynamical proposition in previous communications, that I do not think I am called upon to produce the demonstration here. Tang now the case of the cup-shaped radiometer(No.1035), wemay assume that when the disturbing effect of the incident radiant light or heat, converted into heat of temperature, is just co interbalanced by the tendency of the superficial atoms to take the positions in which they are ordinarily held by the molecular forces, they will, as in the former case, be permanently dis- placed from their neutral positions. But because both the radiating surfaces are bright, the action will be the same on both, so far as regards the amount of expansion caused by the accession of temperature. There will, however, be the differ- 280 Action of the Radiometer with both sides bright. ence, that a given displacement in the normal direction will cause the atoms in a given superficial area to be spread over a larger portion of convex surface than of concave surface, the motion in both cases being from within to without, and the lines of motion being divergent for the convex surface and convergent for the concave surface. On this account there will be, ceteris paribus, greater atomic density at the con- cave surface than at the convex surface, and the latter will be in the condition of the blackened surface of the ordi- nary radiometer. Hence the cup-shaped radiometer will move as if it were pushed on the convex side, as is found ex- perimentally to be the case. The experiments referred to showed that the motion of the radiometer was in the same direction and nearly the same in amount, whether the light fell only on the convex side, or only on the concave side, and that in either case the rate of revolution was about half what it is when the light falls on both sides. These results may be considered to be consistent with the theory, inasmuch as we may draw the inference from the supposed thermo-electrical character of the disturbance, that the state of displacement of the atoms induced by a disturb- ance on one surface is spread equally over both by superficial conduction, and consequently that the action is of the same kind whether one surface or both be illumined. When this radiometer was heated by a hot shade or plunged in hot water, rotation was caused in the opposite direction to that caused by the light. Under either of these circum- stances the superficial atomic density of a vane must be the same throughout in order that its molecular forces may coun- teract the effect upon it of the uniform surrounding tempera- ture. But to satisfy this condition at the convex surface, not only must the tendency of the induced heat to diminish the superficial atomic density by expansion be counteracted, but that also which is due to the divergence of the lines of motion normal to the surface ; whereas at the concave surface the convergence of the lines of motion helps to counteract the ten- dency of the temperature to diminish the superficial atomic density. Hence the molecular force from without to within acts in greater degree at the convex surface than at the con- cave surface. Hence also the interior atomic density dimi- nishes in the direction from the convex to the concave surface, because where the molecular force is greater, the atomic den- sity must, ceteris paribus, be greater. Consequently, as the greater atomic density is on the convex side, the greater velo- city of current and less density of the ether is also on that side, so that the vane is urged in the direction from the con- Mr. M. M. Pattison Muir on Gallium. 281 cave to the convex side. Thus it appears that the motion of the radiometer due to the hot shade or hot water is opposed in direction to that caused by the light. This result accords with the experiment mentioned at the top of p. 314 of the ‘ Proceedings.’ The most essential part of the theory proposed above is the dynamical action of a circulating etherial current. From hydrodynamics we know that sucha current could not beyin to flow in a perfect vacuum, and that it flows with more difficulty in proportion as the vacuum is more complete. This is exem- plified by the difficulty of producing a galvanic discharge in very rare air between distant poles. The proposed theory, therefore, gives a sufficient reason for the decrement of the action of the radiometer as the exhaustion of the air advances towards completion. From this point of view I am wholly unable to admit that the presence of residual gas is the cause of the movement of the radiometer. It seems to me that one might as well argue that because a bell is not heard when rung in an exhausted receiver, the air in the receiver, and not the tongue of the bell, produces the sound when it is heard. I take occasion to say here, as I have said before, that I have been induced to give particular attention to theoretical explanations of phenomena of the radiometer solely on account of the adaptability of such explanations to elucidate the hy- drodynamical theory of the physical forces. Cambridge, March 13, 1877. XXXVI. Observations on Gallium. By M. M. Partison Murr, f.A.S.L., Assistant-Lecturer on Chemistry, the Owens College, Manchester. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, ee your Magazine for 1876 you published a translation, by me, of a short paper written by M. Mendelejeff which ori- ginally appeared in vol. Ixxxi. of the Comptes Rendus, p. 969. In this paper Mendelejeff drew attention to the “ periodic law ”’ announced by him in 1869, according to which “ the proper- ties of the elementary bodies, as also the properties and con- stitution of their compounds, are periodic functions of the ato- mic weights of the elements.” In accordance with this hypo- thesis, the elements may be arranged in certain groups ; remarkable relations are shown to exist between the proper- ties of the members of each group. The third group com- 282 Mr. M. M.- Pattison Muir on Gallium. prises certain of those elements which form oxides having the general formula R, Os, viz. boron, having the atomic weight of 11, aluminium = 27, yttrium = 88, indium = 118, didy- mium =138(?), erbium =178(?), and thallium =204. But when this group is compared with others with which it ought (theoretically) to present certain analogies, it becomes evident that there are several gapsin the series. These gaps M. Men- delejeff has filled with hypothetical elements. Two vacant places occur between aluminium and indium ; to the second of these the hypothetical metal ekaaluminium is assigned. The analogies between this metal and aluminium, on the one hand, and indium, on the other, should be, according to theory, somewhat the same as those existing between zinc and magne- sium and cadmium, or arsenic and phosphorus and antimony. In the paper already referred to, the theoretical properties of ekaaluminium and of some of its salts are detailed. M. Men- delejeff then puts forward the suggestion that the new metal gallium, discovered August 3, 1875, by M. de Boisbaudran, is very probably no other than the hypothetical ekaaluminium. | Since the publication of Mendelejeft’s paper, various notes on gallium and on its salts have been published by the discoverer. In many respects the observed properties of this metal corre- spond with the properties which Mendelejeft’s theory assigns to ekaaluminium. | have tabulated the leading properties of gallium and of its salts, and have placed alongside of these descriptions others, of the properties of the analogous salts of aluminium and indium. I have also tabulated a few of the hypothetical properties of ekaaluminium as detailed by Men- delejeff in the paper already referred to. M. de Boisbaudran does not apparently altogether accept the position assigned to ekaaluminium for his new metal gal- lium. further researches must of course be forthcoming before a decided opinion can be given. Would it not be well that these researches should in the first place take the direc- tion indicated by the hypothetical properties of ekaalumi- nium? Mendelejeff’s hypothesis is at least of much value as a guide to future research. I am, Gentlemen, Yours truly, M. M. Parrison Murr. The Owens College, Manchester. February 24, 1877. (o @) Mr. M. M. Pattison Muir on Gallium. le Aluminium. White, very lustrous, and very ductile. Melt- ing-point over 400°. Not oxidized in air, even at highest temperatures. When in divided state, burns easily in oxygen. Specific gravity 2°67. Not attacked by nitric, but readily soluble in hydrochloric acid. So- luble in potash or soda with evolution of hy- drogen. Precipitated by sul- phuretted hydrogen from neutral or alkaline solutions. Solutions precipitated by sodium carbonate (see column 2). Chloride deliquescent ; solution yields precipi- tate (hydrate) with am- monia, insoluble in ex- cess, but soluble in caus- tic potash or soda. Sulphate easily solu- ble in water, and yields an alum with ammonia or potash. 9 ale Gallium. Nearly white; when melted, remains as lus- trous white liquid at temperatures below the melting-point of the solid metal. Somewhat malleable: may be cut witha knife. Melting- point= 30°15, Heated to redness in alr, non- volatilized, and but superficially oxidized. Crystallizes in octahedra. Specific gravity 5-956. Hardly acted on by nitric acid diluted with its own volume of water. Dissolved by hot nitric acid. Precipitated from alkaline solutions by electric current. Precipitated by H,S before zine, If solu- tion of sulphides of gallium and zine in hy- drochloric acid be treated with sodium carbo- nate, gallium is contained in first portion of precipitate. Solution containing gallium, alu- minium, and indium precipitated with sodium carbonate, first portions of precipitate contain most of gallium; cannot, however, be thus separated from aluminium: indium comes down only after gallium completely precipi- tated. Precipitable by barium carbonate. Gallium chloride deliquescent and easily soluble: solution becomes turbid on dilution with water; precipitate, probably an oxychloride, is with difficulty soluble in hydrochloric acid. Gallium sulphate non-deliquescent, soluble in water. On addition of ammonia and evapo- ration an alum is formed. Solutions of chloride and sulphate yield pre- cipitates (hydrates) with ammonia which are partially soluble in excess of the precipitant. i 9 vo. Indium. Silver-white, ductile, very lustrous. Melting- point = 176°. Un- changed in air at ordi- nary temperature; burns when strongly heated in air. Specific gravity = 7:3-7:4. Insoluble in nitric acid: dissolved by dilute hydrochloric or sulphuric acid. Precipitated from neu- tral solutions, or from solutions containing acetic acid by sulphu- vetted hydrogen. Solu- tions precipitated by sodium carbonate (see column 2). Also by am- monia; latter precipitate insoluble in excess, but dissolved by caustic potash or soda. Chloride very deli- quescent; forms oxy- chloride by heating; soluble in water. Sulphate non-crystal- line. Solution in water apparently forms double salts (alums) with po- tassium sulphate. INI I i sc Gk a a Be ee en a 4. Hypothetical Ekaaluminium. Should be readily obtained by re- duction. Nearly non-volatile. Melt- ing-point tolerably low. Specitic eravity =5'9. Not acted on by air; will decompose water at a red heat. Slowly attacked by acids or alkalies. Hydrate amorphous, insoluble in water, but soluble in acids or alkalies, Solutions should yield precipitate with barium carbonate, Will form a potash alum more soluble, but less easily crystallizable, than the corre- sponding alaminium salt. Formula of oxide, El,O,; chloride, El, Cl,. I do not add the remaining proper- ties of ekaaluminium, because the re- searches of De Boisbaudran upon gal- lium do not allow us to say whether these properties are characteristic of the new metal. If one were to tabu- late the properties of zinc, magnesium, and cadmium, as also those of arsenic, phosphorus, and antimony, I think the general analogies of each of these eroups with the group aluminium, callium, indium would, even now, become apparent. Further, | think that the hypothetical properties of Mendelejeff’s ekaaluminium show a remarkable coincidence with those of eallium, so far as the latter have been examined. [ 284 | XXXIX. Short Reports from the Chemical Laboratory of Tri- nity College, Dublin (Nos. 2 and 3). By J. Eurrson- Reynowps, I.D., MRLA., Professor of Chemistry, Uni- versity of Dublin®. No. 2.—On Franklandite, a new Mineral Borate. ANY analyses have been made from time to time of sodio-calcic borates, brought chiefly from the Peruvian province of Tarapaca. Most of the analyses seem to show that the specimens of borates examined were mixtures of some predominant mineral, such as the well-defined Ulexite, with varying quantities of one or more borates containing a larger proportion of sodium than Ulexite. I have lately had the op- portunity of examining a specimen of a borate from Tarapaca which has the same components as Ulexite, namely sodium, calcium, boron, oxygen, and water, but which is much richer in alkali than that mineral, and which seems to be a nearly pure specimen of the mineral with which I supposed Ulexite to be often associated. The specimen I analyzed was brought from Peru by Mr. Graves, and was kindly placed in my hands for examination by the Rev. Dr. Haughton. The specimen consists of a felted mass of long, thin, inter- laced fibres, which are white in colour and possess a silky lustre. Under the microscope, the fibrous crystals taken from the cleanest portions of the mass were seen to be free from any but traces of granular coating, and presented the same general aspect. The hardness is not greater than 1 ; and the specific gravity proved to be 1°65. The mineral is easily fused, first losmg much water. The taste of the mineral is first slightly saline, owing to the presence of a little admixed common salt, and is afterwards somewhat alkaline. It is slightly soluble in water, but is easily and almost completely dissolved by dilute hydrochloric and nitric acids, the minute residue consisting of particles of clay. When portions of the mineral mass were digested with nearly ice-cold water, a sensible quantity of chloride was dissolved out. The solution, evaporated on a glass micro- scopic slide, afforded the well-known crystals of sodic chlo- ride. A little calcium was also dissolved by the water. In some of my earlier experiments upon this body I was led, through the carelessness of a junior assistant, to suppose that the percentage of chloride present was much greater than it is * Communicated by the Author, having been read before the Royal Trish Academy. On Franklandite, a new Mineral Borate. 285 shown to be in the analysis given further on. The specimen taken for this analysis was carefully picked by myself from the best parts of the mass and the selected portions then mixed. The analytical process was conducted in the following way :— A weighed quantity of the borate was dissolved in pure dilute nitric acid ; to the solution excess of silver nitrate was added, and the precipitated chloride of silver filtered off and de- termined. The excess of silver was then separated from the filtrate by just sufficient hydrochloric acid ; a calculated excess of pure oxalic acid was next added, and the solution then ren- dered alkaline by ammonia. The calcic oxalate thus separated was determined in the usual way. ‘The filtrate from the oxa- late precipitate was then acidulated with hydrochloric acid, and a small quantity of sulphuric acid separated and estimated with the aid of baric nitrate, the excess of the latter being in turn removed by treatment with sulphuric acid. The solution was now transferred to a platinum dish and evaporated to a small bulk, some pure oil of vitriol added, and the heating con- tinued in order to destroy any oxalic acid present. After evolution of gas had ceased, the liquid was allowed to cool and then treated with pure concentrated hydrofluoric acid, and heat applied to volatilize the boric fluoride. The hydrofluoric- acid treatment was twice repeated, and the heating then con- tinued until the temperature ultimately rose to redness. The residue, consisting of sodic and potassic sulphates, was weighed, the potassium present determined with platinic chloride, and from the data obtained the proportion of potassic and of sodic sulphates then calculated. The total water was determined by ignition of a weighed quantity of the mineral in a combustion-tube with pure dry litharge ; the water was collected in a calcic-chloride-tube and weighed, the whole operation being conducted as in the ordinary process of organic analysis. In order to determine by difference the percentage of boric anhydride in the mineral, the small quantity of sulphate pre- sent was assumed to be in the form of calcic sulphate, while the chlorine found was supposed to be combined with the whole of the potassium and with its equivalent of sodium. The residual sodium and calcium were then calculated into their oxides, in accordance with the general practice of mineralogists. The sum of the percentages of impurities, sodic oxide, calcic oxide, and water, subtracted from the hundred parts, then gave the percentage of B, QO; by difference. This result was controlled by a direct determination as potassic boro-fluoride, made in the following way. ‘The borate was dissolved in the least pos- sible quantity of dilute hydrochloric acid ; a slight excess of 286 Prof. J. Emerson-Reynolds on /ranklandite, pure oil of vitriol was then added, and the liquid diluted with twenty volumes of strong alcohol. Calcic sulphate and most of the sodic sulphate separated out; the filtrate when eyapo- rated, after addition of an excess of pure potassic hydrate, was treated with pure hydrofluoric acid, the mixture evaporated to dryness, and the insoluble salts washed away from the result- ing potassic boro-fluoride by solution of potassic acetate (1 to 4 of water) followed bv alcohol. Hstimation of borie oxide by means of the boro-fluoride is always unsatisfactory, owing to the solubility of the body, and to the large volume of po- tassic acetate solution required for the removal of the saline impurities ; nevertheless it is useful as a check on the indireet determination of the boron compound. The numerical value obtained by the latter method is much more worthy of confi- dence, though probably slightly in excess of the true amount. ixperiment, Theory, «hill IL. i) CMO Es deans 43°61 43°76 (by diff. ) 41°81 (direct) Ga eis ciickue a ldcOon.. pea ho ain Lig. NAO eee palin HAO ye, ese.) ore i 27°66 (Na, K)Cl = SE) ena CaSO,+ 2aq. aS = 1°44 sien 3°85 96°15 100°00 If we exclude the impurities present and deal with the residue only (96°15), the analytical data (1.), when discussed in the usual way, lead well to the empirical formula which may be stated thus, according to the custom amongst minera- ere | 8 Na, 0. SCONCE Oy sna Our insight into the constitution of compound borates is so limited that it is scarcely safe to assign to a new member of the class, as I believe this body to be, a “rational ”’ formula ; nevertheless it is possible to express the composition of the compound in such a way as to exhibit very clearly its probable relationship to Ulexite ; for the two minerals may be thus represented :— Ulexite, [2(Na’/BO,) + 2 He BOs] + 2[ Ca’”( BOs), + 2 H, BOs] + 4) Heo: Franklandite, [2Na’BO, + 2 Na’ BO, ] + 2[ Ca’”(BO,). + 2H; BO; ]+9 Hy O. I have ventured to assign to the new mineral the name a new Mineral Borate. 287 “ Wranklandite,”’ with the permission of the distinguished chemist whose researches on the organo-boron compounds have contributed so materially to extend our knowledge of those interesting bodies. Although the formule given above for the two minerals are not in any true sense “ constitutional,” they make one point clear, namely that the substitution af one molecule of sodic oxide (Nay QO) for three molecules of water is capable of con- verting Ulexite into Franklandite, so far at least as compost- tion is concerned. As a chan ge of this kind can evidently be effected by various indirect means, it is to be expected that mixtures of the two borates in different proportions would be found ; and the observed differences in the analytical results afforded by some specimens of native sodio-calcic borates seem to indicate that such mixtures are not uncommonly met with. No. 3.—On the Composition of Lievrite, as determined by Mr. Harly’s method. Of the several methods which have been devised for the analysis of ferroso-ferric silicates, that which has been pub- lished by Mr. William Early *, Demonstrator of Chemistry in this Laboratory, is probably the most easily managed. The advantages attending o its use are chiefly felt in analyzing sili- cates, which are either insoluble in, or attacked with difficulty by the ordinary acids; but it can silee be used with great con- venience in the analysis of silicates easily acted upon by acids. Lieyrite is a silicate belonging to the latter class ; and as us formula of the mineral is ‘by 1 no means definitely fixed, I r quested Mr. Early to analyze by his method a ‘portion oP a particularly fine crystal which I obtained some time ago from the well-known Elba locality, our chief aim being e deter- mine with precision the welenive amounts of ferrous and ferric compounds present in the specimen. The analysis was conducted in the following manner :— 1:54 orm. of the finely and recently powdered mineral were mixed with 20 cubic centims. of hydrofluoric acid (containing 20 per cent. of real acid) ; and the mixture was boiled for five minutes in a deep platinum crucible with a rather loosely fitting cover. 10 cubic centims. of diluted sulphuric acid (1 part to 2 of water) were then added, and the boiling con- tinued for a few minutes. The contents of the crucible were then waslied into a flask with air-free water, and the amount of iron in the ferrous condition determined as rapidly as pos- sible by standard potassic permanganate solution. Another quantity of the mineral was acted upon by strong hydrochloric acid ; perfect decomposition was effected and a gelatinous * Chemical News, October 9, 1874. 288 Prof. J. Emerson-Reynolds on Lievrite. mass formed; the product was evaporated to dryness, and the silica separated in the usual way. The acid filtrate from the insoluble silica was then saturated with chlorine gas, and am- monia afterwards added in slight excess ; the mixture pro- duced was then boiled in a closely covered beaker in order to remove the excess of ammonia, the solution rapidly filtered, and the precipitate collected and ignited with the usual pre- cautions and weighed. The product contained all the iron as ferric oxide, the alumina, the manganese as Mn; O,, and a trace of silica. The silica was separated from this mixture by hydrochloric acid ; and the filtrate was subjected to the double treatment with pure caustic soda for the separation of alumina. The iron and manganese were then separated by the baric- carbonate method. From the weight of iron thus found, that previously ascertained to be present in the ferrous state was deducted; the difference represented the weight of metal in the ferric condition. The filtrate from the first precipitate caused by ammonia had the calcium separated from it as oxa~ late ; and the latter was determined in the usual way; the filtrate from the calcium precipitate was then evaporated to dryness and the residue heated to expel ammoniacal salts ; the product of this treatment was dissolved with the aid of a few drops of hydrochloric acid, the magnesium separated by means of baric hydrate and estimated, while the alkalies in the filtrate were converted into chlorides and weighed, and the potassium separated by platinic chloride. No trace of lithium was de- tected in the mineral. 2°841 grms. of the freshly powdered and unaltered mineral were heated gradually to redness in a hard glass tube connected with a weighed chloride-of-calcium tube ; a current of dry air was at the same time slowly drawn through the apparatus, The water collected weighed -012 grm. =:422 per cent only. The percentage composition of the specimen analyzed by Mr. Early may be thus stated, when the metallic and. other components are calculated as oxides :— SiQ)) deccepme emcee secant 29-93 DENS YR Ah gs Sale Se ea 31°83 Fe, O, AGUODOOOUOOOO NGO ODOC 20°16 Min @) co Saaeeeeee ares. Gaze 2.02 CPi @ emery os SA ean fal: Wied Ona ass 05d sdoce conan 30 AleiOs wowace cccesewaick 36 SIO) Seer me eretiwrsien eiateces onic 20 INa Oe ences “(he Re Aaa Ag) Oe ee 49 Prof. J. Emerson-Reynolds on Lievrite. 289 These data, when discussed in the usual way, give the fol- lowing ratios :— Siar wecaae =°4983 =3°385 =4:00, Oe teas =-7431=5-74=5-96, RS O, seccee 4 OO = 10: “3 R, O;, 6 RO, 48i0,, where 6 RO=4(Fe, Mn)O + 2CaO nearly, neglecting the small amount of alkalies. As the water present in the particularly pure specimen of the mineral analyzed did not reach 0:5 per cent., it is difficult to admit, with Stideler, that it enters into the molecule of the compound; I therefore prefer to regard Lievrite as an anhydrous silicate. Mr. Early’s analysis of the mineral agrees in all essential particulars with those of Rammelsberg and von Kobell, though both those distinguished observers found slightly more iron in the ferric condition. A comparison of the analyses of different specimens of Lievrite by Rammelsberg, von Kobell, Stiideler™, and Early prove that there is little variation in the proportion of Fey to Fe’; J am therefore disposed to regard the former as an essential constituent of the mineral, rather than asa pro- duct of the oxidation of a calcio-ferrous silicate. That the mineral oxidizes in time there can be no doubt; but I have had a number of specimens of Lievrite under observation for nearly ten years, and though two of them were placed in a rather damp case, they sutfered comparatively slight superficial oxidation. If, then, we admit that Lievrite is essentially a dicalcic- ferroso-ferric silicate, we can assign to it the following sym- metrical formula:— 0 0 Fe” ARE) =ci« Fe! RSG) I LENO? 6 fs ( | Ca” = (FeO Ca” O : O O O Fel ‘Si-O neal \Fe// O O- This formula has at least the merit of indicating that the function of the ferric group is probably one of considerable importance, and that, so far from being regarded as an acci- dental constituent of the mineral, it ought to be considered one of the most important components of the molecule of the compound. ; * See Dana’s ‘System of Mineralogy,’ 5th edition, p. 296. Phil. Mag. 8. 5. Vol. 3. No. 18. April 1877. U cr 290 J XL. On Liquid Vortex-Rings. By Joux Trowsripce, S.D., Assistant Professor of Physics, Harvard College*. 5 ba has often been observed by chemists that a drop of coloured liquid falling from a burette or a capillary tube into a liquid of different specific gravity, in which it can dif- fuse, assumes the form of a ring. Vortex motion, by the researches of Helmholtz, Thomson, and Maxwell, is now attracting so much attention that I have thought that a study of the general equations of motion of matter in connexion with a study of the rings would contribute to our knowledge of vortex movement. Professor W. B. Rogers published in the American Journal of Arts and Sciences for 1858 an ex- tended paper on smoke rings and liquid rings, and described various methods of forming them. ‘This paper seems to have been overlooked by recent investigators. It is a singular coincidence that Helmholtz should have published his great memoir on vortex movements in the same year that the article of Professor Rogers, which details purely the experimental side of the subject, appeared on the other side of the Atlantic. Professor Tait’s method of forming smoke rings, which is also referred to by Sir William Thomson in his paper on vortex atoms, is now well known. ‘The apparatus consists merely of a box closed at one end by a tightly stretched cloth, and haying a circular hole of 6 or 8 inches diameter at the other. Clouds of sal-ammoniac vapour are generated inside the box; and rings are expelled by striking the stretched cloth with the hand. Sir William Thomson suggests that two such boxes, placed so that the rings might impinge on each other at any angle, would form a useful apparatus in studying the behaviour of such rings towards each other. At the conclusion of this paper several methods of studying liquid rings will be described. When a drop of liquid falls from a small distance into a liquid of less density, in which it cannot diffuse, the conditions of its motion the instant after it strikes the surface of the liquid of less density are indicated by the general equation of strainst. ‘‘ For each particle we have the component veloci- ties u, v, w parallel to the fixed axes OX, OY, OZ. These have the following expressions, _ da ‘ds dry Tae! Fiigpncl Ar gee X,Y, &, t being independent variables, and «, 8, y functions of them. If the disturbed condition is so related to the initial condition that every particle of the body can pass from its * Communicated by the Author, having been presented at a Meeting of the American Academy of Arts and Sciences, January 14, 1877. + Thomson and Tait’s ‘ Natural Philosophy.’ U Prof. J. Trowbridge on Liquid Vortex-Rings. 291 initial to its disturbed position and strain by a translation and a strain without rotation, 7. e. if the three principal axes of the strain at any point are lines of the substance which retain their parallelism, we must have dB _dy dy _de da_ dB. (1) Getiny cade adie andi ia wi al and if these equations are fulfilled the strain is non-rotational, as specified ; but these three equations express neither more nor less than that adx + Bdy + ydzis the differential of a function of three independent variables.’”’ In other words we have a strain-potential; and in the case of strains rotation is incon- sistent with the existence of a strain-potential. The forces which solicit the particles of a drop when it rests upon the liquid of less density, in which it cannot diffuse, are evidently their mutual attraction, a force arising from the superficial tension of the liquid upon which the drop rests, and a force arising from gravitation. It is evident from a consideration of these forces that, after the drop has suffered a strain at the liquid surface, every particle of the drop cannot pass from its initial position to the next following position by a translation and a strain without rotation; for the drop tends to return from a shape approaching an oblate spheroid to that of a sphere. Then equations (1) do not hold, and a strain-poten- tial does not exist, and the drop must rotate. This rotation is not in general of the ring-form. If, on the contrary, the drop of liquid can diffuse itself in the liquid through which it falis, each particle, with the velocities wu, v, w, is solicited at the moment of impact by a superficial tension, by the force of gravitation, and, on account of the tendency to diffuse, the forces of attraction which tend to make the non- diffusing drop reassume the spherical shape are very small. To assume that each particle of the drop, in the next state to that which it assumes on striking the free surface of the liquid, is translated without rotation, is to assume that each particle is compelled to move in restrained limits which do not exist. If we follow the notation of Poisson* and Helmholtzt, we shall have for the general equations of motion of an internal particle of a liquid, dp dw, du du-~ du Pu alsa deni: denser 1 dp dw dv dv dv ay Nat Mag hah 2 ae saa C5) 1 * Traité de Mécanique. t+ Crelle’s Journal, vol. ly. 1858, U2 292 Prof. J. Trowbridge on Liquid Vortex-Rings. dh dh dh dh 6h Frage diel ey Waa ye oft) beteeiomimtey: fe (3) du dv , dw dat dy We ae ee es. in which p is the pressure at the point x,y, z, X, Y, Z are the components of the external forces acting on a unit of mass, and fh is the density at the point 2, y, z. The forces X, Y, Z are considered to have a potential V, so that x=) ya 9, 7, and the velocities w, v, w a velocity-potential $, so that _¢ ,_@& |,_o Us; tea dae: aaa RMN 3 (6) or udxz + vdy + wdz=dd ; and @ satisfies the equation PE Ph PS _ da. + dy? de > e e e e e (7) which is equation (4) under the conditions expressed in equa- tion (6). We must also have du dv dv dw dw —-du dy de’ de dy de de? * °° ® Wit uaa rade Ye aaa de equations similar to equations (1). Helmholtz has shown that in the case of rotation of a fluid-element, equations (8) become “ Pk = =7E ’ | oH iy, Vs ye err ada fe “‘ and therefore the existence of a velocity-potential is inconsis- tent with the existence of rotation of the fluid-element.”” We have also seen from the equations of strains that the existence of a strain-potential is inconsistent with the rotation of a ma- terial particle ; and therefore, from the conditions of impact, the particles of a drop of diffusing material are in a condition to rotate. Let us now see if vortex movement can arise in a liquid from variation of density and pressure. Following oo Prof. J. Trowbridge on Liquid Vortex-Rings. 293 Helmholtz’s notation, we have, if is a function of 2, y, z, t, oY dv dp dp, dy ent Ge tus Me ar ash anel ceuc( LON) Calling &, n, § the components of the angular velocity, we can obtain their variations with the time by substituting them in succession in equation (10). If we eliminate X, Y, Z from equations (2) by the help of equations (5), and introduce the values of &, 7, € from equations (9), supposing that h is a function of 2, y, 2, ¢, we obtain eee fae dw dv dw 1 (dhdp dhdp eG a) ast ae tae Ge a ay ae ),an and similar expressions for the variations of 7 and ¢. It will be seen that in this case terms of the form 1 (dhdp dhdp independent of &, 7, 8, and depending upon the variations of h and p, enter into the expressions for the variations of the an- gular velocities; and therefore a vortex movement is to be expected in a process of diffusion by a variation of density and pressure without initial angular velocities. This condition can be shown experimentally by dropping a solution of one of the aniline colours into a mixture of glycerine and water. The original ring, after ceasing to move downward in the mixture, breaks up gradually into segments, which in their turn slowly assume the ring form. A mixture of water and glycerine is not necessary; peculiar cup-like figures, indicating the first stage of vortical movement, can be seen whenever a thin stra- tum of one liquid slowly diffuses itself through another liquid of different density. By a consideration of the equations é cE + (uy —u)dt=e (E+ e dt), en+(v,—v)dt=e¢ (n+ ze at), b+ (on, —w)dte( + = it), given by Helmholtz, from which he draws the conclusion that “each vortex-line remains continually composed of the same elements of fluid and swims forward with them in the fluid,” e see, on introducing the new expressions which we have 294 Prof. J. Trowbridge on Liquid Vortex-Rings. OF bn 8 found for = va a 5p equations (11), that we approach nearer and nearer to this conclusion when the variations of h are smaller and smaller. Obviously we should therefore obtain the most perfect liquid rings when the drop and the liquid in which the motion takes place are composed of the same liquid. A drop of water falling into water must form a more perfect ring than that formed by a drop of any coloured liquid of greater density than water; and every drop of water falling into water from a height not too great must necessarily form a vortex-rin The formation of liquid rings is as fascinating and as simple an occupation as blowing soap-bubbles. All liquid drops fail- ing from such a height that the surface of the liquid in which they are about to ditfuse is not too much disturbed to enable the drop to be acted upon symmetrically by the forces at the free surface, will form rings if too great differences of density do not exist. That a drop of pure water will descend through the same liquid in a vortex ring can be shown experimentally by covering the free surface of the water with a fine light powder. Particles of the powder will be carried down by the drop and will be seen to rotate in a ring-shape far below the surface. This fact can be shown also by the employment of any of the aniline colours which are solvent in water, the drop consisting of a coloured solution whose density does not differ sensibly from that of water. The method which I have em- ployed to produce the rings consists merely of a small glass tube, slightly smaller at one end than the other. herself heard in re- turn ; but this is no failure in the law of reciprocity. The explanation of his observations given by Heury depends upon the peculiar action of wind, first explained by Prof. Stokes. According to this view a sound is ordinarily heard better with the wind than against it, in consequence of a curvature of the rays. With the wind a ray will generally be bent downwards, since the velocity of the air is generally greater overhead than at the sur- face, and therefore the upper part of the wave-front tends to gain on the lower. ‘The ray which ultimately reaches the observer is one which started in some degree upwards from the source, and has the advantage of being out of the way of obstacles for the greater part of its course. Against the wind, on the other hand, the curvature of the rays is upwards, so that a would-be observer at a considerable distance is in danger of being left in a sound- shadow. It is very important to remark that this effect depends, not upon the mere existence of a wind, but upon the velocity of the wind being greater overhead than below. A uniform translation of the entire atmosphere would be almost without effect. In particular cases it may happen that the velocity of the wind diminishes with height, and then sound is best. transmitted against the wind. Prof. Henry shows that several anomalous phenomena relating to the audibility of signals may be explained by various suppositions as to the velocity of the wind at different heights. When the distances concerned are great, comparatively small curvatures of the ray may produce considerable results. There is a further possible consequence of the action of wind (or variable temperature), which, so far as I know, has not hitherto beenremarked. By making the velocity a suitable function of height it would be possible to secure an actual convergence of rays in a vertical plane upon a particular station. The atmo- sphere would then act like the lens of a lighthouse, and the intensity ot sound might be altogether abnormal. This may perhaps be the explanation of the extraordinary distances at which guns have sometimes been heard. The difference in the propagation of sound against and with the wind is no exception to the general law referred to at the be- ginning of this communication; for that law applies only to the vibrations of a system about a configuration of equilibrium. A motion of the medium is thus excluded. But the bending of the sound-ray due to a variable temperature, to which attention has 302 Royal Society:—Lord Rayleigh on the Application been drawn by Prof. Reynolds, does not interfere with the ap- plication of the law. An experiment has, however, been brought forward by Prof. Tyndall, in which there is an apparent failure of reciprocity not referable to any motion of the medium*. The source of sound is a very high-pitched reed mounted in a short tube and blown from a small bellows with which it is connected by rubber tubing. The variation of pressure at the second point is made apparent by means of the sensitive flame, which has been used by Prof. Tyndall with so much success on other occasions. Although the flame itself, when unexcited, is 18 to 24 imches high, it was proved by a subsidiary experiment that the root of the flame, where it issues from the burner, is the seat of sensitiveness. With this ar- rangement the effect of a cardboard or glass screen interposed between the reed and the flame was found to be different, ac- cording as the screen was close to the flame or close to the reed. In the former case the flame indicated the action of sound, but in the latter remained uninfluenced. Since the motion of the screen is plainly equivalent to an interchange of the reed and flame, there is to all appearance a failure in the law of reciprocity. At first sight this experiment is difficult to reconcile with the- oretical conclusions. It is true that the conditions under which reciprocity is to be expected are not very perfectly realized, since the flame ought not to be moved from one position to the other. Although the seat of sensitiveness may be limited to the root of the flame, the tall column of highly heated gas might not be without effect ; and in fact it appeared to me possible that the response of the flame, when close to the screen, might be due to the conduction of sound downwards along it. Not feeling satisfied, however, with this explanation, I determined to repeat the experi- ment, and wrote to Prof. Tyndall, asking to be allowed to see the apparatus. In reply he very kindly proposed to arrange a repetition of the experiment at the Royal Institution for my bene- fit, an offer which I gladly accepted. The effect itself was perfectly distinct, and, as it soon appeared, was not to be explained in the manner just suggested, since the response of the flame when close to the screen continued, even when the upper part of the heated column was protected from the direct action of the source by additional screens interposed. I was more than ever puzzled, until Mr. Cottrell showed me another ex- periment, in which, I believe, the key of the diffieulty is to be found. When the axis of the tube containing the reed is directed to- wards the flame, situated at a moderate distance, there is a distinct and immediate response ; but when the axis is turned away from the flame through a comparatively small angle, the effect ceases, although the distance is the same as before, and there are no ob- stacles interposed. If now a card-board screen is held in the prolongation of the axis of the reed, and at such an angle as to * Proceedings of the Royal Institution, January 1875; also Prof, Tyndall’s work on Sound, 3rd edition, of the Principle of Reciprocity to Acoustics. 303 reflect the vibrations in the direction of the flame, the effect is again produced with the same apparent force as at first. These results prove conclusively that the reed does not behave as the simple source of theory, even approximately. When the screen is close (about 2 inches distant) the more powerful vibrations issuing along the axis of the instrument impinge directly upon the screen, are reflected back, and take no further part in the ex- periment. The only vibrations which have a chance of reaching the flame, after diffraction round the sereen, are the compara- tively feeble ones which issue nearly at right angles with the axis. On the other hand, when the screen is close to the flame, the efficient vibrations are those which issue at a small! angle with the axis, and are therefore much more powerful. Under these circumstances it is not surprising that the flame is affected in the latter case and not in the former. The concentration of sound in the direction of the axis isgreater than would have been anticipated, and is to be explained by the very short wave-length corresponding to the pitch of the reed. If, as is not improbable, the overtones of the note given by the reed are the most efficient part of the sound, the wave-length will be still shorter and the concentration more easy to under- stand*. The reciprocal theorem in its generalized form is not restricted to simple sources, from which (in the absence of obstacles) sound would issue alike in all directions ; and the statement for double sources will throw light on the subject of this note. A double source may be thus defined :—Conceive two equal and opposite simple sources, situated a short distance apart, to be acting simultaneously. By calling the two sources opposite, it is meant that they are to be at any moment in opposite phases. At a moderate distance the effects of the two sources are antagonistic and may be made to neutralize one another to any extent by diminishing the distance between the sources. If, however, at the same time that we diminish the interval, we augment the intensity of the single sources, the effect may be kept constant. Pushing this idea to its limit, when the intensity becomes infinite and the interval vanishes, we arrive at the conception of a double source having an axis of symmetry coincident with the line joming the single sources of which it is composed. In an open space the effect of a double source is the same as that communicated to the air by the vibration of a solid sphere whose centre is situated at the double point and whose line of vibration coincides with the axis, and the intensity of sound in directions inclined to the axis yaries as the square of the cosine of the obliquity. The statement of the reciprocal theorem with respect to double sources is then as follows:—If there be equal double sources at two points A and B, having axes A P, B Q respectively, then the * July 13.—I have lately observed that the flame in question is extremely sensitive to one of Mr. F. Galton’s whistles, which gives notes near the limits of ordinary hearing. 304 Royal Society :-— velocity of the medium at B resolved in the direction B Q due to the source at A is the same as the velocity at A resolved in the direction A P due to the source at BK. If the waves observed at A and B are sensibly plane, and if the axes A P, B Q are equally inclined to the waves received, we may, in the above statement, replace “ velocities ” by “‘ pressures,” but not otherwise. Suppose, now, that equal double sources face each other, so that the common axis is A B, and let us examine the effect of in- terposing a screen near to A. By the reciprocal theorem, whether there be a screen or not, the velocity at A in direction A B due to B is equal to the velocity at B in direction A Bdueto A. The waves received at B are approximately plane and perpendicular to A B, so that the relation between the velocity and pressure at B is that proper to a plane wave; but it is otherwise in the case of the sound received at A. Accordingly the reciprocal theorem does not lead us to expect an equality between the pressures at A and B, on which quantities the behaviour of the sensitive flames depends. On the contrary, it would appear that the pressure at A corre- sponding to the given velocity along A B should be much greater than in the case of a plane wave, and then the relative advantage of the position A would be explained. It will be seen that, if the preceding arguments are correct, Prof. Tyndall’s experiment does not bear out the conclusions that he has based upon it with respect to the observations of the French Commission at Villejuif and Montlhéry. No acoustic clouds could explain the failure of reciprocity then observed; and the more probable hypothesis that the effect was due to wind is not incon- sistent with the observation that the air (at the surface) was moving in the direction against which the sound was best heard. Further experiments on this subject are very desirable. «On Supersaturated Saline Solutions.” By J. G. Grenfell, B.A., F.G.S. In making experiments on the sensitiveness of supersaturated solutions to air and greasy surfaces, | was much annoyed by the solutions so frequently crystallizing on the removal of the cotton- wool, as this necessitated boiling the flask again and waiting till it was cool. I noticed that frequently part of the cotton-wool adhered to the mouth of the flask; and it struck me that, in removing this, some fibres must get detached and fall in, carrying with them in all probability crystals of the salt. I soon convinced myself that this was the case, and that cotton-wool is perhaps the worst material that could be chosen for covering these solutions. I now always use paper or tinfoil; and I find that these can be removed many times from the same solution without inducing crystallization. I then found that even the most sensitive solu- tions could be taken up in a clean glass tube and dropped on a clean glass plate without crystallizing, and that they will remain liquid exposed to the air for a very long time, often, in fact, till they dry up by evaporation in modified forms. Twenty drops on a plate give twenty experiments on the effect of air, clean and Mr. J. G. Grenfell on Supersaturated Saline Solutions. 305 unclean surfaces, and evaporation; then the plate is cleaned, and more drops are taken from the original solution till this is used up. The trouble of boiling is thus reduced to a minimum, and the drops can be put upon all kinds of surfaces to test their activity. The slow growth of the modified salts can be watched for hours; and their forms are sometimes peculiar: thus sulphate of soda often gives a single, square, flat pyramid, or a broad well- shaped prism, or occasionally small octahedra round the edge of the drop. The pyramids and prisms change to opaque white when touched, and are apparently the 7-atom salt; the octahedva do not change, and are evidently the anhydrous salt. This fact is interesting, from its supporting the view that it is the anhydrous salt which is in solution. Or, again, a plate with drops may be dried over calcium chloride ; and this sometimes modifies the results, as in the case of ammonia alum. ‘This salt, when allowed to evaporate in air, generally forms a shining semitransparent film of greenish colour with a depression at the top, in which is often a circular opening, while inside small globular concretions of a dull, opaque, milky white eolour are formed; these will remain moist inside for a couple of days or more. When touched with the normal salt, the whole drop becomes brilliant opaque white, quite dry, and apparently increases in volume, as the crust often breaks up and curls out- wards. This modified salt is apparently new. I put some drops over calcium chloride: no film was formed, but the drops crystallized very slowly in the globular forms mixed with little, clear, flat, very thin pointed plates which reminded me much of a particular form of aluminium sulphate. When dry all the drops were brilliant opaque white, and retained a good deal of water. Potash alum forms similar films and globular masses. ‘The mother-liquor of the ammonia alum sometimes slowly deposits short, fine, silky needles with a faint milky tinge and small globular masses. JI have only recently adopted the method of using drops, and have not much leisure for working ; but the field is so wide, and the results already obtained have such an important bearing on the theory of the crystallization of these solutions, that I have ventured to put them forward in their present incomplete state. The most commonly received theory is that of which M. de Gernez is the most prominent advocate—that only a crystal of the same salt causes crystallization, and that these are introduced by the air, which is a vast storehouse of crystals of ail kinds. The following experiments seem to support the crystal theory ; but at the same time they clearly show that the quantity of salts present in the atmosphere is indefinitely less than we have hitherto been led to suppose, and, in fact, they bring that quantity down within the limits of ordinary probability. 1. Put drops of a very strong solution of sulphate of soda on a plate on my laboratory table ; waved a newspaper over them for some time, producing a strong current of air: most of them did Phil. Mag. 8. 5. Vol. 3. No. 18. April 1877. xX 306 Royal Society :— not crystallize, and one slowly dried up in octahedra. I have repeatedly of late boiled sulphuric acid in the laboratory, so that there can be no lack of sodium sulphate in the dust. 2. Drew a strong current of air over drops of sodium sulphate in a glass tube: inactive. 3. Drops of sodium sulphate put upon the leaves of many plants in my garden. They slowly evaporated, giving the 7-atom salt. The leaves were covered with dust, as the garden opens on to a road, and the weather has been hot and dry; we are not far from Bristol, so we might expect to find sulphates. 4, Carried sodium sulphate to an upper room; drops on the wash-hand stand, on the window-sill inside and out, on the iron bars outside: all inactive. Washed my hands and spread a drop with the finger on the window-sill, inside: mactive, Three drops crystallized on the mantlepiece, and one on the window-sill. Several drops on the window-frame evaporated as 7-atom salt. 5. Potash alum on a window-sill outside gave a modified film. 6. Sodium acetate put upon the cork of a large bottle which had stood for two years untouched in my laboratory. The drops were quite thick with dust, but remained liquid for more than 24 hours. 7. Other drops of the same put on the fioor of the laboratory, on the dusty corners of the shelves, on paper, on every place and kind of surface I could find: remained liquid in all cases. | 8. Spread a number of drops of the same on a glass plate, covering nearly the whole of it. Made about half crystallize. Left them exposed for three days; they remained liquid, though the normal salt effloresces slightly. 9. Ammonia alum: many drops on a glass plate; they formed films by evaporation; made a good many crystallize, when they broke open, early in the day: carried them out in a high wind to the house of a neighbour, and brought them back; then late at night put a number of fresh drops on the plate, and several of - them remained liquid all night, 10. Sodium carbonate is not affected by any surface in my laboratory. I have spread a drop over a dirty glass plate so as to cover a good many square inches, and it slowly evaporated, giving crystals. Drops on the floor, shelves, bottles, &c. of the laboratory invariably remain liquid. I could give many other instances, but these are sufficient to show that the air does not ordinarily contain these salts, and that it does not readily catch them up and deposit them on all kinds of surfaces; and yet these salts are remarkably sensitive to crystals of the same kind. The effect of using cotton-wool is a good example of this. Another is this:—Touched a crystallized drop of sodium acetate with a pin; passed the pin repeatedly through my coat: active at once. After touching a crystal the finger needs to be washed carefully. Again, sodium sulphate erystallizes almost invariably on any dirty surface in my labora- tory, and ammonia alum generally. Even the sodium acetate crystallizes at times when I am at work with the same salt close by. Mr. J. G. Grenfell on Supersaturated Saline Solutions. 307 Sodium sulphate crystallizes generally on a clean plate exposed in my laboratory as 10-atom salt, whilst if protected by an inverted beaker it dries up by evaporation, forming the modified salt. So, again, | have had two drops of sodium sulphate liquid all night, and both crystallize within ten minutes of my entering the room in the morning. In my bedroom, however, I left a test-tube containing this solution open all night with the pipette on the mantlepiece. In the morning the solution had not crystallized, while the end of the pipette was covered with a white incrustation, which was inactive in the liquid. The incrustation was again left to dry up, and then contained plenty of water, being evidently the 7-atom salt. For sodium acetate and carbonateitis quite useless to have any cover on the flask or test-tube which contains them, and also for the sulphate in an ordinary room. Care must be taken that crystals are not formed near the mouth of the tube, so as to fallin; but that is the only precaution necessary. Carbonate of soda by evaporation becomes oily like sodium and potassium acetates. I have not yet investigated the composition of the films and crystals which these solutions deposit. Normal sodium acetate when heated leaves a white mass which deliquesces, forming a strongly supersaturated solution. The an- hydrous sulphate also forms a supersaturated solution when added to water, as De Coppet pointed out. I touched a drop of the acetate with the point of a penknife; a little drop crystallized on the penknife, but the drop itself did not, I then repeatedly touched the surface of the drop rapidly with the solidified part and obtained a little rod, formed of separate layers and nearly 4 inch long. At last the rod broke in the drop which instantly crystallized. J have repeated this with carbonate of soda. The factis interesting as showing how very local the crys- tallizing force is. Faraday had an idea that this force might pos- sibly be transferred by wires; but 1 have poured out part of a solution which was crystallizing into a test-tube, where it remained supersaturated. Professor Tomlinson has long maintained with great ingenuity the theory that the cause of crystallization in these solutions is adhesion. To a surface covered with a film of greasy matter the salt adheres, while the liquid does not, and therefore separation follows. I donot think that theory can be sustained in the pre- sence of the following facts :— 1. Rubbed the finger on the palm of the hand, and took up solu- tion of alum from a drop, and deposited on another part of the same plate: inactive. 2. Rubbed oil on the palm of the hand, and repeated: again in- active. 3. Smeared oil over a glass plate: inactive to drops of alum. 4. Rubbed oil on the finger; took up some sodium carbonate, and rubbed it hard on the plate: inactive. 5. Repeated this with sodium acetate. X 2 : 308 Royal Society -— The mere fact, however, that the salts are, as arule, perfectly in- sensible to every kind of surface, wood, paint, paper, glass, and dust of all kinds, seems to me fatal to this theory. A solution of one part of normal sodium sulphate m about six of sulphuric acid possesses some curious properties. This solution, which sets quite firm, can be kept for a week in an open beaker, so that the air apparently has no crystals to introduce; and yet when dropped on to a dirty surface in my laboratory it more often crystallizes than not. It is thus much more sensitive than an aqueous solution of sodium carbonate or acetate. ‘The crystals are apparently a hydrate of the hyperacid salt NaH, (SO,), ; and it is almost inconceivable that the dust should contain crystals of this salt. It is extremely deliquescent, and the excess of acid should certainly be taken up by the dust, and very often by the surface itself. The solution sometimes crystallizes suddenly in the test-tube as though something had fallen in. The crystallized drops will not stand exposure to air for more than 30 minutes or so. Hence, although there is plenty of sulphuric acid in my laboratory, where I have often heated this solution, I find it very hard to believe that the salt exists in this form in any part of the room. The normal salt and the anhydrous salt are without action on the solu- tion. It crystallizes in a test-tube in fine stellate masses, with projecting points on all sides, as alum sometimes does; these ulti- mately coalesce. These erystals are composed of very fine parallel fibres like ferns, and are opaque white. It sometimes sets in long fibres, radiating from different points like aluminium sulphate. Owing to the fineness of the fibres it would be very difficult to free them trom the mother-liquor. My reason for believing them to be a hydrate is this:—In a beaker this solution gradually deposits clear crystals, varying from very fine needles to rhombic plates, prisms, and short, nearly glo- bular, highly modified forms. These are formed near the top, and may perhaps be different hydrates. They are formed, however, at the same time, and at present I believe them all to be the hyper- acid salt. Similar ones are formed by putting the normal salt in the 6 to 1 solution, and this remains liquid, sometimes dis- solving the crystals. An opaque amorphous mass is formed at the same time, which appears to be hydrated, but it also is inactive. A mixture of two parts of acid to one of salt in a flask, when boiled to get rid of all water, sets firmly in a clear mass, in which the opaque variety makes no change. ‘Then if a little water is added the salt turns opaque white wherever the water reaches ; and this is entirely absorbed, the cake remaining quite dry. if this is again melted it deposits clear prisms, leaving a little mother-liquor ; but the opaque variety when introduced from the 6 to 1 solution causes the whole mass to set firmly opaque white and become quite dry. The opacity spreads slowly, and a kind of beard of fine crystals can sometimes be seen growing round the prisms at the edge. Lovely foliated films are often formed at the Mr. J. G. Grenfell on Supersaturated Saline Solutions. 309 same time. The clear crystals are inactive in the 6 to 1 solution, while the opaque is active ; and this isa clear proof of their identity. Solutions of intermediate strength between 2 to 1 and 6 to 1 often deposit in flasks the whole excess in clear crystals, which are sometimes inactive in the 6 to 1 in a test-tube. It is almost im- possible to obtain these solutions supersaturated in flasks, though it may be done with the utmost facility in test-tubes. Out of many trials with one flask I only succeeded once by leaving it to cool on the sand-bath. Ina test-tube they give the same forms as the 6 to 1. The variety of the forms in which these‘ solutions erystallize is truly astonishing, according to tbe preportion of acid and salt, amount of water, and the temperature. A flask once .gave the most exquisite little, flat, open flakes closely resembling snow-flakes ; but I have not been able to reproduce them. In short the relations of these two substances to each other want working out thoroughly. A certain amount of acid added to the salt which is in excess gives a thin liquid, which will not erystal- lize, and a little fine white powder, the anhydrous salt. Two drops of acid in a test-tube half-full of solution cause drops to eya- porate on a plate in octahedra; and when the anhydrous is thrown down on heating the test-tube locally after crystallizing, it is redis- solved, leaving, however, well-marked octahedra just before it all disappears. The most curious property, however, of the 6 to 1 solution is this :—On a clean glass plate it can be spread out into a thin covering of the plate with the handle of a tooth-brush; then with the end of a glass rod scratch a letter hard on the plate, and the letter will come out at once in slowly growing crystals. The effect is certain with the right proportions, and is most striking, as a plate of any size can be used. Scratching has the same effect when the solution is placed on gold or copper, but not on plati- num foil, lead foil, bone, gutta percha, or any soft substance. The effect is of course analogous to that of scratching on the ammonio- magnesic phosphate and on soda water in a clean tumbler. Mr. Tomlinson explains these by supposing that a partial vacuum is formed into which the salt and gas separate. I confess it seems to me more probable that the result is due to vibration. With the same solution of sodium sulphate in acid, but of different strength, scratching is active, and I have tried it in vain on many aqueous solutions. I cannot see why the vacuum should not act equally on all; but it is easy to understand how the molecular vibrations of one un- stable system should be affected by a particular set of vibrations, whilst those of another system should not. The results obtained thus far, then, are :— 1. Exposure to air and dust has no effect on some supersa- turated solutions. 2. The sulphates are the most sensitive. Exposure of a clean glass plate for half an hour to the air of my laboratory caused nearly all the drops of sodium sulphate put upon it to crystallize at once, whilst the same plate recently cleaned is quite inactive. 310 Royal Society. 3. Even the sulphates are unaffected by the dust of the open air and generally of ordinary rooms. 4. Anhydrous salts or modified salts, sometimes new, are pro- duced by the spontaneous evaporation of the solutions in drops. 5. Drops can be rapidly touched on their surface with crystals of the same salt without crystallizing. 6. Greasy surfaces, whether films or lenses, have no effect. 7. The shape of the vessel has sometimes a material influence on the possibility of obtaining a supersaturated solution. 8. Air and dirty surfaces are active on salts which apparently cannot exist in air. 9. Scratching a hard surface will cause a particular solution to crystallize. The crystal theory, modified as it now must be, seems on the whole the best explanation of the phenomena. The case of the hyperacid sodium sulphate, however, remains to be explained. If the crystal theory is true, the order of sensitiveness of the solu- tions should be the order of comparative rarity of the salts; and this remains to be proved. As to the cause of supersaturation, a good many facts seem to show that it is the anhydrous salt which enters into solution. The lower hydrates seem to be first formed, as in the case of sodium sulphate and the alums. In the case of the hyperacid sodium sulphate with two parts acid to one of salt, repeatedly boiled, it seems to be the anhydrous salt which is first deposited. When the aqueous solutions of sodium sulphate and the alums are made to crystallize, the modified salts become opaque white, while the hyperacid salt remains unchanged, and can be obtained unchanged by heating the opaque variety from the top so as to dissolve this, but not the anhydrous. Against the theory that it is the anhydrous sodium sulphate in solution at low temperatures must be set the following fact. Lowel, in his Tables of the solubility of the three forms of sodium sulphate, which are found in all our text-books, gives 412 parts of salt to 100 of water as the maximum solubility of the 10-atom salt; and this is the highest number for any of the three kinds. Now I have dissolved 600 parts of 10-atom salt in 100 of water at 37° C. without throwing down a trace of anhydrous. I then warmed it: at 45° a doubtful trace of anhydrous; at 51° very few ; at 60° still very few ; at 67° about as much as would lie on a little-finger nail; at 75° eight or ten times as much, the liquid nearly opaque; at 80° a large quantity; boiled, the salt thickly covered the bottom of a large flask. Now here the solution at 60° practically retained the whole of the 6 oz. of salt to 1 of water, while according to Lowel it should have retained only 25 OZ. Then between 70° and 80° a sudden change takes place, and a large quantity is seni down. This agrees so far with Loéwel’s Table, as, according to him, at 84° the whole of the excess was practically thrown down. This looks very much like dissociation Geological Society. 311 taking place at that temperature; and that would involve the supposition that it was the 10-atom salt in solution before. The difference in our results springs from the different modes of working. Lowel always maintained a large excess of anhydrous present, whilst I added the salt in small portions, carefully avoid- ing throwi ring down any anhydrous. ‘This is pretty easily done by keeping up a very rapid motion so as to prevent the liquid from getting heated too much at any point. It seems to me that in any case, as the six ounces fairly dissolved, the solubility of the 10-atom salt should be given in those proportions. Further experiments would, I have no doubt, give still higher figures. dn conclusion, I would remark that if the crystal theory of these solutions be accepted we have a test of great delicacy in these drops for the presence of the salts. Interesting experiments might be made as to the power of air to disseminate crystals of a salt thrown into it in fine powder. De Coppet has already remarked that the mass of a solution exerts some influence on its crystallization, and I have shown that the form of the vessel also has a decided effect. The effect again of different vibrations on different solutions is worth trying, as there seems to be no reason why the hyperacid sodium salt should be an exceptional case. A good deal of work has yet to be done before we arrive at a satisfactory explanation of these obscure phenomena. GEOLOGICAL SOCIETY. [Continued from p. 236. ] February 7th, 1877.—Prof. P. Martin Duncan, M.B., F.R.S., Pre- sident, in the Chair. The following communications were read :— 2. “On new Species of Belemnites and Salenia from the Middle Tertiaries of South Australia.” By Ralph Tate, Esq., F.G.8., Pro- fessor of Natural Science in the University of Adelaide. 