dae a we A Virab 3f 4 “a Pale Ro ie BR ae, + he SH Re 4 iids oi Ame Pe eer aR B99 ft ay es Lr ta es Hd Bi fy Ry stos D mes a THE ses ~ LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & E. &e. SIR ROBERT. KANE, M.D. F.R.S. M.R.I.A. WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S. ““Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not. VOL. XXIX.—FOURTH SERIES. / JANUARY—JUNE, 1865. LONDON. TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the Unwersity of London ; SOLD BY LONGMAN, GREEN, LONGMAN, ROBERTS, AND GREEN; SiMPKIN, MARSHALL AND CO.; WHITTAKER AND CO.; AND PIPER AND CO., LONDON :-— BY ADAM AND CHARLES BLACK, AND THOMAS CLARK, EDINBURGH ; SMITH AND SON, GLASGOW; HODGES AND SMITH, DUBLIN; AND PUTNAM, NEW YORK. “‘Meditationis est perscrutari occulta; contemplationis est admirari perspicua..... Admiratio generat queestionem, questio investigationem, investigatio inventionem.”’—Hugo de S. Victore. —“ Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas ; Quid pariat nubes, veniant cur fulmina ceelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” J. B. Pinelli ad Mazontum. CONTENTS OF VOL. XXEX (FOURTH SERIES.) NUMBER CXCIII.—JANUARY 1865. Mr. D. Forbes’s Researches on the Mineralogy of South America | M. C. Martins on the relative Heating, by Solar Radiation, of the Soil and of the Air, on a Mountain and ina Plan .... 10 Mr. C. J. Monro on a case of Stereoscopic Illusion ........ 15 bie eamey on a Gaartic Surface .. 2. cece ee ee ee os 19 Dr. Rankine on the approximate Graphic Measurement of Elliptic ana Trochoidal Arcs, and the Construction of a Cir- cular Arc nearly equal to a given Straight Line. (With a Ne Es oie se hele soe te + ob ib ee De- Ga ae» 22 Dr. Rankine’s Supplement to a Paper on Stream-lines. (With a Plate.).. Re ATE GEIS: Sad A NEOIS, E Sk SI TOP BEF ) Dr. Akin on Calcescence arte 5 tie eh) OO | Prof. Tyndall on the History of Negative Fluorescence...... a ) peer ae aiton the Elistory of Energy ......-...-.-«-.<; 36 | Prof. Magnus on Thermal Radiation. .................... 58 M. de Saint-Venant on the Work or Potential of Torsion. New Method of establishing the ene acme which regulate Pehe Tersion of Blastic Prisms Se taits Se Sars 5s Ope Bad eee a eae Ae Gl Proceedings of the Royal Society :— | Sir W. Snow Harris’s Further Inquiries. concerning the | Laws and Operation of Electrical Force ............ 65 | Proceedings of the Geological Society :— | Dr. Logan on the occurrence of Organic Remains in the Mauremiian Rocks of Canada... 2. 1.0.5 ooo. ee es ee ae 75 Dr. J. W. Dawson on the Structure of certain Organic Remains found in the Laurentian Rocks of Canada .. 76 Mr. T. S. Hunt on the Mineralogy of certain Organic Remains found in the Laurentian Rocks of Canada .. 76 Remarks on the Letter published by Dr. J. Davy in the Decem- ber Number of the Philosophical Magazine, by Sir J. F. W. | MeEreG aris, sO ees to SUR Or LE eee 77 On the Discrimination of Compounds of Sesquioxide of Manga- nese and of Permanganic Acid, by Hoppe-Seyler ....... 78 | On the Construction of Double-scale Barometers, by William ME WC NUT Win oe ne Sk bee he i Pe EM eS egg lV CONTENTS OF VOL. XXIX.—FOURTH ‘SERIES. NUMBER CXCIV.—FEBRUARY. Mr. J. J. Waterston on some Electrical Experiments and In- ductions. (With a Plate.)...-........ 2 5 ee eee Prof. Potter’s examination of the applicability of Mr. Alex- ander’s Formula for the elastic force of Steam to the elastic force of the Vapours of the Liquids, as found by the experi- ments of M, Regnault 2.05... .....6. <2 eee Prof. Cayley on Quartic. Curves. s.2.45)4. gi. - ope ee Mr. A. G. Girdlestone on the condition of the Molecules of Solids) 2") hye waiecers wtece es oat aden ow ei Oke eee Prof,, Wanklyn on Vapour-densities...... 0.22 2) 5 ee Prof. A. vonWaltenhofen on an anomalous Magnetizing of Iron Mr. J. Hunter on the Absorption of Gases by Charcoal...... Dr. Hargreave on Differential Equations of the First Order. Extension of Integrable Forms. . 0. . 220) cee eee Mr. D. Forbes’s Researches on the Mineralogy of South AMMCTICA Oy oc ik 5 be wo es Oe on ee Dr. C. K. Akin’s further Statements concerning the History of Cale€escenee ove he ce hae so ee oe BEE Proceedings of the Royal Society :— Mr. W. Huggins on the Spectra of some of the Nebule., . Prof. Maxwell on a Dynamical Theory of the Electromag- netic Pield. 0.2 56 wot ceo oe deed Proceedings of the Geological Society :— Dr. Hector on the Geology of Otago, New Zealand .... Sir R. I. Murchison on the Glaciers and Rock-basins of New Zealand . Dr. Haast on the Causes which have led to the Excavation of deep Lake-basins in hard Rocks in the Southern Alps of New Zealand . 2.00 Je 00...) Gk eee ee Dr. Haast cn a Sketch-map of the Province of Ni New Zealand . On some Thermio-electric Piles of great ‘activity, by Prof. eis ibunsen2”)) 2. wie: oan On the Radiant Heat of the Moon, by Buys Ballot _ 2 6 On Calorescence, by Prof. Tyndall . : Reply to certain Charges made by Charles Babbage, Esq. - F.R.S., against the late Sir Humphry Davy ............ Simple Method of preparing Thallium, by Prof. R. Bunsen... NUMBER CXCV.—MARCH. Mr. T. R. Edmonds on the Elastic Force of Steam of Maximum Density ; with a new Formula for the expression of such force in terms of the Temperature..*...... ...1-.:2eeeee ee Prof. A.W. Williamson on the Unit-volume of Gases........ Mr. J. J. Waterston on some Electrical Experiments and Induc- tions .. Me Page 81 98 105 108 111 113 116 121 129 136 151 152 157 169 188 CONTENTS OF VOL. XX1IX.— FOURTH SERIES. Dr. C. K. Akin on the Conservation of Force .............. Prof. Favre on the Origin of the Alpine Lakes and Valleys Prof. Bohn on the History of Conservation of Energy, and of its PREECE ENV SICS goa a oa cis shu «! wis « ith Ab ape, otek e ale Be Prof. Tyndall on the History of Calorescence ...... 0.000. Prof. Cayley’s Note on Lobatschewsky’s Imaginary Geometry. Proceedings of the Royal Society :— Mr. H. E. Roscoe on a Method of Meteorological Regis- tration of the Chemical Action of Total Daylight Messrs. De la Rue, Balfour Stewart, and Benjamin Loewy on the Nature of Solar Spots Proceedings of the Geological Society :— Mr. W. Keene on the Coal-measures of New South Wales, with Spirifers, Glossopteris, and Lepidodendron ...... Mr. S. V. Wood jun., on the Drift of the East of England MBMTESPRUISIOMS Mo. ilo so Reve eia « clenae s cobdeideassate 2 Proceedings of the Royal Institution :— Prof. Tyndall on Combustion by Invisible Rays..... On the Heating of the Glass Plate of the Leyden Jar by the discharge, by Dr. Werner Siemens ...... Letter from Sir J. F. W. Herschel, Bart., SE Per conee: Re a recent Communication from Dr. J. Davy, &c. &c... rs On Lunar Influence over Temperature, by J. Park Harrison .. On the Electrical Standard, by Fleeming Jenkin NUMBER CXCVI.—APRIL. Mr. W. G. Adams on the Application of the Principle of the Screw to the Floats of Paddle-wheels ..... Mr. G. C. Foster on Chemical Nomenclature, and chiefly o1 on the use of the word Acid . Dr. H. W. Schroder van der Kolk on the Mechanical Energy 2) Cyc Siie Geil, J UC) a0) 01S) MNRAS seen ed Pe a ee . Dr. Rankine on the Elasticity of Vapours ............. neti Mr. A. C. Ramsay on the Glacial Theory of Lake-Basins .. .. Mr. J. H. Cotterill on an Extension of the Dynamical aes of Least Action - a Dr. Atkinson’s Chemical Notices from Foreign Journals: Prof. Wanklyn on the Constitution of Chromium-Compounds i of the Royal Institution :— r. W. Odling on Aluminium Ethide and Methide...... , eee of the Royal Society :— Mr. W. Huggins on the Spectrum of the Great Nebula in Ee SOLU -Maireeran OmiOm ee 8 oe siete cede die ore Dr. John Phillips on the Planet Mare.) See Proceedings of the Geological Society :— The Rev. P. B. Brodie on the Lias Outliers at Knowle and Wootton Waven in South Warwickshire.......... vl CONTENTS OF VOL. XXIX.— FOURTH SERIES. Mr. T. F. Jamieson on the History of the last Geological Changes in'Seotlamd! i 0(. 0.5/5. 20% So eee oe On a Simple Mode of Determining the Position of an Optic Image,.by A. Kronige.. 565.0 ac. ose. 2 Oe On a Simplified Method of extracting Indium from the Bein: Zincblendes, by M. Weselsky ......... : ee NUMBER CXCVII.—MAY. Prof. Challis’s Supplementary Considerations relating to the Undulatory Theory of Light.” 22.0)... 2-2.) Mr. H. G. Madan on the Reversal of the Bary: of Metallic WAPOUTS). ieee ne Woy Gis sis’ 8 5a oye e eye 0 Mr. D. Forbes on Phosphorite from Spain, ain. ale Wen ep sthel gee aale Prof. Cayley on the Theory of the Evolute . Prof. Adams on the Application of Screw-Blades as Floats for Paddle-wheels**.)0°.)6 0:2 [0 0s. 0 6% 0 = 0 ge ee Dr. A. Matthiessen on the Specific Resistance of the Metals in terms of the B. A. Unit (1864) of Electric Resistance, together with some Remarks on the so-called Mercury Unit. Mr. J.J. Waterston on some Electrical Experiments........ Dr. Atkinson’s Chemical Notices from Foreign Journals ... Mr. J. H. Cotterill on the Equilibrium of Arched Ribs of Uni- FOTM SECON ow. eye eae ore pe + oes er Proceedings of the Royal Society :— Messrs. Warren De la Rue, Balfour Stewart, and B. Loewy’s Researches on Solar Physics....... .<)-- 2! cies eee Dr. H. B. Jones on the Passage of Crystalloid Substances into the Vascular and Non- Vascular Textures of the Body, Prof. A. W. Williamson on the Atomicity of Aluminium. Proceedings of the Geological Society : — Dr. Haast on the Climate of the Pleistocene epoch of New VAAL Grr EEE ee Dr. Bryce on the Drift-beds in the Island of Arran...... Dr. Bryce on the Occurrence of Beds in the West of Scot- land in the position of the English Crag ............ The Rev. H. W. Crosskey on the Tellina proxima Bed near BAIT OTIC §. 6 se byacsctahd $e sh eS oe ec ae ae Mr. E. R. Lankester on the Mammalian fossils of the Red Cra Se ow ER epee ~ ete Sue oe Prof. Phillips on the Geclogy of Harrogate............ Prof. Harkness on the Lower Silurian Rocks of the South- East.of Cumberland, <. i... 2. 11h epe caer Mr. R. Spruce on the Volcanic Tufa of Latacunga...... Dr. Blackmore on the Discovery of Flint Implements in the Drift at Milford Hill, near Salisbury............ Dr. Duncan on the Echinodermata from the South-east coast of Arabia, and from Bagh on the Nerbudda .... Mr. G. Busk and Dr. H. Falconer on the Fossil contents of the Genista Cave at Windmill Hill, Gibraltar........ Page 326 327 328 a9 338 340 344 351 361 370 374 380 390 394 395 398 398 399 399 400 400 CONTENTS OF VOL. XXIX.—FOURTH SERIES. vil Lieutenant Warren on the Caves of Gibraltar .......... 403 Dr.H. Falconer on the asserted occurrence of Human Bones in the ancient deposits of the Nile and the Ganges.... 403 The Rev. J. E. T, Woods on some Tertiary Deposits in the woreny of Victoria, Australia’... 2... 00.0 ose eS 404 Mr. W. Whitaker on the Chalk of the Isle of Tharet.... 404 Mr. W. Whitaker on the Chalk of Buckinghamshire, and or the Chalk of the Isle of Wight ->..!. $f... 2./2 90... 405 On a New Thermo-Element, by M.S. Marcus ..... .. 406 On Production of Magnetism by Turning, by C. B. Greiss. .. 407 On the Alteration of Electromotive Force by Heat, by F. Lindig. 408 NUMBER CXCVIII.—JUNE. Mr. F. Jenkin on the Retardation of Electrical Signals on Land igre ea melig Pda tet) hos so c's 5 cise mao eee wees e s0 tin 409 Dr. Rankine on Rational Approximations tothe Circle .... 421 Sir David Brewster on the Cause and Cure of Cataract ...... 426 Mr. J. H. Cotterill on the Principle of Least Action ..... 430 Prof. Maxwell and Mr. F. Jenkin on the Elementary Relations Between Electrical Measurements........ ..00-- cess cece 436 Prof. Cayley on a Theorem relating to Five Points in a Plane. 460 Prof. A. W. Williamson on Chemical Nomenclature ........ 464 M.Feussner on the Absorptionof Light atdifferent emperatures. 471 Proceedings of the Royal Society :— Prof. Maskelyne on New Cornish Minerals of the Brochan- io & SLAC dae! peat i ge al pian a a 473 Mr. B. Stewart and Prof. Tait on the Radiation from a Revolving Disk . oie 476 Mr. F. Jenkin on the New Unit of Electrical ‘Resistance proposed and issued by the Committee on Electrical Standards appointed in 1861 by the British Association. 477 On an Air-pump constructed on a new Principle, by M. Deleuil. 487 On a Meteor and Meteorites of Orgueil -.............-... 487 On a Phenomenon in the Induction-Spark, by E. Fernet .... 488 NUMBER CXCIX.—SUPPLEMENT. M. A. J. Angstrom on a new Determination of the Lengths of Waves of Light, and ona Method of determining, by Optics, the Translatory Motion of the Solar System. (Witha Plate.) 489 Prof. Cayley on the Intersections of a Pencil of four Lines by a fame O REVO! LANES. 8% 20. Nhe wh. Se es. wi oe 501 Sir David Brewster on Hemiopsy, or Half-Vision : hae 503 Prof. Maxwell and Mr. F. Jenkin on the Elementary Relations between: Electrical Measurements... .........0...00020 0 907 Mr. J. C. Moore on Lake-Basins . ne tae. tr Dao Dr. Atkinson’s Chemical Notices from Foreign Journals... ... 528 vill CONTENTS OF VOL. XXIX.— FOURTH SERIES. ‘Page Mr. E. J. Stone on Change of Climate due to De ree ee of the Marth's ‘Orbit et 22 Sa ee 538 Proceedings of the Royal Society :- ~- Mr. G. Gore on the Properties of Liquefied yr Acid Gas. +. 3a, Ee eons ek 541 Proceedings of the Geological Society :— Dr. Stoliczka on the Character of the Cephalopodous Fauna of the South Indian Cretaceous Rocks.............. 550 Mr. W. Wallace on the Growth of Flos Ferri, or Coral- lordalsArragonite | ..7.2-./ 3.0 20) 220 ee 550 Sir J. F. W. Herschel on some Rhomboidal yeaa ‘of Ironstone, Ge. i). eos ss ie ee er is oul On an Electrical Machine wie a Plate ine Sulphur, by M. Richer. 551 On the Chemical and Mineralogical Characters of the Meteorite of Orgueil, by MM. Daubrée, Cloéz, Pisani, and Des Cloizeaux. 552 Note on the Proragation of Electricity through Metallic Va- pours produced by the Voltaic Arc, by A. De la Rive...... 553 On the Application of the Electric MBE for Bak under Water, by M. Paul Gervais ...... pay PL BO Pex te bus whee een a flew ee Siti sig cots 3 eee 556 PLATES. I. Illustrative of Dr. Rankine’s Papers, on the approximate Graphic Measurement of Elliptic and Trochoidal AXES, and on Stream- lines. II. Illustrative of Mr. J. J. Waterston’s Paper on some Electrical Expe- riments and Inductions. III. Illustrative of Mr. F. Jenkin’s Paper onthe Retardation of Electrical Signals on Land Lines, and M. J. Angstrom’s on a new Deter- mination of the Lengths of Waves of Light. ERRATA. re 248, line 8, for heat read cloud. 252, fig. 2, the line O P, and not I P, should have been produced. — 362, last line in Table II. , for 15: 218 read 15°18. — 363, 3 III. , for pressed 1°668 read hard-drawn 0°1399. — 365, middle of page, for 0°9750 read 0:9742. — 3866, HS for 0:9632 read 0°9625. — 366, bottom of page, for 0°9723 read 0°9716. for 0:9605 read 0°9598. for 0:9620 read 0-9616. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. ‘FOURTH SERIES.] JANUARY 1865. I. Researches on the Mineralogy of South America. By Davip Forszs, f.A.S., &¢.* I. ISMUTH.—This metal occurs in the native state, as well as in combination with oxygen, sulphur, and tellurium, in a small vein in the lower Silurian clay-slates of the mountain Illamput in Bolivia. The mine of San Baldomero opened upon this vein is situated but little under the line of perpetual snow, and has an elevation of between 14,000 and 15,000 feet above the level of the sea. The vein cuts through the lower Silurian strata, here tilted up at a very high angle (nearly vertical), and has to some extent altered these strata: in immediate contact with the vein, a sahlband of from a few lines to some inches in width is seen in the rock on each side of the vein, the thickness of the sahlband being dependent on the relative strength of the vein itself; this is much darker in colour than the less altered rock, and has evidently been altered in chemical composition by the action of the mineral matter of the vein, most probably by the sulphur and arsenic present ; at a greater distance the slates are only hardened or, as it were, baked by heat, and not more altered than that the abundant fossils in them are well preserved —as various species of Homalonotus, Orthis, Arca, Tentaculttes, * Communicated by the Author. + This mountain is in England generally, but erroneously, called Sorata, owing to its being frequently called by the Spaniards “La nevada de Sorata” from the town of that name situated at its base. Its altitude has been determined to be 24,812 English feet above the level of the Pacific Ocean; and consequently it is the highest of all the peaks of the Andes of South America. Phil. Mag. 8. 4. Vol. 29. No. 193. Jan. 1865. B 2 Mr. D. Forbes’s Researches on the Ctenodonta, &c.; in fact hand specimens were cbtained consist- ing of ore and veinstone containing, in the latter, fossils in a perfectly recognizable condition. The geological examination of the environs appeared to prove that this and other veins in the neighbourhood had been pro- duced by the eruption of the large mass of granite (auriferous) further to the west, with which the veins are most probably con- temporaneous. The age of the granite itself was considered to be of the middle Silurian period. The minerals found present in this ven were—Danaite or cobaltiferous mispickel, mispickel, bismuth, bismuth-glance, bis- muth-ochre, carbonate of bismuth, telluric bismuth, gold, apa- tite, iron pyrites, zincblende, tourmaline, epidote, calespar, and quartz. The main mass of the lode was Danaite, which also formed the base for the mining exploration. The native bismuth was found more abundantly on the sur- face of the vein, and became very rare as the workings in the mine increased in depth; it occurred in irregular lumps or masses, and frequently as if wedged in between the walls of the lode. The largest mass found in one piece weighed about 400 pounds, and had one side entirely overlaid with a thin plate of gold of a rather light colour, not more than 0°05 inch in thick- ness, adherent and as if soldered to the bismuth. No crystals of bismuth were observed; but on fracture the basal cleavage was perfect, and the fresh surfaces showed the peculiar reddish-white colour so characteristic of this metal. The specific gravities of two separate specimens quite free from extraneous matter were found respectively to be 9°98 and 9°77 at 60° Fahr. The analysis was conducted as follows :— The arsenic was determined by fusing 25:08 grs. im fine powder, with a mixture of 80 grs. pure nitrate of potash along with 100 grs. pure carbonate of soda in a silver crucible; the mass was extracted with water, acidified by hydrochloric acid, and the arsenic precipitated as arseniate of magnesia and ammonia by the addition of a mixture of ammonia, chloride of ammonium, and sulphate of magnesia. 0270 gr. arseniate of ammonia and magnesia were obtained, equivalent to 0:097 arsenic, or to 0°38 per cent. arsenic in the bismuth. The sulphur was determined by suspending 50:01 grs. bis- muth in finest powder in a solution of potash, and passing a stream of chlorine gas through until all the bismuth was oxidized (this required a very long time) ; the solution was then rendered. more acid by addition of hydrochloric acid to prevent any tellu- rate of barytes being simultaneously precipitated, and the sul- phuric acid precipitated by the addition of chloride of barium. TOL Mineralogy of South America. 3 The precipitated sulphate of baryta weighed 0°26 gr., equivalent to 0:07 per cent. sulphur in the bismuth. The tellurium present was determined by dissolving a fresh portion of bismuth, weighing 45°55 ers., in nitric acid, neutrali- zing with ammonia, then adding sulphide of ammonium in excess, with which it was allowed to stand, being shaken occasionally, for some five days. The insoluble sulphide of bismuth was filtered off and washed with water containing sulphide of ammonium. The filtrate was now treated with an excess of hydrochloric acid, throwing down the sulphide of tellurium along with free sulphur and a little sulphide of arsenic; these were digested with nitric acid until the sulphur was quite pure, filtered, and the solution, previously strongly acidified and heated with hydrochloric acid to reduce all telluric acid present, was treated with a stream of sulphurous acid passed through it until all tellurium present had been thrown down, allowed to stand in an atmosphere of sulphu- rous acid, and then the precipitate was washed with sulphurous acid and dried with proper precautions. ‘The tellurium thus obtained weighed 2°425 grs., equivalent to 5°09 per cent. in the metallic bismuth. | In order to see if any silver was present in the mineral, three several portions, respectively weighing 40°50, 50:0, and 92:0 grs., were cupelled; in no case was any visible trace of silver found, but a faint trace of gold was distinctly observed. According to the above examination, the analysis of the native bismuth will now stand as follows :— Bismuth. . . O4raG Wellurremy 2. °° > 309 Golde ier ee 20" SS trace Arsemie? 0 8 O88 mrumonmere fee) SP et Oy 100-00 From observations on the specific gravity of other specimens of bismuth from this mine, I think it most probable that the percentage of tellurium may vary greatly in different specimens, which is confirmed by the analysis of another specimen from the same mine*, sent some years back to the United States, and which was a portion of the largest piece before mentioned. The analysis is by Mr. F. A Genth, and the results as follows :— Bismuth . . . . 99:914 rome tet es a trace Tellurium. .. . 0:042 | 99-956 * American Journal of Science and Arts, 2nd series, vol. xxvii. p. 247. 4, Mr. D. Forbes’s Researches on the Bismuthine.—As before mentioned, this mineral is found at the San Baldomero mine, where it occurs both in the form of scales incrusting the masses of native metallic bismuth, and by itself in small compact masses having a very highly developed foliated structure. It occasionally occurs in long and fine aci- cular crystals, which sometimes have an iridescent lustre, and frequently are so intermingled with slender needles of black tour- maline as to present a very peculiar and at first glance puzzling appearance. Frequently perfect simgle crystals of mispickel are found im- bedded in the more compact variety. The largest specimens found never exceeded half a pound in weight; in no case were defined crystals obtained, and.in only one case were the needles or plates observed to have terminal faces. Two perfect cleavages, with occasionally a less distinct third cleavage-plane, were present, and the faces of cleavage invariably possessed a brilliant metallic lustre. Hardness was never found above 2, and sometimes appeared rather less. Specific gravity of a pure very compact specimen was found to be 7:16 at 60° Fahr. The chemical examination was conducted as follows :—The de- termination of the sulphur was made by heating 20:02 gers. of the pure mineral in finest powder, with a mixture of 60 grs. pure nitrate of potash along with 70 grs. pure carbonate of soda in a silver crucible ; it glowed gently and became semifused, but did not flow. The mass, on cooling, was digested with water and thrown on to a filter to separate the oxide of bismuth, which was well washed. The filtrate was then acidified with hydrochloric acid and precipitated by the addition of a solution of chloride of barium. The sulphate of barytes thus thrown down was col- lected as usual, and weighed 28°46 grs., equal to 3-926 grs. sul- phur, or 19°61 per cent. sulphur in the mineral. The bismuth was now estimated by dissolving the oxide left upon the filter, as above mentioned, in nitric acid, and precipitating the solution with carbonate of ammonia in excess. The precipitate, well washed and ignited, afforded 18-03 gers. oxide of bismuth, cor- responding to 16-202 grs. metallic bismuth, or 80°93 per cent. in the mineral. An equal amount of the original mineral was examined for arsenic, using the process employed in the case of examining native bismuth for this substance ; no trace however was found*. * I may mention that in analyzing another specimen of this mineral I found 1°90 per cent. arsenic present ; but I satisfied myself that this was due to fine grains of mispickel interposed between the laminz of the mineral. | Mineralogy of South America. 5 Silver, iron, nickel, and cobalt were also specially examined for, but not found present in the mineral. | 42-01 grs. of the mineral in fine powder were now examined for tellurium by the same process as is described in the case of native bismuth. No tellurium, however, was found present. The analysis will therefore stand as follows :— Bismuth . . . 16°20 or 80°98 per cent. SBME oc Pecan O24 4... k POL, 20°12 100-54: Considering the atomic equivalent of bismuth as 106, and that of sulphur as 16, the formula Bi? S* would require the following percentage composition :— Bismuth, 2 atoms . . . 212 or percentage 81°53 Sulphur, 3 atoms . . . 48 18°47 260 100-00 Mispickel—This mineral only occurs crystallized in the San Baldomero mine when in small drusic cavities or close to the walls of the vein, where the crystals are frequently found protru- ding from the surface of the massive mineral and imbedded in carbonate of lime, or, as before stated, in the bismuthine. All the crystals I have observed belong to the trimetric system, and are rhombic octahedrons more or less modified, most generally as twin crystals. Perfect octahedrons are occasionally found, but only when imbedded in the soft bismuthine. No cleavage- planes could be observed. Colour: silver-white to grey-white ; but fresh surfaces tarnish quickly, becoming of a brassy colour on exposure. The specific gravity was found to be 6:255 at 60° Fahr. When heated alone, the mineral first evolves sulphide of arsenic and then metallic arsenic, and leaves sulphide of iron containing a trace of cobalt and nickel. | The chemical analysis was conducted as follows :— 23°42 grs. in finest powder were intimately mixed with 60 grs. pure nitrate of potash previously mixed with 60 grs. pure anhydrous carbonate of soda, and fused in a silver crucible; the mass deflagrated very gently, but a strong smell of arsenic was observed ; it did not flow; the whole on cooling was digested with water, and, after filtration and washing, the filtrate was acidified by hydrochloric acid, and the sulphuric acid precipitated by addition of a solution of chloride of barium. The sulphate of barytes collected amounted to 33°16 grs., equal to 4°575 ers. sulphur, or 19°534 per cent. in the mineral. The insoluble oxides were now dissolved in hydrochloric acid, neutralized by ammonia, and the iron separated from the cobalt, 6 Mr. D. Forbes’s Researches on the nickel, and manganese present by the use of succinate of am- monia with the usual precautions. The succinate of iron, redis- solved in hydrochloric acid and reprecipitated by ammonia, afforded 11°78 grs. sesquioxide of iron, equal to 8°173 grs. iron, or 34°47 per cent. in the mineral. } The solution, or rather filtrate, separated from the oxide of iron was now precipitated by sulphide of ammonium ; this precipitate, — collected, incinerated, dissolved in nitric hydrochloric acid, and precipitated by potash, gave 0°19 gr. oxide of cobalt, nickel, and manganese, which were arsenized and separated according to Plattner’s method by the blowpipe, giving 0°171 quadribasic arsenide of cobalt, equal to 0°104 metallic cobalt, or 0°44 per cent. in the mineral, and 0:09 quadribasic arsenide of nickel, equal to 0:0056 metallic nickel, or 0-03 per cent., whilst the manganese was estimated by the difference. The determination of arsenic was attempted in precisely the same manner as that of the sulphur, as described above; but notwithstanding every precaution, I could not have any confidence in the result, as after three attempts I noticed im each case the smell of garlic indicative of some evolution of arsenic. I therefore modified the process as follows :—20-05 grs. mineral in fine powder was placed in a porcelain crucible and drenched with pure nitric acid until no further oxidation took place. Carbonate of soda was added to take up the superfluous nitric acid, and more carbonate of soda along with nitrate of potash added to make up the same quantities as those used in determining the sulphur. The whole was heated to dryness, removed toa silver crucible and fused ; the residue was digested with water as usual, and the arsenic determined in the filtrate, after acidifying it by hydrochloric acid, as arseniate of ammonia and magnesia, which, when ignited with the usual precautions, gave 18°84 grs.2MgO AsO®, equal to 9°116 gers. arsenic, or 45°46 per cent. arsenic in the mineral*. The results of this examination, when tabulated, will now stand as follows :— ‘Arsenite’. 3.° 1°. 243460 Sulphur. eee Front 92 5 0 eee Manganese ~ .°. + Oa Cobaley Ais gen Niekel 3 2" 8 Pee 100:07 _* Thad the curiosity to make a determination of the arsenic by simply fusing with nitrate of potash and carbonate of soda as before mentioned, and only obtained 38°59 per cent. of arsenic, a loss of 6°87 per cent., which shows how unsafe this method is. : Mineralogy of South America. 7 The formula FeS*?+ FeAs would require— Arsenic, 1 atom . . . 75:0 or percentage 46:02 Sulphur, 2 atoms. . . 3820 a 19°63 Tron, 2 atoms. . . . 560 a 84°35 163:0 100-00 Danaite.—In the analysis of the mispickel above given, I had fully expected to find considerably more cobalt than actually was found; for it must be remembered that this mispickel had -erystallized out of the Danaite, to which it bears a proportion quite insignificant, as the Danaite forms the entire mass of the vein, which occasionally has presented a solid mass of the mineral having a breadth of more than ten feet between the walls. The Danaite was never found crystallized, but formed a com- pact mass, possessing a granular, fibrous, or foliated structure, and more or less crystalline appearance. The specific gravity of the fibrous variety, which probably is the most pure, was found to be 6°94 at 60° Fahr., of the granular variety 5°36; but this was invariably intermixed with more or less quartz or gangue in a very fine state of dissemination. Several analyses were made by the methods described under mispickel, and the following percentages show the average composition derived from their results :— Arsenic ot AVES PAR SS paper ee oa OMe, Mra teP Bal Pe ees Maneanese ~. . °° 8 ST2 Sins he SY eee IN fetes) 2) Oe PoE Pismutie es! C2 POG 100:00 which corresponds to the same formula as for mispickel, allowing a portion of the iron to have been replaced by the cobalt, nickel, and manganese here present. Nickeliferous Mispickel_—F rom Mr. Philip Kroeber I received a specimen of this mineral which I have not before seen described in any of the published works upon mineralogy. The mineral occurs as a vein in the lower Silurian slates in the Cordilleras between La Paz and Yungas in Bolivia, about 5 leagues from Unduavi, at a place called by the Indians Chacaltaya. The geological relations of this vein are very similar to those described in the case of the vein of San Baldomero, and it has doubtless originated from the same cause, the outburst of the same granite. More or less distinct crystals occur, and pertain to the trimetric 8 Mr. D. Forbes’s Researches on the | system. The prisms are found striated parallel to their longer axis, and twins are most common. Lustre metallic; colour tin-white to steel-grey, tarnishing quickly to a greenish-grey tinge. The crystals, when situated in quartz, are frequently coloured a fine green on their surfaces, evidently from the nickel present. The ore also, when exposed to the air and weather, assumes a fine apple-green colour from the same cause. Streak black to dark grey. Fracture uneven, brittle. Specific gravity 4°7 at 60° Fahr. A chemical examination was made by Mr. Philip Kroeber which gave the following results :— Arsenic . . . . 48°683 Sulphur 2c O14 (Gwe Tron: 63 Hib k hg Baa Niekel)) 60) 9. ys) 34074 Cobalt 0'.05.0 0.0.) = Saige Silver's.) 204.4 OFO9G Gold . hg Oe Antimeny™>..)..) . >> -traee 100°203 Mispickel.—Another variety of mispickel, occurring likewise in veins in the lower Silurian formation, is found at Inquisivi in Bolivia, where it is associated with Danaite, native bismuth, and an undetermined and probably new mineral in hexagonal erystals with perfect basal cleavage and having a great resemblance to dark brown zincblende, in a large quartz vein. The crystals obtained were too imperfect for measurement, but evidently belonged to the trimetric system; no defined cleavage-plane was observed. Colour dark steel-grey ; lustre dull metallic; streak dark greyish black. Non-magnetic. Hard- ness 5'5, scratching apatite, but not orthoclase. The specific gravity at 60° Fahr. was found to be 6:170. Before the blowpipe in a closed tube it gave off, first some trace of sulphur, then sulphide of arsenic, and lastly metallic arsenic. In the oxidizing flame it gave off sulphur and arsenic; and with borax glass, slagged off entirely with reaction for iron, but showed no appreciable quantity of copper, nickel, or cobalt present. An assay by cupellation afforded a trace of silver containing gold, which latter appeared present in larger quantity than the silver. The analysis was performed exactly as in the case of the mis- pickel from San Baldomero mine, with the exception that the arsenic was determined as loss. The results were as follows :— Mineralogy of South America. 9 PSD OT ees Bag te OE mn i SO CAG OD SELL I a ahaa ree UC 7 URSTD SS ec a i ear 0 Cobalt, nickel, bismuth, silver, and gold . traces 100:00 which conforms to the usual formula for mispickel, FeS?+ FeAs. I may mention that I examined the Danaite which is asso- ciated with this mineral, and found in various specimens a per- centage of cobalt (with trace of nickel) which varied from 1°81 to 3:9 per cent. metallic cobalt. Antimonial Galena.—Considerable veins of antimonial galena are worked between La Paz and Yungas on the eastern slope of the Andes, chiefly for the amount of silver contained in them. The mines are situated in veins which cut at very high angles through the lower Silurian slates, containing abundant fossils of the genus Crusiana and Boliviana, as well as others not yet determined. ‘Their geological relations are otherwise similar to the veins hitherto treated of in this paper. A specimen from the Mina Pilar was examined by Mr. Philip Kroeber, who has communicated the results to me. The mineral which was ana- lyzed was quite free from gangue, but contained some minute specks of iron pyrites and chalcopyrite; compact but foliated in structure, and in colour of a light steel-grey tint and very lus- trous. Its analysis afforded him— Teadk Aer eS he OS 262:510 Antimony . . . 15°379 Copper Rye AL S246) rom ee Fe 2, hee OP Sag Silvers: 2 ee. O° L90 IMESCHUC. %. os, eS tTAce Sulpnar. te PS O0F 100°200 The associated minerals are quartz, calcspar, carbonate of iron, iron pyrites, chalcopyrite, zincblende, cubic galena, Fahlerz, and a new mineral, in strongly magnetic, copper-coloured crystals, which I have called Kroeberite, and which, though not yet ana- lyzed, appears to be principally a subsulphide of iron. In some specimens also there occurs some mineral containing cobalt, most probably “ Selenkobaltblei,” as the ore was found to con- tain on analysis more than 2 per cent. of cobalt. If we look upon the iron and copper as combined with a portion of the sulphur, forming iron or copper pyrites, we may suppose the mineral here analyzed to pertain to the mineral species Geokronite. I adda tabulated statement of the various 10 M.C. Martins on the relative Heating, by 8 Solar Radiation, minerals considered as compounds of the sulphides of antimony and lead, for the sake of comparison. Specific Name. Formula. Sulphur. |Antimony.| Lead. gravity. : 5:3 Zinckenite. PbS+ Sb?S*?| 21-6 435 | 39:4 5°5 Jamesonite. 3PbS+28b?S?| 20-2 36-2 43°6 5-4 Plagionite. 4PbS+38Sb? 8?| 20°6 38-3 AY: 5°6 Heteromorphite. | 2PbS+ Sb2S*?| 19-2 31:0 49°8 58 Boulangerite. 3PbS+ Sb28?| 17:9 241 58-0 ? Meneghinite. 4PbS+ Sb28S?| 16:7 19°6 63-7 6:40 | Geokronite. SPbS+ Sb2S?|} 16:5 16:7 66°38 6°47 | Do. (Fahlun). © | 6PbS+ Sb28?; 145 14°6 709 Veins of these antimonial-galenas are met with almost every- where, cutting through the Silurian strata of South America. They are generally crystallized, or rather more or less crystal- line; and although they can be procured free from apparent mechanical admixture of other minerals, yet it is extremely diffi- cult to determine the mineral species to which they belong merely by an examination of their external and physical charac- ters, and it is most probable that a closer examination will show the presence of at least more than one new mineral species per- taining to this class. The specific gravities of these varieties differ considerably, yet not sufficiently to be a decisive criterion as to the species; eight varieties of what appeared to be antimonial galena from different mines in the department of La Paz, Bolivia, gave respectively the following specific gravities taken at 60° Fahr. :— 5°25, 5°302, 5°49, 5°49, 6°515, 7:07, 7:20, 7:41; and I have no doubt that on further trial many intermediate numbers would be found; indeed it would seem as if the sul- phides of antimony and lead would combine in any proportion. II. On the relatwe Heating, by Solar Radiation, of the Soil and of the Air, on a Mountain and in a Plan. By M. Cuar.es Martins*. our sun’s rays falling on the top of a mountain ought, theoretically, to be warmer than those which, after traver- sing the lower and denser strata of our atmosphere, reach the adjacent plain, since these strata necessarily absorb a consider- able quantity of the heat of such rays. Observation fully con- firms the prediction of theory in this case. All travellers who have ascended high mountains have been surprised at the great * From the Comptes Rendus de ? Acad. des Sciences, October 17, 1864. of the Soil and of the Air, on a Mountain and ina Plain. 11 heat of the sun’s rays and of the ground, when compared with the temperature of the air in the shade, or with that of the soil at night. As early as 1842, MM. Peltier and Bravais made, from the 10th to the 18th of August, a series of bi-hourly observations on the temperatures of the air and of the soil on the summit of the Faulhorn, a Swiss mountain which rises to a height of 2680 metres above the level of the sea. Experi- ments of a similar kind were made by Bravais and myself, two years afterwards, on the same mountain, between the 2I1st of September and the 2nd of October. The 125 observations comprised in these two series, and which were continued from six in the morning to six at night, both in fair weather and in foul, under cloudy as well as cloudless skies, gave, notwithstand- ing, a mean temperature of 11°°75 for the soil during the day, that of the air being only 5°40. It thus became evident that during the day the soil was heated by the sun twice as much as was the air. We did not know, however, what, during the same period, had been the relative heating of the soil and the air in the Swiss plains. For along time! was anxious to remove this incompleteness, by determining the relative heating of the same kind of soil, at the same moment, on a lofty mountain and on an open plain, when the sky was pure and the air calm. Bagnéres- de-Bigorre and the Pic du Midi appeared to me to possess all the conditions desirable for experiments of this nature. ~The horizontal distance between the two places, as measured on the new map of the Etat-Major, is not more than 14,450 metres, and the two points are under the same meridian. The Pic du Midi, perfectly isolated from the principal chain of the Pyrenees, rises to a height of 2877 metres above the sea—an altitude which merits all confidence, since the Pic du Midi was selected as one of the principal points of the triangulation upon which the new map of France is based. I was moreover able to con- nect, by a single sight through a level, my point of observation im the garden of my friend Dr. Costallat, at Bagnéres, with the system of levels connected with the railways of France. The point in question was thus ascertained to be 551 metres above the level of the ocean, giving a difference of 2326 metres between the alti- tudes of my two stations. Besides this, the valley of Bagnéres has the advantage of not being one of those narrow ones where the reflexion of the sun’s rays increases the temperature; its breadth, in fact, taken from crest to crest of the hills by which it is bounded on the east and west, amounts to 2800 metres. It will be admitted, therefore, that it would be difficult to find in the Alps or im the Pyrenees two stations more favourably situated for the success of the comparative observations which I had in view. These observations, however, would not have been at 12 M.C. Martins on the relative Heating, by Solar Radiation, all comparable with each other had one thermometer been placed at the surface of the natural soil of the mountain, whilst the other reposed on the soil of M. Costallat’s garden; for, as I have elsewhere shown*, superficial soils of different natures are very unequally heated under the influence of solar radiation. In order that the experiments might admit of comparison, it was necessary to observe the heating effect on the same soil at both stations. For this purpose I chose the soil resulting from the decomposition of the wood found in old hollow willow trees ; it is a vegetable soil, since plants, such as briars, honeysuckles, elders, &c., grow thereon very vigorously ; it is moreover homo- geneous, comparable with like soils, and easy to procure in all countries. Its absorbing power is a mean between those of seven other kinds of soil with which [ have compared it; its conducting-power for heat is inferior, however, to that of any of the seven, whilst its emissive power is greater. The experiments were made in the followmg manner :—A wooden box, whose length and breadth were equal to 20 centi- metres, and whose depth was 10 centimetres, was filled with the above soil, and a thermometer with a cylindrical bulb was laid upon its surface—the bulb and the tube, up to zero, being covered with a thin layer of soil. Another thermometer, which had a bent tube, was placed so that the bulb was 5 centimetres below the surface of the willow soil. This box was placed on an iso- lated hillock in M. Costallat’s garden, and another exactly simi- lar one was placed on the summit of the Pie du Midi by my assistant, M. Pierre Roudier, who for twelve years has assisted me in my meteorological researches with great zeal and intelli- gence. Both boxes were buried so that their surfaces were on a level with the natural soils at the two stations. The stratum of atmospheric air between the two boxes was, as already stated, 2326 metres in thickness. Our experiments commenced on the morning of the 8th of September 1864, the sky being admirably pure and the air perfectly calm. Every hour from sunrise to 10 in the morning, and every half hour from the latter period to 3 in the afternoon, we observed, first, the thermometer at the surface of the willow soil; secondly, the thermometer which was imbedded therein ; thirdly, a thermometer with a small bulb placed in the shade and previously well swung (tourné en fronde) ; and lastly a psychro- meter, also placed in the shade. The sky at Bagnéres remained constantly pure, and I was enabled to make all the observations agreed upon. It was otherwise on the Pic du Midi; the mornings were there magnificent, but towards noon czrro-cumult rose from * Annuaire de la Société Météorologique de France, 1863, vol. xi. p. 129 ; and Mémoires de ? Acad. des Sciences de Montpellier, 1863, vol. v. p. 374. of the Soil and of the Air, on a Mountain and in a Phin. 13 the Spanish side, and, driven by a slight breeze from the south, gradually enveloped the Pic. Nevertheless during the three days I was able to select twenty corresponding and perfectly com- parable observations, made alike under a pure sky, in full sun- light and in calm air: these coincidences occurred between 7 in the morning and 2 in the afternoon. With reference, first, to the heating of the superficial soil, the mean of the twenty observations on the temperature of the air in the shade was 22°°3 at Bagnéres, and only 10° 1 at the Pic du Midi. The mean temperature of the surface of the soil was 361 at Bagnéres, and 33°°8 at the Pic. The mean excess of the temperature of the soil above that of the air at Bagnéres had consequently to the like excess at the Pic the ratio of 10 to 17; in other words, it was nearly double onthe mountain. Further, - although the mean temperature of the soil in the plain was 2°3 above that of the soil on the mountain; still, on the 10th of September, between 11 and 11.30 a.m. (after which latter time the Pic became enveloped in clouds), the temperature of the soil at its summit was 6°9 higher than that of the soil at Bagnéres— the mean temperature of the air at the latter station beimg 23°°2, and at the former 13°°8. The absolute maxima observed at the surface of the soil in the twenty corresponding observations were 50°'3 at Bagnéres (2 p.m., September 9, temperature of air in the shade 27°1), and 52°:3 on the Pic du Midi (11.30 a.m., September 10, temperature of air in the shade 13°°2). These experiments place beyond doubt the fact of the greater calorific power of the sun on the mountain than in the plain. I proceed, secondly, to the heating of the soil at a depth of 5 centimetres. I have already stated that the soil resulting from the decomposition of the wood of the willow was penetrated with greater difficulty by solar heat than was any one of the other soils examined, and besides this that it was the best radiator. The physicist will not be at all surprised at this. The greater relative heating power of the sun on the mountain is shown by the thermometers whose bulbs were at a depth of 0°05 of a metre, as well as by those whose bulbs rested on the surface. Thus the mean temperature of the soil at a depth of 0°05 of a metre was 25°°5 at Bagnéres, that is to say, only 3°:2 above the temperature of the air, whilst on the Pic du Midi the first tem- perature was 17°°1, higher consequently by 7 degrees than the temperature of the air surrounding this elevated summit. The mean thermic excess, at Bagnéres and at the Pic, of the soil at a depth of 0-05 of a metre, is therefore as 10:22; that is to Say, on the mountain the excess im question is more than double that in the plain. On the surface of the soil the ratio, as we have seen, was as 10 to 17. Relatively, therefore, the 14 On the relative Heating of the Soil and of the Air. soil at a few centimetres below the surface is still more heated on the mountain than it is im the plain. | | This immense heating of the soil, compared with that of the air on high mountains, is the more remarkable, since during the nights the cooling by radiation is there much greater than in the plain. I have already had the honour of communicating to the Academy (on the 6th of June, 1859) the results obtained by MM. Peltier, Bravais, and myself, by means of Pouillet’s swans- down actinometer, on the summit of the Faulhorn, at an altitude of 2683 metres, and on the Grand Plateau below Mont Blane, at 3930 metres above the level of the sea. I afterwards developed the same subject in a memoir on the causes of the low tempera- tures on high mountains*. _Two corresponding observations of the minima of the air and of the soil at Bagnéres and at the Pic du Midi during the clear nights from the 7th to the 8th, and from the 8th to the 9th of September, will show still more stri- kingly how much more considerable is the cooling of the soil by radiation in the rarefied air of high mountains than in the denser strata of plams. The willow soil beimg, of all those which I tested, the one whose emissive power is greatest, the low tempe- ratures given in the sixth column of the followmg Table, con- taining the results we obtained, will cause no surprise. Lowest Temperatures of the Air and of the Soil during the Night, Bagnéres, altitude 551 |Pic du Midi, altitude 2877 metres. metres. Dates, Lowest temperature Lowest temperature Septem-=|— = 2 a anes Ce Remarks. ee Of the soil at a Of the soil at a ‘| Ofthe| depthof | of the depth of otis 0°00 0°25 alr. 0°00 0°25 metre. | metre. metre. | metre. oO oO ° ° ° fe} Ee ‘ . “7, 8 bra te ThipA Sipe ees 2) 25g ore Hoar-frost on willow soil Dewon the soil of the Pic. 9 14:9 | 12:99 | 18:9 1:3 O-1 | 2-1 It will be seen that the difference between the lowest tempe- ratures at the surfaces of the soil was 13°83 during the night from the 7th to the 8th of September, and 12°8 during that from the 8th to the 9th, the excess bemg in favour of the plain. When the sun rises, his oblique rays impart heat, very slowly at first, to the frozen soil of high mountains: thus, although his rays had already struck the summit of the Pic at 5.30 a.m., it was not until 7 a.m. that the surface of the soil reached a mean temperature of 9°°3; at 11.30 a.m. this tempe- * Annales de Chimie et de Physique, 3 sér. vol. lviti. (1860). Mr. C. J. Monro on a case of Stereoscopic Illusion. 15 rature had risen to 47°°8. Not being in possession of corre- _ sponding afternoon observations, I am not able to fix the time of greatest temperature; I am inclined to think, however, that, as in the case of the air, it occurred about noon. Ramond, in the thirty-five ascents of the Pic du Midi made by him in the course of twelve years in spring, summer, and winter, collected all the plants of the terminal cone, whose height is 16 metres, and whose base covers several ares; he there observed 71 phanerogamous plants. I noticed 131 such plants on the terminal cone of the Faulhorn, whose height is 80 metres, and whose base covers 4 hectares 50 ares (about 11 English acres), the summit being 2683 metres above the level of the sea. Accordmg to the recent Swedish explora- tions, and the account of previous expeditions given by M. Malmgren*, the whole archipelago of Spitzbergen only con- tas 93 such plants. Independently of the original geogra- phical distribution, the temperature of the soil is sufficient to account for the number and the variety of the species which vegetate on the summits of the Alps and of the Pyrenees; they are there heated more by the soil which bears, than by the air which surrounds them, and their respiratory functions are stimu- lated by a strong light. On the other hand, at Spitzbergen, notwithstanding the continual presence of the sun above the horizon during summer, the heat of the sun’s rays, absorbed almost entirely by the vast thickness of atmosphere they have traversed, is incapable of raising the temperature of the soil above that of the air. The soil remains always frozen at a depth of a few decimetres ; and vegetation not being stimulated either by the heat of the air or by that of the soil, the entire flora of the region is limited to a small number of plants capable of living and flourishmg at a temperature but a few degrees above zero. III. On a case of Stereoscopic Illusion. By C. J. Monrot. 1 3 the phenomenon here to be described has not been described before, it is perhaps worth describing for its own sake. If it is well known, it is worth while to point out its bearing on a recently contested point in the theory of binocular vision. In his separate work on the Stereoscope, published in 1856, Sir David Brewster maintained (pp. 78, 81) that when we see or seem to see an object single and solid with two eyes, it is because we see any point with both eyes at the intersection of the two * Petermann’s Miitheilungen, 1863, p. 48. + Communicated by the Author, 16 Mr. C.J. Monro on a case of Stereoscopic Illusion. directions in one of which we see it with each eye. Mr. Abbott* cejects this as an explanation (pp. 106, 107), and denies it as a — vact (p. 107), but is not prepared to give a construction of his own for the apparent place of any point whose images on the two retinas are not similarly situated with reference to the yel- low spots. The apparent places of all points having this pro- perty he determines, as he does the apparent directions of all others, by constructions which only relate to the case of an ob- server looking straight before him, but, at least for the former class of points, are the same as Sir David’s as far as they go (pp. 108, 109). Indeed Mr. Abbott would probably admit that Sir David’s construction was approximately accurate as a geome- trical statement of the facts of ordinary vision. That, on the contrary, it does not in general meet the case of that ‘artificial vision which formed the subject of Sir David’s book, Mr. Abbott has perhaps partly proved}; and the demonstration is completed by the fact that when stereoscopic pictures further apart than the eyes are combined by divergence, the object is given in relief as perfect as that of nature, and does not, in my experi- ence, appear behind the observer. But even in artificial vision, as far as my own eyes are concerned, the theory seems to apply correctly to all cases which, according to that theory, would sug- gest an idea easily adopted by the imagination. Strange to say, in the simplest of these cases, whereas my experience agrees with Sir David’s theory, Sir David’s experience seems to contradict it. In describing the effect of combining an image of each section of a repeated pattern with the conjugate image of another section a certain distance off, he says (Stereoscope, p. 91) “ the surface .... seems slightly curved.” To Mr. Abbott, who seems to speak, like Sir David, of an apparent surface formed on this side of the real one, it looks “ somewhat convex” (Sight and Touch, p. 122). Now if the eyes are taken to be represented by their optical centres, the theory would evidently give a flat surface, * Sight and Touch, an attempt to disprove the received or Berkleian Theory of Vision. By T. K. Abbott, Fellow of Trinity College, Dublin (1864). + He gives a pair of dots in the middle of the page (107), and says that on combining them stereoscopically we do not see the image below or above the paper, but upon it. Now, in the first place, I do see the image below or above the paper according as I combine the pair directly or con- versely. Secondly, the proof meets only half of the proposition. It shows that Sir David’s conditions are insufficient under very trying circumstances : it does not show that they are unnecessary. I venture to use the phrases direct and converse stereoscopic combination, for which I find no equiva- lents in either of the works cited. The combination is direct when the right eye sees the right picture, and the left the left; converse when the right eye sees the left picture, and the left the right. Mr. C. J. Monro on a case of Stereoscopic Illusion. 17 and I presume the error due to this substitution would be some- thing quite imperceptible to the lateral parts of the retina. The eyes are converged indeed upon points very near them, and focused for points further off; and though the disproportionate recession of the optical centres and advance (if there is any advance) of the retina due to this inconsistency would affect all points of the picture alike, it is intelligible, on Mr. Abbott’s principles, that a flattening of the retina, apparently inseparable from its advance, might produce the effect of convexity by draw- ing lateral images a little nearer to the yellow spots. But any illusion depending upon the properties of lateral parts of the retina would disappear upon running the eyes rapidly over the field. Meanwhile, having repeatedly made the experiment both before and after meeting with Sir David’s observations, I have never detected the slightest curvature in the apparent surface, except in two cases—first when the real surface is curved, and secondly when the eyes are at different distances from it. In the cases described the real surface is a flat wall, and the obser- vers are evidently supposed to be looking straight at it: besides, if they had looked obliquely the curvature would have been con- cave, according to the theory ; forthe surface the theory gives is a hyperbolic cylinder asymptotic to the wall. It is difficult, if not impossible, to see this in patterns which vary vertically as well as horizontally; but if the pattern consists simply of vertical lines, nothing can be more vivid than the object sometimes suggested. I combined in this way the images of a straight row of flat vertical bars, about an inch and a half wide and an inch and a half apart, so as to form astereoscopic image beyond them: my nearest eye was about six inches from their plane, to which the line joing the two was inclined at a considerable angle. The bars immediately formed themselves into the alternate faces of a vertical prism, of which the circum- scribing cylindrical surface was apparently asymptotic to the plane of their real position, and came up to a sort of apse quite close to me, and then stretched off indefinitely away from the plane as far as the binocular field extended. The sudden changes of azimuth made by the flat surfaces as they turned the corner of greatest curvature gave the image an effect of solidity as per- fect as that of real nature. Now every test of distance and posi- tion, except that of the intersection of the visual rays, was against the production of the result produced. The very points which the focusing of the eyes affirmed to be the nearest stretched away in the further sheet of the surface; and while the nearly equal illumination of the bars by a single lamp affirmed that they were parallel, they seemed to stand round a very convex surface. So even without positive measurement, which seems impossible, | Phil. Mag. 8. 4. Vol. 29. No. 198. Jan. 1865. C ‘18 Myr.C. J: Monro on a case of Stereoscopic Illusion. and without comparison of estimated with calculated results, which it would be very hard to conduct satisfactorily, I think I may give this phenomenon as a confirmation of Sir David Brew- ‘ster’s view, subject to the qualification above stated, which he applies himself in a particular class of cases at pages 209, 210, and 217. aitd 3 That such a surface is given by the theory is evident. The visual rays approach without limit to parallelism as you run your eyes away along the wall: they are parallel also when the four quantities following are proportional, the distances of the eyes and of the points to be combined from the intersection of the wall by the line through the eyes. When these are propor- tional to one another, they are proportional to their differences. So the direction of the second asymptote is that of the base of.a triangle whose sides are in direction and magnitude the distances between the eyes and between the points to be combined. The latter distance is in these patterns constant in magnitude, and must be positive if the stereoscopic combination is direct, and negative if converse, provided that the directions containing the acute angle are taken to be of the same sign. The surface is cylindrical, because the pomts to be combined in any part of the pattern, and therefore the lines through them from fixed points, and the intersection of these, all have for orthogonal projections points and lines answering the same description in the horizontal plane. 7 For further details, let us confine our attention to this plane. Take for axes the lime through the eyes and the trace of the wall; and, with the above convention as to signs, let the dis- tances of the eyes and of the two other poimts from the origin be a, a’, b, b'. Then, if it is remembered that a, a! and b—J! are constant, the coordinates of the point of intersection of the visual rays will be given by the equations GY a Yy gh ch pe whence 2, a—@ i IQ av + party — (a+ ale + aa'= , the equation of an hyperbola of whose asymptotes the equa- tions are x y _atd a—a't 6—U ad The line given by the last equation cuts the line through the eyes as far on one side of the mid-point between them as the trace of the wall cuts it on the other, and makes with these lines c—, -Prof. Cayley on a Quartic Surface. 19 a triangle similar and similarly situated to that described above without the help of an equation. In the case of direct combination, the aie branch is beyond the wall, and is convex. to the observer; the other branch passes through the eyes; and a short arc, generally near the apse, is in front of them, but, bemg formed by combining points of which one is concealed from the corresponding eye, is invi- sible. The rest is behind the observer, and I suppose none of it can be seen in its proper place; but a small part near the second asymptote is formed by combining points, both of which may be visible, and under favourable circumstances might be combined by divergent visual rays. Where the image would appear, is a curious question. In the case of converse combination, the visible part is on this side of the wall, and is of course concave to the observer. The eurve runs up to the nearest eye, and, though it comes out at the other, is seen no more of. Gibraltar, November 1864. IV. Note on a Quartic Surface. By A. Cayury, F.R.S.* T would, I think, be worth while to study in detail the quartic surface which is the envelope of a sphere having its centre on a given conic, and passing oe a given point. The equa- tions of the conic being z= ae 2 ay = =1, the coordinates of a point on the conic may be en to be e=acos 0, y=bsin 8, z=0, whence, if (a, 8, y) be the coordinates of the given point, the equation of the sphere is (a—acos6)? + (y—bsin 8)? + 2? = (a—acos@)? + (8@—dsin 8)? +49? or, what is the same thing, x? + y? + 2° — a® — B?—y? —2(@—x)a cos 0—2(y—B)bsind=0; and hence the equation of the surface is at once seen to be (v?+ y? 4+ 2?— a? — 6? —v?)? = 4a? (~—a)? + 4b? (y—)?. If a=b (that is, if the conic be a circle), then we may without loss of genevality write @=0, and the equation then is (a? + y? + 2? — a? —y*)? = 4a? § (a —a)? +y° This may be written - wat | 219424 m2 pQ. (a2-+ y? + 22?—a? ~y?— 202)? = — 80% («— Cte tT—), * Communicated by the Author. af 20 Prof. Cayley on a Quartic Surface. which, considering 2 as a constant, is of the form (a? +4? —a)?=16A(x—m) ;sx that is, the section of the surface by a plane parallel to the plane 3 of the conic is a Cartesian. If a and 3 are unequal, but if we still have @=0, the equation of the surface is (a? + y? + 2? — a? —9y?)* = 40?(4@ —a)? 4+ 46y?, There are here two planes parallel to the plane of the conic, each of them meeting the surface in a pair of circles. In fact, writing x*+y?=p, and therefore also y?=p—x*, putting moreover 2?—a*—y?=k, we have (p+ k)?= 4.072? —8a®axr + 4070? + 467(p —2*) ; that 1s, 0? + 4(b29—a?) x? + k2— 40a? + 8a?ax + (2k—4b2)p =0, or, as this may also be written, (1,4(0?—a?), k?—Aa?a?, 4a?x, kK—2b°, OFp, 2, 1)?=0, which is of the form (4, b, Ca gd; Of; a; 1)?=0; and the left-hand side will break up into factors, each of the form p+Ax#2+B (so that, equating either factor to zero, we have p+Av+B=0, that is, v?+y?+Az+B=0, the equation of a circle), if only abe — af *—bg?=0. Writing this under the form b(ac—g’)—af?=0, and substi- tuting for a, b, c, f, g their values, we have b=4(b? —a*), ac—g? =k? —4.0°a* — (k —2b?)? = 4 (07k — 64 — 07a?), af = 16ata?, and therefore the condition is (b?—a?) (67k —b4—a*a?) —ata?=0; that is, 5? }(b?—a?) (k—b") —a’a?! =0, If 52=0, the surface is a pair of spheres; rejecting this factor, we have (b?—a*)(k?— 6?) —a’a?=0; or putting for & its value, the condition becomes (6? —a?) (2? —a? —y?— 6?) —a?a?=0; that is, for each of the values of z given by this equation, the section by a plane parallel to the plane of the conic will bea pair of circles, Prof. Cayley on a Quartie Surface. 21 The planes in question will coincide with the plane of the conic, if only (22 —a2) (2 +245?) + aa? = 0, or, what is the same thing, ba? — (a? — 2)? = 5? (a? —2?); that is, if the point (a, 0, y) be situated on the hyperbola y=0, a 2 maT hae 72 =1. The hyperbola in question and the ellipse z=90, i) 2 a + a =1, are, it is clear, conics in planes at right angles to each other, having the transverse axes coincident in direction, and being such that each curve passes through the foci of the other curve;-or, what is the same thing, they are a pair of focal conics of a system of confocal ellipsoids. The surface in the case in question, viz. when the parameters a, 6, a, 8 are connected by the equation 2 2 ze Y 2-8 B is in fact the “Cyclide” of Dupiu. Itis to be noticed that we have here («—a cos 0)? + b? sin? 6 +9? = a + ry? + b?—2aa cos 0+ (a? — b*) cos? 0; i 2.2 which, observing that «?+?+ 0? is = se gives (2—acos 0)? + 5? sin? 0+4?= (Vee cos 0 — ya J/ a2 — 62) ? so that the radius of the variable sphere is | i ae ace =/ a? —b? cos 0— Jaane If the variable sphere, instead of passing through the point (a, 0, y) on the hyperbola, be drawn so as to touch a sphere of radius /, having its centre at the point in question, then the radius of the variable sphere would be / a2 —b2 cos 8 — ae —/, which is in fact nT, ac =/a—F cos 0— Vea, 22. Dr. Rankine on the approximate Graphic Measurement aaa eee se Op) if aly ; hence if y' be the corresponding value of y, the vanthbie sphere passes through the point ( a, 0, 7) on the hyperbola, and the envelope is still a eyclide. The eyclide as derived from the foregoing investigation is thus the envelope of a sphere having its centre on the ellipse, and touching a fixed sphere having its centre on the hyperbola. It also appears that there are, having their centres on the hyperbola, an infinite series of spheres each touched by the spheres which have their centre on the ellipse; if, instead of one of these spheres we take any four of them, this will imply that the centre of the variable sphere is on the ellipse, and.it is thus seen that the cyclide as obtained above is identical with the cyclide according to the ori- ginal definition, viz. ie envelope of asphere touching four given spheres. _ Cambridge, December 5, 1864. V. On the approximate Graphic Measurement of Elliptic and Trochoidal Arcs, and the Construction of a Circular Are nearly equal to a given Straight Line. By W. J. Macquorn Ran- KINE, C.H., LL.D., F.R.SSL. & B* [ With a Plate. ] HE three following rules are very obvious results of the _application of Simpson’s method of approximate integra- tion to the rectification of curves generated by rollmg; and it is possible that they may have been already published by other authors; but as | do not know of any such publication, and as the rules are useful and convenient, I beg leave to offer them to the Philosophical Magazine. The general proposition of which the rules are particular cases is the following well-known one. Let a plane disk of any figure roll on a plane base-line of any figure: let there be a tracing- point in the disk, and let r denote the rolling radius, or distance of the tracing-point at any instant from the instantaneous centre, or point of contact of the disk and base-line. Then while the disk rolls through the angle ¢, the tracing-pomt describes an arc of the length | rd. To calculate an approximate value of 0 he 7 e e ° this integral, divide the angle ¢ into either 2” or 3n equal inter- * Communicated by the Author. + A process nearly identical with that of Rule I. is apolcd by John Bernoulli to the rectification of the whole ellipse, but not to 2 arcs. (Johannis Bernoullit Opera, vol. i. § 83.) of Elliptic and Trochoidal Arcs, &. 23° vals (the number being the greater the closer the required approximation). Measure the rolling radii corresponding to 0 and , and to each of the intermediate angles, and let them be denoted by 79, 7, 74, &c. Then the mean rolling radius is approximately for 2n intervals (by Simpson’s first rule) 1 = n (75 a 4r) + 215 + 4r., eet 2 on—ot 47 on—1 + 1en)3 and for 32 intervals (by Simpson’ s second rule), 1 Pm = Z(t + Bry + Bry + 27g + 00+ 2 an—3 + Br an—1 + Bran—1 + Pan) 5 and the are described by the tracing-point is approximately equal to a circular arc of the radius rp, subtending the angle >. Rue I. To construct a circular are approximately equal to a given arc CD (Plate I. fig. 1), not exceeding a quadrant, of an ellipse whose semiaxes O A and OB are given. In fig. 2, draw a straight line, in which take EHF=OB and FG=OA. Bisect it in H; and about that point, with the radius HF=H K=0*>9% ec and d in that circle, by laying off He=OC, and Ed=OD. Then divide the are cd into 2n or 3n equal intervals, as the case may be, and measure the distances from the ends of the are and the poimts of division to G: these will be rolling radii of the ellipse, as generated by rolling a circle of the diameter H H inside a circle of the diameter EG, the tracing-point being at the distance H F from the centre of the rolling circle; and the Simpsonian mean (as it may be called) of those rolling radii-will be the radius of the required circular are. Then in fig. 1 describe a circle about O with the radius OA; through C and D draw straight lines parallel to OB, cutting that circle in T' and A; join OI, OA; and about the centre O, with the mean rolling radius already found, describe the cir- cular are MN, bounded by the straight limes OI, OA; this will be the required circular arc approximately equal to the elliptic are CD. sciaan The same circular arc may be drawn, if required, in fig. 2 as. follows :—From any convenient point L in the circumference of the circle F K, draw straight lines through c and d; and about IL as a centre, with the mean rolling radius already found, de- scribe the circular arc mn bounded by those lines. Rute II. Yo construct a circular are approximately equal to a given trochoidal arc, not exceeding the arc between a crest of the trochoid and the adjoining hollow. In fig. 2 make GH= the radius of the rolling’ circle which. , describe a circle. Mark the points 24 On the Measurement of Elliptic and Trochoidal Ares, &c. generates the trochoid; and describe the small circle F K about H with a radius equal to the distance of the tracing-point from the centre of the rolling circle. Take Gy and Go respectively equal to the perpendicular distances of the two ends of the given trochoidal are from the base-line on which the rolling circle rolls. Through y and 6 draw straight lines perpendicular to GH, cutting the small circle incand d. Divide the are c dinto 2n or 8n equal intervals, and measure the distances from the ends of the are and the points of division to G; these will be rolling radii; and their Simpsonian mean will be Zhe radius of | the required circular are. From H draw straight lines through ¢ and d, and about H, with the radius already found, describe the circular are [LY, bounded by these straight lines: this willbe the required circular arc approximately equal to the given trochordal are. Rutz III. To find the radius of a circular are which shall be approximately equal to a given straight line, and shall subtend a given angle. This question is solved by regarding the straight line as form- ing part of an ellipse whose shorter semiaxis is=0. Let PQ (fig. 3) be the given straight line. Construct the triangle P QR, in which Q is a right angle, and P the complement of the given angle; so that R is the given angle itself. Buisect the hypothenuse P R in 8, about which pomt describe a circular arc traversing P and Q. Divide that arc into 2n or 3n equal intervals: measure the distances from its ends and from the points of division to the point R, and take their Simpsonian mean; this will be the radius RT of the required arc TU, which 1s approximately equal to the straight line PQ, and sub- tends the angle PR Q. Remarks.—It is evident that the processes described in the three preceding rules are graphic methods of approximating to elliptic functions of the second kind, and that, if put im an alge- braical form, they would become identical with the method of approximation to the function EK described by Legendre in the Appendix to the first volume of his Traité des Fonctions Ellip- tiques. The amplitude of the function is represented by ¢=MON of fig. 1, ze of fig. 2, =mLnr= = QP or ‘e 3. The modulus in fig. 1 is the eccentricity of the ellipse, in fig. 2 Dr. Rankine on Stream-lines. 25 ee and in fig. 3 unity; and the unit line in fig. 1 is OA, in fig. 2 FG, and in fig. 3 PR. The degree of precision of the approximation depends on the smallness of the intervals into which the amplitude is divided— . the error diminishing somewhat faster than the fourth power of the interval, as Legendre, in the Appendix already referred to, has shown to be the case for every application of Simpson’s for- mula. Thus, in the application of Rule III., the following are examples of the greatest proportionate errors (which are always in excess) :— Intervals of amplitude. — Errors of Rule IIT. ie} 45 s ® . ° s e about a 30 " 73 2500 rE esd (Keke 224 . e ° e e ° 33 8 8) 8) O ee eee ah el os) eau: The errors of Rules I. and II. become smaller than those of Rule III. as the modulus diminishes—that is, as the ellipse ap- proaches to a circle, and the trochoid to a straight line. The following are examples of the errors of Rule I., in the length of a circular are equal to an elliptic quadrant, the major semiaxis being unity :— True length Approximate length by Rule I. (from Eccentricity. = ice? ; pas: ia | Tables). [TW0,intervals| pyyors, | Three intér- | rors, NS 13506 1:3538 0032 1:3520 0014 0-6 ]-4184 1:4195 0011 1:4186 0002 0:5 14675 | 14681 | 0006 | 1-4678 | -0003 Glasgow University, November 19, 1864. VI. Supplement to a Paper on Stream-lines*. By W: J. Macquorn Ranxine, C.H., LL.D., F.R.SS.L. & E. [With a Plate.] 27. Nie following is a demonstration of the proposition, stated in an Addendum to the previous paper, that all waves in which molecular rotation is null, begin to break when the two slopes of the crest meet at right angles :— The profiles of the layers of a series of waves are converted, as is well known, into undulating stream-lines by supposing * In the Philosophical Magazine for October 1864. 26 Dr. Rankine on Stream-lines. — the actual motion of the particles of water to be combined with a uniform translation equal and opposite to the velocity of pro- pagation of the waves. . Thus, let —e be the velocity of the waves propagated m a negative direction, as indicated by the arrow W in Pl. I. fig. 4 and, as in article 13 of the original paper, let e(u—1) and ev be the horizontal and vertical components of the actual velocity of a particle of water in the waves, so that cu and cv shall be the components of the velocity of the same particle in the undulating stream into which the waves are converted, and which flows in a positive direction, as indicated by the arrows S, S!. . The tangent of he slope of a stream-line or wave-line ane point is obviously — ~ The crest of a pay ets is a pout where v=O and uw isa minimum. The latter property distinguishes it from the trough, where v=0 also, but wu is a maximum. The equations of a crest are as follows :-— du 9=05 ai =; A wave begins to break so soon as its crest ceases to be rounded and becomes angular, as at C in fig. 4; and at such a point it is evident that w must vanish as well as v. The ratio of two quantities which vanish simultaneously is equal to the ratio of their differentials. Hence the equations of a sharp crest, mm ad- dition to the equations (I.) and (II.), are the followmg :— dv dt wv eT ay ae dt incur 3 abe d By putting for A the equivalent operation cu dg oe dy’ the preceding equations are transformed into the following. At every crest v=0 : : ‘ (1.) du du ua +y Jy 0; - a) w=0jiso'a: © aisle eee wee dv dx” dy _ 0 “di Ga. bee ee = MIN) u v— 6S Dr. Rankine on Stream-lines. 27 Hquation (1V.) may be reduced to the following form :— dv vjdv du\ wv du | ie — Ta —— 7) ad ue s dy =0. (IV. A) The well-known equation of continuity is du dv Ero hap esa 1h, Otek eh kako) which reduces (LV. 4) to the following : | dv du v du v Ene ee ea VD) whose two roots are as ae : dvd v dx dx? ; --Ees/ du t ae Eset = ANE.) dy dy? and those two roots are i tangents of the slopes that meet at the crest. It is known that in a perfect fluid the quantity known as the mo- ' evdi, AD 4% lecular rotation, or sy — =) 51s either nothing or a constant for each stream-line. The present proposition refers to the case in which . hi ido. 7p an Dn-g rpa, He and consequently the tangents of the two slopes are the two values of the eer (VIL) 2 D -E2J We aie ee8 er iatie) dy? but the product of those if values is =—1; therefore at every sharp or breaking crest of a wave in which there 1s no molecular rotation, the two slopes meet each other at right angles. Q. H. D. 28. The preceding demonstration applies to all waves what- soever in which molecular rotation is null. In waves which, besides having that property, are symmetrical at either side of the crest, each of the slopes which meet at the crest of a wave on the point of breaking is inclined at 45° to the horizon. 29. The figure (which is reduced from a diagram exhibited at the late Meeting of the British Association) represents one-half of a forced wave, such as has been described in articles 13 and 28 Dr. C. K. Akin on Calcescence.. 14 of the previous paper. At C is a right-angled crest; and the full line traversing C is that for which b=1. The dotted continuations of the same line above C satisfy the same equation, but do not belong to any possible wave-surface. The full lines below C are wave-lines for which 0 has a series of values greater than 1, viz. 1,4, 1,4, 1,4, &e.; and the dotted curves above C fulfil the same equations, but are not possible wave-lmes. The dotted lines to the right and left of C are stream-lines for which 0 has values less than 1, such as +3, +9, 7%, &c., and are not continuous wave-lines. Glasgow University, November 19, 1864. VII. On Calcescence. By Dr. C. K. Axtn*, re (eee ESCENCE.—tThe radiescent state of substances is known to originate in three different modes, which may be distinguished by the terms Spontaneous Radiation, Pro- duction, and Reproduction of Rays. As spontaneous radiation may be designated all those phenomena of ray-emission to which, apparently, no immediate cause can be assigned, and which, in the last instance, are probably owing to certain velocities im- pressed on the molecules of matter from all beginning, together with certain intermolecular relations, corresponding in some degree to the primitive tangential tendency and attractive forces which sustain the motions of the solar and planetary systems. Under production of rays may be comprised all those pheno- mena of radiation which are engendered by the agency of finite movement, affinity, cohesion, or electricity ; whilst under repro- duction those instances of radiation may be classed which arise from the incidence or communication of rays derived from dis- tant or contiguous sources. 2. Renovation.—The reproduction of rays derived from distant sources, to which it is wished generally to call attention in this paper, may take place under circumstances of a double nature, and is termed accordingly Diffusion (or Reflexion) and Renova- tion—the term diffusion being common and well known, and that of ‘renovation introduced here with a view to avoid future ambiguity. The important distinction which underlies these terms may be best understood from the language employed by Dr. Young for its elucidation (or rather for some more general * Being the abstract of two papers read before the Mathematical and Physical Section of the British Association at Newcastle, in August and September 1863. Reprinted, with additions and verbal corrections, from No. 39 of the ‘ Reader’ (September 26, 1863). N.B. Paragraphs newly added. will be enclosed within brackets. } . Dr. C. K. Akin on Calcescence: 29 purpose) :—“ It seems highly probable,” he says*, “that light and heat occur to us each in two predicaments, the vibratory or permanent, and the undulatory or transient state—vibratory light being the minute motions of ignited bodies, or of solar phosphori, and undulatory or radiant light the motion of the ethereal medium excited by these vibrations—vibratory heat being a motion to which all material substances are lable, and which is more or less permanent, and undulatory heat that motion of the same ethereal medium, which has been shown by Mr. King and M. Pictet to be as capable of reflexion as lght, and by Dr. Herschel to be capable of separate refraction.” The distinction thus clearly drawn between the separate offices of matter and ether, with reference to radiation upon the whole, is particularly applicable to those which regard the phenomena of ray-reproduction—the “undulatory or transient ” reproduction, or, in current parlance, diffusion, being attributable to the agency of ether, and the “vibratory or permanent” reproduc- tion, or, as designated above, renovation, to the intervention of matter. _ 8. Transmutation.—Of the many phenomena of nature which belong to the domain of renovation, only two (or, rather, one only) have been hitherto investigated—namely, fluorescence and the cognate phenomenon of phosphorescence. Fluorescence may be defined as a case of renovation in which the emitted rays belong to the order of the visible, and the incident, which are the cause of the emitted, either to the same order, or to a higher order, as regards refrangibility, and where emission apparently ceases with incidence; while phosphorescence has to be consi- dered as a case of fluorescence, distinguished from ordinary fluorescence by a sensible protraction of emission beyond the duration of incidence. The phenomena of fluorescence, if not of phosphorescence, are specially interesting from their having evidenced the change of refrangibility to which rays are liable in the act of renovation— visible rays having been transmuted by the agency of fluores- cent matter into visible rays of different colour, and invisible rays actually transmuted into visible rays. As will presently be shown, however, the range of possible transmutations has been hitherto far from exhausted; and besides the transmutations observed in fluorescence, a number of others seem @ priori capable of being effected, some of which it would be highly interesting to realize. For this purpose it is first necessary to consider the constitution of the spectrum of a solar or other similar beam of rays. Any such spectrum, as is well known, * Phil. Trans. for 1802, p. 47. T See English Cyclopedia (Arts and Sciences), vol. iv, p. 124. 30 Dr. C. K, Akin on Caleescence. consists of three compartments, of which the median takes in the visible rays, and the two others, respectively, the rays of greater refrangibility and of less refrangibility than corresponds to visible or ight-rays. In order to avoid circumlocution, and the ambiguity which attaches to the terms actually in use, it is proposed. to adopt in the sequel the following nomenclature for the above-mentioned three classes of rays. The visible rays will be called Newtonic, those of greater refrangibility Ritteric, and finally those of smaller refrangibility Herschellic—the name being formed in each case from that of the discoverer of the particular class of rays. By means of this nomenclature it is _ easy to give a complete list of the transmutations of rays @ priori possible, and eth accordingly 1 is here appended :— (nore 10NS. (1) Of Ritteric rays into Ritteric rays of less refrangibility. - (2) Of Ritteric rays into Newtonic rays. (3) Of Ritteric rays into Herschellic rays. (4) Of Newtonic rays into Newtonic rays of less refrangibility, (5) Of Newtonic rays into Herschellie rays. ) Of Herschellic rays into Herschellic rays of less refran- gibility. (7) Of Herschellic rays into Herschellic rays of greater re- frangibility. (8) Of Herschellic rays into Newtonie rays. (9) Of Herschellic rays into Ritteric rays, (10) Of Newtonic rays into Newtonic rays of greater refran- eibilit (11) Of ne rays into Ritterie rays. (12) Of Ritteric rays into Ritteric rays of greater ae ibility. 4. Degradation and Elevation.—Of the enumerated twelve species of transmutations, the phenomena of fluorescence and phosphorescence afford only instances under (2) and (4); for, as previously stated, these phenomena consist im an emission of light, or Newtonic rays, consequent upon the incidence of either Newtonic or Ritteric rays, subject to the law that m.every case the refrangibility of the emitted rays is less than that of the — incident. This law, which has particular reference to those cases where the incident rays are Newtonic ones, has been found to obtain without exception in all known examples both of fluor- escence and of phosphorescence* ; and, since it comes of itself _* See Phil. Trans. for 1852, p. 499; and Ann. de Chim. et de Phys. vol. lv. pp. 114 and 117 (1859). In a few imstances the meident and emitted rays have been found to be of equal refrangibility. Nice SCD Dr. C. K. Akin on Calcescence. ot true whenever the incident rays are Ritteric ones, the presump- tion has arisen that only such transmutations may actually occur in nature as involve a decrease of refrangibility in the emitted ray as compared with the incident. If such were the case, it is evident that the species of transmutations instanced above from under (1) to (6) would alone be possible, whilst the remainder would be impossible by the nature of things. Among the transmutations the possibility of which is thus more or less directly negatived, the species (8) and (10), forming in some sense the counterpart of those properly comprised under fluores- cence and phosphorescence (namely of (2) and of (4)), it would undoubtedly be of the greatest importance to effect. A simple consideration of well-known facts will show that the transmu- tations (8) and (10) may probably be effected. 5. Calcescence-—The metals, by Professor Stokes, are classed among non-fluorescent substances*, and by M. EH. Becquerel, to whom, as is well known, the most delicate observations on phos- | phorescence are due, among non-phosphorescent substances t— Professor Stokes having been unabie to elicit Newtonic rays from | metals by the means found efficient with fluorescent substances, | and M. Becquerel having been unable to detect any persistency of luminosity in metals exposed to the treatment of the phospho- roscope. On the other hand, it is well known that metals may | be rendered self-luminous or incandescent by contact with flames of high temperature, by electrical and other means; and, though | m0 experiment appears to be on record affording clear evidence of the fact, it is impossible to doubt that the same effect might also be produced by solar radiation of sufficient intensity. If this latter assertion be founded on truth, it must be evident that all metals, in the wide sense of the word, are fluorescent, and most probably also phosphorescent ; for of these phenomena no other definition can for the present be given than that of an emission by renovation of luminous rays on the part of sub- stances irradiated from without, which would clearly be appli- eable to the case of any metal rendered incandescent by means of insolation. Or, if the definitions of fluorescence and phos- phorescence be restricted so as to apply only to facts of the same order as hitherto discovered, namely, to emissions by renovation of luminous or Newtonic rays, on or after incidence of either Newtonic or Ritteric rays, even in that case it may be shown that the metals have a claim to be classed among fluorescent, and then most probably also among phosphorescent substances. Every kind of radiation possesses, with respect to any given * Phil. Trans. for 1852, p. 516—* Metals proved totally insensible.” . + Ann. de Chim. et de Phys. vol. lvii. p. 45 (1859)— Les métaux n’ont donné jusqu’ici aucun effet appréciable.”” ee Dr. C. K. Akin on Calcescence. substance, a certain heating power, which depends (1) on the amplitude of the given ray, (2) on the absorptive power of the given substance for the given ray, and (3) m some unknown manner on the length of undulation of the given radiation. Any kind of radiation may hence be competent to raise any substance whatever to any required temperature by a suitable adjustment of the element of amplitude alone, provided the substance consi- dered be not absolutely pervious to, or an absolute reflector of, the given radiation; more particularly must any species of New- tonic or Ritteric radiation be competent to raise any metal to the fixed temperature of incandescence, if the radiation have sufficient amplitude and be not of that quality which exception- ally may render it liable to absolute reflexion. The conclusions here stated are warranted by all our present knowledge regard- ing the nature of heat, temperature, and radiations. For, how- ever small may appear the calorific effect of the more refran- gible part of an ordinary solar spectrum—whether this be owing to the comparatively small amplitude of the radiations compo- sing it (which we are unacquainted with), or to the peculiar nature of the undulations, which renders them less absorbable or otherwise unfit to produce as great heating effects as the less re- frangible radiations, independently of the effects of dispersion—in no case where actual absorption takes place can this heating effect be absolutely nought*. But metals, by the teaching of experience, do absorb both Newtonic and also Ritteric rayst, the heating effect of which, by an increase or addition of amplitude, may hence be augmented to any wished-for degree, and more parti- cularly be made to result in incandescence—theoretically, and saving practical difficulties. The above considerations clearly demonstrate that, if no other reasons militated to the contrary than the apparent results arrived at by experimenters, it were right to class the metals among fluorescent and also among phosphorescent substances; and, in the next place, what is even more important, that, by means of metals at any rate—and probably by the very substances hitherto distinguished as fluorescent—the opposite transmutations of those which are ordinarily effected by fluorescent matter, and which were believed to be alone possible, might be realized. For it will be evident that incandescence, or an emission of New- tonic rays, which, as proved, might be engendered even by Rit- * Compare the interesting experiments and remarks by Dr. Draper, in Phil. Mag. vol. i. pp. 93-95 (1851). [It is supposed of course that the ab- sorption does not produce any chemical or other similar effects. | 7 With regard to Newtonic rays, the colour of metals is a sufficient proof of their absorptive power. For proof of the absorptive power of metals with regard to Ritteric rays, see the observations by Prof. W. A. Miller, im Proe. Roy. Soc. No. 51. p. 163 (1862). Dr. C. K. Akin on Calcescence. 30 teric rays, will be still more easy to produce by means of Her- schellic rays, to which, for some reason or other, a greater heat- ing power is universally acknowledged to belong, as it will be possible also to produce by any given luminous or Newtonic radiation incandescence of such intensity that some of the New- tonic rays emitted should exceed in refrangibility the incident. In other words, through the production of incandescence by irradiation, or more particularly insolation, the transmutations previously denoted by (8) and (10) might be accomplished. 6. Experiments.—To test the exactness of the preceding infer- ences, the author, conjointly with Mr. G. Griffith, Deputy-Pro- fessor of Experimental Philosophy in the University of Oxford, has instituted the following experiments. At the focus of an ordinary concave glass mirror, measuring some 2’ across*, __ and irradiated by the sun, a piece of platinum-foil was exposed, | attached to the bottom of an opake tube, so that the back side | of the foil might be observed free from the interference of any | extraneous light, such light only being seen as the foil itself | might emit on becoming incandescent. On days of powerful sunshine the platinum became vividly incandescent, and, viewed by means of a pocket-spectroscope (which was inserted in the above-mentioned tube), a spectrum exhibiting all the visible or | Newtonic rays might be observed. On placing, however, in the path of the reflected cone of rays, between the mirror and its focus, a sheet of monochromatic red glass (which, of all sub- stances capable of absorbing the more refrangible part of the spectrum, allows the less refrangible part perhaps the freest ' aecess), the incandescence was found to be extinguished, or at "Teast to become so faint as to be of doubtful visibility. It was ; needless to try, under these circumstances, whether the rays _ reflected by the mirror were capable of producing incandescence -after having traversed a diaphragm allowing access only to Her- schellic rays, and absorbing all the rest. Having found the mirror by itself thus far imefficient, it was intended to resort to an expedient founded on the following con- siderations. Let the heating effect of the rays transmitted by the diaphragm of red glass, in the above experiment, be desig- nated by a, and that of the rays absorbed by the same by £. It having been found, as mentioned before, that («+) was sufficient for the production of incandescence, let the experiment be made as first described—that is to say, the mirror be ex- posed to the sun, the platinum placed in its focus, and the red glass be interposed—but let the platinum besides be connected with a galvanic battery capable of replacing to it the heating effect 8, lost by absorption in the diaphragm; then it appears \ * [The principal focal distance was 23’. | Phil. Mag. S. 4. Vol. 29. No. 193. Jan. 1865. D | 34 Dr. C. K. Akin on Calcescence. necessary that the platinum should become incandescent as here- tofore, when irradiated by the whole cone of rays which is found concentrated at the focus of the mirror. An experiment of this nature (which supposes besides that 8 by itself is not competent to produce incandescence) would be open, however, to exception, in consequence of the dependence of electrical resistance on tem- perature ; but it might be varied in the following manner, in which it. would become entirely unexceptionable. The apparatus being all arranged as above, let an opake screen be at first inter- posed between the mirror and the platinum in its focus; but, on the other hand, let the platinum be rendered incandescent by the agency of the galvanic battery alone with which it is con- nected. Then, breaking this connexion, let the moment be seized at which the platinum, though still hot, ceases to shine, and let at the same instant the screen mentioned above be removed, so as to allow the rays reflected from the mirror to impinge upon the platinum, after having traversed the red diaphragm. These rays being of sufficient calefactory power (as found upon trial) to burn dry paper and pieces of wood, will presumably be com- petent to revive the incandescence of the platinum, if dexterously applied at the very moment of its extinction. The experiment being made either in the first way or in that just described, it would be necessary to observe whether the incandescence pro- duced is visible if looked at through an eye-glass of such a nature as-to be certain that all rays of equal or less refrangibility than those transmitted by the red glass are absorbed, whilst only such as are of higher refrangibility are permitted to reach the observer. Such a medium might be found in certain varieties of green glass, which absorb all the rays of the spectrum of lower refrangubility than the hne D—supposing the so-called monochromatic red glass transmitted only these very rays, and none of greater refrangi- bility. This is generally supposed. On looking, however, at the sun with a pocket spectroscope through the very deepest red glass, it was easy to notice that, besides the rays mentioned, it transmitted, under the circumstances, rays of greater refrangi- bility, extending towards the blue region of the spectrum, but separated from the red and orange by a perfectly dark band; so that it became at least doubtful whether this and other red glass, on being employed for the above experiment in the way described, might not allow rays of higher refrangibility to impinge on the platinum than the green glass is capable of absorbing. The in- vestigation of this pomt and other untoward circumstances did not allow of the experiments suggested to be performed in time to be communicated, except as a project, to the Association*, * The Association have since placed at the disposal of the author and Mr. G. Griffith a grant of money to carry out the experiments suggested by him with a more powerful mirror than wasemployed in the above-described trials. Dr. C. K. Akin on Calcescence. 35 One interesting observation, made in the course of preparing for the preceding experiments, may be worthy of mention. The platinum being rendered incandescent in the focus of the mirror by insolation, a film of water of some 2” thickness, contained between thin sheets of glass, was interposed, and no other dia- _ phragm, when the luminosity of the platinum quite disappeared, just as upon the interposition of the red-glass diaphragm. By the experiments of Masson and Jamin*, the absorption exerted. by glass and water of the thickness described upon the visible or Newtonic rays is extremely small, and according to Professor W.A. Miller+ the same may be pronounced also with regard to the absorption of the Ritteric rays; but, on the other hand, it is well known that glass, and even more so water, very power- fully absorb the invisible Herschellic rays. It is evident,therefore, that the sudden disappearance of the incandescence of the plati- num-foil upon the interposition of the above water-and-glass diaphragm is owing mainly to the abstraction of a great amount of Herschellic rays from the incident beam. Hence it is proved that in the first-deseribed experiment, where all the three species of rays impinge upon the platinum, the Herschellic rays contribute to the production of incandescence—that is to say, of luminous or Newtonic rays—though this does not actually prove that Her- schellic rays by themselves are capable of causing incandescencet. It might, besides, be objected to the above inference, that the ceasing of incandescence, in the case described, might possibly be owing to the loss of luminous and other rays by reflexion at the several surfaces of the diaphragm which had been interposed. This objection, however, may be obviated by simply remarking that, upon employing a thinner film of water—the diaphragm being otherwise similarly constructed, and therefore involving the * Comptes Rendus, vol. xxxi. p. 14 (1850). + Proceedings of the Royal Society, No. 51. { [A diaphragm of green glass acts in the same manner as the water diaphragm ; that is to say, by interposing such glass between the mirror and the platinum at its focus, the production of incandescence is prevented, the incandescence making its appearance as soon as the diaphragm is omitted. It might be (and indeed it has been) said that in this case, as in that of the water, the Newtonic rays which are incident originate vibrations, corresponding to Newtonic rays, on the part of the platinum-particles, and that the function of the Herschellic rays which are added (upon the omis- sion of the water diaphragm, for instance) is only to increase those vibra- tions and to render them perceptible. It is difficult to conceive, however, that an agent which is capable of increasing a certain mechanical effect should not be capable also of originating it; and I am therefore inclined to consider the fact adduced in the text, and the corresponding one relating to green glass, as really, though indirectly, proving the possibility of ray- transmutations implying an elevation instead of a degradation of the rays in the scale of refrangibilities. ] D2 86 Dr. C. K. Akin on Calcescence. same losses of radiation by reflexion, but a smaller loss of Her- schellic rays by absorption—the incandescence was found to con- tinue (though of course its brilliancy was weakened) notwith- standing the interposition of the diaphragm. 7%. Transmutation in Comburescence.—Another class of alieno: mena from which corroboration may be derived that transmuta- tions involving an increase of refrangibility in the emitted beam as compared with the incident—and more especially the transmu- tation of Herschellic into Newtonic rays—are feasible, may yet be briefly adverted to. The glow of a platinum wire heldin the flame of a Bunsen’s gas-burner, of carbon particles in the candle- flame, or of lime in the oxyhydrogen-flame, and no less so the phenomena of coloration to which the introduction of substances capable of vaporization gives rise in alcohol or gas-flames, in the opinion of the author, constitute examples of ray-renovation or transmutation in statu nascent2, so to speak, of the rays. In all these instances the matter introduced into the various flames does not produce any new rays by chemical or other means, but acts simply as a renovating and transmuting agent on the rays emitted by the comburescent or ignited gases with which it is n contact*. The above phenomena in so far are, if not identical, still ex- tremely similar to those of ordinary ray-transmutation ‘by fluor- escence; but there is reason to believe that the transmutations which they evidence are the reverse of those effected by ordinary fluorescence. Perhaps the most trustworthy example for the deduction of such an inference is afforded by the case of the oxy- hydrogen-flame and of lime-light. It is well known that the oxyhydrogen-flame by itself is but sparingly visible, and hence poor in Newtonic rays; it has been found to be little active pho- tographically, and is hence rather deficient in Ritterie rays; yet on the introduction of lime into the flame, the well-known brilliant lime-light is emitted, consisting of a dazzling beam of Newtonic rays, which, to conclude from its powerful photo- graphic effects, observed by Professor W. A. Miller}, is probably accompanied by an intense beam of Ritteric rays. As the oxy- hydrogen-flame, from its great powers of calefaction, must neces- sarily emit Herschellic rays abundantly in its natural state, it admits of little doubt that the Newtonic and Ritteric rays engen- dered by the introduction of lime into the flame arise from a *[It may be interesting to learn what was the opinion of Melloni regard- ing the origin of lime-light, &e. He says (La Thermochr. p. 94) :—* Ce phénoméne tient évidemment a une action de masse. Les gaz sont des corps trés légers; s’1ls peuvent réussir & communiquer leur état d’incan- descence aux corps doués d’une plus grande densité, la quantité de lumiére devra nécessairement augmenter.” + Chemical News for March 21, 1863. Dr. C. K. Akin on Calcescence. ya transmutation of Herschellic rays in the very act of emission. By means of a couple of conjugate mirrors, having in one of the foci an oxyhydrogen-flame, and in the other a piece of lime, the phenomenon of the transmutation of Herschellic into higher rays, thus spontaneously occurring in the production of the common lime-light, might be made to assume the ordinary form of fluorescent phenomena. 8. Conclusion.—In the original communication a third class of experiments promising to effect a conversion of Herschellic rays into Newtonic was adduced, which, from its being almost entirely conjectural, shall be here passed over*. There were also several distinctions mentioned, which most probably will divide ordinary fluorescent phenomena from those to which atten- tion has been directed in this paper. To distinguish these latter phenomena from the former, the term Calcescence was suggested to the author, from calcium, the name of the characteristic che- mical constituent of lime, whose action on the oxyhydrogen-flame suggested the preceding speculations and experimental attempts ; and this term might be applied to all phenomena involving an emission of Newtonic rays by the transmutation of incident Her- schellic rays, or generally an emission of rays of increased refran- gibility as compared with the generative incident. [9. Addenda.—(i) The experiments first tried in the summer of 1863, and briefly described in principle in the preceding pages, were resumed with the aid of more efficient apparatus in the spring of the present year. The mirror employed was one of glass, quicksilvered on the back, of 3! aperture and 34! focus. It was supported at the sides by means of two screws passing through two wooden uprights, properly connected to form a stand. At its vertex, or highest point, a socket was fixed to the mirror, in which a flat bar of iron, possessing the form of an elongated S, was made to rest and held firm by binding screws. The free end of this bar reached somewhat further from the mirror than the principal focal distance, whilst its projection on the plane of the mirror fell a little short of the centre of the mirror. ‘To this end of the bar, which was rounded and perfo- rated, a brass ring or clip was attached, by means of a moveable little brass rod held firm by a binding screw. The ring was placed as nearly as possible concentrical with the mirror, and admitted of a wooden tube, which, when placed so that its nearest end was exactly at the distance of the principal focus from the mirror, was held in its position by means of a screw and nut attached to the brass ring or clip adverted to. At the end nearest to the * |The whole of the paper adverted to has appeared since in the Reports of the British Association for 1863. | 38 Dr. C. K. Akin on Coldescancts mirror, the wooden tube referred to, the diameter of which was about 2", was closed by means of two thin plates of slate cut out at the centre, and between which the platinum-foil in- tended to be rendered incandescent was placed. These plates of slate were designed to close up the tube and render it light-tight, holding at the same time the platinum in its place, and prevent- ing as much as possible caloric conduction*; they rested on a slight circle or shoulder on the interior of the tube, and were prevented from slipping or dropping by means of an ivory rmg screwed on the exterior of the tube. This ivory ring bore, at two points diametrically opposite, two angular pieces of brass of this form | , the sborter and vertical limbs of which had binding screws attached, to make connexion with wires leading to a galvanic battery, whilst the longer and horizontal limbs, near their free extremities, bore each a vertical screw with a flat base made of platinum. ‘The bases of these screws could be screwed down, and made to rest upon the exposed face of the platinum- foil—the upper slate being cut out nearly elliptically, whilst the lower slate was cut out circularly, the diameter of the circle being about equal to the short axis of the ellipse. Thus, when the ivory ring was connected with a galvanic battery, the current passed from one of the angular pieces already described, through the platinum-foil (of about 1” breadth, and 1 to 14" length), to the other angular piece +. The tube thus partially described was about 1’ long, and could be connected with another and similar tube of rather greater length than the semidiameter of the mirror—the two tubes, when connected, forming an angle of 90°. At the interior of this angle a piece of looking-glass was placed, making angles of 45° with each of the two axes of the tube{. By this means, * To some extent the plates of course conduct away the heat of the pla- timum. This circumstance, however, is not without advantage, at least in the case of such experiments as before mentioned, in which it was desired to apply solar radiation subsequent to galvanic heating. In these experi- ments it is desirable that the platinum should remain hot, as long as pos- sible, after the galvanic heating has ceased—a result which was materially aided by the contact of the platinum with a substance such as slate, which, having been itself heated at first by the galvanic current, afterwards re- tained its heat much longer than the platinum, and partially conveyed it back to the platinum. + The thicknesses of the foils varied from 5},” to gogy"'3 some of them were of silver platinized. The screws which rested on the foils were suffi- ciently apart not to interfere with the cone of rays incident on the foils. { The whole of the tube consisted of three parts—one angular, and the two others straight. By joining the latter two parts together, of which one supported the foil and the other the ocular diaphragm, the tube could be used for direct vision, without the intervention of reflexion. The angular or bent piece was sheathed on the outside in brass, and the angle itself was eut off by a circular section, leaving a hole into which was fitted a cork, on Dr. C. K. Akin on Calcescence. 39 an observer placed at the end of the tube, which being parallel to the mirror reached just a little beyond it, might see the inner surface of the platinum-foil without casting a shadow on the mirror, although the mirror faced the sun in the most advanta- geous position, viz. so as to concentrate the solar rays at the prin- cipal focus. : Next after the mirror and the tube, the most important piece of apparatus consisted in the diaphragm or diaphragms by which the solar rays were to be sifted. To avoid every objection, it was intended to have these diaphragms a little larger than the mirror itself, and to connect each as it- might be employed late- rally and all round with the mirror, so as to allow of the inci- dence of no rays upon the platinum except such as had previously passed through the diaphragm. Diaphragms of this size, how- ever, and of the qualities required, were not to be procured; and it was thus necessary to employ much smaller ones, which were placed between the mirror and the platinum in frames supported by stands. In this manner some of the rays incident had to pass twice through the diaphragm, first on incidence, and next after reflexion. To obviate the objection arising from the incidence of side-light upon the platinum, it was proposed to employ a truncated tin cone, the base of which was formed by the dia- phragm itself, whilst the apex gave admittance to the tube supporting the platinum*. In this manner, no rays could reach the platinum but such as had previously passed through the diaphragm; but, on the other hand, the cone itself would have cast a shadow on the mirror, if the latter was placed in its most favourable position. The diaphragms to be employed were of three kinds—(]) red glass, (2) black glass, and (3) iodine dissolved in bisulphide of carbon contained between thin sheets of glass. As regards red glass, we succeeded at last in procuring from Birmingham panes of glass about 1! square, which, tested by the pocket-spectro- scope, cut off all rays of greater refrangibility than the line D. When combined with green glass of the deepest tint, red glass of this description made the sun appear red; which showed that the green glass was slightly transparent to red rays, although when tested by the pocket-spectroscope it cut off all rays of less refrangibility than the line D. Hence it is evident that the analysis by the spectroscope in the case of the red glass also which the piece of looking-glass was mounted. When the looking-glass was properly adjusted, the hole was stopped up light-tight by means of a brass cap, which fitted on the cylindrical borders of the hole. * The cone was pierced in two places, to admit of the wires of the bat- tery, properly insulated from the substance of the cone. ’ 40 Dr. C. K. Akin on Colceeeee a could not be wholly relied upon, as regards its absolute imper- viousness to rays of higher refrangibility than the line D*. As regards black glass, Melloni has published the following numbers, showing its relative permeability to rays from different sources, the incident rays being reckoned as 1007 :— Thiskiess: Alcohol- Incandescent OlAame. flame. platinum. millim. Colourless glass ... 0°88 41°2 52°8 70°6 Black glass......... 0°62 52°6 42°38 37°9 Black glass......... 1°84 29°9 2771 25°3 | M. A. Matthiessen of Altona also has published observations, made on the solar spectrum, which prove the permeability of opake black glass (manufactured at Choisy-le-Roi) to the invisible Herschellic rays{. I consequently tried to procure such black glass both from London and Paris, but only towards the end of last summer I succeeded in getting a specimen from Paris, through Mr. Becker; the absorbing and transmitting powers I have not yet been able to test. Finally, as regards the solution of iodine in bisulphide of carbon, my attention was directed to it by a passage in the work on Heat, by Prof. Tyndall, who has recently pub- lished further experiments on the subject. Considering, however, that the iodine solution must always be placed between glass sheets, and that the transparencies of white and black glass for Herschellic rays seem to be nearly equal, whilst extremely thin sheets of black glass seem capable of excluding the light of the most powerful sources§, perhaps black glass, upon the whole, will appear preferable as a diaphragm to the solution of iodine. Another species of diaphragm required, and to be used as an * However, in no case is it possible to be sure that a given radiation is totally absent; all that it is possible to aver is that it is imperceptible. For this reason it is perhaps equally decisive to prove, in such experiments as those that were to be instituted by means of the above red glass, that the radiation emitted is of greater imtensity than the incident, as to prove that the radiation emitted 1s perceptible, whilst in the mcident beam the same radiation 1s apparently wanting—that is to say, possibly only imper- ceptible. It would be necessary, however, in the former ¢ase not merely to cousider the momentary intensity, but to compare the energy represented by the incident rays with the whole of the energy represented by the cor- responding emitted rays, as long as the emission lasts. + La Thermochrose, p. 178. Compare also the coresponding data in pp. 227, 265, 295, 298, 309, and 310. t Comptes Rendus, vol. xvi. p. 763 (1843). § According to Melloni, black glass of the kind employed im the experi- ments above quoted (“such as opticians employ for the construction of polarizing mirrors ”’) is competent to intercept the hight of “the most brilliant sunshine”’ in thicknesses as smallas 0°596 muillim. (La Thermo- chrose, pp. 289 and 310.) Dr. C. K. Akin on Calcescence. 4.] ocular diaphragm when the red glass was used as an objective diaphragm, was deep-green glass. Pieces of such glass were used for insertion within the angular tube near the end where the eye was placed, and were made moveable from without; so that the incandescence of the platinum, when produced, could be viewed either freely or through the ocular diaphragm. It will be seen that our arrangements were pretty well consi- dered. Unfortunately, when our preparations were nearly ma- tured, my collaborator, Prof. Griffith, as it appeared, was not able to give to the subject so much of his time and attention as it required, and towards August this year the experiments were consequently allowed to drop unfinished. (ii) I have stated in a former Number of the Philosophical Maga- zine my probable inability to pursue the subject-matter of this paper any further, at least experimentally*. Meanwhile I will take this occasion to make some remarks concerning experiments on artificial sources of rays. Our first trials at Oxford were made with a couple of brass reflectors and the flame of the oxyhydrogen jet, in the manner before described ; but, no doubt in a great measure from the - imperfect condition of the reflectors, the trials were not successful. It is evident that, instead of a couple of reflectors, a single re- flector might be made to render practically the same service, the flame and the object to be rendered incandescent being respect- ively placed at any two conjugate foci of the reflector. The oxyhy- drogen jet has the advantage in these experiments of being comparatively deficient in Newtonic and Ritteric rays, which might hence be easily eliminated altogether without much detri- ment to the Herschellic rays. On the other hand, gases are known to be but indifferent radiators as compared with solid bodies, as was shown long ago by Mellonit. Hence it might be preferable perhaps to use lime-light for the purposes here in question, instead of the pure oxyhydrogen-flame, as possibly the -Herschellic radiation of lime-light remaining after the Newtonic and Ritteric rays have been eliminated by proper absorbents might surpass in intensity the similar radiation PERI from the pure oxyhydrogen-flame. Lampblack having been shown by Melloni to be a better absorb- ent of nearly all kinds of radiations than chalk or lime {, incandes- cent coal is presumably a more prolific source of Herschellic rays, the temperature being the same, than incandescent lime. For this reason, coal or coke, rendered incandescent either in the * Since this paper was put im type, I have been led to hope, by author- ized members connected with a great scientific society, that means will be found to set my experiments on foot again. + La Thermochrose, p. 94. { Ibid. p. 96. ~~ 42 Dr. C. K. Akin on Caldbcctnada oxyhydrogen-jet* or by electricity might be preferable to lime- hght for the experiments here spoken of. Coke made incandes- cent by electricity, or the so-called electric hght, presents, with regard to the other sources of rays just mentioned, the follow- ing further advantages: —(1) According to Prof. Stokes the spec- trum of electric light is much more extended in the direction of the Ritteric rays than the solar spectrum}. Now, according to Prof. Draper’s observations, the higher the mazimum refrang'- bility of the rays emitted by any incandescent solid substance, the higher is its temperature, and the greater also is the inten- sity of the rays of lower refrangibility{t. Hence it might seem probable that the joimt intensity of the Herschellic radiations emitted by the electric hght are greater than those of the similar radiations emanating from equal parts of the sun§. (2) The temperature of the electric light, or of the coal points by means of which it is produced, is considered to be higher than that of the oxyhydrogen-flame, and consequently also higher that that of lime-light||. I had frequently desired to test the transmitting powers of the various diaphragms before men- tioned by the aid of the electric lamp, but I had no opportunity of carrying out my design {. (i) Other subjects of experiment, which suggested themselves to me from their relation to the principal subject-matter of this paper, I shall point out here very briefly. (1) One of the first questions which arose in my mind in con- nexion with the explanation of the phenomena of lime-light, &c., was whether in consequence of the ray-transmutations therein taking place the total emission of rays was altered. I later found that Melloni had leng ago shown such to be the case im instances where the transmuting agent is a solid. M. Mag- nus, recently, has shown that the same result obtains also in * According to M. E. Becquerel, however, “‘ coke placed in the flame of the oxyhydrogen blowpipe emits a light but little different from that of a piece of magnesia or lime” (Ann. de Chim. et de Phys. 1863, vol. lxvi. roo. + Proc. Roy. Inst. vol. i. p. 264 (1853). { Phil. Mag. vol. xxx. p. 345 (1847). § Compare, however, the experiments of MM. Fizeau and Foucault in Comptes Rendus, vol. xvii. p. 746 (1844) ; and of MM. De la Provostaye and Desains, ibid. vol. xxxi. p. 515 (1850). || See M. E. Becquerel, Joc. cit. pp. 137 & 139. “| I-have reason to know that, within the last month or so, experiments have been made at the Royal Institution on calcescence, by means of the electric lamp, holding out great promise of success. It is stated that ignited magnesium wire, which emits a light of great brilliancy, is rather deficient in radiations of comparatively low refrangibility ; otherwise a magnesium- wire lamp would offer great advantages as to convenience over any of the other sources of rays above mentioned. Dr. C. K. Akin on Calcescence. 43 instances where the transmuting agent is a vapour*. The increase of radiation exhibited in these experiments, at first sight, appears equivalent toa creation of energy; but, upon consideration, it is easy to see that such need by no means be the case. Some direct experiments might perhaps be made on this point. (2) The experiments before described, in which the platinum was to be heated by electricity previously to the incidence of solar rays, together with a remark mentioned below, led me to pro- pose to myself an investigation of the absorptive powers of solids for rays as dependent on temperature t. (3) In my original paper, since published in the Reports of the British Association for 1863, I suggested an explanation of the phenomena of ray-renovation, according to which the rays emitted in the act of renovation are to be considered as resulting from a species of interference between the incident or absorbed rays and the rays spontaneously emitted by the renovating substance. In order to test this view practically, I intended to try the following experiment. Let a fluorescent substance be placed in front of a thermo-multiplier, and between the multiplier and that substance let an absorbing medium be placed, capable of eliminating New- tonic rays of that very description which the substance in question gives out in the act of fluorescence. The caloric equilibrium being established whilst the substance does not fluoresce, it is evident that, as soon as the substance begins to fluoresce, the calorie equi- librium will be disturbed—supposing that in the act of fluores- cence some of the rays originally emitted by the fluorescent matter get, as it were, consumed (as they must in a case of interference), and supposing also that no merely reflected rays are allowed to pass from the fluorescent substance through the absorbing medium on to the pile. (4) Finally, besides some other points not ripe enough to be here mentioned, I purposed to investigate the Herschellic spectra of the principal incandescent gases, that have recently been exa- mined with regard to their Newtonic spectra. I also intended to endeavour to procure thermographic impressions of Herschellic spectra of all kinds. | London, December 1864. Corrigenda. Vol. xxvii. p. 475, lme 7, for § 207, 1. read art. 2071. — p. 477, line 23, for centripetal read centrifugal. * Pogg. Ann. vol. exxi. p. 510 (1864). 7 In Phil. Trans. vol. xxx. p. 977 (1719), it is stated, regarding a certain metallic mirror, that ‘“the glass [7. e. the mirror] growing hot burned with much less force.” This, I thought, might be a proof of the dependence of absorption on temperature, although it is possible to assume that the fact adverted to may have arisen from some other circumstances. iad VIII. On the History of Negatwe Fluorescence. By Joun Tynvatt, F.R.S. &¢.* A COMMUNICATION from the pen of Dr. Akin, pub- lished in the last Number of the Philosophical Magazine, will, I trust, be my excuse for giving the following brief sketch of my relation to the question of “ negative fluorescence ”—a term which may be provisionally taken to express the changing of the refrangibility of the invisible ultra-red rays of the spec- trum so as to render them visiblet. In the month of June 1852, a scientific gentleman, eminent though young, showed me, in his lodgings in Duke Street, Pic- cadilly, the fluorescence of an infusion of horsechestnut bark, and explained to me the nature of the discovery of Prof. Stokes. In the month of September of the same year, L heard Prof. Stokes lecture on this subject before the Belfast Meeting of the British Association. At that Meeting, moreover, a term was employed by the gentleman who had first enlightened me on the subject of fluorescence, which I have never since forgotten. He said that the light was always degraded (meaning thereby that its refrangibility was always lowered) when fluorescence was exhibited. This lowering of the refrangibility was one of the most prom1- nent characteristics of the phenomena brought to light by Prof. Stokes, and it inevitably provoked the opposite question. In common, I| believe, with many of those who had heard the ex- periments described, I soon afterwards inquired whether it was not possible to elevate refrangibility, and thus to render the ultra- red rays of the spectrum visible, as Prof. Stokes had rendered the ultra-violet ones. I believe I am right in saying that though, owing to the total absence of facts, nothing was published on the subject, the ques- tion of a change of refrangibility, in an upward direction, was not an uncommon topic of conversation among scientific men. Inthe year 1859, moreover, the writer already quoted, and who is also referred to by Dr. Akin, wrote as follows :—“ The thought occurs * Communicated by the Author. + This term was introduced by M. Emsmann in 1861, in the following words :—*‘ Starting from the fact that, in the phenomena of fluorescence hitherto observed, a lowering of the refrangibility or an augmentation of the wave-length occurs—a law which can by no means be regarded as firmly established—we cannot deny all justification to the opinion that a kind of fluorescence must also exist, the essence of which would consist in an ele- vation of the refrangibility or a diminution of the wave-length. The former kind of fluorescence would be that of the chemical rays, which I would propose to call positive fluorescence; the latter that. of the calorific rays, which I would call negative fluorescence” (Pogg. Ann. vol. cxiv. p. 652). In 1863 Dr. Akin introduced the term calcescence to express the same thing. Prof. Tyndall on the History of Negative Fluorescence. 45 involuntarily, that phenoména analogous to those of fluorescence may be discovered, the explanation of which would have to be referred, not to a lowering, but a raising of the refrangibility. Such would be the case if the ultra-red rays of the spectrum could be rendered visible, as the ultra-violet ones have been ”’*. During the last six years, or since the commencement of my researches upon radiant heat, this subject has been frequently in my thoughts; and I helped myself, whenever opportunity offered, to form conceptions of the physical processes involved in negative fluorescence, by observations upon waves of water. But other questions, of a more pressing character, compelled me to postpone the definite experimental examination of this one. © Early in the autumn of 1863 I imagined that I had suc- ceeded in proving one of our commonest experiments to be an illustration of a change of refrangibility, in an upward direction. Having, as I conceived, shown the oscillating periods of the mo- lecules in a hydrogen-flame to be ultra-red, I inferred, at once, that the light emitted by a platinum wire plunged into the flame could only be produced by achange of period. It was not, how- ever, a case of real negative fluorescence, for there was no con- version of invisible rays into visible ones. The change of period occurred, as I then phrased it, “before the heat had assumed the radiant form.” Later on in the year I met, at a Philosophical Club dinner, a gentleman whose own experiments had given himthe right to speak with authority in these matters, and I took my place beside him for the express purpose of learning his matured opinion as to the possibility of converting long waves into short ones. I men- tioned to him the observations which I had been making from time to time on sea-waves in the Isle of Wight, and I then first learned that a gentleman named Akin was trying experiments on this subject. The remarks made on this occasion were restricted to the con- version of radiant heat of slow period ito heat of more rapid period. What I then conceived to be my illustration of conver- sion (namely, the change of the slow periods of a hydrogen-flame into the rapid periods of a platinum wire plunged into the flame) was not referred to. About this time; however, the subject was one of those on which I freely conversed with my more intimate scientific friends. To Dr. Debus, for example, I expounded, early in December 1863, the whole question from beginning to end. On the 23rd of January, a clever and interesting article, entitled ‘‘ Calcescence,” was published in the ‘ Saturday Review.’ The author, Dr. Akin, first proposed an entirely new termi- _* Marbach’s Physikal. Lexicon, vol. vi. (1859) p. 1081. 46 Prof. Tyndall on the History of Negative Fluorescence. nology for the phenomena of radiation. The changes of refran- gibility possible to ight and radiant heat were afterwards dis- cussed, and an experiment was described, by which the author proposed to convert the ultra-red rays of the spectrum into visible ones. In that article there was no mention of the form of conversion which I thought had been established by myself; and having at that time occasion to write to the editor of the ‘Saturday Review,’ I mentioned, in my note to him, my having already accomplished that which Dr. Akin proposed to accomplish. Il informed him that my solution was already some months old, and was now on the verge of publication. I requested him, moreover, if he thought fit, to show my note to Dr. Akin. These facts. are distinctly in the recollection of the Hditor of the ‘Saturday Review,’ who is perfectly willing to corroborate what I have here stated. The supposed change of period exhibited by a platinum wire in a hydrogen-flame, constituted a brief episode in my memoir on “ Molecular Physics,’ read before the Royal Society on the 17th of March 1864. Up to that date I had not the slightest notion that Dr. Akin had ever alluded to the subject. During the exposition of my paper I referred pointedly to Prof. Stokes, with the view of eliciting his opmion as to the reality of the conversion. That opinion, clearly expressed and ably sustained, was not favourable to the conclusion at which I had arrived. Prof. Stokes reasoned thus:—“‘ When oxygen and hydrogen clash together to form aqueous vapour, vibrations of the respec- tive atoms, in short periods, result; but these vibrations of the atonuic constituents are soon imparted to the molecules of the compound formed by their union. Aqueous vapour constitutes, in fact, the ‘ashes’ of a hydrogen-flame; on these ashes the rapid vibrations of the single atoms are expended, thus produ- cing heat of dower refrangibility. When a platinum wire is plunged into a hydrogen-flame, it simply takes up the vibra- tions which, in its absence, are imparted to the ashes; hence the possibility that, in its case also, we have a lowering, instead of a raising of the refrangibility.”” In reply to this striking argu- ment, for which I was quite unprepared, I urged that the plati- num might be brought to incandescence at some distance above the tip of the hydrogen-flame, where the vibrations of the atoms might fairly be supposed to have already expended themselves upon the vapour-molecules. Prof. Stokes, however, retained his opinion that the experiment was altogether inconclusive as to the real point in question. After the reading of my paper, I went to the Isle of Wight, and, while there, an abstract of the paper was published in the Prof. Tyndall on the History of Negative Fluorescence. 47 ‘Reader’ newspaper. Immediately afterwards a letter, ad- dressed to me by Dr. Akin, was forwarded to me, in which he drew my attention to what he had previously written, and expressed a desire to see me. I replied to this letter with all goodwill, and my answer, I have reason to believe, is still in the hands of Dr. Akin. After my return to town he called upon me, and among other things directed my attention to a report in the ‘Reader’ of the 26th of September 1863. In this report I found the following passages:—“The glow of a platinum wire in a Bunsen’s gas-burner, of carbon particles in a candle-flame, and of lime in the oxyhydrogen-flame, and no less so the phenomena of coloration to which the introduction of substances capable of yaporization gives rise in ordinary gas- flames, in the opinion of the author, constitute examples of ray- renovation or transmutation in statu nascenti (so to speak) of the rays;” and again, with reference to the oxyhydrogen-flame, “ it admits of little doubt that the Newtonic [visible] and Ritteric [ultra-violet] rays engendered by the introduction of lime into the flame, arise from a transmutation of Herschellic [ultra-red] rays in the very act of transmission.” . On being made acquainted with these expressions, I did not halt to criticise the grounds of Dr. Akin’s “ opinion,” but I at once wrote the following note, which appeared in the next Num- ber of the ‘ Reader ’:— * Athenzeum Club, April 9, 1864. “Through the kindness of its author, I have this day become acquainted with Dr. Akin’s communication to the ‘ Reader’ of the 26th of December 1863. From conversation with Prof, Stokes, I had obtained a general notion of the experiments in which Dr. Akin has been for some time engaged, but I now learn that on one of the points touched upon in the report of my last investigation—the proposed explanation, namely, of the glowing of a platinum wire in a hydrogen-flame—he has antici- pated me by several months. “Joun TYNDALL.” I afterwards learned that Dr. Akin did not wait for me to set matters right, but had promptly put in his own claim on the 2nd of April. I have thus shown how the idea of negative fluorescence entered my mind; I have explained the nature of my mis- take in supposing that I was the first to recognize, in the heating of a platinum wire in a hydrogen-flame, a change of period, and I have described the reparation made when Dr. Akin’s relation to the subject became known to me. It never occurred to me to criticise the scientific method by which Dr. Akin arrived at his conclusions. I believed them to be correct, and 48 Prof. Tyndall on the History of Negative Fluorescence. freely conceded to his insight what I deemed wanting in his data. But now that he talks of my reasoning being the same as his, save that it exhibits the defect of a missing link, let me inquire what is his reasoning, and what is mine? As far as I can see, he does not reason at all. He founds his “ opinion,” that the radiation from a hydrogen-flame is ultra-red, on the defect of brightness which the flame exhibits. Now the flame of hydrogen, and other gaseous flames, have been over and over again compared, by chemists, with flames yielding solid products of combustion, the defective brightness, in those cases where solid matter was absent, being either referred to the extremely dilute character of the radiation, or to the fact that intense combus- tion generated rays of a refrangibility too high for the purposes of vision. What has Dr. Akin done to prove this notion in- correct? Nothing. He never, to my knowledge, made a single experiment on the radiation of a hydrogen-flame. Again, he speaks of the probable paucity of rays of high refrangibility in a hydrogen-flame, as one ground of his conclusions. On this point let us hear Professor Stokes :—‘“‘ It appears that the feeble flame of alcohol is extremely brilliant with regard to invisible rays of very high refrangibility. The flame of hydrogen appears to _aboundininvisible rays of still higher refrangibility” (Phil. Mag.S.4. vol. iv. p. 892). And again—“ The effect of various flames and other sources of light on sulphate of quinine, and on similar media, mdicates the richness or poverty of these sources with respect to the highly refrangible invisible rays. Thus the flames of alcohol, hydrogen, &c. were found to be very rich in invisible rays” (Pro- ceedings of the Royal Institution, vol. i. p. 264). I have italicized sentences which are diametrically opposed to the as- sumed “poverty of rays of high refrangibility,’ on which Dr. Akin, in part, founds his opinion. My “reasoning,” such as it is, is contained in the December Number of the Philosophical Magazine, p. 457, and at pp. 524 to 526 of the December Supplement. I start from the princi- ple that, from the transparency or opacity of any homogeneous medium to the radiation from any source, we may infer the dis- cord or the accord of the vibrating-periods of the source and medium. I illustrate this principle by a series of experiments on carbonic acid, aqueous vapour, and water. First proving the periods of water to be in accord with those of the ultra-red waves, I give reasons for concluding that the periods of a hydrogen-flame are in accord with those of water. Hence the inference that the periods of a hydrogen-flame are ultra-red, and that, when a platinum wire is raised to whiteness by the heat of such a flame, we must have a change of period. Now these experiments, and the reasoning founded on them, Prof. Tyndall on the History of Negative Fluorescence. 49 may or may not be “‘ rigid ;” but, at all events, they are not the experiments and the reasoning of Dr. Akin. The intelligent reader will now form his own estimate of the gravity of my offence when I ventured to put myself forward as an humble corroborator, by reasoning of my own, of views which I stated to have been previously enunciated by another. With regard to my reading habits, I would simply say that it is hardly becoming on the part of a gentleman in his position to lay down the Jaw, on this head, for the hardworking experimenter. ‘Dr. Akin has, thus far, done little but read and write. I do not object to this, but I do object to his compelling me to adopt his habits. As a matter of principle, I reduce my reading to a minimum; and high as my opinion is of the functions of the British Association, I do not pay strict attention to the news- paper reports of its proceedings. This accounts for the fact that, until Dr. Akin drew my attention to it, 1 was not aware of the existence of the passage which he has cited from the ‘Atheneum.’ That passage, however, imposes no new duty upon me; I have already explicitly recognized the priority of Dr. Akin with regard to the point in question. But the reader of the “ Note on Ray-transmutation ” will have already surmised that the seat of its author’s discontent lies far deeper than this question of a platinum wire and a hydrogen- flame. Let us now inquire into his relationship to the real pro- blem, which may be broadly stated thus :— To raise the refrangibility of invisible rays of long period, so a to convert them into visible rays. | This problem would be solved by raising an incombustible body to a state of incandescence, by perfectly invisible rays of low refrangibility. The consideration of the problem at once limits us to those obscure rays of great intensity which are known to be emitted from highly luminous sources; for it would never occur to any one practically acquainted with the subject, to attempt to produce incandescence by rays emanating from an obscure source. The field of experiment is thus narrowed at the outset, and I am only acquainted with two sources which offer any prospect of success. These are the sun and the electric light. The obscure radiation of the sun was established in the year 1800 by Sir William Herschel, who then proved by far the greater portion of the sun’s thermal power to be due to invisible rays of low refrangibility. I am not aware whether anybody but myself has worked at the invisible radiation of the electric hght, but I may say that this subject has occupied me, at frequent intervals, during the last ten years. Limited thus to rays emitted by luminous sources, the two obvious conditions of experiment are the suitable concentration _ Phil. Mag. 8. 4. Vol. 29. No. 193. Jan. 1865. E b | 50 ~——~ Prof. Tyndall on the History of Negative Fluorescence. of the rays, and the removal of the luminous portion of the radia- tion. Thesecond of these conditions constitutes the main diffi- culty ; and we shall presently see whether the mode of surmount- ing it proposed by Dr. Akin entitles him to compare his per- formance with that of the mathematicians “ who first conjectured the existence of Neptune,” and so on. He described before the British Association, assembled at Newcastle in 1863, three experi- ments. In the first of them he proposed to employ two conjugate mirrors; at the focus of one of which he places a piece of chalk or lime, and at the focus of the other an oxyhydrogen- flame. He proposed to cut off “by absorbents” such visible and ultra-violet rays as the flame emits. ‘ Then,” he says, “if the murrors are of sufficient size to render the temperature of the distant focus approximately equal to that of the flame itself, there is eyery reason to believe that the lime therem contained will shine out.” Six years of hard labour at these phenomena of radiation have rendered such proposals rather amusing to me. The “tem- perature at the distant focus” must, of course, be derived from the rays emitted by the oxyhydrogen-flame, which are reflected in a parallel beam by one mirror and concentrated by the other. It never occurs to Dr. Akin to inquire what fraction of the heat of an oxyhydrogen-flame is disposed of by radiation. He does not at the present moment know whether the tenth, the hun- dredth, the thousandth, or the ten thousandth part of the heat of the flame is thus disposed of. What he imagines is plain enough— namely, that, save some slight losses in his “ absorbent” and at the surfaces of his mirrors, the whole heat of the flame is radiated against one mirror and condensed by the other. He entirely forgets that a flame may be intensely hot, and its radiation extremely feeble, and that this, in an eminent degree, is.the case with the oxyhydrogen-flame. It is not the practical difficulties, which Dr. Akin himself discerns, that I am now speaking of ; it is the radical vice of the conception that a purely gaseous flame, placed in the focus of a mirror, however large, could pos- sibly generate a temperature ‘‘ approximately equal to that of the flame itself,” in the focus of another mirror. In his second, and only rational experiment, Dr. Akin pro- poses to concentrate the sun’s rays by a concave mirror, and to withdraw from the focus the luminous portion of the radiation. But then comes the question, How 1s this to be effected? Dr. Akin replies, “by proper absorbents.” This, as far as I know, constitutes his entire answer to the question. In all that he has written upon the subject I have not been able to find a hint of what the proper absorbent is to be. As a proposed experimental demonstration of a point which Prof, Tyndall on the History of Negative Fluorescence. 51 ean only be decided by experiment, Dr. Akin’s third proposition is, if possible, more hopelessly absurd than his first. These are the “ ideas” of Dr. Akin, which I would have gladly let him enjoy, had he permitted me to do so. The fact is, that although he can fairly claim the eredit of first proposing, in public, a definite series of experiments, with a view to the solu- tion of this question, his Note compels me to state that other and more capable investigators, than he has proved himself to be, abstained from proposing such experiments, simply because they saw more clearly than he did the difficulties involved in the practical treatment of the problem. This, I imagine, sufficiently accounts for a fact which appears to have taken him by surprise, namely, that notwithstanding his having pro- posed so “simple” a plan, “he had vainly endeavoured, for nearly a year, to procure for it a practical trial.” The wished- for opportunity at length came, and the practical trial was made. Concentrating the solar rays by a concave mirror 18 inches in diameter, Dr. Akin found that, when no absorbent was intro- duced, a piece of platinum-foii, held in the focus of the mirror, was rendered incandescent. But when he introduced, between the mirror and the focus, a piece of monochromatic red glass, “which of all substances, capable of absorbing the more refran- gible part of the spectrum, allows the less refrangible part the freest access, the incandescence was found to be extinguished, or at least to become so faint as to be of doubtful visibility ’” (Reader, September 26, 1863, p. 349). It is needless to remark that, even had this experiment succeeded, the question would have still remained unsolved; for a sheet of glass, which permits the most powerful rays of the visible spectrum to pass through it, could not be called a “proper absorbent.” He was afterwards joined by the excellent Assistant Secretary of the British Associa- tion, and in his article in the ‘Saturday Review’ expressed the hope, “that in the course of next summer he will bring his experiments to a successful termination.” The summer came, and a better one for his purpose rarely favoured England —strong sunshine, and plenty of it; and what is the result ? Failure, but no abatement of pretension. “Ihave no doubt,” he says, “ that, with the means at his command and his experi- mental proficiency, Prof. Tyndall! will now realize and ‘ publish’ a discovery which I have assigned the methods for accomplishing, and which I should have probably effected myself, I may say, years ago, had I been seconded as I had hoped, either by persons or by circumstances.” Dr. Akin knows perfectly well how safe it is to boast “now” that he could have made the discovery referred to. He has the best possible reason for havine “no doubt,” viz. the sight of his eyes. / K2 52 Prof. Tyndall on the History of Negatwe Fluorescence. As already stated, the obscure radiation from the electric hght has occupied my attention, more or less, during the last ten years. In 1854 I sought by “ proper absorbents ” to separate the lumi- nous from the non-luminous radiation of this source. In 1858 I again tried to do so; and it was only a few days ago that the last remnant of the black glass, prepared for me for this express purpose by the late Mr. Darker, went to pieces in the condensed beam of my electric lamp. It is not my habit, nor doI think it a commendable habit, to sit down and propose experiments which may, or may not, be capable of realization. At all events if this be done at all, it ought to be done in a magnanimous spirit. The true experimenter knows how frequently the most promising ideas are shattered when he tries to realize them. He 1s forced to be an iconoclast from day to day, breaking down the idols on which his hopes were fixed only to be frustrated. Such a manis not likely to sit down and write out experiments at his leisure, with a view to mounting the high horse of “ Neptune,” and claiming the credit, should anything similar be afterwards exe- cuted. My own experience of an experimenter’s difficulties— difficulties which apparently had never dawned upon Dr. Akin when he made his experiments on paper—are referred to in my book on Heat, page 333. This same book, which is an account of lectures given at the Royal Institution a year and a half before the scientific advent of Dr. Akin, shows me in the act of employing such “ proper absorbents” as were then known. At page 307 I describe experiments in which, by means of a plate of rock-salt, coated with the smoke of a lamp, I cut off the lumi- nous portion of the beam from the electric light. I mark, by a rod, the focus of the invisible transmitted rays, and, bringing my thermo-electric pile into this focus, cause the heavy needles of my coarse galvanometer to dash violently against their stops. A similar experiment, with black glass, is described at page 308. But, though this substance transmitted obscure heat much more copiously than the lampblack, the “ absorbents ” which first filled me with hope, if not with confidence, are mentioned at page 351. These absorbents are bromine, and a solution of iodine—sub- stances suggested primarily by my own researches on the deportment of elementary bodies towards radiant heat*. * Many years ago I was accustomed to explode a mixture of chlorine and hydrogen by placing a lens in front of the electric light and a mirror behind it, causing the foci of both to comecide within the flask which contained the mixed gases. Twenty months before Dr. Akin appeared at Newcastle I used substantially the same arrangement in attempting to obtain an intense focus of invisible rays. It was my friend Dr. Debus who, iu answer to my inquiry about a proper solvent for iodine, proposed bisulphide of carbon. I have since tried many other solvents, but have found none so good. Could we obtain carbon in a state of solution, it also might be found highly pervious to the ultra-red waves. Prof. Tyndall on the History of Negative Fluorescence. 53 In the presence of these published facts, which, as far as I can see, were known to me before the name of Dr. Akin was ever asso- ciated with a physical inquiry, will it be believed that I needed this gentleman's “ideas” to inform me what I was to do with the obscure radiation from the electric light? From Dr. Akin, directly or indirectly, I never derived the fragment of an idea for the work that I have accomplished. My work would have been far more completely done, by this time, had he never existed. His value to me has been purely negative, and that to an extent little dreamt of by the readers of the Philosophical Magazine. The real fact, moreover, is, that ten months ago I performed the thankless task of communicating my ideas to Dr. Akin. I then told him that a solution of iodine, in a rock-salt cell, would ena- ble him to stop the solar light with the least possible detriment to the purely thermal rays. I urged him to try the experiment ; but he objected that rock-salt plates sufficiently large could not be obtained. “ Bring your cell near the focus,” I replied, “and you will not require large plates.’ He rejoined that the plates would be destroyed by the heat; I doubted this, but he finally silenced me by the remark, that he had been actually led to try the solution of iodine by what I had stated in my book regarding it, but that it would not answer. It is the use which, fo his know- ledge, 1 have recently made of this very substance that has roused his ire, and impelled him to the unwarrantable attack which he has made upon me in the last Number of the Philoso- phical Magazine. The true motives of that attack do not at all appear upon the face of it; and this leads me to remark that it is the absence of a frank and open bearing, on the part of this gentleman, which has created difficulties between him and me. In fact, had either of us been other than he is, all difference might have been avoided. If [ had been suspicious, I should have kept him at a distance ; if he had been outspoken, we should have understood each other. There are words placed between inverted commas, in his “ Note on Ray-transmutation,’ which no reader of the Philosophical “Magazine can understand—the meaning of which is known to Dr. Akin and myself alone. For instance, the words “ that very subject,” and the word “attack” are extracted from a private letter, already referred to, as written to Dr. Akin from the Isle of Wight. He possesses that letter; [ now expressly ask him to publish tt in extenso. It is a short note, which will more clearly reveal the spirit in which I proposed to deal with this question, than anything I can now say. At the very time when the proofs of my paper “On Lumi- nous and Obscure Radiation,” on which he has bestowed his malevolent criticism, reached my hands, Dr. Akin was con- 54 Prof. Tyndall on the History of Negative Fluorescence. versing with me at the Royal Institution. I broke the cover im his presence, and, finding that it contained a duplicate proof, handed one directly to him; for I wished him to see what I had there said regarding himself, He read that proof betore I did; and though this occurred ten or twelve days prior to the publication of the paper, or about the 18th of October, the first murmur of his dissatisfaction comes, at once to the publie and to me, in the December Number of the Philosophical Magazine. It is not, I believe, the rule of courtesy in this country to publish private correspondence without some mutual understanding, much less to garble it. But I trust I do not offend against this rule by stating that twenty-four hours before Dr. Akin’s article “ On Ray-transmutation ” met the public eye, I received a friendly note from that gentleman, acknowledging some trifling civilities which it had been in my power to show him, but not containmg the slightest intimation of his attack. During the last days of Octo- ber, and the early part of November, there had passed between Dr. Akin and myself a somewhat voluminous correspondence, which, when it ceased to be useful, I was obliged to end, with an understanding, however, that it should be renewed as soon as hisfeelings had calmed down. I rejoiced to think that the friendly communication above referred to was an evidence that the period of calmness had arrived, and I resolved, if such were the case, to give him an opportunity of associating his name with the experiments I had been making on the invisible radiation of the electric light. The vanity of this resolve is now demonstrated. The words “ will now realize and ‘ publish’ a discovery,” used in the last page of Dr. Akin’s article, are also quite characteristic. No one could infer from these words that I had actually, out of consideration for him, waived all right of making my researches known until the rd of November 1865, for the express purpose of giving him the chance of prior publication. I may add that when I entered into this volun- tary engagement, which, by his own deliberate act, he has now dissolved, I had no notion’ that Dr. Akin had any ‘doubt of his ability to give his attention to scientific researches. The followmg brief summary may, perhaps, spare him the time and trouble of further criticism regarding the “ inconclu- siveness ” of my experiments. 