, » “* ms , r i > z Z » k "i : as 3 A Tt te ar hiee make one is oe Oe La eR a; 1" ] ei - i on y oe is * a 4 Ae eee . a.° ae ae ; EE Sime es Sta ns ae cai Smt a wilige 7 OE ver td toy wd a ps es } GAs en * t -_: t it yr: gas As; = Saucer rich E i, pet : + ~ ! * - ? ' ? | ¥v t ay ay aa : % ay rectal (ao x og | cov ty eka 1m: vib San ae 2 . a = P e CS y hi - Paar Ay Ly i ; Ue! eae 4 CAawe - ny Ne fer a . aan 2 a oa 7 - i i) iy 4 THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.CS. AND WILLIAM FRANCIS, Pa.D. F.L.S. F.R.A.S. F.C.S. ‘“Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib.i. cap. 1. Not. VOL. XL.— FOURTH SERIES. JULY—DECEMBER 1870. LONDON. TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London ; SOLD BY LONGMANS, GREEN, READER, AND DYER; SIMPKIN, MARSHALL AND CO.; WHITTAKER AND CO.; AND KENT 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, queestio 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 cecelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.”’ J. B. Pinelli ad Mazonium. CONTENTS OF VOL. XL. (FOURTH SERIES.) NUMBER CCLXIV.—JULY 1870. Mr. J. Ball on the Cause of the Descent of Glaciers ........ Archdeacon Pratt’s Reply to M. Delaunay’s objection to the late Mr. Hopkins’s Method of determining the Thickness of the Earth’s Crust by the Precession and Nutation of the Earth’s RRR haps Pa phiie inc alias) xi hiajoray> eipithiae.o si ele soe ee £ dh» ae ri Prof. E. Edlund on the Path of Electrical Induction- and Dis- junction-Currents through Gases of various Densities, and between Poles of different shapes .... Mr. A. S.,Davis on a possible Cause of the Bright Line observed by M. Angstrém i in the Spectrum of the Aurora Borealis .. Mr. R. Moon on the Solution of Linear Partial Differential Equations of the Second Order involving two Independent |S TUALSL SEES Eee 9 2 eee a8 kane BOP aor ni ea eae ae Mr. 8. E. Phillips on a Simple Method of Constructing high PPeeeD TVeSIStAMCC jo. alee eis. s.r alas oie '< yee! as o,s eye 4 0 os Prof. von Bezold’s Researches on the Electrical Discharge. . The Rev. J. M. Heath on the Interchangeability of Heat and Bere INC AU NCEIOME econ asia ciievai ees ore cise wie d #0) vis oe 6 wiaie Proceedings of the Royal Society :— Mr. Warren De La Rue, Dr. Balfour Stewart, and Mr. B. Loewy on the Positions and Areas of the Spots observed at Kew during the years 1864-66, also the Spotted Area of the Sun’s visible disk from the commencement of 1832 up to May 1868.. 4 Mr. H. T. Brown on the Estimation of Ammonia i in Atmo- 2 [LEIS S UA Seip ahi Binal area 8 psec pela gage Mr. H. E. Roscoe and Dr. T. E. Thorpe on the Relation between the Sun’s Altitude and the Chemical Intensity Gr Potal SD aylieht ma Cloudless Sky 2.0. 6 eee Prof. C. Piazzi Smyth on Supra-annual Cycles of Tempe- rature in the Earth’s Surface-crust .. The Rev. S. Haughton on the Constituent Minerals of the Granites of Scotland,as compared with those of Donegal. Wed tan. PROSCOe OM VANACIUID: » <6 e aps pis seek Deis apy «© Proceedings of the Geological Society :— Prof Huxley on Hypsilophodon, a new Genus of Dinosauria Prof. Huxley on the Affinity between the Dinosaurian ie liesand Birds ......... Been paen Peg Prof. Huxley on the Dinosauria of the Trias. 53 04 56 08 59 62 68 69 70 IV CONTENTS OF VOL. XL.—FOURTH SERIES, Dr. P. M. Duncan on the Physical Geography of Western Europe during the Mesozoic and Cainozoic Periods.... Mr. 'T. Davidson on the Brachiopoda hitherto obtained from the Pebble-bed at Budleigh-Salterton .............. Mr. S. V. Wood, Jun., on the Relation of the Boulder-clay without Chalk of the North of England to the Great Chalky .Boulderselay of the South. < ...<.« s/s ener Mr. R. Tate and Dr. J. S. Holden on the Iron-ores asso- ciated with the Basalts of the North-east of Ireland Principal Dawson on the Structure of Sigillaria........ Principal Dawson on some new Animal Remains from the Carboniferous and Devonian of Canada ............ Mr. J. W. Hulke ona Crocodilian Skull from Kimmeridge Bay, Dorset) 32 Re eee he Mr. J. W. Hulke on some Teeth associated with two fragments of a Jaw from Kimmeridge Bay .......... Experiments on the Velocity of the Propagation of Sound in Water in a Cast-iron Conduit 8 decimetres in diameter, by Mi. Fr. André sah.) 250 25 SUMS See Se. oe ee Experimental Researches on the Duration of the Electric Spark, by MM: Lucas, and Cazimaith: Uta ae a, ee oe NUMBER CCLXV.—AUGUST. M. Achille Cazin on Internal Work in Gases. (With a Plate.) Mr. W. M. Watts on the Spectraof Carbon .............. Dr. W..J. M. Rankine on Thermodynamics... 5. sen cueuee M. W. Wernicke on the Refractive Indices and the Dispersion of Opaque Bodies (2)... -sitrvese ae aula eee 310 On Tests for the Perfection and Parallelism of Plane Surfaces of Glass, by Wolcott Gibbs, M.D., Rumford Professor in Har- vard University ...... eiabes elas atid» aSeyat bes chante eee 3ll NUMBER CCLXVIII.—NOVEMBER. Prof. F. Zollner on the Temperature and Physical Constitution of the Sun. vw ithiarriates) Os inint UL ia ifs See eee 313 Mr.C. Tomlinson ona Salt that is invisible inits Mother-liquor. 328 Prof. Cayley on the Geodesic Lines on an Oblate Spheroid .. 328 Mr. J. C. Douglas’s Reply to Mr. Templeton’s “‘ Remarks sug- gested by Mr. Douglas’s Account of a New Optometer” .. 340 Mr. F. Guthrie on Approach caused by Vibration. (With a Plate.). . : . 345 Prof. Plateau’s Experimental and Theoretical Researches into the Figures of Equilibrium of a Liquid Mass without se —Ninth, Tenth, Eleventh and last Series ..... . 3805 Proceedings of the Royal Society :— The Earl of Rosse on the Construction of Thermopiles. 369 CONTENTS OF VOL. XL.—FOURTH SERIES, vil Page The Earl of Rosse on the Radiation of Heat from the Moon. Mr. A. Le Sueur’s Observations with the Great Melbourne MLO SCO pees Weil.) ase aane 35 UU: Mig BMigmeocdo & 377 Mr. J. Broughton’s Chemical and siebaa aca she ments on Living Cinchone .... 379 Proceedings of the Geological Society :— Prof. Owen on the Fossil Remains of Mammals in China. 380 Dr. A. A. Caruana on the Fossil Elephants of Malta.... 381 Mr. G. Busk onthe Species of Rhinoceros discovered in a Ficsute-cavern atrOreston in 181G. -).. 2.62. inte 381 Mr. H. Y. Hind on two Gneissoid series in Nova Scotia eemOBINe RY) STUNG WICl Wo. ok. eek uote a he vixeb wi Saran + 382 Mr. E. Billings on specimens of Lower-Silurian Trilobites. 383 Mr. H. Woodward on the palpus and other appendages of Mcaphus, trom the Trenton Limestone ....../.....: 384 Dr. J. W. Dawson on the Structure and Affinities of Si- gillaria, Calamites, and Calamodendron..... PGR TD Ye The Rev. D. Honeyman on the Geology of Arisaig Poe eer lS) Mr. E. R. Lankester on the Newer Tertiaries of “Suffolk and their Fauna....... Bias tr he OOO Dr. Sutherland on an ancient Boulder-clay of Natal . . 888 Prof. R. Harkness on the Distribution of Wastdale- -Crag Blocks, or ‘‘ Shap-Fell Granite cid in West- moreland ... Pe aiclals aoe ie OO Note on Spiral Nebula, by T.S. Aldis, BT eet, 389 On the Molecular Theory and Laws of Electricity, by L. Lorenz of Copenhagen ........ 1... 6. ee cee eee eee eee ees 390 Easy preparation of a eau for oe aie Plateau’s edie by Rudolph Bottger ..... 392 NUMBER CCLXIX.—DECEMBER. Prof. A. De la Rive’s Researches on the Magnetic Rotatory emit OL OIGWIOS oc a uh pala tc dessiho aie, s, niece's bow bee's 393 Dr. J. Clerk Maxwell on Hills and Dales ................ 421 Prot. J. C. F. Zollner on Solar Protuberances.............. 427 The Rev. J. M. Heath on the Principles of Thermodynamics... 429 Mr. R. Moon on the Equation of Laplace’s Coefficients...... 434 Dr. W. J. M. Rankine on the Meteor of November 19,1870.. 440 Mr. IT. T. P. Bruce Warren on a New Method of determining Resistances. . a: athe eed a 441 Notices respecting ‘New Books: — Mr. T. M. Goodeve’s Text-books of Science.—The Ele- ments of Mechanism ,........... Zea sea, ee Reena Hae 445 Vill CONTENTS OF VOL. XL.—FOURTH SERIES. Page Proceedings of the Royal Society :— i Mr. J. M. Heppel on the Theory of Continuous Beams .. 446 Dr. J. W. M.Rankine’s Remarks on Mr. Heppel’s Theory of Continuaus Beams... ..) slice goad. com tf Me ee eae 457 On Leclanché’s Manganese elements, by J, Miller ........ 460 On the Melting of Leaden Projectiles by their impact upon an lron‘Plite; by Eduard Hagenbachwe 7420... eee 462 An Experiment on the Boiling in conjunction of two Liquids which donot mix, by August Kundt ) /.¢ 2227S) 5o ge ee 468 WARGO seicses ig elele gos go ae. ote de Share REM EPS Se «is Sie yy PLATES. I, Illustrative of M. Achille Cazin’s Memoir on Internal Work in Gases. II. Mlustrative of Professor Zollner’s Paper on the Temperature and Physical Constitution of the Sun. III. Illustrative of M. Merz’s Paper on an Object-glass Spectral apparatus. IV. Illustrative of Mr. F. Guthrie’s Paper on Approach caused by Vihration. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. ‘FOURTH SERIES.] JULY 1870. I. On the Cause of the Descent of Glaciers. By Joun Baru, F.R.S. &c.* ao a long period of rest, the controversy respecting the motion of glaciers which occupied so much of the atten- tion of scientific men during the period between 1842 and 1858 has been lately reopened. The Rev. Henry Moseley, who had already in 1855 proposed a theory which failed to obtain the adhesion of men conversant with the facts of glacier-motion, made a communication to the Royal Society in January 1869, wherein he sought to establish the insufficiency of the theory generally accepted by men of science. The mathematical inves- tigation on which he grounded the results given in that paper was communicated to this Journal in May 1869. Having cleared the way by removing from his path the esta- blished theory, Canon Moseley proceeded to prepare for the ad- mission of his own views by two papers which also appeared in this Journal. In August last he published an elaborate mathe- matical investigation of the problem of the “descent of a solid body on an inclined plane when subjected to alternations of tem- perature ;” and this was followed in January last by a paper upon ‘ The Mechanical Properties of Ice,” embodying the results of observations and experiments made by himself and others upon the dilatation, tenacity, and shearing-force of ice. Ata Meeting of the Bristol Naturalists’ Society in December last, Canon Moseley gave a tolerably full exposition of his own theory, and has lately developed the same views, nearly in the same * Communicated by the Author. Phil. Mag. 8. 