3. “On Mawsaurus Gardneri (Seeley), an Elasmosaurian from the baseof the Gault at Folkestone.” By Harry Govier Seeley, Esq., F.L.S., F.G.S8., Professor of Geography at King’s College, London. February 21st, 1877.—Prof. P. Martin Duncan, M.B., F.R.S., President, in the Chair. The following communications were read :— 1. *‘ On possible Displacements of the Earth’s Axis of Figure pro- duced by elevations and depressions of her surface.” By the Rev. J. F. Twisden, M.A., Professor of Mathematics in the Staff College. The object of this paper is to discuss the question of the possi- bility of a displacement of the earth’s axis of figure under the con- ditions indicated in a question (suggesting the possibility of a dis- placement of the axis of figure from the axis of rotation amounting to 15° or 20°) put to mathematicians in a passage of the Anniversary Address delivered to the Geological Society by its President, J. 512 Geological Society :— Evans, Esq., on the 18th February, 1876. The treatment of the question is kinematical; the forces by which the elevations and de- pressions might be effected do not come under discussion. In de- termining numerically the amount of the deviation from the formulas investigated, approximate numbers seem to be sufficiently exact for every useful purpose. ‘The conclusions arrived at are as follows :— (1) The displacement of the earth’s axis of figure from the axis of rotation that would be effected by the elevations and depressions suggested in the question above referred to would be less than 10’ of angle. (2) A displacement of as much as 20° could be effected by the elevations and depressions of the kind suggested only if their heights and depths exceeded by many times the height of the highest mountains. (3) Under no circumstances could a displacement of 20° be effected by a transfer of matter of less amount than about a sixth part of the whole equatorial bulge. (4) Even if a transfer of this quantity of matter were to take place, it need not produce any effect, or only a small effect, on the position of the axis of figure; e. g. if it took place in a way resem- bling that suggested in the question, it would produce a displace- ment amounting to but a small part of 20°. (5) If, however, we suppose a deviation of the axis of figure from the axis of rotation amounting to as much as 20° to have been by any means brought about, the effect would be to cause a sort of tidal motion in the ocean, the greatest height of which would tend to be about twice the depth of the ocean. ‘The author suggests as pro- bable that the effect of this tendency would be to cause the ocean to sweep over the continents in much the same way that a rising tide sweeps over a low bank on a level shore. (6) The notion that a large deviation of the earth’s axis of figure from its axis of revolution may be effected by elevations and accom- panying depressions is at first sight an inviting way of bringing polar lands into lower latitudes, and thereby accounting for the more genial climate that is believed to have once prevailed in such countries as Greenland. The investigation by which the above re- sults have been obtained seems to show that the desired explanation is not to be sought in the direction indicated by Mr. Evans’s question. Whether there is any other agency by which a gradual displace- ment of the pole geographically could be effected is a question of far wider scope than that discussed in the present paper, and one which the author does not profess to determine *. 2. ‘* Note on a Specimen of Diploaylon, from the Coal-formation of Nova Scotia.” By J. W. Dawson, LL.D., F.R.8., F.G.S. * The first draught of the paper, of which the above is an account, was drawn up last August, and was shortly after sent to Mr. Evans. It was written independently of the wider view of the subject taken by Sir W. Thomson in: his Address delivered at the last Meeting of the British Association, and by Mr. G. Darwin in his paper, of which an abstract has been published in No. 175 of the Proceedings of the Royal Society. On the Beds between the Gault and Upper Chalk. 3138 March 7, 1877.—Prof. P. Martin Duncan, M.B., F.R.S., President, in the Chair. 1. * On the Vertebral Column and Pelvic Bones of Pliosaurus Evansi (Seeley), from the Oxford Clay of St. Neot’s, in the Wood- wardian Museum of the University of Cambridge.” By Harry Go- vier Seeley, Esq., F.L.S., F.G.S., Professor of Geography in King’s College, London. 2. “Supplementary Notes on the Fauna of the Cambridge Green- sand.” By A. J. Jukes-Browne, Ksq., B.A., F.G.S. 3. “ On the Beds between the Gault and Upper Chalk, near Folkestone.” By F. G. Hilton Price, Esq., F.G.S. The author described the characters presented by the beds be- tween the Gault and Upper Chalk near Folkestone, indicated the fossils contained in them, and their range in this division of the Cretaceous series, and discussed the classification of the deposits, and their equivalence with those recognized by other writers. His conclusions are shown in the following tabular arrangement :— F. Drew in Whitaker's D’Orbigny. Survey Memoir. Author’s divisions C. Barrois. and zones. Upper Chalk. (Craie compacte). f & VI. Zone of Holaster\ out flints, 138 SS oO subglobosus, 148 feet. | feet. | S 4 Craie argileuse avec] © | Ra banes durs &Amm. > & ) = rhotomagensis. He cs 2'ft.9 in. | i; Cenomanian, | Zone & Amm. va- | v. Zone of Amm. rho- ic 197 feet. 3S rians, tomagensis. \1 feet. | ey \ errr Sy feels ae! Plocoscyphia me- ness not given ; andrina. say about 30 feet. Marne sableuse zone of Taaie as- per, or Warmin- - ster beds, meandrina. 10 feet. 14 feet. Chalk Marl. II. Zone of Plocoscyphia Craie marneuse I Chalk marl, thick- | | | | ) —— Sah Ga Upper Gault. Reger: Baloo XLII. Intelligence and Miscellaneous Articles. ON DIFFUSION AND THE QUESTION, IS GLASS IMPERVIOUS TO GASES? BY G. QUINCKE. T is usual to attribute to all bodies the property of porosity. Respecting the magnitude of the pores or of the molecules of which the bodies consist we know as good as nothing. It might, however, well be possible that composite molecules, especially those with greater molecular weight, occupy a greater space, and constitute bodies with wider pores, than those whose molecular weight is less. A hydrogen molecule would then occupy the smallest space, and it would be conceivable that hydrogen particles might pass through the pores of solid bodies like glass. Opposed as these views may appear to a now very prevalent hypothesis concerning the nature of gases, the question can only be decided by experiment. For this purpose, I have tried for years to force hydrogen and carbonic acid, by pressures of from 40 to 120 atmospheres, through a glass wall of 1:5 millim. thickness, and to determine, by the loss of weight, the quantity of gas that had passed through. One leg of a V-shaped glass tube was a capillary tube of 200 millims. length, closed above; the other was a tube contracted in the middle and open above, 150 millims. long, 8 millims. in diameter, and its wall 1-5 millim. thick. Into the open leg a drop of quicksilver was put ; upon this dilute sulphuric acid was poured ; into the upper part soine sheet zinc was pushed, which was kept from contact with the acid by the contraction of the tube; and then the open end was carefully closed by fusion at a glass- blower’s lamp. Tour tubes thus prepared underwent a double weighing ; and then, by inclining the tubes, the sulphuric acid was brought into contact with the zinc. The pressure of the hydrogen was shown by the diminution of volume of the air in the capillary tube, which served for a mano- meter. Jts amount on the first day, in the different tubes, was | from 14 to 10 atmospheres, rose in five months up to 27-54 atmo- spheres, and in 17 years up to 25-126 atmospheres. During this time the tubes were many times doubly weighed on an excellent balance ; and exactly the same weight, within from 0-1 to 0°3 of a milligram, was always found (8°2556-16°5461 grams). t Another similar tube, with carbonate of lime and concentrated sulphuric acid, in which the pressure of the carbonic acid gas amounted on the first day to 21 atmospheres, after five months to 34 atmospheres, and after seventeen years to 44, showed likewise always the same weight (146361 grams). Thus, according to these experiments, a pressure of from 40 to 100 atmospheres cannot, during a Space of seventeen years, force through 1°5 millim. thickness of glass a perceptible quantity of carbonic acid. While at the commencement the concentrated sulphuric acid wetted the glass sides of the tube, and showed a sharp marginal angle (apparently 0°), gradually in the course of years the angle Intelligence and Miscellaneous Articles. a5 has become obtuse, and the acid flows in the tube with condensed carbonic acid like quicksilver in a glass tube filled with air. In the atmosphere of hydrogen the angle at the margin of the dilute sulphuric acid, which at first likewise wetted the sides, has also increased to about 60°. The glass thus appears to have gradually in the course of years, under the influence of the great pressure, become coated with a thin layer of carbonic acid or hydrogen respectively, which exerts a ditferent attraction from that which glass exerts upon the liquid particles at the margim of the surface. A similar film of gas must have been deposited on the surface of the zinc and obstructed the further chemical action of the acid *. In spite of the negative result of these experiments, I might not conclude that the molecules of hydrogen and carbonic acid have greater dimensions than the molecules or the pores of glass. The distance within which the molecular forces of glass act upon the gas particles is at all events greater than the dimensions of the molecules themselves. The pore-walls of the glass may be coated with a layer of absorbed gas which, through the vicinity of the solid substance, has itself become immovable, and hinders the passage of the gas particles from the interior of the tube into the outer air. It is also conceivable that there is in the pores of the glass a drop-forming liquid with strongly curved surfaces, which prevents the outflow of the gas, like as under ordinary conditions mercury does not flow out of the pores of a wooden vessel con- taining it. A similar objection may be raised against M. Traube’s* otherwise ingenious method of determining the relative magnitude of the molecules of a substance from the possibility or not of its passing through a so-called “ precipitate-membrame.” He brings together two substances soluble in water, A and B, which at their surface of contact give an insoluble precipitate. This precipitate forms a thin porous skin or a network. ‘The meshes are smaller, M. Traube thinks, than the smallest particles of one of the substances (say A) which have contributed to form the precipitate ; for if they were larger, molecules of the substance A would go through them to the substance B and stop up the apertures with newly formed insoluble precipitate. According to this, the thin skin of “precipitate-membrane ” represents a sieve, through which only molecules smaller than its interstices, or smaller than the molecules of the substance A, can pass; substances with larger molecules cannot diffuse through this sieve or precipitate-membrane. But herein the fact is lost sight of that the solid formed by the chemical action of the substances A and B will in general, by selective adsorption, hold different quantities of the three sub- stances A, B, and water at its surface. By the thickness of this * Compare Babinet, Ann. de Chim. (2) t. xxxvii. p. 183; Faraday, Quart. Journ. ii. p. 874; Gmelin, Handb, d. Chem. i. p. 126 (1843); L. Meyer, Pogg. Ann. vol. civ. p. 189 (1858). t Reichert und Dubois-Reymond’s Archiv, 1867, p. 87 seqg., “ Experiments for the Theory of Cell-formation and Endosmosis,” 316 Intelligence and Miscellaneous Articles. adsorbed film of liquid, which has become almost solid, the mag- nitude of the pores of the “ precipitate-membrane ” through which the diffusion takes place is again determined; while the thickness of the adsorbed film may depend upon the velocity with which the insoluble substance of the membrane has been produced. This theory of diffusion through sieve-like precipitate-mem- branes is especially supported by experiments with a watery solution of tannic acid and so-called 6 gelatine—that is, ordinary concentrated gelatine solution which has been kept for a long time heated to 100° C. and has thereby acquired the property of remain- ing liquid even after cooling. gelatine to dry adhering to the lower aperture of a short, light funnel blown from a clean glass tube, and then placed the funnel as a float on a five per cent. solution of tannic acid. After three hours a sac, filled with fluid, had formed out of the gelatine, which was bounded by air in the interior of the funnel, and was penetrated by a glass thread introduced into the upper opening of the funnel without injuring the bottom part adjacent to the tannic acid. A portion of the fluid ascended out of the interior of the sac, by the capillary attraction of the glass thread ; and, emptied into a watch- glass, it gave, with chloride of iron, a deep-black colouring. It appears that the gelatine sac contained in its interior at first much, but after a longer diffusion a less quantity of tannic acid. Thus, in contradiction to the theory of the sieve-like precipitate-mem- branes, tannic acid penetrated from without into the interior of the precipitate-membrane covering the gelatine ; and the process of the diffusion of gelatine and tannic-acid solution is much more com- plicated than it is conceived to be by that theory.—Poggendorff’s Annalen, 1877, No. 1, vol. elx. pp. 118-123. ON COSMIC VULCANISM. BY M, TSCHERMAK. The present is in continuation of a previous paper, on the probable mode of formation of meteorites, in which the opinion was expressed that, judging according to our present knowledge, all stellar systems in their development pass through a volcanic ' phase. The crater-form of the lunar mountains, the eruptive phenomena in the sun, the change of brightness of stars, the nature of meteor- ites (which for the most part resemble volcanic tufas) are all facts which, it may be conjectured, are connected by a common bond. “But the attempt to bring these perceptions under one point of view with our experience of terrestrial volcanoes fails, if based on those hypotheses which have recently come to the front. Intelligence and Miscellaneous Articles. 317 One of these hypotheses, which derives the vulcanism of the earth merely from water penetrating into the glowing depths, is unsuitable for such a generalization, because both the phenomena in the sun and the absence of water on the moon are incompatible with its presuppositions. A second hypothesis, which takes for its principle the conversion of work into heat, and, in accordance with Mallet’s experiments, assumes that volcanic phenomena are condi- tioned by the heat arising from the sinking by contraction of the earth’s crust, meets with a not unfounded opposition from many quarters, since the quantity of heat on which this view rests is so insignificant that, according to the calculation of the propounder himself, it could produce in the most favourable case a rise of tem- perature from 15° to 55°C. The assumption made use of by Nasmyth and Carpenter in order to account for the eruptive formation of the lunar craters, when they referred the former volcanic activity of the moon to con- traction of volume in solidifyimg, is also improbable in itself and incapable of general application. On the contrary, an older hypothesis, which has hitherto met with but little notice, is of high importance for the explanation of cosmic vulecanism. It assumes that the volcanic phenomena of the earth are effected by gases and vapours which are contained ab- sorbed in the supposed fluid interior of the earth, and are evolved as it gradually solidifies. It is true that, as remarked by Angelot, who occupied himself with the consideration of this idea, it is not sufficient for the complete explanation of the earth’s vulcanism ; but it completes the explanation which is based upon the penetration of water into the depths in the most important points, especially in its chemical aspect ; and, besides, it admits of application to the other heavenly bodies, in that it represents their eruptive pheno- mena as a consequence of progressive cooling. This view has moreover the advantage over its competitors, that it is already contained in that more general hypothesis set up by Kant and Laplace for the purpose of making intelligible the forma- tion of the solar system. If the production of the heavenly bodies be conceived as an aggregation into spheres of such materials as are represented in the earth, it must be admitted that the formed globes of glowing liquid contain absorbed matters which may be evolved from them in a gaseous form and occasion eruptions. Observations on many glowing liquid bodies, such as volcanic lavas, cast iron, melted copper and silver, &c., show that, especially under a higher pressure, they are capable of absorbing large amounts of gaseous substances, and giving them out again on solidifymg. Accordingly those materials which, according to modern views, are imagined in the interior of the earth and in the neighbouring heavenly bodies, are of such a nature as to evolve masses of gas on cooling. The application of the above to the sun is self-evident. Meteors are derived from very small stars, which in their rapid cooling fall into eruption, and therewith are in part or wholly disintegrated. The surface-features of the moon can in like manner be traced 318 Intelligence and Miscellaneous Articles. back to a voleaniec stage conditioned by its cooling ; and the absence of an atmosphere can be explained by the nature of the materials which, judging from the small specific gravity of that heavenly body, compose its crust and are capable of confining the volcanic va- pours.—Sittzungsh. der Wrener Akademie, math.-naturw. Classe, 1877, No. vu. pp. 62-64. RESEARCHES ON HEAT-SPECTRA. BY P. DESAINS. In a research published in May 1870 I established that, in the solar spectrum formed by a rock-salt apparatus, the heat accom- panying the luminous rays is about one third of the total heat; on the contrary, in the spectrum of incandescent platinum it is only an insignificant fraction of it. The results are similar when refracting prisms entirely of flint glass are employed. I tried in vain to cause this diiference to vanish by transmitting the radiations from the in- candescent metal through more or less thick layers of water. In my experiments the dark portion of the spectrum of platinum had an extent of about 4°; the interposition of a layer of water of 1 centim. thickness reduced to 2° the length of this obscure spectrum, and diminished its intensity to nearly three fourths of its primitive value ; but the luminous heat still remained a very small fraction of the total heat. Greater thicknesses of water shortened the dark region so as to leave it only a much less extent than in the solar spectrum. Spectra obtained with the electric lamp, on the contrary, may be rendered in their totality much more like those obtained with the rays of the sun, In the electric spectrum, at first, heat is found as far as into the blue. De la Provostaye and I verified this fact more than twenty- five years since; and in some recent experiments, the heat in the luminous part of a like spectrum appeared to me to be about one sixth part of the total heat. It is true this ratio is only half of that found in operating with the solar rays; but if we pass the radiation of the electric lamp through from 3 to 4 centims. of water, we notably reduce the calorific intensity of the dark portion of the spectrum, almost without modifying the luminous heat; and this latter then becomes about one third of the total, just as it does in the solar spectrum. The spectrum thus obtained is nevertheless not absolutely iden- tical with the solar spectrum ; in particular, it has less extent than the latter, especially at the violet end; but the curves representing the intensities in the two spectra exhibit only very slight differences from one another throughout the region comprised between the middle of the green and the portion of the dark spectrum sym- metrical with the blue; and this is especially the calorifically effective region. I will add, in conclusion, that the pile employed in the experiments here described consisted usually of 50 large Bunsen elements; sometimes, however, the number of these elements reached 100. Finally, it will not be useless to call to mind that, according to the usual estimates, the vapour contained in an atmospheric column extending vertically to the limit of the Intelligence and Miscellaneous Articles. 319 atmosphere would form, after condensation, a stratum of water the thickness of which would differ but little from 4 centims.— Comptes Rendus de V Académie des Sciences, Feb. 12, 1877, tome Ixxxiv. pp. 285, 286. ON THE POLARIZED LIGHT OF THE RAINBOW. BY PROF. J. DECHANT. Tn vol. clix. of Poggendorff’s Annalen, M. Schiel communicates the observation that the light of the rainbow is completely polarized. This fact had also previously been observed by Tyndall, in 1870, on the occasion of his journey to Algeria*; and he also states the direction of the polarization, saying, ‘‘ The light of the bow could in all cases be extinguished by a Nicol’s prism the greater diagonal of which was placed tangential to the arc.” The phenomenon finds its satisfactory explanation in the reflec- tion of the light at the back of a rain drop. For, in the first place, the direction of undulation of the lght which arrives at the eye from the rainbow agrees with that of the polarized light produced by reflection. If, namely, the light of the rainbow is extinguished by the Nicol with its longer diagonal held parallel to the tangent to the bow, the undulations of the light itself take place in the direction of the longer diagonal, consequently parallel to the tangent. But parallel to the tangent is perpendicular to the plane which passes through the sun, the rain drop, and the eye; hence it follows that the undulations are perpendicular to the plane of incidence. Secondly, however, the angle under which the rays fall upon the posterior wall of the drop is not far from the angle of complete polarization ; for while the latter for water in air amounts to about 37°, the former averages 40°. Calculating according to Fresnel’s intensity-formula (and taking into account the double refraction in the rain drop) the ratio of the intensities of the light whose undulations are perpendicular to, and of that whose undulations are in, the plane of incidence, we get cos? (a—B) ]2 Ee (a+ a where a denotes the angle of incidence of the effective rays, and fh the angle of refraction. This gives for the extreme red rays (n= 1°3317) 24°5, and for the extreme violet (n=1°3448) 34:9. Thus the rainbow appears from 25- to 35-fold fainter when the Nicol is rotated 90° from the position in which the shorter diagonal is held parallel to the tangent of the bow—which certainly comes very near complete extinction when we consider that the secondary bow already appears tolerably faint whose intensity according to the calculation is yet only 24-fold less than that of the primary. Lastly, we can also indirectly, by an experiment, convince our- selves of the correctness of the explanation above given, if we try to obtain a rainbow with a liquid in which light is not so strongly polarized by refiection at the back of a drop as in water. For this purpose we first seek the exponent of refraction of the liquid with which light would be completely polarized. * In den Alpen, deutsche Ausgabe, 1872, 8. 382. 320 Intelligence and Miscellaneous Articles. If B is the angle under which the rays fall upon the back of the drop, and v the refraction-exponent (from air into the liquid), then 4— tan BP =3 poet. : 1G Aa ee But tan 6 must be also equal to . if complete polarization is to enter; from this we find : n=/2=1°414 ose We must now select a liquid whose refraction-exponent is as distant as possible from V 2, consequently oil of cassia for instance, or sulphide of carbon—of which the first is more suitable for producing a rainbow, since, not to mention that its smell is less unpleasant, it more readily scatters in fine drops, which remain longer floating in the air. Calculation gives as the intensity-ratio of the light whose undulations take place perpendicular to, and of that whose undulations are in, the plane of incidence, for the red rays (n = 1:5945) 6:3, and for the violet rays (1n=1°7025) 2°8. In fact, when oil of cassia is scattered in sunlight before a dark background by a current of air driven through a fine glass tube at right angles above another tube which dips in the liquid, a splendid rainbow is seen, the light of which cannot at any intensity be com- pletely extinguished by the Nicol.—Poggendorff’s Annalen, 1877, No. 1, vol. clx. pp. 123-125. ON THE NATURE OF GAS MOLECULES. BY LUDWIG BOLTZMANN, OF GRAZ. Since the assumption that gas molecules behave as aggregates of material points (atoms) led to results not in accordance with ex- perience, it has been dropped by the author, and the hypothesis is adopted that we are permitted, in calculating the push-action of the molecules, to regard as approximately rigid the aggregate which we designate as a single gas molecule, and which may consist of various corporeal and probably also ethereal atoms. He finds, on the basis of his earlier results generalized by Maxwell and Watson, that then the ratio of the heat-capacities of a gas must be 12 when its molecules have a spherical form. ‘The ratio of the heat- ~capaci- ties becomes equal to 1:4 if the molecules have the form of rigid solids of rotation which are not spheres, and 14 if they are rigid bodies of any other form whatever. These numbers appear to ac- cord at least so far with those found by experiment, that it cannot be said that experiment furnishes any confutation of the theory thus modified. It is also pointed out that the values found experi- mentally for the heat-capacity of gases on this hypothesis are in satisfactory accordance with the heat-capacities of solids. It is self-evident that gas molecules cannot be absolutely rigid bodies ; this is disproved by spectrum-analysis. It may be that the vibra- tions which give rise to gas-spectra are only brief agitations lasting during the collision of two molecules, comparable to the sound- exciting vibrations which ensue when two ivory balls strike one another.—Poggendorfl’s Annalen, 1877, No. 1, vol. clx. p. 175-6, THE LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.) MAY 1877. XLII. On Rotation of the Plane of Polarization by Reflection from the Pole of a Magnet. By Joun Kerr, LL.D., Mathematical Lecturer of the Free Church Training College, Glasgow™. 1. IT WAS led some time ago to think it very likely, that if a beam of plane-polarized light were reflected under proper conditions from the surface of intensely magnetized iron, it would have its plane of polarization turned through a sensible angle in the process or fact of reflection. ‘The known facts upon which this expectation was founded are indicated briefly under the five following heads. (1) The effects discovered by Faraday in his famous polari- scopic experiments in the magnetic field. (2) Many instances in optics to this effect—that a reflected vibration may have its character determined wholly or partly by the refractive power of the reflector, or, more generally, by the specific properties of the reflecting body in relation to transmitted light. Imay adduce Brewster’s law of the polari- zing angle, also Fresnel’s theory of reflection from glass &c., a theory which is still accepted and applied in delicate photo- metric work as affording a good expression of facts, and which treats refraction and reflection as closely related parts of one dynamic whole. I may adduce also the laws of reflection from the surfaces of Iceland spar and other birefringent bodies. It is true that in this last case the catoptric effects are extremely faint in comparison with the dioptric—a fact which is clearly unfavourable to the proposed case of reflection from iron, as contrasted with the resolved cases of transmission through * Communicated by the Author. Phil. Mag. 8. 5. Vol. 3. No. 19. May 1877. ¥ 322 Dr. J. Kerr on Rotation of the Plane of Polarization heavy glass &. But I think that the following facts bear with equal or greater force the contrary way. (3) The enormous differences (in relation to magnetic force) between iron and steel on the one side, and Faraday’s transpa- rent diamagnetics on the other. (4) The effects obtained by Verdet in his application of Faraday’s magneto-optic method to the salts of iron. The strongest instance is that of the perchloride. A dense solution of perchloride of iron in wood-spirit gives a rotation of light contrary to, and nearly twice as great as, that given by heavy glass under the same conditions. (5) The known laws of metallic reflection, particularly the fact that silver, zinc, steel, and other metals are distinguished from each other in a perfectly definite manner as reflectors, each metal having specific relations to the principal component vibrations (perpendicular and parallel to the plane of incidence) with reference both to change of phase and change of am- plitude. The preceding facts were sufficient to suggest a plan of pro- cedure, as well as to give me a strong expectation of success. During the month of August last, in the course of some eareful experiments in the direction thus indicated, I obtained several interesting results which appeared conclusive. Soon afterwards I gave a description of the experiments before the British Association. Since that time I have made one or two additional observations, and have got rid of a serious error into which I had fallen in my first view of the facts. In this paper I propose to give an account of all my principal experiments and views upon the subject. And first, for future reference, I shall lay down the sum of the results in one sentence. The new Fact. 2. When plane-polarized light is reflected regularly from either pole of an electromagnet of iron, the plane of polariza- tion is turned through a sensible angle in a direction contrary to the nominal direction of the magnetizing current; so that a true south pole of polished iron, acting as a reflector, turns the plane of polarization righthandedly. Apparatus and Arrangements. 3. The Magnet.—This is an upright horseshoe electro- magnet, and a very good instrument, I think, of its size. Only one limb of the horseshoe is used at a time, the current being sent through one of the coils, and the observations being made on the enclosed core. Hach of the cores is a solid cylindrical bolt of soft iron, 10 inches long and 2 inches in diameter, which is therefore the diameter of each polar surface. Hach by Reflection from the Pole of a Magnet. 323 of the coils weighs 14 pounds; and the wire makes about 400 turns. The particular coil employed in any case is put into cireuit (generally as a double wire of 200 turns) with a small Grove’s battery of only six cells ; and this is the highest power applied in my experiments. In the circuit is placed also a commutator, which is at my hand, so that, while I watch the polariscope, I have the magnetic state of the core under perfect control. 4. Polar surfaces.—These were originally well planed, and perpendicular to the axes of the cores. For the present pur- pose they had to be smoothed and brightened by polishing, a process which I found troublesome and excessively tedious, from the refractory nature of the material. The polishing was done with fine dry emery powder, applied by chamois leather to one of the surfaces, and by a rubber of fine silk stuff to the other. Hach rubber was backed by a flat and smooth block of iron, which was worked carefully by hand over the end of the core. The last stage of the polishing was similar to the earlier stages, but without new additions of emery. When the process was finished, each polar surface (though not such a speculum as would satisfy an optician) acted as a pretty good plane metallic mirror, its plane perpendicular to the axis of the core. Placed in a room in ordinary daylight, each mirror gave good regular images of all surrounding objects that were in any degree illuminated ; and in a darkened room, the image of a neighbouring candle-flame was generally very good, brilliant, distinct, and sharply and truly outlined, except towards the rim of the mirror, parts not used in the ob- servations. ‘The surface that had been finished by chamois leather was rather more brilliant than the other, but not so perfectly well planed. | I should say here that, from all that I have seen in these experiments and in some earlier trials, I consider the finest attainable polish very desirable. In my present apparatus, I would prefer a much finer polish to any increase whatever of magnetic power (3). 5. Placing of the pieces.—The electromagnet is placed on a solid table, near the edge, and is inclined with its polar surface towards the light by means of a small block placed under the stand. The source of light is a paraffin-flame, narrow and very brilliant, distant a foot or less from the polar surface. Close to the flame stands the first Nicol. The beam of plane- polarized light so rendered is incident horizontally (at an angle of 60° to 80° tothe normal) on the polar surface, and is regu- larly reflected. On this side of the polar surface, a few inches distant, comes the second Nicol, which is supported on a lateral We2 324 Dr. J. Kerr on Rotation of the Plane of Polarization stand, and so placed that, when I look fairly through it, I see the image of the flamein the iron mirror. 6. Principal azimuths of first Nicol.—As the polariscope is worked here in the usual way, by restoration from the best possible extinction, there are only two positions of the first Nicol which are suitable to start from. The plane of polari- zation of the light incident upon the iron mirror must be either parallel to the plane of incidence or perpendicular to it, because in every other case the reflected light is elliptically polarized and therefore inextinguishable by the analyzer. I generally make the plane of polarization coincide with the plane of incidence ; and I manage this in the first place very approximately by trial. I lay the first Nicol with its principal section sensibly horizontal. Looking through the second Nicol, and watching the image of the flame in the polar mirror, I turn the second Nicol quickly through the position of mini- mum intensity backwards and forwards, while the first Nicol is turned slowly, also backwards and forwards, until I obtain a minimum-intensity zero. It is a matter of capital importance in the experiments to have the Nicols placed in this position of pure extinction ; and the arrangement is not so easily made as might be supposed. Perhaps it is from imperfection of polish, and perhaps from the very nature and structure of the reflecting metal; but whatever be the reason, the mirror is never perfectly black in the polariscope ; and though the intensity of the illumination is very faint when the Nicols are in exact position, it is still sufficient to embarrass the observer’s judgment when he has to decide between pure extinction and impure. The difficulty can be overcome by a simple and regular process, as will be seen immediately. In the mean time I assume that we can obtain a pure initial extinction in the polariscope. 7. Submagnet.—I have now mentioned every thing that is of any importance in the arrangements, except one condition, without which I have never obtained any optical effect; and that is, an intense concentration of magnetic force upon the iron mirror. For this purpose I employ a block of soft iron, one of several polar pieces belonging to the magnet, 2 inches square and 3 inches long, which has been planed off at one end into a blunt wedge with well-rounded edge. Two splin- ters of hard wood, which have been thinned and toughened by hammering, are laid upon the sloping polar surface about an inch apart, and parallel to the plane of incidence. Holding the wedge in my left hand, I plant it edge downwards upon the splinters, with its rounded edge perpendicular to the plane of incidence, and right above the centre of the mirror. The by Reflection from the Pole of a Magnet. 325 effect of this arrangement is, that when the circuit of the mag- netizing current is closed, there is a very powerful concentra- tion of magnetic force upon the mirror, and particularly on that part of it which is utilized optically in the experiments, on so much of it, namely, as the chink between wedge and core leaves exposed, on one side to the lamp, and on the other side to the observer’s eye. The lines of magnetic force are sensibly perpendicular to the reflecting surface. The iron mirror is a true polar surface; and its intensely contrasted states, as north, south, neutral, are perfectly under control through the commutator. The wedge intercepts a large part of the image of the flame. The pieces are generally so placed that the part left of the image is a strong middle segment, both top and bottom being eut off. ‘The object now watched in the polariscope is a broad streak of light, crossing the chink at right angles from top to bottom, very sharply defined, and perfectly suitable as an ob- ject in delicate polariscopic work. Splinters of different thicknesses are employed in different experiments, and in variations of one experiment. My only rule is, that the chink between block and core be as narrow as the requirements of the optical observation will allow. Onan average, the width of the chink in the following experiments is about 34, of aninch. The arrangements now described (3..7) are shown simply in the adjacent diagram. Le arm ip L is the source of light, E the observer’s eye, A and B the first and second Nicols, C the wedge of soft iron. 8. First experiment.—The pieces arranged as in the diagram, the chink between block and mirror as narrow as possible, the plane of polarization of the light incident on the polar mirror parallel or perpendicular to the plane of incidence, and the second Nicol turned into the position of pure extinction. The observer now watches the chink through the second Nicol, and works the commutator. When the circuit is closed, the streak of light immediately reappears. The effect is very faint at the best; but it is very distinct and perfectly regular, unless the appa- ratus is in some way out of order, the mirror dimmed, or the battery working below its average power. Under ordinarily L 326 Dr. J. Kerr on Rotation of the Plane of Polarization good conditions, at the instant when the circuit is closed, the light shows itself faintly in proper form, size, and position across the formerly uniform chink, and so continues without sensible change as long as the current passes. Break, and the light immediately disappears. Reverse, and the light again appears and continues till the instant of break, when it disap- pears at once. The beam reflected by the mirror of magnetized iron is cer- tainly not plane-polarized, as is the incident beam (and the reflected beam also before magnetization) ; for when the ight is restored by magnetic force from pure extinction as above, it cannot be extinguished by any rotation of the second Nicol in either direction ; nor (as far as I can judge of these faint effects and with the present means) is the light sensibly weak- ened by any such rotation. The analyzer’s position of extine- tion before magnetization is also (exactly or nearly) the posi- tion of minimum intensity after magnetization. In many repetitions of this experiment, the angle of inci- dence varied from 60° to 80°, and was generally about 75°. 9. At this point I must ask the reader’s attention to several terms; and to the sense in which I shalluse them. By a rota- tion of the first Nicol to the right, I mean a rotation which is right-handed (like the motions of the hands of a -watch which faces the observer) when viewed from the point of incidence on the iron mirror. By the north pole of a magnet, I mean “‘that which points, on the whole, from the north, and, in northern latitudes, upwards ”’*. 10. Second experiment.—Taking this experiment as a con- tinuation of the first, and providing for the best effects, I sup- pose all the arrangements as before: I suppose also that make, break, and reverse of the commutator give bright, black, bright in the polariscope distinctly, however faintly. (1) Leaving the circuit open and every thing else untouched, I simply turn the first Nicol ever so little to the right. The amount of the rotation is important. I have said it was ever so little ; and this generally gives effects distinct enough. But when working for the best results, I determine the displace- ment of the first Nicol by this condition, that the intensity of the light restored in the polariscope by the displacement be * Sir W. Thomson’s papers on Electrostatics and Magnetism, § 445, It will be seen from the quotation that this is,no Inovation of mine. Having had this nomenclature brought to my attention recently by Sir William Thomson and very strongly recommended by him, I made it a matter of careful consideration and have determined to adopt it. Like poles of the great Earth-magnet and of our artificial magnets ought to be similarly named ; and the northern pole of the Harth-magnet cannot with any propriety, be called a south pole. by Reflection from the Pole of a Magnet. 327 sensibly equal to that of the light restored formerly by mag- netization in the first experiment. This being done, I watch the faint light in the polariscope, and work the commutator as formerly. But I must now specify the magnetic states of the mirror. When the mirror becomes a north pole, the light flashes up at once to asensibly higher intensity, which is sustained with- out change as long as the current passes. When the circuit is broken and the mirror demagnetized, the light falls at once from the higher intensity to the primitive faint intensity, and so continues as long as the circuit is open. When the mirror becomes a south pole, the light falls from the primitive faint intensity, down either to perfect extinction or extremely near it. In favourable cases of this kind (that is, in cases properly managed and in a well-darkened room) it is very striking to look at the chink through the analyzer, searching in vain for the faintest trace of the streak of light, and remembering the displacement of the first Nicol. When the circuit is finally broken, the light reappears at once as at first. (2) Leaving the circuit open and every thing else untouched, I watch the faint light in the polariscope, and turn the first Nicol backwards to the left, into the position of extinction and alittle beyond it, regulating the amount of rotation by the in- tensity of the restored light as in the first case. I now watch the light through the analyzer and work the commutator. It would be superfluous to describe the magnetic changes of the iron mirror, and the corresponding changes in the polariscope ; the description would be word for word as before, with one essential alteration. It is the south pole that now strengthens the light, and the north pole that extinguishes or weakens it. This experiment is much more easily managed than the first. Let a good sensible extinction of the streak across the chink be obtained by optical trial in the manner already described (6), the plane of polarization of the incident light being either parallel or perpendicular to the plane of incidence ; and let the first Nicol be turned to the right, so far only as to render the extinction sensibly impure. When the three states of the mirror (north, neutral, south) are now made to succeed one another rapidly, the contrast of bright, faint, dark in the po- lariscope comes out in almost every case very distinctly. Very often I have seen the second experiment give clear effects as now described, in cases where, through partial ex- haustion of the battery, the first experiment gave no sure effect whatever. 11. I have given these two experiments as a simple and exhaustive summary of a large number of observations which 328 Dr. J. Kerr on Rotation of the Plane of Polarization were at first very perplexing, so irregular and apparently in- consistent were the phenomena. ‘The chief cause of my per- plexity I found afterwards to be a very interesting thing ; and that was what I may truly call the exquisite delicacy of the magnetic mirror as a test for fixing the position of the plane of polarization of the incident light. One or two simple notes of actual observations will illustrate this point more distinctly than any general statement could do. Things often happened thus. Working as in the first expe- riment and with ordinary caution, I started from good extinc- tion, and found the north pole restoring the light, and the south pole much the same as open circuit. Trying to obtain better initial conditions if possible, [threw the two Nicols well out of position, and worked them carefully back to good extine- tion ; and now, without any other observable change in the conditions, I found things reversed, the south pole clearly re- storing the light, and the north pole much the same as open circuit. Here the magnetic mirror simply detected the impu- rity of the initial extinction, and characterized it, by strong contrasts of intensity in the polariscope, as due to a slight mis- placement of the first Nicol (otherwise barely or not at all detectable), to the right in the first case, and to the left in the second. Working sometimes with one of the mirrors (that which had been polished by chamois leather, and which was not so well planed as the other), at a particular part of its surface, and at large angles of incidence, I found the upper end of the streak clearly restored by the north pole and the lower end not, while the lower end of the streak was clearly restored by the south pole and the upper end not. There can be no doubt that in this case the magnetic mirror detected a slight differ- ence of slope at those parts of the mirror which reflected the upper and lower ends of the streak. Say that the one part sloped a little downwards to the left, and the other a little downwards to the right; then the planes of incidence at the two places would be out of coincidence with the plane of po- larization of the incident light, to the left in the first case, and to the right in the second. Similarly, I have sometimes seen the right side of the streak restored by the north pole and the left side not, while the left side was restored by the south pole and the right side not. Irregularities and inconsistencies of this kind were explained perfectly by the second experiment as soon as it was discovered. Finally, I observe here that the arrangements for the first experiment are best obtained through those for the second ; and this is a point of some practical importance. Arranging by Reflection from the Pole of a Magnet. 329 the apparatus as for the first experiment and with the greatest eare, I find the effects of the two magnetizations unequal in almost every case. Say that the north pole restores distinctly, and the south pole weakly or not at all. Leaving the circuit open, I turn the first Nicol to the left as little as possible, and then bring the second Nicol into the position of extinction, and test by working the commutator and watching the light in the polariscope. Several careful operations of this kind are sometimes requisite. Summary and Interpretation of the facts. 12. In these experiments light is reflected from an iron mirror at an incidence of 60° to 80°, passing through a first Nicol before reflection and through a second Nicol after. Initial conditions.—The iron mirror unmagnetized, the prin- cipal sections of the two Nicols perpendicular and parallel respectively to the plane of incidence. Essential operations.—Starting thus from pure extinction in the polariscope, we apply any one or two of four operations. Two of these are merely mechanical, extremely small rotations of the first Nicol from its initial position, a right-handed rota- tion (R) and a left-handed (L). The other two are physical, intense magnetizations of the mirror, as a north pole (N) and as a south pole (S). These four operations will be named here and afterwards by suggestive and easily remembered letters as above; and they will be grouped in pairs invariably, R and N together, thus: (R, IN); (hi; S). 13. When any one of the operations is applied singly, the light is restored from pure initial extinction in the polariscope. When any two of the operations are applied simultaneously, and their relations determined by comparison of effects in the polariscope, they are found to be conspiring operations if they belong to the same pair, and contrary operations if they be- long to different pairs. Considering, then, any one of the operations, we see that there are two ways of strengthening its effect in the polariscope, and two ways of weakening it. To strengthen the effect of R, apply either operation of the pair (R, N); turn the first Nicol a little more to the right, or mag- netize the mirror as a north pole. To neutralize or weaken the effect of R, apply either operation of the pair (L, 8); turn the first Nicol a little to the left, or magnetize the mirror as a south pole. To obtain a complete interpretation of the facts, we have 330 Dr. J. Kerr on Rotation of the Plane of Polarization only to assume that the immediate optical effects of the four operations (R, N), (L, 8) are similar in kind for all, and similarly directed for those of either pair, but oppositely di- rected for different pairs. Rand L turn the plane of polari- zation; so therefore, according to this view, do Nand 8S. R and N turn the plane of polarization in one direction; Land turn it in the contrary direction. But even from an optical point of view there is still an important difference between the mechanical operations and the physical; for in the one case (R or L) the full effect of the operation is impressed upon the light before incidence, while in the other case (N or 8) the effect is impressed somewhere and somehow in the very pro- cess of reflection. To get a more definite statement of this interpretation, con- sider the pair of conspiring operations (R, N). In the case of operation N, and to an eye which looks into the polar mir- ror, the nominal direction of the magnetizing current round the core is right-handed (9). In the case of operation R and to the same eye, the direction of rotation of the plane of po- larization, or the direction of rotation of the trace of that plane upon the reflecting surface, is evidently left-handed (9). We infer that a right-handed current gives a left-handed rotation of the plane of polarization. And this completes the first ex- perimental proof of the general statement made in art. 2. 14. To test the truth of this view of the facts, | thought of three methods which appeared accessible :—first, to apply each of the four operations (R, N), (, 8), and to characterize them separately by definite compensating actions in the polari- scope; secondly, to apply the operations N and 8S in com- bination with small permanent rotations of the second Nicol ; thirdly, to return to the case of perpendicular incidence, which I had already tried roughly without success. I shall prepare the way for an account of the first of these methods by a short mathematical discussion. Compensation of effects of operation R. 15. Let the angle of incidence be about 75°; and suppose that the initial conditions are as in the first and second expe- riments (12), and particularly that the direction OX of the vibration is perpendicular to the plane of incidence. The ope- ration R being now applied, and the incident vibration being turned thus through a small angle X OC=a, it is required to find the character of the reflected light, particularly with a view to compensation. The two rectangular components (one in O X) of the incident vibration (¢ in OC) are by Reflection from the Pole of a Magnet. 331 t € COS & COS 27F=» i : t c sin @ cos 277 -> T or, more briefly, acos@ and a’ cos8, where @ is proportional to ¢. Let O Y be perpendicular to O X and to the reflected ray; then, to obtain the components and y of the re- flected vibration in the directions OX and OY, we must apply to the preceding components the known laws of metallic reflection. We find thus z=hacos 86, \ (1) y=ka’' cos (9—¢), where h and & are constants characteristic of the reflecting metal. As the angle of incidence is about 75°, and therefore very near the principal incidence, we may put Oem eG (2) Substituting in (1), and representing the amplitudes by 6 and b’, we find DB's —saaDiCOs ty, y=—O' sin 0. (3) From these equations or otherwise we see that the reflected vibration is elliptic, and that its principal rectangular compo- nents are perpendicular and parallel respectively to the plane of incidence. We see also that the elliptic polarization is left- handed in the case of operation R, and right-handed in the case of Li. Hence a simple method of compensating the effect of the operation R, or of the rotation « of the incident vibration. Introduce a difference of phase 5 between the components & and y by means of a quarter-wave plate, and then turn the second Nicol in the proper direction through a small angle which is definitely related to a. This method I have not had an opportunity of trying. To find another method. Let the elliptic vibration (3) be represented by its rectangular components «’ and 7’, in direc- 332 Dr. J. Kerr on Rotation of the Plane of Polarization tions O X/ and O Y’ inclined at 45° to OX; and let a’ =m cos (0—B), y’ =m cos (0—¥). Identifying the second members of these equations with the proper sums of resolved parts of « and y, we find easily m=}(b?+b?), L/ / fanie= et b? tan y= Be And therefore, if 6 be determined by the equation Dass Oe Me tanio= om te =, tana, 5 (s,.cee eee we see that, finally, x’ =m cos (6+58), \ y’ =m cos (@—8),. 9) By any adequate action upon the reflected ray at any point between the iron mirror and the analyzer, let the component x’ be retarded relatively to y’, so as to undergo a relative change of phase equal to 26. As the components 2/ and 7 have already equal amplitudes, and are equally inclined to O X, it is evident that by this change of phase of «’ the elliptic vi- bration (5) is transformed into a rectilinear in the primitive direction O X. And thus the compensation of effect of the operation R is fully effected, without displacement of the second Nicol. If we assign to : the value 4, which is probably near the truth, as its value in the case of steel, measured both by Jamin and by Senarmont, lies between °5 and °6, and if we give effect to the condition: that @ is a very small angle, we find from equation (4), approximately, 20=2 tan—! pian ee ees h h However, it is sufficient for our present purpose to observe that the compensating change of phase 26 is a small quantity de- termined by «, and of the same order as a, and also of the same sign. 16. The Compensator.—tThis is a slip of plate glass held in the hands, and strained either by flexure round its thickness, or by simple tension or compression from the two ends. In the present experiments the slips used were of the best plate, by Reflection from the Pole of a Magnet. 333 7 inch thick, 2 wide, and 73 long, chosen carefully so as to be quite inactive in the polariscope while unstrained. Suppose one of these slips placed between the mirror and the second Nicol, its surface perpendicular to the reflected ray, and its length parallel to O X'; and let the glass be stretched in the direction of its length. Stretched glass acts upon trans- mitted light as a positive uniaxal with its axis parallel to the line of extension. In this case, therefore, the extraordinary component 2’ is retarded relatively to the ordinary y’; and the method found in the last article gives us this simple rule :-— To compensate the effect of a small operation R or L, the incident vibration being initially directed along O X, at right angles to the plane of incidence, and the reflected vibration being initially cut off by the second Nicol. Leaving the second Nicol in its initial position, and placing the compensa- ting slip between the mirror and the second Nicol, its plate faces perpendicular to the ray, and its length parallel to O X’; stretch the slip along its length in the case of R, and compress it along its length in the case of L. The direction O X/ will be taken as the standard direction of strain: itis at 45° to the plane of reflection, right hand down. — 1%. Third experiment.—All the arrangements are as in the first experiment, the angle of incidence about 75°, and the extinction in the polariscope perfect. As the experiment is a purely optical one, the circuit is kept open. To ensure unifor- mity of optical conditions, the block C is kept in position as in the diagram of (7), and the light is viewed through the chink as formerly. (1) The first Nicol is turned righthandedly through a very small angle, and the light is distinctly restored. The compen- sating slip is introduced between the mirror and the second Nicol in the manner which has just been fully described. When the slip is stretched along its length, say between closely gripping finger and thumb at each end, with a force which increases continuously from zero up to a certain small value, the light restored by displacement of the first Nicol fades away to pure extinction, reappearing and brightening as the tension increases. When the slip is submitted to a longi- tudinal compression which increases continuously from zero, the light increases continuously and very distinctly from be- ginning to end of the increase of compression. (2) The first Nicol is now turned to the left, through the position of extinction, and the light distinctly restored; and the compensator, kept always in the standard position, is stretched and compressed as formerly. ‘Things are precisely as in the first case, except that the effects of tension and com- 334 Dr. J. Kerr on Rotation of the Plane of Polarization pression are reversed, and therefore interchanged. It is now compression that extinguishes the light; tension strengthens it from first to last. When the angle of rotation of the first Nicol is too large, which it may be while still very small, the neutralization by tension or compression is incomplete, the light fading to a very sensible minimum and then increasing; but the extinc- tion is still perfect when the initial intensities have reached much greater values than those obtained by magnetization in the first experiment. I found the present experiment a very interesting one, from the simplicity of the means, the purity of effects, and the beautiful distinctness of the contrasts. However, I do not give the experiment here for its own sake. The only use of it is to characterize the effects of R and Lin the polariscope ; and this work it does perfectly. 18. Fourth eaperiment.—The angle of incidence about 75°, and all the arrangements and procedure as in the first experi- ment, with addition of the compensator. As the intensity in the polariscope is very faint at the best, all proper means are ‘adopted for increasing it—the room well darkened, the battery in good order, the surface of the mirror fresh, the chink be- tween wedge and core merely wide enough to give a good object, and the initial extinction sensibly perfect. When the light is restored from pure extinction by the ope- ration N, and the compensator is placed and strained as in the third experiment, the light is weakened by tension and strengthened by compression, and the weakening by tension proceeds to pure extinction. The effect of the operation 8 is, on the contrary, weakened to extinction by compression, and strengthened from first to last by tension. This is the general result; but some precautions had to be taken in the actual experiment. Sometimes heat from the hand, possibly also from the breath, gave rise in the compen- sating slip to strains which had large effects in the polariscope, effects larger indeed than that to be compensated. In such a case the slip was laid aside and afresh one employed. It was found necessary also to keep the plate faces of the slip accu- rately perpendicular to the reflected beam, as a very small displacement from this direction gave a noxious effect. Ob- serving these and other precautions, and working with proper care, 1 found after some practice that the phenomena were perfectly under control. Sitting down in front of the polari- scope, and getting an assistant to hold the submagnet and work the commutator, I bring the compensator suddenly into the standard position, and find the extinction still pure. ‘The cir- by Reflection from the Pole of a Magnet. 335 cuit is now closed, and the light reappears through the com- pensator. I now compress the slip along its length with a force increasing slowly from zero, and find that the light in- creases continuously and very distinctly as the compression increases. I therefore pronounce the mirror a north pole, which the assistant finds right. To verify by the polariscope, I stretch the slip with a force increasing slowly from zero, and find that the light fades to pure extinction and then brightens. The effects are very faint, but quite unmistakable. In the last-mentioned case, for instance, I put the light out of sight by careful increase of the tension up to a certain small value, and keep it out of sight as long as I please by sustaining the force, straining my eye all the time to catch the faintest glimpse, till the instant when the slip is relieved of strain without change of position ; and then the light reappears as at first. Working similarly in another case, I find these optical effects of tension and compression interchanged, compression extinguishing the light and tension strengthening it; and the mirror is found accordingly to be a south pole. 19. Fifth experiment.—This is a repetition of the second experiment with addition of the compensator ; it is more easily managed than the fourth ; and the results are equally convin- cing. In the first half of the second experiment, as already described (10), the three sets of operations applied successively er (R, Jeli R, (R, S)3 and the intensities in the polariscope in the three cases respec- tively were bright, faint, dark. When the effects in the first and second cases are tested by the compensator, exactly as in the third and fourth experi- ments, they are both compensated to pure extinction by ten- sion, and both strengthened from first to last by compression. And similarly in the second half of the second experiment, the single effect of L and the joint effect of L and 8 are both strengthened by tension, and both weakened down to sensible extinction by compression. 20. Summary of the results obtained in the last three expe- riments. The effects of the operations R and L in the polariscope are compensated respectively by tension and by compression of glass in the standard direction: the effect of N is compensated precisely as that of R, and the effect of S precisely as that of L; the joint effect of R and N is compensated precisely as the separate effects of R and N, and the joint effect of Land S$ precisely as the separate effects of L and 8: and in all these cases the compensation proceeds to sensible extinction. 336 Dr. J. Kerr on Rotation of the Plane of Polarization The four operations (R, N), (, 8) were found in the second experiment to be related to one another, two and two, as con- spiring or contrary ; they are now seen to be related to one another more generally, and in the same combinations, as like or unlike. With reference to effects in the polariscope, the operations R and 8 are as clearly unlike as are the operations R and L, or the operations N and 8; and, on the other hand, and with reference always to eftects in the polariscope, R and N are as clearly like as are any two operations R, or any two operations N. It was assumed, in explanation ‘of the facts brought out in the second experiment, that the optical effects of the four operations (R, N), (, 8) are the same in kind for all, and similarly directed for those of either pair, but op- positely directed for those of different pairs. All the new facts agree with this hypothesis and confirm it. It fae been observed already that the effects of the opera- tions R and L are fully impressed upon the light before inci- dence, while the effects of N and 8 are impressed i in the pro- cess of reflection ; but, as far as we can judge from the present experiments (17, 18, 19), and as far as changes of phase of the principal components are concerned, this difference be- tween the mechanical operations and the magnetic has little influence upon the final effect in the polariscope. We may therefore assume provisionally that, as far as changes of phase by metallic reflection are concerned, the rotation due to mag- netic force is impressed effectively before incidence. We come now to the second method proposed in 14. 21. Siath eaperiment.—Angle of incidence about 75°, initial arrangements as in the first experiment, plane of polarization of the incident light sometimes parallel ; and sometimes perpen- dicular to the plane of incidence, initial extinction as pure as possible. (1) Leaving the first Nicol untouched, I turn the second Nicol righthandedly through a very small angle; and watching ta) oS the faint light thus restored, | work the commutator as for- merly. The operation N strengthens the light; and this effect is distinct and regular. The operation 8 “has sometimes no effect, and sometimes weakens the light, always less distinctly than N strengthens it, and generally less and less distinctly as the rotation of the second Nicol is diminished. (2) The second Nicol is turned to the left from its initial position through a very small angle. N and 8 now inter- change effects; but otherwise the phenomena are as in the first case. The effects obtained in repeated and careful trials were, with few exceptions, as I have now described them; but they were by Reflection from the Pole of a Mugnet. 337 neither so strong nor so pure as those obtained in the second experiment, The strengthening actions of N in (1) and of § in (2) are evidently wh: at was to be expected ; for in (1) the second Nicol leaves the plane of polarization a little to the left, and N turns that plane a little more to the left. But the whole ee deserves a more particular discussion, . To find the intensity of the light which reaches the ob- server's eye in the sixth experiment. Suppose the incident vibration directed along OX (figure of art. 15), at right angles to the plane of incidence. When the second Nicol is turned (righthandedly) through a very small (positive) angle YO D=e, the resolved part of the re- flected vibration (of amplitude 1) i in the direction O D has an amplitude — sine or ac and the intensity of the light trans- mitted to the eye is e’. The effect of an additional operation S is to turn the primi- tive vibration out of the direction OX through a very small (positive) angle p, or to add to the primitive vibration in O X a very small ‘vibr: ition, of amplitude sin p or p, in a direction perpendicular to OX. There are therefore two vibrations presented now to the second Nicol—one in O X and sensibly of amplitude 1 as before, the other in OY and of amplitude k’p or p’, where k’ is a positive number less than 1, an unknown function of the angle of incidence. According to the hypo- thesis advanced in the end of art. 20, the difference of phases of these components has the same value @¢ as if the component ‘in OY were due to an operation R or L. The resolved parts of these components in the direction O D of transmission have amplitudes — sine and p’ cose, or —e and p’; the inten- sity of the transmitted light is therefore equal to e+ p’?