1. By sending the beam from the electric lamp through a sufficiently thick layer of iodine dissolved in bisulphide of carbon, the luminous portion of the radiation may be entirely intercepted, and the non-luminous almost entirely transmitted. 2. The invisible rays, suitably converged, form, at their place of convergence, a clearly defined, but perfectly invisible j ager of the coal-points whence the rays emanate. Mr. P. G. Tait on the History of Energy. 55 3. A piece of zinc-foil placed at the focus of invisible rays, burns with its characteristic purple flame. Chemists know that there is some difficulty in causing this substance to blaze, even in a flame of high temperature. 4, Placing a thin plate of a refractory metal at this focus, a space of this metal, corresponding to the invisible image, is raised to brilliant incandescence. 5. When, instead of a metal, a sheet of carbon, placed in vacuo, 18 brought into the focus of invisible rays, the incan- descent thermograph of the coal-points is also vividly formed. Cutting the sheet of carbon along the boundaries of the ther- mograph, we obtain a pair of incandescent coal-points, larger and less intensely illuminated than the original ones, but of the same shape. Thus, by means of the invisible rays of one pair of coal-points, we may render a second pair luminous. 6. By a suitable arrangement of the carbon terminals a metal on which their image falls may be raised to a white heat. 7. The light of a metal thus rendered white-hot yields, on prismatic analysis, a brilliant spectrum, which is derived wholly from the invisible rays lying beyond the extreme red of the source. 8. When the electric light is looked at, directly, through the © solution employed in these experiments, nothing is seen. 9. When, in a dark room, a suitable screen is placed in the focus of invisible rays, nothing is seen. 10. When a solution of sulphate of quinine, or a piece of ura- nium-glass, is placed in the focus, nothing is seen. 11. When the retina of the human eye is placed at the focus, in which metal plates are raised to incandescence, nothing is seen. The injury to my eyes, resulting from this experiment, was, I believe, less than that produced by the night-labour which the writing of this article has imposed upon me. Royal Institution, December 1864. IX. Note on the History of Energy. By P. G. Tarr, M.A.* i the December Number of the Philosophical Magazine, Dr. Akin has called in question the statement that Newton, in a Scholium to his Third Law of Motion, “ completely enunciated the Conservation of Energy in ordinary mechanics.” He calls attention to the circumstance that the words “ in omni instrumen- * Communicated by the Author. 56 Mr. P. G. Tait on the History of Energy. torum usu” which, for brevity, I omitted in the quotation from the Principia, appear to him to alter the meaning and applica- tion of the passage. Now I consider them to involve precisely that restriction [in ordinary mechanics”’] under which I made the assertion about Newton. In fact the three English words form a perfectly complete, though not literal, translation of the four Latin ones. Any rigid body, subject to such forces as pres- sures, gravitation, &c., is really a machine—whether it be em- ployed for mechanical purposes or not. I took care to indicate the omission of this qualifying clause, though it had, in fact, been supplied in my general statement. I regret that the Treatise on Natural Philosophy, on which Prof. W. Thomson and I have been for a long time engaged, 1s not yet published. The portion bearing on my present subject was printed off considerably more than a year ago. I shall not, however, quote from it, but from a ‘Sketch of Elementary Dy- namics ’* published in October 1863 for the use of students in Glasgow and Edinburgh. In that pamphlet—after quoting Newton’s memorable words—we proceed (p. 30), “In a previous discussion Newton has shown what is to be understood by the velocity of a force or resistance ; 7. e., that it is the velocity of the point of application of the force resolved in the direction of the force, in fact proportional to the vartual velocity. Bearing this in mind, we may read the above statement as follows :— “Tf the action of an agent be measured by its amount and its velocity conjointly ; and if, similarly, the Reaction of the resistance be measured by the velocities of its several parts and their several amounts conjointly, whether these arise from friction, cohesion, weight, or acceleration ;—Action and Reaction, in all combinations of machines, will be equal and opposite.” We then show, in passing, that D’Alembert’s principle is dis- tinctly pointed out, and proceed thus (p. 31): “The foundation of the abstract theory of energy is laid by Newton in an admirably distinct and compact manner in the sentence of his scholium already quoted, in which he points out its application to mechanics. ‘The actio agentis, as he defines it, which is evidently equivalent to the product of the effective com- ponent of the force, into the velocity of the point on which it acts, is simply, in modern English phraseology, the rate at which the agent works. The subject for measurement here is precisely the same as that for which Watt, a hundred years later, introduced the practical unit of a ‘Horse-power,’ or the rate at which an agent works when overcoming 38,000 times the * Edinburgh: Maclachlan and Stewart. Pp. 44. Mr. P. G. Tait on the History of Energy. 57 weight of a pound through the space of a foot in a minute; that is, producing 550 foot-pounds of work per second. The unit, however, which is most generally convenient is that which New- ton’s definition implies, namely, the rate of domg work in which the unit of energy is produced in the unit of time. “ Looking at Newton’s words in this light, we see that they may be logically converted into the following form :— “« «Work done on any system of bodies (in Newton’s statement, the parts of any machine) has its equivalent in work done against friction, molecular forces, or gravity, if there be no acceleration ; but if there be acceleration, part of the work is expended in overcoming the resistance to acceleration, and the additional kinetic energy developed is equivalent to the work so spent.’ “When part of the work is done against molecular forces, as in bending a spring; or against gravity, as in raising a weight ; the recoil of the spring, and the fall of the weight, are capable, at any future time, of reproducing the work originally expended. But in Newton’s day, and long afterwards, 1t was supposed that work was absolutely lost by friction.” This shows that, so far as experimental facts were known in Newton’s time, he had the Conservation of Energy complete ; the cases of apparent loss by impact, friction, &c. were not then understood. The opinion of James Bernoulli on a question of this nature would undoubtedly be valuable, but he seems not to have noticed Newton’s remark. But I must protest against the allowing any weight to that of John Bernoulli, who, while inferior to his brother as a mathematician, was so utterly ignorant of the principle in question as seriously to demonstrate the possibility of a perpetual motion, founded on the alternate mixing of two liquids and their separation by means of a filter. I take this opportunity of mentioning, with reference to Mr. Monro’s paper in the December Number of the Philosophical Magazine, that in the very paper by Professor Thomson in which the word “ naturalist ” is used (after Johnson) for Natural Phi- losopher ; Dynamics is divided, as Mr. Monro suggests it should be, into Statics and Kinetics. The same division is employed in the pamphlet above quoted from. 6 Greenhill Gardens, Edinburgh, December 13, 1864. [ 58 | X. On Thermal Radiation. By Prof. Maenus*. | a previous ‘Note on the Constitution of the Sun” +} I communicated the results of some experiments on the thermal radiating powers of sodium, lithium, potassium, &c. These experiments were made so as to compare the radiation of a platinum plate, heated in a Bunsen’s burner, with that of an exactly equal and similar plate covered with fused carbonate of | soda, of lithia, &e. The great radiating power of these substances appeared to be due not improbably to the circumstance that, at the high temperature to which they are exposed, small particles continually detach themselves, which particles produce the in- tense and peculiarly coloured light of the fame. At the moment of detachment these particles may be regarded as so many points ; so that it appeared possible that the radiation might be deter- mined by them or by the roughness of the surfaces of the glow- ing substances. It is well known, in fact, that rough metallic surfaces do radiate more heat than smooth ones—either in con- sequence of the points which they present, or, as Mellonit and Knoblauch § assert, because their density when rough is smaller than when they are smooth. In order to determine whether the greater radiation of sodium and of other similar substances does in reality depend upon the detachment of such small particles, their radiating powers at 100° C. were compared with that of platinum. For this purpose a small apparatus was expressly constructed; it was heated by steam, and to its radiating surface, which had a diameter of 22 millimetres, several plates could successively be attached. The result was, that even at 100° C. a platinum plate covered with fused sodium was found to radiate much more heat than a pla- tinum plate not so covered. It is difficult to obtain exact mea- surements of the relative magnitudes of these radiations, since the cohesion or tendency to the formation of drops is so strong in carbonate of soda that the substance readily flows to one place on the plate, and not only refuses to distribute itself uniformly over the latter, but frequently recedes altogether from certain patches. Nevertheless the experiments were sufficiently accu- rate to prove that the radiating powers of platinum and sodium have a similar relation to each other at 100°, to that which they have at the temperature of a Bunsen’s flame. It follows from this that the great radiating power of sodium, * Fyom the Monatsberichte for August 11, 1864. + Monatsberichte for 1864, p. 166. Poggendorff’s Annalen, vol. cxxi. p. 510. Phil. Mag. S. 4. vol. xxvii. p. 376. + Thermochrose, p. 90, Remark. § Poggendorft’s Annalen, vol. xx. p. 340. Prof. Magnus on Thermal Radiation. 59 and of other like substances, does not arise from the particles de- tached at a glowing heat. The radiating power of these particles is at most very small, in fact much less important than is stated in the “ Note on the Constitution of the Sun” above referred to. New experiments have shown that when all precautions are taken, so that none of the rays proceeding from solid bodies which do not belong to the flame can reach the pile, the luminous soda-flame scarcely radiates more than the non-luminous flame. The particles of soda in the flame suffice, it is true, to increase its lumimosity; but their mass is too small to augment to any great extent the radia- tion of heat. Although these particles are entirely absent at a temperature of 100°, the radiation of sodium relative to that of platinum is just as great when both bodies have this temperature as it is when they are both raised to a glowing heat. Moreover the radiation of platinum itself varies greatly. When a smooth platinum plate is covered with spongy platinum, either by applying strong heat after pouring a solution of am- monio-platmum on the plate, or by precipitating platinum thereon by a galvanic current, its radiating power becomes so great as to equal, and sometimes even to exceed that of sodium. In the experiments with a Bunsen’s flame we might attribute this augmented radiation to the fact that the spongy platinum, owing to its porosity, assumes a higher temperature than does the smooth plate with which the former is compared; the fact, however, is, that even at a temperature of 100° a plate covered with spongy platinum radiates more heat than a smooth one, and that in the same ratio as when the two are heated in a flame. At 100°, however, when the posterior surface of the plate is warmed, the spongy platinum can in no case be warmer than the plate from which it receives its heat. When the spongy platinum is submitted to the pressure of a polishing-iron its radiating power diminishes, and this radiation continues to diminish according as the sponginess is caused more and more to disappear by pressing, hammering, or in any other manner increasing the density. This circumstance, however, cannot be regarded as a proof that the radiation depends upon the density rather than upon the roughness; for as the density of the spongy platinum increases, the roughness of its surface diminishes. The radiation of so-called platinum-black appeared on this account worthy of examination. This substance, as is well known, consists of platinum solely; its molecular constitution, however, differs from that of spongy platinum, its particles being far more finely distributed. This substance, which can 60 Prof. Magnus on Thermal Radiation. only be employed at low temperatures, was difficult to fix, in consequence of its being heated. I could find no better me- thod of securing this fixity than to press platinum-black lightly on a platinum plate which had previously been smeared uniformly with a very thin layer of fat. On afterwards shaking the plate, the black adheres to it uniformly. Plates so prepared radiate about 25 per cent. more heat than when they are covered with spongy platinum. Lampblack, when distributed in a similar manner over a pla- tinum plate, has a radiating power quite similar to that of pla- tinum-black. Whether the thermal colours of the two are the same or different was not examined. The question whether the magnitude of the radiation is or is not determined by the roughness ‘of the surface is an exceedingly important one in every theory which refers the phenomena of heat to motion. Melloni and Knoblauch, in the memoirs already cited, assert that the radiation depends, not on the form (Gestalt) of the surface, but upon its density solely. None of the inge- ious experiments upon which Melloui bases his assertion, is more conclusive than his observation that rough surfaces do not mvartably radiate more than smooth ones; for example, marble, jet, ivory, quartz, gypsum, and some other substances do not, according to this philosopher, radiate more heat when ina rough than when in a smooth condition. I have found, too, that both the white and black varieties of mica (Glimmer von Miask) as well as several non-metallic substances, deport themselves in a similar manner. Alum in a finely powdered condition fuses at 100°, and its fused surface radiates almost the same as does the rough powder. Powdered sugar scarcely radiates more than fused sugar. On the other hand, Melloni admits that metals in the state of chemical precipitates (e. g. when distributed in a finely divided state over the surface of a Leslie’s cube) possess very great radiating powers. Filings (Fezlspdine) deport themselves in the same manner. They, too, increase the radiation very considerably when distri- buted over the rough surface of the same metal. In order to meet every objection : against this experiment, f spread the filings upon so thin a platinum plate that their most prominent points were not nearer to the thermo-electiic pile than was the ante- rior surface of the thicker rough platinum plate with which the filings were compared. This plate, too, was cut from the same piece of metal which furnished the filings. An experiment with aluminium gave like results. This metal in the reugh, as well as in the smooth condition, is a better radiator of heat than either platinum or silver. sete M. de St.-Venant on the Work or Potential of Torsion. 61 Melloni strives also to refer the greater radiation of powdered bodies, wherever it occurs, to a difference in density. He holds that the separated surfaces of the small particles are less dense than is the smooth continuous surface of the same metal. This view is scarcely tenable. It will scarcely be asserted that filings are less dense than the rough surface of the metal from which they are obtained; nor will it be conceded that platimum-black is less dense than spongy platinum, but merely that it is in a state of greater distribution. We shall consequently be com- pelled to assume that in metals the degree of distribution as weil as the density exerts an influence on the radiating power. Whatever may be the condition of the metal, however, which gives the greatest radiation, whether it be one of less density or greater distribution of the substance, we are always compelled to admit that the vibrating particles of the body, and the ether which immediately surrounds them, are less able to communicate their motion to the external ether when the surface of the metal is smooth than when this surface is rough, or less dense, or when the substance on the surface is in a condition of greater distri- bution. An hypothesis might certamly be found to account for the fact that change of density and distribution alter so greatly the communication of the above motion; and from such an hypo- thesis a simple connexion could be easily deduced between the radiation, absorption, diathermancy, and thermal conductibility of bodies. XI. On the Work or Potential of Torsion. New Method of esta- blishing the Equations which regulate the Torsicn of Elastic Prisms. By M. ps Saint-VENANT*, |e general expression for the potential of elasticity per unit of volume-element, that is to say, for the molecular work ® which a deformed element of an elastic body is capable of vielding during its detorsion or return to its natural and primi- tive state —in other words, the formula for the external work performed m forcing this element from its natural state to the actually supposed state of deformation or tension—is a (Pp Ont? 0,1 Pe O T PyzIyz Epes g... + Pay Joy)? 2 (1) where p,,,..-P,, denote the six components, parallel to the rect- angular coordinate axes, of the pressures per unit of surface, on three small faces drawn through the centre of the element per- * From the Comptes Rendus, November 14, 1864. 62 M.de St.-Venant on the Work or Potential of Torsion. pendicular, respectively, to the coordinates a, y, 2; 0. 0, 0, the dilatations, that is to say, the relative clon gakians of ie cle of the elementary parallelopiped parallel to x,y, 2; and 9.5 9,29 Joy the relative slidings, one over the other and per aie of their dis- tance, of the opposite sides ; in other words, the cosines of the three slightly acute angles formed, after the deformation, by the three pairs of adjacent sides of the parallelopiped*. On substituting the values of the six components p, each of which, as is known, is expressible as a linear function of the six elementary and very small deformations 0, g, an expression for ®, of the second degree, is obtained which contains twenty-one terms, involving the squares and products of these quantities. When, as in the case of the simple torsion of a prism around:a longitudinal axis parallel to that of x, the slidings g,,, g,, alone enter into consideration, this expression reduces itself to lk ! D=3(Gg) +2097), ee) where G and G! are the coefficients of elasticity of sliding in the transverse directions of y and z. It may moreover be demon- strated that each of the terms of the last expression is equal to a — of the quantities of work corresponding to a dilatation 29 xy OY 29.9 and to an equal contraction in the directions, mclined to cael other at an angle of 45°, of the bisectors of the right angles enclosed by the axes of x, y and those of 2, z7. The potential of torsion for the volume corresponding to the unit of length of the prism is equal to the integral of the above quantity, previously multiplied by dy dz, extended over the sur- face of a transverse section. The moment of torsion M, however—that 1s to say, the external transverse force capable, when acting at the extremity of a lever whose length is unity, of maintaining around the longitudinal axis a certain acquired torsion @ which shall develope on the sec- tion the tangential components of pressure p,,, p,,—has mani- festly the value M=\\ dy de(p,,Y—Poy 2) 5 «hie ee (8) and if the force thus applied increases from O to the value M, or until the torsion, per unit of length of the prism, has attained the magnitude @, which latter is that of the angle described by * See Comptes Rendus, 1861, vol. lin. p. 1108, or the formula 200 in the complementary appendix to the new (1864) annotated edition of the Lecons of Navier. t+ See the annotated Lecons of Navier, second note of No. 42 of the his- torical part. ‘Mz. de St.-Venant on the Work or Potential of Torsion. 638 one edge of the base of the prism, the work performed will be Ms. On ee In order that this expression may be equal to the one obtaimed by substituting the value of ®, given in (2), in the integral \\ @dy dz, the following condition must be satisfied identically : 7 alta dz(Ggz_+ Giga) = 5 ( (ay dz(G'g,,y—Gg,,2) 3 (5) provided we limit ourselves to the sufficiently general hypothesis of three planes of symmetry of contexture perpendicular to the axes of x, y, Z, in which case Pry = GG ny PEG eh on tee ae) Now, since for the torsion we have du 5 I oy = ae ple EEE ee ata ey on denoting by u the longitudinal displacement parallel to a of the point (y, z) of the section, the equation (5) becomes, by sub- stitution and reduction, | At py ae du du (du ie If we integrate, partially, the first and second terms according toy and z respectively, we shall detach the simple integrals | (acc i _— éz)|_, [ (ayer (S =f ay) | . (8a) where the indices 0, 1 indicate that the difference between the two values of the 4 must be taken relative to the two intersec- tions of the contour of the section by a parallel to y, and by a parallel to z. At these points we have dz= +dscos (n,y), dy=-+dscos (n, 2), where ds denotes the arc-element of the contour and n the direc- tionof its externally drawn normal; so that the two differences (82) become sums of the form {ds ..., extended over the whole con- 64 M. de St.-Venant on the Work or Potential of Torsion. tour. By this well-known mode of transformation, first employed by Lagrange, the equation (8) to be verified becomes . ds KG —62) cos (n, y) + G! (7 an 0y) cos (n, 2) | | d?u du P 9) —6 {fudyae[e aye + G's ='0. ) Now the squares of the second, and of the first parenthesis, each equated to zero, give precisely and respectively the indefi- nite differential equation applicable to all points of a section, and the definite differential equation having reference to points on the contour; which equations I established in 1847 and in 1853, and presented * as containing, implicitly, the whole theory of the torsion of prisms having any base whatever and composed of matter whose contexture was doubly symmetrical, as in the case to which, for simplicity, we have limited ourselves in the above considerations, Moreover, in the several cases of circular, ellip- tic, triangular, equilateral, &c. sections, | obtained by calculation the same value for the potential of torsion from both its expres- sions Sf dy dz and M : It will be seen that He consideration of the potential or work of elasticity completely verifies the general and special results to which I was led, in a different manner, on establishing the theory of torsion. This consideration, moreover, is evidently connected with the methods of the Mécanique Angi lytique employed by Navier in 1821, and recently verified again by several mathe- matical physicists, amongst whom may “be mentioned the re- gretted Clapeyrou; for his theorem, after supplying the for- gotten factor 4, resolves itself to a particular case of the equa- tion (1). The calculation of the potential of torsion has also, im itself, a practical value; for the helical springs frequently opposed to shocks of different kinds, work almost wholly by the torsion of their threads, as I showed in 18438, and as was also remarked by Binet in 1814, and M. Giulio in 1840, and recently by rail- way engineers. * Mémoires des Savants Etrangers, vol. xiv.; or note to the No. 156 of the Lecons of Navier. sos aes XII. Proceedings of Learned Societies. ‘ROYAL SOCIETY. [Continued from vol. xxviii. p. 479. | June 16, 1864.—Major-General Sabine, President, in the Chair. 6 Bt following communication was read :— “Further Inquiries concerning the Laws and Operation of Electrical Force.” By Sir W. Snow Harris, F.R.S., &c. 1. The author first endeavours to definitely express what is meant by quantity of electricity, electrical charge, and intensity. By quantity of electricity he understands the actual amount of the unknown agency constituting electrical force, as represented by some arbitrary quantitative ‘electrical’ measure. By electrical charge he understands the quantity which can be sustained upon a given surface under a given electrometer indication. Llectrical intensity, on the contrary, is ‘the electrometer indication’ answering toa given quantity upon a given surface. 2. The experiments of Le Monnier in 1746, of Cavendish in 1770, and the papers of Volta in 1779, are quoted as showing that bodies do not take up electricity in proportion to their surfaces. According to Volta, any plane surface extended in length sustains a greater charge—a result which this distinguished philosopher attributes to the circumstance that the electrical particles are further apart upon the elongated surface, and consequently further without each other’s influence.’ 3. The author here endeavours to show that, in extending a sur- face in length, we expose it to a larger amount of inductive action from surrounding matter, by which, on the principles of the conden- ser, the intensity of the accumulation is diminished, and the charge consequently increased ; so that not only are we to take into account the influence of the particles on each other, but likewise their opera- tion upon surrounding matter. 4. No very satisfactory experiments seem to have been instituted showing the relation of quantity to surface. The quantity upon a given surface has been often vaguely estimated without any regard to a constant electrometer indication or intensity. The author thinks we can scarcely infer from the beautiful experiment of Cou- lomb, in consequence of this omission, that the capacity of a circular plate of twice the diameter of a given sphere is twice the capacity of the sphere, and endeavours to show, in a future part of the paper (Experiment 16), that the charge of the sphere and plate are to each other not really as 1°2, but as 1:2, that is, as the square roots of the exposed surfaces; so that we cannot accumulate twice the quantity of electricity upon the plate under the same electrometer indication. 5. On a further investigation of the laws of electrical charge, the quantity which any plane rectangular surface can receive under a given Intensity is found to depend not only on the surface, but also on its linear boundary extension. Thus the linear boundary of 100 square inches of surface under a rectangle 37:5 inches long by 2°66 inches Phil. Mag. 8. 4. Vol. 29. No. 198. Jan. 1865. F * 66 Royal Society :— wide, is about 80 inches ; whilst the linear boundary of the same 190 square inches of surface under a plate 10 inches square is only 40 inches. Hence the charge of the rectangle is much greater than that of the square, although the surfaces are equal, or nearly so. 6. The author finds, by a rigid experimental examination of this question, that electrical charge depends upon surface and linear exten- sion conjointly. He endeavours to show that there exists in every plane surface what may be termed an electrical boundary, having an important relation to the grouping or disposition of the electrical particles in regard to each other and to surrounding matter. This boundary, in circles or globes, is represented by their circumferences. In plane rectangular surfaces, it is their linear extension or perimeter. If this boundary be constant, their electrical charge (1) varies with the square root of the surface. .If the surface be constant, the charge varies with the square root of the boundary. If the surface and boundary both vary, the charge varies with the square root of the surface multiplied into the square root of the boundary. Thus, calling C the charge, S the surface, B the boundary, and u some arbitrary constant depending on the electrical unit of charge, we have C=,%S.B, which will be found, with some exceptions, a general law of electrical charge. It follows from this formula, that if when we double the surface we also double the boundary, the charge will be also double. In this case the charge may be said to vary with the surface, since it varies with the square root of the surface, multiplied into’ the square root of the boundary. If therefore the surface and boundary both increase together, the charge will vary with the square of either quantity. The quantity of electricity therefore which sur- faces can sustain under these conditions will be as the surface. If / and 6 represent respectively the length and breadth of a plane rectangular surface, then the charge of such a surface is expressed by «¥ 216 (146), which is found to agree perfectly with experiment. We have, however, in all these cases to bear in mind the difference between electrical charge and electrical intensity (1). 7. The electrical intensity of plane rectangular surfaces is found to vary in an inverse ratio of the boundary multiplied into the sur- face. If the surface be constant, the intensity 1s inversely as the boundary. If the boundary be constant, the intensity is inversely as the surface. If both vary alike and together, the intensity is as the square of either quantity ; so that if when the surface be doubled the boundary be also doubled, the intensity will be inversely as the square of the surface. The intensity of a plane rectangular surface being given, we may always deduce therefrom its electrical charge under a given greater intensity, since we only require to determine the increased quantity requisite to bring the electrometer indication up to the given required intensity. This is readily deduced, the intensity being, by a well-established law of electrical force, as the square of the quantity. 8. These laws relating to charge, surface, intensity, &c., apply more especially to continuous surfaces taken as a whole, and not to surfaces divided into separated parts. The author illustrates this by examining the result of an electrical accumulation upon a plane Sir W. Harris on the Laws and Operation of Electrical Force. 67 rectangular surface taken as a whole, and the results of the same accumulation upon the same surface divided into two equal and similar portions distant from each other, and endeavours to show, that if as we increase the quantity we also increase the surface and boundary, the intensity does not change. If three or more separated equal spheres, for example, be charged with three or more equal quantities, and be each placed in separate connexion with the electro- meter, the intensity of the whole is not greater than the intensity of one of the parts. A similar result ensues in charging any united number of equal and similar electrical jars. A battery of five equal and similar jars, for example, charged with a given quantity =1, has the same intensity as a battery of ten equal and similar jars charged with quantity =2; so that the intensity of the ten jars taken together is no greater than the intensity of one of the jars taken singly. In accumulating a double quantity upon a given surface divided into two equal and separate parts, the boundaries of each being the same, the intensity varies inversely as the square of the surface. Hence two separate equal parts can receive, taken together under the same elec- trometer indication, twice the quantity which either can receive alone, in which case the charge varies with the surface. Thus if a given quantity be disposed upon two equal and similar jars instead of upon one of the jars only, the intensity upon the two jars will be only one-fourth the intensity of one of them, since the intensity in this case varies with the square of the surface inversely, whilst the quantity upon the two jars under the same electrometer indication will be double the quantity upon one of them only; in which case the charge varies with the surface, the intensity beg constant. If therefore as we increase the number of equal and similar jars we also increase the quantity, the intensity remains the same, and the charge will increase with the number of jars. Taking a given sur- face therefore in equal and divided parts, as for example four equal and similar electrical jars, the intensity is found to vary with the square of the quantity directly (the number of jars remaining the same), and with the square of the surface inversely (the number of jars being increased or diminished); hence the charge will vary as the square of the quantity divided by the square of the surface; and we have, calling C the charge, Q the quantity, and S the surface, 2 =e5 which formula fully represents the phenomenon of a con- stant intensity, attendant upon the charging of equal separated sur- faces with quantities increasing as the surfaces; as in the case of charging an increasing number of equal electrical jars. Cases, how- ever, may possibly arise in which the intensity varies inversely with the surface, and not inversely with the square of the surface. In such cases, of which the author gives some examples, the above for- mula does not apply. 9. From these inquiries it is evident, as observed by the early elec- tricians, that conducting bodies do not take up electricity in propor- tion to their surfaces, except under certain relations of surface and boundary. Ifthe breadth of a given surface be indefinitely diminished, F2 68 Royal Society :— and the length indefinitely increased, the surface remaining constant, then, as observed by Volta, the least quantity which can be accumu- lated under a given electrometer indication is when the given surface is a circular plate, that is to say, when the boundary is a minimum, and the greatest when extended into a right line of small width, that is, when the boundary is a maximum. In the union of two similar surfaces by a boundary contact, as for example two circular plates, two spheres, two rectangular plates, &c., we fail to obtain twice the charge of one of them taken separately. In either case we fail to decrease the intensity (the quantity being constant) or to increase the charge (the intensity bemg constant), it being evident that whatever decreases the electrometer indication or intensity must increase the charge, that is to say, the quantity which can be aceu- mulated under the given intensity. Conversely, whatever increases the electrometer indication decreases the charge, that is to say, the quantity which can be accumulated under the given intensity. 10. If the grouping or disposition of the electrical particles, in regard to surrounding matter, be such as not to materially influence external induction, then the boundary extension of the surface may be neglected. In all similar figures, for example, such as squares, circles, spheres, &c., the electrical boundary is, in relation to sur- rounding matter, pretty much the same in each, whatever be the extent of their respective surfaces. In calculating the charge, there- fore, of such surfaces, the boundary extensions may be neglected, in which case their relative charges are found to be as the square roots of the surfaces only ; thus the charges of circular plates and globes are as their diameters, the charges of square plates are as their sides. In rectangular surfaces also, having the same boundary extensions, the same result ensues, the charges are as the square roots of the sur- faces. In cases of hollow cylinders and globes, in which one of the surfaces is shut out from external influences, only one-half the surface may be considered as exposed to external inductive action, and the charge will be as the square root of half the surface, that is to say, as the square root of the exposed surface. If, for example, we suppose a square plate of any given dimensions to be rolled up into an open hollow cylinder, the charge of the cylinder will be to the charge of the plate into which we may suppose it to be expanded as 1:¥2. In like manner, if we take a hollow globe and a circular plate of twice its diameter, the charge of the globe will be to the charge of the plate also as 1: V2, whichis the general relation of the charge of closed to open surfaces of the same extension. The charge of a square plate to the charge of a circular plate of the same dia- meter was found to be 1: 1°13; according to Cavendish it is as 1: 1°15, which is not far different. It is not unworthy of remark that the electrical relation of a square to a circular plate of the same diameter, as determined by Cavendish nearly a century since, is in near accordance with the formulee C= ¥ S above deduced. 11. The author enumerates the following formule as embracing the general laws of quantity, surface, boundary extension, and inten- sity, practically useful in deducing the laws of statical electrical force. Sir W. Harris on the Laws and Operation of Electrical Force. 69 Symbols. ites €-— Ue (eeieal charge ; Q= quantity ; E = intensity, or elec- trometer ae ; S = surface, B = boundary extension, or peri- meter; A = direct induction; 6 = reflected induction; F = force; p= eric. Formule. C « S, when S and B vary together. Ca Q, E being constant, or equal ie C «/S, B being constant, or equal 1. Ca /B, S being constant, or equal 1. C «,/S.B, when S and B vary together. ] Ea sp (Q@ being constant), for all plane rectangular surfaces. Ew — ,S being constant, or equai 1. E« 2 B being constant, or equal 1. E «+, when§ and B vary together. S? i 1 C ae ® E « Q’, S being constant, or equal 1. Q’ : C eg G2" e e ° ° Py . e e ° . In square plates, C « with side of square. In circular plates, C « with diameter. In globes, C « with diameter. A, or induction « 8, all other things remaining the same. The same for 6, or reflected induction. In circular plates, globes, and closed and open s eee ] ] E x —; or as a S F (=E) « ‘ear ForEa =. S being constant. 2 Generally we have F « D" 12. The author calculates from these laws of charge for circles and globes a series of circular and globular measures of definite values, taking the circular inch or globular inch as unity, and calling, after Cavendish, a circular plate of an inch in diameter, charged to satu- ration, a circular inch of electricity; or otherwise charged to any degree short of saturation, a circular inch of electricity under a given intensity. In like manner he designates a globe of an inch in dia- meter a globular inch of electricity. In the following Table are given the quantities of electricity con- 70 Royal Society :— tained in circular plates and globes, together with their respective intensities for diameters varying from *25 to 2 inches; a circular plate of an inch diameter and 1th of an inch thick being taken as unity, and supposed to contain 100 particles or units of charge. Diameters, Circle. Globe. or See | units of charge. || Particles. | Intensity. || Particles. | Intensity. 0:25 25 0:062 35 0-124 0:50 50 0:250 70 0°500 0:75 75 0-560 105 1-120 1:00 100 1-000 140 2-000 1:25 125 1560 175 3'120 1:40 140 =|. | 1/960 196 3°920 1:50 150 2°250 - 210 4-500 1:60 160 2560 224 5'120 1°75 Li, 3060 245 6°120 2:00 200 4-000 280 8-000 13. The experimental investigations upon which these elementary data depend, constitute a second part of this paper. The author here enters upon a brief review of his hydrostatic electrometer, as recently perfected and improved, it being essential to a clear com- prehension of the laws and other physical results arrived at. In this instrument the attractive force between a charged and neutral disk, in connexion with the earth, is hydrostatically coun- terpoised by a small cylinder of wood accurately weighted, and partially immersed in a vessel of water. The neutral disk and its hydrostatic counterpoise are freely suspended over the circumference of a light wheel of 2°4 inches in diameter, delicately mounted on friction-wheels, so as to have perfectly free motion, and be suscep- tible of the slightest force added to either side of the balance. Due contrivances are provided for measuring the distance between the attracting disks. The balance-wheel carries a light imdex of straw reed, moveable over a graduated quadrantal are, divided into 90° on each side of its centre. The neutral attracting plate of the electro- meter is about 14 inch in diameter, and is suspended from the balance-wheel by a gold thread, over a similar disk, fixed on an insu- lating rod of glass, placed in connexion with any charged surface the subject of experiment. The least force between the two disks is immediately shown by the movement of the index over the gradu- ated arc in either direction, and is eventually counterpoised by the elevation or depression in the water of the hydrostatic cylinder sus- pended from the opposite side of the wheel. The divisions on the graduated quadrant correspond to the addition of small weights to either side of the balance, which stand for or represent the amount of force between the attracting plates at given measured dis- tances, with given measured quantities of electricity. This arrange- ment is susceptible of very great accuracy of measurement. The experiment requires an extremely short time for its develop- ment, and no calculation is necessary for dissipation. ‘The author Sir W. Harris on the Laws and Operation of Electrical Force. 71 carefully describes the manipulation requisite in the use of this instru- ment, together with its auxiliary appendages. He considers this electrometer, as an instrument of electrical research, quite invaluable, and peculiarly adapted to the measurement of electrical force. 14. Having fully described this electrometer, and the nature of its indications, certain auxiliary instruments of quantitative measure, to be employed in connexion with it, are next adverted to. First, the construction and use of circular and globular transfer measures given in the preceding Table, by which given measured quantities of electricity may be transferred from au electrical jar (charged through a unit-jar from the conductor of an electrical machine) to any given surface in connexion with the electrometer. The electrical jar he terms a quantity-jar, the construction and employment of which is minutely explained, as also the construction and employment of the particular kind of unit-jar he employs. 15. Two experiments (1 and 2) are now given in illustration of this method of investigation. Huperiment | developes the law of attractive force as regards quan- tity ; which is found to vary with the square of the number of cir- cular or globular inches of electricity, transferred to a given surface im connexion with the fixed plate of the electrometer, the distance between the attracting surfaces heing constant. Experiment 2 demonstrates the law of force as regards distance between the attracting surfaces, the quantity of electricity being con- stant ; and by which it is seen that the force is in an inverse ratio of the square of the distance between the attracting plates, the plates being susceptible of perfect inductive action. From these two expe- riments, taken in connexion with each other, we derive the follow- 2) 2 ing formula, F ae calling F the force, Q the quantity, and D the distance. It is necessary, however, to observe that this formula only applies to electrical attractive force between a charged and neu- tral body in connexion with the earth, the two surfaces being suscep- tible of free electrical induction, both direct and reflected. 16. The author now refers to several experiments (3, 4, 5, and 6), showing that no sensible error arises from the reflected inductive action of the suspended neutral disk of the electrometer, or from the increased surface attendant on the connexion of the surface under experiment with the fixed plate of the electrometer; as also that it is of no consequence whether the suspended disk be placed imme- diately over the fixed attracting plate of the electrometer, or over any point of the attracting surface in connexion with it. 17. Having duly considered these preliminary investigations, the author now proceeds to examine experimentally the laws of surface and boundary as regards plane rectangular surfaces, and to verify the 3 ] formule C—./, 5. B; and K= SB: sity, S=surface, and B=boundary. For this purpose a series of smoothly-polished plates of copper were employed, varying from 10 inches square to 40 inches long by in which C=charge, K=inten- 72 Royal Society :— 2°5 to 6 inches wide, and about 3th of an aoe thick, exposing - from 100 to 200 square inches of surface. The charges (1) of these plates were carefully determined under a given electrometer indication, the attracting plates being at a coe eant distance. Experiment 7. In this experiment, a copper plate 10 inches square is compared with a rectangular plate 40 inches long by 2°5 inches wide. In these plates the surfaces are each 100 square inches, whilst the boundaries are 40 and 85 inches. The boundaries may be taken, without sensible error, as 1: 2, whilst the surfaces are the same. On examining the charges of these plates, charge of the square plate was found to be 7 circular inches, under an intensity of 10°. Charge of the rectangular plate 10 circular inches nearly, under the same intensity of 10°. The charges therefore were as 7 : 10 nearly, that is, as 1: 1°4 nearly, being the square roots of the boundaries, that is, as 1: V2. Experiment 8. A rectangular plate 37°5 inches long by 2°7 inches wide, surface 101 square inches, boundary 80°5 inches, compared with a rectangular plate 34°25 inches long by 6 inches wide, surface 205 square inches, boundary 80°5 inches. Here the boundaries are the same, whilst the surfaces may be taken as 1:2. On determining the charges of these plates, charge of the rectan- gular plate, surface 101 square inches was found to be 8:5 circular inches under an intensity of 8°. Charge of the plate with double surface =205 square inches, was found to be 12 circular inches under the same intensity of 8°; that is to say, whilst the surfaces are as 1: 2, the charges are as 8°5: 12 nearly, or as the square roots of the surfaces, that is, as 1 : 4/2. Experiment 9. A rectangular plate 26: 25 inches long by 4 inches wide, surface 105 square inches, boundary 60°5, compared with a rectangular plate 40 inches long by 5 inches wide, surface 200 square inches, boundary 90 inches. Here the surfaces are as 1 : 2 nearly, whilst their boundaries are as 2:3. Charge of the rectangular plate surface =105 square inches, 7 circular inches under an intensity of 10°. Charge of rectangular plate surface 200 square inches, 12 circular inches, under the same inten- sity of 10°. The charges therefore are as-7:12 nearly, or as 1:1°7, beg as the square roots of the surfaces multiplied into the square roots of the boundaries very nearly. Experiment 10. A square plate 10 inches square, surface 100 square inches, boundary 40 inches, compared with a rectangular plate 40 inches long by 5 inches wide, surface 200 square inches, boundary 90 inches. Here the surfaces are double of each other, and the boundaries also double each other, or so nearly as to admit of their being considered double of each other. Charge of square plate 6 circular inches, under an intensity of 10°. Charge of rectangular plate 12 circular inches, under the same intensity of 10°. The charges, Sir W. Harrison the Laws and Operation of Electrical Force. 73 therefore, are as the square roots of the surfaces and boundaries conjointly, according to the formula C=¥W/S.B, as also verified in the preceding experiment 9. A double surface, therefore, having a double boundary, takes a double charge, but not otherwise. Neglecting all considerations of. the boundary, therefore, the surface and boundary varying together, the charge in this case will be as the surface directly. 18. The author having verified experimentally the laws of surface and boundary, as regards plane rectangular surfaces, proceeds to consider the charges of square plates, circular plates, spheres, and closed and open surfaces generally. Experiment 11. Plate 10 inches square, surface 100 square inches, boundary 40 inches, compared with a similar plate 14 mches square, surface 196 square inches, boundary 56 inches. Here the surfaces are as 1:2 nearly, whilst the boundaries are as 1 : V 2 nearly. In this case charge of square plate, surface 100 square inches, was found to be 8 circular inches under an intensity of 10°. Charge of the plate, surface 196 square inches, 11 circular inches, under the same intensity of 10°. Here the charges are as 8: 11, whilst the surfaces may be taken as 1 : 2, that is to say (neglecting the boundary), the charges are as the square roots of the surfaces, according to the formula C= VS. On examining the intensities of these plates, they were found to be inversely as the surfaces ; thus 8 circular inches upon the plate surface 100, evinced an intensity of 10°; 8 circular inches upon the plate, surface 196, evinced an intensity of 5° only, or 3 the former, 1 =" Experiment 12. A circular plate of 9 inches diameter, surface 63°6 square inches, compared with a circular plate of 18 inches, or double that diameter, surface 254 square inches. Here the surfaces are as 1: 4, whilst the boundaries or circumferences are as 1: 2. Charge of 9-inch plate, 6 circular inches, under an intensity of 10°. Charge of 18-inch plate, 12 circular inches, under the same in- tensity of 10°. Here the charges are as 1 : 2, whilst the surfaces are as 1:4; neglecting the difference of boundary, therefore, the charges, as in the preceding experiments, are as the square roots of the surfaces. On examining the intensities of these plates, they were found to be inversely as the surfaces; thus 6 circular inches upon the 9-inch plate evinced an intensity of 10°, as just stated; 6 circular inches upon the 18-inch plate had only one-fourth the intensity, or 2°-5, according to the formula E= being inversely as the surfaces, according to the formula E=¢- Experiment 13. A circular plate of 9 inches diameter, surface 63°6 square inches, compared with a circular plate of 12°72 inches diameter, surface 127°2 square inches. Here the surfaces are as 1: 2. Charge of 9-inch plate (surface 63°6 square inches), 5 circular inches, under an intensity of 8°. Charge of 12°72-inch plate (sur- face 127°2 square inches), 7 circular inches, under the same intensity 7A Royal Society. . Te of 8°. The charge8 here are as 5:7, whilst the surfaces are as 1:2; that is to say (neglecting the boundaries), the charges are as the square roots of the surfaces. On examining the intensities of these plates, they were found to be, as in the preceding experiments, inversely as the surfaces. — Experiment 14. Comparison of a sphere of 4°5 inches diameter, surface 63°5 square inches, with a sphere of 9 inches, or double that diameter, surface 254 square inches. Charge of ‘sphere of 4°5 inches diameter (oun 63°5 square inches), 4 circular inches, under an intensity of 9°. Charge of sphere of 9 inches diameter (surface 254 square inches), 8 circular inches, under the same intensity of 9°. Here the charges are as 1: 2, whilst the surfaces are as 1:4. The charges, therefore, are as the square roots of the surfaces, or as 1: V4. On examining the intensities of these spheres, they were found to be inversely as the surfaces, or very nearly, being as 2°°5 and 9° respectively. Experiment 15. Circular plate of 9 inches diameter compared with a sphere of the same diameter. Here the actual surfaces are 63°6 square inches for the plate, and 254 square inches for the sphere, being as 1:4. We have to observe, however, that one sur- face of the sphere is closed or shut up; consequently the exposed surfaces, electrically considered, neglecting one-half the surface of the sphere as being closed, are as 1:2, and the exposed surface of the plate is exactly one-half the exposed surface of the sphere. Charge of plate 8 circular inches, under an intensity of 12°. Charge of sphere 11 circular inches, under the same intensity of 12°. The charges, therefore, are as 8:11, or as 1: 1°4, the exposed surfaces being as1:2. The charges, dhewtone, are as le square roots of the exposed surfaces. On examining the intensities of the plate and sphere, they were found to be in an inverse ratio of the exposed surfaces, as in the former experiments. Haperiment 16. Comparison of a sphere of 7 inches diameter with a circular plate of 14 imches, or double that diameter. In this ease the inner and outer surface of the sphere, taken together, are actually the same as the two surfaces of the plate. The imner surface of the sphere being closed, however, as in the last experi- ment, the surfaces of the sphere and plate, electrically considered, are therefore not equal, and the surface of the plate is twice the surface of the sphere. The surfaces, therefore, open to external induction areas 2: 1. On examining the charges of the plate and sphere, they were found to be as 10:14, or as 1:1°4, charge of sphere being 10 circular inches, under an intensity of 20°, and charge of plate being 14 circular inches, under the same intensity of 20°. The charge of the sphere, therefore, as compared with the charge of the plate, is as 1:2, that is, as the square roots of the exposed surfaces. On examining the intensities of the sphere and plate, they were found to be, as in the preceding experiments, in an inverse ratio of Geological Society. 75 the exposed surfaces. We cannot, therefore, conclude, as already observed (4), that the capacity of the plate is twice that of the sphere. 19. The followimg experiments are further adduced in support of the preceding :— Haperiment 17. A copper plate 10 inches square, compared with the same plate rolled up into an open hollow cylinder, 10 inches long by 3-2 inches diameter. Were, as in the last experiments, although the surfaces are actually the same, yet, electrically consi- dered, the plate has twice the surface of the cylinder, one surface of the cylinder being shut up. On examining the charges of the cylinder and plate, they were found to he, as in the preceding experiments, as 1: V2; that is, as the square roots of the exposed surfaces, and the intensities in an inverse ratio of the surfaces, which seems to be a general law for closed and open surfaces. Experiment 18. A hollow copper cube, side 5:7 inches, surface 195, compared with a hollow copper sphere of diameter equal side of cube, surface 103 square inches nearly. On examining the charges of the sphere and cube, they were found to be as 9:10 nearly, charge of the sphere being 9 circular inches, under an intensity of 10°, and charge of cube being 10 cir- cular inches, under the same intensity of 10°. The charges of a cube, and of a sphere whose diameter equals the side of the cube, approach each other, notwithstanding the differences of the surfaces, owing to the six surfaces of the cube not being in a disjointed or separated state. 20. The author observes, in conclusion, that the numerical results of the foregoing experiments, although not in every instance mathe- matically exact, yet upon the whole were so nearly accordant as to leave no doubt as to the law in operation. It would be in fact, he observes, assuming too much to pretend in such delicate experiments to have arrived at nearer approximations than that of a degree or two of the electrometer, or within quantities less than that of :25 of a circular inch. Ifthe manipulation, however, be skilfully conducted, and the electrical insulations perfect, it is astonishing how rigidly exact the numerical results generally come out. GEOLOGICAL SOCIETY. [Continued from vol. xxviii. p. 562.] Nov. 23, 1864.—W. J. Hamilton, Esq., President, in the Chair. The following communications were read :— 1. “ On the occurrence of Organic Remains in the Laurentian Rocks of Canada.” By Sir W. EK. Logan, LL.D., F.R.S., F.G.S., Director of the Geological Survey of Canada. The oldest known rocks of North America, composing the Lau- rentide Mountains in Canada, and the Adirondacks in the State of New York, have been divided by the Geological Survey of Canada 76 Geological Society. into two unconformable groups, which have been called the Upper and Lower Laurentian respectively. In both divisions zones of limestone are known to occur, and of them at least three have been ascertained to belong to the Lower Laurentian. From one of _ these limestone-bands, occurring at the Grand Calumet on the River Ottawa, Mr. J. McCulloch obtained, in 1858, specimens apparently of organic origin, which were exhibited as such by the author in 1859; and other specimens have also been obtained from Grenville and Burgess. ‘These specimens consist of alternating layers of cal- careous spar, and a magnesian silicate (either serpentine, white py- roxene, pyrallolite, or Loganite)—the latter minerals, instead of replacing the skeleton of the organic form, really filling up the interspaces of the calcareous fossil, as was discovered by Dr. Dawson, to whose paper, and to that by Mr. Sterry Hunt, Sir William refers for further details. 2. “On the Structure of certain Organic Remains found in the Laurentian Rocks of Canada.” By J. W. Dawson, LL.D., F.R.S., F.G.S. With a Note by W. B. Carpenter, M.D., F.R.S., F.G.S. At the request of Sir Wm. Logan, Dr. Dawson carefully ex- amined the laminated material thought by Sir William to have an organic origin, and he found it to consist of the remains of an organism which grew in large sessile patches, increasing at the surface by the addition of successive layers of chambers separated by calcareous laminz. Slices examined microscopically showed large irregular chambers with numerous rounded extensions, and bounded by walls of variable thickness, which are studded with septal orifices irregularly disposed; the thicker parts of the walls revealed the existence of bundles of fine branching tubuli. Dr. Dawson therefore concludes that this ancient organism, to which he gave the name of Hozodn Canadense, was a Foraminifer allied to Carpenteria by its habits of growth, but of more complex structure, as indicated by the complicated systems of tubuli; it attained an enormous size, and, by the aggregation of individuals, assumed the aspect of a coral reef. ” In a note, Dr. Carpenter corroborated Dr. Dawson’s observations on the structure and affinities of Hozodn, but stated also that, as he considered the characters furnished by the intimate structure of the shell to be of primary importance, and the plan of growth to have a very subordinate value, he did not hesitate to express his belief in its affinities to Nummulina. 3. “On the Mineralogy of certain Organic Remains found in the Laurentian Rocks of Canada.” By T. Sterry Hunt, Esq., M.A., F.R.§., of the Geological Survey of Canada. Mr. Sterry Hunt first referred to the structure of Hozoon as made out by Dr. Dawson, and then stated that the mineral silicates oc- curring not only in the chambers, cells, and canals left vacant by the disappearance of the animal matter, but in many cases in the tubuli, filling even their smallest ramifications, are a white pyroxene, a pale-green serpentine and pyrallolite, and a dark-green alumino- magnesian mineral which the author referred to Loganite. The Intelligence and Miscellaneous Articles. 77 calcareous septa in the last case are dolomitic, but im the other instances are composed of nearly pure carbonate of lime. The author then gave the results of a chemical analysis of spe- cimens from the different localities, and deduced therefrom the com- position and affinities of Loganite ; this mineral he considered to be allied to chlorite and to pyrosclerite in composition, but to be distinguished from them by its structure. In conclusion, the author showed that the various silicates already mentioned were directly deposited in waters in the midst of which the Eozoén was still growing or had only recently perished, and that they penetrated, enclosed, and preserved the structure of the organisms precisely as carbonate of lime might have done; and he cites these and other facts in support of his opinion that these sili- cated minerals were formed, not by subsequent metamorphism in deeply buried sediments, but by reactions going on at the earth’s surface. XIII. Intelligence and Miscellaneous Articles. REMARKS ON THE LETTER PUBLISHED BY DR. J. DAVY IN THE DECEMBER NUMBER OF THE PHILOSOPHICAL MAGAZINE. To the Editors of the Philosophical Magazine and Journal. Collingwood, Hawkhurst, Kent, ee nt December 12, 1864, i] HAVE received within a few days a copy of Dr. Davy’s letter to you, forwarded to me by its author, of whose publication in your Magazine I was till then ignorant (but which bears the date of Oc- tober 20th, 1864), in reference to certain charges in a late work by Mr. Babbage. In it he expresses an impression that from what he has learned I would not support Mr. Babbage’s statements respecting a certain conversation alleged by him to have taken place at a Council of the Royal Society held on Nov. 23, 1826, between Dr. Wollaston and Sir Humphry Davy—nor indeed respecting a promise alleged to have been given to me by the latter, that Mr. Babbage should become my colleague in the Secretaryship of the Royal Society then vacant and about to be filled up. From the circumstance of Dr. Davy’s sending me a copy of that letter at so considerable an interval after its publication, I cannot but conclude that he is desirous to be confirmed, or otherwise, respecting this his impression ; and that, in fact, I am to regard his doing soas a call on me to that effect. No one can lament more deeply than myself that this subject should have heen revived after so long an interval, when both the principal parties concerned in it, and so many of those more or less cognizant of its details while in progress, are deceased. Were it not therefore that I was myself a principal means of inducing Mr. Babbage to allow himself to be mentioned to the President as a candidate, and thereby of causing to him a disappointment which it appears he felt most severely, I should assuredly decline responding to Dr. Davy’s appeal. In doing so, however, I shall take care to 78 Intelligence and Miscellaneous Articles. confine myself to those precise particulars to which his expressions regarding ‘myself are directed. And first, as regards the conversation between Dr. Wollaston and the President. In a paper in my own hand-writing, which I can, satisfactorily to myself, identify as having been written either on the 24th or 25th November, 1826, certainly not later, I find it written : «The President was distinctly asked by Dr. Wollaston whether he intended to use the privilege, by courtesy accorded to him, of naming the Secretary, to which no one would object, or fairly to throw it open to the Council. His answer to the former part of the alterna- tive was susceptible of any sense that one might choose to put upon it; to the latter, it was both in Dr. Wollaston’s opinion and my own a hegative.”’ Secondly, as to the question whether the President did or did not promise me that Mr. Babbage should be my colleague. He assuredly never did make to‘me that specific promise, nor, so far as I know, to anyone else. What he did promise me (not me only, but others) with regard to Mr. Babbage’s pretensions, was that the question of the succession to the Secretaryship, as between him and his com- petitor, should be referred to the Council; by which I all along understood (as I suppose anyone would) that the relative claims of the candidates on every ground should be fairly taken into conside- ration at one of its regular morning meetings, and come to be decided on as a matter of free election. Under such circumstances I felt quite confident of Mr. Babbage’s success and Jets in assuring him that I did so. In conclusion, it is with the utmost reluctance that I have written the above in connexion with the name of one for whose distinguished talents and services to science I yield to none in admiration, and I entirely appretiate Dr. Davy’s motives in writing the letter which has given occasion to this from, Gentlemen, . Your obedient Servant, J. F. W. Herscaet. P.S.—The above was written on the date it bears. On considera- tion, however, I concluded that it would be wrong for me to appear in the matter unless called on by both parties. ‘This is so far now the case that I have received a letter from Mr. Babbage, requesting me to allow him to publish certain extracts from a letter of mine bearing reference to the ‘‘ promise” or ‘‘understanding’’ above spoken of. Collingwood, Dec. 20, 1864. ON THE DISCRIMINATION OF COMPOUNDS OF SESQUIOXIDE OF MANGANESE AND OF PERMANGANIC ACID. BY HOPPE-SEYLER. The author has discovered in the spectroscope a method of dis- tinguishing the solutions of permanganates from the sesquisalts of manganese, the latter of which have often a similar coloration to the former. H. Rose, who first described the preparation and properties of + ee ee Intelligence and Miscellaneous Articles. 79 phosphate of sesquioxide of manganese, ascribed the purple colour of the liquid obtained in Crum’s method of testing for manganese, by boiling any manganese compound with nitric acid and binoxide of lead, to the formation of sesquinitrate of manganese, and not, as Crum had done, to the formation of permanganic acid. The author has shown in the most decisive manner that Crum’s view is correct. When a solution, not too dilute, of permanganic acid or its potash salt placed in a glass with parallel sides is brought into the solar spectrum, it produces a very powerful absorption of greenish and yellowish-green light. Solutions of sesquiphosphate of manganese exhibit the same deportment. But if the latter is more and more diluted, the obscurity im the middle of the spectrum gradually dis- appears without showing any absorption bands; while dilute solutions of permanganic acid exhibit five distinct absorption bands, of which the first feeble one (starting from red) lies more towards the Fraun- hofer’s line D, the second dark one is in the middle between C and 6, the third, equally obscure, lies upon E reaching to 4, the fourth is between 6 and F, and the fifth and feeblestisin F. These bands are especially distinct when the spectrum is taken on a paper screen. Sesquichloride and sesquisulphate of manganese show quite a similar deportment to the phosphate, excepting that there are new absorptions in blue and violet. The liquid, prepared according to Crum’s method, shows the five absorption bands in the most distinct manner.—Zeitschrift fur Chemie, No. 3, 1864. ON THE CONSTRUCTION OF DOUBLE-SCALE BAROMETERS. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, In a short paper which you did me the favour to insert in your De- cember Number, it was remarked that there was reason to fear that double-scale barometers were not always properly graduated in this country. I was then unaware of the extent to which barometers with incorrect metrical scales have recently been manufactured by the most eminent firms in London. I have in. my own possession a standard barometer, two mountain barometers, and a mountain aneroid by four of our first makers, and in each of these the metrical scale is erroneous, while a mountain aneroid by Secretan of Paris is affected by a similar error in the English scale. My friend Mr. Tuckett of Bristol, who has been investigating this subject simulta- neously with myself, informs me that all his instruments are like- wise inaccurate. The nature of the error may be explained as follows :— Suppose a standard brass yard, divided to inches, at the normal temperature of 62° F., to be laid beside a standard brass metre di- vided to millimetres at the normal temperature of 32° F., with their zero-points coincident. Then by Guyot’s Tables for converting inches into millimetres, at their respective normal temperatures, each inch of the English standard will correspond with 25°39954 millims. and 30 inches with 761°986 millims., or 762 millims. very nearly. 80 Intelligence and Miscellaneous Articles. Next, suppose the temperature of the standard metre to be increased 30° F., and so to be made equal to the temperature of the English standard. | The coetiicient of the linear expansion ; of brass per degree F. being ...... 000 That for 30° willbe “2022 204. 2. ee OO DSi esen Each length of the standard metre which corresponded with the inch of the English scale will have expanded through a space equal to ‘00795 millim., and the length which corresponded with 30 inches through -238 millim. It is manifest that whatever lengths correspond at the temperature of 62° F. will correspond also at all temperatures common to the two scales. We have therefore the following relations :— At the normal temperatures of the standards. At all common temperatures. linch = 25°39954 millims. linch = 25-3916 millims. 30 inches =761°986 As 30 inches =761°748 ss In a large number of double-scale barometers which have recently been examined by my friends and myself, the metrical reading of 762 millims. has been found to coincide exactly with 30 inches, and therefore to be in excess by nearly a quarter of a millimetre. I ac- cordingly requested one of the makers to inform me on what prin- ciple he made the graduation. His answer was as follows :— * DAG 20°42 Coppers BY EM lis) ase teace trace Brora) 9 Seger) eis oy 40205 0:20 Wrsemc 2718 ber wena OA 0-17 -Insoluble gangue. . . 0°30 1:12 , | 26°91 100-66 — 136 Dr. Akin’s further Statements concerning A second analysis gave the following confirmatory results :— acti ete et deo oe ead se ee Oa Coppers re ue Troe VOUS. ee ee alee irsente 200". antes Insoluble gangue . 0°49 100-00 XXIII. Further Statements concerning the History of Calcescence. By Dr. C. K. Axin*. ; 6 Pane last Number of the Philosophical Magazine contains an article ‘Ou the History of Negative Fluorescence,” by Prof. Tyndall, to which I intend herewith to reply. As this is a per- sonal discussion, of course I shall have to allude to personal matters; but, in doing so, I shall endeavour not to imitate the lancuage adopted by Prof. Tyndall towards myself, more or less, throughout his paper. In stating this, however, I do not wish to padi plam of Prof. Tyndall; for, besides that language of this kind always recoils upon the person who uses it, he has adopted the same tone in his discussions with Professors Tait and Thom- son, and in such excellent company I can very well bear Prof. ‘Tyndall’s contumely. 1. It is now probably from eight to ten years ago that, as a student at the University, and the notions which I was then being taught regarding the nature of heat and radiations being rather vague and inaccurate, I proposed to myself the “ conversion of heat into light” as a problem to be solved in the course of my future scientific career. In the year 1860 I attended the Meet- ing of German naturalists at Konigsberg, at which Professor Knoblauch communicated some new researches of his on the interference of Herschellic rays. I then observed to one of the Konigsberg Professors how much more simple experiments of this kind would be if it were possible to convert Herschellic rays ito visible or Newtonic rays, in a similar manner to that in which Prof. Stokes had shown how to convert Ritteric rays into Newtonic rays. In February 1862 I madea stay at Cambridge, when I had the advantage of seeing the principal experiments on fluorescence performed by Prof. Stokes himself... Having then in my possession a little German treatise which contained a short account of all that had been published at that period on the sub- ject of fluorescence, I began to peruse it; and in the course of that perusal the main ideas which I have since published on the * Communicated by the Author, the History of Calcescence. | 137 transmutation of rays occurred to me*. I immediately commu- nicated on the subject with Prof. Stokes, hopimg that he would enable me to bring my speculations to the test of experiment. Prof. Stokes expressed himself in very high terms on the im- portance of the subject—terms which I have since often repeated to others, and which have frequently encouraged me to persevere when my patience was nearly exhausted; and when, towards midsummer 1862, I left Cambridge, he was good enough to ex- press his regret that it had not been in his power to give me an opportunity of making the experiments I had proposed. In No- vember of the same year, 2. ec. 1862, I went to reside at Oxford, and so much was my mind engrossed by the matter in hand, that the very first time I met Mr. Griffith, then, as now, Deputy Professor of Experimental Philosophy in the University, I broached the subject to him, when I was greatly pleased to find that the matter interested him, and that he was ready to make experiments on it with me. Consequently, in the month in question, or early in the December following, we made some trials with the oxyhydrogen jet; and as these gave no satisfactory result, we began to make experiments on the sun a short time after. These latter exper:ments were continued till June 1868, when I drew up a paper on the subject, which I for- warded to the Royal Society. Being called by urgent private matters to town at that time, it was arranged that, during the week or ten days intervening, the experiments, which appeared then to be in a very forward state, should be completed, so that an account of the result might be presented by me to the Royal Society at the last Meeting of the then session. The expectation founded on this arrangement, however, was not fulfilled, and I was consequently advised to withdraw also the mtroductory papers already forwarded for communication to the Royal Society. Although, in consequence of private circumstances * I may as well state now that the article on fluorescence in Cornelius and Marbach’s Phystkal. Lexicon (the work being one intended for popular circulation and for reference, not for perusal) became first known to me from M.Emsmann’s paper on ‘‘ Negative Fluorescence,’’ published in Pog- gendorff’s Annalen in 1861. It so happened that, at the time when this last-mentioned paper appeared, I was staying at Paris, where I had no access to Poggendorff’s Annalen; and when in the following spring I had an op- portunity of seeing the Annafen at the University Library at Cambridge, the volume in which M. Emsmanun’s paper was published was with the binder; so that the paper became actually known to me only m the winter of 1862-63 at Oxford. In my paper in the Reports of the British Asso- ciation, in which I have duly advertead to M. Emsmann’s publications, I did not think it necessary to mention these facts, as they were of no scientific, but only of personal interest. For an appreciation of the contents of M. Emsmann’s paper I must refer for the present to the historical Appendix in the Reports of the British Association for 1863, p. 99. 138 Dr. Akin’s further Statements concerning which then arose, I could continue to give my time and attention to scientific researches only at a great sacrifice, I yet returned towards the end of June to Oxford, in order to complete the ex- periments, if possible, in time for the Meeting of the British As- sociation, which was to assemble towards the end of the August ensuing at Newcastle; yet, although my return originated in previous arrangements, for reasons which have never been ex- plained to me, no opportunity was given me after my return to proceed with the experiments. The suspense which I then un- derwent, my mind being full yet of other pressing anxieties, has left an indelible mark of pain on my memory. This, however, is not now the question; I will therefore merely state that, although greatly depressed and discouraged in mind, I attended in August the Meeting of the British Association; that I read the papers which I had prepared before the Mathematical: and Physical Section ; and that the Committee of the Section, in con- sequence, resolved to recommend the principal paper I had read for publication in eatenso among the Reports of the Association. The Association further resolved to appomt Mr. Griffith and my- self a committee to carry out the experiments proposed by me, for which purpose a special grant was placed at our disposal. In eonsequence of this latter resolution, I again took up my residence at Oxford in the spring of 1864, although at some sacrifice to my feelings; but the proceedings which I ‘had experienced in the summer of 1863, Iam sorry to say, were soon recommenced, and my plans were again defeated. Instead of a report, I was thus obliged to forward to the President of tlie Mathematical and Physical. Section of the British Association, for the Meeting at Bath in September 1864, a letter of which the following is the substance :—‘“I am sorry to have to state that, owing to the scarcity of clear sunshine at Oxford last summer, and to Mr. Griffith being mostly unable to give his time to our work when the weather happened to be favourable to it, the experiments in- tended to have been made were left in August unfinished. I had the greater reason to feel disappointed at such a conclusion, as the methods and apparatus devised for the purpose appeared, from preliminary trials, competent to effect, im part at least, the proposed object, and as our preparations for the more decisive experiments were in a very forward state.” 2. Meanwhile, in the abstract of a lecture delivered by Prof. Tyndall at the Royal Institution, and which was published in the ‘ Reader’ in March 1864, a sentence had attracted my atten- tion which will presently be mentioned. Being then on the point of writing a letter to the editor of the ‘ Reader’ on a different subject, I took occasion to add the following postscript, which, together with the letter to which it was appended, appeared in the History of Calcescence. 139 the ‘ Reader’ of April 2, 1864:—TI profit by this opportunity to call your attention to your report of Prof. Tyndall’s late lec- ture at the Royal Institution. I suppose it was only by inad- vertence that you said, ‘such a change of period [or of invisible, less refrangible, into visible rays|, Prof. Tyndall believes, occurs when a platinum wire is heated to whiteness by a hydrogen flame,’ &c.; for in your own columns of September 26, 1863, that explanation, communicated by me for the first time to the British Association last year at Newcastle, was published in my name,—a fact which I cannot but believe Prof. Tyndall has referred to.” As an afterthought, and as an act of courtesy to Prof. Tyndall, I wrote to him, a day or two after, a private note, enclosing a set of proof-sheets of my paper on Ray-transmuta- tion, then printing in the Reports of the British Association. In answer to that note, I received a letter from Prof. Tyndall, dated from the Isle of Wight, in which he observed on the “ sin- gular coincidence of thought’’ that had arisen between us, and stated that “the piece of work which he had set before him for attack on his return” to town was a series of experiments on “that very subject ” that engaged my own attention. I was somewhat astonished at this latter statement; for, Prof. Tyndall having read, as he himself informed me, the artiale on ‘‘ Caleescence ” in the ‘Saturday Review,’ was aware that the British Association had confided to Mr. Griffith and myself the task of executing the experiments, for which I had submitted the plans. As to the “coincidence,” real or supposititious, between Prof. Tyndall’s “thoughts” and mine, it could extend only to the explanation of the origin of lime-hght ; and Prof. Tyndall neither then nor has he since ever stated that, before reading of my own method in the ‘Saturday Review,’ he had planned any experiments on cal- cescence similar to those I had submitted to the British Associa- tion. Others, before both myself and Prof. Tyndall, had thought that they had recognized phenomena evincing “ negative fluores- cence,”’ and yet were unable to devise, for the purpose of proving its existence, methods analogous to those adopted in the produc- tion of fluorescence. That Prof. Tyndall had guessed for him- self, or perhaps but remembered, the explanation of lime-light, could form no right on his part to interfere with the experiments I had devised, and was then engaged in working out by authority of the British Association. However, Prof. Tyndall’s letter being on the whole written in a friendly and courteous tone, and knowing the value of a conciliatory spirit, I went to see him a few days after, by appointment, at the Royal Institution. Prof. Tyndall then spontaneously stated to me that he wanted to act towards me in an “honourable and gentlemanly” manner, and that he would do what was ‘“‘most pleasing” to me. At the same time, 140 Dr. Akin’s further Statements concerning — with great eagerness, he proposed to me that we should jointly work out the subject to which our correspondence had referred. With this proposal, for which Professor Tyndall’s letter had already prepared me, I closed with an alacrity equal to that with which it had been advanced, reserving only one pomt. I mentioned that, in consequence of the action taken by the Bri- tish Association, I felt bound to proceed with the experiments on sunlight at Oxford, for which the apparatus had already been constructed, and for making which London was scarcely a fit place; so that the experiments to be made by Prof. Tyndall and myself at London were to be restricted to artificial radiant sources. To this condition Prof. Tyndall cheerfully agreed, observing that he had from the first intended to make experiments only on the electric light; that he was consequently quite satisfied with the arrangement proposed ; and that he had anticipated that there would be no difficulty between us to come to terms. After some more conversation, and on rising to leave, I adverted to “ definite arrangements ”’ to be made for the execution of our agreement. Prof. Tyndall then stated that he was just preparing for his lec- tures at the School of Mines, which would take him from four to six weeks; that he found it difficult to give his mind to more than one subject at a time; and that as soon as he had set up any apparatus, he would write to me that I might come up to town from Oxford, he being sure not to make any experi- ments in my absence. On this understanding I left the Royal Institution, and soon after returned to Oxford. Several weeks had elapsed without my having heard from Prof. Tyndall. Having then occasion to write to him on another matter, I got an answer from him, in which occur these words :—“ I have not been able to think of your subject.” Some three weeks after that I received another short note from Prof. Tyndall, in answer to one of my own, stating that he had been too unwell for some time to write to me. From that time further till October last year, I had no news from Prof. Tyndall. In the first days of that month, however, I returned to town for the winter, and I again called at the Royal Institution. Prof. Tyndall then told me that he had set up some apparatus in the summer (two mirrors, I believe), but that he had obtained no results. In answer to his questions, I stated to Prof. Tyndall that it was not likely that I should continue the experiments begun at Oxford ; and I also referred, as far as I properly could, to the understanding that subsisted between us. Prof. Tyndall, in reply, remarked that he did not intend to take up the subject just then, but that I might rest assured that he “would do nothing” without me. A fortnight after that I had occasion to again call on Prof. Tyndall, when he the History of Calcescence. | 14] showed me the proof of the paper since published in the Philo- sophical Magazine for November 1864, and he invited me to read the paper in his presence, while he was perusing his letters. On reading the very first sentences of the proof, I was somewhat displeased by the marked manner in which Prof. Tyndall alluded in them to the “ difference” between his reasonings and my own on the subject of lime-light. I was still more startled to learn that, whilst a fortnight ago I had been informed by Prof. Tyndall that he was occupied with different matters, he should in the meanwhile have attacked a research intimately related to that which had formed the subject of our agreement. I might have expected that, in the experiments on the spectrum of the oxy- hydrogen-flame, concerning which I was the first to enunciate the views which those experiments were intended to test, Prof. _ Tyndall might have invited me to join him, or, at least, to be pre- sent while they were making—the more so as I was then in town, and daily in the Library of the Royal Institution. However, my astonishment increased when I came to the passage in which Prof. Tyndall expressed his resolution not ‘to publish anything relating to the subject” of “ the production of incandescence” by invisible Herschellic rays till the “ arrangements devised by me had had a sufficient trial.” Considering the agreement that had subsisted all along between us, this statement of Prof. Tyndall was rather puzzling to me. Moreover, abstracting altogether from that agreement, I saw objections in the use of the term “to publish.” An unwary reader might assume that Prof. Tyndall, when writing the sentence above mentioned, had already accomplished what I was searching after, but from generosity towards myself would not publish his results. I, who knew better, and other readers, on the other hand, were obliged to assume that Prof. Tyndall imtended to work out the subject privately, and to defer the publication of his results till the period referred to. A proceeding of this kind I considered an unusual one among men of science, and one fair neither to my- self nor to Prof. Tyndall; as it is ‘searcely possible, or perhaps fit, to keep scientific results secret which are arrived at at a public place like the Royal Institution. An observer of physiognomy would have noticed that the impression which the reading of the passages adverted to had made on me was far from ‘favourable. However, I was not prepared to make any imme- diate remarks, and I consequently merely stated to Prof. Tyndall that, regarding the “‘ arrangements ”’ referred to by him in his paper (meaning the experiments on sunlight begun at Oxford), it was unlikely that I should proceed with them for the future. I further inquired of Prof. Tyndall what day he might be at leisure, when I should be ready to “talk over”? his paper with 142 Dr. Akin’s further Statements concerning him, of which he had given me the proof for private perusal. Prof. Tyndall replied that there was nothing to talk over; and, as I had again adverted to “definite arrangements,” he stated that he had no present intention of prosecuting the matter which had been discussed between us. UponthisI left. I had then reason to expect that I should soon see Prof. Tyndall in a more private manner; and had that expectation been fulfilled, all the com- plication that has since arisen would have probably been avoided. However, some nine days had elapsed without my having seen Prof. Tyndall, when on Saturday the 29th of October 1864, hap- — pening to be at the Library of the Royal Institution, I was ad- dressed by Prof. Tyndall, who had come to the Library with an- other person on some business of their own. On the mvitation of Prof. Tyndall, I followed himi to the Laboratory. On my way there Prof. Tyndall said to me, “I have been working on your subject, and I have succeeded ”?—or other words similar in meaning. Arrived in the Laboratory, Prof. Tyndall rendered — in my presence a piece of platinized platinum-foil incandescent by the rays of an electric lamp, transmitted by a layer of bisul- phide of carbon containing iodine in solution. This experiment was far from being unexceptionable, or of demonstrative power ; yet it held out great hopes that the conjectures I had emitted - were realizable in fact, and on seeing it my sense of pleasure was consequently great enough for a moment to obliterate all other considerations from my mind. From this state, however, I was soon after aroused, when, on leaving, Prof. Tyndall addressed me in these (or similar) words:—“ We shall now make our arrangements, at least you shall see what I intend to publish in MS., and then you shall make your remarks upon it.” Let the reader imagine to himself an emigrant from these islands who, after a stormy voyage, has landed on the Western coast of North America. Guided by geological knowledge, he has sought out a remote uninhabited tract, where he has begun to dig for gold. After many months of hard labour, suffering, and privation, unrelieved by the sympathy of living being, and as yet profitless from the imperfection of his tools, the emigrant’s preseverance begins to flag, when, one evening, he suddenly perceives a man in the distance, who on approaching greets him in a most affectionate manner. The new arrival is an American, who, having heard of the enterprise of the emigrant, and having great faith in the reasons which had led him to suppose that particular spot to be rich in gold, had set out to joi him in his undertaking. The mere advantage of pleasant com- panionship would have been a sufficient inducement for the emigrant to accept of the proposal of joint work for mutual be- nefit which the American is pressing upon him, but the fact that the History of Calcescence. 143 the American has in his possession tools of a superior kind renders his. proposal all the more acceptable. The compact being entered ito by both on the spot, and in terms more or less precise, the American alleges fatigue, and suggests that they should go to ‘rest. On this invitation they both go to sleep, but the American soon rouses himself and begins to work with all his might while his fellow is asleep. Aided by his superior instruments, the American soon reaches with his tool into a gold-bearing vein ; but at the very instant that he gets the first glimpse of the metal he catches also the open eye of his companion. “I am glad to See you are awake,” then observes the American; “just get up and look, here is a pretty large ‘nugget.’ But don’t trouble yourself any further about it. I shall soon bring it myself to the surface, and, of course, you shall have your rights. I intend to state at the mint where I mean to barter this ‘ nugget,’ that you were the first (the emigrant had been in fact the only one) to point out this tract as a gold-bearing region,.and that I have appropriated the ‘nugget’ and ‘claim’ to myself by your free consent.” As the position of the emigrant to the American, so was mine to Prof. Tyndall. For, as he subsequently informed. me, in the paper in which he intended to publish his results, it was his in- tention to state very fully my relation to it, and to show that I was the first to definitely attack it; and it was also his intention to mention that it was by my permission he published his expe- riments. I, at first, proposed to await the publication of Prof. Tyndall’s intended paper, and then to explain the manner of his interfer- ence in public. Wishing to avoid, however, public polemics, upon second thoughts I wrote to Prof. Tyndall a private letter, reminding him of the engagement that subsisted between us, and of all the other things that had passed between-us. In reply, Prof. Tyndall asserted that I had declined in April the proposal for joint work he had made tome. With singular delicacy, Prof. Tyndall stated further that his proposal had been made only on the spur of the moment, and also that, by the experiment he had shown me, he had succeeded in “solving” the question which interested us both. I then wrote again to Prof. Tyndall, stating that, so far from my having declined his proposal in April, I had written and told to several persons that he and I were going to make joint experiments ; I added, however, that, as he now stated that his proposal had been made only upon the spur of the mo- ment, which, I supposed, meant that he had afterwards repented it, [ should be sorry to imsist upon any specific performance of his part of our agreement. I also observed that, however hopeful the experiment which had been shown me might be, it was as yet 144 Dr. Akin’s further Statements concerning far from conclusive ; or else I should not have written privately on the subject, as it would have been too late to carry out our agreement. Several more letters passed between us, the result of which was that Prof. Tyndall volunteered to bind himself not to make known publicly or privately any experiments on ray- transmutation till November 1865 *. When I wrote in reply that, being anxious to see the matter upon which I had been working proved, and not having any hope of being able to pursue the subject myself any further, in the interest of science I would not hold him to the engagement to which he had volunteered to bind himself, Prof. Tyndall answered that, to his regret, he could not accept the release I had offered him, his simple duty appearing to him to be strictly to adhere to the engagement to which he had voluntarily pledged himself. Notwithstanding this, Prof. Tyndall has seized the very first opportunity that offered itself to him to publish, some eleven months in advance, those very experiments which, he had asserted, he could not with any degree of satis- faction to himself publish before November 1865, as there were things more important in his estimation than the mere claims of science. 3. I now turn to reply to Prof. Tyndall’s paper more in de- tail. In doing so, however, I shall not take any more notice of his personal animadversions than will be absolutely necessary for the vindication of my person from the imsinuations levelled against me. My “ Note on Ray-Transmutation,” published in the Supple- mentary Number of the Philosophical Magazine for December 1864, though not exclusively, was principally intended to point out a capital defect in Prof. Tyndall’s published reasoning regarding the origin of lime-light, &c. Prof.'Tyndall does not deny that there is a “missing link” in hisargument; but, adopting a well-known forensic device, he turns round upon me, and charges me with having committed an even greater error. I had spoken, he.says, of the “paucity of rays of high refrangibility in a hydrogen- flame.” Now, Prof. Tyndall quotes passages from the writings of Prof. Stokes, which appear to prove the fact to be the reverse of my assumption. In doing so, however, Prof. Tyndall evidently forgets that, the richer a hydrogen-flame is in invisible Ritteric rays, the more egregious is the oversight he committed in leaving, in his own reasonings concerning the phenomena of lime-light, &c., the Ritteric rays altogether out of consideration. In the paper published in the Reports of the British Association for 1863, I certainly called the oxyhydrogen “poor” in Ritteric rays, because, according to Dr. Miller’s observations,.the pho- * Prof. Tyndall added, however, that he would hold himself at liberty to repeat and develope his experiments “on combustion” by invisible rays. aie en a ae the History of Calcescence. 145 tographic impression produced by an oxyhydrogen-flame in the space of 20 seconds was found to be very faint. The expres- sions of “ poor” and “ rich,”’ however, are well known to be of comparative value only; and Prof. Tyndall is well aware that I grounded my conclusions regarding the origin of lime-light, not upon the poverty or richness of the oxyhydrogen-flame in Ritteric rays in its natural state, but upon the comparative abun- dance of Newtonicand Ritteric rays emitted by the oxyhydrogen- flame and by the lime-light. For the purpose of proving this, I need refer only to the note which Prof. Tyndall certainly had be- fore him in writing his late paper. I there expressly state that I relied in my reasonings upon the probable poverty of the oxy- hydrogen-flame in Ritteric rays, as compared with lime-light, which was later corroborated by the experiments of Dr. Miller*. Not content, however, with showing up imaginary defects in my reasoning on the origin of lime-light, Prof. Tyndall attempts to prove also the existence of ‘radical vices”? in my experi- mental suggestion for the production of calcescence. What I “imagine,” he says, in my first proposal, “is plain enough,” viz. “that the whole heat of the fiame [the italics are Prof. Tyndall’s] is radiated against one mirror and condensed by the other.” And he continues, “It is not the practical difficulties, which Dr. Akin himself discerns, that | am now speaking of; it is the radical vice of the conception that a purely gaseous flame, placed in the focus of a mirror, however large, could pos- sibly generate a temperature ‘approximately equal to that of the flame itself, in the focus of another mirror.” What Prof. Tyndall means by the phrase, “the whole heat of the flame is radiated against one mirror,” [am at a loss to understand ; but the point on which he impugns the validity of my reasoning is stated in the latter part of the sentence quoted, and which is plain enough. Now, I would ask any one, knowing the labours of Fourier and others, what would be the consequence, according to theory, if at one of the foci of a vacuous ellipsoidal envelope of proper form and perfect reflecting power an oxyhydrogen-flame were placed, and at the other focus a piece of platinum, for in- stance? Which is the “amusing ’’ supposition ? 1s it to suppose that the platinum would ultimately attain to the temperature of the flame ? or is it to suppose, as Prof. Tyndall does, that this latter assumption is “absurd?” “As a proposed experimental demonstration,” Prof. Tyndall continues in his urbane language, * of a point which can only be decided by experiment, Dr. Akin’s third proposition is, if possible, more hopelessly absurd than his first.’ At whose door the absurdity lies in the first case, I have already demonstrated ; but this second imputed “ absurdity ”’ is * See Phil. Mag. vol. xxviii. p. 556. Phil. Mag. 8. 4, Vol. 29. No. 194, Feb. 1865. L 146 Dr. Akin’s further Statements concerning indicated in language which I am altogether at a loss to construe. Why “a proposed experimental demonstration of a point which can only be decided by experiment,” should be necessarily “ hope- less” and “ absurd,” because it isa “ proposition,” 7. e.a “ pro- posal,” it is really beyond ordinary reasoning powers to compre- hend. I proposed three experiments by which I hoped, with more © or less certainty, to produce calcescence ; to say that I advanced the mere “ proposition ” as equivalent to a demonstration of fact, which is the only intelligible meaning I can assign to Prof. Tyn- dall’s words, is one of those vagaries of language peculiar to Prof. Tyndall, and to other examples of which I shall yet have to advert. Prof. Tyndall further criticises that of my proposed experi- ments which he allows to be “ rational ”—the “ only rational ” one among the three which I-had suggested. I had hoped to produce incandescence by means of a concentrated solar beam sifted by a diaphragm of monochromatic red glass. ‘It is need- less to remark,” Prof. Tyndall says, “‘ that, even had this experi- ment succeeded, the question would have still remamed unsolved ; for a sheet of glass, which permits the most powerful rays of the visible spectrum to pass through it, could not be called a ‘ proper absorbent.’ ”’ I assert that red glass zs a “‘ proper absorbent.” I had proposed to myself a double object :—first, to produce in- candescence by invisible Herschellic rays; and secondly, to pro- duce visible or Newtonic rays of a given refrangibilty in incan- descent substances, by the incidence of other visible rays of inferior refrangibility—for instance, green rays by the incidence of red rays*. This latter experiment, although less striking to the eye than the transmutation of invisible Herschellic rays into visible or Newtonic rays, would yet possess quite as great an importance as the first experiment in a theoretical point of view ; and for its realization red glass is a “‘ proper absorbent.” I was, however, at no loss regarding absorbents capable of separating the invisible Herschellic rays wholly from the visible or Newtonic rays. From Melloni’s memoirs, I knew that black glass of a certain variety is an absorbent of this kind; and from Prof, Tyndall’s work on ‘ Heat many months before he “ performed the thankless task of communicating to me fis ideas” by word of mouth—lI had learned that a solution of iodine in bisulphide of carbon possessed similar qualities. Ever since 1868 I endea- voured to procure black glass, in which, till lately, I did not succeed ; and in the spring of 1863 (that is, many months before Prof. Tyndall’s thoughts had turned, upon his own showing, to the subject of ray-transmutation as exemplified in the lime-light, * Prof. Tyndall only shows how little he understands the subject even now, when he says that the “real problem ” may be broadly stated thus: —‘‘ To raise the refrangibility of invisible rays of long period, so as to con-~ vert them into visible rays.” the History of Calcescence. 147 &c.) I had caused to be constructed a peculiar diaphragm for the express purpose of containing iodine in solution, and I had made » those observations on the spectrum of that solution which I have adverted to in the Philosophical Magazine for December 1864. Prof. Tyndall asks whether it will be believed that he needed my “ideas” to inform him what he was “to do with the obscure radiation from the electric light ?”? Why should it not be be- lieved? Every one knew that the invisible part of the radiation of the sun is calorifically powerful—at least to the same extent as Prof. Tyndall had shown that of the electric light to be by _ the experiments to which he refers in his last paper. Every one who had read Melloni’s papers knew also that, by means of black glass, the Herschellic rays may be separated from the Newtonic ; and yet nobody knew what he was “ to do” with the obscure radia- tion of the sun. In the article published in the ‘Saturday Review ’ the solution proposed by me for the problem which I had indi- cated was compared with the solution proposed in the case of *Columbus’s egg ;”’ and as in that case, so also in mine, it is easy to say, ew post facto, that anyone might have found the solution, had he but bethought himself of it. 4. As regards Prof. Tyndall’s attempted criticism of my pub- lished papers on the subject of calcescence, to which I have now replied, I might have perhaps saved myself the trouble of an- swering it. One of the Secretaries of the Royal Society wrote to me, after reading those papers, that they showed “a perfect mastery”’ of the subjects treated of ; and relying upon this judgment, I could have afforded to contemn Prof. Tyndall’s ad- verse opinions. I now have to reply to those statements of Prof. Tyndall which concern more my person than my writings. Prof. Tyndall taunts me with “sitting down and proposing experiments which may, or may not, be capable of realization. At all events if this be done at all, it ought to be done in a mag- nanimous spirit,” and not “with a view to mounting the high horse of Neptune.” This phrase, again, appears to me some- what difficult to understand ; but whatever its meaning, Prof. Tyndall totally misrepresents what I havedone. For more than a year I was in possession of and had matured my ideas ere I put pen to paper with a view to publication; and when, in August 1863, I read my papers at the British Association, it was not with a view of mounting any “high horse of Neptune,” but with a view to induce that body to help me to execute the expe- riments I had proposed*. * The readers of the Philosophical Magazine who remember Prof. Tyn- dall’s recent diatribes against Mr. Joule, will but smile at the consistency he exhibits in attempting to cry down at present the value of theoretical speculations unsupported by experiment. L2 148 Dr. Akin’s further Statements concerning Prof. Tyndall regrets that he was not more “suspicious” and I more “ open”; and he employs in this connexion several other expressions in keeping with his usual urbanity. No doubt Prof. Tyndall’s and my own views on this latter sub- ject differ considerably. I have stated already that in Octo- ber 1864 he gave me a duplicate proof of the paper he was then publishing. Having read it m his presence, I proposed to “talk it over” with him, when he replied that ‘there was nothing to talk over.’ Had I shared Prof. Tyndall’s views regarding conduct, no doubt I should have been more “ out- spoken,’ and should have pressed upon him the remarks | wished to make, notwithstanding. As to the “rule of courtesy in this country,” as in others, regarding the publication of pri- vate correspondence, I am very well aware of it, and have acted accordingly. Ihave not published any of Prof. Tyndall’s letters to me, nor have I committed that worse offence than a breach of courtesy, which he seems to be willing to lay at my door. He “challenges” me expressly” to publish the letter which I received from him from the Isle of Wight, and from which I have quoted two words. I hold that letter at Prof. yndall’s disposal, for him to publish it entirely if he chooses to do so. For the vindication of my own good faith, it will be sufficient if I transcribe the whole of the sentence from which I have made the quotation to which Prof. Tyndall objects. It is as follows :—‘ As to the possibility of converting the Herschellic rays into Newtonic rays, I do not entertain a doubt; and indeed the piece of work which I had set before me for attack on my return from this place was a series of experiments on this very subject.” This letter was written in April 1864; the article in the ‘Saturday Review,’ to which it in another part refers, ap- peared in January 1864. This is substantially what I have stated in the Philosophical Magazine for December last. Prof. Tyndall is mistaken in stating that I had written to him a “friendly note” twenty-four hours before my last article was published in this Magazine. I simply wrote to him a formal note, accompanying a book-parcel, which in itself was the indi- eation of a rupture. That both were not sent a week or two earlier was the fault of the bookbinder. It is evidently the same undue reliance on his superiority of age and seniority as a physicist, that, as he fancied, entitled him to adopt a tone of affected disregard towards me, which emboldened also Prof. Tyndall to state that, had I remained ‘silent for some indefinite period, and shown myself sufficiently meek, “he had intended to give me an opportunity of attaching my name to the experiments he had been making.” But im this Prof. Tyndall entirely misrepresents our relative positions. It n-nonane the History of Calcescence, 149 was I who, at his request, had granted him a share in the cul- tivation of a field which I had opened up*, and upon which, as he has himself acknowledged to me, he has since been but trespassing ; and it was not a little preposterous to expect, to say the least of it, that I would consent to accept as a boon, or stoop to petition for, a share in the produce of what was my own undoubted intellectual property. I have understood that the well-known fate of Dr. Mayer, in whose behalf Prof. Tyndall has written so feelingly and mag- nanimously, was brought about by the vexation he encountered in connexion with his speculations on Heat. In former years I should have considered such a statement as a mere piece of senti- mental invention. The experience of the last three years, however, has taught me different; only, while with certain constitutions eontinued vexation of this kind, coupled as it but too often is with troubles of another kind, ake the brain, with different con- stitutions it undermines other, but not less vital, parts of the system. Prof. Tyndall, who is charitable enough to express an implied wish for my non-existence, will no doubt be gratified to learn that the experience I have met with at his hands has acted upon me in the manner he would seem to desire. Yet, strange as it may appear, there are moments when I myself am inclined to palliate his conduct. The colleague of a Faraday, and the successor, virtual or real, of a Davy and a Young, may well consider himself under the obligation to enrich science by at least one signal discovery. Circulars issued by the Royal Insti- tution might ascribe to him the discovery of the Absorption of Heat by Gases; too kind and partial patrons or friends might speak of the ‘‘lustre” of his researches; but Prof. Tyndall well knew that the discovery of the absorption of heat by gases— or even that of the so-called “ principles” of “dynamic radia- tion,”’ and of “ accord and discord ?’—was not his, and that the lustre of his researches, however meritorious some of them might be, had been hitherto far from dazzling. But here there was a genuine discovery, which the best authority on the sub- ject had said would be a great one, and which, though virtu- ally made, yet, beimg still in want of ocular demonstration, almost any one possessed of the necessary instruments might attach his name to. What neither the qualities of his mind nor the genius of the scene of his labours had hitherto supplied him with, seemed thus suddenly placed within Prof. Tyndall’s reach. By writing to the editor of the ‘Saturday Review’t, Prof. Tyndall attempted to claim the discovery in question for * At our interview in April, at which Prof. Tyndall seems to have had a clearer conception of our mutual position than before or ever after, he observed to me that he would not “touch at the subject ” on which I was making experiments unless I *‘ permitted” him. + Prof. Tyndall, having read the article previously referred to in the 150 Further Statements concerning the History of Calcescence. himself. Later, when I myself brought about that immediate communication which he seems to have desired the editor of the ‘Saturday Review’ to establish between us, he claimed, or rather requested, a share in it. But no sooner was that share (perhaps too readily) granted, than his appetite grew again, and he wanted once more the whole. When I checked him in this desire, in November Prof. Tyndall had a momentary qualm ef conscience ; but this appears to have passed off since; and in the last Number of the Philosophical Magazine Prof. Tyndall’s sense of right appears again as obdurate as ever. It would be a blun- der in psychology to suppose that proceedings of this kind — arise from conscious motives, or that they are carried on with a full knowledge of their injustice. Greed is too powerful an instinct to allow of much reflection, and Ambition tco ingenious a sophist not to be able to represent black as white, foul as fair, if need be. However that may be, Prof. Tyndall has assured me that, when I should have achieved and published “ the great experiment ” I was striving to effect, he would muster sufficient greatness of heart not to envy me. I can say, now that Prof. Tyndall has tried to anticipate me, that, whatever advantage he may derive from that fact, I shall not envy him the means by which he has gained it. For my own part, I shall endeavour to console myself with thinking that it is the destiny of some to sow for others to reap. Paris, January 1865. Corrigenda in the January Number. Page 40, line 7 from below, for always read generally. — 42, — 13, for are greater than those read is greater than that. [It is with considerable regret we find ourselves called upon to ‘Saturday Review,’ actually wrote to the editor to say (as he himself is at the pains to state) that he had ‘accomplished already ” what I “ proposed to accomplish.”” This statement of Prof. Tyndall either shows how little he understood, even so late as January last year, the conditions of the problem to be solved; or else it forms an abuse of language rarely exemplified in the annals of science. I intended to produce calcescence by incident rays ; Prof. Tyndall, on the other hand, had guessed (or perhaps only remem- bered what I had emitted before him) that the common phenomena of in- candescence exhibited by solids in contact with flames were owing to an efiect of a similar, but far from identical, nature to that which I mtended to realize; and relying upon this fact, he considered himself justified in saying that he had “ already accomplished ” what I intended to accomplish. Really I am wanting in words strong enough to characterize a statement of this nature. It is as if somebody, having heard that Newton intended to verify the idea of universal gravitation by applying it to the motion of the moon, had asserted himself to have “accomplished” that already, because it had occurred to him that the fall of an apple might be due to the attraction of the earth, Prof. Tyndall invited the editor of the ‘Saturday Review’ to communi- cate to me his letter, with what view he does not state. Prof. Tyndall might have learnt from the editor of the ‘Saturday Review,’ whom he cites as a witness, that he never communicated with me on the subject. Royal Society. | 151 devote so much space to these discussions of purely personal matters ; and although we have, in justice to our subscribers and correspondents, given in this as well as in former instances an additional half sheet, we must now state that after admitting, as in fairness bound to do, the publication of any reply that Prof. 'Tyndall may possibly forward for insertion, the discussion of this subject must close, so far as our pages are concerned.—W. F.] XXIV. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 75. | November 17, 1864.—Major-General Sabine, President, in the Chair. "Bf XE following communication was read:— _ “On the Spectra of some of the Nebule.’ By W. Huggins, Esq., F.R.A.S. ;—a Supplement to the Paper ““On the Spectra of some of the Fixed Stars,’ by W. Huggins, Esq., and W. A. Miller, M.D., Treas. and V.P.R.S. The author commences by showing the importance of bringing analysis by the prism to bear upon the remarkable class of bodies known as nebule, especially since the results obtained by the largest telescopes hitherto constructed appear to show that increase of optical power alone would probably fail to determime the question whether all the nebulee are clusters of stars too remote to be separately visible. The little indication of resolvability, the absence of central conden- sation, the greenish-blue colour, and the intrinsic brightness charac- terizing many of the nebule classed by Sir W. Herschel as planetary, induced the author to select chiefly nebulze of this class for prismatic observation. The apparatus employed is that of which a description is given in the paper, “‘On the Spectra of some of the Fixed Stars,” by the author and Dr. W. A. Miller, to which this is a supplement. No. 4373*, 37 H. IV. Draconis. A bright planetary nebula, with a very small nucleus. The light from this nebula is not com-. posed of light of different refrangibilities, and does not therefore form a continuous spectrum. It consists of light of three definite refrangibilities only, and, after passing through the prisms, remains concentrated in three bright lines. * The strongest of these occupies a position in the spectrum about midway between 6 and F, and was found, by the method of simul- taneous observation, to be coincident with the brightest of the lines of nitrogen. A little more refrangible, a second line is seen. At about three times the distance of the second line, a third, very faint line occurs ; this coincides in position with Fraunhofer’s f’, and one of the lines of hydrogen. SBesides the three bright lines, an exceedingly faint continuous spectrum of the central bright point was perceived. * These numbers refer to the last catalogue of Sir J. F. W. Herschel, Phil, Trans. Part I. 1864, pp. 1-138. 152 Royal Society :—Prof. Maxwell on a - The planetary nebula, 4390, = 6, Tauri Poniatawskii ; 4514, 73 H.IV. Cygni; 4510, 51 H. IV. Sagittarii; 4628, 1 H. TV. Aquarn ; 4964, 18 H. IV., the annular nebula in Lyra 4447, 57 M., and the Dumb-bell in Vulpecula 4532, 27 M., gave spectra identical with the spectrum of 37 H. IV., except that in the case of some of these the strongest only of the three bright lines was seen. It is obvious that these nebulee can no longer be regarded as clus- ters of stars. In place of an incandescent solid or liquid body trans- mitting light of all refrangibilities through an atmosphere which in- tercepts by absorption some of them, such as our sun and _ the fixed stars appear to be, these nebule, or at least their photosurfaces, must be regarded as enormous masses of luminous gas or vapour. On this supposition the absence of central condensation admits of explanation; for even if the whole mass of the gas is luminous, the light emitted by the portion of gas beyond the surface visible to us would be in great measure absorbed by the portion of gas through which it would have to pass, and for this reason there would be pre- sented a luminous surface only. Thesmall brilliancy of the nebulee, notwithstanding the considerable angle which in most cases they subtend, is in accordance with the very inferior splendour of glow- ing gas as compared with incandescent solid or liquid matter. The extreme simplicity of constitution which the three bright lines suggest, whether or not we regard them as indicating the presence of nitrogen, hydrogen, and a substance unknown, is opposed to the opinion that they are clusters of stars. The following nebulee and resolvable clusters gave a continuous spectrum :—4294, 92 M. Herculis; 4244, 50 H. IV. Herculis; 116, 31 M., the Great Nebula in Andromeda; 117, 32 M. Andro- mede ; 428, 55, Andromedee; 826, 26 H. IV. Eridani. In the spectrum of 31 M., the nebulee in Andromeda, and in that of the companion nebula, 32 M., the red and part of the orange are wanting. December 8.—Dr. William Allen Miller, Treasurer and Vice-Presi- dent, in the Chair. **A Dynamical Theory of the Electromagnetic Field.” By Pro- fessor J. Clerk Maxwell, F.R.S. The proposed Theory seeks for the origin of electromagnetic effects in the medium surrounding the electric or magnetic bodies, and as- sumes that they act on each other not immediately at a distance, but through the intervention of this medium. The existence of the medium is assumed as probable, since the investigations of Optics have led philosophers to believe that in such a medium the propagation of light takes place. The properties attributed to the medium in order to explain the propagation of light are— Ist. That the motion of one part communicates motion to the parts in its neighbourhood. 2nd. That this communication is not instantaneous but progres- sive, and depends on the elasticity of the medium as compared with its density. Dynamical Theory of the Electromagnetic Field. 153 The kind of motion attributed to the medium when transmitting light is that called transverse vibration. An elastic medium capable of such motions must be also capable of a vast variety of other motions, and its elasticity may be called into play in other ways, some of which may be discoverable by their effects. One phenomenon which seems to indicate the existence of other motions than those of light in the medium, is that discovered by Faraday, in which the plane of polarization of a ray of light is caused to rotate by the action of magnetic force. Professor W. Thomson* has shown that this phenomenon cannot be explained without ad- mitting that there is motion of the luminiferous medium in the neigh- bourhood of magnets and currents. The phenomena of electromotive force seem also to indicate the elasticity or tenacity of the medium. When the state of the field is being altered by the introduction or motion of currents or magnets, every part of the field experiences a force, which, if the medium in that part of the field is a conductor, produces a current. If the me dium is an electrolyte, and the electromotive force is strong enough, the components of the electrolyte are separated in spite of their chemical affinity, and carried in opposite directions. If the medium is a dielectric, all its parts are put into a state of electric polari- zation,;a state in which the opposite sides of every such part are oppositely electrified, and this to an extent proportioned to the inten- sity of the electromotive force which causes the polarization. If the intensity of this polarization is increased beyond a certain. limit, the electric tenacity of the medium gives way, and there is a spark r “disruptive discharge.” Thus the action of electromotive force on a dielectric produces an electric displacement within it, and in this way stores up energy which will reappear when the dielectric is relieved from this state of constraint. A dynamical theory of the Electromagnetic Field must therefore assume that, wherever magnetic effects occur, there is matter in motion, and that, wherever electromotive force is exerted, there is a medium in a state of constraint; so thatthe medium must be regarded as the recipient of two kinds of energy—the actual energy of the magnetic motion, and the potential energy of the electric displacement. Accord- ing to this theory we look for the explanation of electric and mag- netic phenomena to the mutual actions between the medium and the electrified or magnetic bodies, and not to any direct action between those bodies themselves. In the case of an electric current flowing in a circuit A, we know that the magnetic action at every point of the field depends on its position relative to A, and is proportional to the strength of the cur- rent. Ifthere is another circuit B in the field, the magnetic effects due to B are simply added to those due to A, according to the well- known law of composition of forces, velocities, &c. According to our theory, the motion of every part of the medium depends partly on the strength of the current in A, and partly on that in B, and * Proceedings of the Royal Society June 1856 and June 1861. 154 Royal Society :—Prof. Maxwell on a when these are given the whole is determined. The mechanical conditions therefore are those of a system of bodies connected with two driving-points A and B, in which we may determine the rela- tion between the motions of A and B, and the forces acting on them, by purely dynamical principles. It is shown that in this case we may find two quantities, namely, the ‘‘reduced momentum ” of the system referred to A and to B, each of which is a linear function of the velocities of A and B. ‘The effect of the force on A is to increase the momentum of the system referred to A, and the effect of the force on B is to increase the momentum referred to B. The simplest mechanical example is that of a rod acted on by two forces perpen- dicular to its direction at A and at B. Then any change of velo- city of A will produce a force at B, unless A and B are mutually centres of suspension and oscillation. Assuming that the motion of every part of the electromagnetic field is determined by the values of the currents in A and B, it is shown— ‘ Ist. That any variation in the strength of A will produce an elec- tromotive force in B. 2nd. That any alteration in the relative position of A and B will produce an electromotive force in B. 3rd. That if currents are maintained in A and B, there will be a mechanical force tending to alter their position relative to each other. 4th. That these electromotive and mechanical forces depend on the value of a single function M, which may be deduced from the form and relative position of A and B, and is of one dimension in space ; that is to say, it is a certain number of feet or metres. The existence of electromotive forces between the circuits A and B was first deduced from the fact of electromagnetic attraction, by Professor Helmholtz* and Professor W. Thomsonf, by the principle of the Conservation of Energy. Here the electromagnetic attrac- tions, as well as the forces of induction, are deduced from the fact that every current when established in a circuit has a certain persis- tency or momentum—that is, it requires the continued action of an unresisted electromotive force in order to alter its value, and that this “momentum ”’ depends, as in various mechanical problems, on the value of other currents as well as itself. ‘This momentum is what Faraday has called the Electrotonic State of the circuit. It may be shown from these results, that at every point in the field there is a certain direction possessing the following properties :— A conductor moved in that direction experiences no electromotive force. A conductor carrying a current experiences a force in a direction perpendicular to this line and to itself. A circuit of small area carrying a current tends to place itself with its plane perpendicular to this direction. A system of lines drawn so as everywhere to coincide with the direction having these properties is a system of lines of magnetic * Conservation of Force. Berlin, 1847: translated in Taylor’s Scientific Memoirs, Feb. 1853, p. 114. Tt Reports of British Association, 1848. Phil. Mag. Dec. 1851. Dynamical Theory of the Electromagnetic Field. 155. force ; and if the lines in any one part of their course are so distri- buted that the number of lines enclosed by any closed curve is pro- portional to the “electric momentum ”’ of the field referred to that curve, then the electromagnetic phenomena may be thus stated :— The electric momentum of any closed curve whatever is measured by the number of lines of force which pass through it. If this number is altered, either by motion of the curve, or motion of the inducing current, or variation in its strength, an electromotive force acts round the curve and is measured by the decrease of the number of lines passing through it in unit of time. If the curve itself carries a current, then mechanical forces act onit tending to increase the number of lines passing through it, and the work done by these forces is measured by the increase of the num- ber of lines multiplied by the strength of the current. A method is then given by which the coefficient of self-induction of any circuit can be determined by means of Wheatstone’s electric balance. The next part of the paper is devoted to the mathematical expres- sion of the electromagnetic quantities referred to each point in the field, and to the establishment of the general equations of the electro- magnetic field, which express the relations among these quantities. The quantities which enter into these equations are :—Electric currents by conduction, electric displacements, and Total Currents ; Magnetic forces, Klectromotive forces, and Electromagnetic Momenta. Each of these quantities being a directed quantity, has three com- ponents ; and besides these we have two others, the Free Electricity and the Electric Potential, making twenty quantities in all. There are twenty equations between these quantities, namely Equations of Total Currents, of Magnetic Force, of Electric Cur- rents, of Electromotive Force, of Electric Elasticity, and of Electric Resistance, making six sets of three equations, together with one equation of Free Electricity, and another of Electric Continuity. These equations are founded on the facts of the induction of cur- rents as investigated by Faraday, Felici, &c., on the action of cur- rents on a magnet as discovered by Oersted, and on the polarization of dielectrics by electromotive force as discovered by Faraday and mathematically developed by Mossotti. An expression is then found for the intrinsic energy of any part of the field, depending partly on its magnetic, and partly on its electric polarization. From this the laws of the forces acting between magnetic poles and. between electrified bodies are deduced, and it is shown that the state of constraint due to the polarization of the field is.such as to act on the bodies according to the well-known experimental laws. It is also shown in a note that, if we look for the explanation of the force of gravitation in the action of a surrounding medium, the con- stitution of the medium must be such that, when far from the pre- sence of gross matter, it has immense intrinsic energy, part of which is removed from it wherever we find the signs of gravitating force. This result does not encourage us to look in this direction for the ex- planation of the force of gravity. 156 ; Royal Society. The relation which subsists between the electromagnetic and the electrostatic system of units is then investigated, and shown to depend upon what we have called the Electric Elasticity of the medium in which the experiments are made (7.e. common air). Other media, as glass, shellac, and sulphur have different powers as dielectrics ; and some of them exhibit the phenomena of electric absorption and residual discharge. It is then shown how a compound condenser of different materials may be constructed which shall exhibit these phenomena, and it is proved that the result will be the same though the different substances were so intimately intermingled that the want of uniformity could not be detected. The general equations are then applied to the foundation of the Electromagnetic Theory of Light. Faraday, in his “‘ Thoughts on Ray Vibrations” *, has described the effect of the sudden movement of a magnetic or electric body, and the propagation of the disturbance through the field, and has stated his opinion that such a disturbance must be entirely transverse to the direction of propagation. In 1846 there were no data to calculate the mathematical laws of such propagation, or to determine the velocity. The equations of this paper, however, show that transverse disturb- ances, and transverse disturbances only, will be propagated through the field, and that the number which expresses the velocity of pro- pagation must be the same as that which expresses the number of electrostatic units of electricity in one electromagnetic unit, the stan- dards of space and time being the same. The first of these results agrees, as is well known, with the undu- latory theory of light as deduced from optical experiments. The second may be judged of by a comparison of the electromagnetical experiments of Weber and Koblrausch with the velocity of light as determined by astronomers in the heavenly spaces, and by M. Fou- cault in the air of his laboratory. | Electrostatic units in an bs electromagnetic unit .... } 310,740,000 metres per second, Velocity of light as found by M. Fizeau 314,858,000. Velocity of light by M. Foucault...... 298,000,000. Velocity of ligh a ee y of light deduced from aberra- } 308,000,000. At the outset of the paper, the dynamical theory of the electro- magnetic field borrowed from the undulatory theory of light the use of its luminiferous medium. It now restores the medium, after having tested its powers of transmitting undulations, and the cha- racter of those undulations, and certifies that the vibrations are trans- verse, and that the velocity is that of light. With regard to normal vibrations, the electromagnetic theory does not allow of their trans- mission. What, then, is light according to the electromagnetic theory ? It consists of alternate and opposite rapidly recurring transverse mag- netic disturbances, accompanied with electric displacements, the direc- * Phil. Mag. 1846. Experimental Researches, vol. iii. p. 447. Geoloyical Society. 157 tion of the electric displacement being at right angles to the mag- netic disturbance, and both at right angles to the direction of the ray. The theory does not attempt to give a mechanical explanation of the nature of magnetic disturbance or of electric displacement, it only asserts the identity of these phenomena, as observed at our leisure in magnetic and electric experiments, with what occurs in the rapid vibrations of light, in a portion of time inconceivably minute. This paper is already too long to follow out the application of the electromagnetic theory to the different phenomena already explained by the undulatory theory. It discloses a relation between the induc- tive capacity of a dielectric and its index of refraction. The theory of double refraction in crystals is expressed very simply in terms of the electromagnetic theory. The non-existence of normal vibrations and the ordinary refraction of rays polarized in a principal plane are shown to be capable of explanation ; but the verification of the theory is difficult at present, for want of accurate data concerning the di- electric capacity of crystals in different directions. The propagation of vibrations in aconducting medium is then con- sidered, and it is shown that the light is absorbed at a rate depending on the conducting-power of the medium. ‘This result is so far confirmed by the opacity of all good conductors, but the transpa- rency of electrolytes shows that in certain cases vibrations of short period and amplitude are not absorbed as those of long period would be. The transparency of thin leaves of gold, silver, and platinum can- not be explained without some such hypothesis. The actual value of the maximum electromotive force which is ealled into play during the vibrations of strong sunlight is cal- culated from Pouillet’s data, and found to be about 60,000,000, or about 600 Daniell’s cells per metre. The maximum magnetic force during such vibrations is 193, or about 3, of the horizontal magnetic force at London. Methods are then given for applying the general equations to the calculation of the coefficient of mutual induction of two circuits, and in particular of two circles the distance of whose circumferences is small compared with the radius of either. The coefficient of self-reduction of a coil of rectangular section is found and appiied to the case of the coil used by the Committee of the British Association on Electrical Standards. The results of cal- culation are compared with the value deduced from a comparison of experiments in which this coefficient enters as a correction, and also with the results of direct experiments with the electric balance. GEOLOGICAL SOCIETY. [Continued from p. 77. ] December 7, 1864.—W. J. Hamilton, Esq., President, in the Chair. ao following communications were read :— “On the "Geology of Otago, New Zealand,’ By James Hector M.D., F.G.S. Ina letter to Sir R. I. Murchison, K.C.B., Bohn0., F.G.5. T "i ‘south- western part of the province of Otago is composed of 158 Geological Society. crystalline rocks forming lofty and rugged mountains, and inter- sected by deeply cut valleys which are occupied by arms of the sea on the west, and by the great lakes on the east. These crystalline rocks comprise an ancient contorted gneiss, and a newer (probably not very old) series of hornblende-slate, gneiss, quartzite, &c. East- wards they are succeeded by well bedded sandstones, shales, and porphyritic conglomerates, with greenstone-slates, &c., in patches, all probably of Lower Mesozoic age. ‘Then follow the great auri- ferous schistose formations, which comprise an Upper, a Middle, and a Lower portion; and upon these occur a series of Tertiary de- posits, the lowest of which may, however, possibly be of Upper Mesozoic date, while the upper, consisting of a Freshwater and a Marine series, are unconformable to it, and are decidedly much more recent. In describing the auriferous formations, Dr. Hector stated that the quartz-veins occurring in the schists were not often true “ fis- sure-reefs’”’ (that is, reefs that cut the strata nearly vertically and have a true back, or wall, independent of the foliation-planes) but are merely concretionary lamine that conform to the planes of foliation; the gold occurs segregated in the interspaces of this con- torted schist, but 1s rarely found zn sztu. _ Dr. Hector concluded with some remarks on the early Tertiary volcanic rocks, observing that the period of their eruption must have been one of upheaval, and that the great depth of the valleys, which have been excavated by glacier-action since the close of that period, proves that the elevation of the island, at least in the mountain-region, must once have been enormously greater than it now is. 2. “Note on communicating the Notes and Map of Dr. Julius Haast, upon the Glaciers and Rock-basins of New Zealand.” By Sir RB. I. Murchison, K.C.B., F.R.S., F.G.S. In this note Sir Roderick Murchison states that Dr. Haast has informed him ina letter that he has for the last five years attentively followed the discussions on Glacier theories, that in March 1862 he came, independently of other authors, to the same conclusions in New Zealand that Professor Ramsay did in Europe, and that his views have been printed in his Colonial Reports as Geologist of the Province of Canterbury. Sir Roderick also stated that the constant field and other occupa- tions of Dr. Haast have hitherto prevented his carrying out his intention of writing a paper for the Geological Society; but he has sent the following notes as a résumé of his views. Though opposed to the theory of the excavation of basins in hard rocks by the action of ice, Sir Roderick commended the re- searches of Dr. Haast as showing the mutations of the surface in successive geological periods. _ © Notes on the Causes which have led to the Excavation of ie Lake-basins in hard Rocks in the Southern Alps of New Zea- land.” By Julius Haast, Ph.D., F.G.S. Referring first to the submergence of New Zealand during the Intelligence and Miscellaneous Articles. 159 Pliocene period, and to its subsequent elevation, the author stated that the chief physical feature of the country after that elevation was a high mountain-range, from which glaciers of enormous volume, owing to peculiar meteorological conditions, descended into the plain below, removing in their course the loose Tertiary strata, and thus widening and enlarging the pre-existing depres- sions, the occurrence of which had at first determined the course of the glaciers. The author then observes that, the country having acquired a temporary stability, the glaciers became comparatively stationary, and therefore formed moraines, the materials of which were cemented together by the mud deposited from the water issuing from the glacier; new moraine matter would then raise the bed of the outlet and.dam up the water below the glacier, and from this moment, he believes, the formation and scooping out of the rock-basin begins ; for the ice being pressed downwards, and prevented by the moraine from descending, its force would be expended in excavating a basin in the rock below. 4. “Note on a Sketch Map of the Province of Canterbury, New Zealand, showing the glaciation during the Pleistocene and Recent times, as far as explored.” By Julius Haast, Ph.D., F.G.S. This paper contained a general explanation of a Sketch Map illustrating the past and present distribution of the glaciers on the eastern side of the Southern Alps of New Zealand, as well as the author’s views on the excavation of Lake-basins in hard rocks, as shown by the coincidence between the positions of the lakes and the terminations of the ancient glaciers. XXV. Intelligence and Miscellaneous Articles. ON SOME THERMO-ELECTRIC PILES OF GREAT ACTIVITY. BY PROF. R. BUNSEN. F all substances whose thermo-electric differences have been hitherto examined, and whose electric conductibility is suffici- ently good to enable them to be employed advantageously in thermo- electric piles, bismuth occupies the highest, and an alloy of two parts of antimony with one part of tin the lowest place in the tension series. Experiment has shown me that pyrolusite stands above bismuth in this series, and that copper pyrites occupies a far higher place than even pyrolusite. When copper pyrites is combined with the above alloy so as to form a thermo-electric pair, or, better still—in order to be able to employ greater differences of temperature—when copper pyrites is combined with copper, far stronger currents are obtained han, under the same circumstances, are yielded by any of the ‘er mo-electric piles hitherto in general use. To determine the constants of such a pile the following arrange- 160 Intelligence and Miscellaneous Articles. ment was employed. The adjoin- ing figure represents a plate of copper pyrites 40 millims. broad, 70 long, and 7 thick; into it are inserted, at a distance of 35 mil- lims. from each other, two copper pins of somewhat conical form, and having a mean diameter of 9 millims. Both pins are very care- fuliy cut and platinum-plated, and the upper one has a copper projec- tion 6. This projection being heated by a non-luminous lamp- flame, whilst the lower part of the plate of pyrites, together with - the copper pin fixed therein, is cooled in water, a current is obtained in the closed circuit formed by the copper wires cc, whose intensity after some time becomes constant—care being taken to protect from fluctuations the flame applied to the projection, The constants of this small pile were compared with those of a Daniell’s element, arranged in the customary way. The copper surface which, in this element, was immersed in the liquid opposite to the cylinder of amalgamated zinc had an area of one square decimetre; the liquids consisted of a completely saturated solution of sulphate of copper, and of a mixture of six parts (by weight) of water and one of sulphuric acid. If L denote the effective resistance of a pile, E its electromotive force, w the resistance in the closed circuit, and I the intensity - the current, we have, as is well known, the relation pasta Lt+w The resistance being increased by r, the diminished intensity of the current will be expressed by : L+tw+r To determine E and L, the current was passed through a coil of wire placed, in the requisite manner, at the distance d from a mag- netometer, and the deflections I and 7 were measured which corre- sponded to the resistances (L+w) and (L+w-+r). In all experi- ments w and v had the values 4°46 and 16°00, respectively. The distance d of the coil of wire from the magnetometer was 1 metre with the Daniell’s element, 0°5 of a metre with the pile of copper pyrites, and 0°25 of a metre with the pile of pyrolusite. Accordingly, when comparing the piles, we shall have to employ the formule Te ao 4 AG, He ( +16) id’. Intelligence and Miscellaneous Articles. 161 For the Daniell’s element the following values were found :— After 15 minutes’ Newly filled. vik Mean. I 154-0 141°7 Z 71:0 69-2 L 9-2 10°8 10:0 E 21080 2164-0 2136°0 In the experiments with the above-described plate of copper pyrites four different but constant applications of heat were tried. The fol- lowing series of results were obtained (arranged according to ascend- ing degrees of applied heat):— First. Second. | Third. Fourth. I 98-9 116-0 134°5 150°5 i A1'8 50°7 567 63°5 L 74 79 72 72 145°4 180°2 196-0 218'8 E (ther. elec.) abe pKa is) 1 E (Daniell) 147 11-9 109 . oe L (ther. elec.) peneeeinicll).1 0-74 0°79 0-72 0°72 During the experiments the heat of the water used for cooling rose somewhat over 60° C., and then remained constant at this tem- perature. Although the copper pyrites was heated above the tempe- rature of melting tin, no change was observed either in its interior or on the cut surfaces of the holes pierced throughit. In order not to split the apparatus, I did not applya higher temperature; for it was manifest, from the loosening of the copper pins during the process of cooling, that, when heated, the latter metal expanded more than the pyrites. A still greater electromotive force, however, might readily be obtained by raising the temperature, provided the consequences of unequal expansion were guarded against by cutting the pin, lon- _gitudinally, with a saw down to its axis, and thus enabling it, in vir- tue of its elasticity, to accommodate itself to the aperture. But even at the temperature to which it was exposed, this small pile exhibited a ten times greater action than a bismuth and antimony element, of equal effective resistance, when heated from 0° to 100°C. Ten of the above-described pairs formed into a battery suffice to give all the actions of a Daniell’s element, containing an effective copper surface 14 square centimetres in area. Copper pyrites in its natural state melts easily, at a strongly glow- ing heat, without sensible decomposition; and it may then be cast in any mould whatever. It is a remarkable fact, however, that this substance thereby suffers a change, in consequence of which it sinks far below bismuth in the thermo-electric tension series. Con- sequently it is only the mineral in its natural state which can be Phil. Mag. S. 4, Vol. 29. No, 194, Feb, 1865. M 162 Intelligence. and Miscellaneous Articles. employed for such thermo-electric piles; in that state, however, it can be easily worked into any required form. Pyrolusite, combined with platinum, also gives a pile whose epee motive force can be easily raised to one-tenth of that of a Daniell’s element, without fear of the heat thereby required decomposing the mineral. The upper and lower ends of a small cylinder, 6 millims. in diameter and 50 millims. long, easily cut from a complicated fibrous variety of pyrolusite, were enveloped with platinum wire; and the upper junction, ina cover of mica, was heated directly in a non-lumi- nous, flame, whilst the lower one was immersed in water. An expe- riment therewith, in which, as already remarked, d was equal to 0°25 of a metre, gave I=74:0 and i=68'2; whence result the values L= 183°6 and EK = 217°5. The electromotive force, therefore, amounted again to not less than = of that of a Daniell’s element ; the resistance, however, was 18°4 times that in the Daniell’s ele- ment above described.— Poggendorff’s Annalen, vol. cxxiil. p. 505. ON THE RADIANT HEAT OF THE MOON. To Professor Tyndall, F.R.S., &c. Sir, Utrecht, January 6, 1865. Allow me to trouble you for your duly and highly esteemed opinion on a subject to which I have given considerable time and care, as you may know from my Changements périodiques de température deé- pendants du Soleil et dela Lune, and from the Annalen of Poggendorff. I remember your having written in the Philosophical Magazine*, first, that you could not, as Melloni did, find a heating effect from the full moon’s rays by means of your thermoscope, but that, at the same time, you were of opinion that the smoke of London was an obstacle ; and secondly, that you supposed that the moon’s rays cleared the sky, and that from that cause the earth lost more heat than it gained by the direct action of the moon. I want to know whether this was a lapsus calami, or your real opinion. It is very improbable to me that a source of heat should be in any way a source of cold, even if I could admit Sir John Herschel’s opinion to be a true one—that the moon does clear the sky. I could not find, from many years’ observations, that the sky is more serene when the moon is above than when she is beneath the hori- zon—in other words, that it is clearer about the time of full moon than it is about the time of new moon. As for the influence on the temperature, I have added together all the observations taken on the first day of the moon, from 1729 till now, as wellas all the observations taken on the second, third, fourth, and so on. The result is not the same from 1729 to 1789 as it is from 1789 to now. In et first period I found a greater sum of temperatures 29th, 30th, ‘and the eleven first days. In the second period I find * Vol. xxii. p. 470. on aE | Intelligence and Miscellaneous Articles. 168 just the same as Mr. Park Harrison, viz.a more elevated tempera- ture about new moon; this is also the opinion of the ‘observers who accompanied the late polar expeditions. The whole series gives, ‘however, a ‘sum in favour of the full moon, just as it ought to be. You will agree with me that ifthe new moon really gives @ more elevated temperature at the surface of the earth than the full moon, the question is still more interesting, because the opposite ought to be the case, since the whole earth necessarily Contains more heat about the time of full moon than about the time of new moon. I have thought, at the same time, whether the moon, when it has north declination, imparts a more elevated temperature to our ther- mometer than when it has south declination; and I found it to be so; but the difference is equally variable and small. Now we all admit that other perturbations, a thousand times ‘as great, may totally eclipse for a considerable time the small influ- ‘ence of the moon; but nevertheless it seems to me, when we have 135 years of continued observation, that those perturbations ought to have annihilated themselves. Why is the mean result so small and uncertain, while we are so certain of the heating action of the moon? The explanation that has occurred to me is this :— The moon acts partly directly, and by that part the thermometers are most elevated the second or third day after full moon (the day of the greatest north decliation for our latitude); but it also acts in some measure indirectly, by elevating the temperature of the aqueous vapour in the atmosphere. By the latter action the clouds ‘and the air have a more elevated temperature, and contain more heat, about and after full moon; but some days must elapse before those particles of air and cloud reach the surface of the earth. When fourteen days elapse before they reach the surface, they have an action wholly opposed to the direct action, and thus the two parts ‘of the action of the moon ‘are necessarily neutralizing each other, more or less. : Hence it is that experiments at great elevations, such as those of Prof. Piazzi Smyth at the Peak of Teneriffe, are of the greatest value. Itisone instance among many where they are indispensable. My letter is already too long to give you my numbers. I will publish them, but would like very much to know your opinion before ‘doing so. Probably you have not time and leisure just now to give ‘your attention to this question. Perhaps you may think fit, how- ‘ever, to publish this letter of mine, with verbal correction, in the ‘Philosophical Magazine, together witha few remarks of your own. Excuse me for thus applying to you; it isin order to fix your attention on the subject and to be instructed by your opinion. I am, Most respectfully yours, Buys Bator. {Inthe ‘autumn of 1861 I swept the heavens on several days and M 2 164 Intelligence and Miscellaneous Articles. nights with my thermo-electric pile, and satisfied myself that this instrument is eminently fitted to examine ‘‘the mixed action of our atmosphere and stellar space,” as regards radiation. My observa- tions are referred to in the Philosophical Magazine, vol. xxii. p. 470. I still preserve my little observatory on the roof of the Royal Institu- tion, in the hope of being able to carry out the idea expressed in a note at the page referredto. Until this has been done, any opinion of mine on the questions raised by my distinguished correspondent M. Buys Ballot, would be of little value; but I am glad to see the subject in such excellent hands. It also gives me pleasure to find that M. Poey has recently turned the thermo-electric pile to account in examining the atmosphere of Havana. This zealous observer thinks that his observations regarding the action of aqueous vapour are diametrically opposed to mine: I, however, entertain a strong hope that M. Poey himself will eventually clear up the apparent dif- ference. The experiments demonstrative of the action of aqueous vapour on radiant heat of low refrangibility are, in my opinion, per- fectly conclusive.—Joun TYNDALL. | ON CALORESCENCE. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, While the changing of the ultra-red rays of the spectrum of the electric light into a complete luminous spectrum agrees so far with the phenomena of fluorescence, that in both cases the change of period is wrought by the intermediation of ponderable substances which alter the rate of oscillation, still the fact that the one class of effects is produced in bodies at ordinary temperatures, while the other class requires the temperature of incandescence for their pro- duction, introduces a marked distinction between them. Instead, therefore, of the two words “ negative fluorescence” provisionally adopted by me in an article in the January Number of the Philoso- phical Magazine, I would propose the word Calorescence to express the rendering of bodies luminous by the heat of the ultra-red rays. Joun TYNDALL. A LETTER FROM JOHN DAVY, M.D., F.R.S., ADDRESSED TO THE EDITORS OF THE PHILOSOPHICAL MAGAZINE, IN CONTINUA- TION OF A FORMER ONE, AND ACCOMPANIED BY DOCUMENTARY EVIDENCE CONTRIBUTED BY SIR JAMES SOUTH, F.R.S., AND BENJAMIN GOMPERTZ, ESQ., F.R.S., IN REPLY TO A CERTAIN CHARGE MADE BY CHARLES BABBAGE, ESQ., F.R.S., AGAINST THE LATE SIR HUMPHRY DAVY WHEN PRESIDENT OF THE ROYAL SOCIETY. GENTLEMEN, Referring to my letter to you of the 20th October, published in the Philosophical Magazine for December in reply to certain siamese Intelligence and Miscellaneous Articles. 