4. Vol. 40. No. 264, July 1870. B 2 Mr. J. Ball on the Cause of the Descent of Glaciers. terms, before a London audience, at the theatre of the Royal Institution. The arguments of Canon Moseley have not passed unques- tioned. In March 1869 Mr. James Croll published in these pages a reply to Canon Moseley’s paper shortly before commu- nicated to the Royal Society, wherein, after admitting that the argument directed against the “ ordinary opinion” on the sub- ject of glacier-motion must be considered “decisive,” he attempted to refute the general conclusion by ingenious considerations as to the condition of the molecules of a mass of ice when acted on by external heat. In the ‘Alpine Journal’ for February last, Mr. William Mathews, well known as a successful explorer of the Alps, and familiar with the phenomena of glaciers, has given an able sum- mary of the present state of our knowledge of the causes of glacier-motion, along with a careful analysis of the views of Canon Moseley as developed in his various writings. In the same paper several weighty objections to Canon Moseley’s views are urged by Mr. Mathews; and the result of an interesting ex- periment made by the writer, in conjunction with Mr. A. F. Osler, added a fact of considerable value to the materials avail- able in the discussion. 271 “205 2a ae ee Mean .... 89:76 279... 25:1... 24:9. S233 aa That the deflections first decrease and afterwards again in- crease when the pressure is diminished, indicates that there are several causes for these variations., The magnitude of the de- flection depends on the electromotive force, on the conducting- power of the spark, andon its duration. That the electromotive force decreases with the pressure follows from the fact that the disintegration of the polar surfaces becomes less as the gas 1s rare- fied, because the electrical density of the polar surfaces which is re- quisite for the formation of sparks diminishes with the pressure *, * Tn a previous paper I assumed, without any experimental proofs, that the electrical spark is subject to no perceptible change when a voltaic ' Disjunction-currents through Gases of various Densities. 238 If, now, the conducting-power of the gas, as is probable, increases, and the duration of the spark lengthens, when the gas is rarefied, the result obtained (that the deflections first decrease and then increase) contains nothing inexplicable. Further investigations, however, are needed to enable us to decide with certainty whether the mode of explanation which has been indicated is admis- sible. Tn connexion with the above, experiments were also made with some Geissler’s tubes, in order to ascertain whether the disjunc- tion-current could be perceived in them or not. With three of them, one (according to the label) containing oxygen, another hy- drogen, and the third chlorine, distinct deflections were exhibited; while another, which contained carbonic acid, as well as one with- out label, gave no distinct proof of the existence of a disjunction- current. 4. The current in the voltaic luminous are is well known to occasion a greater disintegration of the positive than of the negative pole. When two equal polar surfaces, between which the discharge from an electrophorus machine has been for some time taking place, are closely examined, it 1s easy to dis- criminate the positive polar surface from the negative; for the former appears more altered than the latter. Hence positive electricity is most active in the disintegration. As positive elec- tricity readily issues from a sharp point without producing there a more powerful disintegration, it must follow that, when one pole consists of a point and the other of a plane disk at right angles to the plane of discharge, the disintegration 1s greatest when the positive current goes from the disk to the point. When, therefore, the discharge goes through the spark from the disk to the point, it is to be expected that the disjunc- tion-current will be stronger—partly because the electromotive force of the disjunction increases with the disintegration, and partly also because the quantity of particles detached from the poles is greater, and therefore the conducting-power of the spark is better. - To test the accuracy of what has here been said, a round brass disk 2°7 millims. in diameter was fastened on one of the two metal rods of the glass cylinder, and upon the end of the other rod a conically sharpened brass point was screwed. current traverses it in either direction ; and on this assumption I have based a method of directly measuring the electromotive force of disjunction. This assumption has been found to be incorrect. The spark undergoes a considerable change by the passage of the voltaic current, so that the de- terminations obtained can only be regarded as valid for the case in which a yoltai¢ current traverses the spark. 24 Prof. E. Edlund on the Path of Electrical Induction- and Experiment 22. The disk The disk The disk negative. positive. negative. "28°9 36°6 27° Deflections shi eae — * ) 27-4 31:9 24:°6 24.0 34-1 25°4 Mean « . 27°1 34:2 25°38 Experiment 23.—The following observations were then made, after the machine had been somewhat altered and the conductions had been reversed, so that the deflections would be towards the opposite side :— The disk The disk The disk negative. positive. negative. 35°4. A7°3 36°5 Deflections.< 34°7 46°3 36°7 34:0 44°3 35°7 42:0 36°2| Mean . « 347 45:0 36:3 Experiment 24.—The conical brass pomt was removed, and in its place a glass tube 3 centims. in length enclosing a plati- num wire a millimetre in diameter was screwed on. The wire reached exactly to the end of the glass tube. Three series of ex- periments were made with this, in which the length of the spark was 1, 2, and 3 millims. It is sufficient to give here only the last, mean numbers :— Length of the The disk The disk spark. positive. negative. 1 millim. 12:0 8:1 Deletion 2 millims. 26:2 19:2 5g 475 37°6 From Experiments 22 to 24, it follows with certainty that the disjunction-currents are strongest when the positive electrical dis- charge proceeds from the disk to the point. The cause, as has already been stated, is that in this case the disintegration of the pole-surfaces 1s most powerful. It is clear that the difference between the two disjunction-currents must become smaller if in- stead of a brass disk a similar one be used of another metal which is more easily disintegrated, so that the mechanical work which the discharge performs in producing the disintegration will be less considerable. If instead of the brass disk a mercury surface be used, the mechanical work which the discharge produces in the spark will consist mainly in imparting velocity to the par- Disjunction-currents between Poles of different shapes. 25 ticles of mercury in their separation from the surface. To in- vestigate this the following series of experiments were made. Experiment 25.—The conical brass point previously used was placed vertically over a porcelain dish which was filled with mer- eury. The mercury was connected by a conducting-wire with the point e, and the sharp point with the point c (see figure, p- 15). From this the following results were :— Mercury Mercury Mercury positive. negative. positive. Mean deflections . 37:2 43°0 40°1 Here, then, the deflection was greater when the mercury was negative; in the foregoing experiments the reverse was the case. Hence the electromotive force of disjunction must have been smaller when sparks were formed between mercury poles than between brass poles. This is confirmed by the following two series of experiments. Experiment 26.—The conical brass point was removed and replaced by a brass knob 17 millims. in diameter, which, as special experiments showed, acted about the same as a disk of the above magnitude. There were thus obtained in two inde- pendent series of observations :— Mercury Mercury Mercury negative. positive. negative. 51°8 35°9 51:9 Mean deflections. 984, 16-9 99-9 Hence the deflections became considerably smaller when the posi- tive discharge traversed the spark from the mercury surface to the brass knob. It might be urged against the above experiments, that the mercury does not retain a level surface while the spark passes, but rises in the form of a peak towards the opposite pole. The smaller deflection when the positive discharge goes from the mercurial surface to the knob would, on this supposition, have been caused by the discharge taking place from the peak to the knob. But there was no such elevation of the surface perceptible. Moreover the deflection, even assuming that a point was formed of the same extent as the brass one, could not have been so small as was observed when the discharge took place from the mercury to the knob, unless we also assume that the mercury itself coope- rated in making the deflection smaller. These experiments merely show that the electromotive force of disjunction between mercury poles is less than that between brass poles; the true ratio be- tween these forces cannot be ascertained by them. In order to examine what takes place when both poles consist of mercury, the followmg method was adopted, 26 Prof. EK. Edlund on the Path of Electrical Induction- and Two vessels, provided in the bottom with exit-tubes and stop- cocks, were filled with mercury and placed so close together that, when the cocks were opened, the mercury-streams were so near each other that a spark could strike across. The mercury was "received in the two separate compartments of a glass vessel placed below. When one vessel was connected with the point e by means of a conducting-wire, and