—2ep! cos o. 23. Before discussing this formula, I proceed to apply similar considerations very briefly to the second experiment. Suppose the direction O X of the primitive vibration still per- pendicular to the plane of incidence, and that positive angles are still those due to righthanded rotations. If two opera- tions, L and 8, be applied simultaneously, the vibration is turned through a small angle e before incidence, and through a small angle p in the process of reflection. The amplitudes of the small reflected vibrations thus generated in the direction OY of transmission may be represented by «’ and p’, where a’ is the ka’ of equations (1) of art. 15, and p’ is the same as in art. 22. According to the hypothesis stated in art. 20, these vibrations are reflected in the same phase, and the inten- sity of the transmitted light is therefore equal to («+ p’)? Phil. Mag. 8. 5. Vol. 3. No. 19. May 1877. Z 388 Dr. J. Kerr on Rotation of the Plane of Polarization To apply this result to the first half of the second experi- ment. By trial we give to « such a value that sensibly a’=p’, and then apply successively the three sets of operations (R,N), (CR), (R, 8). The corresponding intensities in the polariscope are Cre ee Cec ey ee ne which are as the numbers 4,1,0. The actual resuits, as already specified, were bright, faint, black (10). * 24, Returning to the sixth experiment. In discussing the expression e’ + p’’?—2ep! cos , found in art. 22, I shall suppose the rotation of the second Nicol always righthanded, or the angle e always positive. The amplitude p’ is positive for 8, negative for N. The angle @ varies continuously with the angle of incidence, from zero at normal incidence, through 5 at principal incidence (75° or 76°), up to a at grazing incidence. It will be observed that the 5 at principal incidence in the present case is the 37 of equation (2) of art. 15, diminished by the a of reversal due to reflection. (1) When the value of the angle of incidence is consider- ably less than 75°, cos@ has some positive value c, and the additions made to the primitive intensity e’ by the operations N and 8 are p +2ep’c and p?—2ep’c. In this case, therefore, the effect of N in the polariscope is always an increase, and always more pronounced than the effect of 8. | Let e’ be the value of e whichis determined by the equation p’ —2ec=0. When e=e’, the effect of S in the polariscope is reduced to zero; When ee’, the effect of S is a decrease. (2) When the value of the angle of incidence is consider- ably greater than 75°, cos¢ has some negative value —e, and the additions made to the primitive intensity e* by N and S are p’—2ep’e and p” + 2ep’e. Here, therefore, contrary to what holds in the first case, the effect of S isalways an increase, and always more pronounced than the effect of N. Here also, as e increases from zero, the by Reflection from the Pole of a Maynet. 39 addition made to & by the weaker magnetic operation passes from positive, through zero, to negative. (3) In the case of principal incidence, cos¢=0, and the additions made by N and 8 to the primitive intensity e’ in the polariscope are equal and always positive. 25. Seventh experiment, a repetition of the sixth, to test the preceding inferences. (1) Angle of incidence about 70°. All the effects recovered as predicted, and as already obtained roughly in the sixth experiment. Recovered also perfectly at various incidences from 60° to 75°. (2) Angle of incidence very large, about 85°. No sensible effect obtained in any case by application of the operations N and 8, with the arrangements of the sixth experiment, or with those of the second. The reason very probably is that, as the angle of incidence approximates to 90°, the ratio of the ampli- tudes p’ and e becomes excessively small, by diminution of the rotation p towards zero. Angle of incidence about 80°. The effects very faint, but clearly contrary to what was predicted: N strengthens the light as in the first case; S either weakens it or has no effect. (3) Equal positive effects of N and S in the polariscope were never observed at 75° or any other incidence. The hypothesis advanced in 20 is therefore inexact: the rotation due to magnetic force is not impressed effectively before inci- dence. Neither is it impressed effectively after reflection (10...19). The difference of phases of the two reflected vibrations, p’ in O Y, and 1 in O X, has therefore some value A intermediate between ¢ and 0; and the intensity in the sixth experiment is equal to e + p” — ep! cos Ad. Judging from the earlier experiments, second to fifth, I think we are bound to assume that A is very nearly equal to 1: but certainty upon the subject can be reached only through exact measurements. I come now to the third method men- tioned in art. 14. Case of Perpendicular Incidence. 26. Submagnet.—The old wedge C of art. 7 is now in- adequate. The piece which I substitute for it is a block of soft iron, 2 inches square and 3 inches long, rounded at one end into a frustum of a very obtuse cone, of which the small base is hardly 4 inch in diameter. A small boring is drilled through the block, and along the axis of the cone, narrowing regularly from + inch at the flat end ef the block to 74; inch Z 2 340 Dr. J. Kerr on Rotation of the Plane of Polarization at the conical end. The surface of the boring is well dimmed with a coating of lampblack. ‘To ensure perfect stability of position when the piece rests upon its conical end, the original rectangular volume of the block was restored, the part added being a hard stone of plaster of Paris, which was easily moulded to the block of iron in the usual way. This is the first submagnet that gave me good and constant effects in the case of normal incidence ; and it appears to be much the best that I have yet tried. Without a submagnet of some kind, I have never obtained a suspicion of an effect. 27. Placing of the pieces——The old magnet (8) is placed on a solid table near the edge, with its polar surfaces horizon- tal ; and the submagnet just described is laid upon one of the polar surfaces, its conical end downwards, the axis of core and boring coincident, and the block and core separated by a wide ring of writing-paper, or very thin card. Above the lock, as in Norremberg’s polariscope, stands a mirror of un- silvered glass, which receives a horizontal beam from the first Nicol, and reflects it downwards through the boring, perpen- dicularly to the surface Bs EF of the magnetic mirror. In the diagram, HE G | is the polar surface, L RB the source of light, which is the same paraffin-flame as formerly, EI the ob- S$ .-0.- server’s eye, A and B the A first and second Nicols, C the transparent mir- ror. The course of the light? from i to isa! LACFCBE. Allthe * pieces are placed very stably, and the room is well darkened. 28. Highth experiment.—All the pieces are placed as in the diagram, and so that the observer sees at I’, through B, a bright and steady image of part of the flame L: the first Nicol is so laid that the plane of polarization of the light in- cident at OC coincides with the plane of incidence; and the second Nicol is turned into the position of pure extinction. (1) The second Nicol is turned righthandedly through a small angle, giving a distinct but faint restoration. The operation N strengthens the light thus restored; and the operation S weakens and sometimes extinguishes it. (2) The second Nicol is turned lefthandedly through a small angle beyond pure extinction. The results are as in the first case, with reversal of actions of Nand 8. It is now & by Reflection from the Pole of a Magnet. 341 S that strengthens the light, and N that weakens or extin- guishes it. The phenomena now mentioned are very faint, a good deal fainter than those obtained in the second experiment; but they are certain, distinct, and perfectly regular. I need hardly say that this experiment is decisive, and that the effects are certainly due to rotations virtual and actual of the plane of polarization of the light which is presented to the analyzer, the virtual rotations being produced by displacements of the second Nicol, and the actual by the operations N and 8. N conspires with a righthanded rotation of the second Nicol ; and therefore N turns the plane of polarization to the left: S conspires with a lefthanded rotation of the second Nicol ; and therefore S turns the plane of polarization to the right. 29. Ninth experiment.—No change in the arrangements, the initial extinction perfect. (1) The first Nicol is turned righthandedly (from C as point of view) through a small angle, giving a faint but di- stinct restoration. SS strengthens the light thus restored, and N weakens and sometimes extinguishes it. (2) The first Nicol is turned lefthandedly, through pure extinction, to faint restoration. N strengthens the restored light, and 8 weakens or extinguishes it. The phenomena are precisely as in the eighth experiment, and equally distinct and regular, but with reversed relations of S and N to movements of the Nicol: and this was to be certainly expected, because the first Nicol simply carries the plane of polarization with it, while the second Nicol simply leaves that plane behind it. As an illustration of this state- ment, and of the consistency of the results obtained in this article and the preceding, I offer the following optical experi- ment, though it will be to many of my readers unnecessary. 30. Tenth experiment.—The arrangements unchanged, the initial extinction perfect, the circuit kept open. (1) First Nicol to the right, giving a faint restoration. The restored light is weakened to extinction by rotation of the second Nicol to the right ; strengthened clearly, ab initio, by rotation of the second Nicol to the left. (2) First Nicol to the left, giving a faint restoration. The light is weakened to extinction by rotation of the second Nicol to the left ; strengthened clearly, ab initio, by rotation of the second Nicol to the right. These effects are certain and regular ; but sensibly perfect extinctions are obtained only in careful work, and with very small displacements of the first Nicol. 31. Hleventh experiment.—Starting with the same arrange- 542 On Rotation of the Plane of Polarization. ments as in the last three experiments, and working under the most favourable conditions attainable, I have often left the two Nicols in position at pure extinction, and tried the effects of the simple operations N and 8. _ I have certainly got distinct effects many times in such circumstances, and assured myself that they were due to magnetizations of the iron mirror by getting them to appear and disappear at the instants of make and break of the circuit; but the effects were so excessively faint that I could not once characterize them as due to rotation of the plane of polarization. I have no doubt whatever that, with a stronger magnet and a finer mirror, and a more intense light, this experiment would be as satisfactory as any of the preceding. 32. Twelfth experiment: influence of the Submagnet.— The old wedge C of art. 7 has a slit sawn into it at right angles to the edge, as if to divide the block into two equal wedges. The slit is about 54, inch wide, and terminates at the dotted line drawn across the block C in the diagram of 7. Returning to the diagram of art. 27, the bored block is removed, and the slit block put in its place, its largest plane face on the polar surface, and the slit perpendicular to the plane LO F, Block and core are separated successively by six sheets of in- creasing thickness, tissue-paper, thin writing-paper, drawing- paper, pasteboard, thick card-board, and a quarter-inch plank, each of the sheets being perforated properly at Fj!so as to expose the polar surface through the slit. All the other arrangements and the procedure are as in the eighth and ninth experiments. ‘The old effects are obtained under these new conditions, but more faintly at the best. They are certainly strongest with the sheets of pasteboard and card- board, <5 inch to {45 inch thick. With the quarter-inch plank they are barely if at all perceptible. With the first and second sheets, the tissue-paper and thin writing-paper, I could catch no trace of the effects. Summary of Experimental Results. 33. When plane-polarized light is reflected perpendicu- larly from the polar surface of an iron electromagnet, the plane of polarization is turned through a small angle in a direction contrary to the nominal direction of the magnetizing current. When the light is reflected obliquely, the effect in the polariscope is mixed, partly due to magnetic force, and partly due to metallic reflection ; but in this case, as evidently as in the case of normal incidence, the action of the magnetic force is purely or chiefly photogyric, and the plane of polarization Mr. R. H. M. Bosanquet on the Theory of Sound. 343 is turned always in a direction contrary to that of the mag- netizing current. The precise character of the mixed optical effect in the case of oblique incidence can be determined only by exact measurements. This much, however, appears to be clearly proved by the preceding experiments, that the rotation due to magnetization of the mirror is impressed upon the light neither effectively before incidence, nor effectively after re- flection. No effect was obtained in any case without the presence of asubmagnet. I think it certain that the only use of this piece is to concentrate or intensify the magnetic force upon the iron mirror by inductive action. The powers applied were barely adequate to produce all the effects. Some of the phenomena were quite imperceptible when the battery began to work, and afterwards, when it had worked at intervals for three or four hours. Much better effects may certainly be expected with higher electromagnetic powers and finer optical appliances. Glasgow, 26th March, 1877. XLIV. Notes on the Theory of Sound. By R. H. M. BosanQquet, Fellow of St. John’s College, Oxford. [Continued from p. 278. | 2. On the Energy per second of a Pendulum-vibration in Air. J hare flow of energy per second along a column of air transmitting a pendulum-vibration is NZ 74 2p3(™~) or 2x 1.4IIv (=) where p is the density of the air, II the atmospheric pressure, v the velocity of sound, A amplitude of vibration, »X wave-length. This was proved in a paper in the Philosophical Magazine, March 1873. ‘The kinetic and potential energy were esti- mated separately ; each is equal to half the above quantity. ~ This result may be obtained more conveniently by supposing a disk to oscillate in an infinite cylinder. The changes of pres- sure on the two sides of the disk are always equal and opposite ; and the work done in any small movement is the product of the displacement by the difference of the pressures. The total work done by the disk is the energy supplied to keep up the 044 Mr. R. H. M. Bosanquet on the Theory of Sound. two streams of sound which are propagated from it in both directions. Let the axis of the cylinder be the axis of wz, the origin the position of rest of the disk, and y the displacement at any point. Then, on the right, where the transmission is forward, y,=A sin a (vt—«2), dy _ os dx po And on the left, where the transmission is backward. ose * (vt—2). yo=Asin zi (vi+e), diya __ 2aA die Wein And the difference of pressures on the two sides of the disk, where =0, is yy a au (_- dx Ja=0 Cos = (vt+ 2). or, since Oya e tr J - =-9) 2 bic 2x 1411 x2™ cos nt The work done by the disk in passing through the space dy against this ditterence of pressures is this difference x dy, and (4) = ul COs on 0 T T dt *. work done in a quarter vibration 1s T 2A2 1a {co gm = dt = 1-411 oe AT ; xX -, work in a whole vibration mee and in a second, since vibration-number = = —4 x 1-4TTo( m=). And this work produces two streams of pendulum-waves in Mr. R. H. M. Bosanquet on the Theory of Sound. 345 air of amplitude A, so that the work supplied to each stream per second is 2 2 x 14tte(™*) as before. Cor.—Since the maximum velocity in the vibration is awAv ox = V say, we may write the energy per second, 2 (3) Here pv is the mass of air which the sound traverses in a second. Hence the energy transmitted in a given time is the same that the whole mass of air traversed would have if moving with the maximum velocity of the vibration. This is in analogy with the general theorem, that the energy of a body executing pendulum-vibrations is the same as if the mass were arranged on the circumference of a fly-wheel whose radius is the amplitude, and period that of the vibration—a re- presentation of the motion which is frequently convenient. The maximum velocity is the velocity of the circumference of such a wheel; or v=27An. It is consequently indepen- dent of the velocity of transmission. Cor.—NSince the velocity of sound in a gas is subject* to the equation ble puV?. vp=1-4II, where v, p may vary, but II is constant, we have, putting (= = in the last expression, energy per second Hea =, Fig Blige Hence, in the transmission of a vibration of given amplitude and vibration-number through any gas, the energy per second is inversely as the velocity of sound in the gas, or is propor- tional to the square root of the density. This is the case of replacing air by hydrogen in a receiver with a bell hung in it. So long as there is only air present, the energy per second is simply proportional to the pressure ; but if hydrogen be introduced, the velocity of propagation is increased, and the energy per second diminished in inverse ratio. Ultimately when the air is replaced by hydrogen, the “ of its value for air. energy per second is ae * Tf, like hydrogen, it have the same ratio of specific heats as air, 346 Mr. R. H. M. Bosanquet on the Theory of Sound. Cor.—Since the maximum pressure in a transmitted vibra- tion is 1-411 ore P say, and Dr A vi Xr ay v The energy per second may then be written LPY. 3. On the Reflexion of Sound at Gaseous layers of diferent Density™. We confine ourselves to the case of a cylinder, which we suppose to be crossed by layers of gas of different density. Consider first one common surface, and let the velocity of propagation on the side from which the air comes be v, on the other side v’. There will be generally a reflected and a transmitted dis- turbance ; let the amplitude of the incident disturbance be A, reflected - a, = 9) 9) transmitted _,, b. 99 99 The common surface moves with the sum of the amplitudes Jk oh Oe the « one side, and with the amplitude b of the other ; “A. +a=6. The energy per second of A = that of a, b together ; 2 2 6. 2x L4Timint | = Te ohs A?=a?+ab?. Putting 0? =(A+a)?, we find A?1—a«)=@(14+2)4+2Aaz; and, rejecting the solution A= —a, b=0, we have ere or if — =a, v * General formule for a single surface were given by Green. The “object of this communication is chiefly to give an example of the method. The case of oblique incidence loses most of its interest in practical appli- cation to sound, as the necessary conditions for formal refraction are not generally satisfied ; the investigation has been restricted to the simpler case, Mr. R. H. M. Bosanquet on the Theory of Sound. 347 1—w 2A a=A-——, b=——; 1l+2 l+ea : v or, replacing w by w i— 9 Ar! a=A a = = — Vv +v Vv +v The ratio of energy transmitted : original is b? ; na oy @ — Av" _ 4vv’ aS Tes (vv) ~ (e+) v The ratio of energy reflected : original is 2 a v’ —v\? Maes (e,) ; Since v, v’ are symmetrically involved, the division takes place in the same way whether we pass from the denser to the rarer, or from the rarer to the denser medium. Let Ayeh i) =8 (o! +0) a) (ome iS Suppose the sound passes across a layer of gas or heated air (two surfaces); then the following represents the distributions of the sound-energy after reflexions and transmissions at the two surfaces of the layer :— Back. Within the layer. Through. et Or. cet cess eee MANGE cet agen ees ce tian a”. INTIS 5 CH CR peesesb eon Refl. back ef, | Refl. forward «87... «8, Mramsn 2S. tin sscns Refl. back «f°, Refl. forward a8*.., «6%, and so on. 2 The total transmission is = Be 2 Neel wetlecon back is ( —F i 1) 8. Putting for a, @ their values, Bethe. 5: (Avv’)? 2uv’ ae a = (a aan = Pao? trans. a2 PDarv! y—v' 2 (v—v')? (2 +1) B= i +1) (=) Te cay refi, 348 Mr. R. H. M. Bosanquet on the Theory of Sound. The sum of these results =1, as it should be. In these calculations it is supposed that the wave is of such length compared with the thickness of the layer as to prevent inter- ference-eftects. Example.—Sound is transmitted across a layer of hydrogen ; to find the energy per second transmitted and reflected. Density of hydrogen : density of air :: v?: v7::1: 14:44 nearly ; whence v: v’:: 1: 3°8 nearly. Calculating the above expressions, we find that, if energy per second of incident sound be taken as 1, it is divided as follows :— 2 X8i8), oy 400 Transmitted = (sie ti e hate} 9 iS Reflected = (Go) 7°84 Uy pe The transmitted and reflected energy are very nearly equal ; and each is very nearly half that of the incident sound. We can find the value of v : v’ for which the division should be exactly equal between transmission and reflexion. Putting (v—v’)’=2vv’, we find / - = 2+ ./3=3°732 or -268, the one corresponding to passage from air through gas, the other to the reverse. This value is within the limits marked by the square root of the density and Regnault’s determination of the velocity in hydrogen. Regnault’s determination. Square root of density. (These numbers are given correctly in Regnault, Mém. de U Institut, 1868, p. 185. They are accidentally transposed at ». 553 of the memoir, and also in the summary in Tyndall, 2nd edit. p. 381.) As an illustration of the case where the wave-length is not such as to prevent interference, suppose that we are dealing with a layer of the thickness of a quarter wave-length in the gas. Then each successive term of both transmissions and reflexions is the opposite phase from that which precedes it, so that the total energy transmitted is less than the above. The calculations, of which the above is an example, furnish the explanation of Tyndall’s observations about the acoustic opacity of aerial layers of different density. | The observation that the conditions of transmissibility are Mr. O. J. Lodge on Thermo-electric Phenomena. 349 not the same for high and low sounds is probably to be ac- counted for by the fact that the relations which produce inter- ference are not the same in the two cases. As a matter of fact, high sounds are most affected in general by transmission through obstacles or layers of any kind. The reason is, no doubt, that under ordinary circumstances the dimensions considered are comparable with short wave-lengths rather than with long ones. The method given above can be extended to any number of layers by a process analogous to one used in calculating the effect on light ofa pile of glass plates. It is only necessary to remark that the layer behaves like a single surface whose dividing ratios are a a= 1—p” = (75 +1)6: or, remembering that e+ 6=1, eo — Bh Thus for two layers, J ao= so c= 1—a,. pa a ~ 4—32 and for 2” layers, XLV. Reply to the Note of Professor M. AVENARIUS. To the Editors of the Philosophical Magazine and Journal, GENTLEMEN, N the February Number of the Philosophical Magazine, page 156, Professor M. Avenarius does me the honour to notice a communication of mine “On a Mechanical Illustra- tion of Thermo-electric Phenomena ”’ (December Supplement, 1876), wherein I attributed incorrectness to his formula for the electromotive force of a thermo-eiectric couple, =i) (OteO trips oc 5 «6 an imputation which Professor Avenarius rejects. _ Now it is true that this expression, taken by itself and in- dependently of the process by which it was obtained, is not erroneous but quite correct—being, in fact, as he justly 300 =Mr. O. J. Lodge on Thermo-electric Phenomena. observes, of the very same form as the one subsequently given by Professor Tait (1870-71) to express the value of this elec- tromotive force. A few words of explanation are therefore necessary from me. The work of Professor Avenarius in 1863, as detailed in his memoir™, “ Die Thermoelektricitiit, ihrem Urspr unge nach, als identisch mit der Contactelektricitat betrachtet,”” consisted, first of all, in arriving at this expression by means of two hy- potheses, very reasonable and probable at first si ight, but really inconsistent with each other, and one of them flee ; and secondly, in bringing the expression so obtained to the test of experiment, and verifying it in a complete and satisfactory manner between certain limits of temperature. This second part of his work is unassailable ; and as it was performed several years before the similar more extensive experiments of Pro- fessor Tait, it constitutes, so far as I know, the original dis- covery of the actual numerical laws of the electromotive force of a thermo-electric pair. Regarded, then, as an empirical formula expressing with experimental accuracy the electromotive force of a thermo- electric circuit, it is correct; but considered as a formula de- duced from and embodying a certain theory in contact-elec- tricity (which theory one would naturally have supposed to be verified by the verification of the formula), it is erroneous, and has led Professor Avenarius himself to erroneous results. In a subsequent communication to Poggendorft’s Annalent in 1873, to which he now refers me, he admits this to some extent; and in this paper he rraeaTeae full use of the laws dis- covered thermodynamically by Sir William Thomson in 1851, and shows that his own expression is In agr eement with them if the “ specific heat of electricity in a metal”? is assumed to be proportional to its absolute temperature. Professor Tait had pointed this out in a very similar manner a few years pre- viously §; but the original publication of the substance of the 1873 paper took place in the Reports of the University of KKiew for 1870, a copy of which Professor Avenarius has been good enough to send me, as | was unable to find them in the library of ‘the British Museum. Hence it; appears that the priority in this also rests with him. * Poge. Ann. vol. cxix. + See, for instance, Pogg. Ann. vol. cxxii., where the Volta contact- force between two metals at any temperature is supposed to be deduced with the help of thermo-electric measurements, the two distinct pheno-~ mena of voltaic and thermal electromotive force being mixed up and con- fused together. { Vol. exlix. “Kin Beitrag zur Theorie der Thermostrome.” § Proc. Roy. Soc, Edinb, 1870-71. Mr. O. J. Lodge on Thermo-eleciric Phenomena. 351 The errors in the original theory are rather subtle, and are worth pointing out, not for the purpose of casting any slur on the valuable work of Professor Av enarius, but as illustrating the slight though important difference between the present theory “which includes Thomson’s effects, and the two hypo- theses which ignored them and which were also independent of the laws of ther modynamics. First hypothesis. That the electromotive force of a thermal joint is expansible in terms of the (Centigrade) temperature, thus C= tOG A Cb. 8S a ROH GL) Second hypothesis. That in a complete oe fens is no electromotive force anywhere except at the junctions of differ- ent metals, or that the electromotive force of a thermo-electric pair, with two joints at different temperatures, is obtained simply by subtracting the electromotive force of the joint at the temperature ¢, from that of the joint at the temperature ty, or 1D = Cj — €2- ° ° ° ° ° ° Sys (2) Conclusion following from these, the law of Avenarius— Hb Git) fo(@ 2). 2k 5) Now the first hypothesis taken by itself is a tolerably safe assumption, and, as it happens, is actually true as it stands. But when the second hypothesis is also made, the general theory of heat-engines requires the constant ¢ to be zero, which would render most of the subsequent investigation meaningless, and would make (3) entirely discordant with ex- periment. This, in fact, is the very discrepancy which led Sir William Thomson about 1851 or 1852 to see the falsehood of hypothesis No. 2, and hence to the discovery of an electro- motive force between different portions of one and the same - metal at different temperatures, which, under the form of the “electric convection of heat,’ he subsequently caused to be verified by a most laborious series of experiments”. The falsehood of the second hypothesis is fully admitted by Professor Avenarius in 1873 f. The conclusion when considered alone is correct, as I have said above; but the constants 6 and c have not the same mean- ing as they had in (1). If we consider them to have the same value in (1) and (8), we shall be led into error as regards mat- ters of fact, just as Professor Avenarius was. * Phil. Trans., Bakerian Lecture, 1856. Oddly enough this memoir is quoted by Professor Avenarius in the original paper where the Thomscn- effects are ignored. T Pogg. Ann. vol. exlix. footnote, page 374. 352 Mr. O. J. Lodge on Thermo-electric Phenomena. Thus from (1) we observe that e vanishes for two particular temperatures, one of which may be absolute zero, —274; and then the other will be 274— ° , which is Thomson’s “ neutral point,’ and may be denoted by ¢. It attains a maximum value when t= — 2 , which may be called ¢,. From (8) it is plain that E vanishes when t,=¢,, and also when fey eo ts OT Senha Cults (This temperature tm is what Professor Avenarius prefers to call the neutral point; but that is immaterial.) We are thus led to conclude that the vanishing-point of E coincides with the temperature giving a maximum value to e, or that the Peltier effect at a junction of two metals would be greatest for a temperature halfway between two temperatures for which the electromotive force of a complete circuit vanishes ; whereas the fact is that there is no Peltier effect at all at this halfway temperature, and H really vanishes when $(4 + ¢,) equals ¢,, and not when it equals t,. Moreover the metals do change places in the thermo-electric series at the mean temperature where vanishes, a fact which Professor Avenarius (consistently with his hypothesis) would deny *. If we now amend the second hypothesis so as to include Thomson’s effect and start from hypothesis (1), we shall arrive at the correct value for EH in terms of the constants of (1); but it will not be identical with (3). Let us write z instead of the number 274 (or more generally let z be the absolute temperature corresponding to the zero of the scale employed) and then proceed thus. Thermo-electromotive force at a junc- tion of two metals whose Centigrade temperature is ¢, P= ATEN (be ot Sea Difference of electromotive forces at two such junctions whose temperatures are ¢, and ¢, respectively, 5 — = (tf, —) +0(V?—#). Difference of electromotive forces in the two metals when there is a difference of temperature, ¢;—t,, between their ends (Thomson’s effect), €,—€, = ~2e¢h—t) -—E0@—#). . . . | Electromotive force in entire circuit of the two metals, H=e,—e, + €,—€,—(6—Ze)(t,—t,) +4 (#—z). - () * Of. p. 413, vol. exix. Pogg. Ann. Mr. O. J. Lodge on Thermo-electric Phenomena. aoe This being the correct expression in terms of the constants of (1), one is justified in saying that (3) is erroneous—although, as (5) and (3) happen to be of precisely the same form, one is just as good as the other if the constants are arbitrary and have no special meaning assigned to them. In conclusion it may be worth while just to write down the physical meaning of the three constants a, b, and ¢, ot, —-0—2¢, b= S(—2), ¢=—8;,'s « () where ¢, stands for the temperature of the neutral point, b tj=e— mo Be MA ein. Fae) apes. Shen pan Te (7) and 8 stands for J times the difference of the specific heats of electricity in the two metals expressed as a function of the absolute temperature and divided by the temperature. Or, in Avenarius’s (1873) notation, B=, —f2. In Tait’s, B = [tip aaa Ky In Thomson’s, B =i Oqg—O%F By the help of (6) we may remove the constant a from (1) and write it e=d(ze+t)+ce(P—2*), . . . « (8) The temperature for which e is a maximum is t b mia ee) ee (t=). The following Table gives the correct values of a, b, and c for a few junctions, according to the (1863) experiments ot Professor Avenarius, taking z as equal to 274. Metals. | a. | b. C. toe Silver and iron......... 9026 | — -734 | —-0147 | 924 Copper and iron ...... 264-4 + :006 —°0035 275 Silver and zinc ......... —81:9 + °879 +:0043 70 Platinum and lead ... 23'°3 +2°606 +0092 —9 The values of ¢, are explicitly inserted in order to show that the relation a= —zct, is tolerably well satisfied. I am, Gentlemen, Your obedient servant, University College, London. OLIVER J. LODGE. Phil. Mag. 8. 5. Vol. 3. No. 19. May 1877. 2A [ 354 | XLVI. Notice of Crystallographical Forms of Gluucodote. By W. J. Lewis, I.A., Fellow of Oriel College, Assistant in the Mineral Department, British Museum”. [Plate I.] HE mineral from Hikansbo in Sweden is found in large crystals of metallic lustre and dull tin-white colour, imbedded in towanite and pyrites. The crystals are, for the most part, twins, most of them being twinned about the normal to the face (011), so far not described, some about the nor- mal to the prism-face (110). The specific gravity and the prism-angle agree fairly well with those of Breithaupt’s acontite. Glaucodote. Acontite (Br.). Sp. gr. 5°285-6:18. 6:008-6:059. . Prism-angle . . . 69 32 69 31 Brachydome-angle . 100 2 102 0 The one discrepancy consists in the value of the angle of the brachydome {101}, which from direct observation and a calculation by the method of least squares involving all the best angles measured, I make out to be 100° 2’. The angle of the prism varies considerably in different crystals—68° 57’, 69° 62’, 69° 13’, 69° 32’, 69° 40’ having been obtained on fairly good specimens. The planes of the brachydome are much striated, and do not allow of such precise determination. Differences in the brachydome-angle, such as those found in the prism-angle, have been observed, though much more limited in extent. ‘This variation of the crystallographic elements of the mineral is probably to be accounted for by a variation of the quantity of cobalt present. The angle of the prism (=67° 24’) and the cleavage ¢, given in Miller’s ‘ Mineralogy,’ seem to belong to some other mineral. They were not determined by Professor Miller himself; and I have been unable to find out whence they are taken. On the very large crystals are found the forms {010}, {110}, {101}, {102!, {O11}; on smaller crystals have been found the additional forms, {111}, {12 2},{201}. Fig. 1 (Plate I.) is a stereographic projection of these forms. Such simple crystals as I have observed were extended considerably in the direction of the edge of the bra- chydome, but were all broken at one end. On one of these, whose prism-angle measured 69° 193’, a second prism {160} was observed. Its faces were small and not well developed. Assuming the measured angle 69° 194’ for the fundamental * Communicated by the Crystallological Society, having been read December 15, 1876. On Crystallographical Forms of Glaucodote, 355 prism, calculation gives the angle (110, 160)=27° 564’, which agrees very well with that obtained by measurement, at 5AL? The elements and angles given below have been taken from measurements obtained on two good twin-crystals, each about the size ofa cherry. ie prismatic : =(010, 011)=30° 12’; E=(001, 101)=50° 1; a (100, 110)=55° 14’. a:b:c=1:4406: 1: 1:71784. Forms observed: {010}, m{110}, y{201}, U{101}, sf1 02}, nf011}, o{111}, w{122}, p{16 0}. Calculated. Found. mm, = 69 32 69 32 él 100 2 100 1 ls 19 122 19 @O ly i A: ies YY, 134 30 134 314 Ly, 62 44 62 432 my 58 164 58 15 m t 64 55 64 44 nw 16 42 © 16 433 WwW, 33 24 35 27 ow 14 15% Aas mn 44 46 nl 1 = «83 M fh 89 32 89 36 mn 26 224 26 32 The observed angles agree fairly well with those obtained by calculation, with the exception of /s and md. The observa- tion of the latter was one of no great weight; but the former was repeatedly measured with great care. As moreover an increase of 5’ in the angle H involves an increase in Js of 3/ only, I have been obliged to regard the discrepancy as due to a distortion of the face s in the crystal on which the angle was measured. This face s, though large, is generally one of the worst on the crystal. The plane n is but poorly developed, and therefore does not serve for a direct determination of the element D. The plane d is deeply striated parallel to its inter- section with m; the planes / and sare striated parallel to their intersections with one another, s being much the rougher. ZA 2 356 Mr. W. J. Lewis on Forms of Glaucodote. The planes y are pitted and rough. Figs. 2 and 3 are repre- sentations of simple crystals. The twins about (011) are a fresh illustration of the ten- dency to twin about the face of a prism whose angle is near 60°. Fig. 4 isa representation of this twin, in which both mem- bers are shown approximately in equilibrio with the twin-axis vertical. Fig. 5 represents somewhat closely the appearance of a moderately large twin of this kind. The principal crystal, denoted by Roman letters, is projected in the same way as in fig. 1; and to it are attached two smaller crystals twinned about (110), the one represented by Greek letters, the other by barred Greek letters. The intersection of planes which corre- spond is straight and definite, of planes which do not cor- respond (as s and yw) is irregular and indefinite. The elements obtained by measurements on this crystal differ slightly from those given above, as is shown by the following Table:— Calculated. Found. D =30 143 iD D0 22 EF 55 10 i mm, 69 40 69 385 SS, 61 40 61 344 ls 19 122 19 142 ml G4 e2 64 13 ms 72 584 72 53 ™ fh, 48 o04 48 59 One specimen in the British Museum consists of a triple twin, resembling those of chrysoberyl, two of the members being twinned on adjacent faces of the form {011} of the third. Fig. 6 is an orthogonal projection on the plane (1 00) of this twin, in which an attempt has been made to show the appear- ance of the specimen and the relative magnitude of the mem- bers. Fig. 6a shows the simple crystal in the same projection. Twins about the face of the prism {110} have been already observed. These twins generally show the tendency to deve- lop but shghtly in the direction of the twin axis; and I was fortunate enough to get a specimen showing this to a remark- able degree. It is about the size of a penny-piece, and about the thickness of the thick penny of George III. One member is about half the width of the other, the remainder being apparently untwinned without an increase of its thickness. Close inspection, however, shows the existence of twin laminz in this part. Es am | XLVII. Supplementary Note to Professor Des Cloizeaux’s Me- moitr on Humite (Phil. Mag. [V.] vol. i1.). By Professor A. Drs CioizEauxf. GIN CE the communication of this memoir to the Crystallo- logical Society, I have resumed the examination of the optical character of a certain number of crystals of the three types of Vesuvian humite which I received from Professor Scacchi. The results obtained are similar to those which I have already published ; but the crystals of type II. are espe- cially remarkable for the great number of bands twinned round the normal to the base, to which the bands are parallel. In consequence of this twinning, a face a’, for example, is formed very frequently by a portion of a* occupying its proper position, and by a portion of 02 belonging to a twin band. The same coincidence occurs with the corresponding faces a and 0%) a? and h}, b!, and dt, &. Now, no reentering angle being ob- served on these compound faces, their incidences on the base should be equal. It is precisely what one remarks in the cal- culated angles contained in the following Table, and which have been obtained by substituting for two of the elemental angles, which I have borrowed from Scacchi, the following: *» h* =109° 1’ (vom Rath) instead of 108° 58’ (Scacchi). nd? =125° 50's, As 15252) ee b:a:¢:: 419058 : 907949 : 696666. pé 141 50 pa 114 58 pb 135 19 Pier l22: 28 pB 95 19 pd# 135 19 Pe 1385 57 fog 1D pbe 125 50 pot 135 57 Do 1252 *pd3 125 50 pa: 119 52 pa, 103 9 pb? 113 26 pot 119 52 Gao Al pdt 113 26 paz 109 1 Baus dase pm 98 138 *poh 109 1 XLVIL. Note on the Law of Twinning and Hemihedrism of Leucophane. By Emite Bertrand, Parist. ees crystallography of leucophane has been treated of by Professor Des Cloizeaux in his Manuel de Minéralogie, by Mr. Greg (Phil. Mag. [IV. ], vol. ix. p.510), and by Professor + Communicated by the Crystallological Society, having been read April 12, 1877. 358 M. E. Bertrand on the Law of Twinning Von Lang (Mineral. Mittheil. Tschermak, 1871). I have also published a note on this mineral in the Annales des Mines, vol. iii. 1873; but up to the present time two interesting facts concerning it have not been noticed. It is known that leucophane has a very good cleavage parallel to the base, =(001, and that the acute bisectrix of the optic axes is per- pendicular to this cleavage. With a sufficiently large plate it is easy to obtain with the polarizing microscope two direc- tions apparently at 90° to one another, in which the hyperbole and the lemniscates are perceived. In certain cases one finds two crystals separated by a single plane of junction which have the planes of their optic axes orientated at about 90° to one another. In other cases one observes a series of very narrow bands corresponding to as many crystals of which the axes are situated in planes making angles of nearly 90° with one another. By an examination of a great number of cleavages of leucophane, I have succeeded in establishing that these twins are very frequent, especially in plates of some magnitude. I shall describe a very good twin crystal of this kind, which, moreover, presents another peculiarity. It consists of two crystals placed at about 90° to one another, the two bases lying in one and the same plane. Hach of these crystals shows two well-developed faces, b’=11 2, truncating two edges parallel to the base; the two other edges are not truncated in the large crystal; but in the smaller one faces /2=111 are found truncating these edges. Is, then, leucophane hemihedral, and indeed doubly so, as is the case with edingtonite? To prove this, the observation of a large number of crystals will be necessary ; and unfortu- nately crystals of leucophane are veryrare. I have examined a crystal in the collection of Mr. Adam, which presents the same hemihedrism : two edges parallel to the base are modi- fied by 6'=112, and one of the two others by b =1 icf, and Hemihedrism of Leucophane. 359 The fourth edge is not present, owing to the crystal being broken at this part. The British Museum also contains a crystal which I have not examined; but the figure of the crystal published in Tschermak’s Mineral. Mittheil. (1871) shows that the crystal is modified differently on the four edges of the base. This crystal therefore seems to present the same hemihedrism as that noticed above. Without pronouncing definitely on the hemihedrism, | think that there is sufficient probability to justify me in calling attention to the fact, and to encourage an exa- mination as to whether other crystals present the same hemi- -hedrism. Instead of considering leucophane to be hemihedral, one might suppose that it belonged to the oblique system rather than to the prismatic. On this supposition the base would become the plane of symmetry g'=0 10, the bisectrix of the optic axis would be the horizontal diagonal of the base, the faces b'=112 and l?=111 would become m=110 and e=104 respectively. But this supposition would only be admissible if the hemihedrism to which I have called atten- tion were a hemihedrism with parallel faces ; for in the case of a hemihedrism with inclined faces one would not find the four vertical faces necessary for forming the prism. But the twinned specimen of which I have spoken above shows very clearly a hemihedrism with inclined faces. Moreover, if leu- cophane crystallized in the oblique system one would probably observe a crossed dispersion in the polarizing microscope, whereas the symmetry of the dispersion of the colours is most perfect. This does not constitute a proof, but renders it ex- tremely probable that the system is prismatic. I have likewise proved that the trace of the plane of the optic axes on the face p=0 0 1, parallel to the cleavage, coin- cides with the diagonal of this face; for if a twinned plate be examined with the ordinary microscope between two Nicols, the line of separation of the two crystals is observed to be situated very approximately at 45° to the trace of the plane of the optic axes of each of the two crystals, the plane of the optic axes of one crystal being at 90° to that of the other. This coincidence, which is necessary in the prismatic system, but not in the oblique, gives afresh argument in favour of the system being prismatic. We may therefore conclude that the greater part of the erystals of leucophane are twinned and most probably hemi- hedral. It will be interesting to obtain evidence whether other crystals besides those mentioned above present the same hemihedrism. [ 360 ] XLIX. Extension of a Theorem in Continuants, with an im- portant application. By THomas Murr, JA., F.RSE* 1 the Philosophical Magazine for February there appeared, with a demonstration, a solitary theorem in continuants, Which was thought worth placing on record on account of its intrinsic neatness, and not because of any known application to the subject on which continuants bear. Now, however, I am enabled not only to make a generalization of it, but to apply it in demonstrating an extension of an important theorem of Professor Bauer’s regarding the product of two continued fractions. Beginning with the continuant o+ byc, 0 ) 0 —1 6+ = —CPr bole 0 0 0 —1 6+ * — Cy bscs 0 0 0 —1 6 4- in CaP bse, 0 0 ) —1 5+ : — C4", we transform it first into 5+ = by 0 0 0 —¢} o+ Z —cr be 0 ®) 0 —C5 o+ - —Cof bs 0 0 ) —C3 6+ L —C37 b, 0 0 0 —c, 6+ it — Cyr. Now, as before, increasing the elements of the first, second,... rows by 7 times the corresponding elements of the second, third,... rows, we obtain for the continuant an expression in non-continuant form ; then, in this third form, diminishing the elements of the second column by r times the corresponding elements of the first column, diminishing the elements of the third column by 7 times the corresponding elements of the new second column, and so on, there results * Communicated by the Author. On an Extension of a Theorem in Continuants. 361 d+ = —cr by ) 0 0 —(} 5+ = — CoP bs 0 0 0 by(bp— 4) B+b,—a F being the continued fraction given above. Increasing both sides of this by ——7 we have bolbg— ee) B,(bg—«) tae ae ep be Baby 20, b,( bn a) AE (GARG ae: Bra 2 = 037+ 364 Mr. T. Muir on an Extension of Now the fraction F remains unchanged when the sign of a and the signs of all the 6’s are changed ; hence, making this substitution, there results Beet 5.4 bx(bs—*) b3(b;—a@) =i eee a 2 B—b,+63;+ = + 2 F—), B—b3+b,+. bn(On—*) —«) 1 B= ae b, +e and therefore by multiplication we have the remarkable result b eee Z —b, =F gm? = b,(b3—«) E Aa 2) AE | x “8. bn(bp—e) B—a bo(b,—a) * B+5,—a 9 +b,+ aay ae any au €3(b,—a@) cr (C) ; B Tah bs ap by a5 | n he bp(bn—«) Be =| iy where it is easily seen in what cases the fractions may be con- tinued ad infinitum. Putting «=0 in this, we have Professor Bauer’s * first case ; and his second case is obtained on putting e=b—c, and bo, b3, 64... b, b+h, b+2h,... respectively. Further, ifafter these last substitutions we write 2s+h for 8, and h—b for C; there results Huler’s less general theorem { ; and if from this we specialize still further by taking s=a—1, h=2, and b=1, we find the old well-known identity of Wallist, used in the establishment of Brounker’s expression for = —, VIZ. 4 2 HED ey 52 x 2(a+1) ee oa 1 at eu eT De = ee p? Go 2a—1l)+. | Returning to (B) and taking 0, from both sides, we have * Von einem Kettenbruche Euler’s u. s. w. Munchen, 1872. + Comment. Acad. Petropol. vol. xi. 1739, p. 57, § 46. { Arithmetica Infinitorum, Prop. CXCI. a Theorem in Continuants. 365 I'+ab mee es _) b3(b3 — a) TR - : 3 (8) B+ b,—b3+ a Sei tah eaingshiei (nats B+b,—a therefore also, as before, BE + ab by + a) b;(b3;—«) bai gt Sy) 3 B—bs+b,+ bn(bn—&) B—b,+2 Hence we have the curious theorem b,—«a } 1+ See b3(b3—«a) TA ek %) B—6,+ 63+ B—bs3+ bgt, 4 Pon =a) | ae, a: b;(b;—«a) aks 2 3 Bt Os lar, b (by a) B+6, —«@ by a ya x (D) =14+ 25 , b5(b5—a) — b p ale bn—\(bn—2) eee | hb; — a) B Gr Saat agi On—1(0,—2) | rater een J) Again, denoting the continued fractions in (8) and (y) by f and j’ respectively, we obtain from (C), Coots Wa: B—« Bre 1 f ae soft Stray =O, whence and a—B a+ — =p a 6 bw (CD ee: (E) It would be hard perhaps to find a better illustration than is afforded by the foregoing of the great assistance which is de- rived from continuants in the investigation of the subject of continued fractions. Wallis’s theorem was left by him un- proved; and the demonstration of it, as Professor Bauer points 366 Dr. Karl Heumann’s Contributions to out, taxed the vast analytic power of Euler himself. In two different memoirs* it is a subject of inquiry with him; and in one place f he says that he had spent much labour upon it, but that the harder it seemed the more advantage did he hope to draw from the solution. And yet Wallis’s theorem is, as we have seen, one of the simplest cases of the general result here established with comparative ease. Glasgow, February 6, 1877. L. Contributions to the Theory of Luminous Flames. By Dr. Karu Hevmannt. [Plate IT. ] [Concluded from p. 107. | EE a former part of these papers I have declared my belief in the view which regards the separation of solid carbon as the cause of the luminosity of the flame produced by burning hydrocarbonaceous bodies. I have now to prove experimen- tally the justice of this belief, and to demonstrate the existence of free carbon in such flames. The increase in the “ light-effect ” of a gas-flame occasioned by heating the burner-tube has been already traced to the in- crease in the intensity of light of the flame-mantle, and to the simultaneous enlargement of the flame itself. The increase in intensity of the light may be itself traced either to the higher temperature to which the carbon particles are raised, or to the production of a greater number of such particles in a given volume of the flame-mantle. In either case more light will be emitted by any special portion of the flame. Whether both causes are at work when the burner-tube is heated must re- main meanwhile undecided. The increase in size of the flame- mantle, noticed when the burner-tube is heated, has been re- ferred to an earlier separation of carbon in the flame, this separation becoming possible by reason of the high tempera- ture to which the gas has been raised. If this explanation be the true one, it is manifest that any agent, other than heat, capable of producing a separation of carbon in the comparatively cold lower portions of the flame, should also be capable of producing an increase in the size of the flame-mantle. Chlorine and bromine are known to be * “De Fractionibus Continuis Observationes,” Comment. Acud. Petr o- pol. vol. xi. 1739, pp. 32-81; ‘‘De Fractionibus Continuis Wallisii,” Mémoires de U Acad. de St. Péter sbourg, vol. v. 1815, pp. 24-44. + Comment. Acad. Petropol. 1789, p. 41. t Translated, and somewhat condensed, from Liebig’s Annalen, vol. clxxxiv. pp. 206-254, by M. M. Pattison Muir, the Theory of Luminous Flames. 367 capable of producing the former action ; and experiment shows that they can also produce the latter*. Coal-gas issuing from a rather narrow horizontal tube was ignited ; the flame was separated by a space of 1 or 2 centims. from the orifice of the tube. A tube from which chlorine issued was introduced between the burner and the flame: the luminosity of the latter was at once increased ; and the flame at the same time extended itself backwards to the point at which the chlorine entered. The volume of the flame-mantle was thus increased at the expense of the blue zone of the flame. If bromine be employed in place of chlorine, a sooty flame is produced ; this is to be traced to the formation of a gaseous compound of bromine and carbon, and consequent partial cut- ting off of the supply of oxygen. Before deducing a wide generalization, it seemed to me ne- cessary to inquire whether in every case introduction of chlo- rine brought about the result theoretically foretold. The flame of a hydrocarbon may become feebly luminous (1) when the flame-mantle contains a small number of solid carbon particles. This condition is fulfilled in the flame of all substances relatively poor in carbon—for instance, in the flame of ordinary coal-gas. Such flames are rendered more lumi- nous by addition of chlorine or bromine either before or after the gas is ignited. If chlorine be added before ignition, a partial combustion takes place in the innermost portions of the flame; part of the hydrogen unites with the chlorine, while carbon is set free in solid form and renders luminous the hy- drochloric-acid flame within the main flame. Combustion of carbon, and of the hydrogen which is uncombined with chlo- rine proceeds at the outer part of the flame ; inasmuch, how- ever, as the outer portions are comparatively poor in hydrogen but rich in carbon, it follows that an increase in luminosity must take place at ‘these points also. If chlorine be conducted into the centre of a Minar large coal-gas flame, two flames are easily distinguishable. If chlo- rine be mixed with the outer atmosphere in which combustion is taking place, it partially replaces not only the inert nitrogen, but also the oxygen, combining at the same time with hydro- gen, but not at all, or only to a very limited extent, with carbon. ‘The latter is therefore partially deposited as soot. Gases containing little carbon may therefore be caused to burn with a feebly luminous flame by mixing with them sub- stances which at a high temperature partially or completely * Berzelius showed that the flame of alechol is rendered luminous by the introduction of chlorine. See Gmelin-Kraut’s ‘ Handbook,’ 1. pt. 2, p. 18; 6th ed. 368 Dr. Karl Heumann’s Contributions to combine with the hydrogen present, and so produce a hydro- carbon rich in carbon, or set free pure carbon itself. The substitution-products of marsh-gas, CH; Cl and CH Cl,, are gases fulfilling these conditions. While marsh-gas burns with a feebly luminous flame, the flame of methyl chloride (CH;Cl) is smoky and strongly luminous. Chloroform (CH Cl;) also burns at the surface of a wick with a luminous flame. Hydrogen containing a little chloroform vapour burns with a brilliant although non-smoky flame ; if a large quan- tity of chloroform be present, the flame becomes somewhat opaque and deposits much soot. In each of these cases hy- drochloric acid is produced. The flame of a hydrocarbon may become feebly luminous, or even non-luminous when (2) the temperature is not sufficiently high to cause separation of solid carbon. ‘Two cases here pre- sent themselves. A low temperature may be occasioned by withdrawal of heat by extraneous causes, as when a luminous flame is brought into contact with cold substances, or by the action of admixed gases which absorb heat, and so reduce the original temperature of the flame. These flames may be so hot as to cause to glow a piece of platinum wire held within them, and yet not hot enough to bring about a deposition of carbon from the hydrocarbonaceous material of the gas. On the supposition already put forward, chlorine ought in either case to render the non-luminous flame luminous. A small luminous flame was rendered non-luminous by causing it to play upon a porcelain basin. (I have already shown that withdrawal of heat is here the cause of non-lumi- nosity.) So soon as chlorine or bromine vapour was brought into the blue flame, it became luminous and deposited soot upon the basin. This experiment proves that the flame be- came non-luminous because the temperature was not attained at which carbon is deposited, and that so soon as carbon was separated, even by other means than increase of temperature, luminosity returned. The blue flame of mixed coal-gas and carbon dioxide, coal- gas and air, or coal-gas and carbon monoxide, when mixed with a little chlorine became very luminous ; this was espe- cially noticeable with the flame of mixed coal-gas and air, because this flame is possessed of a higher temperature than the others ; and I have already shown that the temperature at which deposition of carbon takes place in flames admixed with indifferent gases is higher than that at which the same phenomenon occurs in the case of flames not so admixed. The luminosity of a hydrocarbon flame may be diminished (3) by the temperature not being sufficiently high to maintain the Theory of Luminous Flames. 369 the separated carbon in such a condition as that it shall emit light. Such flames (the flame of turpentine for instance) become luminous when their temperature is increased ; this may be done by admitting air or oxygen. The admission of chlorine to such flames may be shown experimentally to have no effect in increasing luminosity. Frankland has put forward the suggestion that the soot de- posited from luminous flames does not consist of carbon, but of a mixture of heavy hydrocarbons whose vapours have been condensed upon the cold body introduced within the flame. Stein * has pointed out that in this case increase of tempera- ture should cause the soot to again assume the gaseous form ; experiment proves that this is not so. The absorptive power of carbon for gases seems to me to explain the fact that the soot deposited from | luminous flames does not consist of pure carbon. Stein’s analyses show 99:1 per cent. of carbon and 0-9 per cent. of hydrogen. I have shown that admission of chlorine to flames containing decomposable hydrocarbons causes an increase in the luminosity of these flames, and that this increase is attended with deposition of soot. Can it be supposed that this soot consists of condensed heavy hydrocar- bons? Frankland has himself told us that to obtain pure carbon from the soot deposited from luminous flames it is ne- cessary to heat the deposit in chlorine. If chlorine be then capable of decomposing hydrocarbons at a red heat with pro- duction of pure carbon, it can scarcely be the means of bring- ing about the formation of heavy hydrocarbons in the flame itself. In the case of flames rendered luminous by admission of chlorine, free carbon is evidently separated ; and as the phenc- mena attending the luminosity of lames of high temperature present no points of difference from the same phenomena in the case of flames containing chlorine, the conclusion is that in the high-temperature flames free carbon is also separated. It has been already shown that when a porcelain rod is held in a gas-flame, the lower surface (that is, the surface opposed to the stream of burning gas) is alone at first covered with soot, and that a thin fiim of soot is formed on the upper sur- face only after the expiry of a considerable time. This experiment affords direct proof of the presence of solid carbon particles in the luminous flame. If the action of the cold object were to condense the vapours of hydrocarbons, such condensation would of course take place equally around the cold object ; but the facts of the experiment show that the deposition is a purely mechanical operation exactly compa- rable with the deposition of dust upon the walls of a room. * Journ. Pract. Chem. (N.8.) oar vill. p. 402. Phil. Magis. 5. Wold. No. 19 Moy 1377. 2B 370 Dr. Karl Heumann’s Contributions to Further, the fact experimentally proved, that the surface of a body heated to redness may become cov ‘ered with soot, 18 op- posed to Frankland’s hypothesis : if the deposition consisted of condensed hydrocarbons, it could only take place upon surfaces relatively colder than the flame itself. If the space iImmedi- ately over the flame of burning turpentine be examined, it is seen to contain flaky particles of sooty matter. A hydrogen- flame brought into this layer becomes surrounded by a conti- nuous luminous mantle ; the flame of a Bunsen lamp becomes crowded with glowing particles. No glowing particles can be distinguished by the eye or by means of the microscope in a luminous gas-flame, by reason of the rapidity with which the current of gas is carried upwards. These small particles are stopped in their upward course by any solid body brought into the flame, or by the comparatively still layers of air; they thus become more compact and dense, and so bring about the deposition upon themselves of further numbers of particles until there is finally formed a visible cloud of soot or smoke. A solid body, or even a layer of air, while stopping the rush of solid particles, simultaneously lowers the temperature of the flame. In order to render visible the production of masses of solid matter, two blowpipe-nozzles, through each of which a stream of gas issued, were arranged horizontally opposite to one another. _ By regulating the distance between the nozzles a perfectly circular homogeneous flame was obtained ; by bring- ing the nozzles rather nearer to one another and slightly altering their inclination, the flame assumed a half-moon shape. The lower part of this flame was but slightly luminous, but was filled with little glowing points (fig. 1, Plate II.). The flame being in a kind of whirling motion, these little points were swept upwards and passed away as sparks from each horn of the half-moon. By bringing a porcelain plate over these points, the little particles were obtained in the form of coarse- grained soot. The appearances described become more appa- rent by causing the gas to issue under diminished pressure; but in this case the regulation of the flow is more difficult. Another experiment was arranged in which the little par- ticles of carbon were caused to form a larger and visible mass by projection against a solid body. A platinum basin hung vertically was heated on the concave side by means of a Bun- sen’s lamp ; a coal-gas flame about 5 centims. in length was caused to issue from the narrow circular orifice of a tube which was held by a clamp, and directed so that the flame struck the basin a little below the centre. By regulating the distance between this tube and the basin, a halfmoon-shaped flame the Theory of Luminous Piames. 371 was obtained crowded with little glowing particles which as- cended with a spiral motion, escaping from each horn of the half-moon (fig. 2). Lhe separation of solid carbon within a coal-gas flame is thus rendered visible to the eye. The experi- ment further shows that in an ordinary coal-gas flame the solid particles are very small but numerous, and that, when a number of these are gathered together in a special part of the flame, that part becomes continuously luminous. Frankland looks upon the fact of the transparency of lumi- nous flames as militating against the view that they contain solid particles. We know, however, that many substances containing solid matter (for instance, paper soaked in oil) are more or less transparent. Stein has also shown that it is very difficult to distinguish ordinary letters placed behind a gas- flame consisting of several layers, or behind the flame of a pe- troleum lamp. My own experiments confirm those of Stein, and prove that the lower non-luminous portion of a gas-flame is much more transparent than the upper luminous portion, and that it is almost impossible to distinguish an object when viewed through several layers of such flame, the same object being seen when viewed through a single layer. The eye becomes dazzled by the light of the flame, and so incapable of sharply distinguishing objects which emit lesser degrees of light. Tested in the sunlight, all non-luminous or slightly Juminous flames appear exceedingly transparent, luminous flames appear transparent only when viewed in thin layers, and smoky flames only when viewed in small masses. Frankland asks how a luminous flame can be so transparent as it is if it contain particles of solid carbon. ) tannous and stannic chlo- Arsenic and its salts (white- } © rides (blue colour)... .... yellow, COLOUT)) esi. 0 ere 2 Be Manganous chloride(greenish Antimony and its salts ‘a SOlOUE) A SRE eo ee ree (whitish colour) ........ D) 5 Gold chloride (greenish Mercuric chloride. a CoMlORE Hoetacis)s «ks srain'es Magnesium chloride. Cuprous and cupric chlorides Silver chloride. (blue and green colours), . \ ‘QUIT PU snOnUUOD ‘shonutyUOD eayoedg If the substances which are brought into the flame be non- volatile at the temperature of the flame, yellowish-white light is alone emitted, the flame appears very luminous and affords . * In one of Davy’s early papers I find an experiment described in which cupric chloride was used to bring about luminosity in a flame, 374 Dr. Karl Heumann’s Contributions to a continuous spectrum. If the metal or oxide which is sepa- rated in the flame be partially volatilized, one part of it may remain in the solid form and so impart luminosity to the flame, while another portion may become gaseous and so impart colour to the flame. The luminous portions of such flames show a continuous, the coloured portions a line-spectrum. Those substances which do not cause a non-luminous flame to become luminous may also be subdivided into those (salts of lead, of alkalies, alkaline earths, except magnesia, &c.) which are easily volatilized and therefore colour the flame while affording line-spectra, those (arsenic and antimony com- pounds) which afford continuous spectra while also imparting a colour to the flame, those (mercuric chloride) which vola- tilize almost immediately without producing any noticeable effect upon the flame, and, lastly, those (magnesium and silver chlorides) which, although undergoing decomposition with the production of solid matter, nevertheless do not cause luminosity because the solids produced are not carried into the flame. ‘The metal or oxide which is separated in the various experiments may be obtained by bringing a porcelain basin into the flame. If it be true that the luminosity is due in the foregoing ex- periments to solid matter separated within the flame while the colour is caused by heated vapours, we should expect to find the luminous flames casting shadows upon a white background e e e . cr) . when viewed in sunlight, while the coloured flames would cast no shdaows. Experiment has proved the correctness of this expectation in every case. The flames of burning magnesium and of coal-gas contain- ing oxygen and metallic zine both cast very distinct shadows ; these flames contain magnesium and zinc oxides respectively, substances which remain solid at high temperatures. From these experiments I think we may draw the follow- ing inference :— Luminous flames which owe their luminosity to the presence of finely divided solid maiter produce characteristic shadows when viewed in sunlight. But is the converse of this true? Do luminous flames which produce shadows in sunlight owe their luminosity to the presence of solid matter ? To this question, in the absence of experimental evidence, I should answer no; for it is possible that luminous flames consisting only of heated gases may, when viewed in sun- light, cause an appearance similar to that of a true shadow. We know that the electric light, when passed through the Theory of Luminous Flames. 