165 charges brought against the late Sir Humphry Davy, when President of the Royal Society, and also to the letter addressed to you by Sir John Herschel, which appeared in the same Magazine for January, partly in answer to mine, but less clear and satisfactory than I had expected, may I beg the favour of you to allow the following corre- spondence, in further vindication of the character of my brother, to have a place in the next Number of your periodical? A sense of duty impels me to make this request, and I trust that a sense of justice will induce you to comply with it. I am, Gentlemen, Lesketh How, Ambleside, Your obedient Servant, January 19, 1865. Joun Davy. Dear Srr James,—I have to request your attention to a letter addressed by Sir John Herschel to ‘The Editors of the Philoso- phical Magazine and Journal,” and published in the Philosophical Magazine of this month. As you were present at the Council of the Royal Society, held on the 23rd November, 1826, I shall feel obliged if you will acquaint me whether you consider the statements contained in that letter to be perfectly accurate. I am, yours faithfully, Lesketh How, near Ambleside, Joun Davy. January 3, 1865. Letter from Sir James South, F.R.S., to Dr. John Davy, F.R.S. The Observatory, Campden Hill, Kensington, January 11, 1865. Dear Dr. Jonn Davy,—Before I received your letter to me of the 3rd inst., my attention had been directed to Sir John Herschel’s letter in the Philosophical Magazine of this month. I can, dear Dr. John Davy, assure you it was with great surprise I read the representations of Mr. Babbage and Sir John Herschel, in reference to the Secretaryship of the Royal Society in 1826, because I knew them to be painfully inaccurate. Sir John Herschel, Mr. Gompertz, and I are the only members now alive who constituted the Council of the Royal Society on November 23, 1826, and I therefore, immediately after my perusal of Sir John Herschel’s letter, communicated in the following letter with Mr. Gompertz, in order to ascertain what he knew upon the subject. Observatory, Kensington, January 2, 1865. My pear Mr, Gomprrrz,—May I be permitted to direct your attention to the accompanying passages marked in red ink, contained in Mr. Babbage’s work entitled ‘“‘ Passages from the Life of a Philo- sopher,” and in the Philosophical Magazine of December 1864 and January 1865? It is stated by Mr. Babbage (p. 186), that at the Council of the Royal Society, held Nov. 23rd, 1826, Dr. Wollaston, in reference to the Secretaryship, ‘‘ asked Sir Humphry Davy if he claimed the 166 | Intelligence ond Miscellaneous Articles. nomination as a right of the President, to which Sir Humphry gil replied, that he did; and then nominated Mr. Children.” It is likewise stated by Sir John Herschel (Phil. Mag. Jan. 1865, p. 78), that “the President was distinctly asked by Dr. Wollaston Pit the Council of the Royal Society, Nov. 23, 1826] whether he intended to use the privilege, by courtesy accorded to him, of naming the Sécretary, to which no one would object, or fairly to throw it open to the Council. His answer to the former part of the alter- native was susceptible of any sense that one might choose to put upon it; to the latter, it was both in Dr. Wollaston’s opinion and my own a negative.’ You and I were present at that Council from the commencement to its end. May I be permitted to ask you whether you remember having heard any conversation such as that which has been stated by Sir John Herschel and Mr. Babbage? I assert, that no such conversation took place. May I also be permitted to ask you, asa then member of the Council, whether you ever heard it even surmised, that Sir Humphry Davy had promised to appoint Mr. Babbage to the office of Secre- tary of the Royal Society, and had then violated that promise ? Iam, my dear Mr. Gompertz, Yours sincerely, Benjamin Gompertz, Esq., F.R.S. J. Sours. My respected old friend lost not a moment in replying to it, as follows :— Kennington Terrace, Vauxhall, January 2, 1865. ‘My pzar Sir J amxs,—In reply to your letter of the 2nd inst., I beg to state that I never heard the conversation alluded to by Sir John Herschel and Mr. Babbage, at the Council of the Royal Society, on November 23, 1826; and I never heard that Sir Hum- phry Davy had promised the Secretaryship to Mr. Babbage. I write this with the wish that, if you think it necessary, you should publish it. Yours very sincerely, To Sir James South, F.R.S. Benin. GoMPERTZ. There are, however, ‘some additional facts which in my opinion establish that your late brother, Sir Humphry Davy, did not, either directly or by implication, promise that he would appoint Mr. Bab- bage to the Seeretaryship of the Royal Society, and consequently - that Sir Humphry was not guilty of the mala fides of which he has been so recklessly accused. On November 14, 1826 (the Council of the Royal Society was held on the 23rd of November), I received a letter from Sir John Herschel (then Mr. Herschel), of which the following is a copy :-—= Sloane Street, . Tuesday, Nov. 14, 1826. _ Dear Sovurn,—I am sorry not to have met with you, as I wanted to have had some talk with you about the Secretaryship of the Royal Intelligence and Miscellaneous Articles. 167 Society. 1 have endeavoured to ascertain Babbage’s sentiments upon the subject, and I think I see them pretty distinctly, and that in such light as makes me very desirous to have some personal com- munication with you about it. Knowing that you yourself have formed something of a wish re- specting it, I think you will be enabled to judge how high an idea I have formed of what may be expected from a disposition like yours, when I tell you that the object of my calling was to induce you yourself to name fim to our President as a proper person to fill the, office, if he has not already his eye on him. My reasons I will explain vivd voce; and if you do not see the force of them, at least you will have no cause to blame the feeling which gives them weight with me. Yours very sincerely, J. F. W. HErscue. Immediately after the perusal of this letter, I went to the residence of Sir Humphry Davy (Park Street, Grosvenor Square), and was accompanied near to the house by Sir John Herschel, but who re- fused to accompany me into it. Not finding- him (Sir Humphry) at home, I wrote a letter, of which the following is a copy, and left it for him on his library table :— Nov. 14, 1826. My pear Sir Humpury,—During many weeks I have not heard anything which gives me more pleasure to communicate, than the fact I have just arrived at, namely, that Mr. Babbage would probably accept the office of Secretary to the Royal Society, were you to offer it to him. Most sincerely praying that nothing may have yet transpired to cause you to think of any one else, in which I feel sure every scien- tific member of the Society joins me, I remain, trusting you will forgive the warmth of my expressions, Yours very. truly, J. Sourn. In order personally to urge the claims of Mr. Babbage upon the consideration of Sir Humphry Davy, I called at his residence again in about half an hour after I had left the foregoing letter. Sir John Herschel walked with me near to the house, but he would not enter it and see Sir Humphry with me. Sir Humphry was at home, he received me very kindly, and told me Herschel had given him information which had much surprised him, namely, that 1 would have accepted the Secretaryship it it had been offered to me; that he thought my never having given him the slightest idea I would take the office was not a friendly act towards him, » I replied, I had thought very little of the matter, but that, having met Mr. Babbage on Ludgate Hill a few days ago, I asked him if he would take the Secretaryship, and his reply was, ‘“‘I would see the Society d d first ;’ that I walked with him as far as Troughton’s, and repeated my question, to which he returned the same answer ; 168 Intelligence and Miscellaneous Articles. that I then said, “If no one better can be found, I perhaps might take it, were it offered me, but I will not ask for it.” Sir Humphry Davy then said to me, ‘‘If you will now take the Secretaryship, no one else shall have it; to which IJ replied, ‘My dear Sir Humphry, the thing is impossible. In the letter that you have in your hand I have solicited you to give the appointment to — Mr. Babbage, and I would cut my right hand off sooner than you and Wollaston should say of me, as both of you said of...... thac’ hewwent.to hee. to get the Clerkship of the Irons for Children, but that he came back, having secured it for himself!” *” Sir Humphry then said, ‘‘I have not given the place to Children, nor have I actually promised it to him, but I wiLt not GIVE IT TO BABBAGE.” Under the foregoing facts and circumstances, it would be an unjus- tifiable encroachment upon your time, if I were at greater length to trespass upon your attention, except it be to remark— “‘ Facilis descensus Averni ; Sed revocare gradum, superasque evadere ad auras, Hic labor, hoc opus est.” I am, dear Dr. John Davy, Yours very faithfully, J. Sours. P.S.—You have my permission to publish this letter.—J. 8. SIMPLE METHOD OF PREPARING THALLIUM. BY R. BUNSEN. In a large sulphate-of-zinc works at Goslar, a lye is evaporated, obtained from the Rammelsberg pyrites which is so rich in thallium that pounds of this metal can be readily obtained from it. It con- tains, besides other constituents, 21°74 per cent. of sulphate of zinc, 0:536 of sulphate of cadmium, 0°05 of chloride of thallium, and 0°28 of sulphate of copper. Mixed with an equal volume of hydrochloric acid, an immediate precipitate of chloride of thallium is obtained. When iodide of potassium is added to it in the presence of an ade- quate quantity of hyposulphite of soda, iodide of thallium is preci- pitated, mixed, however, with some subiodide of copper if the quan- tity of hyposulphite is insufficient. But as the addition of these sub- stances hinders the production of white vitriol, I have found a way which is not only simpler, but which also introduces an essential improvement in the manufacture. It consists in placing in the cold lye sheets of zinc, by which copper, cadmium, and thallium are pre- cipitated. In this way, from acubic metre of the lye, for 7°4 kilogs. of zinc, 6°4 kilogs. of a spongy metallic precipitate were obtained, which was rapidly washed out in a flannel bag. Besides some lead and zinc, this contained 4:2 kilogs. of cadmium, 1°6 kilog. of cop- per, and 0°6 kilog. of thallium. When digested with water to which some sulphuric acid was added from time to time, the cadmium and thallium dissolved with disengagement of hydrogen, leaving the copper. To the sulphuric acid solution, 0:5 kilog. of iodide of potassium were added, which precipitated 0-97 kilog. of chemically pure iodide of thallium, which was readily washed by decantation. —Liebig’s Annalen, January 1865. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. (FOURTH SERIES.] MARCH 1865. XXVI. On the Elastic Force of Steam of Maximum Density ; with a new Formula for the expression of such force in terms of the Temperature. By THomas Rows Epmonps, B.A. Cantab.* 4 pkg laws of steam and other vapours, in relation to elastic force, density, quantity of heat, and temperature, possess claims on the attention of mankind which are not surpassed in interest or importance by the claims of any other branch of phy- sical science. The foundation for the knowledge of these laws must be sought in observations and experiments of great variety, extent, and accuracy. The best of such observations (as is gene- rally acknowledged) are those of M. Regnault, made by order and at the expense of the Government of France. The report of M. Regnault to the Government of his nation was made in the year 1847. His Report fills the twenty-first volume of the Mémoires de ? Académie des Sciences de Institut de France. It is divided into ten memoirs on steam and allied subjects. The eighth memoir, entitled “ Hlastic Forces of Steam,” contains the materials now presented for consideration. Among the laws of steam desired to be known, the most im- portant has generally been acknowledged to be the law which indicates the relation between temperature and elastic force of steam confined with water in a closed vessel—such as the boiler of a steam-engine. On the application of heat to such a vessel, the enclosed water will continually diminish by conversion into steam, and the enclosed steam will continually increase in density and elastic force until the point of condensation or saturation is attained, or, which is the same thing, until the maximum den- * Communicated by the Author. Phil. Mag. 8. 4. Vol. 29. No. 195. March 1865. N 170 Mr. T. R. Edmonds on the Elastic Force of sity appropriate to the given temperature is attained. The elastic force of such steam is measured by the height of a column of mercury contained in a tube of which the open end is inserted in the boiler containing both water and steam. At a given tem- perature, when the elastic force ceases to increase, the contained steam must be of maximum density. It is to be noted that when, by increasing the temperature, the whole of the contaimed water has been converted into steam, any further addition to the tem- perature cannot further increase the density of the steam, which then becomes “dry” or “superheated ” steam, a kind of steam which is not here taken into consideration. The problem offered for solution is this:—Given the tempe- rature of the water and steam contained in the boiler, it is required to find, either by experiment or calculation, the corre- sponding elastic force when such force is constant and at its maximum. This problem has been completely solved by M. . Regnault so far as experiment is concerned, and this for all ordinary ranges of temperature and pressure—extending from 130° Centigrade above to 180° Centigrade below the boiling-point of water, or from a pressure of twenty-seven atmospheres to a pressure of only the two-thousandth part of one atmosphere. What remains to be desired is, the knowledge of the law which connects together the experimental results, and which will enable a person to determine by calculation the elastic force at every other temperature from the known elastic force at any one temperature. At different times during the last fifty years there have ap- peared various empirical formule intended to express approxi- mately the elastic force of steam of maximum density m terms of the temperature. The comparative merits of several of these formule have been discussed by the two commissions (on steam, &c.) appointed by the French Government, viz. by MM. Dulong and Arago in their Report of the year 1829, and by M. Regnault in his Report made in the year 1847. The conclusion arrived at by M. Regnault is, that one only of these empirical formule yields results sufficiently near the truth to render it capable of being usefully applied to purposes of interpolation. The favoured formula is well known as that of M. Roche, who was formerly professor in a college or military school at Toulon. It was pub- lished in 1829, or before that year. This formula, when reduced to its simplest terms by making P=1 when ¢=0 (the former quantity representing elastic force, and the latter temperature measured on the thermometric scale), is the following : t log Pee ATi’ Steam of Maximum Density. 171 which formula, when expressed in series, becomes log P,=At {1 —Mé+ M*?—M°8+ &e.}. The earliest of the empirical formule referred to is that of our own countryman Dalton, who suggested, as the foundation of useful formule of interpolation, the principle, that the elastic forces increase in geometrical progression, whilst the tempera- tures increase in arithmetical progression. Thus Dalton’s for- mula of interpolation would be los FP = Az, a formula consisting of one term only, and that term being the first of the series (above given) constituting the Roche formula. M. Regnault (at page 587 of the volume* cited) makes a valuable remark which 1s applicable to the two empirical formule just mentioned, as well as to other empirical formule relating to steam. The remark is, that such formule express correctly only the first, or only the first and second terms of the series consti- tuting the true formule. That isto say (applying and extending the principle), if the true formula, expressed in series of ascend- ing powers of ¢, were log P;= At+ Bi? + Ce + &e., then the approximate formula of the first degree would be log P;=A¢é, which is that of Dalton. And the approximate formula of the second degree would be log P;= At + Bd? + &c., of which Roche's formula is an example, the first and second co- efficients A and B being identical with the first and second coefficients of the formula expressing the true law. Proceeding in the same course, it may safely be said that if an approximate formula of the third degree were discovered, it is highly pro- bable that such formula would coincide with the true formula, not only in the first three terms, but in all the succeeding terms of the two series, and that such formula would be as great an improvement on the Roche formula as the latter is an improve- ment on the formula of Dalton. The general character of the law of variation according to tem- perature of the elastic force of steam of maximum density, may be easily perceived on inspection of the tabulated values of these forces as given either by MM. Arago and Dulong or by M. Reg- nault. If the logarithms of these forces, separated by equal intervals of temperature (as 5 or 10 degrees Centigrade), be written under one another in a vertical columr, and the differ- ences of the consecutive logarithms be taken, the series thus formed of the quantities A log P will evidently be composed of terms uniformly decreasing with the temperature, from the very * Mémoires de ? Académie, &c., vol. xxi. 172 Mr. T. R. Edmonds on the Elastic Force of low to the very high temperatures. It will be readily seen that, for short ranges of temperature, the successive values of A log P are In near agreement with Dalton’s law, and that for moderate ranges the values of A log P are in near agreement with Roche’s law. The result of the inspection (if carried to a sufficient degree of minuteness) can hardly fail to be the conviction that there exists a fixed and simple law of connexion between the force and temperature, and that Roche’s law is only an approxi- mation (and not a very close one) to such fixed and simple law. The manifest uniformity of decrease with temperature of the finite differences of the logarithms of the observed elastic forces of steam of maximum density is indicative of similar uniformity of decrease of the differential or indefinitely small differences of these logarithms. If the elastic force (P) be a funetion of the temperature (¢), and if the finite differences (A log P) are known in terms of the temperature, then the differentials (d.log P) are similarly known; and conversely. The existence of an exact law being assumed, the simplest expression of that law will be contained in the differential (d.log P) in terms of the tempera- ture (f). If such differential can be obtained from the observa- tions of M. Regnault, and if such differential is of a simple form and readily integrable, the law which governs the elastic forces at all temperatures will be ascertained. The Table given by Regnault as the final result of his obser- vations on the elastic forces of steam is found at page 624 of the volume cited. In this Table the forces are stated in millimetres of mercury for every degree Centigrade, from 32° C. below the freezing-point of water to 230° C. above that point. At the temperature 100° C., taken as the boiling-point of water, the force is 760 millims., which is taken to represent the pressure of one atmosphere. ‘There is also given in the same Table a column of differences or increments of forces for all consecutive intervals of one degree of temperature. By means of this column the value of the rate of increment of the force P, and consequently the value of d.log P, may be easily obtained for any required temperature. The differential of hyperbolic logarithm P is = which is the limit of ~ when the intervals of temperature are indefinitely di- minished. By taking AP equal to halfthe sum of the increment preceding and the increment following the value of P for a given temperature, and then dividing by P, we get the mean value of the rate of increment per degree ( ar or Tani for the inter- P rps val of two degrees, one of which precedes and the other follows the Steam of Maximum Density. | 173 given temperature. When the intervals taken are small (as one degree Centigrade), such mean value coincides exactly, so far as observations are concerned, with the rate of increment per degree of the force existing at the middle point of the interval or at the given temperature. Such rate of increment per degree is the hyperbolic logarithm & taken to represent — According to the known properties of hyperbolic logarithms, when the rate of increment of force is constant throughout any interval (as one degree taken as a unit), and when such interval is divided into an infinite number (gq) of equal parts, then we have for the constant ratio of increase of force for such infinitely small interval (a - *) =e7, and consequently for the total unit inter- val containing qg such parts, Mee es € us *) =e '=e*=1]+r, if it is known that the force unity under a constant rate of incre- ment becomes (1 +7) at the end of the unit interval. From the above equation we obtain the following two values of « in terms of r:— l #=com log (1+7) x p and, by expressing hyperbolic logarithm in terms of its corre- sponding number, ey & a=r— a == 3 — XC. In the above equations the indefinitely small quantity ~ represents dPy SAP _ d.log P= = = = xX 7 AP The values of poor the rates of increment of force P for every tenth degree of temperature, commencing with 380° C. below the freezing-point of water, have been obtained in the manner above described from M. Regnault’s principal and adopted Table, and are contained in the last column of Table I. SAE hereunto annexed. The ratios of these quantities (+) to one another are the same (or very nearly the same), at the same tem- peratures, as the ratios of the differentials (d.log P). On com- paring together these ratios a, it is found that they all bear a 174 Mr. T. R. Edmonds on the Elastic Force of ; BS Lees very simple relation to one another, which is that of (=): to: (5 VF The quantities a and a+¢ represent temperatures measured from an ideal fixed point which has been called the absolute zero of temperature. The quantity a represents the absolute temperature of the point adopted as the zero of the thermometrical scale in use. The quantity ¢ represents the number of degrees in either direction measured on such scale. The exponent 7 LU is the hyperbolic logarithm of 10, and is sth to.2;302585. From what has preceded, it ensues that if # be the hyper- bolic logarithm representing the ratio of increment of the elastic force P at the absolute temperature a, then the hyperbolic logarithm representing the rate of increment of elastic force at any other absolute temperature (a+7¢) will be We = i =e a ee _ k - (a :) 6 (1+ -) Using differentials, we may say that if - = ? then will 0 1 d.log P,= ae “\ =a(1 ate tba, The above differential of log P; yields on integration the equa- tion following, by which is expressed im logarithms the ratio of elastic force of steam of maximum density at any thermometric temperature, ¢ to the elastic force at, aes temperature a, whence ¢ is measured ; - hyp log P,= oe (i+ 3). } 4 The quantity n is put for G ~1)= 1302585. The above equation, otherwise expressed, 1s. aas,_ f\—n kaa —n pee EOD _ (ltt tO OF. The quantity eis the base of the hyperbolic system of loga- rithms, and is equal to 2°7182818, and k is the modulus of the common. or decimal system of logarithms, and equal to "4342945. By means of the formule above, given, the values of (P;) the elastic force, and («;) the rate of increment per degree of such Steam of Maximum Density. 175 force, have been calculated for all temperatures differing by in- tervals of 10° C., beginning at the absolute temperature 246°, and ending at the absolute temperature 506°. These values are exhibited in Table I. annexed hereto. They are placed side by side with similar values for the same temperatures, which have been deduced directly from M. Regnault’s principal Table printed at page 624 of vol. xxi. of the Mémoires de I Académie, &e. On inspection and comparison, it will be seen that the two different series of results are in close coincidence with one another in nearly all parts of the scale. The only exception worthy of note occurs for temperatures below +10° C. But in this part of M. Regnault’s Table the elastic forces, as well as the incre- ments of elastic forces, have lost the regularity and uniformity - of progressive increase or decrease which is remarkable at all temperatures above 10° C. On account of the want of uniformity at. this part of the scale, very little weight can be attached to the slight discrepancies here existing between M. Regnault’s adjusted Table and my theoretical Table. The errors of observation amount apparently to about one part in one thousand for any temperature above 10° C., and about one part in one hundred for temperatures below that point. The extreme error (when the two compared at the same temperature are in opposite directions) might thus amount to one in five hundred at temperatures above, and one in fifty at temperatures below 10° C. It is only within these limits that the present new theoretical Table differs from M. Regnault’s adjusted Table and the selected observations adopted by him. M. Regnault informs his readers (page 589) that, in the ad- justment of his chief Table, all his definitive calculations have been executed by using only the formula of M. Roche or that of M. Biot for purposes of interpolation. The formula of M. Biot is this: log P=a+la’+ cf’, the five constants contained requiring for their determination five observed values of P separated from one another by equal intervals of temperature. M. Regnault afterwards says (page 599) ¢hat the formula of interpolation (EK) which he has used for all temperatures below the freezing-point of water, or 0° C., is P=a-+ be, which formuia is a modification of Biot’s general for- mula, obtained by cutting off the third term and substituting P for log P. At page 598 M. Regnault states that he has used another formula (D), wherein log P, for all temperatures between 0° and 100° C., is represented by the general formula of Biot. At page 600 it is stated that another formula (F), wherein log P is represented by the general formula of Biot, has been used for all interpolations between 100° C. and 230° C. It thus appears 176 Mr. T. R. Ednionds on the Elastic Force of that M. Regnault’s adjusted Table is a composite Table consist- ing of three separate series, each regulated by its specific con- stants, whether three or five in number. When this mode of construction is taken into account, it will not be expected that such a Table will be in complete harmony with a theoretical Table deduced from one uniform law throughout the whole range of temperature observed. Disagreement between Tables so differently constructed is most likely to occur at the tempera- tures 0° and 100° C., the points at which the different series ot Regnault are intended to join one another. At page 606, however, M. Regnault gives another formula (H) according to Biot, with five special constants, which formula is intended to be applied generally to the whole range of tempe- rature observed, and to prove to the reader that the single formula (H), with its five special constants, will yield nearly the same results as those contained in the principal or adjusted Table of M. Regnault, and obtained by three sets of constants, amounting to thirteen in number. The greatest proportional difference between the elastic forces of steam, as given by Regnault’s ad- justed Table and by my new theoretical Table, occurs at the temperature 0° C., or at the temperature of melting ice. But the elastic force at the same temperature given by the general formula (H) already described, differs from the result of my formula in an opposite direction. The elastic force at tempera- ture 0° C. is, in millimetres, 4°60 according to Regnault’s ad- justed Table; in my theoretical Table it is 4°52 millims.; whilst by the general formula (H) it is 4°48 millims. This will be seen on reference to Table II. hereunto annexed. In the same Table II. is included a column (extracted from page 608) of elastic forces, at intervals of 10° C., measured on a copper engraving which contains a geometrical construction of the results of M. Regnault’s observations, and which represents by a continuous curve the elastic forces observed at every tempera- ture, or which represents rather those observations which were thought most worthy of being relied upon. The values exhi- bited according to this “graphic curve” (as it is designated by M. Regnault) are of doubtful authority in respect of the small deviations at temperatures below 10° C. from the law now offered as the true law; for it is not improbable that M. Regnault, biassed by his favourable opinion of the formula of Roche, has selected for adoption those experiments which were most in harmony with that erroneous formula. The general formula above given for the elastic force in terms of the temperature may, by expanding the exponential ¢ + a): by the binomial theorem, be expressed in the series following : Steam of Maximum Density. 177 j nt+lt n+l nt+2?2? n+l n+2 n+38 eee et 8 ae a a et 2 3 = kat | 1 —1-151292- a= 1-267414°, 13682905 -~ ie. b. The above series, representing the true law of elastic force of steam, may be used to show in what manner Roche’s law and two other approximate laws may be formed. According to the true law, and also according to the three approximate laws, the common multiplier of all the terms of the four different series is ket—the quantity « being the hyperbolic logarithm represent- ing the rate of increase per degree when the thermometric tem- perature is 0 or dt. Also the true law as well as the three ap- proximate laws agree in having their two first terms the same, kat (1— "42 T). Itis at the third term only that the varia- tions begin. The three approximate formule are these :— n+1 log P:= kat (1 “+ ‘) ine (No. 1), —1 WHA L) (No. 2, or Roche's formula), log P,=kat Ql + Bae log P,=kate 2 2 (No. 3). = or = =m, we shall have for the three approxi- mate formule for log P,, Putting t —m —! ket (1 = ‘) » kat (a +m -) , and kate”, a | a The coefficients of the third and fourth terms of the above three approximate formule are, omitting the common multiplier ke, as follows :— + 1:238383 —1:300835 (No. 1), + 1:325473 —1°526007 (No. 2), + °662736— °252668 (No. 3). The coefficient of the third term of the true formula being 1:267414, it will be seen that the coefficient of the same term in Roche’s formula is ‘058059 in excess, and in formula No. 1 is ‘029081 im defect. That is, Roche’s approximate formula 178 Mr. T. R. Edmonds on the Elastic Force of deviates from the true formula at the third term exactly twice as much as approximate formula No. 1 does. The Roche formula, as given above, differs considerably from the Roche formula used by M. Regnault. In the correct for- mula, A=ka and M= - are constant for all temperatures, begin- ning with ‘=0. Jn the modified formula used by M. Regnault and others, A and M are made to vary (ina small degree) accord- ing as ¢ varies. For example, in the pure Roche formula, where P is taken equal to unity at —20° C., the value of A or ke is "037679, and the value of M or - is (0044973. In the mixed Roche formula, constituted by changing A and M, in order to force the formula to give true values of P at 100° C. and at 220° C. (as M. Regnault has done for the Roche Table, con- tained in column 5 of Table II. hereunto annexed), Ais changed to 0382382, and M to :004774. The consequence of these alte- rations of the constants belonging to the real curve at its origin is to produce a fictitious curve of great irregularity, more espe- ‘cially at points near those of forced coincidence with a real curve belonging to an equation whose constants are really constants. As an instance of the defect of the Roche formula constituted as above, I may mention that the true elastic forces (yielded by the new formula) at temperatures —20° C. and 0° €. are -92 and 4°52 millims. respectively, whilst the elastic forces at the same temperatures given by the Roche formula constituted as above are ‘92 and 4°59. The error thus found to exist in the Roché formula is 459—4°52, or ‘07 millim. at the temperature 0°C., when —20° C. is taken as the point of departure. This error is a near representation of the whole of the discrepancy, at temperature 0° C., between the forces given by the new formula and by M. Regnault in his adjusted Table. A comparison may be usefully instituted between the laws of variation with temperature of the elastic force (P) of steam of maximum density and of the elastic force (p) of a perfectly elas-- tic gas, or vapour of constant density. It is generally acknow- ledged that the equation p=1+ . represents the elastic force of' a perfectly elastic gas of constant volume and density when raised to the temperature ¢, compared with a unit of elastic force possessed at temperature 0°. We have consequently, on dif- ferentiating, &. Steam of Maximum Density. 179 | dt i It has already been shown that d.log P=«——_.. On di- 1 : QQ) a viding the latter equation by the former, we have Lelie _ aa(1 + “) =a —" = gge-™ ; Dae ae 8 Bigs : on putting p=1+ - =e‘! so that ¢;=hyp logp, then d.logP : » de, integrating, we get — log P=constant ent =} | em : n n =aae—™ and d.log P=aae—™4 dt ; which agrees with the general equation first obtained. 1 It has been shown that d.log P varies as (i +") * and ay d.logp as Q -- *) . The quantity a, which is common to both expressions, is the most important constant in the laws of steam and other vapours, and probably in the laws of liquids and solids also. At the zero of the Centigrade thermometer (the temperature of melting ice) a is equal to 276 Centigrade degrees. This number represents the absolute temperature of melting ice, measured from an ideal fixed point at which all heat disappears. This number approaches very near to the recipro- cal of the coefficient of expansion of gases whose elasticity is nearly perfect, and probably would be found exactly equal to such reciprocal if a gas of perfect elasticity could be found. At the zero of the Centigrade thermometer, in atmospheric air of the ordinary density for that temperature, the coefficient of ae G? nearly as determined by M.. Regnault (page 73). According to the same authority (page 120), the coefficients of expansion of different gases ap- proach nearer to equality with one another according as their densities diminish; and he believes that it is not improbable that the supposed law, that all gases have the same coefficient of expansion, may be true when their densities are indefinitely diminished. In air of the temperature of melting ice and of density 4°810, he found (page 110) the coefficient of expansion 1 1 to be a5 5606? and in air of density 0°144 to be Ea Accord- ing to these two experiments, there is a difference of 4°°8'C. in expansion per degree is ‘(003665 = 180 Mr. T. R. Edmonds on the Elastic Force of the place of the absolute zero of temperature in respect of densi- ties of air in the proportion of 33 to 1. Ifa further reduction in the density of the air in a similar proportion could have been effected, it is not improbable that a coefficient of expansion equal 1 to sng nearly would have been obtained, which coefficient of expansion is the constant quantity ( for temperature 0° C.) involved in all M. Regnault’s experimental results on the elastic forces of steam of maximum density at different temperatures. When the value of the constant a has been determined for any fixed temperature, the only constant remaining to be deter- mined is « in the general formula for the ratios of elastic forces at all temperatures. As has been said, this quantity is the hyperbolic logarithm representing the increment per degree of the elastic force at the precise absolute temperature a° of the point fixed as the origin of thermometrical temperature 7°. In the construction of my theoretical Table, I have found it most convenient to adopt 100° C. as the origin of the thermo- metrical scale, so that the value of a in this case is 376°, being 100° added to 276° when the latter is the value of a for the tempera- ture of melting ice. The whole range of temperature observed by M. Regnault is comprised between 130° above the tempera- ture of 100° C., and 130° below that temperature. Consequently if ¢° be reckoned from 100° C., all thermometrical temperatures referred to may be expressed in terms of the absolute tempera- ture (a+t) or (a—t), wherein a=876, and ¢ is any quantity not exceeding 130°C. The lowest absolute temperature observed is 246°, and the highest 506°. When the value of « has been obtained for any absolute temperature (a), the value of a; for any temperature greater by i. ¢° may be obtained from the equation e,=a, ( + -) *. The value which I have adopted for « at 376° absolute temperature is ‘038580. When this number is inserted in lieu of & in the general formula, we get, first, when ¢ is positive, hea f\-"| _ kx 0858 x 376 LiNm com log Py “ae {a—(1+ 2)" } =o (tae) f t —n — 4-48'7960 {1-(14 wa) \. Secondly, when ¢ is negative, t —n com log P_;= — 44879604 ¢ = a —_ i} : Steam of Maximum Density. 181 By means of these two equations have been calculated the theo- retical elastic forces given in all four of the Tables hereunto annexed. On inspection of the last two columns of Table I. hereunto annexed, it will be seen that my theoretical values of a; coincide at the same temperature almost exactly with the values of az directly obtained from the adjusted Table of M. Regnault for all temperatures above + 10 degrees of the Centigrade thermometer. It is, however, to be remarked that my adopted theoretical value of « for 100° C., which is ‘0358, differs more from M. Reg- nault’s experimental number at the same temperature than it ought to do if the smaller differences between theory and expe- riment existing before and after that temperature are to be taken asa guide. ‘This discrepancy, however, is easily accounted for by the statement already made, that M. Regnault’s adjusted Table is a composite Table formed in three sections, two of which touch one another, but do not unite together, at the temperature 100° C. The general equation for the ratio of the elastic force at tem- perature ¢° to elastic force at temperature 0° having been ob- tained, there remains to be added for practical purposes a com- mon multipher to take the place of unity previously used to express the elastic force at temperature 0°. The standard of measurement of force usually adopted is either the height or the weight of a vertical column of mercury which is in equilibrium with the ordinary pressure of the atmosphere. The height of the column of mercury adopted to represent one atmosphere is 760 millimetres, or 29°9218 English inches. The pressure or weight of such a vertical column of mercury amounts to 2116°4 pounds avoirdupois on the square foot, or to 14°7 pounds on the square inch. Lither of the above four quantities may be called H, and used as a multiplier in the general equation for the ratios of P at different temperatures. The equation for practical use will then become P,=H x ge CT oe Sige and using common logarithms, log P;=logH + ee) 1 (a Sb ey. It is not difficult, though somewhat laborious, to calculate from the general formula the value of log P for every degree of temperature. The properties of the formula are, however, such that all the desired results can be obtained without incurring the labour of making a direct use of the formula, except for obtaining the values of log P for two temperatures only. If a 182 Mr. T. R. Edmonds on the Elastic Force of Table of five columns be formed, the first column denoting abso- lute temperatures from 246° to 506°, the second column denoting values of log P, the third column denoting values of A log P, the fourth column denoting values of log A log P, and the fifth column denoting values of A log A log P, it will be found that the quantities in the fifth column are the reciprocals of the numbers in the first columm nearly. In other words, it is found that A log A log P=—_ nearly. Even when intervals so a great as 10° C. are taken, the differences are very small between the numbers in the fifth column and the reciprocals of the abso- lute temperature. In order to form by the use of logarithms a Table of elastic forces of steam of maximum density for intervals of one degree Centigrade, or one degree Fahrenheit, nothing is required beyond, Ist, a Table of reciprocals of numbers repre- senting absolute temperatures; 2ndly, the value of A log P for any one specific interval of temperature; and 3rdly, the value of log P for any one specified temperature. The remarkable property just mentioned is consequent on the form of the differential coefficient of log P;, which is either Parnes or a @ + Ve. ay a Calling this «,, and taking the ratio of two consecutive coefficients at unit intervals, we get 1 er +¢+ Ny Fe(1 4. 1 ne a, d.log P; a+t a+t which becomes, when the intervals of temperature are indefinitely diminished, testa (1 +H tae Set bola ty att Taking common logarithms of both sides of the former of the above two equations, we get Ot aa a+t com log —= -7, com log t or, which is the same thing, (com log #;41—com log a;) = — (hyp log (4+ ¢+1)—hyp log (a+2)). That is to say, the differences between the common logarithms of the rates of increment of the elastic forces are equal to the differences of the hyperbolic logarithms of the corresponding ab- solute temperatures. This is another way of expressing the essen- tial principle involved in the law of steam of maximum density. 3 Steam of Maximum Density. 188 It may also be shown from the general formula, on putting A log P,=log oe that Ep 1 ]|—= log P,4,—log Prt k 2k ao: oe). 1 Toe Poclog Pej= Ege H = 107 = 10"? neatly. k 2 By taking the ratios of two consecutive differential coefficients of log P corresponding to the temperature ¢~—} and ¢+43, we get d.log Pry: _ a+t+$ a ig yt: d.log Py_a atti—4% but d. loy Pas A log Piii—A log P, ly: d.log Py_2 ~ Alog P;—A log P:_1 2 eee consequently o 3 GEN wii ie) A log Py (Gaye = the last being a formula which gives the ratio to one another of consecutive values of A log P, with great accuracy. A log P Equating the two values thus obtained of Aloe Pay > we get, on taking common logarithms, : 1 1 at+t+4 If Q be taken to 4 —10 a+l1 ae a+t Qo Qa, a Qs-1 , or i 1 QF =10 Ga asa), Qo | and, taking common a pase of each Bae ] ee + &e ae . : Bat = 7 = “atts” Now taking, according to the second of the above two equa- tions, the value of ores we get, on substituting for ¢ the num- t bers 1, 2, 8, and ¢ in succession, and taking 10 as the unit of temperature, 1 Q, oS 4 (ON8 1 LOSS EP oan 376410—5/ ~~ \881/ ” Bp 1 QF « 87-642:04+°5\ *_ 40-1)" Oy. 376+4+2-0— are oOo)" a 3917.” Prat log —* =: ie Ors, P,; — 5 Si i Qt gg Fe BFE-HERS _ 87-14% t-—1 On multiplying together the quantities on the same sides of the equations, we have O07 5G. Q, [39-1 401 eit Q,°0,°Q, Or” L331" 391 eee 1 OF) Sage oat a alt sa.) = (1 +353 Consequently, taking the common logarithm, 38° = This is a formula by means of which A log P; may be ascertained for any temperature, with considerable precision, when A log P for any other temperature is previously known. Among other formulz it may be useful to mention the fol- lowing :— com log Q;= com log bes — com log (a +> Steam of Maximum Density. 185 A log P,= log ae t 1 ae Ja B, Be Bs = ka (1+) 4-aht ap at p) the values of the coefficients B,, B,, &c. being the same as in the original formula for log P; expanded in a series. The above series being of great convergency, will often be found useful in supplying defects from using logarithms to seven places of deci- _ mals, when logarithms to ten places are not at hand. In the formula for log P, one of the factors, viz. 41 —_ (1 a \"j , 1s sometimes incapable of being correctly expressed beyond the fifth decimal place by means of the ordinary Tables of loga- rithms to seven places. TasieE I.—Elastic Force of Steam of Maximum Density, and rate of Increment per degree, according to Regnault and ac- cording to a new formula. (Regnault’s Table, p. 624, vol. xxi. Meém. de l’ Académie, &c.) Elastic force in Temperature. hundredths of one atmosphere. Increment per degree Centigrade. Fahren- Centi- Abso- New Regnault. New Regnault. heit. grade. lute. formula. formula. —22 —30 246 "049 ‘051 | -09509 | -09326 — 4 —20 256 12) "122 | -08676 | -083°50 +14 —10 266 278 °275 | 07943 | :07979 32 0 276 095 “605 | :07296 | -07359 50 +10 286 1-198 1:206 | -06722 | -06645 68 20 296 2-286 2:288 | -06210 | -06179 86 30 306 4:156 4151) :05753 | :05744 104 40 316 7235 7°224 | 05342 | -05346 122 50 326 12-11 12°10 | :04972 | -04980 140 60 | 336 19°58 19-58 | :04638 | -04646 158 70 346 30°66 30°67 | 04335 | -04339 176 80 356 46°65 46°66 | -:04060 | -04060 194 90 366 69-12 69:14 | 03809 | 03808 212 100 376 100-00 | 100-00 | -08580 | -03571 230 110 386 14153 | 141:50 | 03370 | -03373 248 120 396 196:32 | 196:22 | 03177 | :03175 266 130 406 267°33 | 267:15 | 03000 | -02999 284 140 416 357°88 | 357:59 | 02837 | -02836 302 150 426 471:64 | 471-22 | -02685 | -02685 320 160 436 612-59 | 612-05 | :02546 | -02547 338 170 A46 785°04 | 784-44 | 02416 | -02418 356 180 456 993-53 | 992-96 | -02296 | -02298 374 190 466 (1242-9 |1242-5 702184 | -02187 392 200 476 |1538-2 |1538-0 02080 | :02083 410 219 486 |1884:5 {1884-9 701983 | -01985 428 220 496 |2287:°3 |2288°2 701892 | -01894 446 230 906 |2751:8 = |2753°5 01807 | -61809 Phil, Mag. 8. 4. Vol. 29. No. 195. March 1865, O 186 Mr. T. R. Edmonds'on the Elastic Force of TaBLE I].—Elastic Force of Steam of Maximum Density, ac- cording to new formula, compared with the Elastic Forces indicated by the three elementary Tables from which the ad- jyusted Table of M. Regnault has been formed. poe (The force is stated in millimetres of mereury. One atmosphere equal to 760 millimetres = 29°9218 English inches.) Observa- zune a New a ee Biot formula | Roche fonanla pee Centi- formula. | ,COPPE?, ; 2 Table, Se 2 eae page 608. page 615. aes page 608. _30 371 -37 | (Not stated.) | (Not stated.) "386 — 20 "920 Ol |x “91 |x 9] 927 —10 2-111 9-08 1:97 2-12 2°093 0 4:520 4:60 4-48 4:60 4°600 +10 9-105 9°16 9:05 9-22 9:165 20 17°37 17°39 17°30 17°62 17°39 309 31°58 31:55 31:50 32°04 31°55 40 54:98 54°91 | * 54°91 55°71 54:9) 50 92:06 91:98 92-02 93°11 91:98 60 148-82 148°79 148-83 150°19 148-79 70 233°03 233°09 233°1] 234:°61 233°09 80 35451 354°64 354°64 356:06 394°64 90 525-33 525°45 525°45 526°42 525°45 100 760-00 760:00 | * 760:00 |x 760:00. | - 760-00 110 1075-6 1073°7 1075-4 1073°7 1075°4 120 1492-0 1489:0 1491°3 1487°] 1491°3 130 2031-7 2029°0 2030°3 2022-7 2030°3 140 2719-9 2713-0 2717°6 2705°6 27176 150 3084°4 3072°0 3981-2 3563°9 3581°2 160 4655-6 4647:0 |x 4651-6 4628°5 4651-6 170 5966-2 5960°0 5961:°7 5932-8 5961-7 180 7550°8 7545°0 7546°4 75129 7546-4 190 9446-0 9428°0 9442-7 9407-1 9442-7 200 =|11690 11660 11689 11656 11689 210 {14822 14308 14825 14302 14825 220 =117383 17390 * 173890 x 17390 17390 230 (20914 20915 20926 20965 20926 The three formulz for log P above referred to are Z —1°302585 of 1—(1+7) fs a+ ba! +c’; and A¢ x (1+ Mz)’. * Assumed points of coincidence with observations marked on engraved plate of copper. 187 Steam of Maximum Density. 6LIG:LZ 9-0¢ 0-81 : IZ¥06- 0£080- 1802-1 9.07 91020. 91020. 9.65 OT LEL8-2S 9-69 0-21 ty ee | L8FZ6- I LL¥80- LEI@-1 98h ' gg0z0- || 8g0z0- : 9.86 OL ESF8-81 9-8 O-TI - , | PPSTG I 0Z880> 0SZ2-1 vey - O1Z0- ZO1Z0: gle OL 0Z88-ST 9:Lb 0-01 : ‘eee L¥996- I LS60- 9182-1 9.9% . 9P1Z0- ChIZO- | 9.0% OL O8ZF-Z1 9-99 0-6 « ae Z6L86- 2% I 96160: O1Sz-T 86120: $61Z0- gsr OL 186-6 9-7 0-8 0.7% 68600: T 6ZZ0I- 96961 SPEC: P¥ZC0- 9.1% OL Z8V8-L 9:P7 0-4 is ae - 63280- I ZLLOL- GI83-1 = $6860: £62Z0- g.er OL Z9SL-9 9-87 0:9 ep ae BESS: I 9SSII- 68621 oan LYEZ0- ShEZ0- g.cr OL LOLLY 9-ZP 0: any 0L8L0: I LS6II- 6LIE-T — POZO: GOPZ0- 9.1% _ OT 6115-8 9-1F OF 0.0% SLZ0I- I 699Z1- 1882-1 a €9FZ0- E9PZ0- 9.0r OT VEL9-Z 9-07 0-8 ae SELZI- I SOFEL: L198-1 Be GZSZ0- 95920: 9.68 _ OL $896-1 9-68 0:2 oe | P9IZSI- I LIZ I- [L88-1 = 16&Z0- 16520: g.se Ol Slr 9-8 OL Gest. = a a cgost: |, Slr 0000-1 9-48 0 ‘d sory. So, V *(2) © Ri a ° . , D 1oyeM “SUOTIOVIT *suoloRTy 1-9 . Mei fel Sot d Zo V segoat an tee ee jo aaiodes qes[NA ut [euoop ut d Soy ‘a 301 V Bo, |. 4d 1-9 @SVoIOUI JO O1y *soroydsourye =[10q, 09 oATVL OI snk ae ieee es ie oe! é Ss) I-2q ur 90103 =? q I I aes T +9 201 Ga mol “a =: da | Ttae So] ‘ainjzerodura,y, d “AvISUO(T WINUWIXeT\T JO WRI}g JO 9d010,q OTYSeTT 94 Jo ‘ommyerodimay, 03 Surpaovoe osvoiouy Jo me] oY} ‘opeactyuay SeoIsop QT Jo sTeadozut Joy “SuLMOYS—'] I] FTAV O02 188 Prof. Williamson on the Unit-volume i Gases. Tasie [V.—Exhibiting by Logarithms (when the unit of Tempe- rature is 10 degrees Centigrade) the law of Increase of the Elastic Force of Steam of Maximum Density, ue A log P being equal to te nearly. att Absolute Alog A log P Absolute log P. A log P. log A log P. = = nearly). , sir ak (a+t). 46886930) | —.. B co) 3°0831720 | oo ey | Tecoscy | 0390873 «| 25-6 "4436980 -3306190 | 5193278 0376088 26°6 7743170 -3041360 “4830679 "0362599 27°6 20784530 2806050 ‘4480954 0349725 28°6 3590580 9595970 | -4142997 0337957 29°6 "6186550! 5497750 38] 6114 ‘0326883 30°6 8594300 9938458 “3499490 0316624 o1-6 1'0832758 2085734 -3192588 0306902 32°6 °2918492 -1947596 -2894989 0297599 33°6 "4806088 1899111 -2605748 0289241 34°6 6688199 1707984 9394837 0280911 39°6 8396183 1603817 | -2051548 0273289 36°6 37°6 00000000 1508529 1785537 0266011 37°6 38°6 °1508529 0259142 38°6 1421149 | -152639 10252622 | 39-6 1340841 | -1273773 0246295 -| 406 1198671 | -0787001 40-6 4270519 39°6 -2929678 41-6 5537435 42-6 6736106] j1a5568 | .ossoo03 | 0284798 42-6 43-6 | -7871694 -0229334 43-6 a ‘1077178 | -0322874| - 44-6 8948872 : ; 0224372 44-6 -1022940 | -0098502 45:6 9971812 maa “0219279 45-6 0972573 | 2°9879223 | | 46-6 | 1-0944385| 994 0214525 46-6 0925699 | 9664698 | |< 47-6 1870084 0210253 47-6 Of) -0881951 | -9454445 | | 48:6 | 2752035 0205793 486 0841134 | -9248652 496 | -3593169| ‘Donoosa | -go4zogg | (0201588 49-6 506 | -4896153 XXVIII. On the Unit-volume of Gases. By Professor A. W. Witiiamson, P.C.S., F.R.S., &¢.* Hoe many years the term volume has been employed by che- mists in a specific sense in relation to the weight of gases and vapours. When a chemist speaks of a volume of hydrogen or nitrogen, &c., he is understood to refer to that particular quantity of the gas which is equal in volume to sixteen parts by weight of oxygen. When we say that alcohol, according to the formula C? H® O, is a two-volume vapour, we thereby say that the weight represented by this formula, namely forty-six parts * Communicated by the Author. mn, Prof. Williamson on the Unit-volume of Gases. 189 of alcohol, occupies twice the bulk of sixteen parts of oxygen, or the same bulk as thirty-two parts of oxygen. Before the rectification of the atomic weight of oxygen, the unit-volume was defined as being the volume of eight parts by weight of oxygen. But retaining the principle of that original definition, viz. that the unit-volume is the volume of one atom of oxygen, we now use volumes double as great as the old volumes, while referring to an atomic weight of oxygen double of what was formerly in use. : ; A more convenient way of describing the unit-volume now in use is to call it the volume of one part by weight or one atom of hydrogen, and this definition is now generally coming into use. One important advantage of the rapidly prevailing system of applying the term “ two volumes ” to the volume of two parts by weight of hydrogen (or one molecule of free hydrogen), is that we thus obtain an exceedingly easy means of calculating the density of gases and vapours on the hydrogen scale. Thus when we say that the molecule of steam occupies two volumes, we thereby assert chat H?O, or eighteen parts by weight of steam, occupy twice as great a volume as one part by weight of hydrogen, and our statement contains the data for cal- culating the density of steam compared to that of hydrogen ; for it amounts to saying that two volumes of steam weigh eighteen, while one volume of hydrogen weighs one; so that one volume of steam weighs nine times as much as one volume of hydrogen. Again, the molecule of chlorosulphuric acid, SO? Cl?, is stated to occupy two volumes in the state of vapour, so that this weight (S=382, 0?=382, Cl?=71), 135, is as bulky as two parts by weight of hydrogen, and our vapour has accordingly a density of 67-5. Or when we say that a molecule of marsh-gas occupying two volumes requires four atoms of oxygen, occupying four volumes, for its complete combustion, and that the product is a molecule of carbonic acid occupying two volumes, and two molecules of steam occupying four volumes according to the equation CH* + 04 = CO? + (H?0)?, 2vols. 4vols. 2 vols. 4 vols. we similarly supply the data for calculating the density of each of the aériform bodies named. Thus CH* weighing sixteen, and occupying two volumes, is eight times as heavy as two vo- lumes of hydrogen. O* weighing sixty-four is of course sixteen times as heavy as its own bulk of hydrogen. CO? weighs forty- four and occupies two volumes, proving that it has a density of 22; and the density of steam is found in like manner. 190 Prof. Williamson on the Unit-volume of Gases. The great convenience of this hydrogen scale of densities, which is already leading to its general adoption, arises from the fact that it enables the chemist to calculate with facility the density of any gas or vapour from a knowledge of its molecular weight. For inasmuch as every molecule, with very few appa- rent exceptions, is found to occupy two volumes in the state of vapour, the vapour-density of every compound is equal to half its molecular weight. For some years past I have been in the habit of using an ex- tension of this natural system of volume-notation, which affords the means of calculating with rapidity the absolute volume of a given weight of a gas or vapour, or inversely the absolute weight of a given volume. This extension consists simply in substitu- _ting the word “ gramme” for “ part by weight ” in the definition of volume. A volume of hydrogen is the bulk of one gramme of hydrogen at the normal temperature and pressure, and a volume of any gas or vapour is a bulk of that gas or vapour equal to that of one gramme of hydrogen. According to the determinations of oxygen, which are less affected by errors of manipulation than the determination of hydrogen, a volume is 11°19 litres at O° C. and 760 millims. ‘mercurial pressure. For most purposes the volume may be de- fined as 11°2 litres. ! ; | In order to show the advantages derivable from this absolute volume, it will be best to take a few examples of calculations per- formed ‘by the aid of it. Thus, it is required to find the volume of oxygen obtainable by the decomposition of one kilogramme of potassic chlorate. The formula KC1O tells us that the molecule of chlorate weigh- ing 122°5 contains 48 parts of oxygen, so that the proportion 122°5 :48=1000: 2 gives us 391°8, say 392 grammes, as the weight of oxygen contained in our kilogramme of chlorate. In order to reduce this to litres, we have from the density of oxygen _(O=16= 1 vol.) the proportion 16: 11:°2=392:y, whence y _ =274-4 litres as the measure of oxygen obtainable by the com- plete decomposition of a kilogramme of chlorate. 2. Given 500 grammes of zinc, required the volume of hy- drogen obtainable by its action on sulphuric acid. The equation Zn + H? SO*= H? + Zn SO% tells us that sixty-five parts by weight of zine displace two parts by weight of hydrogen from its sul- phate; and 65:2=500: 2 gives us 15°384 grammes as the weight of hydrogen ; and this number, multiplied by 11-2, gives us 174°3 as the number of litres of hydrogen. 3. Given 150 grammes of paraffine, find the volume of air required for its combustion, assuming for paraffine the formula Prof. Williamson on the Unit-volume of Gases. 191 (CH?)*. According to the formula (CH2)"+ (09)"= (CO2)*-+ (H? 0)", we find that 14 parts by weight of paraffine require 48 of oxygen for their combustion; so that 150 grammes require 514°3 grammes of oxygen, equal to 385-7 litres; 21: 100= — 385°7 : # gives us 1830°6 litres of air. 4. Given a room of 80 cubic metres capacity full of air at 15°C. and 760 millims. pressure, what weight of oxygen does it contain? The proportion 105°4977 : 100=80:z gives us 75°8 cubic metres as the volume of our air reduced to 0° C.; and this multiplied by 2, gives us 15-918 as the volume of the oxygen, whence 15°918: z=11'2: 16 gives us 22°740 grammes as the weight required. 5. Required the weight of a litre of ether-vapour, measured at 100° C. ~The formula C* H!®?O= 2 vols., gives us 37 grammes as the weight of 11:2 litres at 0° C., whence 3°305 grammes for one litre at O° C. 2:42 grammes is therefore the weight at 100° C. These examples will no doubt suffice to explain the use of this constant, and the advantage derivable from it; and I have found that students of chemistry learn its use very easily, and, aided by it, are enabled to compute rapidly the answers to numerical questions involving a transition between measures of weight and measures of volume. It appeared most natural to start from weight in fixing an absolute volume, because our symbols are used to denote certain relative weights of elements, and ought to be used as the basis of every calculation. Equivalent calculations may easily be made by the aid of an absolute volume defined in grains and cubic inches. One grain of hydrogen at the normal temperature and pressure measures nearly 44°5 cubic inches, and 44°5 cubic inches would be the -unit-volume of gases for those who use grains and cubic inches “instead of the metrical system. The merest beginner in science understands when he is told that a volume means 11°2 litres, and can easily calculate problems relating to gases, with the aid of this constant. After using the absolute volume for some time, he learns to see the same rela- tions between the volumes of gases in a more general and abstract manner, but the only philosophical beginning for him is an absolute volume defined intelligibly in itself. pees] XXVIII. An Account of some Electrical Experiments and Induc- tions. By J. J. Warerston, Esq. [Concluded from p. 98. ] On the Integral of Electric Force and its mode of distribution in space, as deduced from the elementary laws established by Ca- vendish and Harris. ©: 51. T O prove that the attraction between parallel electrified conducting surfaces is constant at all distances of the quan- tity of electricity engaged between them is constant, suppose two Leyden jars or magic panes exactly the same in every respect, except that the glass of one (L) is twice as thick as that of the other (M). If it takes 100 unit-jars to charge L so that the balance electro- meter of Harris connected with its charging side requires 10 grains, there will be required 200 unit-jars to charge M to the same intensity as measured by the electrometer. The attractive force between a square inch of the two coatings of M is four times the attractive force between a square inch of the two coat- ings of L. Let us suppose the charge of L to be increased by another 100 unit-jars, making the whole charge 200. The force between a square inch of the two coatings of L is now four times what it was with the charge 100. The “force is therefore equal to that of a square inch of M, and the quantity of electricity on a square inch is the same in both, while the distance between the coatings isin Ltwice thatin M. The electrometer connected with the charging side of L now requires 40 grains. Suppose the sides of a magic pane to be separated by a dielectric plate capable of compression, and which yields stiffly to the attractive force exerted through it from the opposite sides. The quantity remaining constant, the static force is constant, and the intensity of the free part of the charge diminishes as the square of the distance between the opposite surfaces. 52. The coated surfaces of the magic pane may be supposed to be perfect concentric spheres, in which case no free electricity is required to enclose and confine the charge, which is wholly engaged and symmetrically placed. This form given to the magic plane simplifies the subject, and enables us without em- barrassment to arrive at an accurate conception of the integral of the force. Let the sphere A (fig. 25) with conducting surface be situated concentrically within the spherical shell B, also composed of con- ducting matter. We suppose A to be charged with 100 unit- jars of positive electricity. On the inner surface of B we have negative electricity induced ; and the quantity is the same as on A, because they mutually engage ; but the density is less, because On some Electrical Experiments and Inductions. 193 the surface is greater, the ratio being the inverse square of the radii. Suppose 100 radial lines like ad to be drawn equidistant, and let ¢ represent an extremely thin disk of metal perpendicular to one of the radi. We know that on the inner side of ¢ negative electricity appears, and on the outer positive. These are shown by the arrow-heads, or rather what are more correctly to be taken as V marks. Thus c towards J presents a positive entrant or male aspect, and ¢ towards a presents a negative recipient or female aspect. Upon each of the 100 radial lines we may ima- gine an infinite number of such disks without any disturbance of the electricity between the concentric spherical surfaces; and if each is marked like c with the symbol of the electricity that is developed on each side, we shall have each of the 100 lines re- presented thus >>pp>pr-, which exhibits the nature of the static polarizing power that exists in the space between a and bd. The intensity of this force depends on the distance between the lines, diminishing as the distance increases. To obtain a clear idea of this, we may suppose another disk d similar to c and close to it. We may also imagine these disks to be extended all round so as to become spherical surfaces C, D concentric with A. The electric equilibrium will not be disturbed. We have next to suppose the electricity or electric lines between A and C to be discharged, also those between D and B. We shall then have remaining the electri- city between C and D. Let the radius of A be considered as unity, and that of C be denoted by 7; we may then represent cd by dr, Let D be supposed immoveable, and C moveable and expansible. The force that attracts C to D is uniform through the element of space dr, and is proportional directly to the spherical surface C, that is to r?, the spherical surface of A being unity, and inversely as the square of the density of electricity upon C, that is to =: the density upon A being considered unity. Hence the static force 2 of C towards D is thus - = “. [supposing the static force of A, when as originally charged towards an exterior concentric sphe- rical surface at distance dr (the electricity being supposed engaged between the two as in the case of C and D), to be unity], and the space through which this static force acts being dr, the differen- tial of the work performed by the surface C in expanding to D by the influence of the electric force is = the integral of which is 1— = This gives us the value of the work performed by the spherical surface A expanding to infinity under the influence of the 194 Mr. J. J. Waterston on some Electrical electricity with which it is charged. This value is expressed by unity, which means the static force at A acting through the radius of A. 53. Compare the charge on A with a charge of equal density on another sphere Z with twice the radius of A. The quantity of electricity on Z must be four times that on A to have equal density with it; and the density being equal, but the surface of Z four times that of A, the static force on Z is four times the static force on A; and as the integral is that force acting through _the radius of the respective spheres, it comes to pass that the integral of the charge on Z is eight times the integral of the charge on A; and the quantity of electricity on a square inch of the surface of Z, although equal to the quantity on'a square inch of A, has twice its mechanical equivalent. This may seem somewhat of a paradox ; but a little considera- tion as to the rate of divergence of the electric lines will make it clear. Thus let cd (fig. 26) represent the space occupied by an electric line or root on the surface of the sphere A, and ef the same on the surface of Z, 6 being their common centre. Now, the density being the same, cd=ef=a, and ¢@ is the static force common to both. These lines on proceeding outwards diverge, _ so that if cd or @ becomes ep in 6 distance out from the surface of A, ef or « becomes ep in 26 distance out from surface of Z. The statice force of both being ¢, we have ¢6 the first dynamic increment of a line issuing from surface of A, and 26 the first dynamic increment of a line issuing from the surface of Z. All the successive increments have the same ratio, therefore the inte- grals have also this ratio. 54. Thus we see by clear induction from the elementary laws established by the experiments of Cavendish and Harris, that,an electrically excited surface contains only the roots of lines of force, in which lines the mechanical power of the electricity resides. Work is, as it were, stored up in these lines, and the static intensity at a point in one of them depends on the close- ness of the neighbouring lines at that point only. The closer they are packed the more intense the longitudinal force, and the more intense the lateral force of repulsion. Indeed these forces, as they increase and diminish together, seem to be identical, or a mode of reaction. The repulsive tension exists in the plane mn (fig. 27) transverse to the electric lme /p/ in which the con- tractile tension is manifested. When two bodies charged with the same electricity are brought closer together, the lines become more closely packed. Mecha- nical power, or work, requires to be expended in order to force the bodies closer together, 7. e. to force the electric limes closer together. _ The lateral repulsion of the lines has to be overcome, Experiments and Inductions. 195 and that increases in a high inverse ratio of their mutual. dis- tance, and produces a proportionally intense longitudinal con- tractile static tension. The mutual distance varies at every point of a line, and responsively so does the transverse repulsive ten- sion and its dependent longitudinal contractile tension. Let the disk c (fig. 25) have a magnified representation in fig. 28, and let it be composed of a double film of metal ¢, c,, the two films being perfectly close together, yet not cohering. We may further imagine these double films to extend all round to form concentric spherical surfaces as before (52). It will be remarked that we have negative or V roots developed on c,, and positive or A roots on ¢, the lateral repulsive tension acting in the space between these roots on both sides of the -duplex film c; but on the side c, it produces a longitudinal strain in one direction, 7. .e. towards a; and on the side c, it pro- duces an equal longitudinal strain in the reverse direction, 2. e. towards d or 0. tit Let a, x, b, z (fig. 29) represent four rods jointed at their ex- tremities ; press a and b towards e, this will press z and z from c in opposite directions. A rough notion may thus be obtained of the lateral and longitudinal strain that exists on every part of an electric lme—the lateral convergent being the ad pressure, and the longitudinal divellent beimg the @ z. The lateral force affects the position of the lines, and thence of their polarized roots on conducting surfaces; but it is the longitudinal strain at the polarized roots that immediately pro- duces the phenomena of motion and discharge. The motor phe- nomena resulting from the strain at the roots sometimes assume the appearance of attraction and sometimes of repulsion in adja- cent bodies, as, from the lateral action of the lines, the roots happen to be distributed more on their near or their opposite sides. 55. If we examine closer this quantitative relation between the lateral and longitudinal forces, we shall find a certain simplicity that is worth keeping in remembrance. Suppose two planes at the infinitesimal distance dr to cut the lines at right angles. The lines intersect these planes in points, each ‘point, as p, fig. 80, being the centre of a certain extent of surface which may be denoted by a, and dr may be viewed as the ~ axis of a cylinder whose area is adr. This area is small when the lines are closely packed, and vice versd. What relation does the static intensity of the longitudinal force at p bear to the area of this infinitesimal cylinder ? The force, as it has been proved from Harris (51), is as the square of the density of electricity, or as the square of the num- ber of points ina square inch. Thus « being the area of one 196 Mr. J . J. Waterston on some Electrical point, the number in a square inch is o = and the force on a iy gh futiahel square inch is as 3 but the number being a z the force of each one is & —: a Thus it appears that the fundamental law of action is that the static longitudinal pull at p is inversely as the area of the infini- tesimal cylinder edr. Now to fix this in the mind, we may ima- gine the cylinder to be a reality, and, however great or however small, to contain the same constant quantity of an elastic fluid, which will thus be more compressed when @ is small than when it is large. Further, let us suppose a valve or pressure-gauge at p, or rather two small pistons, acting one in the direction pi,, and the other in the direction pl,, under the influence of the elastic fluid contained in the cylinder. This elastic fluid, when of double density, exerts double pressure, according to the law of Mariotte; so that it is not difficult, by keeping this little arti- ficial arrangement in view, to retain a distinct idea of the distri- bution of force in an electric line. How Nature accomplishes this curious arrangement of force, and supports it from two excited material terminals, is of course a profound mystery; but that it does exist is, I submit, a fact inductively established. We have no choice, we cannot deviate from it, if we regard accuracy in the conception of the potential nature of electricity. It is a theory, not an hypothesis; a system proved from Harris’s observations, not a system coined in the imagination. | 56. With regard to practically determining the mechanical equivalent of a given charge (that is, a given quantity of elec- tricity on a given surface), the only difficulty is from the portion that is free—how to ascertain its amount and allow for it. The following occurs as perhaps practicable with Harris’s appa- ratus. [The unit-jar as a measure of quantity seems to be unex- ceptionable ; would it not be well to have an arrangement for an absolute-unit standard measure ?| Suppose we wish to compute the integral of a charge of g unit- jars given to a sphere 10 inches in diameter, having a surface of 314 square inches. Let B be a circular conducting plate of 100 square inches mounted horizontally in a perfectly insulated con- dition, and at the distance of an inch let A, another circular plate of the same size, be suspended by newly high-dried silk lines to one side of abalance. Let a charge be given to B by unit-jar, while a free conductor touches A ; and after removing the free conductor from A, let the weight required to raise A be measured as in Harris’s experiments. Next let B be touched with a free conduc- Experiments and Inductions. 197 tor, and, the distance A B continuing to be 1 inch, let the weight required to raise A be again measured. Let the first weight be denoted by m, and the second by 2, and let the charge given to B at first be ¢ unit-jars. The forces at the constant distance AB being as the square of the quantities of engaged electricity between the opposite surfaces, we have Wm:Vn::1: 3 and oq / is the charge which, engaged between two surfaces m of 100 square inches at the distance of 1 inch, engenders the force m of apparent attraction. Now ¢ — upon 100 square inches gives electricity of same density as 3:14 ¢ ah — upon 314: square inches, the surface of the sphere of 10 inches diameter : compare this charge with g. The force of apparent attraction follows the ratio of the square of the charge; hence we have on [x 8:14:92: B14xm: n=, m D n that is, the value of the weight that, acting through 5 inches, the radius of the sphere, expresses the integral of its electric charge —its work-representative. On the Arrangement of Electric Lines into Systems. 57. From the simplest system, viz. that of lines issuing from the surface of an insulated conducting sphere, we may pass to others where exact mathematical treatment seems hardly possible as yet. But one or two salient points arrest the attention. 58. Free electricity in a conducting surface of unequal curva- ture, as the solid S B with a sharp and blunt end (fig. 31). a. The mechanical equivalent of a line upon such a surface increases in going from the blunt to the sharp end. The lateral force of the roots lying in the small circle a, resolved perpendicular to that circle, must equilibriate the lateral force of those in the larger circle 6 similarly resolved. This requires closer packing at a than at 6. The number in a x their lateral force should be equal to the number in 6 x their lateral force. Let a be the length of one circle, and 6 that of the other; m the number in 2 2 a, and m the number in 6. Then = and (*) represents the area of each root respectively; and since the lateral force at the ° 2 2 . root is inversely as the area, we have (=) and. G) representing 198 Mr. J. J. Waterston on some Electrical the lateral force at each root. respectively in the circles a and b. Multiplying these by the number of roots m and n, we have me a. — Bz 2 at b @ we have the ratio of the density at 6 to that at a as 1 to b? m? | . Se ee p2\4 Bm? which by substitution is equal to (=). itteh tok Hence “ = pp and the density at a being “3? ind 6. Suppose a continuous metallic envelope to intersect all the lines that radiate from the surface of SB beginning at a certain point P. If P were at an infinite distance from S B, it is evident that. the envelope would be spherical : so at intermediate distances such envelopes would graduate between the extremes of such a surface as SB and a perfect sphere, while those close to the pri- mary 8B would be less contrasted than it in the curvature of its extremities.. The surface would be similar to S B, but less and less pointed as the distance is greater. c. The mechanical action of the electric roots on S B being at each perpendicular to the surface, the integral of all these forces, resolved in one direction, ought to be zero, because all the lines being supposed free, and no discharge taking place at the sharper end, the body is at rest; the static pull at the surface 1 is equal in all directions. 59. Free electricity of the same kind on two adjacent insu- lated conductors. a. While the excited bodies are forced together, the lines are closer packed and have their integral power augmented, me- chanical power being converted into electric tension, and vice versd. When they fly from each other, electric tension is con- verted into mechanical force or work, e. g. the two hemispheres H, K (fig. 82); when separate and equally electrified, their collec- tive surface measures six great circles, when in close contact it measures only four. 6. The repulsion between H and K is immediately caused by the increased quantity of electricity accumulated on the off sides of the hemispheres (leading to a preponderance of root pullings on these sides), which is effected by the lateral repulsion of the lines that issue from H on those that issue from K bending them round. c. The disposition of the electricity on the adjacent sides of the hemispheres as they approximate must be peculiar. The lines belonging to one that lie next to the lines belonging to the other, as ab, ed (fig. 32), while approximating at a and ¢ and ex- ternal to these points lying adjacent, and forming part as it were of one system, must at the lower part b and d diverge to these Experiments and Inductions. 199. roots on different surfaces, thereto form the interior terminals enclosing a space in which no electric lines exist. I have found this confirmed by experiments made with circular plates 5 inches in diameter stuck on cylinders of lac (fig. 34). Narrow slips of gold-leaf about 14 inch long were stuck on at three or four points in a line passing through the centre, so that when the plate was charged they rose on end, and would stand thus for an hour (d, g). When the twin-plate p, equally charged, was brought down parallel to g, there was a certain distance (about 3 inches) at which they dropped suddenly dead as it were; and looking through a lens at them when the distance was reduced to about 2 inches, there was not the slightest appearance of electric ex- citement at the edges of the leaves when p was tilted a little so as to disturb the general equilibrium of the system of lines. It appears that in such cases, when bodies similarly electrified are made to approach, we are compelled to admit the existence of a series of inner terminal lines acting laterally outwards and sideways, and sustained by their contractile tension. (See 60.) 60. When insulated conductors charged with different electri- cities approach each other, the charge becomes more engaged and less free. The mechanical integrals of the lines diminish, and electric tension is converted into work. - When forced sepa- rate it 1s vice versa. Let Q and R (fig. 86) represent two equal spheres segmented at g and r so that there should be equal and parallel circular planes opposing each other at those points. Suppose these spheres to be equally charged with the opposite electricities, and to move backwards and forwards in the line Q R—an impervious dielectric medium, such as a mica plate, intervening between. the circles g, 7 to prevent discharge when close together. When Qand Rare at a distance, almost all the electricity upon them is free and distributed over their spherical surface (fig. 36) ; when they are close together, almost all the electricity is engaged (fig. 37), and to be found in the opposite circles g, 7 separated by the thin impervious non-conducting film. While approaching, they are impelled by the prepondering force of the electricities (or root pulling) on the near sides, and work or dynamical force is engendered. The electric lines collapse, and their integral force is expended by being converted into motion. They are to a certain degree discharged; but complete discharge has not taken place, for the roots are still polarized, and by applying force the spheres may be withdrawn from each other and work reconverted into electric lines. Let us consider the equilibrium of the lines in an intermediate position such as fig.85: what is the force that packs close together the lines on the near surfaces? The condition of equi- 200 Mr. J. J. Waterston on some Electrical librium among the lines requires that they be pressed as much inwards towards gr as outwards; but tracing round the sphe- rical surface till we come to the extreme outward points opposite q and 7, it is obvious that, although the excited roots of these pomts may have others adjacent mutually repellent on all sides, yet the lines that issue from these extreme points must in their curvilinear course /m, uv take directions that cannot have juxtaposition except at the issuing points on the surface. What, then, prevents them yielding to the repellent forces of the imte- rior adjacent lines? Let m (fig. 38) represent an ultimate me- tallic chemical atom im an electric line PN. If such a condition could be realized, there is every reason to believe that the side towards N would be positively electrified, and the side towards P negatively electrified, as represented by the V symbols, and that it is thus being pulled equally from both sides with intensity in accordance with the nearness of adjacent lines. Now let us sup- pose a similar atom situated at each symbol thus (fig. 39). We have, instead of an electric line, a line of electrified molecules each of which is drawn by an equal force in opposite directions, giving to the whole line a longitudinal contractile tension. Now supposing such a line to be curved, this contractile force will engender a lateral compressing power towards the concave side ; and as all the disengaged electricity in this system consists of lines similarly curved, 7. e. with similar convexity one over the other, the lateral packing power is cumulative, and the central ’ engaged lines will be packed together by means of the curvili- nearly derived power of the whole of the system exterior. The proof of the existence of this contractile power in a line is obtained by employing the method of concentric films as in 52. Suppose B and all the concentric films to contract simulta- neously and concentrically upon A by the electric action between the adjacent surfaces in degrees respectively proportionate to their distance from it. Here is a system of lines expending their integral, and in doing so exerting a contractile force throughout, which must therefore have had a contractile tension as potential antecedent, a force acting at each point of a line towards its opposite extremities. A line composed of india-rubber has a contractile force which might be thus defined ; but it differs from an electric line in this, that in the rubber line the force is the same at every point; but in the electric line the force depends on the distance of adjacent lines, and is thus variously distri- buted according to circumstances. Thus, e. g., in the concen- tric spherical arrangement of 52. the contractile tension dimi-- nishes outwards regularly. When the electric lines are closely engaged, the contractile tension must be nearly uniform. In the systems figs. 84, 35 it may be small at the root, gradually Experiments and Inductions. 201 increase for a certain distance, obtain a maximum, and then di- minish. Generally it must be in a continual state of change according to the varying condition of the system to which it belongs. | 61. In the magic pane the free part of the charge compresses the engaged part by the contractile tension of the free lines. These by their lateral repulsion tend to fill up unoccupied space, and thus bend round the engaged lines and acquire the lateral packing power by their longitudinal tensile force when thus bent. Fig. 40 is intended to give an idea of the charging of a magic pane. The line B pressed forward by A (intended to represent the lines engendered by the machine) arrives at the balls 4, /. The ball / cuts the line, and so do the opposite surfaces of tne magic pane. The part of it between & and / remains, and so _ does the part between the coatings of the magic pane. The part c between / and the near surface of the magic pane con- tracts and discharges itself along the conducting wire w; the exterior part D escapes to the ground by the free conductor x after the centre part N has been pressed into the magic pane. The lines between & and / accumulate until discharge takes place, which may be looked upon as a signal that a certain number « of lines have crossed over and left segments packed into the magic pane. The spark appears after the unit quantity has entered the jar. The propelling force (from the machine) required to bring up @& of course increases as the charge M increases ; but when brought up, it is probable that discharge between k, J destroys the same constant number of lines, and thus that the unit-jar correctly measures quantity, its coatings 2,7 beg viewed as prolongations of the surfaces of the respec- tive balls. . Remarks. In experiments such as 1, 3,5, 6, the phenomena are, strictly speaking, examples of convection or conveying of polarized par- ticles (except 50, 5c) to non-conducting matter, upon which they adhere without being depolarized. They all tend to prove that electricity is never separate from matter even in discharge. _ (8.) It seems probable (since a small ball throws off stars) that a brush consists of a symmetrical succession of polarized molecules—at least when discharged upon a non-conducting surface, upon which they cling still in an excited condition, and therefore must act repellent upon the next in succession (see 4). The breadth of the fosse is evidently caused by capillarity. (7.) In this experiment the thin shell-lac coating of the con- ductor becomes charged as magic pane with one side only coated. Viewed in the dark, the brush was of eccentric forms. (8 a.) Is aremarkable effect that I do not recollect having seen Phil. Mag. 8. 4. Vol. 29. No. 195. March 1865. P 202 Mr. J. J. Waterston on some Electrical mentioned before, although it can hardly have escaped the notice of experimenters. (8 5, &c.) Are due to a similar quality of shell lac, and probably other non-conducting surfaces. If the electric fire consists of strongly excited molecules, we may remark that when in such condition of excitement, and moving probably with inconceivable velocity, they appear not to obey any ordinary law of projectile force. They seem for the time to form part of the polarized ether, and to be in the grasp of an agent of transcendant attri- butes. As it is in the spark, so must it be in the lightning, the amazing mechanical effects of which must be due to the matter issuing from the surfaces of discharge. (9.) Such phenomena might be anticipated of a heterogeneous body consisting of a perfect dielectric substance (if such a sub- stance really exists, but clear amber is not) containing conducting particles equally distributed throughout its mass, each one par- ticle being separate and isolated from itsneighbour. The appa- rent induction at first seems evanescent; but in subsequent experiments it will be remarked that, if exposure lasts for some minutes, persistent inductive excitement appease the surface adjacent to the one excited. (10.) We may remark in this, that while brush discharge and convective discharge of less intensity (1) takes place upon a non- conducting surface, the: spark discharge does not take place without forcing it open: the coating is lifted up at both dis- charging surfaces, therefore metallic particles issue from both. Is such the case in lightning between the cloud and the ground ? Does the flash consist of luminous water on one side, that of the cloud? ‘Towards the ground there may be many surfaces of discharge, at each of which polarized molecules issue giving rise to so many different foci of explosion. (21.) This effect is what would take place by separation of polarized molecules from the metal that strokes the wax surface, because the excitement is located on the surface stroked. Yet it is difficult to see that this is likely, the wax beg much softer than the metal, especially when it is steel—as the side of a steel blade. (22.) The rate of dischar ge diminishes with the intensity : combustion being chemical action, and chemical action being also electric action, the electrically- excited molecules of the oxygen, carbon, or hydrogen may fly to the excited body under the influ- ence of its induction, which though weak may yet be stronger than that of the combining element. From 29d. it appears that molecules do actually proceed from the flame to the near surface of the wax screen, which, with the B. D. and intermediate air as dielectric, becomes a char ged magic pane arrangement, the B. D. forming one side and the screen the other. ” . = Experiments and Inductions. 203 (24, 25, 26.) Here there is evidence, especially in 25., that the flame or match acts in discharging the B. D. partially, as if unconnected with the electroscope. In this it differs from the action of points, which could not discharge the B.D. without charging the electroscope, although the discharge would of course be more limited than if the plate of the electroscope were a free conductor. (27, 28.) Why should not the brass disk be discharged under the same conditions that discharge the excited sulphur ? (30.) This is proof of induction acting in curved lines, which Faraday was the first to direct attention to (Experimental Researches, 1218, 1231). Not entertaining the possibility of such curved action taking place in a vacuum, he holds that the inductive force is enabled to bend round in consequence of the molecules of air being polarized, and one leading the action to the others in straight lines. In § 63 of paper in Phil. Trans. for 1834, Harris states that the operation of electricity on distant bodies by mduction is quite independent of atmo- spheric pressure, and is precisely the same im vacuo as in air. (31.) The free part of the charge which issues from the exterior surface of the inside coating gradually diminishes, and the engaged or masked portion between the coatings consequently expands, and the free part comes to issue from the exterior sur- face of both coatings. So the electroscope shows latterly the action of that nearest to it, which again is removed by touching the outer coating. See 34. (35.) The diminution of the excitement probably takes place by discharge (the exact nature of which remains to be discovered). This must take place, not only on the excited side, but all over. Now remark that the discharge of the electric lines that takes place on the excited side is the total of each line discharged ; but the discharge that takes place on the side opposite the excited side is the discharge of lines that pass through the cake, so it must leave undischarged that part of each line that lies between the two surfaces, having negative root on «and positive on 8. A charged magic pane without coatings is thus gradually formed and gradually also discharged. _ It is the engaged lines becoming gradually disengaged that at last brings out the posi- tive electricity on the surface opposite to that originally negatively excited. : (37.) The inductive effect on a wax surface is very marked in this and other experiments. If a B. D. charged negative is placed resting on a cake of sulphur, it induces gradually a per- sistent positive on that part of the surface of the sulphur upon which it rests. Time is required. See 39, 40. (88.) When first discharged this double cake has positive on P2 204: On some Electrical Experiments and Inductions. the whole of the outside surface, top, bottom, and sides, which is completely engaged by the negative on the two interior surfaces. No free charge is required to hold the engaged lines together ; the condition is similar to the concentric spheres of 52. _ (41, 42.) The appearance of positive on 8 depends on a partial discharge having spontaneously taken place during the elapsed time, as in 35. (43.) The lower cake positive by induction; the upper by © partial discharge of a few of the negative lines that pass upwards through the three cakes. It is remarkable that the mductive power is limited in its action to the surface in contact with the surface excited. . (44.) In this, as in 36., the surface in contact with the excited surface appears to share, to a small extent, its excitement, as if conduction had actually followed very slowly behind induction. (45.) The permanent effect on the cylinder was similar to the temporary effect on a conducting cylinder of the same size, the charged B. D. being supposed close to but not touching it. (47.) This is a very instructive experiment; there was no actual loss of charge, only an apparent loss, so long as the cake was on the electroscope and the contact surface inductively _ excited. (53.) The large radius of the hoop appendage that characterizes Winter’s electric machine gives slow divergence to the electric lines that issue from it. See 53. This gives them, as part of the system of electrical lines that imcludes the lines between the spark balls, great power of lateral compression upon them previous to the spark. The thunder-cloud as a charged surface is an extreme example of the spark-producing power of slowly converging electric lines. (58 a.and58c.) The distribution computed from 58 a. subjected to the equation in 58c¢., ought to stand the test. In an ellipsoid or spheroid it might be practicable to execute the calculation, and thus obtain further confirmation of the law of mutual depen- dence of the lateral repulsive and root-pulling or contractile force. In conclusion I may mention that the theory of electric lines here given was deduced from Harris’s experiments about twelve years ago; since which time I have been in the habit of applying it to the published results of experimentalists, and thus continually testing it. It is very suggestive of new experiments. Some of the simpler sort of these I have been able to make, but there are others, chiefly with respect to the production of light and mechanical effect, that require greater means and appliances, not to mention aptitude; for to suggest and to execute are spe- Dr. C. K, Akin on the Conservation of Force. 205 cialities that do not always go together. The main end and purpose of these would be to obtain some idea as to the working arrangements between the ether—that higher potential form of matter in which the might of the Infinite resides—and ordinary molecules, the agents of its development. If we confine our attention to the planetary movements, nothing seems clearer than that its density must be inappreciable. On the other hand, were we to make legitimate inferences from the most obvious phenomena of radiant heat, there is evidence that its density may not differ much from that of water, and at least that it is quite impossible that its non-resistance to the celestial motions can be owing to its extreme rarity. Edinburgh, December 4, 1864. XXIX. On the Conservation of Force. By Dr. C. K. Axin*. aoe and another controversy of a very different nature, prevented my noticing hitherto Professor Tait’s answer to my remarks published in the last December Num- ber of this Magazine. Professor Tait begins by calling atten- tion to the fact that, although omitting the words ‘in omni instrumentorum usu” from the passage which he quoted from Newton’s scholium, he indicated the omission by dots. The readers of this Magazine will have seen that in reproducing from Pro- fessor Tait’s paper the paragraph in question, I took care to cause the dots also to be inserted, to which I made special refer- ence in my remarks. On this point, therefore, there can be no misunderstanding. But when Professor Tait says that “in ordi- nary mechanics ”’ is the ‘‘ perfectly complete” free rendering of the above Latin words, I can only partially agree with him. No doubt the rendering is free, “ not literal,” and in some instances it might also be correct ; but I contend that in the present case it is not properly admissible. In the sentences preceding the one cited both by Professor Tait and myself, Newton instances expressly the cases of the “ balance,” “pulley,” “clocks,” “screw,” and “ wedge”; and in my opinion, therefore, the free English translation of “in omni instrumentorum usu,” as appli- cable to the case in hand, is not ‘in ordinary mechanics,” but as given by Motte, ‘in the use of all sorts of machines,” or something like it. Professor Tait allows that “‘in Newton’s time, and long after- wards, it was supposed that work was absolutely lost by friction ” —in other words, that Newton himself supposed it to be so; but, considering that it was known that friction excites heat, as well * Communicated by the Author. 206 Prof. Favre on the Origin of as the other facts I have mentioned, I cannot agree with Professor Tait “that, so far as experimental facts were known in Newton’s time, he had the Conservation of Energy complete.” In the case of any other man it might appear ungenerous to look too closely into claims to a scientific discovery put forward on his behalf by well-meaning advocates, especially when there is not any better- entitled competitor in the field; but in the case of Newton, whose head is already so thickly covered with laurels, this remark could not apply. I cannot help thinking that the principle of the Con- servation of Force, in its widest sense, was discovered by no single person, but was only gradually evolved and developed; and lam mistaken if we are already in full possession of its meaning. Professor Tait protests against the allowing of any weight to the opinion of John Bernoulli “on a question of this nature,”’ because he “ seriously demonstrated the possibility of a perpetual motion.” Iam not aware that, in point of theory, “ perpetual motion” is impossible; although, no doubt, “ perpetual work” is But waiving altogether this point, would it not be possible also on such a principle to impugn the value of any opinion of New- ton—for instance, on the subject of light, on the plea that his fundamental notion of the nature of light was wrong? Like many others, I am anxious for the appearance of Pro- fessors Tait and Thomson’s long-promised treatise; and in the meanwhile the “Sketch of Elementary Dynamics,” published for the use of the students of Glasgow and Edmburgh, might perhaps with advantage be made more accessible to students in general than I have understood it to be. London, February 1865. XXX. On the Origin of the Alpine Lakes and Valleys. A Letter addressed to Sir Roderick I. Murchison, K.C.B., by M. At- PHONSE Favre, Professor of Geology in the Academ y of Geneva, and Author of the Geological Map of Savoy*. SIR, Geneva, 12th January, 1865. [ AM glad that you have asked my opinion of the new theory, according to which the Alpine lakes have been excavated or scooped out by glaciers; and of that which also explains the origin of the Alpine valleys by means of the erosion produced by glacial action. -* Communicated by Sir Roderick J. Murchison, K.C.B., D.C.L., F.R.S., &e. + A great isany arguments against these theories have been advanced in various memoirs, as in those of Mr. Ball (Phil. Mag. 1863, vol. xxv. p- 81), Desor (Revue Suisse, 1860), Studer (Archives des Sc. Phys. et Natur. 1863, vol. xix.), &c. However unwilling I may be to reproduce the arguments which they have already employed, it is almost impossible not to revert to them occasionally. the Alpine Lakes and Valleys. 207 IT am a strong partisan of the notion of the transport of erratic blocks by ice, at the period of the great extension of the glaciers, and as a Swiss [ am attached to this theory, which is worthy of the term national. But, at the same time that I acknowledge it to be accompanied by certain difficulties, I can- not comprehend the two other theories, although they have the advantage of being advocated by able men of science. Amongst these is to be counted Professor Ramsay, a highly distinguished geologist, to whom long practice on the Geological Survey of Eng- land has given great powers of observation and a sure eye (coup ail), Mons. de Mortillet, who is well acquainted with the Alps, and Professor Tyndall, whose works on physics hold the first place. Not that I do not sincerely respect the opinions of the learned authors who have developed these views, and who have done so, I acknowledge, with considerable ability. It is evident, indeed, that existing glaciers abrade the rocks on which they move, inasmuch as they polish them. But this action is so feeble, that I cannot see how it has been inferred therefrom that it has been able to scoop out deep lake-basins many hun- dreds of feet below the mean level of the valleys, even on the supposition that it has been exerted during very long periods. I understand still less how this same action could have excavated valleys many thousands of feet deep in a great rock-mass like that of the Alps. A limit must be set to certain effects. This limit exists in all geological questions, and it is indispensable to establish it. On seeing a dune on the sea-shore, twenty or thirty metres high, formed by means of grains of sand driven by the wind, shall I be right in concluding that m some hundreds of thou- sands of years this same dune could attain the height of the Alps or that of the Himalaya ? I have no wish to maintain that the glaciers have not exerted any influence on the forms of lakes and valleys. It seems to me to be impossible that masses so considerable as those which moved in the valleys during the glacial epoch, should not have fashioned, more or less, the borders of these depressions. But I cannot become an advocate of the belief that glaciers are the original cause of the formation of lake-basins and valleys. I believe both to be a direct consequence of the formation of. mountains, and that they both owe their origin to movements of the earth’s crust. Let us now leave these general arguments, and arrive at more precise facts relative to the origin of the Lake of Geneva. According to all glacial theories, the union of all the glaciers of the Valais at Martigny, to a portion of those of the main body (massif) of Mont Blanc, formed one enormous glacier, to which 208 Prof. Favre on the Origin of the name of the Glacier of the Rhone has been given. This glacier evidently discharged itself into the Swiss plain by the valley which extends from Martigny to Villeneuve, and had a mini- mum thickness of 23800 to 2600 feet *. This great glacier extended itself over the plain. It covered all the bottom of the basin of Lake Leman with moraines, boulders, clay, and scratched pebbles. The distribution of these materials has often been studied; they are spread over the two banks of the lake; but I do not think that any conclusion can be drawn from their examination, either for or against the hypo- thesis which I am desirous of examining. In the course of its slow but continuous movement, the enor- mous glacier abutted eventually against the Jura. As M. Char- pentier has stated, it is remarkable that the maximum height of the traces which it has left should be near Chasseron, a moun- tain situated to the north-west of Yverdun, just opposite the valley of the Rhone. The blocks there attain an elevation of 3000 feet above the Lake of Neuchatel +. Thence the upper limit of the boulders falls successively to- wards the north and south, in such a manner that we may apply the term medzan to the line which connects the mouth of the Rhone near Villeneuve with Chasseron. North of the median line the higher line of the blocks rejoins the plain in the environs of Soleure. The glacier terminates there, and has left at its ex- treme limit the remarkable blocks of Steinhof, near Soleure. South of the median line the glacier has left incontestable traces over all the southern extremity.of the Swiss plain. It has gone beyond the limit of this plain in passing Mont Sion, south of Geneva, and the defile of Fort de l’Ecluse. These facts have long been known; but it is a matter of surprise (reasoning according to the hypothesis of the excavation of the basin of the lake by the glacier) that the lake has not been hollowed out in the direction of the median line—that 1s to say, from the mouth of the Rhone to Chasseron—but in a curve which bears no rela- tion to that line. This bend in the lake nearly follows the base of the great mountains which are situated on the southern bank, at least so far as the large lake is concerned. The depth of the basin is evidently connected with the neighbourhood of the mountains, and the inclination of the strata; it is thus that near Meillerie, where the mountains are elevated and the strata vertical, the lake at- * Charpentier, ‘ Essai sur les Glaciers,’ pp. 270, 271. I am led to believe that the glacier rose above this limit, and that if blocks are not met with above it, it is owing to their having rolled towards the bottom. + Charpentier, ibid. the Alpine Lakes and Valleys. 209 tains its maximum depth (265 metres near Meillerie, and 300 metres a little further west*). Nevertheless it is probable that in this locality the bed of the lake is of the same nature as its banks, that is to say, lime- stone, and that the ridges there consist of very hard lime- stone. Further westward, where the lake is situated in Tertiary Mollasse much softer than the limestone, it only attains a depth of from 30 to 40 metres. This fact is of considerable importance. It seems to me inexplicable, on the supposition that the glacier hollowed out the basin of the lake ; on the other hand, it is easy of explanation in connecting the depression of the lake with the inclination of the strata. Near Meillerie the beds of hard limestone are vertical and highly contorted, and there the lake is deep; nearer Geneva the softer beds of Mollasse descend from the two sides of the lake beneath its waters with a gentle inclination, and there the lake is shallower. This proves the relation between the depth of the lake and the flattening of the beds, as has been already stated by M. Studer; and I will show further on, that it is connected with the reversal of the same beds. Let us now turn to another point. I consider that the observations made in the neighbourhood of Geneva have contributed to the origin of that theory of the erosion of the lakes, which | oppose. These observations may be summed up as follows. Below the Lake of Geneva there are found considerable accu- mulations formed in their upper part of glacial deposits (clay with scratched pebbles and transported boulders), and in their lower part of the older drift of Necker. This latter deposit is different from the old drift of the greater number of the savants who have written upon the geology of France. We have also in our country this old drift, which is that which I have distinguished in the explanation of my geological map of Savoy by the name of terrace-gravel (alluvion des terraces). It contains Elephas primigenius. Overlying the glacial drift, this last is higher than the older drift of Necker, upon which I am desirous of making a few remarks. This last is composed of rolled pebbles and sand, often bound together by a calcareous cement. No striated pebbles are seen amongst them. The principal characters of this accumulation in our district consist in its bemg of older date than the glacial deposit, in being placed below the Lake of Geneva, and in enclosing pebbles (such as those of euphotide) which could not have been derived from the Valais, whence the Rhone glacier proceeded. * Chart of the principal soundings of Lake Leman, by H. T. De la Beche, 1827. 210 Prof. Favre on the Origin of These: pebbles must consequently have passed over the de- pressions of the lake. But how could they do so, since their transport appears to be anterior to the development of the glacier? That is the difficulty, and it is this which has given rise to the notion of the theory of excavation, in which it is supposed that the pebbles of the older drift have been heaped up by pre-glacial currents in the depths of the lake, and that when the glacier reached them it excavated that portion of the lake which had been filled up. It is supposed, then, that it has produced a great excavation, and that it then spread before it all this enormous mass of pebbles which it drew from this great depression. This idea, generalized and applied to other localities, has produced the hypothesis which is known by the name of the theory of excavation. I think I have been impartial in this explanation. To this theory I believe I am able to offer objections which seem to me to be very serious. In the first place, when the glacier originally began to carry away from the depths of the Lake of Geneva all the enormous mass of pebbles which is now deposited lower down, how did it effect it? Did the glacier slide over the solid rock without leaving any interve- ning mass of these pebbles between the two? For if it left beneath it no pebbles, it ought to push before it an enormous mass of this débris, such a mass as can with difficulty be repre- sented—a mode of action which would be the more singular, because nothing amongst existing causes countenances this sup- position, no part of the glacier beg seen to push before it an accumulation of rolled pebbles. If, on the contrary, the glacier covered these rolled pebbles again, the excavation seems to me to be very difficult, because the glacier moulds itself upon its under surface, and causes the pebbles of the underlying bed of mud to advance very slightly. Moreover, according to one or the other of these suppositions, [ am unable to comprehend how the deposit of older drift could be accumulated below Geneva without any admixture of clay or glacial mud having been produced. But there is an objection which appears to me to be still more opposed to the theory of excavation. The supporters of this theory assign to the glacier which formerly mvaded our lake a force sufficiently great to enable it to remove, from a depth of 800 metres near Meillerie, all the pebbles of the older drift*. Nearer Geneva the lake is not so deep, and the glacier had still, at this point, the necessary power to scour out of the bed of the lake all those pebbles ; for we know that this glacier has extended several leagues further, * Mortillet’s Theory. the Alpine Lakes and Valleys. 211 and that it has passed over Mont Sion and the defile of Fort de ?Ecluse. But about a kilometre below Geneva (at the wood of La Batie) th older drift is visible, as I have stated, covered by the glacial deposit over a very large area. At this point one is compelled to conclude that the glacier has not had the power to remove this older drift, and that it has spread itself over it. Is it not evident that ‘the glacier has been supposed to possess immense power above Geneva, and that there is a clear proof that it did not possess that force below the city in question? I believe, then, that the truth lies in the fact that a glacier can slide over a deposit of rolled pebbles without cutting a way through them. Consequently the ancient glaciers have not had the power to remove, near Geneva, the older drift on which they have left their traces, and, for a still greater reason, they have not had the power to remove the rolled pebbles from the bottom of the lake. The rolled pebbles which constitute the older drift below Geneva, and which are placed beneath the glacial drift, seem to me to have been transported by the torrents which were given out by the glaciers of the Rhone and Arve when they reached the neighbourhood of our city. ‘They have been rounded after leaving the glaciers. This is perceptible ales existing glaciers when they reach a plain. In such cases there is nearly always a certain area of deposit occupied by rolled pebbles, which are fashioned, sorted, and levelled by the torrent. The pebbles which form part of the older drift, and which are evidently derived from the Valais, have traversed the depression of the lake when it was filled with ice. They have made the journey in question in the form of erratic blocks or gravel, and were rolled only when they reached the torrent at the base of the glacier. Subsequently, when this deposit was formed and levelled, the advancing glacier has passed over it; and, on retiring, it has left on its surface the glacial mud, the scratched pebbles and the erratic blocks which we see there even at the present day. I have endeavoured to show that the theory of excavation was insufficient to account for the accumulation of the glacial deposits, and I ground my opinion on the weakness of the ex- cavating power of the glacier, as is proved by the presence of the glacial drift reposing on a light deposit formed of rounded pebbles; for a still stronger reason I cannot believe that a glacier has ever excavated the basin of the lake or a valley. If these depressions had been formed by the glaciers, how shall I explain why there is no lake in the Valley of the Arve, in the valley of Chamouny, or in the Val d’Aoste? The glaciers have, nevertheless, remained for a longer period im those higher 212 Prof. Favre on the Origin of valleys, before, during, and after the glacial epoch, than in the valley of the Lake of Geneva. The valleys of Savoy and the Valais bear a clear relation to the structure of the mountains. They present a remarkable regularity. They are nearly all at right angles to or parallel with the general direction of the Alps. Amongst the former cases is noticed the valley of the Rhone from Martigny to the lake ; that of the Dranse, which has its outlet near Thonon; that of the Arve, from Sallanche to Geneva; the valley of Lake Annecy; that of the Isére between Moutier and Albertville, and between Tigne and Bourg St. Maurice, the valley of Chapier, that of Courmayeur, &c. Amongst those which are parallel with the chain of the Alps, are the valley of the Rhone above Martigny, the valley of Chamouny, of the Allée-blanche and Entréves, the valley of Illiers, the valley of Megéve, and that of the Isére below Albertville, and between Bourg St. Maurice and Montiers. Amongst these may we not reckon the depression in the Lake of Geneva between that town and Rolle, and which is parallel to the great anticlinal axis of the Mollasse? This axis extends from Saléve to Lausanne, passing by Boisy, and is continued onwards to Bavaria*. As to the eastern parts of the lake, the direction of which is from west to east, shghtly south-east, and which is consideredewith reason as being partly placed in a depres- sion (cluse), it bears a relation to the curved form of the mountains which lie on its southern bank+. To prove this, it is necessary to enter into minute details with regard to the direction of the various parts of the chain, which would be out of place here ; but I may quote an old and classical authority that nobody will call in question, and this quotation will show that the lake presents nearly the form of the mountains. “ The ordinary direction of these ranges aud of these valleys,” says De Saussure f{, when speaking of the region lying on the right bank of the Arve (between the Arve and the Rhone), ‘is nearly that of the entire chain, which in our country extends from the north-east to the south-west. But this general direction varies in some places and undergoes local inflexions. One sees from the summit of the Mdle that the chains of mountains, which in its * Bull. Soc. Géol. de France, 1864, vol. xix. p. 928. Archives, 1862, vol. xiv. p. 217. | + It is not on the south bank only of the Lake of Geneva that the chains of mountains assume a circular or semicircular outline. This form is still more developed in the mountains of the left bank of the Arve than in those of the opposite bank. See, m reference to this subject, a note which I have published in the ‘ Reports of the British Association for the Advancement of Science,’ 1860 (Trans. of Sect., p. 78). t Voyages, § 280. gg. the Alpine Lakes and Valleys. 213 neighbourhood run nearly north-east, follow for a great dis- tance the curve of the lake, and towards the frontier of the Valais take an easterly direction, as does the lake itself between Rolle and Villeneuve.” This form may be recognized in my geological map of Savoy. These great features, so characteristic of the region of the Alps which border upon us, establish an evident relation be- tween the form and position of the lake-basin, the orography of the ground, and the cause which has elevated the mass of the Alps above the mean level of the continent. The position of most of the Alpine lakes reveals to us, again, the relation which subsists between the mountains and the lake-basins: nearly all lie either on the borders of the Alps, or at the junction of the beds of Mollasse with hard calcareous chains. They frequently even penetrate the interior of the chains—allowing that the marshes, which are almost always at their upper end, form part of the lakes. Such are the lakes of Geneva, of Thun, Lucerne, those of Zurich and Wallenstadt (which form only one lake in a geo- graphical point of view), and also the Lake of Constance. In the Bavarian and Austrian Alps, again, are found the lakes of Wal- chen, Kochel, Schlier, Mond, Atter, Traun, &c., all on the borders of the Alps. Is this very remarkable position the result of chance? or is it not likely that in the law of the structure of the Alps there is a circumstance which has determined the formation of the lake-basins. This had been pointed out by De Saussure when, in describing the mountains lying on the right bank of the valle of the Arve, he remarked that the innermost turned their backs towards the exterior part of the Alps*, but that the outer chains turn their backs to the central chain; that is to say, that their curves are brought up on a line with the Lake of Geneva. Since the time of De Saussure light has been thrown on the question, and the papers which you yourself have published have contributed largely to the elucidation of this subject}. It is now recognized that over the greater part of the enormous distance which separates the environs of Geneva from the eastern Alps of Austria, there is a prolonged reversal of strata, so that very often the older beds repose upon the newer. One can understand that such a great disturbance in the strata should have produced a subsidence in those which are beneath the surface by a sort of reciprocating movement (bascule). As regards the Lake of Geneva in particular, this reversal has been clearly pointed out on the two banks—on the northern at * Voyages, § 281. + Quart. Journ. Geol. Soc. 1848, vol: v. pp. 182, 195, 197, 200. 214 On the Origin of the Alpine Lakes and Valleys. Playaux near Vevey, and on the southern at Voirons, east of Geneva. These two mountains are both situated on the borders of the Alpine chain. In order properly to grasp the relation which subsists between the overthrow of the strata along this line and the great depths of the lake, it is necessary to mark on the map the soundings of the lake by De la Beche, the positions of the crests of the Voirons, the Allinges south of Thonon, and of Playaux near Vevey *. The principal soundings of the lake placed opposite Meillerie and Evian may likewise (and perhaps it is the most easily effected) be marked on the geological map of Savoy. Then Voirons and Playaux should be joined by a line (but not by a straight line, because the chains on the borders of the lake are curved) drawn through Calvairé (Voirons), Allinges, the point where the Alpine Macigno (M) (Affleure) descends to a level with the bed of the Dranse, at a distance of four kilometres from Thonon and the city of Evian. Such a line as this would terminate towards Playaux, passing over the northern bank of the lake between Corsier and St. Saphorin. This course shows pretty nearly the line of the reversal of the strata situated on the flanks of the Alps; and, presenting a certain parallelism to the denudations of the different rocks traced on my geological map of Savoy, if passes through the midst of the soundings which indicate the greatest depth of the lake. Con- sequently this depth bears a relation to the reversal of the beds. It is in such fractures, I am confident, that the true cause of the origin of these lake-basins is to be found. From a summary of these facts it may be concluded— Ist. That the Lake of Geneva deviates much from the median (central) line of the great glacier or glaciers which extended from the Rhone to the Jura. 2udly. That these ancient glaciers not having had the power to remove the older drift below Geneva, have not been able to pro- duce in the lake-basins what is called their excavation (Vaffouille- ment). If they could not scoop out these basins, still less have they excavated the adjacent valleys which terminate in them. 3rdly. The valleys and the basins of mountain-regions are related to the cause which has given to the mountains their orographical characters, and to the strata their greater or less inclination. * This mountam, called Pleyaux or Playaux, is indicated on the Federal map by the name of Pléiades. To facilitate the indication of it on my geological map of Savoy, on which it is not marked, I should say that it lies 6 kilometres from the mouth of the stream which discharges itself into the lake between Vevey and Corsier, and 63 kilometres from the point of Montreux. On the History of Conservation of Energy. 215 4thly. We have seen, in fact, that, so far as the Alpine lakes ge- nerally are concerned, and as regards that of Geneva in particular, their position has been determined along a line of overthrow, or re- versal of the strata. We have seen that the form of the Lake of Geneva was caused, in the eastern part, by the curvature of the mountains on its southern banks, and in its western part by its parallelism with the great anticlinal axis which traverses Switzer- land. Finally, we have remarked that the greatest depth of the Lake of Geneva lies along the line of reversed strata which occurs at the junction of the Alps with the pla. Consequently the sort of basin to which this lake belongs is not the result of a cause acting on the surface of the globe, but is what may be termed a volcanic effect (that word being used in the sense assigned to it by Humboldt), viz. the influence exerted by the interior forces of a planet on its external crust in the different stages of its cooling. Accept, &c. &c., ALPHONSE Favre. P.S.—Since the dispatch of my previous letter, I have read - with extreme interest your Address to the Geographical Society of London, of the 23rd May, 1864, with which you have been so good as to favour me. I find in that address a clear and precise summary of the state of the question, and valuable evidences derived from many parts of the world. . I perceive in it, again, with pleasure that we are of the same opinion respect- ing the excavation of lakes and the erosion of valleys by glaciers. You make use of several highly important arguments against that view of the question, and you have already developed the idea on which I have dwelt—viz., that the form of the Lake of Geneva is divergent from the direction of the most powerful or central portion of the glacier of the Rhone, which advanced from the Valais in the direction of Yverdun, following what I have termed the median line. Pray, Sir, oblige me by inserting this remark at the end of my letter of the 12th of January.—A. F. Geneva, January 22, 1865. XXXI. On the History of Conservation of Energy, and of its application to Physics. By Professor Boun*. T is an old experience, that great and fruitful ideas make their entrance into the world neither suddenly nor in a state of complete perfection ; they generally require a certain time of de- * Communicated by the Author. 216 Prof. Bohn on the History of Conservation of Energy, velopment and growth, during which they may be said to belong to different persons. He who first expresses an idea with perfect clearness and exactness is commonly regarded as the discoverer, although in fact there be more than one entitled to this name. Now this rule is also applicable to the question concerning the author of the idea of transmutation of work of one kind into work of another kind. This question, however, is complicated by a circumstance which creates a difficulty in all researches on the history of force, vis viva, of conservation of energy, and others: these terms, as well as those of “ work,”’ “ momentum of force,” “momentum of activity,’ “dynamical effect,” ‘ mechanical power,” “quantity of action,” “quantity of movement,” and such like, are used by different authors, frequently even by one and the same writer, in a different sense, and in so undefined a manner that a sort of translation into the more precise scientific language of the present day is required in order to clearly show the meaning of the authors. In the Philosophical Magazine, 8. 4. vol. xxvin. pp. 473, 474, Dr. C. K. Akin quotes a few sentences from Placidus Heinrich and Dr. Mohr, which he considers as the earliest statements of the “allotropy of force.” It appears to me, however, that it is essen- tially left to the individual judgment of the reader whether he will or will not find in those sentences a certain proof of the author’s firm conviction of possible transmutation of common mechanical work into heat or electricity, and vice versd. In my opinion the following remark of L. N. M. Carnot is more striking and less ambiguous than the above-mentioned quotations of Dr. Akin. “ Vis viva can figure either as the product of a mass and the square of its velocity, or as the product of a moving power and - a length ora height. In the first case it is a vis viva properly called, in the second it is a latent vis viva.” This seems to show that, according to Carnot’s meaning, the vis viva consumed in raising a weight or performing other work is latent or stored up, and may be again employed in reproduc- tion of a motion, or in the performance of another work at the cost of the first done work. This appears more evidently from another passage from Carnot :— “All effects of propelling powers (forces mouvantes) may be compared to the raising of a weight to a certain height, and con- sequently to a ws viva, be it a real or a latent one.’ For these statements I refer to Carnot’s Prineipes de Péquilibre et du mouvement ; they are surely to be found in the edition of 18038, perhaps already i in the first (of 1783), whereon, not having the books at hand, | am not able at present to decide. For the same reason I was unable to quote literally; but I trust and of its application to Physics. 217 that I have succeeded in giving an exact statement of Carnot’s meaning. It must be left to the reader to decide on the import- ance of these sentences of Carnot. As to the statement of Professor Faraday quoted by Dr. Akin, I can only declare my perfect concurrence with the latter. In researches on the priority of physical truths, the preference is most justly allotted to those publications which for the first time treat a question by measure and numbers. The first quan- titative study of the reciprocal transmutation of different kinds of work originated, as far as I know, from Baron Liebig. In the fourth* of his “Chemical Letters” (Beilage zur Allgemeine Zei- tung vom 30 September 1841) he surveys the expectations which were at the time in question set on electromagnetism as a me- chanical power for propelling ships, &c. In order to show the amount of clearness then pervading the ideas of the celebrated chemist on the subject in question, it would be necessary to transcribe some pages of the letter quoted. I content myself, however, with reproducing a few words :— “ Warme, Hlectricitat und Magnetismus sind in einer ahnlichen Beziehung einander aequivalent wie Kohle, Zink, und Sauerstoff. - Durch ein gewisses Maass von Electricitat bringen wir ein entspre- chendes Verhaltniss von Warme oder von magnetischer Kraft hervor, die sich gegenseitig aequivalent sind. Diese Electricitat kaufe ich mit chemischer Affinitat, die, in der einen Form verbraucht Warme, in der andern Hlectricitat oder Magnetismus zam Vorschein bringt. Mit einer gewissen Summe von Affinitat bringen wir ein Aequivalent Electricitat hervor, gerade so, wie wir umgekehrt durch ein gewisses Maass von Hlectricitat Aequi- valente von chemischen Verbindungen zur Zerlegung bringen. Die Ausgabe fiir die magnetische Kraft ist also hier die Ausgabe fiir die chemische Affinitat,” &c. Another passage is the following :— * Aus nichts kann keine Kraft entstehen; in dem berihr- ten Fall wissen wir, dass sie durch Aufldsung (durch Oxy- dation) des Zinks hervorgerufen wird; allein abstrahiren wir von dem Namen, den diese Kraft hier tragt, so wissen wir, dass ihre Wirkung in einer andern Weise hervorgebracht werden kann,” &e. It is worth while to compare the first words of the latter quotation with Dr. Mayer’s sentence, “ex nihilo nil fit— nil fit ad nihilum,” such being the basis of his speculations in 1845. With regard to Dr. Akin’s remarks upon Huyghens (at p. 472 of No. 191 of the Philosophical Magazine), I finally beg leave to * The twelfth in the edition of 1851 of the Chemische Briefe, p. 202 et seq. Phil, Mag. 8. 4, Vol. 29. No, 195, March 1865, Q 218 Prof. Tyndall on the History of Calorescence. refer to Lagrange, Mécanique Analytique, 8° édit. par M. Ber- trand, vol. i. pp. 215, 217, or to Montucla, Histoire des Mathé- matiques, vol. ii. p. 618, and more particularly vol. i. o 622. Giessen, January 28, 1865. XXXII. On the History of Calorescence. By Joun Tynvat1, F.R.S., &c.* qr: the 26th of May, 1859, I eS to the Royal Society “Note on the Transmission of Radiant Heat through Gaseous Bodies.” The question had occupied me some time ; but as the experimental difficulties were very great, I published the Note referred to in order to enable myself to vanquish those dif- ficulties at my leisure. All the time at my disposal in 1859 and 1860 was devoted to the subject, and towards the end of 1860 I was so far advanced as to be able to prepare a memoir, which was presented to the Royal Society on the 10th of January, and, being chosen as the Bakerian Lecture for that year, was read . on the 7th of February, 1861. In that memoir the comparative deportment of elementary and compound gases towards radiant heat is for the first time announced. I had attempted to make radiant heat an explorer of molecular condition, and had found that the simple gases possessed a power of transmission immensely greater than that of the compound ones. In the autumn of 1861 I pursued the subject, and by purifying more perfectly the elementary gases, rendered the differences between them and the compound ones still more vast. I then turned my attention to solids and liquids, and confirmed Melloni’s experiments on the diather- mancy of lampblack ; I also tried to render the substance more transparent to invisible heat-rays by ridding it of the hydro- carbons which attach themselves to it during its formation. I next examined the element. bromine and found it eminently diathermic; I tried sulphur dissolved in bisulphide of carbon and found it still more so. I finally operated on a solution of iodine in bisulphide of carbon, and found that a layer of it, sufficiently dense to intercept completely the light of the noon- day sun, offered a scarcely sensible obstacle to the passage of the rayaerle calorific rays t * Communicated by the Author. + The same @ priori considerations which led to the discovery of the iodine, point also to red glass coloured by the element gold, instead of that coloured by the suboxide of copper, as most suitable for experiments on ray-transmutation. The colouring matter of the former appears to be without sensible action upon the invisible heat-rays; and the rays trans- mitted through it are competent to raise platinized platinum to a white heat. Prof. Tyndall on the History of Calorescence. 219 This fact is thus announced in a footnote at page 67 of the Philosophical Transactions for 1862 :—“A layer of bromine, suf- ficiently opake to intercept the entire luminous rays of a gas- flame, is highly diathermanous to its obscure rays. An opake solution of iodine in bisulphide of carbon behaves similarly. The details of these experiments shall be published in due time: they were publicly shown in my lectures many months ago.—June 138, 1862.” Turning to my published lectures on Heat as a Mode of Motion,” I find at page 357 one of these experiments described in the following words :—“ I cannot use iodine in a solid state, but happily it dissolves in bisulphide of carbon. I have the densely coloured liquid in this glass cell. I throw the parallel electric beam upon the screen ; this solution of iodine completely cuts the light off; but if I bring my pile into the path of the beam, the violence of the needle’s motion shows how copious is the trans- mission of the obscure rays.”’ Turning back to page 307 of the same work, I find experiments on smoked rock-salt and black glass described as follows :—“ Here is a plate of rock-salt coated so thickly with soot that the light, not only of every gas-lamp in this room, but the electric light itself is cut off by it. I inter- pose the plate of smoked salt in the path of the beam; the light is intercepted, but this rod enables me to find with my pile the place where the focus fell. I place the pile at this focus; you see no beam falling on the pile, but the violent action of the needle instantly reveals, to the mind’s eye, a focus of heat at the point from which the hght has been withdrawn.” I would ask the reader to picture any experimenter standing by a focus of invisible rays, the exposure to which, for an instant, of the face of my thermo-electric pile caused the heavy needles of a coarse galvanometer to dash against their stops. Could he escape the temptation to put his hand there? I did so fifty times, trying moreover to concentrate the radiation by pushing out my lens. The camera of my electric lamp was fur- nished with a concave reflector, at the centre of which stood the carbon-points whence issued the electric hght. The rays were converged by a lens in front; and when the points were at their proper elevation, the focus of the lens coincided with that of the mirror. Causing the two foci to coincide, and con- verging the rays as much as possible, I cut off the hight by the solution of iodine, and brought in succession my hand, my cheek, pieces of brown paper and of lead-foil into the dark focus. It was simply a substitution of these bodies for the face of my thermo-electric pile. But while the action on the skin was almost intolerable, I obtained neither the charring of the paper nor the fusion of the foil. I knew that a large portion of the radiant heat Q2 220 Prof. Tyndall on the History of Calorescence. of the lamp was lodged in the lens in front of it, and in the sides of the cell containing my solution of iodine; and I deter- mined, as soon as I could turn my thoughts to it, to be Lawes that lens and that cell by rock-salt ones. At that time my experiments on the action of aqueous vapour -as an absorbent of radiant heat were at variance with those of an eminent natural philosopher. Respect for him, and the de- sire to place my results beyond the pale of doubt, determined my course of action. The autumn of 1862 was devoted to the preparation of a memoir “On the Relation of Radiant Heat to Aqueous Vapour,” which was presented to the Royal Society on the 20th of November, and read on the 18th of December of that year. In the autumn of 1863 I completed my demonstration of the action of aqueous vapour on radiant heat, and at the same time executed further experiments on dissolved iodine, illustra- tive of its extraordinary transparency to heat-rays of ultra-red refrangibility. My course was now cleared, and my thoughts reverted at once to the experiments which I had suspended more than two years before. I went to the Isle of Wight in March 1864 with my ideas perfectly defined and ripe for execution. While there, under circumstances which I have fully described in my article “On Negative Fluorescence,” published in the January Number of the Philosophical Magazine, I received a note from Dr. Akin, a Hungarian gentleman who had arrived in this country in the early part of 1862, and who was personally unknown to me. His name had been mentioned to me by Professor Stokes ; I had read an article from his pen published in the ‘ Saturday Review,’ and he now forwarded to me a proof of a Report presented by him to the British Association assembled at Newcastle in 1868. In this Report three experiments were proposed: two of them were impracticable, but they nevertheless showed ability, while the third seemed to offer a promise of real success. These were not the experiments that I had proposed to make ; I did not intend to experiment on the sun, for his beams are unattainable where I work; I intended to operate with the radiant source with which the constant practice of the previous eleven years had rendered me familiar, and to realize ideas of which the origin has been indicated above, but which, with the caution of a man who knows the difference between conception and performance, I did not publish in detail. The reader will now be in a posi- tion to appreciate the use which Dr. Akin has made of the fol- lowing note written to him at the time :— “Clarendon Hotel, Chale, Isle of Wight, Wednesday. “My prar Sir,—I have read the proof which you have been kind enough to send me with extreme interest. Being a truant from the Prof. Tyndall on the History of Calorescence. 221 Sections at Newcastle, I did not know that you had brought the subject forward there. Professor Stokes, however, informed me that you were engaged on the question, and I had similar information from the ‘Saturday Review.’ «There is certainly a most singular coincidence in the thoughts which have passed through both cur minds on some of the points in question. As to the possibility of converting the Herschellic into © the Newtonic rays I do not entertain a doubt; and indeed the piece of work which I had set before me for attack on my return from this place was a series of experiments on this very subject. “‘T have devised a very perfect means of sifting the Herschellic from the Newtonic rays, and with the latter alone I have strong hopes of being able to produce incandescence. But you have entered this field before me, and although the question lies directly in the way of my own inquiries, [ should like to do in the matter what would be most pleasing to you. I shall be in town on Saturday next, at the Royal Institution at noon; could you not look in upon me there ? ** Yours very sincerely, “ Joon TynpaLu.” In the December Number of the Philosophical Magazine, p- 559, Dr. Akin employs the following language with refer- ence to this letter :—‘“‘I must be allowed to express here a doubt whether Sir Humphry Davy, for example, or any other predecessor of Professor Tyndall at the Royal Institution, hav- ing read in a public print. that two persons were engaged in making researches on a certain subject with the aid and sanction of the British Association, would have chosen ‘ that very subject’ for ‘attack’ some little time after.” I, on the other hand, may be permitted to express the assured conviction that Sir Humphry Davy would never have given Dr. Akin the chance of garbling his language as he has here garbled mine. The reader will com- pare the words “ attack” and “ that very subject,” as held in the claws of his inverted commas, with the same words as they occur in my note, and draw his own conclusions as to the temper of the quoter. The fundamental error of Dr. Akin consists in his interpreting the attitude assumed by me in the foregoing note, as one which, under the circumstances, he had a right to expect. What most men would have regarded as an act of free courtesy on my part, Dr. Akin interprets as an acknowledgment of his imordinate clams. He does not seem to understand why, of my own free will, I conceded to him a position which I should unquestionably have refused had it been demanded as a right. As I have already stated to him, “there was nothing in the circumstances of the case to prevent me from working at the subject, restricting myself to a due reference to his labours.” Had I been aware that my note had excited his “ astonishment,’ I should have acted 222 Prof. Tyndall on the History of Calorescence. very differently towards him. Had he urged “ the authority of the British Association,” I should have informed him that I could not recognize its authority in such a matter. At the same time I should have known that the eminent leaders of that body would never countenance Dr. Akin in the attempt to shut me out of a field of inquiry which I had virtually entered before him, and which consideration for him as a stranger had alone caused me to relinquish. To render this assurance doubly sure, I wrote to General Sabine, who knows more about the constitution of the British Association than any other living man, and who, with the kindness which I have always exper ienced at his hands, promptly wrote to me the following reply :— «Dear T'ynpaLt,—Viewing your inquiry simply as an admini- strative question, Dr. Akin’s Report on the Transmutation of Spec- tral Rays in the British Association Reports for 1863 indicated a very wide field of experimental researches. In aid of these the General Committee made a grant of £45 to Mr. Griffith and himself. A part of this grant was expended in apparatus to be employed by those gentlemen in the spring or early summer of 1864, the results of which were designed by Dr. Akin to be presented by himself to the Meeting of the British Association at Bath in the September of ‘that year. For this purpose Dr. Akin went to Oxford to join Mr. Griffith, but from some unexplained cause their purpose was frus- trated, and 1864 passed without the experiments being made. ‘The grant, however, did not lapse, as part of it had been expended in apparatus, which it appears to be still Dr. Akin’s intention to employ (though not at Oxford where there is sunshine, or in Lon- don where there is no sunshine suitable for the purpose). Such, so far as I can collect them, is a statement of the facts. «The object of the British Association in making such grants is to aid the progress of science, by enabling those, who may be so dis- posed, to make experiments, but by no means to retard its progress by discouraging others from approaching the same ground. One cannot read, I think, Dr. Akin’s Report in 1863 without the impression that there is work enough in the subject for a dozen at least of active experimenters. He may have had an advantage (and properly used it _ is a great one) in meditating longer than others on the laurels that may be gathered, but he who desires to be foremost in the field must be ‘ prompt in action’ where there are so many competitors. ‘“« Always truly yours, “‘ KDWARD. SABINE.” I also wrote to Sir William Armstrong on the same subject. As President of the British Association at Newcastle, Sir William Armstrong does not think himself entitled now to speak, but as a private individual he states that the British Association ‘ could not, even if they proposed anything so foolish, confer upon Dr. Akin any exclusive privileges in the matter.” Prof. Tyndall on the History of Calorescence. 223 It was in answer to the express desire of Dr. Akin to see me that I informed him at the end of my note from Chale that I should be in town on the following Saturday. Hecame. Ihave since ransacked my memory for the details of our interview; and > though I cannot recall the whole of them, the essential ones are perfectly clear to me, while the result is as vivid to my mind as the occurrence of yesterday. Without waiting to obtain the knowledge of Dr. Akin’s character that ten minutes’ conversa- ‘tion might have given, I remarked that although he and I had reached the same point by independent routes, he was the first to publish definitely his ideas, and that, therefore, I would not interfere with him. I stated that although my plans were pre- pared, I was perfectly willing to suspend them. Dr. Akin’s reply was that he was delighted to find the subject taken up, and was only anxious to see it prosecuted to a successful issue, Of these words I have the most distinct recollection. I did not know at the time that the note written to him on the previous Wednesday had excited his “ astonishment”; nor did I know that he had come, as he has since informed me, expecting that I would make him an offer that we should work together; but pleased by his apparent frankness, on the spur of the moment I used these words :—‘‘ We might perhaps attack it together.” I use the phrase “spur of the moment” because it strictly represents the fact, but they who know me best will be the last to believe me capable of retreating from a position assumed even on the spur of the moment. And had Dr. Akin agreed to my proposal, no matter what consequent penalties it might have involved—and they, I doubt not, would have been great—I should have carried it out to the letter. But he did not agree to my proposition. He said that he had associated himself with Mr. Griffith at Oxford, and that he was compelled to fulfil his engagement with that gentleman. Let me here remark that neither Dr. Akin nor myself pro- fesses to remember the whole of what occurred during this inter- view; and when he spoke of his being bound to Mr. Griffith, some conyersation followed, the precise terms of which I do not recollect ; but it drew from Dr, Akin a proposition, which I do remember perfectly well. 1 will allow him to supply what I have here forgotten. In a letter written to me more than three months ago, he affirms that when he declared himself bound to Mr.Griffith at Oxford, I rejoined :—“‘ Can we not make it a triple alliance ?”’? His reply was, ‘‘ No, leave us the sun at Oxford, but as regards experiments on artificial rays, I shall be happy to co- operate with you separately.” Of the words “ triple alliance” I have no recollection, but they are so like what I should use under the circumstances, that I do not doubt the correctness of Dr. 224: Prof. Tyndall on the History of Calorescence. Akin’s memory regarding them. But I do remember his proposal to work with me in London and with Mr. Griffith at Oxford, and it caused me to pause. Neither in its tone nor in its terms did it please me, and to it, by neither word nor sign, did I ever show the shghtest symptom of assent. In his last published account of this conversation Dr. Akin omits all reference to my proposal and his refusal of a “triple alliance,’ and represents me as accepting his counterproposition without reservation or qualification. ‘To this conclusion Profes- sor Tyndall cheerfully agreed, observing that he had from the first intended to make experiments on the electric hight; that he was consequently quite satisfied with the arrangement proposed.” Though there seems now no shade of doubt upon Dr. Akin’s mind regarding my acceptance of his offer, still I think there was a slight shade upon it four months ago. In a letter written to me on the Ist of last November, after reminding me of his offer to cooperate with me in London, leaving the sun to himself and Mr. Griffith © at Oxford, he continues thus :—“ If there was no ‘ closing’ with any offer, it must have been on your part, and as regards this last-mentioned offer, which I made in answer to your own” *. This passage, I submit, indicates a condition of mind and memory somewhat different from that which prompted the unqualified assertion “to this condition Professor Tyndall cheerfully agreed.” When I wrote to Dr. Akin from the Isle of Wight, my desire and intention was to allow him ample scope for the realiza- tion of his ideas, and during our conference this intention was * Here is the extract in extenso: it is taken from Dr. Akin’s second letter to me, the word “closing” beg placed between inverted commas, because in myreply to Dr. Akin’s first letter I had reminded him that he had not “closed” with my proposal :— “DEAR Sir,—I have just received your letter of today, and intend to shortly reply to such portions as seem to me to require it. ** As regards the way in which your attention was turned to the subject which is im question, of course you are the best as well as the only autho- rity, and I have no intention of challenging any statement on your part, deliberately made, and where there are no facts within my knowledge pro- ving that your recollection misleads you. Such, however, I believe to be the case in reference to what occurred at the Royal Institution m April, in the course of our conversation. You then spoke of a ‘triple alliance’ (those were the words you used). I replied, ‘ Leave the sun to us at Oxford,’ but added that, as regarded experiments on artificial sources of rays (the expressions, I believe, were ‘the other two experiments,’ meaning those described in my paper), I should be happy to cooperate with you se- parately. If there was ‘no closing’ with any offer, it must have been on your part, and as regards this last-mentioned offer, which I made in answer to your own.” ©? That was after I had said that I was bound to Mr. Griffith.” Prof. Tyndall on the History of Calorescence. 225 revived. I resolved then and there not to interfere with Dr. Akin, to suspend the experiments I had planned, and leave the subject entirely in his hands throughout the summer. During the months of April, May, and June my assistant was employed, under my direction, on an investigation which he afterwards published in the August Number of the Philosophical Maga- zine, while I occupied my leisure with other matters. The naked facts stand thus:—On Wednesday the 30th of March, I write to Dr, Akin stating that I had devised a series of expe- riments to be undertaken on my return to town. On the very day of my arrival the execution of these experiments is post- poned, and not a word is heard of them until the end of October. Meanwhile Dr. Akin had pursued his experiments at Oxford, and had sent in the following Report of his performances to the President of the Physical Section of the British Association. The document is dated from the Cavendish Club, London, 15th September, 1864. “‘ T am sorry to have to state that, owing to the scarcity of clear sunshine at Oxford last summer, and to Mr. Griffith being mostly unable to give his time to our work when the weather happened to be favourable to it, the experiments were left in August unfinished. I had the greater reason to feel disappointed at such a conclusion, as the methods and apparatus devised for the purpose appeared, from preliminary trials, competent to effect, in part at least, the pro- posed object, and as our preparations for the more decisive experi- ments were in a very forward state. Meanwhile I have received fresh testimony from several esteemed quarters to the importance of the research thus partially accomplished, which makes me féel yet deeper regret at seeing the matter after two years’ labour, and nearly three years’ thought and trouble—some of it unexpectedly galling— still in abeyance.” After the Bath Meeting of the British Association, Dr. Akin also wrote thus to the President of the Association :—“I now beg leave to state that, after the experience of the last two years, it would be a hopeless undertaking for me to con- tmue at Oxford the experiments begun there. Moreover I am not sure whether, after the end of the present year, I shall be able to give my attention any longer to scientific researches.” Supposing Dr. Akin to be perfectly satisfied in his own mind that he had entered into a definite engagement with me, does it not seem odd that he should not have hinted at this engagement, either in his Report or in his ietter? When he stated that he had abandoned hope in Oxford, it would surely have been natural to add that he had not abandoned it in London. The fact seems to be that Dr. Akin had no clear con- 226 Prof. Tyndall on the History of Calorescence. sciousness at the time that such an engagement existed, and that anger now supplies him with a power of memory which in his calmer moments he did not enjoy. I went to Switzerland early in July, and from Pontresina wrote to my assistant, describing the apparatus I had intended to employ, and desiring him to have it prepared for me. One portion of it consisted simply of the substitution of a rock-salt lens for the glass one of the electric lamp, and a rock-salt cell for the glass one that I had used in 1862. With this arrange- ment I executed the experiments “on luminous and obscure radiation ”’ described in the November Number of the Philoso- phical Magazine. Nay, abandoning the rock-salt altogether, and employing a glass lens of somewhat shorter focus than that made use of in 1862, with a battery of sixty cells, I obtained all the results with the electric lamp there described. In not the slightest particular does this arrangement differ from that which I had employed two years and three-quarters previously, We have the same source of rays, the same mode of conver- gence, and the same absorbent to intercept the lumimous por- tion of the radiation. And yet it is from this, my own ground, which I had taken up practically before he had perused the “little German treatise which first taught him what had been done” on the subject of fluorescence, that Dr. Akin would fence me out. Experiments on combustion could not decide the question of ray-transmutation. ‘“‘Intimately connected” they assuredly were,—so intimately, indeed, that the man who could neglect to pass immediately from the one to the other, would be unfit for the vocation of a natural philosopher. Was I, then, out of con- sideration for Dr. Akin, to keep my platinum-foil or my silver- leaf away from the focus of dark rays, lest it should become in- candescent there? My duty to science ruled otherwise ; and as no bond or promise existed to contravene that duty, I resolved not to let the autumn pass as Dr. Akin had the summer, without making some attempt to realize my ideas. He had already tried, failed, and announced his failure. Still, however, wishing to treat him with the utmost consideration, I resolved, while for- warding the work of science, to leave the chance of prior publica- tion open to Dr. Akin. I determined to hold back whatever results [ might obtain until he would be either able to precede me, or could so far merge his individual interests in the larger interests of science, as to be willing to see the results published. This he deems an unusual proceeding on my part, and so it as- suredly was, But from first to last my proceeding towards him was unusual. In relation to any other man it would have been +e ee Sn le ee apo Prof. Tyndall on the History of Calorescence. 