the other with the point e, de- flections so distinct were obtained, as soon as the machine was set to work, that there could be no doubt in reference to the elec- tromotive property of the mercury in the above respect. The same experiments were repeated after the mercury had been replaced by water containing sulphuric acid. Although a slight spark, which was very distinct in the dark, passed between the two jets, no evident deflections were observed which could be ascribed to the disjunction-current. Notwithstanding this negative result, I doubt not that water is an electromotor in this respect, although the means at my disposal were not suitable to show this. rine 5. I have shown in a previous paper that, when induction-cur- rents which result from voltaic induction have the opportunity of traversing the spark of an electrical discharge, those currents which tend to traverse the spark in the same direction as the discharge can most easily penetrate it. The spark acts thus like an electrical valve: of the two opposite induction-currents, that passes in greatest proportion which is in the same direction as the discharge. That the other also passes to some extent may be seen from the appearance of the spark. When the induction- coil is inserted in the circuit between e and g (sce figure, p. 15) the spark is duller, and cannot strike across such a distaneé between the knobs as when the coil is removed—affording a proof that the induction-current, which arises at the commencement of the spark and goes in the opposite direction to the discharge, does in fact partially traverse the spark. In this case, therefore, the intensity of the spark is diminished by the mduction ; its curve of intensity is, as it were, flattened. When, on the contrary, the in- duction-coil is placed between e and k, the intensity of the dis- charge increases in consequence of the fact that the induction- current formed at the commencement of the spark now traverses it in the same direction as the discharge; the spark has a greater striking-distance than when the coil is removed ; its intensity is increased. Now it might possibly be maintained that the reason why the deflection of the disjunction-current is diminished by the introduction of the induction-coil between e and g, or be- tween e and f, is not that that induction-current which has the same direction as the discharge traverses the spark in greatest proportion, but that it is to be sought in the fact that the eurve Disjunction=currents between Poles of different shapes. 27 of intensity of the spark undergoes a change in form, although both induction-currents pass with equal facility. That this cannot be the case can be easily seen from the following con- siderations. We assume for a moment that both induction-currents tra- verse the spark in exactly equal proportions; the electricities which have passed are then exactly equal, whether the induction- coil is in the circuit or not ; and therefore it is solely the change in the curve of intensity of the spark when the induction-coil is in- serted between e and g or between e and & which causes the diminution in the deflection of the disjunction-current. But it is to be remarked that the intensity of the spark increases when the induction-coil is inserted between e and &, while it decreases when the coil is between e and g; two entirely opposite changes in the intensity would thus both have the same effect—that is, a di- minution in the deflection produced by the disjunction-current. This would only be possible if the deflection which the disjunction- current produces when there is no induction were really a maxi- mum, so that a change in the shape of the spark in either direction could not increase the deflection. But that this deflection is not a maximum follows from the fact that the introduction of the in- duction-coil in all cases diminishes the deflection, whether there is a greater or a smaller distance between the knobs, or whether . there is or is not a bridge in front of the galvanometer, whether the condensers have greater or smaller coatings, or whatever be the other circumstances on which the form of the curve of intensity of the spark depends. Hence it follows that the two induction-currents cannot traverse the spark in equal pro- portion. : | But, instead of this, we might say that it is not those induc- tion-currents which traverse the spark in the same direction as the charge which pass most easily and in greatest proportion, but this is the case with the currents which go in the opposite direction to the discharge, and therefore in the same direction as the disjunction-currents. The latter, it is true, are added to the disjunction-current and thereby increase the deflection ; but, on the other hand, they produce so great a diminution in the dis- integration of the poles, that, on the whole, the deflection is thereby diminished. Many proofs may be adduced for the ab- surdity of this opinion ; but the question is most easily settled by the following experiments. We assume for the moment that that induction-current which is in the opposite direction to the discharge, or in the same direc- tion as the disjunction-current, most readily penetrates the spark, and, in the manner just described, effects the diminution observed in the deflection. To acquire a better.idea of this matter, we 28 Prof, E. Edlund on the Path of Electrical Induction- and may conceive it as follows:—The induction-current in question produces a disintegration of the polar surfaces; and this gives rise to a disjunction-current which is in the opposite direction to the former disjunction-current, and therefore diminishes the de- flection of the magnetic needle. Now, from experiments 22 to 24, we know that the greatest disjunction-current is obtained when the valve has such a position that the discharge which the disintegration causes goes from the disk to the poimt. Hence it follows that the greatest diminution in the deflection must oc- cur when the induction-current in question goes from the disk to the point, or, what is the same thing, when the discharge goes from the point to the disk. Subsequent experiments show, how- ever, that the fact is quite the reverse, and therefore that the assumption, that that induction-current which is opposite in di- rection to the discharge is the one which traverses the spark most readily, cannot be correct. In these experiments the brass disk previously mentioned was fastened to one rod of the glass cylin- der, and the platinum wire surrounded by a glass tube was firmly screwed to the other rod. The pressure of air in the glass cylinder was 1 atmosphere. Experiment 27.—The valve was first of all so arranged that the positive discharge of the machine went from the wire to the disk. There was thus obtained :— Without induc- Coil between Without tion-coil. e and k. coil. Mean deflections . . 371 6°2 37'°6 The valve was then reversed, so that the discharge went from the disk to the wire :— Mean deflections . . 47:4 8:5 46:2 In the former case, then, the induction produces a diminution in the deflection of 31:°2= = — 6-2) ; andin the latter case, of 88'°3 divisions. Hence the diminution in the deflection in the first case was not greater, but less than in the latter. Experiment 28.—This experiment was in all respects like the preceding, except that the mduction-coil was inserted between e and g. The discharge of the machine went first from the wire to the disk :— Without Coilbetween Without coil. e and g. coil. Mean deflections . . 38-4 aie, 38°7 The valve reversed, so that the discharge went from the disk to the wire :— Mean deflections . . 45°0 5 43°6 : Disjunction-currents between Poles of different shapes. 29 This last experiment therefore confirms the preceding. Hence it cannot be the induction-current opposite in direction to the discharge which most readily traverses the spark, but must be the other. As it is now certain that the induction-current which has the same direction as the discharge most readily traverses the spark, another conclusion can be drawn from the preceding experiments ; for they show that the diminution in the deflection of the magnetic needle which the induction-current causes is greater when that current traverses the spark from the disk to the point than when its direction is opposite. An induction-current which traverses a spark does so most readily when it can go from the disk to the point. This result, which holds for the case in which the spark passes in a space filled with air, is essentially the same as that which Professor Riess found for the spark in rarefied air. 6. We now proceed to the case in which the electrical dis- charge traverses a spiral, and thereby produces induction in an adjacent spiral. -When the latter spiral is connected with a gal- vanometer and its ends are in metallic connexion, no deflection is obtained, because the two induction-currents are equal and in opposite directions. If, on the contrary, the spiral is opened so wide that formation of sparks takes place, the magnetic needle makes a deflection which indicates that the inducing current is -in the same direction as the discharge-current. When the spark is formed in a space containing air, this holds, under ordinary circumstances, whatever be the shape of the poles. We really have not less than four currents—that is, two induction-currents and two disjunction-currents. When the galvanometer is in- serted in the conduction and not provided with a suitable bridge, the system of currents is still more complex. Both induction- currents have the same electromotive force; and if the spark opposed the same resistance to each, there would be no action upon the galvanometer. As regards the disjunction-currents, their electromotive forces can by no means be equal. The first mduction-current, or that which is in the opposite di- rection to the discharge, must break through a dense layer of air ; and as this cannot occur without a more considerable tension of the electricity, a powerful disintegration of the polar