375 burning hydrogen which has been coloured yellow by the presence of sodium chloride, is partly absorbed thereby, and that the light which passes on shows a dark absorption- band. So also sunlight is more or less absorbed when passed through various glowing gases. As sunlight already shows dark lines corresponding with light spectral lines of sodium, barium, calcium, copper, &ec., it is not to be expected that flames coloured by these metals in the gaseous state should cause absorption of any part of the sun’s rays. But it is otherwise with colourless luminous flames. Such flames ab- sorb portions of the rays of almost every part of the solar spectrum. These flames must therefore cause a shadow-like appearance on the screen, unless the absorption be too trifling to allow of our eye detecting the relatively dark spaces. That the eye is unable to detect any dark spaces, I have proved experimentally. I have not succeeded in obtaining any flame owing its luminosity only to strongly heated gases which is capable of throwing an appreciable shadow on a white screen when viewed in sunlight. That the flames of carbon monoxide, sulphur, selenium, sulphuretted hydrogen, and carbon disul- phide should cause no shadow (although affording continuous spectra) may perhaps be chiefly due to the small quantity of light emitted by them. But it was also found that the exceed- ingly luminous flames of arsenic, phosphorus, and phosphu- retted hydrogen burning in oxygen, as also of oxygen and nitric oxide in carbon disulphide, produced no appearance of a shadow on the white screen. The absorption caused by these flames upon the sunlight was therefore tco small to admit of detection by the unaided eye. On account of their volatility, arsenious and phosphoric oxides must be present in the gaseous condition in the flames produced by burning arsenic and phos- phorus in oxygen. These flames are therefore transparent : it is only at some distance above the flames that the products of combustion assume the solid form ; the white smoke so produced casts a deep shadow on the screen. From an extended series of observations, we conclude that _luminous flames consisting only of gases and vapours are in- capable of producing an appreciable shadow when viewed in sunlight; lighter and darker streaks, due to the varying den- sities of the vapours, of course appear in the images of these flames thrown on the screen. The appearance of a shadow is therefore proof of the presence of suspended solid matter in the flame causing the shadow. Ii follows from this that the luminous flames of hydrocar- bons contain solid matter, inasmuch as they produce very sen- sible shadows. It is evident that this solid matter can be 376 Dr. Karl Heumann’s Contributions to nothing else than carbon. The shadow test therefore supplies us W ith a means of detecting the presence of solid carbon in such flames. Some time after writing the foregoing pages I noticed a memoir by G. A. Hirn entitled “ Sur les “propriétés optiques de la flamme des corps en combustion, et sur la température du soleil”’*. In this paper Hirn describes the behaviour of various flames when viewed in sunlight; his conclusions, however, are directly opposed to those which I have deduced. Hirn starts with the assumption that luminous hydrocarbon- flames contain solid carbon, lumincus phosphorus-flame con- tains solid pentoxide of phosphorus &e.—that the transparency of these flames is due to a change, brought about by the high temperature, in the optical properties of the solid particles con- tained in the flames, whereby these particles become transpa- rent and incapable of reflecting light. I shall endeavour to show that Hirn’s conclusions are in- valid. In his preliminary assumption Hirn takes no notice of Knapp’s experiments, which show that the decrease in lumino- sity of hydrocarbon-flames, brought about by admitting air, is not to be traced to oxidation of the carbon, inasmuch as pure nitrogen causes the same result f. Frankland’s supposition that the luminosity of hydrocarbon-flames is not due to the presence of solid carbon had been disputed by no one when Hirn’s paper appeared. Frankland had shown, five years previous to the appearance of Hirn’s paper, that phosphorus pentoxide is volatilized at temperatures lower than that of the flame of phosphorus burning in oxygen, and that there- fore the luminosity of this flame cannot be due to the presence of solid phosphorus pentoxide. Of Hirn’s assumptions—that the luminosity of hydrocarbon- flames is due to the presence of solid carbon, and that the lumi- nosity of phosphorus burning in oxygen is due to the pre- - sence of solid phosphorus pentoxide—the first was unproved at the time he wrote, and the second is untrue. Light reflected from a solid body is known to be polarized. Hirn found the light from ordinary hydrocarbon-flames, as also the light from burning phosphorus, to be non-polarized ; he also failed to detect evidence of polarization in the light coming from the flame of the blast-furnace. He found, how- ever, that the white smoke rising from the phosphorus-flame emitted polarized light, as did also the smoke coming from the blast-furnace when the furnace-doors were opened. He con- cluded that the flame of the furnace owes its brilliancy to the * Ann. Chim. Phys. [4] vol. xxx. p. 319. t+ Journ. Pract, Chem. | 2] vol. i. p. 425, the Theory of Luminous Flames. 3717 presence of those metallic salts which appear in the solid form when the doors are opened. This conclusion tacitly assumes the presence of solid matter in the flame of the blast-furnace, Hirn does not appear to have examined the spectrum of this flame ; and, so far as our knowledge extends, the contrary assumption to that made by Hirn appears quite as credible as his. Hirn thus assumes that the light from a flame which con- tains solid matter must show evidence of polarization, and that the absence of polarized light is only to be accounted for _by supposing that the solid particles become optically altered at a very high temperature, and lose their power of reflecting light. It appears to me that the facts observed by Hirn would be much better explained by regarding the absence of polarization as proof of the absence of solid particles in the flame. This explanation would apply to the phosphorus- flame, and perhaps also to the flame from the blast-furnace. I have, however, convinced myself by experiment that the non-recognition of polarized rays in the light coming from a flame is not proof of the absence of solid matter in that flame. The amorphous carbon present in the luminous flames of ordinary combustible hydrocarbons refiects almost no light ; these flames show no traces of polarized light when examined by means of the polariscope. The hght from many other non-homogeneous bodies is also devoid of noticeable polarized rays. We cannot, therefore, assume mo the hight emitted by a flame containing a small quantity of finely divided solid matter must show such a number of polarized rays as shall be recognizable by the polariscope. Hydrogen-flames, rendered luminous by the presence of platinum chioride, osmic acid, ammonium chromate, ferric and cupric chiorides, &c., showed no traces of polarized light when examined by means of Arago’s and Savart’s polariscopes ; yet these flames certainly contained solid matter. The flame of hydregen containing chromyl dichloride also failed to show polarized light: the smoke of this flame, and also of the turpentine-flame, when examined in sunlight, afforded evidence of polarization. 1 am inclined to trace the polarizing action of the smoke in these cases to the presence of condensed water, tarry matter, hydrochloric acid, &e., which substances would be present as gases in the flame itself, I cannot, therefore, regard the non-detection of polarized light as proof of the absence of solid matter in flame ; much less can I agree with Hirn’s- statement, that “the solid par- ticles lose their power of reflecting light at a white heat.” 378 Dr. Karl Heumann’s Contributions to In the second section of his paper Hirn notices a statement made by Offret*, who, reasoning from Arago’s observation that the luminous effect of a flat gas-flame, as measured by the photometer, is the same whether the broad or narrow end be turned towards the instrument, concludes that the luminous gas-flame is conpletely transparent. Hirn shows from his own observations that Arago’s statement is not quite correct, and that the broad side of the flame always emits a little more light (about one fifth more) than the narrow side of the flame. Offret mentions the well-known fact that the light from an oil-lamp or candle, when thrown through the electric or lime light, casts a shadow on the opposite wall: he, and Hirn also, regards this phenomenon as due to refraction caused by the heated, and therefore thin, layers of gas. I have, however, shown that luminous flames throw true shadows when .carefully examined, and that these shadows are independent of the darker and lighter bands caused by refraction. In section 3 of his paper Hirn examines the transparency of the flame of petroleum-lamps for light emitted from flames of the same kind. An old-fashioned shadow photometer was employed. A system of eight large lamps placed one behind another, served as the source of light. Hirn’s observations and calculations led him to the conclusion that the light from such lamps suffers a greater diminution by passing through the hot gaseous products of combustion, than by passing through the luminous flames themselves. The method of calculation adopted by Hirn appears to me to be altogether erroneous. By applying what I must regard as a more rational method of interpretation to Hirn’s results, I find that there is a decided decrease in luminosity brought about by the action of the separated carbon upon the light passing through the flames of these lamps, over and above that occasioned by refraction in passing through the heated layers of gas f. Hirn discusses the transparency of flames for light from foreign sources in the fourth section of his paper: he again unfortunately chooses the flame of burning phosphorus. From the fact that the flame of burning phosphorus causes no shadow, while the smoke, so soon as it becomes visible to the eye, does cast a shadow, Hirn concludes that the solid phos- phorus pentoxide suspended in the flame is transparent ; we * Essay presented to the Société d’ Agriculture, Douai. + [The original paper contains Hirn’s numbers, with a description of his, and of Heumann’s method of calculation: the latter method is cer- tainly much the more rational. Hirn’s photometric process is also shown by his own results to be very faulty.—M. M. P. M.] the Theory of Luminous Flames. 579 have long known, however, that the oxide does not exist in the solid form in the flame. I have noticed a faint shadow cast by the flame of phos- phorus burning in air; but as this shadow disappears on substituting oxygen for air, | conclude that in the former combustion the temperature is scarcely high enough to ensure the complete conversion of solid into gaseous matter. Hirn further says that the flame of a petroleum-lamp throws no shadow on a screen when viewed in sunlight, but that when the flame is rendered smoky the smoke causes a most marked shadow. From the detailed description of Hirn’s experiment, it is evident to me that he placed the screen at too great a distance from the flame. He also obtained no distinct shadow when the sunlight was sent, by means of a looking-glass, through a series of eight petroleum-flames. On account of the interference between the flames, and also on account of their distance from the screen, this result is not to be wondered at”. The petroleum-flame employed by Hirn was surrounded by -a glass cylinder, which seriously interfered with the distinct- ness of the shadow produced. It is not possible, by removing the screen further and further from the flame, to obtain a clearly defined shadow much exceeding in size the dimensions of the flame itself. If, however, the sunlight be collected by a convex lens, and be thrown on the flame, a large and well-defined shadow may be obtained; the eye is also less fatigued by the glare of the white screen. Fig. 7 represents the shadow thrown by a non-smoky coal- gas flame, burning at the orifice of a tube 7 millims. in width : fig. 8 represents the appearance on the screen after removing the luminosity of this flame by admission of carbon dioxide. If the flame was rendered wholly or partially non-luminous by the introduction of a piece of metal, the shadow wholly or partially disappeared: emission of light and production of shadow are therefore closely related to one another. The flat flame of a very small bat’s-wing burner produces no shadow ; but if the flame be turned edgeways towards the screen, a small but distinctly perceptible shadow is produced. in the first instance the layer of luminous flame is too thin to cause the production of a shadow ; if an ordinary-sized burner * Hirn remarks that the smoke arising from a petroleum-flame ap- peared white when illuminated in a dark room. This is, I think, due to reflection of light from the smoke, chiefly from the particles of water, tarry matter, &e., the black smoke being itself nearly invisible against the dark background. 380 Dr. Karl Heumann’s Contributions to be employed a shadow is obtained. This shadow is most dis- tinct towards the outer edges of the flame, where the thick- ness of luminous matter attains a maximum. Fig. 9 represents the shadow thrown by the flame of an ordinary burner. Fig. 10 represents the shadow produced by directing the small flame against the screen. Figs. 11 and 12 show the forms of shadows produced by adding an excess of benzol vapour to the gas (coal-gas or hydrogen) issuing from ordi- nary burners. Similar appearances result with the flame of hydrogen rendered luminous by admission of chromyl dichloride. These experiments show that the shadows in- crease in intensity as the thickness of the luminous layer in- creases, or, in other words, that the intensity of the shadow is dependent upon the number of carbon particles which pre- vent the passage of the sun’s rays through the flame. Hirn blew lycopodium powder into a flame ; before the powder was completely ignited the flame produced a shadow ; after complete ignition, however, no true shadow was obtained. i have carefully repeated this experiment, and find that a flame containing a considerable quantity of lycopodium pow- der produces a marked shadow. Hirn probably used too little of the powder, or placed his screen at too great a distance from the flame. It is of course to be expected that the shadow produced by a flame in which the lycopodium powder is undergoing thorough combustion should be less marked than that formed by a flame which contains unburned lycopodium : in the former case the shadow is due to the presence of sepa- rated carbon only. The sole experiment of Hirn which is capable of interpre- tation in terms of his theory only, is that in which the light of burning magnesium wire was passed through the flames of eight petroleum-lamps: the increase in the light-effect of these eight flames was equal to the total light-effect of the magnesium when burned by itself. But Hirn’s previous ex- periments showed that the hight from two petroleum-lamps loses 39°9 per cent.* when passed through stx other similar flames ; it is scarcely possible therefore that the light of burn- ing magnesium could suffer no diminution in luminosity when passed through eight petroleum-flames. Hirn’s photometric process is, as his own results show, altogether untrustworthy. Hirn says that the flame of the blast-furnace is completely transparent : this may be so. His conclusion, that this flame contains solid matter, but that this sod matter is optically * Calculated according to my method. the Theory of Luminous Flames. 381 changed at the high temperature of the flame, is, I think, based upon no solid foundation of fact. Hirn describes experiments with coloured flames (Bengal fire, &c.). His conclusion, that these flames contain much solid matter, although they cast no shadow, is evidently in- correct. ‘The colour is, of course, due to vapour, not to solid matter. ; Lastly, Hirn regards the petroleum-flame as diathermanous ; but even ‘admitting that this fame allows more or less the pas- sage through it of. heat-rays (a problem which I am not in a condition to examine experimentally), this would not contra- dict the demonstrated fact of the presence of solid carbon in ordinary luminous flames. I think I have now shown that Hirn’s hypothesis, viz. that solid bodies when raised to a white heat lose their power of reflecting light and become transparent, is without experi- mental support, and therefore cannot be maintained. In the attempt to discover the causes of the luminosity of flame, it is necessary that the observer should be acquainted with the physical as well as with the chemical data which he vill be required to examine. A want of this twofold know- ledge has already led many to view the phenomena of lumi- nous flames either from the purely physical, or from the purely chemical standpoint ; in either case the result has been disastrous. In conclusion, I would once more draw attention to the observations of W. Stein. If soot be present in the form of vapour in luminous flames, the application of a high tempera- ture, after condensation, should cause it to again assume the gaseous form; but this is not the case. Further, the soot deposited from a coal-oas flame does not contain more than 0-9 per cent. of hy drogen. I would now gather together the Proofs of the Presence of Solid Carbon in Luminous Hydro- carbon-flames. (1) Chlorine causes an increase in the luminosity of feebly- luminous, or non-luminous, hydrocarbon-flames. Inasmuch as chlorine decomposes hydrocarbons at a red heat, with separa- tion of carbon, it follows that the increased luminosity is due to the production of solid carbon particles. (2) A small rod held in the luminous flame becomes rapidly covered on its lower surface (the surface opposed to the issuing gas) with a deposit of soot. The solid soot is evidently driven against the rod. If the soot were present as vapour in the juminous flame, its deposition would be due to a lowering of 3882 Messrs. Wanklyn and Cooper on the Determination the flame-temperature, and would therefore take place on all sides of the rod. (3) A strongly heated surface also becomes covered with a deposit of soot. This would not be possible if the deposit were the result of the cooling action of the surface upon the flame. (4) The carbon particles present in the luminous flame become visible when the flame is caused to rush against another jlame or against a heated surface. The separated particles are rolled together into larger masses, so that the luminous mantle becomes filled with numerous glowing points. The soot of such a flame is very coarse-grained. (5) The luminous mantle of a flame is not altogether transparent: the thicker the flame-layer and the greater the number of solid particles contained therein, the less trans- parent does it become. The transparency of a luminous jlame as no greater than that of the (approwimately) equally thick stratum of soot which rises from the flame of burning turpen- tine, and which is universally allowed to contain many solid carbon particles. ‘The luminous flame of hydr ogen, containing solid chromic oxide, is as transparent as the hy drocarbon- flame. (6) Those flames which undoubtedly owe their luminosity to the presence of finely divided solid matter, produce charac- teristic shadows when viewed in sunlight. The only luminous flames which do not produce true shadows are those which consist of giowing vapours and gases. Luminous hydrocarbon- jlames produce strongly marked shadows in sunlight; these jiames therefore contain finely divided solid matter. That this solid matter can be nothing but carbon is evident from the fact that other substances, capable of remaining solid at the temperature of these flames, are absent. These proofs are, I think, sufficient to convince every one that the luminous flames of hydrocarbons actually contain solid carbon particles. Darmstadt, Chemisches Laboratorium des Polytechnicums. LI. On a Method of determining the Anount Prove Compounds in Vegetable Substances. By J. ALFRED W ANK- LYN, Corresponding Member of the Royal Bavarian Academy of Saviano , and We JCOornR*. eae phy solomen doctrine that the animal does not pro- duce proteine compounds, but simply transforms those proteine substances which it has taken in as food, lends great * Communicated by the Authors. of Proteine Compounds in Vegetuble Substances. 388 importance to the determination of the amount of proteine compounds in different kinds of vegetable food ; and such a determination becomes of the utmost importance both to the physiologist and from a practical point of view. Hitherto, however, this desideratum has been very imper- fectly supplied, and the chemist has ver y inadequately an- swered the question as to the proteine value of the different vegetable foods. Gluten, legumen, vegetable caseine, vegetable albumen, as the various proteine substances occurring in vege- tables have been called, vary much in properties. Some of them are soluble and others are insoluble in water ; and some are soluble in alcohol; and it would be difficult to draw up any general method of extracting the proteine compounds from vegetables so as to be enabled to weigh the proteine compound in a state of purity. Resort has therefore been had to ele- mentary analysis; and chemists have deduced the amount of proteine compounds from the percentage of nitrogen found on submitting the food to ultimate analysis. To this procedure there are several objections which have, apparently, not been sufficiently insisted upon. Taking the ease of wheaten flour (which is much more favourable than many other cases), the percentage of nitrogen is a little short of 2°00; yet neither the Will-and- Varrentrapp process nor the Dumas process of nitrogen-determination, as it 1s gene- rally carried out, is at all adequate to the valuation of the pro- teine substance in flour. The Will-and-Varrentrapp process, as those who have a eritical knowledge of it are aware, is subject to special failure when it is applied to proteine substances, and is not a deter- mination of nitrogen in these instances. The Dumas method, as usually practised, is uncertain when it is apphed to determine a minute quantity of nitrogenous substance in presence of a large quantity of non-nitrogenous organic matter. Possibly, if carried out with extraordinary care and extraordinary precautions, the Dumas process might become available for the purpose in view ; but those persons who have practical knowledge of the difficulties besetting this particular case will admit that extraordinary care would indeed be required, and that the process would be too imprac- ticable for general employment. The method by which we seek to accomplish the task before us is, we believe, especially adapted for this description of work. We propose to measure the amount of proteine substances in vegetables by the amount of ammonia which the vegetabies generate when they are subjected to the action of a boiling solution of potash and permanganate of potash ; in fact, we 384 Messrs. Wanklyn and Cooper on the Determination have made a special adaptation of the well-known ammonia process of water-analysis to the case of vegetable proteine. The working details of our process are as follows :— Into a litre flask a carefully weighed gramme of the ve- getable substance to be analyzed is placed, and 20 cub. centims. of decinormal solution of caustic potash is added, and then water is added until the litre-mark is reached by the level of the liquid. The contents of the flask are then shaken up so as to ensure thorough mixture. In this manner we obtain a liquid of such a strength that each cubic centim. contains 1 milligramme of the flour or other vegetable substance to be operated upon. 10 or 20 cub. centims. of this liquid (4. e. 10 or 20 milligrammes of the vegetable substance) are conve- nient quantities to work with. The next step is to get the retort in order as for a water- analysis, and to place in it 300 or 500 cub. centims. of good drinking-water, and to add 50 cub. centims. of a solution con- taining 10 grms. of potash and 0:4 grm. of permanganate of potash (such as is used in water-analysis), and to distil until the residue in the retort no longer yields the slightest trace of ammonia. That having been done, 10 or 20 cub. centims. of the liquid containing the vegetable substance are to be added and the distillation proceeded with. The vegetable substance will then be attacked, and its proteine will yield ammonia, which will distil over and may be measured b means of the Nessler tests. For further details of the man- ner of carrying out work of this description we would refer to the ‘Treatise on Water-2 analysis, which is now sufficiently well known to chemists. It was shown some years ago that egg-albumen yields about one tenth of its weight of ammonia when submitted to such a process as the above, and that solutions containing different quantities of eg g-albumen yield ammonia exactly propor- tional in amount to the strength of the solutions of albumen. Our experiments warrant a parallel statement in the case of vegetable proteine ; and in the Table about to be given, the ammonia, multiplied by 10, gives a fair approximation to the actual quantity of vegetable proteine in the different samples. As will be observed, cur experiments include many descrip- tions of wheaten, pea-, rice-, maize-flour, oats, barley, malt, rye, and arrowroot. The last-named is important as showing a very small proportion of proteine. The peas tote was ground from the peas in our own labora- tory, and passed through a very fine sieve. ‘The rice-flour was likewise of home mantiacture ; and the same is true of maize and the malt. The rest were not powdered in the laboratory. Samples of wheaten flour :— of Proteine Compounds in Vegetable Substances. 385 Percentage Name of sample. of ammonia. 1. Cambridgeshire extra-superfine... 1:10 2. Another sample a oie) 3. Household flour, Waterloo Bridge. 1:13 PRCOUMURY HOUT, oestieoe cas suuerecsiaces 1:08 Pew be MGI COMSHITE) \saiace0isse nace ie 1°05 SIMS UE Ol keene clas c ck icles Rnkelnd acer. 1:00 Piper MTV AIAN 3 6 0.gai0 03:24 onle cigs 'ge csereheniss 1°10 S-eenother Hiumearian: ......0......+: 1-05 9. a Me ibhaat ict Setaicttes oA seats dots 1:07 mpm Datblay Paris) ...c0 (that is, if the mirror is posztive), the minor axis is oriented in the upper right-hand quadrant. 2. If 8<0 (that is, if the mirror is negative), the same axis is oriented in the upper left-hand quadrant. 3. If é=0 (that is, if the mirror is neutral), the minor axis vanishes. tan 2rp?= 4. If d=+ = (that is to say, under the principal incidence), the minor axis remains oriented at 45°, whatever may be the orienta- tion of the initial vibration. 5. Under this incidence, when the polarizer is rotated, Airy’s fringes become transformed into Dove’s rings. Let @ be the azi- muth obtained; it is that of the restored polarization, connected with the factors of alteration of the amplitudes by the formula h t = =, an @ B This method is convenient for the study of reflection in general and also of the laws of Cauchy and Jamin; moreover it is delicate. Indeed, if you employ ordinary glass as the mirror, and observe under an incidence near the polarization-angle, you will recognize that the extremities of the minor axis have an appreciable devia- tion; and yet the elliptical polarization is so little evident that it escaped Fresnel. An interesting experiment consists in arranging in succession three mirrors—of steel, of alum, and of fluorine. The first and the third, being one positive, the other negative, present two contrast- ing positions of the fringe en semelle; the second, being neutral, offers the transitory phenomenon of conserved rectilineal polariza- tion.—Comptes Rendus de V_ Académie des Sciences, March 26, 1877, tome Ixxxiy. pp. 604-606. NOTE ON MOLECULAR VOLUMES. BY F. W. CLARKE, §.B., PROFESSOR OF PHYSICS AND CHEMISTRY. Several years ago, in a series of papers upon atomic or molecu-_ lar volumes, I pointed out some curious multiple relations connecting both elements and compounds*. For example, I found that a simple relation of this kind connected the alkaline metals with each other; * Silliman’s American Journal, March and May, 1869; September, 1870. Intelligence and Miscellaneous Articles. 399 and, later, that the haloid salts of some of these metals had mole- cular volumes multiples of that of hydrogen. For this latter relation, however, my materials were meagre. I had then the specific-gra- vity determinations for LiCl, NaCl, KCl, NaBr, KBr, Nal, and KI, or seven compounds in all. ‘To these I added, though unsatisfac- torily, the corresponding salts of silver, making a list of ten bodies closely related, and giving volumes multiples of 5:5, the value as- signed by Kopp to hydrogen in its liquid compounds at their boiling-points. This relation I am now able to extend, partly by new density-observations of my own, to include at least twelve compounds not in my earlier list. My own determinations, in addition to those I have already given for the alkaline fluorides, are as follows :—Rubidium chloride, 2°209, 19°; rubidium bromide, 2°780, 17°°5; rubidium iodide, 3°023, 22°; lithium bromide, 3°102, 17°; lithium iodide, 3-485, 23°. Now let us tabulate the material. The first column contains the symbol of the substance, the second its density with authority ‘given, the third its molecular volume as found, the fourth its volume calculated, the fifth a theoretical density deduced from this volume. The calculated volumes are of course the exact multiples of Kopp’s hydrogen value, and will be seen at once to agree closely with the results of experiment. ‘The real variation between fact and theory, however, will be best seen upon comparing the two columns of densities. The differences here are always less than 0:1. ) iE II, il. IV. V. Lik | 2:295, Clarke. 11°33 11:00 2°363 LiCl | 1:998, Kremers. 21:27 22°00 1:932 LiBr | 3°102, Clarke. 28°05 27:50 3164 Lil BAO bs 38°45 38°50 3°481 Nak | :2:558,__—s«,, 16-41 16°50 2°545 NaCl | 2:145, Bruignet. 27°27 27°50 2:127 NaBr | 3:079, Kremers, 30°45 33°00 3121 Nal | 3°450, Filbol. 43°48 44-00 3409 KF 2°096, Clarke. 28°20 27°50 27113 KCl | 1°945, Kopp. 38°35 38°50 1937 KBr | 2'672, Playfair, Joule.| 44°57 44-00 2°707 _ KI 3°056, Filhol. 54:35 55:00 3°020 RbF | 3:202, Clarke. 32°64 33°00 3167 RbCl e| 2209... 54:78 55:00 2-200 RbBr Zit sOie © 4; 59°53 60°50 2°735 Tjolk paler Seo 70°29 71°50 2972 Here, now, we have sixteen compounds of a single type, every one of which agrees with the rule. In each case the molecular volume comes out a multiple of 5°5, or very nearly. Only one substance in the list seems to be in any way abnornal, namely, rubidium fluoride, with its volume of 33. The other fluorides in this group have volumes less by 11 than those of the corresponding chlorides; but in this case the difference is 22. A curious progressive relation is also worth noting. If we compare the five chlorides given in the Table we shall see that, upon arranging them in the order of their mole- cular weights, the differences between successive members of the series increase as we ascend. Thus LiCl and NaCl differ by 5:5, 400 Intelligence and Miscellaneous Articles. NaCl and KCl by 11, KCl and RbCl by 16°5. This regular differ- ence-increase is certainly suggestive of some law yet to be clearly made out. A similar relation to Kopp’s hydrogen-volume is also afforded by the two other compounds. Sodium hydride (Na,H), discovered by Troost and Hautefeuille*, with a density of 0°959, has a molecular volume of 49-1, or very nearly 5°5x9. Still more interesting is iodine monochloride, so carefully studied by Hannay?. At 0° the solid substance has a specifie gravity of 3-263, and a molecular volume of 49:8, thus varying only 0°3 from a multiple of 5:5. At 101° the chloride boils, and at 98° its density is 2-958, having a volume of 54°9. Probably an absolutely correct determination at its boiling-point would give a value of 55. So we may say that iodine monochloride, both as a solid at 0°, and asa liquid at its boiling-point, has molecular volumes multiples of that of hydrogen. As for the haloid salts of silver, they cannot with certainty be included among the substances connected by this multiple relation. The fluoride agrees fairly, however, having a density of 5°852, Gore, and a molecular volume of 21°7 instead of 22. The chloride and iodide may be forced to agree by selecting out the density-determi- nations of certain investigators, and rejecting other decidedly dis- cordant data. The bromide does not agree atall. A determination of my own for precipitated AgBr gives a density of 6-215, 17°, and a corresponding volume of 30°25. Other determinations are even more discordant than this. Silver salts generally have molecular volumes equal or nearly equal to the corresponding sodium com- pound, that of sodium bromide being 33:0. Silver fluoride, it will be seen, diverges also from the sodium salts. For thallium our data are insufficient. Its monochloride has a molecular volume approximating to a multiple of 5°5, but not closely enough to be satisfactory ; the sesquichloride does not even approximate. At some future time I hope to be able to revise and extend our specific- gravity determinations for this class of thallium salts. Now to sum up. Including the silver and thallium salts we know the densities of twenty-five substances containing only univalent elements. Of these, twenty have molecular volumes multiples of that of hydrogen, three are doubtful, two apparently disagree. We may therefore safely assert the following general law, subject to possible exceptions :—Hvery compound containing only elements of the hydrogen group has a molecular volume an even multiple of that of hydrogen. This is probably but a hint of some more general regu- larity connecting other elements and other groups. Postscript.—Since the above pages were written, there has been ublished by Johnson a density-determination for potassium tri- iodide, KI, (Chem. News, vol. xxxiv. p. 256). This determination, 3°498, corresponds to a molecular volume of 120-1. 121 is an exact multiple of 5:5, and gives a theoretical density of 3-472. The mul- tiple relation now holds good in twenty cases out of twenty-five. Silliman’s American Journal, April 1877. * Comptes Rendus, vol. \xxviui. 970. + Journ. Chem. Soc, II. xi. 818. THE LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIBS.] SONG VSiCt: LV. Onsome Effects of Dissociation on the Physical Proper- ties of Gases. By W. M. Hicxs, M.A., Fellow of St. John’s College, Cambridge*. (poe following pages contain an attempt to discover what effect the dissociation of an elementary or compound gas has upon its physical constants. That dissociation must exist to some extent at all temperatures is exceedingly probable; and if so, it must necessarily affect the physical properties of the gas; and especially we might suppose that it would pro- duce variation from Charles’s law, and perhaps explain the difficulty hitherto experienced in accounting for the ratio 1°408 of the specific heats of a permanent gas. It was under this belief, and also with some hope of throwing a little light on the chemical changes which take place in compound gases, and on mixing different gases, that I undertook the mathema- tical investigation of it. I. 1. Before we can apply mathematical reasoning to the con- sideration of dissociation, it will be necessary to have some hypothesis on the manner in which it takes place. Our hypo- thesis should be one which, while being as simple as possible, is likely to contain the essentials of what really takes place, even though it may not be correct in all its details. Dissocia- tion of a compound gas is that state in which the compound molecules of a gas are split up into their component parts and exist together uncombined. I shall suppose the same also to * Communicated by the Author. Phil. Mag. 8. 5. Vol. 3. No. 20. June 1877. 2D 402. Mr. W. M. Hicks on some Eifects of Dissociation take place in an elementary gas, the molecule being composed of two atoms. How the atoms are bound together we do not know ; but, from what we can gather, there seems to be some attractive force between them which at very close quarters changes into a repulsive one. Equilibrium is sustained by the attraction between the two atoms and their motion about one another. If, then, the two atoms of a molecule become sepa- rated, there seem only two ways of accounting for it. Hither their relative motion becomes so large as to overcome the force of attraction ; or some external force must act upon them, which can be nothing else than a reaction between them and some other molecule. The latter is the hypothesis I have adopted in the following investigation. 2. I consider the atom to be smooth, spherical, and perfectly elastic, and, in order to bring the dissociation under mathe- matical treatment, suppose (1) That when a molecule experiences a blow greater than a certain blow c, it breaks up into its component atoms, (2) That when two atoms impinge with a blow less than ec, they combine to form a molecule. Now it is exceedingly improbable that any of these sup- positions is absolutely true ; but yet I venture to think, since the mathematical form would be similar, that the state of such a gas would differ only slightly from that of real gases. As was said before, the reaction between two molecules is pro- bably a varying one, and it is unlikely that they ever come into real contact ; still the mean effect will be similar to the case under our hypothesis. We must look upon ¢ as a mean blow for different directions of incidence, or as some quantity which in the real state determines whether the molecules will break up or not. For instance, if the force between two atoms were inversely as the square of the distance, ¢ would determine whether the resulting orbit of two atoms coming together would be an ellipse, or a parabola or hyperbola. So also the radii of action must be taken as average quantities. Further, it is not likely that they are absolutely independent of the temperature ; for it is conceivable that as the internal energy . increases they will fly further apart, and thus become more liable to blows from the other molecules. Neither are we perhaps warranted in assuming that ¢ is constant ; since ¢ constant involves the invariability of the distance of the two atoms; for if the distance increased, the force between would diminish, and therefore c also. Nevertheless, although numerical results would be affected by this cause, the general laws would be of the same form in the two cases; and in either case our experimental knowledge is neither wide on the Physical Properties of Gases. 403 enough, nor exact enough, to enable us to deduce exact numerical results, 3. In the present paper I first consider the problem, To find the number of blows greater than c, between two sets of moving particles, per unit of time, in unit of volume. This is then applied to find the dissociation at any tempera- ture, and a quadratic obtained, the positive root of which gives the ratio of molecules to free atoms in the gas ; and it is shown that the resulting state of the gas is a stable one. This ratio is used to investigate the relation between the tem- perature and pressure ; and it is shown that Charles’s law is not rigorously exact, though within ordinary ranges of tem- perature it is very nearly so; reasons are also given why for the permanent gases c should be large, compared with the mean blow at ordinary temperatures. Next the specific heats are considered ; and it is proved that for a diatomic molecule, in which the atoms are smooth and spherical, or the energy of rotation of the atoms is unaffected by external causes, the ratio of the specific heats is about 1:4 ; it is also shown that the specific heats are almost rigorously constant at ordinary temperatures. ‘This concludes the present paper ; in what is to follow I intend to discuss the properties of a compound gas of the type HCl. 4. When we pass to the consideration of a compound gas, even of the simplest form, additional difficulties are introduced, as equations of a high order appear whose algebraical solution is impossible, and from which therefore it will be extremely difficult to deduce general laws. All we seem able to do is to take one or two particular cases, and learn what we can about them. For instance, in the case of a gas of the lype HCl, i.e. in which two monatomic gases combine to form a gas whose molecule is diatomic, we get three equations of the second degree between three unknowns. In general, when two gases A and B are mixed together, there will always be a certain proportion of a new gas C whose molecule is com- posed of atoms of A and B, and the proportions of free atoms and molecules of A and B will be altered. When the excess of the number of combinations of free atoms of A with B over the number of molecules of C destroyed in any time is greater than the number of combinations of free atoms of A to form A and of free atoms of B to form B, then the propor- tion of A and B decreases, whilst that of C increases, and we get a chemical change. This will explain why often the mere presence of another gas D will produce a change of A and B into C ;.for the action of D on A and B may cause more of their molecules to be broken up than of C, while at the same 2D2 404 Mr. W. M. Hicks on some Hffects of Dissociation time not many more of its own are ; therefore, since the com- binations of A and B atoms into C molecules are destroyed more slowly than the combinations of A and B atoms into A ‘and B molecules, the gases A and B after a time change into C. 5. In a similar manner we may explain the result obtained by Andrews, that if nitrogen be mixed with carbon dioxide, the mixture may be subjected to very high pressure without the carbon dioxide being condensed. When a gas condenses, we must suppose that molecules combine with molecules to form larger aggregations, and that this continues until the whole gas is condensed into a liquid. When the temperature is below a certain degree, the change from the gaseous to the liquid state takes place around nuclei, in which the molecules get entangled, and which the energy of agitation is not great enough to destroy ; in this case a mist is formed, and we see the gas condense. But when the temperature is higher than a certain degree (the critical temperature), the energy of agitation is so great that an aggregation greater than the average gets broken up as soon as formed, and the gas passes into the liquid form by having its particles uniformly pressed more closely together; no separate nuclei are formed to diffuse the light passing through, and we can see no change take place. The nitrogen molecules and atoms act in the same way to break up the carbon dioxide aggregations as soon as formed, and hence prevent it from condensing. 6. The fact that two states of a gas are possible under the same conditions, as for instance 2 N+O and N, O, is easily explicable, as it is quite clear that in general there will be more than one way in which the losses of the different molecules may be equal to their gains. In other words, the equations of high order, which we obtain, have several positive roots, which give a stable state of the gas: as the tempera- ture rises, one such state may become unstable ; in this case we shall get a sudden change into one of the other stable states, with a transformation of energy, answering In ex- perience to an explosion with evolution of heat. Jb: 7. Let N be the number of molecules of mass m, in unit of volume, and N‘ the number of molecules of mass m,. Also let a, 8 be the velocities of mean square in the two systems respectively, and s the mean effective distance between mole- cules of the first kind and of the second. Consider a molecule of the first kind moving with velocity v; the number of such whose velocities lie between v and v+6év on the Physical Properties of Gases. 405 AN oe ae. ve ~#dy*; and let us find the number of collisions in Ta unit of time between one of these (m,) and the second system of molecules. The number of molecules of the second kind in unit of volume whose velocities lie between wu and w+6u is 4N’ V 783 between @ and 6+66 with the direction of motion of m, is tsin 066. The relative velocity of m, with these 18 uP we du. The proportion of those moving at angles = Vu? +v" + 2uv cos =r, say ; . and the number of collisions in unit of time is | ie aN ,*.. re TST. ve. uve & sin 0dud0=N rsin @ dé, say. 8. We have now to find the proportion of those that strike with a blow greater than a given quantity (c,say). Consider a molecule of the second system striking m, at an arcual dis- tance @ from the point of directimpact. The relative velocity of the surfaces before impact is 7 cos @, and as the molecules 2M : M+ My 0805 and this must be >c. If, therefore, ¢, be such an angle that 2mm, 7 Cos P5=(, + mMz)c, all those molecules that fall within a small circle whose radius is ssin ¢, will strike with a blow >c. The proportion required of the whole number of impacts is therefore qs? sin? : m,+m,)c\? Oe ee ein’ d= 1 — eu) =1-(£) , Say ; Ts" QmyMer r are supposed perfectly elastic, the blow will be and the whole number of collisions required te 1.2 =Nr{ i (2) sin 050. 9. The number of molecules of the second kind with veloci- ties between wand w+ dou, and making an angle between @ and 9+64 with direction of m, is ae sin O8Ou20~ Su. Therefore the number of those with velocity uw which have a * See Maxwell, Phil. Mag. January 1860. - 406 Mr. W. M. Hicks on some Effects of Dissociation velocity r relative to m = Sa, 6, 60u7e -B Pa 405, where uw +v?+2uv cos 9,=7r". For the same value of « when r becomes r+6r, 9, becomes é;+066,, where : ? sin 6,69, = — — 6r 1001 me and the above number becomes oul ———_ ¢ —BSu ror. B80 To find the number of molecules impinging on m, with rela- tive velocity between rv and r+6r, this must be multiplied by 7s’r and integrated with respect to wu over all possible —w—v 2 2 r values of w, 1. e. for such that Sar lies between +1, or uw MEO S20. U~Vcis 1— ae Ae Hence the whole number of impacts of the second system on m, with a blow >c between molecules of the first and second kinds per unit of time is ales 2 oe _ (r+0)? 3p eel ei) al fe }ve #& dvdr. This may - put in the form 4ANN’s? ('* (v—h)2 (v+h)2 12 — 283 4 (7? — )e- ee a i fe ya =e ¥ }udv, e on the Physical Properties of Gases. 407 where 2, 028? lS 2 82 and y = ae The second integral *-F 00 v2 3 Ann» =| (othe Pdv=h/ry= va ie = (a? +6) Hence the whole integral An/ a@NN’s? : Re NTE _ a ie ; hee —C”?\re &+8 dr (a? + 27)? Jo! =2VaNN's Va? + Be +8. @ Aen tae : Let 5 be the common mean kinetic energy of molecules in each system. Then 9 ay) Mya =Mofp = 0; also ,__ M4 +My . 2MaMe es Hence the number of blows >c in a unit of volume per unit of time between molecules of the first and second kinds respec- tively is mi+Mo Cc? 2V/ c@NN’s? ee / Oe Amys ee Os. M4 Nbo The law of variation of the number for the same pair of gases is of the form EO App’V te #¢, where p, p’ are the densities of the two gases, ¢ is the absolute temperature, and A and ¢, are constants. It is probable that c or ¢, will vary with the amount of internal energy of the mo- lecules, and will diminish as the temperature increases. Putting c=0, we find the whole number of collisions to be oV TNN’s? aE Rua las yet My1Mg as has been shown by Maxwell*. Hence the number of coili- * Phil. Mag. January 1860 408 Mr. W. M. Hicks on some Effects of Dissociation sions which impinge with a blow c 1s given by an expression of the form de-#”; hence the num- ber of blows between ¢ and c+ 6c == NiLCe gin OCN; hence the mean blow CO 2a Cer? de == 0 No. of blows > 0 ak ass aa! Gas Tm = —=} ave"? da = —= ( e-P da=t Wi Ts Vp V bh Jo pe 2a. T, eam Amn, ee PR dn 4 m+my, m+ ms or c’ is proportional to the square root of the temperature. We may therefore express the number of blows >c¢ in the form m,+m sen Oe. INN’s? (mi) ce 2, M4Mg IIL. Case of an Elementary Gas. 11. We will now employ the foregoing formula to investi- gate the effect of dissociation on an elementary gas whose molecule is diatomic. _We shall suppose the dissociation to occur through a molecule receiving a blow >c; also that if two atoms come within a mean distance s, so that they would impinge with a blow e ieee ea Me e and, m = half the number of molecules destroyed The number of on the Physical Properties of Gases. 409 collisions of a molecule and atom with a blow >c a 39 _ 30 =Arvy/ rs <" e@ 8méd J : 2m = the number of molecules destroyed. The number of colli- sions of two atoms with a blow aé, or, substituting for &, ere) 1l>a—va' +), which is clearly the case, and the value of & therefore gives a stable state. The condition may be stated in a different form as follows. When w increases through the root, /(«y) must change from positive to negative. From this again we see that the positive root of by?—2ary—x?=0 gives a stable state. For when «=O the expression is positive, and when «=~ it is negative, whence, as there is only one positive root, /(@y) must change from positive to negative as 2 increases through it. 13. The expression above found for & gives twice the ratio of molecules to free atoms in the gas at any given tempera- ture @. The proportion of molecules to the whole number of moving particles in the gas is therefore = oy = suppose whilstthe whole number of moving particles =2y+2=4 —— = : N. In order to obtain some idea of the law of variation of the pro- portions of molecules and free atoms with the temperature, I have traced the curve in fig. 1. The abscissee denote the tem- Rigel. Asynptote 0 ‘5Oo G, perature measured in terms of @,, whilst the ordinates give the proportion of free atoms to moving particles. The particular SHS : curve represented belongs to the case where s;= On (which seems very likely the case) and s=3s, (or the radius of action of a molecule equal to the sum of the radii of action of the atoms of which it is composed) ; but the general form of the curve does not depend on the values of s, s1, so, and only varies very slightly with their variations. It is noticeable that there on the Physical Properties of Gases. 411 are two periods when the variation of the proportions is small, viz. when the temperature is small compared with 0, (less than yo 8) and when it is greater than @). The curve, “ok course, has an asymptote at a “distance 1 from the origin; if we regard this as the line of abscissee, the ordinates measured from it ¢ give the values of 7. 14. In considering the pressure of the gas we may treat it asa mixture of two. We shall therefore have p=s .2mav?+2m. 2yv?, where vj, v. are the velocities of mean square in the two cases; and therefore 2mv? =mwv;=XO, where @ is the absolute tempe- rature and % some constant, whence NEC GES) aI ey a5} Poe 2 =3 (et W= 3 Spe M=3 (1+ tae) =«(1+ )p0, say. If there were no dissociation, we should have, calli ling P the pressure in this case, Koos Fig. 2 shows the relations of p and Pina gas where s= Fig. 2. hence Bess 2 §25 O G (s) the abscissz represent the temperature, and the ordinates the corresponding pressures in the two cases. The bend in the curve between °5@, and 1°56, is noticeable. 15. According to the ordinary theory P=xpt, where t is the temperature measured from a certain zero-point, which is very slightly different for the different permanent gases. Ac- cording to the above theory p=xp(1+)0, where @ is the mean kinetic energy of translation of the particles composing the gas. Now, in the formula P=xpt, the temperatures are 412. Mr. W. M. Hicks on some Liffects of Dissociation measured by comparison with the temperature of mercury or some other substance ; and all we can deduce is that when the temperature increases a certain degree, the pressures of all the permanent gases increase in very nearly the same ratio with. one another ; but we have no proof that what we consider equal increments of temperature corresponds to exactly equal increments of mean kinetic energy. ‘This is generally ac- knowledged and the temperatures measured by the “air- thermometer ”’ are supposed to be correct, whilst the varia- tions from the law P=xpét (when ¢ is measured by the mercury- thermometer) are set down to the account of the unequal ex- pansibility of mercury at different temperatures. But even on this supposition all that experiment tells us is that, in the formula P=xpt, « is the same forall permanent gases, and tis measured from nearly the same zero-point. Tor instance, suppose that €is the same for all gases at the same tempera- ture ; then, (1+ ¢)@ being the same at the same temperature for all gases, we should find in our experiments that « is the same and ¢ is measured from the same zero. But if we could by some means measure @ correctly and then apply our corrections to the temperatures as given by the mercury- rmometer, we should find that the coefficient of expansion the ter, hould find that the coefficient of e sio of mercury increases still more with the real temperature than is apparent from our comparisons of air and mercury, suppo- sing, as is done, that equal increments of the pressure of air correspond to equal increments of temperature, and not, as on the theory of dissociation, to equal increments of the quantity (1+ 0)0. Since itis highly probable that the relations between s, s1, s9 are the same for all gases, the only condition that (1+¢)0 H may be the same is that @, or ee may be the same, which 0 m : would mean that, if two molecules are to break up, the relative velocity of the two impinging directly must be such—not that the minimum blow is the same in all gases, but that the vis viva must be the same, or that the force of cohesion is propor- tional to the square root of the mass. As I see no likely hy- pothesis on which this may be the case, I think it is not pro- bable that (14 )@ is rigorously independent of the kind of gas. But that the theory may agree with experiment, it is not necessary that (1+¢)@ should be rigorously the same for all gases ; in fact, experiment tells us it is not so, although the variation is very small. 16. If for all the permanent gases 0, be small compared with our ordinary temperatures, then our ordinary tempera- tures are some multiples of 6, and the range within which on the Physical Properties of Gases. 413 experiments have been made is also some multiple of 6,. Moreover a slight difference in the values of @, for the differ- ent gases would givea greater difference in the law of pressure as the temperature increases. If, on the other hand, @, be great, so that ordinary temperatures are <-+/50,, then as we have seen before, the variation and dissociation is small, and the more so as the maximum range of the Centigrade tempe- ratures would all be small fractional parts of 6). Here also variations of @, would not produce much difference be- tween different gases at ordinary temperatures. We should be led therefore to suppose that 0, is in general large. This is also supported by the fact that it is highly probable that at ordinary temperatures the dissociation of the permanent gases is small. [or the sake of illustrating this and also to obtain some idea of the magnitude of the variations involved, we will consider more fully the case of two gases, in one of which @,=100°, and in the other =5000°, the degrees being Centi- grade and measured from absolute zero, 7. e. —273° C. 17. In Tables I. and Il. below, column 1 gives the tempe- rature ; column 2 the dissociation at the given temperature, the dissociation being measured by the proportion of free atoms to moving particles in the gas; column 3 gives the value of 1+€ in the formula p=«p(1+)@, and which we may call the expansibility ; whilst column 4 gives the ratio PL Zs (Po, 9 being the pressure and temperature at 27° C.). Po 0 0 Taste I. (@,=—173° C.). ¥ ER Ay g 6. ya : — 24 Dy Wore a 5 Eres ne 0 —273 0 ] —173 “610 1-439) 0°873 — 73 "728 lesyal 0:953 27 "785 1-6473 il 127 °820 1°695 1:029 227 *845 1-732 LEOat 527 "858 1°752 1-063 oo 1 2 NAL 414. Mr. W. M. Hicks on some Effects of Dissociation Tasue Il, (6,=5000°—= 4727-0.) 2y Pp 0. Pa wellaes. ok Po 8, —273 0 1 — 73 ‘O0C00 10000 | 27 ‘0017 1:0008 1 127 0096 1:0048 1:0048 227 ‘0269 10136 10136 327 ‘057 10268 10260 527 “116 10617 10610 | 727 "182 11003 1-0994 12274 313 1:1850 11841 1227 “459 12970 12961 Co 1 2 | 19984 18. From Table II. we see that at ordinary temperatures the dissociation is very small when @,=5000°, even up as high as 700° C.; whilst when 6,=100° or —173° C., the dis- sociation is always large, even down to —200° C. Also the expansibility in the first case between temperatures 0° C, and 100° C. varies as much as in the second case between 0° C. and 300° C., though when we get to high temperatures the expan- sibility changes more slowly in the first case than in the second. In the second case the expansibility is almost con- stant between 0° C. and 100° C., and even up to 300° changes only slightly. Again, a difference of 10 per cent. in the value of @, in different gases will produce a difference in their ex- pansibilities at ordinary temperatures of ‘004 when @, is small and about —173° C., and of -00065 when @, is large and about 4727° C. In other words, if 8 be —173° C. in one gas and the value of @, in the other gas vary to the extent of 10°, the difference in their expansibilities will vary to the extent of ‘004; whilst if in one @, be 4727° C. and the value of 6, in the other vary to the extent of 500°, the difference in their expansibilities will vary to the extent of ‘00065. These three reasons, viz. (1) smallness of dissociation, (2) constancy of expansibility, (38) near equality of expansibilities of different gases, lead us to believe that in the case of the permanent gases @) is large compared with ordinary temperatures. Still there may be gases whose 4 is small. It is possible that mercury vapour is such a gas,-and that this accounts for the fact that its molecules are monatomic, viz. that the temperature at which it exists is a large multiple of its 4, and that therefore the dissociation is large. on the Physical Properties of Gases. 415 19. In considering the effect of dissociation on the specific heats of gases, we may not treat them as a mixture of two whose proportions remain constant; for in raising the temperature, not only is work done in increasing the kinetic energy of translation and internal motion, but also in destroying a cer- tain proportion of molecules. Let, as before, z be the number of molecules, 27 the number of atoms present when the tem- perature is 6. Let 4, A, be the ratios of the whole energy to that of translation in molecules and free atoms respectively. Then we have, if Q is the quantity of energy present in unit of yolume, and I the potential energy of combination of a single molecule, Q=F2mv? . rye +4mvr?. 2r.y + Le = (Ayw + 2r.y)AO + Iw. Let a quantity 6Q of heat be applied, the volume being constant. Then 6Q= { (a5 =p + Daga CL NO + Oaee+ Dray n+ 1 lao = Kile, where c is the specific heat at constant volume. Also 2Z(e@+y)=N; dz . ds ays "dé zy dO = And dh eles y+ 20)0 SE + Aart Bray — = alas and if c’ is the specific heat at constant pressure, dv c ae Now p= 3 a +)N0. If V be the volume occupied by the gas and N’ the number of atoms in it, N = We Hence pV=ra (+083 = pag =z {it+t+e ds 416 Mr. W. M. Hicks on some Effects of issociation where p is constant ; Nit ee SAN =) - ; daet (1th +08 ’ dt as OS +14e Cone TO. dy feds dt oe rica ae Tae dt Dade In the above we have neglected the variation of the poten- tial energy of molecules except in the case where they are broken up. The above formula is greatly simplified if we consider, as is highly probable, that a molecule has twice the number of degrees of freedom of a free atom—in other words, 2r\.=A,; we then get dt of go ae cum ay EG ON GO. 20. If the atoms be smooth and spherical (as has been sup- posed throughout the present paper), any internal energy an atom may have must be unaffected by change of temperature ; and in this case A, = 2. The blow just sufficient to break up a molecule is c; if this acted in the most favourable manner, the work done in sepa- 2 cts =2r6,. Hence is a2nee rating a molecule would be 2m If we put I=2n6,, SK Ga ° 1-0 75 If 0) is small and about 100°, 7. e. —173° C., we find from on the Physical Properties of Gases. 417 Table I. that, at a temperature of about 70° C., L+E=1671, 4% =-00048, 6=350; whence it follows that cl — =1°609. C If @ is large and about 5000° or 4727° C., Table II. gives us for a temperature of 70° 1+ €=1:0028, . = ‘00004, whence f Aon, Cc In the above we have confessedly taken I too large, as we showed that 2X) was its superior limit; if we were to take T=2)8@ x 4, we should get | C {/ — =1°403. c / The value of - for the permanent gases is about 1°408. Not only does this result confirm our former conclusion that 8, is very large, but it adds largely to the probability of the general theory here set forth, since the great difficulty of the kinetic theory of gases hitherto has been to explain the / C value of — for the permanent gases whose molecules are C diatomic. Mercury vapour which has simple molecules, or is monatomic, and which therefore has no dissociation, has the value given by the ordinary theory, as has been shown re- cently by Messrs. Kundt and Warburg. 21. To satisfy experience, it is further necessary to show that c does not vary much within the ordinary range of temperature. We have ; _” be Ue, eh de a1 208, dé where « is a fraction. Hence ders PE dé => —rAKNG, ae? ° Phil. Mag. 8. 5. Vol. 3. No. 20. June 1877. ee 518} 418 Mr. R. H. M. Bosanquet on the Theory of Sound. Now ne is throughout very small, and varies very slowly, dé 2 so that 2 is extremely small. In fact, from Table II. we see that at 100° C. oe is somewhere about ‘00000048. de” [To be continued. | LVI. Notes on the Theory of Sound. By R. H. M. BosanQuET, fellow of St. John’s College, Oxford. [Continued from p. 349. | 4. On Combined Wave-systems. f aes principle that a stream of sound may be regarded as a flow of energy, which cannot of itself increase or di- minish in quantity, enables us to deal with certain simple cases of combined wave-systems. I restrict myself for the present to the case of plane waves. Prop. 1.—If two equal and similar pendulum wave-systems, travelling in opposite directions, meet in air, they form a sta- tionary wave which will carry the whole energy of both. Let Yyy=a sine! (vt—2), r Yg=a sina” (vt + x) be the two equal systems travelling opposite ways; the more general equations can always be reduced to this form by suit- able choice of the origins of space and time. Then Y=yity.=2a nee cos a, 7 adY¥ dare ome 20 di ame Ne on NT eas sae eget nee dg = eRe any Pra en dY When ¢=0, Y=0 and —— =0, or there is no displacement dx and no pressure anywhere along the stationary wave, but there is a maximum velocity, dY Aarrv es 27x atm | N >) Mr. R. H. M. Bosanquet on the Theory of Sound. 419 when ¢= t (quarter period), there is no velocity anywhere, but there is a maximum displacement, 2r Y= 2a cos 7% and a maximum pressure, ADO ame 1411. > n> a. Consider a tube having the length of the velocity of sound, in which such a stationary wave is maintained by the trans- mission from the opposite ends of the equal and opposite wave- systems. ‘The energy in the tube is to be found. We have shown that the form of energy alternates entirely between potential and kinetic. In either form it is identical in distribution and magnitude with the kinetic or potential energy of an ordinary wave of transmission in air of the same amplitude; so that there is only one quantity in the stationary wave where there would be two in the ordinary wave of trans- mission. The energy in the tube of length v is therefore 1:4 IIv (=). ee Ca 2a,)) or half that in a wave of transmission of amplitude A. And this may be written 2 2 {2 x 14 He(=*) ie which is twice the energy of either single stream, or the sum of both. Cor.—Putting «=0, we have the conditions of a loop sur- face; and it follows withous difficulty that, If a disk of air oscillate with maximum velocity V and without change of density, the energy per second through the disk consists of two equal and opposite streams each = “ee V? per second, making a total transfer of - V’ per second through the disk. (Section unity.) 7 Prop. 1I.—If any two wave-systems of the same wave- length (pitch, or periodic time) meet in air, travelling in opposite directions, their direct superposition carries the energy of both. By 1D) 420. Mr. R. H. M. Bosanquet on the Theory of Sound. Let y,=a sin “T (via), You b - (vt +z) +a cos 5 (vt — x) }y GY fh 3 Te 222 Qa a Se (0 cos > (vt + “)—a cos —- (vt — x)). The total energy in any disk dz, estimated as kinetic + poten- tial, is (Phil. Mag. [4] vol. xlv. p. 174) 7 al on, 2 t\al *’\ae) S° The coefficient of 2ab disappears from this expression, leavin g only the terms involving a’ and 6”, which give on integration the same value of the energy per second as the sum of the values for the component streams. This, of course, includes the result of prop. I. Prop. I1I.—If two equal and similar pendulum wave-sys- tems, in the same phase and travelling in the same direction, join each other in air, they cannot be superposed without alteration. Let each of the wave-systems have an amplitude a; then, if they are simply superposed, the combined stream has an am- plitude 2a, and the energy per second carried by the combined stream is four times that of each of the single streams, or twice the sum of the energy of the two streams together. Hence the energy required for the superposition is twice the total energy supplied, and simple superposition cannot take place. Cor.—Reflexion will generally take place at. the point of junction. Prop. 1V.—Two equal and similar wave-systems, in the same phase and travelling in the same direction, join each other in air ; to determine the transmission and reflexion. Let A be the amplitude of each of the original streams, a that of the reflected stream, b that of the transmitted stream. At the common surface, 2A+a=b; Mr. R. H. M. Bosanquet on the Theory of Sound. 421 and equating values of energy per second, 2M =a? +b’; eliminating A, we find a+b=0. The reflected and transmitted streams are equal; and each of them is equal to either of the original streams. This proposition finds an application in some cases of inter- ference. The circumstances supposed here cannot, however, be realized in an accurate manner physically ; for the two ori- ginal streams can only be kept apart before their junction by travelling in different channels. In this case there are two reflected streams, and the solution is different. Prop. V.—Two equal and similar wave-systems, in the same phase and travelling in the same direction by two sepa- rate channels, join each other by the two channels uniting into one, of the same size as either ; to determine the transmission and reflexion. At the common surface at the entry to the channel of union, 2(A+a)=), 2(A?—a’) =G’=4(A+a)’, whence A’?+4Aa+3a?=0, (A+a)(A+3a)=0. A+a=0 involves b=0 and is inadmissible ; Ps [Aleta b=4A; or and of the total energy incident per second, 8 is transmitted in the combined vibration, the remaining } being reflected back along the paths of the incident wave-systems. These circumstances may be realized in the case where the wave-length is great compared with all the dimensions, so that any difference of direction between the original and united channels becomes immaterial. Prop. V1.—In the general case, where two systems of the same wave-length join in air, to determine the reflexion and transmission, considering one channel, 7. e. under the circum- stances of prop. IV. Let A, B be the amplitudes of the incident wave-systems, y the difference of phase, a the amplitude of the reflected system, b the amplitude of the transmitted system. 422 Mr. R. H. M. Bosanquet on the Theory of Sound. ne yy=Asin = (vt—w), y2=Bsin 127 wa) ty}, A+ty2=C sin | oT (eta) +D \, where C?=A’?+ B’+2AB cosy. It is clear that this combined vibration cannot generally be transmitted unaltered ; for the energy per second would be altered by a term depending on 2AB cos ¥. Proceeding as before, we have, equating the values of the amplitude at the common ee C+a= whence A? + B?+ 2AB cosy =(b—a)’, and, equating values of energy per second, A?+ B?=a’?+0?; whence A? + B?—2AB cos y=(at+ 6)’. Let A? + B?—2AB cosy=C”, then C =b—a, C/=b+a, C—C’ : 9 Tam Nh) C+C’ 2 os whence, if we draw from a point O two radii equal to A, B respectively, enclosing the angle y, and complete the paralle- logram of which they form two sides, half the difference of the diagonals is the reflected amplitude a, and half the sum of the diagonals is the transmitted amplitude 6. The diagonal through O is of course C, the amplitude derived by geome- trical superposition. The ratios of energy in the above case are :— transmitted b? incident A? + B? 4 A?B? cos? pa yf cot See): 4( i (A? + By? 2 Mr, R. H. M. Bosanquet on the Theory of Sound. 