227 more than fair; in relation to him it has proved to be worse than useless. Late in the day of the 29th of October, I obtained the incan- descence of platinum foil by the dark rays of the electric light. The layer of iodine, however, was too thin to wholly intercept the light, while the battery had been enfeebled by long-continued previous action. On the following morning it was freshly charged, the number of cells being increased from fifty to sixty. Removing from the back of the camera the little reflector which I had made use of in 1862, I mounted it on a retort-stand, and with it converged the rays from the lamp. The mirror was silvered behind, and the reflected rays had therefore to pass to and fro across a plate of glass of considerable thickness. Not- withstanding this, however, and the employment of a much thicker layer of dissolved iodine, the platinum, when placed in the dark focus of the mirror, became vividly incandescent. Almost immediately after the performance of this experiment I found Dr. Akin in the library of the Royal Institution. With- out a moment’s hesitation I invited him to accompany me to the laboratory, and there almost simultaneously with myself he saw the result which I had obtained*. Not one word of remonstrance or complaint escaped him on this occasion ; not a syllable to indicate that he believed me in any way pledged to him. He made some critical remarks as to the experiment being made in daylight. He was moreover struck with the thickness of the layer of iodine employed, observing that the layer used by him at Oxford was a thin one, which did not cutoff the light. He finally expressed himself delighted to see the experiment, and we quitted the laboratory together. I walked with him upstairs, and there at the eleventh hour ex- pressed my desire not to interfere with him, and to leave, if he wished it, the subject still in his hands. His reply was, “ It will all depend on the manner of publication.” Knowing my own willingness to do him the amplest justice in any publication of mine, I responded, “‘ You shall see my manuscript before I publish.” My intention when I parted from Dr. Akin was to give a brief account of the experiment at the first meeting of the Royal Society, but I had not definitely made up my mind. On the evening of the day to which I now refer I thought and spoke of associating myself with Dr, Akin for the further prosecution * Dr. Akin had informed me that he was collecting materials for a “‘ His- tory of Force,’’ and needed access to a good library. Deeming his work both useful and honourable, to enable him to prosecute it I introduced him to the libraries both of the Royal Institution and the Athenzeum Club. f 228 Prof. Tyndall on the History of Calorescence. of the inquiry. On the following Monday, however, I received a letter from this gentleman which entirely changed the aspect of affairs, and in which he informed me that, on thinking over the experiment I had showed him, his mind had become greatly agitated. He referred to our interview in April, and to what he asserted had occurred between us since. Like his last article in this Journal, that letter consisted of a single broken fibre of truth in a tissue of error. I then went through the assertions of Dr. Akin one by one, pointed out where they were exag- gerated, where he had unduly intensified language, and where his statements were, as I believed, at direct variance with facts. His last paper. furnishes some illustration of the intensification of language which I then sought to correct. In my reply to his intimation that I had appropriated his ideas, I stated that “my work would have been far more completely done by this time had he never existed.” Dr. Akin’s version of this state- ment of a fact is this:— Professor Tyndall, who is charitable enough to express an implied wish for my non-existence, will no doubt be gratified to learn that the experience 1 have met with at his hands has acted upon me in the manner he would seem to desire.” It was sufficiently evident from Dr. Akin’s correspondence that he was very much disappointed. He had been “ greatly depressed and discouraged in mind” at Newcastle. “ An indelible mark of pain” had been left upon his memory by the treatment he received at Oxford ; and now his misfortunes culminated on find- ing, in London, the goal at which he aimed attained by another. Still that other, though sorely irritated, was less anxious to avail himself of his success than to show Dr. Akin “how lightly he valued the whole matter when a question of good faith came into play.” The letter which contained my corrections of Dr. Akin’s misapprehensions concluded thus :— * And now for a few concluding words :—I cannot help express- ing my deep regret that you did not write to me in a different manner. I should have gone almost any length to gratify you, had you adopted another tone; and I shall prove my sincerity in writing thus, by doing that which still remains in my power to do. I have to say, then, that from this 3rd of November 1864 to the 38rd of November 1865 I shall not make known, publicly or privately, any experiments on ‘ ray-transmutation.’ Nearly seven months ago I was, as you know, ready to take this subject up. Out of deference to you I did not do so; so that at the termination of the period referred to I shall have held back for nearly nineteen months. That you will be able to release me long before, by the actual performance of this experiment, is almost beyond a doubt; and in this event I hope to muster sufficient greatness of heart not to envy you.” i i Prof. Tyndall on the History of Calorescence. 229 Dr. Akin has the assurance to upbraid me with having, in the | face of this promise, seized the first opportunity to publish my results. My promise was given in order to enable him to perform honest work, and not to indulge in aggression. I halted that he might move on. The arrangement left open to him another summer, during which he might renew the in- vestigation that had broken down at Oxford, with the assurance, moreover, that the object at which he aimed was no longer a doubtful one. Not satisfied with this arrangement, he continued to complain, and I was at length obliged to end a profitless and apparently interminable correspondence with these words :—“ I have now only to add, that when you have so far overcome the agitation of mind to which you so frequently refer, as to be able to look at this question with the eyes and mind of a philosopher, IT shall be happy to communicate with you. But no possible good can arise from a continuance of this correspondence. Hence, as far as | am concerned, it is for the present at an end.” Dr. Akin then wrote to me his fifth letter, and ended it by the statement that, although he could scarcely allow himself to hope much for the future, he wished, nevertheless, to say that whenever I should be pleased again to communicate with him he would be happy to hear from me. This letter was dated from Harley Street, November 9, 1864. For nearly three weeks I heard nothing from or of Dr. Akin, but he meanwhile was not idle. Silently, and without a word — of warning to me, he concocted his “ Note on Ray-transmutation” for the December Number of the Philosophical Magazine. After the completion of that article, and twenty-four hours previous to its publication, he wrote to me commencing his letter with “ Dear Sir,” and ending it with “ Believe me yours very faithfully.” On the very day of its publication he sent me a second note with some- what similar termini; but neither of them breathed a whisper of his attack. During my correspondence with Dr. Akin I availed myself from time to time of the wisest advice within my reach ; and the verdict of my advisers was now prompt and emphatic. From the legal, the scientific, and the general world, I heard the unanimous opinion that Dr. Akin’s act of war cancelled every treaty subsisting between us, and rendered the act of publication a duty to science as well as to myself. To sum up :— : 1. Dr. Akin affirms that I have interfered with an investiga- tion which he had originated and to which he had secured an exclusive right. I assert, on the contrary, that my inquiries have been the di- rect result of labours commenced before Dr. Akin was heard of in this or any other field of scientific inquiry; and that even if 230 Prof. Tyndall on the History of Calorescence. they had not been, the assumption of any such right of exclu- sion is inadmissible. : 2. Dr. Akin affirms that he closed with alacrity with a pro- position of mine to work out, in conjunction with him, a certain subject. But Dr. Akin admits that he did not “close” with my first proposition, on account of his tie to Mr. Griffith. He further admits that he declined the “triple alliance”? between Mr. Griffith, Dr. Akin, and myself, which was next suggested by me. Finally, he produces no evidence to show that I proposed or accepted any other arrangement ; and I categorically deny that any other arrangement was proposed or accepted by me. 3. Dr. Akin’s words imply that I have availed myself of his ideas or suggestions, to anticipate his results. I answer thus :— It has been shown in the foregoing article that early in the year 1862 I formed foci of invisible rays, and also illustrated in my public lectures the heat of such foci; that I employed for this purpose the condensed rays of the electric light, and inter- cepted the lumimous part of the radiation by an absorbent of extraordinary properties discovered by myself. Sir William Herschel had tried to render the ultra-red rays of the solar spectrum visible by condensation, having first sepa- rated them, by prismatic analysis, from the visible rays. But the idea of forming intense foci of invisible rays by concentrating the total radiation of a luminous source, and removing the visible rays by an absorbent, is, I believe, entirely mine. 4. In the autumn of 1863 Dr. Akin proposed to obtain an intense focus of invisible rays by converging the sun’s beams and intercepting the luminous part of the radiation by absorb- ents which he did not name. In making this proposition, Dr. Akin had, without a word of acknowledgment, appropriated an idea which I had in substance enunciated and applied more than a year and a half previously. 5. The only particular in which Dr. Akin was in advance of me—and this not in thought, but in publication—was that he was the first to express the belief that the dark rays of the sun, when detached from the luminous ones by my method, would be competent to raise platinum-foil to incandescence ; and that if they did so we should have for the extra-red end of the spec- trum phenomena analogous to those of fluorescence. 6. In consequence of the precision with which he had enun- ciated this idea, and also in part on account of his being a foreigner, working, as I conceived, against difficulties in this country, I somewhat Quixotically permitted him during the whole of last summer to pursue his idea undisturbed. He had tried, failed, and reported his failure to the British Association Prof. Cayley on Lobatschewsky’s Imaginary Geometry. 231 assembled at Bath, before my experiments on calorescence had commenced. | _ If have not waited longer before publishing the results of my experiments, as I once proposed to do, it is because by his un- warranted and unprovoked attacks, Dr. Akin has forfeited all claim to the position in which I had voluntarily, but unwisely, placed him. Royal Institution, February. [The Editors have received a letter from Dr. Akin, in which he begs to enter a public and formal protest against the note appended to his communication in the last Number of the Magazine by W. F., and claims to. have the last word in this discussion. As Dr. Akin commenced the controversy in the December Number, and in that of February has had every opportunity of placing all the evi- dence he deemed necessary before our readers, we cannot admit the justice of his claim, and abide by the decision already given. —Txue Eprirors. | XXXIII.—WNote on Lobatschewsky’s Imaginary Geometry. By A. Cayitzy, Esq.* NG down the equations cos A + cos B cos C em |G sin B sin C f t cos B+ cos C cos A a a oa sin C sin A : cos C+ cos A cos B at, am Asin 4 where A, B, C are real positive angles each COs ty COS at cos bi COS Ct (I have, as mentioned above, replaced Lobatschewsky’s Ot by their complements): the relation between the angles A, B, C and the subsidiary quantities a’, 0’, c' which replace the sides, is given by the formule 1 _ cosA+ cos BeosC, cosa! sin B sin C 1 _ cosB+cosCcos A cos b! sin C sin A s 1 __cosC + cos A cos BL cosc! sin A sin B I do not understand this; but it would be very interesting to find a real geometrical interpretation of the last-mentioned system of equations, which (if only A, B, C are positive real quantities such that A+B+C<7; for the condition, A, B, C each <37, may be omitted) contains only the rea/ quantities A, B, C, a’, U', c'; and is a system correlative to the equations of ordinary Spherical Trigonometry. It is hardly necessary to remark that the equation = = COS A COS @ Royal Society. 233 is Jacobi’s imaginary transformation in the Theory of Elliptic Functions. See, as to this, my paper “On the Transcendent 1 aid. 7 log tan (q + : ui),” Phil. Mag. vol. xxiv. (1862) pp. 19-22. Cambridge, January 21, 1865. XXXIV. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 157.] December 22, 1864.—Dr. William Allen Miller, Treasurer and Vice- President, in the Chair. NHE following communication was read :— MB “Ona Method of Meteorological Registration of the Chemical Action of Total Daylight.”’” By Henry E. Roscoe, B.A., F.R.S. The aim of the present communication is to describe a simple mode of measuring the chemical action of total daylight, adapted to the purpose of regular meteorological registration. This method is founded upon that described by Prof. Bunsen and the author in their last Memoir* on Photochemical Measurements, depending upon the law that equal products of the intensity of the acting light into the times of insolation correspond within very wide limits to equal shades of tints produced upon chloride-of-silver paper of uniform sensitive- ness—light of the intensity 50, acting for the time 1, thus produ- cing the same blackening effect as light of the intensity 1 acting for the time 50. For the purpose of exposing this paper to light for a known but very short length of time, a pendulum photometer was constructed ; and by means of this instrument a strip of paper is so exposed that the different times of insolation for all points along the length of the strip can be calculated to within small fractions of a second, when the duration and amplitude of vibration of the pen- dulum are known. The strip of sensitive paper insolated during the oscillation of the pendulum exhibits throughout its length a regu- larly diminishing shade from dark to white; and by reference to a Table, the time needed to produce any one of these shades can be ascertained. The unit of photo-chemical action is assumed to be that intensity of light which produces in the unit of time (one second) a given but arbitrary degree of shade termed the standard tint. The reciprocals of the times during which the points on the strip have to be exposed in order to attain the standard tint, give the intensities of the acting light expressed in terms of the above unit. By means of this method a regular series of daily observations can be kept up without difficulty ; the whole apparatus needed can be packed up into small space; the observations can be carried on without regard to wind or weather ; and no less than forty-five sepa- rate determinations can be made upon 36 square centimetres of sen- sitive paper. Strips of the standard chloride-of-silver paper tinted in the pendulum photometer remain as the basis of the new mode * Phil. Trans. 1863, p. 139. Phil. Mag. 8. 4. Vol. 29. No. 195. March 1865. R 234 Royal Society :-— ‘of measurement. Two strips of this paper are exposed as usual in the pendulutn photometer : one of these strips is fixed in hyposul- phite-of-sodium solution, washed, dried, and pasted upon a board furnished with a millimetre-scale. This fixed strip is now graduated in terms of the unfixed pendulum strip by reading off, by the light of a soda-flame, the position of those points on each strip which possess equal degrees of tint, the position of the standard tint upon the unfixed strip being ascertained for the purpose of the gradu- ation. Upon this comparison with the unfixed pendulum strip depends the subsequent use of the fixed strip. A detailed descrip- tion of the methods of preparing and graduating the strips, and of the apparatus for exposure and reading, isnext given. The following conditions must be fulfilled in order that the method may be adopted as a trustworthy mode of measuring the chemical action of light : — ist. The tint of the standard strips fixed in hyposulphite must remain perfectly unalterable during a considerable length of time. 2nd. The tints upon these fixed strips must shade regularly into each other, so as to render possible an accurate comparison with, and graduation in terms of, the unfixed pendulum strips. 3rd. Simultaneous measurements made with different strips thus graduated must show close agreement amongst themselves, and they must give the same results as determinations made by means of the pendulum photometer, according to the method described in the last memoir. _ The fixed strips are prepared in the pendulum apparatus, and afterwards fixed in hyposulphite of sodium. A series of experi- ments is next detailed, carried out for the purpose of ascertaining whether these fixed strips undergo any alteration by exposure to light, or when preserved in the dark. Two consecutive strips were cut off from a large number of different sheets, and the point upon each at which the shade was equal to that of the standard tint was deter- mined. One half of these strips were carefully preserved in the dark, the other half exposed to direct and diffuse sunlight for periods vary- ing from fourteen days to six months, and the position of equality of tint with the standard tint from time to time determined. It appears, from a large number of such comparisons, that in almost all cases an irregular, and in some cases a rapid fading takes place immediately after the strips have been prepared, and that this fading continues for about six to eight weeks from the date of the prepara- ‘tion. It was, however, found that, after this length of time has elapsed, neither exposure to sunlight nor preservation in the dark produces the slightest change of tint, and that, for many months from this time; the tint of the strips may be considered as perfectly unalterable. The value of the proposed method of measurement entirely depends upon the possibility of accurately determining the intensi- ties of the various shades of the fixed strip in terms of the known intensities of the standard strips prepared in the pendulum photo- meter. The author examines this question at length, and details two methods of graduating the fixed strips, giving the results obtained in several series of determinations, in order that the amount of experi- oh oy eige i. iy ha aad On the Registration of the Chemical Action of Daylight. 235 mental error may be estimated. Curves exhibiting the graduation of several strips are also given; and from these the author concludes that the determmations agree as well as can be expected from such photometric experiments, the mean error between the positions 40 and 80 min. on the strip in one series of graduations not exceeding 1 per cent. of the measured intensity. To each fixed strip a Table is attached, giving the intensity of the light which must act for 1 second upon the standard paper, in order to produce the tints at each millimetre of the length of the strip. The methods of exposure and reading are next described. The exposure of the paper is effected very simply by pasting pieces of standard sensitive paper upon an insolation band, and inserting the band into a thin metal slide having a small opening at the top and furnished with a cover, which can be made instantly to open or close the hole under which the sensitive paper is placed. When one ob- servation has thus been made, and the time and duration of the inso- lation noted, the remaining papers can be similarly exposed at any required time; and thus the determinations can he very easily car- ried on at short intervals throughout the day. The reading-instrument consists of a small metallic drum, fur- nished with a millimetre scale, and upon which the graduated strip is fastened. ‘The drum turns upon a horizontal axis, and the inso- lation band, with the exposed papers upon it, is held against the graduated strip, so that by moving the drum on its horizontal axis the various shades of the strip are made to pass and repass each of the papers on the insolation band, and the points of coincidence of tint on the strip and on each of the exposed papers can be easily ascertained by reading off with the monochromatic soda-flame. In the next section of the paper the author investigates the accuracy and trustworthiness of the method. ‘This is tested in the first place by making simultaneous measurements of the chemical action of daylight by the new method and by means of the pendulum photometer, according to the mode described in the last memoir, upon which the new method is founded. Duplicate determinations of the varying chemical intensity thus made every half-hour on four separate days give results which agree closely with each other, as is seen by reference to the Tables and figures showing the curves of daily chemical intensity which are given in the paper. Hence the author concludes that the unavoidable experimental errors arising from graduation, exposure, and reading are not of sufficient magnitude materially to affect the accuracy of the measurement. As asecond test of the trustworthiness and availability of the method - for actual measurement, the author gives results of determinations made with two imstruments independently by two observers at the same time, and on the same spot. The tabulated results thus ob- tained serve as a fair sample of the accuracy with which the actual measurement can be carried out; and the curves given represent gra- phically the results of these double observations. From the close agreement of these curves, it is seen that the method is available for practical measurement. In order to show that the method can be applied to the purposes R2 236 Royal Society :— of actual registration, the author gives the results of determinations of the varying intensity of the chemical action of total daylight at Manchester on more than forty days, made at the most widely differing seasons of the year. These measurements reveal some of the interesting results to which a wide series of such measurements must lead. They extend from August 1863 to September 1864; and Tables are given in which the details of observations are found, whilst the varying chemical intensity for each day is expressed graphi- cally by a curve. . Figure showing curves of daily chemical intensity at Manchester, In spring, summer, autumn, and winter. As a rule, one observation was made every half-hour ; frequently, however, when the object was either to control the accuracy of the measurement or to record the great changes which suddenly occur when the sun is obscured or appears from behind a cloud, the deter- minations were made at intervals of a few minutes or even seconds. Consecutive observations were carried on for each day for nearly a month, from June 16th to July 9th, 1864; the labour of carrying out these was not found to be very great, and the results obtained are of great interest. By reference to the Tables, it is seen that the amount of chemical action generally corresponds to the amount of cloud or sunshine as noted in the observation ; sometimes, however, a considerable and sudden alteration in the chemical intensity occurred when no apparent change in the amount of light could be noticed by the eye. The remarkable absorptive action exerted upon the chemically active rays by small quantities of suspended particles of water in the shape of mist, or haze, is also clearly shown. For the purpose of expressing the relation of the sums of all the various On the Nature of Solar Spots. 237 hourly intensities, giving the daily mean chemical intensities of the place, a rough method of integration is resorted to: this consists in determining the weights of the areas of paper inscribed between the base-line and the curve of daily intensity, that chemical action being taken as 1000 which the unit of intensity would produce if acting continuously for twenty-four hours. The remarkable differences observed in the chemical intensity on two neighbouring days is noticed on the curves for the 20th and 22nd of June 1864: the integrals for these days are 50°9 and 119, or the chemical actions on these days are in the ratio of 1 to 2°34. The chemical action of light at Manchester was determined at the winter and summer solstices, and the vernal and autumnal equinoxes : the results of these measurements are seen by reference to the accom- panying curves. The integral for the winter solstice is 4°7, that of the vernal equinox 36°8; that of the summer solstice 119, and that of the autumnal equinox 29°1. Hence, if the chemical action on the shortest day be taken as the unit, that upon the equinox will be represented by 7, and that upon the longest day by 25. The results of simultaneous measurements made at Heidelberg and Manchester, and Dingwall and Manchester, are next detailed. From the integrals of daily intensity the mean monthly and annual chemical intensity can be ascertained, and thus we may obtain a knowledge of the distribution of the chemically acting ‘rays upon the earth’s surface, such as we possess for the heating rays. January 26, 1865.—Major-General Sabine, President, in the Chair. The following communication was read :— “* Researches on Solar Physics.—Series I. On the Nature of Solar - Spots.” By Warren De la Rue, Ph.D., F.R.S., Balfour Stewart, A.M., F.R.S., &c. and Benjamin Loewy, Esq. After giving a short sketch of the history of their subject, the authors proceed to state the nature of the materials which had been placed at their disposal. In the first place, Mr. Carrington had very kindly put into their hands all his original drawings of sun-spots, extending from November 1853 to March 1861. In the next place, their materials were derived from the pictures taken by the Kew heliograph. A few pictures were taken by this instrument at Kew Observatory in the years 1858 and 1859. In July 1860 it was in Spain doing service at the total eclipse. In 1861 a few pictures were taken at Kew, while from February 1862 to February1863 the instrument was in continuous operation at Mr. De la Rue’s private observatory at Cranford, and from .May 1863 until the present date it has been in continuous operation at Kew under Mr. De la Rue’s ‘superintendence. A Table was then given from which it was deduced that the number of groups observed at Kew from June to December 1863 inclusive was 64, while that observed by Hofrath Schwabe during the same interval was 69. In like manner, the number at Kew between January and November 1864 inclusive was 109, while during the same interval Hofrath Schwabe observed 126. It thus appears that Schwabe’s numbers are somewhat larger than those of Kew; but probably, by means of a constant corrective, the one series may be made to dovetail with the other. 238 © Royal Society :— The authors then attempted to answer the following questions :-- (1) Isthe umbra of a spot nearer the sun’s centre than the penum- bra, or, in other words, is it at a lower level ? (2) Is the photosphere of our luminary to be viewed as composed of heavy solid, or liquid matter, or is it of the nature either of a gas or cloud ? (3) Is a spot (including both umbra and penumbra) a pheno- menon which takes place beneath thelevel of the sun’s photosphere- or above it ? In answering the first of these, it was shown that if the umbra is appreciably at a lower level than the penumbra, we are entitied to look for an apparent encroachment of the umbra upon the penum- bra on that side which is nearest the visual centre of the disk. This, in fact, was the phenomenon which Wilson observed, and which led him to the belief that the umbra was nearer the sun’s centre than the penumbra. _ Two Tables are then given, showing the relative disposition of the umbra and penumbra for each spot of the Kew pictures available for this purpose. In the first of these, this disposition was estimated from left to right, this being the direction in which spots advance across the visible disk by rotation; while in the second Table this disposition was estimated in a direction parallel to circles of solar longitude, and in this Table only spots having a high solar latitude were considered. From the first of these Tables it was shown that, taking all those cases where an encroaching behaviour of the umbra in a right and left direction has been perceptible, 86 per cent. are in favour of the hypothesis that the umbra is nearer the centre than the penumbra, while 14 per cent. are against it. It also appeared that, taking all. available spots and distributing them into zones according to their distance from the centre, this encroaching behaviour is greatest when spots are near the border, and least when they are near the centre. From the second Table, in which only spots of high latitude were considered, it was shown that, taking all those cases where an encroaching behaviour of the umbra in an up-and-down direction has been perceptible, 80-9 per cent. are in favour of the hypothesis that the umbra is nearer the centre than the penumbra, while 19-1 per cent. are against it. The result of these Tables is therefore favourable to this hypothesis. The authors next endeavoured to answer the following question :— Is the photosphere of our luminary to be viewed as composed of heavy solid, or liquid matter, or is it of the nature either of a gas or cloud ? It was observed that the great relative brightness of faculee near the limb leads to the belief that these masses exist at a high eleva- tion in the solar atmosphere, thereby escaping a great part of the absorptive influence, which is particularly strong near the border ; and this conclusion was confirmed by certain stereoscopic pictures produced by Mr. De la Rue, in which the facule appear greatly elevated. It was remarked that faculze often retain the same appear- ance for several days, as if their matter were capable of remaining suspended for some time. Geological Society. 2039 A Table was then given, showing the relative position of sun-spots and their accompanying faculze for all the Kew pictures available for this purpose. From this it appeared that out of 1137 cases 584 have their facule entirely or mostly on the Jeft side, 508 have it nearly equal on both sides, while only 45 have it mostly to the right. It would thus appear as if the luminous matter being thrown up into a region of greater absolute velocity of rotation fell behind to the left ; and we have thus reason to suppose that the faculous matter which accompanies a spot is abstracted from that very portion of the sun’s surface which contains the spot, and which has in this manner been robbed of its luminosity. Again, there area good many cases in which a spot breaks up in the following manner. A bridge of luminous matter of the same apparent luminosity as the surrounding photosphere appears to cross over the umbra of a spot unaccompanied by any penumbra. There is good reason to think that this bridge is above the spot; for were the umbra an opaque cloud and the penumbra a semi-opaque cloud, both being above the sun’s photosphere, it is unlikely that the spot would break up in such a manner that the observer should not per- ceive some penumbra accompanying the luminous bridge. Finally, detached portions of luminous matter sometimes appear to move across a spot without producing any permanent alteration. From all this it was inferred that the luminous photosphere is not to be viewed as composed of heavy solid, or liquid matter, but is rather of the nature either of a gas or cloud, and also that a spot is a phenomenon existing below the level of the sun’s photosphere. The paper concluded with theoretical considerations more or less probable. Since the central or bottom part of a spot is much less luminous than the sun’s photosphere, it may perhaps be concluded that the spot is of a lower temperature than the photosphere; and if it be supposed that all the sun’s mass at this level is of a lower temperature than the photosphere, then we must conclude that the heat of our luminary is derived from without. GEOLOGICAL SOCIETY. [Continued from p. 159. ] December 21, 1864.—W. J. Hamilton, Esq., President, in the Chair. The following communications were read :-— 1. ‘‘ On the Coal-measures of New South Wales, with Spirifers, Glossopteris, and Lepidodendron.”’ By W. Keene, Esq. Communi- cated by the Assistant-Secretary. The prevailing rock in New South Wales is a sandstone, which is called the ‘‘Sydney Sandstone” by the author, and is the most recent deposit in the colony. Its upper beds contain certain shales, called the ‘‘ False Coal-measures”’ by Mr. Keene, and the ‘‘ Wya- namatta Beds” by the Rev. W. B. Clarke, the position of which is 800 feet above the true Upper Coal-seam. On approaching the latter, Vertebraria australis and Glossopteris are met with; and these 240 | : Geological Society. plants accompany the entire series of the Coal-measures, from the topmost to the lowest seam. ‘The workable seams of coal were stated to be about eleven in number; and the author remarked that towards the two lowest seams Pachydomus, Bellerophon, &c. were found; Spirifer abounds near the lowest seam, as well as Fenestella and Orthoceras; but the Vertebraria and Glossopteris, occur throughout, while Lepidodendron has been found in coarse grits below the Coal-measures. Mr. Keene then described a lower fossiliferous limestone uncon- formable to, and much older than, the Coal-measures; and gave a sketch of the geology of the Peak Downs Range, in Queens- land. He concluded by referring to his large collection, sent to England some time ago, and now in the Bath Philosophical Institu- tion, for further evidence of the age of the Coal-beds of New South Wales, which he believes to be as old as those of Europe. 2. «On the Drift of the East of England and its Divisions.” By S. V. Wood, jun., Esq., F.G.S. In this paper the author divides the Drift of the country extend- ing from Flamborough Head to the Thames, and from the Sea on the East to Bedford and Watford on the West, as follows :—a, the Upper Drift, having a thickness of at least 160 feet still remaining ' in places. 6 and c, the Lower Drift, consisting of an Upper series (5), having a thickness from 40 to 70 feet, and a Lower series (c¢), with a thickness, on the coast near Cromer, of from 200 to 250 feet, but rapidly attenuating inland. c¢ comprises the Boulder-till, and overlying contorted Drift of the Cromer coast, which along that line crop out from below 6 a few miles inland. c also, in an at- tenuated form, ranges inland as far south as Thetford, and probably to the centre of Suffolk, cropping out from below 0 by Dalling, Wal- singham, and Weasenham, and appearing at the bottom of the valleys of central Norfolk. 6 consists of sands, which on the east coast everlie the Fluvio-marine and Red Crag, but change west and south into gravels, which pass under a and crop out: again on the north, south, and centre of Norfolk, and west of Suffolk and Essex, ex- tending (but capped in many places by a) over most of Herts. ‘The Upper Drift (a) consists of the widespread Boulder-clay, which overlaps b, for a small space, on the south-east in Essex, and again at Horseheath, near Saffron Walden, but overlaps it altogether on the north-west, resting on the secondary rocks in Huntingdonshire and Lincolnshire. The distribution of 6 indicates it as the deposit of an irregular bay, afterwards submerged by the sea of a, which over- spread a very wide area. a@ now remains only in detached tracts, having been extensively denuded on its emergence at the beginning . of the post-glacial age, so that wide intervals of denudation (sepa- rating the tracts) indicate the post-glacial straits and seas which washed islands formed of a. The author considers the so-called Norwich Crag of the Cromer coast as not of the age of the Fluvio- marine Crag of Norwich, but as an arctic bed forming the base of c, into which it passes up uninterruptedly. The author regards the beds 6 as identical with the fluvio-marine gravels of Kelsea, near Royal Institution. 241 Hull, and the Kelsea bed not to be above a, as hitherto supposed, but below it, having been forced up through a into its present posi- tion. He also regards the Upper Drift (a) as the equivalent of the Belgian Loess, and the beds 6 as the equivalent of the Belgian Sables de Campine. ROYAL INSTITUTION OF GREAT BRITAIN. Jan. 20,1865. ‘On Combustion by Invisible Rays.” By Pro- fessor Tyndall, F.R.S. &c. Passing in review the researches and discoveries of the two Herschels, and the experiments of Melloni, Franz, and Miller on the dark rays of the sun, the lecturer came to the invisible radia- tion of the electric light, and to the distribution of heat in its spectrum. The instruments made use of were the electric lamp of Duboscq and the linear thermo-electric pile of Melloni. The spectrum was formed by means of lenses and prisms of pure rock- salt. It was equal in width to the length of the row of elements forming the pile; and the latter being caused to pass through its various colours in succession, and also to search the space right and left of the visible spectrum, the heat falling upon the pile, at every point of its march, was determined by the deflection of an extremely sensitive galvanometer. As in the case of the solar spectrum, the heat was found to aug- ment from the violet to the red, while in the dark space beyond the red itrose toa maximum. The position of the maximum was about as distant from the extreme red in the one direction, as the green of the spectrum in the opposite one. The augmentation of temperature beyond the red in the spectrum of the electric light is sudden and enormous. Representing the thermal intensities by lines of proportional lengths, and erecting these lines as perpendiculars at the places to which they correspond, when we pass beyond the red these perpendiculars suddenly and greatly increase in length, reach a maximum, and then fall somewhat more suddenly on the opposite side of the maximum. When the ends of the perpendiculars are united, the curve beyond the red, re- presenting the obscure radiation, rises in a steep and massive peak, which quite dwarfs by its magnitude the radiation of the luminous portion of the spectrum. Interposing suitable substances in the path of the beam, this peak may be in part cut away. Water, in certain thicknesses, does this very effectually. The vapour of water would do the same; and this fact enables us to account for the difference between the distribution of heat in the solar and in the electric spectrum. The comparative height and steepness of the ultra-red peak, in the case of the electric light, are much greater than in the case of the sun, as shown by the diagram of Professor Miller. No doubt the reason is, that the eminence corresponding to the position of maximum heat in the solar spectrum has been cut down by the aqueous vapour of our atmo- sphere. Could a solar spectrum be produced beyond the limits of the atmosphere, it would probably show as steep a mountain of in- ar VN wl Th tah tag 242 - 7 Royal Institution :-— visible rays as that exhibited by the electric light, which is practically uninfluenced by atmospheric absorption. Having thus demonstrated that a powerful flux of dark rays accompanies the bright ones of the electric light, the question arises, Can we separate the one class of rays from the other ? In the lecturer's first experiments on the invisible radiation of the electric light, black glass was the substance made use of. ‘The specimens, however, which he was able to obtain, destroyed, along with the visible, a considerable portion of the invisible radiation. But the discovery of the deportment of elementary gases directed his attention to other simple substances. He examined sulphur dissolved in bisulphide of carbon, and found it almost perfectly trans- parent to the invisible rays. He also examined the element bromine, and found that, notwithstanding its dark colour, it was eminently transparent to the ultra-red rays. Layers of this substance, for ex-. ample, which entirely cut off the light of a brilliant gas-flame, transmitted its invisible radiant heat with freedom. Finally he tried a solution of iodine in bisulphide of carbon, and arrived at the extraordinary result that a quantity of dissolved iodine sufficiently opake to cut off the light of the midday sun was, within the limits of experiment, absolutely transparent to invisible radiant heat. This, then, is the substance by which the invisible rays of the electric light may be almost perfectly detached from the visible ones. Concentrating by a small glass mirror, silvered in front, the rays emitted by the carbon-points of the electric lamp, we obtain a con- vergent cone of light. Interposing in the path of this concentrated beam a cell containing the opake solution of iodine, the light of the cone is utterly destroyed, while its invisible rays are scarcely, ii at all, meddled with. ‘These converge to a focus, at which, though nothing can be seen even in the darkest room, the following series of effects has been produced :— A piece of black paper placed in the focus, is pierced by the in- visible rays, as if a white-hot spear had been suddenly driven through it. The paper instantly blazes, without apparent contact with any- thing hot. A piece of brown paper placed at the focus soon shows a red-hot, burning surface, extending over a considerable space of the paper, which finally bursts into flame. The wood of a hat-box similarly placed is rapidly burnt through. A pile of wood and shavings, on which the focus falls, is quickly ignited, and thus a fire may be set burning by the invisible rays. A cigar or a pipe is immediately lighted when placed at the focus of invisible rays. His Royal Highness tlhe Comte de Paris performed this experiment at the lecture. Disks of charred paper placed at the focus are raised to brilliant incandescence; charcoal is also ignited there. A piece of charcoal, suspended in a glass receiver full of oxygen, is set on fire at the focus, burning with the splendour exhibited by this substance in an atmosphere of oxygen. The invisible rays, though they have passed through the receiver, still retain sufficient power to render the charcoal within it red-hot. Prof. Tyndall on Combustion by Invisible Rays. 243 A mixture of oxygen and hydrogen is exploded in the dark focus, through the ignition of its envelope. A strip of blackened zinc-foil placed at the focus is pierced and inflamed by the invisible rays. By gradually drawing the strip through the focus, it may be kept blazing with its characteristic purple light for a considerable time. This experiment is particularly beautiful. Magnesium wire, flattened out and blackened, burns with almost intolerable brilliancy. The effects thus far described are, in part, due to chemical action. The substances placed at the dark focus are oxidizable ones, which, when heated sufficiently, are attacked by the atmospheric oxygen, ordinary combustion being the result. But the experiments may be freed from this impurity. A thin plate of charcoal, placed in vacuo, is raised to incandescence at the focus of invisible rays. Che- mical action is here entirely excluded. A thin plate of silver or copper, with its surface slightly tarnished by the sulphide of the metal, so as to diminish its reflective power, is raised to incandescence either 7m vacuo or in air. With sufficient battery-power and proper concentration, a plate of platinized platinum is rendered white-hot at the focus of invisible rays; and when the incandescent platinum is looked at through a prism, its ight yields a complete and brilliant spectrum. In all these cases we have, in the first place, a perfectly invisible image of the coal-points formed by the mirror; and when the plate of metal or of charcoal is placed at the focus, the invisible image raises it to incandescence, and thus prints itself visibly upon the plate. On drawing the coal-points apart, or on causing them to approach each other, the thermograph of the points follows their motion. By cutting the plate of carbon along the boundary of the thermograph, we may obtain a second pair of coal-points, of the same shape as the original ones, but turned upside down; and thus by the rays of the one pair of coal-points, which are incompetent to excite vision, we may cause a second pair to emit all the rays of the spectrum. The ultra-red radiation of the electric hght is known to consist of ethereal undulations of greater length, and slower periods of re- currence, than those which excite vision. When, therefore, those long waves impinge upon a plate of platinum and raise it to incan- descence, their period of vibration is changed. The waves emitted by the platinum are shorter, and of more rapid recurrence, than those falling upon it, the refrangibility being thereby raised, and the invisible rays rendered visible. ‘Thirteen years ago Professor Stokes published the celebrated discovery that by the agency of sulphate of quinine, and various other substances, the ultra-violet rays of the spectrum could be rendered visible. ‘These invisible rays of high refrangibility, impinging upon a proper medium, cause the molecules of that medium to oscillate in slower periods than those of the ‘incident waves. In this case, therefore, the invisible rays are ren- dered visible by the lowering of their refrangibility; while in the experiments of the lecturer, the ultra-red rays are rendered visible by the raising of their refrangibility. To the phenomena brought to light by Professor Stokes, the term fluorescence has been applied by 244 Intelligence and Miscellaneous Ariicles. their discoverer, and to the phenomena brought forward on Thursday week at the Royal Society, and on the evening of the following day — at the Royal Institution, the lecturer proposes to apply the term calorescence. It was the discovery, more than three years ago, of a substance opake to light, and almost perfectly transparent to radiant heat— a substance which cut the visible spectrum of the electric light sharply off at the extremity of the red, and left the ultra-red radiation almost untouched—that led the lecturer to the foregoing results. They lay directly in the path of his investigation, and it was only the diversion of his attention to subjects of more immediate interest, that prevented him from reaching, much earlier, the point which he has now at- tained. On this, however, the lecturer could found no claim, and the idea of rendering ultra-red rays visible, though arrived at inde- pendently, does not by right belong to him. The right to a scientific idea or discovery is secured by the act of publication ; and, in virtue of such an act, priority of conception as regards the conversion of heat-rays into light-rays, belongs indisputably to Dr. Akin. At the Meeting of the British Association, assembled at Newcastle in 1863, he proposed three experiments, by which he intended to solve this question. He afterwards became associated with an accomplished man of science, Mr. Griffith, of Oxford, and jointly with him pur- sued the inquiry. Two out of the three experiments proposed at Newcastle are, the lecturer believed, impracticable ; but the third, though not yet executed, may nevertheless be capable of execu- tion. In that third Dr. Akin proposed to converge the rays of the sun by a concave mirror, to cut off the light by ‘‘ proper absorbents,” and to bring platinum-foil into the focus of invisible rays. It is quite possible that, had he possessed the instrumental means at the lecturer’s disposal, or had he been sustained as the lecturer had been, both by the Royal Society and the Royal Institution, Dr. Akin might have been the first to effect the conversion of the dark heat-rays into luminous ones. For many years the idea of forming an intense focus of invisible rays had been perfectly clear before the lecturer’s mind, and in 1862 he published experiments upon the subject. He had then discovered the properties of iodine, and had made use of this substance as an absorbent, in the manner subsequently proposed by Dr. Akin. The effects observed by him in 1862 at the focus of invisible rays, were such as no previous experimenter had witnessed, and no experimenter could have observed them without being driven to the results which formed the subject of the evening’s discourse. Still publication is the sole test of scientific priority, and it cannot be denied that Dr. Akin was the first to propose definitely to change the refrangibility of the ultra-red rays of the spectrum, by causing them to raise platinum-foil to incandescence. XXXV. Intelligence and Miscellaneous Articles. ON THE HEATING OF THE GLASS PLATE OF THE LEYDEN JAR BY THE DISCHARGE. BY DR. WERNER SIEMENS. AS’ it seemed probable to me that the glass plate of the Leyden jar must be heated by the charge and discharge, I arranged an ap- Intelligence and Miscellaneous Articles. 245 paratus by which even small heating-effects could be recognized with certainty. The result of the experiments made therewith quite an- swered my expectations. The construction of the apparatus is as fol- lows :—I covered with silk a fine iron and equally fine German-silver wire. These wires were cut into pieces about a decimetre in length, and each German-silver wire soldered to an iron wire. ‘These wires were so laid upon a glass plate covered with a cement of resin and shell-lac, that the solderings of 180 wires, without touching, occupied a space of about a square decimetre. By pressing with a warm iron the wires were fused into the cement and thus fastened upon the plate. After the adjacent free ends of the wires were soldered together so as to form a battery of 180 elements, a second glass plate, also covered with cement, was laid with the cemented surface upon the first. By careful heating, the cement between the glass plates was softened, and a portion of it, with the individual air-bubbles which it enclosed, pressed out. The thermo-pile stood thus in a surface of cement free from air, exactly in the middle of a glass plate about 5 millims. in thickness. The middle of the glass plates covering thus all the inside solderings was provided on both sides with tinfoil armatures about a decimetre square, which were furnished with insulated wires. ‘Ihe free ends of the thermo-pile were also furnished with copper wires, by which they were connected with a delicate reflecting galva- nometer. ‘The entire apparatus, including the external solderings, was carefully protected from any change of temperature. A short succes- sion of charges and discharges, by means of a voltaic inductor of about an inch striking-distance, was sufficient to drive the scale of my gal- vanometer out of the field, and this, too, in the direction due to the heating of the solderings between the armatures. After the charges the deflection returns very slowly to zero. It disappears entirely only after some hours. It is independent of the direction of the dis- charge, and apparently proportional to the number of charges, and to the striking-distance to which the apparatus was charged. The motion of the scale begins at once, and then proceeds regularly. But if one of the armatures be touched with the finger, the scale remains stationary two or three seconds before beginning its motion, which usually terminates outside the field of view. The heating-effect observed can be due neither to conduction through the mass of glass, nor to compression by attraction of the armatures, nor, finally, to penetration of electricity into the glass-mass nearest the armatures. The first objection is directly answered by the arrangement of the apparatus and the experiments described. Any heutine by compression would be equalized by the subsequently equally strong cooling on expansion, and could therefore produce no permanent heating, even if the extremely small contraction were suffi- cient. Nor could a penetration of electricity into the mass of glass nearest the coatings be the cause of the heating, as the deflection did not begin at once, but only after the lapse of some seconds. But if we assume, with Mr. Faraday, that the charge and discharge depends ona progressive molecular motion in the insulator which separates the coatings, the fact of the heating of this insulator is no longer surprising.— Berliner Berichte, 1864, p. 612. ‘ 246 Intelligence and Miscellaneous Articles. — A LETTER FROM SIR J. F. W. HERSCHEL, BART., TO THE EDITORS OF THE PHILOSOPHICAL MAGAZINE AND JOURNAL, IN REFER- ENCE TO A RECENT COMMUNICATION TO THAT WORK OF DR. J. DAVY, ETC. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, Collingwood, February 12, 1865. In reference to the communication from Dr. Davy in your Journal for this month, I have only a few words to say. If the conver- sation between Dr. Wollaston and Sir Humphry Davy, the pur- port of which I stated in my letter to you of December 20, 1864, did not take place, I must have been dreaming when I wrote down, within forty-eight hours from the time of its occurrence, the state- ment in question. If so, the dream has been a singularly persistent one, as J still retain a clear recollection of that conversation having taken place, and of its general purport, though not of the particular words used; and I have, moreover, before me the copy of a letter which J wrote to Mr. Davies Gilbert on the 27th of June, 1827, enclosing my formal resignation of the Secretaryship, in which the opinion expressed by Dr. Wollaston on that occasion respecting the President’s right or courtesy of nomination is alluded to. This letter I subjoin; observing merely that, as Mr. Gilbert was present at the - Meeting of the 23rd of the previous November, the allusion to a matter of which he was personally cognizant requires no further explanation. | (Copy.) ** Devonshire Street, June 27, 1827. «Dear Sir,—I have sent a copy of the enclosed to each member of the Council, the President excepted, you acting as his delegate. which I hope will satisfy all points of propriety. «‘T should retire from the office of Secretary, I will confess, with more regret had it not been recently pressed on my attention with somewhat of a painful distinctness, that that office, by the usages of the Royal Society, although elective by a majority of its members, is yet regarded as being held at the nomination of the individual filling the office of the President; and had it not even been advanced by an authority, to which on all occasions I feel disposed to bow with just reverence, that the exercise of such power of nomination is and ought to be regarded as an act of patronage on the President’s part. «‘ When I accepted the office of Secretary, I assuredly regarded it in no such light, considering myself honoured by the election of the Society to an office so important to its interests, and which had been dignified by the tenure of a Hooke anda Wollaston. Although I never will subscribe to a doctrine which, by lowering the dignity of that office in the eyes of those who may hereafter fill it, cannot but tend to abate their zeal in the discharge of its duties by leading them to regard as a matter of mere routine and clerkship what ought to be executed in the spirit of an important scientific trust— yet I cannot but most deeply lament that such an opinion should exist :—-and offer it as my individual and humble, but fixed, senti- Intelligence and Miscellaneous Articles. 249 timent that unless very distinctly disavowed in all future cases, the interests of the Royal Society and of science will suffer materially. “«T remain, dear Sir, very sincerely yours, (Signed) «J. F.W. Herscuer.” “ Davies Gilbert, Fisq., V.P.R.S.,45 Bridge Street, Westminster.” It can hardly be necessary for me to recall to Dr. Davy’s recollec- tion that I have nowhere asserted that the President had promised the Secretaryship to Mr. Babbage, or either directly or by implica- tion promised to appoint him to, or to give him, that office. I have the honour to be, Gentlemen, Your obedient Servant, ei sity J. F. W. Herscuer. _ LUNAR INFLUENCE OVER TEMPERATURE, To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, With great deference and respect for Dr. Buys Ballot, I cannot but express a very strong conviction that the value of results derived from a tabulation of mean temperatures of the different days of the moon’s age for the last seventy-five years (from 1789 to 1865) far outweighs any that attaches to the sixty years previous. In an inquiry into lunar influence over*temperature, the most de- licate and accurate instruments are essential in order to detect effects which may often require to be measured by tenths and hundredths of a degree (Fahr.). No thermometer, however, of great accuracy existed between 1723 and 1789; and even if any had been available, it would seem extremely doubtful whether observations 130 years ago were made with sufficient regularity and care, or at the exact hours requisite to obtain true mean results. In Dr. Buys Ballot’s work, Les changements périodiques de température, p. 22, there is a passage which of itself would suggest a doubt on this point. It is remarkable, too, that the existence of cold after full moon first becomes apparent in the sums of temperature at Harlem shortly after the date of the invention of Six’s self-registering spirit-ther- mometer. My results (which also show cold in the second half of the luna- tion) completely accord with conclusions arrived at by Bouvard, Schibler, Flaugergues, and other physicists, who have sought for lunar influence over rain, cloud, the serenity of the sky, &c. I have consequently from the first attributed the occurrence of heat and cold in the lunation to the presence or absence of cloud asa known cause of the phenomenon. ‘here is indeed no meteorolo- e'cal fact more certain than that the greatest cold occurs under a clear sky, whether in the polar regions or the desert of Sahara, and that heat is retained in the ground and lower strata of the air by the agency of cloud*. As regards the want of perfect regularity in the action of the moon, Dr. Buys Ballot’s suggestion that it may be due to her influ- ence being partly direct and partly indirect, is worth careful consi- * As shown by Glaisher, in the Phil. Trans. 248 Intelligence and Miscellaneous Articles. deration. But it is consistent with my theory to attribute it also to the fact that the existence of cloud and vapour is due to the sun and the winds, and consequently the action of the moon, though con- sistent, cannot be regular or constant. For example, if no clouds are formed at the}: eriod of new moon and first quarter, the earth’s radiant heat passes away into space, and the result is cold at a time when curves of mean temperature for a series of lunations, show feat; and so in like manner, if more heat than the moon is able to disperse occurs in the second half of the lunation, where the curves indicate cold, the result, pro hac vice, would be a higher temperature than the average. Lastly, as the moon’s hemisphere turned towards the earth does not, as it would appear, attain its maximum heat until the last quarter (and it is probable also. that it does not part with all its radiant heat till several days after new moon), if any further expe- riments are made with the thermo-electric pile, would it not be well to try for heat at the third quarter, and that in a lunation in which the moon takes the longest time in passing from the full, and so receives the greatest amount of heat from exposure to the sun’s rays ? Your faithful Servant, Ewhurst, February 14, 1865. J. Park Harrison, P.S.—The cloud-dispelling power of the moon has been observed not only by Sir John Herschel, but by Baron Humboldt, M. Le Verrier, the late Radcliffe observer (at Oxford), and Mr. Nasmyth ; I am not aware if anyone but Sir John Herschel has attributed it to the radiant heat of our satellite. ELECTRICAL STANDARD. To the Editors of the Philosophical Magazine and Journal. 6 Duke Street, Adelphi, London, W.C., GENTLEMEN, February 7, 1865. I have the honour to inform you that copies of the Standard of Electrical Resistance chosen by the Committee on Electrical Stand- ards appointed by the British Association in 1861, can now be pro- cured by application to me as Secretary to the Committee. A unit coil and box will be sent on the remittance of £2 10s. The Standard is a close approximation to 10,000,00 Pere a Weber’s absolute electromagnetic system, determined according to new andcareful experiments made by different members of the Com- mittee, and the copies are constructed of an alloy of platinum and silver in a form chosen as well adapted for exact measurement. The want of a generally recognized standard of electrical resistance has been universally felt, and led to the appointment of the Com- mittee. They now desire me to express a hope that the motives which have led to their present choice, and which are fully explained in the several reports published by them, will induce you to assist in procuring the general adoption of the new standard, I remain, Gentlemen, Your obedient Servant, . (Signed) FLEEMING JENKIN, Secretary to the Committee. THE LONDON, EDINBURGH, anno DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] APRIL 1865. XXXVI. On the Application of the Principle of the Screw to the Floats of Paddle-wheels. By W. G. Avams, M.4., F.G.S., Fellow of St. John’s College, Cambridge, Lecturer on Natural Philosophy at King’s College, London*. is eres following calculation is an attempt to apply the mathe- matical laws of fluid-motion, as far as they may be de- pended on, to an important practical question with regard to paddle-wheel steamers, viz. the comparison of the pressure of a fluid on a float in the form of the surface of a screw, with the pressure on the ordinary flat float, so as to discover whether any advantage would be gained by having the floats of paddle-wheels made in the form of a screw-surface. This application of the prin- ciple of the screw has been conceived by Dr. Croft of St. John’s Wood, who has tested it by means of small working models with very satisfactory results, both as to the speed when the boat is either lightly or heavily laden, and also as to the steadiness of the pulling power. In all cases on the small boat, the new is superior to the old paddle-wheel when they are of the same dia- meter, and even when the new wheel is narrower than the old one. It has also been tried on larger boats, and the two kinds of floats have been compared; and the results have been in favour of the new principle, there being no large waves or strong backward current in the case of the new wheel, and the velocity and steadiness of motion being greater than in the paddle-wheel with flat floats. This principle is now being applied, under Dr. Croft’s directions, to one of Her Majesty’s steamers. Suppose A B (fig. 2) to be the axis of the paddle-wheel, and AG * Communicated by the Author. Phil, Mag. 8. 4, Vol, 29. No. 196, April 1865. S 250 Mr. W. G. Adams on the Application of the and BH two parallel radii on opposite rims of one wheel, C E F D the axis of two screw surfaces CE K G and D FLH of opposite kinds, the outer edges G K and. H L being at the circumference of the wheel, and the angles'which they make with H G at G and H being each half a right angle; C HE, EF, and F D are equal to one another, so that between the floats a vacant space is left equal in breadth to either of them. K Lis a rod connecting the free corners of the floats, and the planes K EM and LF N are per- pendicular to the axis. These two floats take the place of one of the ordinary flat floats ; and I propose to compare the pressure on them, and the power necessary to sustain it for a given speed of revolution with the pressure, and the corresponding power, in the case of the ordinary paddle-wheel. ~ Before entering into the calculation, it will be well to notice some of the peculiar features of this paddle-wheel, which will probably prove to be not among the least of its advantages. If it is possible to judge from the conduct of a small model, they certainly appear to be decided advantages. 1. The floats enter the water gradually, the pomts K and L being first immersed, and the whole gradually following ; so that there is no sudden jerking of the steamer when a float enters the water, as in the case of the ordinary wheel, where the jerking is ‘so violent at starting as to cause vibrations up and down by the bending of the ship from stem to stern. . The absence of this jerking and the quivering motion will be no slight comfort to those on board. 2. These floats do not carry all the water before them, or cause a strong backward current and so diminish the pressure on the ‘succeeding floats as in the ordinary wheel, but, as there is a vacant space between the floats equal in breadth to one-third of the breadth of the wheel, the water in this space is only slightly dis- turbed, and this disturbance is not sufficient to cause any very great motion at the point where the next float enters the water ; also since the water runs off the floats both outwards and inwards, and not in the direction of motion, there will be no large waves formed in the wake of the ship; so that the power which is ex- pended in the ordinary wheel in producing large waves is in this case usefully expended in increasing the speed of the ship; this is fully borne out in the case of Dr. Croft’s working models ; also the water thrown under the ship on both sides will help to buoy it up. In these points it would seem that Dr. Croft’s wheel is likely to be superior to the ordinary wheel, whether the floats of the latter are feathering floats or not. 3. In the new wheel, when the float is coming out of the pete, the water runs ae sideways readily, and is not car ried up with ( & Principle of the Screw to the Floats of Paddle-wheels. 251 the float, as it must be when the only way for it to run off is in the direction of the motion of the float ; hence by this method all the back-water is got rid of; and this is perhaps one of the greatest advantages - which this wheel has over the ordinary wheel without feathering floats. 4, Again, the new wheel will work shethes it be only slightly immersed or whether the water rises nearly up to the axis of the wheel; and it seems to have the greatest advantage over the or- dinary wheel when they are both deeply laden. There are other important features which might be pointed out; but these [ have no doubt Dr. Croft will ‘take an oppor- tunity of bringing before the notice of the scientific world; but I have mentioned these few points to show that it is not unlikely that this invention may lead to our more steady and more rapid onward progress by means of paddle-wheel steamers. Two questions still remain: Can sufficient hold on the water be obtained by means of the new floats? and if so, what power will be necessary to obtain it? To these questions it is proposed to give a mathematical solution, based on the laws of resistance on surfaces in motion through fluids, which laws, although they are not sufficiently perfect to give absolute results im any par- ticular case, may yet be employed to compare the pressures on two surfaces under similar conditions, and so in this case may be expected to show whether the new wheel is any improvement on the old, either in getting up the same speed with less power, or in getting up a greater speed with engines of the same horse- power. Fig. 3. Fig. 1. By the mathematical thee y, the resistance perpendicular to the surface on any part of a surface in motion through ‘a fluid, where the direction of the motion makes an angle @ with the perpendicular to the surface, is $«p,v* cos*a, where p, is the S 2 252 . Mr. W.G. Adams on the Application of the density of the fluid, « the area, and v the velocity of that por- tion of the surface. The effect of this resistance in a direction inclined at an angle 8 to the normal, will be measured by 4xp,v? cos*a cos B. : Suppose A BG H to have made half a revolution round A B from left to right, so that the floats are in their lowest posi- tion, then the direction of mo- tion of any point of the surface being perpendicular to the line drawn from it perpendicular to the axis, we must find the angle between the direction of motion and the perpendicular to the surface, and also between the perpendicular to the surface at that point, and the perpendi- cular to the plane A BHG, since the motion of the vessel is _ perpendicular to this plane. If _@ be the former angle and 8B the latter, then the resistance R=4xp,v? x cos’« cos 8. Also the power of engine required will be measured by that part of the resistance perpendicular to the surface (4«pjv* cos*«), which acts in a plane perpendicular to the axis AB, multiplied byits distance from that axis—in other words, the moment of the resistance about the axis of revolution. To express these inclinations and portions of surface mathe- matically, we must have recourse to the ordinary notation of Geometry of Three Dimensions. The surface of this screw is traced out by a straight rod, as O P, which slides uniformly along a fixed rod, as CD, at right angles to it, and at the same time twists uniformly about that fixed rod. It will be familiar to all as the surface formed by the edges of the stairs in a spiral staircase, and the steepness of the stairs will depend on the relation between the sliding and the twisting motion, and also on the distance from the shaft. If the fixed rod C D be taken as the axis of z, and C G as the axis of w, then the equation to the surface CG EK is Fig. 2, isi af 0 —-—ycos-= Tr y T where, in this particular case, CG=r, since the angle between GK and HG at Gis 45°. If OP, the distance of any point P from the axis of the surface =p, then p?=2*+y?, and the * Principle of the Screw to the Floats of Paddle-wheels. 258 angle which O P makes with the plane GC DH (the plane of & Z) =<, the surface being a conoid, of which the helix is the directrix, and which is inclined at an angle of 45° to the plane of xy, at a distance r from the axis. Hence ne. Ame cad nea an YG Sts The inclination of the normal at any point to the axis of = is fh ae *) (« eS sin © oe Zz a eho r2+(wcos=+ysin = =r, suppose. cos—2 which is equal to cos~! —-© 2 Jr? + p? Hence an element of the surface at the point P is ey vee ee dy. The inclination of the normal to its trace on the plane of x y is % Jr + p? This trace is perpendicular to O P in the plane P OT (fig. 3), and therefore makes an angle O PI with the direction of motion of the point P. Let AC=OI=a, and let the inclination of OP ( =) to the plane of xz be denoted by 0, and let the angle PIO=¢; then the angle OPI=0—¢ sé o— x(a+xz)+y? Hig HOtECO 8 COTY (at aley Vata e a being the inclination of the normal to the direction of motion of P, we get cos! p+acos @ Oe aly: +7 *V(atayP+y? Also, @ being the inclination of the normal to the axis of y (the direction of the required resistance), cos a=sin y cos (9—d) = reos@O WV 724 p2 p24 pe Also, if w be the angular velocity of the wheel, then the velocity of the point P=wxIP=0X/(a+2)?+y*. cos 6 = sin y cos 0= ————— 954. . Mr. W.G. Adams on the Application of the Hence R=}p,v« cos’a cos 8 $p,0°4(a+2)? ty} (te dan dy) = = jp orn tem Or eb, ay oe or, taking polar coordinates, es: 2 R=3p,o°r . aa — aS Again, the perpendicular distance from the axis A B on the trace of the a in the plane of zy is p+acos 6. ‘Therefore M, the moment about the axis A B = 4p,v*« cos’ sin y(p +4 cos 8) lets cos 0)? do dd. 2+ pP * ane —— ge (p +a cos 2. reosO | Pe lettre va dp dd. = po" Each float extends to a distance (a+r) from the axis A B, 4. e. to the circumference of the wheel. Therefore for the limits of p a? + p?+ 2ap cos = (a+7r)’, or p+acosO= V/ r+ 2ar+a° cos", The limits for p are af 7 + 2ar +a? cos* 0— acos @ and 0. The limits of integration for 0 will be one-third of the ratio of the breadth of the wheel to the length of CG. In the example worked out, C G has been taken =2A G, and the breadth of the wheel GH has been taken shghtly greater than CG for convenience ; so that the limits for 0 are rather more than 4 or 20°, and O, and the breadth of the wheel is to its radius as 7: 10. The expressions for the resistance and moment about the axis admit of integration with respect to p without any restriction : (0 +4 cos 0)? cos 8 =t pare (fete cosdh cond +p? dp d0 ee (0? +r?) cos 8+ 2ap cos? 6 + (a? cos? @—r?) cos 0 =? P)@ re Pn ere eee 9 : ' 2 =4 per? {f feos 0 ap do+ | {a cose. ape? dé | 2 eos? @—r?) | ae eee 7 Jee ao | | | |, r -p* dp dé | Principle of the Screw to the Floats of Paddle-wheels. sl p,o°r? (fe cos. 0 dé fe cos* 9 log (1+5)z0 Cy: kame fer ond. tan" do }, between proper limits, = por Ar V7? + 2ar + a® cos? O—a cos 0} cos 0 dé + (a cos? log { 14 ( E+ Part a cost Oa oon? L x _ The moment of the sdsiilwne’ on cne float +acos 0 M=3 p, na((erecr dp d0 an ile dp dO +80 cos 0 dp dé) pare r 3ar? cos @—a® cos? 0 _ffietenta te yan between proper limits, =i pw v= | (apt Sap cos 0 d9 D anck G12) 2 1 (Oe ee ong (14 La {Petes tans ten ap 2. ae | r te 05 WV 72 + Qar + a? cos? 0+ 5a cos 6. seen i 5. a eo. ae i ee 1 V 72 + Qar + a2 cos? 0—acos 0 | aa foo OE hog {i+ |( ee cos 6 2 r 255. y} a6 Tig = o case tan™*( V 72 + 2ar+ a* cos* O—a cos 0.0} ; a 256 #$Mr.W.G. Adams on the Application of the Bar? cos 0—a® cos? 6, _, Wr? -+2ar +a? cos? O—a cos 9 ae ES say 4 ——-- ‘ Now let a= Then ase aoe oan =po%{ (4/1 +1+ “7 i | cos 0 dé cos? 0 (ay, cos? 8 cos 0? + (OFF tog | 1+ 2 fo) ee bao 4:— cos? @ ‘ut: (y/ cos*@ cos @ a 2+ 1, ) ao}. The resistance on the two floats will be equal to one another. Therefore the resistance on a pair of floats (i =4p,0'r4 {( “8+ cos? 0— cos 0) cos 6 dO CUA) iho 2 + fog (1+ (EH 8 8 08 cost 8.40 ‘gir age -{ (4—cos? 0) cos 6 tan BAiee 4 wo} Also the moment of resistance on a pair of floats Ae cos*@ 5 cos? 0 \/ cos? ) =tp,0°r {((2+ ri 4 +2 cos 6 2+ A dé a Se 2 —{a — 3 cos? @) log { se (a cosy oe zs } dé — cos 0 (3 —4cos?6) tan feo a0 } = 45, ot 2+ cos0(4/ 8+ cos?6—cos6)}d0 Mor 14 ee do og | * 2 +f cos log { 1 (So shea’ ams do —{p cos 6 tan- ‘e Store ja 6 Principle of the Screw to the Floats of Paddle-wheels. 207 —\z(4— cos70) qian (Ot eon con ap iz To find the value of these expressions for the resistance and ‘ moment, the method of Integration by Quadratures has been em- ployed, the values of the functions to be integrated being found at intervals of 5° between the limits 0 and 20°, which limits make the ratio of the breadth to the radius of the wheel the same as that of 7 to 10. The value of the circular measure of 5° is °087266. Values of the Functions to be integrated, the Integrations being taken between O° and 20°. : Let . (,/8 + cos? 0—cos6) =2¢. cos 0. cos? @. 29. 2q cos 0. = BL -999048 -9980898 2:000635 | 1:998731 + 22 999048 -998098 2000635 | 1:998731 7 991445 982963 2:005714 | 1:988555 123 -976296 °953154 2015886 | 1:968101 17 953717 909576 2°031174 | 1:937165 222 923879 853553 2:051613 | 1°895442 4—cos? 0 log, (1+4@’). jlog, (1+-9”) . cos?é. tan—* q.cos 9.| tan—* g.cos@ > . a 693465 692146 784209 1:177960 + 25 *693465 °692146 *7 84809 1:177960 74 696004 684146 780093 1:176785 123 -701090 °668250 °770643 1:174015 173 °708733 644647 756422 1168832 224 718950 613663 737407 1:160105 Hence the expressions for the resistance with their differ- ences are :— Poe or 7519017) © aL isso 94701 — Shear Bee — "033579. a . ia rd 12h 1462837 — ‘iogny "015778 17} 1-412980 — pagoay —014628 221 1349000 The expressions for the moment are :— or Reese. th AEM. coneenn 7 sees 121 1-639906 ~~ 017176 Tees 2 P0601 -azag. 7008078 174 | 1614657 — paorg, — 007535... 224 1:581873 258 . Mr. W.G. Adams on the Application of the To find the accurate values of the integrals of these functions, suppose a is one of the angles for which the value is known, then we must integrate for the variable angle 6 between the. limits +24° and —22° on each side of a, and then add the. results of the integrations. Let O=cx-+a y : where c is the ee measure of 5°, so that the limits fot a are +3 and — : If f,(0) and Fi be the mean of the first differences and the second difference corresponding A one of the values of a, then POTTY) 1 a )3 therefore : (Ae)de=afl0)+ F410 + Fhl0) and * fle) .e. da = e{f(0) +p f,(0)}. peer | The sum of the second differences (which is the same as the last of the first differences) divided by 24, = — ‘002666 for the resistance, and | = — ‘001866 for the moment. Hence the correction for the resistance = — 002666 .c¢, and the correction for the moment == —'001366.c¢; therefore the resistance becomes ge é aieeeiee — 002666 } =10,rt x c(5°881484) =4p,.7r* x ‘518256=4 pw*(rad)* x ‘101384, and the moment becomes $p,@?r'c {6577423 —-001366} =1p*r? . ¢x (6576057) = 40,077" x 573869 =10,?(rad)®° x 075572,— the resistance and moment being expressed in powers of the radius of the wheel for the sake of comparison with the resist- ance and moment on a flat float. Now considering the resistance and moment on a flat float where the radius of the wheel and the length and breadth of the float are in the ratio of 10:6:8 respectively. In this case the resistance on one float Principle of the Screw to the Floats of Paddle-wheels. 259, = 39/2)" + (Yor) ye pap =p) x for X 37° {1—(7%)°} =p, x 74x +1314. The moment = kpeoer? 85x 11 —(qh)4} =10m/r° x 1138985. On comparing these results, we see that when the two wheels are revolving with the same angular velocity, the resistance and moment on the new float are less than on the old, but the ratio between the work done and the power required to perform it is greater in the case of the new wheel than in that of the old, in the ratio of 7 to 6; so that the advantage is on the side of Dr. Croft’s invention. If the difference of the powers of the two be ‘spent in increasing the angular velocity of the new wheel, then the resistance will be eeteater in the new wheel than in the old, im the ratio of 7 to 6; and the angular velocities in this case would be in the ratio of 6 to 5. The mathematical theory takes no account of the shone of the water; so that the results of the above calculations are quite separate from the other evident advantages stated in the early part of this paper. Also, since the floats enter the water gradu- ally, and since the water is less disturbed, it is plain that the angular velocity of the new wheel may be increased in the above ratio without causing the floats to ap through the water and do no work. Another case, where the results may be more easily obtained from the expressions after the first mtegration, is that in which the axis of the wheel is the axis of the screw-surface, and where the inner portion of the surface up to a distance of one-third of the radius from the axis is cut out, so that a=0, and the limits of integration for p are r and - Hence R=}p0%"{ /°2—$)e0s 0dd—2/)(5 —tan~'} Joos edo} =1p,w7r* x sin 0 x ‘406, and M= pore /2{1-4 (4)2 do — isles )d0=4p,w?r? x Ox 301 very nearly. 260 Mr. W. G. Adams on the Application of the Hence if these wheels be of the same breadth as in the first case, the resistance and moment are not so great as in the other case, but are nearly in the same proportion. If the breadth of. the wheel be three-fourths of the radius, then the same resistance will be produced by the same power as in the first case considered. It will now not be difficult to arrive at the expressions for the resistances and moments, taking into account the velocity of the steamer. If v be this velocity, the expression for the resistance when the float is in a vertical position is oe 3 {fie - ree ~~ cos 0. ie (p+. cos ) —v cos 0} 2dp. dO — vee as 8 salod +acos @)—v cos 6} *dp dd, Also the moment ; 6 = aA bee a (9 -+acos 0)—v cos 0! "dp dO. Hence the resistance on one float becomes +acos 0)? cos 0 apyat of | (eres ey eee pda 20 cos?@ — yoyo ( ie 5 dp d0 —4p)7?v(2aa—v) ff oF 5 Ap dé. And the moment on one float becomes ++ acos 6) 3p,@” {| ergo p ee = dp dé — pr. no (etacos ens? COS? aaa ae { Bae 9 10 dO +4p,73v? .a A (ee 8 ap These integrals are the same as those which have already been found ; and the results arrived at are these :— | Principle of the Screw to the Floats of Paddle-wheels. 261 Resistance on 4 pair . floats =16,0*r af: 513256—~ x: 284563——” 5 OT ali Ee. 259202; and the moment of the resistance on them = $p,0%4" x 493765. The angular velocity should be such that v, the rate of the steamer, is not greater than =~ Let => : then the resistance =5 port x 149092 i : po? (rad)4 x 029450 ; and the moment =5) wr? x *184054 =5 po? (vad)® x “024288, The corresponding expressions may be obtaimed for the flat float by taking (wp —v)? for the square of the actual velocity of a point of the surface, instead of w*p?; and the results obtained are :— Resistance =5 pM, at B14 x 153 + oo »X 2x 18} =5 p,@/274 x frau oy Me “051 + S x “02 | | Moment 2 =5 popes "1140— +1314 x ae x 153 } 2 =; peer? { 1140— a x 0438+ > x ‘017 / the velocities being the same in both cases. If the relation between the angular velocities be such that the resistances are the same, then the moment in the case of the new wheel will be less than in the old, the ratios being as 96°88 to 100; so that not only can the same hold be obtained on the water by means of the new floats, and so the speed be kept up, but the power of 262 . Mr. G. C. Foster on Chemical Nomenclature, © the engine required to do it is about 3 per cent. less. The angular velocity of the new wheel will be greater than that of the old in the ratio of 1175 to 1, or nearly in the ratio of 6 to 5. We may conclude, then, that for a velocity of ten miles an hour in a steamer with paddle-wheels of 15. feet radius, the number of revolutions a minute should not be less than 18: and with this number the relations between the resistances and moments are those given above, which show an advantage in favour of the new wheel. With a less number of revolutions the part of a float nearest to the axis will tend to stop rather than to propel the boat. For a velocity of 18 miles an hour, the number of revolutions a minute in the new wheel should not be less than 30, for the same reason ; and then the same hold is obtained on the water as in the ordinary wheel making 25 revolutions a minute, and that with less power of engine. By still further increasing the angular velocity in the new wheel as compared with the old, so that the number of revolutions a minute are as 3 to 2, the ratio of the resistance to the power producing it is 10 per cent. greater in the new wheel than in the old. Since . it appears that the angular velocity of the new wheel may be made much greater than that of the old (provided marine engines will admit of such an increase in the rate of revolution) without causing the floats to slip through the water, it follows that this increase will give the new wheel a great advantage over the old with Bae to speed. XXXVII. On Chemical Nomenclature, and chiefly on the use of the word Acid. By G. C. Fostur, B. A., Lecturer on Na- tural Philosophy in Anderson’s University, Glasgow*. iB forming a nomenclature for any science, two distinct requirements must be kept in view as having each to be supplied. In the first place, a convenient general language must be provided, to serve as a medium for the ordinary every- day transactions of the science; and in the second place, there must be what. may be called the legal language of the science, —a language whose terms are, as far as possible, strictly defined, and have an exact and generally recognized value. It is this second stricter language which constitutes the more technical part of scientific nomenclature, and it is this alone which it is either desirable or possible to alter or reform in accordance with. any par ticular state of scientific opinion, The general language of a science will always, in the main, take care of itself; and at, any given period it usually contains a ‘lar ge admixture of terms— once technical, but now no longer used for purposes of accu- Communicated by the Author. and chiefly on the use of the word Acid. . 263 racy—which, like fossils in a rock, tell of the successive changes by which the existing state of things has been brought about. The more strictly technical language, on the other hand, is always formed with more or less premeditation, and is therefore, toa corresponding extent, under control and capable of being re- formed. The existence of such a language and its preservation in the highest possible state of efficiency are of the utmost scien- tific importance ; for, although none but a pedant would im all cases employ it (when the use of more popular expressions could lead to no ambiguity), it is quite certain that accurate language is an essential imstrument of accurate thought, and that the progress of any science will be greatly retarded unless its lan- guage is such as to admit of its facts and theories being stated with any required degree of precision. These general remarks are meant as answer, by anticipation, to the objection, so often urged to attempted reforms in Chemical Nomenclature, that the proposed modes of expression would be too troublesome for general use. It is contended that this objection, even when real, is by no means necessarily conclusive. A particular innovation might render important services as a part of what has above been called the legal language of the science, although it might never come into general use, from the fact that it corresponded to a degree of precision beyond that required for ordinary purposes. Our aim should be to render our language such that it may be in the power of every chemist to know accurately the ideas which he will convey to the minds of others by his use of it. The extent to which each one avails himself of its resources must, of course, be left to his own discretion. At the present time, one of the most important questions which has to be considered, in relation to chemical nomencla- ture, is as to the use of the term Acip. The sense in which this word has been employed of late years has been gradually becoming more uniform than it was previously; and those che- mists who regard the now prevalent usage as the correct one might well have been content to watch, without attempting to hasten, its still further spread, were it not that a return toa former and, as they consider, improper use of the term has quite recently found an advocate of no less authority than Pro- fessor Williamson, President of the Chemical Society*. : This distinguished chemist desires to apply the term acid to the class of substances now very frequently called anhydrides or anhydrous acids, and to call, for imstance, N?O° nitric acid, N? 0? nitrous acid, (C? H?QO)?0 acetic acid, SO? sulphurous * “Remarks on Chemical Nomenclature and Notation,” by Professor Williamson: Journ. Chem. Soe. vol. xvii. p. 421 (December 1864).- _- 264 Mr. G. C. Foster on Chemical Nesephalature. acid, SO? sulphuric acid, &. Among the arguments urged by Professor Williamson in support of this proposal, one of the most forcible is founded upon what he says was the original meaning of the word. “There are perhaps no words in use among chemists of which the original meaning was so clear as the word acid, and the correlative word base. They were intro- duced to describe bodies of opposite properties, which are more or less completely lost in the salt or compound of acid and base” (page 423). And again, “I submit that it is not allow- able to use any word in a sense inconsistent with its established meaning and use, unless one has the most ample evidence that it cannot again be wanted, and will not again be used, for its original pupose. Words may be considered as the property of the ideas which they are used to denote, and the words ‘acid’ and ‘base’ belong to the idea of compounds of fundamentally opposite properties, which unite to form one or more molecules of a comparatively neutral compound ” (page 424). No doubt Dr. Wilhamson’s definition of the words acid and base would have met with very general, though not universal, acceptance fifty years ago; but if we wish to ascertain the “ ori- ginal ”” meaning of these words, we must go much further back, and then that meaning becomes anything but particularly clear. There can be no doubt that sourness was the property whose possession in common by different substances first led to the use of the term acid as a generic name for a class of bodies. Corrosiveness came afterwards to be regarded as an important mark of acidity; but at no time previous to Lavoisier does it ap- pear that the meaning of the word acid was defined with anything like precision. In addition to sourness and corrosiveness, the power of reddening many vegetable blues, of precipitating sulphur from solution of liver of sulphur, of causing effervescence with alkaline carbonates, and of destroying more or less completely the causticity of alkalies, was considered characteristic of acidity ; but how far chemists were from using the word acid to denote any very clearly definable idea, is sufficiently proved by the fact that, in the latter half of the last century, limestone was sup- posed to become caustic when burned by absorbing an acid (acidum pingue) from the fire, and that its power of rendering the “ mild alkalies ” caustic was due to its imparting to them this same acid*. Until the time of Lavoisier, the substances known as acids were regarded as members of the general class of salts, which was commonly divided into salia acida, salia alcalina, and salia * The acidum pingue of Meyer was the last form of an idea which had been previously put forth by Van Helmont and by Stahl. (See Watts’s * Dictionary of Chemistry,’ vol. i. pp. 40 & 115.) | | and chiefly on the use of the word Acid. 265 media vel composita. The separation of acids from neutral and alkaline salts, and their recognition as a distinct class, resulted chiefly from Lavoisier’s discovery of the presence of oxygen in several of the best-known acids, and his consequent conclusion that they were in reality a particular class of oxides*. This view was of course applicable with strictness only to the anhydrous acids, but it did not for a good while occasion any difficulty in the application of the word acid: the essential nature of the dif- ference between the bodies since known as anhydrides, and the bodies formed by their union with water, although insisted upon by Davy, was not generally recognized until experiment had shown how different was the behaviour of these two sets of sub- stances respectively with ammonia and almost all organic com- pounds. But these investigations had been pursued only a very little way before it became evident, to all who took the trouble to examine the question, that it was utterly illogical and unphilo- sophical to continue to designate by the same name bodies which differed so essentially from each other as did many of those which had been hitherto classed indiscriminately as acids. Laurent and Gerhardt, whose teaching contributed more than that of any other chemists to set this point ina clear light, got rid of the in- consistency by strictly confining the application of the name acid to salts of hydrogen, such as SO*H?, and calling the bodies (actually or conceivably) produced from these by loss of water, such as SO?, anhydrides. In retaining the term aczd for SO* H? and its analogues, rather than for SO® and its analogues, they undoubtedly followed the prevailing usage of chemical language ; for though the latter class of bodies were described as acids in all systematic works on chemistry, yet in perhaps ninety-nine cases out of a hundred, when an acid was spoken of as taking part in or resulting from a reaction, it was a hydrogen-salt, and not an anhydrous acid, that was meant. Hence the course which they adopted obviously involved a much smaller departure from esta- blished usage than the choice of the other alternative would have done; andif this was true twenty years ago, it is true to so much greater an extent now that the reversal of Laurent and Gerhardt’s system would necessitate the rewriting of almost the whole of organic chemistry. Hence it appears that, so far from the original meaning of the word acid having been clear, it would be more correct to say that this word was never used in a strictly scientific and logical sense at all, until Gerhardt defined acids to be salts whose 5ase was wholly composed of hydrogent. * See particularly his Trazté élémentaire de Chimie, vol. i. p. 163. + Précis de Chimie Organique (Paris, 1844), vol. i. p. 70; Introduction a Pétude de la Chimie par le Systeme Unitaire (Paris, 1848), p. 103. Phil. Mag. 8. 4. Vol. 29. No. 196, April 1865. T 266 Mr. G. C. Foster on Chemical Nontonbheure, The original meaning of the term base is perhaps even less clear than that of the word acid. According to Kopp* it was in- troduced by French authors, and occurs frequently from about the year 1730. With regard to its earliest meaning, he says, “The following passage from Rouelle’s ‘ Memoir on the Neutral Salts’ (1754) may give some idea of the sense connected with the use of this word :—‘J’ai étendu le nombre des sels autant qu’il était possible, en définissant génériquement le sel neutre, un sel formé par union d’un acide avec une substance quel- conque, qui lui sert de base et lui donne une forme concrete ou solide.’ (Stahl employs a periphrasis similar to the above to express what we now call a base; in his Specimen Becherianum [1702], he denotes the substance which is contained in chloride of sodium in combination with an acid as materia illa, que salt corpus prebet.)” The word “base” occurs very frequently in the writings of Lavoisier, but with him, as m the above quota- tien from Rouelle, it appears to have retained very much of its etymological meaning of foundation, and not im any degree to suggest the possession of properties opposed to those of acids. The following passage may serve to illustrate his use of the term :— I] est infiniment rare d’y trouver [in the vegetable kingdom] un acide simple, c’est-a-dire qui ne soit composé que d’une seule base acidifiable. Tous les acides de ce régne ont pour base ’hydrogéne et le carbone, quelquefois l’hydrogéne, le carbone et le phosphore, le tout combiné avec une proportion plus ou moins considérable d’oxygéne. le régne végétal a également des oxides qui sont formés des mémes bases doubles et triples, mais moins oxygénées ” (Traité élémentaire, vol. i. pp. 124, 125, edit. 1789). The modern word equivalent to ‘ base’ in this passage would evidently be ‘ radical,’ as is clearly shown by the one which follows :—‘‘Il faut done distinguer dans tout acide, la base acidifiable 4 laquelle M. de Morveau a donné le nom de radical, et le principe acidifiant, c’est-a-dire, oxigéne ” (Ibid. p. 69). The limitation of the term base to salifiable bases only, seems to be of comparatively recent introduction, and is probably due to Berzelius; but even with this limitation it has never been confined exclusively to bodies of any one class. ver since the expression salifiable base came into use, it is probable that almost all chemists have been agreed in considering it as applicable to sub- stances as variously constituted as those represented by the for- mule KHO, K?0, PbO, NH?. In the following passage, how- ever, Professor Williamson seems to imply. that Gerhardt confined the word base to basic hydrates only :—“‘ In fact he [Gerhardt] systematically apphed the term acid to hydrogen-salts, giving _ * Geschichte der Chemie, vol. iii. p. 69. | : | and chiefly on the use of the word Acid. 267 the name anhydride to acids, and leaving bases, however anhy- drous they might be, entirely unprovided with a corresponding name” (page 424) ; but I am not aware from what part of his writings such a limitation can be inferred. It is quite true, however, that Laurent and Gerhardt pointed out that, as a matter of fact, the bases which took part in a great many reactions were not anhydrous oxides (as they had hitherto been commonly re- presented) but hydrates, and that they laid great stress upon the importance of recognizing this fact in the chemical equations by which those reactions were expressed. But not only can I not admit that original usage is in favour of that application of the terms “acid” and “ base”? which Dr. Williamson recommends ; it appears to me that one at least of the arguments by which he tries to show that the salts of hy- drogen ought not to be called acids, can be used with equal force against the employment of that name in the sense which he de- fends. In page 4:26 he says,— “ But it is not only true that the bodies misnamed Weare are acids ; it is equally true and certain that the hydrogen-salts cannot with any consistency be called acids: for when two hy- drogen-salts—say hydric nitrate and potassic hydrate—react on one another, we cannot call the process a combination of nitric acid with potash, without putting in the background, and to some extent concealing, the fact that water is formed, quite as much as potassic nitrate. Learners of chemistry who have been told that an acid is a thing which combines with a base, natu- rally and consistently wish to omit any mention of the water in their description of the process, and they have to be told that this supposed acid really is a salt of hydrogen possessing acid properties, and the so-called base is a hydrogen-salt with strongly basic properties, the two on coming together undergoing double decomposition, just as truly as potassic chloride when mixed with argentic nitrate.” Without dwelling upon the facts that chemists who call hydrogen-salts acids, do not want to call the process above de- scribed “‘a combination of nitric acid with potash,” and that they would not tell learners of chemistry that ‘an acid is a thing which combines with a base,” we may remark that a pre- cisely similar difficulty would m some cases arise for learners from the adoption of Dr. Williamson’s definition of acids. When ete acetic “acid,” (C? HO)? O, aceto-benzoic “ acid,” - yee \ O, or thiacetic “ acid,” (C? H? O)?S, reacts with a base, say water, H* O (which is the first base in the list of examples on page 429), we cannot call the process a combination of the acid with the base, without putting in the background, and to some extent T ; 268 Mr. G. C. Foster on Chemical Nomenclature, concealing, the fact that it is in reality a double decomposition, just as truly as the change which occurs on mixing potassic chloride with argentic nitrate. Possibly Professor Williamson might reply to this, that he never asserted that double decompositions could not occur between acids and bases; but that is not now the precise ques- tion. If the impossibility of correctly describing the reaction which takes place between the two bodies NHO® and HKO as the combination of an acid with a base is a reason for not calling NHO? nitric acid, the lke impossibility im the case of the bodies (C? H? O)?0 and H?O is an equally good reason for not calling (C? H? QO)? O acetic acid. Nevertheless, although it appears to me that the are: consis- tent and logical sense in which the word acid can be used, is the sense defined by Laurent and Gerhardt, it seems to me unnecessary to retain it at all as a strictly scientific term. I most fully agree with what Professor Williamson says in a pas- sage which follows immediately the one last quoted :— “T hold that it is inconsistent and highly inconvenient to apply to the double decompositions which take place between hydrogen-salts of acid properties and hydrogen-salts of basic properties, any terms which conceal the fact of their close ana- logy with other double decompositions ; and that the hydrogen- salts ought to be designated by terms similar in form and gene- ral arrangement to the terms applied to the salts of other metals.” If we regard the salts of hydrogen as constituted like the salts of any other metal, the application to them of the name acid becomes incorrect if it implies any peculiarity of constitution, and superfluous if it does not. When we want to speak of acids as a Class, they are accurately and conveniently indicated as hydrogen-salts; while individual acids may equally well be de- noted by such names as hydric sulphate, hydric nitrate, hydric chloride, &c., the systematic adoption of which is urged by Dr. Williamson. The word acid will certainly long remain as a part of popular, and even of ordinary chemical language, and hence the im- portance of trying to ascertain its correct application; but its strictly scientific significance has passed away. It indicates a distinction to which we now know that no real difference cor- responds. Lastly, it is necessary to say a few words as to the nomencla- ture of the substances upon which Dr. Williamson is wishful to bestow the name acid. The term “ anhydride,” by which Laurent and Gerhardt designated these bodies, has been very justly ob- jected to on the sround that, in applying it to any object, we merely state that that object is not one of an infinite number of On the Mechanical Energy of Chemical Actions. 269 things which it might be, but we do not say what it zs. This, again, isa term by the total abandonment of which I venture to think that the language of chemistry would be improved rather than impoverished. The so-called anhydrides are exclusively oxides (or sulphides) ; and there seems to be no good reason for applying to them a nomenclature different from that which is employed for other bodies of the same class. By simply calling these bodies what everyone admits that they are, namely, OXIDES, we avoid all the objections that can be urged against calling them either acids or anhydrides, and we obtain names— such as sulphurous oxide, sulphuric oxide, acetic oxide, benzoic oxide—which are at once intelligible to every chemist. In support of this suggestion, I may be allowed to quote in conclusion part of a letter received a short time ago from Mr. Watts, a gentleman whom all recognize as a high authority on such a subject :— “‘T quite agree with you that owide is a much better term than anhydride for things like SO?, P? O°, &c. Indeed I should have denoted them in that way throughout the ‘ Dictionary,’ had it not been that some vested interests seemed to stand in the way. I allude to terms like carbonic oxide, nitric oxide, &c., which, being already appropriated, could not be applied to the anhydrides CO* and N*O°. But the difficulty may be com- pletely got over by calling CO carbonic oxide, CO? carbonic dioxide, N* O° nitric pentoxide, &c. As to the term ‘acid,’ I really don’t see why it should not, as you suggest, be superan- nuated altogether, excepting as a trivial name for certain well- known compounds which people in general will perhaps never be induced to call by any other name.” XXXVIIT. On the Mechanical Energy of Chemical Actions. By Dr. H. W. ScuropER van DER Koxx*. N a communication on “ Dissociation,” M. H. Sainte-Claire Deville sets out from the view that all chemical compounds are ultimately decomposable into their constituents by a suffici- ently elevated temperaturet. He supposes the molecules thus * Translated from Poggendorff’s Annalen, vol. cxxii. p. 439 (July 1864), by G. C. Foster, B.A. The author says, in a foot-note to the original, ‘This paper wag already written when I again encountered the same ideas in Clausius’s recently published paper (Pogg. Ann. vol. cxxi. p. 1), where he says that in the principle of Transformations a general natural tendency to transformations in one definite direction expresses itself, and that this tendency comes into account also in the changes of state of material bodies.” + Fortschritte der Physik, 1860, p. 379. Phil. Mag. S. 4. vol. xx. p. 448. 270 Dy. van der Kolk on the Mechoniteal separated to be, at a lower temperature, capable either of com- bining spontaneously (that is, by mere cooling) or of remaining separate. From this point of view, therefore, compounds may be divided into two groups,—the first contaming those which, when decomposed by heat, are recomposed again when cooled ; and the second, those in which this does not take place. There seems to me to be a connexion between this property and the following. It is known from Favre and Silbermann’s experiments that in many cases of chemical combination heat is evolved, while in a’ few cases heat is absorbed; accordingly, chemical compounds may be divided into two series from this point of view also. The way in which this property is connected with that previously referred to, will become clear from the fol- lowing considerations. If we figure to our minds a body, at first in some definite con- dition, at 0° C. for example, and then suppose heat to be ap- plied to it, it will at a given temperature have taken up a given quantity of heat. This heat goes partly to raise its temperature, partly to cause molecular changes (so-called internal work), and partly to perform external work. This whole quantity of heat increases continually as the temperature rises. Hlevation of temperature, as well as change of state of aggregation from the solid to the liquid, and from the liquid to the gaseous state, always requires absorption of heat. In order to find the quantity of heat existing in the body after the process, we must deduct from the total quantity the portion which is converted into ex- ternal work. The quantity of heat then remaining is called by Thomson* the mechanical energy of the body in the given state. According to the suppositions we have made, this is not an ab- solute measure of the energy, but indicates how much more energy is accumulated in the body than was in it in a given condition at O° C. Kairchhoff}+ has called the influence which the body exerts upon external matter, while passing from the first condition to the second, the effective function (Wirkungsfunc- tion) of the body for this change. This is therefore, with the contrary sign, the exact equivalent of what Thomson calls its energy. According to this, every body possesses, in a given condition, a given quantity of energy. Let us now suppose two bodies, such as oxygen and hydrogen, which can combine by an electric spark. Before confbination, each contains a certain quantity of energy ; by the combination heat is generated ; and if the vapour of water which is formed is cooled down to the temperature ex- isting before the combination, the quantity of energy which the * Phil. Mag.S. 4. vol. ix. p. 523. + Poggendorff’s Annalen, vol. cui. p. 177. Energy of Chemical Actions. 271 water-vapour contains less than was contained in its constituents will be exactly equal to the amount of heat set free. It will be understood that the combination of oxygen and hydrogen is here supposed to take place in a closed space, and therefore without any development of external work; otherwise this must also be taken into account. If aqueous vapour is decomposed at the same temperature, as much energy must be given to it as was set free by the combi- nation. Accordingly, two cases are possible: either the body possesses more energy than its constituents, or it contains less. In the first case, heat is produced by the decomposition of the body ; in the second case it is destroyed. Heat is therefore set free when we heat a compound of the first class until decomposition begins: The components will then no longer recombine spontaneously by subsequent cooling, for the quantity of energy contaimed in them is not sufficient for the formation of the compound body at the same temperature. Combination would be possible only if one of two cases occurred : either the body must take heat from surrounding matter, whose temperature never exceeds, but is at most equal to its own; or there must be a sudden cooling of the body formed. So far as I know, such a case of cooling has not hitherto presented itself. The law developed above may accordingly be enunciated thus : Bodies which evolve heat when decomposed by elevation of tem- perature are not reproduced by subsequent cooling. Hence follows, as a direct consequence, the connexion of the above-named properties. Let us test this law by means of Favre and Silbermann’s results*. J. Nitrous oxide evolves heat when decomposed. There exists therefore less energy in nitrogen and oxygen when they are sepa- rate, than when they are combined in the form of this compound ; accordingly they do not recombine when afterwards cooled. This conclusion is not affected by Favre and Silbermann’s explanation that ozone comes into play here. 2. Binoxide of hydrogen evolves heat on decomposition ; and hence again there exists more energy in H? 0?, than in H?O and @ when they are separate. By cooling, the combination is not reproduced. 3. Oxide of silver appears likewise to give off heat when de- composed ; and it is not formed again by cooling. 4, According to Favre}, hypochlorous and chloric acids evolve * Annales de Chimie et de Physique, 3 sér. vol. xxxvi. p. 1. t+ Theses presentées a la Faculté des poeners de Paris (Mallet-Bache- lier, 1853). In this work (p. 52), Favre has already remarked that 272 Dy. van der Kolk on the Méciened heat when decomposed ; they break up when heated, and are not reproduced on cooting. The following additional examples may be iste from Deville’s paper referred to above—namely, chioride, iodide, and sulphide of nitrogen, which are suddenly decomposed with evo- lution of heat by elevation of temperature, but are not reproduced by subsequent cooling. The law above stated holds good also for the transformations’ of dimorphous or polymorphous sub- stances from one condition to another. 1. When Arragonite is heated, it changes into cale-spar and evolves heat; Arragonite therefore contams more energy than calc-spar, and hence the opposite change does not take place on cooling. 2. Crystals of sulphur eed by fusion (and belonging to the Fifth System) change at a low temperature, with evolution of heat, into crystals of the same form as those of native sulphur (which belong to the Fourth System). Again, therefore, more energy is contained in the substance in its first condition than mm the second, and accordingly the inverse process does not occur at low temperatures. 8. Plastic sulphur (soufre mou) lkewise evolves heat while passing into ordinary sulphur, and hence contains more energy than this. Ordinary sulphur therefore cannot of-itself change into the plastic modification, but the opposite change can occur. 4, Deville* speaks of a third modification of sulphur, which is insoluble in sulphide of carbon. By warming, this variety is converted into common sulphur; and it follows from the expe- riments of Fordos and Gelis+, that it takes up heat during the change, thus exhibiting the opposite behaviour to that of plastic sulphur. ‘This insoluble modification accordingly contains less energy than ordinary sulphur, and apparently it does not change spontaneously into the latter. Devillet kept some fragments at the ordinary temperature, which were unchanged after six years. Herein lies the explanation of the following observations by Favre§. He finds that in the formation of sulphurous acid from ordinary sulphur, and its further oxidation to sulphuric acid by means of chlorine, each equivalent evolves 67,212 thermal units - (the equivalent of hydrogen being taken as 1 gramme), whereas by direct oxidation by means of hypochlorous acid only 64,110 thermal units are evolved. In the last case, however, the less the above-named compounds do not form of themselves after decomposi- tion; but he merely deduces this from the observed phenomena, and does not give it as in any way a consequence of a general theory. * Ann. de Chim. et de Phys. 3 sér. vol. xlvu. p. 94. + Ibid. p. 108. t Ibid. p. 100. § Theses, &c., p. 43. - Energy of Chemical Actions. 278 energetic insoluble modification was employed ; and since in this experiment the components contained less energy than in the former one, but the resulting sulphuric acid the same quantity in both cases, the difference between the energy of the reagents and that of the products, that is, the heat evolved, was less in the second case. 5. It is pointed out in the same memoir (Favre, Théses, &c., p. 25) that 1331 units of heat are absorbed in the conversion of opake arsenious acid into the vitreous modification. Hence more energy exists in the second modification than in the first ; and in reality vitreous arsenious acid changes spontaneously into the opake variety, but the opposite change takes place only on heating. 6. Red phosphorus possesses more energy than common yel- low phosphorus* ; nevertheless it does not of itself change into the latter. This, however, does not at all contradict the theorem ; for this does not say that the transformation will occur in every case, but only that, if transformation does take place, the body passes into a state in which it contains less energy. 7. Ozone also may be quoted as an example. It contains more energy than ordinary oxygen, into which it is changed by heating, no doubt evolving heat at the same time. Subsequent cooling does not reproduce the ozone. ; In accordance with the foregoing facts, it may be established as a general theorem, that— When a body on heating passes from one condition to another with evolution of heat, it does not return to its first condition upon subsequent cooling. The examples already given may suffice to illustrate this theorem. It is possible that exceptions will come to light; but if so, they must be such as can be referred to the two cases stated above. It is of course understood that the chemical affinity between molecules must also be taken into account, and we can imagine this sufficiently powerful to draw from surrounding objects the energy required for the combination. Something of * [There appears to be a mistake here: according to Favre’s experiments, as reported in Liebig and Kopp’s Jahresbericht for 1853, p. 24, the trans- formation of 31 grammes of red phosphorus (1 gramme-atom) into com- mon phosphorus is attended with the absorption of 28,246 thermal units. This result, taken in connexion with the comparative ease with which yel- low phosphorus changes into the red modification, harmonizes better with the principles which the author is seeking to establish, than his own state- ment contained in the text. In Miller’s ‘ Elements of Chemistry’ (3rd ed. vol. 1. p. 220), however, it is stated that when red phosphorus is heated to the temperature at which it is converted into yellow phosphorus, “the whole mass suddenly passes back imto the ordinary form, with a copious evolution of heat.”—TRANSL. | 274 Dr..van der Kolk on the Menilinkonl this kind takes place in freezing-mixtures, where the cooling is a secondary consequence of the powerful molecular forces; but similar phenomena do not seem to have been observed in the case of simple combination accompanied by absorption of heat. The converse theorem to the above is as follows:—. _ If heat is absorbed in the case of a decomposition caused by ele- vation of temperature, an action of the opposite kind will occur on subsequent cooling. This theorem cannot be referred to a theoretical basis, - and therefore cannot be looked upon as proved ; it receives, however, frequent confirmation, as the following examples show. Carbonate of lime absorbs heat, according to Favre and Sil- bermann, when decomposed by heat, and therefore does not con- tain as much energy as its components taken together. Accord- ingly, lime and carbonic acid combine again on cooling. It is worthy of remark that Arragonite, which contains more energy, absorbs scarcely any heat when decomposed. It is the same with the slaking of lime. A great deal of heat is given off, and consequently hydrate of lime contains much less energy than its components. By heating, it is decomposed, and it re-forms spontaneously on cooling. Heat is evolved in the formation of carbonic acid and water ; consequently these compounds possess less energy than their constituents. Their elements, however, unite only at a high temperature; and if therefore, as stated by Deville, they are decomposed by the mere action of heat, this decomposition must take place at a still higher temperature than that at which they are formed. At low temperatures, nevertheless, no combination occurs, notwithstanding that the components contain much more energy than the products. ‘This is connected with the mode of action of chemical affinity, which at low temperatures is not suffi- ciently powerful to cause the formation of these compounds, although they contain so much less energy. In order that a compound may be produced, two general conditions must be fulfilled: (1) there must be chemical force or affinity sufficient for combination; and (2) there must be the energy necessary for combination. There is to a certain extent an analogy between these conditions and those involved in the existence of a galvanic current, which requires not only a difference of tension, but, in addition, the energy needed for the production of the current, and generated by the chemical processes which go on in the battery. One cause alone is in both cases insufficient. Here therefore we may speak of reversible and non-reversible pro- cesses. If a body is changed by elevation of temperature and evolves heat, it comes into a new condition in which it contains less energy than before, and therefore cannot possibly. return of Energy of Chemical Actions. 275 itself to its previous condition of more energy. ‘This is accord- ingly a non-reversible process. If, on the other hand, heat is taken up during the change, the body in its new condition pos- sesses more energy than before, and hence it may come to pass. that it returns spontaneously on cooling to its former state. The first case will be of most frequent occurrence, for here the second condition is of necessity always fulfilled. Hence it appears that evolution of heat in combination is the rule, and absorption of heat the exception. As examples of reversible processes, we may also mention the phenomena of latent heat in fusion and vaporization. Bodies which have undergone these changes always possess more energy in their new condition than they did previously, and they accord- ingly return of themselves to their former state on cooling. This is analogous to the well-known theorem of the dynamical theory of heat, which states that heat can never be transferred from a lower to a higher temperature without the expenditure of work. Many long-familiar principles at once take their places among the consequences which follow from these considerations. For instance, (1) the heat of combination remains the same whether the combination takes place suddenly at once or by several stages; (2) the heat of combination of a compound body is in general less than the sum of the heats of its constituents. The following examples may be taken as illustrating the ap- plication of the laws of mechanical energy to the explanation of chemical processes. 1. It is well known that the electric spark can occasion the - combination of gases in two perfectly distinct ways. A mixture in equivalent quantities of hydrogen and oxygen, of chlorime and hydrogen, or of carbonic oxide and oxygen, com- bines suddenly with evolution of heat, and in unlimited quantity, under the influence of a single spark. Other gaseous mixtures (such, for instance, as nitrogen and oxygen) combine only gradually along the path of the spark itself. No evolution of heat takes place, and the combination of the gases ceases as soon as no more sparks are passed. In the same category we may also place the formation of ozone by means of the electric spark. In the first case, the energy of the components exceeds that of the compound. A sufficient quantity of energy is therefore at hand; but combination does not occur, because the first con- dition (a sufficiently strong affinity) is not fulfilled. Under these circumstances, the electric spark mcreases the power of affinity: combination takes place between a few atoms of hy- drogen and oxygen, and the heat thereby developed causes 276 . Dr. van der Kolk on the Mechanical further combination, since, at least within certain limits, the strength of chemical affinity increases with the temperature. In other compounds (nitric acid, for example) the components possess less energy than the body formed. In such a case the spark must not only cause a possible increase of affinity, but it must in addition furnish the needful energy; each spark, how- ever, yields only a limited quantity of work, so that the entire mass of such a mixture can never be made to combine by a single spark. ; According to Favre and Silbermann*, 1 gramme of hydrogen evolved 7576 units of heat by its conversion into ammonia ; ammonia therefore contains less energy than its components. Its behaviour with the electric spark is, however, peculiar. Ac- cording to Buff}, gaseous ammonia is gradually decomposed by powerful electric sparks; but it 1s also stated that nitrogen and hydrogen combine under the influence of the spark. But since it is nevertheless impossible that the same spark should produce two completely contrary effects, there must necessarily be some difference between the two cases, which further researches will bring to light. This calls to mind the well-known facts of the decomposition of water-vapour by iron turnings, and the for- mation of water when hydrogen is passed over oxide of iron {. 2. Some cases of so-called catalytic action receive a higher explanation on this theory. Platinum causes hydrogen and oxygen to combine to form water, but it does not unite nitrogen and oxygen into nitrous oxide. These facts are connected with the principles that have been developed above. It is evident that the platinum can only modify the affinity ; for masmuch as it does not itself undergo any alteration, it is impossible that it © should develope energy. It can only occasion the formation of compound bodies in cases where the required energy is already present in the constituents, and not when, as with protoxide of nitrogen, the constituents contain less energy than the com- pound. In hke manner platinum converts ozone into oxygen, a body which contains less energy, but cannot bring about the op- posite change. ‘ It is thus explained how it happens that the electric spark and platinum produce the same effect (formation of water) upon explosive gas, but contrary effects upon ozone and oxygen—the electric spark converting oxygen into ozone, and platinum con- verting ozone into oxygen. It is stated that oil of turpentine, when, shaken with oxygen, * Ann. de Chim. et de Phys. 3 sér. vol. xxxvil. + Fortschritte der Physik, 1860, p. 501. t [By an obvious oversight the original has Kupferdrahtspdne (scraps of copper wire) and Kupferoxyd (oxide of copper) eke Energy of Chemical Actions. 277 causes the formation of ozone without itself undergoing any modification. Such an action would certainly be catalytic, and would contradict the theory that has been put forward. But it is not difficult to discover a source of energy in this experiment. By shaking, the oil is doubtless heated, since the external work performed must transform itself into heat; accordingly it is only needful that the oil should be heated somewhat less than would otherwise be the case, in order to furnish sufficient energy for the formation of the very small quantity of ozone which results*. 3. In the memoir already citedt, Deville discusses a condi- tion which he calls Dissociation, intermediate between a state of firm combination and one of decomposition. This condition is supposed to arise when the molecules are separated from each other to a certain distance. The fact that melted platinum causes the formation of explosive gas when it is thrown into water, is what gave rise to these considerations. In this case the platmum can only act upon the aqueous vapour which is formed. Regnault has shown that at about 1000° C. aqueous vapour is decomposed by melted silver, which absorbs its oxygen. On the other hand, the heat evolved by the combustion of explo- sive gas suffices for the fusion of platinum, producing a tempe- rature which the author estimates at at least 2500° C. He ex- presses surprise that the combination of hydrogen and oxygen should develope a much higher temperature than that which occurs in the decomposition. He seeks an explanation in dis- sociation, in which state he supposes water-vapour to exist at 1000° C. The atoms of chlorine and hydrogen are regarded as already in the state of dissociation at the common temperature. The author cites, as cases where decomposition occurs sud- denly and with evolution of heat, without previous dissociation, the chloride, iodide, and sulphide of nitrogen. Lastly, he com- pares the three conditions of firm combination, dissociation, and decomposition, with the three states of aggregation. This last comparison appears to me very defective. In fact there is no great difficulty in seeing that the author’s dissocia- tion coincides in general with the state in which only one of the two necessary conditions of chemical action pointed out above is fulfilled. In chlorme and hydrogen there is a sufficient supply of energy, and all that is wanting is an increase in the strength * [But does the oii of turpentine remain quite unaltered ? or is agitation absolutely necessary? There is no apparent reason for supposing that shaking favours the formation of ozone otherwise than by renewing the surface of contact between the oxygen and oil of turpentine. On the other hand, there is reason to believe that light plays an important part in the action. (Cf.Schonbein, Chem. Soc. Quart. Journ. vol. iv. p. 135, foot-note.) —TRANSL. | { Forischritte, &c. 1860, p. 380. Phil. Mag. S. 4. vol. xx. p. 451. 278 Dr. van der Kolk on the Mechanical of affinity, such as day-light, for imstance, suffices to produce. The same applies to chloride of nitrogen, &c., and even in the case of the decomposition of water there is nothing that need surprise us. Water contains less energy than its components. If, there- fore, these do not combine, this is due to the non-fulfilment of the first condition, or want of a sufficiently strong affinity. If we represent this affinity as =O when no combination occurs in presence of sufficient energy, in the case before us the affinity is =O at the ordinary temperature, it acquires a certain value at higher temperatures, and it disappears again at a still higher temperature—namely, that at which water-vapour is decomposed by heat alone. It is not decomposed by itself at 1000°; but if it is in contact with melted silver, the metal can, in the first place, furnish the energy needed for the decomposition*; and in the second place it can exert a different action on the two com- ponents of the vapour, and thus weaken their mutual affinity. The silver has therefore in this case a twofold action. Were simple decomposition to occur at 1000°, without any- thing further, it would certainly be surprising; but in presence of melted silver this is not the case. The development of a higher temperature by the combustion is quite another question. A product is formed containing less energy than the substances from which it is produced; conse- quently energy is set free in the form of heat and raises the temperature of the resulting water-vapour. ‘This temperature can be calculated from the known values of the heat of combi- nation of water and of the specific heats of hydrogen, oxygen, and water, and is found to be about 6800° C.+ In this calcu- lation, however, it is assumed that no heat is communicated to the surrounding medium. But a temperatnre as high as this must immediately fall; and when we determine it, it is doubtless already much lower. According to Deville’s experiments, how- ever, it may amount, under favourable conditions, to at least 2500° C. Now the melted platinum can, in the first place, supply the requisite energy; and secondly, the metal very probably acts differ- ently at this high temperature on the two constituents of aqueous vapour. Otherwise this would become a problem of molecular forces. The phenomena of dissociation cited by the author appear to [* How? Why should silver at 1000° impart to aqueous vapour more energy than the latter would receive by contact merely with the sides of a porcelain or platinum vessel at the same temperature ?—TRANSL. | + Lecons de Chimie et de Physique, professées a la Société Chimique de Paris (1861), p. 65. : Energy of Cheinical Actions. — 279 me, therefore, quite explicable by the theory of energy, without _ the help of any hypothesis concerning the distances of the molecules. __ 4. Kirchhoff discusses the heat of combination in his memoir on the effective function, and demonstrates that in general it must alter with the temperature*, This follows also as a direct con- sequence of the following considerations. Let explosive gas be converted into water at different temperatures, e. g. at 50° and 100° C., in a closed space, and therefore without development of external work; the heat of combination can be the same in both cases only if the difference between the quantities of energy contained in the water and in the explosive gas at the two tem- peratures is the same. This again implies that aqueous vapour and explosive gas take up equal quantities of heat when they undergo equal elevations of temperature—in other words, that under constant volume the specific heat of water-vapour is the same as that of explosive gas. This cannot in general be assumed. Kirchhoff finds for this difference between the specific heats of water-vapour and explosive gas, upon two distinct hypotheses, 0:0417 and 0°212 unit of heat per 1°C. We find similarly, in the case of the formation of carbonic acid from carbonic oxide and oxygen, 0:0049 unit per degree and per gramme. _ Since the alteration of the specific heat with the temperature has been determined for only a few substances, this difference cannot yet, in most cases, be exactly stated. 5. The heat of combination is in general regarded as a mea- sure of chemical affinity; but although experiment shows on the whole a greater heat of combination in the case of stronger combinations, many striking exceptions nevertheless present themselves which make it impossible to accept this as a fully proved principle: Thus phosphoric acid has a greater heat of combination than sulphuric acid, although the latter displaces it from its compounds. Potash is a stronger base than lime, but evolves less heat than lime does by union with nitric acid. Oxide of silver neutralizes the properties of acids more com- * Poggendorff’s Annalen, vol. ciii. p. 203. [This had been distinctly implied some years previously by Thomsen (of Copenhagen) in his Thermo- chemical Investigations(Pogg. Ann. vol. Ixxxvili. p. 349,1853, No. 3). Itis perhaps also allowable to refer to Watts’s ‘Dictionary of Chemistry,’ vol. iu. p- 117, where the probability is pomted out that the thermal effect of a given chemical change is not absolutely constant, but is affected by the circum- stances under which the change takes place, and where (before the publi- cation of the present memoir, and in ignorance of what had been said by Kirchhoff) the writer deduces the almost necessary variation of the heat of chemical action with the temperature, from considerations regarding specific heat essentially the same as those insisted on by Kirchhoff (Joc. cit.) and by the author in the text.—TRANSL. | | 280 Dr. van der Kolk on the Mechanical pletely than oxide of copper, and can even displace the latter oxide from its combinations, actions which are dependent on affinity ; its heat of combination is, nevertheless, smaller than that of oxide of copper*. It follows from this, that it is not possible to deduce one from another the force of affinity and the heat of combination ; we have in fact here to deal with two magnitudes of totally distinct kinds—energy and affinity; and to take one as a measure of the other, seems to me no more allowable than to take the electromotive force of the closed gal- vanic circuit as equal to the tension of the electrodes when the circuit is open. The heat of combination, denoting the differ- ence between the quantities of energy contained in the reagents and products, is a measure of the stability. Water+, with the heat of combination 29,413, is more stable than hydrochloric acid, whose heat of combination is 23,783. Decomposition can take place only if a quantity of energy equivalent to the heat of combination is restored to the compound; and accordingly decomposition may sometimes be possible in the case of hydro- chloric acid, under circumstances in which it is not possible for water. But it does not follow from this that decomposition will actually take place every time this condition is fulfilled; che- mical affinity comes also into account, as is shown by the exam- ple of explosive gas, where the requisite energy is present in full measure, but no combination occurs at the ordinary temperature. lf the heat of combination must thus be regarded as only a very imperfect measure of the force of affinity, it is impossible * None of these examples can be taken as conclusive that the heat of chemical action ought not to be regarded as the measure of the chemical affinity concerned. This will be evident if we examine each in succession. }. According to Favre and Silbermann, one equivalent of potash evolves 16,083 units of heat by combination with 1 equiv. of sulphuric acid, and 17,766 units of heat by combination with 1 equiv. of phosphoric acid (to form the dipotassic phosphate ?); according to Andrews, however, the quantities of heat evolved are respectively 15,900 and 14,200. But, ad- mitting Favre and Silbermann’s results to be probably the most accurate, it would be difficult to prove that sulphuric acid does completely displace phosphoric acid from phosphate of potash. 2. Why is potash called a stronger base than lime? If im some cases it displaces lime from its combinations, it is in other cases itself displaced by lime ; moreover the remarks made upon the next example apply here also. 3. The fact that oxide of silver can sometimes displace oxide of copper from its salts is not more surprising than that it can displace oxide of hy- drogen. The change is in both cases madequately stated as the mere replacement of one oxide by another; it ought rather to be regarded as a double decomposition in which oxide of silver is decomposed and oxide of copper is formed,—a change which corresponds to the evolution of 15,772;f units of heat, and may therefore well compensate a possible absorption of heat in other parts of the process.—TRANSL. | T Debray, Lecons de Chim. et de Phys. 1861, p. 63. Energy of Chemical Actions. 281 to take it as any measure at all where combination is accom- panied by absorption of heat, and the chemical affinity would therefore be a negative quantity. In the example of water, already considered, we saw that the affinity, or the tendency to combine, where sufficient energy is present, changes with the temperature, and is accordingly a variable quantity. In like manner it is different in different bodies. If, for example, one acid displaces another from its combinations, the first has a greater affinity for the base than the second. For the most part, however, in such cases as these, as always in precipitation, changes in the distribution of energy take place, whereby the matter is complicated. We can speak of pure effects of affinity only when the quantity of energy is the same before and after the combination. This is always the ease, according to Favre and Silbermann, where two salts mutually decompose each other in solution without precipitation. In such experiments, however, it is often very difficult to state how the decomposition occurs. It is doubtless by no means easy to give a good definition of affinity. That which is commonly given*, namely, that it is the force which brings about the combination of bodies, and which retains the substances thus formed in their new conditions, has the disadvantage of being ambiguous; we may doubt whether both these meanings always coincide. In what has gone before, the affinity of two bodies has always been taken to mean the total effect which they exert upon each other, account having been already taken of the energy. In this respect the definition is more negative than positive. The application of the theory of energy may perhaps give us a clearer insight into this also. The combinations and decom- positions are known experimentally; they depend upon two causes, one of which, the energy, can be determined ; and it may thus be possible, from the result and the first cause, to acquire a nearer knowledge of the second. But since this affi- nity is different between each pair of substances, such investiga- tions as these demand an exact acquaintance with the specific properties of the various chemical substances. The further development of this subject belongs therefore more to che- mistry than to physics. It is worthy of being further remarked that the function of energy in these combinations very often coincides with that of Stahl’s phlogiston. Just as carbon was considered as containing a large quantity of phlogiston, which escaped when the carbon was burned into carbonic acid, and the amount of which was connected with the heat of combination, so likewise carbon and oxygen in the separate state contain more energy than the * Favre, Théses, &c., p. 1. Phil. Mag. 8S. 4. Vol. 29. No. 196. April 1865. U 282 On the Mechanical Energy of Chemical Actions. carbonic acid formed from them; and this difference ‘is, as it were, indicated by the heat of combination. It is obviously impossible to do more in this short communi- cation than to point out the general features of the application of the theory of energy to a few cases of chemical action ; but what has been said may suffice to prove the importance of this theorem in the region of chemical phenomena. Maestricht, March 1864. Postscript to the foregoing Memoir *. The principle that the heat of combination cannot be taken as a measure of affinity can perhaps be rendered intelligible as fol- lows. When a freely falling bay comes suddenly to rest, we must assume that its vis viva, }mv?, is converted into heat, pro- vided no other effects are produced. Supposing we could mea- sure this quantity of heat accurately, as well as the final velocity of the falling body, each experiment would furnish a demonstra- tion of the principle of the conservation of energy; and this result would be the same in whatever part of the earth the expe- riment was made. The variations and other properties of gravity upon the earth would nevertheless remain quite unknown to us. This case is analogous to the one we are considering. We measure the heat of combination, which may be taken as the measure of the energy or vis viva expended, that is to say, of a product one factor of which is the affinity or force of chemical attraction, and the other the change of position which occurs under the influence of this force. This change of position is no doubt much more complicated than in the case above considered, inasmuch as the force cannot be regarded as by any means inde- pendent of the mutual positions of the molecules. But as the positions of the molecules are entirely unknown, nothing can be predicated of the forces; and as the properties of gravity in the case supposed. above, so here the chemical forces remain quite unknown to us. | The action of these forces manifests itself in the combinations which occur as a consequence of chemical affinity. A stronger acid displaces a weaker one from combination because the affinity of the former for the base is greater than that of the latter. Now in Favre and Silbermann’s experiments we certainly find in general the greatest heat of combination developed by the strong- est combinations; im some cases, however, we find the opposite. There is nothing at all strange in this ; for there is, strictly speak- ing, no connexion at all between the two magnitudes, and we have reason to be surprised rather at the prevailing agreement than at the occurrence of exceptions. July 1864. * Poggendorff’s Annalen, vol. cxxii. p. 658 (August 1864). [ 283 ] XXXIX. Elasticity of Vapours. By W. J. Macquorn RaAnkINE, C.E., LL.D., F.RSS.L. & E. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, i, M* ALEXANDER, quoted by Professor Potter in the Philosophical Magazine for February, was surely mistaken when he claimed as new, in 1848, the formula p=(a+ 6T)® for the pressures of saturated vapours. The general formula of which it is a particular case, p= (a+06T)», was first proposed by Dr. Thomas Young nearly sixty years ago. The same formula, with the index n=5, was used by Arago and Dulong in 1829*, and with the index n=6, by Tredgold about 18287. 2. The history of that and many other formule is given by M. Regnault in his Relation des Expériences &c., vol. 1. pp. 582 et segg. He gives the preference, for purposes of interpolation, to the formula proposed by Biot in 1844, logp=a+ba’ +c", the five constants a, b, c, a, 8 being deduced from five experi- mental data for each fluid. 8. Young’s formula, it is true, contains three constants only, a, b, and n; but, as M. Regnault has shown, it is deficient in exactness. It has, in particular, two faults,—that for a certain temperature, T= — 7 it makes the pressure of the fluid disap- pear, and become negative below that temperature, which is exceedingly improbable; and that it makes the pressure of every vapour increase without limit as the temperature rises—a result contradicted by the experiments of M. Regnault, which (as he states in vol. i. p. 647) point to the conclusion, that “the elastic force of a vapour does not increase indefinitely with the temperature, but converges towards a limit which it cannot exceed.” 4. The first of those faults, but not the second, exists in Roche’s formula, 4 a ae ar. 1+mT 5. So far as 1 am aware, no formula has yet appeared, con- taining three constants only, which agrees so closely with experi- ment as that which I proposed in the Edinburgh Philosophi- * Mémoires de ? Intut. + Treatise on the eam-Engine. U 284. Dr. Rankine on the Elasticity of Vapours. cal Journal for July 1849, viz. be log p=a—7 — 93 where ¢ denotes the absolute temperature, measured from the avsolute zero, 274° C. below melting ice, and a, 0, and ¢ are determined from three data for each fluid. (For values of those constants for various fluids, see also the Philosophical Magazine for December 1854, and ‘A Manual of Prime Movers,’ p. 237). This formula, besides agreeing very closely with experiment at all temperatures, gives the following results :—That every sub- stance can exist in the state of vapour at all temperatures above the absolute zero; and that the pressure of saturation of every vapour tends towards a limit as the temperature increases,—the latter result being in accordance with the conclusion deduced by M. Regnault from his experiments. 6. It may be remarked that if vapours at saturation were perfectly gaseous, it can be proved from the laws of thermo- dynamics that their pressures of saturation would be given by the formula 7 where ¢ is the specific heat of the gas at constant volume, c’ its specific heat at constant pressure, c’ the specific heat of the liquid, 6 the total heat of gasefication of the fluid at the abso- lute zero, from which ¢ is reckoned, and a a constant to be de- termined by experiments on the pressure corresponding to a given boiling-point. So far as I know, this proposition has not before been published ; but its demonstration will be obvious to any one acquainted with the principles of thermo-dynamics. When the formula is applied to steam, it gives pressures agreeing very closely with actual pressures of steam from 0° to 160° C. ; but above the latter temperature the effect of the deviation of the vapour from the perfectly gaseous condition becomes consi- derable; so that at 220° C. the pressure given by the formula for a perfect gas is about one-fiftieth part less than the actual pressure. I am, Gentlemen, Your most obedient Servant, W. J. Macquorn RANKINE. Glasgow University, Feb. 18, 1865. P.S.—Since the above was written, I have seen the formula proposed by Mr. Edmonds in the Philosophical Magazine for March 1865. In the notation of the present paper, that formula Prof. A. C. Ramsay on the Glacial Theory of Lake-Basins. 285 is thus expressed : wer=if-(0F} It obviously possesses the same general: character with my for- mula of 1849; viz. it makes the pressure a function of the reciprocal of the absolute temperature, containing three con- stants, vanishing at the absolute zero, and converging towards a limit when the temperature increases indefinitely ; and it is satis- factory to me to see that Mr. Edmonds, by an independent investigation, has arrived at a result which thus agrees in the main with mine.—W. J. M. R. March 1865. XL. Str Charles Lyell and the Glacial Theory of Lake- Basins. By A. Go RAMSAY, /.R.S.. VP.G.8.* 1 a Sir Charles Lyell’s new edition of the ‘ Elements of Geo- logy,’ he has devoted several pages to the discussion of the theory of the “connexion of the predominance of lakes with glacial action,” and he does me the honour, by a number of coun- ter arguments, to combat the views I advanced in 18627. In the opening passage he adopts that part of my reasoning in which I first insisted, as a significant fact, on the connexion of multitudes of lakes with regions high and low in all latitudes that have been thoroughly subjected to ice-action, and their comparative rarity in countries where the signs of glacial action have not been observed{. It is with satisfaction that I now see * Communicated by the Author. + “On the Glacial Origin of certain Lakes,” &c., Journal of the Geological Society, vol. xvii. p. 185 (Proc. March 5, 1862). + On this subject Sir Charles observes, *‘ It has been truly remarked that lakes are very common in those countries where erraties, striated boulders, and rock-surfaces, with other signs of glaciation, abound, and that they are comparatively rare in tropical and subtropical regions. When travelling over some of the lower lands in Sweden, far from mountains, as well as over the coast-region of Maine in the United States, and other districts in North America, I was much struck with the innumerable ponds and small lakes, of which counterparts are described as equally characteristic of Fin- land, Canada, and the Hudson’s Bay territories.’ These are the very regions to which I directed attention in my Memoir of 1862; and my attention having been directed by a geologist of distinction to the passage quoted, I was led to infer that by accident I had done injustice to the published views of Sir Charles Lyell. It was therefore with a sense of relief that, on referring to his two journeys in North America and other writings, I failed to find any allusion to the subject. I mention it now lest others should draw the same inference that I did. As far as lam aware, I first drew special attention to the fact in connexion with the Glacial Theory. 286 Prof. A. C. Ramsay on the Glacial Theory of Lake- Basins. this fact stated as a piece of common knowledge in a manual so popular as Sir Charles Lyell’s is sure to be. Some physical geologists may doubtless marvel that Sir Charles, writing of lakes that “run in great rents and faults,” is still of opinion that the existence of such rents and faults in connexion with valleys “is no more than may be said of most of the longi- tudinal and transverse valleys in every mountain-chain ;” but I will not argue that point, and I may forget the assump- tion when I find it coupled with the admission of the truth of the principle I endeavoured to establish, that mountain-lakes do not lie in gaping fractures, and that fractures, wherever we know them by eye, are almost always close*. Sir Charles, I am glad to see, also approves of my argument to show that the Alpine and other lake-basins are not the result of special subsidences; and the admission of all these points by him will help no doubt by-and-by to procure the adhesion of readers who do not think or have no opportunity of observing for themselves. Those who go so far take so many steps in the right direction—steps, I think, which may in the long run lead them to accept my theory altogether. But though there is this partial agreement in some details, including the direct power of ice “in scooping out shallow basins where the rocks are of unequal hardness’’ (Antiquity of Man), Sir Charles does his utmost to disprove the possibility of glaciers on a great scale having been the means of scooping out by slow erosion large lake-basins, such as those of the Alps, Scotland, Sweden, or North America; and I now propose, as briefly as I can, to examine some of the arguments to which he seems to attach the greatest weight. The erosion, then, of large rock-basins is untenable because even if ice, in descending a steep slope, “scoop out one of those cavities called tarns,”” yet we must suppose that it loses all power of extending the cavity, being unable to cut a gorge through the lower margin of the tarn; and “ this dimi- nished force of erosion, wherever the ice has to ascend a slope, or to move horizontally, seems adverse to the hypothesis of the formation of lakes of considerable length and depth by glaciers.” In my last paper, published in the Philosophical Magazine for October 1864, some months before the appearance of the ‘Elements,’ I discussed for the second time what I believe to have been the peculiar scooping effects of huge glaciers that issued from the slopes of great, yet comparatively narrow valleys into the wider plains that they overspread, or into flats near the * Attributed by Sir Charles to Mr. Jukes, who m an admirable article in the ‘ Reader,’ March 12th, 1864, used in my favour, and with new illus- trations, the arguments which I employed i in my original memoir. Prof. A. C. Ramsay on the Glacial Theory of Lake-Basins. 287 mouths of the valleys themselves, and still within their bounds. And though Sir Charles has not met the arguments urged either in my first or second paper, except by implication, I am constrained by the circumstances of the case to repeat them in a manner that I*hope cannot be misunderstood. This may be done in a very few words. Every physicist knows that when such a body as glacier-ice descends a slope, the direct vertical pressure of the ice will be proportional to its thickness and weight and the angle of the slope over which it flows. If the angle be 5°, the weight and erosive power of a given thickness of ice will be so much, if 10° so much less, if 20° less still, till at length, if we may imagine the fall to be over a vertical wall of rock, the pres- sure against the wall (except accidentally) will be nz. But when the same vast body of ice has reached the plain, then motion and erosion would cease, were it not for pressure from behind (excepting what little motion forward and sidewards might be due to its own weight). This pressure, however, must have been con- stant as long as supplies of snow feli on the mountains, and there- fore the mert mass in the plain was constantly urged onwards ; and because of its vertical pressure its direct erosive power would necessarily be proportional to its thickness, and greater than when it lay on a slope; for it would grate across the rocks, as it were, unwillingly and by compulsion, instead of finding its way onwards more or less by virtue of gravity. Indeed the idea is forced on the mind, that the sluggish ice would have a tendency to heap itself up just outside the mouth of the valley and there attain an unusual thickness, thus exer- cising, after its descent, an extra erosive power. Further, as I have said elsewhere, when the glacier spread well out upon the plain, far beyond the mouth of the valley, it would of necessity thin more and more by melting; and this seems to me a very obvious reason why, its weight being lessened, the waste of under- lying matter by erosion would decrease towards what are now the mouths of those lake-basins which Sir Charles, following the supposition of the late Dr. Falconer, allows were filled with ice during the glacial period. These propositions seem to me so obvious, that I should scarcely have thought it necessary to re- state them ; but if they be mere fallacies, it is singular that no one has yet thought it worth while to refute them. Sir Charles himself seems to allow that the ice may have had “ to ascend a slope ”’*. The remark that in a “ part of a valley from which a gla- cier has retreated in historical times, no basin-shaped hollows are conspicuous,” is met, if we think of it, by the foregoing * To discuss the details of this subject would involve a repetition of what I have already printed, and this I must necessarily avoid. Geolo- gical Journal, /. c.; Phil. Mag. October 1864, &c. 288 Prof. A. C. Ramsay on the Glacial Theory af Lake- Basins. observations ; for the extreme end of the petty glaciers of to-day have only a small erosive power, and not one that I know in the Alps has ever in historical times been protruded in mass on and well over a plain. When a glacier les on a slope, it needs little reflection to show that its tendency will by no means be to pro- duce “ cup-and-saucer-shaped cavities ”’*. The argument that the constant occurrence of transverse rents in the same part of a glacier proves that the ice “ cannot saw through and get rid of the obstacles which impede the free- dom of its onward march,” reads strangely after the admission that ‘ everywhere we behold proofs that the glacier, by the aid of sand and pebbles, can grind down, polish, and plane the bottom.” Neither the mountains that bound nor the valleys under the glaciers can possibly preserve the same relative de- tails of feature till all shall be worn away ; and the position of the obstacles as constants can no more be considered indestruc- tible than the Falls of Niagara, which Sir Charles Lyell has long ago shown may retreat till Lake Erie itself shall be drained. Another point seems to require explanation. At the beginning of the subject (p. 168) it is stated that lakes are exceedingly common in all regions that have been glaciated, and rare in tro- pical and subtropical regions; and at page 170 it is observed that ‘such basins, large and small, are met with i all latitudes.” Now I have specially guarded myself against being supposed to assert that all lake-basins have been formed by ice; but if “such basins, large and small, ate met with im all latitudes,” which I doubt (except among mountains which maintain or have main- tained glaciers), their relative proportions in different lati- tudes deprives the argument of much or of any value; and for other reasons the same may be said of the remark “that there are lacustrine deposits of all geological epochs, attesting the existence of lakes at times when no one is disposed to attribute them to the agency of ice.” There may have been lakes of all geological epochs; but I should like to see proofs adduced ; and very few of them are mentioned in the ‘ Klements.? Where are the lakes of the Silurian strata, which themselves embrace more epochs than one, if unconformities constitute epochs? And though Sir Charles compares the Old Red Sandstone fish to * See my paper “ On the Erosion of Valleys and Lakes,’ Phil. Mag. October 1864. I have often thought that the absence or scarcity of lakes on the southern flanks of the Himalayah i is due to the well-known steepness of the valleys, and their occurrence in numbers on the north is owing to the opposite circumstance. Tarns I know there are on frag- mentary flats on the mountains on the south side. But I can only judge from maps and descriptions, and therefore dare not positively assert it. After the publication of my first memoir, Dr. Hooker wrote me a letter confirmatory of these views, which were till then new to him. Prof. A. C. Ramsay on the Glacial Theory of Lake-Basins. 