surfaces thereby ensues. The second induction-current, or that which goes in the same direction as the discharge, instantaneously follows the first, strikes therefore, in the spark, air already rarefied, and the disintegration is less. On this account the first induction-current must produce the most powerful disjunction- current. ‘This latter current, which goes in the same direction as the second induction-current, produces the deflection of the magnetic needle. Hence the capacity of the first induction-cur- 30 Prof. E. Edlund on the Path of Electrical Induction- and rent to produce the strongest disjunction-current need not be ascribed to any special property of it, as it is sufficiently ex- plained by the fact that the formation of sparks commences with this current. When the poles are in an enclosed space, from which the air can be exhausted, the electromotive force of the disjunction diminishes in proportion as the air is rarefied. Finally the electromotive force of induction, which does not de- pend on the density of the layer of air traversed by the spark, begins to be greater than the former, and then the deflection of the magnetic needle mainly depends upon the induction- currents. Professor Riess* has shown, by means of the electric valve which he has devised, that when this is inserted in the path of an induc- tion-current, the following relations take place when the density of the air and the position of the valve are altered. When the spark is formed under a pressure of one atmosphere, there is obtained on a galvanometer inserted in the circuit a deflection im the same direction as that which would be obtained with the second indue- tion-current. Here, as regards the direction of the deflection, it is immaterial whether the second induction-current goes from the disk to the point, or vice versd. When the current in ques- tion goes from the disk to the poimt and the air is gradually exhausted from the valve, the deflections of the magnetic needle are always in the same direction, but their magnitude gradually diminishes at first, increasing again on subsequent rarefaction. When, on the contrary, the valve is so applied that the second in- duction-current goes from the point to the disk, the deflection diminishes more rapidly with the rarefaction, and afterwards changes to a deflection towards the opposite side, which increases when the rarefaction is increased. These details could not well have been sufficiently ex plained before the discovery of disjunction-currents ; but now the explanation follows spontaneously. The deflection obtained when the valve was full of air did not arise, as has been hitherto assumed, from the second induction-current, but from the dis- junction-current, which is caused by the firs¢ induction-current. When the air is rarefied, the disjunction-current becomes feebler, and the induction-currents begin to have more and more effect ; at last they determine the direction of the deflection. Now, from the results of experiments 27 and 28, we know that the induction- current can traverse the spark most readily when it goes from the disk to the point. If, therefore, the valve is so applied that the second induction-current goes from the disk to the point, the di- rection of the deflection must remain unaltered when the air is * Abhandlungen iiber die Lehre von der Reibungs-EHlectricitat. Berlin, 1867, p. 316. Pogg. Ann, vol, exx,-p. 513, : ve Disjunction-currents between Poles of different shapes. 31 gradually rarefied. But the deflection is not caused during the | whole time by the same current: in the unrarefied air the direc- tion of the deflection is chiefly determimed by the disjunction- current, and in the rarefied air by the second induction-current. If, on the contrary, the valve is applied.so that the first induc- tion-current goes from the disk to the point, this current acquires the upper hand and determines the direction of the discharge when the air is rarefied; hence in this case the deflection must alter its direction when the air is gradually rarefied. In the space filled with air the disjunction-current has the upper hand; in rarefied air the jist induction-current is the more powerful. By the foregoing investigations we have obtained a simple means of experimentally proving whether a given deflection of the magnetic needle is caused by a disiunction- or by an in- duction-current. Experiments 22 to 24 show that when the spark is formed between the disk and the point, the disjunction- current is most powerful when the discharge goes from the disk to the point, or, what is the same thing, when the disjunction- current goes from the point to the disk. LHxperiments 27 and 28, on the contrary, have shown that when an induction- current produces a deflection, this is greatest when the induc- tion-current goes from the disk to the point. If, therefore, the current which produces the deflection first goes from the disk to the point, and thereupon by reversing the valve a greater deflection is obtained, it is a case of a disjunction-current ; but if the deflection is smaller when the valve is reversed, an in- duction-current is the cause. This holds, without exception, when the deflection is produced either by a disjunction- or by an induction-current only. When both currents act simulta- neously and to the same extent, this rule, as may be easily seen, may, under certain circumstances, be misleading. M. Riess has already found that, when the valve was full of air, the greatest deflection was obtained when the second induc- tion-current (which, in his opinion, determines the direction of the deflection) went from the point to the disk. This, however, as we have seen, is a proof that the deflection was caused hy a disjunction-current. The subsequent series of experiments pata this observa- tion, and prove afresh that the deflection in the case in question ‘was caused by a disjunction-current. The expression ‘ Disk positive,” signifies that the second induction-current went from the disk to the point ; and the expression the “ Disk negative ” signifies the contrary. 32 On Electrical Induction- and Disjunction-currents. Experiment 29.— Disk Disk Disk positive. negative. positive. Mean deflections . . 19°6 30°8 22°8 Experiment 30.— Mean deflections . . 12:3 19:2 12:2 We can hereby explain the peculiarity that, in that position of the valve which gives the smallest deflection in a space filled with air, the deflection remains unaltered towards the same side when the air in the valve is rarefied. On a superficial consideration, it may seem absurd to sup- pose that the disjunction-current can produce upon the magnetic needle an action many times as powerful as the discharge by which itis caused. It might be thought that the direct action of the discharge upon the magnetic needle must be just as great as when this current first produces a disjunction-current which subse- quently exerts magnetic action. Yet it may easily be seen that this discrepancy is only apparent. That electricity consists of motion is indubitable; but this presupposes something which moves, whether it is the smallest particles of a body, the ether, or any other body. Now, if the mass set in motion in the electrical discharge be called M, and its velocity V, MV? is its vis viva in the discharge. If, in like manner, m denotes the mass in motion in the disjunction-current, and v its velo- city, mv® is the vis viva of the disjunction-current. This latter quantity cannot be greater than the former, but smaller; for the entire vis viva of the discharge never passes to the disjunction- current. If, now, the deflection of the magnetic needle were pro- portional to the vis viva of the current which acts upon it, the de- flection which the disjunction-current causes could not possibly be greater than that which the discharge could directly produce ; but the action upon the magnetic needle is not proportional to the vis viva, but to the intensity; that is, proportional to mv ; and this a may readily be many times as great as MV, although mv? must always be less than, or at most equal to MV?. If, for sistance M=1 and V=100, MV?=10000 ; if m=10000 and v1, MV?=mv?, but mu= 100MV. In the electrical dis- charge the mass moved is inconsiderable, but its velocity is large; in the disjunction-current the reverse is the case. By the mechanical work which the discharge performs in the spark, one of these forms of motion is changed into the other. I will remark, in conclusion, that in my opinion it would be desirable to revise the electrical investigations which were insti- tuted before the discovery of the electrical disjunction-current, and in which electrical sparks and an enclosed circuit occurred. However trustworthy the observations, the explanations could scarcely be either correct or complete when this mode of de- velopment of electricity was unknown, [ 383 ] IV. On a possible Cause of the Bright Line observed by M. Angstrom in the Spectrum of the Aurora Borealis. By A. S. Davis, B.A., Mathematical Master, Leeds Grammar School. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, | ie a letter upon “A Theory of Nebulz and Comets,” published in your Magazine for last month, I endeavoured to show that there are grounds for believing that the solid or liquid bodies composing a meteoric band are surrounded by very rare and extensive atmospheres. I assumed that the meteoric bodies are so numerous and the atmosphere of each so extensive, that in the neighbourhood of the sun, and as far from it as the tails of comets are formed, the atmospheres of the different bodies encroach upon one another, and so form a continuous envelope of gaseous matter about the sun. As the tails of comets are known to extend to a much greater distance from the sun than the distance of the earth, we must admit that the earth is moving through this gaseous envelope. Though the matter which forms it is exceedingly rare, yet it must be much condensed in the neighbourhood of a large attracting body like the earth. The question then arises, is there any evidence of the existence of such gaseous matter in our atmosphere ? I think that the spectrum of the aurora borealis indicates the existence of this matter in the higher regions ofthe atmosphere. The spectrum of an aurora observed by M. Angstrém* con- sists mainly of one bright line not belonging to any known ter- restrial substance, besides several very faint atmospheric lines and some faint bands of light. This proves that there exists in the upper regions of the atmospherea kind of matter not known to exist in,an appreciable quantity in the lower strata. More- over, M. Angstrom has found the same bright Ime in the spec- trum of the zodiacal light, which shows that this matter is of the same kind as that which exists in the sun’s envelope. From the great superiority in the brightness of this line in the auroral spectrum, compared with the atmospheric lines, we might beled to suppose that the matter to which it is due either exists in larger quantities than the elements of the atmosphere in those regions from which the light comes, or else that the electrical currents render it more luminous than the other matter present. This, however, is not necessarily the case; for the light due * Poggendorft’s Annalen, May 1869, and Phil. Mag. September 1869. Phil, Mag. S. 4. Vol. 40. No, 264, July 1870. D 34 On the Bright Line in the Spectrum of the Aurora Boreals. to the luminosity of the atmospheric elements will, in its pas- sage through the non-luminous lower strata of the atmosphere, _ be very greatly diminished, owing to absorption; whilst the light due to any substance not present in the lower strata will be almost wholly transmitted to the eye. Thus the relative in- tensity of the rays due to the different kinds of matter will, when they reach the eye, be very different from their relative in- tensity before their passage through the atmosphere*. The absence of a corresponding dark line in the solar spec- trum shows, I think, that the quantity of the gaseous matter is very small; and this, taken in conjunction with the brightness of the line in the auroral spectrum, shows that it is confined to the higher parts of the atmosphere. | Auroras are known to occur in the lower parts of the atmo- sphere, in the region of the clouds; and some have been observed so low as to appear against a mountain as a background. It would be interesting to know whether such auroras would exhibit the same spectrum as that observed by M. Angstrom. M. Angstr6m asserts, as a deduction from his observations, that the aurora is not due to electricity. The only other way in which it seems possible to account for luminous matter in the atmosphere is by supposing chemical action to be taking place, and, as all chemical action between the constituents of the atmo- sphere must have ceased long ago, if ever there was any chemi- cal affinity between them, we must suppose that this chemical action is taking place between the elements of the atmosphere and the newly introduced gaseous matter. I do not, however, see that M. Angstrém’s observation affords any ground for be- heving that the aurora is not the light due to electrical discharges, ; A. 8. Davis. Roundhay Vicarage. June 10, 1870. * I wish here to point out that the light from a nebula may be due to only one of the different gases composing it; for the light due to the other gas may be wholly absorbed in passing outwards through its non-lumi- nous portions. The presence of lines in the spectrum of a nebula due only to one kind of matter, is therefore no proof that it is not composed of more than one kind of matter. V. On the Solution of Linear Partial Differential Equations of the Second Order involving two Independent Variables. By R. Moon, M.A4., Honorary Fellow of Queen’s College, Cam- bridge*. | Mate following method of treating the problem offered to us in the solution of the General Linear Partial Differential Equation of the Second Order, in the cases which are not amen- able to Monge’s method, may be found to possess both interest and value. dz d?z d?z 0=R-, Ge dade aye ee a ytUEty, Atk) where R,8,T,P,Q, U, V are functions of x ii y only; and assume z=A+Ad(u) +A,67!(u) +Agb72(u) +R, &e.,. (2) where u,A, A, A,, Ao, &c. are functions of # and y only, and | ode. =/¢ an oe . Our assumption gives us dz dA du moe ep A gy dada de?) (ni Mt 4 ou) +(A E+ Ft) bw) + &e, ie dix dz _ dA | Ny 5 du “sb att Gt aye tee OZ it d?A (u) da®~ dx® ji ae yA du, 4 du $/(u) : ig ip da ae dul... 4A, du du oo) + (A eA aa tA ge t ge) ow) Hi? dA, du, , du oy i? + (Ao Skt Oe ae etd gee)? + &e. * Communicated by the Author. 5) 6 d?z d? A du du I Dilly Bagh \ teat © dxdy dxdy vay dudu | dA du ‘(haat oy dudu | dA, du = Grae it dz dy* (A aa da dA. du Seedy” ia ee +e. ; dz dx Mr. R. Moon on the Solution of Linear Partial Ada re dy dx +Aaa (u) dy de 4g tH RY 5g dy dx M1 ~— wt dA, du du at) $-(u) dy dx adh y + Ton when in the latter we put y for z. 2y and we shall have an expression for ie identical with that for Substituting these values in (1) and equating to zero the co- efficients of d"(u), d'(u), d(u), b —(u), &e., we get one ot 47ot ype = 7 TUALY, . (3) o=Re “+85 T+ ray, (4) O= (ene Si) 7 + (s# ere +(RS tet Siew * TG +P E+ + QR), j= (or id +8) as +(Si+ +2P a z +(RoSt8 pel get eae ae eos cant e+e Pa +a i= (enG 4st) oe * (Sae+ Ra) ay * (Ba Seay * Tar meee 7) he a + 8igq tT ae TE tQG) +UA, Xe. &e. Differential Equations of the Second Order. 37 If aj, ag be the roots of O= Ra? +S8a+T, we shall have _ du y du Qe du du Tide.) aim ~ da"? dy Hence if the integrals of the equations O=dy+a,dz, O=dy + a,dzr be respectively ®,=const., w.=const., @, Or @, may be substituted at pleasure for u in (2). The equations which succeed (4) may be written dA dA DT are dA dA a Ad As v— We dy tet Ye &e. &e. The integral by Lagrange’s method of any one of these equa- tions, as (5), will be of the form A,=L.x(o) +M, where LL, M are functions of # and y; y is arbitrary; and o = const. is the integral of O=dy—adz. Hence if these values were substituted in (2), and we then put g(u) = a constant, as we may do, we should have the given equation (1) satisfied by an integral of the form z=F je, Y, x(w)?, where F is a definite, and y an arbitrary function; from which it would inevitably follow that the given equation is soluble by Monge’s method, whereas by hypothesis it is not so soluble. We must assume, therefore, the arbitrary function in each case to be zero; so that, in order to find A, A,, &c., we may take the equations . 38 Mr. R. Moon on the Solution of Linear Partial dA Oo= dg tb’ e . e e e e e (6) dA ; o= “Te teat e e ° ° e (7) dA O= Fe TB Aat Ye &e. &e. where du ay) aU du du ?) =i du du ; 2h +8 hi d?A d?A d?A dA div a ge dady t git Page eg, ee | Te he +e ue dae dy d*A, d?A, dA, dA, dA, . ae a dae ele ee ie ae dx dy &e. &e. (6) gives us pe Oe ae where ¢ is constant, it being understood that, if 8 contains y, the latter variable must be eliminated before the integration by means of the equation a @= const., and the constant so introduced must be eliminated after jatess gration by means of the same equation. Hence we shall have A xc foes, Ay =c,eS Bde — @fBe | deg . ry 6 S842, As = Coe S Pe eW fae dr : y,e/8%, &e. &e. It is clear, however, that the substitution of these values would give rise to a term in z =e SO. Soh(u) + cy P-"(u) + egh-*(u) + &e.}., =e SPA Ae (u) 5 Differential Equations of the Second Order. 39 so that, in effect, we may in the above values of A, A,, &c. put e=1, a oyese, = Se. =0; 2. e. we shall have fv [gal Pra, Ay= —eS Pa \ dar . ye SP%*, A,=—eV/ Baa dee yoelh™, &e. &e.; as to which it is to be observed that no constants are to be in- troduced in the integrations, all such having been accounted for. Take the case where R=1, and S and T are constant, and we get U=Y+A#, OY U=Y+4,2 5 the first of which values gives B= Pat? a, — If we take we shall have And the substitution of this value in (8) gives us h(h—1)a*—? + Pha*—1 + Ux" {= oes _ k+h(h—1) oes Fw a — Ag ‘ if we assume heap mae xv where & is constant ; “i —w" f de se hy, A Ue aa Also ede EF tad AS no h-3 pe ED. 41) (42) + P(A) 4 Uae}. A ay Gq] gr 3 Gla) th bat. @;—A\ h-—3 peg AMES) f+ (l- 1) weepnry, fA A, A= me 40 On Linear Partial Differential Equations of the Second Order. ie = where / is constant ; Soy = {k+h(h—1)} $k+(h—1)(h—2) —ih ener (a,—4)* 1.2 Similarly we shall arrive at se 23 (a, —4a)° &e. &e. 4 h(h—1t {k+ (h—1) (h—2) —Uh ... Sh (A —7 +2) (h—r +1) -—(r— (4 — 42)’ aoe plas bre a ae If hf is fractional or negative, we shall, on the particular as- sumptions above introduced, always have an integral of the assumed form, the number of terms being finite or infinite ac- cording to circumstances, though as to the practical value of the integral so obtained in the latter case I am not prepared to ex- press an opinion. | The condition to be satisfied in order that A, may vanish and that the expression for z may have a finite number of terms when h is not a positive integer, is, that we have O=k+ (h—r4+2)(A—r+1)—(r—-1), the only conditions limiting the quantities h, k,/,r being that they are all constant, and that r is, and f/ is not, a positive integer. When h/ is a positive integer and r=A, we shall have A, con- stant; whence it follows that upon this supposition the series will always terminate when U=O, The well-known equations Wen ed’ 2 nn) = —— 2 dx? dy? a4 P) are readily solvable by the foregoing method. | It remains to be remarked with respect to the first term of the series for z, that since (3) is of precisely the same form as (1), any value assigned to A must be different from avy derivable from the general expression for z—as, for instance, a solution obtained upon a particular hypothesis not necessarily implied by Ona Simple Method of Constructing high Electrical Resistance. 41 the terms of the problem submitted to us—for example, on the assumption that one of the partial differential coefficients p, q, 7, s, ¢ vanishes. 6 New Square, Lincoln’s Inn, June 20, 1870. VI. On a Simple Method of Constructing high Electrical Re- sistance. By Samurt HK. Puixuies, Jun.