423 reflected a a incident A?+ B? Gr ie ise 4 A?B? cos oe) (as: ak ae : = or the incident wave-systems differ in phase by quarter of a period. When the phase-difference is either zero or half a period, the transmission is a minimum and the reflexion a maximum ; the values are :— The transmission is complete only when y= 2 A2+ B”’ B? RB Transmission = Reflexion where A >B. (For C—C’=—2a, and C+C’=2b; andC, C’ are essen- tially positive quantities. ) Prop. VII. In the general case where two systems of the same ee clonuth travelling in the same direction by two separate channels, join each other by the two channels uniting into one, of the same size as either; to determine the trans- mission and reflexion, 7. e. under the circumstances of prop. V. Following the notation of the last proposition, we have for the common amplitude at the entry of the channel of union, Cea ee io vaare: eC) A’ + B?+ 2AB cos y= (b—2a)= whence and, equating values of energy per second, BF AB? Da? HOP aah iyoity el 9 rm, (A) A?+ B?—2ABcosy=O0” =b? + 4ab. whence From this and (1), b?—26C—C”?=0 b= oe Ae and from (1), 424 Mr. J. R. Harrison’s Experimental Researches The ratios of energy are :— transmitted 0” incident ~ A’?+B? if —2AB cos y+4Cr/ A?+ B?—AB cosy). =o t= ep ne single reflected stream a incident —~ A? + B? 1} AB cosy+20¥V A?+ B?— AB 208 Oh =) 24 eee eee '* AG is If y=0, or cosy=1, and A=B, we have the case of prop. V. This determines the employment of the upper signs before the roots in the present results, in which case these results coin- cide with those of prop. V., giving § of the whole transmitted, and the remaining 4 divided between the reflected streams. If cos y=0, or the component systems differ in phase by 4 of a period, the whole energy is transmitted, or the geometrical composition takes place unaltered. This is immediately seen from the vanishing of the term (2AB cosy), by which C? dif- fers from A’ + B’. In all these discussions it has been assumed that the incident wave-systems were not subject to constraint, which would pre- vent them from yielding to the reflected impulse ; and in cases of interference in air constraint is frequently absent. But where the two -wave-systems are supplied, say, by tuning- forks close to the point of meeting, the forks are capable of maintaining their movement unchanged and acting as a con- straint. Under these circumstances more work is done by the sources, and the geometrical composition of the systems is maintained. In the next note I propose to apply the principle of the flow of energy to the divergence of sound in air. LVIIL. Huperimental Researches on the supposed Diathermancy of Rock-Salt. By JouN Rusaton HARRISON*. [Plate III.] T is almost universally accepted that pure rock-salt trans- mits more than 92 per cent. of the total radiation from heated bodies. I would ask permission to glance for a moment at the mode of experiment by which Melloni arrived at this conclusion. * Communicated by the Author. on the supposed Diathermancy of Rock-Salt. 425 A thermopile is placed at a distance from the source of heat, the radiation from which causes a deflection of the galvano- meter-needle. This arrangement completed, the substances to be examined are introduced between the source and the pile, their different powers of absorption and transmission being determined by the different values of the deflections. Taking a single instance, it is assumed that a plate of ice 35 of an inch thick absorbs all the incident radiation from copper heated to 400° C.; while a rock-salt plate of the same thickness transmits 92°3 per cent. of the total radiation from the same source of heat. That the ice does absorb the heat is proved by the liquefaction of the substance; but that 92°3 per cent. of the total radiation passes through the salt is not, I think, equally certain ; in fact the experiment points, not to diathermancy, but to the unequal absorptive powers of the different substances examined. In 1869* Professor Magnus endeavoured to account for the diathermancy of rock-salt by saying :-—“ The great diather- mancy of rock-salt does not depend on a small absorbing- power for different kinds of heat, but upon the circumstance that it emits only one kind of heat, and only absorbs this one, and that almost all other bodies at a temperature of 150° C. emit heat which only contains a small portion, or none at all, of the heat which rock-salt emits.”” There will be little doubt that this conclusion is based upon the doctrine of periods, although the result of another experiment with fluor-spar, noticed in the same paper, is fatal to that conclusion. It is less, I think, from an experimental point of view than from unsuccessful attempts to explain why a solid substance should be diathermanous, that any one would be led to doubt | the value of Melloni’s conclusions; and here I would state that the experiments recorded in this paper, by which opposite results have been obtained, were not originally suggested by any apparent inefficiency in the mode of experiment adopted by this great philosopher. The apparatus by which these results have been obtained is as follows:—Two thermometers, each 3 inches long, with bulbs zo of an inch diameter, registering from 0° to 200° C. One of these thermometers is enclosed in a rock-salt case 384 inches long, bored out so that the bulb stood at a distance of 7, of an inch from the salt ; the scale of the thermometer is plainly visible through the salt case, which consists of two pieces, as shown in tig. 1, afterwards cemented together with a thin film of transparent glue. The sides of the case are 4/5 of an inch * Philosophical Magazine for November 1869. 426 Mr. J. R. Harrison’s Hxperimental Researches thick ; a few threads of unspun silk wound round the head of the thermometer-tube hold it in position. This I will call the “ enclosed’’ thermometer, and the other the “‘naked’”’ one; both thermometers are fixed to one cork and placed in a glass tube. The whole apparatus is seen in fig. 2. C is the cork with thermometers attached, the bulbs of which are at a distance of one inch from each other; T, a glass tube 12 inches long and 14. inch internal diameter containing them; V, a glass vessel 8 inches long and 4 inches internal diameter, fitted with a cork to admit the tube T; this vessel is filled with water at the boiling-temperature ; t, a tube to convey the steam given off by the water to condenser K. The mode of pertorming the experiment is as follows:— The thermometers being in their places, the tube containing them is placed in a freezing-mixture and allowed to remain till both thermometers register O° C. The water in the vessel V is heated by the aid of a spirit-lamp which is withdrawn when the water boils ;« when ebullition has ceased the tube is taken from the freezing-mixture and quickly passed into the vessel V, and the rise of both thermometers noted from minute to minute, When the enclosed thermometer has reached its maximum temperature, the tube is then withdrawn, placed in the freezing-mixture, and the descent from minute to minute noted. The result of the experiment is seen in the following Table :— Registration of both thermometers at commencement of experiment, 0° C. jaked thermometer, Enclosed thermometer. After the gain in After the gain in lapse of 1 minute, 35°; temp. 35° | lapse of 1 minute, 9°; temp. 9° ” 2 9 5d ”? 20 ”7 2 ”? 20 ” iat 5 oO D 9 3 28 9 8 ” a ”? 69 ” 5 ” 4 ” 39 : ” 7 ”? D ”? 70 ” 1 ” 5 ” 40 7 9) ee le 0 ” Ore nee ” 5 ” 7 ” 71 (max ) ” ] 9 7 9 49 9 4 ” 8 ” 71 9 0 ” 8 ” 52 ” 3 ” 9 ” 71 0 9 9 ” 55 ”? 3 5 10 ni Loss 1 ‘i 10. yy 88 _ 3 ” ila ” 70 ” 0 9? 11 ” 60 ” 2 ” 12 ” 69 39 1 ”? 12 PP 61 ” i ” 13 ” 69 ” 0 ”? 13 ” 62 ”7 I ” 14 ” 68 ”? 1 ” 14 ” 63 3” 1 9 15 ” 67 ” 1 ”? 15 ”? 63 9? 0 ” 16 ”? 66 ” 1 ” 16 ” 63 9 0 3 17 ya ote os 1 35 It ~,,, -G4(@max.)i,, 1 18 Nt ial 49) 4 0 > Le iam vo Loss 1 pe EY ip lee: 9 1 yu elo ie gee ” 0 ” 20 ” 64 ” 0 ”? 20 ”? 63 ” 0 ” 21 9 62 ” 2 ” 21 ” 62 ”? 1 on the supposed Diathermancy of Rock-Salt. 427 The tube containing the thermometers was then placed in the freezing-mixture. Naked thermometer. Enclosed thermometer. After the gain in After the gain in lapseof 22minutes, 35°; temp. 27° | lapse of 22 minutes, 52°; temp. 10° ” 23 ip me: ” 19 » Delay 40 " 12 * 24 8 ” 8 yr aah e 30 1 10 ”? 25 ” 9) ” 3 ”? 25 7 20 ”? 10 ” 26 ” 3 ” 2 ” 26 ” 17 ” 3 ” 2 ” 0 ” 3 ” 27 ” 15 ”? 2 After the After the lapseof 5 0 Oy, | Tapseioi”. 8) sk, 7 i 8 ” 5 ”? 0 0 ”? 5 ”? 3 ” 4 ” 5 ”? 0 0 ” 5 ” 1 ”? 2 ag) 0 0 r 5 O ” 1 It will be noticed that the naked thermometer reached its maximum temperature 71° C. in seven minutes, at which time the enclosed thermometer registered 49° C. The former remained stationary at 71° C. for two minutes, and then slowly descended; after the lapse of ten minutes from the time it first reached its maximum, and seventeen minutes from the commencement of the experiment, it had fallen 6° C. and now registered 65° C. During this time the enclosed thermometer steadily increased in temperature, and now registered its maxi- mum (64° C.), it having risen 15° C., while the naked ther- mometer had fallen 6° C. This reverse action proves beyond doubt that the heat incident on the bulb of the enclosed ther- mometer had been radiated from the salt as an independent source, and not diathermanously transmitted. The following experiment, though void of numerical value, is still, [ think, interesting, as a different source of heat is em- ployed. The apparatus used is shown in fig. 3: T is a test- tube with foot, 8 inches long and 14 inch internal diameter ; t, a second tube passed into the first and held in position by means of a cork, ¢ (this inner tube is ? of an inch internal diameter, and stands half an inch higher than the outer one); P, a pivot fixed in the inner tube to support the source of heat —a round bar of hot copper 2 inches long and half an inch cross section ; UC, a movable German-silver cap open at both ends and polished on both sides; its smallest circumference passes into the inner tube, and its larger circumference passes into the outer one. One surface of a piece of white blotting- paper is coated with a thin layer of melted white wax, care being taken that the wax does not penetrate through; when this layer is dry, others are applied till the texture of the paper is well filled. The experiment is performed as follows:— 428 Prof. EH. Edlund on the Thermal Phenomena of the The outer tube being filled with water, the bar of copper heated to a dark red is placed in the inner tube, the cap ad- justed, and a rock-salt plate 35 of an inch thick shaped thus placed on the_to pof the cap, the blotting-paper with its waxed surface downwards brought immediately over but not touching the salt: the heat ascending melts the wax, and a well-defined outline of the rock-salt plate is produced on blotting-paper, and then spreads towards the edges. Different shaped plates were used with similar results. In performing the experiment care must be taken that the heated copper stands fairly perpendicular under the centre of the cap. LVIII. On the Thermal Phenomena of the Galvanic Pile, and Electromotive Forces. By Ki. Hpuuny*. Sal Ih ines the experiments which have been instituted for the purpose of studying the thermal phenomena of the galvanic pile and its conductors the conclusion has been drawn, that the heat which arises in consequence of the pas- sage of the current through the entire conduction (including the pile itself) during a certain time is exactly equal in quan- tity to that which is produced in the pile by chemical pro- cesses during the same time,—that is to say, provided that the current performs no external work (for example, induc- tion, chemical decomposition, &c.); and among the pro- cesses mentioned, only those must be understood which are primary and in direct connexion with the formation of the current. In the following, to distinguish these two quantities of heat from one another, we will name that which is occasioned by the passage of the current through the conductors the gal- * Translated from a separate impression, communicated by the Author from Poggendorff’s Annalen, vol. clix. pp. 420-456, Galvanic Pile, and Electromotive Forces. 429 vanic, and that which arises from the chemical processes in the pile the chemical heat. Then it has been inferred, from the experiments which have been made, that, under the presuppo- sition mentioned, the chemical is equal in amount to the gal- vanic heat. Calling the galvanic heat gw, according to Joule’s law gw= Milt, where M is a constant, 7 denotes the current- intensity, / the resistance of the conduction and the pile toge- ther, and ¢ the time during which the current is in action. Therefore, if H denotes the electromotive force of the pile, we can also write gu=MUit, from which, in consequence of the inference drawn, we obtain kw= MIHit, if kw signifies the heat evolved by the primary chemical processes in the pile. IRfn denotes the number of chemical equivalents decomposed by the action of the current at the positive-pole plate of the pile, ac- cording to the law of electrolysis n= mit, m denoting a constant which is independent of the nature of the electrolytic liquid. Hence we conclude that kw= oD , and therefore that, for one equivalent, kw= zea , from which it follows that the quan- tity of heat which is produced in the pile by the primary che- mical processes while one equivalent is decomposed at the positive pole is a measure of the electromotive force of the ile. If the galvanic is in reality precisely as great as the primary chemical heat, we may consequently say that the whole effi- cacy of the current consists only in this, that it conducts the chemical heat to all parts of the closed circuit, and deposits at each place exactly as much as corresponds to the resistance at the same place—although of course it is very difficult to form a clear conception of the actual physical processes that take place in this conduction. If by direct measurement of the heat produced in the pile itself it were to be found that its amount is greater than that of the galvanic heat occasioned by the passage of the current, or, in other words, exceeds the heat which the current calls forth in a metallic conduc- tor whose resistance is equal to that of the pile, we should have to admit that this excess was derived from the secon- dary processes which may take place in the pile and have nothing in common with the formation of the current. In this way also it has been attempted to explain such surplus heat in the cases in which it has been observed :—If a chemi- cal-decomposition cell ora voltameter be inserted in the circuit, so that the current has opportunity to decompose water, for example between platinum poles, then, according to the way of regarding it now presented, all the primary chemical heat | | | 430 Prof. EH. Edlund on the Thermal Phenomena of the arising in the pile cannot pass over into galvanic heat, but a part of it is expended for the mechanical work necessary for generating the electromotive forces of polarization and the chemical decomposition in the cell. We can imagine this brought about by the store of chemical heat requisite for this work being carried by the current from the pile into the decomposition-cell, where it is employed for the purpose mentioned. Consequently no other change of temperature can arise in the decomposition-cell than that which is occa- sioned by the passage of the current through the electrolytic liquid. The heat generated in the decomposition-cell must therefore be equal to that which is produced whén the current passes through a metallic conductor the resistance of which is equal to that of the liquid. Now, as by direct measurement the quantity of heat produced in the decomposition-cell has been found greater than the galvanic, the cause of this has been sought in the secondary chemical processes which may take place there and are independent of the current. 2. I have already, some years since *, given another expla- nation of the thermal phenomena in question. It was, in brief, the following :—If the current does no external work, its total action consists in calling forth heat in the conduc- tor through which it passes. After the current has ceased, no other products of the activity of the pile are found but the chemical changes in the pile and the heat which has arisen, partly in the pile itself, and partly in the conductors. It is evident, however, that the amount of this heat must be equivalent to the chemical changes; that is, in other words, the quantity. of heat generated must be exactly equal to that which would have resulted from the same chemical changes if no current had taken place; for otherwise either chemical work or heat would have been obtained out of nothing. The current has therefore, upon the whole, generated no heat at all; its total heat-production is equal to nil. But we know that the current does a certain amount of mechanical work in order to overcome the resistance of the galvanic conduc- tion ; and this work changes into heat. Therefore the cur- rent brings forth in the conduction an actual production of heat. But, because the total heat-production of the current must be equal to nil, this can only happen through a con- sumption of heat occurring at some place or other in the conduction ; and of course the place can be no other than that where the electromotive force has its seat. We conse- quently arrive at the result that, in order to produce the cur- * Ofversigt af K. Vetenskaps Akademiens Forhandlingar, 1869; Pogg. Ann. vol, cxxxvil. p. 174. Galvanic Pile, and Electromotive Forces. 431 rent, the electromotive force consumes a quantity of heat ex- actly equal to the quantity generated by the current in over- coming the resistance of the galvanic conduction. The heat- consumption of the electromotive force is accordingly equal to gw; yet it does not hence follow that it is not also equal to kw, or that gw and kw have not the same magnitude, If only a single electromotor is inserted in the closed circuit, keeping the same notation as before, we have gu=MPlt=MEtt ;s therefore in unit time a quantity of heat is consumed which is proportional to the product of the electromotive force and the intensity of the current. Thus, during the solution of one equivalent of zinc, the total amount of heat gw consumed by the electromotor = oH K. This holds, even if / be changed— that is, even if the current-intensity be increased or diminished. Are two electromotors E and E’ acting in the same direction ? then in unit time the total heat-consumption in both must be M(H + E’)i,, if i, denotes the intensity of the current produced ; hence, evidently, MHz, is consumed in the former, and MH, in the latter. When H is greater than EH’ and the one elec- motor acts in the opposite direction against the other, the total quantity of heat consumed becomes M(H —Hi’)z,,, if 7,, denotes the current-intensity. In the first electromotor the quantity Mi, of heat is now consumed; but this is greater than the total quantity generated by the current in consequence of the galvanic resistance. In the other electromotor, therefore, a quantity of heat equal to MH’7,, must be generated. Conse- quently, when the current traverses the electromotor in the same direction in which the electromotive force acts, a quan- tity of heat is consumed which is proportional to the product of the electromotive force and the current-intensity; but if the current goes in the contrary direction, just as great a quantity of heat is produced instead”. From this it is evident that these two ways of considering the subject agree in one respect, namely that, according to both, the sum of the heat which the current produces upon the whole is equal to nil; but in the one case the heat produced in the pile by the chemical processes is regarded as con- veyed to the different parts of the circuit ; while in the other heat is supposed to be generated by the current everywhere in the circuit ; yet the total quantity of heat produced is equal * The unitarian view of the nature of electricity leads direct to the same result. See ‘‘Théorie des phénoménes électriques,” p. 45 (K. Ve- tenskaps Ak. Handl, Bd. xii. No. 8: also Brockhaus, Leipzig). 432 Prof. BE. Edlund on the Thermal Phenomena of the to that which is consumed by the electromotive force. In other respects the two views lead to divergent results: for example, according to one view the quantity of the primary chemical heat is equal to that of the galvanic, wherefore the former also gives a measure of the electromotive force ; ac- cording to the other these two quantities may be different, and consequently the primary chemical heat cannot serve as a measure for the electromotive force, Xe. In order to determine which of these two views accords best with experience, we will more closely consider the expe- riments which have been instituted for the purpose of studying the thermal phenomena of the pile and of the current. For brevity, we will name the first-cited method of consideration No 1, and that proposed by me No. 2. 3. Favre* has endeavoured, by direct experiments, to answer the question, Is the whole of the galvanic heat which arises in the circuit derived merely from that which is gene- rated by the chemical processes? Jor this he made use of a mercury calorimeter with two muffles situated close to one another, of the same nature as the calorimeter which Favre and Silbermann had previously employed in their determina- tions of the heat developed in chemical processes. The pile he used consisted of a glass tube filled with water containing sulphuric acid, in which were placed the two pole-plates, amalgamated zine and platinized copper (Smee’s pile). It was closed with a fine platinum wire, which was of unequal length and thickness in different experiments. The hydrogen evolved in the pile was collected and measured. The experi- ment was first made in this way :—The pile was enclosed in one muffle, and the platinum wire in the other ; at the same time it must be remarked that the copper wires connecting the pole-plates with the ends of the platinum wire, and which were outside of the calorimeter, were so thick that no perceptible development of heat could take place in them. When, therefore, the experiment was thus arranged, the calorimeter indicated the total sum of the heat which was developed in the pile and the entire circuit while | the current was in action; and since the quantity of the hydrogen gas developed was at the same time known, it was easy to calculate what the sum of the heat would have been if the experiment had been continued until one equiva- lent of zinc in the pile was dissolved. Thereupon the experi- ment was varied by leaving the platinum wire outside of the calorimeter, in consequence of which the galvanic heat which arose in the wire had no effect upon the calorimeter. The * Annales de Chimie et de Physique, (2) t. xl. p. 293 (1854). Galvanic Pile, and Electromotive Forces. 433 difference between the indications of the calorimeter in the two cases was consequently equal to the galvanic heat which was developed in the platinum wire. The results of the different ex- periments will be seen from the followimg Table. Column a gives the length of the wire ; 0, the deflection of the calorimeter in heat-units (the gram being taken as unit of weight) when both the pile and “the platinum wire were enclosed in the calorimeter ; c, the corresponding deflection when the plati- num wire was excluded from the calorimeter ; b—c, the dif- ference between these two deflections, or the galvanic heat de- veloped in the wire ; and gw the quantity, thence obtained by calculation, of the galvanic heat in the pile and the platinum wire together. Diameter of the wire =0°265 millim. | a. b. C. b—c. gw. millim. it 25° | 18092 | 13127 4965 ! 50 | 18247 | 11690 cosr_ | f (9682 100 | 18185 | 10439 7746 ean 200 | 18022 8992 9030 In another series of experiments, in which.a thinner wire was used, the following results were obtained :— Diameter of the wire =0°175 millim. a b c b—e gw millim 50 18082 9955 8127 50 18173 10101 8072 12040 100 18066 8381 9685 Cane (fy OO Ay dln! Santee, BeclKupp sabes 10837 As the preceding Tables show, the value of gw increases as the resistance becomes greater ’and therefore the current- intensity less. According to Favre and Silbermann, there are developed, Heat-units. in the combination of one equivalent of 1 42451 zinc (38 grams) with oxygen. . in the combination of the oxide with ~ 10455 sulphuric acid . . On the other hand, in the decomposi- are con 34462 tion of one equivalent of. eae sumed. . 18444 Phil. Mag. 8. 5. Vol. 3. No. a ae ISIC Ce 2 434° Prof. KE. Edlund on the Thermal Phenomena of the The mean, 18124, of the numbers found in the above expe- riments differs only about 300 heat-units from the last-men- tioned sum; wherefore the two may be regarded as equal, But according to both views, No. 1 and No. 2, this equality must exist ; and so we have no clue to enable us to judge in what way the galvanic current is produced ; whether we take No. 1 or No. 2 as the correct way of considering, in this re- spect we come to the same result. The calculation of the quantity of galvanic heat developed by the -current in the entire circuit (a calculation not carried out by Favre in these experiments) shows that it amounts on the average to 10837 thermal units, not much more than the half of the chemical heat. The circumstance that, as results from the above experi- ments, the galvanic heat gw developed by the current in the entire circuit increases when the resistance is increased and consequently the current-intensity is diminished, is confirmed by Favre’s later experiments with Smee’s pile *. In one oi these experiments, the length of the platinum wire being shortened from 7000 to 250 millims., the galvanic heat was lessened from 18018 to 14424 thermal units ; the chemical heat he found somewhat greater than before, namely 19834 units. While the chemical heat, as we know beforehand, is constant and independent of the inserted resistance, the gal- vanic heat, on the contrary, became less when the resistance was dimminishee and consequently the intensity of the current was augmented. In all these experiments, however, the che- mical was greater than the galvanic heat. In the following experiments, on the contrary, the galvanic exceeded the chemical heat ; for there appeared in the pile an actual consumption of heat, so that its temperature sank on the passing of the current, instead of risingf. One of the pole-disks of the pile employ ed consisted of platinum, the other of zine or cadmium; and both were immersed in hydro- chlorice acid. The closed pile was first put into the calorimeter without any exterior resistance, by which a measure of the total chemical heat was obtained. Afterwards the pile was furnished with a considerable exterior resistance and then en- ciosed in the calorimeter, but so that the resistance was left outside. ‘The chemical heat amounted, for the cadmium-pla- tinum pile, to 7968 units, and for the zinc-platinum pile to 15899; but when the resistance was left outside of the calo- rimeter, there was observed, in the cadmium-platinum pile, a * Comptes Rendus, t. xlvii. p. 599 (1858), and t. Lxyii. p. 1012 (1868), + Ibid. t. Ixviii, p. 1800 (1869). ~ Galvanic Pile, and Hlectromotive forces. 435 lowering of temperature 1288, and, in the zinc-platinum pile, 1051 thermal units. Favre * has also, with the aid of the mercury calorimeter, determined how much chemical and galvanic heat is liberated in some piles of another construction during the solution of one equivalent of zinc f. We will here take into consideration only the numerical values obtained by Favre for the piles of Daniell and Grove. If kw denote all the chemical, and gw all the galvanic heat, he obtained for Daniell’s pile kw=25060, gw=23998, and consequently kw—gw=1067 thermal units; for Grove’s pile kw=41490, guw=46447, and consequently kw—gquw=—4957 units ; so that in Daniell’s pile the chemical heat is only about 1000 units greater than the galvanic, while in Grove’s pile the galvanic is greater than the chemical heat. Consequently, when this pile is closed with a conducting wire of great resist- - ance, the pile itself'is cooled during the passage of the current, while the conducting wire is heated. We may add that Raoult also has determined by direct ex- * Comptes Rendus, t. 1xix. p. 34. +t The following was the method of observation here employed :—The pile to be investigated was enclosed in one mufile of the calorimeter. As the progress of the chemical processes could be determined with great accuracy by measuring the hydrogen which was evolved in the Smee’s pile, such a pile was also placed in the calorimeter, and connected with the other pile, so that the current passed through both. ‘The rheostat, which connected the two poles, was also enclosed in the calorimeter. Thus the calorimeter gave the chemical heat developed in both piles. The quantity of heat shown by the calorimeter while half an equivalent of hydrogen was being evolved in the Smee pile was now observed—that is, during the time that the chemical processes in the two piles together corresponded to one equivalent. When a Daniell’s and a Smee’s pile were placed in the calorimeter, 22447 heat-units were in this way obtained. The quantity of chemical heat for one equivalent of hydrogen, in the Smee’s pile employed, was determined, by speciai trial, at 19834 thermal units, or 9917 fora half-equivalent. Consequently, if the quantity of che- mical heat corresponding to | equivalent for the Daniell’s pile be called z, we shall have 5 +9917 =22447, whence 2=25060, A fresh experiment was then made, in which the Smee’s pile and the rheostat resistance were taken out of the calorimeter, so that the Daniell’s pile alone remained within. The outer resistance was so great, that the heating caused by the current in consequence of the resistance in the pile itself could be neglected. With this arrangement, the calorimeter now eave the difference between the chemical and the galvanic heat, or gk — gw. In this way was obtained, during the evolution of one equivalent of hydro- gen in the Smee pile, gk—gw= 1067 thermal units. Subtracting this number from 25060, we get 23995, which denotes the galvanic heat of the Daniell pile. Favre proceeded in the same manner in his investigation of the other piles. 2 2 436 Prof. E. Edlund on the Thermal Phenomena of the periments the galvanic heat of Daniell’s pile, and found that it amounts to 23900 thermal units, which agrees closely with M. Favre’s result*. If the difference which is almost always found between the quantities of the chemical and the galvanic heat is caused by the secondary chemical processes which may take place in the pile, we must assume, in accordance with what has been said above, that these processes bring forthin some piles a produc- tion, in others a consumption of heat. Favre thought at first that the galvanic heat was exactly equal in quantity to the chemical ft. Subsequently he shared the view already ex- pressed by others, that the cause of the difference in question in Smee’s pile lay in this, that the hydrogen at the negative platinum disk was separated in the active state, or in statu nascenti. As afterwards the hydrogen leaves the platinum disk and escapes upward through the liquid, it passes over into its ordinary condition, in which process heat is liberated, which probably raises the temperature of the liquid, but does not augment the electromotive forcet. But the unexpected relation shown by the cadmium-platinum and zinc-platinum piles charged with hydrochloric acid finally convinced him that this also could not be the true explanation §. In order, therefore, to explain the difference in the ordi- nary Smee’s pile, we must assume that heat is evolved on the transition of the hydrogen from the active to the ordinary state, and that this heat merely raises the temperature of the liquid in the pile, without affecting the electromotive force. In the two piles last mentioned, with hydrochloric acid as the liquid, hydrogen separates im statu nascenti upon the negative platinum disk; but here, in order to account for the difference in question, we must assume that cold is generated when the hydrogen passes from the above-mentioned state into its ordi- nary condition—an assumption which contradicts the prece- ding one. Favre, on this account, ascribes this fact to other, secondary chemical processes which may occur in the pile ; but he does not specify in what those processes are to consist. The fact that the galvanic heat which is developed in Smee’s pile by the current increases with the inserted resistance, Favre has endeavoured to explain by assuming that the ratio between the primary and secondary processes 1s, as to its mag- nitude, dependent on the intensity of the current. * Ann. de Chim. et de Phys. [4] t. iv. p. 892 (1865). + Ibid. [3] t. xl. (1854). + Comptes Rendus, t. xvii. p. 1012 (1868). Compare with this Bosscha’s investigation in Poge. Ann. vol. cil. (1858). § Ibid. t. Ixviii p. 1300 (1869). Galvanic Pile, and Electroinotive Forces. 437 From the foregoing it follows without doubt that it is very difficult to employ the mode of representation No, 1 for the explanation of the thermal phenomena which take place in the galvanic pile and its circuit. Hven if we leave out of con- sideration that it is by no means easy to understand in what manner the heat is conveyed from the pile to the different con- ductors outside of it, it may yet be truly said that it has been attempted to attribute the difference between the amounts of the chemical and the galvanic heat to causes whose presence cannot with any certainty be proved, and the actions of which are still less determined quantitatively. It appears to me that such a way of explaining cannot, from a scientific point of view, be called a good one. The question takes ano- ther form when representation No. 2 is employed. The as- sumption that the electromotive force expends a certain quan- tity of vis viva or heat to produce the work of the current is fuily justified, because it is valid also for forces different in nature from the electromotive. That the consumption of heat by the electromotive force must be equal to the production of heat by the current is self-evident ; yet it does not’ by any means necessarily follow that this heat-consumption is exactly equal to the quantity of heat which is generated by the chem1- cal processes in the pile. Himploying representation No. 2, the experiments cited in the foregoing show that the heat-consumption occasioned by the electromotive force in the zinc-platinum and cadmium- platinum piles with hydrochloric acid for the electrolytic liquid, is greater than the heat-production brought about by the che- mical processes which take place in these piles, but that the ratio in the Smee pile is inverse. It is easy to understand that the consumption of heat, and consequently also the quan- tity of galvanic heat in the entire circuit, in the Smee pile, must be less when the external resistance is diminished. The negative platinum disk in this pile is polarized by hydrogen ; and when currents so feeble as those which occur in these ex- periments are in question, the polarization increases with the intensity of the current. Therefore, when the external resist- ance is little, the electromotive force of the polarization musv be relatively great, and consequently the total electromotive force of the pile become inconsiderable. It is therefore evi- dent that the heat-consumption of this force, and consequently also the galvanic heat developed by the current, must dimi- nish with the resistance. We have therefore no need to have recourse to unknown causes in order to account for the results obtained by the experiments instituted. 4, For determining indubitably which of the two repre- 438 Prof. E. Edlund on the Thermal Phenomena of the sentations, No. 1 or No. 2, deserves to be preferred, we obtain the best clue from the experiments instituted in order to mea- sure the heat-phenomena in a chemical-decomposition cell or voltameter. With this view Raoult employed partly water acidulated with sulphuric acid, and partly a solution of sul- phate of copper as electrolytic liquid, and with the help of a mercury calorimeter measured the quantity of heat which arose in the decomposition- cell over and above the quantity occa- sioned there by the passage of the current in consequence of the resistance™. If W is the total heat developed in the vol- tameter, and qu (as before) the heat which the passage of the current occasions in consequence of the resistance (or the gal- vanic heat), W—gw 1 was measured. This heat-difference, which Raoult calls the local heat, may in the following be de- noted by L. By special experiments Raoult moreover mea- sured the polarization-electromotive force produced in the voltameter during the passage of the current. ‘This electro- motive force may “be denoted by e, and that of an element of the Daniell pile by d. The series employed consisted, in the dif- ferent experiments, of from two to twelve Daniell elements. The numbers cited below under L denote the number of heat- units which were developed in the voltameter during the libe- ration of one equivalent of hydrogen or copper. As, more- over, it cannot be necessary to describe more closely the arrangements in the experiments, we may here add only that, with the decomposition of the sulphuric-acid water, the two poles in the voltameter consisted of platinum wires in the first two experiments (A and B)—while in the third experiment (C) only the positive pole consisted of platinum, the negative being formed of a thick wire of copper. In all three experi- ments with the copper solution the positive pole consisted of a thick wire of platinum, and the negative of one of copper. As may readily be understood, the voltameter alone was en- closed in the calorimeter, and the piles stood outside of it. The following were the results obtained :— On the decomposition On the decomposition of the water. of the sulphate of copper. e é 7 lig rh L. A. 2°04 + 14898 Aer led) +7594 Be 4575 + 7596 B. 1:58 +7997 C..22:16 +17626 C. 1:36 +2821 From this we see that in both cases a considerably greater - * Ann. de Chim, ct de Phys. [4] t. iv. p. 411; see also t. ii. p. 317. Galvanic Pile, and Electromotive Forces. 439 quantity of heat is produced than the galvanic which is caused in the voltameter by the passage of the current ; and this happens notwithst anding it might be supposed, in consequence of the chemical decomposition of the liquid, that the result would be a cooling. Raoult is of opinion that the cause of the heating in this case is to be sought in secondary chemical processes occurring in the voltameter, which have nothing to do with the current. He supposes that the constituents of the electr olyte, which cover the electrodes and cause the polarization, are easily de- composable, and on their decomposition give rise to a heat- production in the same manner as takes place with the hyper- oxide of hydrogen—that the decomposition of these products first takes place after they have left the electrodes and begin to ascend through the liquid, in consequence of which this is heated by them without the current being at all affected. In my view, this explanation is unsatisfactory; on the other hand, heat-production is in this case a necessary consequence if we start from representation No. 2. According to this way of representing it, if a current passes through an electromotor in the direction required by its elec- tromotive force, a quantity of heat is consumed which is pro- portional to the electromotive force, mult tiplied by the inten- sity of the current; but if the current goes in the opposite direction, just as oreat a quantity of heat is generated. I, therefore, the current is permitted to traverse the electromotor during so long a time that an equivalent of the electrolyte is decomposed, the quantities of heat consumed or generated become proportional to the electromotive force. Consequently there arises in the voltameter a source of heat, because the electromotive force of the polarization acts in the opposite di- rection against the current which is passing through. It has been mentioned above that the galvanic heat-development i in a closed Daniell pile during the liberation of an equivalent of copper amounts to 23900 heat-units; and according to No. 2 exactly so much heat must, during the same time, be con- sumed by the electromotive force of the pile. With the help of this datum it is easy to calculate the magnitude of the above-mentioned source of heat in the various oe instituted by Raoult; for we need only multiply 5 — with the last-mentioned number. But, moreover, heat is suing by the chemical decomposition in the voltameter. For each equivalent, 34462 thermal units are consumed, according to Favre and Silbermann, in the decomposition of the water ; and, according to Raoult, 29605 in the decomposition of the 440 On the Thermal Phenomena of the Galvanic Pile. salt of copper. If from the quantity of heat developed by the electromotive counterforce the last-mentioned quantity of heat, consumed by the decomposition, be subtracted, we actually obtain, as the following Table shows, the values observed by Raoult of the surplus heat L. In the decomposition of water. L. A (2:04 x 23900). 48756-34462 = + 14294 Bev oslo G, by y 41825-34469 4) 7368 Cc ye youl: BING94 234469 So: gD In the decomposition of sulphate of copper. A (1°59 x 23900). 38001 —29605 = + 8396 Bo, = ~Ss«37762—29605—= 4 8157 C 4, 4 + 82504—29605 = +2899 Indeed the calculated do not differ more from the observed numbers than can be accounted for from the unavoidable errors of observation occurring in experiments of this sort. Hence it follows that, to account for the thermal phenomena occurring in the voltameter, there is no need to have recourse to the secondary chemical processes which may take place there, the nature and amount of which are more or less un- known*; the theoretical view above presented under No, 2 perfectly suffices for their explanation. 3 5. Some experiments made by Favre, on the development of heat in the voltameter, fully confirm what is here alleged f. In a mercury calorimeter (No. 1) provided with seven mufiles, in the first five mufiles five equal Smee’s elements were en- closed, and in the sixth a rheostat consisting of a platinum wire with so great a resistance that the resistance of the remaining parts of the circuit, in comparison with it, could almost be neglected. On the solution of one equi- valent of zinc in each element, the calorimeter indicated the quantity of chemical heat & developed in the five elements. * Raoult, in order to show that the occurrence of secondary chemical rocesses is necessary for the production of the heat in this case, makes an inference which might be rendered in the following manner :— When the voltameter is inserted in the circuit, the electromotive force of the series is thereby diminished by e, and the entire circuit is thus deprived of a quantity of heat which is equal to 28900 x = This heat is expended in the production of chemical decomposition in the voltameter. But as the quantity of heat expended for this is less than that above-mentioned, the difference must be made good by the occurrence of secondary chemical processes. + Comptes Rendus, t. Ixvi. p. 252; Pogg. Ann. vol. cxxxy. p. 300 (1868). On the Mode of the Propagation of Sound. AAT The same experiment was then repeated, with only this differ- ence, that a voltameter was enclosed in the seventh muffle. In this the quantity of heat k—a was obtained, where a (as shall presently be shown) denotes the quantity of heat which was consumed in the chemical decomposition of the electro- lyte in the voltameter. In this way Favre found, as the equi- valent for the chemical decomposition of water, 34204, and for the decomposition of sulphate of copper 26568 thermal units. Thereupon the following experiments were made :—The voltameter was taken out of the calorimeter No. 1, and placed in another calorimeter, No. 2; while the series and rheostat remained in No. 1. It was now found that calorimeter No. 1 indicated, on the electrolysis of water, 54235 heat-units less than in the first experiment—that is, when the series and rheo- stat were enclosed in No. 1 and no voltameter was inserted in the circuit. When the voltameter contained the copper- solution, 38530 units of heat less than in the first experiment were obtained in the same calorimeter. The calorimeter No. 2 gave, in the former case, a heating of 20335, and, in the latter, one of 12445 units. Upon this Favre asks, What can be the reason that the large quantity of heat that has disappeared in the series is again found in the calorimeter No. 2? This cause, he con- tinues, cannot be referred to the physical resistance of the vol- tameter; for this is so insignificant that it might almost be neglected in comparison with the resistance of the rheostat. According to his view the cause is to be sought in the cir- cumstance that the substances which take part in the chemical processes (oxygen, hydrogen, &c.) are found now in statu nascenti, now in the ordinary state. This explanation appears to me quite unsatisfactory. Hiven if it be assumed that such secondary chemical processes take place in the voitameter, they can certainly cause a heating of the voltameter, but they cannot possibly account for the great loss of heat which takes place in the series and rheostat. [To be continued. | LIX. Mode of the Propagation of Sound, and the Physical Con- dition determining its Velocity on the Basis of the Kinetic Theory of Gases. By 8. ToLvVER PRESTON®. I; Se the kinetic theory of gases is now generally ac- 7 cepted by physicists, affording, as it does, a rational explanation of the physical qualities and deportment of gases - * Communicated by Professor Clerk Maxwell. 442 Mr. S. T. Preston on the Mode of in agreement with experiment, it becomes a point of interest to inquire how the propagation of sound (or the propagation of waves in gases generally) would be explained by the aid of the kinetic theory. Since; in accordance with this theory, the molecules of gases are in motion among each other in straight lines, colli- ding among themselves, it would appear somewhat difficult to form a distinct idea as to the mode of propagation of a wave ina gas and the condition determining the rate of propagation, unless some law or guiding principle could be conceived of according to which the molecules moved. Now I think it will be found, on considering the subject, that there is a guiding principle governing the motions of the molecules of a gas among each other. I propose to show that the mo- lecules of a gas in a fixed vessel under the influence of their mutual collisions tend to arrange their motions in such a way that an equal number of molecules move at any instant in any two opposite directions; or a self-acting adjustment goes on among the molecules of a gas in such a way that when an imaginary plane is placed in any position outside the vessel, the number of molecules which at any instant are approaching the plane is equal to the number which at the same instant are receding from it. 2. This will be found to be a simple condition following necessarily from the conditions of equilibrium of pressure of a gas; for if a preponderating number of molecules were moving in any special direction in a gas, this would be fol- lowed by an increased pressure in that direction, whereas ob- servation shows that this is not the case, or the pressure of a gas is uniform in all directions. This therefore proves that the motion of the molecules which produces this pressure is uniform in all directions (and does not take place in one di- rection in preference to another), and therefore that the num- ber of molecules moving in any direction at a given instant is equal to the number moving in the opposite direction. It might be said that some of the molecules moving in one direc- tion might happen to possess a less velocity than some of those moving in the opposite direction, and therefore an increased number of molecules would be required in that direction in order to produce an equilibrium of pressure ; but it is to be observed that a space of any perceptible capacity encloses a vast number of molecules, so that every conceivable velocity of motion is encountered as much in one direction as in the opposite direction, and all inequality is thus equalized. It is not asif it were a case of a few molecules—say a dozen, when the mean velocity of the six moving in one direction might the Propagation of Sound. 443 happen to be considerably different from the mean. velocity of the six moving in the opposite direction ; but since it is a case of millions of molecules, all inequalities are equalized. It is evident, therefore, that in order that equilibrium of pressure may exist in a gas, or in order that the molecules in their mutual collisions may balance each other’s effects, as many molecules must be moving in one direction as in the opposite, so that the vis viva in two opposite directions is equal. If, for example, in any portion of a gas, such asa cubic foot, the number of molecules moving towards one ima- ginary bounding plane of this cubic foot were greater than the number moving towards the opposite bounding plane, the whole cubic foot of gas would tend to be propelled bodily in that direction towards which the greater number of its molecules was moving, thus producing a current, whereas no such currents in gases are observed. Indeed, according to actual observation, each portion of a gas however small, ap- pears to be at rest. The portion of the gas could only be at rest under the condition that it exerted a uniform pressure in all directions ;: for if it exerted a less pressure in any given direction, it would be reacted upon by the surrounding gas and propelled from that side towards which it exerted the least pressure. Since, however, any portion of the gas, however. small, appears to be at rest, it follows that this portion of the gas must exert a uniform pressure in all directions, and there- fore that the motion of the molecules composing this portion of the gas must take place uniformly towards all directions, i. é. aS many molecules must be moving in any one direction as in the opposite. 3. As a direct corollary to this, it may be shown that there is a self-acting tendency for this form of motion to be kept up; or, in other words, a mechanical self-adjustment is conti- nually going on among the molecules of a gas to produce a special character of motion, viz. that the motion of the molecules takes place uniformly towards all directions, or the numbers of molecules moving in any two opposite directions are equal— that, therefore, if by any artificial means the motion of the iWolecules of a gas could be interfered with or changed, they would, when left to themselves, automatically return back to the above regular form of motion. This evidently follows from the consideration that, since the equilibrium or uniformity of pressure requires that the motion of the molecules should take place uniformly towards all di-+ rections, and since any disturbance of this form of motion would disturb the equilibrium of pressure, and since the equi- librium of pressure is self-adjusting, the uniformity of motion 444 Mr. S. T. Preston on the Mode of (or the motion of the molecules towards all directions) which produces this equilibrium of pressure is therefore also neces- sarily self-adjusting. This fact will be at once evident by sup- posing an ooh eme case. Thus, supposing the component mo- lecules of an imaginary cubic (oat of gas to have their motion interfered with in such a way that the molecules only move longitudinally (i. e. in directions parallel to each other), then this cubic foot of gas will cease to exert any transverse or lateral pressure ; for a pressure cannot be exerted at right angles to the line of motion. The pressure of the surrounding gas will therefore cause this cubic foot of gas to collapse late- rally-(owing to the absence of a lateral opposing pressure); and in this act of collapse, by the lateral inrush of the sur- rounding gas, the molecules of this cubic foot will receive a forcible lateral. acceleration which they previously wanted, the irregularity of motion being thus soon corrected and the equilibrium of pressure restored. Itis clear that in the actual fact no such state of things as this could occur ; for the rapid interchange of motion going on among the molecules of a gas necessarily corrects any incipient disturbance of the equili- brium of pressure immediately on its occurrence—a continual self-acting adjustment thus going on which entirely prevents any abnormal movement of the molecules from developing itself, the movement of the molecules equally towards all directions being thus automatically maintained. To summa- rize, therefore, we observe :— That a special form of motion is required to produce equi- librium or uniformity of pressure in all directions within a gas, viz. uniformity of motion in the molecules of the gas towards all directions (so that an equal number of molecules are moving in any two opposite directions); and, further, that this uniformity of motion is self-adjusting, or the gas itself automatically adjusts the motion of its molecules, so that they move uniformly towards all directions. 4. Mode of the Propagation of Waves.—These considers tions enable the mode of propagation of waves in a gas to be illustrated in a very simple manner. Thus, since the mole- cules of a gas move in such a way that an equal number of molecules are moving in any two opposite directions, we may. therefore represent the molecules of a gas by a row of spheres or ivory balls (fig. 1), colliding among each other in such a way that at any given instant half are Fig. 1. moving in one direction and half in the opposite. The odd balls 1, 3, &c. may be supposed to move simultaneously in one direction, during the time that the even balls 2, 4, &e. move Sie ae a Laas t ' 1 Sem { 1 ' 4 the Propagation of Sound. 445 simultaneously in the opposite direction, the balls continually rebounding from each other and maintaining an equilibrium by their collisions. In the annexed diagram I, II, II, IV, V, may serve to illustrate the different WS phases of the movement. The balls 1, letisieic 2, 3,4 may be supposed to be controlled id biota Raa i: by the two plane surfaces A and B, al ie | 34 from which the end ones rebound, the fff |<} sisi whole row thus maintaining an equili- ' an bie a brium. Hach ball simply performs an Vr oe art one oscillatory movement within the limits Vj 37}*$ | nae Gas of space bounded by the dotted lines in the diagram—all the odd balls (or half the row) moving simultaneously in one direction, whilst all the even balls (or the other half of the row) move simultaneously in the reverse direction. To assume the balls to move simultaneously merely serves to simplify the conceptions without altering in the least the true conditions of the case. In the actual fact, of course, inthe case of a gas, some of the molecules would be moving obliquely to such an imaginary line ; but since the molecules maintain an equilibrium by their collisions, it cannot alter the ease in the least if we assume for simplicity the motions to be straight; or, indeed, the resolved component of the motions in the direction of the line can be taken. The row of colliding balls, like the colliding molecules of a gas, thus maintain a perfect equilibrium, the row not tending bodily as a whole to be propelled. in any particular direction, but simply tending to open out or expand, and to separate the controlling sur- faces A and B. The oscillatory form of motion of the balls fulfils that condition, that the row of balls, as a whole, main- tains a fixed position while its parts are in motion, just as a portion of a gas maintains a fixed position while its parts are in motion. 5. To illustrate now the way a wave is propagated by a gas, we may suppose that a forward and backward motion is communicated to the plane A in the form of a vibratory motion ; also the plane B may be supposed removed and the row of spheres extended indefinitely from the plane A, the movement of vibration of the plane being also supposed slow compared with the normal velocity of the spheres. In that case the sphere 1 would strike against the plane A a number of times during one forward swing of the plane. On the commencement of the first forward swing of the plane, the plane advancing towards the sphere 1, the latter receives a small increment of velocity, which it transfers by collision to sphere 2, the two spheres simply exchanging velocities 446 Mr. 8. T. Preston on the Mode of according to the principles of impact of equal masses. The sphere 1 therefore returns towards the plane with its origi- nal normal velocity unchanged, and receives a second similar increment of velocity from the plane, which it again trans- fers, &c. The sphere 2 at once transfers to sphere 3 the in- crement of velocity received from sphere 1, the sphere 2 re- turning with its original normal velocity to repeat the process, The same considerations apply to all the spheres ; and in this “way during one forward swing of the plane A,a succession of small increments of velocity are propagated in the form of a wave by exchange of motion along the line of spheres (or the waye consists in a peculiarity in the motion of the spheres such that they move forward with a velocity somewhat greater than the normal velocity, and backward with the normal ve- locity), the velocity of transmission of the wave being that of the spheres themselves, assuming that the diameter of the spheres is small compared with their mean distance, as is true of the molecules of gases. The length of this pulse or half-wave evidently must depend on the time taken by the plane to make one swing or semivibration ; or wave- length is proportional to vibrating-period. The wave-length will also evidently depend on the normal velocity of the spheres. By the backward swing of the plane, to finish one complete vibration, the plane A moving or receding from the sphere 1, the latter will be slightly retarded ; and thus a suc- cession of small decrements of velocity, forming the second half of the wave, is transmitted in precisely the same manner along the row of spheres: or the second half of the wave con- sists in a peculiarity in the motion of the spheres such that they move forward with a velocity somewhat less than the normal velocity and backward with the normal velocity. 6. Itis of course clear, as before remarked, that in the ease of a gas the molecules in their mutual collisions would not all be moving in the direct line of propagation of the wave at the instant of its passage, but some of them more or less obliquely to the line of propagation ; so that, for this cause, the rate of propagation of the wave would be necessarily, to a certain extent, slower than the normal velocity of the molecules them- selves. This, however, does not aifect in the least the prin- ciple involved ; and therefore the above mode of illustration serves to give a perfectly just idea of the physical process by which, through the normal motion of the molecules of a gas, changes of velocity experienced by the molecules or “ waves” are propagated to a distance through the gas in accordance with the kinetic theory. @. Cause producing the Oscillation of the Mass of Air.—It is the Propagation of Sound. 447 a known fact that, when a sound-wave passes through a mass of air,the mass of air oscillates, as a whole, backwards and forwards (within small limits). It will therefore be necessary to explain how this takes place in accordance with the kinetic theory, Taking the illustrative case of the row of spheres, we have observed that when no wave is passing, each sphere is nor- mally oscillating backwards and forwards within definite limits ; or all the alternate spheres, or half the row, move forward, whilst the other half moves backwards. We have observed that when a wave passes, each sphere, after it has transferred the increment of velocity foward, returns back- wards with its normal velocity; 7. e. the sphere is only affected with the increment of velocity when it moves forwards, and not when it moves backwards. The sphere therefore makes its forward movement with a greater velocity than its backward movement ; and accordingly the sphere gains more ground at its forward movement than it loses at the backward movement 3 and as-this occurs at each oscillation of the sphere, and the sphere oscillates a great number of times backwards and for- wards during the passage of the wave, there is a gradual gain of ground by the sphere. The same applies to all the spheres forming the first half of the wave, so that all the spheres affected by the increment of velocity are pushed eae for- ward tain the time that the increment of velocity forming the first half of the wave passes. | The same considerations apply to the molecules of a mass of air, which are accordingly pushed bodily forward during the time that the first half of a wave of sound passes; and thus the mass of air oscillates forward as a whole during the passage of the half-wave. This forward movement of the mass of air is naturally ac- companied by a condensation of the air. , 8. Precisely the same considerations (conversely) apply to the decrement of velocity experienced in the second half of the wave. The spheres now make their forward movement with a decrement of velocity and their backward movement at their normal velocity; so that their forward movement is made at a less velocity than their backward movement; and thug (conversely) ground is lost by the spheres, or they are shifted bodily backwards during the time the decrement of velocity forming the second half of the wave passes. The same ap- plies to the molecules of a mass of air, which is accordingly shifted bodily backwards during the passage of the decrement of velocity constituting the second half of the sound-wave ; and thus the mass of air oscillates backwards and forwards during the time the complete wave traverses it. By the back- ward-shifting of the mass of air, a rarefaction ensues. 448 Mr. 8. T. Preston on the Mode of 9. The Physical Condition determining the Velocity of Sound. —It must evidently follow, as a necessary consequence from the above considerations, that the velocity of sound in a gas must be proportional to the velocity of the molecules of the gas; so that, therefore, the numbers expressing the velocity of sound in different gases and the numbers expressing the velocities of the molecules of different gases must be propor- tional to each other. This is found to be true. Thus, for example, the velocity of the molecules of hydrogen is known to be four times as great as that of the molecules of oxygen; so the measured velocity of sound in hydrogen is four times its measured velocity in oxygen. 10. The velocity of sound ina gas is, as was to be expected from the reasons before referred to, a certain fixed proportion slower than the normal velocity of the molecules of the gas. Thus the velocity of the molecules of hydrogen at 0° C. is 6050 feet per second, whereas the velocity of sound in hydro- gen at 0° C. is 4164 feet per second. The constant ratio ex- pressing the relation between the velocity of sound in a gas and the velocity of the molecules of the gas is given by the number 0:688 very nearly; or the velocity of sound in a gas is 0-688 time the velocity of the molecules of the gas ; so that the velocity of sound in a gas may be simply got by multiply- - ing the known velocity of its molecules by this constant. It would seem probable that by taking into account the oblique motions of the molecules in their collisions along the line of propagation of the wave atall conceivable angles, by a system of averages, the absolute value of the velocity of sound in a gas could be determined independently as an a priori problem, direct from the molecular velocity, by mathematics”. 11. The fact that the velocity of sound in a gas is simply pro- portional to the velocity of its molecules cannot surely but be regarded as a far more simple and satisfactory physical con- dition governing and determining the velocity of scund than the vague idea of “ elasticity,” or (as assumed) that the velo- city of sound in a gas is proportional to its “ elasticity.”’ The definite physical conception of the velocity of the molecules themselves which by their interchange of motion propagate the wave, is surely far preferable to the vague idea of “ elasti- city’ governing the velocity of the wave. 12. Velocity unaffected by Density or Pressure.—According to the principles involved in the kinetic theory, therefore, the velocity of sound in a gas is dependent on nothing else but the velocity of its molecules ; or, whatever conceivable condi- tions the gas may be subjected to (such as change of density * See Postscript (2). the Propagation of Sound. 449 or pressure), the velocity of sound will remain unaltered so long as the velocity of the molecules remains unaltered. Thus, if the density of a gas (or air) be changed by forcing fresh air into the same space, the velocity of sound will remain unaltered, simply because the velocity of the molecules remains unaltered. The old theory would assume that the velocity of sound has remained unaltered in this case because increased density (or increased number of air-molecules) has a power of diminishing the velocity of the sound-waye, while, on the other hand, the increased pressure of the air against the sides of the vessel (considered to represent increased “ elasticity ’’) has a power of increasing the velocity of the wave, and that the two actions counteract each other, and therefore the velocity of the wave has remained unaltered. Contrast this with the | simple and realizable explanation of the kinetic theory, viz. that the velocity of the wave has remained unaltered simply because the velocity of the molecules which propagate it has remained unaltered. 13. Clausius has demonstrated that, for a gas to fulfil Mariotte and Gay-Lussac’s laws :— (1) ‘The space actually filled by the molecules of the gas must be infinitesimal in comparison with the whole space occu- pied by the gas itself.”’ (2) “‘ That those portions of the path of a molecule through- out which the molecular forces are of influence in sensibly altering the motion of the molecule either in direction or velo- city must be of vanishing value compared with those portions of the path throughout which such forces may be considered as inactive.”’ ¥ Since, therefore, the portion of a molecule’s path through which it is acted on by other molecules of the gas is vanish- ingly small compared with the range of its path throughout which it is not so acted on, there is therefore practically no distance action between the molecules of a gas, which accord- “ingly can only influence each other by direct impact. The only way, therefore, one molecule of a gas can influence ano- ther is by moving up to it and striking against it. The only way, therefore, a wave or small impulse can be propagated from molecule to molecule through a gas is by the molecule pos- sessing the impulse moving up toand striking against another molecule ; and therefore the velocity of propagation of such wave or impulse must depend solely and entirely upon the velocity with which the molecule moves; or the sole conceiv- able cause regulating the velocity of an impulse propagated from molecule to molecule is the velocity of the molecule itself, or the velocity with which the molecule traverses its free path. ~ Phil. Mag. 8. 5. Vol. 3. No. 20. June 1877. 2G 450 Mr. 8. T. Preston on the Mode of This is an inevitable certainty by the acceptance of the kinetic theory ; and therefore it is clear that a change of density of the air, by adding to the number of air-molecules (as when air has been forced into a vessel), cannot possibly influence the velocity of propagation of a wave by the air so long as the molecular velocity remains constant. 