239 living genera in African and American rivers, is he prepared to follow Mr. Godwin-Austen’s opinion, that much of the Old Red Sandstone, as distinct from Devonian rocks, is a lacustrine de- posit ? With respect to the Coal-measure strata, constant refer- ence is made in the ‘Elements’ to their formation in deltas or lagoons; but no mention is made of great deep inland lakes. Indeed the word Jake is only once used in the description of this formation, and it is immediately qualified by the word lagoon. Has any one yet described Permian lakes? though I believe they will be found. And even in his account of rock-salt, Sir Charles does not assert that the salt of the Trias was formed _ in far inland continental lakes supersaturated with salt, though he refers to those of Asia; and he again insists rather on la- goons, as in the Runn of Cutch or the Bahr Assal, near the Abyssinian frontier, or the possibility of salt now forming in the Red Sea. Are there any Liassic, Oolitic, or Cretaceous lakes de- scribed? On the contrary, all their freshwater formations are either said to be deltoid, or the manner of their formation is left _in the dark. It is true that lakes have been described of very late Hocene (?) and of Miocene age ; and there the record of them begins and ends till we come to post-pliocene and recent times. It is therefore by no means yet a piece of common knowledge “ that there are lacustrine deposits of all geological epochs.” But if “ lacustrine deposits” are “ of all geological epochs,” has no one spoken of ‘the agency of ice” in past times? or has no one written of anything that might suggest that idea to an unbiased mind? Let us look to this. Mr. John Carrick . Moore has described conglomerates in the Lower Silurian rocks of Wigtonshire, which might well be called boulder-beds; fora prodigious number of the enclosed masses of gneiss and granite (which Mr. Moore has pointed out to me on the ground) range from a foot up even to six feet in diameter, and all of them have been derived from ancient strata (perhaps Laurentian) of aregion now unknown. The conglomerate of the Old Red Sandstone of several parts of Scotland and the North of England is so lke the “ Upper boulder-drift” of many parts of Britam, though consolidated, that other geologists besides myself have spent hours in search- ing it for scratched stones; but, for chemical reasons connected with pressure, which Mr. Sorby will appreciate, none have yet been found, if they ever existed there*. Mr. Godwin-Austen has been so bold as to attribute the transport of blocks in the French carboniferous rocks to floating ice ; and I invite any one to examine the ice-scratched erratics * The Rev. J. G. Cumming long ago suggested the glacial origin of the Old Red conglomerates of the Isle of Man. 290 Prof. A. C. Ramsay on the Glacial Theory of Lake- Basins. of the Permian strata in the Jermyn Street Museum, and then to judge if the subject as described by me does not, to say the least, deserve the measure of attention which it has received in the Manuals of Professor Phillips*, Professor Jukes, and Mr. Page. | I feel convinced that the same conclusions which I drew for the Rothliegende of part of England will yet be extended to much of that of Northern Germany; for though marls and gravels are interstratified with it, these, as im our post-pliocene drift, are exceptional, and the main characteristic of this vast formation (2600 feet thick) in the Thiiringerwald is the flattened and subangular nature of its blocks, some of which are of large size. Similar erratic deposits are now forming in Baffin’s Bay and the Western Atlantic. Mr. Godwin-Austen long ago suggested the ice-borne character of great blocks in the New Red Sandstone of Devonshire; and the Oolitic strata of the east of Scotland contain such numbers of huge angular blocks, that their possibly though scarcely pro- bably glacial origin constantly suggested itself to my mind when . I noted the facts during a journey with Sir Roderick Murchi- son in 1859. The local character of the blocks, chiefly but not entirely Oolitic, is adverse to the view ; but the smashed condition of many of the shells in the interstratified oolitic clays is analo- gous to the state of the shells in the upper drifts all over Britain. It may not be generally known that Escher von der Linth is aware of boulders in the cretaceous strata of the Alps, and God- win-Austen has suggested a similar origin for boulders some- times found in the British chalk ; and surely, though unnoticed by him in the ‘ Elements,’ Sir Charles is conversant with the clear-sighted observations of Gastaldi, who attributes the for- mation of certain conglomerates (with scratched stones), and the transport of the huge boulders that lie in them, to the agency of floating icebergs that, descending into a miocene sea, broke from Alpine glaciers, and carried their freights to the neighbeour- hood of what is now Turin, from the far-off region where the Lago Maggiore at present lies. Geologists, then, some of them of the highest eminence, have actually written of “the agency of ice” im several geological epochs; and, whether in these epochs or in others mentioned above, it is clear that erratic- and boulder-phenomena not easily to be accounted for exist in many formations, these phenomena . being not unlike those that are brought about by floating ice in the present day. The subject of the ancient agency of glaciers and floating ice is indeed far too prominent to be disposed * Professor Phillips does not agree with me, but still in a note he takes care to notice my opinion. Prof. A.C. Ramsay on the Glacial Theory of Lake-Basins. 291 of without examination, and rejected, for all but post-pliocene time, in half a dozen lines, as if indeed, even in a Manual of stratigraphical geology, the older strata exhibited no perplexing phenomena that might induce anything to be said on the sub- ject worth attention. In the case of the Miocene ice-work of the Alps, which, having seen it with Gastaldi, I have long con- sidered to have been proved by him, some persons may con- sider it suggestive that lacustrine phenomena do occur on the flanks of the Alps in the same formation; and if any of the boulder-conglomerates of the Old Red Sandstone be ice-formed, and Mr. Godwin-Austen’s suggestion be true, the conjunction occurs again. ‘It would, indeed, be the most perplexing of all enigmas,” says Sir Charles, “if we did not find that lake-basins were now, and had been at all times, a normal feature in the phy- siognomy of the earth’s surface, sincewe know that unequal move- ments of upheaval and subsidence are now in progress, and were going on at all former geological epochs.” Here again we find the assumption of “ lake-basins at all times,”’ Just as if it were a fact familiar to geologists that such lake-basins had always ex- usted, whereas, eliminating lagoons, the statement seems to be only derived from two or three circumstances relating to strata of tertiarytimes. Traces of estuarine beds are more frequent; but this is another matter altogether. ‘To me the absence of lake-deposits is not at all perplexing,—first, because the preservation of all superficial terrestrial phenomena (as opposed to marine) has been, for obvious reasons, rare in the world’s history, except in strata of very late date; and secondly, because | believe that the conditions for the formation of innumerable lakes like those of North America, Scandinavia, the Highlands, the Alps, and other glacier mountain-regions, were probably comparatively rare in the earlier history of the earth. That accidental lakes, due to volcanos, and a few of them perhaps to unequal movements of upheaval and subsidence, may have existed at all times is perhaps certain; and it would do no harm to my theory were I to concede that all the known and accepted lakes of Miocene and Hocene (?) times, and older ones if they existed, were formed by the pro- cesses to which Sir Charles adheres. These preliminary points regarding past times being stated lead, in the ‘ Elements,’ to the special discussion of Sir Charles Lyell’s proposition as to what was in his opinion the real cause of the formation of the larger lakes that flank the Alps; for, except in a vague manner, he does not grapple with the origin of the unnumbered lake-basins that are strewn over the face of such a country as North America. ‘“ We need but little reflec- tion,” he remarks, “ to discover that when changes of level are in progress, some of the principal valleys can hardly fail to be 292 Prof. A. C. Ramsay on the Glacial Theory of Lake-Basins. converted in some parts of their course into lakes of considerable magnitude,” because otherwise we should have to assume “ that the greatest elevatory movement always conforms to the central axis of every chain,” or to that “of every watershed.” “ But sometimes upheaval will be in excess in the lower part of the valley, and at other times (which would equally produce lake- basins) there would be an excess of subsidence m the higher regions, the alluvial plains below sinking at a less rapid rate, or being, perhaps, stationary.” And here I must be allowed to remark that these considerations did not escape me when I wrote my memoir “On the Glacial Origin of certain Lakes”; but I rejected them (I now see, unwisely) as random surmises, not comparable in value to the various hypotheses I discussed, and as I believe disproved, viz., that the great Alpine lakes “ lie in simple synclinal troughs,” or in ‘ areas of mere watery erosion,” or in mere “lines of dislocation,” or “in areas of special sub- sidence.” I shall now show why I rejected and still reject both of the above suppositions proposed in the ‘ Elements.’ Referring to ‘The Antiquity of Man,’ Sir Charles very pro- perly assumes tnat the large valleys of the Alps were of pre- glacial origin,—a good and asound assumption, founded on de- finite proofs as old as the days of Charpentier, if not older, and one I had occasion in this Magazine to show may have ori- ginated in subaérial actions that have been going on ever since the close of Miocene times*. No one, therefore, ever dreamed that ‘‘ the rivers had been idle for a million of years or more, leaving to glaciers the task of domg, in comparatively modern times, the whole work of excavation.”? But the question he proposes to solve is, how, controverting my proposition of glacier- erosion, parts of these valleys may have been converted into lakes. Let us take the Lago Maggiore as an example. If in this case upheaval was “in excess in the lower part of the valley,” what would the result be ? From the deepest part of the lake to its efflux is a distance of about twelve miles, and the average angle from the deepest part to the efflux is 2° 21’, and, giving every advantage to any one who prefers upheaval ‘in excess in the lower part of the valley,” I will assume that the axis of movement lay on a line comeident with the deepest part of the lake, or, in other words, that the hinge, so to speak, of the movement lay there. Before the up- ward movement began, the whole slope must have been down- ward towards the valley of the Po, otherwise the drainage would have been dammed up; and it needs little reflection to see in that case that the point which is now the efflux of the lake must have been 2625 feet, or say 2650 feet lower than at present, so * Phil. Mag. November 1862. Prof. A.C. Ramsay on the Glacial Theory of Lake-Basins. 293 as to bring it at the least to a level a little lower than what is now the deepest part of the lake. Without this the onward southern flow of the water could not have been established. But in that case the plain of the Po outside the present efflux of the lake must also have been at the least 2650 feet lower than at present, that is to say, before the tilting began; in which case the plain must have been about 2000 feet below the level of the present sea, and liable to be covered with deposits of that post-pliocene epoch. But no trace of these deposits exists, and they have never even been imagined ; for the post-pliocene deposits of the valley of the Po are older than the ancient glaciers. The only escape from this is to suppose that when these movements took place the whole region lay so high (from 2000 to 3000 feet higher than at present) that elevations and de- pressions had no immediate relation to existing sea-levels. But though Sir Charles alludes to upheaval “in excess in the lower part of the valleys,” he rejects it in the case of the Alpine valleys, and prefers another hypothesis to account for the actual existence of the lakes as they now stand; and this I shall now examine. “The Alps,” he observes, “are from 80 to 100 mules across. Let us suppose a central depression in this chain at the rate of 5 feet in a century, while the intensity of the move- ment gradually diminishes as it approaches the outskirts of the chain, till at length it dies out in the surrounding lower region.” Thus in time the valley-slopes that originally all declined out- wards and downwards from the central elevations of the moun- tains, would in the lower regions, by depression of the central ridges, by degrees acquire a reverse slope, that is to say, towards their ends they would slope inwards to the mountains, and by this process the drainage would become dammed up by rock, and lake-basins would be formed. Now, to test this idea, we must take the distance between the efflux of lake and lake on the opposite sides of the chain. From the cutflow of the Lago Maggiore to that of the lake at Lucerne, the distance is roughly about ninety- three miles im a straight line; and if we measure another line as far as the north end of the Lake of Zurich, the distance is about 112 miles. It will make no material difference in my argument which line I take; but let us take the latter, for it is clear that the rule of subsidence ought to apply to the lakes in general on both sides of the Alps. corre- sponding to the monohydriodate. When the mixture of these two acetates is treated with caustic potash, a dihydrate is obtained. It boils between 210° and 220°, and is remarkably stable ; its composition, H 6 4 Q2—(6 Flo C5 H4 O2=CS H 4 (HOY is the same as that of hexylic glycol. When this dihydrate is treated with strong hydrochloric acid or with hydriodic acid, the dihydrochlorate or dihydriodate are respectively obtained. On the Constitution of Chromium-compounds. 313 Besides these biatomic compounds of diallyle, there is a mono- atomic series, the starting-point of which is the monohydriodate of diallyle, €° H}!° HI, obtained from the dihydriodate by the loss of one molecule of HI. For the reduction of nitro-compounds, Zinin first introduced the use of sulphuretted hydrogen; and Béchamp subsequently showed that a mixture of iron filings and acetic acid is an ex- tremely energetic reducing agent. Sulphuretted hydrogen acts in such a manner that a single atom of hyponitric acid, NO?, is replaced by NH?; while acetic acid and iron filings act so that all the NO* present is replaced by NH*. Beilstein* has recently made some experiments on the reducing action of a mixture of tin and hydrochloric acid. He finds that its action is very ener- getic; in all cases the whole of the hyponitrous acid, NO?, is converted into the group NH?. ‘Thus nitrosalicylic acid is con- verted into amidosalicylic acid, in accordance with the equation G7 H° (NO?) 02+ 6Sn+ 6 HCl= €7H°(NH?)03 + 2 H?@+6S8nCl. Nitrosalicylic acid. Amidosalicylie acid. In a similar manner dinitrotoluole, G7 H® (NO?), is converted into toluylene-diamine, GC’ H® (NH*)?; and picric acid, C°H3(N0?)%0, into picraminet, €° H? (NH?). XLII. On the Constitution of Chromium-Compounds. By J. Aurrep WanKLyN{]. P A NHE researches of Deville and Troost on the vapour-densi- ties of the metallic chlorides have led to various attempts to revise the atomic weights of most of the metals. One of the most obvious ways of dealing with the case of iron and of the different metals belonging to the iron family (including of course chromium), was to represent the metal asa six-atomic element, 1. FeVi=112; Crvi=105 Fe Cle Cr Cle. This view, which has been advocated by several chemists, in- volves, among other inconveniences, a very complex formula for the protochlorides, or else the assumption that the protochloride is an unsaturated compound. In a paper published in the spring of 1862$, Erlenmeyer * Liebig’s Annalen, May 1864. T Phil. Mag. vol. xxv. p. 540. { Communicated by the Author. § Zeitschrift fir Chem. und Pharm., p. 129. Phil, Mag. 8. 4. Vol. 29. No. 196, April 1865. ¥ 314 _ Mr. J. A. Wanklyn on the Constitution ~ proposed to look upon ferric chloride as a compound of the second order of complexity, and showed that on this supposi- tion the atomic weight of iron might be 28 or 56. Among other possible views of the constitution of iron-com- ounds (and he extended them to the other metals u the 1 iron- family), Erlenmeyer proposed this : Belv = 56. 1 . . ¥e Cl* Hypothetical. 2 . . ¥Fe?Cl* Ferrous chloride. 3 . . Fe? Cl® Ferric chloride. | Of course, on the same principle, chromium-compounds would be represented thus :— Criv=52'5. 1 . . €r Cl* Hypothetical. 2 . . Gr?Cl* Chromous chloride. 3 . . &r?Cl® Chromic chloride. In atomicity these metals would be like carbon, compounds 2 and 3 being chlorine representatives of the iron and chromium ethylene, Fe? H*, and ethyl-hydride, Cr? H®. When either these hypothetical chlorides shall have been discovered, or representatives of them shall have been found, this theory will have acquired claims on the attention of chemists. There is a chromium representative of the hypothetical chlo- ride. It is chlorochromic acid. The analysis and vapour-density of chlorochromic acid agree with the formula Gr 0? Cl*. That chlorochromic acid and the proto- and sesqui-chlorides of chromium are of different orders of complexity is proved by the difference in their boiling-points. If anyone maintains the formula of sesquichloride of chromium to be Gr Cl°, he is at once involved in this absurdity, that there are two chromium-compounds differing only in this, that in the one there is a certain atom of chlorine, and in the other this certain atom of chlorine is replaced by 9?, but that whilst the former boils at a red ‘heat, the latter (with the oxygen in it) boils a little above the boiling- -point. of water. It is therefore quite certain that, whilst chlorochromiec acid con- tains only Gr in the standard volume, sesquichloride of chromium must contain at least €r?. From the close analogy subsisting between sesquichloride of chromium and sesquichloride of iron (the vapour-density of which requires Fe*Cl°); it also follows that the molecule of chromic chloride (sesquichloride of chromium) must be €r? Cl®. The relation of chlorochromic acid to chromic chloride having of Chromium-compounds. 315 been thus satisfactorily disposed of, the next question relates to the function of the 0? in the chlorochromic:-acid. Has this 0? a two or a four saturating power? The*well-known oxidizing energy of those compounds, such as Brodie’s organic peroxides, which are admitted to contain (Q?)", leads us to see in the extra- ordinary energy of chlorochromic acid an argument that the oxygen is (07)". Thus chlorockromic acid becomes Cr - which is the analogue of Carrying out the theory systematically, we should v write the chromates on the same type: thus (Q2)" KO! KO! ’ Cr is neutral chromate of potash. The establishment of the rational formule of chromium-com- pounds is of course an important step towards the establish- ment of the rational formule of analogous compounds. It must have weight in fixmg the constitution of the aluminium-com- pounds, the formule of which have been recently (as it appears to me with little probability) deduced from vapour-density deter- minations cf aluminium-ethyle and aluminium-methyle taken at temperatures at which these bodies have undergone decom- position. In place of the hypothesis of Messrs. Buckton and Odling, that aluminium-methyle is not a true gas at 130° C. but becomes a true gas at above 200° C., an hypothesis which appears to me to be very unphilosophical, I would suggest that aluminium- methyle, if it should not experience an ordinary decomposition at about 200° C., may perhaps react upon the mercury of the bath, or, more interesting still, resolve itself into 2 Al? Me®=3 Al Me*+ Al. Hither of these suppositions would be compatible with all the data which are as yet published. London Institution, March 17, 1865. Y 2 [ 316 ] z XLIV. Proceedings of Learned Societies. ROYAL INSTITUTION OF GREAT BRITAIN. Feb. 3, “¢ y¥N Aluminium Ethide and Methide.” By William Od- 1865. ling, M.B., F.R.S. The symbols by which the atomic proportions of a few of the prin- cipal metallic elements are usually represented, together with the relative weights of these several proportions, are shown in the fol- lowing Table :— Eathium. 2), 2% Li 7 Magnesium... Mg 24 VIG eicee cette est 65 Arsenic ...... “4 As 75 Silver Ag 108 ARAM Ss Batic ones Sn 118 Mereury'. «2 / He 200 Lead . . 23.27 sb 5 207 Bismuth ye css Bi 210 It is observable that the atomic proportions of the metals range from 7 parts of lithium, through 108 parts of silver up to 210 parts of bismuth. Now itis found that all these different proportions have substantially the same specific heat, so that 7 parts of lithium, 108 parts of silver, and 210 parts of bismuth, for instance, absorb or evolve the same amount of heat in undergoing equal increments or decrements of temperature. Hence, taking silver as a convenient standard of comparison, the atomic proportion of any other metal may be defined to be that quantity of the metal which has the same specific heat as 108 parts of silver. Many of the metals unite with the halogen radicals chlorine and bromine, as also with the organic radicals ethyle and methyle, to form volatile compounds, which may be conveniently compared with the chloride and ethide of hydrogen. Now it is found that the several proportions of metal or hydrogen contained in equal volumes of these gaseous chlorides or ethides, are their respective atomic pro- portions; so that equal volumes of chloride or ethide of hydrogen, zinc, arsenic, tin, mercury, lead, and bismuth, for instance, contain 1, 65, 75, 118, 200, 207, and 210 parts of hydrogen or metal respec- tively. Hence the molecule of chloride of hydrogen, HCl, being conventionally regarded as constituting two volumes, the atomic pro- portion of a metal may be defined to be that quantity of the metal which is contained in two volumes of its gaseous chloride, or bro- mide, or ethide, or methide, &c. These two definitions having reference respectively to the specific heats of the metals, and the molecular volumes of their gaseous com- pounds, lead in all cases to the same conclusion. Thus 200 parts of mercury is the quantity of mercury which has the same specific heat as 108 parts of silver, and is also the quantity of mercury contained in two volumes of mercuric chloride, mercuric ethide, &c, Dr. Odling on Aluminium Ethide and Methde. 317 The atomic proportions of the different metals unite with 1, 2, 3, 4, &c. atoms of chlorine and ethyle, to form the two-volume mole- cules of their respective chlorides and ethides, as shown below :— 2 vols. 2 vols, 2 vols. H Cl H Et gC? He Et? ZnEt” Bi Cl Bi Et? As Et? Sn Cl* Sn Et* PbEt* Or, two volumes of the gaseous chlorides of hydrogen, mercury, bismuth, and tin, for instance, are found to contain respectively 35°5 parts, twice 35°5 parts, three times 35°5 parts, and four times 35°5 parts of chlorine. Aluminium, which is one of the three most abundant constituents of the earth’s crust, and the most abundant of all its metallic con- stituents, enters into the composition of a large number of native minerals of great value in the fine and useful arts, and also forms extremely well-defined artificial compounds, possessing a high degree of chemical interest. Nevertheless chemists are not at all agreed as to the atomic weight which should be accorded to the metal, or as to the molecular formule of its principal compounds. The quantity of aluminium which has the same specific heat as 108 parts of silver, is found to be 27°5 parts; and analysis shows that this quantity of aluminium combines with three times 35°5 parts of chlorine to form chloride of aluminium. Accordingly the atomic proportion of aluminium should be fixed at 27°5 parts; its chloride be formulated as a trichloride thus, AICI’ ; and its other compounds be represented by corresponding expressions, as shown in the left- hand column of the following Table, instead of by the heretofore- used more complex expressions shown in the right-hand column :— ~ AE 27°5. Al 13°75. AICl? ea ds Ohiornde, Fe ae AP Cr Na AICl?* jn oe odi0-chloride’.... - Na AlCl Na’ Al F® ..». Cryolite fas) Near EY Na?’ Al O° sees Aluminate ods > Nae ALO: FE. AIO? j# s. */Diaspore ese? etd Ale OF ie le. O° 3... Alum!) bea de. AS? 6? i? AlSrO* -...... Felspar five, Ie ARSE Oo P AlO* ac) Ehosphate Spee ES Bele e But the quantity of aluminium contained in two volumes of its gaseous chloride was found by Deville to be 55 parts instead of 27°5 parts, while the quantity of chlorine was found to be siz times 35°5 parts instead of three times 35°5 parts. Hence, relying exclusively upon molecular volume, the atomic weight of aluminium would be 55, and the formula of chloride of aluminium Al Cl’. This conclu- sion, however, is inadmissible for several reasons, and chiefly because it would make the atomic proportion of aluminium possess a specific heat twice as great as that belonging to the atomic proportion of any other metal, 318 Royal Institution. To evade this difficulty, some chemists have proposed to accord to the molecule of aluminic chloride the formula Al? Cl’, whereby an indivisible proportion of metal would be habitually represented by a divisible symbol; for it is agreed on all hands that the proportion of aluminium contained in the molecule of aluminic chloride is the smallest proportion of aluminium found in any aluminic compound whatsoever; that it is incapable of experimental division by any pro- cess whatsoever; and consequently that, so far as our present know- ledge goes, it 1s an indivisible or atomic proportion. Now there are undoubtedly certain bodies, elementary and com- pound, of which the ascertained vapour-densities, and consequent volumes, no matter how accounted for, are, as a mere matter of ex- periment, discordant with the chemical analogies of the respective bodies; but in most instances these anomalous results are rendered unimportant by other determinations of vapour-density, either of the same bodies raised to higher temperatures, or of associated bodies having a more decided volatility. Hence arises the question whether the ascertained volume of aluminic chloride, which is discordant with the specific heat of aluminium, may not be anomalous in a similar manner, and whether the anomaly may not be corrected by an ex- amination of other more volatile aluminic compounds. The methide and ethide of aluminium recently obtained by Mr. Buckton and the speaker are, so to speak, varieties of aluminic chloride in which the chlorine has been replaced by methyle and ethyle, and are at the same time far more volatile and manageable than the typical chloride. Now it has been found that two gaseous volumes of the methide and ethide of aluminium contain only 27°5 parts of aluminium, united with three atomic proportions of methyle and ethyle; and accordingly their molecules have to be expressed by the formule AJ]Me’ and AlEt’ respectively. In other words, the ~ normal results obtained with the methide and ethide correct the anomalous result obtained with the chloride, and confirm the atomic weight and molecular formule deducible from the specific heat of aluminium. That the ascertained vapour-density of aluminic chloride is oily anomalous receives a further corroboration from the behaviour of aluminic methide itself.’ At 220° and all superior temperatures the vapour-density of this compound shows that two volumes of its vapour contain 27°5 parts of aluminium and three times 15 parts of methyle ; but at 130° its vapour-density, corrected for alteration of tempera- ture, becomes very nearly doubled, or, in other words, two volumes of its vapour contain very nearly 55 parts of aluminium and siz times 15 parts of methyle. According, however, to the well-known rule, based on the separate researches of Cahours and Deville, the mole- cular formula of a body must be calculated from its permanent or ultimate, and not from its variable or initial vapour-density ; whence the high vapour-density of aluminium-methide at 130° does not at all interfere with our attributing to its molecule the formula AlMe’, deducible from its vapour-density at 220° and upwards, and harmo- nizing with the specific heat of metallic aluminium. , Royal Society. 319 Aluminium-ethide and methide occur as colourless liquids. The ethide boils at 194°, and does not freeze at —18°. The methide boils at 130°, and solidifies at a little above 0° into a beautiful crystalline mass. Both liquids take fire on exposure to the air, and explode violently by contact with water. They are produced from mercuric ethide and methide respectively by heating these compounds for some hours in a water-bath, with excess of aluminium clippings. This process was obviously suggested by Frankland and Duppa’s new reaction for making zinc-ethide, methide, amylide, &c. Al’+ 3HgEt?=Hg’ + 2AlEt’. ROYAL SOCIETY. [Continued from p. 239. ] January 26, 1865.—Major-General Sabine, President, in the Chair. The following communications were read :— “ On the Spectrum of the Great Nebula in the Sword-handle of Orion.” By William Huggins, F.R.A.S. In a paper recently presented to the Royal Society*, I gave the results of the application of prismatic analysis to some of the objects in the heavens known as nebule. Hight of the nebule examined gave a spectrum indicating gaseity, and, of these, six belong to the class of small and comparatively bright objects which it is convenient to distinguish still by the name of planetary. These nebule pre- sent little indication of probable resolvability into discrete points, even with the greatest optical power which has yet been brought to bear upon them. The other two nebulz which gave a spectrum indicative of matter in the gaseous form, are 57 M, the annular nebulain Lyra, and 27 M, the Dumbbell nebula. The results of the examination of these nebulze with telescopes of great power must probably be regarded as in favour of their consisting of clustering stars. It was therefore of import- ance to determine, by the observation of other objects, whether any nebulee which have been certainly resolved into stars give a spec- trum which shows the source of light to be glowing gas. With this purpose in view I submitted the light of the following easily resolved clusters to spectrum analysis. 4670. 2120 h. 15 M. Very bright cluster; well resolved ” +. 4678, 2125 h.2M. Bright cluster, well resolved.” Both these clusters gave a continuous spectrum. I then examined the Great Nebula in the Sword-handle of Orion. The results of telescopic observation on this nebula { seem to show * On the Spectra of some of the Nebulz, Phil. Trans. 1864, p. 437. Tt The numbers and descriptions are from Sir John Herschel’s Catalogue, Phil. Trans. 1864, part 1. “The general aspect of the less luminous and cirrous portion is simply nebulous and irresolvable; but the brighter portion immediately adjacent to the trapezium forming the square front of the head, is shown with the 18-inch reflector broken up into masses, whose mottled and curdling light evidently 820 Royal Society :—Mr. W. Huggins on the Spectrum that it is suitable for observation as a crucial test of the correctness of the usually received opinion that the resolution of a nebula into bright stellar points is a certain and trustworthy indication that the nebula consists of discrete stars after the order of those which are bright to us. Would the brighter portions of the nebula adjacent to the trapezium, which have been resolved into stars, present the same spectrum as the fainter and outlying portions? In the brighter parts, would the existence of closely aggregated stars be revealed to us by a continuous spectrum, in addition to that of the true gaseous matter ? The telescope and spectrum apparatus employed were those of which a description was given in my paper already referred to. The light from the brightest parts of the nebula near the trapezium was resolved bythe prisms into three bright lines, in all respects similar to those of the gaseous nebulee, and which are described in my former aper. These three lines, indicative of gaseity, appeared (when the slit of the apparatus was made narrow) very sharply defined and free from nebulosity ; the intervals between the lines were quite dark. When either of the four bright stars, «, 2, y, 0 Trapezii was brought upon the slit, a continuous spectrum of considerable bright- ness, and nearly linear (the cylindrical lens of the apparatus having been removed), was seen, together with the bright lines of the nebula, which were of considerable length, corresponding to the length of, the opening of the slit. The fifth star y’ and the sixth a are seen in the telescope, but the spectra of these are too faint for observation. The positions in the spectra of a, 3, y, 6 Trapezii, which corre- spond to the positions in the spectrum of the three bright lines of the nebula, were carefully exafnined, but in no one of them were dark lines of absorption detected. The part of the continuous spectra of the stars a, 0, y, near the position in the spectrum of the brightest of the bright lies of the nebula, appeared on a simultaneous comparison to be more brilliant than the line of the nebula, but in the case of y the difference in brightness was not great. The corresponding part of 6 was perhaps fainter. In consequence of this small difference of brilliancy, the bright lines of the adjacent nebula appeared to cross the continuous spectra of y and 6 Trapezii. Other portions of the nebula were then brought successively upon the slit; but throughout the whole of those portions of the nebula which are sufficiently bright for this method of observation the spectrum remained unchanged, and consisted of the three bright indicates, by a sort of granular texture, its consisting of stars, and when examined under the great light of Lord Rosse’s reflector, or the exquisite defining power of the great achromatic at Cambridge, U. S., is evidently perceived to consist of clustering stars. There can therefore be little doubt as to the whole consisting of stars too minute to be discerned individually even with these powerful aids, but which become visible as points of light when closely adjacent in the more crowded parts . . . .”—Sir John Herschel, ‘Outlines of Astronomy,’ 7th edi- tion, pp. 651, 652. \| | of the Great Nebula in the Sword-handle of Orion. 321 lines only. The whole of this Great Nebula, as far as it lies within the power of my instrument, emits light which is identical in its characters ; the light from one part differs from the light of another in intensity alone. The clustering stars of which, according to Lord Rosse and Pro- fessor Bond, the brighter portions of this nebula consist, cannot be supposed to be invisible in the spectrum apparatus because of their faintness, an opinion which is probably correct of the minute and widely separated stars seen in the Dumb-bell nebula, and to which reference was made in my former paper. The evidence afforded by the largest telescopes appears to be that the brighter parts of the nebula in Orion consist of a ‘‘mass of stars;”’ the whole, or the greater part of the light from this part of the nebula, must there- fore be regarded as the united radiation of these numerous stellar points. Now it is this light which, when analyzed by the prism, reveals to us its gaseous source, and the bright lines indicative of gaseity are free from any trace of a continuous spectrum, such as that exhibited by all the brighter stars which we have examined. The conclusion is obvious, that the detection in a nebula of minute closely associated points of light, which has hitherto been con- sidered as a certain indication of a stellar constitution, can no longer be accepted as a trustworthy proof that the object consists of true stars. These luminous points, in some nebulee at least, must be regarded as themselves gaseous bodies, denser portions, probably, of the great nebulous mass, since they exhibit a constitution which is identical with the fainter and outlying parts which have not been resolved. ‘These nebulz are shown by the prism to be enor- mous gaseous systems ; and the conjecture appears probable that their apparent permanence of general form is maintained by the continual motions of these denser portions which the telescope reveals as lucid oints. : The opinions which have been entertained of the enormous distances of the nebulz, since these have been founded upon the supposed extent of remoteness at which stars of considerable brightness would cease to be separately visible in our telescope, must now be given up in reference at least to those of the nebulze the matter of which has been established to be gaseous. It is much to be desired that proper motion should be sought for im those of the nebulz which are suitable for this purpose ; indications of parallax might possibly be detected in some, if any nebulze could be found that would admit of this observation. If this view of the greater nearness to us of the gaseous nebulze be accepted, the magnitudes of the separate luminous masses which the telescope reveals as minute points, and the actual intervals existing between them, would be far less enormous than we should have to suppose them to be on the ordinary hypothesis. It is worthy of consideration that all the nebulee which present a gaseous spectrum exhibit the same three bright lines; in one case only, 18 H.IV., was a fourth line seen. If we suppose the gaseous substance of these objects to represent the “nebulous fluid”? out 322 Royal Society :— of which, were to the hypothesis of Sir Wm. Herschel, stars are to be elaborated by subsidence and condensation, we should expect a gaseous spectrum in which the groups of bright lines were aS numerous as the dark lines due to absorption which are found in the spectra of the stars. Moreover, if the improbable supposition be entertained, that the three bright lines indicate - matter in its most elementary forms, still we should expect to find in some of the nebulee, or in some parts of them, a more advanced state towards the formation of a number of separate bodies, such as exist im our sun and in the stars; and such an advance in the process of formation into stars would have been indicated by a more complex spectrum. My observations, as far as they extend at present, seem to be in favour of the opinion that the nebulee which give a gaseous spectrum, are systems possessing a structure, and a purpose in relation to the universe, altogether distinct and of another order from the great group of cosmical bodies to which our sun and the fixed stars belong. The nebulous star « Orionis was examined, but no peculiarity could be detected in its continuous spectrum*. ‘Further Observations on the Planet Mars.’ By John Phillips, M.A., LL.D., F.B.S. F.G.S. — The return of Mars to his periodical opposition with the sun has enabled me to offer a few observations on this planet, in addition to those which on a former occasion I had the honour to present to the Society +. Among the subjects then suggested for considera- tion was the permanence of the main features of light and shade which had been recognized by many observers. Another question requiring attention referred to the fogeiness or seeming cloudiness of the planet, also noticed by many observers, some of whom repre- sented what might be thought effects of currents in the atmosphere round him. Again, it was a matter for further research whether the colours of what we suppose to be land and sea (the reddish hue of the land, and the grey aspect of the sea) were capable of expla- nation by any peculiarity of the soil or atmosphere, and whether, from the phenomena of snows visible about the poles and elsewhere, the climate of Mars could be estimated on trustworthy grounds. My observations are too few to furnish answers for ail these ques- tions ; but I have something to say in reply to some of them, though the distance of Mars from the Earth during the late opposition was too great to allow of such close scrutiny as in 1862. First, then, in respect of the permanence of the main features of the planet. I submit several drawingst made between the 14th * Admiral Smyth appears to have always maintained that the results of telescopic observation on the nebulz were insufficient to support the opinion that all these objects were probably of stellar constitution. See his ‘ Cycle of Celestial Objects,’ vol.i. p.316; and his ‘Speculum Hartwellianum,’ pp. 111-114. + Phil. Mag. S. 4. vol. xvi. p. 312. hi Preserved for reference in the Archives; an equatorial projection is given in Plate IT. Oe — Dr. Phillips on the Planet Mars. 823 November and 13th December (both inclusive), the dates being marked on each, for comparison with others made in 1862, partly by Mr. Lockyer, partly by myself; from which it will immediately appear that no appreciable change has occurred in the main outlines of land and sea, in the longitudes observed. A certain fogginess has been noticed, especially on the 18th and 20th November, such as does not commonly occur with Jupiter or Saturn ; but it seemed to be due to no essential circumstance of the planet, for it grew less and less as the observation approached the meridian. The colour of the larger masses of land is the same as formerly ob- served, but fainter from distance; and the sea is grey and shadowy, but without the very distinct greenish hue which was’ noticed in 1862. Finally, the snows round the south pole appeared much less extensive than in 1862, and were not really observable with distinctness except on a few evenings. Snowy surfaces, scarcely more defined, but much more extensive, were observed in parts of the northern regions, not immediately encircling the pole (which was invisible), but in two principal and separate tracts estimated to reach 40° or 45° from the pole. On one occasion (30th November) two practised observers (Mr. Luff and Mr. Bloxidge) noticed with me one of these gleaming masses of snow, very distinct—so much so, that, as happened with the south polar snow in 1862, it seemed to project beyond the circular outline—an optical effect, no doubt, and due to the bright irradiation. This white mass reached to about 40° or 45° from the pole, in the meridian of 30° on my globe of Mars. Another mass was noticed on the 14th and 18th November, in long. 225°, and extending to lat. 50°. In each case the masses reached the visible limb. The small extent of the snow visible at the further pole may be truly the effect of the position of the planet. If we remember that on this occasion the axis of Mars was nearly (within about 6° or 8°) at right angles to the line of sight, while in 1862 it was ob- lique (about 26°), we shall perceive that though the snow about the south pole were really as extensive in 1864 as it appeared to be in 1862, it could not possibly appear even nearly so large, and in fact could barely be seen (as it was) under the very small angle which it would subtend on the limb. There may, however, have been really less snow round the south pole, in consequence of the longer action of the summer heat on Mars in 1864 than in 1862. The ruddy tint of the surface of the broad tracts of land is so con- stantly observed in these parts as to claim to be regarded as charac- teristic of some peculiarity in them—some special kind of terrestrial substance for example *. On the other hand, the tint is so much * “Tn this planet we discern, with perfect distinctness, the outlines of what may be continents and seas. Of these, the former are distinguished by that ruddy colour which characterizes the light of this planet (which always appears red and fiery), and indicates, no doubt, an ochrey tinge in the general soil, like what the red sandstone districts on the earth may possibly offer to the inhabitants of ~ Mars, only more decided. Contrasted with this (by a general law in optics) the seas, aS we may call them, appear greenish.”’—Herschel’s Astronomy (ed. 1833), p- 279. ; 324: Royal Society. like that of our evening clouds as to suggest the probability of its being due to the deep atmospheric zone which has been often ascribed to this planet, though perhaps, until of late years, on in- sufficient grounds*. On this head spectral analysis will probably enlighten us. If, however, there be such a deep covering of atmo- sphere, it might explain some facts regarding the climate which other- wise appear unaccountable. Some considerable amount of vaporous atmosphere there must be, to give origin to the beds of snow which alternately invest and desert the opposite poles, if indeed either pole be ever quite free from snow. In different Martial years the extent of the snow appears nearly the same under nearly similar conditions. Compare, for instance, Herschel’s drawing for August 16, 1830, with my sketch for Sep- tember 27, 1862 ¢, and that now presented for November 20, 1864. Snows appear to have been observed in mass as far from the south pole as lat. 40°. This occurred in April 1856, according to a draw- ing by Mr. De la Rue: snow in lat. 50° or perhaps 45° North is the result of my observations during this late opposition. Assuming. this to be the geographical limit of the freezing mean winter tem- perature, we see at once that it differs but little from that of the earth, on which the isothermal line of 32° varies, according to local peculiarities, from the latitude of 40° to that of 60°. If the snows on the land of Mars be compared with those on the northern tracts of Asia and America, they will be found not to extend further. And as the snows, if they do not actually disappear, are reduced to small areas about either pole in zfs warm season, thus showing the mean summer temperature there to be not less than 32°, this confirms the general impression that the variations of the climate of Mars are comprised within nearly the same thermic limits as those of the earth. In all the broad belt of 30° or 40° from the equator, the temperature seems to be such as always to allow of evaporation; between that limit and the pole, snows gather and disperse according to the season of the year, while for about 8° or 10° more or less round the pole, the icy circle seems to be perennial. The relative mean distances from the Sun of Mars and the earth being taken at 100 and 152, the relative solar influence must be on Mars 100 to 231 on the earth; so that the surface of the more distant planet might rather be expected to have shown signs of being fixed in perpetual frost, than to have a genial temperature of 40° to 50°, if not 50° to 60°, as the earth has, taken on the whole. How is this to be accounted for? Of two conceivable influences which may be appealed to, viz. very high interior heat of the planet, and some peculiarity of atmosphere, we may, while allowmg some value to each, without hesitation adopt the latter as the more immediate and effective. To trace the effects in detail must be impracticable; but in the general we may remark that as a diminution of the mass of vaporous * <‘Tt has been surmised to have a very extensive atmosphere, but on no suffi- cient or even plausible grounds.’”’—Herschel’s Astronomy (ed. 1833), p. 279, note. T Treatise on Astronomy (ed. 1833), pl.1. $ Phil. Mag. S. 4. vol. xxvi. p. 314. Geological Society. 825 atmosphere round the earth would greatly exaggerate the difference of daily and nightly, and of winter and summer temperature, so the con- trary effect would follow from an augmentation of it. Applying this to Mars, we shall see that his extensive atmosphere would reduce the range of summer and winter, and of daily and nightly tempera- ture. It would, moreover, augment the mean temperature by the peculiar action of such an atmosphere, which, while readily giving passage tothe solar rays, would resist the return of dark heat-rays from the terrestrial surface, and prevent their wasteful emission into space*. This effect obtains now on the earth, which is ren- dered warmer, as well as more equable in temperature, by the atmo- sphere than it would be without it. It is conceivable that it may obtain upon Mars to a greater degree, even without supposing the atmosphere to be materially different in itsnature from that round the earth, or the surface of Mars to have any specially favourable or exceptional characters for the absorption and radiation of heat. It seems, however, requisite to suppose a greater communication of heat from the interior of the planet; for otherwise the additional vapour, to which the warming effect is in the main to be’ ascribed, could not probably be supported in the atmosphere. On the whole we may, perhaps, be allowed to believe that Mars is habitable. Here, so far as direct observations upon the aspect of Mars are available, we may pause. The researches of the Radcliffe Observer, lately in Oxford, and formerly at Greenwich, have, however, brought into view a peculiarity in the constitution of this planet which deserves special notice. Its figure is spheroidal, as might be expected from the general laws of planetary form ; but it is spheroidal in so high a degree as to be quite exceptional in this respect. Computing by the known rotation-velocity, and the admitted measures and mass of Mars, its ellipticity should be about =},. Mr. Main’s observations with the splendid Oxford Heliometer give as the most probable result, the large fraction of as for 1862. This excellent astronomer has continued his observations during the late opposition. My own attempts to obtain the ellipticity with the micrometer eye- piece reading to 0''-2 of are failed to give satisfactory measures. The ellipticity, indeed, seemed to be small, and was merely observable, not really measurable or even to be approximately estimated by the help of this apparatus. GEOLOGICAL SOCIETY. [Continued from p. 241.] January 11, 1865.—Sir R. I. Murchison, Vice-President, in the Chair. The following communications were read :— 1. “On the Lias Outliers at Knowle and Wootton Waven in South Warwickshire.”’ By the Rev. P. B. Brodie, M.A., F.G.S. The author gave a description of the Liassic outliers at Knowle * Life on the Earth, 1860, p. 163-65. Tyndall’s Researches, Proceedings of the Royal Society, February 1861. 826 Geological Society. and Wootton in South Warwickshire. At Knowle, eleven miles S.E. of Birmingham, the Lower Lias is represented by limestone and shales containing Ammonites planorbis, Saurian remains, Ostrea, Modiola, &c.; below these beds with Ammonites planorbis, dark shales were seen resting on the New Red Marl; amongst the shales occurs a micaceous sandstone with Pullastra arenicola, which else- where prevails low down in the series, in close connexion with the bone-bed. ‘The greater outher at Wootton Park, near Henley, ex- hibited more clearly the succession of the deposits, from the beds with Pecten Valoniensis up to the limestone with Lima gigantea, &c. 2. “On the History of the last Geological Changes in Scotland. By T. F. Jamieson, Esq., F.G.S. The history of the last geological changes in Scotland, as given in this paper, was divided into three periods, namely, the Preglacial, the Glacial, and the Postglacial. The absence of the later Tertiary strata from Scotland leaves the history of the Preglacial period very obscure; but the author con- sidered it in some degree represented by some thick masses of sand and gravel (apparently equivalent te the Red Crag of England) on the coast of Aberdeenshire ; and he stated that there were indica- tions of the Mammoth having inhabited Scotland during this period. The Glacial period was divided into three successive portions, namely, (1) the Period of Land-ice, during which the rocky surface was worn, scratched, and striated, and the boulder-earth, or glacier- mud, was formed; (2) the Period of Depression, in which the glacier-marine beds were formed; and (3) the Period of the Emer- gence of the land to which belong the valley-gravels and moraines, and during which the final retreat of the glaciers took place. To the Postglacial period Mr. Jamieson referred that of the formation of the submarine forest-beds, which he considered was succeeded by a second period of depression, and this again by the elevation of the land to its present position. It is in the old estuary beds and beaches formed during the Second Period of De- pression that the author finds the first traces of Man in Scotland, while the Sheil-mounds with chipped flints he referred to the same epoch as the blown sand and beds of peat, namely to the most recent period, during which the land was raised to its present level. Mr. Jamieson described in great detail the deposits representing each of these periods, and concluded his paper with lists of shells from the different beds, showing the percentage of the species that are now found in the British, Southern, Arctic, N.E. American, and North Pacific regions. Se a ba XLY. Intelligence and Miscellaneous Arias. SIMPLE MODE OF DETERMINING THE POSITION OF AN OPTIC IMAGE. BY A. KRONIG. Qs looking with one eye at two points which form no, or at all events a very small visual angle with one another, it is easily de- termined whether one of the points is more distant, and which it is. It is merely necessary, while continuing to look at the two points, to move the eye at right angles to the direction of its axis, and to ob- serve the simultaneous apparent motion of the two points. ‘That point which moves in the same direction with the eye is the most distant. In the annexed figure, let A be the eye which looks at the ae Be Q es B two points Pand Q. Let A, P, and Q be in the same right line. The eye is now moved from A to B. The two points P and Q thereby diverge from one another by the angle P B Q, and Q appears to move in the same direction as the eye (to the right, for instance), but P in the opposite direction. Inversely, when P appears to move in the same direction as the eye, it follows that P is more distant from the eye than Q. . Imagine now an optical apparatus which projects an objective pic- ture of any object. If the image is not sufficiently bright to be caught upon a screen, the law (that of two unequally distant points the further moves in the same direction as the eye) furnishes an easy means of finding the position of animage. The eye is so placed that it views the image. A needle-point is then brought by the hand, or still better by means ofa fixed stand, into such a position that the point covers any part of the picture. ‘The head is then moved some- what on one side. If now either the needle-point or the point of the picture moves in the same direction as the eye, this point is further removed from the eye than the other, which moves in the opposite direction. By successively shifting the needle-point, the position is readily found in which, when the eye is moved, the needle-point coincides with the point of the picture considered. This is the position of the image. If the needle-point, after it has been approached to the reflecting or refracting apparatus till it touches, still appears to move in an opposite direction to the eye, the image is subjective, and not objective. In order to extend the same process to subjective images, it would first be necessary to prove experimentally and directly that the image produced by a plane mirror actually occupies the position hitherto ae 328 Intelligence and Miscellaneous Articles. assumed. For this purpose two equal threads stretched vertically by weights might be used, and a plane mirror without edge be so adjusted that the reflected piece of the one thread falls in a straight line with the directly seen parts of the other in each position of the eye. After the position of the image produced by a plane mirror has thus been fixed, the discovery of the position of other subjective pictures will be possible by means of a transparent and at the same time reflecting plane-parallel plate on which a luminous point is reflected. ‘The plate is to be so arranged that the reflected picture of the luminous point covers a point of the image in question. An assistant must move the luminous point until the reflected and re- fracted image no longer move towards each other in any motion of the eye. ‘The directly measured distance of the reflected point from the plane-parallel plate is equal to the required distance of the sub- jective image produced by the optical apparatus from the same plate. —Poggendorff's Annalen, vol. cxxiil. p. 655. fo ON A SIMPLIFIED METHOD OF EXTRACTING INDIUM FROM THE FREIBERG ZINCBLENDES. BY M. WESELSKY. The roasted and levigated blendes are treated with a mixture of ten parts of hydrochloric and one of nitric acids; the solution, separated from silica and the liberated sulphur, is greatly diluted with water, and carbonate of soda added until a precipitate first begins to form. The solution is boiled, hyposulphite; of soda being added until no more sulphurous acid escapes, and the precipitate, which at first is yellowish and flocculent, has become black, when it readily settles down. The solution contains, besides all the iron and zinc, small quantities of arsenic and copper, and also part of the indium. ‘The black precipitate consists of the sulphur-compounds of arsenic, lead, copper, &c., and contains the rest of the indium. Without removing it, freshly-precipitated carbonate of baryta in excess is added to the liquid when it is cold, and the whole allowed to stand for twelve hours. ‘The precipitate, which, besides the above sulphides, contains all the indium and the excess of carbonate of baryta, is well washed, the air being excluded, and is then treated with dilute hydrochloric acid. In this way the carbonate of baryta and the indium are dis- solved. ‘To remove a small quantity of sulphides which pass into solution, sulphuretted hydrogen is passed into the acid solution; and baryta is removed by sulphuric acid. Oxide of indium is separated from any possibly adhering oxides of iron or zinc by means of car- bonate of baryta. From experiments with which M. Weselsky is at present occupied, it appears that, under suitable circumstances, indium may be com- pletely precipitated by hyposulphite of soda, by which the applica- tion of carbonate of baryta is quite avoided.— Bulletin der Akademie in Ween, vol. vil. p. 1869. ——— = THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] MAY 1865. XLVI. Supplementary Considerations relating to the Undulatory Theory of Light. By Professor Cuauuts, F.R.S., F.R.A.S.* Q* a review of the arguments by which I have now for a long time maintained that the phenomena of light are referable to the vibrations and pressures, as mathematically de- termined, of a continuous elastic fluid the pressure of which varies proportionally to its density, I have found that there are certain points of the reasoning which require rectification or confirmation. To discuss these points is the object of the pre- sent communication. (1) By pure reasoning, founded on admitted principles, I have ascertained that the vibratory motion of the supposed elastic fluid is composite independently of particular modes of disturb- ance, and that each component consists of vibrations partly parallel and partly transverse to an axis. The former of these results is at once applicable in accounting for the composition of light as indicated by prismatic analysis, “and the other in the explanation of facts of polarization. As the reasoning also showed, independently of arbitrary disturbances, that for small vibrations udz + vdy +wdz is an exact differential, the motion relative, as above stated, to an axis is analytically expressed by the equation (d. fob) =udz + vdy + wdz, f being a function of x and y only, ¢ a function of z and ¢ only, and the axis of the motion coinciding with the axis of z. In fact this equation gives df a dg | =$9, w=; * Communicated by the Author. Phil, Mag. 8. 4. Vol. 29. No. 197, May 1865. Z = 330 Prof, Challis on the Undulatory Theory of Light. and we may assume / to be such that, where e=0 and y=0, a a ly a an es | The details of the reasoning here referred to are given in the proof of Proposition X. contained in an Article on the Princi- ples of Hydrodynamics in the Philosophical Magazine for December 1852. In the same Article are investigated exact expressions for the functions f and ¢, and the rate of propaga- 2 tion of the motion along the axis is found to be a/ 1+ , a and X having the usual significations, and e being a constant such that, where =O and y=0, a2 a iy? + 4e=0.. As e is necessarily a positive quantity, it follows that the rate of propagation, as determined by hydrodynamics, 1s greater than a. It is further evident, putting «a for the rate, that if x be a nu- merical constant, its value should be determinable exelusively on hydrodynamical principles. This is what I have attempted to do in a communication to the Philosophical Magazine for Fe- bruary 1853; but having recently discovered that the mathema- tical reasoning there given requires correction, 1 propose now ‘to enter upon the discussion of this point. The determination of the constant e depends on the integra- tion of the equation Of OF ape = P +4ef=0, | 7 being any distance from the axis of motion. The integral is not obtainable in a finite form, but it may readily be shown that the following series for f satisfies it, viz. 024 08,6 felis a" age erage For finding e it 1s required to ascertain the large values of 7 that make f vanish. This problem is solved by Sir W. Hamilton in a memoir on Fluctuating Functions in the Transactions of the + &e. Royal Insh Academy (vol. xix. p. 313), and by Professor Stokes in the Transactions of the Cambridge Philosophical Society (vol. ix. part 1. p. 182). I hesitated to accept the equation (52) ia the latter memoir, because it contains quantities R and S representing series that are convergent for a certain number of terms and then become divergent, which yet are employed as if they were wholly convergent. Whatever be the answer to this Prof. Challis on the Undulatory Theory of Light. 331 objection, it is certain that the equation obtained by Professor Stokes for large values of 7, viz. f=(2ar Ve e)—# 2(cos 2 VW er+ sin 2 / er), approaches the true integral in proportion as 7 is larger. In fact this equation is the exact integral of the differential equation df, & Ae 2) die + 4ef= Ae which evidently differs less from the foregoing differential equa- tion as ris larger. Hence it appears that the consecutive large values of 7 which cause f to vanish, increase by the common dif- ference api By peculiar reasoning applied to the infinite /e roots of the equation f=0 (Phil. Mag. for February 1853), I found the common difference to be ultimately a But from € the preceding argument it must be concluded that that reasoning is not legitimate, and that some error is involved in the treat- ment of the infinite roots. It will therefore be necessary to de- termine the rate of propagation by a new investigation, employ- ing for the purpose the above expression for f. This I proceed to do by a course.of reasoning analogous to that which was fol- lowed in the previous investigation. In the article already cited, containing Proposition ae the following equations to the first approximation are obtained :— i: Qi ai En? Ng's dp _ p=m cos ~ ee 0 e=a/ 14 We CET aa Also if wand @ be respectively the velocities parallel and trans- verse to the axis of z, we have w= fa i: and a=¢ = The fore- _ going expression for f may be put a the form (4arra/ e) —? cos (2/ er — 7) ; and as r is assumed to be very large, it may be supposed to have the constant value 7, outside the cosine, and the general value %%+h under the cosine, h being always very small compared to %, Then patting, for brevity, hy for the constant coefficient, and ¢ for 2 Ve To— - we shall have S=fo cos (2 Veh+e), 4 = —2 Vefysin (2 Veh+c'). Z 2 332 Prof. Challis on the Undulatory Theory of Light. | Consequently w= LET a6, (2 Veh+e) sin = (g—xKat+c), w= —2m V ef, sin (2 VW eh+c') cos o (z—xat+c), c= — PT MIT wos (2 Veh+c') sin 52 (¢—xKat+c). Hence it follows that w= =. Suppose now another series of waves, exactly equal to the first, to be propagated in the contrary direction ; and let z) be the coordinate of a position at which the velocity parallel to the axis is constantly zero. Then if in general z=z,)+-J, and if w', w', and o! be respectively the result- ing velocities and condensation, we shall have w= — oe cos (2 Veh +c!) (sin= (1— rat) + sin ac xat) ), ol = — 2m V ef, sin (2 Veh+ 0) cos’ (I— rat) +08" (4 Kat))), ___ 2amkfy — ae OT ee a ces (2 Vch-+e)(sin = (J—xat) —sin x (I+ «at)). From the first and second of these equations it appears that wo! Wer w! 7 5 a 271 hasan es tan (2 Veh +c’) cot > Let now the distance 7, apply to positions at which the trans- verse velocity is always zero; and in order to get rid of the ne- gative signs, and to avoid double signs, let c’=(2n4+1)a7. Then supposing / and / to represent very small equal distances from a point (79, Zp), where the velocity is constantly zero, we have ultimately @'o_ Ver tan2Veh _ er? Wo a Ql ie tan —— an This result informs us that the changes of condensation produced by the flow of the fluid to or from any point of no velocity are due to the longitudinal and the transverse motions in a constant ratio. It hence follows that the changes of condensation at any given point of a single series of waves are due at each instant to the longitudinal and transverse motions in the same ratio.. In Prof. Challis on the Undulatory Theory of Light. 300 fact, from the foregoing values of w and a, it will be seen 2 that the ratio of aa = is that of e to = Hence if 6h=06/, we have aes = = which is clearly the ratio in which the two velocities contribute to the changes of condensation. I 2 By substituting a for a in the value of «, we obtain for the "0 I velocity of propagation i 1+ =): which shows that the 0 excess of the velocity above the value a is caused by the trans- verse velocity, and that, because the changes of condensation are due to the transverse as well as the longitudinal velocity, they are more rapid than they would be if due to the latter alone, and the rate of propagation of a given state of density is consequently accelerated. Reverting now to ." expressions for w! and o!, if (2n+1)7r be substituted for a2 SU. * for 2, and «! for ae the following equations may be obtained :— wl Bue cos (sin <7 (h—«lat) + sin (i+dat)), a etd fog d= a oat ( sin Sr — (h—x'at) — sin = (h+« 'at)). At the same ee a Pen! sn east sin ™ (+m) oe 2a pesca f oe ) 1__ “TMK Lee co 7 sin 5 (J—xat) — sin = (c+ Kat) }. Hence the transverse motion and condensation may: be repre- sented by equations exactly analogous to those which represent the longitudinal motion and eon at and the two motions are correlative to eachother. If * be substituted for e in the xn2 value of «,we obtain ay es 1+ = Also x= — Me afiniaee +53 Thus the velocities of propagation «a and x’a are each greater than a, because, as already explained, the transverse and longi- tudinal motions both contribute to the changes of condensation. But the ratio of these velocities is that of X to N, as evidently should be the case, since the propagations over these breadths occupy necessarily the same time. 334 — Prof. Challis on the Undulatory Theory of Light. - There remains another consideration which must be brought to bear on the determination of the velocity. of propagation. a , We found above the general relation ae between the lon- situdinal velocity and condensation in a single series of waves. The analogous relation obtained by the process of reasoning that has been usually adopted in questions of this kind isw=ace. But that process does not take into account that the total motion is composed of separate longitudinal and transverse motions relative to aves. The factor = is wholly due to the lateral spreading which accompanies the condensations and rarefactions propagated along and parallel to the axis of motion, which has the effect of diminishing the rate of change of the density in the direction of propagation, and thus making the effective elasticity of the fluid, ceteris paribus, less than the actual in the ratio of 2 a : ° ° ° ° ° + . 72 to a?. But just in the proportion in which the effective elasticity is caused by lateral spreading to be less than the actual in the direction of propagation, it must, by a reciprocal action, be made greater than the actual in the transverse direction, and accordingly be increased in the ratio of «?a? to a?. Thus the ratio of the latter effective elasticity to the other is «+, and the © ratio of the corresponding velocities of propagation is x. Now ! we have proved that this ratio is 1 Hence, substituting in the expression for x, we have i. n=a/ ies vor r— = 1, Consequently the numerical value of «x? is obtained by-the solu- tion of a cubic equation which has one real positive root and two imaginary roots. The value of « will be found to be 1°2106. Hence, taking a=916°322 fect, the resulting velocity of propaga- tion is 1109-8 feet. The value by observation, as given by Sir J. Herschel in the Encyclopedia Metropolitana, is 1089-7 feet. The difference 19°6 feet might be lessened in some degree by calculating the corrections of the observations for temperature according to Regnault’s coefficient of expansion. But probably the principal part of the difference is due to the circumstance that the theoretical reasoning assumes the fluid to be perfect, and.it may be that atmospheric air is not strictly such. It seems hardly to be accounted for that a course of reasoning involving considerations so various and peculiar as those which have been gone through above, should have conducted to a result differing a Prof. Challis on the Undulatory Theory of Light. 335. from observation by no larger amount, unless the principles of the reasoning are fundamentally correct. I may here state that the point of no velocity might have been taken on the axis of motion instead of being at a great distance from it, inasmuch as the motion contiguous to the axis may be supposed to consist of two equal sets of longitudinal and transverse motions ; and each set might be treated independently of the other. By conduct- ing the reasoning in this way I obtained the same results as by the other method. If it be objected that when the effect of the development of heat on the rate of propagation 1s taken into account the mathematical result is contradicted by experiment, I reply as follows :—It is evident, from the mutual relation of the longitu- dinal and transverse motions above described, that we have had under consideration a case of free expansions and contractions due to successive generations and filings up of a partial vacuum. Now it is admitted, I believe, that experiment has decided that “n such a case there is no change of temperature. Consequently the rate of propagation remains unaffected. The case of develop- ment or absorption of heat when air is suddenly let into, or abs- tracted from, closed spaces, and when, in consequence, work is done, has no analogy to this. Upon the whole I seem entitled to conclude that I have at length succeeded in solving the diffi- cult problem of determining mathematically the rate of propaga- tion in a continuous elastic fluid. The results obtained are essential to the undulatory theory of polarization. (2) I proceed, in the next place, to advert to a communi- cation 1 made to the Philosophical Magazine for January 1857, entitled “On the Transmutation of Rays of Light.” In the course of the article I have enumerated various inferences re- lating to phenomena of light, which had been deduced by means of the analysis I had applied to the undulatory theory ; and to one of these, which is numbered (4) in the order of the series, I wish how to call attention. That deduction is expressed in the following terms :—‘‘ When the ether in motion suffers disturb- ance by encountering atoms actually or relatively at rest, and the original motion 1s a simple series of vibrations of the usual type, or is compounded of several such motions with parallel axes and different values of m, A, and c, the result of the disturbance may in either case consist of ari indefinite number of separate ‘motions having their axes 10 various directions, and having values of m, X, and c altogether different from the values of these quantities in the original motion.” Further on I remark that “ when the circumstances of the disturbance are as supposed in (4), light may produce new light, which may differ from the original light in intensity, colour composition , and direction of 836 Prof. Challis on the Undulatory Theory of Light. propagation. This effect I have called a ‘Transmutation of Rays;’ and I beg it may be understood that in making use of these terms I mean only to express a result deduced from the mathematical theory.” In writing the last sentence I had in mind the statement made by Professor Stokes, that change of refrangibility always took place from a greater to a less refrangibility. As there was nothing im my theory of Transmutation which pointed to such a limitation, and as the experimental evidence for it appeared to be only negative, I preferred stating the theoretical results in all their generality, without citing any experiments bearing upon them. But now that the experiments of Dr. Tyndall have shown that this law of transmutation applies to the less refrangible as well as to the more refrangible rays, and that there may be change from less to greater refrangibility, I feel at liberty to say that the theory is in complete accordance with these experimental results. I take this occasion to remark that the term ‘‘ Transmutation of Rays,” which has acquired special interest since Dr. Tyndall’s experiments have shown that it expresses a law of nature, was originated by me, on purely theoretical grounds, in the commu- nication here referred to, published more than eight years ago, and has since been adopted without any reference to its oc- currence in that communication. (3) In my Theory of the Composition of Colours, contained in the Philosophical Magazine for November 1856, I have endea- - voured, under section (5), to give reasons for a dean be- tween “ terrestrial light,” that is, light which has been reflected, refracted, or generated by terrestrial substances, and direct solar light. I was induced to do this by the persistent assertion of experimenters that a composition of yellow and blue solar rays does not produce a green colour, whereas the composition of such rays emanating from yellow and blue terrestrial sub- stances undoubtedly produces green. More recently, an ex- periment by Sir J. Herschel, described in the ‘ Proceedings of the Royal Society’ (vol. x. No. 35, p. 82), has led me to infer that the distinction I sought to account for does not really exist. This experiment renders it very probable that in cases in which green is not perceived to result from a mixture of yellow and blue solar rays, the rays are of too great intensity for the eye to distinguish the colour. At least Sir J. Herschel found, after concentrating a solar spectrum by an achromatic lens, so as to bring the yellow, green, and blue spaces pretty close together, that, on diminishing the intensity of the light, the green appeared to be so diffused as to encroach greatly on the yellow and blue spaces. When making the experiment of covering white paper with alternating parallel spaces, not inconsiderable in breadth, Prof. Challis on the Undulatory Theory of Light. 337 of yellow and blue colours made by chalk pencils, I constantly found that even when the eye was near enough to distinguish the spaces easily, the whole appeared to be suffused by a tinge of green. Now, although this diffusion in both kinds of ex- periment may be referable to the manner in which the organ of sight is acted upon by the rays, it proves not the less that a combination of yellow and blue has the same effect in producing green, whether the light come directly from the sun, or is what I called terrestrial hight. For this reason I withdraw the dis- tinction I endeavoured to establish between solar light and ter- restrial light. With reference to the same subject, I take this opportunity to state that I have made experiments for showing the effects of combining colours by means of revolving disks, the disks _being divided into spaces covered alternately with the two colours to be compounded. The apparatus I used was pro- fessedly made according to directions contained in Professor Maxwell’s paper on this subject, and among the different sets of colours was one which was intended to show that yellow and blue combined do not produce green. The result in this in- stance was certainly a dirty white; but according to my sight the blue and the yellow had scarcely any resemblance to pris- matic blue and yellow. On substituting for them the very same chalk colours that I used in the above-mentioned experiment of parallel spaces, I found that the result was decidedly green. It may be that the colours I used were not pure colours; but the fact that one appeared blue and the other yellow was owing to the predominance of blue or yellow solar rays, and the predominant tint of the compound was determined ac- cordingly. For these reasons, drawn, it will be seen, in part from per- sonal observations, I hold that sunlight and terrestrial light are not essentially different, and that, in accordance with the ma- thematical theory of the composition of colours given in the above-cited article, combinations of yellow and blue, with either kind of light, have the effect of producing green. (4) It having been suggested to me to employ Angstrom’ S values of A, given in Poggendorff’s Annalen for November 1864, for testing my Theory of the Dispersion of Light con- tained in the Supplementary Number of the Philosophical Magazine for December 1864, I have calculated as follows for this purpose. It was considered sufficiently accurate to obtain the values of X for the rays C, D, F, and G from those for the rays B, E, and H, and the given values of uw by mere interpola- tion, and to regard the differences of the results deduced from the old and the new values of X as the same that would have pee 338 Mr. H. G. Madan on the Reversal of been obtained by calculating strictly according to the theoretical formula (@). According to this principle, it is only necessary to apply these differences to the values of X previously calcu- lated from Fraunhofer’s data, to obtain the values that would be given by Angstrém’s data. These calculations having been gone through, the comparison, to the third place of decimals, of the observed and calculated values of X for the two sets of data stands as follows :— Excess of calculation. Excess of calculation. dX by dX by . Ray. Ba rR) ** Fraunhofer. Flint-glass Oil of Angstrom. Flint-glass Oil of Nowe Cassia. No. 13. Cassia. B 2-541 0-000 0-000 2:5397 0-000 0-000 C 2-422 +0:003 +0-006 2:4263 — 0-602 +0-001 D 2-175 —0-001 —0-001 2:1786* — 0-003 —0 003 E 1:945 0-000 0-000 1:9484 0-000 0-000 F 1-794 +0-002 — 0-003 1:7973 +0-003 —-001 G 1587 +0-005 — 0-004 1-5923 +0 004 — 0-003 H 1-464 0-000 0-000 1-4672 0-006 0-000 It appears from this comparison that the excesses of calculation are somewhat smaller with Angstrom’ s values than with Fraun- hofer’s, especially in the case of oil of cassia, the more refractive substance. With this communication I conclude the series of arguments by which I maintain that the Undulatory Theory of Light rests legitimately on no other than a hydrodynamical basis. Cambridge, April 22, 1865. XLVIL. On the Reversal of the Spectra of Metallic Vapours. By H.G. Manan, F.C.S. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, April 11, 1865. \ AY I be allowed to mention a simple and convenient + method of illustrating one of the most important points m Bunsen and Kirchhoff’s spectrum discoveries, viz. the reversal of the spectra of metallic vapours; the most familiar example of which is the reversal of the sodium-line D? I have tried most of the various methods proposed for effect- ing this object, but none have appeared to me so easy and effective as the following. * This value applies to the middle of the double line. | the Spectra of Metallic Vapours. 339 It consists simply in directing the spectroscope upon a frag- ment.of sodium burning in oxygen gas. The incandescent metal gives, of course, a continuous spectrum; but the rays, in passing through the cooler atmosphere of sodium-vapour which surrounds the metallic nucleus, are selectively absorbed, and the dark double line D, or Naa, appears with great distinctness on the bright spectrum. As, however, the fragment of sodium is soon consumed, I have used an apparatus resembling that employed for making phosphoric anhydride, by which pellets of sodium may be added as often as required. A moderate-sized deflagrating-jar is placed in a dish of sand. In it 1s suspended a shallow iron cup, and through the same cap which carries the latter is passed a short wide glass tube, so as to be directly over the centre of the cup. Through the sand and under the lower edge of the jar passes a bent glass tube, con- nected with a caoutchouc bag of oxygen, and serving to intro- duce a continuous slow stream of the gas to replace that con- suined by thesodium. The spectroscope should first be adjusted as to position and focus by bringing it to bear on a candle placed on the opposite side of the jar, so that its flame may just be seen over the edge of the iron cup. Then, while the jar is fillmg with gas, the cup may be withdrawn, a pellet of sodium placed in it and heated over a spirit-lamp until it begins to burn, and lastly immersed in the jar. Fragments of sodium may be added as required through the glass tube, and will readily burn if the mass of soda in the cup be not allowed to cool below dark red- ness. The experiment may thus be carried on as long as de- sired; and, of course, two or more spectroscopes may be arranged round a single deflagrating jar. _ I have not yet tried whether the spectrum thus produced can be thrown on a screen, the deflagrating-jar being enclosed in a Duboscq’s lantern ; but, from its brilliancy in the spectroscope, I have little doubt that it could be thus shown. The idea of this method occurred to mé about a year ago, and I have shown it to many in Oxford; but it seemed so obvious an expedient that I thought it must have been already described. As, however, I have been unable to find any account of it, I venture now at any rate to bear my testimony to its efficacy. The same method is of course available in the case of other volatile andoxidizable metals, as lithium, zinc, magnesium. T remain, Queen’s College, Oxford. Yours, &c., H. G. Mapan. [40.4 XLVI. On Phosphorite from Spain. By Davin Forsss, F.R.S., &¢.* feo mineral was some time back forwarded from Spain for the purpose of being submitted to chemical examination ; it was stated to occur in the district of Estramadura in South- ern Spain in large quantity. The specimens received, though in large blocks, consisted of the pure phosphorite, apparently uncontaminated and unaccom- panied by any other minerals; the mineral itself was massive, and, on breaking, the fracture was uneven and earthy, disclosing at the same time a slightly radiating dendritic structure, but no trace whatever of crystallization. The colour of fresh fracture was chalk-white, but weathered surfaces frequently showed a dirty or rusty white colour externally. Lustre earthy; opake ; streak and powder dead white. Hardness about 4°5 on the scale, or immediately below apa- tite, by which it was scratched. The specific gravity was taken on two distinct specimens, and found to be 3:00 and 2°92 re- spectively at 60° F. When the powdered mineral was heated over a lamp in the dark or thrown on to a nearly red-hot plate of iron, it quickly glowed, emitting an extremely beautiful and slightly greenish- yellow light, which passed off before the mimeral attained a visibly red heat. As Mr. Phipson, in his treatise on Phospho- rescence, states that minerals which, after having been heated, no longer emit the characteristic phosphorescent light upon reheat- ing, again recover their fluorescent property upon being exposed to the sunlight, the experiment was tried several times and with various modifications, but failed even after many days’ exposure to the sun’s rays: this was also the case when the mineral, after heating once, was cooled in the dark and again reheated. In order also to see if the loss of moisture in the first heating had any relation to the phosphorescent property, another portion, after heating, was thrown into water and kept in the sun under water for many days; on being air-dried and reheated no signs of phos- phorescence could be detected ft. In order to examine whether, as 1s the case with the mineral Gadolinite {, the phenomenon of fluorescence, on heating, might * Communicated by the Author. + Mr. Phipson states that the fluor-apatites only are phosphorescent, and that this is not the case with the chlor-apatites. On examination, however, the fine crystallized true chlor-apatites from Krageroe in Norway emitted, on heating in the dark, a most distinct slightly greenish-yellow hight, though not quite so bright as the above phosphorite. { Gadolinite, when heated, glows suddenly and increases in density, being, after ignition, about 5 per cent. specifically heavier than before. Mr. D. Forbes on Phosphorite from Spain. 341 not be accompanied by a change in its specific gravity, two ex- periments were made upon fragments of the mineral, which, after having had their specific gravity determined, were heated to visible redness for some time, and, after cooling, a second deter- mination of their specific gravity was made. In both cases a somewhat higher result was obtained after ignition than before, the exact numbers being as follows :—before ignition the specific gravities of the specimens were 3°00 and 2°92, but after ignition 3°12 and 2°98 respectively. As the mineral was found to lose weight upon ignition (amounting to 1°44 per cent.), the specific gravity of the mineral after ignition was calculated from the weight of the mineral left behind after heating, and not from the weight of the phosphorite actually employed in the first instance, from which weight the specific gravity of the unignited mineral had been calculated. It seems, however, not improbable that the increase of specific gravity may really be due to the mineral becoming less porous, or contracting, on losing the water (probably only hygroscopic), and not connected at all with the phenomenon of phosphorescence. Before the blowpipe the mineral behaves as follows :—A thin fragment heated in the platinum-points remains unchanged, but at a very strong heat becomes rounded off at the edges, and, provided the mass operated upon is sufficiently small, ultimately fuses with great difficulty to a milk-white enamel. During this heating, in general no coloration of the outer flame can be per- ceived; but if the fragment be moistened in strong sulphuric acid and introduced into the point of the blue flame, a distinct bluish-green colour, quickly passing over, 1s seen at the moment of contact of the mineral with the flame. In both open and closed tubes some little moisture is observed ; and if a rather larger amount be heated in a bulbed tube and the evolved moisture tested, it will be found to feebly redden blue litmus paper, and give a somewhat yellow colour to Brazil-wood paper. When heated with carbonate of soda it fuses with effervescence, part of the mass is absorbed by the charcoal, and a white resi- duum is left upon the surface. Heated with borax-glass it dissolves to a transparent glass, somewhat yellow when hot, but colourless after cooling—a change no doubt owing to a small amount of iron present in the mineral itself. The glass, if sufficiently saturated, becomes milk-white ; and if supersaturated with the minerat, becomes opake. Phosphate of soda* dissolves the phosphorite with much more * Instead of using the microcosmic salt or phosphate of soda and am- monia, | find it much better to use the anhydrous phosphate of soda left behind on heating microcosmic salt until all water and ammonia are evolved. ‘The reactions in both cases are precisely similar. 342 Mr. D. Forbes on Phosphorite from Spain. facility and in larger quantity than borax-glass, and forms aclear colourless glass, which, however, if supersaturated, becomes a white enamel. | i aia A portion of the mineral in the state of powder was placed in a small leaden capsule and drenched with strong sulphuric acid. Hydrofluoric acid was eyolyed upon gently heating the capsule, and etched deeply letters written through a film of wax varnish coating a glass plate with which the leaden capsule was covered. The analysis of the mineral was conducted as follows :— 31:05 grains in powder were heated for some time to redness in a platinum crucible; upon cooling; the diminution in weight amounted to 0°45 gr., equivalent to 1°44 per cent., which loss was considered as water; the powdered mineral had become much darker in colour during ignition, and on cooling had as- sumed a reddish-brown tint. In order to determine the amount of carbonic acid present, this gas was displaced by the action of hydrochloric acid upon 100 grs. of the powdered mimeral placed in a previously tared thin glass apparatus, from which the gases were evolved after passing through a tube containing chloride of calcium. The loss of carbonic acid was found to be 0°45 gr., or equivalent to 0-98 per cent. carbonate of lime in the mineral. Sulphuric acid was also distinctly observed, but in quantity too smali for estimation unless an unusually large amount of the mineral had been operated upon. For determining the fluorine a thin glass bulb was employed, closed by a cork through which two tubes passed, the one for evolving the gaseous products, and the other, reaching to the bottom of the bulb, for passing a stream of air through it in order to displace and drive off the hydrofluosilicie acid which remained behind in the apparatus at the termination of the Operation ; a sufficient quantity of pure strong sulphuric acid was now placed in the bulb along with 10 grains pure silicic acid (precipitated from hydrofiuosilicice acid), and the whole boiled to expel any moisture present, and weighed. 50-00 grs. phospho- rite in powder were then introduced, and the whole heated and weighed several times during two days; the ultimate loss was found to be 2°66, or 5:32 per cent. terfluoride of silicon ; and as, according to Wohler, 100 terfiuoride of silicon 1s equivalent to 72°79 fluorine, this would afford 3°87 per cent. fluorine, or 8°01 fluoride of calcium. : The insoluble matter was estimated by dissolving 36°94 grs. in nitrohydrochloric acid and collecting the insoluble remainder, which was found to weigh 0:42 gr., or 1:41 per cent. 20:09 grs. were now digested with strong sulphuric acid, which evolved fumes of hydrofluoric acid, and the mass then Mr. D. Forbes on Phosphorite from Spain. 343 extracted with alcohol to dissolve the phosphoric and excess of sulphuric acid, and afterwards well washed with a saturated aqueous solution of sulphate of lime, after which the sulphate of lime was dried, incinerated, and w eighed 23°03 grs.; deducting from this weight 0:15 for the insoluble matter ‘contained in it, gives 22°88 ers. sulphate of lime, equivalent to 9:44 lime, or 47°29 per cent. lime. From the wash-water 0:07 gr. pyrophos- phate of magnesia was obtained by the usual method, repre- senting 0:025 gr. magnesia, or 0°12 per cent. 20°01 grs. were dissolved in NO®, filtered from the inso- luble residue, and the filtrate precipitated by a solution of nitrate of silver, which produced a minute precipitate, which on ignition gave. 0:08 chloride of silver, equivalent to 0:02 chlorine, or 0°10 per cent. corresponding to 0°16. chloride of lime in the mineral. The excess of silver was removed as ehloride from the filtrate, which now only gave, with chloride of barium, indications of sulphuric acid too small for accurate determination. The solu- tion was now boiled and neutralized by carbonate of baryta, a solution of soda added in excess, and then a solution of carbo- nate of soda to precipitate all excess of baryta. The precipitate, which was now filtered off, evidently from its colour contained all the iron present, which was demonstrated when, on boiling the filtrate (previously acidified with a little hydrochloric acid) with a little chlorate of potash and precipitating with ammonia, no iron was obtained, and only pure alumina fell, which was col- lected, and, on ignition, gave 0°35 gr., or 1°75 per cent. in the phosphorite. In order to determine the phosphoric acid, 14°28 grs. were dissolved in nitric acid filtered from insoluble matter, and a solu- tion of molybdate of ammonia, previously supersaturated with nitric acid, added in great excess, and allowed to stand two days, taking the precaution to test whether sufficient molybdate of ammonia had been added. The beautiful yellow precipitate of phosphomolybdate of ammonia, after separation, was then dis- solved off the filter by addition of ammonia, and this solution precipitated by chloride of magnesium. The precipitated phos- phate of ammonia and magnesia was now collected and inci- nerated with the usual precautions, and gave 9°74 pyrophos- phate of magnesia =6°303 phosphoric acid, or 44°12 per cent. ; the filtrate, which, after having separated the phosphoric acid by the molybdate of ammonia, still contained the bases, was placed in a corked flask with ammonia in excess and sulphide of ammonium also in excess, and allowed to stand some twelve hours. The insoluble matter containing the iron and alumina _was then filtered off, washed with water containing sulphide of ammonium, and then dissolved in nitrohydrochloric acid ; a little 344: Prof. Cayley on the Theory of the Evolute. pure sulphur was removed from this solution, and then ammonia added to precipitate the alumina and sesquioxide of iron. These were not separated, but after washing were ignited, and afforded a weight of 0°42 gr., equivalent to 2°94 per cent.; and sub- tracting from this the 1°75 per cent. alumina previously deter- mined, we have 1:19 per cent. as the amount of sesquioxide of iron present in the mineral. The results above, when tabulated, will give the following percentage composition :-— Fluoride of calcium . . 8 Ol Chloride of calcium . . O16 Lame oy es Masneésia 242 5a gn ae A Tuanttia lao He fod vsdppe pea eS Sesquioxide of iron. . . 1:19 Phosphoric acid. . . . 44°12 Sulphuric acid .jt./-5 5 fobs Carbonic acid . . . . 0-40 Insoluble matter . . . 1:41 Water e0.4%--1444, Sime Si alien 99°63 XLIX. On the Theory of the Evolute. By A, Cayuey, F.R.S.* ysis ec to the generalized notion of geometrical mag- nitude, two lines are said to be at right angles to each other when they are harmonics in regard toa certain conic called the Absolute; this being so, the normal at any point of a curve is the line at right angles to the tangent, and the Kvolute is the envelope of the normals. Let the equation of the absolute be O=(4, b,¢, f, 9, hXa, y, z)=0, and suppose, as usual, that the inverse coefficients are (A, B, C, F, G, H). Consider a given curve U=(* a, y, z)"=0, and suppose, for shortness, that the first differential coefficients of U are denoted by L, M, N. Then we have to find the equation of the normal at the point (z, y, z) of the curve U=0. The condition that any two lines are harmonics in regard to the absolute, is equivalent to this, viz. each line passes through the pole of the other line in regard to the absolute. Hence the normal at the point (x, y, 2) is the line joing this point with the pole of the tangent. Now, taking (X, Y, Z) as current co- * Communicated by the Author. : Prof. Cayley on the Theory of the Evolute. 345 ordinates, the equation of the tangent is LX+MY+NZ=0. The coordinates of the pole of the tangent are therefore (A, H, @XL, M, N): (H, B, FXL, M, N) :(G, F, CXL, M, N). And the equation of the normal is | Xx , Y Z 0. ~ xv ) y 9 2 (A, H, GXL, M,N), (H, B, FXL, M,N), (G, F, CLL, M, N) The formula in this form will be convenient in the sequel; but there is no real loss of generality in taking the equation of the absolute to be 2?+y4?+2?=0; the values of (A, B,C, F, G, H) are then (1, 1,1, 0, 0,0), and the formula becomes Me Vat Pai tis) & L, M, N where it will be remembered that (L, M, N) denote the derived functions (0,U, 0,U, 0,0). The evolute is therefore the envelope of the line represented by the foregomg equation, say the equation (=O, considering therein (z, y, 2) as variable parameters connected by the equa- tion U=0. As an example, let it be required to find the evolute of a conic; since the axes are arbitrary, we may without loss of generality assume that the equation of the coniciszz—y?=0. The values of (L, M, N) here are (z, —2y, x). Moreover the equation is satisfied by writing therein w:y:z=1:6:6?; the values of (L, M, N) then become (6?, —20, 1) and the equation is 1 ; 0 ; 6? xX : Me ; Z (A, H, G9, —1)’, (H, B, FXO, —1)’, (G, F, CX, —1)? or developing, this is xX G—2Fe?+ Cé —H*+2Be3— Fe? ) sa A@—2H+ Gé? - Goi+2K6—C) +Z ( Hé?—2B6+F —A@®+2H?— Gé =0, which I leave in this form in order to show the origin of the Phil. Mag. 8. 4, Vol. 29. No. 197. May 1865. 2A 346 Prof. Cayley on the Theory of the Evolute, different terms, and in particular in order to exhibit the destruc- tion of the term 6? in the coefficient of Y. But the equation is, it will be observed, a quartic equation in 0, with coefficients which are linear functions of the current coordinates (X, Y, Z). The equation shows at once that the evolute is of the class 4; in fact treating the coordinates (X, Y, Z) as given quan- tities, we have for the determination of 0 an equation of the order 4, that is, the number of normals through a given point (X, % Z), or, what is the same thing, the class of the evolute, 1s = 4. iA! The equation of the evolute is obtained by equating to zero the discriminant of the foregoing quartic function of @; the order of the evolute is thus =6. There are no inflexions, and the diminution of the order from 4.8, =12, to 6 is caused by three double tangents. | I consider the particular case where the conic touches the absolute. There is no loss of generality in assuming that the contact takes place at the point (y=0, z=0), the common tan- gent being therefore z=0; the conditions for this are a=0, h=0, and we have thence C=0, F=0. Substituting these values, the equation contains the factor 0; and throwing this out, it is X(—H6 + (B+26)6 ag +¥( A®— 2He ) +2( — A &48HO—(B+2G))=0, or, what is the same thing, ; G(-H X+AY ) +0((B+2G)X—2HY—A = Z) ue 4 ? 3H ° Z) + ( | —(B+2G)Z)=0, where it will be observed that the constant term and the coefii- cient of @ have the same variable factor Z, where Z=O is the equation of the common tangent of the conic and the absolute. The evolute is in this case of the class 8. It at once appears that the line Z=O is a stationary tangent of the evolute, the point of contact or inflexion on the evolute being given by the equations Z=0, (B+2G)X—2HY=0. The equation of the evolute is found by equating to zero the discriminant of the cubic function ; the equation so obtained has the factor Z, and throwing this out the order is =3. The evolute is thus a curve a Prof. Cayley on the Theory of the Evolute. 347 of the class 3 and order 8, the reduction in the order from 3.2, =6, to 3 being caused by the existence of an inflexion. Comparing with the former case, we see that the effect of the contact of the conic with the absolute is to give rise to an in- flexion of the evolute, and to cause a reduction =1 in the class, and a reduction =3 in the order. _ ne I return. now to the general case of a curve U=(« (a, y,2)"=0. | Using, for greater simplicity, the equation x*?+ y?+2?=0 for the absolute, the equation of the normal is Oe. Xi Ba ped: Lv »Y 7 * 0,U, ro POP 0,U we may at once find the class of the evolute; in fact, treating (X, Y, Z) as the coordinates of a given point, the two equations U=0, 0O=0 determine the values (x, y, 2) of the coordinates of a point such that the normal thereof passes through the point . (X, Y, Z); the number of such points is the number of normals which can be drawn through a given point (X, Y, Z), viz. it is equal to the class of the evolute. The points in question are given as the intersections of the two curves U=0, Q=0, which are respectively curves of the order m, hence the number of in- tersections is =m. It is to be observed, however, that if the curve U=O has nodes or cusps, then the curve Q=0 passes through each node of the curve U=0, and through each cusp, the two curves having at the cusp a common tangent; that is, each node reckons for two intersections, and each cusp for three intersections. Hence, if the curve U=O has 6 nodes and « cusps, the number of the remaining points of intersection is =m?—26—Sx. The class of the evolute is thus =m?~—26 —3x. The number of inflexions is in general =O. If, however, the given curve touches the absolute, then it has been seen in a par- ticular case that the effect is to diminish the class by 1, and to give rise to an inflexion, the stationary tangent being in fact the common tangent of the curve and the absolute: I assume that this is the case generally. Suppose that there are @ con- tacts, then there will be a diminution =@ in the class, or this will be =m?—25—3x—86; and there will be @ inflexions ; there may however be special circumstances giving rise to fresh in- “ag i and I will therefore assume that the number of inflexions 1 ty’, : 2A2 348 Prof. Cayley on the Theory of the Evolute. Suppose in general that for any curve we have m, the order, Ny 55 Class, 6, ,, number of nodes, K, 33 33 cusp 8, T, 9 9 double tangents, tess ys inflexions. Then Pliicker’s equations give t—K=3(n—m), T—O=3i(n—m)(n+m—9); and we thence have | t—K+7T—b=3(n—1)(n—2) —1(m—1)(m—2), or, what is the same thing, 4(m—1)(m—2) —6—K=4(n—1)(n—2) —7T—1. Now M. Clebsch in his recent paper “ Ueber die Singulari- taten algebraischer Curven,” Credle, vol. lxiv. (1864) pp. 98-100, has remarked (as a consequence of the investigations of Riemann in the Integral Calculus) that whenever from a given curve another curve is derived in such manner that to each point (or tangent) of the given curve there corresponds a single tangent (or point) of the derived curve, then the expression d(m—1)(m—2)—8—K, =}(n—1)m—2)—T—1, has the same Tenwa in the two curves respectively, or that, writing m', n', !, x, 7', o' for the corresponding quantities in the second curve, then we ; have 4(m—1) (m—2) —8—K« = 4(n—1) (n—2)—T—-1 =3(m!—1) (mn! —2) —9) d= Hal 1) (el —2)—a! =A and con sequently that, knowing any ¢wo of the quantities m’, n’, Oni sth >.49, the remainder of them can be determined by means of this relation and of Pliicker’s equations. The theorem is applicable to the evolute according to the foregoing generalized definition* ; and starting from the values n! =m? —26—3«—8, | a we find in the first instance 7! =3(n! —1)(n! —2) —3(m—1)(m—2) +6 +n—d; * M. Clebsch in fact applies it to the evolute in the ordinary sense of the term, but by madvertently assuming «’=k instead of =0 he is led to some incorrect results. Prof. Cayley on the Theory of the Evolute. 349 and substituting in the equation m! =n! (n! —1)—27'— 31, we find | m! =2(n!—1) + (m—1)(m—2) —26—2e—U; and the equation s! —«! =3(n' —m’) gives also k= —3(n!—m') +0, whence, attending to the value of n’, we find the following sys- tem of equations for the singularities of the evolute, viz. n' =m?—2 o—3 k— 8, m'=3m(m—1)—6 6-8 Kc—20—U, of ye i, K =3m(2m—8) —126—15«—30—27, and the values of 7! and 6! may then also be found from ee equations m! = n!(n! —1)—2r! bes n! =m! (m'—1)—26'— I have given the system in the eee form, as better exhi- biting the effect of the inflexions; but as each of the @ sun” with the absolute gives an inflexion, we may write o’=@ +0", where, in the absence of special circumstances giving rise to any more inflexions, !'=0. The system thus becomes n! =m? —2 o—3 K— 9G, =3m(m—1)—6 6—8 «—380—", d= 6+", Kk! =3m(2m—8) —126 —15«—50—2u!, so that each contact with the absolute diminishes the class by 1, the order by 38, and the number of cusps by 5 I remark that when the absolute becomes a pair of points, a contact of the given curve m means one of two things: either the curve touches the line through the two points, or else it passes through one of the two points: the effect of a contact of either kind is as above stated. Suppose that the two points are the circular points at infinity, and let m=2, the evolute in ques- tion is then the evolute of a conic, in the ordinary sense of the word evolute. We have, in general, class =4, order =6; but if the conic touches the line infinity (that is, in the case of the parabola), the reductions are 1 and 3, and we have class =3, order =3, which is right. Ifthe conic passes through one of the circular points of infinity, then in like manner the reduc- tions are ] and 3; and therefore if the conic passes through each of the circular points at infinity (that 1s, in the case of a circle), 300 Prof. Cayley on the Theory of the Evolute. the reductions are 2 and 6, and we have class =2, order =O, which is also right; for the evolute is in this case the centre, regarded as a pair of coincident points. That this is so, or that the class is to be taken to be (not =1 but) =2, appears by the consideration that the mmnteber of normals to the circle from a given point is in fact =2, the two normals being, however, coincident in position. To complete the theory in the general case . where the abso- lute is a proper conic, I remark that, besides the inflexions which arise from contacts of the given curve with the absolute, there will be an inflexion, first, for each stationary tangent of the given curve which is also a tangent of the absolute; secondly, for each cusp of the given curve situate on the absolute. Hence, if the number of such stationary tangents be =A, and the num- ber of such cusps be =p, we pape write e/= +, and there- fore also /=O+2X+ p. I remark also that we have —26—3«=— m(m—1)+n, —66—8«= —3m(m—2) +7, and therefore also —126—15«= — 6m? + 15m—8n 4 82. The general formule thus become n= m+ n —- 6 A m=8m + .—20— J, = ie Ke! =6m—3n+ 81—30—2/. If instead of the given curve we consider its reciprocal in regard to the absolute, then 7 m,n, 6, k,T, 6; Or, wm; J=O+A+p are changed into n,m, 7, t,0,k; O,p,rX3; J=O+p4tr respectively. And for the evolute of the reciprocal curve we have n= nt+m — 6 7d, m' =3n + «—20—7, tie , « =6n—38m+ 8e—30—", which, attending to the relation .—-«=3(n—m), are in fact the same as the former values; that is, the evolute of the given curve, and the evolute of the reciprocal curve are curves of the same class and order, and which have the same singularities. Cambridge, February 22, 1865, | bie Ie L. On the Application of Screw-Blades as Floats for Paddle- wheels. By W.G. Avams, M.A., F.G.S., Fellow of St. John’s College, Cambridge, Professor of Natural Philosophy i in King’s College, London*. GQ INCE my former paper on this subject was communicated to the Philosophical Magazine, experiments (an account of which appeared in the ‘Times’ of the 5th of April) have been made at Portsmouth with Dr. Croft’s new wheel, on Her Ma- jesty’s private yacht ‘ Elfin,’ with very satisfactory results, show- ing in the very first trial that the new wheel is superior to the wheel with ordinary flat floats, and very nearly comes up to the wheel with feathermg floats, even with a much smaller surface exposed to the pressure of the water. One of the points especially worthy of notice is the fact that “no vibration whatever was experienced on board’’; so that it is no longer a mere matter of theory, but also true in practice, that with the new wheel the sudden jerking and quivering motion have no existence. In my former paper it is stated that if the number of revolutions be such that v is greater than or, then the part of the float nearest to the axis will tend to stop rather than to propel the boat. This must certainly be the case where the radius of the paddle-wheel is small, as in the case of the ‘Elfin,’ and may also be the case in a larger vessel. This diffi- culty may be obviated by cutting away the part of the float near- est to the axis; and I propose to consider the effect of sucha | change on the resistance and moment about the axis, in order to determine whether the float is rendered thereby more or less efficient. I also propose to investigate the expressions for the resistance and moment on a screw-blade whose pitch is different . from 45°, and to determine the efficiency when the pitch is what 1S practically considered most advantageous. The equations giving the resistance and moment on one float are these :— a | (po +a cos 0)? cos 8 R=4 Pe dp dé 2p Cos —¥ pvor { (Fee? eee dp — bpp doualny 2 | (roa ay +p * Communieated by the Author. B02 Prof. Adams on the Application of Serew-Blades 2 : i = 9,07 { cos 0 dé +a cos” @ log (a + Pao O\ gio\l 2 7 — HE 88 cos 0 tan 20 | —4 por? Yeos Olog (1 ta} e) do—3 4p,v wna nye f 228 ¢ tan = 19,04 {fe cos 0 d0+ (: cos* 0 log (1 “+ ede 2 “a _ 3 008" 6) cos 8 tan-} é dO el 2 (co:*@log(1+ 8 p Fa — 2 . 2) cos? 6 tan-1© 240} @Or\r @r 1 M=Jp,o° { i COST iy do | r+ p? emit vaya ((eraced)ens? p ee ae ° dp d 2 +'Lp,e%7 ay aoe dp d0 +4. py a A » & Od (3 pdé + (80p cos 6 dé a log (1 + £) dd 2 sini e tte -{*2 cos 6— a? cos tan12 a0 } r 2 —+p,2vor® {fe cos 6 dé +e cos? 6 log Q “+ - dé 2 aos? Tiaat oot cos 8 tan 1. dé \ +4 p,v “8 cos? @ log @ + e) d0 +4p,v?ar? costatan-1p 0 3a? T ip? ap 1— —;-cos? 0 | eI CO WICC baci mn 2 oN = sper {45 72 io \3 ; 7 cos dé { “ log(1 ay 2 -{(s-! = cos? a)" cos@.tan-! = dd _ wv a p Tae al ih cos 6d0 + { cos? @ log Qa + F) dé 2 th — - cos? 0) cos 6 tan—! 2 eo + ms 5 sr cos 0 log (1 _ 5 dO 4+- ooh 00s 6 tan-12 Pao}. ————————_—. = as Floats for Paddle-wheels. 353 Suppose that a portion of the screw-blade nearest the axis of breadth kr is cut away, then this will be the lower limit for p in the integration. If only that part of the float were cut away which tends to stop the boat, then the lower limit of integration would be given by the equation (p)+ acos 0) —v cos 9=0, or po=(= —«) cos 7 Vv a = 2) cos 8. or Vi Or if the part cut away be of the same width throughout, then =(=-°) OO Nar! P)? or (=. = CVn f or 7 Supposing, as before, that a= = then v mee foal 2 =3(1+2h) Without these suppositions the quantities 4, - and — are in- dependent of one another; and it may be considered doubtful whether (1) they should have the same values for wheels of dif- ferent radu, or (2) whether the above are the best hypotheses which can be made. It is only by repeating the calculations for different cases that these points can be theoretically determined. Taking the above values of - and — the resistance on both floats becomes £p,or* 1 2h eos 6d0 + log (1+?) \ cos? 6d —2tan—! i 00s 0d6+itan-} cos? 6 dé — (1+2h) log, (1+) { cose 0 dé —ttan—! iA cos 6 dé + 2k?. tan-! & | cos 6 dé } 354 Prof. Adams on the Application of Screw-Blades | =1 pw°r4 {2k sin @—hlog, (1 +42) (0-+4 sin 26) —2tan- k sind | + 2k? tan—! k (sin @—4 sin® 6)} | = 4 p,w°r' {(k— tan— k) x *68404—k log, (1 +k?) x *67046 +k? tan-1kx 65737} =1p,w'r $23 (:22801 — °67046 + °65737) — k? (18681 —°33523 + °21912) + &e.? = bp, 0774 {h3 x *21492 —K? x 02071. The moment on the two floats becomes 1 ppo*r? $120 + 8(k—tan-? k) sin O— log, (1+) x 8 +2log, (1+#?)(@+4sin 20) +7 tan—'k (sin @—4 sin? 8) — (142k) [(k—tan—'k)2sin0 + slog, (1 + k?)(0+ $sin2@) +4 tan—1k (sin @—t sin? 6) | 4+ 4(1 +24)? [log,(1 + 4?)(0 + 4sin26) + 2tan-"k(sind —1sin?6)] } = 1p wr? {(k—tan—' k) (sind —4ksin 8) + (# —log, (1+ k?)) x 9 —tklog (1 +h?) (0+ 3sin20) + Shlog (1 + k?)(0 + $sin2@) +i? tan—' k (sin 0—1 sin? @)} | =1p,0r° \(3- ‘ya —4k) sin 0+ . 0— . _ a )O+8 sin 26) } + e (0+ 4 sin 20) + (e- (sin 6— sin? 6) \ = 4p, 0% §13(-11401 —-38523 + 32868) + k4( —:45604 + °17453 + °33523) — k°(:06840 —-16761 + -10956)} =} pw*r? $k? x 10746 + 4 x 053872 —k? x 01035}. * Hence the resistance on a pair of floats e = tp, w?r* {518256 — (1+ 2k) x *234563 —4(1 —4k?) x *259202 — k? x +21492 + kh? x :0207} | = 4 p,w*r4 {-149092—-k x 469126 + k? x 518404 —F? x -21492 +k? x 0207}. as Floats for Paddle-wheels. — 355 And the moment of the resistance on them = $ pwr? {573869 — (1 + 2k) x 513256 +4 2 (1+ 2k)? x 493765 —k? x 10746 —K* x 05372 +k? x -01035 } = p,@°r? {184054 —k x 582747 + h? x 493765 — kh? x *10746 —k* x (053872 +k? x -01035}. 1. When the vessel is going at a uniform speed, the amount of useful work done by the resistance in a unit of time is Rv, and the amount done by the engines is Ma, therefore be is a measure of the efficiency of the paddle-wheel. (1) In the case investigated in my former paper k=0; therefore Ro _ 7149092 1 _ Mo °184054 ~* 2 (2) Now, if we suppose that all the portions of the floats which are within a distance of half the radius from the centre of the wheel to be cut away, then k=4. Substituting this value for & we get ='405. Resistance =4 p, w*r* x 04266, Moment =43p,o*r? x ‘05674. Now = 5 (1+24). And Flin the vessel is going at full speed, the measure of the efficiency is Rv i ‘04266 5 4266 ema ea}; 6 bee (3) If we suppose that the innermost portion of the float is at a distance from the centre equal to two-thirds of the radius of the wheel, then K=4, and we get Resistance = 3 p,@ 274 x ‘01856, Moment =4p,?r> x ‘02465. Also . a a ie g (L+ 2h) =r; 1856 i therefore the efficiency = 9465 465 = =e 7Da. If the velocity of the vessel be 10 knots an hour or 1000 feet 356 Prof. Adams on the Application of Screw- Blades in a minute nearly, and 2 the number of revolutions a minute, then 2a77n=o and 1000 gt 2= a If, as in the case of the ‘ Elfin,’ the radius of the ais is bh feet nearly, then therefore 3000 90 14+2k= a aie nearly ; therefore if =A showing that, if the number of revolutions a minute be 45, then all that portion of the blade should be cut away which is within a distance of the axis of the wheel equal to two-thirds of the radius ; 7. e., half the blade should be cut away. In the trials with the ‘ Elfin’ (see the report in the ‘ Times’ of April 5th) the area of immersed screw-blades when complete was 72 feet; hence theoretically, with forty-six revolutions a minute, rather more than half the blade should be cut away, leaving an area of about 35 feet; practically it was found that the speed was the greatest when the area was reduced to 32:7 feet, show- ing a very close agreement between the theoretical and experi- mental results. (4) If the radius of the paddle- wheel be 9 feet, then r=6 feet, and Jaf +2k). If we again suppose the velocity to be 10 knots an hour or 1000 feet in a minute, and the number of revolutions a minute to be 33, then v 1000 oa 200 and £=4, or one-third of the float should be cut away. If the number of revolutions a minute be only 28, then v _ 1000 o 166 and k=4, showing that im this case one half of the blade should be removed, or that no part of it should be at a less distance from the centre than two-thirds of the radius of the wheel. —5, =6 nearly, te =43, then s=4, and for a velocity of 10 knots an hour @ as Floats for Paddle-wheels. 357 the number of revolutions a minute must be 36. The efficiency Rv _ :060871 vote "060871 3 _ neg Mo ‘079887 ~ wr — -079887 * 4°" (5) In the case of the flat float with paddle-wheels of the same radius and making the same number of revolutions with the same speed, the efficiency Rv 0234 so ae 0234 1 557: Ma 02D ar 02h, 887674 so that the flat float is not so advantageous as the screw-blade with the portion nearest the axis cut away. Cases (4) and (5) may be compared with the case which fol- lows, so as to determine whether it is more advantageous to have screw-blades with the inner portions cut out, or complete screw-blades of the same size, but having their axis at a distance from the centre of the wheel greater than one-third of the radius. Another point to be considered is, what should be the pitch of the screw-blade at the circumference of the wheel? If vy be the pitch, then the blade extends to a distance (a+7 cot y) from the axis of the wheel, a+r being, as in the case already consi- dered, the distance from the axis to the point where the pitch is 45°. Therefore for the superior limit of p in this case a* + p?+ 2ap cos O= (a+r cot y)?=r? cot? y(1+A)? [where a=”r cot y], or a (./1+2X+2? cos? 6—X cos 6) . cot y. Considering the float to be a complete screw surface having its axis at a distance a=rAcoty from the centre of the wheel, the lower limit for p will be 0. Let (\/1 +22X+2? cos? 9—X cos 6) cot y=q. Then the expressions for the resistance and moment on one float are these : R=3p, of (ag cos 0d0 +f cot y cos? @ log (1+ q?) dé -{a —* cot? y cos? 0) cos 8. tan“! g. dd “ — cos? O log (1+?) dO — Kea = ee 3? =! } in (20 cot y 2 )heo @ .tan-! q.d0 358 Prof. Adams on the Application of Screw-Blades =sp0%t (og cos 6d? — \ tan—! qg cos 0d0 ae @ cot y— 5) feos 6 log (1 + q°)d0 2) (cos? o.. tan gi } u oe y- =) {eos 9 .tan-!qd0 -, Q M=4p,o?r® { iC dO + {ae cot y cos 0d@ ts (3 (1—8n? cot? y cos? 8) log (1+ g?) dO -{e—. cot? y cos? 6). A. cot y cos 6 tan—! gdO ay = [2 cos 6d@ +fr cot y cos? @ log (1+ 9?)d8 -fa —n? cot? y cos? 8) cos @ tan! gid | 1 v* 2 2 +3. as J cos 8 log (1 + q?) dé 2 4 <= - cot feos Otan-! q. ao } 2 = por" {\t do— {3 log (1+ 9*)d@ +o cot y. g cos 0d6 — fa cot y.tan—!q.cos 0d0 +2 @ cot y— =| {a cos 0d0— \tan-'q cos @. a | v v : +4 @ cot y— = (80 Cot ae feos # log (1+ g?) dé +2 cot @ cot y— 2). cos? 6. tan—! gd0 - : “4 od OO J These equations for R and M will apply to all cases by giving different values to A, y, and the limit of 0, and by putting g=k if any portion of the screw-blade of width kr be cut away,—re- membering that the radius of the wheel =r coty(1+A), and that the axis of the screw-blade is at a distance equal to Ar cot y as Floats for Paddle-wheels. 359 from the axis of the wheel. It may be noticed that if the velo- city of the vessel be equal to the velocity of rotation of the edges of the blade nearest to the axis, then v a =X cot y. In practice it is found that the efficiency of a screw is greatest when its pitch is about 25°; with this pitch the limit of 6 must be increased, otherwise the breadth of the wheel will be dimi- nished ; also it appears from the above cases, and from the experiments already made, that the distance from the axis of the screw-surface to the axis of the wheel should not be less than half the radius of the wheel. If then we take A=1 and y=263°, so that cot y=2, then g=2( V3-+ cos? @—cos 8). If the limit for 0 be 25°, then the breadth of the wheel will be +2ths of the breadth in the case which has been already inves- tigated. With these values of X and y we get R= ror{ (iy cos 6dé — {tan q. cos 0d@ vihge 2 Q +(2 s) feos 8 log (1-+ 9°) dé eX? =5 (2- =) feos @.tan-'gq. ao. wr 2 M=tpor{ (¢ dé + (24 cos 0 dO — | 2 tang. cos 0 d0 , : 3 +2(2— =) | s cos 6 d0— \ tan—'q . cos 646 | S 4 (2 5) =| (6— 2) feos @ log (1+ q*) dé Q +2 (2- 2) {oss @.tan-} gdb }. 360 Application of Screw-Blades as Floats for Paddle-wheels. Values of the Functions to be integrated, the limits of integration being 0° and 25°. cos 0. g- gcos@. | tan—1q¢.cos0. 21 | -999048 | 2-000954 | 1:999050 | 1-106286 2 | -991445 | 2-008582 | 1:991398 1-099373 121 | -976296 | 2:025916 | 1:977894 1-085919 173 | -953717 | 2047096 | 1-:952350 1-064724 221 | -923879 | 2:0783836 | 1-920132 1-036906 271 | -887011 | 2117912 | 1:878611 1:002026 q°. log, (1+g?). [loge (1+ 9’) .cos’®.| tan_* g . cos 0. 23 | 4-003818 1-610201 1:607138 1:104182 4 | 4034400 1:616294 1:588757 1-080642 123 | 4:104337 1:630090 1-553727 1035043 173 | 4:190604 1:646850 1:497935 "968447 221 | 4319480 1671375 1:426608 “885054 274 | 4:485553 1:702117 1:339206 “788382 Hence, by the same method as in my former paper, ae *r4J -388103 + (2— =) x 669379 v \2 4 (2- ~) 442383 |b, M= 1pyo%4 1-820900 ty (2- = x 776207 + (2- =) (s— -)x 334690 @r @r v 2 + (2— >.) x 884766 }. @r (6) If the radius of the paddle-wheel be 9 feet, then (1+A)rcoty=9, and r=2, or 7 equals 1th of the radius. Supposing the speed of the vessel to be 10 not an hour, and the engines to be making 36 revolutions a minute, then v — =A ®@ TS) be and (2- =| = @r In this case the velocity of the vessel will be equal to the velo- Dr. Matthiessen on the Specific Resistance of Metals. 361 city of rotation of the edge of the blade nearest to the axis, and for one float R=}p w*r* x 388103 =4p,w* (radius)* x ‘001516, M=$p,*r? x 1°320900 =4p,0? (radius)° x ‘001290. Tueref pre the efficiency at full speed Rv _ 001516 ie 001516 1 Mo -001290 * w(rad.) -001290 * 2 showing that a screw-surface which has the part nearest to the axis cut away is not so advantageous as a complete screw of the same size which has its axis at a greater distance from the cen- tre of the paddle-wheel. In consequence of the proximity of the paddle-wheel to the side of the vessel, it is found that the inner blades do not throw the water under the vessel, but against the side, so that it can- not escape; hence it has been found necessary to make all the screw-blades on the same wheel of the same kind, and to place them so as to throw the water outwards. As the pressure pro- duced on the water is precisely the same with a left-handed as with a right-handed screw, it is quite clear that the results of the mathematical investigation will be equally trustworthy, whether the corresponding screw-blades be of the same or of opposite kinds. = G0 5 LI. On the Specific Resistance of the Metals in terms of the B. A. Unit (1864) of Electric Resistance, together with some Remarks on the so-called Mercury Unit. By A. Matruinssen, F.R.S., Lecturer on Chemistry in St. Mary’s Hospital*. A’ the B. A. unit will doubtless come into general use, it may not be out of place to give the resistance of the metals and some of the alloys in terms of it. Mr. Hockin and myself have determined +, in terms of this unit, the values of the re- sistance of certain lengths and weights of wires of several metals and one alloy; and when reduced to the same length and weight, namely, a metre long and gramme weight, we found their resist- ances to be, for hard-drawn wires, * Communicated by the Author. t+ Not yet published. These experiments were carried out for the Com- mittee appointed by the British Association to report on Electrical Stand- ards, and will appear in their Report of 1864. Phil. Mag. 8. 4. Vol. 29. No. 197. May 1865. 2B 362 Dr. Matthiessen on the Specifie Resistance of the Metals TABLE I, Resistance in terms of B.A. unit (1864). Coppet s)he ke we (Oe Silver os. eS oe lige Gold: 328 TAS Oa Lhéade G0 RO ie ae ee Merenry’ .4 6... toe Gold-silver alloy. . . 1:668 _ These values are called by Professor William Thomson and Mr. Jenkin the specific resistances of the metals at O° referred to unit of mass and length. When carrying out the above determinations, we did not think of taking the specific gravity of the wires employed, as our object was only to see to what accuracy we could reproduce resistances by using wires of the above metals, &c. We employed the length weight in preference to the length section, knowing that the weight of a wire may be much more accurately determined than — its section, whether deduced directly from the measurements of the diameter or indirectly from the specific gravity, the determi- nation of the latter introducing a certain error. Of course, in endeavouring to reproduce resistances, it is wise to avoid the use of any unnecessary values ; and it is just as well, and certainly a much more accurate method, to determine a resistance in length weight than in length section. A strict comparison with former values will not be possible, owing to the above fact. Approximately, we may compare them by using the following specific gravities :— TaBxe II. Conducting-power Resistance in terms of hard-drawn wires of the B. A. unit. of metre length and Specific gravity. millimetre diameter. Silyer* .. ©... 10:50 0:02048 48°83 Copper* . 8:95 0:02090 47°85 Gold*....1.. 19:27 0:02742 36°47 Lead* . . 11°391 0:2527 3°957 Mercury . 18°595 1:224: ‘ 0°8172 Gold-silverf 15°218 0°13899 7°148 Or taking the conducting-power of the gold-silver alloy, 7°148 =15:03, the following will be the values of the conducting- powers of the metals and some of their alloys :— * Of cast specimens. © + Of the wire. in terms of the B. A. Unit (1864) of Electric Resistance. 363 = Taste III. (Temperature of all, 0° C.*) ve . , Specific conducting-power Ss ae A ae in terms | of metre length dat aa: of the B. A. unit. metre diameter. Hard- | An- Hard- An- | drawn. Pressed. nealed. | drawn. Pressed. nealed. | SLE) ee 0:02103 | ....... O-01937.\.- AZ-56. he check 51-63 Copper ...........- 002104)... 002057 47:53 | ...... 48-61 lie ee BE ee W02697 | 0250. 0:°02650| 37-08 | ...... 37°73 | Whe ee. oe, POSTE GA t Wee 26-66 | Magnesium ......| .+-- Oe Ree eae O-OS106 1.) .2cc0st ., bape 19°58 7 i ee ee pelo ECS 4 tg a 13-80 Se OSS cco, «| Y cakes 11°28 Pallaiiny 2.022012.) 203.5. Boag Spas PO ULAGy | 58 or eae — 877 | Platinium. ........- De st By gece dat OPLIGE be nok.8d oe 8-58 | oo ee er eh 1 2k ee, Sate A 8-19 | ll eS Pretesemee OnI2aeeew tore 1 eee 799 | Lob ee ee ee (GUS. 8 3 OTRO i 5 ks Pa 6°23 | es ee O1ZOL | sere | sees 5:88 SS a eee | 922906 | rere, | seeeee 4°36 ie pe ago O-2527) ee So 3-96 | Arsenite “2...2.:..... babs Ae 0°4417 Abia sok Hee [A Sed 2-27 Anemmony }sici2c.|.s.3.-- 0:4571 | EME Nes Dap pees 2-19 SO es CREE ae RR 0-591 ULL ree 1! EA al Mi Btn 0-788 cereal } — Meare at 3:18 Se | German silver ...| ...... 02695 | oteeees 3°71 | Gold-silver alloy...| | ...... (MIE Es sana gee Bees 7148 | The platinuin-silver alloy contains 66°6 per cent. silver, and is that alloy which has been used for making the copies of the B. A. unitt. On comparing these values with those deduced from the actual ones found, as given in the second Table, we find a difference with the silver of about 3 per cent. This is explained in our paper by the fact that the silver wire used was drawn in a peculiar manner; and on referring to another paper{, like differences will be found in the conducting-power of silver. The differences in the other cases will be chiefly due to not using the correct spe- cific gravities; thus, for instance, the specific gravity of copper used was 8°95. Siemens§ found it to vary for wire between 8°89 and 8°92; using the value 8°91, we find the conducting-power to be 47°64. * Phil. Trans. 1864, p. 197, value for lead given in the Table is wrong; it ought to be 8°32, and not 8°23 (see Phil. Trans. 1862, p. 16). Tt Report of the British Association, 1864. t Phil. Trans. 1862, p. 6. § Poggendorff’s Annalen, vol. ex. p. 18. 2B2 364 Dr. Matthiessen on the so-called Mercury Unit. Again, the specific gravity of gold used is 19°27. The specific gravity given in Gmelin’s ‘Chemistry’ for gold wire is 19°3 to 19-4. Using the value 19:4, we find the conducting-power to be 36-72. The differences between the values obtained for the mercury (namely, about 3 per cent.) show how difficult it is to obtain good results with this metal when only ordinary care is taken in experimenting. No doubt these differences are due to the manner of calibrating and deducing the values for the diame- ters of the tubes employed in my first experiments, published in 1858*; and when determining at a later period} the influence of temperature on its conducting-power (finding with the one tube we used nearly the same value), we did not think it neces- sary to repeat the determination. The value given by Mr. Hockin and myself is, as will presently be shown, probably the correct one. In my papers on the conducting-power of metals and alloys, I have advocated the use of the gold-silver alloy as a ready and practical means, where only ordinary care is employed, of repro- ducing resistances. Here, again, we find my statements correct, for the values deduced by it agree well with the old ones, especially the lead one, a metal which has been recommended by Mr. Hockin and myself as eminently fit for the reproduction of resistances where great care isemployed{. Of course it is to be hoped that no one will try to reproduce any unit by means of this or any metal, now that the B. A. unit has been issued §; for they will certainly not obtain such accurate measures (without an enormous trouble and expense) as the copies of the B. A. unit at present issued by the Committee appointed by the British Asso- ciation; and as proof of the correctness of this statement, I would draw the special attention of those who would endeavour to reproduce a unit, first, to what has been stated in the Reports of the Committee published in the Transactions of the British Association, and secondly, to the remarks I am now about to make on the sco-alled mercury unit. It is defined as the resistance of a column of mercury a metre long and a square millimetre section at 0°. Now it may be asserted :— lst. That no true mercury unit has been issued. 2nd. That the units issued from time to time have not the same resistance. lst. That no true mercury unit has been issued. This assertion * Phil. Trans. 1858, p. 383. T Ibid. 1862. { The specific gravity of lead is said not to alter on _being hammered or rolled (Reich, Journ. of Pract. Chem. vol. lxxvui. p. 730). § Copies of which may be obtained from the Seeretary to the Committee (see Phil. Mag. vol. xxix. p. 248). Dr. Matthiessen on the so-called Mercury Unit. 365 is based on the fact that for the calculations the wrong specific gravity of mercury has been used, viz. 18°557 at O° instead of 13°595 as found by Regnault, Kopp, Balfour Stewart, and Neumann. These observers all give the same value for the spe- cific gravity of mercury at 0° as compared with water at 4°. (Their values only vary up or down 0-007 per cent. from the above value, the maximum being 13°596, and the minimum being 13-594.) These data prove either that no true mercury units have been issued, or if 13°557 be the true specific gravity of mercury at O°, then the experiments of Regnault, Kopp, B. Stewart, and others must be all incorrect—a highly improbable result ; in fact, one is irresistibly led to the conviction that it is utterly impos- sible that those distinguished observers can all have made such mistakes, and therefore that the value used, viz. 13°557, is wrong, and the units issued, supposing them to be otherwise quite correct, will each have a resistance about 0°3 per cent. greater than it ought to be. | 2ndly. That the units issued from time to time have not the same resistance. In the Exhibition of 1861 were two sets of coils said to be reproductions of the mercury units ; now the one set was exhibited by Siemens (London), the other by Sie- mens (Berlin), and when the two sets were compared with each other they showed a difference of about 12 per cent. The value of the resistance of these two units in terms of the B. A. unit is as follows :— Siemens (London). . . . 0°9750 Siemens (Berlm) . . . . 0-'9682 These values have been obtained in the following manner :— Mr. F. Jenkin, in his Report on Electrical Instruments (Jurors’ Report, 1862, p. 82), gives a Table containing the values of different coils, and on reference it will be seen that the coil whose resistance equals a mile of pure copper, &c., is equal to 13:95 Siemens (London) and 14°12 Siemens (Berlin) units. Now, when I adjusted this mile coil for Messrs. Elhots Brothers, I made another coil of the same resistance of different German- silver wire, and arranged it in a perfectly different manner from the coil tested by Mr. F. Jenkin. On comparing these two coils with each other after the lapse of three years, they were found exactly equal, showing that they had not altered ; for it is hardly probable that two different specimens of wire put up in different methods should alter in resistance to a like extent. . Again, another proof of the mile coil not having altered is the following. Mr. F. Jenkin sends me the following value :—Thom- son’s coil (one in my possession, a duplicate of that sent to 366 Dr. Matthiessen on the so-called Mercury Unit. Weber) was found by him in 1861 equal to 4°025 Siemens (London) units. That Thomson’s coil had not altered during this time was proved by comparing it again with a coil of wire of the gold- silver alloy which I made, and compared with the coils before they were sent to Weber in 1860. The new comparison agreed identically with the first one. Thomson’s coil =4°025 8. (London) units =15°543 of an arbi- trarily chosen unit, made for my own experiments, Mile coil. =53'780 ditto; and therefore the mile coil =13°93 Siemens (London) units, proving that the mile coil has not altered, for Mr. Jenkin gives the value equal 13°95*, showing a difference of rather more than 0°15 per cent., a difference, considering the roundabout way the value is arrived at, which is very small; in fact it is much smaller than the differences of which I have now to speak. Now the mile coil equals in resistance 13°59 B. A. units. Mile coil equal 13:95 Siemens (London) units, 33 99 14°12 ” (Berlin) units, therefore Siemens (London) unit. . . . . . =0:9750B.A. units. a (Berlin) Po Se * =0-9632 i A new unit issued by the ane in 1864. = 0°9564. - It would be of interest to know which of these units Messrs. Siemens consider the correct one. Owing, however, to their using the wrong specific gravity for mercury, the values for com- parison with others must be corrected by multiplying them b 13559 Y 73-595 of mercury of a square millimetre section at O° according to 33 ——-~—» when we arrive at the following values for a metre True value in B. A, units. Siemens (London) unit, . . . 0°9723. 4 (Berlin) 3770). 2 2 Opes (TS64) ee eer Meanie) oie 0:9620 Value deduced from experiments made by Mr. Hockin and maa bo 9619 (1864) i From the above we see how Be the Siemens (Berlin) coil * Mr. Jenkin informs me that the values given in his Table may possibly be 0'1 per cent. wrong ; he does not think that any of them are 0°25 per cent. wrong. Dr. Matthiessen on the so-called Mercury Unit. 367 “agrees with the last value; andas the true value for the resist- ance of the mercury unit, as defined by Messrs. Siemens, we may take 0-961 B.A. units, a value differmg from their 1864 issue by about 0°5 per cent., and when corrected for specific gravity, by about 0°8 per cent. Now why do these differences exist? Are we not led to think from the papers written by these gentlemen, and others working in their laboratory, that the reproduction of the mercury unit is the most simple thing possible? I will quote what one of them says on the subject. Mr. R. Sabine states*, ‘Following this method, every electrician may inexpensively and with little trouble make himself a standard measure.... The mercury unit has there- fore been reproduced in Dr. Siemens’s laboratory twenty-one times, six times in the first determination, five times in the second, and ten times in the present. And,allowing for the unfortunate misrepresentation of the measure by individual errors of the measuring-apparatus used in the comparison of the first tubes, the agreement between them all is greater than could be gua- ranteed between any two single electrical measurements with different measuring-apparatus....From the foregoing results it follows that, by the method of direct production proposed by Dr. Siemens, much greater exactness has been attained than by means of any other of the methods of determination or copy- ing.” I cannot allow the above passage to pass unnoticed, for it will be apt to mislead many who have not worked in this field of research. In the first place, we are told that this method of reproducing resistances is inexpensive and causes very little trouble. It may be inexpensive to those who possess first-rate apparatus for normal weighings or measurements, normal thermo- meters, &c.; for with first-rate apparatus only normal results can be obtained. Then, as to the trouble; does anybody for a mo- ment suppose that a standard measure can be reproduced with a little trouble? Would it not take any observer weeks to re- produce with accuracy a resistance which can be relied en? must not such an observer check and recheck every determi- nation he makes? must not he be sure all his instruments are graduated accurately ? and he can only be sure of this if they are carefully tested by himself, or by perfectly reliable persons ; and, what is of very great importance, must he not be sure that he deals with an absolutely pure metal? Did not Mr. C. W. Sie- mens himself state at the meeting of the Royal Society when remarks had been made upon Mr. Jenkin’s paper on the B.A. unit, that he was loth to give up the use of the mercury unit, as he was afraid the B. A. unit could not be accurately reproduced, * Phil. Mag. vol. xxv. p. 172 (1863). 368 Dr. Matthiessen on the so-called Mercury Unit. for experience in reproducing the mercury unit had taught him the great difficulty of such operations? I think Mr. Sabine’s sentence that I refer to would have been more correct if thus written :— Following this method, every electrician may, with perfect apparatus, &c., and with a very great deal of trouble, by taking some weeks for his determinations, together with the use of all precautions to ensure normal results, as well as employing proper constants and coefficients for deducing and correcting the values so obtained, make himself a standard measure. In the second place, we are told that the unit has been re- produced twenty-one times, and that, allowing for the unfor- tunate misrepresentation of the measure by individual errors of the apparatus used in the comparison of the first tubes, the agreement between them all is greater than could be guaranteed between any two single measurements with different measuring- apparatus. The first tubes show, as I have elsewhere pointed out, a maximum difference between the calculated and observed resistances of 1°6 per cent., and this differenee is said to be caused by errors in the measuring-apparatus. Assuming this to be the case, it proves that the precautions to be adopted in adjusting the appa- ratus must be very great. For if in Dr. Siemens’s hands, with his skill and with such good apparatus as is described in his paper, such errors can occur in his endeavours to reproduce this unit, how much more are errors to be feared from others who have not such good apparatus at their command! As to the agreement between the other reproductions being more accurate than an two measurements with different apparatus, the following facts will constitute a good answer. 1. The Messrs. Siemens’s reproductions, they state, agree within 0:05 per cent. Two coils* were compared with each other some years ago (the one German silver, the other gold silver), and now, with different apparatus and by a different ob- server, they were again compared : the ratio of their resistances was found absolutely the same. 2. The Messrs. Siemens have issued an 1864 mercury unit. Now four different copies of this have been compared with four different copies of the B. A. unit with four different measuring- apparatus, and by four different observers +, and the ratios of the resistances, as determined by the four observers, do not vary between each other more than 0-02 per cent. - | In the third place, we are told that, by direct production, much greater accuracy has been attained than by any other method of determination or copying. * See Report of Electrical Standard Committee, 1864. + See Report on the B. A. Unit, by F. Jenkin, Proc. Roy. Soc. No. 74. Dr. Matthiessen on the so-called Mercury Unit. 369 Copies of a unit may be made, I maintain, to any accuracy required: all the B.A. units agree together, when issued, to within 0-01 per cent., of course at the temperature stated on them : they are all kept a month after making; if during that time they alter in the least, they are taken to pieces and remade ; out of fifty already made, only two have had to be altered, the cause of failure being in both cases faulty soldering. This statement, together with the above fact of the four dif- ferent copies of the 1864: mercury unit agreeing so well together, prove that copies of a unit can be, and are, made to agree together much more accurately than it can be reproduced even when great care is taken. If the reproduction of a unit be so easy a matter, how are we to explain the large differences observed in the copies of the different issues of the mercury unit. The simple truth is that the reproduction of any unit, where great accuracy is required, is exceedingly difficult. Take, for instance, the repro- duction of the normal pound by Professor Miller of Cambridge: one would think, at first sight, nothing easier; but when we enter into the minor details, we find how difficult the problem was to solve. It would have been better if, instead of reproducing the unit from time to time, Messrs. Siemens had done what the Com- mittee on Electrical Standards appointed by the British Associ- ation have done—namely, first determined the value of their unit as accurately as possible, and then made copies of it in several different materials. It is not possible that all these copies will alter to a like extent by age, and it is very probable that most of them will not alter at all: they will, of course, be tested from time to time; and at the Kew Observatory, where they will be deposited, arrangements will be shortly made for comparing also, from time to time, at a small cost, the coils issued by the Com- mittee, thus offering a ready means of ascertaining whether the coils issued are constant or not. The coils issued by the Com- mittee are copies of the B. A. unit, and at the temperature marked on them are correct to within O-Ol per cent. By using these coils, the results of different observers become comparable. The Committee of Electrical Standards do not wish to imply that the resistance of their unit is exactly equal to 107 22°, Weber’s electromagnetic units, but only a close approximation to it. If in a few years’ time new and more ac- curate determinations be made, then, supposing a correction required, the copies of the B. A. unit (1864) being all exactly equal to one another, will have a small value to be added to or subtracted from their resistance, and all the comparisons made with them corrected by the same coefficient. 370 Mr. J. J. Waterston on some Electrical Kxpermments. Had the Messrs. Siemens followed this plan, then the use of the wrong specific gravity would not so much influence the value of their coils as means of comparison, as the differences in the values of the coils themselves ; for when we find a Siemens unit used, we must first discover what value it has, because, as already pointed out, the different issues have different values. LIL. On some Electrical Experiments. By J.J. Waterston, Esq. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, . Ec § 30 of the paper on Electric Experiments, I have in- advertently stated that the leaves of the electroscope diverged with negative electricity, stead of positive. The experiment was mneant to direct attention to a simple mode of proving, by means of a Leyden jar and electroscope, that the force of electric induction is capable of acting in curved lines, a fact which appears to deserve that distinct announcement due to a fundamental characteristic of the electric force. Suppose we take a coated plate of glass properly insulated, and- charge it highly with positive electricity on the side A, and ne- gative on the opposite side B. After leaving it in this charged state for a few seconds, let an electroscope be brought with its cap near the centre of A, but not touching it : the leaves are found to diverge with positive in consequence of the free positive on the outer side of coating A acting inductively on the cap of elec- troscope, exciting upon it negative, and on the gold-leaves a cor- responding amount of positive. In the same way, if we remove the electroscope from near A and place it on the opposite side close to centre of B, the leaves will diverge with negative from the action of the free negative on the outer side of B. While the electroscope is thus stationed close to B, let A be touched: the leaves-increase their divergence, showing that the free negative on the outer side of B has received an augmenta- tion. The electroscope is then to be immediately removed to the opposite side, and the cap made to touch the centre of coat- ing A. The leaves do not open, there is no longer electric excitement on the outer side of A: it has been discharged by touching. If we gradually remove the electroscope further away from the plate, but still keep it opposite the centre of A, the leaves diverge with negative more and more until a certain maxi- mum is attained, after which they gradually sink as the distance is further increased. The imductive action cannot come from any part of the adjacent coating A, which is altogether positive; it Mr. J. J. Waterston on some Electrical Experiments. 371 must therefore be supplied from B, the free negative on the outer side of which thus acts not only on the B side of the plate, but on the A side also, to attain which it must pass round the edges of the coating A. Faraday supposes this to take place by means of the action of contiguous particles of air; and hence it is to be presumed that it is his belief that a charged pane could not exist in an illimitable vacuum, or at least that the electricity on B could not affect an electroscope on the side of A, because there would be no conti- guous particles to transmit the force. This hypothesis has been supposed to be further supported by the apparent augmentation in the force of induction that takes place when a plate of lac or sulphur is interposed between the charged body and a neighbouring conductor ; and the term specific inductive capacity, applied to denote the degree of the special fa- culty of transmitting the mductive power belonging to the parti- cles of a given non-conducting body, seems to be now established, Harris having published experiments as supporting Faraday’s views, and teaching them in his elementary treatise. As this term appears to me inapplicable to matter in rela- tion to electric phenomena, I beg to submit the following experi- ment as demonstrating the non-existence of such a quality. An insulated brass disk (the B. D. of previous experiments) is suspended over the cap of the electroscope at the distance of 2 inches above it. A cake of sulphur, 4 inches in diameter and 3 -an inch thick, is provided with handles of sealing-wax projecting about 10 inches from each side. It is examined to see if there is any excitement upon A; and if any, discharge is effected by presenting it to a flame. The B. D. is charged from an electro- phorus so that the leaves of the electroscope diverge to about 60°. The cake of sulphur, supported by its handles (which enable the hands of the operator to be kept at such a distance as not to influence the electroscope), is brought horizontally into the space between the B. D. and cap of the electroscope. Itis then moved parallel up and down ; now close to the cap, then close to B. D. When close to B. D., the leaves are not at a higher angle than before its imtroduction; but on bringing it down towards the cap the angle increases a little, and when quite close to it the angle increases considerably, and this notable augmentation takes place within a distance of about 1 of an inch from the cap. The experiment requires to be promptly per- formed, because the sulphur soon becomes inductively excited in the manner peculiar to non-conductors and as, to a certain degree, developed in the previous experiments. On first bringing the cake between the B. D. and the electroscope, the leaves descend a little just as the edge cf the cake passes in between the outer 372 Mr. J.J. Waterston on some Electrical Experiments. edges of the B. D. and cap. Next let us take a metallic disk of the same diameter as the cake, and having also applied similar insulating handles, introduce it and move it up and down between the B. D. and cap without touching either. The leaves of the electroscope will be found to be acted upon in the same way as before, but in a greater degree. I submit that if the sulphur had a greater capacity than air of transmitting induction, the leaves of the electroscope ought to rise higher when the cake is close to the charged B. D. than when it is close to the cap of the electroscope. In the latter case the increase of the angle of the gold-leaves was fully as great as when the electroscope was brought half an inch nearer to the B.D. In the former case no increase of induction was apparent. The same experiment, repeated with sealing-wax and gutta- percha plates, showed similar results, but more striking. When close to B. D..the inductive force was less than through air; when close to the cap it was greater. [Gutta percha shows some curious abnormal effects, especially when heated and _ soft. Although it is then still a perfect non-conductor, it seems to absorb the inductive force like a sponge.] A change in the shape or size of the non-conducting plates modifies the result, exactly in the same manner as the conducting plates, though always in a Jess degree. The proper way of studying the sub- ject would therefore seem to be to experiment with conducting and non-conducting plates of the same size, and guard against the effect of induction upon the non-conducting surfaces, which seems to be a phenomenon ofa special kind, that stands in need of further elucidation. [I have not been able to arrive at any distinct law of action. The transition from one kind of induction to the other may be conveniently studied in a warm room during dry weather, by placing a shade of thin glass over the electroscope, of such size that the round top may be about an inch above the cap, the agent being an insulated brass disk (the B. D.) charged induc- tively from an excited plate of sulphur. If we moisten the out- side of the shade with a sponge and bring the excited B. D. close to the top, but not touching, there is of course no effect on the electroscope, the surface is opake to the electric force; the in- duction is confined to the aqueous surface opposite the B.D. . As the shade dries we observe a slight effect on the gold-leaves, which becomes more and more apparent as the glass resumes the dielectric condition. Let the shade be now heated before a clear fire, and replaced, when cool, over the electroscope. We may now study the effect of moving the excited B. D. to and fromthe top of the shade. If the action is performed without pause, the leaves open and shut in the regular normal way ; but _ Mr. J.J. Waterston on some Electrical Experiments. 