* A‘ present resistance-coils are mostly made with German- silver wire; and a set of coils equalling 10,000 B.A. units _ forms a box of convenient size. But in electrical research resist- ances of several million units are often useful; and to produce such with wire in the ordinary way would be both expensive and cumbrous. Latterly Mr. Hockin has used selenium for this purpose. Fine glass tubes with a platinum wire blown in at each end and filled with different fluids, according to the resistance required, have also been largely used; but these latter necessarily give very variable results, owing to polarization and electrolysis; and the former, I believe, are somewhat difficult to construct. Requiring a high resistance for some experiments, I made one as follows :—Upon a strip of vulcanite, 6 inches long by 1 inch _wide, I ruled several pencil lines with an ordinary H.B. pencil in such a manner as to produce a continuous line about ;%, of an inch wide and 4: inches long. At the extremities of the line I rubbed the pencil plentifully over a space as large as a six- penny piece, upon which | firmly screwed two binding-screws by means of “nuts” underneath, and, gently dusting off all su- perfluous plumbago, varnished the whole with several coats of pure shellac varnish. The above arrangement gave me a resistance of slightly over two million B.A. units. It was constructed three months ago, and up to the present time the resistance has remained very con- stant. I have tested it repeatedly with 100, 200, and 800 cells, and have always obtained the same result within very small limits. It is also beautifully steady with prolonged battery contact. Mr. G. Preece has kindly tested a resistance made in the above manner for me, and finds it very constant, only getting an alteration of about 0°5 per cent. for 5° F. I have mounted a vulcanite slab with twenty binding-screws, giving a wide range of varied resistances by combination or otherwise, and hope shortly to make some experiments with the view of determining the ratio of its alteration by difference of temperature. -* Communicated by the Author. [ 42] VII. Researches on the Electrical Discharge. By Professor von Brzotp*, [T the course of the further investigation on the connexion I have recently described} as existing between the mode of discharge and the character of the dust-figures thereby pro- duced, I strongly felt the necessity of producing the phenomena in question by a more simple apparatus than Ruhmkorff’s. The first experiments with charged Leyden jars, as well as with the ordinary electrical machine without condensing-arrange- ments, soon showed that with these means only simple figures (that is to say, discharges) could be obtained. The observation of the spark is sufficient to prove that the discharge which, with a good conducting circuit only inter- rupted by a break, is alternating, is changed into a simple one by inserting a test-platet; for while in the first case the spark is brilliantly luminous, it appears in the second only as a narrow purple line with a bright point towards the positive electrode. | In order, therefore, to obtain alternating discharges even when the test-plate was interposed, no way was left but the use of a suitable branch or return conductor. If this conductor (which goes to earth) is continuous (that is, nowhere interrupted by a break), it is to be expected that the discharge of the conductor through which the electricity is led to the plate will ensue directly after the charge,—that is, that in this conductor one or more alternations of electricity will take place. In experiments made with such return conductors, various entirely new and surprising facts were observed which seem suited to serve as starting-points for new inquiries. But, before I begin the description of these new facts, I must first mention a simple experiment, which indeed teaches nothing essentially new, but yet contributes materially to the under- standing of the following. If the otherwise insulated coating of the test-plate is placed in conducting communication with the source of electricity, while the needle which at other times serves as conductor is connected with the earth, a positive discharge upon the glass surface pro- duces a negative figure, and conversely. If the coating be perfectly insulated, while two conductors (A * Communicated by the Author, having been read before the Bavarian Royal Academy of Sciences, February 5, 1870. , _ T Phil. Mag. 8.4. vol. xxxix. p. 392. ~ By test-plate (Probeplatte) I shall in the sequel mean the plate, coated on one side, on which the figures are formed. Prof. von Bezold’s Researches on the Electrical Discharge. 43 and B) are placed upon the upper uncoated surface, one of which is connected with the source of electricity Q (fig. 1), and the other by a wire E with the earth, at each discharge a Fig. 1. positive and a negative fi- gure will be simultaneously formed. - These experiments teach x = that a positive (negative) ji- Zener gure is obtained when either positive (negative) electricity is added, or negative (positive) taken away. _ § 1. This being premised, the above-mentioned experiments shall now be described. One of the first was made according to the following scheme (fig. 2). From the positive conductor of ee ae ry Fig. 2. an electrieal machine a wire was led to one knob of a spark- micrometer F. From the other knob two wires conducted, one (H) directly to the earth, the other (D) to the conductor A. The lower coating of the plate was also connected with the earth by means of the wire H/. In my opinion, two kinds of results were by this means to be expected. For it was conceivable that either no figure at all would be formed upon the plate, and the whole of the electricity would be immediately conveyed to the earth by the good conducting-wire, or that at most a small part would reach the plate and then again pass back through E to the earth. I therefore expected either no figure at all, or a small positive compound figure—that is, a yellow star with a red spot. ~The result was nevertheless the exact opposite. A figure was formed ; it was not positive, however, but negative, a red irre- gular jagged ring with a yellow radiating centre. Hence the discharge had not only not divided at the two branches, but the electricity, flowing to the earth in the shortest way through KH, took with it electricity of the same kind from the branch A E’. Not only the very surprising nature of the experiment, but: 44: Prof. von Bezold’s Researches on the Electrical Discharge. also the circumstance that it was not always unequivocally suc- cessful (for the figures were at times scarcely perceptible) made it desirable to repeat the experiment with another source of electricity. The electrical machine was therefore replaced by the inductorium, one pole being connected with the spark-mi- crometer and the other with the earth. The knobs of the elec- trometer were gradually moved apart. As long as the striking-distances were small, figures were formed which were of the same kind as that of the electricity passing across the break ; that is, when the negative pole of the inductorium was connected with the micrometer, negative figures were formed, and vice verséd. But as the striking-distance be- came greater, the diameter of these figures diminished. While, for instance, in one series with a striking-distance of 1 mullim. negative figures of about 15 millims. diameter appeared, when the striking-distance was 10 millims. this diameter diminished to 2 millims. On continuing to increase the distance between the knobs, the figures ceased for a while, until when the striking- distance was more than 15 millims. they again occurred, and were decidedly positive in character. Hence there was here a complete transformation of pheno- mena. While with small striking-distances the path of the cur- rent is that represented in fig. 2 by the dotted arrows, with greater striking-distances another path appears, denoted by the perfect arrows. Working with positive electricity, positive figures are first obtained, which, when the distance is increased, continually diminish, then disappear for awhile, and are ultimately replaced by negative ones. The transformation first occurs in this case with greater striking-distances than is the case in working with negative electricity. These, as well as many similar differences in the phenomena, according to the kind of electricity used, doubtless owe their origin to the circumstance that equally intense discharges of the two electricities produce figures of entirely different sizes. Hence also it may arise that, so frequently, alternating discharges of a decidedly negative character* produce figures which at first sight might be taken for positive, while the converse never oc- curs. For if we imagine a negative and a positive discharge passed successively to the same position on the plate, the former must far exceed the latter in intensity if it be not concealed by traces of the latter. Yet though there are so many minute points to be discussed * By an alternating discharge of a positive character I mean one in which the algebraic sum of the quantities of electricity discharged is positive, and vice versa, Prof. von Bezold’s Researches on the Electrical Discharge. 