14. Obviously when air has been foresd into a vessel and thereby its density increased, this has simply the effect, by adding to the number of molecules, of increasing the number of collisions among the molecules ; but this cannot affect in the least the velocity of propagation of the sound-wave, for the simple reason that it cannot affect the velocity of the mole- cules. So the increased pressure of the air against the sides of the vessel (considered to represent increased “ elasticity ’’) cannot possibly influence the velocity of the sound-waye, this increased pressure being merely due to an increased number of molecules colliding against the sides of the vessel. The above considerations may perhaps be made more ob- vious by imagining the case of a number of couriers pro- pagating a message with no intervening mechanism through which they can communicate with each other (as in analogy with the molecules of a gas). Then the velocity of propaga- tion of the message will solely depend on the velocity of the couriers themselves. Increased number of couriers (corre- sponding to increased number of molecules in a gas or in- creased density) will have no effect on the velocity of propa- gation of the message, provided the velocity of each courier remains the same. So with the molecules of a gas, which according to the kinetic theory, are interchanging motion among themselves with no means of acting upon each other excepting by direct impact. Thus the velocity of a wave in a gas can be determined solely by the velocity of its mole- cules, and by nothing else; or the sole physical condition de- termuning the velocity y of sound in a gas is the velocity of its molecules. 15. Variation of Specific Gravity.—So, therefore, also vari- ation of specific gravity in gases can have no influence on the velocity of the sound-wave, unless the molecular velocity be changed. One known consequence of the kinetic theory is, that equal volumes of different gases all contain the same number of molecules, so that therefore the specific gravity of a gas is proportional to its molecular weight. A cubic foot of oxygen contains the same number of molecules as a cubic foot of hydrogen; but the specific gravity of oxygen is sixteen times that of hydrogen, and the oxygen molocale is sixteen times as heavy as the hydrogen molecule, and (as is known) ss. the Propagation of Sound. 451 the molecules of hy drogen are moving four times as fast as the molecules of oxygen; and on this account the wave is propagated four times as fast, not because the propagating molecule is heavy or light. 16. Case of Heated “Rar efied Air.—When air unconfined and free to expand is heated, the velocity of sound is found to beincreased. This, according to the old theory, is considered to be due to the diminished densit, 'y of the air, or the diminished number of molecules attendant on the expansion of the air.- Now, in accordance with the kinetic theory, this increased velo- city of propagation of the wave is simply explained by the in- creased velocity of the air-molecules which propagate it, atten- dant on the application of heat to the air, the motion of the molecules representing the “ heat ” and their velocity being a measure of the “temperature.” The increase in the velocity of the molecules of air attendant on the application of heat pushes the surrounding air back, and causes the heated portion to be rarefied, thus diminishing its density. The density of the heated portion may therefore be taken as a convenient measure of the velocity of its component molecules, upon which the velocity of propagation of the sound-wave depends. Thus it may be a convenient rule that the velocity of sound in heated rarefied air is inversely proportional to the square root of the density of the air, the cause of this being that the molecu- lar velocity is itself inversely proportional to the square root of the density (7. e. in air free to expand and change its den- sity). The diminished density of the heated rarefied air can- not, however, be said to be the cause of the increased velocity of the sound-wave ; ; the diminished density is rather the effect of the increased molecular velocity, which itself is the cause of the increased velocity of the wave. 17. So the velocity of sound in different gases is found to be inversely proportional to the square root of the specific gravities of the gases: but this is simply due to the fact that the specific gravity of a gas is as its molecular weight; and the molecular velocity, upon which the velocity of pro- pagation of the sound-wayve depends, is itself inversely pro- portional to the square root of the molecular weight. 18. Case of Heated Confined Air.—When air (or any gas) is confined in a vessel so as to prevent expansion and then heated, the velocity of sound is found to be augmented. This augmentation of velocity, according to the kinetic theory, is due to the same cause as in the previous case (when the air was unconfined), viz. to the increased telat y of the air mole- cules attendant on the application of heat. According to the old theory, the augmented rate of pr spagtion of the wave is 2G 2 y a 452 On the Mode of the Propagation of Sound. now referred to increased “ elasticity’ of the air (represented by the increased pressure of the confined air upon the sides of the vessel). This increased pressure upon the sides of the vessel, however, is only due to the increased velocity of the air- molecules which impinge against the sides of the vessel, and whose velocity has been augmented by the application - of heat (and whose motion represents the heat”). The in- creased pressure of the heated air may serve as a convenient means for estimating the augmentation of molecular velocity, upon which the augmented velocity of propagation of the sound-wayve depends. ‘Thus it may be a convenient rule that the velocity of sound in heated (confined) air (of unchanged density) is proportional to the square root of the “ elasticity ”’ of the air (as measured by the pressure), the reason of this being that the velocity of the molecules of air (which deter- mines the velocity of the propagation of the wave) is itself pro- portional to the square root of the pressure. The augmented: pressure of heated confined air is evidently not itself the cause of the increased velocity of propagation of the wave ; but the augmented pressure (“elasticity”) is the effect attendant on the increased velocity of the molecules of air, which increased velocity is itself the cause of the augmented velocity of propa- gation of the wave. 19. The result of these considerations may therefore be summarized as follows :— That the velocity of propagation of a wave (such as a wave of sound) in a gas is solely determined by, and proportional to, the velocity of the molecules of the gas; that this velocity of pro- pagation of the wave is not affected by density, pressure, or by the specific gravity of a gas, or by any thing else excepting the velocity of its molecules. 20. This, it may be observed, is a condition following inevi- tably on the acceptance of the kinetic theory ; and surely the very simplicity of this relation as affording a definite physical conception of the condition determining the velocity of sound, and as giving an insight into its mode of propagation, would be by itself sufficient to recommend it over the old system. If any thing I have written should serve to divert the atten- tion of others more competent than myself to this interesting subject, the purpose of this paper will have been served. 67 PS. (1). It is proper for me to add that this paper is not wholly original, but the perusal of a paper by Mr. J. J. Waterston in the ‘ Philosophical Magazine’ (Jan. 1859, Sup. to vol. xvi.) formed the starting-point of the present paper. The method of illustrating the propagation of a wave by means of a line of spheres is due to Mr. Waterston ; but the Mr. W. J. Lewis’s Crystallographic Notes. 453 investigation as to how the special motion assigned to the line of spheres can properly represent the character of the motion of the molecules of a gas in its normal state is my own, no special investigation of this kind being contained in Mr. Waterston’s paper. To Mr. Waterston, however, is mainly due the initiative in this subject. As I should be sorry to claim any originality that I did not possess, I would respect- fully direct the attention of readers to the portion of Mr. Waterston’s paper bearing on this subject. PS. (2). Professor Clerk Maxwell, to whom this paper was communicated, and who has taken a kindly interest in the sub- ~ ject, has worked out mathematically the velocity for a wave or impulse propagated by a system of particles moving among _each other according to the conditions of equilibrium inves- tigated in the first part of this paper—the diameter of the particles being assumed so smallas to be negligible compared with their mean distance, and the particles being further as- sumed spherical, so that there is no movement of rotation developed at the encounters (which would involve loss of velocity). Under these premises, the velocity of the wave was found to be = (or 0°745) into the mean velocity of the particles. In most gases the velocity of sound is slightly less than this. This is referable to the movements of rotation deve- loped at the encounters of the molecules (which calculably would delay the wave to a certain extent). In vapour of mercury, according to the determinations of Kundt and War- burg, the velocity of sound is exactly a into the molecular velocity. London, May 1877. LX. Crystallographic Notes. By W. J. Lewis, W.A., Fel- low of Oriel College, Oxford, and Assistant in the Mineral Department, British Museum*. [Plate IV. ] Barium Nitrate. | ieee autumn my friend Mr. T. Davies, of the British Museum, kindly brought me a fairly large crystal with a very large number of faces on it. It had been found at the * Communicated by the Crystallological Society. Read April 12, 1877, 454 Mr, W. J. Lewis’s Crystallographic Notes, bottom of a reagent-bottle which had been put aside for many years. The solution, owing to a faulty stopper, had all eva- porated, leaving this single crystal. The label had been lost; so, after a crystallographic investigation, I scraped off a very small portion from a part on which were no crystal-faces. By means of this I was able to determine that the crystal was one of barium nitrate. I have thought that a description of its crystallography would be interesting, both on account of the remarkable development of its faces and its decided tetar- tohedrism. The facts already known about barium nitrate are that it crystallizes in the cubic system, shows a hemi- hedrism with parallel faces, and has the forms {100}, {111}, and 7{210}. 7 The forms observed on the crystal in question are a= {10 0}, Peril 24), h= wri 24 nn er oo Leonie s=x{211}, o=«{111}. A glance at the stereographic pro- jection (fig. 1, Plate IV.) of these forms shows that t, n, and { occupy alternate octants, and that o, s, and h occupy the remaining octants. The forms¢ and h are complementary, and make up the hemihedral form with parallel faces 7{1 24}. The physical character of the faces of this form in adjacent octants manifests, however, the tetartohedrism of the crystal; for the faces h are large and smooth, the faces ¢ small and rough. The faces are tetartohedral and well developed in alternate octants ; they are for the most part bright; but the most care- ful examination in the remaining octants failed to discover the slightest trace of corresponding planes. Similarly the faces o, which are large and bright, were found only in alternate oc- tants. The faces / are fairly developed and bright. The faces s are very small but fairly bright. The faces of the cube a are large and bright. The principal zones on the crystal are those containing the planes antl, a,,s,,0, at,ths,h, ol,n,u.: These aterded considerable aid in seeking for traces of planes, and also in some instances in determining the real positions of some of the badly developed faces. ‘The following are the most im- portant angles of the combination, with which the measure- ments accorded well:— at, 29 12 an 82 19 ie Laas 31 Gly Gal dy oe Gn, OV al on, €2 585 at, 64° 734 an, 59 32 * on ie ee The stereographic projection (fig. 1.) shows very clearly the zones and the arrangement of the poles. Fig. 2 is an ortho- gonal projection on one of the faces of the cube; and fig. 3 is Mr. W. J. Lewis’s Crystallographic Notes. AD55 one in which the axes have been projected in the usual manner. To avoid confusion, the small planes s have been omitted in the latter figure. The crystal is elongated in a direction nearly coinciding with the normal to a face of the tetrahedron. An oval ring seems to have been first deposited; and on this the erystal has grown, vaulting itself on the lower surface so as not to cling to the bottle. There were no definite crystal- faces to be seen on this concave portion. The top is also irre- gular and indefinite. The crystal introduced into the polari- zing microscope between crossed Nicols depolarized the light. Hxact experiments on the rotation of the plane of polarization could not be made without destroying the crystal. On some crystals of barium nitrate crystallized out of solution during the course of a few weeks, the forms «{111}, «{111}, {101}, and «{1 22! were found. The planes «{1 11}! seemed to be smoother and brighter than those of «{111!; andthe edges of the former carried the planes «{1 2 2}. Sphene. On acrystal from the Tyrol, obtained by me some years ago, two rough ill-developed planes are situated on the quoin formed by the two planes n= {1 2 3} and the base c= {00 1}. They look almost like the result which would be produced by slightly grinding down this quoin. The exact symmetry of the two planes, as also the frequency of their occurrence, show them, however, to be really planes. Hessenberg, who devoted considerable attention to this mineral, has noticed similar faces on the crystals from the Zillerthal, described in his Min. Notizen, vi., and has introduced them in two of the figures of these crystals.. As this part of the Notizen is out of print, I have copied one of these figures (fig. 34), in which the small triangular dotted planes are those under consideration. Hes- senberg says that he found them more or less clearly deve- loped on almost all the crystals from this locality. He ex- presses, however, his conviction that the rough portion is only a continuation of the plane n. Lately I obtained several crystals on which these planes were very fairly developed, of one of which fig. 4 is a projec- tion. They give such excessively bad reflections, that it was only by observing with a ray of sunlight thrown into the room by a mirror, and by slightly oiling the surfaces, that reliable measurements were obtained. ‘The form calculated from these measurements is {3, 3, 10}, adopting the axial system given in Miller’s ‘Mineralogy.’ The following are the angles ob- served and calculated :— 3 456 Lord Rayleigh’s Acoustical Observations. Observed. Calculated. iby Setar See gee 10 59 N, DP cecccccccees 33 dd4 sient) DP, coccceessees 22 d35 22 ail Gis Wacseiteniiniarecit 423 2 474 Gold. Measurement of a large though imperfect crystal in the British Museum showed it to be a combination of the cube with the tetrakishexahedron {410% and the triakisoctahedron {811}. As the faces were very dull, and but rough measure- ments could be obtained, I was glad to confirm this observa- tion by the examination of a crystal showing the same com- bination in Mr. Ludlam’s beautiful collection, which he was good enough to lend me. The angles measured on the latter crystal agree fairly well with the calculated angles. Measured. Calculated. (ATOMS TY 1 eons 9 52 (410,401) Te ari AC NIU) 19 44 I saw recently a very beautiful crystal of the same combi- nation in the collection of the Ecole des Mines, Paris. In the two former the planes {811} are deeply striated parallel to their intersection with the faces of the cube. LXI. Acoustical Observations. By Lorp Rayieten, JA., PRS.* Perception of the Direction of a Source of Sound. 7% a paper with the above title, communicated last year to the Musical Association and afterwards published in abs- tract in ‘Nature,’ I brought forward the fact that we are unable to distinguish whether a pure tone (obtained from a tuning-fork and air-resonator) is immediately in front of or immediately behind us—although with other sounds, and no- tably with the human voice, there is in general no difficulty. In order to make the experiment satisfactorily, it is necessary to provide two similar forks and resonators and to place the observer between them. At a given signal both forks are struck, but one of them only is held over its resonator. If this precaution be neglected, the noise attending the excita- tion of the fork vitiates the experiment. Subsequently to the reading of my paper, it occurred to me that if the ordinary * Communicated by the Author. Lord Rayleigh’s Acoustical Observations. 457 view as to the functions of the two ears be correct, there must be other ambiguous cases besides those already experimented upon. To the right of the observer, and probably nearly in the line of the ears, there must be one direction in which the ratio of the intensity of sound as heard by the right ear to the intensity as heard by the left ear has a maximum ‘value ereater than unity. For sounds coming from directions in front of this the ratio of intensities has a less and less value, approach- ing unity as its limit, when the sound is immediately in front. In like manner, for directions intermediate between the direc- tion of maximum ratio and that immediately behind the ob- server, the ratio of intensities varies continuously between the same maximum value and unity. Accordingly, for every direction in front there must be a corresponding ‘direction be- hind for which the ratio of intensities has the same value; and these two directions could not be distinguished in the case of a pure tone. The only directions as to which there would be no ambiguity are the direction of maximum ratio itself, and a corresponding direction of minimum ratio on the other side of the head. The attitude of my mind with respect to this result was, I confess, one of considerable scepticism. A great number of miscellaneous experiments had been made with forks as well as with other sources of sound; and I thought that, if these ambiguities had existed, indications of them must have been erceived already. It was therefore with some curiosity that took the first opportunity, last September, of submitting the matter to the test of experiment, the same forks (making 256 vibrations per second) being used as on previous occasions. The decision was soon given. An observer facing north, for example, made mistakes between forks bearing appr oximately north-east and south-east, though he could distinguish without a moment’s hesitation forks bearing east and west. In all such experiments it is necessary that the observer keep his head perfectly still, a very slight motion being sufficient in many cases to give the information that was previously wanting. A suggestion was made, in the discussion that followed the reading of my paper before the Musical Association, which I thought it proper to examine, though I had not much doubt as to the result. In order to meet the difficulty in the ordi- nary view as to the functions of the two ears arising out of the fact that a 256-fork seems to be heard nearly as well with the ear turned away as with the ear turned towards it, it was suggested that possibly the discrimination between forks right and left depended on something connected with the commence- 458 Lord Rayleigh’s Acoustical Observations. ment of the sound. It might be supposed, for example, that we are able to recognize which ear is first affected. On trial, however, it appeared that the power of discrimination was not weakened, although the observer stopped his ears during the establishment of the sound. When one ear is stopped, mistakes are made between forks right and left; but the direction of other sounds, such as those produced by clapping hands or by the voice, is often told much better than might have been expected, The Head as an Obstacle to Sound. The perfection of the shadow thrown by the head depends on the pitch of the sound. I have already menticned that it appears to make but little difference in the audibility of a pure tone with a frequency of 256, whether the ear used be turned towards or from the source. But the case is very different with sounds of higher pitch, such as that of an ordinary whistle. The one that I employed was blown from a loaded gas-bag, and gave a very steady note of pitch f”. A hiss is also heard very badly with the averted ear. This observation may be made by first listening with both ears to a steady hiss on the right or left, and then closing one ear. It makes but little difference when the further ear is closed, but a great dif- ference when the nearer ear is closed. A similar observation may be made on the sound of running water. For the same reason a hiss or whisper, coming from-a person whose face is averted, is badly heard. Under these circumstances even ordinary speech is difficult to understand, though the mere intensity of sound does not seem deficient, Reflection of Sound. In many cases sound-shadows appear much less perfect than theory would lead us to expect. The anomaly is due in great measure, I believe, to an error of judgment, depending on the enormous range of intensity with which the ear is capable of dealing. The whistle of a locomotive is very loud at a distance of ten yards. At a mile off the intensity must be 30,000 times less ; but the sound still appears rather loud, and would robably be audible under favourable circumstances even when enfeebled in the ratio of a million to one. Tor this reason it is not easy to obtain complete shadows; but another difficulty arises from the fact that there are generally obstacles capable of reflecting a more or less feeble sound into what might other- wise be a nearly complete shadow. An attempt to examine this point led me to a few simple experiments on the reflection of sound, which may be worth recording. Lord Rayleigh’s Acoustical Observations. 459 The principal obstacle throwing the shadow was the corner of a large house; and among the sources of sound tried were the human voice, tuning-forks, whistles steadily blown, and a small electric bell, of which the last (which was employed in Professor Reynolds’s acoustical experiments) proved to be as convenient as any. The source was placed close to the south side of the house, at a distance of eight or ten yards from the south-west corner, while the observer took up a corresponding position on the west side. With these arrangements the sound- shadow was pretty good, though far from perfect. When, however, a flat reflector, such as a drawing-board of moderate dimensions, was held at the proper angle by an assistant placed at some distance outwards from the corner, the augmentation of sound was immense, and the hearer realized for the first time how very good the shadow really was. A screen made by stretching a ‘Times’ over a hoop about 21 feet in diameter gave apparently as good a reflection as the drawing-board ; but when calico was substituted for the paper the reflecting-power was very feeble. By wetting the calico, however, it could be made to reflect very well. These results are in agreement with the striking experiments described by Professor Tyndall. Audibility of Consonants. I suppose it must have been noticed before now that the s sound is badly returned by an echo. Standing at a distance of about 150 yards from a large wall, I found that there was scarcely any response to even the most powerful hiss. Sh was heard a little better; m, k, p, g pretty well; r very well; h badly ; ¢ badly; 6 seemed half converted into p by the echo. The failure of the hiss seems to be the fault of the air rather than of the wall, for a powerful hiss heard directly at a dis- tance of 200 yards had very little s left in it. Interference of Sounds from two unsonant Tuning-forks. In ordinary experiments on interference the sounds are only approximately in unison, and consequently the silences result- ing from antagonism of the vibrations are of only momentary duration. I thought it of interest, therefore, to arrange an experiment in which the sounds should be pure tones, abso- lutely in unison, and should proceed from sources at a consi- derable distance apart. With the aid of electromagnetism the solution of the problem was comparatively easy. An intermit- tent electric current, obtained from a fork interrupter making 128 vibrations per second, excited by means of electromag- nets two other forks, whose frequency was 256, These latter ee ee 460 Lord Rayleigh’s Acoustical Observations. forks were placed at a distance of about ten yards apart, and were provided with suitably tuned resonators by which their sounds were reinforced. The pitch of both forks is necessarily identical, since the vibrations are forced by electromagnetic forces of absolutely the same period. The arrangement was successful; and with a battery-power of two Grove cells sounds of fair intensity were obtained. With one ear closed it was possible to define the places of silence with considerable accu- racy, a motion of about an inch being sufficient to produce a marked revival of sound. Ata point of silence, from which the line joining the forks subtended an angle of about 60°, the apparent striking up of one fork, when the other was stopped, had a very peculiar effect. : Symmetrical Bell. I do not know whether it has ever been noticed that there ought to be no sound emitted along the axis of a symmetrical bell. It is easy to see that at any point of the axis any effect, whether condensation or rarefaction, which may be produced by one part of the surface of the bell must be neutralized by other parts, and that therefore on the whole there can be no variation of pressure during the vibration. The experi- ment may be made with a large glass bell (such as those used with air-pumps), set into vibration by friction with the wetted finger carried round the circumference. If the axis of the vibrating bell be turned exactly towards the observer, the sound is feeble as compared with that heard when the position of the bell is altered. The residual sound may be due to want of symmetry, or more probably to reflexion from the ground, which last cause of error it is almost impossible to get rid of. Octave from Tuning-forks. When a vibrating fork is held over an air-resonator in tune with itself, the sound emitted is very approximately a pure tone; but when the fork is placed in contact with a sounding- board, the octave may generally be perceived by a practised ear, and is often of remarkable loudness. By means of a reso- nator tuned to the octave the fact may be made apparent to any one. ‘This result need not surprise us. By the construc- tion of a fork the moving parts are carefully balanced, and the motion is approximately isolated. In the ideal tuning-fork, composed of equal masses moving to and fro in a straight line, the isolation would be complete, and there would be no ten- dency whatever to communicate motion to surrounding bodies. In an actual fork, however, even if the direction of motion of the masses were as nearly as possible perpendicular to the Lord Rayleigh’s Acoustical Observations. 461 stalk, the necessary curvature of the paths would give rise to an unbalanced centrifugal force tending to set the sounding- board in vibration. The force thus arising is indeed of the second order, and might probably be neglected, were it not that the apparatus is especially suited to bring it into pro- minence. 3 In order to test the soundness of this view as to the origin of the octave, the following experiment was contrived. A 256 tuning-fork was screwed on to a resonance-box intended for a 512 tuning-fork, and therefore approximately in tune with the octave of the first fork. When a powerful vibration was excited by means of a bow, the octave sound was predomi- nant, and but little could be heard of the proper tone of the fork. In order to place the two sounds on a more equal foot- ing, a resonator, consisting of a bottle tuned by pouring water into it to a frequency of 256, was brought near the ends of the vibrating prongs. By adjusting the distance it was easy to arrange matters so that at the beginning of the vibration neither sound had a conspicuous advantage. But, as the am- plitude of vibration diminished, the graver tone continually gained on its rival, and was left at last in complete possession of the field. The purity of the remaining sound could be tested at any time by the perfection of the silence obtained by removing the air-resonator. This arrangement may be recom- mended to any one who wishes to practise his ears in hearing octaves. From the above experiment (in which, if desired, the ear may be replaced by Konig’s manometric flames), it appears that the octave sound is to be attributed to a motion of the second order, which is rendered important by the peculiar iso- lation of the motion of the first order. The harmonic sounds heard when suitably tuned resonators are presented to the free ends of the prongs, though also dependent on orders of the motion higher than the first, have a somewhat different origin. Influence of a Flange on the Correction for the Open End of a Pipe. In theoretical investigations* as to the amount of the cor- rection to the length of an open pipe due to the inertia of the external air, it has been usual, for the sake of facilitating the calculations, to suppose that the open end is provided with an infinite flange. Even with this simplification no exact solution of the problem has been obtained. It has been proved, how- ever, that, provided the wave-length be sufficient in relation * * Helmholtz, Crelle,1860. Alsoa memoir by myself ‘On Resonance,” Phil. Trans. 1871. 462 Lord Rayleigh’s Acoustical Observations. to the diameter of the pipe, the addition which must be sup- posed to be made to the length is very nearly equal to, though somewhat less than, °8242R, and is certainly greater than ‘785 R*, R being the radius of the pipe. It is obvious that the removal of the flange would make a considerable difference, probably reducing the correction be- low the lower limit above mentioned. In the absence of any theoretical estimate, I thought it desirable to make an experi- mental determination of the effect of a flange, and ordered some years ago a pair of similar organ-pipes of circular section for the purpose. My idea was to tune the pipes to unison, and then to count the beats when the pitch of one of them was slightly lowered by the addition of a flange ; but the experi- ment lay in abeyance until last winter. Instead of tuning the pipes to unison, I preferred simply to count the beats before and after the addition of the flange, which consisted of a large sheet of stiff millboard perforated witha hole sufficiently large _ to allow the passage of the pipe. In this way it appeared that the effect of the flange was to reduce the frequency by nearly 14 out of about 242. If we take the velocity of sound at 1123 feet per second, corresponding to 60° F., the calculated effective length of the pipe is about 28 inches, and the radius isl inch. Thus the correction to the length due to the flange is the same fraction of 28 inches that 14 is of 242, or is equal to about -2R. Combining this result with the theoretical esti- mate above referred to, we may conclude that the whole cor- rection for an open end, when there is no flange, must be about °6 R. Mr. Bosanquet, to whom I communicated the result at which I had arrived, informs me that he has since determined the correction for a flange as ‘25 R. The Pitch of Organ-pipes. The whole correction to the length of an organ-pipe, neces- sary to make it agree with Bernoulli’s theory, is considerably greater than any of those spoken of under the preceding head- ing. According to the rule of Cavaillé-Coll, the addition for an open pipe of circular section amounts to as much as 34 R, whereas for a simple tube open at both ends it should be only about 1:2 R. This discrepancy is, I believe, often attributed toa peculiar action of the stream of air by which the pipe is excited. Of course it is not to be denied that some disturbance arises from this source, as is proved by the dependence of the pitch on the strength of the wind; but the near agreement between * See note to a paper “On the approximate Solution of certain Pro- blems relating to the Potential,” Math. Soc. Proc. vol. vii. No, 93, Lord Rayleigh’s Acoustical Observations, 463 theory and measurements by Wertheim and others, on the pitch of resonators caused to speak by a stream of air, has always seemed to me to prove that a comparatively small part only of the whole discrepancy is to be explained in this way. Onthe other hand, it is obvious that-the ‘‘ open ”’ end at the base of the pipe is very much contracted, and that the correction thence arising may be several times as great as that applicable to the upper end, where the pipe retains its full section. Iwas therefore anxious to ascertain what was the proper note of an organ-pipe, regarded as a freely vibrating column of air, and thus to estimate in what proportion the two causes of disturb- ance contribute to the final result. There are two methods by which the pitch of a resonator may be determined without the use of a stream of air. The simplest, and in many cases the most accurate, method con- sists merely in tapping the resonator with the finger or other hammer of suitable hardness, and estimating with the aid of a monochord the pitch of the sound so produced. In attempting, however, thus to determine the pitch of the organ-pipe, I found a difficulty arising from the uncertain character of the sound, and the results were by no means so accordant as I desired. Possibly an observer gifted with a more accurate ear than mine would have been more successful. The other method is one of which I have had a good deal of experience, and which I can generally rely upon to give results of mode- rate accuracy. It consists in putting the ear into communi- cation with the interior of the resonator, and determining to what note of the scale the resonance is loudest. I have gene- rally found it possible thus to fix the pitch of a resonator to within a quarter of a semitone. In the present case a small hole was made in the side of the pipe near the centre ; and over the hole a short piece of tube was cemented, which could be put into communication with the ear by means of a rubber tube. In this way the effective length of the pipe was deter- mined to be 28°7 inches, 4°7 inches more than the actual length. As a check upon this estimate, I closed the upper end of the pipe with a plate of wood and again determined the note of maximum resonance. ‘The effective iength of the pipe was now 29°] inches, so that the correction due to want of openness at the lower end amounted to 5:1 inches. If weadd -6 as a correction for the upper end, we obtain as the corrected length of the pipe in its ordinary condition 29°7 inches. The difference between this and 28°7, obtained directly, is greater, I think, than can be ascribed to errors of experimenting, and is possibly connected with the excessive magnitude of the cor- rection in relation to the wave-length of the sound. The 464 Notices respecting New Books. actual note of the pipe, when blown in the ordinary way by a wind of pressure measured by 23 inches of water, corresponded to an effective length of 28 inches, so that the blown note was actually higher in pitch than the note of maximum resonance. So far, therefore, from the depression of pitch in an organ- pipe below that calculated from the actual length, according to Bernoulli’s theory, being principally due to the action of the wind, it would appear that in the absence of a peculiar action of the wind the depression would be even greater than it is. Too much stress, however, must not be laid on a single obser- vation; and all I would maintain is, that by far the larger part of the depression of pitch is due to the insufficient openness of the lower end of the pipe. May 9, 1877. LXII. Notices respecting New Books. The Elements of Machine Design: an Introduction to the Principles which determine the Arrangement and Proportion of the Parts of Machines, and a Collection of Rules for Machine Design. By W. CawrnornE Unwin, B. Sc., Assoc. Inst. Civil Engineers, Professor of Hydraulic and Mechanical Engineering at the Royal Indian Cwil Engineering College. London: Longmans, Green, and Co., 1877. [Text-Books of Science, small 8vo. Pp. 326.] HE author takes as a motto for his work an extract from Reuleaux’s ‘ Theoretical Kinematics,’ of which the following is part :—‘‘ Machine design has been removed by Redtenbacher from its incorrect position as a part of Applied Mechanics, and established on a footing of its own. Its province is to show how the parts of the machine are to be proportioned so as to resist deformation. In order to accomplish this fully, they must be considered both with reference to the external forces acting on the machine, and the corresponding molecular forces within its substance.” These words serve as a general description of the author’s aim; and accordingly he begins the volume with an account of the theory of the strength of materials, with a view to its application to the questions which form the subject of the volume. These may be briefly enumerated as fastenings, pipes, shafts, bearings, gearing, linkwork, and valves. It is almost needless to say that, though to ensure a due degree of strength is an important element in design- ing machinery, many other points are brought under notice; and accordingly the work is not so exclusively occupied with the ques- tion of strength as the motto might lead the reader to expect. Thus, in the chapter on toothed gearing, our author first considers the cases of shafts driven by rolling contact, and proceeds to show the need of teeth for transmitting force by this means. After briefly mentioning the materials employed, he defines the parts and proportions of teeth, investigates the conditions which deter- Notices respecting New Books. 465 mine their form, and gives rules for describing cycloidal and invo- lute teeth. He then takes the question of the strength of teeth, goes on to give rules for the construction and proportion of wheels, and ends the chapter with some articles on screw-gearing. This very brief account of the contents of a single chapter will perhaps serve to indicate the sort of treatment which the subject receives at our author’s hands, as well as to show how much is taken up directly with the question of strength, viz. about a fourth part in the case of the present chapter. A similar remark would apply to other chapters. The work seems to have been executed with great care and with an ample knowledge of the subject. It will doubtless be very useful to students of mechanical engineering; and those whose interest in mechanics is of a less practical kind will find a good many inter- esting questions worked out clearly and accurately. The author of such a work as that before us has one great dif_i- eulty to contend with. He is obliged to consider the extent of the mathematical knowledge which his readers may be presumed to have; and in order to render his work useful to as large a class as possible, he is obliged to take some things for granted which admit of being proved. What should be taken for granted and what proved is a question that must be settled by a sort of com- promise; and as the author may be presumed to have given it a great deal of attention, his opinion, as expressed in the selection that he makes, is prima facie entitled to great weight; we do not, ‘ however, think that.in the present case Mr. Unwin has been always very happy. At all events, we think that we were entitled to expect that the omissions should be obviously consistent with each other, that where matters are not referred to their ultimate principles they should, at all events, be referred to important pro- positions (to what may be called secondary principles), and that when algebraical formule are given without proof they should be accompanied with sufficient explanations to ensure their being understood. It would be easy to point out examples of failure in each of these respects, which might with advantage be rectified in a second edition. Thus, on p. 186 it is taken for granted, with- out so much as a reference, that the work lost in the friction of teeth is proportional to p H(R, + R,) + R,R,; while on p. 207-8 the formula for the tensions of a rope stretched over a fixed eylinder (T, = T, e*°) is proved at full length. It is hard to see why both should not be assumed, or both proved. In the former case the reader’s attention should be drawn to the fact that a point capable of proof is beimg taken for granted; this, however, is not done on p. 186. Again, on p. 30, where the subject dis- cussed is the strength of a beam subject to simple bending, we are told that the beam will be of adequate strength when the bending- moment equals fZ, Z being ‘‘ the modulus of the section—that is, a function of the dimensions of the section which is proportional to the moment of resistance of the section;’ and on p. 35 a table is given of the values of Z for certain forms of section. Here every Phil. Mag. 8. 5. Vol. 3. No. 20. June 1877. 2H 466 Notices respecting New Books. thing is arbitrary unless the reader knows more than he finds. in the book, whereas, if the author had gone back a single step, and stated the connexion between Z and the moment of inertia of the cross section, the reader would have seen that nothing more was being assumed than certain geometrical results which are to be found proved in many text-books*. On p. 54, and elsewhere, Poncelet’s formule for approximating to (a + 6’) are used, but not a word is said to indicate the degree of approximation obtained by them. When a student is informed that if « and 6 are un- known he may write 0°83(a +4 6) for /(a’ + 0’), he certainly ought to be told that in doing so he is liable to an error of rather more than a sixth part of the whole, either in excess or defect. A somewhat glaring example of a formula given without the needful explanations occurs on p. 31, where, in an article on Continuous Beams, the author gives the equation which expresses the ‘‘ Theorem of Three Moments :” he states in connexion with the equation that the bending-moments at the extreme points of support are zero. Now, if the reader happens to know more about the subject than the author tells him, he will be able to understand the article, and will see that as far as it goes it is quite correct. If, however, he attempts to use the equation with no more information than the book supplies, we should feel no certainty as to the result: e. ¢., let the beam be supported on the two extreme points and an inter- vening point (A, C, and B), and let the reader suppose that B is eradually brought nearer and nearer to C; when it reaches C he will probably expect that as B is now at the extreme point the bending-moment at it will be zero. The equation, however, tells him that it equals one fourth part of the moment of the weight of the beam. The explanation of this seeming paradox would hardly occur to him, viz. that when the beam is said to est on three sup- ports this means that when B and C are less than a certain dis- tance apart the end of the beam must be pressed down on O, and that when they come into coincidence the force by which this is done must be infinitely great. Again, when the author states, almost parenthetically, that the pomts of support are at the same level, the unlearned reader is not likely to understand that the sameness of the level is an essential condition of the truth of the formula, and that a very small difference between the heights of the points of support would render the equation quite inapplicable. It would be easy to name cases in which a difference of no more than an exceeding small fraction of an inch would completely alter the conditions of the question. * On a subsequent page (p. 50) the relation is stated, but not in such a way as to invalidate what is said above. a ce LXIII. Proceedings of Learned Societies. ROYAL SOCIETY. (Continued from p. 392. ] Nov. 16, 1876.—Dr. J. Dalton Hooker, C.B., President, in the Chair. NHE following paper was read :— “Experimental Contributions to the Theory of the Radiometer.” —Preliminary Notice. By William Crookes, F.R.S. &c. Instead of bringing another preliminary notice before the Society, I should have preferred reserving the announcement of my new results on the Repulsion resulting from Radiation until they were fit to be offered ina more complete form; but the radiometer is now so much occupying the attention of scientific men, and results of experiments with this and allied instruments are appearing so frequently in the scientific journals at home and abroad, that were I not to adopt this method of bringing the results of my more re- cent experiments before men of science, I might find myself anticipated in some or all of the conclusions at which I have arrived. On June 15th last I mentioned to the Society that the re- pulsion resulting from radiation increases up to a certain point as I exhaust the air from the torsion-apparatus. After long- continued exhaustion the force of radiation approaches a maximum, and then begins to fall off. I have since succeeded in experi- menting at still higher exhaustions, and with different gases in the apparatus; and by means of a McLeod gauge attached to the mercury pump I have been able to measure the atmospheric pressure at any desired stage of exhaustion. I have not only measured the force of repulsion, but also the viscosity of the residual gas; and from the results I have plotted the observa- tions in curves, which accompany this paper, and which show how the viscosity of the residual gas is related to the force of repulsion exerted by radiation. These curves must not, however, be con- sidered as representing more than the broad facts; for I have not included in them my final observations, which in all probability will introduce modifications in them. In plotting these curves I have supposed my scale ta be 1000 metres long, and to represent one atmosphere. Halfway up the scale therefore, or 500 metres, represents half an atmosphere; 999 metres up the scale represents an exhaustion of 7,5, of an atmo- sphere: each millimetre, therefore, stands for the millionth of an atmosphere. My results have principally been obtained at the top of the scale ; and it is the last quarter of a metre which supplies the diagrams ac- companying this paper. When the residual gas is air, the viscosity (measured by the ee rithmic decrement of the arc of oscillation) is practically con- stant up to an‘exhaustion of 250 millionths of an atmosphere, or 0-19 millim. of mercury, having only diminished from 0°126 at the 2H 2 468 Royal Socvety :— normal pressure of the atmosphere to 0-112. It now begins to fall off: at 200 millionths it is 0-110, at 100 millionths it is 0:096, at 50 millionths it is 0°078, at 20 millionths it is 0°052, at 10 millionths it is 0°035 ; and at 0-1 of a millionth of an atmosphere the log. dec. has fallen to about 0-01. Simultaneously with this de- crease in the viscosity,£ the force of repulsion exerted on a black sur- face by a standard light varies. It increases very slowly till the exhaustion has risen to about 70 millionths of an atmosphere ; at about 40 millionths the force is at its maximum; and it then sinks very rapidly, till at 0-1 millionth of an atmosphere it is less than one tenth of its maximum. On continuing the curves of the log. dec. and the force of radiation, and assuming “that the torsion-fibre of glass has no viscosity, it is most probable that they both would come to zero when the last traces of an atmosphere had been taken out of the apparatus. The oxygen diagram differs from that of air. The log. dec. is 0126 at the atmospheric pressure ; it falls to 0-111 at a pressure Mr. W. Crookes on the Radiometer. 469 of 250 millionths of an atmosphere; at 100 millionths it is 0°105, at 50 millionths it is 0°093, at 20 millionths it is 0-068, and at 2 millionths it is 0°02. The force of repulsion in oxygen increases very steadily up to an exhaustion of about 40 millionths of an at- mosphere ; it is at its maximum at about 30 millionths, and thence declines very rapidly. | ; Hydrogen gives a remarkable diagram. The viscosity at the normal pressure is measured by a log. dec. of 0:063; at 250 millionths of an atmosphere it is 0°057, at 100 millionths it is 0°052, at 50 millionths it is 0°046, whence it rapidly sinks. The force of repulsion increases slowly up to an exhaustion of 250 millionths, then quickly until it attains its maximum at about 50 millionths, and it then rapidly declines. The force of repulsion is very great in a hydrogen vacuum, being in comparison with the maximum in an airvacuum as 70 to41. Neither is it necessary to get so high an exhaustion with hydrogen as with other gases to obtain considerable repulsion. This shows that in the construc- tion of radiometers it is advantageous to fill them with hydrogen before exhausting. Carbonic acid has a viscosity of about -01 at the normal pres- sure, being between air and hydrogen, but nearer the former. On approaching a vacuum, the force of repulsion does not rise very high, and soon falls off. Before working with this apparatus I thought that monohy- drated sulphuric acid evolved no vapour, and I therefore freely used it for cleaning out the pump and for drying the gases. I can even now detect no vapour-tension; but a comparison of the eurves, with and without sulphuric acid, shows that the presence of this body modifies the results. One of my curves represents the action of the residual sulphuric anhydride gas. The experience thus gained has led me to adopt phosphoric anhydride for drying the gases. I can detect no ill effects from the presence of this agent ; and I have been able in consequence to push the rarefaction to higher points than before. The McLeod gauge will not show the presence of mercury va- pour. It is therefore possible that I have a greater pressure in the apparatus than is here stated. I have, however, entirely failed to detect the presence of mercury vapour at any great distance from the mercury in the pump; and the tube packed with gold- leaf, which I frequently interpose between the pump and the apparatus, shows no trace of bleaching, and exerts no appreciable effect one way or the cther on the results. With this pump, assisted sometimes by chemical absorption, it is not difficult to exhaust a radiometer to such a point that it will not move toa candle placed a few inches off; but I have not yet succeeded in stopping the movement of the beam in the torsion- apparatus. A long series of observations have been taken, at different degrees of exhaustion, on the conductivity of. the residual gas to the spark from an induction-coil. Working with air, [ find that ata pressure 470 | Royal Society :— of about 40 millionths of an atmosphere, when the repulsive force is near its maximum, a spark, whose striking-distance at the normal pressure is half an inch, will illuminate a tube having aluminium terminals 3 millimetres apart. When I push the exhaustion further, the 43-inch spark ceases to pass; but a l-inch spark will stall illu- minate the tube. As I get nearer toa vacuum more power is required to drive the spark through the tube; but at the highest exhaustions I can still get indications of conductivity when an im- duction-coil actuated with five Groye’s cells, and capable of giving a 6-inch spark, is used. When so powerful a spark is employed there is great danger of perforating the glass, thus causing a very slight leakage of air into the apparatus. The log. dec. now slowly rises, the repulsive force of the candle increases to its maximum, and then slowly diminishes to zero, the log. dec. continuing to rise till it shows that the internal and external pressures are identical. With a fine perforation several days are occupied in going through these phases, and they take place with such slowness and regularity as to afford opportunities for getting valuable observations. The improvements now added by Mr. Gimingham to the pump render it so easy to obtain high exhaustions, that, in preparing experimental radiometers, I prefer to exhaust direct to one or two millionths of an atmosphere. By keeping the apparatus during this exhaustion in a hot-air bath heated to about 300° C. for some hours, the occluded gases are driven off from the interior surface of the glass and the fly of the radiometer. The whole is then allowed to cool, and attenuated air from the air-trap is put in in small quantities at a time, until the McLeod gauge shows that the best exhaustion for sensitiveness is reached; if necessary, this point is also ascertained by testing with a candle. Working m this way, 1 can now do in a few hours what formerly required as many days. In this manner, employing hydrogen instead of air for the gaseous residue, and using roasted mica vanes set at an angle with the axis, as described further on, I can get very considerably increased sensitiveness in radiometers. JI am still unable, however, to get them to move in moonlight, The statements made by an observer nearly a year ago, that he obtained strong rotation by moonlight, must therefore be considered erroneous. My most sensitive torsion- balance will, however, move easily to moonlight. The above-mentioned facts, in addition to what has already been published, leave no reasonable doubt that the presence of residual eas* is the cause of the movement of the radiometer. But few theories are sufficiently strong not to require reinforcement ; and in the present case very much remains to be ascertained as regards * It is a question whether the residual gas in the apparatus, when so highly attenuated as to have lost the greater part of its viscosity, and to be capable of acquiring molecular movement palpable enough to overcome the inertia of a plate of metal, should not be considered to have got beyond the gaseous state, and to have assumed a fourth state of matter, in which its pro- perties are as far remoyed from those of a gas as this is from a liquid. Mr. W. Crookes on the Radiometer. 471 the mode of action of the residual gas. The explanation, as given by Mr. Johnstone Stoney, appears to me the most probable; and haying stood almost every experimental test to which I have submitted it, | may assume for the present that it expresses the truth. According to this the repulsion is due to the internal movements of the molecules of the residual gas. When the mean length of path between successive collisions of the molecules is small compared with the dimensions of the vessel, the molecules rebounding from the heated surface, and therefore moving with an extra velocity, help to keep back the more slowly moving mole- cules which are advancing towards the heated surface; it thus happens that though the individual kicks against the heated surface are increased in strength in consequence of the heating, yet the number of molecules struck is diminished in the same propor- tion, so that there is equilibrium on the two sides of the disk, even though the temperatures of the faces are unequal. But when the exhaustion is carried to so high a point that the molecules are sufficiently few and the mean length of path between their successive collisions is comparable with the dimensions of the vessel, the swiftly moving, rebounding molecules spend their force, in part or im whole, on the sides of the vessel; and the onward crowding, more slowly moving molecules are not kept back as before, so that the number which strike the warmer face approaches to, and in the limit equals, the number which strike the back, cooler face; and as the individual impacts are stronger on the warmer than on the cooler face, pressure is produced, causing the warmer face to retreat. I have tried many experiments with the view of putting this theory to a decisive test. The repulsive force being due to a reac- tion between the fly and the glass case of a radiometer, it follows that, other things being equal, the fly should revolve faster in a small bulb than in a large one. - This cannot well be tested with two different radiometers, as the weight of the fly and the amount of friction would not be the same in each; but I have constructed a double radiometer which shows this fact in a very satisfactory manner. It consists of two bulbs, one large and the other small, blown together so as to have a wide passage between them. In the centre of each bulb is a cup, held in its place by a glass rod; and in the bulbs is a small four-armed fly with roasted mica disks blacked on one side. The fly can be balanced on either cup. In the smaller bulb there is about a quarter of an inch between the vanes and the glass, whilst in the larger cup there is a space of half aninch. The mean of several experiments shows that in the small bulb the fly rotates about 50 per cent. faster than in the large bulb, when exposed to the same source of light. One of the arms of another radiometer was furnished with roasted mica disks blacked on alternate sides. The other arm was furnished with clear mica disks. The two arms were pivoted in- dependently of each other; and one of them was furnished with - a minute fragment of iron, so that by means of a magnet I could oxet e+ So ee SE i 472 Royal Society :— bring the arms into contact, theblack surface of the mica then having a clear plate of mica in front of it. On bringing a lighted candle near the instrument, and allowing it to shine through the clear plate on the blackened mica, the clear plate is at once driven away till the arm sets at right angles to the other. Two currents of force, acting in opposite directions, can exist in the same bulb. I have prepared a double radiometer in which two flies are pivoted one over the other, and having their blackened sides turned in opposite directions. On bringing a lighted candle near, the flies rapidly rotate im opposite directions. Experiment shows that the force can be reflected from a plane surface in such a manner as to changeits direction. If an ordinary radiometer is exposed to light the black surface is repelled, owing to the excess of pressure acting between it and the glass. If, however, a plate of mica were to arrest this force and reflect it back again, the motion should be reversed. Experiment shows that this is the case. A two-disk radiometer was made, having flat opaque mica disks blacked on one side. In front of the black surface of the mica, about a millimetre off, is fixed a large disk of thin clear mica. On bringing a candle near, the molecular pressure streaming from the black surface is caught by the clear plate and thrown back again, causing pressure behind instead of in front; and the result is rapid rotation in the negative direction, the black side now moving towards the light. To still further test this view of the action, I made another radio- meter, similar to the above, but having a clear mica disk on each side of the ordinary mica vane. This prevents the reflection of the pressure backwards, and causes it to expend itself in a vertical plane, the result being an almost total loss of sensitiveness. The above actions can be explained on the ‘“ evaporation and condensation ” theory, as well as by that of molecular movement ; and I therefore devised the following test to decide between these two theories. A radiometer has its four disks cut out of very clear and thin plates of mica, and these are mounted in a some- what large bulb. At the side of the bulb, in a vertical plane, a plate of mica, blacked on one side, is fastened in such a position that each clear vane in rotating shall pass it, leaving a space between of about a millimetre. If a candle is brought near, and by means of a shade the light is allowed to fall only on the clear vanes, no motion is produced; but if the light shines on the black plate, the fly instantly rotates as if a wind were issuing from this surface, and keeps on moving as long as the light is near. This could not happen on the evaporation and condensation theory, as this requires that the light should shine intermittently on the black surface in order to keep up continuous movement. By cutting a thin plate of aluminium into the form of a spiral, then drawing it out corkscrew fashion, biacking the upper surface and suspending it on a point, a spiral radiometer is made, which rotates like a screw on exposure to light. Here also the black surface need never be in darkness, the pressure acting continuously Mr. W. Crookes on the Radiometer. 473 between the black side of the spiral and the cylindrical tube in which it is mounted. The experiments with the double radiometer of different sizes showed that the nearer the absorbing surface was to the glass, the greater was the pressure produced. ‘To test this point in & more accurate manner, a torsion-balance was fitted up with a glass suspending-fibre and reflecting-mirror, as described in my previous papers. At one end of the beam is a disk of roasted mica blacked on one side. In front of this black surface, and parallel to it, is a plate of clear mica, so arranged that its distance from the black surface can be altered as desired, at any degree of exhaustion, without interfering with the vacuum. This apparatus is very sensitive, and gives good quantitative results. It has proved that when light falls on the black surface molecular pressure is set up, whatever be the degree of exhaustion. At the atmo- spheric pressure this disturbance can only be detected when the mica screen is brought close to the black surface, and it is in- appreciable when the screen is moved away. As the barometer- gauge rises, the thickness of the layer of disturbance increases. Thus, retaining the standard candle always the same distance off, when the gauge is at 660 millims., the molecular pressure is re- presented by 1 when the space separating the screen from the black surface is 3 millims., by 3 when the intervening space is reduced to 2 millims., and by 5 when the space is 1 millim. With the gauge 722 millims. high, the values of the molecular pressure for the spaces of 3, 2, and 1 millim. are respectively 3, 7, and 12. When the gauge is at 740 millims., the corresponding values for spaces of 3, 2, and 1 millim. are 11, 16, and 23. With the gauge at 745 millims., the molecular pressures are represented by 30, 34, and 40, for spaces 3, 2, and 1 millim. When the gauge and ba- rometer are level, the action is so strong that the candle has to be moved double the distance off, and the pressures when the inter- vening spaces are 12, 6, and 3 millims. are respectively 60, 86, and 107. A large series of observations have been taken with this apparatus, with the result not only of supplyimg important data for future consideration, but of clearing up many anomalies which were noticed, and of correcting many errors into which I was led at earlier stages of this research. Among the latter may be men- tioned the speculations in which I mdulged as to the pressure of sunlight on the earth. : Hitherto most of my experiments had been carried on with bad conductors of heat. ‘lo get the maximum action of a radiometer it appeared necessary that no heat should pass through to the back surface, but that all should be kept as much as possible on the surface on which the light fell*. At first I used pith; but since * T have already shown that when a ray of light from any part of the spec- trum falls on a black surface the ray is absorbed and degraded in refrangibility, warming the black surface and being emitted as radiant heat. In this sense only can the repulsion resulting from radiation be called an effect of heat. 474 Royal Socrety :— learning the advantage of raising the whole apparatus to a high temperature during exhaustion, I have used roasted mica lamp- blacked on one side for the vanes ; for this purpose it is almost per- fect, being a good absorber on one face, a good reflector on the other, a bad conductor for heat, extremely light, and able to stand high temperatures. Many experiments have been tried with metal radiometers, some of the results being recorded in previous papers which I have read before the Society; but being less sensitive than pith or mica instruments, I had not hitherto worked much with them. I now tried similar experiments to the above, using the best conductors of heat instead of the worst; and for this purpose thick gold-leaf was selected for the surtace on which to try the action of radiation. An apparatus was constructed resembling a radiometer with an opening at the top, capable of being closed with a plate of glass. Through this I could introduce disks of any substance I liked, mounted in pairs on an aluminium arm rotating on a needle- point. The first disks were of gold-leaf, blacked on alternate sides. After exhaustion, a candle repelled the black surface of cne of the disks, but, to my surprise, it strongly attracted the black surface of the other disk. I noticed that the disk which moved the negative way was somewhat crumpled, and had the outer edge curved so as to present a slightly concave black surface to the candle. I soon found that the curvature of the disk was the cause of the anomaly observed ; and experiments were then tried with disks of gold and aluminium—the latter being chiefly used as being lighter and stiffer, whilst it acted in other respects as gold. A radiometer the fly of which is made of perfectly flat alummium plates, lampblacked on one side, is much less sensitive to light than one of mica or pith; but, as I proved in my earlier papers, it is more sensitive to dark heat. Exposed to light, the black face of a metal radiometer moves away as if it were black pith. When, however, it is exposed to dark heat, either by grasping the bulb with the warm hand, dipping it mto hot water, or covering it with a hot glass shade, it rapidly rotates in a negative direction, the black advancing, and continuing to do so until the temperature has become uniform throughout. On now removing the source of heat, the fly commences to revolve with rapidity the positive way, the black this time retreating as it would if light shone on it. Pith or mica radiometers act differently from this, dark heat causing them to re- volve in the same direction as light does. The outer corners of the aluminium plates, which were mounted diamond-wise, were now turned up at an angle of 45°, the lamp- blacked surface being concave and the bright convex. On being exposed to a candie, scarcely any movement was produced; when one vane was shaded off the other was repelled slightly, but the turned-up corner seemed to have almost entirely neutralized the action of the black surface. A greater amount of the same corner was now turned up, the fold going through the centres of adjacent sides. Decided rotation was now produced by a candle, but the black Mr. W. Crookes on the Radiometer. ; 475 surface was attracted * instead of repelled. Dark heat still caused the opposite rotation to light, repelling the black surface. The plates were now folded across the vertical diagonal, the black surface being still inside and the bright metal outside. The actions with a candle and hot glass shade were similar to the last, but more decided. The plates were now flattened, and put on the arms-at an angle, still being in the vertical plane. When the bright surface was out- side, scarcely any action was produced by a candle; but when the lampblacked surface was outside, strong repulsion of the black was produced, both with a candle and with a hot shade. The square aluminium plates were mounted in the experimental apparatus, one being attached to the arm by the centre of one of the sides, and the other by an angle. The opposite corner of the one mounted diamond-wise was turned up atan angle. The outer convex surface of the diamond plate was blacked, and the side of the square plate facing the same way was also blacked, so that either two black or two bright surfaces were always exposed to the ight, instead of a black and a white surface, as is usual in ra- diometers. As might have been expected, both these black surfaces were repelled; but the turned-up corner of the diamond-mounted plate proved so powerful an auxiliary to its black surface, that strong rotation was kept up, the square plate being dragged round against the action of light. Folding the plates with the angle horizonta! has not so decided an action as when the fold is vertical. Sloping the plates and disks of a lampblacked mica radiometer so as to have the black outside, and consequently more facing the side of the bulb, greatly increases its sensitiveness. The above experiments show that shape has even a stronger in- fluence than colour. A convex bright surface is strongly repelled, whilst a concave black surface is not only not repelled by radiation but is actually attracted. I have also tried carefully shaped cups of gold, aluminium, and other metals, as well as cones of the same materials. I will briefly describe the behaviour of a few typical radiometers made with metal cups, which I have the honour of exhibiting to the Society. No. 1035. A two-disk cup-shaped radiometer, facing opposite ways; both sides bright. The disks are 14°5 millims.in diameter ; and their radius of curvature is 14 millims. Exposed to a standard candle 3°5 inches off, the fly rotates continuously at the rate of one revolution in 3°37 seconds. A screen placed in front of the concave side so as to let the light shine only on the convex surface, repels the latter, causing con- tinuous rotation at the rate of one revolution in 7°5 seconds. When the convex side is screened off so as to let the light shine only on the concave side, continuous rotation is produced at the | * JT use the word attraction in these cases for convenience of expression. IT have no doubt that what looks like attraction in these and other cases is -really due to vis a tengo. 