373 if the B. D., when close to the top of the shade, is kept in posi- tion for a few seconds, the leaves sink a little (showing a decre- ment A of the inductive force acting on the electroscope, although there is no decrement of the charge on B.D.) ; and on removing it they shut and then open with the opposite electricity, and the extent of the opening corresponds to the decrement A, thus showing that the top of the glass shade has been inductively excited by B.D. But this excitement is evanescent, the leaves subside in a few seconds. The explanation of such phenomena that first presents itself is, that the outer surface of the shade is a partial conductor ; but if this were the case, how is it that on bringing theB. D. into contact with the glass shade it does not lose charge, although its intensity is much greater than the induced excitement which so quickly passes away? The lesser intensity cannot be conducted more easily than the greater. Insulating the glass shade, by resting it upon sulphur, makes no difference. It appears to be a constrained local polarization, in which the work-equivalent of the charge is partially expended in effecting a change of molecular condition ; but there is no separation of the electricities accompanied with conduction, as takes place on a truly conducting metallic surface subject to the inductive in- fluence of a charged body. Faraday’s view of static induction has led him to give a defi- nition of disruptive discharge, which I think is also unfortunate as tending to close further inquiry in the very direction most likely to lead to important discovery in the dynamical conditions affect- ing the relations of molecules to the higher potential medium. In recent educational works it is mentioned, not as a conjecture, but as an established fact, that “the particles of the intervening dielectric are brought up to a highly polarized state, until at length the tension on one particle rising higher than the rest, and exceeding that which it can sustain, it breaks down; the balance of induction is thus destroyed, and the discharge is com- pleted in the line of least resistance.”” In my tenth and eleventh experiments it may be remarked that the disruption that accom- panies discharge is hike what is caused by mechanical impulse of matter pressing with sudden and short-lived force. If this idea is kept in view and arrangements made in accordance with it, experiments on the discharge of high-tension electricity would, I believe, assume a new and exciting interest, and lead; if well planned, to a deeper insight into the arrangement of force in nature than we could otherwise hope for. T remain, Gentlemen, Your obedient Servant, Joun James WaTERSTON. Edinburgh, March 20, 1865. ire 7¢ eee LI. Chemical Notices from Foreign Journals. By E. Atkinson, Ph.D., F.C.S, [Continued from p. 313.] W ITH a view to finding an effectual method of separating from each other Mosander’s three bases, yttria, erbia, and terbia, Popp undertook an investigation of yttria. He has pub- lished the results of his investigation separately, and has given a summary of it in Liebig’s Annalen*, from which the following is taken. As distinct oxides he considers that erbia and terbia have no separate existence, or rather they are not the oxides of hitherto unknown metals, but are identical with the oxides of cerium and didymium. Mosander’s oxide of yttria contains both alkali and lime. Hence erbium and terbium, which have heretofore been regarded as elements, though not altogether without some doubt, must now be struck from the list. Pure yttria is separated from its accompanying earths by means of carbonate of baryta, which completely precipitates oxides of cerium and didymium even in the cold, but not yttria. It is necessary that the cerium be present as sesquioxide. When freshly precipitated, yttria closely resembles hydrate of alumina, and is of a pure white colour. A tinge of red indicates that it contains oxide of cerium. Ignited, it is a heavy yellowish-white powder, which, if quite white, contains alkali and lime. Hy- drated oxide of yttria corresponds approximately to the formula YO, 2HO. It is a strong base, and expels ammonia from its salts when boiled. In its relations to the alkalies it shows close analogies with magnesia. : All the yttria salts have a distinctly hght rose-colour, which is not caused by the presence of manganese or didymium, but is peculiar to them, and which they lose when they are dehy- drated. It is characteristic of the yttria salts that when a solution is interposed between the prism of a spectroscope and a strongly luminous gas-flame, five black lines are seen, which are quite dif- ferent, both in number, position, and intensity, from the similar lines of didymium. One of these lines is in the deep violet, and the other in the extreme red. The combining proportion of yttrium was determined afresh, inasmuch as Berzelius, who found the number 40, had evidently worked with impure yttria. Popp used the sulphate which separates from a boiling solution of sulphate of yttria, and which Berzelius had employed. The yttria was precipitated by means of oxalic acid, and the oxalate ignited and weighed. From the * August 1864. Chemical Notices :—M. Popp on Yttria. 375 relation of the sulphuric acid to the yttria found, Popp deduces the number 42 as the combining proportion of yttria, which, assum- ing that it has the composition YO, gives 34 for the combining proportion of yttrium. The metal yttrium was reduced from the chloride of ammo- nium and yttrium by means of sodium, in a manner analogous to that by which magnesium is prepared. While moist it is a black glittering powder, which, while drying, becomes lighter, owing to oxidation. When quite dry it does not oxidize in the air; at ordinary temperatures it only slowly oxidizes in water ; on boiling, the oxidation is more rapid, but even then is not complete. It is readily dissolved by dilute acids with disen- gagement of hydrogen. Heated on platinum foil, yttrium burns with intense lustre ; in pure oxygen the combustion is most brilliant; the colour is not of such a pure white as is that of magnesium and alumi- nium ; it inclines towards reddish. By the properties of the metal, as well as those of its com- pounds, yttrium is allied to magnesium ; and by its property of bemg precipitated by ammonia it is the connecting link between the alkaline earths and the earths proper. Some of the best-defined and most important of its salts are the following. The sulphide of yttrium is difficult to prepare. The best results are obtained by passing dry bisulphide-of-carbon vapour mixed with dry hydrogen over heated yttria. Chloride of yttrium, YC1+6HO, erystallizes in rhombic very deliquescent plates. Chloride of yttrium is non-volatile and a chloro-base; it forms with chloride of mercury easily soluble deliquescent crystals, which have the formula YC],2HgC1+6HO. Sulphateof yttria,2YOSO?+5HO, has the peculiarity that its solubility diminishes proportionally to the increase of temperature. At 30° to 40° its solution becomes turbid, and on boiling, all the salt separates out as a heavy crystalline powder. Nitrate of yttria, dissolved in alcohol and evaporated over alcohol, forms well-defined rhombic plates, which are deliquescent and have the composition YO NO®+3HO. Carbonate of ytiria, YO CO? +3 HO, is obtained, by precipitating a solution of yttrium with carbonate of sodium, as a gelatinous precipitate, which, digested with an excess of carbonate of soda, is converted into small white crystalline needles. The acetate of yttria is the most easily crystallizable of all the salts ; it has the composition YO Ac+2HO. Redtenbacher has described to the Vienna Academy of Sciences* an improved method of separating the metals potassium, rubidium, * Bulletin, No.8. 1865. 376 M. Redtenbacher on Cesium and Rubidium. and ceestum, which depends on the solubility of the alums of these three bases. All three alums are easily soluble in hot water; but while 100 parts of water at 17° C. dissolve 13°5 of potash-alum, they dis- solve 2°27 of rubidium-, and 0°619 of czsium-alum. Hence at 17°C. potash-alum is thirteen times, rubidium-alum fifteen times, _ and cxsium-alum eighty-eight times as soluble as the correspond- ing platinum-salts. And while the solubility of the alums in the different cases is as Potassium. Rubidium. Cesium. 22 : 4, : 1, that of the platinum-salts is 15 simerke : 1. By this deportment a way is opened for the separation and preparation of these metals on a large scale. Schiel describes* the following as a lecture experiment. A test-tube containing peroxide of silver, drawn out in the middle and sealed, is introduced into a well-dried stoppered gas-bottle, which is then filled with chlorine. The flask being closed, the tube is broken by shaking; the chlorine becomes paler, and im a few minutes the flask is full of colourless oxygen gas. The proportions of peroxide and chlorine must be those of their equi- valents. The peroxide is readily prepared by passing ozonized oxygen over dry oxide of silver. Poppt designates the following as the best of two methods which he gives for separating oxide of cerium from the oxides of lanthanum and didymium, with which it is usually associated. The three oxides, dissolved in acid, are approximately neutralized without producing a permanent precipitate. An adequate quan- tity of acetate of soda is added and then an excess of hypo- chlorite of soda, and the whole boiled for some time. The cerium is deposited as a bright-yellow precipitate, the other bodies remain in solution. The filtrate must not become turbid on the addition of hypochlorite and boiling; by careful and suffi- cient addition of hypochlorite in the first case, one treatment is sufficient, and every trace of cerium is precipitated free from lan- thanum and didymium. The yellow precipitate contains much water; it dries to a brownish-yellow, transparent and easily pulverizable. mass. It has all the characters of a peroxide, and is doubtless CeO?, it is formed in the same way as the peroxides of lead and manga_ * Liebig’s Annalen, December 1864. + Ibid. September 1864. M. Marignae on the Silico-tungstates. 377 nese. It dissolves in hydrochloric acid with disengagement of chlorine, yielding a solution of a clear saffron-yellow colour, which diminishes on dilution, and disappears completely on boiling. Nitric and sulphuric acids dissolve the peroxide with a reddish- yellow colour, forming corresponding compounds of the oxide. Popp finds that the peroxides of nickel and cobalt are formed in the same manner as that of cerium. Marignae* has found that when a solution of acid tungstate of potash or soda is boiled with gelatinous silicic acid, the liquid assumes an alkaline reaction, and is now found to contain a new acid in which 1| equiv. of silica is united with 12 equivs. of tung- stic acid, Si0? 12 W0O®, which he calls silico-tungstic acid. It is a powerful acid, which is easily separated from its salts, forms two splendidly crystallized hydrates, and salts which for the most part are soluble and crystallize well. Under the same circumstances as above, acid tungstate of am- monia gives rise to another acid in which an equivalent of silica is united with ten of tungstic acid, $107, 1OWO%, and which Marignae names silico-decatungstic acid. It is more difficult to obtain pure; its hydrate does not crystallize ; and from the very soluble character of its salts, it is difficult to obtain them in crystals. The acid itself is not very stable; when heated, a small quan- tity of silica separates out, and a new acid is obtained containing silica and tungstic acid in the same proportions as in silico- tungstic acid, but which in other respects is totally different, and which has accordingly been named tungsto-silicic acid. It forms a soluble and deliquescent hydrate, which can, however, be ob- tained in well-formed crystals. It forms a series of salts isomeric with the silico-tungstates, but differing from them in crystalline form, and in the amount of water of -crystallization, and also in being somewhat more soluble. All these acids are quadribasic, if the salt with 4 equivs. base is to be taken as neutral, and are formed when the acids act upon the carbonates of a base. The most frequent salts are those with 2 or 4 equivs. base; the first crystallize most easily. They have a great tendency to form double salts; hence it is that ammonia does not precipitate a solution of silico-tungstate of alumina, and that alumina, magnesia, carbonate of lime, &c. are dissolved by silico-tungstate of ammonia. As the salts of the acids are easily soluble, and contain a large quantity of tungstic acid, their solutions have a remarkably high specific gravity. The solution of silico-tungstate of soda has the specific gravity 3°05, so that glass, quartz, and most rocks float upon this, which is moreover a very mobile liquid. * Comptes Rendus, vol. lviui. p. 809. Phil. Mag. 8S. 4. Vol. 29. No. 197. May 1865. 2C 378 M. Weltzien on the Determination of Nitric Acid. Silico-tungstic acid crystallizes at ordinary temperature in thick quadratic pyramids, and which contain 29 equivs. water of crystallization, according to the formula SiO? 12W 02 4HO + 29Aq: if it crystallizes at somewhat higher temperature, or at ordinary temperature in the presence of alcohol, hydrochloric acid, or sul- phuric acid, it forms a hydrate which only contains 18 equivs. water of crystallization, and of a different crystalline form. At 100° the acid retains, besides the basic water, 4 equivs. of water of crystallization. On heating at 220° it loses the latter, but retains 2 equivs. of basic water: these appear necessary for the constitution of the acid; they are only removed at the temperature of red heat. wet Tungsto-silicic acid crystallizes with 20 equivs. of water of crystallization, and has the formula 12 W0O3, SiO? 4HO +20Aq. It is acted upon by heat in the same way as silico-tungstic acid. Marignac has made a crystallographic investigation of the salts of these acids; and although relations to other compounds have not been found (since these acids appear to belong to a new type of combination), they have furnished a number of interesting results. These, as well as reasons against Persoz’s proposal to change the formula of tungstic acid, Marignac discusses at length. Weltzien* describes a method for the quantitative estimation of nitric acid in waters. It consists in determining it as ni- trogen gas. The water to be investigated is evaporated, and by a careful addition of carbonate of soda, the lime and mag- nesia are precipitated as carbonates, and any nitrate of lime or magnesia 1s converted into nitrate of soda. The filtrate from this precipitate is evaporated to dryness, and mixed with finely divided copper reduced from the oxide by hydrogen. ‘This mix- ture is heated in a somewhat long combustion-tube in the usual mode of determining nitrogen, all the atmospheric air having been previously expelled by carbonic acid. Weltzien gives a number of analyses of the waters of the town of Carlsruhe inyes- tigated by this method, and also, to show its accuracy, determi- — nations made with known quantities of nitrates. His analyses of the town well-waters show in a marked degree the influence of population in increasing the quantity of nitrates. They show also the completeness with which any nitrogenous organic matter becomes oxidized into nitrates. * Liebig’s Annalen, November 1864. M. Lamy on Thallium. ah 379 According to Lamy*, phosphoric acid forms with thallium a series of phosphates, for the most part very soluble, and varied in their composition and properties like the corresponding com- He of the alkaline metals. They are as follows :— Nentral phosphate of thallium . PO*,2TIO,,HO+HO Acid ts pe , PO’, TIO, Z2BO Basic Ms » PO?, 3110 Neutral pyrophosphate i eis: PO? 2810 Acid pyrophosphate __,, . PO, TIO, HO Metaphosphate _ we PO, TiO. _ All these salts are white, and almost all soluble in water and - Insoluble in alcohol. They are distinguished from the alkaline phosphates by the fact that they give a white precipitate with hydrochloric acid, and also with nitric acid, provided their solu- tions are neither too hot nor too dilute. The phosphates and pyrophosphates give a white precipitate of tribasic phosphate with the alkalies, while they are not precipitated by alkaline car- bonates, nor even by alkalies in the presence of these carbonates. After a description of these phosphates, M. Lamy offers some considerations on the position of thallium. In previous re- searches on thallium he had classed this metal by the side of the alkaline metals, in which he had the countenance of M. Dumas. My. Crookes, on the other hand, places thallium near the heavy metals—principally on account of the insolubility of some com- pounds, such as the peroxide, the protochloride, the iodide, sul- phate, and phosphate of thallium, the facility with which the pro- toxide is dehydrated and loses most of its solubility, the high atomic weight of the metal, the ready reduction of its salts by zinc, and generally most of its physical properties. M. Lamy, while admitting the insolubility of its bromide, &c., points out that thallium forms soluble higher chlorides, a soluble fluoride, and a soluble double fluoride with silicitum. Hethinks the physical properties of secondary importance, but principally relies in support of his view on the following considerations. The hydrated protoxide of thallium is very soluble in water, strongly alkaline and caustic like potash ; its carbonate is soluble and alkaline like that of potash; there are phosphates and arse- niates varlous in composition and properties, like the correspond- ing alkaline compounds; the sulphate is soluble, and has most of the properties of sulphate of potash, with which it 1s isomor- phous ; there is analogy of properties and isomorphism in the case of the thallium and potassium alums; and this analogy is also met with in the case of the double sulphates of the magnesia * Comptes er April 10, 1865. 2C2 380 Mr. J. H. Cotterill on the Equilibrium of series, and in the paratartrates and bitartrates.. Like the alka- lies, it forms double salts, the number of which increases the more this curious metal is studied. It forms neither subnitrate nor subacetate; but its acetate, distilled with arsenious acid, fur- nishes cacodyle. Lastly, thallium has, like the alkaline metals, and them alone, the characteristic property of forming thetic alcohols. M. Lorin desonthes a rnode of reduction which is an applica- tion of the following property. An ammoniacal salt, a simple — or a compound base, gives in general, in the presence of zinc and water, a disengueement of hydrogen—frequently at the ordinary temperature, but better towards 40° and upwards. This property has been verified on about fifty ordinary salts of ammonia, and on a small number of salts of methylamine, ethyl- amine, TRL and naphthylamine. The quantity of hydrogen appears to be a function of the equivalent of the acid. An equivalent of sulphate of ammonia gave at least an equivalent of hydrogen. Of the ordinary metals, iron is the only one which approaches zinc in its action on ammoniacal salts, though it is less intense. The concurrence of zinc, iron, ammonia, and an ammoniacal salt are the best conditions for accelerating the production of hydrogen. The rapidity of the disengagement is almost equal to that for dilute acids. One exception is met with in the case of nitrate of ammonia, which on dilute solution gives protoxide of nitrogen at a tempe- rature near 50°. LIV. On the Equilibrium of Arched Ribs of Uniform Section. By James H. Corrzritt, B.A., Scholar of St. John’s College, Cambridget. dy pas object of this article is to show how to find approxi- mately the thrust, shear, and bending moment on any section of an arched rib acted on by given forces under given circumstances ; the method is founded on the principle of Least Action, which in a former article was employed in the case of straight beams. Let transverse planes be drawn indefinitely near to each other, meeting in the centre of curvature at any point, cutting off a small portion of the rib. Let the forces which may be acting on the rib, whether distributed or detached, be supposed to act at points in the line joining the centres of gravity of its trans- * Comptes Rendus, April 10, 1865. ~ Communicated by the Author. Arched Ribs of Uniform Section. 381. verse sections, or, as it will be called hereafter, the axis of the rib; it is plain that this supposition, which is exactly true for the weight of the rib, will in other cases produce no consider- able error. Also let the stress on any section of the rib be resolved into a shear F, a thrust H, and.a bending moment M ; and let it moreover be supposed that the shear and thrust may be considered as concentrated at the centre of gravity of the section. These suppositions being made, we have for equilibrium of the small portion, by resolving tangentially and normally and taking moments, Hd¢é=d¥ + pds, Fdd +dH=gds, dM =F .ds, where d@ is an element of the angle which the section consi- dered makes with a given section ; ds an element of the axis; p the normal pressure estimated per unit of length of the axis and reckoned positive when acting inwards; g the tangential pres- sure per unit of length of the axis, reckoned positive when tend- ing to increase d. If p be the radius of curvature of the axis, these equations may be written, dk dd +pe=H, eet db =P; dM dd en Differentiating the first equation and adding it to the second, we have ad? daz it 8? web whence F=K+F,.cos¢+ H,.sin @, where F,, Hy are arbitrary constants, Ge d GG) fein} a¥ aK 1 Ue a +pp=pp+ dp +H). cos ¢—F). sin , € 382 My. J. H. Cotterill on the Equilibrium of and a =F.p=Kp+F,).p.cos6+H),.p.sng; p p : ate i) Kpdp+F,. { i lbos d+ Hof “ov siniguaceaintc. 0 0 0 Thus M, H, and F are expressed in terms of known functions of ¢, and three undetermined constants which, if no distributed forces act on the rib, are the shear, thrust, and bending moment on the initial section. In these expressions shear is reckoned posi- tive when it tends to draw away from the centre of curvature that portion of the rib which is fowards the algebraical increase of @, thrust when it tends to move the same portion towards the increase of d, and bending moment when tending to twist the same portion in the direction of ¢. Now it may be that something is known about the stress on one or more sections, and in that case one or more of the con- stants will be definite ; but in general it is impossible to deter- mine them without a knowledge of the physical constitution of the rib, because their values entirely depend on that constitu- tion. But if the nature of the material be known, so that the work done in it by the action of the forces can be estimated, then will the actual values of the constants be such as to make that work the least possible, and the differential cvefficients of that work with respect to the constants will furnish the means of find- ing their values. I proceed, therefore, to find the general values of those coefficients, supposing that the rib 1s composed of homogeneous material stramed with the limits of perfect elas- ticity. Before doing so, however, I may remark that it is frequently convenient to use rectangular equations of equilibrium ; the rib is to be divided into plates by planes parallel to the axis, and differential equations obtained expressing the equilibrium of one of those plates*. 2. When a straight beam is subjected to a bending moment, the strain being supposed within the limits of perfect elasticity, then it is known that the stress at different poimts of any transverse section varies uniformly, vanishing at points situated in a straight line, through the centre of gravity of the section, parallel to the axis of the applied couple. In effect, considerations of symmetry show that any particles originally in two transverse planes will, after application of the d * Tt is worth remarking that ga= 7; J pp! is the equation of a linear £ p dg P q arch. Arched Ribs of Uniform Section. 383 bending moment, still be in two transverse planes, whence the geo- metry of the question shows that the elongation and shortening of lines in the beam parallel to its axis will be proportional to their distances from some line situate in a transverse section, and that consequently the stress must vary uniformly; and since, moreover, the total amount of the stress is a couple, the line of no stress or neutral axis must pass through the centre of gravity of the section. Now, if the beam be curved, the same considerations of sym- metry apply to show that particles originally in two transverse sections will still be in two transverse sections ; but since those transverse sections are not parallel in their original positions, the geometry of the question is different, and consequently the stress does not vary unifermly, nor does the neutral axis pass through the centre of gravity of the section. By the method indicated, the law of variation of the stress, and the deviation of the neu- tral axis from the centre of gravity, might be determined, and also the maximum stress on the section. But it is probable that the introduction of terms depending on the curvature of the beam would not add materially to the accuracy of the results ; for in general not only does a bending couple act on the beam, but also forces which cause a shear on most of its sections; and the accuracy of the above conclusions is thereby disturbed to an unknown though (from the values of the coefficients of direct and transverse elasticity of the materials used in construction) small extent; and this error, in cases where the curvature is moderate in proportion to the depth, may probably be as great as the error produced by neglecting the curvature of the beam. We may take therefore M2 EH? v=({ri 4 saa f us as a first approximation to the work done. In cases in which the angle subtended by the rib is considerable, and in which, moreover, the distribution of the load differs much from that which is necessary for the equilibrium of a linear arch of like form, then, the thrust being small, the work done is almost en- tirely done by the bending moment, and a sufficient approxima- tion is given by M? M?p cn | eee —— ; vera acre Be “a Reference will be subsequently made to cases in which these con- ditions are not satisfied. - Using this formula, if the value of M given above were sub- stituted and the result integrated throughout the beam, the result 384 Mr. J. H. Cotterill on the Equilibrium of would oe the potential, by differentiation of which the values of the constants could be determined; but inasmuch as this func- tion is of great complexity, it is necessary to proceed otherwise, and calculate the several differential coefficients separately. ha differentiation, dU (Mp dM p : iF = I dF db= HE pcos db dp; so that if we merge the factor EI in U, *9 = (of p. cusp. dd d¢ ; so also Chas aus = = moj p.sin d.dd. dd, 3 eae dU ou, = | Mp. a. In calculating these coefficients for a given form of beam, it is convenient to observe that they consist of two parts—one due to the arbitrary constants, and the same for every load, and the other due to the mode of distribution of the load. If the beam be acted on by detached forces, then the portion due to-the con- stants must be estimated afresh for every part of the rib lying between those detached forces; but the portion of the coefficients due to the distributed load may be taken throughout the rib, without reference to any detached forces which may act upon it*, 3. I proceed to calculate the values of the parts of the coeffi- cients due to the arbitrary constants in the case of a circular rib of radius 7. Here p=r, and consequently the coefficients are Cy cy = a) M .sind.dd; am =", M(1—cos ¢).d¢ ; 2/9 (9) 0 ae =|" Mudd ; and so far as the arbitrary constants are concerned, M=M,+F).r.sin¢@+ Hor(1— cos ¢). On substitution and integration, we find * It is of course supposed that the change of form of the rib is incon- siderable ; otherwise a preliminary question would have to be solved— namely, to find p as a function of d by means of the calculus of variations. Arched Ribs of Uniform Section. 385 apa {3 —1sin 26} + Hor? {4 . cos 2— cos 6—F} + Mor?{1—cos $}, dU dH, = Fy? {2—cos +408 26} + Hy7?{5G—2. sin f+ jsin2g>} +M,7?(¢—sin 9), dU dM, =F, 72{1— cos } +Hyr?(d— sin ¢) ze. Myr¢. These values enable all questions to be solved concerning a circular rib loaded at detached points only. For example, let it be required to determine the bending moment at a given point of one of the rings of a chain composed of circular links. First, suppose the links not to be strengthened by the addition of a cross bar; then, supposing measured from the point of contact of two links, Hp=0, Fp=— a? where W is the © weight which the chain carries; so that we have only to deter- mine M,, which is done from the equation dU dM, where @==7,, because U must be estimated through half the ring up to the point of contact of the other ring in contact with it. = — J r°(1—cos $) + Myrp=0, The same result must manifestly be obtained if = = ; in either case | M)= heap 7 The stress on any section is therefore given by F=F,.cos$+Hy.sing=— +. c0s d, H=Hp).cos@—F,. sin d= £ . Sin d, M=M,+F).7r.sing+H)7(1—cos ), Wr ee =2 arising , oe: sin d. 2a If the links had each of them a central bar placed at right angles to the line of action of W, then H, would be undetermined, and = W. 386 Mr. J. H. Cotterill on the Hquilibrium of the equations for determining M, and H, would be ea oo, ay F, being replaced by — i A. I shall next “ the parts of the coefficients Ase to a continuous load on a circular rib. First, for the parts due to the weight of the rib, let w be the weight of the rib per unit of length of the axis, so that the weight of a frustum cut off by planes very near to each other is w. ds; then we have P= COs@, C=. sino, hee \er d K= {14 a f { op- pi? eA) et ; sur} 1+ = {2.sin ht =—wr.d.cos d, ) ) M =| Kpdgd= —we(’ h.cosd.dd =—wr\d.sng+ cosP—lt, On substitution of this value of M in the general values of the coefficients formerly given, the parts of those coefficients due to the weight of the rib are found to be Co = — Ir" {2g($—sin 24) —B. cos 26 +8. cos p—5}, 5 ; | Se = — Jor" {26 (cos 26—4.. cosp—6) +24 sin $—8 .sin 262, | (0) i =wr Sd(cosp+1)—2.sin pt, | If the rib be supposed loaded with a vertical load of uniform horizontal intensity w', then p=w'.cos?d; g=w'.singd.cos¢. And by a similar process we find for the parts of the coefficients * The consideration of the small amount of work done in compressing the central bar is omitted. The question has been inadvertently treated as if W were a thrust instead of a pull on the chain; to obtain results correct in sign, W must be changed into —W wherever it occurs. ie Arched Ribs of Uniform Section, 387 due to such a load, dU v 7 if, OM ath le Gamera or a mae {sind@—fsnsh+sin2d—2g}, p * 0 oT = jw? {4 sin 26—S}. J 0 By means of these two sets of equations, combined with the set given above for the arbitrary constants, all questions concerning circular ribs loaded as described can be solved. It is to be ob- served that ¢ is supposed measured from the crown of the rib. The values of F, H, M at any point distant ¢ from the crown are F =K+F,.cos¢+H,.sin 9, H=pr+ = +H,.cosd—F,.sin ¢, © ‘ M=r{ Kdd + For sin d+ Hor(1— cos d) + Mo, where p =w.cosd+w'.cos* d, K=—ur.¢.cosd—3w'r. sin 2¢. For example, suppose a semicircular rib under a vertical load of uniform horizontal intensity w! but of inconsiderable weight. Also let the rib be hinged at its crown and fixed firmly at its springing ; then, since the initial section is at the crown F,=0, M,=0, and H, is determined from the equation ae == Uj7tle 0 value of this coefficient being taken from (B) and the corre- sponding value in the preceding section. Hence we get, remembering that 6= s Hy? -2} +4ulr4{1+4—7} =0, whence Ho=hw'r. aint = 2w'r approximately. And therefore | F =—1w’'r sin 2¢ + 2w'r . sin , H =w'r .cos’ 6—w'r . cos 26+ 2w'r . cos ¢, M =jw'r?(cos 26 — 1) + 2w'r?(1 — cos 9), 088 Mr. J. H. Cotterill on the Equilibrium of which equations determine the stress on every section. From them it appears that 3w'r is the horizontal thrust nearly; also that M, which for small values of d is ie ea increases to a maximum negative value when cos#=%, then diminishes to zero ‘and changes sign when cos¢=1], ‘herman increasing positively to the springing when its value is 4w'r 5. By aid of the general expressions given in by the coeffi- cients may be determined for a rib of any form (such that p is a simple function of ¢) loaded in any manner, though the pro- cesses are of great complexity, which, however, is probably un- avoidable by any method. In cases in which the thrust is very great, it is moreover necessary to take the work done by it into account, whereby a large number of fresh terms will be introduced into the coefficients, but the process is rather com- plex than difficult. When the rise of the rib is small compared with its span, and it has a vertical load, it is simpler to use rectangular equations of equilibrium ; but it is unnecessary to enter into details, as the process is similar to the one already employed. The results are the same as those Professor Ran- kine has obtained in his work on Civil Engineering. Care must be taken to include every part of the structure im which work is done; thus if abutments yield, the work done in over- coming their resistance must be estimated and added to U. In the case of stone and brick arches, not only is work done in the arch ring, but also-in the mass of material resting on it. The same law of Least Action, however, governs the distribu- tion of the work; and if it were possible to estimate its whole amount, the problem of the arch might, by application of that law, be completely solved. In my former article 1 endeavoured to show that if X, Y, Z be the components of one of the forces acting on a perfectly elastic body, uw, v, w the displacements of its point of application pro- duced by the action of the forces on the body, then oy sy dU Pom. aw aZ =W. But the reasoning is not so conclusive as the following. Since | 2U=2{Xu+Yv+ Zu} 2.6U=>{Xdu+ Yb.v4+Z.6w} +2{u.dX+v.6Y¥+w. 6Z}; but > {Xdu 4 Y .0v-+-Z. owl is the increment of energy ex- pended, which, by the law of conservation of energy, is equal to Arched Ribs of Uniform Section. 389 dU, the increment of work done ; therefore we have also SU=¥ (udX-+08Y + w OZ}, whence the above equations follow. ay at dU d¥, dH, dM, initial section from its original position produced by the action of the a on the rib. Thus in the case of the chain of circular In particular are the displacements of the links alee is the stretching of each link; and when multi- = it dF plied by the scaebectat links, would give the stretching of the whole chain by the action of the weight Ww. March 1865, er Se NOTE. This article is intended chiefly to illustrate the application of the principle of least action, many details are therefore omitted which are necessary to complete a practical solution of the problem. Also the simplest cases have been chosen, to avoid, as far as possible, the inherent complexity of these problems. If a chain hang beneath the rib and carry part of the load by ver- tical struts, then, the form of the chain being known, the load on each strut is known in terms of H!, the unknown horizontal tension of the chain; for otherwise the form of the chain would not be pre- served. Supposing the struts indefinitely many in number, the in- 2, tensity of the load on the chain is H’, ay ; a being got from the equation to the chain (z horizontal). The intensity of the vertical load on the rib is consequently less- 2 : ened by the quantity H’, a and the coefficients a a at must be calculated, together with a new coefficient *TTU in terms 0 of H’, and the other quantities involved, U can now be made a minimum, and the four constants F,, H,, M,, H', determined, whereby the problem will be fully solved. If the chain take the thrust of the rib, then H,=H_",, and there are only three coefficients. The general problem of the stiffened suspension bridge is a particular case of this more general problem. The elasticity of the chains can be taken into account by estimating the work done in them in terms of H!.. Many other See of the same general class, that is, where the law of variation of stress is known, and its absolute amount is re- quired, may be advantageously treated by application of the principle of least action; in a future article I hope to consider some cases in which the law of variation is required. [ 390 ] LY. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 325.] February 2, 1865.—Major General Sabine President, in the Chair. NHE following communications were read :— « Researches on Solar Physics.—Second Series. On the Beha- viour of Sun-spots with regard to Increase and Diminution.” By WarrenDe la Rue, Ph.D., F.R.S., Balfour Stewart, A.M., F.R.S., and Benjamin Loewy, Esq. One of the authors of this paper having been led, from a preli- minary investigation, to suspect that the behaviour of sun-spots with respect to increase and diminution refers to some extraneous. influ- ence, they resolved to investigate the behaviour in this respect of the spots observed by Carrington, in addition to the Kew photograms up to the present date. The authors have thus examined materials embracing a period of ten years, and in this paper state the result. The nature of their examination is thus described :— If we imagine great circles of ecliptical longitude to be drawn from the sun’s centre, every point of the sun’s surface as it moves round by rotation will of course pass successively through each of those great circles, and every one of the planets will do the same as they move round by their own proper motions. And if we imagine the plane of the paper to denote the plane of the ecliptic, and project upon this plane each body of our system, we shall havea scheme similar to the above, in which ADB, the inner circle, may represent the sun himself, the next circle, let us say the orbit of Venus, the next that of our earth, while the outer may denote the orbit of Jupiter. To an observer looking down upon our system from the north, all motions will be in the direction of the arrow-heads, that is to say, in a direction contrary to that of the hands of a watch, or left-handed, while ecliptical circles of longitude will be represented Royal Society. 391 by the various radii proceeding from the centre C, the angular dif- ference between the two radii denoting the angular difference between the two correspondin glongitudes. If the observer be stationed at the earth, all points of the solar surface will advance by rotation from left to right across the visible disk ; while the radii vectores of the inferior planets Mercury and Venus, which move faster than the earth, will appear to the terrestrial observer to have a left-handed rotation, in such a manner that the planet Venus will move from its place in the diagram to opposition, and ultimately come round to conjunction from the Jeff. On the other hand, the superior pla- nets, which move more slowly than the earth, will appear to the _ terrestrial observer to have a right-handed rotation, im such a manner that Jupiter will proceed from his place in the diagram to opposition, and ultimately come round in conjunction by the right. Also the point B, which occupies the central position of the visible solar disk, will have the same heliocentric longitude as the earth. Let us make the central longitude, or longitude corresponding to the position of the earth at the time of observation, our meridian, and let us reckon as negative all longitudes less than 180° to the left, and as positive all those less than 180° to the right. In this way a spot or point of the sun’s disk, as it comes round by the left limb, will have the longitude —90, while, as it disappears by the right limb, its lon- gitude will be +90. Hence also the longitude of Jupiter in the diagram will be —ACB, while that of Venus willbe +BCD. Ifthe angle ACB is very large, we may say that Jupiter is much to the left, and if BCD is large, we may say that Venus is much to the right. In the examination to which the spots have been subjected, it has been endeavoured to ascertain, as nearly as possible, at what longi- tude any spot breaks out, or at what longitude it reaches its maxi- mum and begins to wane. Very often, however, we are not able to assign the exact longitude of such an occurrence; but yet, as will be seen in the sequel, we are able to determine, in a general way, the behaviour of spots. . The examination was made in the following manner. Mr. Carring- ton’s original drawings were examined by two observers noting the behaviour of each spot, and the results again compared with Car- rington’s published maps, which give the behaviour of spots from day to day ; ultimately a list was obtained, no spot available for compa- rison being left out. A similar process was followed with regard to the Kew pictures. It is to be remarked, that in making the examinations of the Car- rington pictures, both observers were ignorant of the planetary confi- gurations; and that although with regard to the Kew pictures one observer knew the corresponding planetary configurations, yet his judgment, being checked by his fellow-observer, could not be biassed by any previous speculative views. Ina Table given, showing the behaviour of sun-spots from the beginning of 1854 to the end of 1864, it is seen that different spots occurring about the same time on the sun’s disk behave themselves in the same manner; so that if one spot, after making its appear- 3892 Royal Society :— ance, increases until the centre line, another will do the same; oF if one spot breaks out on the left or on the right, half the other spots about the same period have a tendency to break out on the same half. Examples of these are referred to in the Tables. The authors suppose that this peculiarity of behaviour of spots can only be explained by reference to some influence from without. Suppose that such an influence, of a nature unfavourable to spot- production, exists, then, as spots are brought round to it by rota- tion, they will gradually wane; and, on the other hand, as the surface departs from it, spots will break out. But while there is good evidence for believing in the existence of some such influence, it is a very difficult thing to determine its nature, and one which can only be done very imperfectly with our present knowledge. The authors attempt to answer the following questions. Is this influence stationary? or, if moveable, can it be traced to any of the planets of our system ? The behaviour of each series of groups is then compared with the positions of the three planets, Mercury, Venus, and Jupiter, at the same date ; these planets being imagined to be the most influential ; since the first, though small, is very near the sun, the second is both near and tolerably large, while the last, although distant, is of very great mass. In answer to the first question, Is the influence stationary? it may be remarked that if it be so, the difference of behaviour noticed at different periods must be due to the position of the earth, or point of view at these periods with reference to the stationary influence, and hence in similar months of different years we should have a similar behaviour; but it cannot be found from investigations that there is any connexion between a certain behaviour of sun-spots and a certain period of the year, and hence there is no reason to suppose that the external influence is fixed. In the next place, does this influence, if moveable, move faster or slower than the earth? If faster, it will proceed from conjunction to opposition, passing over the sun’s disk from left to right. If we view it as one unfavourable to the production of spots, then, at first, when it is near conjunction, or a little to the left, the sun’s surface to the right, receding from it, will break out into spots ; but as the in- fluence moves on to the right, spots will come towards it from their first appearance, and will consequently decrease from the first. But if, on the other hand, the influence move more slowly than the garth, it will move from conjunction to opposition, from right to left; that a tendency of spots to form on the disk will he followed by a tendency to increase, not decrease, after making their appearane. The order of the consecutive phenomena will thus be different in the two cases. It is shown by a Table that a tendency of spots to break out is fol- lowed. by a tendency of spots to decrease after making their appear- ance, and it is thereby concluded that the influence moves faster than the earth. This would seem to point to either Mercury or Venus as the agent in this matter, but the behaviour varies too De la Rue, Stewart, and Loewy on Solar Physics. 393 slowly to be caused by the former. Venus, therefore, appears to be the influencing agent; and whether the behaviour of spots ap- pears to depend on the position of this planet with reference to the earth, or point of view, the following Table, in which the spot- behaviour is compared with the corresponding position of Venus, will show No. of © =e e ae Behaviour. Position of Venus. 1. Increase to centre. A good deal to left. 2. Break out. Conjunction. 3. Decrease. To right. 5. Increase. Near opposition. 6. Break out. Near conjunction. 7. Increase. Opposition. 8. Break out. Near conjunction. 9. Uncertain behaviour. To right. 11. Increase to centre. Near opposition. 12. Increase past centre. Near opposition (to the left). 13. Break out. Near conjunction, 15, Decrease. To right. 17. Increase to centre. Near opposition. 18. Increase past centre. Near opposition (to the left). . Break out. Near conjunction. To right. Near opposition. Near conjunction. To right. Near opposition. Near opposition (to the left). Near conjunction. 22. Stationary behaviour, 24. Increase to centre. _ 25, Break out. *26. Uncertain behaviour. 27. Increase to centre. 28. Increase past centre. 29. Break out. 31. Decrease shortly after aide melt appearance. na 32. Increase to centre. Near opposition. It will be seen from this Table that the behaviour of spots appears to be connected with the position of Venus in such a manner that spots dissolve when that part of the sun’s surface in which they exist approaches the neighbourhood of this planet ; while, on the other hand, as the sun’s disk recedes from this planet, spots begin to break out and reach their maximum on the opposite side. There are a few cases in which Venus and Jupiter are opposed to one another; the authors do not, however, suppose that these instances are sufficient to prove the fact of an action due to Jupiter, but think it right, in alluding to them, to state at the same time the opposed position of the two planets, since this may furnish a pos- sible explanation of the uncertain behaviour of spcts by which these series are characterized. The results of this paper may be stated briefly as follows :— * Venus and Jupiter are here opposed to one another. Phil. Mag. 8. 4. Vol. 29. No, 197. May 1865. Peat 394 Royal Society :— Observed fact.—Spots appearing about the same time on the sun’s disk behave in the same manner as they pass from left to right. Legitimate deduction.—The behaviour of spots is influenced by something from without, and from the nature of the spot-behaviour the authors conclude that this influence travels faster than the earth ; and finally, they find that the behaviour of spots appears to be deter- mined by the position of Venus in such a manner that a spot wanes as it approaches this planet by rotation, and, on the other hand, breaks out and increases as it recedes from the neighbourhood of the planet, reaching its maximum on the opposite side. . In conclusion, it is not meant in this paper to convey the idea that Venus is the cause of the ten-yearly period of sun-spots, but merely that there is a varying behaviour of spots which appears to have reference to the position of this planet, or, putting aside the influ- one agent, appears to have reference to certain ecliptical longi- tudes. “On the Rapidity of the Passage of Crystalloid Substances into the Vascular and Non-Vascular Textures of the Body.” By Henry Bence Jones, F.R.S. In a Letter to the Secretary. . Dear Dr. Suarpey,—I am anxious that you should read to the Royal Society a short note containing the results of some ob- servations I lately made on the rapidity of the passage of crystal- a substances into the vascular and non-vascular textures of the ody. It occurred to me that it might be possible to trace the passage of substances from the blood into the textures of the body by means of the spectrum-analysis, and with the assistance of Dr. Dupré some very remarkable results have been obtained. Guinea-pigs have chiefly been used for the experiments. Usually no lithium can be found in any part of their bodies. When half a grain of chloride of lithium was given to a guinea-pig for three successive days, lithium-appeared in every tissue of the body. ~Even in the non-vascular textures, as the cartilages, the cornea, the crys- talline lens, lithium would be found. a Bs Two animals of the same size and age were taken; one was given 3 grains of chloride of lithium, and it was killed in eight hours ; another had no lithium ; it was also killed, and when the whole lens was burnt at once, no trace of lithium could be found. In the other, which had taken lithium, a piece of the lens, ,th of a pin’s head in size, Showed the lithium ; it had penetrated to the centre of the lens. In another pig the same quantity of chloride of lithium was given, and in four hours even the centre of the lens contained lithium. ~ Another pig was given the same quantity, and it was killed in two hours and a quarter. The cartilage of the hip showed lithium faintly, but distinctly. The outer portions of the lens showed it slightly ; the inner portions showed no trace. To a younger pig the same quantity was given, and it was killed in thirty-two minutes. Lithium was found in the cartilage of the hip ; i the aqueous humour; distinctly in the outer part of the lens and very faintly in the inner part. Prof. Williamson on the Atomicity of Aluminium. 395 In an older and larger pig, to which the same quantity was given, lithium after one hour was found in the hip and knee joints very faintly ; in the aqueous humour of the eye very distinctly ; but none was found in the lens, not even when half was taken for one trial. Chloride of rubidium in a three-grain dose was not satisfactorily detected anywhere. When 20 grains had been taken, the blood, liver, and kidney showed this substance ; the lens when burnt all at once showed the smallest possible trace ; the cartilages and aqueous humour showed none, probably because the delicacy of the spectrum- analysis for rubidium is very much less than that for lithium. A patient who was suffering from diseased heart took some lithia- water containing 15 grains of citrate of lithia thirty-six hours before her death, and the same quantity six hours before death. The crys- talline lens, the blood, and the cartilage of one joint were examined for lithium: in the cartilage it was found very distinctly; in the blood exceedingly faintly ; and when the entire lens was taken, the faintest possible indications of lithium were obtained. Another patient took lithia-water containing 10 grains of carbo- nate of Jithia five hours and a half before death: the lens showed very faint traces of lithium when half the substance was taken for one examination ; the cartilage showed lithium very distinctly. I expect to be able to find lithium in the lens after operation for cataract, and in the umbilical cord after the birth of the foetus. I am, yours truly, H. Bence Jones. February 9.—Major-General Sabine, President, in the Chair. The following communication was read :-— **Note on the Atomicity of Aluminium.” By Professor A. W. Williamson, F.R.S., President of the Chemical Society. In the ‘‘ Preliminary Note on some Aluminium Compounds,” by Messrs. Buckton and Odling, published in the last Number of the Society’s ‘ Proceedings*,’ some questions of considerable theoretical importance are raised in connexion with the anomalous vapour- densities of aluminium ethyle and aluminium methyle. The authors have discovered that the vapour of aluminium methide (Al’ Me‘) occupies rather more than two volumes (H=1 vol.) at 163°, when examined by Gay-Lussac’s process, under less than atmospheric pressure. The boiling-point of the compound under atmospheric pres- sure is given at 130°, and the compound accordingly boiled a good deal below 130° at the reduced pressure at which the determination was made. The vapour was therefore considerably superheated when found to occupy a little more than two volumes. When still further superheated up to 220° to 240°, it was found to possess a density equivalent to.rather less than four volumes at the normal tempera- ture and pressure. The aluminium ethyle was found to have a density decidedly in excess of the formula Al? Et® = 4 vols., but far too small for Al? Me® =2vols. From their analogy to aluminic chloride, Al? Cl’=2 vols., * See also pp. 313 and 316 of the present volume of this Journal. D2 396 : Royal Society :— the methide and ethide might be expected to have vapour-volumes | corresponding to Al? Me® = 2 vols., Al? Et® = 2 vols. The authors seem, however, more inclined to doubt the truth of the general prin- ciples which lead us to consider these hexatomic formule the correct ones, than to doubt their own interpretation of the observations already made upon the new compounds. Even if the vapour-volume of aluminie chloride had been unknown to us, there were ample grounds for assigning to aluminium methide a molecular formula Al’ Me*, and a vapour-density corresponding to Al’ Me’ = 2 vols. ; for,the close analogy of aluminie and ferric salts is erfectly notorious, and the constitution Fe* O° for ferric oxide settles Al’ O* as the formula for alumina. With regard, however, to the chlorides of these metals, it might be supposed that the formula Fe Cl’ and AlCl’ would be the most probable molecular formule ; and Dr. Odling, in his useful Tables of Formule, published in 1864, expressed an opinion in favour of these formule by classing as ano- malous Deville’s vapour-densities, which correspond to the higher formule Al? Cl’, Fe? Cl’. Itis well known that Laurent and Ger- hardt, whose penetrating minds raised so many vital questions of chemical philosophy, laid down a preliminary rule that every molecule must contain an even sum of the atoms of chlorine, hydrogen, nitro- gen, and metals. According to this rule, the formule Al? Cl’ and Fe’ Cl’ would have no greater probability than the formule Fe Cl’, AICI’; and judging by that rule, Dr. Odling naturally preferred the simpler formule. ‘Since Gerhardt’s time chemists have, however, extended to the greater number of metals the arguments which proved oxygen to be biatomic; and we now know that the alkali-metals, the nitrogen series, silver, gold, and boron, may count with the atoms of chlorine, hydrogen, &c. to make up an even number in each molecule, but that the greater number of metals must not be so counted; for that in each molecule in which they are contained the sum of the atoms of chlorine, hydrogen, nitrogen, potassium, &c. must be even, just as much as if the atom of the diatomic or tetratomic metal were not in thecompound. In a paper ‘‘ On the Classification of the Elements in relation to their Atomicities,’’ I had occasion to point out that inasmuch as iron and aluminium belong, partly by their own pro- perties, partly by their analogies, to the class of metals which do not join with chlorine, &c. in making up an even number of atoms, the number of those other atoms in each molecule must be even in itself, just as if iron or aluminium were not there ; and that. accord- ingly the formule Fe?’ Cl’, Al? Cl° are really quite normal. In like manner I showed that the vapour-density of calomel, HgCl = 2 vols., is anomalous, as containing in a molecular velume a single atom of chlorine, although, in accordance with Gerhardt’s rule, Dr. Odling had classed it asnormal. I certainly understood that my able friend accepted my suggestion in this case at least, for he speedily brought forward theoretical and experimental facts in confirmation of it. These examples serve to show that it was to be expected that the ethyle and methyle compounds of aluminium would contain an even _—— Prof. Williamson on the Atomicity of Aluminium. 397 number of atoms of ethyle and methyle in each molecule, and that their formule would accordingly be AP Me’®, Al’ Et’. It remains for us to consider how the deviation from our theore- tical anticipations in the case of aluminium ethyle and the partial deviation in the case of aluminium methyle ought to be treated. _ Fortunately we have the benefit of some experience to guide us in this matter, for a considerable number of other compounds have been found to occupy in the state of vapour nearly double the volume which corresponds to one molecule; but, with very few exceptions, all of them have already been prov ed to have undergone decomposition, so as to consist of two uncombined molecules. Thus sal-ammoniac is admitted to have the molecular formula NH‘ Cl; yet in the state of vapour this quantity occupies the volume of nearly two molecules, viz. four volumes. Has the anomaly led us to doubt the atomic weight of chlorine, nitrogen, or hydrogen, or to doubt any other of the results of our comparison of their com- pounds? or has it led chemists to diffusion experiments with its va- pour, proving it to contain uncombined HCl and NH’, each occupy- ing its own natural volume? Has it not been proved that at the temperature at which sal-ammoniac vapour was measured, its con- stituents mix either without evolving heat (that invariable function of chemical action), or, according to another experimentalist, with evolution of far less heat than of the whole quantity of hydrochloric acid and ammonia combined, on coming together at that high tem- perature ? Again, SO* H? is known to represent the formula of one molecule of hydric sulphate, yet the vapour formed from it occupies nearly the bulk of two molecules. Has this fact cast any doubt on the atomic weights of the elements S$, O, or H? Or has it led to the discovery of peculiarities in the constitution of the vapour which would pro- bably have escaped notice had they not been anticipated by theory, peculiarities which go a long way towards bringing the apparent anomalies within the law? Nitric peroxide, N? O*, was considered, from our knowledge of other volatile compounds of nitrogen, to be anomalous in its vapour- volume being N?O*=4 vyols.; and we have been shown by the experiment of Messrs. Playfair and Wanklyn, that the anomaly almost disappears when the compound is evaporated by the aid of a per- manent gas at a temperature considerably below its boiling-point, as its theoretical molecule N? O* is then found to occupy the two volumes which every undecomposed molecule occupies. This explanation seems to me to be the more entitled to grave consideration on the part of the discoverers of the new aluminium compounds, from the . fact that the evidence in favour of it has been admitted to be con- clusive by Dr. Odling, who classes nitric peroxide by the formula N? O* = 2 vols. among compounds with normal vapour-densities, in virtue of the fact that at low temperatures it can be obtained with that density, though having half that density at higher temperatures. The arguments for admitting that the low vapour-densities of the aluminium compounds are anomalous are even stronger than those which are admitted in the case of nitric peroxide; for it did require 398 al Geological Society :— very severe superheating to get the aluminium compounds to near four volumes, whereas it required very ingenious devices to get nitric peroxide out of the four-volume state. Such guiding principles as we have acquired in chemistry are the noblest fruits of the accumulated labours of numberless patient experimentalists and thinkers; and when any new or old fact ap- pears to be at variance with those principles, we either add to our knowledge by discovering new facts which remove the apparent incon- sistency, or we put the case by for a while and frankly say that we do not understand it. The decision of the atomic weight of aluminium has involved greater difficulty than was encountered in the case of most other metals, owing to the fact of our knowing only one oxide of the metal, and salts corresponding to it; but the analogies which con- nect aluminium with other metals are so close and so numerous, that there are probably few metals of which the position in our clas- sification is more satisfactorily settled. We may safely trast that the able investigators who are examining these interesting com- pounds will bring them more fully than now within the laws which regulate the combining proportions of their constituent elements ; for, as it now stands, the anomaly is far less than many others which have been satisfactorily explained by further investigations. Meanwhile aluminium is a metal singular for only appearing in that pseudo-triatomic character in which iron and chromium appear in their sesquisalts. GEOLOGICAL “SOCIETY. [Continued from p. 326. | | January 25, 1865.—W. J. Hamilton, Esq., President, in the Chair. The following communications were read :— 1. “‘ Notes on the Climate of the Pleistocene epoch of New Zea- land.” By Julius Haast, Ph.D., F.G.S. The main feature in this communication was a notice of the oc- currence of bones of the Dinornis in the moraines of the extinct glaciers of New Zealand. In support of the author’s opinion that the extinction of that bird was due to the agency of man at a some- what recent date, it was observed that the present Alpine flora furnished a large quantity of nutritious food quite capable of sustaining the life even of so large a creature; and as the fruits of these plants were at present applied to no apparent purpose in the economy of nature, the author argued the former existence of an adequate amount of animal life to prevent an excessive development of hier a This part, he considered, was played by the Dinornis. = On the Order of Succession in the Drift-beds in the Island of fence: By James Bryce, M.A., LL.D., F.G.S. In a paper read last year before the Royal Society of. Edinburgh, the Rev. R. B. Watson described all these beds as Boulder-clay, and did not assign the Shells which he had discovered in them to any particular part of the deposit. Dr. Bryce dissented from this view, and in this paper pointed out the various causes of error likely On Drift-beds in the West of Scotland. 399 to mislead an observer in examining such accumulations. He then deseribed the various sections of the deposits, and showed that the lowest bed is a hard tough unstratified clay,: full of striated, smoothed, and polished stones of all sizes, but totally devoid of fossils, and that it is, in fact, the true old Boulder-clay of the geo- logists of the West of Scotland. The Shells are entirely confined to a bed of clay of open texture, containing a few small stones; it rests immediately on the Boulder-clay as above defined, and is succeeded by various drift-beds, consisting of seams of clay and sand inter- mingled, containing stones that are rarely striated, and without Shells. Dr. Bryce then discussed the probable origin of these drifts, and the amount of depression which the land had sustained before the Shell- bed was deposited over the Boulder-clay, which he considered to have been formed by land-ice emanating from central snow-fields, and covering the whole surface of the country. 3. * On the Occurrence of Beds in the West of Scotland in the position of the English Crag.” By James Bryce, M.A., LL.D., F.G.S. In consequence of the results arrived at from the investigation of the Drift-beds of Arran, Dr. Bryce determined to examine all the recorded cases of fossils occurring in the Boulder-clay, the Chapel Hall case having, however, been already undertaken by the Rey. H. W. Crosskey. The most celebrated case is that of the occurrence of Elephant-remains at Kilmaurs, near Kilmarnock, in Ayrshire; and the author showed, from a section of the quarry exposed for the purpose by Mr. Turner, of Dean Castle, which corresponded exactly with one already furnished to him by an aged quarryman, that the Elephant-remains, the Reindeer’s horn, and the Shells, all occurred in beds below the Boulder-clay, and not im that deposit, as has always been stated. ‘The same conclusion was arrived at respecting the occurrence of Elephant-remains at Airdrie and Bishop briggs and of Reindeer’s horn with Shells at Croftamie; and the author concluded by discussing the question whether the fossils belong to the Upper Crag period, or merely indicate a downward extension of the Arctic fauna which characterizes the beds directly above the Boulder-clay, as described in the last paper. 4, “On the Tellina proxima Bed at Chapel Hall, near Airdrie.” By the Rev. H. W. Crosskey. One of the most perplexing cases in Scotland, upon any theory of the formation of Boulder-clay, has been the alleged occurrence at ‘Chapel Hall of a clay-bed containing Tellina prozxima, intercalated between two masses of true Boulder-clay. The Shells were first found by Mr. James Russell in sinking a well; and the case was made known by Mr. Smith, of Jordan Hill, in a paper laid before the Geological Society in 1850. At the author’s request, Mr. Russell had sunk another well 7 yards from the former, from an examina- tion of which Mr. Crosskey satisfied himself that the bed above that containing the Shells is not the true Boulder-clay, but an upper Drift, and that the Shells occurred in a hollow of the lower clay, or true Till, filled up with a clay-deposit of an age interme- 400 . Geological Society :— diate between that of the other two. He therefore considers that this can no longer be regarded as one of fossils occurring in the true Boulder-clay. February 8, 1865.—W. J. Hamilton, Esq., President, in the Chair, a following communications were read :— . “On the Sources of the Mammalian fossils of the Red wee kiss on the Discovery of a new Mammal in that Deposit allied to the Walrus.” By E. Ray Lankester, Esq. The Mammalian fossils of the Red Crag were stated to belong to three groups :—(1) the teeth of Coryphodon, &c., derived from Lower Eocene strata; (2) the other terrestrial Mammalia; and (3) the Cetaceans. The Molluscan fauna of the Red Crag was cited in proof of its identity in age with the Upper or Yellow Crag of Antwerp, which contained none of the Red Crag Mammals. ‘The underlying Middle and Black Sands of Antwerp contain far larger percentages of extinct forms and very abundant Cetacean remains. The deposits at Darmstadt and in the South of France, containing terrestrial Mammalia similar to those of the Red Crag, are also ante- rior to the Yellow Crag of Antwerp. The Red Crag was thus shown to include Mammalian fossils found nowhere else excepting in strata of an earlier age. The probabilities therefore were, that these various Mammalia were not indigenous to the Red Crag, but were derived from the breaking up of earlier strata; and this supposition was supported by lithological evidence, which the author gave in detail, and discussed the chemical and mineralogical questions involved. Further evidence of the extraneous nature of the Mammalian fossils was also adduced, in the fact that teeth of Rhinoceros and Mastodon occurred at the base of the Coralline Crag ; and other less conclusive facts were cited. The great abundance and perfect condition of teeth of Carcharodon and Ziphioid Cetaceans in the Middle Crag of Antwerp, their absence in the Yellow Crag of that locality, and their presence in a much rolled, indurated and fragmentary condition in the Red Crag, often with portions of their previous sandy matrix adhering, was considered as conclusive evidence with regard to the Cetacean remains. Mr. Lankester then described the tusks of an animal allied to the Walrus, but probably much larger, which he proposed to call Tri- chechodon Huzleyi. ‘The minute details of form and structure were entered into, and the author stated that the teeth called Balenodon by Professor Owen belonged really to two genera, Zzhpius and ee as shown by the remains from the Middle Antwerp beds, 2. “ Note on the Geology of Harrogate.” By Professor John Phillips, M.A., F.R.S., F.G.S. The cuttings on the North-eastern Railway, combined with sec- tions exposed in several quarries, have enabled the author to trace the range of the Millstone-grit, Calcareous roadstone, and Yoredale Shales near Harrogate; and have also thrown some light on the relation of the Permian to the more ancient rocks. Prof. Phillips was also enabled to refer the mineral springs, with greater con- fidence than heretofore, to a deep source along an axis of movement ; —— On the Lower Silurian Recks of Cumberland. 401 and to suggest that the Harrogate roadstone probably corresponds to the Main, or 12 fathom, limestone at the top of the Yoredale series. These results, the arguments and facts in support of them, and the inferences obtainable from their consideration were given by the author in this paper, which was illustrated by a horizontal section from Wharfe, on the 8.E., through Harrogate, to Nid on the NW. ; February 22, 1865.—W. J. Hamilton, Esq., President, in the Chair. The following communications were read :— 1. ‘“‘ On the Lower Silurian Rocks of the South-East of Cumber- land and the North-East of Westmoreland.” By Professor R. Harkness, F.R.S., F.G.S. The district described in this paper consists of a narrow hand of country on the western side of the Pennine Chain; it possesses external features which indicate a geological structure different from that of the Pennine escarpment, and from that of the adjacent country on the west, from which it is separated by the Pennine fault. Prof. Harkness described the Lower Silurian rocks occupy- ing this narrow tract in some detail, and showed them to consist of Skiddaw Slates, with interstratified greenstone porphyry and ash, and a band of fossiliferous shale.. He also gave, in illustration of the structure of the country, a section from Melmerley Scar to Romanfell, and one from Milburn to Dunfell, together with a geolo- gical sketch-map of the narrow Lower Silurian tract in question. In conclusion the author described a fault which brings the Skid- daw Slates against the Coniston Limestone, and another, which cuts through the Lower Silurian rocks of the district, having a course at right angles to the former, and nearly parallel to that of the Great Pennine fault. 2. ** Note on the Volcanic Tufa of Latacunga, at the foot of Coto- paxi; and on the Cangaua, or Volcanic Mud, of the Quitenian Andes.” By R. Spruce, Esq. The Voleanic Tufa described in this paper is not only used for building-purposes, but also by the smiths instead of charcoal, as when heated to redness it emits considerable heat, but very little flame. The author then described the large deposits of Volcanic Mud, called Cangaua, which are met with throughout the central valley of the Quitenian Andes. This mud is compact, slightly argillaceous, and more or less saline, and occurs in rock-like masses, yielding very slowly to atmospheric agency, or even to running water. 3. “ On the Discovery of Flint Implements in the Drift at Milford Hill, Salisbury.” By Dr. H. P. Blackmore. Since the discovery of Flint Implements in the Higher-level gravel at Fisherton on the west of Salisbury, a large number of very excellent weapons have been obtained from the Drift-gravel of Milford Hill. This deposit is of the same age as the Fisherton beds; but it is situated on the opposite side of the Avon, imme- diately to the east of Salisbury. 402 Geological Society :— Dr. Blackmore described the materials composing the gravel of Milford Hill, and discussed the nature and power of the forces which had brought them together. He then described the position, thickness, and physical relations of the deposit, stating that the gravel is from 10 to 12 feet thick on the top of the hill, becoming thinner and gradually dying away on the sides. The hill itself is quite isolated, being separated from the surrounding higher land by river-valleys ; its highest point is about 100 feet above the present level of the rivers. In making a cutting on the south-eastern side of the hill, a bed of sand containing four species of land-shells was discovered near the base of the gravel. No other fossils have been found in the deposit, with the exception of a single tooth of a species of Hquus. Dr. Blackmore concluded by describing the implements them- selves, which nearly all belong to the long-pointed type, thus con- firming the opinion of Mr. Evans, that this form is mainly charac- teristic of the Higher-level gravels. March 8, 1865.—W. J. Hamilton, Esq., President, in the Chair. The following communications were read :— 1. ‘* On the Echinodermata from the South-east coast of Arabia, and from Bagh on the Nerbudda.” By P. Martin Duncan, M.B, Sec. G.S. In this paper Dr. Duncan described eight species of Echinoderms, only one of which was new, from Ras Fartak and Ras Sharwén on the scuth-east coast of Arabia, and four from Bagh on the Ner- budda. He also mentioned five determinable species of other classes from each locality. Of these fossils, Memiaster similis, D’Orb., and Pecten quadricostatus, Sow., were alone common to the two localities; but with the exception of the new Echinoderm, which was named Cottaldia Cartert by Dr. Duncan, all the species occur in European Cretaceous rocks. He considered the fossils from the two localities to belong to the same period, and discussed the question of the correlation of the deposits containing them with those of Europe, coming to the conclusion that they were most pro- bably of Cenomanian rather than Neocomian age, and of later date than the Pondicherry series; but he also remarked ‘that it is im- possible to determine their exact contemporaneity, the vertical range of many of the species being so great, and the parallelism of the allied European Cretaceous beds not exact. In conclusion, Dr. Duncan discussed several questions arising out of a comparison of fossils from distant localities, especially the specific identity of similar specimens occurring in different forma- tions, or in distant regions 5 also the variability of certain species, and the idea of ‘‘ homotaxis.” 2. “On the Fossil contents of the Genista Cave at Windmill Hill, Gibraltar.” By George Busk, Esq., F.R.S., F.G.S., and the late Hugh Falconer, M.D., E.R. S., F.G.8. This ‘was a letter addressed by the authors to His Excellency the Governor of Gibraltar, General Sir W. J. Codrington, K.C.B., &c., On the Gibraltar Caves and their Fossils. 403: and containing the results of their examination of the Genista Cave. Referring first to Capt. Brome’s report for a description of the general features of that cave, the authors stated that the rock of Gibraltar abounds in both seaboard and inland caverns, the Genista Cave being one of the latter class. It has been traced downwards to a depth of 200 feet; but the external aperture has not yet been discovered ; it was stated to be full of the remains of Quadrupeds and Birds, some of the former being now wholly extinct, others ex- tinct in Europe and repelled to distant regions of the African con- tinent (as the Hyena brunnea), while others, again, live now either on the rock or in the adjoining Spanish peninsula. A list of the species to which these remains were referable was then given, and it was inferred that there had been a connexion by land, either circuitous or direct, between Europe and Africa at no very remote period. The authors observed that the wild animals whose remains were dis- covered lived and died upon the rock during a long series of ages, and they gave a detailed account of the manner in which they con- sidered the bones were introduced into the cave. ‘They also recom- mended the formation of a local collection of these and other spe- cimens, urged the appointment of a geologist to make a geolo- gical survey of the rock, and concluded by expressing their opinion of the value and importance of Capt. Brome’s exploration of the Genista cavern. March 22, 1865.—W. J. Hamilton, Esq., President, in the Chair. The following communications were read :— : 1. ‘‘ Notes on the Caves of Gibraltar.” By Lieutenant Charles Warren, R.E. The principal caves at Gibraltar are St. Michael’s, Martin’s, Glen Rocky, Genista, Asylum Tank, Poco Roco, and three under the Signal Station, on the eastern face of the rock. The author de- scribed the salient features of St. Michael’s Cave, stating that it is a portion of a transverse cleft through the rock, and was probably open to view at no very remote historical period; and he briefly noticed the cave at Poco Roco, which he considers to be a portion of the fissure which extends from Bell Lane, in the town, to the village of Catalan Bay, the noise of blasting having been heard on more than one occasion through the apparently solid rock. In con- clusion Lieut. Warren offered his services in the event of a geolo- gical survey of Gibraltar being undertaken. 2. ‘*On the asserted occurrence of Human Bones in the ancient fluviatile deposits of the Nile and the Ganges, with comparative remarks on the Alluvial Formation of the two Valleys.” By the late Hugh Falconer, M.D., F.R.S., F.G.S. In this communication the author brought together the few in- stances on record of the occurrence of mammalian fossil remains in the Valley of the Nile, and instituted a comparison between the Alluvial deposits of the Nile and those of the upper part of the Valley of the Ganges which had come under his own observation. Ac- cording to certain statements, fossil human bones have been met 40 4 Geological Society :— with in both of these subtropical valleys; and Dr. Falconer remarked that at the present time the consideration of the general inferences to which these cases lead may probably be of some use. After discussing at some length the cases in which human and other Mammalian bones had been stated to occur in the Valley of the Nile, Dr. Falconer described the general features of the Alluvial deposits of the valleys of the Ganges and Jumna, stating what organic remains had been found in them. In a comparison of the two regions, Dr. Falconer observed that there are striking analogies between the Alluvial deposits occurring along the banks of the Nile on the one hand, and the Ganges and Jumna on the other, the most obvious being the great abundance, in both cases, of argillacev- calcareous concretions, forming an impure kind of travertine, and in the lowermost beds horizontal deposits of the same material; but that in its poverty of vertebrate remains the former, so far as it has been explored, is a remarkable contrast to the latter. _ Dr. Falconer then reverted to an opinion expressed by Sir Proby Cautley and himself many years ago, namely, that the Colossochelys Atlas may have lived down to an early epoch of the human period, and become extinct since; and he concluded with some general observations on the question of the antiquity of the human race, suggested by more recent discoveries. April 5, 1865.—Sir R. I. Murchison, Vice-President, in the Chair. The following communications were read :— 1. “On some Tertiary Deposits in the Colony of Victoria, Aus- tralia.” By the Rev. J. E. T. Woods, F.L.S., F.G.S. The author first referred to a former paper on the Australian Tertiary strata, and then described the beds of Muddy Creek, near Hamilton, mentioning the principal fossils occurring therein, espe- cially a species of Trigonia; he also stated that the same formation occurs at Harrow, on the River Glenelg, about sixty miles to the north-east, as well as in Tasmania. In discussing the age of these »eds he adopted Professor M‘Coy’s views, that they are of Lower Miocene date; but he considered the Mount Gambier limestone to be more recent, probably older Phlocene, and the Murray River de- posits as possibly holding an intermediate position; the latter he therefore considered to represent the Upper and Middle Miocene of Europe. Older than all these are certain strata occurring at Port Phillip and elsewhere, which the author referred to the Upper Eocene period. In conclusion Mr. Woods gave a sketch of the salient features of the Bryozoon-faune of the deposits occurring at Hamilton and Mount Gambier, chiefly for the purpose of showing that the latter is much the more modern of the two. In a note, Dr. Duncan enumerated the species of Corals which had been sent him by Mr. Woods; but he stated that, although they had a very recent aspect, no exact geological date could safely be as- signed to them. 2. “ On the Chalk of the Isle of Thanet.” By W. Whitaker, Esq., B.A., F.G.S., of the Geological Survey of Great Britain. | In this district a bed of comparatively flintless chalk overlies one On the Chalk of Buckinghamshire, &c. _ 405 with many flints. The higher division, or Margate Chalk, contains but few scattered flint-nodules, and shows well-marked N.W.andS.E. joints. The lower division, or Broadstairs Chalk, on the other hand, is less jointed, and has many continuous layers of flint. The beds form a very flat arch, as may be seen along the coast from Kingsgate to Pegwell, between which places the flinty chalk rises up from below that with few flints. It is remarkable that in this neighbourhood the Thanet beds are conformable to the Chalk, the green-coated nodular flints at the bottom of the former resting on a peculiar bed of tabular flint at the top of the latter. 3. “ On the Chalk of Buckinghamshire, and on the Totternhoe Stone.” By W. Whitaker, Esq., B.A., F.G.S., &c. In carrying on the geological survey of Buckinghamshire, the Totternhoe Stone (with its underlying chalky marl), which had been sometimes thought to be the representative of the Upper Greensand, was traced south-westwards into a part where that formation was fairly developed, and was then found to overlie it. The divisions of the Chalk in Buckinghamshire are, in ascending order,— (1) Chalk-marl, with stony layers here and there, and at top. (2) The Totternhoe Stone, generally two layers of rather brownish sandy chalk, hard, with dark grains of small brown nodules. (3) Marly white chalk, without flints. (4) Hard-bedded white chalk without flints, forming generally a low ridge at the foot of the great escarpment. (5)*The thick mass of white chalk without flints, or with a very few flints in the uppermost part, and at top. (6) The ‘“chalk-rock,” already described in the Society’s Journal, a thin hard bed or beds, with green-coated nodules. (7) The Chalk with flint, the lowermost part only coming on near the top of the escarpment, the rest bed by bed over the tableland southwards, the angle of dip being rather more than that of the slope of the ground. . *©On the Chalk of the Isle of Wight.” By W. Whitaker, ian B.A., F.G.S., &c. The chief object of this paper was to show that here, as in Oxford- shire, &c., the division between the chalk with flints and chalk without flints is marked by a peculiar bed (“ chalk-rock’’), hard, of a cream-colour, and with irregular-shaped green-coated nodules, which may be seen in many of the pits on the southern flank of the chalk-ridge, where, however, it is very thin. The author disagreed with the inference that the chalk was eroded before the deposition of the Tertiary beds, which has been drawn from the irregular junction of the two in the cliff-sections, and thought that the irregularity had been caused rather by the forma- tion of “‘ pipes” after the deposition of the latter, although he did not deny that there was other evidence of denudation of the Chalk before the deposition of the Tertiaries upon it. [ 406 ] LVI. Intelligence and Miscellaneous Articles. _ ON A NEW THERMO-ELEMENT. BY M. 8S. MARCUS. ih (ea author has given the following account of the prepa and construction of his new thermo-element : — 1. The electromotive force of one of the new elements is sth of that of a Bunsen’s element, and its resistance is equal to 0°4 of a metre of normal wire. $ Six such elements can decompose acidulated water. 3. A battery of 125 elements disengaged in a minute 25 cubic centims. detonating gas; the decomposition took place under unfa- vourable circumstances, ‘for the internal resistance was far greater than that of the interposed voltameter. 4. A platinum wire half a millim. in thickness introduced into the circuit of the same wire is melted.. 5. Thirty elements produce an electro-magnet of 150 pounds lifting-force. 6. The current is produced by heating one of the junctionsof the ele- ments, and cooling the second by water of the ordinary temperature. To construct this battery, it is necessary, on the one hand, to pro- cure two electromotors suitable for a thermo-element, and, on the other, to have such an arrangement of the elements, and of the means for heating and cooling, as will ensure as favourable a result as pos- sible. The former constituted the physical, the latter the construc- tive part of the problem. In solving the first part of the problem it was the author’s endea- vour— a. To use such thermo-elements as are constructed of metals as far apart as possible in the thermo-electric series, and b. Such as permit great differences of temperature without using ice, —which is only practicable if the bars possess as high fusing-points as possible. c. The material of the bars must not be costly, and the bars themselves must be easily constructed. d. The insulation used for the elements must be able to resist high temperatures, and must possess sufficient solidity and elasticity. As neither the usual bismuth-antimony couples nor any combi- nation of the other simple metals satisfy these conditions, M. Mar- cus availed himself of the circumstance that alloys, in the thermo- electric pile, do not stand between the metals of which they consist, and was thereby led to the following alloys, which completely satisfy the above requirements :— For the positive metal— 10 parts of copper, EMS zinc, Gs jj ENREl: An addition of one part of cobalt increases the electromotive force. For the negative metal— 12 parts of antimony, 5 53 zinc, 1 part of bismuth. Intelligence and Miscellaneous Articles. 407 By repeated remelting, the electromotive force of the alloy is in- creased, Or he used a combination of Argentane (known as Alpacca, from the Triestinghofer metal-manufactory) with the above negative metal; or an alloy of 65 parts of copper, 31 dg zinc as positive metal, and an alloy of 12 parts of antimony, Spee zinc ‘as negative metal. The bars are not soldered together, but bound by means of screws. The positive metal melts at about 1200° C., the negative at about 600° C. As in this element it is only the heating of the positive metal which influences the development of electricity, the arrangement has been made that only this is heated, while the negative metal receives heat by conduction. By this arrangement it is possible to apply temperatures of even 600°, and consequently to attain greater differences of temperature. An interesting illustration of the conversion of heat into electri- city is the fact, that the water which is used for cooling the second point of contact of the element becomes warm very slowly as long as the circuit is closed, but pretty rapidly if it is open. The thermo-pile in question was constructed with a view to being used with a gas-flame. ‘The individual elements consist of bars of unequal dimensions; the positive electrical bar is 7” long, 7" broad, and 3" thick; the negative electrical bar is 6” long, 7'” broad, and 6” thick. Thirty-two such elements were screwed together, so that all positive bars were upon one, and all negative on the other side, and thus had the form ofa grating. ‘The battery consists of two such gratings, which are screwed together in a roof shape, and are strengthened by aniron bar. As an insulator between the iron bar and the elements, mica was used. Besides this, the elements, where they came into contact with the cooling water, were coated with so- luble glass. An earthen vessel filled with water was used for cooling the lower contact sides of the elements. The entire battery has a length of 2 feet, a breadth of 6 inches, and a height of 6 inches. M. Marcus communicated further, that he had constructed a furnace which was intended for 768 elements. They represent a Bun- sen’s zinc-carbon battery of thirty elements, and consume per diem 240 pounds of coal.— Sitzungsbericht der Akademie in Wien, No. 8, 1865. —_—— ON PRODUCTION OF MAGNETISM BY TURNING. BY C. B. GREISS. On a visit to the central workshop of the Nasseu Railway, I was struck by the perfect winding of the shavings of cast steel, which were just like a thin rope; and on investigating a specimen. I found that it had two well-pronounced magnetic poles. Subsequently I obtained from the same place a number of shavings of different ma- terlals—cast steel, puddle steel, and soft iron. By means ofa not at all delicate magnetic needle I found that they all possessed po- 408 Intelligence and Miscellaneous Articles. larity ; only one required the application of a finer needle. They had all therefore, by being turned, obtained permanent magnetism, even those which were of soft iron, and which can neither be permanently magnetized by touch nor by the voltaic current. One of the turnings, 7 feet in length, when broken formed two complete magnets. When a turning of puddle steel was broken it exhibited two poles at the fracture, but not so strong by magnetic as the original ones. Even a piece half an inch in length had two poles. No connexion could be perceived between the direction of the winding and the occurrence of the poles, analogous to what prevails in magnets on Ampére’s theory. In one north pole the windings were in the direction in which the hand of a watch moves, in another in the opposite direction. I found, however, that the turnings had all a sharp edge on one side, but somewhat jagged on the other. The sharp edge is obviously formed where the chisel attacks the metal, so that it can be easily determined where the winding begins and where it ceases. ‘Taking this into account, I found that zn all cases a south pole was formed where the turning began, and a north pole where it ceased. In five or six of the pieces the magnetism was stronger than in others. This phenomenon did not originate in the length of the turning nor in their nature, that is, whether of cast steel, puddle steel, or soft iron. But I observed that all turnings whose spires, looked at from the south pole, were in the opposite direction to the motion of the hands of a watch, had a stronger magnetism than those whose spires, looked at from the south pole, coincided in direction with the motion of the hands of a watch.—Poggendorfft’s Annalen, September 1864. ON THE ALTERATION OF ELECTROMOTIVE FORCE BY HEAT, BY F. LINDIG. The following summary is given by the author of the results of an investigation on this subject. : 1. Some of the electrical tensions are dependent on the tempera- ture of the exciters, and change more or less with them. Thus, for instance, copper in sulphate of copper, amalgamated zinc in sulphate of zinc and chloride of zinc, and unamalyamated zinc in solution of chloride of sodium, show an increase of force when warmed; while with the ordinary measuring-instruments this cannot be with cer- tainty shown in the case of sulphuric acid and solution of common salt. 2. The change of force is not always in the same direction: thus, while it decreases with the temperature in the case of copper in sul- phate of copper, and amalgamated zinc in chloride of zine and in sulphate of zinc, with unamalgamated zinc it increases in solution ‘of common salt. 8. The change is not in all cases proportional to the change of temperature between the temperatures + 2° and 85°, as is distinctly seen in the case of zinc in sulphate and chloride of zinc. 4. In accordance with (1) and (2), a Daniell’s element is not con- stant with changing temperature when zinc is surrounded with dilute sulphuric acid or solution of common salt.—Poggendorff’s Annalen, September 1864. Se THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. (FOURTH SERIES.] JUNE 1865. LVII. On the Retardation of Electrical Signals on Land Lines. By ¥Fiermine Jenin, Esq.* [With a Plate. ] N various papers on the theory of the electric telegraph, Professor W. Thomson has investigated the effect produced on electrical signals by lateral induction, and has deduced the laws by which, when certain constants peculiar to each circuit are known, we can calculate the modifications that will occur in any signal, or series of signals, in consequence of transmission through that circuit. The nature of these modifications, which are most marked in the case of submarine cables, may be described as follows. 1. The abrupt well-defined electrical changes produced at the sending-end of the circuit, by making or breaking contact with the battery, are replaced at the receiving-end by changes more or less gradual. ‘Thus, when a current is sent into a cable by suddenly completing the circuit, no sensible effect whatever is at first observed at the further end (supposed in connexion with the earth). After a little while a weak current arrives, and this gra- dually increases until, after a certain time more or less long, a maximum is reached, when, if the insulation were perfect, the received current would be equal to that sent. 2. If the signals be sent in such rapid succession that sufficient time does not elapse between each change of contact for the re- ceived current to acquire this maximum and again fall to zero, then the total magnitude of the change at the receiving-end will be * Communicated by the Author, being an extension of a paper read at the Meeting of the British Association at Bath. Phil. Mag. 8. 4, Vol. 29. No. 198. June 1865. 2H 410 Mr. F. Jenkin on the Retardation of less than that produced at the sending-end ; so that as the rapi- dity with which the signals succeed one another is increased, the variations in the received currents diminish, and above a certain speed no sensible change whatever in the electrical currents in- dicating a signal can be observed, however strong the currents produced near the sending-end of the cable may be. 3. The changes in the received currents corresponding to sig- nals sent are not constant even on a given cable with a given battery, but vary according to the electrical condition of the cir-, cuit, produced by the signals immediately preceding ; so that a given signal at the sending-end does not produce an invariable and constant effect at the receiving-end, but a variable and in- constant effect, depending on preceding signals. Thus when the ordinary electrical signals are sent through a long submarine cable in quick succession, the received signals are not only re- tarded, but, if sent too quickly, they are weaker than those that would have been received through an aérial line of equal length, resistance, and insulation, they are also confused and unintelli- gible, and at a still higher speed are wholly obliterated. The phenomena, as exhibited in long submarine cables, are so marked, and their commercial importance so great, that they have been the subject of considerable study, although even now the constants required for the rigorous application a Professor W. Thomson’s theory are imperfectly known*. Fig. 2, Plate III. is a reduced copy of the curve given by Pro- fessor W. Thomson in the Philosophical Magazine for December 1855, and represents the gradual arrival of an electric current at the further end of a long wire in connexion with the earth, when the near or sending end of the line is connected with the battery for a time sufficiently long to allow the current to reach its maximum. The horizontal ordinates represent times in func- tion of a certain quantity a, and the vertical ordinates the strengths of the current at those times. Thus after a time 6a, the current reaches about 65 per cent. of its maximum strength, ; kel? A ; The quantity a= = lee (5), where k = the resistance of the conductor per unit of length in absolute electrostatic mea- sure, ¢ its absolute electrostatic capacity per unit of length, and Zits length. /1is of course known; k can be pretty accurately calculated from existing data; c is imperfectly known for sub- * There are not many long and perfectly insulated cables in the world on which the necessary experiments can be tried. The Malta Alexandria cable, belonging to H.M. Government, was singularly adapted for these experiments when first laid; but no use whatever has been made of it for this or any other scientific pur pose. Electrical Signals on Land Lines. All ae cables, and hitherto has been quite unknown for land ines. | The mathematical expression for the above curve will not be found in that paper. The following series, for which the writer is indebted to Mr. Charles Hockin, allows the curve to be easily constructed. Let C be the maximum current, and let a have the value given above; then calling # the current at any time ¢, we have t = ot Me = CET ON 2 UON 2 055 (BN SONG #04 1-916) -(@) + (4) —G) +G)-s} The series for uniform imperfect insulation may also be found interesting. Let n express the quotient of the number expressing resistance to loss from one unit of length of the conductor, divided by the resistance of the same unit of length to conduction along itself, then for uniformly imperfect insulation (the case of a*sound sub- marine cable) we have the current Me t 1 1 Nn—e Nn ann a 2 1 ce Bae | (4) Jn 4t +1, on ae ot 1s Aid: 3\ 7 1 3\" I oy ana (i) if iP (3) Figah (3) + 8} } A nn? * 9 nm? * 16 na In the curve as thus drawn, the maximum current will, when graphically represented, be equal to 10a. The object of the present paper is to show the application of the theory to land or aérial lines, and especially to fix an ap- proximate value for the quantity c. The investigation of this sub- ject has hitherto been neglected, inasmuch as the effect of induc- tion in aérial lines is absolutely insensible when any of the ordi- nary methods of signalling are employed. The charge induced on a conductor separated from all surrounding conductors by many feet of air is exceedingly small, and the time required to allow the received current to reach a maximum is correspond- ingly short—so short, indeed, that the speed of transmission appears to depend on the skill of the manipulator and the deli- cacy of the receiving-instruments alone; but when automatic signalling arrangements are employed capable of transmitting a ‘very greatly increased number of words in a given time, the re- tardation due to lateral induction becomes of importance even on moderate lengths of aérial lines. 2H 2 412 Mr. F. Jenkin on the Retardation of One good example of the kind of instrument alluded to is afforded by Professor Wheatstone’s automatic arrangement, with which, ona single circuit, 600 letters per minute can be transmit- ted, each indicated by about three dots on an average, requiring, when reverse currents are used, that they shall be transmitted at the rate of 3600 per minute, or 60 per second. Other automatic arrangements, for instance that of the Che- valier Bonelli, differing exceedingly in most points from that above mentioned, have this in common, that the number of dis- tinct currents required per minute is exceedingly great; and when these arrangements are used on long aérial circuits, the phenomena of induetion place a limit to the number of messages that can be sent in a given time, precisely as the induction in submarine cables limits the capability of the line with ordinary hand-signalling. It becomes, therefore, of importance to the inventors and introducers of these inventions to know where to expect this limit to the rate of transmission, or to the distance over which messages can be sent at a given rate. This consi- deration led the writer to examine whether any existing experi- ments gave the data required; and he found that a paper by M. Guillemin, published in 1860*, afforded, for the particular lines of which he made trial, much of the information wanted. M. Guillemin himself appears to have imperfectly understood the theory of Professor W. Thomson; but it is somewhat difficult to be certain as to his views on this point, owing to a very curious coincidence. Ohm, in his paper “ On the Mathematical Law of the Galvanic Circuit,” published in 18277, not only considers the case of the permanent current which exists according to the well- known relation between electromotive force and resistance known par excellence as Ohm’s Law, but also considers the condition of the current when increasing from nothing to its maximum. Ohm does not suppose that this change can take place instanta- neously, and upon purely hypothetical grounds he arrived at an expression of the law according to which the increase must take place. ‘This law was wholly unsupported by any practical experiment, and appears at the time to have attracted little or no attention. It is, however, exactly that which was later discovered by Professor William Thomson in a more complete form, and with a knowledge of experimental results justifying his conclusions. Ohm’s expression is du d*u Vat X da?’ where u is the potential at the time ¢, and at a point at the * Annales de Chimie et de Physique, 3 sér. vol. 1x. Tt Vide Tayloc’s Scientific Memoirs, vol. ii. * Electrical Signals on Land Lines. 413 distance x from the origin of the cable, y is the specific con- ducting-power of the wire, andy a purely hypothetical quantity, the existence of which Ohm cannot prove, but which he regards as a specific capacity for electricity analogous to the specific capacity of a body for heat, proportional, therefore, to its length and section. Professor William Thomson’s expression is pol _ a Di ee where v is the u of Ohm’s expression, and k and c have the meanings given above. Thus, if we write uf = ke, the two expres- sions become identical. The difference between Ohm’s statement and that of Thomson is simply, that whereas the former assumed a certain quantity for which he can give no value, and of the existence of which he can give no proof, the latter uses a quan- tity, c, of which he can not only prove the existence, but calcu- late the amount from independent data. Ohm was wrong in supposing the capacity for electricity analogous to that for heat, and proportional to the section of the wire ; and therefore no value applicable to all wires even of one metal could be found by ex- periment for his constants. M. Guillemin starts with Ohm’s expression, uses his phraseology, and apparently still believes y to be a specific capacity proportional to the section of the line and the material employed. He is well aware of the existence of the statical charge, but does not appear to have understood its connexion with the phenomena he observed. The results, however, of M. Guillemin’s experiments are, as was to be expected, in accordance with the completed theory, and allow the constants required for its application to land lines to be calculated with some accuracy. The direct measurement of the retardation of a single signal im the manner which has been practised for submarine cables would be exceedingly difficult, if not impossible ; for not only is the retardation on a long line so trifling as to be measured by a few hundredths of a second, but during that exceedingly short interval it would be necessary, if accurate information were wanted, to measure the gradual increase of the electrical current from nothing toa maximum. The direct measurement of the statical charge, from which the retardation could be readily calculated, could hardly be made on land lines as usually insu- lated, owing to the loss of electricity by the posts; the experi- ment would be further vitiated by the so-called polarization at the moist surfaces of the insulators, tending to send a reverse current to that employed to charge the cable. Some indirect 414, Mr. F, Jenkin on the Retardation of method of observing the phenomena was therefore wanted, and that employed by M. Guillemin leaves little to be desired. Figs. 3 and 4 will assist in rendering these experiments intel- ligible. Fig. 3 represents the series of changes produced in the electric current at the receiving-end of a wire by a succession of uniformly long signals, where each contact used to charge and discharge the line is continued for a sufficiently long time to allow the current in each case to rise to its maximum and fall again to zero; c, ¢, ¢, represent the commencement of the charging contacts, and 6, b,, 5, the commencement of the dis- charging contacts. M. Guillemin’s experiments have for their object the defini- tion of the curves cb and bc, each of which is identical with that given in fig. 2; and this object he obtains as follows :— In fig. 4, A L D represents his circuit, formed by a wire leaving Paris and passing through say Tours and Mans back to Paris by a different route. E and E, represent the earth-plates, two in number, G a gal- vanometer, B the battery. The receiving-end of the line D was kept constantly in connexion with the earth and with one end of the galvanometer-coil. The end A of the line, by means of a cylinder suitably arranged and revolving at a given uniform speed, could be alternately connected with M and N (that is to say, with the battery and earth) for short periods, variable.at will, but generally equal to ;!,th or sth of a second. The length of these contacts corresponds to the times indicated by the distance separating c and binfig.3. These contacts sent a succession of signals round the line to be received at D, where they produced a series of changes in the electric current, such as are represented in fig. 8. This current, it will be observed, does not pass through the galvanometer; but the end F of the galvanometer- coil is so connected with the revolving cylinder, that a contact at F can be established for a very short time, represented by the short space r in fig. 3 (equal, say, to +o!5 th of a second), and commencing at any given interval ¢ after the contact with the battery at A has been made. very time such a short contact at D has been completed, a fraction of the received current pass- ing at the moment 1s diverted, and passes through the galvano- meter, tending to deflect the needle. The galvanometer bemg sensitive, a small fraction of the whole current deflects it suffi- ciently for the purpose of observation; this derivation exercises very little influence on the whole resistance of the circuit, and does not sensibly disturb the rate of variation in the current received at D. ‘The constant succession of impulses thus given to the galvanometer-needle, produce a constant deflection indi- cating the strength of the varying received current at a time ¢ Electrical Signals on Land Lines. 415 after the contact with the battery at A has been made. The curve of arrival is perfectly defined by using the time ¢ and the observed strength of current as coordinates (the time 7 remain- ing constant); and quite similarly the curve showing the gradual cessation of the current after the earth-contact has been made at the sending-station, is obtained by making the galvanometer- contact at F at intervals of time ¢ after the connexion is made between A and M. By this simple plan, although the time during which the current varies may not exceed in all a few hundredths of a second, the rate of increase or decrease can be perfectly observed. It is to be regretted that M. Guillemin used a simple detector instead of a measuring-galvanometer, by the deflections of which the relative strengths of the current might have been accurately compared. Data are also want- ing as to the resistance of the lines on which the experiments were made, also as to their insulation and some other points of interest. ‘These omissions prevent us from being able to cal- culate with much accuracy the constant ¢ required for the mathe- matical theory, and render it uncertain whether slight discre- pancies between the theoretical and the observed curves are due to the imperfect method, or to necessary conditions on the lines themselves not taken into account by the theory. M. Guillemin’s results confirm the conclusion that the time required to transmit a signal through a uniform conductor, or, more exactly, to allow the received current to reach a certain proportion of its maximum strength, varies as the square of the length of that conductor. He believes that the electromotive force of the battery does exercise a small influence on the rate of transmission, which is contrary to theory; but the effect ob- served, if any, is very small, not amounting to 10 per cent. when the battery is doubled, and may perhaps be accounted for by considering the improvement which a powerful battery effects on the insulation by producing polarization. The effect of the resistance was not tested, nor does M. Guil- lemin seem to have apprehended the manner in which this ele- ment enters into the calculation. No experiment on this point, however, is required, as the truth of the theory in this respect has been abundantly proved. The comparison between the theoretical and observed curves may be made as follows:—M. Guillemin, with a wire 570 kilo- metres long and 4 millims. in diameter, obtained the results given in the three first lines of the following Table :— 416 Mr. F. Jenkin on the Retardation of TasuE I. Times, in ten-thousandths 17 50) 85 127 |146 1195 Of @/SECONG 220. o<.ncnsee Deviations, in degrees ...... 0°5 25 | 11-5 18-5 | 22 24°2 | 26°5 Percentage of maximum 1-9 9-4 | Al +0 83 91 AeViatiON fies ksi5k eng. ue Times expressed in func- tion of a according to 16 2:2 A] 65 85 | 106 theoretical curve......... Value of a obtained by di- viding the numbers in {| 19.6 the first line by those in WHE MOUTH ie coavece- ree 23 21 19°5 | 17 16:5 _ The meaning of the figures in the Table will be made clearer by an example, thus: 127 ten-thousandths of a second after the signal had been sent, the received current caused a deflection of 18°°5 in the galvanometer, showing that the current had reached 70 per cent. of its maximum strength. The fourth line expresses the fact that, according to Professor Thomson’s theory, this fraction of the maximum strength corresponds to a - period of 6°5 a; and the last line gives the corresponding value of.a (i. e. the quotient of 127 by 6°5). If M. Guillemin’s results were in exact accordance with theory, the value of a would be constant from whatever part of the observed curve it might be calculated. We find, however, that the value is least of all at first, rapidly increases, and again slightly decreases. The small value of a obtained from the shortest period of time is possibly due to the want of propor- tionality between the galvanometer-deflections and the observed current. Still more probably it is due to the difficulty of making an exact observation of so small a deflection as half a degree. We may therefore reject the first result from our cal- culations. Between one or two degrees and twenty, there is often a pretty good agreement between the deflections shown by the common detector and the current passing through it. We find, therefore, as was to be expected, that in passmg from 10 per cent. to 70 per cent. of the maximum current, the value of a varies little. Between 70 and 90 per cent. the values of a again diminish, showing a more rapid increase than would be due to theory. We may therefore say that the observed curve is some- what flatter than the calculated one, resembling in this respect the curves obtained by the writer in experiments on a submarine cable, and due possibly to a similar cause, viz. varying insulation caused on the land lines by the polarization of the moist film on the insulators—and possibly to electromagnetic induction produ- cing currents in the neighbouring wires. Electrical Signals on Land Lines. 417 Tables II. and III. contain the results of two more sets of observations on a line 550 kilometres long. M. Guillemin’s paper contains many other Tables; but those selected appear fair examples. TaBLeE IT, Times, in ten-thousandths 17 133 |50 |65 Fre 136 146 |162 |170 Di SCEODE, coco ccceddes Deviations, in degrees ...... 0} 2 |12 {29 | 42 | 48-7) 4: | 45-5) 46 Percentage of maximum .o| or GOWEAINOW 6. o.6:sguc0~ 0 scone ID ti EE EN el Se Times expressed in func- tion of @ according | 1 | 1:8) 3:2} 5-7; 10:0} 11:0} 11:5] 18:0} 14:0 the theoretical curve ... Value of a obtained by di- viding the numbers in ; the first line by those a ty 48 i 15-6) 11-4) 10°3| 12-4; 12-7} 12 | 12 PRIOPIOUTLN, csv cecccavcves In Table II. it may be suspected that the effect of imperfect proportionality between the higher galvanometer-deflections and the current makes the agreement between the theoretical and experimental curves better than it should be. This impression is confirmed by the result of Table III., expressing the results of experiments in which the arrangements differed from those which gave Table II. only in the resistance of the circuit of deri- vation through the galvanometer—a change which diminished the range of the deflections, but can have produced very little altera- tion in the true received current. TABLE III. Times, in ten-thousandths . ‘ GE ASCCOUE .65..2.0500026. | 7 Pe De & 103 136 | 150 Deviations, in degrees ...... 0°5 ] 4 10 20 23 24°5 Percentage of maximum GEVIALION: fo 2.5+..000 nen 005 ‘ ; : bie ee y fi 28 Times expressed in func-— tion of a according to 15 18 2°6 4°] 80 | 11 the theoretical curve ... Value of a obtained by di- viding the numbers in f ’ : : ; ; the first line by those in ee es = PRS TOUTE o56 cscccceencens This series, like Table I., would give a curve considerably flatter than that due to the simple theory. The effect of imperfect insulation would not bring the theore- tical curves nearer toM.Guillemin’s results. Imperfect insulation, instead of flattening, rather sharpens the curve, as may be seen from the following Table, calculated by the series given above 418 Mr, F. Jenkin on the Retardation of for the length of 350 miles, and with the degree of insulation given by good lines in bad weather. TABLE LV. Times after making con- | tact, = ule pg aiee toda Be a Calculated strength of cur- rent with perfect insula- tion for any strength and 0°64 3°88 6:46 8-58 9°99 length of current, maxi- Ditto with (7=20007 l) oso | 485 | 7-5 Ord 9:99 imperfect 400 an an insulation. | 74000) l| 1-06 ]- 5:56 | 815 | 964 | 9:99 It is clear that the curves represented by these ordinates depart still more from those given by the experiments; and we may therefore presume that the experiments were tried in fine weather, when the insulation was much better than the above. The calculation of c, the electrostatical capacity per metre, may be made as follows. Taking Table I., we find the mean value of a from the last column, neglecting the first number, to be very nearly nineteen and a half 10-thousandths of a second. The resistance of one kilometre of iron wire, 4 millims. in diameter, is about 9°27 B. A. units, or say 92,700,000 absolute electromagnetic =. This value is obtained from the value of Messrs Digney’s resistance-coils expressing one kilometre of iron wire, and exhibited in the International Exhibition for 1862. The value there given from Professor Weber’s determination of the metre-second is 100,800,000, and the value taken in the present paper results from the more accurate determination of the Committee on Electrical Standards. The resistance of one metre of the wire is therefore taken as 9:27 x 10* in electromagnetic units. To convert this into electrostatic measure, it must be divided by (810,740,000)? (vzde Report of British Association for 1863, p. 159); henee lad x LOF 5 aia = 9-656 x 10% equal nearly to 9°6 x 10~"’. 1=570,000; and if we take a equal to 0:00194 second and substitute pie values in the equation given above, we obtain the eel 213. The meanvalue of a from TableI1. value Pe of ie Electrical Signals on Land Lines. 419 for 550 kilometres, excluding the first observations as before, is 0-00132 second; from Table III. it is 0:'00153 second. This last value ought to have coincided with the previous one. The mean of the two is 0:'00142 second: substituting this value for a, and 550,000 for / in the above expression, we obtain as the value of c, 0168. This number should have agreed with the value 0°213 deduced from Table I. The discrepancy shows that it would be of little use to follow out minutely the results to be obtained from every series observed by M. Guillemin. We are not informed of the resistance in the batteries or at the. recelving-end ; the resistance of the lines can only be looked on as the roughest approximation. The state of insulation of the lines is not known, and the de- flections observed are not truly proportional to the currents. With all these sources of error, little dependence can be placed on the accuracy of the result; but M. Guillemin has indicated a method by which correct results might be obtained, and has shown that the phenomena of retardation observed on land lines of the usual construction in France is such as would be produced by an electrostatic capacity of between say 0°15 and 0:25 in electrostatic measure. This result is equivalent to saying that the capacity of a metre length of the wire is equal to that ofa sphere between 0°15 and 0°25 metre radius, supposed in space at a distance from all conductors; or the capacity of a foot of the wire is equivalent to the capacity of a sphere between 0°15 and 0°25 foot radius under the same conditions. This result may be compared with the theoretical capacity of a perfectly insulated wire supposed to be suspended in the air at uniform distances above an infinite flat conducting plane, and approached by no other conductor. The capacity of the wire _under those circumstances would be a eel bap 2 log where h = the height of the wire above the plane, and D its dia- meter (vide article by Professor William Thomson headed “ Tele- graph, Electric,” Encyclopedia Britannica, eighth edition). Taking h= 3 metres and D = 0:004 metre, the above expression gives C = 0-067, or less than half the smallest value obtained from experiment. It is clear that no better agreement was to be expected ; for the conditions in practice are far from agreeing with the postulates of the theory. The above calculated value will be increased by the approach of the posts to the wires, by the proximity of the other conducting-wires, by the capacity of 420 On the Retardation of Electric Signals on Land Lines. the insulators (which will probably vary considerably according to the weather), and possibly by the effects of polarization at the points of support. (The value does not vary rapidly with the variation of height above the ground.) The apparent capacity, measured by the method M. Guillemin adopts, will also be affected by the dynamic induction from wire to wire, the effect of which will be to make the capacity appear larger. Consider- able variations may therefore be expected to be observed between different lines, even where a wire of the same diameter is used ; and the state of the weather may sensibly affect this capacity. The number of signals which may be sent on a land line, of the construction used in M. Guillemin’s experiments, may be deduced from the Table calculated by Professor Thomson, pub- lished by the writer, and now given in an abridged form. TABLE V. Period of dots in function of «, Amplitude in percentage ad kel? 1 107% of maximum. current. re ge og ; DON es oe eae Eee 2°97 cAI By ae rene Dara CTS 6°31 BrO Sete cul oy ak pi vee ae gee O20 re ee et ee ee ee 1S Uae aaa trem arenas 2/10) 7 Sih Se oct diet Ge pen ee ee Qi hee he Mas, oe, Pe ht eee LON Oi Bes SCY Sa eee The first column represents the period of time occupied by two equal contacts at the sending-end of a telegraph wire, the first contact being made with the battery end, and the second with earth. The time is expressed in seconds, and must be calculated. from efor any given conductor. The second column repre- sents the total variation in the received current which will be produced when a regular succession of contacts is sent at the speed given in the first column. The maximum variation, 2. e. that produced by a permanent contact with the battery, is called 100. The value « may be calculated for a given line, using for the resistance per metre of the conductor in B. A. measure, di- vided by 9°656 x 10°, and using the values of ¢ given in this paper, 7. e. from 0°15 to 0:25. As an example, if we take c=0°20, then « on a line 500 kilometres long would be 0°00112 second. By inspection of the Table, we find that a period of 10a is re- quired to produce a variation in the received current equal to one-third of the maximum current that would be received when Dr. Rankine on Rational Approximations to the Circle. 421 kept permanently flowing through the wire. Itis very doubtful whether in practice a smaller variation than this would be avail- able for practical signalling by any of the automatic plans yet invented for aérial lines. This would give for the duration of the shortest signal 0'0112 second, equivalent to about 90 signals per second, or about 5400 per minute; on the Morse alphabet this would correspond to 360 words per minute. On a line of 1000 kilometres this speed would be reduced to 90 words per minute. Thus Professor Wheatstone’s automatic instruments, alluded to in the beginning of this paper, may be expected to transmit at their © full speed over a line 500 kilometres (or say 300 miles) long ; but their speed would necessarily be reduced on a line of double that length, unless, by augmenting the section of the conductor, the value of k be reduced. ‘The value of c would at the same time be increased by doing this; but, as will appear from the formula given above for the suspended wire, its value will not be materially affected within practical limits. The value of k in British electrostatic measure for one foot of No. 8 iron wire is not far from 7°7 x 107“, whereas the value of / in British measure for a foot of the French wire is about 9x10~™. This differ- ence in the value of & makes a difference of about 15 per cent. in the length of the line over which a given speed of signalling could be maintained. By similar means we can calculate the number of words per minute which could be transmitted by any system over any given line. It is to be hoped that experiments will soon be made which will determine the value of c in such a way as to supersede the rough approximation arrived at in the present paper. LVIII. On Rational Approximations to the Circle. By W. J. Macquorn Ranxine, C.L., LL.D., F.RSS.L. & E* iL ol “ena common method of approximating to the ratio which the circumference of a circle bears to its diameter by means of a series of inscribed and circumscribed regular polygons, though practically convenient, is unsatisfactory as regards the illustration of certain general principles, because of the irration- ality of the successive steps of the approximation,—the cir- cumferences of the whole of the regular polygons, with the exception of the inscribed hexagon and circumscribed square, being computed by successive extractions of the square rout, and expressed by means of surds. 2. The object of the present paper is to show how, by using arreguiar inscribed and circumscribed polygons, an indefinite * Communicated by the Author. 422 Dr. Rankine on Rational Approximations to the Circle. series of approximations of any degree of closeness to the cir- cumference of a circle may be obtamed, consisting wholly of rational quantities, computed by the operations of common arit - metic only. 8. This process is not to be recommended for practical use, because of the extreme length of the calculations required by it ; but it appears to me to be worthy of some attention on account of its great simplicity in principle. 4 The method of this paper is so obvious that I was at first unwilling to believe that it could be new; and I now publish it only because I have not been able to find or to hear of any pre- vious publication of it. 5. The following lemarnatays or preliminary propositions, are already well known. Lemma I. Prostem.—To construct an angle whose sine and cosine (and therefore its tangent also) shall be rational frac- tions, and whose sine and tangent shall not differ by more than a given fraction (-) of the tangent. It is well known that if a and 6 be any two whole numbers, a? + b?, a? —b?, and 2ab represent the sides of a rational right- angled triangle ; and therefore either of the acute angles of that triangle fulfils the conditions of the problem. Thus, let @ be the angle opposite the side 2ab; then 2ab a* — b? 2ab sin 6= Pome y cos = a3 tan = 5 5. cel) a tan 0 To fulfil the condition that tan @— sin d= mn 7 We must have anes a? + b?=m’ and consequently OF (2m A) bao eotias ee) Having, then, m the first place assumed any arbitrary value for 6, take for a® any integer square which is not less than (2m—1)b?, and find the required sine, cosine, and tangent by the equations (1). Q.E.F. 6. Lemma II. THrorrm.—lIf the sines and cosines (and therefore the tangents) of two or more angles are rational frac- tions, so also are the sine, cosine, and tangent of any angle formed by adding or subtracting those angles; because these quantities are computed from the sines and cosines of the given angles by addition, subtraction, multiplication, and division. For example, in the case of two angles 6 and ¢, Dr. Rankine on Rational Approximations to the Circle. 423 sin (9+¢)=cos¢sin 0+ cos@ sng; cos (9+¢)=cosdcos OF singsin G; tan 0+ tan d fan tt) 1} tan d tand This theorem includes, as a particular case, the proposition that if the sine and cosine of an angle are rational fractions, so also are the sines, cosines, and tangents of all multiples of that angle. The known formule for the sine and cosine of a multiple angle are here given for convenience of reference. Let cosO@=c, sn@=s; then a1 ag 1%: eh aoe cr—434__ &e, (3) pe: n cosn0@ =c”—n. n—l n— 2 3 7. Proposition [. Tozrorrem.—/J/ all the sides of a polygon inscribed in a circle, save one, are known to be equal to the sides of rational right-angled triangles of which the diameter of the circle as the hypothenuse, then the remaining side of that polygon also is equal to the side of a triangle of the same sort; and consequently the perimeter of the polygon is commensurable with the diameter of the circle. sin 26 =nc"—!s—n ora ew ee For the ratios of the given sides of the polygon to the dia- meter are the sines of a set of angles whose sines and cosines are rational fractions; and the ratio of the remaining side to the diameter is the sine of the sum of those angles, which, by Lemma II., is a rational fraction also, as well as the cosine of that sum ; whence the ratio of the perimeter of the polygon to the diameter of the circle is the sum of a set of rational fractions. Q. E. D. 8. Proposition II. Tororem.—/f tangents be drawn to the circle at the angles of the before-mentioned inscribed polygon, so as to make the corresponding circumscribed polygon, every side of that polygon (and therefore its perimeter) will be commensurable with the diameter of the circle. For each of the parts (which may be called half-sides) into which each side of the circumscribed polygon is divided by its point of contact with the circle bears a ratio to the diameter ex- pressed by a rational fraction (being half the tangent of one of the before-mentioned angles) ; and the ratioof the perimeter of the polygon to the diameter of the circle, bemg the sum of those fractions, is a rational fraction also. Q. H. D 424 Dr. Rankine on Rational Approximations to the Circle. 9. Provosition III. Prostum.—Upon a given circle to construct an inscribed polygon and the corresponding circumscribed polygon, so that the perimeters of both shall be commensurable with the diameter of the circle, and shall not differ from each other by more than a given fraction = of the perimeter of the circumscribed polygon. First sotution.—By Lemma I., find the sine, cosine, and tangent of an angle (@) which shall be rational fractions, and such that the difference between the tangent and sine shall not exceed = of the tangent. Then by the ordinary rules (referred to in Lemma II.) com- pute successively the sines of the multiples of that angle, sin 26, sin 80, &c., until a sine is arrived at, say sin 70, less than sin 0*. Then the inscribed and circumscribed polygons will each have n+1 sides; n of the sides of the inscribed polygon will be equal to each other, and to the diameter of the circle x sin 8, and the remaining side to the diameter x sinn@; and 2n of the half- sides of the circumscribed polygon will be equal to each other, and to the diameter of the circle x = and the remaining two half-sides will be equal to each other, and to the diameter tan (—n6) ono yaa | Thus the ratios of the perimeters of the inscribed and circum- scribed polygons to the diameter of the circle will be respectively inscribed polygon a acios =nsin d+sin nd, BGS (5) circumscribed polygon diameter =ntan@+tan(—né@);. (6) both of which ratios are rational fractions ; and the difference be- tween them is less than = of the greater of them. Q. H. F. SECOND soLuTIoN.—Proceed as before until sin n@ is found less than sin @; then find sin (n+1) 6, which will also be less than sin@. The inscribed and circumscribed polygons will each now have n+2 sides; 2+ 1 of the sides of the inscribed polygon * The value of » might be found with the aid of trigonometrical tables, by taking the greatest whole number in the quotient = ; but this would be a departure from the principle of using none but the elementary processes of arithmetic. Dr. Rankine on Rational Approximations to the Circle. AQ5 will be equal to each other, and to the diameter of the circle x sin@; and n+] of the half-sides of the circumscribed polygon tan gn the remaining side of the inscribed polygon and the remaining pair of half-sides of the circumscribed polygon will have for their arithmetical ratios to the diameter respectively sin (n+1)@ and tan (—n—1)0 2 first side and the (x +1)th side of the inscribed polygon, and the corresponding parts of the circuniscribed polygon, will overlap each other, the closing side of the one and pair of half-sides of the other must run backwards, and must be subtracted in the computation of perimeters. Thus the ratios of the perimeters to the diameter will now be will be equal to each other, and to the diameter x , but will be negative; which means that as the inscribed polygon ui Qa a ri = (n+ 1) sin §— sin (n+1)@, 2 (7) circumscribed polygon diameter both of which ratios are rational fractions, and the difference =(n+1) tan @—tan (—n—1)8, (8) between them is less than — of the greater of them. Q. E. F. 10. Prorosrtion IV. PRosirem.—ZIJn solving the previous problem, to ensure that the denominator of the ratio of the peri- meter of the circumscribed polygon to the diameter shall contain any given factor (f). ‘In applying Lemma I., make either a—b or a+6 a multiple of the given factor; that is to say, having chosen an arbitrary value of b, make BP TT FSI DY APE) and determine the multiplier & by trial, so as to satisfy the con- dition expressed by equation (2), viz. a= (kf+b)? = (2m—1)0%, . . . « (10) 2__ 42 Then cos d= op will contain the given factor f, which will therefore be a factor in the denominator of tan 0, and of the tan- gent of every odd multiple of @, as may be proved by considering the results of dividing equation (4) by equation (3). Then, in solving the problem of Proposition III., use the firs¢ solution if n is odd, and the second solution if 7 is even ; and the denominator of the ratio of the perimeter of the circumscribed polygon to the diameter will contain the given factor. Q. E. F. | 11. It is easy ‘to see that there are an endless variety of Phil. Mag. 8. 4. Vol. 29. No. 198. June 1865. 2F 426 Sir David Brewster on the Cause ways of constructing rational polygons, as they may be called, the methods described in Propositions III. and IV. having been chosen merely as the simplest. For example, in a circle whose diameter is 1, let there be an inscribed rational polygon one of whose sides is sin@. Then if ¢ be any angle less than 0, and such that sin ¢ and cos ¢ are rational, sin @ and sin (@—@) will ~ be two of the sides of a new rational inscribed polygon, subtend- ing together the same arc that is subtended by sin @ in the ori- ginal polygon ; and to the new inscribed polygon will correspond a new circumscribed polygon, which will be rational also, — Glasgow University, April 1865. LIX. On the Cause and Cure of Cataract. By Sir Davip Brewster, K.H., F.R.S.* Y attention was called to the subject of Cataract, in con- sequence of having, about forty years ago, experienced an incipient attack of that complaint, and studied its progress and cure. While engaged in a game at chess with Sir James Hall, who was a very slow player, I amused myself in the intervals with looking at the streams of light which radiated from the flame of a candle in certain positions of the eyelids. In one of these observations I was surprised by a new phenomenon, of which I did not immediately see the cause. The flame of the candle was surrounded with lines of light, of an imperfectly triangular form, some parts of which were deeply tinged with the prismatic colours. Upon going home from the chess club, this optical figure was seen more distinctly round the moon, and of course it appeared, with more or less brightness, round every source of light. Having been engaged in examining the structure of the crys- talline lens in animals of all kinds, I soon discovered the cause of the phenomenon which I have described. The lamine of the crystalline lens had separated near its centre, and the separation had extended considerably towards its margin. The albuminous fluid, the liquor Morgagni, which so wonderfully unites into one transparent body, as pure asa drop of water, the mass of toothed fibres which compose the crystalline lens, had not been suffi- ciently supplied ; and if this process of desiccation had continued, the whole laminz of the lens would have separated, and that state of white opacity have been induced which no attempt has ever been made to remove. The continuance of this affection of the lens was naturally a * From the Transactions of the Royal Society of Edinburgh, vol. xxiv. part 1, Communicated by the Author, and Cure of Cataract. 427 subject. of much anxiety, and I never entertained the slightest hope of a cure. My medical friends recommended the use of what were then called Eye Pills, but having received no benefit from them, and having learned from experience the sympathy between the eye and the stomach, I used every day, and copi- ously, the Pulvis salinus compositus, and at the end of about eight months, when playing at chess in the same apartment, I had the happiness of seeing the lamine of the lens suddenly brought into optical contact, and the entire disappearance of the luminous and coloured apparition with which I had been so long haunted. | In speculating on the process by which the crystalline lens is supplied with the necessary quantity of fluid, it occurred to me that it might be derived from the aqueous humour, and that cataract might be produced when there was too little water and too much albumen in the fluid which filled the aqueous chamber. Upon this hypothesis, incipient cataract might be cured in two ways :— Ist. By discharging a portion of the aqueous humour, in the hope that the fresh secretion, by which the loss is repaired, may contain less albumen, and counteract the desiccation of the lens. 2nd. By injecting distilled water into the aqueous chamber, to supply the quantity of humour discharged from it. The first of these methods I knew to be practicable and _ safe, from the fact that a surgeon in the Manchester Infirmary, many years ago, tapped the aqueous chamber of a female patient forty times, in the vain hope of curing a case of conical cornea, which he attributed to an excess of aqueous humour. The frequent repetition of this operation shows how rapidly the humour is secreted, and how reasonable it is to suppose that, in the case of cataract, a healthier secretion might be produced under medi- cal treatment. Although the second method, of injecting distilled water into the aqueous chamber, presents greater difficulties, yet they do not appear to be insuperable. In 1827, when I happened to be in Dublin, I mentioned this method to the celebrated compara- tive anatomist, Dr. Macartney, who considered it quite practi- cable. He mentioned to me that a foreign oculist, whose name I forget, had actually injected distilled water into the eye of a patient with the view of supplying the aqueous humour that was lost during the extraction of the lens. My attention was recalled to these suggestions for treating incipient cataract, by the results of a series of experiments on the changes which take place in the crystalline lenses of the sheep, the cow, and the horse after death. In these experiments, 428 Sir David Brewster on the Cause which were published in the Philosophical Transactions for 1837, the lenses were placed in a glass trough of distilled water, and exposed to polarized light; and the changes thus produced were indicated by variations in the number and character of the polar- ized rings, and more palpably by the gradual enlargement of the lens. The distilled water passed through the elastic capsule of the lens. The lens increased in size daily, and at the end of several days the capsule burst, leaving the lens in a disorganized state, the outer laminz being ‘reduced to an nein Goo pulp by the water admitted through ‘the capsule. These experiments have an obvious importa in reference to the cause and cure of the two kinds of cataract to which the human eye is subject. The aqueous humour is im immediate contact with the capsule of the crystalline lens. When, there- fore, the humour contains too little water, the lens has not a sufficient supply of the fluid which keeps its fibres and laminee in optical contact, and hence the laminz separate, and the lens becomes opake and hard. When, on the contrary, the aqueous humour contains too much water, the capsule introduces the excess into the lens, and produces the more dangerous affection of soft cataract, in which it is difficult either to depress or extract the lens. In order to cure the first of these kinds of cataract, we must discharge a portion of the aqueous humour, and either supply its place by injecting distilled water, or leave it to nature to sup- ply a more healthy secretion. In or -der to cure the second kind, we must supply the place of the discharged humour with a solu- tion of albumen; or, as in the first case, leave to nature the production of a more albuminous secretion. These views have received a remarkable confirmation from recent experiments on the artificial production and removal of cataract in the eyes of animals. Dr. Kind, a German physiolo- gist, whom I met at Nice in 1857, informed me that he had pro- duced cataract in guinea-pigs by feeding them with much salt, and that the cataract disappeared when there was no salt in their food. More recently, Dr. Mitchell*, an American physician, produced cataract by injecting syrup into the subcuticular sacs of frogs; and Dr. Richardson+ did the same by injectmg syrup into the aqueous chamber of the recently dead eye of a sheep. In the experiment of Dr. Mitchell, the cataract was removed from the living eye of the frog by surrounding the animal with water; and in that of Dr. Richardson, the cataract was removed from the dead eye of the sheep by replacing the syrup with dis- tilled water. * American Journal of the Medical Sciences, January 1860. + Medical Times and Gazette, March 31, 1860. and Cure of Cataract. 429 Neither Dr. Mitchell nor Dr. Richardson seem to have been acquainted with my experiments on the changes in the lens after death, published in 1837, and with the theory of the cause and cure of cataract there referred to, nor with the distinct state- ment of it published in 1836* and, twenty years later, in 18567. Dr. Richardson, however, has borne ample testimony to its prac- ticability and safety, when he suggests, almost in my own words, “that it would be worth while, in the earliest stage of cataract in the human subject, to let out the aqueous humour, and to refill the chamber with simple water.” And he has borne still stronger testimony to its value by congratulating “ Dr. Mitchell in having been the earliest experimentalist to elucidate the synthesis of cataract, and to take the first steps towards a rational interpre- tation of the disease.” The tendency of the human crystalline lens to indurate or soften, by a defect or excess of water in the aqueous humour, may occur at any period of life, and may arise from the general state of health of the patient; but it is most likely to occur at that age (between 40 and 60, and often much earlier) when the lens experiences that change in its condition which requires the aid of spectacles. This change commences at one part of the mar- gin of the lens, where its density is either increased or dimi- nished. Its action in forming a picture on the retina thus becomes unsymmetrical, and vision is sensibly impaired. But when the change has taken place round the margin of the lens, its symmetrical action is restored, and by the use of spectacles the vision becomes as perfect as it was before the change. If glasses are not used when the change is completed, the eye must either strain itself or use a strong light, to produce distinct vision im reading the small] type and the imperfect printing which characterizes the daily press; and by both these processes it will, in a greater or less degree, be injured. It is a strange delusion, arising either from ignorance or vanity, which induces most people to put off the use of spectacles as long as possible. From the instant they are required, spec- tacles of different focal lengths ought to be used for the different purposes for which distinct vision is required; and the eyes should never do any work, unless they can do it with perfect distinct- ness and satisfaction. There is no branch of the healing art where science comes so directly and immediately to the relief of impaired functions as that which relates to vision, and none where science has been so imperfectly applied. When the change in question takes place, the eye requires to be carefully watched, - and used with the greatest caution; and if there is any appear- * Reports of the British Association, 1836, p. 111; and 1837, p. 12. t+ North British Review, vol. xx. p. 167 (November 1856), 430 Mr. J. H. Cotterill on the Further Application ance of a separation of the fibres or lamin, those means should be adopted which, by improving the general health, are most likely to restore the aqueous humour to its usual state. Nothing is more easy than to determine the condition of the crystalline lens; and by the examination of a small luminous object placed at a distance, and the interposition of small apertures, and small opake bodies of a spherical form, we can ascertain the exact point in the lens where the fibres and laminz have begun to separate, and may observe from day to day whether the disease is gaining ground or disappearing. [Since the preceding paper was read, I have seen a remark- able work, entitled Htudes Cliniques sur [ évacuation de ? Humeur Aqueuse dans les Maladies de ? Gil, par Casimir Spirino (Turin, 1862), pp. 500. M. Spirino had, in the course of little more than a year, operated upon forty-five cases of cataract. In many of these the cataract was perfectly cured, and in others the sight was improved. ‘The first case was that of a lady of eighty-one, who had cataract in both eyes. After thirty-two evacuations of the aqueous humour by the same aperture, and almost always two or three times at the same sitting, both cataracts disap- peared, the lady was able to read, without glasses, Nos. 3 and 4 of Jaeger’s scale, at the distance of 4 or 5 inches, and even to thread a small needle. | LX. Further Application of the Principle of Least Action. By James H. Correrizy, B.A., Scholar of St. John’s College, Cambridge*. ? N two former articles of this Magazine the principle that the work done, in a system in equilibrium of elasticity, 1s a minimum, has been applied to cases in which the !aw of varia- tion of internal stress is supposed to be known, and it is required to find the absolute amount of that stress. I shall now consider some cases in which it is required to find the law of variation, chiefly with a view to verify-the statement made in a former article, that the results obtained are identical with those obtained by other methods. 1. A thick hollow cylinder is exposed to fluid pressure, the material being perfectly elastic ; it is required to find the law of variation of the principal pressures. Symmetry shows that the principal pressures must be parallel and perpendicular to a radius of the cylinder. Let p and g be these pressures ; then if a concentric cylinder, radius r and thick- ness or, be conceived divided into equal parts by a longitudinal * Communicated by the Author. of the Principle of Least Action. — 431 plane, 20 {pr}. Sr is the force with which these parts are pressed fai, and this force is also equal to 2gcér, where cis the length of the Rona so that dp g= F ertaper Now the work done is by Clapeyron’s theorem proportional to if (p+q)?—kpq}rdr (since p and-g are principal pressures) , k being a constant depending on the nature of the material*, We must therefore have {[e2@+0-m1%+ {2(p +9) —kp}8q|rdr= for all forms of dp 5g consistent with d. 6p dg=Sp+r. a whence, by the rules of the calculus of variations, {2(p + q)—kg—A}r+ S4n08} =0, 2(p+q)—kp+r=9, where Ais an unknown ‘ee of r, Eliminating X, we obtain ae kk (p+q)= £5278 p+q) —Kpr° ; but dp ld ptq= ees a Sp 77h (4-8) {pr} = 54 22 + (4—apr | 5 whence dp gg OP. 2r re = constant, and c = 3 + C9; Cy ie T C95 * The work done in a parallelopipedal element will not be altered by a quantity of the same order by supposing its sides inclined at an infinitesimal angle. The third principal pressure is parallel to the axis of the cylinder, and may be supposed zero without at all affecting the result. 432 Mr. J. H. Cotterill on the Further Application two equations which determine the law of variation required. These results agree with those obtained by M. Lamé and Pro- fessor Rankine. 2. A thin perfectly elastic sprmg is bent by the action of forces acting on it; it is required to find its form. Here the work done in the spring is very approximately a ds, where M is the bending moment at the poit consi- dered, EF the modulus of elasticity, ds an element of are-of the spring-curve. Consequently { M?ds must be a mimimum; but it is shown in works on applied mechanics that Mo 8 where p is the radius of curvature of the spring at the point considered ; and it follows therefore that a must beaminimum. Adopt- ing this principle, the problem is discussed in Jellet’s ‘ Calculus of Variations,’ where it 1s ascribed to D. Bernoulli. 8. A solid smooth hard cylinder fits into a semicircular recess in an indefinite solid of hard material, lined with a thin layer of soft material; to find the law of variation of the pressure on the cylinder. Here, if the pressure at an angular distance 6 from the bot- tom be p, the work done will be approximately proportional to \p?d0, which integral must consequently be a minimum, subject to the condition that (2p. cos 0.1. a6 shall be equal to half 0 the load on the cylinder. Consequently {{p? + 2kp cos 03d0 must bea minimum, where £ is an arbitrary constant. Therefore p=-—kcos@; but if W be the load, = 2r(*p cos 0 dé 0 —2rk | * cos 6 d0=—1 ark; 0 whence ill, 2W TY and 2W = —.,.cos0@ P TT ? an equation which gives the law of variation of the pressure, and of the Principle of Least Action. 433 shows that its maximum intensity is double of its mean inten- sity. The conditions necessary for the truth of this solution may perhaps be approximately realized in the case of a shaft and its bearing. 4. In the most general case of the equilibrium of elasticity, U the work done is given by the equation x {iV 2 2 : 2U0= N,+N,+N ea it NotNs} _N,N,+N,N,+N.Nj—T2—-T2—T.2 bb dx dydz, where N,, N., Nz are the intensities of the normal pressures on three faces of the element perpendicular to the axes of z, y, z respectively, ‘T,, T,, T the intensities of the tangential stress on the element parallel to the planes yz, xz, xy respectively, and Aw are constants depending on the nature of the material which is ‘supposed homogeneous, and of perfect elasticity. The notation, to facilitate comparison, is the same as that employed by M. Lamé. This value of U must now be made a minimum, subject to three equations of condition necessary for the equilibrium of the element, namely, ANVeaTeclid Pio 5 Pig’ a ae dE pe d Nagin dV yah de t dy t de =” he Nt, dN Mondial endzhan (Lamé, Lecons sur [ Klasticité, chap. 7.) Applying Lagrange’s process, we obtain three equations, of which one is ey 2 elie 2 pop (N4+N,+Ny}— ets — i da’ and three other equations, of which one is 27, _ dy , dy be dz ~~ dy $1, $a, pz being unknown functions of a, y, z. 43,4 Mr. J. H. Cotterill on the Further Application - Now if with M. Lamé we take _N,+N,4+N; ON+ 26 3 we have No+Ns=(8A+2u)0—N,, — and the first equation becomes 2(14 ~)e— BA+ 2h pe _ thy, be ps fe dat or Nant eke The two other equations may be reduced in ce manner ; also from the second set of equations, dps a T=) a het sg dy with two other symmetrical equations. Now on comparing these equations with M. Lamé’s (p. 65, equations (1)), they are seen to be identical on supposing $= 2u, gh o=2v, $,=2w; and thus it appears that the results of the ap- plication of the principle of Least Action are identical with those obtained by M. Lamé, which furnishes an independent proof of the principle in the case of perfect elasticity. Before leaving the subject, I will make some general remarks in conclusion. Though nothing has been strictly proved, except that the va- riation in the work done in a perfectly elastic body due to a change in the resisting forces is zero, yet it 1s sufficiently evident that the work is a minimum. That is, of all values of the work possible on the supposition that the resistances in terms of which the work is expressed may be not merely resisting or (as they have been called) “passive” forces, but applied or “active” forces, the least is that which corresponds to the passive forces. I think that, seen from this point of view, the principle of Least Action is nearly self-evident, even without the confirmatory evi- dence that the variation in the case of a perfectly elastic body is zero; for the change of a force which is really an effect, mto a force which is really a cause, must increase directly or indirectly the total effect. On the other hand, the energy expended may be said to be a maximum. ‘That is, of all values of the energy expended by the really active forces possible on the supposition that those forces may be active which are really passive, the greatest value physi- cally possible corresponds to the passive forces. Thus a weight of the Principle of Least Action. 435 placed on a beam descends as low as possible; for if any possible different values of the passive forces would enable that weight to descend, it would certainly descend and produce those values. But there is a restriction imphied in the words “ physically pos- sible,” namely, that the energy expended cannot exceed a certain limit consistently with the physical constitution of the mass of matter; and the function representing the energy expended is not a maximum in the technical sense of the word. It is just the same in the case of the principle of least resistance: each re- sisting force is indeed the least possible; but its limiting value depends on the constitution of the whole mass, and it is not, properly speaking, a minimum, though the least possible. In my first article I attempted to state the conditions imposed by the physical constitution of the mass; they were framed with the view of avoiding any assumption as to its continuity. They may perhaps seem arbitrary and insufficient ; but whatever dif- ficulty there may be in stating these conditions correctly, it is clear that (as was poimted out for the conditions stated) they must be introduced in the act of expressing the work in terms of the forces; and this, which is confirmed by the fact that the function representing the work is susceptible of a minimum value, is the reason why results can in general be obtained by the prin- ciple of least action, but only in peculiar cases by the principle of least resistance. The principle employed in these articles has a manifest ana- logy to the dynamical principle of least action, so that I have ventured to use the same name and even to call it an extension of that principle, and they may perhaps be cases of a gene-_ ral law. But it is not my intention at present to attempt to develope this analogy; the object of this imperfect sketch has simply been to show that the distribution of the resistance of matter to the action of force is governed by a law of Least Action, and that that law is capable of being applied to all, and may advantageously be applied to some of the cases where it is required to find that distribution. Unless Bernoulli’s principle mentioned above be an instance, I am not aware that such a method has been hitherto used, and it therefore may perhaps be new. From want of opportunity, however, I am un- acquainted with much that has been done on this subject. I especially regret that I have not seen the new edition of the Lecons of Navier, referred to by M. de St. Venant in a paper translated in the Philosophical Magazine for January 1865. April 30, 1865. Norte. If U, the work done in a body, be conceived to be expressed in 436 Prof. Maxwell and Mr, F, Jenkin on the Elementary terms of the displacements of the points of application of the forces acting on its surface, on the supposition that the passive forces are replaced by any active forces which can be in equilibrium with the — applied forces, then, since oU= df Xou+ Yov+Zéwt, where uw, v, w are the component displacements of the point of appli- cation of the force whose components are X, Y, Z, we have dU = x dU SSH. dU = 7. du dv dw equations which express a property of U analogous to the well-known property of the potential energy of a particle consequent on its vici- nity to an attracting body, and to the properties of the accumulation of vis viva of a dynamical system. LXI. On the Elementary Relations between Electrical Measure- ments. By Professor J. Cuerk Maxweii and FLEEMING JENKIN, Esq.