45 in reference to this experiment, what has been communicated shows sufficiently that in electrical currents phenomena may occur similar to those observed in the motion of liquids and named suction- phenomena, practically applied, for instance, in Giffard’s injec- tor, or in the well-known inhalation-apparatus. § 2. These curious observations gave rise to further experi- ments on the division of discharge-currents. Here also alternating discharges gave more constant results than simple ones, and care was therefore always taken to procure a suitable return-current. The above experiments prove that a single wire cannot serve for this purpose; and therefore the secondary coil of a Ruhmkorff’s instrument was used (fig. 3). Fig. 3. When now the electrical machine was slowly worked, until a spark passed, the compound positive figures appeared on the plate in great regularity. - When the current was branched off by a short wire D, and the branch current also led to the plate by a conductor B, two per- fectly like figures appeared, as was to be expected. When, on the contrary, the branch wire had a length at all considerable (some- thing more than a yard), the figures exhibited a decided difference in magnitude; for as soun as the length of the wire exceeded this limit the figure at B was always greater than that at A, even when the branching commenced quite near the end of the conducting-wire (1 centim. above the plate). As the branch wire D was lengthened, the difference in size of the two figures be- came more striking, until, when D=6°4 millims. and F=4'0 millims. (F being the striking-distance), the figure at A was re- duced to a small star, and many times was not even formed. This experiment obviously shows that Ohm/’s laws hold for stationary currents but not for the electrical discharge, as indeed all theoretical investigations have hitherto shown; for while no electricity at all passes to the plate by the very short branch A, 46 Prof. von Bezold’s Researches on the Electrical Discharge. it takes, at any rate apparently, the path, of many hundred times that length, through the wire D. If the wire D be still more lengthened, the phenomenon at first remains, within tolerably wide limits, unchanged; and not until the length has nearly doubled does the figure at A become again larger, until with still more considerable lengths the difference in magnitude of the two figures again quite disappears. In this case it was immaterial whether a thick or a thin, a good or a bad conducting-wire was used, or whether it was tied in a tight knot or made to describe an arc of a circle. I have not yet worked with spirals. The phenomenon being so entirely novel, I thought it would be interesting to investigate the deportment of the wire D in various positions. Hence an alteration was made which is represented in fig. 4. The conductors A, B, C are placed upon the plate and are connected with each x : other by two wires, D and a Beate D’. If, now, the lengths are so chosen that at C as large, and at A, on the contrary, as small a figure as possible is formed, the figure at B is larger than that at A and smaller than that at C. But if the length of the wire is » more considerable, the sizes of thefigures AandC becomemorenearly equal, while B, with a suitable choice of the ratio D : D', becomes very small or even quite disappears. With a striking-distance of 4°3 miliims., and the lengths AF=50 centims., D=6°2 metres, D’'=8:1 metres, the figures at A and C were large, while at B. very small stars only appeared. If any one of the conductors be raised from the plate, the figures at the other conductors will not be in the least altered. This experiment teaches the new fact that the connexion of the conductor with a blind-ending wire is sufficient materially to alter the figure formed at the conductor, or to make it disap- pear. The experiment becomes most instructive when close to the conductor A a second spark-micrometer (jf, fig. 5) is in- troduced, one of whose knobs is connected with A, while the other leads to the wire D (fig. 5). If, then, the spark-micro- meter f be first of all adjusted for a great distance and this distance be gradually diminished, it will be seen how from the moment the spark passes at f the figure at A becomes different Prof. von Bezold’s Researches on the Electrical Discharge. 47 —yelatively disappears. But if we consider that with alterna- ting discharges the wire D is again immediately discharged, it Fig. 5. follows that in such a process electricity first passes into the extreme end of the wire D and is again immediately expelled— that, in short, motions take place which are perfectly comparable toa reflection. This consideration leads to an hypothesis on the peculiar changes in magnitude which the dust-figures undergo with the branchings described ; for if electrical waves are driven into a wire, and after reflection at its end return the same way, the progressing must interfere with the reflected waves and produce phenomena which are analogous to those observed with organ- pipes. The observations hitherto communicated exhibit this analogy in a high degree; and we may well venture to compare the places in which maximum and minimum figures appear with vibrating loops and nodes. The hypothesis that we have here to do with phenomena of interference acquires probability from the circumstance that the experiments only succeed satisfactorily with alternating dis- charges, while with simple discharges differences in magnitude of the various figures are observed, but not, by far, to the same extent. § 3. A slight modification was made of the above-described ex- periments, which formed another starting-point for new inves- tigations. If the end of the wire D (fig. 3) be again connected with the first conductor A as represented in fig. 6, with a suitable length of the wire, the figure can also be made to disappear. This experiment formed really the starting-point for all those I have previously mentioned ; yet I have deferred its description till now, because it is not suited to facilitate the comprehension of the above experiments. I thought at first I had met with an analogue of Savart’s interference-experiment for sound-waves, and supposed. the path of the current to be that represented by the dotted 48 Prof. von Bezold’s Researches on the Electrical Discharge. arrows. The experiments with the blind-ending wire, as well as the circumstance that the distance of the two branching-points Fig. 6. upon A exerted no decided influence, necessarily militated against this view. To remove all doubt as to this, I made several breaks in the wire, so as to form a succession of sparks. The knobs of this second micrometer were here approached to within a distance of from 0:01 to 0:03 millim.; for I thought that in the case in which the current rushes from both sides into the wire there must be a place where both sets of waves meet. When the mi- crometer is placed just at this point, the tension on both sides must simultaneously reach the same height, and there is there- fore no reason for the formation of a spark here, while one may be expected in all other positions. The spark indeed failed to appear when the micrometer was in- serted in the middle of the loop, and reappeared as soon as tt was moved by only a few decimeters on either side. It is thus proved that the path of the current is represented by the perfect arrows ; and, on the other hand, the small retardation which the electrical discharge-current experiences by traversing a wire of a few deci- metres 1s made visible. I first of all sought the conditions under which this experi- ment on retardation succeeds most strikingly. I found it best Fig. 7. il to use directly the discharge of a Ruhmkorff’s apparatus, on the plan represented in fig. 7. The inducing current was produced i i Prof. von Bezold’s Researches on the Electrical Discharge. 49 oy a Grove’s element, and the distance in the spark-micrometer F was made =2 millims., as neither larger nor smaller distances gave such good results, Under these circumstances it was sufficient, in order to produce a spark, if one wire D was even only 1 decimeter longer than the other. When, on the contrary, they were of the same length, a spark never appeared. Yet it can be instantaneously evoked if, by touching one of the wires with the knob of a Leyden jar, the symmetry of the two current-paths is disturbed. In these experiments also the material and thickness of the wire exerted not the smallest influence. Whether I used a sil- vered copper wire of 0:06 millim. diameter, or an iron wire of 0:23, or a copper wire of 0:8 millim. diameter, the spark never appeared when both wires were of the same length. Hence the velocity of the propagation of electricity is the same for all stretched* wires. _ Yet in the form above described, the experiment is not very striking, as we can only work with very small distances in the accessory micrometer f. I endeavoured therefore to alter it in such a manner that it would be visible to a whole audience. Experiments with small Geissler’s tubes have led to no decisive result. On the contrary, with lengths of some metres at least, the retardation may be very beautifully shown in the following manner :— Ifa discharge (negative) (best of all, ofa Ruhmkorff’s appara- tus) be divided, as above, just behind the spark-micrometer into two branches, and if one of them be connected with the coating of the perfectly insulated test-plate, while the other is led by the conductor A to the upper uncoated surface, a positive, a negative, or no figure at all can be made to appear, according as the upper branch is larger, smaller, or as long as the lower one. Indeed the experiments must succeed one another in a definite order if they are intended to support the opinion that they owe their origin to differences in time. For if we remember that it is immaterial whether positive electricity be imparted to the plate * Spirally-coiled wires will, it may be presumed, give a different result. Phil, Mag. 8, 4, Vol. 40. No, 264, July 1870, E 50 Prof. von Bezold’s Researches on the Hlectrical Discharge. or negative be extracted, it will be understood that a positive charge produces a positive figure when the electricity reaches the poimt of the conductor before it reaches the coating—that is, when D, isshorter than D,. Tf, on the other hand, the dis- charge reaches the coating first, the conductor will be traversed by the induced electricity in the opposite direction ; and hence a negative figure must be formed upon the glass surface when D, is shorter than D,. In the course of the motion this in- duction discharge must meet, in the wire D,, the electricity coming direct from F, and thereby a compound character will be imparted to the