476 Roya! Society. rate of one reyolution in 6°95 seconds, the concaye side being attracted. These experiments show that the repulsive action of radiation on the convex side is about equal to the attractive action of radiation on the concave side, and that the double speed with which the fly moves when no screen is interposed is the sum of the attractive and repulsive actions. No. 1037. A two-disk cup-shaped aluminium radiometer, as above, lampblacked on the concave surfaces. In this instrument the action of light is reversed—rotation taking place, the bright convex side being repelled, and the black concave attracted. That this attraction is not apparent only, is proved by shading off the sides one after the other. When the light shines only on the bright convex side no movement is produced ; but when it shines on the black concave side, this is attracted, producing rotation. No. 1038. A cup-shaped radiometer similar to the above, but having the convex surfaces black and the concave bright. Light shining on this instrument causes it to rotate rapidly, the convex black surface being repelled. No movement is produced on letting the light shine on the bright concave surface ; but good rota- tion is produced when only the black convex surface is illuminated. No. 1039. A cup-shaped radiometer like the above, but blacked on both sides. | With this a candle causes rapid rotation, the convex side being repelled. On shading off the light from the concave side the rotation continues, but much more slowly ; on shading off the convex side the concave is strongly attracted, causing rotation. When either of these four radiometers is heated by a hot shade or plunged into hot water, rotation is always produced in the opposite direction to that caused by the hight. On removing the source of heat the motion rapidly stops, and then commences in the opposite direction (7. e. as it would rotate under the influence of light), the rotation continuing as long as the fly is cooling. Chilling one of these radiometers with ether has the opposite action to ex- posing it to dark heat. The vanes of radiometers have also been formed of metal cones, and of cups and cones of plain mica, roasted mica, pith, paper, &e. ; and they have been used either plain or blacked on one or both surfaces. These have also been balanced against each other, and against metal plates, cups, and cones. The results are of conside- rable interest, but too complicated to explain without great expen- diture of time and numerous diagrams. The broad facts are con- tained in the above selections from my experiments. The action of light on the cup-shaped vanes of a radiometer probably requires more experimental investigation before it can be properly understood. Some of the phenomena may be explained on the assumption that the molecular pressure acts chiefly in a direction normal to the surface of the vanes. A convex surface would there- fore cause greater pressure to be exerted between itself and the Intelligence and Miscellaneous Articles. 477 bounding surface of glass than would a concave surface. In this way the behaviour of the cup-shaped radiometer with both surfaces bright, No. 1035, can be understood, and perhaps also that of Nos. 1038 and 1039. It would not be difficult to test this view experi- mentally, by placing a small mica screen in the focus of a concave cup, where the molecular force should be concentrated. But it is not easy to see how such an hypothesis can explain the behaviour of No. 1037, where the action of the bright convex surface more than overcomes the superior absorptive and radiating power of the concave black surface; and the explanation entirely fails to account for the powerful attraction which a lighted candle is seen to exert on the concave surfaces in Nos. 1035, 1037, and 1039. LXIV. Intelligence and Miscellaneous Articles. RESEARCHES ON THE METALLIC REFLECTION OF POLARIZED OBSCURE HEAT-RAYS. BY M. MOUTON. I HAVE employed, in these researches, one of the apparatus ordi- narily used by M. Desains for studying heat-spectra. Polarized in a determinate azimuth, the light and heat traversed first a plate of flint glass suitably inclined to the plane of incidence, and intended to nnul the effects produced by the prism*. The pencil, reflected, then dispersed and analyzed, was finally resolved into a very pure spectrum, the luminous portion of which was directed to the slit of the thermoelectric pile. The breadth of this slit was 1 millim. ; that of the red band of the luminous spectrum 4 millims., and the total extent of the luminous spectrum about 4 centims. I operated on three wave-lengths (X,, A,, A,) distributed in the obseure portion of the spectrum, and sensibly symmetric in refer- ence to the extreme red :—A,, of the yellow; X,, of the blue-green ; and X,, of the indigo. ‘The method of experiment rests on princi- ples established by M. Jamin in his “ Etudes de la réflexion métal- lique de la lumiére”?:— 1. Every ray initially polarized in any other azimuth than zero and 90° becomes, after reflection, elliptic. 2. After passing through a spar prism, of which only the extra- ordinary image is utilized, an elliptic ray presexts, when the prin- cipal section of the prism coincides with the major axis of the ellipse, a maximum of intensity—with the minor axis, a minimum; and if we study these intensities in pairs of azimuths a and a+ 90°, going from the major to the minor axis, the first predominates over the second as long as a@ is comprised between the major axis and 45°, becoming inferior to it as soon as « passes beyond that bisec- trix of the axes. Thus the source of heat is only required to be constant during each pair of observations, a period which is ren- dered very brief by a special movement permitting the analyzer to be rotated rapidly through 90°. The azimuth of the bisectrices of of the axes of the ellipse can thus be determined within 1 degree. * Fizeau and Foucault, Ann. de Chim. et de Phys. 3° série, t. xxx. p. 147. + Ibid. t. xix. p. 321 seqg. 7 478 Intelligence and Miscellaneous Articles. 3. The azimuth of the incident vibration can thus be brought to be such that the two principal components of the reflected vibration will be equal. This azimuth is again determined by pairs of obser- vations whose only inferiority to the preceding is their not having a constant sum (the source being so), but which, like them, have the advantage of being swift, grouped in pairs independent of one another, and terminated by two equal values of the galvanomeiric deflections. 4. If we designate by w the azimuth of the bisectrices of the axes of the ellipse (the incident ray vibrating at 45°), by a the azimuth of the incident vibration which renders the two principal reflected components equal, by @ the difference of phase produced by the reflection, and, lastly, by I and J the absolute numbers by which the reflection multiplies the amplitude of the principal components, we have the two relations cot 2w I Ee Al i cos c=:—__—. and = = tana to determine = and 6*. au 2a ali } JJ If the Tables (p. 479) be compared with that given by M. Jamin? for the red, the analogy is remarkable. In each of them the rate is seen to increase with the incidence, pass through rt at 76° with the red, at 79° with X,, at 82° with X,, and at 83°°5 with X,. To these in- cidences always corresponds a minimum value of the amplitude- ratio. Let us now turn our attention to the two quantities which “ enter as constants into the formule of metallic reflection, viz. (1) the incidence of the polarization restored after two reflections from parallel mirrors, (2) the polarization-azimuth of the reflected ray under this incidence when the initial azimuth is equal to 45°”. The first is the incidence for which the difference of rate is a quarter of an undulation ; it is therefore 79° for d,, 82° for X,, 83°°5 for \,. As to the second, if we designate it by /3, we haye T2 tan —— whence tan b=tan’? a; we then find for 6 the values 15° 40’ for X,, 14°°5 for d,, and 13° 20! for X,. And, on comparing these results with the Table$ in which M. Jamin has given the values of these two principal quantities, proceeding from the violet to the red, we see that the azimuths of the restored polarization, which diminish for steel from the violet to the red (from 21° to 16° 20'), continue to do so beyond, while the principal incidences, which increase from the violet to the red (from 73° to 77° 52'), continue the series of their increasing values in proportion as we advance into the obscure radiations. Permit me, in conclusion, to express my acknowledgements to M. Desains: his assistance and daily counsels have been a great help to me in carrying out this investigation.— Comptes Rendus de P Académie des Sciences, April 2, 1877, tome Ixxxiv. pp. 650-653. * See M. Jamin’s ‘‘ Discussion théorique,” Ann. de Chim. et de Phys. 3° série, t. xix. p. 276. + Ibid, t. xix. p. 317. } Ibid. t. xxii. p. 313. § Ibid. p. 316. 479 iscellaneous Articles. Intelligence and Mi Extract from a Table of Experiments. (Wave-length \,; incidence 80°; mirror of steel; mcident vibration 45°.) Investigation of w. Investigation of a. Azimuths of the | ,C@!vanometer- | 4 7imuths of the | Galvanometer ; Analyzer deflections in mil- : Incident vibration. analyzer. F : analyzer. deflections. ins. to 80 centims. 0°. 90°. ° fe) Qo ° fe) 70 150 58 125 30 105 110 70+90 100 58+90 | 126 29 102 100 60 130 Value at the axes. 60+90 120 13 65 56 120 13+90 185 56+90 128 Therefore w=58°, a=29°. Results of Experiments made on polished Steel. Wave-length )j. Wave-length dg. Wave-length X,. | Difference of | Ratio of amplitudes. Ratioofamplitudes. Sas Ratio of amplitudes. Incidence. jrate as a func-|— — Incidence. | Difference Incidence, | 2#erence tion of Ay, | Anol t of rate. I | LES i ngle a. | 7 a. y a. tr 2 (Vea ° ° ° 9° 70 0179 3D 0:70 70 0-130 32°5 0:64 75 0-120 31 0-60 75 0:200 33 0:65 75 0:155 32 0:62 80 0:207 29 0°55 79 0253 28 0:53 80 0-202 29 0-55 81 0212 27°5 0:52 80 0:260 29 0:55 — 81 0:224 27 0-51 82 0-225 27 0:51 82 0°320 30 0:58 82 0:247 27 0-51 83°5 0:250 26 0:49 83 0-296 29 0°55 480 Intelligence and Miscellaneous Articles. ON THE DIFFUSION OF VAPOURS THROUGH CLAY CELLS. BY DR. J. PULUJ. The apparatus for the experiments in this investigation con- sisted ‘essentially of a clay cell enclosed in a tin-plate box, and connected with a cooling-apparatus and a vertical glass tube. A moderate current of air passed through the box, while the vapour flowed into the cell, and, striking past at the walls of it, diffused reciprocally with the air in the box. The surplus vapour, as well as the air that had diffused through, passed into the cooling- apparatus, where the former condensed, and the air, saturated with - vapour at the temperature of the room, flowed into the glass tube. The volume of this air was measured by means of soap-films or very thin disks of mica suspended by soap-water in the tube, by which the pressure could be preserved equal on the two sides of the cell. ‘The outflowing air from the box passed through an ab- sorption-apparatus, the increase in weight of which consequently gave the quantity of vapour that had diffused through in a fixed time ; and from this the volume of the vapour was calculated. Two series of experiments, carried out with steam between 123°-8— 145°°3 and 136°-6-144°:9 C., gave the result, that, while the ratio of the volumes of the transdiffused air and vapour remains constant and is almost exactly equal to the square root of the reciprocal value of the vapour-density, the velocity of the diffusion increases with the temperature. Experiments with the vapours of alcohol and ether gaye for this ratio somewhat higher values than the numbers cal- culated from the theoretical vapour-densities. The deviation which had been already observed from Graham’s law is not of equal amount in the case of every vapour; and the author makes it appear not improbable that the forces acting between the molecules of substances and their vapours, which with some vapours are _ even more striking, may modify the square-root ratio, and that a case would not be inconceivable in which a vapour of greater density would diffuse through a porous plate more rapidly than one of less density, as is the case with absorbent films of liquid—a reversal of the diffusion-ratio which has also been observed in the osmosis of liquids. Meanwhile it is to be regarded as certain that the vapours investi- gated diffuse through clay cells in nearly the imwerse ratio of the square root of their densities. In the appendix to his memoir, the author discusses Dufour’s experiments on the diffusion of dry and moist air through porous plates, demonstrates the inadmissibility of Dufour’s assumption that dry air diffuses more rapidly. than moist of which the density is less than that of the former, remarks that certain experiments made by Dufour himself must be left unexplained by that assump- tion; and, starting from the presupposition of the result obtained from the experiments he has described, that aqueous vapour diffuses more quickly than mr, gives a complete explanation of the experi- ments of Dufour.—Sttzungsh. der k. Akademie in Wien, math.- naturw. Classe, 1877, No. vii. pp. 69-71. THE LONDON, EDINBURGH, axp DUBLIN PelLOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. SUPPLEMENT vo VOL, III. . FIFTH SERIES. LXY. The Influence of Light upon the Electrical Resistance of Metals. By Dr. R. Bornstein, Assistant in the Physical Institute, Heidelberg University *. | ieee object of the experiments described in this paper is to prove the more general occurrence of a class of phe- nomena which had hitherto been noticed only within narrow limits, but which, nevertheless, were of such a nature as to excite considerable interest among physicists in general. - The experiments are connected with the fact, which has been noticed within the last few years, that the electrical resistance of the metalloids selenium and tellurium diminishes if either of these bodies be exposed to the action of luminous rays; and they have shown that the same phenomenon occurs in the case of metals—that is to say, in the case of platinum, gold, and silver. No other substances have as yet been examined ; but the similarity in the behaviour of these three metals renders it extremely probable that sensitiveness to light is not, as one was hitherto inclined to think, a property peculiar to selenium and tellurium, but that we are here dealing with a general property of all metals. Both these metalloids are ill adapted for proving the phe- nomenon of sensitiveness to light, inasmuch as they occur in different and partially crystalline modifications, which behave differently as regards the passage of electricity, and can be converted, by means of heat, from one modification into the other. Consequently the effect which is ascribed to light may also, in certain circumstances, be produced in selenium and tellurium by the action of heat; and it is only certain definite modifications of these metalloids which show the reverse behaviour. This, however, is absolutely necessary in order to prove that the observed diminution of resistance is * Translated and condensed by R. EH. Day, M.A., the Owen’s College, Manchester. Phil. Mag. 8. 5. No. 21. Suppl. Vol. 3. 21 482 Dr. R. Bornstein on the Influence of Light really due to light, and not to a rise of temperature, which always accompanies any exposure to radiation. The metals that have been examined differ from selenium and tellurium in this respect, that their resistance invariably increases with the temperature ; and when they are exposed to light, the ob- served change in their conductivity arises from the differential action of two causes, namely the direct action of light and the rise of temperature ; and the existence of the first of these may be considered as proved beyond question, if the observed change consists in a diminution of the resistance. Now, in the case of platinum, gold, and silver, phenomena have been observed which are exactly similar to those already noticed in the case of selenium and tellurium ; and their detec- tion was effected by giving these metals such a form that the surface was very large as compared with the mass, so that as much as possible of the mass was exposed to the incident luminous rays. Jor the exposure a collimating tube with a slit was employed, a lens like that in use in spectroscopic experiments, and a flint-glass prism of 45° refracting angle, placed in the position of minimum deviation for sodium- light. The achromatic collimating lens had a focal length of 260 millims., and a diameter of 26 millims. In front of the slit was a Bunsen burner, the flame of which was coloured in the usual manner by means of a bead of salt on a platinum wire. When an observation was to be taken without expo- sure to light, the flame was extinguished, and the slit was covered with a piece of black paper. In a few cases sunlight was used—sometimes the direct rays, and on other occasions the ray after its refraction through a prism being employed. The actual observations consisted in comparing the measured resistances of the metallic bodies when unexposed, with their resistances when exposed to light. In order to avoid any risk of error, two different methods of measuring the resistance were employed—the measurement by the Wheatstone bridge arrangement, and the measurement of a resistance according to Weber’s method of ‘‘ damped vibra- tions.” Among the experiments a few were also made with induced currents; and though they are inconclusive as re- gards the action of light, they are put forward with the rest because they enable us to draw some interesting inferences concerning the action of a current upon its conductor. In employing the first method, two equal metallic bodies were simultaneously observed while one and then the other was alternately illuminated; and the ratio of their resistances, under these circumstances, was determined each time inde- pendently. This method of procedure had this advantage, upon the Electrical Resistance of Metals. 483 that the two metallic bodies under comparison were, except as regards the illumination, continuously under the influence of identical conditions. The “ damping”’ method did not per- mit of two metallic bodies being simultaneously observed, and was therefore employed to determine the resistance of one body at frequent successive intervals, during which it was alter- nately in the dark and under the influence of the luminous rays. This method afforded no security against any possible influence which alterations of temperature, and other changes, might have upon observations which succeeded one another after any considerable interval of time. Nevertheless the ma- jority of the experiments have been carried out according to this method, and far more favourable results have thereby been obtained than with the Wheatstone bridge. The explanation of this lies in the fact that the “damping” method is much better adapted for working with electrical currents of very weak intensity ; so that changes in the resistance, or other influences, can only very slightly affect the currents which are employed in the measurement. While in the first of these methods a Leclanché cell was employed as the electromotor, in the latter method the currents generated in the coils of the galvanometer by the oscillations of the magnetic needle were found to be sufficient ; and it appears that just this par- ticular difference between the two methods had an important influence on the results, and therewith also on the applicability of the methods. The author then gives a general summary of the results already obtained by other observers for selenium and tel- lurium, and then proceeds to describe his own experiments. KHeperiments with the Wheatstone Bridge. In these, as well as in all the following experiments, the connecting wires were always coated, and the junctions were earefully soldered. Whenever a connection was made by means of a mercury-cup, the wires dipping into it were amal- gamated. The apparatus employed in the first of the methods was of the form commonly known as the Wheatstone bridge. The electromotor, a Leclanché cell, was connected directly with a commutator, and a key, which usually kept the circuit open, but closed it on being pressed down with the hand. A second commutator was also employed for the purpose of interchanging the two resistances whose ratio was required. With the bridge-wire itself there was included a galvano- meter, having a copper damper and a reflecting scale; and one end of this bridge wire was connected in the usual manner with a metal slider, movable along the measuring- 212 484 Dr. R. Bornstein on the Influence of Light wire. The bridge-wire was of German silver, 1150 millimetres long; and to each end there was attached a spiral of copper wire. By this arrangement the sensitiveness of the apparatus became very much greater than it had been when the German- silver wire, originally intended for this purpose, was alone employed. To prevent any changes of temperature by radia- tion, the two spirals were covered with paper shades during the experiments, and the German-silver wire was protected against any heat radiated from the observer’s body by a strip of wood; and before each observation its temperature was rendered uniform by fanning it with a piece of cardboard. The true position of the slider was calculated from two posi- tions differmg by one millimetre, on the assumption that within these limits the variations in the deflection of the gal- vanometer and the position of the slider were proportional to one another. In each of these two positions of the slider, the first deflection of the galvanometer-needle was read off for both directions of the battery-current; and then the second commutator was made use of, and the whole repeated. Hight readings were consequently taken for each determination of the resistance, which was calculated from them by means of a formula determined empirically for this piece of appa- ratus. Hxperiments were first made upon two very thin platinum wires, which were obtained from what is called Wollaston wire, by dissolving off the outer layer of silver with nitric acid. ‘To hold them a box-shaped enlargement was made at that part of the telescope, belonging to the spectroscope em- ployed, where the cross-wires are usually situated. This por- tion, which was of brass, had four slightly conical holes at right angles to the axis of the telescope ; and brass plugs were fitted, air-tight, into these holes, and insulated by means of vulcanite collars. The plugs were connected on the inside with platinum clips, all insulated with vulcanite ; and between these clips the two platinum wires were stretched. Their ends were soldered to the clips; and they were placed in the same plane and parallel, symmetrically situated, and at right angles to the axis of the telescope ; and by means of the con- nexions already described they could be separately joined up, from the outside, in an electric circuit. This box containing the wires was closed on the side towards the object-glass by a piece of plate glass, and on the opposite side by an eye-lens, so that it could be connected with an air-pump and exhausted. It appeared afterwards that no change in the experimental results was produced when this space was exhausted to a pressure of 15 millimetres of mercury ; and consequently this upon the Electrical Resistance of Metals. 485, arrangement, which, by the way, was intended for a different purpose, was no longer employed. The eye-piece was adjusted so that when the slit in the collimator was illuminated the two platinum wires, and a silver wire stretched horizontally in front of the slit, appeared equally distinct in the field of view. When the wires were vertical, and one of them was illuminated from the slit, then half a turn of the telescope about its axis brought the second wire within reach of the rays, and placed the first wire in darkness. The apparatus was covered with a black cloth, so as to prevent any light but that coming from the collimator and prism from falling upon the object-glass of the observing-telescope. The two platinum wires were each 14 millimetres long, and had each an elec- trical resistance of about 13 Siemens’s mercury units ; their thickness might therefore be calculated at 0:01122 millim., if we assume the law of propagation of the electrical current to be the same in such thin conductors as it is in thicker ones. The wires were connected with the bridge arrangement; and their resistances were repeatedly compared while one and then the other was alternately illuminated. The results of these experiments, in which sodium-light was employed, showed most clearly a diminution of resistance by the action of light, and also that, in the course of the ex- periments, the sensitiveness to light invariably diminished, until finally it was overbalanced by the heating-effect. If the wires were renewed, or whenever any pause occurred in the experiments, the effect of the illumination came out again more strongly. The mean of the results obtained from 98 observations with each wire, gave 0°0125 per cent. as the mean diminution of resistance of each platinum wire owing to the illumination. Further experiments, according to the same method, were carried out with two strips of gold leaf, the arrangement of which was as follows :—A rectangular plate of glass, about 40 x 70 millims., was coated at opposite ends with tinfoil, so that there was a clear space, 24 millims. wide, right across the glass ; a slip of gold leaf, suitably cut, was then floated on water, and was lifted out by this prepared glass plate in such a manner that it formed a conducting link between the two tinfoil coatings. When the water had evaporated, the gold leaf held firmly to the foil below. If a drop of soft solder be made to fall on the tinfoil it holds firm enough to admit of copper wires being soldered to it; and after both of the tinfoil coatings had thus been fitted with connecting wires, the under side of the glass was covered with black paper, the black side being turned towards the glass. Two such glass plates were 486 Dr. R. Bornstein on the Influence of Light then cemented side by side in an upright position on to a larger glass plate, so that the gold leaves were parallel and vertical ; and then the arrangement was placed in the position previously occupied by the observing-telescope in the appa- ratus already employed; and the gold leaves were included in the circuit by means of their connecting wires, just in the same way as the platinum wires had been. A simple slot in the table which carried the whole of the apparatus allowed the glass plate, carrying the gold leaves, to be rapidly slid along, so that one and then the other was alternately within reach of the rays coming from the prism. All the other arrangements remained exactly as before. The length of each of the gold leaves, between the tinfoil coatings, was 24 millims., and its width 9 millims., while its resistance was about 3 mercurial units. The results obtained in these experiments corresponded exactly with those previously arrived at with the platinum wires; and we may therefore combine them briefly as fol- lows : Platinum and gold exhibit a diminution of resistance in con- sequence of illumination—the diminution, vt is true, being quan- titatively of small amount, but qualitatwely quite sufficient clearly to establish the reality of the fact. Experiments with Weber's Magneto-Inductor. In all the experiments in which the Wheatstone-bridge arrangement was employed the changes of conductivity, due to exposure to light, which could be detected in platinum and gold, were very small, hardly amounting to more than 0°01 per cent. It was impossible to tell from these experiments whether there was any secondary action, connected with the method of observation, which interfered with the luminous effect; for both the metallic bodies which were examined on each occasion were, throughout the experiment, in exactly the same circumstances, the only difference consisting in their illumination. If any unfavourable influence was present, it would be present invariably, and therefore could not be de- tected by any comparative experiments. But, as soon as the earlier experiments had shown that there was in all proba- bility a real diminution of resistance in consequence of illu- mination, it appeared desirable to discover a second method, which would establish the same fact in another way. The first point consisted in separating the metallic bodies under examination ; and henceforward each of them was always ex- perimented upon by itself. One of the gold leaves, already referred to, was first examined, the method of illumination upon the Electrical Resistance of Metals. 487 being the same as before. The electromotor consisted of a Weber’s ma gneto-inductor. The bar magnet, by whose motion the electric currents were induced, was ei in an upright, cylindrical, wooden frame, at the upper and of w rhich was a string, leading over a pulley to the observer’s place, who was thus able to raise or depress the bar magnet at will. The bar magnet was thus made to move in the direction of its axis, which coincided with that of a fixed spiral of copper wire surrounding it. The induced currents were observed by means of a multiplier, wound with thick wire, which had a powerful copper damper and a reflecting scale, its oscillating magnet, which weighed one pound, being suspended by an iron wire from the lid. The resistance of the inductor coil was equal to 2°325 mercurial units, and that of the multiplier 1:223 units; and the two together with the metallic body under examination, and the necessary connecting wires, com- pleted the circuit. The mode of carrying out an observation is due to Weber, and has been fully described by him™*. The resistance of one of the pieces of gold leaf was then determined several times in succession, during which it was alternately unexposed and then exposed to the light of a sodium-flame ; and the pees! results of these experiments may be There was a difference in the resistance of about 0-035 per cent. to be accounted for by the exposure to light; but there was also a permanent increase of resistance developed in the gold leaf by the passage of the electric current. Jor instance, it was found, at the conclusion of one series of experiments, that the resistance of the unexposed gold leaf had increased by 1°25 per cent. of its original value, owing to the passage of the electric current ; but on resuming the experiments the next day with the same piece of gold leaf, this after-effect had apparently disappeared, and the gold leaf had regained its original resistance. Now this increase of resistance during the passage of elec- tricity cannot be regarded as due to any heating by the elec- tric current; for the change went on increasing uniformly during the whole period of the first set of observations, which extended, with several interruptions, over a period of nine hours. Moreover any heat developed in the strip of gold leaf must have been communicated very quickly to the glass plate which was immediately connected with it; and there is * Weber, Elektrodynamische Maashestimmungen, I1., insbes. iiber Widerstandmessungen, Abh. d. kgl. stichs. Gesellschaft d. Weis Bd. I. S. 351. 1852. 488 Dr. R. Bornstein on the Influence of Light no doubt that this always took place in the interval between any two consecutive inductive impulses; for the duration of these currents was indefinitely small as compared: with the intervals of time which elapsed between them. During the whole time of the experiments the temperature of the room increased from 13°°7 to 14°38 C., and therefore could not have been the cause of this observed increase in the resistance. Since the same phenomenon was confirmed by a number of further observations on other days, it appears conclusively proved that The mere passage of electrical currents increases the resist- ance of the thin layer of gold by more than one per cent., the effect remaining for the space of about one day. Haperiments by the Damping Method. In seeking for a further method which would enable the sensitiveness to light of metallic plates, which were being traversed by an electric current, to be observed in a manner free from any disturbing secondary actions, the object to be aimed at was to employ a current of minimum intensity, without, however, diminishing the accuracy of the measure- ments. It seemed as if this would be satisfactorily effected by employing the “damping” method due to W. Weber*, which consists in joining up the conductor, whose resistance is required, with a galvanometer, and observing the oscil- lations of the galvanometer-needle. In this way the metallic plate under examination was only traversed by the feeble currents induced in the coils of the galvanometer by the swinging magnetic needle; and, except in the first few ex- periments, the metallic plate itself was included in the circuit only at the moment when the deflections of the needle were being read. The disturbing influence of the current was thus reduced to a minimum: of course it was impossible to get rid of it entirely; and, moreover, this is not required for qualitative experiments, since, fortunately, it operates in the same way as heating would do, and thus can never be mis- taken for the direct luminous effect. In the majority of the experiments carried out by this method the source of light consisted of the flame of a Bunsen burner coloured with salt, the rays being sent as before through the slit, prism, and lens, onto the metallic plate ; on a few subsequent occasions sunlight was employed. - The experiments were made with gold, platinum, and silver. Gold was employed as before, in the form of strips of gold * Weber, Ee ece Maasbestimmungen, AbA. der kgl. siichs. Ges. d, W. Bd, I. 8. 374. 1852. upon the Electrical Resistance of Metals. 489 leaf upon glass ; platinum, as a very thin film, burnt in on plate-glass, appearing of a grey colour by transmitted light ; and silver in layers of varying thickness on plate glass, the layers being of a bluish colour by transmitted light. The platinum held so firmly to the glass, that the thin connecting wires could be soldered to it directly. In the case of silver it was necessary first to cover the points intended for the con- nexions with a galvano-plastic layer of copper; and then the connecting wires could be soldered on to the layer of copper thus produced. The plates were then fixed to suitable stands, so that the longer side, which was parallel to the line joining the points of connexion, was vertical. The illumination invariably took place on the metallic side. The dimensions of the gold plates employed were 24 x 9 millims.; and they had a resistance of 3 mercury units. Those of the platinum plates were about 50 x 16 millims., with a resistance of 175 units; while the dimensions of the silver plates were about 65 x 17 millims., with a resistance of 4°853 units. The experiments consisted in determining, by the above method, the resistance of the metallic plate, first when unex- posed, and then when exposed to light. Exposure to light was thus found to produce a diminution of resistance, the maximum of which amounted to 3, 4, and 5 per cent. for the respective resistances of the platinum, gold, and silver plates. These values, moreover, did not by any means remain con- stant in different experiments, although these were carried out, as far as possible, under similar conditions. On the con- trary, whenever, in order to ensure similarity in the external conditions, several experiments were made in quick succession with the same metallic plate, it always became less sensitive to light; in fact, in a few instances the opposite effect was eventually produced, just as if the rays were now only able to generate a rise of temperature. The experiments always suc- ceeded best when the particular metallic plate had not been experimented upon for some days; and when, in such cases, the observations were continued for any length of time, it was very evident that, owing to the duration of the experi- ments, the sensitiveness to light diminished, but again in- creased after every pause. The same thing had also been noticed, but less distinctly, in the experiments with the Wheatstone bridge. It might appear open to question, whether the cause of this phenomenon, which has come out in the course of the experiments, is to be sought for in the electrical currents, or in the illumination, since both exerted their influence simultaneously ; but, on comparing the experi- 490 Dr. R. Bornstein on the Influence of Light mental methods here employed and the results obtained, we shall see that in the first method, where the more powerful currents were employed, there was, ceteris paribus, a much smaller sensitiveness to light; and we may therefore conclude that The diminution of conductivity produced by the electrical current, which was described above as an electrical after-effect, is accompanted by a diminution in the sensitiveness to light. In all the previous experiments a coloured gas-flame had been employed as the source of light. In order to test, in this respect, the facts which had been discovered, a few of the thin silver plates were exposed to sunlight, and the change in their conductivity was examined therewith. At first the direct rays of the sun were allowed to pass through the closed window ; and the effect produced was found to corre- spond to that due to a rise of temperature ; so that either there was no direct luminous action, or else it was overpowered by the heat developed in the silver and glass by the sunlight. The window was then opened, and by means of a glass con- denser the sun’s rays were brought to a focus at a short dis- tance in front of the silver plate, since, when focused upon it, they generated too much heat. Under these circumstances, the surprising result was obtained that here again exposure to light produced an increase of 3:7 per cent. in the electric conductivity. These experiments therefore prove that “ The metals platinum, gold, and silver, just as was already known in the case of selenium and tellurium, eaperience, under the action of luminous rays, an increase in their electric con- ductivity, the magnitude of which, as far as the observations go at present, may amount to from 3 to 5 per cent. of the total conducting-power.”” Having thus stated the prominent facts, it appears neces- sary to refute an objection which might possibly be made. It appeared, as was described above, that thin layers of different metals experience, under the action of luminous rays, a change in their resistance which is contrary to that which the resistance of thicker pieces of the same metals was proved to undergo by heating ; and hence it was inferred that the phenomenon which had been noticed could not be due to any rise of temperature. It was therefore necessary to show that the electrical resistance of platinum, gold, and silver, when used in these thin layers, increases with a rise of temperature, just as it does in the case of larger pieces. This is, @ prior, by no means certain, since we are almost entirely ignorant of the molecular constitution of these thin metallic plates. It upon the Electrical Resistance of Metals. 491 therefore seemed desirable to test this point by experiment. For this purpose the Wheatstone bridge was employed, and the resistance of a thin metallic plate was compared with a known copper-wire resistance. In this case the electric cur- rent, which was generated by a Daniell’s cell, was kept on continuously, and every thing was so arranged that from the commencement there was a small deflection of the galvano- meter-needle. This would necessarily increase whenever the resistance of the lamina increased, while a diminution in the electromotive force of the cell could only slightly diminish the deflection. All the different specimens of thin metallic plates employed in the above experiments agreed with one another in the following phenomena. At first the deflection increased, owing to the effect of the current—considerably in the case of silver, but less so in the case of gold and platinum ; then, when a large copper soldering-iron, which had previously been heated to a dull red by a glass-blower’s lamp, was brought near the plate under examination, the intense radia- tion from it produced a considerable increase in the deflection, which, on the removal of the hot iron, diminished again very slowly, at all events much more slowly than did the tempera- ture of the heated metal plate. Hence it follows that, at any rate for ordinary temperatures, the resistance of the thin metal plates increases by heating, just as it does in the case of larger pieces of metal. And, moreover, it appears to follow, from what has just been described, that the heating produces in the thin metal plates an after-effect similar to that produced by the electric current. The question as to the relative effect of different kinds of light is naturally connected with these results. In order to elucidate this point, different portions of the solar spectrum were employed as sources of light, in a few experiments which in other respects were arranged exactly like the pre- vious ones. Unfortunately the season and the weather have been very unfavourable for the employment of sunlight, and the author has in consequence been unable to carry out many experiments on this point. As far as they go, however, they appear to indicate that, for very thin layers of silver, the maxi- mum luminous effect is in the blue and violet, the minimum in the green ; for gold leaf the maximum is in the orange, yellow, and violet, and the minimum in the green and blue. At present the author does not consider himself entitled to give a decided opinion, on account of the paucity of experi- mental data on this point; but as soon as the weather and other circumstances permitted, he intended to determine accurately, for as many different metals and different thick- 492 Dr. E. J. Mills on Cumulative Resolution. nesses of metal as possible, the luminous effect of the differ- ent colours, in order to base thereupon some further infer- ences. It is clear that experiments in this direction will be of the highest interest as regards our knowledge of optical and electrical phenomena. The results of this investigation are as follows :— The property of experiencing a diminished electrical resist- ance under the influence of luminous rays is not confined to the metalloids selenium and tellurium, but belongs also to platinum, gold, and silver, and in all probability to metals in general. The electrical current diminishes both the conductivity and also the sensitiveness to light, of its conductor; and both of these, after cessation of the current, gradually acquire their former values. LXVI. On Cumulative Resolution. By Evuunp J. Miuts, D.Se., P.R.S.* 1. J F a substance, or mixture of substances, combine with itself m times, and each time lose a particular fraction of itself according to a fixed law, it may be said to undergo cumulative resolution. The body undergoing cumulative reso- lution will, in the sequel, be termed the diapolyte; and it will be spoken of as cumulatively resolved, or diapolyzed, with respect to what it loses (the apolyte) in the manner above expressed. One of the most frequent forms of cumulative resolution is represented by the following general equation :— nA, BgC,...—(n—m)A, B,C,... SA eon) ine Bi(g—b)-+-mb Cag eine eee When n becomes exceedingly large with respect to m (in which case it will be denoted by v), the right-hand side of the equation becomes VLA G@-a) Bee—v) Cg-e) +++]. I shall apply the term cumulate to a product having this general formula, and thus obtained, and designate it by the special symbol ~), which will always include a numerical value, unless when used as an operator. In the latter case an expression ii X=Y is to be interpreted thus,—‘ The substance X becomes the substance Y when n units of it lose (x—m) units of apolyte by way of cumulative resolution.” * Communicated by the Author. Dr. E. J. Mills on Cumulative Resolution. 493 In many cases of chemical action the diapolyte is capable of forming but one cumulate only ; but in others a succession of cumulates occurs, each cumulate becoming in turn a diapolyte. Observing that the first cumulate is affected by v, we have to operate with V tn[ Aaa) Be-s) Oa ee “A —(n—m)A, B, C,} 5) which leads to the second cumulate; &c. &ce. Proceeding thus we obtain the following series of cumulates: — 0) = [A BeC,...]; 2) =v [Ag-a Bis) Cg—e---]3 2) =V"[A(e—20) Bis—28) Cy—20) ++ «J 38) = v*[ Aca—sa) Bee—30) Cis) ee all 3 &e. &e. While these differ in composition by a uniform amount, their operator v proceeds by powers ; and the curve represent~ ing the relation of v to their difference is a logarithmic curve. T have not yet met with an instance in which the series even- tually vanishes. It may appear at first sight unreasonable to suppose that bodies of indefinitely high symbolic value, and consequently of indefinitely low specific heat, can possibly exist. We are, however, as yet ignorant of the exact connexion between the specific heat of such bodies and their chemical formule; and a great deal of the evidence we possess points to the conclusion that in their case the ordinary law breaks down. The con- ception, moreover, of a purely expanding series is familiar to chemists*. It may be that many or all of the cumulates, at the instant after their formation, undergo katamerization }; if so, they can then possess specific heat on the ordinary terms. It is sufficient if some portion of a cumulate is left to undergo the continuous inflictions of the resolving power. In any event the “ composition,”’ or symbolic coefficients, of the cumu- late would remain undisturbed; and the entire process can therefore be followed by practical analytical operations. I will now consider some typical cases of cumulative resolution. 2. AMMONIC CARBONATES.—The obscurity surrounding the formation of these salts has been gradually increasing; and the latest experimental researches, while solving some parti- cular problems in connexion with them, have left the more general ones for the most part untouched. The formulee of the different ammonic carbonates (omitting * The paraffin series, Cn Han+2, is an instance, though here the con- ception is an erroneous one. t+ Katamer, the reverse of a polymer. 494 Dr. E. J. Mills on Cumulative Resolution. hydration water), are derivable, with one exception*, from the equations aN, Hy CO;—(n—1) NBSO=N,, 7 Hears © Ornan ee 1) =v NH; CO2], and 2n NA; CO; =@==1), COSSNF ElenC nO) tae a ee (2) 4) =LN2 H, COz] 2) =v Ny Hy CO,] &e. Xe. &) == aie This will be evident from the following Tables, in which r denotes the ratio of N to C in the known carbonates, as above referred to. TaBLE I. (Kquation 1). nr PIN: SL aiken ets cactuaeete 2 Pee eset sce aateaee satiate PA aT | (0): | cased caleciee coseeeues ppl) fel Ua RLS eran el ery | AD S50 Oro. vae ce eae ne WS yAP3P to) TiS Giive dessiecatopremiata the ties Gate Cod A135) fs ail screens Gaara meniaae Dis es POO ee ar eke qatueeeees 32: 2 7 0 a ee err ae eA ome BOS cones ea one aher 4:8 DL) OT eee eeseeeseeeseeeees Lica TABLE II, (Hquation 2). n T= IN Ch OO) Herne cia ta sreittarcBitiotes Ove (116 Steere tia se aa ODD de tetattcr e's cs ccc 2 As IY eee ete « Ris ere staie Leo) DOU vate mamectas cick iga'e's 4:3 Or (hrc teeta ceaseless 3 802 ACTA DB eee ca 32: 2 tO), cereale ch cists ae Sy RPS. COL deena tether saesies (Res LD! 25 cine teatcnnitensts stas Dee aS CE} | ME Math tclds'e ieee Dita * Rose’s nine-fourths carbonate, already recognized as quite isolated in its composition. Dr. BE. J. Mills on Cumulative Resolution. 495 According to these Tables, the different ammonic carbonates may be produced either by deammoniating diammonic car- bonate, or by decarbonating hydroammonic carbonate. We have also to note the relations n+1 1b a eae mato, n 2n °2 n+l and 1179 =— De These relations are graphically expressed by rectangular hyperbolic curves. A drawing of the equation to 72 is here Beets bend Aa eee | esplution. Je] | | e | | | given, where the dots represent portions, at present un- known, of the resulting curve. Considered as far as the first cumulate, all the values of 7, lie between —1 and +2. 3. AMMONIC SULPHIDES.—Aqueous solutions of these bodies are gradually converted by exposure to air into ammonia, water, and sulphur. n NH;S—(n—1)He=Nn Hane Sn Seven Sy] ee © The terms corresponding to n=1, n=2 are known. The equation to the cumulate suggests the possible presence of a sulphur derivative of hydroxylamine. 496 Dr. E. J. Mills on Cumulative Resolution. 2nN, Hs S—(n—1) §(2nH3) Ho} =Nony2 Henye Son + (2) 1) =v [N, H, 8], 2)=v'LN2 Hy &], Ke. Ke. @)=v"[8 .]- Of this series, the ratios in the first, fourth, fifth, and seventh cumulates are known. The decompositions themselves, how- ever, admit of various modes of representation, according to the starting-point selected. 4. Manaanic Oxipes.—The derivatives of manganic dioxide can be represented as follows,— 2n MnO, —(n — 1)O.= Miron Oonyo- Known ratios of Mn to O correspond to the following values Of ns vizio. lel? 2 io andiec. Ferric OxyCHLORIDES.—When ferric chloride is treated with water, it decomposes, eventually producing a body whose composition is very near to that of ferric oxide. Its formula shows that there must be six distinct stages in this continuous process. These are united, for the first time, in the equations n Fey Cle. 3H, O—(n—1) HCl= Fen Clon4, HO"*! Osn, 1) =v [Fe Cl, H; Og], 2) =V'[ Fe, Cl, Hy Os], &e. &e. ) =v Fe, Os]. Ferric compounds of the above nature are somewhat repul- sive to analysts; and hardly an attempt at their formule appears in systematic works. 5. Bismutsic Nrrrates.—The acticn of water on normal bismuthic nitrate is necessarily represented as containing three distinct continuous stages :— n Bi, O3.3 No O;s—(n—1)Nz O5= Bion Oan « Nan+2 O1on+s- 4) =v [Bi, O3. Ny Oyo], 2) =v"[ Bi, O;. N2 05], 8) =v*[ Bi, Os]. In the first stage, ratios are known for n="1 and 1; for the second, n=2; for the third, n=§, $, 4,1, and o. 6. StticatEs.—A large number of silicates are derivable Dr. E. J. Mills on Cumulative Resolution. - 497 from two silicic hydrates, of which the second is the cumulate of the first. nv H, SiO,—(n—1) laid Hees Si, Oct: aD =v | H, 8i03], 2) == iO || - After the first cumulate, the second series is vH2 Si, Oon41. For the mixed series, mH,S8iO, + nH, Si03—(m + n—2)H20 = Hom4sSinsnOsm+on+23 whence i) =v| H, SiO, . S105] . Series 1.—Peridote*, phenakite, zircon, almandine, grossu- laria, tetrethylic silicate (n=1). Analcime? (n=1°3). Okenite (n=2). Magnesite, Labradorite (n=3). Diopside, enstatite, chlorophzite, amphigene, pyrophyliite, tale, emerald, diethylic silicate C= Oe): Series 2.—Anorthite (n='5). Fremy’s hydrate (n=1°5). Diethylic disilicate (n=2). Dovyeri’s hydrate (n=3). Mixed Series.—Orthose (n=4, m=2), Analcime (n= —1, m=5). Fuchs’s hydrate (n= ax, m= o&). Before proceeding to the consideration of carbon compounds, it is necessary to consider the relation of homology to cumu- lative resolution. 7. Homotocy.—lIf we take any starting-point X, and pro- ceed to form homologues X.CH,, X.2CH,, X.3CH,, K&e., we have in general X.C, H»,. When, therefore, n becomes very large, the composition of a member of any homologous series is undistinguishable from that ofan olefine. Such com- position is moreover attained by a perfectly continuous ap- proach. Take, for example, the fatty alcohols, C, Hen+. 0, which are homologues of water: 1) is evidently vCH,, as must also be the case with the aromatic alcohols C,, H.,-5O * T have taken Wurtz’s authority for the formule (Legons de Phil. Chim. p. 181. In this place will be found some of the earlier suggestions of a theory). Phil. Mag. 8. 5. No. 21. Suppl. Vol. 3. 2K 498 Dr. EB. J. Mills on Cumulative Resolution. and any other homologous series. Hyentually, then, all ho- mologous series tend to become the same. The complexity of any member of such series as the above clearly depends on the value of n and on the ratio r of C to H; and these are its only variables. We have, in the series of fatty alcohols, ae ae "On +2? a hyperbolic relation between 7 and n. — Up), if J, is the heat required for the change of state at the pressure p”,; for during the contraction the work Phil. Mag. 8.5. No. 21. Suppl. Vol. 3. 21 514 On the Steam and Hoar-frost Lines of Water-substance. p’’(u',—u,) is done on the mass. Hence (v/—w!'y)(to 9! —P'o) = Uo Mo) Loo =p) $Il, + pl (u/o— Mo) But, by the above assumption, o,=v, and p'5=p =p", also wand u, may both be neglected in comparison with v,, of which they are less than the 200,000th part. The equation in its simplified form therefore becomes Voto A numerical value for this difference is thus found: if the pressure of 1 millim. of mercury be taken as unit pressure, 423°55 then J =ja59g =31'153 ; also )=80, PVA iy (calculated by theory) ; whence 2 0-048. M. Kirchhoff remarks :—‘ This difference is too small to be safely inferred from Regnault’s experiments. It is interesting, however, to remark that a difference of the same sign and order of mag- nitude as the theory requires is furnished by the numbers which Regnault gives as the results of his experiments.” For M. Regnault’s empirical formula for the pressure of steam over ice gives o/)=0°361, and that for the pressure of steam over water gives a)=0'329; whence w)>—a,=0°082. The lines therefore cut each other ; and the angle of intersec- - tion is re-entrant downwards as a)<@)’. M. Kirchhoff’s numbers do not agree so well as the above, since he assumed that both the above empirical formule give the same value for p at O° C., whereas the one gives 4°610 and the other 4-600. M. Moutier has lately taken up the same line of reasoning, in a paper, ‘‘ Recherches sur les vapeurs émises a la méme température par un méme corps sous deux états differents,” published in Annales de Chimie et de Physique, [5] i. (1874) p- 848. He has, however, assumed that o/=a@; whence it would follow that at no temperature could water and ice have the same vapour-tension. This mistake has been corrected in the ‘ Proceedings’ of the Royal Society, 1874, xxii. p. 461, by Prof. Riicker, who reasons from Prot. James Thomson’s con- clusions, but without exactly reproducing M. Kirchhofi’s result. May 15th, 1877. Pn tebe] LXIX. On a Modification of Mance’s Method of measuring Battery Resistance. By Otiver J. Lopes, B.Sc.* [Plate V.] HE modification here suggested consists simply in using a galvanometer and condenser instead of a galvanome- ter alone, so as to detect variations in ditterence of potential instead of variations in current. By this change it is converted into a strictly nuil method. Moreover it is now possible entirely to get rid of the eflects of variations in the electromotive force of the battery, which are very annoying in any of the ordinary methods and prevent ac- curate measure. This is accomplished by breaking the galva- nometer-circuit the instant aiter the battery is short-circuited. Hig. 1 (Pl. V.) is a diagram of the connexions for measuring the resistance of the battery d, with the keys shown on a large scaie: m partially short-circuits the battery when depressed ; nm closes the galvanometer and condenser circuit unless de- pressed. The two keys are electrically independent ; but the stand of the upper one is balanced so as to rest partly on the spring of the lower one (which must be strong). On depress- ing the upper key, the first effect is to close the circuit marked ry at the point m; the second, and immediately succeeding, effect is to break the circuit marked g at the point n. The same object would be accomplished: more conveniently by a single double-contact key made on purpose, as shown in fig. 4. The object of the double key is fully explained below. A BUD represents a box of resistance-coils; a and 6 are large and equal resistances ; and ¢ will be equal to d, the resistance of the battery, whenever the galvanometer-needie is unaftected by pressing down the keys. Resistance-measurements in general. Consider the arrangement of six conductors joining four points (commonly known as the Wheatstone’s bridge) as form- ing the edges of a tetrahedron or triangular pyramid (fig. 2). lt is obvious, (1) that, as far as position is concerned, every con- ductor has precisely the same properties as any other, and (2) that any one conductor is adjacent to four of the others and opposite to the remaining one. Call the resistances of pairs of opposite ones a and ¢, 6 and d, r and g, and let electromotive forces be caused to act in any manner through any of them ; then it can be shown that when ac=6d, r and g are “ conju- gate conductors,” or that variations in the conductor r have no effect whatever on the current in g, and vice versd, no * Communicated by the Physical Society. 21:2 516 Mr. O. J. Lodge on a Modification of Mance’s matter whether these variations are simple changes of resist- ance or the introduction of new electromotive force. By ascertaining, then, whether the insertion or removal of batteries at r has any eitect on a galvanometer at g, one can observe whether the relation ac=6d is or is not fulfilled, and can change one of these resistances until itis. For the case when a, 6, c, and d are simple metallic conductors, this is Wheatstone’s method of comparing their resistances. Again, reciprocally, when this relation is fulfilled, no change in g can affect the current through the battery in 7; and therefore, if this battery in ris the only electromotive force in action, a change in the resistance of g does not affect the cur- rent at all anywhere. Hence a galvanometer in, say, d will show a constant deflection whether the resistance of g is O or o , whenever ac=bd; and this is Thomson’s method of mea- suring the resistance of the galvanometer d. Furtuer, from what has been said, there is no objection to an existence of electromotive force in any or all of the con- ductors, provided tt remains constant; for it will be equally pos- sible to observe whether changes in r (of any sort) have any effect on the current in g; and if not, then ac=hd, as before. For the case when d is a battery of constant electromotive force, this is Mance’s method of determining its resistance. But it must now be observed that although changes in r may have no effect on the current in g, they must affect very essentially the current every where else, and therefore through the battery d. This battery ought, then, to preserve its electro- motive force constant in spite of variations taking place in the strength of its current—a thing which no known battery is capable of doing. ‘The electromotive force of every battery is really a function of the current itis producing and of the time it has lasted. In cells called constant the dependence of elec- tromotive force on current and time is only slight; but in none does it disappear. This fact that the current * and consequently, to some extent, the electromotive force of the battery are made to vary by the process of measuring its resistance, constitutes a great appa- rent defect of the method ; but it is an irremediable defect, and is not peculiar to this particular method. It is in fact impos- sible to measure the resistance of a battery without varying the strength ofthe current passing through it, by any method founded, as all our methods are, on a measurement of current or of difference of potential. In other words, just as it is im- * Professor Clerk Maxwell, in describing this method (‘ Electricity and Magnetism,’ i. p. 411), says that “ the current in the battery is not in any way interfered with during the operation ;” but this must be a mistake. Method of Measuring Battery Resistance. 517 possible to measure any resistance whatever without the pas- sage of a current through the resisting body, although it is quite easy to measure an electromotive force without any cur- rent circulating through the electromotor, so, although a current of constant strength is sufficient to give a measure of the resistance of a homogeneous conductor, such as a metallic wire of uniform material, or a homogeneous liquid, or any thing else which contains no internal electromotive force, yet a vari- able strength of current is necessary to determine the resis- tance of an electromotor. And the reason of this is apparent, viz. that the opposition experienced by a current in passing through an electromotor is of two kinds—one due to the proper ohmic resistance, the other due to the electromotive force ; and with only one strength of current it is no more possible to tell how much of the opposi- tion is resistance and how much is electromotive force, than it is to obtain the values of two unknown quantities from one equation. We may either take two measures of the strength of current and then eliminate one of the unknown quantities algebraically, or we may use a contrivance (like Mance’s method) by which one of them (viz. electromotive force) is eliminated electrically ; but two strengths of current are just as essential in the latter case as in the former, as also it is just as necessary that the two unknown quantities shall remain constant. Itis possible that the resistance, as well as the electromotive force, of a battery does not accurately fulfil this condition, but that it varies to some extent with the current ; in so far as it does this, however, it is not a definite thing, and is incapable of accurate measurement. I have entered into this matter at some length because the slip in Maxwell is getting repeated in other books (cf. Cum- ming’s admirable ‘ Introduction to the Theory of Electricity,’ p- 162) ; and it is as weil to get clear on the subject. The difference of potential required to force a current of strength C through an electromotor of resistance R and internal electromotive force ¢ is H=RC+e. Various methods may be applied to measure E and C; but no observation of a single value of E and C can determine R unless eis known. Another observation with a different value of E and C must be made; and then e can either be eliminated directly, or one can employ an indirect means of effecting its elimination, provided it remain constant. (If it does not remain constant, and if the law of its variation is unknown, no amount of experiments can eliminate it.) It is true that a 518 Mr. O. J. Lodge on a Modification of Mance’s single strength of current will suffice to determine R after e is known; but in the determination of ¢ another and quite dif- ferent strength of current (viz. zero) was employed. A curious illustration of the impossibility of measuring the resistance of an electromotor by means of a constant current was noticed the other day in the physical laboratory at Univer- sity College by Mr. H. F. Morley, who has found that the cur- rent produced by a certain form of gas-battery is, within very wide limits, almost independent of the resistance of its circuit. He endeavoured to measure the internal resistance of this bat- tery by means of its own current, but found it quite imprac- ticable. Variation of the Electromotive Force of a Battery. In what precise way the electromotive force of an ordinary cell depends on the current passing through it and on the time that current has lasted, lam not aware of any experi- ments which afford us information. eule a t law like the fol- lowing seems not improbable. t o Hate B4 Re Oe where ¢ is the time the cell has been in action through the re- | sistance It; so that the rate of change of Hi is proportional to ~ the excess of the strength of current it is producing over the minimum strength to which it will ultimately fall, or di K—B pen. Ee ° 5 ° . ° ° (2) p is a number which may be constant, or it may be a function of the current or of ¢; but for a cell making any pretensions to constarcy, it must be small. A and B are constants such that A+B is the initial and B, the final, value of E. At any rate we may, I think, reasonabl ly assume that E is - not affected instantaneously, however much the resistance of the circuit R is changed, but that it takes a certain time to change its value appreciably ; Goulet aye ntly, if we only change R for an instant of time and then restore it to its ori- ginal value, H may be regarded as constant. It is this fact, I apprehend, which gives “Mance’s method its practical value, and renders it superior to the somewhat similar methods of Siemens and Thomson, because in it the change of resistance of » can be made very rapidly without disturbing the galva- nometer, and need only last a few seconds. The shortest time, however, is sufficient for some variation to take place in the battery; and accordingly a kick of the needle is usually Method of Measuring Battery Resistance. 