* Part 1.—Jntroductory. A, OPe CTS of Treatise—The progressive extension of the electric telegraph has made a practical knowledge of electric and magnetic phenomena necessary to a large num- ber of persons who are more or less occupied in the construc- tion and working of the lines, and interesting to many others who are unwilling to be ignorant of the use of the network of wires which surrounds them. ‘The discoveries of Volta and Galvani, of Girsted, and of Faraday are familiar in the mouths of all who talk of science, while the results of those discoveries are the foundation of branches of industry conducted by many who have perhaps never heard of those illustrious names. Between the student’s mere knowledge of the history of discovery and the workman’s practical familiarity with particular operations which can only be communicated to others by direct imitation, we are in want of a set of rules, or rather principles, by which the laws remembered in their abstract form can be applied to estimate the forces required to effect any given practical result. We may be called on to construct electrical apparatus for a particular purpose. In order to know how many cells are required for the battery, and of what size they should be, we require to know the strength of the current required, the elec- tromotive force of the cells, and the resistance of the circuit. If * Reprinted from the Reports of the British Association for 1863. Relations between Electrical Measurements. 437 we know the results of previous scientific inquiry, and are ac- quainted with the method of adapting them to the case before us, we may discover the proper arrangement at once. If we are unable to make any estimate of what is required before construct- ing the apparatus, we may have to encounter numerous failures which might have been avoided if we had known how to make a proper use of existing data. All exact knowledge is founded on the comparison of one quantity with another. In many experimental researches con- ducted by single individuals, the absolute values of those quan- tities are of no importance; but whenever many persons are to act together, it is necessary that they should have a common understanding of the measures to be employed. The object of the present treatise is to assist in attaining this common under- standing as to electrical measurements. 2. Derwation of Units from fundamental Standards.—Kvery distinct kind of quantity requires a standard of its own, and these standards might be chosen quite independently of each other, and in many cases have been so chosen; but it is pos- sible to deduce all standards of quantity from the fundamental standards adopted for length, time, and mass; and it is of great scientific and practical importance to deduce them from these standards in a systematic manner. Thus it is easy to understand what a square foot is when we know what a linear - foot is, or to find the number of cubic feet in a room from its length, breadth, and height—because the foot, the square foot, and the cubic foot are parts of the same system of units. But the pint, gallon, &c., form another set of measures of volume, which has been formed without reference to the system based on length; and in order to reduce the one set of numbers to the other, we have to multiply by a troublesome fraction, difficult to remember, and therefore a fruitful source of error. The varieties of weights and measures which formerly pre- vailed in this country, when different measures were adopted for different kinds of goods, may be taken as an example of the principle of unsystematized standards, while the modern French system, in which everything is derived from the elementary: standards, exhibits the simplicity of the systematic arrange- ment. In the opinion of the most practical and the most scientific men, a system in which every unit is derived from the primary units with decimal subdivisions is the best whenever it can be introduced. It is easily learnt; it renders calculations of all kinds simpler ; itis more readily accepted by the world at large ; and it bears the stamp of the authority, not of this or that legis- lator or man of science, but of nature. 438 Prof. Maxwell and Mr. F. Jenkin on the Elementary The phenomena by which electricity is known to us are of a mechanical kind, and therefore they must be measured by mecha- nical units or standards. Our task is to explain how these units may be derived from the elementary ones; in other words, we shall endeavour to show how all electric phenomena may be measured in terms of time, mass, and space only, referring briefly in each case to a practical method of effecting the observation. 3. Standard Mechanical Units.—In this country the standard of length is one yard, but a foot is the unit popularly adopted. In France it is the ten millionth part of the distance from the pole to the equator, measured along the earth’s surface, accord- ing to the calculations of Delambre ; and this measure is called a metre, and is equal to 3:280899 feet, or 39:37079 inches. The standard unit of time in all civilized countries is deduced from the time of rotation of the earth about its axis. The side- real day, or the true period of rotation of the earth, can be ascer- tained with great exactness by the ordinary observations of astro- nomers; and the mean solar day can be deduced from this by our knowledge of the length of the year. The unit of time adopted in all physical researches is one second of mean solar time. The standard unit of mass is in this country the avoirdupois pound, as we received it from our ancestors. The grain is one 7000th of a pound. In the French system it is the gramme, derived from the unit of length by the use of water at a stan- dard temperature as a standard of density. One cubic centi- metre of water is a gramme = 15:48235 grains =:00220462 lb. A Table showing the relative value of the standard and derived units in the British and metrical systems is given in § 55. The unit of force adopted in this treatise is that force which will produce a unit of velocity in a free unit mass, by acting on it during a unit of time. This unit of force is equal to the weight cf the unit mass divided by gy, where g is the accele- rating force of gravity = 32:088 (1+ 0°005133 sin? X) in Brit. units | at the level or =9°78024 (1+ 0:005133 sin? A) in met. units { of the sea, d being the latitude of the place of observation. A unit of force still very generally adopted is the weight of the standard mass. ‘ The value of the new unit is 3 times the old or gravitation unit. The unit of work adopted in this treatise is the unit of force, defined as above, acting through the unit of space (vade § 55). 4. Dimensions of Derived Units.—Every measurement of which Relations between Electrical Measurements. 439 we have to speak involves as factors measurements of time, space, and mass only ; but these measurements enter sometimes at one power, and sometimes at another. In passing from one set of fundamental units to another, and for other purposes, it 1s useful to know at what power each of these fundamental mea- surements enters into the derived measure. Thus the value of a force is directly proportional to a length and a mass, but inversely proportional to the square of a time. This is expressed by saying that the dimensions of a force are LM . , : “pz 3 in other words, if we wish to pass from the English to the French system of measurements, the French unit of force ; 3°28 x 15:43 2 will be to the English as ued cs Tt: or.as 90°6 to. 1: because there are 3°28 feet in a metre, and 15°43 grains in a gramme. If the minute were chosen as the unit of time, the net 1 unit of force would, in either system, be 3600 of that founded on the second as unit. A Table of the dimensions of every unit adopted in the present treatise is given in § 55. Part I1.—The Measurement of Magnetic Phenomena. 5. Magnets and Magnetic Poles.—Certain natural bodies, as the iron ore called loadstone, the earth itself, and pieces of steel after being subjected to certain treatment, are found to possess the following properties, and are called magnets. If one of these bodies be free to turn in any direction, the presence of another will cause it to set itself in a position which is conveniently described or defined by reference to certain ima- ginary lines occupying a fixed position in the two bodies, and called their magnetic axes. One object of our magnetic mea- surements will be to determine the force which one magnet exerts upon another. It is found by experiment that the greatest manifestation of force exerted by one long thin magnet on another occurs very near the ends of the two bars, and that the two ends of any one long thin magnet possess opposite qua- lities. This peculiarity has caused the name of “ poles ” to be given to the ends of long magnets; and this conception of a magnet, as haying two poles capable of exerting opposite forces joined by a bar exerting no force, is so much the most familiar that we shall not hesitate to employ it, especially as many of the properties of magnets may be correctly expressed in this way ; but it must be borne in mind, in speaking of poles, that they do not really exist as points or centres of force at the ends of the 440 Prof. Maxwell and Mr. F. Jenkin on the Elementary bar, except in the case of long, infinitely thin, uniformly mag- netized rods. If we mark the poles of any two magnets which possess simi- lar qualities, we find that the two marked poles repel each other, that two unmarked poles also repel each other, but that a marked and an unmarked pole attract each other. The pole which is repelled from the northern regions of the earth is called a posi- tive pole; the other end the negative pole. The negative pole is generally marked N by British instrument-makers, and is sometimes called the north pole of the magnet, whereas it is obviously similar to the earth’s south pole. The strength of a pole is necessarily defined as proportional to the force it is capable of exerting on any other pole. Hence the force f exerted between two poles of the strengths m and m, must be proportional to the product mm,. The force, f, is also found to be inversely proportional to the square of the distance, D, separating the poles, and to depend on no other quantity ; hence we have, unless an absurd and useless coefficient be introduced, ee ON et eee 1) from which equation it follows that the unit pole will be that which at unit distance repels another similar pole with unit force; f will be an attraction or a repulsion according as the poles are of opposite or the same kinds. The dimensions of the unit magnetic pole are T 6. Magnetic Field.—It is clear that the presence of a magnet in some way modifies the surrounding space, since any other magnet brought into that space experiences a peculiar force. The neighbourhood of a magnet is, for convenience, called a magnetic field; and for the saine reason the effect produced by a magnet is often spoken of as due to the magnetic field instead of to the magnet itself. This mode of expression is the more proper, inasmuch as the same or a similar condition of space may be produced by the passage of electrical currents in the neighbourhood, without the presence of a magnet. Since the peculiarity of the magnetic field consists mm the presence of a certain force, we may numerically express the properties of the field by measuring the strength and direction of the force, or, as it may be worded, the intensity of the field and the direction. of the lines of force. This direction at any point is the direction in which the force tends to move a free pole; and the intensity, H, of the field is necessarily defined as proportional to the force, /, with which it Relations between Electrical Measurements. 441 acts on a free pole; but this force, /, is also proportional to the strength, m, of the pole introduced into the field, and it depends on no other quantities; hence . Ht yo hivanth. Ae Shae: et and therefore the field of unit intensity will be that which acts with unit force on the unit pole. 2 The dimensions of H are Ls L?T The lines of force produced by a long thin bar magnet near its poles will radiate from the poles, and the intensity of the field will be equal to the quotient of the strength of the pole divided by the square of the distance from the pole; thus the unit field will be produced at the unit distance from the unit pole. Ina uniform magnetic field the lines of force, as may be demonstrated, will be parallel; such a field can only be pro- duced by special combinations of magnets, but a small field at a great distance from any one pole will be sensibly uniform. Thus, in any room unaffected by the neighbourhood of iron or mag- nets, the magnetic field due to the earth will be sensibly uni- form ; its direction will be that assumed by the dipping-needle. 7. Magnetic Moment.—In reality we can never have a single pole entirely free or disconnected from its opposite pole; and it is time to pass to the consideration of the effect produced on a material bar magnet in a magnetic field. In a uniform field two equal opposite and parallel forces act on its poles, and tend to set it with the line joming those poles in the direction of the force of the field. When the magnet is so placed that the line joining the poles is at right angles to the lines of force in the field, this tendency to turn or “couple,” G, is proportional to the intensity of the field, H, the strength of the poles, m, and the distance between them, /; or Bnd Hey) ceed yl hoondo Sy ml, or the product of the strength of the poles into the length between them, is called the magnetic moment of the magnet; and from equation (3) it follows, that, in a field of unit intensity, the couple actually experienced by any magnet in the above position measures its moment. ‘The dimensions of the unit of | = M2 magnetic moment are evidently ase 8. Intensity of Magnetization.—The intensity of magnetiza- tion of a magnet may be measured by its magnetic moment divided by its volume. Phil. Mag. S. 4, Vol. 29. No. 198. June 1865. 2G 442 Prof. Maxwell and Mr. F. Jenkin on the Elementary The dimensions of the unit of magnetization are therefore oe the same as in the case of intensity of field. 9. Coefficient of Magnetic Induction—When certain bodies, such as soft iron, &c., are placed in the magnetic field, they become magnetized by “induction”; so that the intensity of magnetization is (except when great) nearly proportional to the intensity of the field. In diamagnetic bodies, such as bismuth, the direction of magnetization is opposite to that of the field. In paramagnetic bodies, such as iron, nickel, &c., the direction of magnetization is the same as that of the field. : | The coefficient of magnetic induction is the ratio of the inten- sity of magnetization to the intensity of the field, and is there- fore a numerical quantity, positive for paramagnetic bodies, negative for diamagnetic bodies. 10. Magnetic Potentials and Equipotential Surfaces—If we take a very long magnet, and, keeping one pole well out of the way, move the other pole from one point to another of the mag- netic field, we shall find that the forces in the field do work on the pole, or that they act as a resistance to its motion, according as the motion is with or contrary to the force acting on the pole. Ifthe pole moves at right angles to the force, no work is done. The magnetic potential at any pomt im a magnetic field is measured by the work done by the magnetic forces on a unit pole during its motion from an infinite distance from the mag- net producing the field to the point in question, supposing the unit pole to exercise no influence on the magnetic field in ques- tion. The idea of potential as a mathematical quantity having different values at different points of space, was brought into form by Laplace*. The name of potential, and the application to a great number of electric and magnetic investigations, were introduced by George Green, in his Essay on Electricity (Not- tingham, 1828). An equipotential surface in a magnetic field is a surface so drawn that the potential of all its points shall be equal. By drawing a series of equipotential surfaces corresponding to poten- frals 15001. oes co n, we may map out any magnetic field so as to indicate its properties. | ) The magnetic force at any point is perpendicular to the equipotential surface at that point, and its intensity is the reci- procal of the distance between one surface and the next at that * Mecanique Céleste, liv. u1. Relations between Electrical Measurements. 443 point. The dimensions of the unit of magnetic potential are L? Mt él 11. Lines of Magnetic Force. —There is another way of explo- ring the magnetic field, and indicating the direction and mag- nitude of the force at any point. The conception and applica- tion of this method in all its completeness are due to Faraday *. The full importance of this method cannot be-recognized till we come to electromagnetic phenomena ($$ 22, 23, & 24). A line, whose direction at any point always coincides with that of the force acting on the pole of a magnet at that point, is called a line of magnetic force. By drawing a sufficient number of such lines, we may indicate the direction of the force in every part of the magnetic field; but by drawing them according to rule, we may indicate the intensity of the force at any point as well as its direction. It has been shownyt that if, in any part of their course, the number of lines passing through unit of area is proportional to the intensity there, the same proportion between the number of lines in unit of area and the intensity will hold good in every part of the course of the lines. All that we have to do, therefore, is to space out the lines in any part of their course, so that the number of lines which start from unit or area is equal to the number representing the inten- sity of the field there. The intensity at any other part of the field will then be measured by the number of lines which pass through unit of area there; each line indicates a constant and equal force. 12. Relation between Lines of Force and Equipotential Sur- faces.—The lines of force are always perpendicular to the equi- potential surfaces; and the number of lines passing through unit of area of an equipotential surface is the reciprocal of the distance between that equipotential surface and the next in order—a statement made above in slightly different language. _ {tna uniform field the lines of force are straight, parallel, and equidistant ; and the equipotential surfaces are planes perpen- dicular to the lines of force, and equidistant from each other. If one magnetic pole of strength m be alone in the field, its lines of force are straight lines, radiating from the pole equally in all directions; and their number is 4am. The equipotential surfaces are a series of shares) whose centres are at the pole, and whose radii are m, 3m, im, im, &c. In other magnetic arrangements these lines and surfaces are more complicated ; * Experimental Researches, vol, ii. art. 3122 et passim. t Vide Maxwell on Faraday’s Lines of Force, Cambridge Phil, Trans. 1857. 2G2 4Ad, - Prof. Maxwell and Mr. F. Jenkin on the Elementary but in all cases the calculation is simple, and in many cases the lines and surfaces can be graphically constructed without any calculation. . Part III.—Measurement of Electric Phenomena by their Electro- magnetic Effects. 13. Preliminary.—Before treating of electrical a the exact meaning in which the words “ quantity,” “ current,” “electromotive force,” and “ resistance’’ are used will be ex- plained. But, in giving these explanations, we shall assume the reader to be acquainted with the meaning of such expressions as conductor, insulator, voltaic battery, &c. 14. Meaning of the words “Electric Quantity.’—When two light conducting bodies aré connected with the same pole of a voltaic battery, while the other pole is connected with the earth, they may be observed to repel one another. The two poles pro- duce equal and similar effects. When the two bodies are con- nected with opposite poles, they attract one another. Bodies, when in a condition to exert this peculiar force one on the other, are said to be electrified, or charged with electricity. These words are mere names given to a peculiar condition of matter. If a piece of glass and a piece of resin are rubbed together, the glass will be found to be in the same condition as an. insulated body connected with the copper pole of the battery, and the resin in the same condition as the body connected with the zine pole of the battery. The former is said to be positively, and the latter negatively electrified. The propriety of this antithesis will soon appear. The force with which one electrified body acts on an- other, even at a constant distance, varies with different circum- stances. When the force between the two bodies at a constant distance, and separated by air, is observed to increase, it is said to be due to an increase in the quantity of electricity ; and the quantity at any spot is defined as proportional to the force with which it acts, through air, on some other constant quantity at a distance. If two bodies, ‘char ged each with a given quantity of electricity, are incorporated, the single body thus composed will be charged with the sum of the two quantities. It is this fact which justifies the use of the word “ quantity.” Thus the quality in virtue of which a body exerts the peculiar force described is called electricity, and its quantity is measured (ceteris paribus) by measuring force. The quantity thus defined produced on two similar balls simi- larly circumstanced, but connected with opposite poles of a vol- taic battery, is equal, but opposite; so that the sum of these two equal and opposite quantities is zero; hence the conception of positive and negative quantities. Relations between Electrical Measurements. 445 In speaking of a quantity of electricity, we need not conceive it as a separate thing, or entity distinct from ponderable matter, any more than in speaking of sound we conceive it as having a distinct existence. Still it is convenient to speak of the inten- sity or velocity of sound, to avoid tedious circumlocution ; and quite similarly we may speak of electricity, without for a moment imagining that any real electric fluid exists. The laws according to which the force described varies, as the shape of the conductors, their combinations, and their distances are varied, have been established by Coulomb, Poisson, Green, W. Thomson, and others. These will be found accurately de- scribed, independently of all hypothesis, in papers by Professor W. Thomson, published in the Cambridge Mathematical Journal, vol. i. p. 75 (1846), and a series of papers in 1848 and 1849. 15. Meaning of the words “ Electric Current.’—When two balls charged by the opposite poles of a battery, with opposite and equal quantities of electricity, are joimed by a conductor, they lose in a very short time their peculiar properties, and assume a neutral condition intermediate between the positive and negative states, exhibiting no electrical symptoms whatever, and hence described as unelectr ified, or containing no electricity. But during the first moment of their junction, the conductor is found to possess certain new and peculiar properties: any one part of the conductor exerts a force upon any other part of the con- ductor; it exerts a force on any magnet in the neighbourhood ; and if any part of the conductor be formed by one of those com- pound bodies called electrolytes, a certain portion of this body will be decomposed. These peculiar effects are said to be due to a current of electricity in the conductor. The positive quantity, or excess, is conceived as flowing into the deficiency caused by the negative quantity ; so that the whole combination is reduced to the neutral condition. This neutral condition is similar to that of the earth where the experiment is tried. If the balls are continually recharged by the battery, and discharged or neutral- ized by the wire, a rapid succession of the so-called currents will be sent; and it is found that the force with which a magnet is deflected by this rapid succession of currents is proportional (ceteris paribus) to the quantity of electricity passed through the conductor or neutralized per second; it is also found that the amount of chemical action, measured by the weights of the bodies decomposed, is proportional to the same quantity. The currents just described are intermittent ; but a wire or conductor, used simply to join the two poles of a pattery, acquires perma- nently the same properties as when used to discharge the balls as above with great rapidity; and the greater the rapidity with which the balls are discharged, the more perfect the similarity of 446 Prof. Maxwell and Mr. F. Jenkin on the Elementary . the condition of the wire in the two cases. The wire im the latter case is therefore said to convey a permanent current of electricity, the magnitude or strength of which is defined as pro- portional to the quantity conveyed per second. This definition is expressed by the equation =. 7.11 1 ee where C is the current, Q the quantity, and? the time. A per- manent current flowing through a wire may be measured by the force which it exerts on a magnet; the actual quantity it conveys may be obtained by comparing this force with the force exerted under otherwise similar conditions, when a known quantity is sent through the same wire by discharges. The strength of a permanent current is found at any one time to be equal im all parts of the conductor. Conductors conveying currents exert a peculiar force one upon another ; and during their merease or decrease they produce currents in neighbouring conductors. Similar effects are produced as they approach or recede from neighbouring conductors. The laws according to which currents act upon magnets and upon one another will be found in the writings of Ampére and Weber. : 16. Meaning of the words “ Electromotive Force.”’”—Hitherto we have spoken simply of statical effects; but it 1s found that a current of electricity, as above defined, cannot exist without effecting work or its equivalent. Thus it either heats the con- ductor, or raises a weight, or magnetizes soft iron, or effects chemical decomposition ; in fine, in some shape it effects work, and this work bears a definite relation to the current. Work done presupposes a force in action. The immediate force pro- ducing a current, or, in other words, causing the transfer of a certain quantity of electricity, is called an electromotive force. This force 1s necessarily assumed as ultimately due to that part of a circuit where a “degradation” or consumption of energy takes place: thus we speak of the electromotive force of the vol- taic or thermoelectric couple; but the term is used also inde- pendently of the source of power, to express the fact that, how- ever caused, a certain force tending to do work by setting elec- tricity in motion does, under certain circumstances, exist between two points of a conductor or between two separate bodies. But equal quantities of electricity transferred in a given time do not necessarily or usually produce equal amounts of work; and the electromotive force between two points, the proximate cause of the work, is defined as proportional to the amount of work done between those points when a given quantity of electricity is transferred from one point to another. Thus if, with equal,cur- rents in two distinct conductors, the work done in the one is Relations between Electrical Measurements. 4.4.7 double that done in the second in the same time, the electromotive force in the first case is said to be double that in the second; but if the work done in two circuits is found strictly proportional to the two currents, the electromotive force acting on the two cur- rents is said to be the same. Defined in this way, the electro- motive force of a voltaic battery is found to be constant so long as the materials of which it is formed remain in a similar or con- stant condition. The above definitions, in mathematical lan- guage, give W=ECz, or W 5 has hot ate ee where E is the electromotive force, and W the work done. Thus the electromotive force producing a current in a conductor is equal to the ratio between the work done in the unit of time and the current effecting the work. This conception of the relations of work, electromotive force, current, and quantity will be aided by the following analogy:—A quantity of electricity may be compared to a quantity or given mass of water; currents of water. in pipes in which equal quantities passed each spot in equal times would then correspond to equal currents of electricity ; electro- motive force would correspond to the head of water producing the current. Thus if, with two pipes conveying equal currents, the head forcing the water through the first was double that forcing it through the second, the work done by the water in flowing through the first pipe would necessarily be twice that done by the water in the second pipe; but if twice as much water passed through the first pipe as passed through the second, the work done by water in the first pipe would again be doubled. This corresponds exactly with the increase of work done by the electrical current when the electromotive force is doubled, and when the quantity is doubled. Thus, to recapitulate, the quality of a battery or source of electricity, in virtue of which it tends to do work by the transfer of electricity from one point to another, is called its electromo- tive force, and this force is measured by measuring the work done during the transfer of a given quantity of electricity between those points. The relations between electromotive force and work were first fully explained in a paper by Prof. W. Thomson “ Qn the application of the principle of Mechanical Effect to the Measurement of Electromotive Forces,” published in the Philo- sophical Magazine for December 1851. 17. Meaning of the words “ Electric Resistance.” —It is found by experiment, that even when the electromotive force between two points remains constant, so that the work done by the transfer of a given quantity of electricity remains constant, nevertheless, by modifying the material and form of the conductor, this transfer 448 Prof. Maxwell and Mr. F. Jenkin on the Elementary may be made to take place im very different times; or, in other words, currents of very different magnitudes are produced, and very different amounts of work are done in the unit of time. The quality of the conductor in virtue of which it prevents the performance of more than a certain amount of work in a given time bya given electromotive force is called its electrical resistance. The resistance of a conductor is therefore inversely proportional to the work done in it when a given electromotive force 1s main- tained between its two ends; and hence, by equation (5), it is inversely proportional to the currents which will then be pro- duced ‘in the respective conductors. But it is found by experi- ment that the current produced in any case in any one conductor is simply proportional to the electromotive force between its ends; hence the ratio C will be a constant quantity, to which the re- sistance as above defined must be proportional, and may with convenience be made equal ; thus E RoE a an equation expressing Ohm’s law. In order to carry on the parallel with the pipes of water, the resistance overcome by the water must be of such nature that twice the quantity of water will flow through any one pipe when twice the head is applied. This would not be the result of a constant mechanical resistance, but of a resistance which increased in direct proportion to the speed of the current ; thus the electrical resistance must not be looked on as analogous to a simple mechanical resistance, but rather to a coefficient by which the speed of the current must be multiplied to obtain the whole mechanical resistance. Thus if the electrical resistance of a conductor be called R, the work W is not equal to CRt, but Cx CR xz, or WC, |, eee eee) where C may be looked on as analogous to a quantity moving at a certain speed, and CR as analogous to the mechanical resist- ance which it meets with in its progress, and which increases in direct proportion to the quantity conveyed in the unit of time. 18. Measurement of Electric Currents by thetr Action on a Magnetic Needle.-—In 1820, Oersted discovered the action of an electric current upon a magnet at a distance; and one method of measurement may be based on this action. Let us suppose the current to be in the circumference of a vertical circle, so that in the upper part it runs from left to right. Then a magnet sus- E * By equation (5) we have W=CEz#; but by equation (6) R= @; hence W=C’Rt.—Q.E.D. Relations between Electrical Measurements. 449 pended in the centre of the circle will turn with the end which points to the north away from the observer. This may be taken as the simplest case, as every part of the circuit is at the same distance from the magnet, and tends to turn it the same way. The force is proportional to the moment of the magnet, to the strength of the current as defined by § 15, to its length, and Inversely to the square of its distance from the magnet. Let the moment of the magnet be mi, the strength of the cur- rent C, the radius of the circle 4, the number of times the cur- rent passes round the circle n, the angle between the axis of the magnet and the plane of the circle 0, and the moment tending to turn the magnet G, then G=mlC . 2rnk 700s 8, FF MAR ANC SES) which will be unity if m/, C, k, and the length of the circuit be unity, andif @=0°. The unit of current founded on this relation, and called the electromagnetic unit, is therefore that current of which the unit of length placed along the circumference of a circle of unit radius produces a unit of magnetic force at the centre. The usual way of measuring C, the strength of a current, is by making it describe a circle about a magnet, the plane of the circle being vertical and magnetic north and south. Thus, if H be the intensity of the horizontal component of terrestrial mag- netism, and G the moment of this on the magnet, G=m/H sin 0, whence the strength of the current Bee elie 6 =5-, Htan te ah, eprrentrve (9) where & is the radius of the circle, n the number of turns, H the intensity of the horizontal part of the earth’s magnetic force as determined by the usual method, and @ the angle of deviation of the magnet suspended in the centre of the circle. As the strength of the current is proportional to the tangent of the angle 0, an instrument constructed on this plan is called a tangent galvano- meter. The instrument called a sine galvanometer may also be used, provided the coil is circular. The equation is similar to that just given, substituting sin @ for tan 0. To find the dimensions of C, we must consider that what we observe is the force acting between a magnetic pole, m, and a cur- rent of given length, L, at a given distance, L,, and that this force = T2° Hence the dimensions of C, an electric current at L? M2 thus measured, are ieee 19. Measurement of Electric Currents by their mutual action 450 Prof. Maxwell and Mr. F. Jenkin on the Elementary on one another.—Hitherto we have spoken of the measurement of currents as dependent on their action upon magnets; but this measurement in the same units can as simply be founded on their mutual action upon one another. Ampére has investigated the laws of mechanical action between conductors carrying currents. He has shown that the action of a small closed circuit at a dis- tance is the same as that of a small magnet, provided the axis of the magnet be placed normal to the plane of the cireuit, and the moment of the magnet be equal to the product of the current into the area of the circuit which it traverses. Thus, let two small circuits having areas A and A, be placed at a great distance D from each other in such a way that their planes are at right angles to each other, and that the line D is in the intersection of the planes. Now let currents C and C, circulate in these conductors; a force will act between them tending to make their planes parallel, and the direction of the currents opposite. The moment of this couple will be fe ee ae if Sea Hence the unit electric current conducted round two circuits — of unit area in vertical planes at right angles to each other, one - circuit being at a great distance, D, vertically, above the other, will cause a couple to act between the circuits of a magnitude = The definition of the unit current (identical with the unit founded on the relations given in § 18) might be founded on this action quite independently of the idea of magnetism. 20. Weber's LElectro-Dynamometer.—The measurement de- scribed in the last paragraph is only accurate when D is very great, and therefore the moment to be measured very small. Hence it is better to make the experimental measurements in another form. For this purpose, let a length (/) of wire be made into a circular coil of radius 4; let a length (/,) of wire be made into a coil of very much smaller radius, 4,. Let the second coil be hung in the centre of the first, the planes being vertical and at the angle @. Then, if a current C traverses both coils, the moment of the force tending to bring them parallel will be ea eae Sie a sin 0. POE roe eS This force may be measured in mechanical units by the angle through which it turns the suspended coil, the forces called into play by the mechanical arrangements of suspension being known from the construction of the instrument. Weber used a bifilar suspension, by which the weight of the smaller coil (10) | | £ Relations between Electrical Measurements. 451 was used to resist the moment produced by the action of the currents. 21. Comparison of the Electromagnetic and Electrochemical action of Currents.—Currents of electricity, when passed through certain compound substances, decompose them ; and it is found that, with any given substance, the weight of the body decom- posed in a given time is proportional to the strength of the cur- rent as already defined with reference to its electromagnetic effect. The voltameter is an apparatus of this kind, in which water is the substance decomposed. Special precautions have to be taken, in carrying this method of measurement into effect, to prevent variations in the resistance of the circuit, and conse- quently in the strength of the current. This subject is more fully treated in Part V. $§ 58, 54. 22. Magnetic Field near a Current.—Since a current exerts a force on the pole of a magnet in its neighbourhood, it may be said to produce a magnetic field ($ 6), and, by exploring this field with a magnet, we may draw lines of force and equipoten- tial surfaces of the same nature as those already described for magnetic fields caused by the presence of magnets. When the current is a straight line of indefinite length, like a telegraph-wire, a magnetic pole in its neighbourhood is urged by a force tending to turn it round the wire, so that this force is at any poit perpendicular to the plane passing through this point and the axis of the current. The equipotential surfaces are therefore a series of planes passing through the axis of the current, and inclined at equal angles to each other. The number of these planes is 47C, where C is the strength of the current. The lines of magnetic force are circles, having their centres in the axis of the current, and their planes perpendicular to it. The intensity of the magnetic force at a distance, k, from the current is the reciprocal of the distance between two equipoten- tial surfaces, which shows the forces to be oe The work done on a unit magnetic pole in going completely round the current is 47C, whatever the path which the pole describes. | 23. Mechamcal Action of a Magnetic Field on a closed Con- ductor conveying a Current.—When there is mechanical action between a conductor carrying a current and a magnet, the force acting on the conductor must be equal and opposite to that acting on the magnet. Every part of the conductor is therefore acted on by a force perpendicular to the plane passing through its own direction and the lines of magnetic force due to the magnet, and equal to the product of the length of the conductor 452 Prof. Maxwell and Mr. F. Jenkin on the Elementary into the strength of the current, the intensity of the magnetic field, and the sine of the angle between the lines of force and the direction of the current. This may be more concisely expressed by saying that if a conductor carrying a current is moved in a magnetic field, the work done on the conductor by the electromagnetic forces is equal to the product of the strength of the current into the number of lines of force which it cuts during its motion. Hence we arrive at the fallowvinie general law, for determining the mechanical action on a closed conductor carrying a current and placed in a magnetic field :— Draw the lines of magnetic force. Count the number which pass through the circuit of the conductor, then any motion which increases this number will be aided by the electromag- netic forces, so that the work done during the motion will be the product of the strength of the current and the number of additional lines of force. For instance, let the lines of force be due to a single magnetic pole of strength m. These are 477m in number, and are in this case straight lines radiating equally in all directions from the pole. Describe a sphere about the pole, and project the circuit on its surface by lines drawn to the pole. The surface of the area so described on the sphere will measure the solid angle sub- tended by the circuit at the pole. Let this solid angle =o, then the number of lines passing through the closed surface will be mw; and if C be the strength of the current, the amount of work done by bringing the magnet and circuit from an infi- nite distance to their present position will be Cmw. This shows that the magnetic potential of a closed circuit carrying a unit current with respect to a unit magnetic pole placed at any point is equal to the solid angle which the circuit subtends at that point. By considering at what points the circuit subtends equal solid angles, we may form an idea of the surfaces of equal potential. They form a series of sheets, all intersecting each other in the circuit itself, which forms the boundary of every sheet. The number of sheets is 47rC, where C is the strength of the current. The lines of magnetic force intersect these surfaces at right angles, and therefore form a system of rings, encircling every point of the circuit. When we have studied the general form of the lines of force, we can form some idea of the electromag- netic action of that current, after which the difficulties of nume- rical calculation arise entirely from the imperfection of our mathematical skill. 24. General Law of the Mechanical Action between Electric Currents and other Electric Currents or Magnets.—Draw the 3 Relations between Electrical Measurements. 453 lines of magnetic force due to all the currents, magnets, &c., in the field, supposing the strength of each current or magnet to be reduced from its actual value to unity. Call the number of lines of force due to a circuit or magnet, which pass through another circuit, the potential coefficient between the one and the other. This number is to be reckoned positive when the lines of force pass through the circuit in the same direction as those due to a current in that circuit, and negative when they pass in the opposite direction. If we now ascertain the change of the potential coefficient due to any displacement, this increment multiplied by the product of the strengths of the currents or magnets will be the amount of work done by the mutual action of these two bodies during the displacement. The determination of the actual value of the potential coefficient of two things, in various cases, is an import- ant part of mathematics as applied to electricity. (See the mathematical discussion of the experiment, Appendix D. Brit. Assoc. Reports, 1863, p. 168.) 25. Electromagnetic Measurement of Electric Quantity—A conducting body insulated at all points from the neighbouring conductors may in various ways be electrified, or made to hold a quantity of electricity. This quantity ($ 14) is perfectly definite in any given circumstances; it cannot be augmented or dimi- nished so long as the conductor is insulated, and is called the charge of the conductor. Its magnitude depends on the dimen- sions and shape and position of the insulated and the neighbour- ing conductors, on the imsulating material, and finally on the electromotive force between the insulated and the neighbouring’ conductors, at the moment when the charge was produced. The well-known Leyden jar is an arrangement by which a consider- able charge can be obtained on a smail conductor with moderate electromotive force between the inner and outer coatings, which constitute respectively the “insulated” and “neighbouring ” conductors referred to in general. We need not enter into the general laws determining the charge, since our object is only to show how it may be measured when already existing; but it may be well to state that the quantity on the charged insulated conductor necessarily implies an equal and opposite quantity on the surrounding or neighbouring conductors. We have already defined the magnitude of a current of elec- tricity as simply proportional to the quantity of electricity con- veyed in a given time, and we have shown a method of measu- ring consonant with this definition. The unit quantity will therefore be that conveyed by the unit current as above defined in the unit of time. Thus, if a unit current is allowed to flow for a unit of time in any wire connecting the two coatings of a 454 Prof. Maxwell and Mr. F. Jenkin on the Elementary Leyden phial, the quantity which one coating loses, or which the other gains, is the electromagnetic unit quantity*. The mea- surement thus defined of the quantity in a given statical charge can be made by observing the swing of a galvanometer-needle produced by allowing the charge to pass through the coil of the galvanometer in a time extremely short compared with that oc- ' cupied by an oscillation of the needle. Let Q be the whole quantity of electricity in an instantaneous current, then C4 Q=2——sin 3%,”. Mae i ea where C, = the strength of a current giving a unit deflection (45° on a tangent or 90° on a sine galvanometer), ¢ = half the period or time of a complete oscillation of the needle of the gal- vanometer under the influence of terrestrial magnetism alone, and 7 = the angle to which the needle is observed to swing from a position of rest, when the discharge takes place. C, is a con- stant which need only be determined once for each instrument, provided the horizontal force of the earth’s magnetism remain unchanged. In the case of the tangent galvanometer, the for- mula for obtaining it has already been given. From equations (9) and (12) we have for a tangent galvanometer Q= 5 Hisin di, 2) geht aeiaGpay where, as before, A = the radius of the coil, and n = the number of turns made by the wire round the coil. } The quantity in a given charge which can be continually repro- duced under fixed conditions may be measured by allowing a succession of discharges to pass at regular and very short mter- vals through a galvanometer, so as to produce a permanent de- flection. The value of a current producing this deflection can be ascertained ; and the quotient of this value by the number of discharges taking place in the “ second” gives the value of each charge in electromagnetic measure. To find the dimensions of Q, we simply observe that the unit of electricity is that which is transferred by the unit current in the unit of time. Multiplying the dimensions of C by T, we find the dimensions of Q are L? M?. 26. Electric Capacity of a Conductor.—lIt is found by experi- ment that, other circumstances remaining the same, the charge on an insulated conductor is simply proportional to the electro- motive force between it and the surrounding conductors, or, in other words, to the difference of potentials (47). The charge * Weber calls this quantity two units—a fact which must not be lost sight of in comparing his results with those of the Committee. Relations between Electrical Measurements. 4.55 that would be produced by the unit electromotive force is said to measure the electric capacity of a conductor. Thus, generally, the capacity of a conductor S = = where Q is the whole quan- tity in the charge produced by the electromotive force E. When the electromotive force producing the charge is capable of main- taining a current, the capacity of the conductor may be obtained without a knowledge of the value either of Q or E, provided we have the means of measuring the resistance of a circuit in elec- tromagnetic measure. For let R be the resistance of a circuit, in which the given electromotive force, EK, will produce the unit deflection on a tangent galvanometer, then, from equations (6) and (12), we have tsindi wR, where ¢ and 2 retain the same signification as in equation (13) 25). . Direct Measurement of Electromotive Force.—The meaning of the words “electromotive force”? has already been explained (§ 16). This force tends to do work by means of a current or transfer of electricity, and may therefore be said to produce and maintain the current. In any given combination in which elec- tric currents flow, the immediate source of the power by which the work is done is said to produce the electromotive force. The sources of power producing electromotive force are various. Of these, chemical action in the voltaic battery, unequal distribution of temperature in circuits of different conductors, the friction of different substances, magnetoelectric induction, and simple elec- tric induction are the most familiar. An electromotive force may exist between two points of a conductor, or between two points of an insulator, or between an insulator and a conductor, —in fine, between any points whatever. This electromotive force may be capable of maintaining a current for a long time, as in a voltaic battery, or may instantly cease after producing a current of no sensible duration, as when two points of the atmo- sphere at different potentials (§ 47) are jomed by a conductor ; but in every case in which a constant electromotive force, H, is maintained between any two points, however situated, the work spent or gained in transferring a quantity, Q, of electricity from one of those points to the other will be constant; nor will this work be affected by the manner or method of the transfer. If the electricity be slowly conveyed as a static charge on an insu- lated ball, the work will be spent or gained in accelerating or retarding the ball; if the electricity be conveyed rapidly through a conductor of small resistance, or more slowly through a con- S=2 . (14) 456 Prof. Maxwell.and Mr. F. Jenkin on the Elementary ductor of great resistance, the work may be spent in heating the conductor, or it may electrolyze a solution, or be thermoelectri- cally or mechanically used; but in all cases the change effected, measured as equivalent to work done, will be the same, and equal to EQ. Hence the electromotive force between two points is unity, if a unit of mechanical work is spent (or gained) in the transfer of a unit of electricity from one point to the other. This general definition is due to Professor W. Thomson. The direct measurement of electromotive force would be given by the measure, in any given case, of the work done by the trans- fer of a given quantity of electricity. The ratio between the numbers measuring the work done, and the quantity trans- ferred, would measure the electromotive force. This measure- ment has been made by Dr. Joule and Professor Thomson, by determining the heat. developed in a wire by a given current measured as in (§ 18)*. 28. Indirect Measurements of Llectromotive Force.—The direct method of measurement is in most cases inconvenient, and in many impossible; but the indirect methods are nume- rous and easily applied. The relation between the current, C, the resistance, R, and the electromotive force, E, expressed by Ohm/’s law (equation 6), will determine the electromotive force of a battery whenever R and C are known. A second indirect method depends on the measurement of the statical force with which two bodies attract one another when the given electro- motive force is maintained between them. This method is fully treated in Part IV. (43). The phenomenon on which it is based admits of an easy comparison between various electromotive forces by electrometers. This method is applicable even to those cases in which the electromotive force to be measured is inca- pable of maintaming a current. The laws of chemical electro- lysis and electromagnetic induction afford two other indirect methods of estimating electromotive force in special cases (54 and 81). 29. Measurement of Electric Resistance.—We have already stated that the resistance of a conductor is that property in vir- tue of which it limits the amount of work performed by a given electromotive force in a given time, and we have shown that it thud may be measured by the ratio G of the electromotive force between two ends of a conductor to the current maintained by it. The unit resistance is therefore that in which the unit electromotive force produces the unit current, and therefore per- forms the unit of work, in the unit of time. If im any circuit * Phil. Mag. S. 4. vol. 11. (1851), p. 551. Relations between Electrical Measurements. — 457 we can measure the current and electromotive force, or even the ratio of these magnitudes, we should, zpso facto, have measured the resistance of the circuit. The methods by which this ratio _ has been measured, founded on the laws of electromagnetic in- duction, are fully described in Appendix D (Brit. Assoc. Re- ports, p. 163). Other methods may be founded on the measure- ment of currents and electromotive forces described in 18, 19, 20, 27, and 28. Lastly, a method founded on the gradual loss of charge through very great resistances will be found in Part IV. (45). The equation (25) there given for electrostatic measure is applicable to electromagnetic measure when the capacity and difference of potentials are expressed in electro- magnetic units. 30. Electric Resistance in Electromagnetic Units is measured by an Absolute Velocity —The dimensions of R are found, by comparing those of E and C, to be = or those of a simple velo- city. This velocity, as was pointed out by Weber, is an absolute velocity in nature, quite independent of the magnitude of the fundamental units in which it is expressed. The following illus- tration, due to Professor Thomson, will show how a velocity may express a resistance, and also how that expression may be inde- pendent of the magnitude of the units of time and space. Let a wire of any material be bent into an are of 571° with any radius, k. Let this are be placed in the magnetic meridian of any magnetic field, with a magnet of any strength freely sus- pended in the centre of the arc. Let two vertical wires or rails, separated by a distance equal to k, be attached to the ends of the arc; and let a cross piece slide along these rails, inducing a current in the arc. Then it may be shown that the speed required to produce a deflection of 45° on the magnet will mea- sure the resistance of the circuit, which is assumed to be con- stant. This speed will be the same whatever be the value of f, or the intensity of the magnetic field, or the moment of the magnet. In this form the experiment could not be easily car- ried out; but if a length, /, of wire be taken and rolled into a circular coil at the radius 4, and the distance between the ver- 2 tical rails be taken equal to = then, if the resistance of the cir- cuit be the same as in the previous case, the deflection of 45° will be produced by the same velocity in the cross piece, measuring that resistance; or, generally, if the distance between the rails 2 be Ps then p times the velocity required to produce the unit deflection (45°) will measure the resistance. The truth of this Phil. Mag. 8. 4. Vol. 29. No. 198. June 1865. 2H 458 Prof. Maxwell and Mr. F. Jenkin on the Elementary proposition can easily be established when the laws of magneto- electric induction have been understood (31). 31. Magneto-electric Induction.—Let a conducting circuit be placed in a magnetic field. Let C be the intensity of any cur- rent in that circuit; HE the magnitude of the electromotive force acting in the circuit. Let the circuit be so moved that the number of lines of magnetic force (11) passing through it is increased by N in the time 7, then (23) the electromagnetic forces will contribute towards the motion an amount of work measured by CN. Now Q, the quantity of electricity which passes, is equal to C¢; so that the work done on the current is EQ or CEt. By the principle of conservation of energy, the work done by the electromagnetic forces must be at the expense of that done by the electromotive forces, or CN+CHi=0; or dividing by Cé, we find that ee = (15) or, in other words, if the number of lines of force passing through a circuit be increased, an electromotive force in the negative direction will act in the circuit measured by the number of lines of force added per second. If R be the resistance of the circuit, we have by Ohm’s law ( quation 6) H=CR; and therefore N= —Ht=—RCt=—RQ;. .. . (16) of, in other words, if the number of lines of magnetic force passing through the circuit is altered, a current will be produced in the circuit in the direction opposite to that of a current which would have produced lines of force in the direction of those added, and the quantity of electricity which passes, multi- plied by the resistance of the circuit, measures the number of additional lines passing through the circuit. The facts of magneto-electric induction were discovered by Faraday, and described by him in the First Series of his “ Expe- rimental Researches in Electricity,” read to the Royal Society, November 24th, 1831. He has shown* the relation between the induced current and the lines of force cut by the circuit, and he has also described the state of a conductor in a field of force as a state the change of which is a cause of currents. He calls it the electrotonic state; and, as we have just seen, the electrotonic state may be measured by the number of lines of force which pass posh the circuit at any time. * Experimental Researches, 3082, &e. Relations between Electrical Measurements. 459 The measure of electromotive force used by W. Weber, and derived by him (independently of the principle of conservation of energy) from the motion of a conductor in a magnetic field, is the same as that at which we have arrived; for, from equa- tion (15), we find that the unit electromotive ‘force will be pro- duced by motion in a magnetic field when one line of force is added (or subtracted) per unit of time ; and this will occur when in a field of unit intensity a straight bar of unit length, forming part of a circuit otherwise at rest, is moved with unit velocity perpendicularly to the lines of force and to its own direction. - ToW.Weber, whose numerical determinations of electrical mag- nitudes are the starting-point of exact science in electricity, we owe this, the first definition of the unit of electromotive force ; but to Professor Helmholtz* and to Professor W. Thomsont, working independently of each other, we owe the proof of the necessary existence of magneto-electric induction, and the deter- mination of electromotive force on strictly mechanical principles. 32. On Material Standards for the Measurement of Electrical Magnitudes.—The comparison between two different electrical magnitudes of the same nature, e. g. between two currents or between two resistances, is in all cases much simpler than the direct measurement of these magnitudes in terms of time, mass, and space, as described in the foregoing pages. Much labour is therefore saved by the use of standards of each magnitude; and the construction and diffusion of those standards form part of the duties of the Committee. Electric currents are most simply compared by “ electro-dyna- mometers ” (20)—instruments which, unlike galvanometers, are ractically independent of the intensity of the earth’s magnetism. hen an instrument of this kind has been constructed, with which the values of the currents corresponding to each deflection have been measured (19), (20), other instruments may easily bé so compared with this standard that the relative value of the deflections produced by equal currents on the standard and the copies shall be known. Hence the absolute value of the current indicated by each deflection of each copy will be known in abso- lute measure. In other words, in order to obtain the electro- magnetic measure of a current in the system described, each observer in possession of an electro-dynamometer which has been compared with the standard instrument will simply multiply by a constant number the deflection produced by the current on his instrument (or the tangent or sine of the deflection, Pes to the particular construction of the instrument). * Paper read before the Physical Society of Berlin, 1847 (vide Taylor’: s Scientific Memoirs, part 2. Feb. 1853, p. 114), tT Reports of the British Association, 1848; Phil. Mag. Dec. 1851. 2H 2 460 Prof. Cayley on a Theorem relating Electric quantities may be compared by the swing of the needle of a galvanometer of any kind. They may be measured by any one in possession of a standard electro-dynamometer, or resist- ance-coil, since the observer will then be in a position directly to determine C, in equation (12), or R, in equation (14). — Capacities may be compared by the methods described (26) ; and a Leyden jar or condenser (4:1) of unit capacity, and copies derived from it, may be prepared and distributed. The owner of such a condenser, if he can measure electromotive force, can de- termine the quantity in his condenser. The material standard for electromotive force derived from elec- tromagnetic phenomena would naturally be a conductor of known shape and dimensions, moving in a known magnetic field. Such a standard as this would be far too complex to be practically useful: fortunately a very simple and practical standard or gauge of electromotive force can be based on its statical effects, and will be described in treating of those effects (Part IV. 43). A practical standard for approximate measurements might be formed by a voltaic couple, the constituent parts of which were in a standard condition. .It is probable that the Daniell’s cell may form a practical standard of reference in this way, when its value in electromagnetic measure is known. This value lies between 9 x 107 and 11 x 107. Resistances are compared by comparing currents produced in the several conductors by one and the same electromotive force. The unit resistance, determined as in Appendix D (Brit. Assoc. Reports, p. 163), will be represented by a material conductor ; simple coils of insulated wire compared with this standard, and issued by the Committee, will allow any observer to measure any resistance in electromagnetic measure. [To be continued. | LXII. On a Theorem relating to Five Points in a Plane. By A, Cayizy, F.R.S.* eee triangles, ABC, A’B/C’ which are such that the lines AA', BB’, CC! meet in a point, are said to be in perspec- tive; and a triangle A/B/C’, the angles A’, B’, C’ of which lie in the sides BC, CA, AB respectively, is said to be inscribed in the triangle ABC; hence, if A’, B’, C’ are the intersections of the sides by the lines AO, BO, CO respectively (where O is any point whatever), the triangle A!B’C’ is said to be perspectively inscribed in the triangle ABC, viz. it is so inscribed by means of the point O. We have the following theorem, relating to any triangle * Communicated by the Author. to Five Points in a Plane. 461 ABC, and two points O, O'. If in the triangle ABC, by means of the point O, we inscribe a triangle A'B/C’, and in the triangle A'B/C’, by means of the point O’, we inscribe a triangle «Py, then the triangles ABC, «Sy are in perspective, viz. the lines Az, BS, Cry will meet in a point. This is very easily proved analytically ; in fact, taking 2=0, y=0, z=0 for the equations of the lines B'C’, C'A', A’B! respec- tively, and (X, Y, Z) for the coordinates of the point O, then the coordinates of (A, B, C) are found to be (—X, Y, Z), (X, — Y, Z), (X, Y, —Z) respectively. Moreover, if (X’, Y', Z') are the co- ordinates of the point O’, then the coordinates of («, 8, y) are found to be (0, Y', Z'), (X!, 0, ¥), (X!, Y', 0) respectively. Hence the equations of the lines Az, BB, Cy are respectively Peet 1 ry, 2p =O) pa miele. —X, Y, Z X,—Y, Z Xo¥y=Z ery”: -Z! ee OOS Zt x @ that is, ) z( YZ'—Y'Z)+y/( Z'X) +2(—XY! =O; z(—YZ! \ty( ZX'—Z'X) +2( XIV} =0, ze( MDH ZX... \+-e{ ..SY'—K'Y)=0, which are obviously the equations of three lines which meet in a point. But the theorem may be exhibited as a theorem relating to a quadrangle 1234 and a point O'; for writing 1, 2, 3, 4 im place of A, B, C, O, the triangle A'B’C! is in fact the triangle formed by the three centres 41.23, 42.31, 43.12 of the qua- drangle 1234, hence the triangle in question must be similarly related to each of the four triangles 4238, 431, 412,123; or, forming the diagram B LQ s0uisi-s AP IB) Aeey Be PQ PLA ADS Gy Ae he | 2 seo Ok Ll A S. we have the following form of the theorem: viz. the lines a4, B3, y2 meet in a point P, a3, B4, yl ”? 9 Q, a2, Bl, y4 5) 9 R, al, 62, 8 ” ” S, 462 Prof. Cayley on a Theorem relating or, what is the same thing, we have with the points 1,2, 3, 4 and the point O! constructed the four points P,Q, RS such that 18, 2R, 3Q, 4P meet in a, O89 1B, 40,38 i 32a 88,°4B/\1Q, 22) bon ve ae The eight points 1, 2, 3, 4, P,Q, R, S form a aoe such as the perspective representation of a parallelopiped, or, if we please, a cube; and not only so, but the plane figure 1s really a certain perspective representation of the cube ; this identification depends ~ on the following two theo- rems :— 1. Considering the four summits 1, 2, 3, 4, which are such that no two of them belong to the same ‘edge, then, if through any point O we draw | the line OA! meeting the lines 41, 23, 33 OB! 39 39 Ai2, 31, 99 OC’ 99 ) 43, 12, and the lines Oz, O8, Oy parallel to the three edges of the cube respectively, the three planes (OA!’, Ox), (OB! OB), (OC’, Or) will meet in a line. | 2. For a properly-selected position of the point O, the lines OB', OC’, Oc will lie in a plane, 3) OC'" OA’, Os 33 33 3 9 | OA’, OB’, Oy 29 99 ‘ In fact for such a position of O, projecting the whole figure on any plane whatever, the lines Ol, 02, 03, O4, OP, OQ, OR, OS, Oa, OB, Oy, OA', OB', OC' meet the plane of projection in the points 1, 2, 3, 4, P, Q, R, S, a, 6, y, A’, B’, C' related to each other as in the last-mentioned form of the plane theorem. To prove the two solid theorems, take O for the origin, Ox, O8, Oy for the axes, (a, 8, y) for the coordinates of the summit S, and 1 for the edge of the cube, the coordinates of 1 are +1, 8, Y; PP) 2 EP) a; B +- I, Y> eee By) hy Bo ae OCR ec 4 99 a+, 6+1, y+I. to Five Points in a Plane. 463 The equations of the line OA’, or say of the line O/41, 23), are those of the planes O 41, O 28, viz. these are ¥ rY¥ 2 =0, [% y 52 =0; . a+t1,8 » a, B+1, ¥ id a+1, B41, y+1 a, B »ytl that is, a(B—y)— (a+1)(y—2)=0, aB+ytl)—e (y+z)=0. ‘Writing for shortness - M=e+6+y+1, these equations give 2a(a+1) ] ped a ; (M + 2rya) (M+ 208) ‘M+ 2ya “M+2a08" or completing the system, for lme OA! we have 2s a eee? are Vote) Giese Tee Y= (N+ Qya)(M +208)’ M+2ye M4208” for line OB! we have pe Se eR +) lige © 2°" MA 2By* (M+2a8)(M +287)" M+2a8 for line OC! we have ve Be) ee a" M+ 28y° M+2qa "(M+ 2By)(M + 2ya) The equations of the lines Ox, OS, Oy are of course (y =O, z=0) ; (g=0, =0), (ex=0, y=0) respectively ; and we therefore see at once that the planes (OA’, Oa), (OB’, O8), (OC’, Oy) meet ina ine, viz. im the line which has for its equations | e ° — 1 e 1 ° bee Sain e 3 PY 2= NET 2By M+2ya°M+2a8 The lines OB!, OC’, Ox will lie in a plane, if only 4B + +2), (M+2By)? ° (M+ 26y)?=4B8y(8+1)(y+1]), or, as this may be written, . M? + 4y(a+8+y=1+By)=48y(By+8+y+]); ° that is, 464, Prof. Williamson on Chemical Nomenclature. that is, M?+ 4a6y=0, or, what is the same thing, (a+B+y+1)?+4aBy=0; | and from the symmetry of this equation we see that when it is satisfied ; the lines OB’, OC’, Oc will lie in a plane, 33 OC’, OA’, Og 32 33 ” OA!', OB’, Oy ” 9 viz. this will be the case when the point O is situate in the cubic surface represented by the last-mentioned equation; this com- pletes the demonstration of the solid theorems. | It is clear that considering five pomts 1, 2, 3, 4,5 im a plane, then, since any one of these may be taken for the point O! of the foregoing theorem, the theorem exhibited im the first instance as a theorem relating to a triangle and two points, and afterwards as a theorem relating to a quadrangle and a point, is really a theorem relating to five points in a plane. There are, of course, five different systems of points (P, Q, R, 8), correspond- ing to the different combinations of four out of the five points. Cambridge, March 6, 1865, LXIII. On Chemical Nomenclature. By ALEXANDER W. Wituiamson, E.R.S., F.C.S.* | HAD some weeks ago the honour of submitting to the consideration of the Chemical Society a few practical sug- gestions on the subject of chemical nomenclature, framed in the hope of diminishing the inconsistencies which prevail in it at present, and of aiding the development of its best tendencies. My chief proposal was to adopt, as systematically as possible, terms such as mercurous nitrate, Hg?(NO%)?; mercuric hydro- nitrate, Hg HO NO®; hydric sulphate, H? SO*; potassic hydrate, KHO; hydropotassic sulphate, HKSO*; hydrodisodic phos- phate, H Na? PO*; sodic sulphate, Na*SO*; sodic disulphate, Na? S? 0”, &c. ; ferric oxydisulphate, Fe?O (SO*)?; ferric dioxy- sulphate, Fe? O? SO, &c. The result of two evenings’ discussion of the subject was to show that the principles of such nomencla- tureare, upon thewhole, approved, and the names formed inaccord- ance with those principles offer altogether greater proportional recommendations than any other names which are before che- mists. “* Communicated by the Author. Prof, Williamson on Chemical Nomenclature. 465 In the course of the discussion which took place on the sub- ject, I had occasion to point out that, inasmuch as salts in which the base is hydrogen, such as hydric nitrate, hydric sulphate, hydric phosphate, &c., are admitted to be analogous in their constitution and properties to the salts of the regular metals, such as silver, potassium, &c., it is desirable, when describing their reactions, to designate them by names bearing a corre- sponding analogy to the names of thesalts of silver, potassium, &c.; that in describing the reactions of double salts containing as base partly hydrogen, partly some heavier metal, such as com- mon rhombic phosphate, H Na? PO‘, it is not only desirable to introduce the name of the hydrogen in a form similar to that of the other metal, but it is really not possible to obtain systematic and consistent names without representing in them the metallic functions of the hydrogen; that when hydrogen is in the place of an acid or chlorous constituent of a salt, it must be described by a term which represents the fact of its having such functions. In fact it is not allowable to apply to hydrogen-salts names which conceal their analogy with other salts, or which imply the absence of saline constitution in hydrogen-salts. Thus it isa faulty expression to say that the common process for preparing so-called nitric acid consists in the action of sulphuric acid on potassic nitrate, forming potassic bisulphate and nitric acid; for such an expression conveys the idea of a mere displacement of one acid by another, whereas the process is admitted to be an’ interchange of half the hydrogen in hydric sulphate with potas- sium in potassic nitrate, forming hydropotassic sulphate and hydric nitrate. It was admitted by all who spoke on the subject at the Che- mical Society, that hydrogen-salts must in exact language be named similarly to other salts; and one distinguished member mentioned that, in describing to students such a reaction as the above, he uses such terms as sulphate of hydrogen and nitrate of hydrogen. It was at first supposed by some members that I advocated the immediate introduction of systematic and accurate names ito common and popular language. The learned member felt alarm at the danger of having to speak of mercurous chloride instead of “ calomel,’ manganic peroxide instead of “ manga- nese,” hydric sulphate instead of “sulphuric acid,’ &c.; and manufacturers would certainly not have received with favour a proposal to give up the term “soda” for sodic carbonate, to say arsenious acid instead of “ arsenic.” I accordingly hastened to explain that my suggestions towards improving our systematic nomenclature were only expected, if adopted, to react gradually upon the popular language, and that 466 - Prof, Williamson on Chemical Nomenclature, for the present Herb Enh ordering a couple of carboys of “sulphuric acid” or “nitric acid”’ as heretofore, meaning those compounds which in ms stematic language are designated “ hydric sulphate” and “hydric nitrate”; but that when I have to explain to learners the reactions of those hydrogen-salts, I should give them the systematic names which correspond to their composition. The popular and trivial names by which they are known are abbreviations formed so as to point to the essential or characteristic constituent. It is not practicable to send out real sulphuric acid, SO®; but manufacturers and con- sumers know that the value of oil of vitriol is not in the water which it contains, but in the “real acid.” In like manner, the common crystals of hydrated sodic carbonate are valuable in proportion to the percentage of soda, Na?O, which they contain, and they are not unreasonably named after their characteristic constituent. There was, on the part of one or two distinguished members of the Society, a feeling that the retention of the words acid and base in their established signification of ‘electro-negative oxides ”’ and “ electro-positive oxides”’ might be inconvenient im presence of the fact that chlorine forms with hydrogen a very acid salt, and that some other elements also form acid hydrides. But when it is admitted that H* SO* is a salt, though of very acid proper- ties, that HNO? and H? PO8 are also ver y acid salts, and that in scientific language they must be designated as salts, it really is not surprising that HCl, HBr, &c. should be salts of considerable acidity, and it is not LG al a to call them salts of hydrogen in systematic nomenclature. The fact that we cannot remove the elements of water from hydric chloride and make Cl?—Q, whilst we can remove water from hydric sulphate and make sot O, is: really no reason against classing, side by side, hydrogen-salts with compound radicals such as NO®, SO*, PO*, &c., and those. with elementary radicals such as Cl, Br, &c. Since my suggestions have been published Mr. Foster has published in the Philosophical Magazine a paper “ On Chemical Nomenclature, and chiefly on the use of the word Acid.” In this paper Mr. Foster expresses assent to the form of names of which I had recommended the systematic adoption ; and he says, “If we regard the salts of hydrogen as constituted like the salts of any other metal, the application to them of the name acid becomes incorrect if it implies any peculiarity of constitution, and superfluous if it does not.” Now, as Laurent and Gerhardt did admit and assert that the salts of hydrogen are constituted like the salts of any other.metal, and as Mr. Foster is doubtless perfectly aware that they did so, the above sentence is a distinct condemnation of Gerhardt’s proposal of applying the word acid Prof, Williamson on Chemical Nomenclature. 467 to salts with hydrogen as base. And coupled, as it is, with Mr. Foster’s admission that these hydrogen-salts ought, in systematic language, to be called hydric sulphate, hydric nitrate, &c., it does convey Mr. Foster’s assent in a very full manner to the principle of the proposal which I made on the subject of Nomen- - glature. The general form of Mr. Foster’s paper is, however, that of an argument against my proposal; and the paper contains some statements to which my silence would probably seem to give a consent, which I really cannot give. It must have been from inadvertence that Mr. Foster speaks of my wishing to apply the name acid to such bodies as CO”, SO®, Si0?, &c. ; for I merely remarked that the name that belongs to them is wanted by its owners, and that it does not suit the hydrogen-salts to which Gerhardt wanted to transfer it. Mr. Foster goes into an elaborate exposition of what he con- ceives to be the original meaning of the word acid, and speaks of that “original meaning” as “anything but particularly clear.” He might safely have called it “ particularly cloudy.” Every chemist knows that the great Berzelius epitomized the prevailing definition by saying that an acid is an electro-negative oxide, and a base is an electro-positive oxide. No definition is complete and perfect; but_this definition is certainly clear, and it does point to differences of properties among chemical com- pounds which are the most characteristic and important known to us. I cannot see any chance whatever of the words acid and base being given up; for they describe conveniently the chief differences of properties by which we classify compounds chemi- eally. Mr. Foster’s remark, that ‘‘ the strictly scientific signifi- cance of the word acid has passed away,”’ and that the word indi- cates “a distinction to which we now know that no real difference corresponds,” must be taken as referrig to Gerhardt’s misuse of the word acid, as describing salts with basic hydrogen. He might have gone a step further in condemnation of that misuse of the word, and have shown that the word acid never has had any scientific significance as applied to hydrogen-salts. Mr. Foster quotes from my note (but apparently misunder- stands) the statement, “In fact he [Gerhardt] systematically applied the term acid to hydrogen-salts, giving the name anhy- dride to acids, and leaving bases, however anhydrous they might be, entirely unprovided with a corresponding name.” If bodies such as HNO?, H? SO, H? PO? were considered to be entitled to the name “acid,” then for precisely similar reasons, bodies such as. KOH, Ba(OH)? would be entitled to the name “base’’; and if the bodies N?0°, SOQ, P?0°, &c. formed by dehydrating these so-. called acids are called ‘‘anhydrides,” then some corresponding and , 468 Prof. Williamson on Chemical Noneniate distinctive name should be given to the bodies K?O, BaO, &c., formed by dehydrating the so-called bases. The absence of any such term is a deficiency sufficiently grave to make one pause in adopting the term anhydride in systematic language, until the idea which it represents is duly applied to the other great class of chemical compounds; but I cannot, with Mr. Foster, call it a “limitation”; and as I have not said that Gerhardt imposed any “limitation ” in the matter, I may fairly be excused from accept- ing Mr. Foster’s challenge to show where Gerhardt imposed it. If Mr. Foster were to deny my statement that the anhydrous bases are unprovided by Gerhardt with a name corresponding to that of anhydride for the acids, I might probably beg the favour of his quoting chapter and verse in support of his denial, But as matters now stand, the two great classes of chemical compounds are called acids (such as CO?, SO®, Si0?, &c.) and bases (such as K*O, CaO, Fe? O?, &c.). Whoever wants to take their names from them for the use of their hydrates must at least give them new names which will do as well. And he will certainly not be permitted to take the two names from the two classes of bodies, and put them off with one name between them. Ger- hardt seems to have thought that he would be permitted to do . so, but the single substitute (anhydride) which he offered is ad- mitted to be not only insufficient but absolutely unacceptable. Perhaps the most important advantage which chemists have gained by representing all substances of known composition by typical formule, has been the increased clearness with which they have been able to compare the properties of bodies with one another, without the mind being encumbered by conven- tional differences of form. Even elements are now for the most part represented by formulze analogous to those used in repre- senting compounds; free hydrogen being HH lke HCl, free oxygen being OO like CaO, free phosphorus being P? P like H?N, &c. The one great difference which stands forth above all other chemical differences, is that which is described in various terms, all more or less similar in import to acid or acid-like and basic or base-like. We have long since admitted that this fun- damental difference is a difference in the degree in which various substances exert analogous effects, a weak acid acting like a base under the influence of a very strong acid, and a weak base acting like an acid to a very strong base. Among simple and well-known compounds this difference is most markedly repre- sented by oxides such as SO, P? 0°, SO?, CO?, CaO, K?O, PbO, Bi? 0%, &c.; and every chemist knows that compounds of the former class are electro-negative to those of the latter class, electro-negative oxides being called acids, and electro-positive oxides being called bases. It is admitted that hydrogen-salts Prof. Williamson on Chemical Nomenclature. 469 must be represented and named like other salts ; hydric nitrate, or hydric phosphate like potassic nitrate or potassic phosphate, and potassic hydrate or calcic hydrate like potassic nitrate or calcic nitrate; and Gerhardt’s attempt to apply to bodies of the first class the name acid is, in the words of Mr. Foster, “incorrect if it implies any peculiarity of constitution [different from other salts], and superfluous if it does not.” Mr. Foster might, how- ever, as above remarked, have added that Gerhardt’s definition of the word acid is simply in itself devoid of meaning. He quotes it thus: Acids are “salts whose base [the italics are mine] is wholly composed of hydrogen.” A person ignorant of the meaning of the words acid and base could surely not ascertain from his inner consciousness which is the acid and which the basic constituent in any of the followmg compounds, KOH, HNO?, BaO? H?, SO* H?; and Gerhardt’s pretended definition would afford him no aid in ascertaining which of these compounds are to be called acids, which bases. One is almost tempted to suspect Mr. Foster of bitter irony when he calls this definition * strictly scientific and logical.” Although different in form, it is not one bit more reasonable than the Munchausen (or Ivish ?) feat of ascending to the moon by the aid of a mile-long chain, the traveller first fastening his chain by one end at a point one mile up, then climbing up by the chain to that point, and so on. But I am sorry to say that Gerhardt’s disciple is even in a worse plight than the aéronaut, he is so unfortunately circumstanced that even if his chain were fastened one mile up, he could not climb up it. For if, as a preliminary to the understanding of Gerhardt’s dictum, we are told how to find out which is the acid and which the basic constituent of a given compound, we find that this preliminary information is inconsistent with Gerhardt’s dictum, and prevents our making any use of it. By the aid of a battery anybody could find out which are electro-negative, which the electro-positive oxides derivable from the above com- pounds; but Gerhardt would then reject the result as inappli- cable to his purpose. It has always seemed to me that the most plausible objection to the use of the terms acid and base in the sense of electro-nega- tive oxide and electro-positive oxide was the fact that some acids, such as SO%, P?O0°, Si0?, &c., may be put in contact with bases such as BaO, K*O, &c. without manifesting any strong tendency to combine with them; and observations of this kind led some chemists to say that, in their chemical properties, these so-called acids do not behave like acids, and that it is therefore reasonable to deprive them of the name acid. Now the fact is that these acids always do combine with bases when brought in contact with them in the fluid state, and they combine with more force ATO Prof. Williamson on Chemical Nomenclature. than that with which’their hydrates react on basic hydrates. It is well known that when two saline molecules such as SO*4 H? and BaO? H? react on one another with liberation of water and formation of a salt, the force of combination, as measured by the heat evolved, is less than that which the acid and base exert in direct combination; for the process of double decomposition ‘separates the water from SO? and from BaO, and in doing so absorbs just as much heat as was evolved when water combined with SO? and with BaQ; so that the force with which the two hydrates react on one another is by so much less than that with which SO? combines with BaO. Mr. Foster expresses an objection to applying the term ‘ com- bination ” to the reaction of such bodies as anhydrous acetic acid (C? H3 O)? O on water, because by a process of double decompo- sition the two molecules, acid and water, give rise to the forma- tion of two new molecules; but if his objection is admitted to have weight, it applies equally to the reaction of free chlorme on free hydrogen, where two molecules of the elements form two molecules of the compound by a process of double decomposition. If such reactions as that of chlorine on hydrogen, and of anhy- drous acetic acid on water, are not combinations, the word might perhaps be retained for such reactions as the combina- tion of carbonic oxide and chlorine; or SO? and water, where two molecules unite to form one; but if Mr. Foster seriously proposes such a restriction of the word, it will be time enough to consider it. The present usage is to describe as combinations those reactions in which the resulting molecules are less various than the original molecules, as in the cases of O?+ (H?)?=(H?0)?; Cl?+K?=(CIK)?; N?0°+ H?O=(NO?H)?; (C?H30)?0 + H?0= (C?H40?)?, &e. ; and, in like manner, to describe as decompositions those reactions in which the products are more various than the materials, as SO4 H?=S0? + H? O; Pb (NO?)?= PbO +0+4 N? 0}; (C? H8 KO?)?=C? H®O+CO? K*?; (HgO)?=2Hg+0?, (e s 0) + S04 H? = =(6s “ 0) + H20+80!H2, Many of these processes are known to consist of a series of double decompositions, and the fact is often mentioned in allu- ding to them; but it does not seem likely that we should abandon the use of the terms combination and decomposition. Mr. Foster has discussed in his paper what he calls the ori- ginal use of the words acid and base, which is sufficiently cha- racterized by his own words, “ anything but particularly clear.” On the Absorption of Light at different Temperatures. 471 He has also discussed Gerhardt’s misuse of the word acid. His conclusion that the word had better be given up, would be quite worthy of serious consideration if the words were only used in those improper senses. But the words acid and base really mean something not only true, but of fundamental importance, which we are constantly obliged to consider and speak of in chemistry ; and I am quite sure that it would be utterly beyond my power to take from them their established meaning, even if I wished to do so. There is at present a considerable amount of incon- sistency in the prevailing use of these, as of most other scientific terms; and Mz. Foster’s interesting paper affords further argu- ments than those which I had given in favour of abandoning as speedilyas practicable the misuseof the terms which has crept into partial use through popular disregard of water in hydric sul- phate, and which Gerhardt unsuccessfully endeavoured to incor- porate with scientific language. I have not discussed the propesal to call both acids and bases oxides, because it has not as yet received sufficient development to enable me to form any opinion upon it beyond the obvious objections which present themselves at first sight to so grave a change. Thus MnO, Mn? 0?, MnO?, MnO?, Mn? O7 are at pre- sent conveniently distinguished by names, calling the last two acids, and the first two oxides; and so also CO and CO? are very conveniently distinguished by the words oxide and acid. Another circumstance which would alone have been sufficient to prevent my offering any opinion on this proposal is the fact above explained, that it is founded on Mr. Foster’s opinion that the word acid is not clear and is unworthy of being retained. University College, London, May 16, 1865. _LXIV. On the Absorption of Light at different Temper atures. By M. Frussner*. g haa prismatic examination of light which has passed through absorbent media has been continually acquiring greater im- portance ever since Stokes called attention to its practical utility. In particular it is interesting to examine the alterations in ab- sorption which take place on mixing two absorbing substances which exert no chemical action upon each other, and the altera- tions caused by changes of temperature. Professor Melde of Marburg has described} the odie ~ * From the Monatsber. d. koniyl. preuss. Akad. d. Wissensch. z. Bs March 30, 1865, p. 144. 7 Poggendorff’s Annalen, vol. exxiv. p. 91. 472 On the Absorption of Light at different Temperatures. produced in the position of the absorption-bands of a solution of carmine by mixing it with other coloured solutions, and was thus the first to call attention to phenomena of this nature. The following observations, on analogous phenomena presented by indigo, had been already made by the author at the date of Professor Melde’s communication. It is well known that indigo gives a spectrum in which a com- paratively narrow red band is followed by an absorption-band, of greater or less breadth according to the concentration of the solution, while after this there comes a bright band which attains its maximum of intensity in the blue, and lastly the violet end of the spectrum again suffers absorption. Now if a small quan- tity of a solution of sulphate of copper is mixed with such a solution of indigo, the red line disappears immediately, and after a short time the second bright band begins to approach the red end of the spectrum, and finally extends in this direction to the extent of about one-eighth of the breadth of the entire spectrum. The indigo solution, however, must not contain any free sulphu- ric acid; for if only one drop of this acid is added to it the first spectrum reappears. It thus becomes a question whether the change above described does not depend on the formation of a new chemical compound. On adding dichromate of potassium to the indigo instead of sulphate of copper, a much smaller alte- ration takes place. The red band then remains unchanged, and after adding several drops we observe only a displacement of the limits of the green towards the red end, the maximum displace- ment amounting to about one-thirtieth of the total breadth of the spectrum. The solutions examined by the author with respect to altera- tions of absorption caused by changes of temperature, were ferric chloride, cupric chloride, cupric sulphate, sulphate of cupram- monium, dichromate of potassium, sesquinitrate of nickel, proto- chloride of cobalt, and dichloride of platinum. In all these an alteration was manifest, namely in all cases an increase of ab- sorbing power with rise of temperature; but this was much greater in the case of chlorides than with the other salts. Chlo- ride of copper, for instance, when employed at the proper degree of concentration, becomes completely opake at the boiling-point. And it is worthy of remark here, that the part of the spectrum which remains longest visible as the temperature is raised, does not coincide exactly with the part which is the last to disappear when the thickness of the stratum is gradually imcreased ; so that the point of maximum intensity of the spectrum comes ata different place in the heated substance from that which it occu- pies at ordinary temperatures. The behaviour of chloride of cobalt is also interesting. At Royal Society. 473 common temperatures and at the proper degree of concentration this substance shows two luminous bands, one of which is very intense and embraces the whole of the red and yellow, and part of the green ; the other, comparatively weak, is situated in the violet. On applying heat, this violet band gradually diminishes in in- tensity, and two new bands of absorption, of which previously no trace was visible, appear in the red. They increase very rapidly in breadth, especially the less refrangible of the two, as the temperature rises; so that, when the boiling-point is ap- proached, they have completely obliterated the entire bright band in which they appeared, with the exception of a very nar- row weak stripe in the extreme red. In order to explain these phenomena, one might be disposed to assume that the elevation of temperature occasioned chemical changes to take place in the liquids—that, for instance, a fewatoms of water were fixed or given off—were it not that, so far as the observations have yet gone, a sudden alteration of absorbing- power never occurs, but the changes take place in a perfectly gradual manner. On the other hand, these phenomena are quite analogous to those observed by Brewster* and others in relation to the ab- sorbing-powers of certain gases, in which, as the temperature rises, the absorption-bands increase in number and width. LXV. Proceedings of Learned Socteties. ROYAL SOCIETY. [Continued from p. 398. ] Feb. 23, 1865.—John P. Gassiot, Esq., Vice-President, in the Chair. NHE following communications were read :— «< On New Cornish Minerals of the Brochantite Group.” By Professor N. Story Maskelyne, M.A., Keeper of the Mineral Depart- ment, British Museum. On a small fragment of Killas from Cornwall, a discovered, several months ago, a new mineral in the form of minute but well- formed crystals. The specimen had come from Mr. Talling, of Lostwithiel, a mineral-dealer, to whose activity and intelligence I am indebted for the materials that form the subject of this paper. After a little while he found the locality of the mineral, and sent me other and finer specimens; but these specimens proved to con- tain other new minerals besides the one already mentioned. Two of these minerals are described in this paper, and a third will form the subject of a further communication. I. Langite. The first of these minerals which I proceed to describe is one tu * Phil. Mag. S. 3. vol. viii. p. 386. Phil, Mag. S. 4. Vol. 29, No. 198. June 1865. 2-1 ATA Royal Society :—Prof. Maskelyne on New which I have given the name of Langite, in honour of my friend Dr. Viktor von Lang, now of Gratz, and lately my colleague in the British Museum. It occurs in minute crystals, or as a crystalline crust on the Killas, of a fine blue with a greenish hue in certain lights. The crystals are prismatic. The forms observed are (1 00), (001), (110), and (20 1) & (010), the normal inclinations giving the fol- lowing angles, which are the averages of many measurements :— 110110—56 16 100 110=61 52 001 201=51 46 conducting to the parametral ratios 7 a:6:c=1:0°5347 : 0°6346. The crystals are twinned after-the mauner of cerussite, the twin axis being normal to the plane (1 1 0). 110 (110) 110=112 33 100 (110) 100=123 44 7 110 (110) 110= 67 26 Cleavages seem to exist parallel to001and100. The planes 001 and 100 arevery brilliant. The plane of the optic axes, as seen through a section parallel to the plane 0 0 1, is parallel to1 00. The normal to 00 1 would seem to be the first mean line, and it is nega- tive. .The optical orientation of the mineral is therefore b, ¢, a. — The crystals are dichroic. a 1. Seen along axis c, c, greenish blue. b, blue. 2. Seen along axis a, c, darker greenish blue. a, lighter bluish green. The specific gravity of Langite is 3°48 to 3°50. Its hardness is under 3. It will not abrade calcite. Before the blowpipe on charcoal it gives off water, and fumes and becomes reduced to metallic copper. Insoluble in water, it is readily dissolved by acids and ammonia. Heated, it passes through (1) a bright green, and (2) various tints of olive-green, till (3) it becomes black. Water is given off the whole time, and finally it has a strongly acid reaction, The first stage corresponds to the loss of one equivalent of water ; the second reduces its composition to that of Brochantite; at the third it loses all its water. The chemical composition of Langite is represented by the for- ort 3Cu" H’, O,4 Cu" 80,4 2H’, O, which requires the following numbers :— Calculated Average percentage. found. 4 equivalents of copper.......... 126°72=52:00 52°55 4 equivalents of oxygen ........ 32> =13'13 13°27 1 equivalent of sulphuric anhydride 40° =16°41 16°42 9 equivalents of water .......... 45> =18°46 18°317 243°72 100-00 100°56 Cornish Minerals of the Brochantite Group. A75 I have met with a small and old specimen of Connellite with a twin erystal of Langite associated with it. Il. Waringtonite. To a Cornish mineral associated with Langite, emerald to verdigris- green in colour, occurring in incrustations generally crystalline, and seen occasionally in distinct individual crystals aggregated loosely on the Killas, I have given the name of Waringtonite, in honour of my friend Mr. Warington Smyth. The crystals are always of the same form, that, namely, of a double-curved wedge. A narrow plane, 001, is very brilliant and without striation. It appears to be a cleavage-plane. A second, but scarcely measurable plane, 100, di occurs at right angles to it, truncating the thin ends of the wedge. The prism planes in the zones 010, 001, and 010, 100 are uni- formly curved. The planes of two prisms seem to exist in the zone 010, 001, but the angles, as approximately measured by the gonio- meter, are not very reliable ; one of them, however, may be pretty confidently asserted to be very near 28° 30', which is the mean of many measurements on four crystals. Seen in a microscope fitted with an excellent eyepiece goniometer, planes of polarization in the crystals are evidently parallel and perpendicular to the planes 1 00, 001; but whether a plane of polarization bisects the acute angle of the wedge, 7. e. is parallel to 019 orto 100, or whether 100 is equally inclined to the planes forming the wedge—in short, whether the crystal is oblique or prismatic, it is very difficult to determine. The mineral frequently presents itself, moreover, in what appear to be twinned forms; but the angles between the planes 100 in the two individuals are not sufficiently concordant, as measured on dif- ferent crystals, to justify a speculation on the symbols of a twin face. Several analyses of Waringtonite concur in establishing its for- mula as 3Cu"H', O,+ Cu! SO,+ H',O, as is seen by the following numbers :— Percentage as Average calculated. found. . 4 equivs. copper ........ ==126°72 = 53°99 54:48 4 equivs. oxygen.......... SN B2%;, » S3p113°63.4 » (eale0137756) ] equiv. sulphuric anhydride = 40° = 17°04 16°73 4 equivs. water .......... = 36° = 15°34 14°64 234:72 =100-00 99°606 It also contains traces of lime, magnesia, and iron, and appears to be generally mixed with a small proportion of another mineral, which is probably Brochantite, as Brochantite occurs in distinct crys- tals on some of the specimens of Waringtonite. Its specific gravity is 3°35 to 3°47. Its hardness is 3 to 3°5, being harder than calcite, and about equal in hardness to celestine. The entire difference of its crystallographic habit, the absence of the striation and marked prismatic, forms so characteristic of Brochantite, its habitually paler colour, lower specific gravity (an Bro- A76 Royal Society :— chantite G=3°87 to3°9), and hardness sufficiently distinguish it from that mineral. The mountain-green streak offers an available means of contrasting Waringtonite and Brochantite with Atacamite, the streak of which is of a characteristic apple-green. M. Pisani has published analyses of the two above-described mi- nerals. In the former (possibly from having driven off part of the water in the preliminary desiccation of the mineral) he has found less water than I consider it really to contain, and he has conse- quently given to Langite the formula of Waringtonite. The green mineral which he has analyzed and described as Bro- chantite seems, from his analysis, to have contained a slight admix- ture of the ferruginous matrix, and also differs from mine in the esti- mate of the water. I confined my preliminary. desiccation to a careful treatment of the bruised mineral with dried and warm blotting-paper, as many hydrated minerals of this class yield up part of their water when long exposed. to a perfectly dry air, or to a temperature of 100° C. “‘ Preliminary Note on the Radiation from a Revolving Disk.” By Balfour Stewart, M.A., F.R.S., and P. G. Tait, M.A. The authors having been led by perfectly distinct trains of reason- ing to identical views bearing on the dissipation of energy, have had preliminary experiments made on the increase of radiation from a wooden disk on account of its velocity of rotation, both in the open air and im vacuo. These experiments were made with a very delicate thermo-electric pile and galvanometer. In the experiments in the open air the disk was of wood; its diameter was 9 inches, and it was made to rotate with a velocity somewhat less than 100 revolutions in one second. A sensible effect was produced upon the indicating galvanometer when the disk was made to rotate, and this effect appeared to be due to radiation, and not to currents of air impinging against the pile. In amount it was found to be nearly the same as if the disk had increased in temperature 0°75 Fahr. In the experiments in vacuo the diameter of the wooden disk was over 12 inches; its velocity of rotation was about 100 revolutions in one second, and the pile was nearer it than when in air. Under these circumstances, with a vacuum of 0:6 in,, an effect apparently due to radiant heat was obtained, amounting to nearly the same as if the disk had increased in temperature 1°°5 Fahr. Bearing in mind the increased diameter of the disk, the effect is probably equivalent to that obtained in air, and these preliminary experiments would tend to show that when a wooden disk is made to revolve rapidly at the surface of the earth, its radiation is increased to an extent depending on the velocity; and it would appear that this effect is not materially less in a vacuum of 0°6 in. than in the open air. The authors intend to work out this and allied questions experi- mentally, and hope, if successful, to communicate the result to this ~ Society. Mr. F. Jenkin on the New Unit of Electrical Resistance. 477 April 6.—Major-General Sabine, President, in the Chair. _ The following communication was read :—: ** Report on the New Unit of Electrical Resistance proposed and issued by the Committee on Electrical Standards appointed in 1861 by the British Association.”” By Fleeming Jenkin, Esq. Sir Humphry Davy, in 1821*, published his researches proving a difference in the conducting-power of metals and the decrease of that power as their temperature rose. This quality of metals was examined by Snow Harris, Cumming, and E. Becquerel, whose table of conducting-powers, compiled by the aid of his differential galva- nometer, and published in 18267, is still frequently quoted, and is indeed remarkable as the result of experiments made before the publication by Ohm, in 1827{, of the true mathematical theory of the galvanic circuit. The idea of resistance as the property of a conductor was intro- duced by Ohm, who conceived the force of the battery overcoming the resistance of {the conductors and producing the current as a result. Sir Humphry Davy, on the contrary, and other writers of his time, conceived the voltaic battery rather as continually reprodu- cing a charge, somewhat analogous to that of a Leyden jar, which was discharged so soon as a conductor allowed the fluid to pass. The idea of resistance is the necessary corollary of the conception of a force doing some kind of work§, whereas the idea of conducting- power is the result of an obvious analogy when electricity is con- ceived as a fluid, or two fluids, allowed to pass in different quantities through different wires from pole to pole. When submitted to measurement, the qualities of conducting-power and resistance are naturally expressed by reciprocal numbers, and the terms are used in this sense in the early writings of Lenz (1833) ||, who, with Fechner 4, and Pouillet**, established the truth of Ohm’s theory shortly after the year 1830. The conception of a unit of resistance is implicitly contained in the very expression of Ohm’s law; but the earlier writers seem to have contented themselves with reducing by calculation the resist- ance of all parts of a heterogeneous circuit into a given length of some given part of that circuit, so as to form an imaginary homoge- neous conductor, the idea of which lies at the basis of Ohm’s reason- ing. These writers, therefore, generally speak of the resistance as the ‘reduced length” of the conductor, a term still much used in France (vide Daguin, Jamin, Becquerel, De la Rive, and others). The * Phil. Trans. 1821, vol. cxi. p. 425. t Ann. de Chim. et de Phys. vol. xxxii. 2nd series, p. 420. t Die galvanische Kette, mathematisch bearbeitet, 1827; also Taylor’s Scien- tific Memoirs, vol. ii. p. 401. § The writer does not mean by this that electrical and mechanical resistance are truly analogous, or that a current truly represents work. || Pogg. Ann. vol. xxxiv. p. 418. - € Maasbestimmungen, ete. 1 vol. 4to. Leipzic, 1851. Elémens de Physique, p. 210, 5th edition; and Comptes Rendus, vol. iy, p. 267. 478 Royal Society :— next step would naturally be, when comparing different circuits, to reduce all resistances into a length of some one standard wire, though this wire might not form part of all or of any of the cir- cuits, and then to treat the unit length of that standard wire as a unit of resistance. Accordingly we find Lenz (in 1838*) stating that 1 foot of No. 11 copper wire is his unit of resistance, and that it is 19°9 times as great as the unit he used in 1833+, which was a certain constant part of the old circuit. In the earlier paper the resistances are treated as lengths, in the later as so many “‘ units.”’ Lenz appears to have chosen his unit at random, and apparently without the wish to impose that unit upon others. A further advance is seen when Professor Wheatstone, in his well-known paper of 1843, proposes | foot of copper wire, weighing 100 grains, not only as a unit, but as a standard of resistance, chosen with reference to the standard weight and length used in this country. To Pro- fessor Wheatstone also appears due the credit of constructing (in 1840) the first instruments by which definite multiples of the resistance- unit chosen might be added or subtracted at will from the circuit {. He was closely followed by Poggendorff§ and Jacobi||, the descrip- tion of whose apparatus, indeed, precedes that of the Rheostat and Resistance-coils, although the writer understands that they acknow- ledge having cognizance of those inventions. Resistance-coils, as the means of adding, not given lengths, but given graduated resist- ances to any circuit, are now as necessary to the electrician as the balance to the chemist. t In 1846 Hankel used as unit of resistance a certain iron wire ; in 1847 I. B. Cooke** speaks of a length of wire of such section and conducting-power as is best fitted for a standard of resistance. Buff++ and Horsfordtt m the same year reduce the resistance of their experiments to lengths of a given German-silver wire, and as a further definition they give its value as compared with pure silver. To avoid the growing inconvenience of this multiplicity of standards, Jacobi $§ (in 1848) sent to Poggendorff and others a certain copper wire, since well known as Jacobi’s standard, desiring that they would take copies of it, so that all their results might be expressed in one measure. He pointed out, with great justice, that mere definition of the standard used, as a given length and weight of wire, was insufficient, and that good copies of a standard, even if chosen at random, would be preferable to the reproduction in one laboratory of a standard prepared and kept in another. The present Committee fully indorse this view, although the definition of standards based on weights and dimensions of given materials has since then gained greatly in precision. Until about the year 1850 measurements of resistance were con- fined, with few exceptions, to the laboratory; but about that time * Pogg. Ann. vol. xlv. p. 105. + Pogg. Ann. vol. xxiv. p, 418. { Phil. Trans. 1843, vol. exxxiu. p. 303. § Pogg. Ann. vol. li. p. 511. || Pogg. Ann. vol. lii. p. 526; vol. liv. p. 347. | Pogg. Ann. vol. Ixix. p. 255. ** Phil. Mag. New Series, vol. xxx. p. 385. +f Pogg. Ann. vol. Ixxii. p. 497. > tt Pogg. Ann. vol. lxx. p. 238, and Silliman’s Journ. vol. v. p. 36. §§ Comptes Rendus, 1851, vol. xxxiii. p. 277. Mr. F. Jenkin on the New Unit of Electrical Resistance. 479 underground telegraphic wires were introduced, and were shortly followed by submarine cables, in the examination and manufacture of which the practical engineer soon found the benefit of a knowledge of electrical laws. Thus in 1847 the officers of the Electric and International Telegraph Company used resistance-coils made by Mr. W. F. Cooke, apparently multiples of Wheatstone’s original standard, which was nearly equal to the No. 16 wire of commerce ; and Mr. C. F. Varley* states that, even at that date, he used a rough mode of “distance testing.” In 1850, Lieut. Werner Siemens + published two methods for determining, by experiments made at distant stations, the position of “a fault”—that is to say, a con- nexion between the earth and the conducting-wire of the line at Some point between the stations. In one of these plans a resistance equal to that of the battery is used, and the addition of resistances is also suggested ; and Sir Charles Bright, in a Patent dated 1852t, gives an account of a plan for determining the position of a fault by the direct use of resistance-coils. Since that time new methods of testing for faults and of examining the quality of materials employed, and the condition of the line, have been continually invented, almost all turning, more or less, on the measurement of resistance; greater accuracy has been continually demanded in the adjustment of coils and other testing-apparatus, until we have now reached a point where we look back with surprise at the rough and ready means by which the great discoveries were made on which all our work is founded. The first effect of the commercial use of resistance was to turn the “feet”? of the laboratory into “miles” of telegraph wire. Thus we find employed as units, in England the mile of No. 16 copper wire §, in Germany the German mile of No. 8 iron wire, and in France the kilometre of iron wire of 4 millimetres diameter. Several other units’ were from time to time proposed by Langsdorf ||, Jacobi4], Marié- Davy**, Webertt, W. Thomsonft, and others, with a gradually increasing perception of the points of chief importance in a standard ; but none of these were generally accepted as the one recognized measure in any country. To remedy the continually increasing evils arising from the discrepancies invariably feund between dif- ferent sets of coils, Dr. Werner Siemens (in 1860$$) constructed standards, taking as unit the resistance of a column of chemically pure mercury 1 metre long, having a section equal to 1 millimetre square, and maintained at the temperature of 0° Centigrade||||. * Letter to writer, 1865. t+ Pogg. Ann. vol. lxxix. p.481. + Patent No. 14,331, dated Oct. 21, 1852. § A size much used in underground conductors, and equal in resistance to about double the length of the common No. 8 iron wire employed in aérial lines. || Liebig’s Ann. vol. lxxxv. p. 155. { Pogg. Ann. vol. lxxvii. p. 173. ** Ann. Chim. et Phys. 3rd series, vol. ix. p. 410. tt Pogg. Ann. vol. lxxxii. p. 337. t{ Phil. Mag. Dec. 1851, 4th ser. vol. iip.551. §§ Pogg. Ann. vol. cx. p. 1. "||| Dr. Siemens, while retaining his definition, has altered the value of his standard about 2 per cent. since the first issue; and it is doubtful whether even the present standard represents,the definition truly: his experiments were made by weight; and in reducing the results to simple measurements of length he has used a specific gravity for mercury of 13°557 instead of 13°596 as given by Regnault, 13595 by H. Kopp, and 13:594 by Balfour Stewart. 480 Royal Society :-— Dr. Siemens supposed that this standard could be reproduced without much difficulty where copies could not be directly obtamed. Mer- cury had been proposed before as a fitting material for a standard by Marié-Davy and De la Rive; but Dr. Siemens merits especial recognition, as the coils and apparatus he issued have been made with great care, and have materially helped in introducing strict accuracy *. The question had reached this point when (in 1861) the British Association, at the suggestion of Professor W. Thomson, appointed a Committee to determine the best standard of electrical resistance. This Committee, aided by a grant from the Royal Society, has now issued a new standard, the subject of the present paper. The writer has hitherto described those units only which are founded on a more or less arbitrary size and weight of some more or less suitable material; but measurements of resistance can be con- ceived and carried out entirely without reference to the special qualities of any material whatever. In 1849 Kirchhoff} had already effected a measurement of this kind; but it is to W. Webert that we owe the first distinct proposal (in 1851) of a definite system of electrical measurements, according to which resistance would be measured in terms of an absolute velocity. This system of measures he called absolute electromagnetic measure, in analogy with Gauss’s nomenclature of absolute magnetic measure. The Committee have decided that Weber’s proposal is far preferable to the use of any unit of the kind previously described. Setting aside the difficulties in the way of their reproduction, which are by no means contemptible, : arbitrary material standards, whether of mercury, gold, silver, plati- num, or any other material, would be heterogeneous isolated units without any natural connexion with any other physical units. The unit proposed by Weber, on the other hand, forms part of a sym- metrical natural system, including both the fundamental units of length, time, and mass, and the derived electrical units of current quantity and electromotive force. Moreover it has been shown by Professor W. Thomson§, who accepted and extended Weber's pro- posal immediately on its appearance, that the unit of absolute work, the connecting link between all physical forces, forms part of the same system, and may be used as the basis of the definition of the absolute electromagnetic units. The full grounds of the choice of the Committee could only be ex- plained by a needless repetition of the arguments given in the reports already made to the British Association. It will be sufficient here to state that, in the absolute electromagnetic system, the following equations exist between the mechanical and electrical units :— W=C’Rz, io a ae) where W is the work done im the time ¢ by the current C conveyed ~ _* Many of the different units described above were represented by resistance- coils in the International Exhibition of 1862: wide Jury Report, Class XIII. p. 83, where their relative values are given : vide also Appendix A. to present paper. t Pogg. Ann. vol. Ixxvi. p. 412. { Ibid. vol. lxxxii. p. 337. § Phil. Mag. Dec. 1851, 4th series, vol. ii. p. 551. 1-000 62-48 ppenpIx A.—Relative 0°3187 0:3348 0:6655 0:9607 1-000 1-005 EOLT. 10456 0:0968 10:20 10-90 1419 26°75 60:03 —=— German Miles. 0-005307 --0:005574 | 901108 0:01655 0-01666 001675 0°01695 10-1613 \( 9-1700 M 9-1815 14 9.9365 2€ 0.4457 59 1.000 0°01741 [To face page 480. | Observations. Calculated from the B. A. unit. From an old determination by Weber. No measurement made; ratio be- tween Siemens (Berlin) and Ja- | cobi taken from ‘‘ Weber’s Gal- | vanometrie.”’ (Measurement taken from a deter- mination in 1862 of a standard! | sent by Prof. Thomson ; does not| 4 agree with Weber’s own measure- ment of Siemens’s units ; by We- ber 1 Siemens’s unit =1-025 x 10") metres-second. { Measurement taken from threecoils issued by Messrs. Siemens. Measurement taken from coils exhi- bited in 1862 by Messrs. Siemens, Halske & Co. (well adjusted). Measurement taken from coils exhi- bited in 1862 by Messrs. Siemens, Halske & Co. (well adjusted). Hqual to 10,000,000 == ac- second cording to experiments of Stand-| ard Committee. From coils exhibited in 1862 (pretty well adjusted). From coils exhibited in 1862 (in- differently adjusted). From coils exhibited in 1862 (badly adjusted). From a coil lent by Dr. Matthies-, sen (of German-silver wire). From coils lent by Mr. Varley (well adjusted). (From coils exhibited in 1862 by | Messrs. Siemens, Halske & Co. * inufacture coils with this unit, Description. Absolute fons ern | second netic units (new determination) Absolute foot secon netic units (old determination) a% 10’ electro-mag- Twenty-five feet of a certain ae per wire, weighing 345 grains... Absolute metre: x 107electro-mag- second netic units determined by Weber (1882): ccscc:<.. rece ies One metre of pure mercury, one square millimetre section at 0° O. One metre of pure mercury, one square millimetre section at 0° C. One metre of pure mercury, oo} square millimetre section at 0° C. British Association unit ........:...++ One kilometre of iron wire, four millimetres in diameter (tempe- rature not known) One kilometre of iron wire, four millimetres in diameter (tempe- rature not KNOWM)..+.....++seseenes One kilometre of iron wire, four millimetres in diameter (tempe- rature not KNOWN), ....000-s0ss. One English standard mile of pure annealed copper wire 3; in. dia- meter at 15°-5 C. One Mnelish standard mile of one special copper wire sy inch in diameter.....+.+-++« (DEBE OSCCIREECS One German mile=8238 yards of i iron wire 4 inch in diameter (temperature not Inown*) ...... Name. foot 7 second ZOE Absolute Thomson’s unit ......... Weber’s absolute 2 eee second Siemens 1864 issue...... Siemens (Berlin) Siemens (London) ...... 'B. A. unit, or Ohmad... Absolute foot 7 second PSE 3015 —— Digneyeractmasavcecsssanss Matthiessen....se....-..+++ Warley. .....cscssssveeserrss German mile ...........- 44-57 84:01 188:4 Thomson’s old unit. 2871 2/988 3004 3:040 3123 28:94 30:50 32:56 42-43 79:96 179'4 1-444 Apprnpix A.—Relative Values of various Units of Electrical Resistance. Weber's absolute metre «107, second 0:3316 0:3483 0:6925 1-000 Siemens 1864 issue. 0:3187 0:3348 0:6655 0:9607 1-000 1005 1-017 10456 0:0968 10:20 10:90 1419 26°75 60:03 Siemens (Berlin). 0:3168 0:3328 0:6618 0:9556 0:9950 1:000 1:012 1-039 9:634 10:15 10:84 14:12 26:61 59°71 Siemens (London). 03131 0:3289 0:9443 0:9829 0:9881 1-000 1-026 9-520 10:13 10°71 13:95 26:30 59:00 B, A. unit, or Ohmad. 0:3048 0:3202 0:6367 0:9191 0:9563 0:9625 0:9742 1000 9:266 9-760 10:42 13:59 25°61 57-44 Digney. 0:03289 0:08455 0:06869 0:09919 0:1033 0:1038 0:1050 0:1079 1-000 1:054 1-125 1-66 2-763 6:198 Bréquet. 0:03123 0:03279 0:06520 0:09416 0:09799 0:09852 0:0997 01024 0:9491 1-000 Swiss. 0:08071 0:06106 0:08817 0:09177 0:09227 009337 00959 0:8889 0:9365 2:456 5509 * Messrs. Siemens do not now manufacture coils with this unit, which has been abandoned by them in favour of the mercury unit giyen above. [Lo face page 480.] Matthiessen. 0:02357 0:04686 0:06767 0:07047 0:07081 0:07166 0:0736 0:6822 0-7187 0:7675 1-000 1-885 4:228 Varley. 0:01190 0:01251 0:02486 0:03591 0:03737 0:03757 0:03802 0:03905 0:3620 0:3814 0:4072 0:5306 1-000 2243 German Miles, 0:005307 0:005574 9:01108 0:01655 0:01666 0:01675 0:01695 0:01741 01613 01700 0:1815 Observations. Calculated from the B, A. unit. ee an old determination by Weber. No measurement made; ratio be- tween Siemens (Berlin) and Ja- | cobi taken from ‘* Weber's Gal- yanometrie.”” Measurement taken from a deter- mination in 1862 of a standard sent by Prof. Thomson ; does not agree with Weber’s own measure- ment of Siemens’s units ; by We-| ber 1 Siemens’s unit =1:025 x 107) metres-second, Measurement taken from three coils { issued by Messrs. Siemens, Measurement taken from coils exhi- bited in 1862 by Messrs. Siemens, Halske & Co. (well adjusted). Measurement taken from coils exhi- bited in 1862 by Messrs. Siemens, Halske & Co. (well adjusted), Equal to 10,000,000 ™2"** ac. second cording to experiments of Stand- ard Committee. From coils exhibited in 1862 (pretty well adjusted), From coils exhibited in 1862 (in- differently adjusted). From coils exhibited in 1862 (badly adjusted). From a coil lent by Dr. Mafthies- sen (of German-silver wire), From coils lent by Mr. Varley (well adjusted). (From coils exhibited in 1862 by | Messrs, Siemens, Halske & Co, * iy | 4 { o { ] | | x sat eves s ee im he — 5 ~ Mr. F. Jenkin on the New Unit of Electrical Resistance. 481 through a conductor of the resistance R. This equation expresses Joule and Thomson’s law. E Eee Sti Seta sy nites ree where E is the electromotive force. This equation expresses Ohm’s law. CL ee (3) expressing a relation first proved by Periny. ater Q: is the quantity of electricity conveyed or neutralized by the current in the time ¢. Finally, the whole system is rendered determinate by the condition that the unit length of the unit current must produce the unit force on the unit pole (Gauss) at the unit distance. If it is preferred to omit the conception of magnetism, this last statement is exactly equi- valent to saying that the unit current conducted round two circles of unit area in vertical planes at right angles to each other, one circuit being at a great distance D above the other, will cause a couple to act between the circuits of a magnitude equal to the reciprocal of the cube of the distance D. This last relation expresses the proposal made by Weber for connecting the electric and magnetic measure. These four relations serve to define the four magnitudes R, C, Q, and E, without reference to any but the fundamental units of time, space, and mass; and when reduced to these fundamental units, it will be found that the measurement of R involves simply a velocity, 7. e. the quotient of a length by a time. It is for this reason that the metre |, foot second second as the common non-absolute unit of work involving the product of a weight into a length is styled kilogrammetre or foot-pound. The Committee have chosen as fundamental units the second of time, the metre, and the mass of the Paris gramme. The metrical rather than the British system of units was selected, in the hope that the new unit might so find better acceptance abroad, and with the feeling that while there is a possibility that we may accept foreign measures, there is no chance that the Continent will adopt ours. The unit of force is taken as the force capable of producing in one second a velocity of one metre per second in the mass of a Paris gramme, and the unit of work as that which would be done by the above force acting through one metre of space. These points are very fully explained in the British Association Report for 1863, and in the Appendix C to that Report by Professor J. Clerk Maxwell and the writer *. metre The magnitude of the secon absolute measure of resistance is styled ——_—.., precisely is far too small to be practically con- venient, and the Committee have therefore, while adopting the system, chosen as their standard a decimal multiple 10° times as great as Weber’s unit ea melee , or 10” times as great as the metre second second This magnitude is not very different from Siemens’s mercury unit, which has been found convenient in practice. It is about the twenty-fifth part of the mile of No. 16 impure copper wire used as * [See pp. 409, 507 of the present volume of this Magazine. | 482. Royal Society :— a standard by the Electric and International Company, and about once and a half Jacobi’s unit*. It was found necessary to undertake entirely fresh experiments in order to determine the actual value of the abstract standard, and to express, the same in a material standard which might form the basis of sets of resistance-coils to be used in the usual manner. These expe- riments, made during two years with two distinct sets of apparatus by Professor J. C. Maxwell and the writer, according to a plan devised by Professor W. Thomson, are fully described in the Reports to the British Association for 1863 and 1864. The results of the two series of experiments made in the two years agree within 0:2 per cent., and they show that the new standard does not probably differ from true absolute measure by 0'1 percentt. It is not far from the mean of a somewhat widely differing series of deter- minations by Weber. In order to avoid the inconvenience of a fluctuating standard, it is proposed that the new standard shall not be called “‘ absolute mea- ey but that it shall receive a seconds distinctive name, such as the B. A. unit, or, as Mr. Latimer Clark suggests, the ““Ohmad,” so that, if hereafter improved methods of determination in absolute measure are discovered or better experi- ments made, the standard need not be changed, but a small coefficient of correction applied in those cases in which it is necessary to convert the B. A. measure into absolute measure. Every unit in popular use has a distinctive name; we say feet or grains, not units of length or units of weight; and it is in this way only that ambiguity can be avoided. There are many absolute measures, according as the foot and grain, the millimetre and milligramme, the metre and gramme, &c. are used as the basis of the system. Another chance of error arises from the possibility of a mistake in the decimal multiple used as standard. For all these reasons, as well as for convenience of expression, the writer would be glad if Mr. Clark’s proposal were adopted and the unit called an Ohmad. Experiments have been made for the Committee by Dr. Mat- thiessen, to determine how far the permanency of material standards may be relied on, and under what conditions wires unaltered in di- mension, in chemical composition, or in temperature change their resistance. Dr. Matthiessen has established that in some metals a partial annealing, diminishing their resistance, does take place, ap- parently due to age only. Other metals exhibit no alteration of this kind; and no permanent change due to the passage of voltaic currents has been detected in any wires of any metal—a conclusion contrary to a belief which has very generally prevailed. The standard obtained has been expressed in platinum, in a gold- sure,” or described as so many * This last number may be 30 per cent. wrong, as the writer has never been in possession of an authenticated Jacobi standard, and has only arrived at a rough idea of its value by a series of published values which afford an indirect com- parison. t Vide Appendix B. Mr. F. Jenkin on the New Unit of Elecirical Resistance. 483 silver alloy, in a platinum-silver alloy, in a platinum-iridium alloy, and in mercury. Two equal standards have been prepared in each metal; so that should time or accident cause a change in one or more, this change will be detected by reference to the others. The experiments and considerations which have led to the choice of the above materials are fully given in the Report to the British Associa- tion for 1864. The standards of solid metals are wires of from 0°5 millim. to 0°8 millim. diameter, and varying from one to two metres in length, insulated with white silk wound round a long hollow bobbin, and then saturated with solid paraffin. The long hollow form chosen allows the coils rapidly to assume the temperature of any surronnd- ing medium, and they can be plunged, without injury, into a bath of water at the temperature at which they correctly express the standard. The mercury standards consist of two glass tubes about three-quar- ters of a metre in length. All these standards are equal to one another at some temperature stated on each coil, and lying between 14°°5 and 16°°5 C.- None of them, when correct, differ more than 0:03 per cent. from their value at 15°°5 C. Serious errors have‘occasionally been introduced into observations by resistance at connexions between different parts of a voltaic circuit, as perfect metallic contact at these points is often prevented by oxide or dirt of some kind. Professor Thomson’s method of inserting resist- ances in the Wheatstone balance (differential measurer) has been adopted for the standards, but in the use of the copies which have been issued it has been thought that sufficient accuracy would be attained by the use of amalgamated mercury connexions. In the standards themselves permanence is the one paramount quality to be aimed at; but in copies for practical use a material which changes little in resistance with change of temperature is very desirable, as otherwise much time is lost in waiting till coils have cooled after the passage ofacurrent ; moreover large corrections have otherwise to be employed when the coils are used at various temperatures ; and these temperatures are frequently not known with perfect accuracy. German silver, a suitable material in this respect, and much used hitherto, has been found to alter in resistance, in some cases, without any known cause but the lapse of time, since the change has been: observed where the wires were carefully protected against mechanical or chemical injury. A platinum-silver alloy has been preferred by the Committee to German silver for the copies which have been made of the standard. These have been adjusted by Dr. Matthiessen so as to be correct at some temperature not dif- fermg more than 1° from 15°°5 C. The resistance of platinum-silver changes about 0031 per cent. for each degree Centigrade within the limits of 5° above and below this temperature; this change is even less than that of German silver. The new material seems also likely to be very permanent, as it is little affected by annealing. The form of the copies is the same as that of the standard, with the exception of the terminals, which are simple copper rods ending in an amalga- mated surface. Twenty copies have been distributed gratis, and notices issued that others can be procured from the Committee 484: Royal Society: — for £210s. . The Committee also propose to verify, at a small charge, any coils made by opticians, as is done for thermometers and barome- ters at Kew. Dr. Matthiessen reports, with reference to the question of repro- duction, that given weights and dimensions of several pure metals might be employed for this purpose 2f absolute care were taken. The reproduction, in this manner, of the mercury unit, as defined by Dr. Siemens, differs from the standards issued by him in 1864 about 8:2 per thousand if the same specific gravity of mercury be used for both observations*. Each observer uses for his final value the mean of several extremely accordant results. It is therefore to be hoped that the standard will never haye to be reproduced by this or any similar method. On the other hand, four distinct observers, with four different apparatus, using four different pairs of standards issued re- spectively by Dr. Siemens and the Committee, give the B. A. unit as respectively equal to 1°0456, 1:0455, 1°0456, and 1-0457 of Sie- mens’s 1864 unit. It is certain that two resistances can be compared with an accuracy of one part in one hundred thousand—an accuracy wholly unattainable in any reproduction by weights and measures of a given body, or by fresh reference to experiments on the abso- lute resistance. ‘The above four comparisons, two of which were made by practical engineers, show how far the present practice and requirements differ from those of twenty and even ten years ago, when, although the change of resistance due to change of tempera- ture was known, it was not thought necessary to specify the tem- perature at which the copper or silver standard used was correct. The difficulty of reproducing a standard by simple reference to a pure metal, further shows the unsatisfactory nature of that system in which the conducting-power of substances is measured by compa- rison with that of some other body, such as silver or mercury. Dr. Matthiessen has frequently pointed out the discrepancies thus pro- duced, although he has himself followed the same system pending the final selection of a unit of resistance. It is hoped that for the future this quality of materials will always be expressed as a specific resistance or specific conducting-power referred to the unit of mass or the unit of volume, and measured in terms of the standard unit resistance, that the words conducting-power will invariably be used to signify the reciprocal of resistance, and that the vague terms good and bad conductor or insulator will be replaced, in all writings aiming at scientific accuracy, by those exact measurements which can now be made with far greater ease than equally accurate measurements of length. There is every reason to believe that the new standard will be gladly accepted throughout Great Britain and the colonies. Indeed the only obstacle to its introduction arises from the difficulty of explaining to inquirers what the unit is. The writer has been so much perplexed by this simple question, finding himself unable to answer it without entering at large on the subject of eiectrical mea- * If Dr. Matthiessen uses the sp. gr. of 13°596, as given by Regnault, the difference from Dr, Siemens’s standard is 5 per thousand Mr. F. Jenkin onthe New Unit of Electrical Resistance. 485 surement, that he has been led to devise the following definitions, in which none but already established measures are referred to. metre The resistance of the absolute ——— is such that the current ge- second nerated in a circuit of that resistance by the electromotive force due to a straight bar 1 metre long moving across a magnetic field of unit intensity* perpendicularly to the lines of force and to its own direction with a velocity of 1 metre per second, would, if doing no other work or equivalent of work, develope in that circuit m one second of time a total amount of heat equivalent to one absolute unit of work—or sufficient heat, according to Dr. Joule’s experiments, to heat 0°0002405 gramme of water at its maximum density 1° Cen- tigrade The new standard issued is as close an approximation as could be obtained by the Committee to a resistance ten million times as great metre - second. | in a magnetic field of unit intensity, would require to move with a velocity of ten millions of metres per second to produce an electro- motive force which would generate in a circuit of the resistance of the new standard the same current as would be produced in the cir- cuit of one es resistance by the electromotive force due to the C as the absolute The straight bar moving as described above motion of the bar at a velocity of one metre per second. The velo- city required to produce this particular current} being in each case proportional to the resistance of the circuit, may be used to measure that resistance, and the resistance of the B. A. unit may therefore metres second It is feared that these statements are still too complex to fulfil the purpose of popular definitions, but they may serve at least to show how a real velocity may be used to measure a resistance by using the velocity with which, under certain circumstances, part of a circuit must be made to move in order to induce a given current in a circuit of the resistance to be measured. That current in the absolute system is the unit current, and the work done by that unit current in the unit of time is equal to the resistance of the circuit, as results from the first equation stated above. Those who from this slight sketch may desire to know more of the subject will find full information in the Reports of the Committee to the British Association in 1862, 1863, and 1864. The Committee continue to act with the view of establishing and issuing the correla- tive units of current, electromotive force, quantity, and capacity, the standard apparatus for which will, it is proposed, be deposited at Kew along with the ten standards of resistance already constructed with the funds voted by the Royal Society. * Gauss’s definition. + This current is the unit current, and, if doing no other work or equivalent of work, would develope, in a circuit of the resistance of the B. A unit, heat equivalent to ten millions of units of work, or enough to raise the temperature of 2405 grammes of water at its maximum density 1° Centigrade. be said to be ten millions of metres per second, or 10" 4.86 | Royal Society. APPENDIX B, The followmg Table shows the degree of concordance obtained in the separate experiments used to determine the unit. The deter- minations were made by observing the deflections of a certain magnet when a coil revolved at a given speed, first in one direction, and then in the opposite direction. The first column shows the speed in each experiment ; the second shows the value of the B. A. unit in terms of 10’ a as calculated from the single experiments. A differ- ence constantly in one direction may be observed in the values ob- tained when the coil revolved different ways. This difference de- pended on a slight bias of the suspending thread in one direction. The third column shows the value of the B. A. unit calculated from the pair of experiments. The fourth shows the error of the pair from the mean value finally adopted. In the final mean adopted, the 1864 determination was allowed five times the weight allowed to that of 1863. 1 2. 3. 28 Value of B. A. unit in t £ 197 metres Value from mean | Percentage error of igeeed second: of each pair of | pair of observations Time of 100 revo- lutions of coil, in Difference in two values 1864 and 1863=0:16 Probable error of two experiments .... =0°08 33 22 seconds. as calculated from experiments. from mean value. each experiment. eae emt | ou | moe mez roe} oo | po soz) amet || gana | 00 7 | 8018) | gga | ons peor | oaset) | game | 0 ae | wage) | roms | 40a we | Gg) |. 10m 17 ms | 1908) | oom | gm waa | cae) | ime | 40a nai | 3084) | og | ons i Probable error of R (1864).......... =(°1 per cent. | Probable error of R, (1863).......... = 0°24 us [487] LXVI. Intelligence and Miscellaneous Articles. AIR-PUMP CONSTRUCTED ON A NEW PRINCIPLE. BY M. DELEUIL. "THE machine is intended for industrial purposes, as it is only pur- posed to try to obtain, in a relatively short time, a vacuum of 18millims. of mercury for the size of vessels commonly worked with, and of 8 millims. for the usual sizes of the laboratory. The principle on which I have gone has much analogy with that which guided M. Isoar, ten or twelve years ago, in his superheated steam-engine, which consisted in using steam at high pressures, acting on pistons of small section working with great velocity, and not rubbing against the sides of the cylinder. I imagined that if, in making a vacuum, I caused a metallic piston to move in a cylinder perfectly ; and only leaving between it and the cylinder the thickness of a sheet of letter- paper, the fluid could not pass from one side to the other of the pis- ton, provided that its length was equal to at least twice its diameter, and it was provided with grooves 8 cr 10 millims. apart. Expe- riment has shown that with such a piston, without any great ve- locity, a vacuum of from 8 to 18 millims. may be attained, according to the capacities. The fluid itself serves as packing for the piston. I thus, at the same time, destroy the resistance due to the friction of the piston in the barrel and the stopping up of the valves (by suppressing the oil used to lubricate the pump), as well as the wear and tear of the cylinder. .This machine is double-acting, and can be used as com- pression-pump up to the limit of two atmospheres, as it can pump gas from a reservoir, and compress it in another without appreciable loss of gas.—Comptes Rendus, March 20, 1865. METEOR AND METEORITES OF ORGUEIL. On the evening of the 14th of May, 1864, a very bright fireball was seen in France throughout the whole region from Paris to the Pyrenees. Loud detonations were heard in the neighbourhood of Montauban, and a large number of stones came down near the vil- lages of Orgueil and Nohic. The passage of the meteor was wit- nessed by a large number of intelligent observers, since it occurred early in the evening. Numerous accounts of its appearance have been published in the Comptes Rendus. This fall of meteorites is of peculiar interest. While we have over a hundred large fireballs and detonating meteors whose paths through the atmosphere have been computed with more or less precision, there are only four or five of them from which stones have been known to come. Of these four or five, only one, the Weston meteor, has been so well observed that we can speak with confidence of its path. 488 Intelligence and Miscellaneous Articles. The published accounts show that the Orgueil meteor was first seen at an altitude greater than 55 miles, that it exploded at an altitude of about 20 miles, and that it was descending in a line in- clined at the least 20° or 25° to the horizon. The “velocity must have been not less than 15 or 20 miles per second. This example affords the strongest proof that the stone-producing meteors and the detonating meteors are phenomena not essentially unlice.—Sillimany S American Journal for March 1865, PHENOMENON IN THE INDUCTION-SPARK. BY E. FERNET., The disengagement of heat which the induction-spark produces in the air exerts upon the path of this spark an influence which seems to be shown by the following. experiment. Two small straight brass rods about 2 decimetres in length, each upon an insulating support, are placed almost vertically and parallel to each other at a distance of a few centimetres; they are then moved.somewhat apart above, so that they form below a very acute angle. They are then both united with the ends of the induction- coil of a Ruhmkorff’s apparatus. The sparks which pass at each oscillation of the commutator appear first, as is natural, between the two nearest points of the bars—that is, at the bottom. But they soon leave this and appear at a higher part, until they reach the highest, when this discharge suddenly ceases. The spark now passes below, and the same series of phenomena is repeated. ‘The duration of the impression has, moreover, the effect that not merely one line of light is seen, but several are seen close together—a sort of ladder with very brilliant rounds in the dark, which slowly and regularly ascends between the vertical bars, breaks off, and then again begins from below without ever exhibiting the inverse direction. These results appear to be explained by the heating in the dis- charge. ‘The passage of each spark produces in the air a consider- able increase of temperature, the air expands, ascends, and thus the upper layer, though longer, offers less resistance, in consequence of which the second spark passes here. ‘The passage of the second acts just in the same way upon the third, and so forth, until the dis- charge takes place on the uppermost points. ‘The air continues to ascend; but the spark betakes itself where the layer of air is shortest, that is, to the lowest point. This explanation is supported by a change of the experiment. For if the bars are placed in a herizontal, and not a vertical plane, still somewhat divergent, no displacement is observed, but the spark always passes between the nearest points. This is also the case if the bars are vertical but converge above. Even in the first position of all, the ascent of the spark can be suddenly suppressed, if a current of air from above is directed upon it.—Compies Rendus, vol. lix. p- 1005. THE LONDON, EDINBURGH ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. SUPPLEMENT to VOL. XXIX. FOURTH SERIES. LXVII. On a new Determination of the Lengths of Waves of Light, and on a Method of determining, by ,Opties, the Trans- latory Motion of the Solar System. By A. J. ANGsTROM*, [With a Plate. ] I. N the Note on Fraunhofer’s lines which I had the honour of communicating to the Royal Academy in October 1861, I spoke of my intention of revising the lengths of luminous waves, as determined by Fraunhofer}, and of extending these deter- minations to all the remarkable lines of the spectrum, in order with their help to obtain the wave-lengths for the metal-spectra. The weather last summer was, on the whole, scarcely favour- able to such experiments on the solar spectrum, nor are these experiments by any means complete. Nevertheless, sce my measurements of the principal lines of Fraunhofer are sufficiently numerous and self-accordant to secure my results from any essential change, I have deemed it of some interest to examine whether, and to what extent, these new determinations agree with those obtained by Fraunhofer himself—the more so because no new measurements on the wave-lengtlis of light have, to my knowledge, been made since Fraunhofer closed his wonderful investigations. I employed in my experiments an optical theodolite constructed by Pistor and Martins in Berlin, and a glass grating made by the optician Nobert in Barth. The theodolite was provided with two telescopes, the second of which served as a sight-indicator (Sehzeichen). In reading off, two microscopes were used, and one division of the micrometer corresponded to an angle of 2!"1. The eyepiece is also provided with a micrometer arrangement : the screw-head is divided into 100 parts; and when the telescope * From Poggendorff’s Annalen, vol. cxxii. p. 489; to which journal the paper was communicated by the Author after its publication in the Oefver- igt af K. Vet. Akad. Forh. 1863, No. 2. + Poggendortt’s Annalen, vol. cxvii. p. 290. Phil. Mag. 8.4. No. 199. Suppl. Vol. 29. 2K 490 M.A. J. Angstrom on anew Determination is adjusted on an infinitely distant object, every scale- disasion corresponds to 1-308. The glass grating prepared by Nobert is particularly well constructed. In a space 90155 Par. lines broad, there are 4501 lines drawn by a diamond. - Errors of division, as tested by Nobert with a microscope which magnified 800 tRE, lie below 0:00002 of a Par. line. The breadth, as given by Nobert, was chines ie comparison with a standard prepared by the mechanician Baumann of Berlin, and which was a copy of the one made by the same artist for Bessel. As a proof of the excellence of this glass grating, I may state that Fraunhofer’s lines can be seen therewith in the third and fourth spectrum, and that in distinctness and richness of detail these lines far exceed those which are obtained by the refraction of light through a flint-glass prism. During the observations the grating was always placed per- pendicularly to the incident rays. This was accomplished, first, by always giving to the unscratched side of the grating a position suck that the image of the heliostat-aperture reflected by it coin- cided with the aperture itself; secondly, by adjusting on the heliostat-aperture the moveable telescope used in the observations; and thirdly, by fixing the axis of the second telescope so as to coincide with the prolongation of the optic axis of the first. The scratched side of the glass grating was always turned from the incident light and towards the moveable telescope, being placed in the middle over the rotation-axis of the imstrument. The observations were calculated according to the known formula esinO=ma, where e, or the distance between two scratches on the grating, had, according to the above remark, the value e=0:000166954: of a Par. inch, W denotes the required wave-length, © the observed angle, and m the order of the spectrum. As the values of X thus obtained have reference to air, they must be dependent upon its temperature and barometric pressure; I have consequently always noted these two elements, although under ordinary circumstances their mfluence on the measure- ments was found to be appreciable. The changes in the tem- perature of the grating itself exercise a somewhat more important action; nevertheless since, at the time the observations were made (September and commencement of October), the temperature of the room only oscillated between 13° and 18° C., I have like- wise omitted this correction. of the Lengths of Waves of Light. 49] _ That no appreciable errors can have thereby arisen in the mean yalues thus obtained—values which may be regarded as true for 15°C. and the mean barometric pressure—is readily seen on calculating the magnitudes of these corrections. Assuming the refraction-coefficient of air to be | n= 1:000294, — to be a constant magnitude, independent of temperature and pressure, and the value of e, moreover, to hold for 15° C., w. obtain the following corrected value :— esin® log X= log ——— — 0:36 (¢,°—15°) + 0:09(7,°—15°) __ | | —0:04(H —0™-76), whence we conclude that the correction for log» amounts to +0°45 (¢°—15°) —0°14 (H —0™76), expressed in units of the fifth decimal place. | Accordingly a change of 2 degrees in temperature produces a change of 2” in the value of the angle ©, if © be assumed equal to 25°; this error is comparable with the error of adjustment itself. For smaller values of © the error will of course be smaller. The angle © is also subject to a correction dependent upon the absolute motion of the instrument in the direction of the path of the incident ray; this correction, however, is almost in- appreciable for the observations upon which the numerical values in the following Table are founded. The wave-lengths are, like those of Fraunhofer, expressed in units whose magnitude is equal to 0°00000001 of a Par. inch. TasBLEe I.—Wave-lengths, in ths of a Paris inch. . 100, 500: 000 2K 2 i - : ] : é ee | Eg 5 : at : aS E Bea. |S) D. 18 PR = ba 1s F. |5 GS ie. Le) 6 Ee oS 5) oO S) SS) s) o | a) S| iS z. 3 z. z a z z. n Nn nN RR op) R | N n | — —— es ey [eae —|—| Si — —— 539-91) j 2496: 50) 1 | 2178-69) 3 | 1948-25) 1 | 1916-51] 1 | 1797-38) 1 | 1592-32) 2 | 1467-19) 1 | 1454: 88 2939°54| 2 | 2426-28} 2 | 2178-53! 3 | 1948-21] 3 | 1916-64! 3 | 1797-37 3 | 1592-53) 1 | 1467-58) 4 | 1453-39 2529-76 3 | 2426-23) 2 | 2178-62) 2 | 1948-24) 2 | 1916-46} 2 | 1797-21) 3 | 1592-22) 2 | 1467-32) 3 | 1453-74 2426-33) 3 | 2178-64) 1 | 1948-20) 1 | 1916-53] 4 | 1797-27) 2 | 1592-16) 2 | 1466-66)-2 | 1453-89 | 2426:25) 1 | 2178-57| 4 | 1948-25] 3 | 1916-56] 1 | 1797-05) 1 | 1592-50) 2 | 1467-12) 1 2426:27| 2 | 2178-61) 4 | 1948-24| 3 | 1916-49] 4 | 1797-20 3 | 1592-32) 2 | 1467-34) 4 | | 2178-56) 2 | 1948-23] 3 | 1916-43) 4) 1797-11, 2)... 1466:98) 3 |2178°48) 4 | 1948-32! 