519 observed, like that produced by an extra current, which is very — annoying. The modification which I have to propose, how- ever, renders possible so great a virtual diminution of the per iod of contact that this disappears. Modification of Mance’s Method. There is also a practical objection to the ordinary form of Mance’s method, not relating to its essentials, but to its sen- sibility and convenience, which the modification is intended entirely to remove. It is this :—The galvanometer in g, whose function it is to indicate any change in the current in that branch, has always a certain current passing through it, and its needle is therefore deflected more or less, according to the sensibility of the gaivanoineter; but the great produced by an ordinary cell whose resistance one wishes to measure is usually such as one does not care to pass through a delicate instrument, even if the excessive deviation it produces be cor- rected by external magnets. A rough galvanometer is there- fore generally employed, and the needle is brought back reasonably near its mean position by magnets placed near it. But the needle being thus constrained by immersion in a powertul magnetic field, is by no means under favourable Pe and only comparatively large changes in the eur- rent can be indicated by it. To remedy this defect and to make the method a nul/ one, my first idea was to use a differential galvanometer and to send through its second wire a current from an auxiliary battery equal and opposite to the current produced in its first wire by the cell whose re- sistance is being determined, so as really to neutralize instead of merely to overpower its action on the needle. Or, without using a Hane val galvanometer, we may balance the eiec- tromotive force in the galvanometer circuit by means of an auxiliary closed battery circuit after the manner of Poggen- dorff. If either of these arrangements be adopted, we can use a sensitive Thomson’s galvanometer, and its needle may be as nearly astatic as we choose. But it is not easy to get the two batteries under such similar conditions that they shall constantly oppose one another exactly ; and though these ar- rangements may be useful in some cases, they are rather com- plicated and the adjustments somewhat dificuit to make. The next alteration which suggested itself consisted in inter- posing a condenser in the galvanometer circuit (see fig. 3). This effectually prevents any continuous circulation of electri- city in that branch; and the galvanometer therefore remains at zero after the condenser has acquired its full charge ; but any variation in this charge is indicated by a throw of the 520 Mr. O. J. Lodge on a Modification of Mance’s galvanometer-needle proportional to the amount of variation. The quantity of electricity flowing into or out of the condenser through the galvanometer-coil will be equal to the variation of potential, Y, taking place between its terminals multiplied by S, its statical capacity ; and the throw of the galvanometer- needle # will be proportional to this quantity multiplied by the galvanometer-constant I, which depends directly on the num- ber of turns of wire on it. The resistance of the galvanometer is quite immaterial. If H is the strength of the magnetic field in which the needle hangs and T the time of a complete oscillation of the needle in that field, we have atheos ekaTalnSING m5 = aT (3) By using, therefore, a galvanometer with a very large number of turns, and a condenser of great capacity, one can increase the sensitiveness of the method to any extent. The investigation of the distribution of currents throughout the circuit becomes very simple now that there is no con- tinuous current through the branch g. The connexions are shown in fig. 8, where AC is the branch 7, whose resistance can be changed at pleasure from infinity to something near rero. Let A, B, C, D, be the potentials of the four corners ; let d be the resistance of the battery we wish to measure, e¢ its electromotive force, and wu the strength of the current passing through it. We want the difference of potential B—D to be wholly independent of the potentials of A and C, which will be altered by changing *. Now as there is no current through g, we have the same current passing through 0 as through a—that is, es Q a aig ete Ab+Ca a b atb similarly De (A—e)e+Cd , aa c+d ; hence _p— (A—C)(bd=ac) + ec(a +b) which shows that the difference of potentials between the ter- minals of the condenser is independent of the potentials A and C as soon as the condition bd—ac=0 is satisfied. We may conveniently write the above expression in terms of the strength of the current w passing through the battery Method of Measuring Battery Resistance. 521 d; thus, since A—C=e—(c+d)u, A ee mee (4) So, if ac=bd, the difference of potential B—D is quite inde- pendent of the current through the cell (except in so far as the electromotive force ¢ depends upon it) and is equal to = EC a which are the same thing. c The current wu is of course dependent on the resistance r of the branch AC, being Pas (at+b+r)e , (5) (a+b)(e+d)+r(atb+cet+d)’ ~ so we may also write the above difference of potential in terms of this resistance 7, thus : rn ah at+b)c+r(O+e re ionin (at+b)(e+d)+r(at+tb+e+d) ~~ CP) All the differential coefficients of this with respect to r contain the factor ac—bd; consequently when this factor vanishes this quantity is independent of r. Conditions for Sensitiveness. To find out what are the values of a, b, and ¢ which give the greatest sensitiveness, we can subtract the value of B—D when 7 is infinite from its value when » is zero, and can make this quantity a maximum when the condition ac=dd is nearly fulfilled. The quantity which has to be a maximum is u/s dia aN a e(ac—bd) ee Os = Gada eb texay The resistance d is supposed to be given ; so let us define the others with reference to it, putting c=)Ad, a=pd, and b= Awd=Am(1—z)d, where z is a small quantity ; then the above quantity becomes ee A[LZE 4 Considered as a function of A, this is a maximum whenA=1 ; 1 : it has in fact the same value whether AX=n or - Considered as a function of mw, it has no maximum, but it is greatest when p is infinite, though it does not increase fast after pu is tolerably large ; the curve is, in fact, a rectangular hyperbola with asymptotes y=1 and w=—1; and 1 is its greatest value for positive values of uw. Accordingly the most sensitive arrange- 522 Mr. O. J. Lodge on a Modijication of Mance’s ment is obtained when »=1 and when “4=« —+that is to say, when ¢ is equal to d (the resistance to be measured), and when a and 6 are equal and as large as convenient. When these arrangements are made, the maximum value of y, or the change in the difference of potential between the terminals of the condenser brought about by depressing the key, is, when c is nearly equal to d, Eig), gee ane Ye jee OF Sey) and this is the quantity to be inserted in equation (3). The sensitiveness is evidently directly proportional to the electromotive force of the cell: but it is independent of its re- sistance; 7. é. a high- resistance is measured with as great pro- portional accuracy as a low one. But it must be remem- bered that when the resistance to be measured is great, the re- sistances a and b should be as great also; if they are not as great as d, the sensitiveness falls off very appreciably. But, as said before, there is really no limit to the sensitiveness of the method; for the size of the condenser and the length of wire on the galvanometer may be increased to any extent. Practical Details. The condenser I have used is a small standard one with the dielectric of mica; and it las a capacity of slightly over one micro-farad. ‘The galvanometer is a Thomson astatic by Elliott, with a resistance of about 7000 ohms. The two branches a and 6 of the resistance-coiis, forming the equal arms of the bridge, were 1000 ohms each, being the iargest resistance conveniently available in the box of resistance-coils used. But when the resistance to be measured is large (say over 500 ohms) it is better to have a and 6 greater than this ; ; and they may then be made of Muirhead’s carbon-paper (fig. 4). A strip 2 feet long by half an inch broad will have a resistance of about 14000 ohms; and the galvanometer terminal B may be con- nected with its middle so as to divide it into two halves repre- senting aand b. Wxact equality in the two arms is not essential, as it is easy (and, indeed, generally advisable) to eliminate any errors of this sort by a method analogous to double weighing. Connect a and 6 to a commutator in such a way that it is easy to interchange them end for end (see fig. 4), and balance the resistance d “by the coils ¢ ; then inter rchange a and 6 and balance again; this time we may ae anamountc’. Then it is easy to see that d= ./(cc’), whatever the ratio of a to b; for in the first case we have d.;c=a:b, and in the second adz¢=0 a0 live andi are mearly equal, their arithmetic Method of Measuriny Battery Resistance. 523 mean may be taken instead of their geometric, as being easier to calculate. Use of a Double-wire Galvanometer as an Electrometer. When a differential galvanometer, or a galvanometer with two long fine wires wound side by side, is employed, a sepa- rate condenser is not absolutely necessary ; for the galvano- meter itself has a certain capacity, and in order to charge one of its wires up to the potential B, and the other down to the potential D, a certain quantity of electricity must flow into the one wire and out of the other, and any variation in this quantity will affect the needle (though the galvanometer-con- stant has only half its ordinary value). yen when a separate condenser is used the capacity of the differential galvanometer may be taken advantage of, by connecting the terminals of the condenser to its two middle screws (instead of joining them di- rectly to each other by a wire and inserting the condenser as in fig. 3), so that both condenser and galvanometer get charged instead of oniy the condenser. The defect of this method is, that the insulation between two silk-covered wires is not very perfect, and there is a slight leakage, which maintains a slight continuous deflection of the needle when the two outer screws are joined up to a battery; moreover the statical capa- city of an ordinary fine-wire differential galvanometer is not very great. But I think it may be often convenient to use a doubie-wire galvanonieter as an eiectromoter in this way. For instance, rapidly to compare the electromotive force of any number of cells, join them up to the outer screws of the galvanometer with disconnected wires one after the other ; the kick in each case measures the electromotive force of the cell. It might also be used to measure very high resistances. It is quite possible, and indeed very probable, that this method has been suggested before. Elimination of Variations in Electromotive Force. It has been stated above that if only momentary variations are made in the resistance 7, or in the value of uw, we can con- sider e, the electromotive force of the battery, constant. The plan I adopt is to make the effective variation of r, or the va- riation which is to have any influence on the galvanometer, very short indeed. And this is done by arranging that the key m which closes the circuit of 7 shall break the galvano- meter circuit g, the instant after, at the point n, as shown in figs. land 4. For an instant, then, uis varied; and if the resistances are not balanced so that ac=bd, a certain quantity of electricity will enter or leave the condenser through the 524 On Mance’s Method of Measuring Battery Resistance. galvanometer ; but variations in e (due to the changed w), which would produce the same effect on the galvanometer, no matter how much the resistances were balanced, have no time to take place before the galvanometer circuit is broken; and then no further change has any effect. This works very well in practice ; and the resistance of a cell can be really deter- mined when producing a current through a definite resistance, viz.at+b+c+d. This cannot be done accurately by any other method that I know of. Measurement of any Liquid Resistances. The method may be applied to determine the resistance of electrolytes in general. A long tube containing the electro- lyte surrounded by a jacket of water at a known temperature is interposed in the battery circuit d, the battery being one whose resistance is small and can be depended on; and the re- sistance of the two together, battery and tube, is measured. The tube is then removed, and the resistance of the battery determined alone ; the difference of course gives the resistance of the electrolyte in the tube. The tube can then be filled with mercury and the measurement repeated. The amount of polarization of the electrodes is of no more consequence than the electromotive force of the battery, provided the gas given off is not allowed mechanically to obstruct the current; and the effect of variations in its amount are reduced to a mini- mum by the method just described for the battery. It is well to make the tube end in a couple of globular receivers with two necks, very much like Dewar’s electrometer, and to plunge large electrodes into these globes (see T, fig. 4). Their position in the globes is not of very much consequence ; neither is a bubble or two of gas on their surface ; the principal part of the resistance is offered by the liquid in the tube. If a ther- mometer is kept in each receiver and the liquid be allowed to flow backwards and forwards through the tube once or twice before observing, its temperature may be known without sur- rounding it with a jacket. But of course this does not apply accurately when it is required to raise its temperature much above that of the atmosphere. Since the sensitiveness depends on the electromotive force of the battery, it is well to use one or two Grove’s cells. Fig. 4 is a complete diagram of the connexions, showing the arrangement for interchanging a and b by means of a commutator, and also showing a key which will break the galvanometer circuit at the instant required and act instead of the extemporized arrangement of two keys depicted in fig. 1. The lower spring carries a block which presses up against a screw connected with the galvanometer, except when it is forced down by the upper spring. This Mr. N. 8. Maskelyne on Ludlamite. 525 block is insulated from the spring, which carries it, but is connected with the point B. The interval elapsing between the breaking contact at m and the making at 7 is, and must be, utterly inappreciable. or the shortest practicable inter- val is sufficient to allow the currents to adjust themselves, unless a and } are extravagantly large resistances ; and if it is not exceedingly short, disturbances will occur due to varia- tions in the battery. The diagrams purposely show the galvanometer, and not the condenser, connected with the breaking-key n, because leak- age of the condenser is sure to occur to some extent when its circuit is broken, and, in order that this may not in the least signify, one terminal of the galvanometer must be insulated, University College, London. LXX. Additional Note on Ludlamite. By N. Story Masketyne, F.R.S.* HE column of calculated angles incorporated in my notice of Ludlamite is vitiated by an error traceable to the erroneous reading of a figure in the calculation of one of the fundamental angles; and a consequent revision, at somewhat greater leisure, of the relative weights to be attached to the measurements of the different angles on the various crystals, has enabled me to offer a closer approximation to the true ele- ments of Ludlamite than I was able to give at the time the measurements were published. The subjoined data therefore present a better theoretical representation of the crystallo- graphy of Ludlamite than that published in the Philosophical Magazine of January last. System oblique, the elements of the crystal being Os OO = 42° 46 onl 101036374 OOO S67 47 otherwise, a: b: c=1: 0°4439 : 0°8798. n= 100° 33’; 7. e. the axial angle Z X=79° 27’. ac =79 27 ee =65 414 fem=85 403 eg — 21) Os mn’ =48 37 éq =68 31 | da’==54 40 cp =61 253 at =26 494 or =44 364 ka’=31 564 ap =04 1 b=. 283 kq= 60 581 wl.==8o, 122 dq =58 153 ai o— lO) AT bq =22 302 pn=d3 238 6) 262250) qa’=72 1%4 * Communicated by the Author. [526 ] LXXI. Notices respecting New Books. The Amateur Mechame’s Practical Handbook, describing the different Tools required in the Workshop, the Uses of them, and How to Use them; also Examples of different kinds of Work, with full De- scriptions and Drawings. By ArtHurR H. G. Horsox. London: Longmans, Green, and Co. 1877. (Small 8yo, pp. 114.) fees book contains a number of instructions for performing different kinds of work, particularly metal work, such as an amateur mechanic is likely to undertake. ‘The principal tools which he is supposed to have are a lathe, a drilling and planing machine, as well as vice, bench, and hand tools. He is expected to be able to use them: e.g. he should be able to turn a ecrank- shaft, bore out a cylinder, cut a screw, and make a universal chuck. He should also be able to make drawings and patterns. Although it is scarcely worth the trouble, yet, at a pinch, our amateur ought to be able to make his own iron castings. The case is different with brass castings; by making them he will save both time and money. He is supposed to be well otf for space; for he should have a separate room for pattern-making, When thus furnished he will be prepared to execute works of considerable difficulty, such as to make a horizontal engine; and accordingly a chapter is devoted to describing the process. ‘The boiler, however, is a more difficult matter ; so this may be “ selected.” Still, “if you are at a loss for a job, you will find it some amusement to make a boiler yourself;” and therefore instructions are given for making a vertical boiler. For though “horizontal boulers may be used,” yet when the size is small ‘‘ they do not answer so well as the upright ones.” When all is made, the amateur will have his reward; “he lights the fire in his boiler, turns the steam on, and excitedly looks for the first turn of the fly-wheel. If the engine be a success, he will in that one turn of the fly-wheel pass one of the pleasantest moments of his life.” It will be seen that our author is enthusiastic about his pursuit ; still ke gives his amateur some very good and sensible advice: thus, he tells him how to profit by a visit to a mechanical engineer’s works, and, again, advises him to learn not only how to mend his tools, but even for the most part to make them. This advice, if followed, would in many eases save his readers a good deal of money, by enabling them to find out whether they have in them the genuine spirit of the amateur mechanic: “ Buy but few tools at first, you will soon find out your wants as you go on. Make as many as you can ; and with diligence in using them, and exercising care and patience, in the course of twelve months you will find yourself amply repaid for your trouble.” Very true! If you are not pre- pared to make and mend your own tools, you have not the root of the matter in you, and had better give it up. Royal Society. 527 Memoirs of the Geological Survey. Explanation of Map 48 E.S.E and adjoining part of 48 N.E. The Geology of the Kastern End of Essex (Walton-Naze and Harwich). By W. Wuitaker, B.A. Lond., F.G.S. London, 1877. (8vo, pp. 32.) This short memoir completes the geological descriptions, by the Geological Survey, of the area directly bordering the estuary of the Thames, and is supplementary to the author’s longer memoir on the Geology of the London Basin, 1872. It is also the first memoir issued by the Geological Survey which notices the Crag Formation, so rich in fossils, and valuable as a source of the phos- phatic nodules and fossils, called ‘“ coprolites,” used in making artificial manures. The London Clay and its cement-stones come to be first de- scribed ; then the Red Crag of Beaumont, Walton-Naze, and near Wrabness and Harwich, is carefully noticed, in brief, both from the author’s recent observation on its dwindling remnants, and from the results of the long-continued researches of the Messrs. Wood, Prof. Prestwich, and others. ‘The old gravels, sands, and brick-earths, and the later alluvium, blown sand, and shingie, also receive attention. In noting the physical features of this clay district, with its local cappings of gravel, and its alluvial flats, the great waste of the seacliiis is of course mentioned. We may sug- gest that if the Government were to apply a small sum of money to allow of the Coast Guard making accurate periodical measure- ments, from the sea to inland marks, on those parts of the British coasts subject to great degradation, some definite bases for calcu- lating the continuous loss “of land, and occasional gain from the sea, would be obtained before many years have elapsed. Several valuable well-sections are recorded by Mr. Whitaker in Appendix I.; and Mr. Etheridge gives some carefully revised lists of fossils in Appendix 14k LXXII. Proceedings of Learned Societies. ROYAL SOCIETY. {Continued from p. 477. ] Dec. 14, 1876.—Dr. J. Dalton Hooker, C.B., President, in the Chair. _ following paper was read :— *¢ Note on the Photographic Spectra of Stars.” By William Huggins, D.C.L., LL.D., F.R.S. In the year 1863 Dr. Miller and myself obtained the photograph of the spectrum of Sirius. “ On the 27th January, 1863, and on the 3rd March of the same year, when the spectrum of this star (Sirius) was caused to fail upon a sensitive collodion surface, an intense spectrum of the more refrangible part was obtained. From want of accurate adjustment of the focus, or from the motion of the star not being exactly 528 Royal Society :— compensated by the clock movement, or from atmospheric tremor, the spectrum, though tolerably defined at the edges, presented no indications of lines. Our other investigations have hitherto pre- vented us from continuing these experiments further; but we have not abandoned our intention of pursuing them’’™*. I have recently resumed these experiments by the aid of the 18-inch speculum belonging to the Royal Society’s telescope in my possession. Considerable delay has arisen from the necessity, for these observations, of a more uniform motion of the driving- clock. For this purpose, Mr. Howard Grubb has successfully applied to the clock the control of a seconds’ pendulum in electric connexion with a sidereal clock. This system works quite satis- factorily. The prisms employed are made of Iceland spar, and the lenses of quartz. After an extensive trial of different photographic processes, preference has been given to dry plates. The apparatus is so arranged that a solar or electric spectrum can be taken on the same plate, for the purpose of comparison, with the spectrum of the star. Spectra have been obtained of Sirius, Vega, Venus, the Moon, &c. I do not purpose in this preliminary notice to describe in detail the arrangements of the special apparatus which has been con- structed, nor to offer the results of the experiments in their present incomplete state to the Royal Society. Still I venture to hope that, even in this early stage of the inquiry, the enlarged copy of the spectrum of Vega (a Lyra) which accompanies this note may not be regarded as altogether unworthy of attention. After exposure to the light of Vega, the dry plate was allowed to remain in the instrument until the following morning, when a solar spectrum was taken upon it through the half of the slit which had remained closed when the instrument was directed to the star. The photograph shows seven strong lines, all of them slightly shaded at the sides. The two lines which are least refrangible coincide with two known lines of hydrogen in the solar spectrum. It is expected, by means of an apparatus now in the course of construction, to obtain also any finer lines which may be present in the spectrum of this star, as well as to extend the photographic method to stars which are less bright. I need not now reter to the many important questions in con- ae with which photographic observations of stars may be of value. * Phil. Trans. 1864, p. 428, On Rotation of the Plane of Polarization of Light. 529 December 21.—Dr. J. Dalton Hooker, C.B., President, in the | Chair. The following papers were read :— ““On the Rotation of the Plane of Polarization of Light by Reflection from the Pole of a Magnet.” By George Francis Fitz- gerald, M.A. At a meeting of the Dublin Scientific Club on Monday the 6th November, Professor Barrett gave the Club an account of Mr. Kerr’s experiments on the rotation of the plane of polarization of a ray of light when reflected from the surface of the end of a magnet, to which additional interest was attached by the reading of a letter from Mr. Kerr to Professor Barrett giving an account of the mode of making and of the last results of his experiments. At the time I proposed trying whether any similar effects would be produced by reflection from the surface of a crystal of quartz cut perpendicularly to the axis, as | was led to think there might be, owing to the similarity of the rotatory polarization of quartz and of substances under magnetic action. Following out that clue, I obtained the following explanation of Mr. Kerr’s experi- ment, and was enabled, through Professor Barrett’s kindness in helping me to verify my recollections of Mr. Kerr’s letter, to make sure that my theory explains the facts. Faraday has shown, in the nineteenth series of his experimental researches, that a ray of plane-polarized light, when transmitted through any solid (diamagnetic?) transparent medium under the action of a powerful magnet, has the plane of its polarization rotated in that direction in which a positive current must circulate round the ray in order to produce a magnetic force in the same direction as that which actually exists in the medium. Verdet, however, discovered that in certain ferro-magnetic media (as, for instance, a strong solution of perchloride of iron in wood-spirit or ether) the rotation is in the opposite direction to the current which would produce the magnetic force. Now Fresnel’s explanation of the rotatory power of quartz has been applied by Professor Maxwell, in his ‘ Electricity and Mag- netism, vol. i. p. 402, to explain the similar, though not identical, phenomenon of magnetic rotation of light. He there, in § 812, gives this explanation in the following words :—“ A plane-polarized ray falls on the medium. ‘This is equivalent to two circularly polarized rays, one right- and the other left-handed (as regards the observer). After passing through the medium the ray is still plane- polarized, but the plane of its polarization is turned, say, to the right (as regards the observer). Hence of the two circularly pola- rized rays, that which is right-handed must have had its phase accelerated with respect to the other during its passage through the medium. In other words, the right-handed ray has performed a greater number of vibrations, and therefore has a smaller wave- length within the medium than the left-handed ray which has the same periodic time.” ‘This is the same as saying that the velocity Phil, Mag. 8. 5. No. 21. Suppl. Vol. 3. 2M 530 Royal Society :—Mr. G. F. Fitzgerald on of the right-handed ray is less within the medium than the left- handed, or that the refractive index for right-handed rays is greater than for left-handed in a medium that rotates light to the right. Hence, from what Verdet has shown, it appears that, in a ferro- magnetic substance, for a ray of light travelling from the south to the north pole, the magnetic action is such as to make the refractive index for right-handed circularly polarized rays less than for left- handed ones; for in this case the plane of polarization is turned to the left, for it is a right-handed current that would produce the magnetic force. By applying this to the case of light reflected from the south pole of a magnet, we get what I believe to be the true explanation of Mr. Kerr’s interesting experiment. In like manner, as in the case of a transmitted ray, I consider the incident plane-polarized ray to be the resultant of two circularly polarized ones, one right- and the other left-handed. Now, for the right-handed one, the refractive index at the surface of the south pole of the magnet, being a ferro-magnetic substance, is less than for the left-handed ray. Hence if each of the two circularly polarized rays be sup- posed to be the resultant of two plane-polarized rays, one polarized in the plane of incidence and the other at right angles to it, the intensities of these four rays being equal, it is evident that the intensities of the pair of reflected rays corresponding to the left- handed ray will be greater than the corresponding intensities of those due to the right-handed ray. Hence the two rays which were polarized perpendicularly to the plane of incidence, and which originally destroyed one another, will, after reflection, have a component in the direction of the vibration of the left-handed ray after reflection. Now, on account of the change of direction of the ray on reflection, this latter is towards the right. This is completely explained in M. Jamin’s ‘Cours de Physique,’ vol. ii. part 2, p. 674, where he shows that a ray the azimuth of whose plane ‘of polarization was originally towards the right is by re- flection turned towards the left. Hence the result of reflection is to furnish two rays, one polarized in the plane of incidence, and the other at right angles to it. The phases of these rays will, in general, be different ; for they dittered by 90° before reflection, and, except at the polarizing angle for iron, this difference of phase would not be completely destroyed, so that the resultant would generally be an elliptically polarized ray the direction of whose major axis would make a small angle towards the right with the plane of incidence ; and at the polarizing angle for iron this ellipse would become a plane-polarized ray whose plane of pola- rization was turned towards the right, which I understand to be the direction in which Mr. Kerr observed it to be turned—although from some ambiguity as to the meaning of right and left rotations in a ray, arising from not specifying whether it is relative to the direction in which the ray is going or in which it is observed, I am not quite sure whether I understand Mr. Kerr correctly. Rotation of the Plane of Polarization of Light. 531 Also from the fact that there are exceptions* to the rule that rota- tions are positive for diamagnetic and negative for ferro-magnetic substances, neutral chromate of potash being diamagnetic, yet pro- ducing a negative rotation, I should be rather inclined to deduce the direction of the rotation that would be produced, if iron were transparent, from Mr. Kerr’s experiment. It would be quite easy to deduce the difference of the refrac- tive indices of iron for the two circularly polarized rays if we knew the amount by which the plane of polarization is turned ; but it would be necessary to employ MacCullagh’s or Cauchy’s formule for the intensities of the reflected rays; and these are so compli- cated that it is hardly worth while going through the calcula- tions, as the effect Mr. Kerr has observed seems only barely obser- vable. Similar effects must, of course, occur in the cases of diamagnetic substances, organic solutions, and quartz; but the amounts in these cases would be entirely beyond the range of observation of our present instruments ; for in quartz, for instance, the difference of the refractive indices of the two circularly polarized rays is only 000008. Observations confirmatory of the foregoing Explanation. Since sending my explanation of Mr. Kerr’s experiment I have made some experiments in confirmation of it. The instruments, with the exception of the electro-magnet, which was kindly lent to me by Mr. Yeates, are the property of Trinity College, Dublin, and were placed at my disposal by Professor Leslie. The electro-magnet I used is of the horseshoe pattern, with movable’ soft iron armatures, a face of one of these being well polished. The magnet was placed vertically, and the armatures were arranged on the poles so that the polished face was vertical and a vertical edge of the other armature parallel and very close to this face. A folded piece of paper was inserted at the top be- tween the edge and the face to prevent their being drawn together when the magnet was set in action. Two Nicol’s prisms were so _ placed that a horizontal beam of light traversing one of them was reflected down the other by the polished face from that part of its surface which was opposite the edge. A beam of sunlight was now transmitted through the apparatus and observed on emerging from the second Nicol. The following | results were thus obtained:—When the light was polarized by the first Nicol, either in or perpendicularly to the plane of incidence, and when it had been extinguished by the analyzer, as soon as the electro-magnet was set in action the light immediately reappeared. On now slightly moving the analyzer the light could be partly ex- tinguished; but no motion of the analyzer could make the field as black as it had been before the magnetism was excited, thus con- clusively proving that what was produced was an elliptically * Unless, indeed, these soy, ie the nature of the solvent, Dad Royal Society:—Mr. H. Tomlinson on the Increase polarized ray, as I had anticipated. When the light was reflected from a south pole the plane of polarization was rotated to the right of the observer, which is the direction of rotation assumed in my explanation. I next covered a portion of the polished face with gold leaf, as Professor Barrett had suggested ; and now the light reflected from this diamagnetic substance was unaffected by the magnetism, as I had also anticipated. I exhibited all these effects to Mr. Stoney, who entirely confirmed my observations. The angle of incidence in the experiments described above was about 60°. If the incidence were either perpendicular or grazing, the theory which I have proposed would lead to the conclusion that the angle between the major axis of elliptic polarization and the original plane of polarization would vanish. If, accordingly, the observation can be made at a perpendicular incidence, and if the Nicol’s prisms be so placed as to extinguish the light before magnetizing the iron, then on exciting it light ought to reappear, as it does at oblique incidences; but the field should not become darker on moving the analyzer. I attribute great weight to the verification of my theory arising from the fact that the polarization of the reflected ray is found by experiment to be in general elliptic, and also from the fact that there is no appreciable effect when gold, a diamagnetic substance and therefore feeble, is substituted for iron. Since communicating my paper, I learn, through Professor Stokes, that when Mr. Kerr’s paper was read before Section A of the British Association, both he and Sir W. Thomson spoke of the possibility of connecting Mr. Kerr’s result with a powerful double refraction of the same kind as the feeble double refraction shown by transparent substances under the influence of magnetism. It is a connexion of this kind which I have endeavoured to de- monstrate. “On the Increase in Resistance to the Passage of an Electric Current produced on Wires by Stretching.” By Herbert Tomlinson, B.A., Demonstrator of Natural Philosophy, King’s College, London. The object of this inquiry was (1) To determine the relation between increased resistance to the passage of an electric current and stretching force. (2) To ascertain how much of the increased resistance in each case is produced by mere increase of length and diminution of section of the stretched wire. In order to determine the increase of resistance from stretching, the wires were each divided into two parts, about 14 ft. in length ; one end of each part was fastened to a stout hook firmly fixed into a block of wood. These two hooks were about 8 inches apart, and the block of wood in which they were fixed was securely fastened across two uprights placed resting against a wall of the room, so that the weights, which were attached to the other ends wn Electric Resistance produced in Wires by Stretching. 538 of the wires, might swing clear of the table. The two parts of the wire were joined at the top, about 2 inches below each hook, by a small piece of copper wire, which was securely soldered on to each part of the wire so as to connect them. ‘Towards the lower extremities of the two parts, about 5 inches above the points of attachment of the weights, two copper wires of small resistance were soldered so as to connect the wires with a Wheatstone- bridge arrangement. ‘The increase of resistance was measured by means of a sliding scale of platinum wire divided into millimetre divisions, each equal to :00166 ohm. As the object was to obtain the temporary, and not the permanent, increase of resistance, which permanent increase was found more or less with all the wires, weights slightly heavier than those intended to be used were first put on and then taken off. Afterwards the wire was balanced as nearly as possible by German-silver wire without the sliding scale, and then very exactly with the sliding scale, which was connected with one of two resistance-coils of 100 ohms each, which formed the other two sides of the bridge. The weights used were then carefully put on to the wires, and the increase of resistance measured by means of the sliding scale; the weights were next taken off again, and the sliding scale used for balancing once more. If there was any slight difference, as sometimes occurred, between the readings of the sliding scale before the weights were put on and after they were taken off, the mean of the two readings was taken. In order to secure still greater accuracy, as many as eight or ten trials were frequently made with each particular weight, and the mean of all the trials taken. In this manner 4 pianoforte steel wires, 1 wire of commercial steel, 3 iron wires, and 4 brass wires were examined with several different weights. The wires taken were of various sections, and. it was found that in each case the increase of resistance was “‘ exactly proportional to the stretching force,” the stretching not being carried beyond the limit of elasticity of each wire. The resistance of a cubic centimetre of each wire was then determined, also the increase of resistance which a cubic centimetre of each wire would experience when stretched by a force of 1 gramme im the same direction as the passage of the current was calcu- lated from the observations made. The former values varied from 1574:8 x 107° to 1882:4 x 107° in the case of steel, from | 1200°8 x 107° to 1291-0 x 107° in the case of iron, and from 656°7 X10 to 782:2x10~° in the case of brass; the latter values varied from 2982x107” to 3511x107” in the case of steel, from 2557 x10” to 271210” in the case of iron, and from 1565x107” to 1843x107” in the case of brass, the numbers in each case representing so many ohms. 584 Royal Society :— On dividing the latter values by the former, it was found that the increase per unit of resistance for a stretching force of 1 gramme on a cubic centimetre of each wire was nearly the same for wires of the same material, but differed with wires of different materials. ‘The mean increase per unit of resistance was for the steel wires 1875°5x10, fortheiron ,, 2132-2x10”, —12 and for the brass ,, 2244:9x10 “, the greatest departure from the mean value being for the steel less than 2°7 per cent., for the iron about 3-0 per cent., and for the brass about 8°5 per cent. The temporary increase of length which a cubic centimetre of each wire would experience on being stretched with a force of 1 gramme was then calculated from observations which had been made in the usual manner with the cathetometer; this increase of length was found to vary in the case of 3 steel wires from 508210 * to 5665x107”; in the case of the iron wires from 4896 x10 * to 5988x107’ and in the case of 1 brass wire was 10120 x 107”. On dividing the increase per unit of resistance for a stretching force of 1 gramme on a centimetre of the material by the increase of length produced by the stretching force, so as to obtain the in- crease per unit of resistance when the wires are stretched 1 centi- metre, a mean value of 3°525 was obtained for the steel wires, 3°951 for the iron wires, and 2°203 for the brass wires—thus showing that, though the increase per unit of resistance for a eiven stretching force is greater in brass than in iron or steel, the increase per unit of resistance for a given lengthening of the wire is much greater both in iron and steel than in brass. The torsional rigidity of the wires was next ascertained by the method of vibrations, several trials being made with different lengths of each wire; the results for different lengths of the same wire agreed very closely indeed. From the values of torsional rigidity and the increase of length, the diminution of section was calculated for a cubic centimetre of each wire when stretched with a force of 1 gramme, assuming the wire to be isotropic. Next the increase of resistance which would result from mere lengthening of each wire and diminution of section was determined, and it was ascertained that, on sub- tracting this latter value from the total observed increase of resistance, there was a considerable residue in the case of the steel and iron wire, also a residue not so great in the brass. This residual increase of resistance probably arises from increased Mr. W. Spottiswoode on Stratified Discharges. 535 space in the line of flow of the current between the particles of the wire produced by the stretching force. The conclusions to be drawn from the experiments are :— 1. That the temporary increase per cent. of resistance of a wire when stretched in the same direction as the line of flow of the current is exactly proportional to the stretching force. 2. That the increase per cent. of resistance, when a cube of each material is stretched by the same weight, is greater in iron than in steel wire, and greater in brass than in iron; also that the increase is nearly the same for different specimens of the same material. 3. That the increase per cent., when a cube of each mate- rial is stretched to the same extent, is much greater in iron and steel than in brass. 4. That there is a residual increase in each case over and above that which would follow from mere increase of length and diminu- tion of section; that this residual increase is much greater in iron and steel than im brass, and greater in iron than in steel. February 15, 1877.—Dr. J. Dalton Hooker, C.B., President, in the Chair. The following paper was read :— «On Stratified Discharges.—III. On a rapid Contact-breaker, and the Phenomena of the Flow.” By William Spottiswoode, M.A., F.R.S. in a paper published in the Proceedings of the Royal Society, vol. xxi. p. 455, I have described a form of contact-breaker de- signed for great rapidity and steadiness of action. It consisted of a steel rod which vibrated under the action of an electro- magnet. Asregards sharpness of break and steadiness of definition in the striz, this instrument left little or nothing to be desired. But, as explained in the paper above quoted, an alteration in the current not only affected the steadiness directly, hut also reacted on the break itself. The effects due to an alteration of the current alone thereby became masked, and the study of the laws relating to such changes was rendered more difficult, or altogether impracticable. In order to obviate this inconvenience I devised another form of contact-breaker, in which the vibrating rod and electromagnet were replaced by an arrangement purely mechanical in its action, and therefore entirely under control. This instrument consists essentially of a wheel platinized at the edge, on which a platinum spring rests. In the circumference of the wheel a number (40 in the first instance) of slots were cut, and filled with ebonite plugs so as to interrupt the current. The breadth of the slots was about -04 inch, and that of the teeth about *5 inch. The wheel was connected with suitable driving gear, so as to give from 250 to 2000 currents from the coil in each direction per second. A 4-inch coil was found sufficient to produce the effects; but the 18-inch coil by Apps, mentioned in former communications, was preferable. With the wheel, as with the electromagnetic break, a very slight strength of current was 536 Royal Society :-— required ; but, on the other hand, high tension in the primary was found necessary. In many of the experiments accordingly from 10 to 20 of the smallest Leclanché cells usually made were em- ployed with the small, and from 20 to 50 with the large coil. But these were afterwards replaced by a double fluid battery suggested by my assistant, Mr. P. Ward, and described at the end of this communication. For some time the experiments were conducted with the platinum spring resting on the wheel; and the effects were varied by altering either the pressure of the spring or the velocity of the wheel ; but the gradual abrasion of the platinum through friction proved to be a fruitful source of irregular results. This irregularity of action, at all times difficult to compensate, and sometimes insuper- able, was fortunately removed by a simple although delicate ad- justment. It was, in fact, found that actual metallic contact between the spring and wheel was not necessary, provided that a layer or cushion of conducting material were interposed. Such a layer was formed by a thin film of liquid drawn out by a thread leading from a reservoir and resting on the wheel. Various fluids were tried; but the simplest, and on the whole the best, proved to be dilute sulphuric acid, in the proportion of 1 drop of acid to 6 drams of water. Generally speaking the better conductor the fluid is, the better are the obtained results but, owing to the insulating slots being very narrow in this instance, a comparatively weak mixture of acid and water was necessary. In one wheel, where the insulating slots are 7 in. wide, a mixture 36 times as strong may as advantageously be used. ‘The spring, which under these circumstances became unnecessary, was replaced by a point, the adjustment of whose distance from the wheel was simpler and more accurate. This arrangement gave excellent results, even when the number of currents per second was reduced in some cases to 250; added to which the unpleasant and disturbing noise of the friction was entirely avoided. Wheels having different numbers of teeth were also constructed, and (what was perhaps of more importance) having teeth of different breadths, so as to give with the same velocity of rotation contacts of different duration. The breadth of the ebonite plugs, or length of interruption of the current, was immaterial, so long as the current was efliciently broken. It did not appear, however, that with the same tube more could be obtained with wheels having different numbers of teeth, than with the same wheel at different speeds. Butit was found that for different tubes different wheels occasionally gave better results. With the contact-breaker here described effects similar to those produced by the rapidly vibrating break were obtained. ‘The striz were formed in a regular manner, and advanced or receded, or remained at rest, in a column usually unbroken, so long as the velocity of the wheel was maintained without change ; and even in the longer tubes, where the striz, of the double discharge, advanced or receded towards both ends at the same time, and appeared some- Mr. W. Spottiswoode on Stratified Discharges. 537 times compressed and at others dilated, the phenomena always maintained their characteristic features. The condition of the striz here described, whether flowing or sta- tionary, may be comprised under the general term “ steady ;” and when there is no motion in either direction, they may be speci- fically denominated as “ stationary.” Two questions here presented themselves :—First, what are the conditions necessary for the production of steady striz? Secondly, what are the conditions and circumstances of the advance and retreat, in other words, of the flow of steady striz ? With a view of ascertaining the nature of the distinction between the ordinary and the steady striz, careful observations were made with the revolving mirror. It having been noticed that when the wheel break moved slowly ordinary or irregular strize were produced, and that when it moved rapidly steady striz resulted, it seemed probable that the latter effect might be due to the short time of contact, and to the consequent absence of many of the features described in Part II. of these researches. This is, in fact, identical with the suggestion there made, that the fluttermg appearance was due to the unequal duration of the striz themselves, and to the irregular positions of the points at which they were renewed at successive discharges of the coil. And such, in fact, proved to be the case ; for as the speed of the wheel was increased the dura- tion of the discharges diminished ; the image as seen in the mirror became narrower and simpler in its configuration, until, when the steady effect was produced, each discharge showed only a single column of striz of a width proportional to the apparent width of the slit. The proper motion, implied by the inclination of the individual striz to the vertical, was still perceptible, and was directed, as usual, towards the negative pole. From a comparison of the number of striz as seen by the eye with those seen in the revolving mirror, it was found that the striz so formed were of the kind called “ simple” in former communi- cations. Andthe phenomena of the flow may therefore be considered to be due to the different positions taken up by the strize in successive discharges. If in each discharge the strize occupy positions in advance of those occupied in a previous discharge, the column will appear to advance ; if the reverse be the case, they will appear torecede. If the positions remain unchanged, the column will appear stationary. The following consequence of this explanation of the flow will readily occur to the reader, viz. that the rapidity of the flow will increase with the extent of advance made by the striz in each successive discharge, until that advance amounts to half the distance between two contiguous striz. Before this is attained the flow will have becume too rapid to be followed by the unassisted eye, and can - only be observed by the aid of the mirror. When this rate of advance has been exceeded, the flow will appear to be reversed. If the rate of advance still continues to increase, the rapidity in the reverse direction will appear to decrease until the advance amounts 538 Royal Society. to the entire distance between two contiguous strie, when it will apparently be reduced to zero; the striz will then again appear stationary. Experiments appear to confirm this view of the case. Experiments were next instituted with a view of ascertaining the connexion between the flow and resistance. Starting from a con- dition of current and break for which the striz were stationary, it was found that an increase of resistance, introduced generally in the primary circuit, produced a forward flow, 7. ¢. from the posi- tive towards the negative terminal, while under similar circum- stances a decrease of resistance produced a backward flow. Fur- thermore, if after producing a forward flow the resistance be continually increased, the flow after increasing in rapidity so as to become indistinguishable by the unassisted eye, gradually appears - to become slower, and ultimately to reverse itself, in accordance with the law suggested above. Another form of contact-breaker was also occasionally used. The principle upon which it was based was the sudden disruption of a thin film of conducting liquid by a discharge between the electrodes of a circuit. The mode of effecting this was to make one electrode terminate in a platinum plate fixed in a horizontal position, and supplied with a uniform film of dilute sulphuric acid ; the other in a platinum point, the distance of which from the plate is capable of delicate adjustment by means of a screw. LElectro- motive force required for this break is not less than that of 5 cells of Grove. As soon as the current passes, the fluid between the plate and point will be decomposed and electrical continuity broken. This done, the fluid flows back again, and continuity is restored. By a proper adjustment of the supply of fluid and of the distance of the electrodes (the latter varying from ‘05 inch to ‘001 inch), the number of disruptions may be made to attain_1000 per second. The currents delivered by this form of break are exceedingly uni- form, and the effects produced are quite equal in delicacy to those produced by the electromagnetic or by the wheel break. The elements used in the battery to which allusion was made in the early part of this paper are zinc and carbon. The zinc is immersed in dilute sulphuric acid in the proportions of 1 volume of acid to 7 of water; and the carbon in a saturated solution of bichromate of potash with 1 volume of sulphuric acid to 7 of the solution. The carbon and bichromate solution are held in a porous cell. The absence of nitric acid permits this battery to be used in a room ; while the fact that the zine is attacked only when the circuit is complete, renders it unnecessary tolift the plates out of the fluid when notin use, as in the bichromate battery. The only limit to the time during which this battery may be left untouched, appears to be the period when the bichromate salt finds its way mto the outer cell, so as to attack the zinc independently of electrical action. But this does not take place to an extent materially to affect the action for some months. Geological Society. 539 GEOLOGICAL SOCIETY. [Continued from p. 395. | April 25th, 1877.—-Prof. P. Martin Duncan, M.B., F.R.S., President, in the Chair, The following communications were read :— 1. “On the Upper Limit of the essentially Marine Beds of the Carboniferous System, and the necessity for the establishment of a ‘ Middle Carboniferous Group.’” By Prof. E. Hull, F.R.S8., F.G.S. The author, in this paper, divided the whole of the Carboniferous rocks into successive stages from A to G inclusive, taking the Car- boniferous beds of Lancashire as a type, and showed that these stages could be identified over the whole of the British Isles. It was only recently that their determination had been made in Ire- land, so that until now the materials had not existed for a complete correlation of the series in the British Islands. The following is an abbreviated statement of the representative stages in descending order :— Essentially Freshwater or Estuarine, with one or two Marine Bands. Stace G.—Upper Coal~measures of Lancashire (2000 ft.) and other English coal-fields. Red Sandstones &c., of Bothwell and Ayz, in Scotland. Absent in Ireland. - Srace F.—Middle Coal-measures of Lancashire &c., with prin- cipal coal-seams (5000 ft.). Flat coal series of Scotland. Present in Ireland (Tyrone, Kilkenny.) Essentially Marine. Stace E.—“ Gannster Beds” (Phillips), with marine shells and thin coals (2000 ft.), in Lancashire. ‘ Pennystone series” of Coal- brook Dale, South Wales, &c. ‘Slaty black-band” series of Scot- land. Present in Ireland (Kilkenny, Dungannon, Lough-Allen coal-fields); also in Belgium, Rhenish Provinces, and Silesia, with numerous marine shells. Stace D.—Millstone-Grit series of England and Wales. 3500 ft. in Lancashire ; “‘ Moorstone Rock” of Scotland ; “ Flagstone series ” of Carlow and Kilkenny; Millstone Grit of Fermanagh and Leitrim, with coals and marine shells. Stace C.—Voredale Beds. 3000 feet in Lancashire; Upper Limestones and “ Lower Coal and Ironstone series” of Scotland ; Shale series of Kilkenny and Carlow; Ironstone shales of Lough Allen, with marine shells. Stace B.—Carboniferous Limestone. Mountain Limestone of Derbyshire; “Scaur Limestone” in Yorkshire; ‘“ Lower Lime- stone” (Roman camp) of Scotland; Carboniferous Limestone of Ireland. Stace A.—Lower Limestone Shale of England. Calciferous Sand- stone series (‘‘ Tuedian,” Tate) of N. of England and Scotland ; Lower Carboniferous Sandstone, N. of Ireland; Lower Carboniferous slate, with Coomhola grits, with marine shells, 8. of Ireland. (In Scot- land, estuarine or lacustrine.) 540 Geological Society. Paleontological Results—On making a census of the Molluscan and other fossils from the various stages above that of the Carboni- ferous Limestone (Stage B) as determined by the Paleontologist of the Geological Survey, some interesting results were obtained, showing the prevalence of marine conditions up into stage EK, and a general change in the character of the fauna in the succeeding stages. Including only the area of the British Islands, it was found that no fewer than 37 genera, with 74 species, of decidedly marine forms, occur in the Gannister-beds (Stage E), of which all the genera and about 40 species were known in the stage of the Car- boniferous Limestone. The series includes Phillipsia, which has been found by Dr. F. Romer in the representatives of Stage E in Silesia. On the other hand, of the whole number of species in stage E (Gannister beds) only 6 are known in the overlying stages F and G, these being characterized by the prevalence of bivalves of supposed lacustrine or estuarine habitats, variously called “« Unio” and ‘“ An- thracosia.” Of the few species of marine genera known in stage F (Middle Coal-measures), about 5 or 6 species are peculiar to itself, according to the determination of the late Mr. Salter. Such a remarkable difference in the fauna of the Upper and Middle Coal-measures, as compared with that of the Gannister beds, constituted, in the author’s opinion, sufficient grounds for drawing a divisional line between these two divisions of the Carboniferous series. Of the several existing methods of classification adopted by different authors, none of them appeared sufficiently to recognize the paleontological distinctions and characteristics of the several formations. The large number of genera and species which are now known to range up from the Carboniferous Limestone into the Gan- nister beds, and no higher, indicated the proper horizon for a divi- sional line, in fact a paleontological break at the top of the Gan- nister beds. On the other hand, the mineral and paleontological differences between the Carboniferous Limestone and the overlying Yoredale series * were sufficient to justify their separation into distinct divi- sions; while the Yoredale, Millstone-Grit, and Gannister series are related by close mineral and paleontological resemblances. With a view, therefore, of bringing the classification of the Car- boniferous series into harmony with the character of the representa- tive faunas, and the physical features of the successive stages, the author suggests that stages C, D, and E, composed of essentially marine beds, should be united into a Middle Carboniferous group ; while stages F and G would remain as at present, in the Upper Carboniferous, their fauna being essentially of freshwater. The series, as thus amended, would be as follows :— Upper Carboniferous Group. Stage G. Upper Coal-measures .............. Essentially BS Middle ‘Coal=Measures 2.0 <0. ce ee freshwater. * In the south of Ireland there is strong evidence that the Yoredale beds (‘‘Shale-series”) are unconformable to the Carboniferous Limestone. 99 Intelligence and Miscellaneous Articles. 54] Middle Carboniferous Group. Stage E Lower Coal-measures or Gannister Beds Essentially eee AMilistone-Giit series "i i' 0... sce sss Hi ee Voredale senes 6. os. sac ne cement P Lower Carboniferous Group. Stage B. Carboniferous Limestone series ...... Essentially ma- 5, A. Lower shales, slates, Carboniferous and rine (except Calciferous Sandstone series ...... { in Scotland). The author then proceeded to show, by reference to the writings of Dr. F. Romer of Breslau, of M. De Koninck, M. Charles Bar- rois, &c., that stage E with its marine fauna, is represented both in Germany, Belgium, and France, as well as in the British islands, so that the classification would hold good over Western Europe, which was a sufficiently extensive area to justify the establishment of a distinct group of strata. 2. “ On Coal-pebbles and their Derivation.” By H. K. Jordan, Esq., F.G.S. In this paper the author endeavoured to explain the mode of production of pebbles of coal in the clays and sandstones of the South-Wales Coal-field and elsewhere, the occurrence of which had been long since noticed by Sir William Logan and Sir Henry De la Beche. His opinion is that the pebbles in question are derived either from the seam of coal above which they are found, or from a seam of coal which formerly existed in the same, or approximately in the same position, and which has been destroyed by erosion, the effect of strong currents of water, which distributed the grains of sand and other materials upon the coal-seam. LXXIII. Intelligence and Miscellaneous Articles. ON THE EMPLOYMENT OF A SILVERED GLASS AS A CAMERA LUCIDA. BY A. TERQUEM. {\VERY one knows how fatiguing is the prolonged use of the camer lucid usually employed for drawing objects in relief or microscopic objects. Nevertheless this apparatus is very convenient when we wish to reproduce the outline of objects of which the per- spective is difficult to obtain directly, such as certain physical appa- ratus: photography cannot always be employed, when the sketch is not to reproduce integrally the object itself with all its details. I have found that, for the usual camera lucida with either one or two reflections, a glass semi-silvered by Foucault and Martin’s process can be substituted with great advantage. For this purpose it is sufficient to leave the glass in the silver bath from one to two minutes at the most, according to the strength of the reducing agent and, especially, according to the external tempera- ture, the influence of which on the reduction of silver is consi- derable. 542 Intelligence and Miscellaneous Articles. I have made use of a simple plate of glass having a breadth of 1 decimetre anda length of 1°5. Semi-silvered glass has great reflecting-power, and yet remains very transparent; it presents merely a slight brown shade. It is known that M. Foucault advised the investing with this semi-silvering the objectives of telescopes for viewing the sun, in order to arrest nearly the whole of the rays of obscure heat*. When the glass is silvered, washed, and dried, the silver (which might be removed by the slightest friction) is fixed by coating the glass with a transparent varnish. For this purpose it is heated to about 40°, and the following varnish is poured upon the silvered face :—alcohol, 100 cubic centims.; mastic tears, 10 grams. The thin film of resin which adheres is very transparent and has a very even surface. The reflecting-power of the glass is slightly diminished, but is still sufficient. ‘The silvered surface could be covered with another glass plate ; but this would give rise to mul- tiple reflection, which is avoided by using the varnish. The glass is then fixed, when the varnish is dry, by one of its edges, in a nipper fitted to a foot, permitting various inclinations to the horizontal to be given to the glass ; if the object to be drawn is vertical, the angle of 45° should evidently be preferred. The paper on which the drawing is to be made is fixed beneath. It is indispensable that above the glass a sight-piece be placed, to give the eye a perfectly fixed position. If the object has a strong relief, the images of the various parts are formed at different dis- tances behind the glass, and the perspective changes with the po- sition of the eye; it is the same with the coincidence of the points on the paper and the different parts of the image to bedrawn. The sight-piece consists simply of a small slip of blackened cardboard pierced with a small aperture ; this can be supported by the appa- ratus which sustains the glass. If the illumination of the object, placed at a suitable height and distance before the inclined glass, be in a certain correspondence with that of the drawing-paper, the image of the object, the pencil, and even the line of the drawing as it is being executed can all be seen at the same time without any fatigue. The conditions of the illumination can be easily realized by the aid of screens or shutters. The advantage of this camera lucida over that generally used arises from the reflection taking place over a large surface, which gives more intensity, and especially from the circumstance that the simultaneous visibility of the pencil and the image is independent of the position of the eye of the observer, depending only on cer- tain conditions of illumination which can be easily regulated before commencing the execution of the drawing. It would be easy, by taking two parallel glass plates, one semi-silvered and the other having received a thick coat of silver, to make a camera lucida that * The same arrangement would be very advantageously employed in photographic enlarging-apparatus, where the solar heat sometimes cracks the plates. Intelligence and Miscellaneous Articles. 543 could be fitted to microscopes, and more convenient than those at present employed. NOTE ON THE SENSATION OF COLOUR. BY C. 8. PEIRCE. It may, perhaps, be worth while to notice a few consequences of three theories concerning colour which are usually regarded with some fayour. First Hypothesis—The appearance of every mixture of lights depends solely on the appearances of the constituents, without distinction of their physical constitution. This I believe is estab- lished. Second Hypothests——Hvery sensation of light is compounded of not more than three independent sensations, which do not influence one another. This is Young’s theory. It follows that, if we de- note the units of the three elementary sensations by 2, 7, and k, every sensation of hght may be represented by an expression of the form Xi+Yj+Zk. Third hypothesis—The intensity of a sensation is proportional to the logarithm of the strength of the excitation, the barely per- ceptible excitation being taken as of unit strength. Negative loga- rithms are to be taken as zero. This is Fechner’s law. It is known to be approximately (and only approximately) true for the sensation of light. From this it follows that, if w, y, z be the relative proportions of a mixture of three lights giving the elementary sensations 7, 7, k, the sensation produced by the mixture is Tlogw.2+J logy.7+K logz.k, where I, J, K, are three constants. From these principles it follows that, if a light giving any sen- sation such as that just written have its intensity increased in any ratio 7, the resulting sensation will be Llogra.i+J log ry .j+Klogrz.k =llogw.1+ Jlogy.j+Klogz.k+logr(Li+J7+ Kk). Thus the result of increasing the brilliancy of any light must be to add to the sensation a variable amount of a constant sensation, lit+Jj+Kk; and all very bright light will tend toward the same colour, which may therefore be called the colour of brightness. Moreover, if the three primary colours be mixed in the proportions in which each by itself is just perceptible, the sensation produced will be logr(Ll2+J7+K£), and can only differ by more or less. Now I find in fact that all colours are yellower when brighter. If two continuous rectangular spaces be illuminated with the same homogeneous light, uniformly over each, but unequally in the two, they will appear of different colours. 544 Intelligence and Miscellaneous Articles. If both are red, the brighter will appear scarlet ; 39 99 green 39 > yellowish 5 2» 2» blue 9 ” greensh ; », veolet i blue. If we have the means of varying the wave-length of the light which illuminates the fainter rectangle, we can improve the match between the two, by bringing the fainter toward the yellow. Such motions will converge toward a certain point of the spectrum which they will never cross—a point a little more refrangible than D and having a wave-length of 582.10-° mm., according to Angstrém’s map. If both rectangles be illuminated with this light, the fainter appears white or even violet ; but if it be varied in wave- length with a view of improving the match, it will be found to return to the same point with the utmost precision. It appears, therefore, that, if our hypotheses are correct, the colour log r (Li+J7+K“) is like that of the spectrum at A=582, only that it contains less blue or violet, and is consequently of greater chromatic intensity. Jt further follows from Fechner’s law that, if any light be gra- dually reduced in brightness, one element of the sensation will disappear after another—and that when very faint it will exhibit only one primary colour, which is the one which it contaims in greatest proportion relatively to the proportion in the light which has the colour of brightness. Now although this does not seem to be exactly the case, yet we do get some approximation to it. It is true that any light whatever, when sufficiently faint, appears white, owing to the self-luminosity of the retina. We cannot therefore, unfortunately, get sight of the primary colours by re- ducing the light of three parts of the spectrum. But we may, as has often been suggested, make use of the principle of contrast. If any red spectral light be sufficiently reduced, it will perfectly match any less-refrangible light. We may therefore say that a faint spectral red in contrast with a bright ight of the same kind, excites with approximate purity one of the elementary sensations. The same thing is true of the violet; and therefore a rich violet may be taken as another primary colour. In my book entitled ‘Photometric Researches,’ the printing of which is nearly complete, I show reason to think that the pure green has a wave-length intermediate between Hand’.