4 | 1916-47) 4 ical 2539-73| 2426:29| | 2178-59 1948-24 1916°50 1797:27| ~| 1592-34) 1467" 18)" 1453-98 er BD CR | Spectrum. : | 492 M.A. J. Angstrom on anew Determination The difference of the wave-lengths corresponding to the two D lines, as measured in the third and im the fourth spectrum, amounts to 2°226,—that between the wave-lengths corresponding to the two E lines being only 0°395, as measured in the third spectrum. Fraunhofer has given two different series of values for the wave-lengths of light. The first series was obtained by mea- surements with wire gratings, and it is upon this that Cauchy founded his calculations in the Mémozre sur la Dispersion. It contains the following numerical values (8) :— B. C. D. E. F. G. IF 2541, 2425, 2175, 1943, 1789, 1585, 1451. Comparing these values with the corresponding ones in the foregoing Table, which I will call the series (a), the following differences («— ) are obtained :— —1°3, +13, +3°6, +5°2, +83, +7:4, +162. The differences increase, as will be seen, towards the violet end of the spectrum, and are there very considerable. This arises from the difficulty, when using gratings so coarse as those | employed by Fraunhofer, of accurately distinguishing the dark lines at the violet end of the spectrum. The best of all the gratings employed by Fraunhofer is, with- out doubt, that which he denoted as No. 4, and with which he observed the line Keven in the thirteenth spectrum. - This grating gives, in general, values which agree better with my own. For the lines C, D, and E the agreement is nearly perfect. The grating in question gave, in fact, the values B. C. D. E. F. G. iam 2542, 2426, 2178, 1947, 1794, 1586, 1457. I conclude from this that the disagreement between the series («) and (@) must arise principally from errors of observa- tion, which, with the wire gratings used by Fraunhofer, were unavoidable. The other series of values of wave-lengths given by Fraun- hofer is of a somewhat later date. It will be found in Gilbert’s Annalen der Physik, vol. \xxiv., as well as in Herschel’s ‘Optics,’ Schwerd’s Beugungs-Erscheinungen, and other works. This series, on account of its exactitude, appears to have been held by Fraun- hofer in greater esteem than the older ones. It contains the following values (vy) :— C. vs B, K. G. H. 2422, 2175, 1945, 1794, 1587, 1464; and gives, when compared with the series («), the differences (a-y)i 44-3 43:6, £32, +33, 45-4, 43-1. of the Lengths of Waves of Light. | 493 The values of the wave-lengths contained in the series (vy) depend on measurements of the first interference-spectrum of a glass grating which was considerably finer than the one I em- ployed. According to Fraunhofer’s statement, in fact, e=0°0001223 of a Par. inch, Since, however, the number of marks in this grating of Fraun- hofer’s amounted only to 3601, the breadth reduces itself to 5°2833 Par. lines; and consequently it must have been considerably less luminous than that of Nobert. In another respect, too, Fraunhofer’s grating, although an excellent one, appears to me to have been inferior to that of Nobert; for the line B could not be mea- sured even in the first spectrum, and the lines from C to G were not visible in any of the spectra beyond the second. Nevertheless, since almost all the differences (a—y) have the same value, a constant error appears to be indicated, either in my measurements or in those of Fraunhofer. That an error of this character cannot have affected the value of © in my mea- surements, is evident from the fact that the value of this angle was obtained from mutually agreeing observations on four dif- ferent spectra. The introduction of such an error into Fraun- hofer’s measurements is equally inadmissible, since on calculating the wave-lengths of the lines from C to G (which Fraunhofer also observed in the second interference-spectrum, though he did not introduce them into his calculation), the following mutu- ally according values are obtained from the two spectra :— Cc. D. E. F. G. First spectrum . 2422-00, 2174°58, 1944°81, 1793-98, 1586°89; Second spectrum. 2421°54, 2174°36, 1944°63, 1793-92, 1588-07. It is only for the line G that the difference is somewhat greater. The reason of the differences (a—y), therefore, must arise from an erroneous determination of the value of e; which latter may have been caused either by a wrong enumeration of the lines in one of the two gratings, or by an incorrect estimation of their breadth. In order to make the two values of the wave- lengths for the line D agree, in the series (#) and (y), by alter- ing the value of e, the breadth of Nobert’s grating would have to be diminished by 0:0128 of a Par. line =0:001025 of a Par. inch, or the number of lines in the grating zncreased by 6. _ The same object would be attained by increasing the breadth 494 M. A. J. Angstrom on anew ai of Fraunhofer’s grating by 3 0:00061 of a Par. inch, or wr by diminishing the number of lines by 5. That the second decimal is wrong in the above breadth (=9-0155 lines) of Nobert’s grating is not probable; far more so is the supposition of an error of about half this ‘magnitude in the estimation of the breadth of Fraunhofer’s grating, espe- cially since the microscope, forty years ago, had not reached its present high degree of perfection. Fraunhofer, moreover, was compelled to strengthen the extreme lines of his grating, in order to see them more distinctly when measuring, a circumstance which may possibly have affected the positions of these two lines. Besides the fact that my measurements agree with the results which Fraunhofer obtained by means of the grating No. 4, there is another reason in favour of the assumption that the ‘differ- ences (a—y) arise from an incorrect value of e in Fraunhofer’s glass grating. For the above-cited memoir of Fraunhofer’s contains measurements made with another glass grating for which e had the considerably greater value of 0:0005919 of a Paris inch. Fraunhofer made no use of these measurements, probably because this grating proved to be far less perfect, the spectra on one side of the axis being twice as intense as those on the other. On calculating these measurements, however, we obtain the fol- lowing values corresponding to the lines from D to G:— D. E. F. G. Spectrum. a a | | | ee Qe eeo) OAV PU tee, ts 2177-48 | 1947°18) 1796-10 | 2177-64 1947-23) 1796-09 | 1590-90 3 2 I OU 2176°80| 1946-63 | 1795-99 | 1591-07 2177°55 | 1947-25 | 1796°39 | 1590°16 2177°34| 1947:10| 1796:14| 1590°71 These values, compared with the series (c), indicate a constant difference; here, however, the differences amount only to 1:25, 1:14, 1:18, 1°63, or to about one-third of those last given. Now, since this last grating was nearly five times as coarse as the former, and probably also broader, it must have been easier to determine accurately its corresponding e. This circumstance of the Lengths of Waves of Light... -. 495- tends to increase the probability of the existence of an error in the value of e corresponding to the finer grating. The values of the wave-lengths obtained by means of Nobert’s grating, therefore, appear to me to merit a greater confidence than that which Fraunhofer’s can justly claim. Eb As already stated at the commencement of this paper, I have not limited my measurements to the principal lines of Fraun- hofer. I have measured, with the circle, the angle © for all the stronger lines at a distance from each other of from 10! to 20’, and determined with the eyepiece-micrometer the positions of the remaining intermediate lines. The measurements, moreover, were repeated in the second, third, and fourth spectra, in order to verify their exactitude. The following Table contains some of these results, those wave- lengths alone being given which correspond to the strongest and most prominent lines of the solar spectrum. Most of these lines belong to iron or to lime, and have consequently a double interest, since they present themselves also in the gas-spectra of these substances. In order to give the reader a visible image of the position and breadth of these lines in the solar spectrum, I have added a figure (Plate III. fig. 1), which correctly shows their respective positions as presented by a prism of sulphide of carbon having an angle of 60°. An are of 2' corresponds in the figure to a length of one millimetre. Tasie II.—Wave-lengths, in hundred millionths (=13) of a Paris inch. Spectra in which cor- ee responding lines -are Remarks. observed. ae length. A 2812 iB 2539°7 C C7 2426-29 2312-2 Earth’s atmosphere ...| Strong line. 22873) 2279°6 2276:8 | 2269-4 ‘| Iron and calcium ...... Group of strong lines. 22677 | 2262°1 D { 2179-70 eee Two groups of lines. Ov C2 bO 1) (—) [=y) €© ~] —_ Le ¢ ~ SS a 5 ee ee 496 M.A.J. Angstrom on a Method of determining, Tasxez II. (continued). Line. ™ A agen 1454:0 Wave- length. oe | eee 2060°1 2016:9 2013'6 2013-1 2007°3 2005-3 1998-4 1997-9 1985-8 1985-3 1984-2 1983-5 1974-2 1969-6 1968-1 1965-3 1953-2 1948-44 1948-04 1946°8 1934-6 1936-4 1919-6 191650 1912-39 1911-10 1910-49 1903-4 1832-70 1819-1 1818-4 1808-3 1801-1 1797-27 1632-2 1628°5 1620°4 1604:°3 1598°8 1592:34 1579°1 15747 1571-2 1562-4 1532-0 1515-9 1505°3 1502-0 1495:2 1480°4 1467-2 Spectra in which cor- responding lines are observed. Iron. Remarks. Saeed 99 stiedads ccenmatetees Strong line. 97 Teoveccacteressoevene 7 Iron and calcium. 99 ” Iron. 99 SCOCOCrcebebOOesceuseor Hydrogen. Iron. 9 Hydrogen. Tron. 39 Calcium BCrGoeeseeeeeseseb se ron? .cesane cece ne Unknown. Tron: 4 sc. Wee atoms mee COCesecoeesesevecstes Weak. Double line, like E. Double line, like E. .| Double line, like E. Iron when weakly incandescent gave but one of these lines; when strongly incandescent, however, a third was visible. Double. Double line. Double line ; several weak lines were also visible between g and h. Very strong line. Strong line. by Optics, the Translatory Motion of the Solar System. 497 IIT. In a lecture given on October 6, 1860, to the Royal Scien- tific Society of Upsala, I explained a method of determining the motion of the solar system by observations on the interfer- ence-bands of a glass grating. I then showed that if we assume the propagation of the undiffracted rays, passmg through the openings of the grating, to be uninfiuenced by the motion of the instrument, the same must be true of the formation of the interference-bands on both sides; consequently, also, that when a telescope is used in the observations the customary aberration must ensue, and be proportional to the ratio between the motion of the telescope, im a direction perpendicular to its axis, and the velocity of light along this axis. Hence, the velocity of light being taken as the unit, if 4 be the velocity of the instrument in the direction of the incident light, then for an angle ©, under which, e. g., the D line in an interference-spectrum is observed, the velocity of the telescope perpendicular to this direction will be Asin ©, which accordingly must be the expression for the aberration. If the angle © were observed for two positions of the instru- ment in which the velocities in the path of the incident rays were / and h', we should then have — AG=(h—h)smO, . en es (YE) or, since 2@ is the angle immediately given by observation, A .20=2(h—/A’/) sin ©. Puttmg A(=—A') equal to the velocity of the earth in its orbit, this equation gives A.20=81"-6sin ©; and since, for the double line D in the fourth spectrum, 20 = 62° 55! 44!!-2, we deduce NL 2A A426, a magnitude capable of being readily observed. Two questions have here to be answered by observation. The one has reference to the actual existence of the phenomenon, and may be most readily answered by applying the method to the known orbital motion of the earth; the other has reference to the employment of the method, when proved to be accurate, to the determination of the translatory motion of the solar system. The experiments hitherto made cannot in any respect be con- 498 -M.A.J. Angstrém on a Method of determining, sidered as quite decisive. Last midsummer the weather was unfavourable to my observations, and at the end of October the latter were not sufficiently numerous to furnish an answer even to the first of the above questions. I should not in fact have alluded to the subject had not M. Babinet, in the Academy of Sciences, proposed a method of deter- mining the translatory motion of the solar system identical with the one which, two years ago, I submitted to the Royal Scientific Society of Upsala. A small difference exists, however, in our calculations. I had assumed the motion of the grating to have no influence on the angle ©, whereas Babinet introduces, on this account, the cor- rection h(1— cos @) tan ©. The truth of this formula may in fact be readily established by help of the adjoining figure, in which e sin @ denotes the distance traversed by light during the time that the gra- ting describes the distance — hesm@ in a direction contrary to that of the incident rays. The difference of path for the two interfermg waves will consequently, through the motion of the grating, be diminished by he (li — cos @) sin ©, a magnitude which, when equated to —ecos 0 dO, gives : d® = —h(1— cos ®) tan ©. The value of d® will, of course, be positive when the instru- ment moves in the same direction as the light. The expression thus obtained, added to fhe one in the formula (1), gives for the total variation af the angle © the value AO=(h—/')tan O ; and if, moreover, h= —/h!=20"-4, and 2@=62° 55! 41", then will A20=49"8, Hence in the special case under consideration, the variation of the angle 2 is increased by 7”-2 in consequence of the motion of the grating. The observations on which the numerical values of Table I. by Optics, the Translatory Motion of the Solar System. 499 are based were all (with a few exceptions) made at or near mid- day. On this account I thought that the corrections due to the motion of the instrument might be neglected in calculating the results, since in the final mean such corrections must, for the most part, disappear. In proof of the accuracy of the theory here established, I will give a few of the observations made last year at the commence- ment of October. They have reference to the double line D in the fourth interference spectrum. The light was always inci- dent from south to north. The second telescope and the grating were readjusted every day. Tape III. Time of observation, sre in 1862 aS Remarks. ee ee Sc h (eo) i i/ 11-4 a.m. - 2 a Mean of three observations. 5 P.M. | 62 56 7 Mean of six observations. Oct. 0} 3:74pm. | 6256 0 Mean of six observations. 9-5 A.M. 62 55 51 by) pee 62 55 58 Mean of two observations. 3°75 P.M. 62 56 7. From the mean value of the wave-lengths corresponding to the line D given in Table I. we deduce 2@, = 62° 55! 41""-2=d5; and since this value must be very nearly free from any error due to the motion of the instrument, it ought to agree with that fur- nished by the observations in Table III., after applying to the latter the corrections due to the motion of the instrument. If X be the velocity of the solar system im a direction deter-- mined by the coordinates of the equator, D=34°°5 and A=259%8, the magnitude of the motion of the instrument from north to south, due to the motion of the solar system, will be X cos b=X [cos D sin P cos (A— >) — sin D cos PJ, where P denotes the altitude of the pole, and > the sidereal time of the observation. For Upsala, therefore, we shall have the formula X [0-718 cos (259°-8— *) — 0-284]. The velocity of the instrument, in the above direction, due to 500 On the Translatory Motion of the Solar System. the earth’s annual motion is equal to hcosb,=h§ cos D, sin P sn[© —*]—sm D, cos P}, where — sin D,=sin 28° 38! cos ©. In this formula © denotes the right ascension of the sun, P and > the same magnitudes as before, and h=20""4 the velocity of the earth expressed by the angle it “subtends at the centre of a circle whose radius is the velocity of light. The total correction of the angle ¢, therefore, will be Ag=24!"-9[cos 6, +n cos bj, since X=nh and 40"-8 tan © =24!-9. If by means of this last formula, and under different assump- tions for the value of n, we calculate the correction for each angle g@ in Table Iil., and afterwards add these corrections to their respective angles, the resulting values of ¢ 4- Ad, subtracted from the assumed true value of 2@,, that is to say, from =—02° Do 40. will give the following : TaBLe lV. bo>—(¢+A¢) Po—# n=0. | n=t. oe n=1 dl il di di il + 3 +3 + 4 +4 an aa | +9 sus +3 = 2 —26 =o — 6 a —13 —19 42 aT ee) —% 10 17 my —12 _% —18 —— | —10 —10 i — 26 — | —10 —10 —16 The sums of the squares of the differences are respectively 2267, 462, 419, 427, 719. So far as we can conclude from the above observations, the influence of the earth’s annual motion appears to be verified ; that of the motion of the solar system is less perceptible. Never- theless it is obvious that if we were to assume that motion to be zero, or to be equal to that of the earth in its orbit, the agree- ment between the observations would be worse than under the assumption that the magnitude of the motion in question is Intersections of a Pencil of four Lines by a Pencil of two Lines. 501 somewhat more than one-third of that of the earth. Between this result, and what we already know of the motion of the solar system through astronomy, there is no great divergence. I hope during the present year, however, to be able to con- tinue my spectrum-experiments, and to have a better opportu- nity of determining, numerically, the magnitude of the motion of the solar system. In the present paper my object has merely been to show the possibility of solving, optically, this interesting problem in physical astronomy. LXVIII. On the Intersections of a Pencil of four Lines by a Pencil of two Lines. By Professor Cayuey, F.R.S.* LUCKER has considered (‘“ Analytisch-geometrische Apho- rismen,” Crelle, vol. xi. (1834) pp. 26-32) the theory of the eight points which are the intersections of a pencil of four lines by any two lines, or say the intersections of a pencil of four lines by a pencil of two lines: viz., the eight points may be con- nected two together by twelve new lines; the twelve lines meet two together in forty-two new points; and of these, six he on a line through the centre of the two-line pencil, twelve lie four together on three lines through the centre of the four-line pencil, and twenty-four lie two together on twelve lines, also through the centre of the four-line pencil. The first and third of these theorems, viz. (1) that the six points lie on a line through the centre of the two-line pencil, and (3) that the twenty-four pomts lie two together on twelve lines through the centre of the four-line pencil, belong to the more simple theory of the intersections of a pencil of three lines by a pencil of two lines; the second theorem, viz. (2) the twelve points lie four together on three lines through the centre of the four- line pencil, is the only one which properly belongs to the theory of the intersections of a pencil of four lines by a pencil of two lines. The theorem in question (proved analytically by Plucker) may be proved geometrically by means of two fundamental theo- rems of the geometry of position: these are the theorem of two triangles in perspective, and Pascal’s theorem for a line-pair. I proceed to show how this is. Consider a pencil of two lines meeting a pencil of four lines in the eight points (a, 0, c,d), (a', b', c,d’); so that the two lines are abcd, a'b'c'd' meeting suppose in Q; and the four lines are aa', bb', cc!, dd' meeting suppose in P ; then the twelve points are * Communicated by the Author. 502 Intersections of a Pencil of four Lines by a Pencil of two Lines. a'd.clb, ad'.cb!, a'c.d'b, ac!. db' lymg in a line through P, alb.d'c, ab!.dce, a'd.b'c, ad'. bc! a 3 alc. bid, ac. bd', alb.cd, ab!.cd' . pf where the combinations are most easily formed as ee > viZ.; for the first four points starting from the arrangement r ; (or any other arrangement having the diagonals ab. cd), and thence writing down the four expressions acd ac ade ad ob” a0 oD Oe we read off from these the symbols of the four pots; and the like for the other two sets of four points. ' Now, considering the points. (a, b, e) and (a', b',c’), fhe points ab!.a'b, ac!.a'c, be'. b'c lie in a line through Q; and similarly the points ab!.a'b, ad'.a'd, bd'.b'd lie in ae through Q; which lines, inasmuch as they each contain the points Q and ad’. a'b, must be one and the same line; considering the combinations (b, c, d), (0', ¢, d'),the line in question also passes through cd'.cd; that is, the six points ab!.a'b, ac!.a'c, ad’. ald, be'.b'c, bd’. id, cd. cd lie in a line through Q, which is in fact the before-men- tioned first theorem. Hence the points ab!.a'b and cd’ .c'd lie in a line through Q; or, calling these points M and N respect- ively, the triangles Maa’, Mbt’, Nec’, Ndd' are in -perspective. Hence, considering the two triangles Maa’, Ndd' (or, if we please, the complementary set M6d', Nec’), the corresponding sides are Ma, Nd meeting in ad’. de’, Ma', Nd! : ab .d'e a’ , dd! us iD Weg that is, the points ad! .dc', a'b .d'c lie in a line through P. Similarly ad'.a'd and dc! .d'c lie in a line through Q; or, call- ing these points H, I respectively, the triangles Haa!, Hada, 16d’, Icc' are in perspective ; and considering the combination Hdd’, Idd! (or, if we please, the complementary set Haa’, Icc'), the cor- responding sides are Ha, Ib meeting in ad'. be’, Ha’, Id! i a'd. cb, aa', bb! be Poe that is, the points a'd.c'b, ad!'.cb! lie in a line through P. It remains to be shown that the two lines through P, viz. the line containing ab!.dc! and a'b.d'c, and the line’ contaming ad’. be! and a'd.cb', are one and the same line. This will be Sir David Brewster on Hemiopsy, or Half-Vision. 503, the case if, for instance, ab!. de! Ia__4 ae and ad’. bc also lie in a line through P. We have the points (a, db, d) in a line, and the points (0’, ¢’, a’) in a line; the points a, d, !, c! are also called A, B’, B, A’ re- spectively ; ad’, bb! meet in C, be, dd' in C'; hence, considering the hexagon ad'db'bc', the lines ad', b'b meet in Coats ea, be *,, has aeee. ., AA!. BBY; C’ and hence these three points lie in a line; or, what is the same thing, the lines AA’, BB’, and CC! meet in a point, that is, the triangles ABC, A'B'C’ are in perspective; the corresponding sides are AB, A'B’, that is, ab’, cd meeting in ab! .c'd, BORIC: bb, dd 5 Poet ie MOA, ad', be! . ad' . bc; and these three points lie in a line; that is, the points ab’. dd and ad'. bc! lie in a lime through P. Hence the line through ab! . dc! and a'b.d'c and the line through ad’. bc! and a'd.cb! are one and the same line; that is, the points ab! . de’, a'b . d'c, ad' . bc’, a'd . b'c lie ina line through P. This proves the existence of one of the lines through P; and that of the other two lines follows from the symmetry of the figure ; it thus appears that the twelve points lie four together on three lines through P. Cambridge, April 11, 1865. LXIX. On Hemiopsy, or Half-vision. By Sir Davip Brewster, K.H., F.R.S.* HE affection of Half-vision, or Half-blindness as it has been called, was first distinctly described by Dr. Wollaston, in a paper “ On Semidecussation of the Optic Nerves,” published in the Philosophical Transactions for 1824. “It is now more ..* From the Transactions of the Royal Society of Edinburgh, vol. xxiv. part 1. Communicated by the Author. Ee GO a 504: Sir David Brewster on Hemiopsy, or Half. Vision. than twenty years,” he says, “since I was first affected with this peculiar state of vision, i consequence of violent exercise I had taken for two or three hours before. I suddenly found that I could see but half the face of a man whom I met, and it was the same with every object I looked at. In attempting to read the name Johnson over a door, J saw only son, the commencement of the name being wholly obliterated from my view. In this instance, the loss of sight was towards my left, and was the same, whether I looked with my right eye or my left. This blindness was not so complete as to amount to absolute black- ness, but was a shaded darkness, without definite outline. The complaint lasted only about a quarter of an hour.” In 1822, Dr. Wollaston had another attack of hemiopsy, with this differ- ence, that the blindness was to the right of the centre of vision; and he has referred to three other cases among his friends; but in these the affection was accompanied with headache and indi- gestion. In republishing Dr. Wollaston’s paper in the Annales de Chimie et de Physique*, M. Arago says that he knows four cases of hemiopsy, and that he himself had experienced three attacks of it, followed by headache above the right eye. In the ‘ Cyclopzedia of Practical Surgery,’ published in 1841, Mr. Tyrrell describes Hemiopsy as “‘ Functional amaurosis from general] disturbance.” He informs us that ‘he has experienced this form of amaurosis several times,” and that he has been con- sulted by several fellow-sufferers of both sexes. In all these cases the affection was attended with severe headache, giddiness, and gastric irritation, sometimes preceding, and sometimes fol- lowing the attack. In the accounts which have been given of these tataent cases of hemiopsy, no attempt has been made to ascertain the optical condition of the eye when it is said to be half-blind, or to determine the locality and immediate cause of the complaint. Dr. Wollaston describes the blindness as a shaded darkness with- out definite outline. M. Arago says nothing about darkness ; and the insensibility of the retina, of which he speaks, must mean its insensibility to visual, and not to luminous impressions. Mr. Tyrrell, on the other hand, simply states that the obscurity takes place in different portions of the retina, and varies in its extent at different times. Having myself experienced several attacks of hemiopsy, I have been enabled to ascertain the optical condition of the retina when under its influence, and to determine the extent of the affection, and its immediate cause. In reading the different cases of hemiopsy, we are led to infer * 1824, vol. xxvii. p. 109. Sir David Brewster on Hemiopsy, or Half-Vision. 505 that there is vision in one-half of the retina, and blindness in the other. But this is not the case. The blindness, or insen- sibility to distinct impressions, exists chiefly in a small portion of the retina to the right or left hand of the foramen centrale, and extends itself irregularly to other parts of the retina on the: same side, in the neighbourhood of which the vision is uninjured. In some cases the upper half of the object is invisible, the part of the retina paralyzed being a little below the foramen centrale. On some occasions, in absolute darkness, when a faint glow of light was produced by some uniform pressure upon the whole of the retina, I have observed a great number of black spots, corresponding to parts of the retina upon which no pressure was exerted. In the case of ordinary hemiopsy, as observed by myself, there is neither darkness nor obscurity, the portion of the paper from which the letters disappear being as bright as those upon which they are seen. Now this is a remarkable condition of the retina. While it is sensible to luminous impressions, it is in- sensible to the lines and shades of the pictures which it receives of external objects; or, in other words, the retina is in certain -parts of it in such a state that the light which falls upon it is irradiated, or passes into the dark lines or shades of the pictures upon it, and obliterates them. ‘This irradiation exists to a small degree, even when the vision is perfect at the foramen centrale, and it may be produced artificially in a sound eye, on parts of the retina remote from the foramen, and as completely, though temporarily, as in hemiopsy. In order to prove this, we have only to look obliquely at a narrow strip of paper placed upon a green cloth—that is, to fix the eye upon a point a little distant from the strip of paper. After a short time the strip of paper will disappear partially or wholly, and the space which it occu- pied will be green, or the colour of the ground upon which it is laid*. This temporary insensibility of the retina in the part of it covered by the picture of the strip of paper, or its inability to maintain constant vision of it, can arise only from its being paralyzed by the continued action of light,—an effect not likely to be produced, and never observed, in the ordinary use of the eye. The insensibility of the retina in cases of hemiopsy, and the consequent irradiation of the light into the space occupied with the letters, or the objects which disappear, though a pheno- menon of the same kind as that which takes place in oblique vision, has yet a very different origin. The parts which are in these cases affected extend irregularly from the foramen centrale * Letters on Natural Magic. Lett. II. p. 13. Phil. Mag. 8. 4. No. 199. Suppl. Vol. 29. 2 L 506 Sir David Brewster on Hemiopsy, or Half-Vision. to the margin of the retina, as if they were related to the distri- bution of its blood-vessels and hence it was probable that the paralysis of the corresponding parts of the retina was produced by their pressure. This opinion might have long remained merely a reasonable explanation of hemiopsy, had not a phenomenon presented itself to me which places it beyond a doubt. When I had a rather severe attack, which never took place unless I had been reading for a long time the small print of the ‘ Times’ newspaper, and which was never accompanied either with head- ache or gastric irritation, I went accidentally mto a dark room, when I was surprised to observe that all the parts of the retina which were affected were slightly luminous, an effeet invariably produced by pressure upon that membrane. If these views be correct, hemiopsy cannot be regarded as a case of amaurosis, or in any way connected, as: has been supposed, with cerebral disturbance. | Dr. Wollaston endeavoured to explain the phenomena of he- miopsy, and the fact of single vision with two eyes, by what he calls the semidecussation of the optic nerves, a doctrine which Sir Isaac Newton had suggested, and employed to account for single vision*. A fibre of the right-hand side of the optic nerve is sup- posed to semidecussate or divide itself into two fibres, sending one to the right side of the right eye, and another to the right side of the left eye, while a fibre on the left-hand side of the optic nerve also semidecussates, sending one fibre to the left side of the left eye, and another to the left side of the right eye. Hence Sir Isaac ‘Newton drew the conclusion, that an impression on each of the two half-fibres would convey a single sensation to the bram; and hence Dr. Wollaston concluded that hemiopsy in one eye must be accompanied with hemiopsy in the other. Ingenious as these explanations are, the anatomical facts by which alone they could be supported have not been established. Dr. Alison}, who has adopted the opimion of Newton, and rea- soned upon it, admits that the anatomical evidence is still defect- ive; and the late Mr. Twining f has adduced nine cases of disease in the optic nerves and thalami, which stand in direct opposition to the hypothesis of semidecussation. Dr. Mackenzie, too, adopting the same view of the subject as Mr. Twining, distinctly asserts that “the great mass of facts in Pathology and Experi- mental Anatomy, touching this question, go to prove that injuries and. diseases affecting one side of the brain, instead of hemiopsia in both eyes, produce amaurosis only in the opposite eye.” * Optics, p. 320. + Edinburgh Transactions, vol. xii. p. 479. { Trans. Med. Soc. Calcutta, vol. ii. p. 151; or Edinburgh Journal o Science, July 1828, vol. ix. p. 143. Elementary Relations between Electrical Measurements. 507 The two great facts of hemiopsy in both eyes, and of what is called single vision with two eyes, do not require the hypothesis of semidecussation to explain them. If hemiopsy is produced by the distended blood-vessels of the retina, these vessels must be similarly distributed in each eye, aud similarly affected by any change in the system; and consequently must produce the same effect upon each retina, and upon the same part of it. In explaining single vision with two eyes, we have no occasion to appeal to double fibres in the optic nerves, or to corresponding points on the retina. There is, in reality, no such thing as single vision, that is, a single image seen by both eyes. With two sound eyes every object is seen double, and it appears single only _ when, by the law of visible position, the one image is placed above the other. But even in this case the object is seen double, by means of two dissimilar images of it which are not coincident. By shutting the right eye we lose sight of a part on the right side of the double image, which is seen only by the right eye; and by shutting the left eye we lose sight of a part on the left side of the double image, which is seen only by the left eye. If one eye gives a better picture than the other, the duplicity of the apparently single image is more easily seen. By shutting the good eye the imperfect picture is seen, and by shutting the bad eye we insulate the perfect picture. It is difficult to understand how optical writers and physiologists should have so long de- manded a single sensation for the production of a single picture from the two pictures imprinted on the two retinas. If we had the hundred eyes of Argus, the production of an apparently single picture would have been the necessary result of the Law of Visible Position. LXX. On the Elementary Relations between Electrical Measure- ments. By Professor J. CuerK Maxwetut and FLEEMING JENKIN, Esq. [Concluded from p. 460. ] Part IV.—Measurement of Electric Phenomena by Statical Effects. 33. AULe CTROSTATIC Measure of Electric Quantity. By the application of a sufficient electromotive force between two parts of a conductor which does not form a circuit, it 1s possi- ble to communicate to either part a charge of electricity which may . be maintained in both parts, if properly insulated (14). With the ordinary electromotive forces due to induction or chemical action, and the ordinary size of insulated conductors, the charge of 212 ee 508 Prof. Maxwell and Mr. F. Jenkin on the Elementary electricity in electromagnetic measure is exceedingly small; but when the capacity of the conductor is great, as in the case of long submarine cables, the charge may be considerable. By making use of the electromotive force produced by the friction of unlike substances, the charge or electrification even of small bodies may be made to produce visible effects. The electricity in a charge is not essentially in motion, as is the case with the electricity in a current. In other words, a charge may be per- manently maintained without the performance of work. LElec- tricity in this condition is therefore frequently spoken of as sta- tical electricity; and its effects, to distinguish them from those produced by currents, may be called statical effects. The pecu- liar properties of electrically charged bodies are these :— 1. When one body is charged positively (14), some other body or bodies must be charged negatively to the same extent. 2. Two bodies repel one another when both are charged positively, or both negatively, and attract when oppositely charged. 3. These forces are inversely proportional to the square of the distance of the attracting or repelling charges of electricity. 4. If a body electrified in any given invariable manner be placed in the neighbourhood of any number of electrified bodies, it will experience a force which is the resultant of the forces that would be separately exerted upon it by the different bodies if they were placed in succession in the positions which they actually occupy, without any alteration in their electrical con- ditions. From these propositions it follows that, at a given distance, the force, f, with which two small electrified bodies repel one another is proportional to the product of the charges, g and q,, upon them; but when the distance varies, this force, f, is in- versely proportional to the square of the distance, d, between them. Hence fe... ee When g and q;, are of dissimilar signs, f becomes negative; 7. e. there is an attraction, and not a repulsion. This equation is incompatible with the electromagnetic definitions given in Part III., and, if it be allowed to be fundamental, gives a new defi- nition of the unit quantity of electricity, as that quantity which, if placed at unit distance from another equal quantity of the same kind, repels it with unit force. 34. Electrostatic System of Units—This new measurement of quantity forms the foundation of a distinct system or series of units, which may be called the electrostatic units; and mea- Relations between Electrical Measurements. —-509 surements in these units will in these pages be designated by the use of small letters: thus, as Q, C, &c., signified quantity, current, &c., in. electromagnetic measure, so g, ¢, e, and 7, &c., will represent the electrostatic measure of quantity, current, electromotive force, resistance, &c. The relations between current and quantity, between work, current, and electromotive force, and between electromotive force, current, and resistance, remain unchanged by the change from the electromagnetic to the electrostatic system. 35. Ratio between Electrostatic and Electromagnetic Measures of Quantity.—Since the expression forming the second member of equation (17) represents a force the dimensions of which are LM ian : L? M2 72 the dimensions of g are a The dimensions of the unit of electricity, Q, in the electromagnetic system are L? M? (25). Hence, since in passing from the one system to the other we must employ the ratio a this ratio will be of the dimensions Tk that is to say, the ratio O is a velocity. In the present treatise this velocity will be designated by the letter v. The first estimate of the relation between quantity of electri- city measured statically and the quantity transferred by a cur- rent in a given time was made by Faraday*. A careful experi- mental investigation by MM. Weber and Kohlrauschf not only confirms the conclusion that the two kinds of measurement are consistent, but shows that the velocity =O is 310,740,000 metres per second—a velocity not differing from the estimated velocity of light more than the different determinations of the latter quantity differ from each other. v must always be a con- stant, real velocity in nature, and should be measured in terms of the system of fundamental units adopted in electrical mea- surements (8) and (55). A redetermination of v (46) will form part of the present Committee’s business in 1863-64. It will be seen that, by definition, the quantity transmitted by an elec- tromagnetic unit current in the unit time is equal to v electro- static units of quantity. 86. Electrostatic Measure of Currents.—In any coherent sys- tem, a current is measured by the quantity of electricity which passes in the unit of time (15); if both current and quantity * Experimental Researches, series ii. § 361, &e. + Abhandlungen der Kénig. Sachsischen Ges. vol. ii. (1857) p. 260; or Poggendorff’s Annalen, vol. xcix. p. 10 (Aug. 1856). 510 Prof. Maxwell and Mr. F. Jenkin on n the wernt are measured in electrostatic units, then eee | eS , 3 1 L?M2 The dimensions of c are therefore qa and in order to reduce a current from electromagnetic to electrostatic measure, we must multiply C by v, or exoOy! 2) ae) 37. Electrostatic Measure of Electromotive Force.—The sta- tical measure of an electromotive force is the work which would be done by electrical forces during the passage of a unit of elec- tricity from one point to another. The only difference. between this definition and the electromagnetic definition (16 and 27) consists in the change of the unit of electricity from the electro- magnetic to the electrostatic. Hence, if g units of electricity are transferred from one place to another, the electromotive force between those places being e, the work done during the transfer will be ge; but we found (27) that if EK and Q be the electromagnetic measures of the same quantities, the work done would be expressed by wie hence ge=QEH; but (35) . : g=vQ, therefore a0) e= ae A . 5 5 5 2 5 (20) Thus, to reduce electromotive force from electromagnetic to electrostatic measure, we must divide by v. LM? T 38. Electrostatic Measure of Resistance.—If an electromotive force, e, act on a conductor whose resistance in electrostatic measure is 7, and produce a current, c, then by Ohm’s law The dimensions of e are i C Substituting for e and c¢ their equivalents in electromagnetic measure (equations 19 and 20), we have but (eq. 7) Relations between Electrical Measurements. _- 511- and therefore | Pea RES) aha nee To reduce a resistance measured in electromagnetic units to its electrostatic value, we must divide by 2. | T ; The dimensions of r are po the reciprocal of a velocity. 89. Electric Resistance in Electrostatic Units is measured by the Reciprocal of an Absolute Velocity.—We have seen from the - last paragraph that the dimensions of r establish this proposi- tion ; but the following independent definition, due to Professor . Ny. Thomson, assists the mind in receiving this conception as a necessary natural truth. Conceive a sphere of radius 4, charged with a given quantity of electricity Q. The potential A the sphere, when at a distance from all other bodies, will bee = 7 (40, 4), and 47). Let it now be discharged throngh a certain oe ance, r. Then, if the sphere could collapse with such a velocity that its potential should remain constant (or, in other words, that the ratio of the quantity on the sphere to its radius should remain constant, during the discharge), the time occupied by. its radius in shrinking the unit of length would measure the resistance of the discharging conductor in electrostatic measure, or the velocity with which its radius diminished would measure the conducting-power (50) of the discharging conductor. Thus the conducting-power of a few yards of silk in dry weather might be an inch per. second, in damp weather a yard per second. The resistance of 1000 miles of pure copper wire, 7. inch in diameter, would be about 0:00000141 of a second per metre, or its conducting- -power one metre per 0°00000141 of a second, or 708980 metres per second. 40. Electrostatic Measure of the Capacity of a Conductor. — The electrostatic capacity of a conductor is equal to the quantity of electricity with which it can be charged by the unit electro- motive force. This definition is identical with that given of capacity measured in electromagnetic units (26). Let s be the capacity of a conductor, g the electricity in it, and e the electro- motive force charging it ; then Di SG Mis tes i eens hia “Aoi tcs ben A From this equation we can see that the dimension of the quantity sis a length only. It will also be seen that SOS PAHOA BION DOT naan where S is the electromagnetic measure of the capacity of the conductor with the electrostatic capacity s. 512 Prof. Maxwell and Mr. F. Jenkin on the Elementary The capacity of a spherical conductor in an open space is, in electrostatic measure, equal to the radius of the sphere,—a fact demonstrable from the fundamental equation (17). Experimentally to determine s, the capacity of the conductor in electrostatic measure, charge it with a quantity, g, of electri- city, and measure in any unit its potential (47) or tension (49), e Then bring it into electrical connexion with another conductor whose capacity, s,, is known. Measure the potential, e,, of s and s, after the charge is divided between them; then g=se=(st+5,)e, and hence gE ge) rr In this measurement we do not require to know e and e, in absolute measure, since the ratio of these two quantities only is required. We must, however, know the value of s,; and hence we must begin either with a spherical conductor in a large open space, whose capacity is measured by its radius, or with some other form of absolute condenser alluded to in the following paragraph. 41. Absolute Condenser. Practical Measurement of Quantity. —As soon as the electromotive force of a source of electricity is known in electrostatic measure, the quantity which it will pro- duce in the form of charge on simple forms is known by the laws of electrical distribution experimentally proved by Coulomb. Simple forms of this kind may be termed absolute condensers. A sphere in an open space is such a condenser, and the quantity it contains 1s se (equation 23). A more convenient form isa sphere of radius x, suspended in the centre of a hollow sphere, radius y, the latter being in communication with the earth. The capacity, s, of the internal sphere is then, by calculation, paces MMT y—x By a series of condensers of increasing capacity we may mea- sure the capacity of any condenser, however large. The compa- rison is made by the method described above (40). Thus, the practical method of measuring quantity in electrostatic measure is first to determine the capacity of the conductor containing the charge, and then to multiply that capacity by the electromotive force producing the charge (43). 42. Practical Measurement of Currents:—The electrostatic value of currents can be obtained from equation (21) when e and r are known, or from equation (19) when v and C are known, Relations between Electrical Measurements. 513 or by comparison with a succession of discharges of known quan- tities from an absolute condenser. 43. Practical Measurement of Electromotive Force.—The rela- tions expressed by equations (17) and (23) show that in any given circumstances the force exerted between two bodies due to the effects of statical electricity will be proportional to the electro- motive force or difference of potential (47) between them. This fact allows us to construct gauges of electromotive force, or in- struments so arranged that a given electromotive force between two parts of the apparatus brings an index into a sighted posi- tion. In order that the gauge may serve to measure the electro- motive force absolutely, it is necessary that two things should be known,—first, the distribution of the electricity over the two attracting or repelling masses (or, in other words, the capacity of each part); secondly, the absolute force exerted between them. For simple forms, the distribution, or capacity of each part, can be calculated from the fundamental principles (33); the force actually exerted can be weighed by a balance. By these means Professor W. Thomson* determined the electromotive force of a Daniell’s cell to be 0:0021 in British electrostatic units, or 0:0002951 in metrical electrostatic unitst. This proposition is equivalent to saying that two balls of a metre radius, at a dis- tance d apart in a large open space, and in connexion with the opposite poles of a Daniell’s cell, would attract one another with (0:0002951)? 0:000,000,00888 a force equal to 4d? 2 absolute units, or gramme weight. An apparatus by which such a measurement as the foregoing can be carried out is called an absolute electrometer. It will be observed that, although the definition of electromotive force is founded on the idea of work, its practical measurement is effected by observing a force, inasmuch as when this force exerted be- tween two conductors of simple shape is known, the work which the passage of a unit of electricity between them would perform may be calculated by known laws. 44. Comparison of Electromotive Forces by their Statical Effects. —This comparison is simpler than the absolute measurement, inasmuch as it is not necessary, in comparing two forces, to know the absolute values of either. Instruments by which the comparison can be made are called electrometers. Their arrange- * Paper read before the Royal Society, February 1860. Vide Proceedings of the Royal Society, vol. x. p. 319, and Phil. Mag.S.4.vol.xx.(1860) p.233. + [Note added May 5, 1865.—In electromagnetic measure this would make the electromotive force of a Daniell’s cell equal to about 91,700. Other observers have found a value of about 100,000 (metrical system, based on metre, gramme, and second). | { This value was erroneously given in the original paper. 514 Prof. Maxwell and Mr. F. J ne on the Elementary ment is of necessity such that the force exerted between two given parts of the instrument shall be proportional to the differ- ence of potential between them. This force may be variable and measured by the torsion of a wire, as in Thomson’s reflect- ing electrometer ; or it may be constant, and the electromotive forces producing it may be compared by ‘measuring the distance required in each case between the two electrified bodies to pro- duce that constant force. The latter arrangement is adopted in Professor Thomson’s portable electrometer, first exhibited at the present Meeting of the Association. The indications of a gauge or electrometer not in itself absolute may be reduced to abso- lute measurement by multiplication into a constant coefficient. 45. Practical Measurement of Electric Resistance.—The elec- trostatic resistance of a conductor of great resistance (such as gutta percha or india rubber) might be directly obtained in the following manner :—Let a body of known capacity, s (40), be charged to a given potential, P (47), and let it be gradually dis- charged through the conductor of great resistance, r. Let the time, ¢, be noted at the end of which the potential of the body has fallen to p- The rate of loss of electricity will then be t P| Hence p=P, * and 4 = log. ©. Hence sr sr p t mae Pie (27) s log.— : P — from which equation 7 can be deduced if s, ¢, and the ratio — be known ; ¢can be directly observed ; s can be measured (40) ; and the ratio —can be measured by an electrometer (44) in con- stant connexion with the charged body. This ratio can also be measured by the relative discharges through a galvanometer, first, immediately after the body has been charged to the poten- tial P, and again when, after having been recharged to the po- tential P, it has, after a time 7, fallen to potential p. (This latter plan has long been practically used by Messrs. Siemens, although the results have not been expressed in absolute mea- sure.) Unfortunately, in those bodies, such as gutta percha and india rubber, the resistance of which is sufficiently great to make ¢ a measurable number, the phenomenon of absorption due to continued electrification* so complicates the experiment as to * Vide British Association Report, 1859, Trans. of Sec. p. 248, and Report of the Committee of Board of Trade on Submarine Cables, pp. 136 & 464. Relations between Electrical Measurements. 515 render it practically unavailable for any exact determination. The apparent effect of absorption is to cause r, the resistance of the material, to be a quantity variable with the time ¢, and the laws of the variation are very imperfectly known. 46. Experimental Determination of the Ratio, v, between Elec- tromagnetic and Electrostatic Measures of Quantity.—In order to obtain the value of v, it is necessary and sufficient that we should obtain a common electrostatic and electromagnetic mea- sure of some one quantity, current, resistance, electromotive force, or capacity. There are thus five known methods by which the value can be obtained. (1) By a common measure of quantity. Let a condenser of known capacity, s, be prepared (40). Let it be charged to a given potential P (47). Then the quantity in the condenser will be sP in electrostatic measure. The charge can next be mea- sured by discharge through a galvanometer (25) in electromag- netic measure. The ratio between the two numbers will give the value of v. The only difficulty in this method consists in the measurement of the potential P entailing the measurement of an absolute force between two electrified bodies. This method was proposed and adopted by Weber*. (2) By a comparison of the measure of electromotive force. The electromotive force produced. by a battery, in electrostatic measure, can be directly weighed (43). Its electromotive force, in electromagnetic measure, can be obtained from the current it produces in a given resistance (28). The ratio of the two num- bers will give the value of v. This method has been carried out by Professor W. Thomson, who was not, however, at the time in possession of the means of determining accurately either the absolute resistance of his circuit or the absolute value of the current Tt (3) By a common measure of resistance. We know (29 and 45) how to measure resistances in electromagnetic and electro- static measure. The ratio between these measures is equal to v*, The measure of resistance in electrostatic measure is not as yet susceptible of great accuracy. (4) By a comparison of currents. The electromagnetic value of a current produced by a continuous succession of discharges from a condenser of capacity s can be measured (18, 19). The electrostatic value of the current will be known if the potential to which the condenser is charged be known. The ratio of the two numbers is equal to v. * Poge. Ann. August 1856, vol. xcix. p. 10. Abhandlungen der Kén. Sdachsischen Gesellschaft, vol. iu. (1857), p. 266. + Paper read before the Royal Society, February 1860. Vide Proceed- ings of the Royal Society, vol. x. p. 319, and Phil. Mag. S. 4. vol. xx. p. 233.. 516 Prof. Maxwell and Mr. F. Jenkin on the Elementary (5) By a common measure of capacity. The two measure- ments can be effected by the methods given (26 and 40). The ratio between the two measurements will give v?. This method would probably yield very accurate results. Part V.—Electrical Measurements derived from the five ele- mentary Measurements ; and Conclusion. 47. Electric Potential.—The word “ potential,” as applied by G. Green to the condition of an electrified body and the space surrounding it, is now coming into extensive use, but is perhaps less generally understood than any other electrical term. lec- tric potential is defined by Professor W. Thomson as follows*. “The potential, at any point in the neighbourhood of or within an electrified body, is the quantity of work that would be required to bring a unit of positive electricity from an infi- nite distance to that point, if the given distribution of electricity remained unaltered.” 3 It will be observed that this definition is exactly analogous to that given of magnetic potential (10), with the substitution of the unit quantity of electricity for the unit magnetic pole. (Analogous definitions might be given of gravitation-potential, heat- potential ; and every one of these potentials coexist at every point of space quite independently one of the other.) In an- other papcr} Professor Thomson describes electric potential as follows :—‘‘ The amount of work required to move a unit of elec- tricity, against electric repulsion, from any one position to any other position, is equal to the excess of the electric potential of the first position above the electric potential of the second position.” The two definitions given are virtually identical, since the po- tential at every point of infinity is zero, and it will be seen that the difference of potential defined in the second passage quoted is identical with what we have called the electromotive force between the two points (16 and 27). When, instead of a difference of potentials, the potential simply of a point is spoken of, the difference of potential between the point and the earth is referred to, or, as we might say, the elec- tromotive force between the point and the earth. The potential at all points close to the surface and in the in- terior of any simple metallic body is constant; that is to say, no electromotive force can be produced in a single metallic body by mere electrical distribution ; the potential at the body may there- * SiGe read before the British Association, 1852. Vide Phil. Mag. 1853, 9 oie Pages read before the Royal Society, February 1860. Vide Proceed- ings of the Royal Society, vol. x. p. 334, and Phil. Mag. S. 4 vol. xx. p. 323. Relations between Electrical Measurements. 5 Wa fore be called the potential of the body. The potential of a me- tallic body varies according to the distribution, dimensions, position, and electrification of all surrounding bodies. It also depends on the substance forming the dielectric. In any given circumstances, the potential of the body will be simply proportional to the quantity of electricity with which it is charged ; but if the circumstances are altered, the potential will vary although the total amount of the charge may remain constant. In a closed circuit in which a current circulates, the potential of all parts of the circuit is different; the difference depends on the resistance of each part and on the electromotive force of the source of electricity, 7. e. on the difference of potentials which it is capable of causing when its two electrodes are separated by an insulator or dielectric. The different parts of a conductor moving in a magnetic field are maintained at different potentials, inasmuch as we have shown that an electromotive force is pro- duced in this case. The potential of a body moving in an elec- trie field (7. e. in the neighbcurhood of electrified bodies) is con- stantly changing, but at any given moment the potential of all the parts is equal. The use of the word “ potential” has the following advantages. It enables us to be more concise than if we were continually obliged to use the circumlocution, “ electro- motive force between the point and the earth;” and it avoids the conception of a force capable of generating a current, which almost necessarily, although falsely, is attached to “ electromotive force.” Equipotential surfaces and lines of force in an electric field may be conceived for statically electrified bodies ; these surfaces and lines would be drawn on similar principles and possess ana- logous properties to those described in a magnetic field (10). It is hardly necessary to observe that the magnetic and the electric fields are totally distinct, and coexist without producing any mutual influence or interference. The rate of variation of electric potential per unit of length along a line of force is at any point equal to the electrostatic force at that point, 7. e. to the force which a unit of electricity placed there would experience. The unit difference of potential is identical with the unit electromotive force; and the electro- meter spoken of as measuring electromotive force measures po- tentials or differences of potential. 48. Density, Resultant Electric Force, Electric Pressure.— The three following definitions are taken almost literally from a paper by Professor W. Thomson*. Our treatise would be in- * Paper read before the Royal Society, February 1860. Vzde Proceed- ings of the Royal Society, vol. x. p. 333 (1860), and Phil. Mag.S. 4.vol. xx. p. 322. 518 Prof. Maxwell and Mr. F. Jenkin on the Elementary complete without reference to these terms, and Exolestar Thom-. son’s definitions can hardly be improved. | “ Kiectric Density.—This term was introduced by Coulomb to designate the quantity of electricity per unit of area in any part of the surface of a conductor. He showed how to measure it, though not in absolute measure, by his proof-plane. “ Resultant Electric Force.—The resultant force in air or other insulating fluid in the neighbourhood of an electrified body is the force which a unit of electricity concentrated at that point would experience if it exercised no influence on the electric dis- tributions in the neighbourhood. The resultant force at any point in the air close to the surface of a conductor is perpendi- cular to the surface, and equal to 4p, if p designates the elec- tric density of the surface in the neighbourhood. *€ Kilectric Pressure from the Surface of a Conductor balanced by Air.—A thin metallic shell or liquid film, as for instance a soap- bubble, if electrified, experiences a real ‘mechanical force in a direction perpendicular to the surface outwards, equal im amount per unit of area to 27p*, p denoting, as before, the electric density at the part of the surface considered. In the case of a soap- bubble its effect will be to cause a slight enlargement of the bubble on electrification with either vitreous or resinous electri- city, and a corresponding collapse on being perfectly discharged. In every case we may consider it as constituting a deduction from the amount of air-pressure which the body experiences when unelectrified. The amount of deduction being different at dif- ferent parts according to the square of the electric density, its resultant action on the whole body disturbs its equilibrium, and constitutes in fact the resultant electric force experienced by the body.” 49. Tension.—The use of this word has been intentionally avoided by us in this treatise, because the term has been some- what loosely used by various writers, sometimes apparently ex- pressing what we have called the density, and at others diminu- tion of air-pressure. By the most accurate writers it has been used in the sense of a magnitude proportional to potential or difference of potentials, but without the conception of absolute measurement, or without reference to the idea of work essential in the conception of potential. We believe also that it has not been generally, if ever, applied to that condition of an insulating fluid in virtue of which each point has an electric potential, although no sensible quantity of electricity be present at the point. The expression “tension” might be used to designate what we have termed the potential of a body. The tension be- tween two points would then be equivalent to the electromotive force between those points, or to their difference of potentials, and would be measured in the same unit. Relations between Electrical Measurements. - 519 50. Conducting-Power, Specific Resistance, and Specific Con- ducting- Power. ~ Conducting-Power, or Conductivity.—These expressions are employed to signify the reciprocal of the resistance of any con- ductor. Thus, if the resistance of a wire be expressed by the number 2, its conducting-power will be 0°5. Specific Resistance referred to Unit of Mass.—The specific re- sistance of a material at a given temperature may be defined as the resistance of the unit mass formed into a conductor of unit length and of uniform section. Thus the specific resistance of a metal in the metrical system is the resistance of a wire of that metal, one metre long, and weighing one gramme. The Specific Conducting-Power of a material is the reciprocal of its specific resistance. Specific resistance, referred to unit of volume, is the resistance opposed by the unit cube of the material to the passage of elec- tricity between two opposed faces. It may easily be deduced from the specific resistance referred to unit of mass, when the specific gravity of the material is known. Specific conducting-power may also be referred to unit of volume. It is of course the reciprocal of the specific resistance referred to the same unit. It is somewhat more convenient to refer to the unit of mass with long uniform conductors, such as metal wires, of which the size is frequently and easily measured by the weight per foot or metre; and itis, on the other hand, more convenient to refer to the unit of volume bodies, such as gutta percha, glass, &c., which do not generally occur as conducting-rods of uniform sec- tion, while theird imensions can always be measured with at least as much accuracy as their weights. 51. Specific Inductive Capacity.—Faraday* discovered that the capacity of a conductor does not depend simply on its dimen- sions or on its position relatively to other conductors, but is in- fluenced in amount by the nature of the insulator or dielectric separating it from them. The laws of induction are assumed to be the same in all insulating materials, although the amount be different. The name “inductive capacity” is given to that qua- lity of an insulator in virtue of which it affects the capacity of the conductor it surrounds, and this quality is measured by refer- ence to air, which is assumed to possess the unit inductive capacity. The specific inductive capacity of a material is therefore equal _ to the quotient of the capacity of any conductor insulated by that material from the surrounding conductors, divided by the capacity of the same conductor in the same position separated * Experimental Researches, series xi. 520 Prof. Maxwell and Mr. F. Jenkin on the Elementary from them by air only. It is not ee that this view of induction may be hereafter modified. 52. Heat produced in a Conductor by a Current.—The ark done in driving a current, C, for a unit of time through a con- ductor whose foe x R, by an electromotive farce , is EC=RC? (§ 17). This work is lost as electrical energy, and is transformed into heat. As Dr. Joule has ascertained the quan- tity of mechanical work equivalent to one unit of heat, we can calculate the quantity of heat produced in a conductor in a given time, if we know C and R in absolute measure. In the metrical series of units founded on the metre, gramme, and second, if we call the total heat O, taking as unit the quantity required to raise one gramme of water one degree Centigrade, we have RC?*¢ O= tar" 8 "Wie nets) In the British system, founded on feet, grains, and seconds, with a unit of heat equal to the quantity required to raise one grain of water one degree Fahrenheit, we must substitute the number 24861 for 4157 in the above equation. 53. Electrochemical Equivalents—Dr. Faraday has shown* © that when an electric current passes through certain substances and decomposes them, the quantity of each substance decom- posed is proportional to the quantity of electricity which passes. Hence we may call that quantity of a substance which is decom- posed by unit current in unit time the electrochemical equiva- lent of that substance. This equivalent is a certain number of grammes of the sub- stance. The equivalents of different substances are in the pro- portion of their combining-numbers ; and if all chemical com- pounds were electrolytes, we should be able to construct experi- mentally a table of equivalents, in which the weight of each sub- stance decomposed by a unit of electricity would be given. The electrochemical equivalent of water, in electromagnetic measure, is about 0-02 in British, 000927 in the metrical system. The electrochemical equivalents of all other electrolytes can be de- duced from this measurement with the aid of their combining- numbers. 54, Electromotive Force of Chemical Affinity.— When two sub- stances having a tendency to combine are brought together and enter into combination, they enter into a new state, in which the intrinsic energy of the system is generally less than it was before; that is, the substances are less able to effect chemical changes, or to produce heat or mechanical action, than before. * Experimental Researches, series vii. t ‘009375 by Weber and Kohlrausch. Relations between Electrical Measurements. 521 - The energy thus lost appears during the combination as heat or electrical or mechanical action, and can in many cases be measured*. The energy given out during the combination of two sub- stances may, like all other forms of energy, be considered as the product of two factorst—the tendency to combine, and the amount of combination effected. Now the amount of combina- tion may be measured by the number of electrochemical] equiva- lents which enter into combination; so that the tendency to combine may also be ascertained by dividing the energy given out by the number of electrochemical equivalents which enter into combination. If the whole energy appears in the form of electric currents, the energy of the current is measured by the product of the electromotive force and the quantity of electricity which passes. Now the quantity of electricity which passes is equal to the number of electrochemical equivalents which enter on either side into combination. Hence the total energy given out, divided by this number, will give the electromotive force of combination. Thus, if N electrochemical equivalents enter into combination under a chemical affinity I, and in domg so give out energy equal to W, either as heat or as electrical action, then NI=W. But if W be given out as electrical action, and causes a quantity of electricity Q to traverse a conductor under an electromotive force E, we shall have W=EQ. By the definition of electrochemical equivalents, : EN; therefore t=; or the force of chemical affinity may in these cases be measured as electromotive force. This method of ascertaining the electromotive force due to che- mical combination, which gives us a clear insight into the mean- ing and the measurement of “ chemical affinity,” is due to Pro- fessor W. Thomson ft. The field of investigation presented to us by these considera- * Report of the British Association, 1850, p. 63; and Phil. Mag. S. 3. vol. xxxu. See papers by Professor Andrews, and Favre and Silber- mann, ‘On the Heat given out in Chemical Action,”” Comptes Rendus, vols. xxXXVl. and xxxvil. +t See Rankine “On the General Law of Transformation of Energy,” Phil. Mag. 1853. { “On the Mechanical Theory of Electrolysis,” Phil. Mag. Dec. 1851. Phil. Mag.8. 4. No. 199. Suppl. Vol. 29. 2M 522 Prof. Maxwell and Mr. F. Jenkin on the Elementary tions is very wide. We have to measure the intrinsic energy of substances as dependent on volume, temperature, and state of combination. When this is done, the energy due to any combi- nation will be found by subtracting the energy of the compound from that of the components before combination. As the tendency to increase in volume is measured as pressure, and as the tendency to part with heat is measured by the tempe- rature, so in chemical dynamics the tendency to combine will be properly measured by the electromotive force of combination. 55. Tables of Dimensions and other Constants :— _ Fundamental Units. Length = L. Time=T. Mass= M. Derived Mechanical Units. 2 Work =W= ae - Force =P= ae - Velocity =V= Derived Magnetical Units. Strength of the pole of a magnet . m=L? T7’ M? Moment ofa magnet . . . . . mi=L? T"' M? Intensity of magnetic field . . . H=L°?T~' M? rit Electromagnetic System of Units. Quantity of electricity . . . . . Q=Iix M? Strength of electric current . . . C=L?T”’ M3 Electromotive foree . . . . . . E=LeT”? M2 Resistance of conductor. . . . . R=LT™” Electrostatic System of Units. Quantity of electricity . g=L? T™ Mi Strength of electric currents . . . c=Lz T* M2 Electromotive force. . . . . . esela TM? Resistance of conductor. . . . . r=L°'‘T Let v be the ratio of the electrostatic to the electromagnetic unit of quantity (385 and 46); then v=310,740,000 metres per second approximately, and we have c=vC Hew v q=vQ r=aR s=e78 Relations between Electrical Measurements. 528 TaBxe for the Conversion of British (foot-grain-second) System _ to Metrical (metre-gramme-second) System. Number of Number of trical units ' British units paved oe 3 Lon: Log. Leseanres is a British unit. metrical unit. Rerior WE 2522es2 et S..: 0:0647989 | 2°8115678| 1°1884321| 15-43235 2. For L, ? R, 4 and V.| 0:3047945 | 1-4840071| 0-5159929| 3-280899 r 3. For F (also for se} grains and metre- $| 0:0197504 | 2-2955749'| 1-7044250| 50-6320 grammes) .....0..- ua eat sei Mis atv. dec aed ts 0:0060198 | 3-7795820 |, 2-2204179 | 166-1185 5. For H and Seaer 0-461085 | 1-6637804| 0:3362196| 2:16880 chemical equivalents. uy Gor @, ©, and ec... 01.0. 0-140536 | 1-1477874| 0-8522125| 7-11561 7. For E, m,g, andc ...| 0-0428346| 2-6317949 | 1-3682051| 23-3456 a ee eee 0:0359994 | 2-5562953| 1-4437046| 27-7782 British System.—Relations between Absolute and other Units. One absolute { force —0-0310666 weight of a grain sl faeces (ob! unit of work foot-grains 4 Soe = 382°1889 absolute units of faces London \ one foot-gram work. One absolute f force _ 1 unit weight unit of work g unit weight x unit length g in British system =382-088 (1+0-005133 sin? X), where X= the latitude of the place at which the observation is made. Heat.—The unit of heat is the quantity required to raise the temperature of one grain of water at its maximum density 1° Fahrenheit. Absolute mechanical equivalent of unit of heat =24861=772 foot-grains at Manchester. Thermal equivalent of an absolute unit of work = 0000040224. Thermal equivalent of a foot-grain at Manchester = 0-0012953. Electrochemical equivalent of water =0:02, nearly. Metrical System.—Relation between Absolute and other Units. One absolute J force _ 00809821 weight of a gramme unit of work metre-gramme At { the weight of a gramme aisisesalcaluromniuct force Paris or metre-gramme work. One absolute f force _ 1 unit weight , unit of work” g unit weight x unit length everywhere. g in metrical system =9°78024(1 + 0:005133 sin? 2X), where »X = the latitude of the place where the experiment is made. Heat.—The unit of heat is the quantity required tc raise one gramme of water at its maximum density 1° Centigrade. 2M2 everywhere. at Paris. 524 Prof. Maxwell and Mr. F. Jenkin on the Elementary Absolute mechanical equivalent of the unit of heat =4157-25 =423°542 metre- grammes at Manchester. | Thermal equivalent of an absolute unit of work =0-00024054. Thermal equivalent ofa metr-grm.at Manchester =0:00236154. Electrochemical equivalent of water =0-0092, nearly. 56. Note to the Table of Dimensions, by Professor Clerk Maa- well.—All the measurements of which we have hitherto treated are supposed to be made in the same medium—ordinary air ; but Faraday has shown that other media have different proper- ties. Paramagnetic bodies, such as oxygen and salts of iron, when placed in media less paramagnetic than themselves, behave as paramagnetic bodies; but when placed in media more para- magnetic than themselves, they behave as diamagnetic bodies. Hence magnetic phenomena are influenced by the nature of the medium in which the bodies are placed, and the system of units and of measurements which we adopt depends on the nature of the medium in which our experiments are made. If we made our experiments in highly condensed oxygen, magnets would attract each other less, and currents would attract each other more, than they do in common air; and the reverse would be the case if we worked in a sea of melted bismuth. Now if we take into account the “coefficient of magnetic induction ” of the medium in which we work, and instead of assuming that of common air to be unity, assume it proportional to the density of that part of the medium to which the mag- netic ak is due, we shall have the repulsion of two poles =— where mm! are the two poles, w the density of the magnetic medium, and 7 the distance. Now a density isa mass, M,, divided by L’, the unit of volume. Hence the dimensions of MM ‘ m are Te - ; or if we can measure the density of the mag- netic medium in the same unit of mass as that employed for other purposes, the dimensions of m will be simply those Tv? of H will then be qe or a velocity. If we suppose the density of the magnetic medium to be taken account of in the electromagnetic units, their dimensions become Quantity of electricity . = L?, or equivalent to an area. Z Strength of current. . C= T ; M Electromotive force. . H= 7 M Resistance of conductor R= LT Relations between Electrical Measurements. 525 The electromagnetic unit of quantity of electricity is equal to the electrostatic unit multiplied by a certain velocity, depending on the elasticity of the magnetic medium, and proportional or probably equal to the velocity of propagation of vibrations in it. Hence the dimensions of Electrostatic quantity . . . . g=LT Electrostatic current. . . . . e=hL ‘ L Electrostatic electromotive force e= ite ’ M hresistanee?..). 0.105 2 ee) rs ie As we have no knowledge of the density, elasticity, &c., of the magnetic medium, we assume it as having a standard state in common air; and supposing all measurements to be made in air, the original table of dimensions is sufficient for expressing mea- surements made according to one system in terms of any other system. 57. Magnitude of Units and Nomenclature.—In connexion with the system of measurement explained in this treatise, two points hitherto unmentioned deserve attention—first, the abso- lute magnitude of the units, and secondly the nomenclature. The absolute magnitude is in most cases an inconvenient one, leading to the use either of exceedingly small or exceedingly large numbers. Thus the units of electromagnetic resistance and electromotive force and quantity, and of electrostatic cur- rents, are inconveniently small; the unit of electrostatic resist- ance is inconvyeniently large. Decimal multiples and submulti- ples of these units will therefore probably have to be adopted in practice. The choice of these multiples and submultiples forms part of the business of the Committee. The nomenclature hitherto adopted is extremely defective. In referring to each measurement, we have to say that the number expresses the value in electrostatic or electromagnetic absolute units: if a multiple is to be used, this multiple will also have to be named; and further, the standard units of length, mass, and time have to be referred to, inasmuch as some writers use the pound and some the grain, some the metre and some the milli- metre, as fundamental units. This cumbrous diction, and the risk of error imported by it, would be avoided if each unit received a short distinctive name in the manner proposed by Sir Charles Bright and Mr. Latimer Clark, in a paper read before the British Association at Manchester, 1861. [ 526 ] LXXI. On Lake-Basins. | By Joun Carrick Moors, Esq., F.G.S., &c.* ROFESSOR RAMSAY, in his able memoir in defence of his Glacial Theory of Lake-Basins, in the April Number of this Magazine, lays down principles of the erosion produced by _a sliding body which, with the greatest deference, I cannot believe to be sound. His words are, “ Every physicist knows that when such a body as glacier-ice descends a slope, the direct vertical pressure of the ice will be proportional to its thickness and weight and the angle of the slope over which it flows. If the angle be 5°, the weight and erosive force of a given thickness of ice will be so much, if 10° so much less, 20°, less still, till at length, iff we imagine the fall to be over a vertical fall of rock, the pressure against the wall (except accidentally) will be nz. But when the same vast body of ice has reached the plain, then motion and erosion would cease, were it not for pressure from behind.” By “the direct vertical pressure of the ice,” the Professor means that resolved portion of the weight which is at right angles to the slope; and this resolved portion, which is stated rather loosely to be proportional to the angle, is proportional to the cosine of the angle, a function which up to 90° diminishes as the angle increases. It does not appear to have struck Professor Ramsay as strange, that by his theorem the erosive force is nothing at 90°, comes into operation as the angle declines from 90°, goes on increasing sine limite as the angle diminishes, and just when we expect it to be a maximum, we are told it is nal as the angle vanishes. It seems to me that Professor Ramsay has taken a wrong measure of the erosive foree. He says “the weight or ero- sive force,” as if the words were equivalent. But mere weight does not erode; weight in motion will. A body slidmg down a slope will tend to erode with a force compounded of the pressure perpendicular to the slope and the velocity. Now the velocity of sliding ice (as has been shown by Hopkins) is nearly uniform, and therefore may be taken as proportional to the force in the direction of the motion—that is, as the sine of the inclination 6; therefore the erosive force is as the pressure vertical to the plane x sin@; that is, as weight x cos@x sin @; that is, as weight xsin26. This expression is in accordance with Professor Ramsay’s theory, that when the angle is 90°, the erosion is 0; and again, when the angle is 0, the erosion is nothing : but it is quite discordant from his view, that the erosion is greater at an * Communicated by the Author. Mr. J. C. Moore on Lake-Basins. 527 angle of 5° than at one of 10°, &e. In fact the maximum will be at 45°; and this I believe to be in accordance with what takes place in rivers with highly-inclined beds. At steep rapids the erosion is considerable ; but when the angle becomes almost im- perceptible, the river, so far from cutting down its bed, often raises it by deposition of sediment. As soon as the glacier reaches the plain, erosion by sliding ceases ; and if it moves, it must be by propulsion ; and if it ex- cavates, the materials ground down must be removed. It is difficult to conceive how this can have been effected but by run- ning water; and that is contrary to the idea of a rock-basin. In those cases where a glacier has been seen to be forced up a slope, is it certain that the rock with the same slope extended quite across the valley? May not one side of the bottom of the valley have been higher than the other? so that while the ice was forced up the slope on one side, the rest of the glacier with water issuing from under it may have been sliding down the other side. But if there is to be no river, then how were, say, the last 100 feet of depth of the Lake of Geneva excavated? It is not “le premier pas qui coute,” but “le dernier.” Even granting that the enor- mous mass which the problem supposes could be forced up a slope, what becomes of the fine fluid mud into which the rocky contents of the lake had been ground? The advancing face of the glacier cannot be presumed to have forced the water before it, for it is fissured in all directions; and though a glacier is said sometimes to thrust pebbles before it, the watery mud would always subside into the depths. Professor Ramsay, in his memoir published last October, admits that a quasi-plastic body constantly pressed from behind, when opposed by a high impassable barrier like the Jura, would spread itself out in the direction of least resistance. On this I would observe that it was not the height of the Jura which formed the impassable barrier: the glacier merely felt the re- sistance of a rock at its own level, and, in obedience to the law, which I cordially accept, turned aside in the direction of least resistance. And on the same principle I.should expect the Rhone glacier, on issuing from the gorge, to crawl along the plain, as glaciers are known to do, instead of seeking out resist- ance by burying itself 1000 feet among hard rocks. [ 528 ] LXXII. Chemical Notices from Foreign Journals. By K. Atkinson, PhA.D., F.C.S. [Continued from p. 380. ] } i ERRMANN* has investigated the action of nascent hydro- gen on benzoic acid. When an excess of this acid in water is heated nearly to boiling, and sodium-amalgam added, the nascent hydrogen is almost entirely consumed; and if neu- tralization and solution of the acid are prevented by the gradual addition of hydrochloric acid, the following changes occur: the liquid smells strongly of oil of bitter almonds; during the ad- dition of the hydrochloric acid benzoic acid separates along with an oily body; as the reaction continues, the former finally dis- appears, while the latter alone remains in solution. When, in the course of the above reaction, the liquid had become alkaline, it was distilled until the odour of oil of bitter almonds was no longer perceived. In this way an aqueous dis- tillate was obtained containing oil-drops; on shaking this with ether, and subsequently distilling off the ether, an “oily liquid was obtained which proved to be benzylic alcohol, C!* H® 02, the formation of which from benzoic acid is thus expressed : — C4 HS 04144H=2HO+C"™ H8 O?. By exhausting the alkaline residue in the above case with ether, a heavy aromatic oil was obtained, which after some time solidified to a crystalline magma. The liquid from which this had been extracted by ether was returned to the retort, and again treated with sodium-amalgam until an oil was separated which did not solidify in the cold. The above crystalline substance, when boiled with water, was partly dissolved ; on cooling, a body was obtained which crys- tallized in laminx. The melting-point of this substance is 116°; it is unaltered by boiling with potash, but by destructive distillation is resolved completely into oil of bitter almonds. The body has the formula C*® H!4 O4, and is isomeric with hy- drobenzoin, obtained by Zinin by the action of zine and sul- phuric acid on oil of bitter almonds. From its formula it might be a compound of benzoic aldehyde with an aldehyde richer by two atoms of hydrogen. The third substance separated from the alkaline solution by hydrochloric acid is a volatile oily acid with an extremely un- pleasant odour, strongly suggestive of valerianic acid. It forms salts, which cannot be crystallized, but readily attract moisture, and are decomposed on exposure to the air in consequence of oxidation of the acid. As it was impossible to get good results * Liebig’s Annalen, October 1864. Von Oefele on a new Class of Sulphur Compounds. 529 by the analysis of the acid or of the salts, the ether was made, and thus the formula of the acid was found to be C!4 H!9 O04, It contains hence four atoms of hydrogen more than benzoic acid ; and it forms an intermediate member between the acids which correspond, as regards carbon, in the aromatic and fatty acid series :— . Benzoie acid *%., .- ~~... C™ HS..O* Intermediate acid . . . C%4H'°Q4 anthyle acid (svc sO BOA Herrmann calls this acid Benzoleic acid; it is distinguished from the fatty acids only by greater specific gravity. When monosulphide of ethyle and iodide of ethyle are heated together under suitable conditions, Von Oefele* has found that they combine and form a compound crystallizing in small lamine which contains the elements of one atom of sulphide of ethyle and one atom of iodide of ethyle. Its chemical deportment leads to the view that it is the iodide of a radical consisting of three Csi atoms of ethyle and two of sulphur, C*H® +S?, which Oe6efele C* H® calls Triethylsulfine. The body can also be obtained by distilling a mixture of alcoholic solution of monosulphide of potassium with iodide of ethyle. When the aqueous solution of the iodide is treated with nitrate of silver, iodide of silver is at once precipitated, and the solution contains nitrate of triethylsulfine ; or if it is treated with freshly precipitated oxide of silver, iodide of silver is obtained with hy- CEA | drated oxide of triethylsulfine, C*H® -S?O, HO. The solution C* H® filtered off from the iodide of silver has a strongly alkaline reac- tion, readily attracts carbonic acid, precipitates solutions of the metals just as does potash, and, when evaporated in the exsiccator or in a vacuum, yields a crystalline body. It so readily attracts moisture that an analysis could not be made. Its salts are ob- tained by neutralization with the corresponding acid; they are difficult to crystallize, and are very deliquescent. A plati- num-salt, however, was obtained, in splendid dark reddish- yellow prisms, which had the composition C45 C* He | S? Cl+ Pt Cl?. GAH? * Liebig’s Annalen, October 1864. 530 - M. Vogt on Naphthylie Mercaptan. Oefele has also found* that when monosulphide of ethyle is gradually added to fuming nitric acid, an energetic action ensues, the result of which is the formation of a body which crystallizes readily in thin large-sized colourless plates. This body has the composition C® H!°S?0*, and Oefele names it Diethylsulphan, ; : considering its epee to be a = S? 04, analogous to sulphobenzole, Gr Hs PS? O*, which he names diphenylsulphan. Diethylsulphan melts at 70°, and boils at 248° C., distilling without decomposition. Treated with nascent hydrogen, it is reduced to monosulphide of ethyle. Vogt+ showed that the chloride of phenylsulphuric acid, by the action of nascent hydrogen, yielded phenylmercaptan. Schertel{ shows that by applying this reaction to the chloride of naphthylsulphurie acid (which Kolbe and his pupils name chloride of naphthyl-sulphan (Naphthylsulfanchlorid)), the corre- sponding mercaptan of naphthylic alcohol is obtaimed, a change expressed by the following equation, C0 H7 §? 04 C1+6H=C” H8 §?+ HC]+ 4HO. Chloride of Naphthylic naphthylsulphan. mercaptan. The change is effected by adding the substance to a mixture of zine and sulphuric acid from which hydrogen is being disengaged. On distilling the liquid, an oil passes over, which, after appro- priate purification, has the following properties :—colourless, highly refringent, of unpleasant but not intense odour, not miscible with water, but soluble in alcohol and ether. It has the specific gravity 1:146, and boils at 285° C. Like other mercaptans, it readily exchanges an atom of hydrogen for metals. 20 F]7 The naphthylmercaptide of mercury, : - BS is a light pale yellow powder; the corresponding compounds of copper, 20 7 . Y, ae and of lead, i pb rS* are also insoluble preci- pitates. When naphthylmercaptan is dissolved in strong ammonia and the solution left to spontaneous evaporation, after some days transparent well-defined crystals are formed,’ belonging to the klinorhombic system. These are the bisulphide of naphthyle, C20 H7S?, the production of which, supposing the previous * Liebig’s Annalen, October 1864, p. 86. + Phil. Mag. S. 4. vol. xxii. p. 302. t Liebig’s Annalen, October 1864. M. Linnemann on Benzhydrole. 531 formation of naphthylmercaptan ammonium, takes place in con- sequence of oxidation; thus C20 H7 : NEP S?+ O=C* H’ S?4+ HO+ NH?. Napthylmer- ofr, captan ammonium. Linnemann* has continued his investigations+ of benzophe- none, G!? H!°Q, the acetone corresponding to benzoic acid. He finds that benzoate of lime, when distilled with lime, yields this body along with benzole in about the proportion of two of the latter for one of the former. Benzophenone has a great ten- dency to crystallization, and is readily obtained in large crystais. It unites with bromine, but not without the formation of hydro- bromic acid, and the bodies formed are not of a very definite nature. Linnemann had previously found that by the action of nascent hydrogen on benzophenone a body was formed which he called Benzhydrole, and assigned to it the formula €!3 H!4 9, which sub- sequent analyses show ought to be G'9H!*O. This body has many of the properties of a monatomic alcohol, but differs in that, when oxidized (as, for example, by chromic acid) it repro- duces benzophenone, and not an aldehyde. Ifthe benzhydrole is treated by strong nitric acid, oxidation first takes place, form- ing benzophenone, which is then converted into binitrobenzophe- none, C!8 H§ (NO?)?0. Benzophenone thus behaves exactly like acetone. That sub- stance, when treated by nascent hydrogen, yields an alcohol isomeric but not identical with propylic alcohol, and called ac- cordingly isopropylic alcohol. This isopropylic aleohol when oxidized yields the body acetone from which it was formed, instead of propylic aldehyde as is the case with ordinary pro- pylic alcohol. Benzhydrole also differs in another important respect from ordinary alcohol, inasmuch as it readily forms with bromine bibrominated benzhydrole, C'? H!° Br? @. This body con- sists of a hght glistening white mass, which is seen, under the microscope, to consist of small acicular crystals. Benzhydrole resembles the alcohols in that it readily forms compound ethers; it differs in that, as yet, it has not been pos- sible to form a chloride or iodide of the alcohol. The action of the chloride of phosphorus is simply a withdrawal of water with 13 11> the formation of benzhydrolic ether, ee Q. This body is also formed by keeping benzhydrole for some time at the boil- * Liebig’s Annalen, January 1864. +t Phii. Mag. S. 4. vol. xxv. p. 539. 5382 M. Linnemann on Benzhydrole. ing-temperature under the ordinary atmospheric pressure ; it is then split up into the ether and water, thus, 13 11 13 lil pica HH }O=Gu ju }O+HPO. It is the first instance of a monatomic alcohol being decom- posed in this way by the simple action of heat. It is obtained in clear adamantine crystals belonging to the rhombic system. When to benzhydrole dissolved in absolute alcohol a small quantity of sulphuric acid is added and the mixture left for some days, an oil is separated on the subsequent addition of water, which has the formula GC H!®O. It is a mixed ether, ethyl- 11 benzhydrolic ether, ve _ fo, and is a colourless liquid of the consistency of glycerine. ‘ This body exhibits a remarkable deportment towards light. Shortly after distillation it is a colourless liquid; but kept, it becomes coloured. ‘This colour arises from the action of light; for when the liquid is kept for some time in the dark it disappears. The coloration reappears after some time when brought into diffused daylight, but imme- diately when brought into the sunlight. By incident light the liquid appears of a beautiful green, and by transmitted of a pale yellow. The colour, besides depending on the light, appears to de- pend on a certain position of rest, for it disappears when the liquid is moved backwards and forwards. It is also lost by warming. If the colour has been destroyed by exposure to dark, by agita- tion, or by heat, it may be brought back by exposure to direct sunlight. Yet, strangely enough, this condition is transient ; for when the liquid has been kept for some months it is colour- less, and does not regain its previous properties, even by distil- lation. But in any condition of the liquid, when a cone of light is transmitted through it, it is highly fluorescent, the conver- gent light being of a beautiful blue. Besides acetic benzhydrolic ether (which has also these remark- able luminous properties) and benzoic benzhydrolic ether which Linnemann formerly described, and which description he now completes, he has prepared other ethers. The succinic benz- 18 Y{11)2 hydrolie ether, C4 W402 ee consists of small lustrous laminz which melt at 142°. This compound experiences, by the action of heat, a singular change, which is expressed by the following equation :— as de} ee= C fe }O* +2613 HI10, It is decomposed into succinic acid and a hydrocarbon which, M. Linnemann on Benzpinakone. 533 when appropriately purified, forms small well-shaped rhombic plates of considerable thickness. It melts at 209° to 210° C. When, to an alcoholic solution of benzophenone, sulphuric acid is added and then zinc, a slow disengagement of hydrogen takes place; and after some time a substance difficultly soluble in alcohol forms, and coats the zinc like a white crust. When this is purified it is obtained as a brilliant white mass, consisting of small needles. It has the formula €?6 H®? 02, and is derived from two molecules of benzophenone by the assimilation of two of H. It stands to benzophenone just in the same relation as pinakone to acetone. Thus, 26° H°Q + H?=C° H4 02, Acetone. Pinakone. 2015 994 H2= 6% H2 92, Benzophenone. Linnemann has assigned to it the provisional name benzpinakone. Standing, as regards its composition, between benzophenone and benzhydrole, it is readily converted into either; thus, boiled with a dilute solution of chromic acid, it yields the former, C2 H2 624 9-203 H19 94 H20; Benzpinakone. Benzophenone. while by the reducing action of sodium-amalgam it is changed into the latter, C6 2 O24 H2=2033 B20. Benzhydrole. Benzpinakone can neither be distilled nor melted without an alteration of its physical properties. In both cases it is con- verted into a body isomeric with benzpinakone, and which is called isobenzpinakone. This is a colourless syrupy liquid which boils at 297°5, and does not solidify even at —15°. By keep- ing, however, for a few months at the ordinary temperature it becomes solid. Both modifications of benzpinakone have the same chemical reactions. The above investigations show that the hydrogen disengaged from an acid solution acts quite differently to that from an alka- line solution. A similar investigation of the behaviour of acro- leine towards zine and hydochloric acid, by Linnemann*, has shown that the products here obtained also differ from those produced by hydrogen disengaged in alkaline solutions. The action on the acid is very energetic, and requires to be mode- rated by mixing an ice-cold ethereal solution of acroleine with equally cold hydrochloric acid, gradually adding the mixture to * Liebig’s Annalen, January 1865. 534 M. Linnemann on the Action of Hydrogen on Acroleine. the zinc. Two of the bodies produced are allylic and propylic alcohol, which remain dissolved in the aqueous solution of chlo- ride of zinc ; besides these, there is an insoluble substance which partly forms a. deposit and partly is dissolved in an ethereal layer which floats on the liquid. By exhausting the entire liquid with ether, the whole of this substance is obtained in solution. The solution of chloride of zinc containing the two alcohols was distilled, and the distillate dehydrated by carbonate of pot- ash and again distilled, and this distillate dehydrated by anhy- drous sulphate of copper. In this way a volatile liquid was obtained, consisting of about one volume of propylic and six of allylic alcohol. It was impossible to separate these completely by fractional distillation, for their boiling-points are so near, though ample evidence of the identity of the two substances was obtained from their reactions; and to effect the complete separation, the mixed alcohols were treated by hydriodic acid, by which they were converted into iodides. Iodide of allyle, €? H° I, readily unites with mercury to form a compound, €° H®T Hg”, while iodide of propyle is unaffected by mercury: advantage was taken of this deportment to separate the two iodides. The properties of the iodide of allyle were found identical with those of that prepared from glycerine. From the iodide of propyle, G® H7 I, propylic alcohol was obtained identical with that obtained from acetone, and which is therefore isopropylic alcohol. The ethereal solution contained the above-mentioned insoluble substance, and also some chlorine and sulphur organic com- pounds. When, however, the ethereal solution was evaporated, these latter became carbonized and completely decomposed ; and hence the first purification consisted in distilling and redistill- ing the liquid until it passed over without decomposition. An oily liquid was left, which could not be obtained of quite con- stant boiling-point; freshly distilled it is colourless, but rapidly becomes brown on standing, and has a peculiar camphorous odour. It has the formula €° H!° 02, and stands to acroleine in the same relation that pinakone and benzpimakone do respectively to acetone and benzophenone, thus, 203 H40 + H2 = C&HE?2. Acroleime. New body. The chemical relations of this new substance, to which the name acropinakone is provisionally assigned, have not yet been com- pletely examined, and the author is still engaged upon the sub- ject. His researches show that the action of the hydrogen from an acid solution on acroleine gives rise to three bodies, whose formation may be thus collated :— M. Friedel on the Synthesis of Acetone. 535 GHtO + H? = CHO. | Allylic alcohol. G?H*0+42H* = CHa. Propylic alcohol. 26°H*6 + H? = C&HO% « Acropinakone. Linnemann* has also found that pinakone exists in two is0- meric modifications—a liquid one, which boils at 176° or 177°, and dissolves in water, from which it soon separates as a crystal- line hydrate; the solid pinakone is a snow-white crystalline mass which melts at 35° to 38°, gradually softening first, and boils at 171° to 172°. The distillate is a colourless thickish liquid, which soon solidifies. Both these modifications unite with water and form one and the same hydrate, €° H*O0?+6Aq; pinakone forms besides, as Fittig has shown, several hydrates. Freund found some time agot that the synthesis of acetone could be effected by the action of chloride of acetyle on zinc- methyle; thus 3 Zu me a +26? H3 0 Cl=Zn" Cl? + 2¢3 He 9. Chloride of Chloride Acetone. — acetyle. of zinc. methyle. Friedel{ has now found that the synthesis of acetone can also be accomplished by another reaction, in which he makes use of chloracetene, G* H® Cl, the interesting body obtained by Harnitz- Harnitzsky§, by the action of phosgene gas on aldehyde. When this substance acts upcn methylate of sodium, chloride of sodium is formed and acetone; thus, €? H® Cl+ € H3 NaO=NaCl+ CG? H®°O. A quantity of sodium corresponding to the chloracetene was dis- solved in methylic alcohol and the excess evaporated. On gra- dually adding chloracetene to the mixture, kept cool, a brisk reaction was established, chloride of sodium was formed, and, when the mass was distilled, a distillate was obtained consisting of acetone mixed with a little methylic alcohol. As the boiling- points of the two liquids are very close, separation could not be effected by fractional distillation, and the mixture was accord- ingly treated by permanganate of potash, by which methylic alcohol is oxidized very much more readily than acetone. In this * Liebig’s Annalen, (Suppl. 3) vol. i. part 3. 7 Phil. Mag. S. 4. vol. xx. p. 201. £ Comptes Rendus, May 1, 1865. § Phil. Mag. S. 4. vol. xvii. p. 430. 536 MM. Borsche and Fittig on the Preparation of Allylene. . way acetone was obtained pure, as evidenced by its boiling-point, its analysis, and its combining with sulphite of soda. Borsche and Fittig*, in an investigation of acetone, describe some of its derivatives, and a new mode of converting that body into allylene gast. When chlorine is passed into acetone, hydro- chloric acid is formed, which remains dissolved in the acetone. On distilling the liquid, torrents of hydrochloric acid are given off, and a distillate is obtained consisting of unchanged acetone along with dichlorinated acetone, G? H* Cl* ©, a body which, when suitably purified, has a pleasant ethereal odour, and boils at 120°. When this body is treated with pentachloride of phosphorus, it is acted on in the same way as is acetone; that is, it pees its atom of oxygen for two of chlorine. The decomposition takes place according to the equation C3 H4 Cl264+ PCh=G? H4 Cl4+ PCA. Dichlorinated Chloride of di- acetone. chlorinated acetone. The reaction requires, however, for its completion a lengthened action of the pentachloride. The new compound, €® H*Cl4, is a colourless oil of not unpleasant odour, which boils at 153°. It is isomeric with Cahours’s quadrichlorinated propylene, the boiling-point of which, however, is about 50° higher. When chloride of dichlorinated acetone is treated with either caustic potash or ammonia, it 1s resolved into a body, €? H? Cis, which is isomeric but not identical with trichlorinated propylene, and which Borsche and Fittig call csotrichlorinated propylene. From its formula, chloride of dichlorinated acetone can be regarded as the chloride of a tetratomic hydrocarbon, G?H*"Clt ; this is, in fact, the case; the hydrocarbon is the gas allylene. The action of sodium on the chloride is at first feeble, soon begins to be extremely violent, and requires to be moderated. It was found best to dissolve the chloride in four times its volume of rectified benzole before adding the sodium; by warm- ing or by cooling, the action could then either be accelerated or moderated. The allylene was given off as gas, and was absorbed by passing it into an ammoniacal solution of subchloride of cop- per, with which it forms a well-defined compound—copper- allylene. When this compound was treated with hydrochloric acid, allylene gas was disengaged, the identity of which was de- termined by converting it into the bromide, €* H* Br?®, and the tetrabromide, €? H* Br+, already described by Oppenheim ft. * Liebig’s Annalen, January 1865. + Vide antea, p. 306. { Ibid. p. 307. M. Harnitz-Harnitzsky on the Synthesis of the Fatty Acids. 587 - Harnitz-Harnitzsky, who succeeded in effecting the synthesis of benzoic acid by adding carbonic acid to benzole*, has nowt extended this reaction to the series of hydrocarbons homologous with marsh-gas, and has thus artificially prepared acetic acid, and its homologue, caproic acid. Synthesis of Acetic Acid—When marsh-gas was passed, together with oxychloride of carbon, into a vessel heated to 120°, a reaction took place which is represented by the followmg equation :— CH* + COCl? = @ H°OCl + HCL. Marsh- Phosgene Chloride of gas. gas. acetyle. Some of the chloride of acetyle thus formed was condensed in the apparatus, and by its properties can be readily identified ; but the greater part was collected in a vessel connected with the receiver, and containing caustic soda, by which it was completely decomposed, forming chloride of sodium and acetic acid, which _ then united with soda, forming acetate of soda. The decompo- sition of chloride of acetyle by the soda is thus expressed :— ©? H3 06 Cl+ NaHO=€? H4 02+ NaCl. Chloride of Acetic acid. acetyle. In like manner Harnitz-Harnitzsky has prepared chloride of caproyle by the action of oxychloride of carbon on hydride of amyle; and this, by its action on water, gave caproic acid, thus, CH? + COC = CH" OCl + HCl; Hydride of | Chlorocar- Chloride of amyle. bonic acid. caproyle. C6H' OCl+H20=—€% H!2 02+ HCl. Caproic acid. Under the class of acetals may be ranged all compounds of aldehydes with monoatomic alcohols. They have their origin in the combination of two equivalents of alcohol with one of alde- hyde, with loss of water. Wurtz has described the existence of a similar compound, produced by the union of glycol with alde- hyde under elimination of water. Harnitz-Harnitzsky and Menschutkin{ have completed this group, by announcing the existence of a similar class of bodies derived from the triatomic alcohols the glycerines, and which they call glycerals. They * Vide antea, p. 310. + Comptes Rendus, May 1, 1865. + Ibid., March 20, 1865. Phil. Mag. 8. 4. No. 199. Suppl. Vol. 29. 2N 588. ~—- Mr. E. J: Stone on Change of Climate are formed in accordance with the following equation :— C H® 0% + aldehyde — H? O= glyceral. Glycerine. wet ©? He Acetoglyceral, H ‘0%, is formed by heating glycerine with | C2 14 aldehyde in closed tubes for thirty hours to a temperature of 170°-180°. On distilling the contents of the tubes, a body is obtained which passes over between 184°-188°, and is the sub- stance in question. It is a dense liquid, slightly soluble in water. Freshly distilled it is almost inodorous ; but exposed to the mois- ture of the air, the odour of acetic aldehyde soon appears. C8 H5 Cs Heé Valeroglyceral, H po and benzoglyceral, H } , have C5 Fy10 C7 He been prepared by analogous methods. In his general investigations on organic acids, Kekulé had | observed that, by the action of sodium-amalgam on aconitic acid, _an acid richer in hydrogen was produced. This observation has been pursued by Wichelhaus*, who has found that the acid thus formed is identical with an acid obtained by Maxwell Simpson by the action of potash on cyanide of allyle: the acid received no name from its discoverer, but Kekulé has proposed for it the name carballylic acid. The formation of this acid from aconitic acid is thus expressed :— , C5 H6 08 + 2H = C8 H8 68, Aconitic acid. Carballylie acid. LXXIII. On Change of Climate due to the Excentricity of the | Earth's Orbit. Lo the Editors of the Philosophical Magazine and Journal. 03 Harley Street, GENTLEMEN, May 23, 1865. HAVE received the followmg communication from Mr. _ Stone, of the Observatory at Greenwich, in reply to some questions put by me to the Astronomer Royal on the subject of Mr. Croll’s valuable paper “On the Physical Cause of the Change of Climate during Geological Epochs,” which appeared in the August Number of your Magazine for 1864. Feeling sure that it will.be of use to Mr. Croli and those geologists and astrono- mers who may be following up the important line of investiga- * Liebig’s Annalen, October 1864. due to the Excentricity of the Earth’s Orbit. = 539 tion lately opened up by him, I have asked Mr. Stone to allow his calculations to be printed, without waiting till others of a more complicated kind, and bearing on the same subject, are completed. ‘I have the are to be, Gentlemen, Your obedient Servant, -CuHartes LYELL. To Sir Charles Lyell, Bart., F.R.S., &. Royal Observatory Greenwich, STR, May 12, 1865. The Astronomer Royal has placed in my hands your letters of 1865, March 6, March 20, and May 8, together with Mr. Croll’s papers, which I return: in part reply to your letters I have the honour to forward the following information. Assuming the sun’s mean horizontal equatorial parallax =8"-943, and the Astronomer Royal’s value of the equatorial semidiameter of the earth — 3962°822 miles, I find the mean distance of the sun from the earth = 91 400,000 miles. From Leverrier’s paper in the Connaissance des Temps, 1843, I extract the following values of the excentricity of the earth’s orbit :— Porshe year 1800: .-. | =0°0168 Maximum value . . . . =0:0778 From computation, I find for the values of the excentricity 210,065 years ago the value 0:0575. These data give me the following results :— Greatest dis- Least distance Years ago. lane 3 ® | of @ from ©. Difference. 65 92935521 89864479 | 3071042 210065 96655504 86144496 10511008 Maximum POEL Ee 98506355 84293645 14212710 I consider that as the differences given above are nearly as 3:11:14, whatever climatic changes may have taken place through the existence of the absolute maximum excentricity, corresponding and very slightly inferior changes must have taken place about 210,065 years ago. As this period may therefore turn out to be geologically interesting, I forward the values of the excentricity and longitude of the perihelion of the earth’s orbit about this period. ‘The longitudes are referred to the mean 2N2 ee 540 Change of Climate due to Excentricity of Earth's Orbit. line of equinoxes for the year 1800, and are given merely to show the degree of rapidity of change of its position. TABLE. Longitude of ® Years ago. Value of e. perihelion. 170,065 0-0437 298 7 180,065 0-0476 209 22 190,065 0:0532 190 4 200,065 0:0569 168 18 210,065 0:0575 144 55 220,065 (0-0497 124 33 230,065 0:0477 102 49 I may mention that the above represents the maximum state of the excentricity during the last 500,000 years. With respect to the precession of the equinoxes, although it would not be correct to assume the uniformity of motion during the immense periods of time here under consideration (for the accumulative error would become large), it will certainly lead to no sensible error to assume its values at the time 210,065 years ago as not very different from the present one. It will be seen from the Table, that the change of excentricity and longitudes of perihelion are exceedingly slow as compared with the motion of the line of equinoxes; that if Mr. Croll’s theory is correct, we must have had, when the excentricity is larger, alternate changes of climate from one of extreme cold to one of great equability. The main point of the argument, as I undated it, of change of climate depending upon the excentricity of the earth is as follows. It is true that the amount of heat received varies but very slightly with changes in the excentricity; but the mean temperatures will depend as much upon the heat radiated off as upon that received; the amount of heat radiated off will certainly be less the shorter the time the temperature is below the mean, and the less it sinks below the mean; hence, ceteris paribus, a warm winter and a short one must raise the mean temperature, and a cold winter and a long one must lower this mean (the mean temperature). The effects produced, however, are terribly involved. I have the honour to be, Sir, Your obedient Servant, E. J. Stone. ps4 4 LXXIV. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 486. | May 4, 1865.—Major General Sabine President, in the Chair. [SHE following communication was read :— “On the Properties of Liquefied Hydrochloric Acid Gas.” By George Gore, Esq. In a former communication to the Royal Society “‘ On the Proper- ties of Liquefied Carbonic Acid,’ printed in the Philosophical Trans- actions for 1861 (also in the Journal of the Chemical Society, vol. xv., page 163) *, I described a mode of manipulation whereby various solid substances were introduced into that liquefied gas whilst under very great pressures (varying from 500 to 1100 pounds per square inch), and the action of the liquid upon them observed. The experiments described in the present paper were made in a similar manner, but with some improvements in safety of manipu- lation, and in the mode of discharging the tubes, so as to recover the immersed solids in a satisfactory state. . The glass tubes in which the gas was condensed were about ;3,ths of an uich internal diameter, and fully 3ths of an inch external dia- meter. Hach tube was, before bending, 114 inches long; it was bent, at 14inch and 61 inches respectively from one end, to the form already described in the paper referred to, thus giving 5 inches in length for the salt, 5 inches for the acid, and 11 inch for the liquefied gas. These distances are essential ; for if the quantities of acid and salt are not properly proportioned to each other, and to the remain- ing space in the tube, the liquefied product will be very small. The curve in the tube between the acid and the salt should be very gra- dual, and the other bend much less so. The end of the tube con- taining the salt should be constructed open, with a flange, and be closed securely by a plug of gutta percha in the same manner as the upper end. The materials used were strong sulphuric acid and fragments of sal-ammoniac. Each tube was placed in a deal frame or box 10 inches high, 8 inches wide, and 4 inches from front to back, open at the back, and with a front or door of wire gauze. The tube was supported by a cork fitting into a hole in the side of the frame, and was secured within a notch in the cork by a ligature of wire. By means of this arrangement the acid and salt were brought into mutual contact by turning the box itself, without incurring the danger of putting one’s hand inside the box and turning the tube alone, as in the former experiments. ‘ The annexed figures (1 & 2) represent the position of the box, Ist, when charged and ready for the decomposition of the sal-ammoniac ; and 2nd, after the decomposition is completed. The arrows indicate the direction in which the box is turned. The action at first should be very slow ; otherwise the bubbles * The reader is referred to the above communication for details of information respecting the apparatus employed and manipulation adopted. | | 542 Royal Society :—Mr. G. Gore.on the of gas will convey the sulphuric acid into the short end of the tube, and endanger the purity of the liquefied hydrochloric acid. The action of the acid was less violent than when generating carbonic acid, and the process was less frequently stopped by clogging of the tube. The liquefied gas was condensed in contact with the various solid bodies by application (from behind) of cotton wool, wetted with ether, to the short end of the tube, as in the former experiments. ~Each tube was discharged of its contents by taking hold of it with an ordinary wooden screw clamp support, and immersing its Iower end in a vessel of nearly boiling water behind a protecting screen. The explosion quickly occurred, generally without fracture of the tube, and the substances operated upon could in nearly all cases be readily extracted for examination without suffering injury by coming into contact with the saline contents of the tube: Pow- dered substances, however, were frequently lost during the discharge, owing to the sudden expansion of the gas in their pores expelling them from the small glass cup. The great degree of pressure (probably about 700 pounds per square inch and upwards) to which the various substances were subjected, frequently made them very hard. Fig. 1. Fig. 2. oi QE The chief inconvenience met with in these experiments arose from the action of the liquefied acid upon the upper gutta-percha stopper, causing the acid to become dark red-brown and opaque, and preventing accurate observation of the substances—also, on _ discharge of the tube, causing the glass cup and its contents to become coated with a tenacious film of gutta percha. To obviate this inconvenience as much as possible, the inner end of the upper stopper was carefully coated with melted paraffin. During the early part of each experiment, the liquefied acid was repeatedly poured back, and redistilled by the application of ether, in order to free it from colour imparted to it by the stopper, and also to make its solvent or other action upon the immersed body more rapid. The action of the liquid acid upon the bodies was only Properties of Liquefied Hydrochloric Acid Gas. 543 continued a few days; and in many cases the acid was not in a liquid state the whole of the time, but only at intervals; in all cases, how- ever, the period of immersion was abundantly sufficient for the liquefied acid to produce its full effect. The effects in nearly all cases were of so distinct a character, and the conditions under which they were produced so definite, as not to require repetitions of the experiments; but those which were in any respect uncertain were repeated, and those also which were of an important or striking character were likewise repeated, in order to remove the least shadow of a doubt that might be raised respecting them. The liquid acid is a very feeble conductor of electricity. Two fine platinum wires, immersed in it ths of an inch in length and th of an inch asunder, and connected with a series of 10 Smee’s ele- ments, evolved no perceptible bubbles of gas, and produced only a moderate deflection (amounting to 23 degrees) of the needles of a sensitive galvanometer; and this amount of conduction might pos- sibly have been due to a minute trace of oil of vitriol mixed with the liquid acid. In a second similar experiment, with the wires zigth of an inch apart, not the slightest conduction occurred on using the same battery-power, but by employing the secondary cur- rent of a strong induction-coil with condenser attached, conduction and a steady deflection of the needles of the galvanometer (26 degrees) took place, gas being freely evolved from the negative wire only. On separating the brass points of the secondary terminals beyond the distance of the thickness of a thin address card, sparks ceased to pass between those points, and gas was evolved copiously in the liquid acid, apparently in the mass of the acid between the two platinum wires as well as at the wires themselves; two similar platinum wires in dilute hydrochloric acid in the same circuit evolved very little gas. It is probable that much of the gas evolved in the liquefied acid was not a product of electrolysis, but simply the acid itself volatilized by the thermic or other action of the current. No sparks occurred at any time in the liquid acid. It is evident there- fore that liquefied hydrochloric acid gas is a very bad conductor of electricity, but it is not nearly so powerful an insulator as liquefied carbonic acid gas. The followmg experiments illustrate its chemical, solvent, or other action upon various substances immersed in it. The quantity of the solid substances employed was in nearly all cases very small in proportion to that of the liquid acid in contact with them, and in many cases did not amount to one-twentieth of its volume. A piece of charcoal remained unchanged at the end of ten days, the acid beg in a liquid state in contact with it at intervals. A fragment of fused boracic acid did not lessen in bulk or alter m appearance in seven days. White phosphorus was undissolved and unchanged in nine days, and remained equally inflammable. A fragment of ordinary sulphur did not dissolve or alter in several days. Fragments of vitreous black selenium did not dissolve or change in six days. Iodine dissolved rather freely, and quickly 544 Royal Society :—Mr. G. Gore on the formed a purple-red solution. A piece of pentachloride of phos- phorus softened in the gaseous acid, and dissolved quickly and com- pletely in the liquid acid, forming a colourless solution. A fragment of sesquicarbonate of ammonia swelled and became full of fissures in the gaseous acid, but neither evolved gas nor dissolved when the liquid acid came into contact with it; after three days’ intermittent immersion in the liquid acid, the saline residue evolved no gas on immersion in dilute hydrochloric acid. A piece of sal-ammoniac, immersed almost constantly during nine days, remained undissolved and unchanged. Potassium evolved no gas when the liquid acid came into contact with it ; after eight days it was sometimes enlarged in bulk, and from the outset it was of a white colour ; it did not at all dissolve. Ina second experiment the results were precisely similar ; after three days’ intermittent immersion the saline residue showed no signs of contain- ing free potassium on immersing it in dilute hydrochloric acid. An- hydrous carbonate of potash in powder evolved no gas on first coming into contact with the liquid acid; after three days’ occasional immer- sion it remained undissolved, and the residue evolved no carbonic acid on immersion in dilute hydrochloric acid. A crystal of chloride of potassium did not dissolve or change in appearance by four hours’ immersion in the liquefied acid. Powdered chlorate of potash im- parted a yellow colour to the liquid acid, and did not lessen in bulk during three days’ constant immersion; the upper gutta-percha stopper became quite white at its inner end. A crystal of nitrate of potash became of a brownish colour before the gas liquefied, and remained undissolved after six days’ intermittent immersion; the upper gutta-percha stopper was unusully acted upon, and of a nan- keen colour. Sodium became white and swelled largely before the gas liquefied. No visible gas was evolved by it in the liquid acid. After three days’ intermittent immersion the residue contained no sodium in the metallic state, and no portion of it imparted a blue colour to damp litmus paper. Anhydrous carbonate of soda in powder immersed one hour and a quarter in the liquid acid evolved no visible bubbles of gas, and lost its alkaline reaction (with litmus paper) to about three- fourths of its depth. A fragment of fused sulphide of sodium pro- duced a slight sublimate of a yellowish-white colour in the gaseous acid, and turned of a yellowish-white colour. It evolved no visible gas in the liquefied acid*. After three days’ variable immersion it was of a yellowish-white colour, and somewhat enlarged in bulk ; the residue evolved no sulphuretted hydrogen by immersion in dilute hydrochloric acid, and its solution gave a perfectly white precipitate with acetate of lead, and imparted no dark colour to sulphate of copper. Precipitated carbonate of baryta in powder evolved no visible gas * Probably the sulphuretted hydrogen set free was in a liquid state, and there- fore no bubbles of gas appeared. I found by experiment that hydrochloric acid and hydrosulphuric acid, generated together and condensed into a liquid state, did not form two separate strata of liquid. Properties of Liquefied Hydrochloric Acid Gas. 545 by immersion in the liquid acid; it remained undissolved and un- changed in appearance during three days’ immersion; the residue evolved a minute quantity of gas by contact with dilute hydrochloric acid. Precipitated carbonate of strontia in powder behaved like carbonate of baryta; the residue, after three days’ immersion, was lost during the discharge. A minute fragment of anhydrous Bristol lime exhibited no solution or alteration by nearly constant immer- sion during eight days in the liquid acid. On removal from the tube, it imparted a strong blue colour to neutral litmus paper by slight friction. On fracture it was found similarly alkaline through- out, and exhibited a slight change of colour, extending from its sur- face to the centre, as if the gas or liquid had been forced into its pores. In a second experiment of three days’ intermittent immer- sion, precisely similar effects were obtained. Several minute frag- ments of very soft marble were immersed in the liquid acid at in- tervals during seven days. No gas was evolved when the liquid touched them. On removal from the acid, their physical characters appeared unaltered; they were insoluble in water, but quickly dis- solved in dilute hydrochloric acid, with copious evolution of gas. A fragment of bone-earth did not dissolve or alter in appearance during seven days. Bright magnesium ribbon slowly became dull in the liquid acid, without visible evolution of gas; after seven days’ intermittent im- mersion it was still (with the exception of a thin film) in the metallic state. Ina second experiment of three days’ constant immersion, similar effects occurred ; the residue dissolved and floated in dilute sulphuric acid, with copious evolution of gas. A wire of magnesium and one of platinum immersed in the liquid acid, and connected with a sensitive galvanometer, evolved no perceptible electric current, and only a barely perceptible current after two days of constant im- mersion. Calcined magnesia in powder did not dissolve or alter in appearance during four days’ nearly constant immersion. Oxide of cerium (containing some oxide of didymium and lanthanum) re- mained undissolved and unchanged in colour during nine days; the residue was insoluble in water. Metallic aluminium became dull in the gas, and quickly dissolved, with evolution of gas, when the liquid acid came into contact with it, and formed a colourless solu- tion. A wire of aluminium and one of platinum, immersed tth of an inch apart in the liquefied acid, and connected with a sensitive galvanometer, produced a steady deflection of 123 degrees, the alu- minium being positive; the deflection gradually increased to 17 degrees in one hour, and two layers of liquid formed, the lower one brown in colour, and the upper one nearly colourless. The conduc- tivity of the liquid acid was probably increased by the metallic aluminium dissolved in it. Precipitated alumina did not visibly alter or dissolve during six days; the residue deliquesced in damp air. Precipitated silica in powder did not dissolve or visibly alter during four days. Precipitated titanic acid in powder (pale flesh- colour) slightly dissolved in seven days. A fragment of fused tungstate of soda did not alter in bulk during 546 Royal Society :—Mr. G. Gore on the ten days; it had then acquired a superficial green colour. Molybdic acid in powder turned dark green, but remained undissolved at the end of nine days. Native sulphide of molybdenum remained un- dissolved and apparently unchanged during two days. Molybdate of ammonia in powder became yellowish green in the gas; it became grass-green in colour in the liquefied acid, but did not dissolve in four days. Sesquioxide of chromium in powder did not dissolve in six days, but became of a dull blackish-brown colour. A fragment of anhydrous yellow chromate of potash became red before the gas liquefied, but did not dissolve or otherwise alter in the liquid acid. Sesquioxide of uranium became of a paler yellow colour in the gas, but did not dissolve in the liquid acid in six days; the residue was entirely soluble in water. Precipitated black oxide of manganese in powder, and free from water, became quite white in the gas; it re- mained white in the liquid acid without evolving visible bubbles of gas, and did not lessen in bulk in seven days. A erystal of perman- ganate of potash softened and swelled in the liquid acid, but did not dissolve in five days; it remained of a dark colour; the residue placed in distilled water produced no coloration. A. crystal of metallic arsenic remained perfectly bright and un- changed in bulk during three days’ immersion. Arsenious acid in powder quickly liquefied in the gas, and dissolved to a colourless solution in the liquid acid. A crystal of arsenic acid softened before _the gas liquefied, and dissolved quickly and freely in the liquid acid to a colourless solution. Bisulphide of arsenic in powder did not dissolve in six days, but became slightly less red and_more yellow ; a slight yellowish-white sublimate occurred in the tube during the generation of the gas. ‘Teriodide of arsenic in powder slightly dis- solved to a purple-red liquid; apparently only a trace of its iodine was extracted, as its bulk was not visibly less in three days. A crystal of bright antimony remained perfectly bright and unchanged after nine days’ intermittent immersion. Precipitated teroxide of anti- mony became partly liquid before the gas liquefied ; it dissolved in the liquid acid quickly and rather freely, and made a colourless solution. Oa woe, together with chromic iron 0°49, magnetic iron 12°03, nickeliferous sulphide of iron 16°97, water and supposed organic substances 14:91=100. This gives for the oxygen ratio of the oxides and silica 9°98: 13°90=8 : 4. Pisani proved the presence of magnetic iron by dissolving the mineral in hot nitric acid, which decomposed the silicate and the sul- phides, and left a black magnetic residue. The nickel was proved to Intelligence and Miscellaneous Articles. . (553 exist as sulphide by treating the substance with sulphide of ammo- nium, which dissolved out sulphide of nickel. The stone contains 55°60 per cent. of silicates; and taking into account the water deter- mined by Cloéz, the oxygen ratio of the silicate is that of serpentine. If the alumina is due to anorthite, it will give 2°42 per cent. of this felspar contained in the meteorite. Subsequent observations by Des Cloizeaux, Pisani, Daubrée, and Cloéz prove that this remark- able meteorite contains minute rhombohedral crystals of a double carbonate of magnesia and iron, and Cloéz obtained a little more than a half per cent. of carbonic acid from a portion of the meteorite operated upon.—Silliman’s American Journal for March 1865. NOTE ON THE PROPAGATION OF ELECTRICITY THROUGH METALLIC VAPOURS PRODUCED BY THEVOLTAIC ARC. BYA.DELA RIVE. In following out my investigations upon the propagation of elec- tricity in greatly rarefied elastic fluids, I have been led to study this propagation in the vapours of various metals. The apparatus that I make use of for this purpose consists of a large glass balloon, furnished with four tubulures and supported on afoot. The two tubulures at the extremities of the horizontal diameter are furnished with leather plugs traversed by metal rods, to which are fitted the metallic or charcoal points, which serve to produce voltaic arcs by means of a Bunsen’s battery of 60 to 80 pairs. The two tubulures situated at the extremities of the ver- tical diameter serve for the passage of two brass rods, terminated by metal balls, between which passes at the same time the electric jet of a Ruhmkorff’s apparatus. ‘The balloon, after a vacuum has been produced in it, is filled with thoroughly dried nitrogen, which is rarefied to a pressure of from 2 to3 millims.; then the electric jet is passed through, its intensity being measured by means of the pro- cess of derivation described by me in a previous communication. After the constancy of this intensity has been ascertained, the horizontal metallic points are brought near to each other, so as to produce the voltaic arc, which acts here solely as a source of heat. Care must be taken to maintain this arc for some minutes; then at a certain moment the intensity of the electric jet is seen to be con- siderably increased; at the same moment the colour of this jet, which was of a deep rose in the nitrogen, acquires quite a different tint, which varies according to the nature of the conducting points between which the voltaic arc passes. This new appearance lasts for some moments after the cessation of the arc; and it is even at this period that it is most remarkable, as it no longer has to suffer by contrast with the dazzling light of the arc. The voltaic arc was successively produced between points of silver, copper, aluminium, zinc, cadmium, and magnesium, and between two points of gas-coke, all these materials being capable of acquiring a gaseous state in consequence of the high temperature which is pro- duced. With points of silver and zinc the electric jet exhibits a very distinct blue colour, darker with zinc than with silver. With points of copper the tint is a very dark green; with cadmium apple- Phil. Mag. 8. 4. No. 199. Suppl. Vol. 29. 20 554 Intelligence and Miscellaneous Articles. green; with magnesium very bright green; and with aluminium whitish green. With coke-points the colour of the jet is bright blue, which becomes bluish when the are ceases; this is due to the pro- duction of a little carburetted hydrogen gas, as I have ascertained directly. It is in the upper part of the balloon, to which the metallic vapours produced by the voltaic arc ascend, that these effects are most dis- tinct. The streaks or stratifications of the electric light are still more marked in these vapours than in rarefied gases. The augmentation of the intensity of the jet is most considerable in the vapours of silver and copper. The galvanometer passes sud- denly from 30° to 60° at the moment when the jet indicates, by its change of colour, that it is transmitted through the vapours of those ‘metals. The increase, although less, is still very distinct in the ‘vapour of aluminium. It is much less, only from 10° to 20°, with the vapours of zinc, cadmium; and magnesium. Lastly, the increase is very great with the vapour arising from the are formed by two coke-points; but here the effect is more complex in consequence of the production of small quantities of carburetted hydrogen gas, which it is difficult to avoid. I have also employed iron and platinum points. With the former I have certainly observed a change in the colour of the electric jet and a slight augmentation of its intensity; with the latter no effect was produced, except that the excessive elevation of the tempera- ture caused an appreciable increase in the conductibility of the rare- fied nitrogen, but too slight to be in any way compared with the augmentations of which I have spoken above. This last experi- ment proves that it is not to the heating of the rarefied nitrogen, but to the presence of the metallic vapour produced by the voltaic arc, that the very distinct augmentation of the conductibility above indicated is due. ‘This does not imply that the temperature has no influence; its influence is, on the contrary, very sensible, and is manifested in all rarefied gases by a considerable increase in their conducting-power. I have already determined this increase for a great number of gaseous substances, and I shall make known the results that I have obtained in this respect when my work is more complete. I will not conclude this notice without indicating en passant a phenomenon which I had the opportunity of observing in trying to — produce the voltaic arc with points of various alloys, namely, that at these high temperatures all these alloys are decomposed. To observe this decomposition more satisfactorily, I take as the negative electrode a plate of coke; the puint of alloy serves as the positive electrode, and consequently becomes heated and vaporized. Alloys of copper and zinc, copper and tin, copper and aluminium, platinum and silver, and of iron and antimony have all been decomposed at these high temperatures, and I have collected upon the plates of coke particles of the constituent metals of the alloys very distinctly sepa- rated. This is a case of dissociation by heat, which indeed might easily have been foreseen, and which comes as an addition to those curious examples indicated by M. H. Sainte-Claire Deville in his beautiful investigations.—Compies Rendus, May 15, 1865, p. 1002. Intelligence and Miscellaneous Articles. 555 APPLICATION OF THE ELECTRIC LIGHT (GEISSLER’S TUBES) FOR LIGHTING UNDER WATER. BY M. PAUL GERVAIS. Of late years the electric light has been used for illumination under water. In the Channel and in the Mediterranean attempts were made by means of water-tight receivers of glass, in which works a regulator for bringing in contact carbons made incandescent by a battery, the elements of which are on board a vessel on which the trials are made. The part serving as lantern is sunk under water. In some cases these attempts have been successful, and the light thus prodnced has been utilized either for submarine works or in fishing, which this method seemed to render more productive by attracting the fish. Yetthe use of such apparatus is costly, and the manipulation difficult; moreover the light is in many cases too bright, and, besides, the entire arrangement is liable to numerous accidents, such as, for instance, the spilling of the liqvid owing to the motions of the vessel. There are, moreover, circumstances in which a less brilliant light is sufficient and even preferable. It would, therefore, be useful to construct an apparatus capable of working under water, and such that its totalimmersion would not stop its working. Ithought that these results might be arrived at by means of Geissler’s tubes, placing them in connexion with an exhausted receiver containing the ele- ments of a battery and a coil for producing the electrical current by which these tubes are made luminous; and M. Ruhmkorff has con- structed for me the following apparatus :— Our receiver is a sort of bronze box mounted on four small feet, and the cover of which is made to fit hermetically by means of screws and of a vulcanized india-rubber washer. A ring on the cover serves to suspend the entire apparatus. The exhausted box contains two bichromate-of-potash elements closed in their turn by plates. The poles of the current furnished by the element can at pleasure be connected with the coil, and the induced current, by means of insulated wires, passes through the bottom of the apparatus to a Geissler’s tube. This tube, of an appropriate form and filled with carbonic acid, is enclosed in a thick glass cylinder provided with copper armatures, and into which water cannot penetrate. This is the illuminaticg part of the apparatus. With this instrument a soft but distinct light is obtained, re- sembling that which military engineers and miners now use. In some respects it resembles that which phosphorescent animals emit, though itis more intense. It can be seen ata considerable distance, ~ even when the apparatus is worked under water at a depth of seve- ral metres. It cannot be doubted that it will attract fish as does the phosphorescence of certain species, and it might also be used to illu- minate closed spaces situate below the surface of the water, or for making floating signals. Captain Deroulx has seen this apparatus work in the port of Cette last September. In this experiment the apparatus was immersed for nine hours, and it illuminated during six hours under these conditions. The duration of its phosphorescence may be greater. A second trial at Port Vendres also succeeded.--Comptes Rendus, March 27, 202 556 INDEX to VOL. XXIX. ACETONE, on the synthesis of, 535; on the conversion of, into allylene, 536. Acetylene, researches on, 305. Acid, on the use of the word, 262, 464. Acids, fatty, on thesynthesis of the,537. Acroleine, on the action of hydrogen on, 533. Adams (Prof. W. G.) on the applica- tion of the principle of the screw to the floats of paddle-wheels, 249, 35 L, _Air-pump, description of a new, 487. Akm (Dr.) on calcescence, 28, 136; on the conservation of force, 205. Aldehydes, on the propylic and buty- lic, 309. Allylene, on the preparation of, 306, 536; on the action of bromine and iodine on, 307. Aluminium, on the ethide and methide > Of, 316; on the atomicity of, 395. Angstrom (A. J.) on a new determi- nation of the lengths of waves of hght, 489. Antimony, on native sulphides of, 10. Ares, on the approximate graphic measurement of elliptic and tro- choidal, 22. Arragonite, on the growth of coral- loidal, 560. _ | Atkinson (Dr. E.), chemical notices by, 305, 374, 528. Barometers, on the ¢onstruction of double-scale, 79. Beilstein (M.) on the reducing action of tin and hydrochloric acid, 313. Benzhydrole, researches on, 531. Benzoie acid, on the action of nascent hydrogen on, 528. Benzole series, on the synthesis of hydrocarbons of the, 31]. Benzpinakone, on the constitution of, 533. Berard (M.) on some compounds of iodine with acetylene, 505. Berthelot (M.) on iodide of acety- lene, 305. Bismuth, analysis of native, 3. Bismuthine, analysis of, 5. Bohn (Prof.) on the history of the conservation of energy, 215. Borsche (M.) on the preparation of allylene, 536.. Brewster (Sir D.) on the cause and cure of cataract, 426; on hemi- opsy, 903. Bunsen (Prof. R.) 6n some thermo- electric piles of great activity, 159; on a simple method of preparing thallium, 168. Busk (G.) on the fossil contents of the Gibraltar caves, 402. Butylene, researches on, 307. Butyric acid, on the synthesis of, 308. Buys-Bailot (M.) on the radiant heat of the moon, 162. Cesium, on the separation of, 376. Calcescence, researches on, 28, 136. Calorescence, researches on, 28, 136, 164, 218. Cataract, on the cause and cure of, 426. Cayley (A.) on a quartic surface, 19; on quartic curves, 105; on Lobat- schewsky’s Imaginary geometry, 21; on the theory of the evolute, 344; on a theorem relating to five pomts in a plane, 460; on the in- tersections of a pencil of four lines by a pencil of two lines, 501. Cerium, on the separation of, 376. Challis (Prof.) on the undulatory theory of light, 329. INDEX. Charcoal, on the absorption of gases s~ by, 116. Chemical actions, on the mechanical energy of, 269. nomenclature, observations on, 262, 464. — notices from foreign journals, 305, 374, 528. Chromium-compounds, on the con- stitution of, 313. Circle, on rational approximations to the, 421. Claus (M.) on the synthesis of cro- tonic acid, 309. Climate, on change of, due to excen- tricity of the earth’s orbit, 538. Cotterill (J. H.) on an extension of the dynamical theory of least action, 299, 430; on the equilibrium of arched ribs of uniform section, 380. Crotonic acid, on the synthesis of, 309. Danaite, analysis of, 7. Davy (Sir H.) on certain statements respecting the late, 77, 164, 246. De la Rive (A.) on the propagation of electricity through metallic va- _ ponrs, 553. De la Rue (W.) on the nature of solar spots, 237, 390. Deleuil (M.) on a new air-pump, 487. De Luynes (M.) on butylene, 307. Diallyle, researches on, 3) 1. Dynamical principle of least action, on an extension of the, 299, 380, 430. Edmonds (T. R.) on the elastic force of steam of maximum density, 169. Electrie light, on the application of the, for lighting under water, 555. Electrical experiments and _ induc- tions, on some, Sl, 192, 370. force, on the laws and opera- tion of, 65. machine constructed of sulphur, on an, 551. measurements, on the elemen- tary relations between, 436, 507. signals, on the retardation of, on land lines, 40). standard of resistance, on the, _ 248, 361, 477. Electricity, on the propagation of, _ through metallic vapours, 553. Electromagnetic field, on a dynamical _ theory of the, 152. Energy, on the history of, 55, 215; 557 on the mechanical, of chemical actions, 269. Equations, differential, of the first order, on, 121. Erithyrite, on the action of hydro- chloric acid on, 307. Ethvlene-gas, preparation of, 306. Evolute, on the theory of the, 344. Falconer (Dr. H.) on the fossil con- tents of the caves at Gibraltar, 402; on the occurrence of human bones in the ancient deposits of the Nile and Ginzes, 403. Favre (A.) on the origin of the alpine lakes and valleys, 206. Fernet (E.) on a peculiar phenome- non produced by the induction- spark, 488. Feussner (M.) on the absorption of light at different temperatures, 471. Fittig (M.) on the synthesis of hy- drocarbons of the benzole series, 311; on the preparation of ally- lene, 536. Fluorescence, on the history of nega- tive, 44. Forbes (D.) on the mineralogy of South America, 1, 129; on phos- phorite from Spain, 340. Force; on the conservation of, 205, 215. Foster (Prof. G. C.) on chemical nomenclature, 262. Friedel (M.) on a new method of preparing allylene, 306; on the synthesis of acetone, 535. Gases, on the absorption of, by char- coal, 116; on the unit-,olume of, 188. Geological Society, proceedings of the, 75,157; 239,325, 398, 450: Geometry, note on Lobatschewsky’s imaginary, 231. Gervais (P.) on the application of the electric light, for hghtmg under water, 599. Girdlestone (A. G.) on the condition of the molecules of solids, ]08. Gold, analysis of native, 129. Gore (G.) on the properties of lique- fied hydrochloric acid gas, 541. Greiss (C. B.) on the production of magnetism by turning, 40/7. Hargreave (Dr. C. J.) on differential equations of the first order, 121. Harnitzsky (M.) on the conversion 558 INDEX. of benzole into benzoic acid, 310; af the synthesis of the fatty acids, 37. Harris (Sir W. S.) on the Jaws and operation of electrical force, 65. Harrison (J. P.) on lunar influence over temperature, 247. Heat, on the alteration of electro- motive force by, 408. Hemiopsy, observations on, 503. Herrmann (M.)onthe action of nascent hydrogen on benzoic acid, 528. Herschel (Sir J. F. W.) on certain statements respecting Sir H. Davy, 113240: Hoppe-Seyler (M.) on a spectroscopic method of distinguishing solutions of permanganates from the sesqui- salts of manganese, 78. Hugeins (W.) on the spectra of some nebule, 151; on the spectrum of the great nebula in the sword- handle of Orion, 319. Hunter (J.) on the absorption of gases by charcoal, 116. Hydrochloric acid gas, on the pro- perties_of liquefied, 541. Indium, on the preparation of, 328. Induction-spark, on a peculiar phe- nomenon of the, 488. Iron, on an anomalous magnetizing of Ld. Jenkin (I’.) on the retardation of elec- trical signals on land lines, 409; on the elementary relations be- tween electrical measurements, 436, 507; on the new unit of electrical resistance, 477. Jones (H. B.) on the passage of li- thium into the textures of the body, 394. Kronig (A.) on a simple mode of determining the position of an optic image, 327. Lake-basins, on the glacial theory of, 206, 285, 526. Lamy (M.) on the phosphates of thallium, 379. Langite, description of the new mi- neral, 473. Leyden jar, on the heating of the glass plate of the, by the discharge, 244. Liebermann (M.) on the action of iodine on silver-allylene, 31:7. Light, on the undulatory theory of, 329; on the absorption of, at dif- ferent temperatures, 471; ona new determination of the lengths of waves of, 489. Lindig(F.) on the alteration of electro- motive force by heat, 408. Linnemann (M.) on benzhydrole, 531; on the action of hydrogen on acro- leine, 533. Lithium, on the passage of, into the. textures of the body, 394. Lobatschewsky’s imaginary geome- try, note on, 2351. Loewy (B.) on the nature of solar spots, 237, 390. Logan (Sir W. E.) on the Laurentian rocks of Canada, 75. Lorin (M.) on a new mode of reduc- tion, 380. Madan (H. G.) on the reversal of the spectra of metallic vapours, 338. Magnetic phenomena, on the mea- surement of, 439. Magnetism, on the production of, by turning, 407. Magnus (Prof.) on thermal radiation, 58. Manganese, on a spectroscopic me- thod of distinguishing certain com- pounds of, 78. Marcus (S.) on a new thermo-element, 406. Marignac (Prof.) on the silico-tung- states, 377. 4 Mars, observations on the planet, 322. Martins (C.) on the relative heating, by solar radiation, of the soil and of the air, 10. Maskelyne (Prof.) on new Cornish minerals, 473. Mathews (W.) on the construction of double-scale barometers, 79. Maxwell (Prof. J. C.) on a dynami- cal theory of the electromagnetic field, 152; on the elementary rela- tions between electrical measure- ments, 436, 507. Mercury unit, on the, 361. Metals, on the specific resistance of the, 361. Meteorites of Oreueil, on the, 487; on the chemical and mineralogical characters of the, 552. Michaelson (M.) on propylie and bu- tylic aldehydes, 309. Mineralogy of South America, re- searches on the, 1, 129. | INDEX. Minerals, descriptions of new Cornish, 473. Monro (C. J.) on a case of stereo- scopic illusion, 15. Moon, on the radiant heat of the, 162. Moore (J. C.) on lake-basins, 526. Naphthylmercaptan, researches on, 530. Nebulz, on the spectra of, some, 151. Nitric acid, on tke estimation of, in waters, 378. Odling, (Prof. W.) on aluminium ethide and methide, 316. Oefele (M. von) on a new class of sulphur-compounds, 529. Oppenheim (M.).on the action of bro- mine and iodine on allylene, 306. Optic image, on a simple mode of determining the position of an, 327. Orion, on the spectrum of, 319. Phillips (Prof. J.) on the planet Mars, 322. Phosphorite from Spain, analysis of, 340, Photo-chemical researches, 233. Pisani (M.) on the chemical compo- sition of meteorites of Orgueil, 552. Plane, on a theorem relating to five points in a, 460. Popp (M.) on yttria, 374; on cerium, 376 /6. Potter (Prof.) on the applicability of _ Alexander’s formula for the elastic force of steam to the elastic force of the vapours of liquids, 98. Prisms, new method of establishing the equations which regulate the torsion of elastic, 61. Quartic surface, note on a, 19. -— curves, on, 105. Radiation, researches on thermal, 58 ; from a revolving disk, note on, 476. Ramsay (Prof. A. C.) on the glacial theory of lake-basins, 285. Rankine (W. J. M.) on the graphic measurement of elliptic and tro- choidal ares, 22; on stream-lines, 25; on the elasticity of vapours, 283; on rational approximations to the circle, 421. Rays, on combustion by invisible, 559 Redtenbacher (Prof.) on cesium and rubidium, 379. Richer (M.) on an electrical mache constructed of sulphur, 551. Roscoe (Prof. H. E.) on a method of meteorological registration of the chemical action of total daylight, 2335 Royal Institution, proceedings of the, 241, 316. Royal Society, proceedings of the, 65, 151, 233, 319, 390, 473, 541. Rubidium, on the separation of, 376. Saint-Venant (M. de) on the work or potential of torsion, 61. Schéyen (M.) on the synthesis of butyric acid, 308. Schroder van der Kolk (Dr. H. W.) on the mechanical energy of che- mical actions, 269. Screw, on the application of the prin- ciple of the, to the floats of pad- dle-wheels, 249, 351. Semenoff (M.) on the preparation of ethylene gas, 306. Siemens (Dr. W.) on the heating of the glass plate of the Leyden jar by the discharge, 244. Silico-tungstates, on the, 377. Solar radiation, on the relative heat- ing of the soil and of the air by, 10. -—— spots, on the nature of, 237, 390. system, on a new method of determining the translatory motion of the, 489. Solids, on the condition of the mole- cules of, 108. Spectra, on the reversal of the, of metallic vapours, 338. ee on the elastic force of, 98, 69. Stereoscopic illusion, on a case of, 15. Stewart (B.) on the nature of solar spots, 237, 390; on the radiation from a revolving disk, 476. Stone (E. J.) on change of climate due to excentricity of the earth’s orbit, 538. Stream-lines, observations on, 25. Sulphur-compounds, on a new class of, 529. Tait (Prof. P. G.) on the history of energy, 90; on the radiation from a revolving disk, 476. eporn: on lunar influence over, 4/. 560 INDEX. Thallium, simple method of prepa- ring, 168; ov the phosphates of, - 379. Thermo-electric piles of great energy, en some, 159. Thermo-element, on a new, 406. Tin, analysis of native, 133. Tollens(M.) on the synthesis of hydro- carbons of the benzole series, 311. Torsion, on the work or potential of, 61. Tyndall (Prof.) on the history of ne- gative fluorescence, 44, 218; on combustion by invisible rays, 241. Valleys, on the origin of the Alpine, 206. Vapour-densities, note on, 111. Vapours, on the elasticity of, 283; on the reversal of the spectra of metallic, 338. Vogt (M.) on naphthylmercaptan, 530. Waltenhofen (Prof. A. von) on an peg magnetizing of iron, Wanklyn (Prof. J. A.) on vapour- densities, 111; on the constitution of chromium-compounds, 313. Waringtonite, description of the new - mineral, 475. | Waterston (J. J.) on some electrical experiments and inductions, 81, — 192, 370. Weltzien (M.) on the estimation of nitric acid in waters, 378. Weselsky (M.) on a method of ex- tracting indium, J28. Williamson (Prof. A. W.).on the unit- volume of gases, 188 ; on the atomi- city of alumimium, 395; on chemi- mical nomenclature, 464. Wurtz (M.) on diallyle, 311. Yttria, researches on, 374. END OF THE TWENTY-NINTH VOLUME. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREDT. Phil. Mag. Ser. 4 .Vol. 29. PUT. J. Basire sc. JS Basirve se. | Lhil. Mag. Ser. 4-Vol.29. Pl.I. 8 Ce >2>HID>>>> a J Basire se. i i } f i ennai teams emi aia J Basire se. a nl a Sy a) Cenc oe aa yee Seer A ress i ae ig «JANUARY 1865. “No. 193. j : Prajohed the First Day of every Month.—Price 2s. 6d. THE I : LONDON, EDINBURGH, ano DUBLIN gm ; ‘PHILOSOPHICAL MAGAZINE, | } ey AND i JOURNAL OF SCIENCE. | . 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ATKIN: SON, Peres to the Council.” January 3, 18665. Just published, price 38s., Vol. XXIII. Part ILI. of the TRANSACTIONS OF THE ROYAL SOCIETY OF EDINBURGH. CONTENTS. | I. Description of the Lithoscope, an Instrument for distinguishing Preciouen a PLE and other bodies. By Sir David Brewster, K.H., F.R.S. (Witha © , Plate § II. On the Agrarian Laws of ict ous, and one of Mr. Grote’ s Canons of His- — torical Criticism. By Professor Blackie. W Til. Onthe Limits of our Knowledge respecting the Theory of Parallels. By | Professor Kelland. a IV. On the Temperature of certain Hot Pprua in the Pyrenees. BY R. E. Scoresby-Jackson, M.D., F.R.C.P. V. On Superposition. By Professor Kelland. Part ee (Continued from Vol. XX. p. 273.) (With a Plate.) VI. On the Variations of the Fertility and Foainats of Women according to Age. 4 _By J. Matthews Duncan, M.D. > VII: On the most Volatile Constituents of American Peerolemn By Edmund : ~ Ronalds, Ph.D. y VIIT. On Sun Spots, and their Connexion with Planetary Configuraticns. By © Balfour Stewart, Esq., M.A., F.R.S. % IX. On the Freezing of the Evo of the Common Fowl. By John Davy, M.D., _ F.R.SS. Lond. and Edin., &e. Communicated by Professor Maclagan. X. On the Morphological Relationships of the Molluscoida and Ceelenterata, and of their leading Members, inter se. By John Denis Macdonald, RN. EF R.S., Surgeon of H.M.S. ‘ Icarus.’ XI. On the Great Drift Beds with Shells in the South of Anee By the Rev. Robert Boog Watson, B.A., F.R.S.E. (With Two Plates.) _ : XII. On the Principal Deities of the Rigveda. . By J. Murr, Esq., D.C.L., LL.D. XIII. The Law of the Volumes of Aériforms extended to Dense Bodies. By the Rev. J. G. Maevicar, M.A., D.D., Moffat. . XIV. Biographical Sketch of Adam Ferguson, LL.D., F.R.S.E., Professor of Moral Philosophy in the University of Edinburgh. By John Small, M.A., Librarian to the University. XV. Onthe Reputed Metrological System of the Great Pyramid. 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[ADVERTISEMENTS continued on 3rd page of Cover. SUPPLEMENTARY NUMBER. No. 199.- Published the First Day of every Month.—Price 2s. 6d. : THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE, AND | JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson’s ‘ Annals of Philosophy.’ CONDUCTED BY SIR DAVID BREWSTER, K.H. LL.D. F.R.S. L.& E. &c. SIR ROBERT KANE, M.D. F.R.S. M.R.I.A. WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S. FOURTH SERIES. N° 199.—_ SUPPLEMENT. JUNE 1865. This SuprLemeEnt to Vol. XXIX. is published with the regular Number for June, and should be delivered with it to Subscribers. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Pubiishers to the University of London. Sold by Longman, Green, Longmans, ind Roberts; Piper and Co.; Simpkin, Marshall and Co.; Whittaker and Co.; and H. Bailliére, London :—and by A. and C. 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