figure. Between these two arrangements with entirely opposite eaules there must obviously be some in which no figures are formed, as there is no reason why one should be formed in preference to the other. This must be the case when the electricities from both sides arrive simultaneously—that 1s, when D, and D, are of the same length*, The experiments completely fulfilled these theoretical antici- pations. With cither kind of electricity, figures of both kinds are obtained when the lengths of the wires are rightly chosen. To many a one who makes the experiment under not quite favourable circumstances this statement may appear incorrect, apart from the case in which, owing to perfect equality of the two branches, no figures at all are formed ; for it may occur that the whole of the figures seem at first sight positive, whatever be the circumstances and whatever be the kind of electricity worked with. The cause lies simply in the circumstance that the compound negative figures belong in this case to that group which have already a strongly positive character, and even, at first, can scarcely be recognized as negative; but the considerable dif- ference in magnitude which occurs after a change of poles is sufficient at once to remove any doubt as to the true nature of the figures, and to prove the agreement of the expemments with theoretical anticipations. To sum up, the following results were obtained :-— 1. When an electrical discharge, after traversing a spark-interval, is offered two paths to the earth (a short one, and a long one in- terrupted by a test-plate), with small striking-distances the discharge 2s divided. With greater distances the electricity takes only the shorter path, and even carries with it electricity of the same kind jrom the other branch. 2. Lf electrical waves be sent into a wire insulated at the end, * There may probably in this case be a small difference in favour of the upper wire, since the electricity coming from below has to spread over ‘ thé entire coating. On the Interchangeability of Heat and Mechanical Action. 51 they will be reflected at that end. The phenomena which accom- pany this process in alternating discharges appear to owe their ort- gin to the interference of the entering and reflected waves. do. An electrical discharge travels with equal rapidity in wires of equal length, without reference to the materials of which these wires are made. VIIi. On the Interchangeability of Heat and Mechanical Action. By the Rev. J. M. Hearu*. Hh doctrine of the equivalence of heat and mechanical action, and that of the conservation of energy, are the expression of one and the same thing to those who believe that heat is motion, and therefore itself a fori of force or energy. They both alike express this-—-that when the action of force, continued through a space, results in motion or heat, or vice versd, there has been a true conversion, a change of one form into another, and that when no motion results there is no con- version. The selfsame expression \ fds expresses indifferently the pressure accumulated at any point in a fluid mass by the action of all the particles situated upon a given line upon it, or the accumulation of the same force upon a single particle which should move through the line for which the integral is taken. But the resuits are not identical. The forces which accelerated the moving particle have done their work and are extinguished ; they now exist only in the form of the motion they have created. But the corresponding fluid pressures have done no work (it the creation of motion is work), and have never become any thing else than the pressures they were at first. If we bear this in mind, the great problem of the science of thermodynamics (how much out of a given gross amount of force (P) applied as a load to the piston of a gas-chamber will generate its mechanical equivalent in heat or motion) becomes one of extreme simplicity. The force P divides itself into two parts, p = the pressure of the gas below employed in neutrali- zing the resistance opposed by the gas to motion, and P—p the remainder, which is wholly effective in producing motion. The separate functions which these two portions of the force respec- tively discharge are given by the two equations j (R—p)dv= 4>mv?+C and \(p p—p)dv= const., where v is the volume of the gas. And it appears very obvious that the first of these is the answer to the question, How much of the whole force P is converted into motion or heat? * Communicated by the Author. 52 On the Interchangeability of Heat and Mechanical Action. But this conclusion is now generally ignored, or rather set aside, in favour of a very different one, founded, as I am forced to think, upon a misconception of the very important elementary question in kinetics, How is a weight lifted up? The quantity of heat gained or lost, we are told, in the supposed case depends upon the work expended upon its generation, or upon that done by its destruction. In the first case, if the piston descends through the space dv, the work expended is | Pdv or Pov. In the second case, if the gas drives the piston up before it, the v+du ; work done is pdv. In which it may be observed, en pas- e/v sant, that the constancy of P affects the form of the result very materially when it descends and causes condensation, but has no influence upon it when it is raised. But the far more serious objection to the doctrine is, that weight raised or resistance over- come is precisely that kind of work done by a force in which no conversion into heat or motion takes place at all; and it excludes the only case in which such conversion does take place, which, as we have shown, is that in which force acting upon matter free to move, itself passes into motion. From the second of the above equations, af (p—p)dv=c, we see that so long as the forces above and below the piston remain equal to each other no vis viva is generated. The piston may rise or it may descend, but the motion will not be due to either of the antagonistic forces, whose function it is to reduce each other to nullity. The office of the elasticity of gas in raising a superincumbent weight is simply and exclusively that of giving it statical support at every point of the rise. The force P—p generates acceleration, the forces p—p make unaccelerated rise or fall possible: and it is the singular infelicity of the modern doctrine that heat is created by the expenditure of work, that the definition of the work ex- pended does not include the case in which alone motion or heat is created, and does include only the cases where no motion or heat is created. I do not think I can more distinctly contradict every part of the received doctrine on this subject than by stating simply what appears to me to be unquestionable, as truth—that no force employed in equilibrating resistances ever becomes converted into heat, and that no heat is ever generated except by forces acting on bodies verging on the state of motion, and offering no resistance to the action of the forces. Milland, June 21, 1870. LN OB wi IX. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from vo}. xxxix. p. 462. ] March 10, 1870.—Warren De La Ruz, Esq., Vice-President, in the Chair. TINHE following communication was read :— “* Researches on Solar Physics.—No. II. The Positions and Areas of the Spots observed at Kew during the years 1864-66, also the Spotted Area of the Sun’s visible disk from the commencement of 1832 up to May 1868.” By Warren De La Rue, Hsq., Ph.D., F.R.S., F.R.A.S., Balfour Stewart, Esq., LL.D., F.R.S., F.R.A.S., &c., and Benjamin Loewy, Esq., F.R.A.S. The paper commences with a continuation for the years 1864-66 of Tables II. and III. of a previous paper by the same authors; it then proceeds to a discussion of the value of the pictures of the sun made by Hofrath Schwabe, which had been placed at the dis- posal of the authors; and the result is that these pictures, when compared with simultaneous pictures taken by Carrington and by the Kew heliograph, are found to be of great trustworthiness. From 1832 to 1854 the pictures discussed are those of Schwabe, who was the only observer between these dates; then follows the series taken by Carrington, and lastly the Kew series, which began in 1862. A list is given of the values of the sun’s spotted area for every fort- night, from the beginning of 1832 up to May 1868, and also a list of three-monthly values of the same, each three-monthly value being the mean of the three fortnightly values which precede and of the three which follow it. These three-monthly values are also given for every fortnight. , A plate is appended to the paper, in which a curve is laid down representing the progress of solar disturbance as derived from the three-monthly values; and another curve is derived from this by a simple process of equalization, representing the progress of the ten- yearly period. The values of the latter curve, corresponding to every fortnight, are also tabulated. From this Table are derived the follow- ing epochs of maxima and minima of the longer period :— Minimum Noy. 28, 1833. PERATIRUTD o, 6 is. ois sss Dec. 21, 1836. Minimum Sept. 21, 1843. a THAWLs 6 ube) zo nds Nov. 14, 1847. Minimum April 21, 1856. “E20 Gi i rs Sept. 7, 1859, Minimum Feb. 14, 1867. This exhibits a variability in the length of the whole period. Thus we have between Ist and 2nd minimum...... 9°81 years, 2nd and 3rd do. Ree 2 28 ore adeAtindote siti) vis/ee.s 10°81 oP ) 33 Mean of all the periods........ 11°07 years. 54 Royal Society :—Myr. H. T. Brown on the Estimation Another fact previously noted by Sir J. Herschel is brought to light—namely, that the time between a minimum and the next maxi- mum is less than that from the maximum to the next minimum. Thus the times from the mmimum to the maximum are for the three periods 3:06, 4:14, and 3°37, while those from the maximum to the minimum are 6°75, 8°44, and 7°44 years. In all the three periods there are times of secondary maxima after the first maximum ; and in order to exhibit this peculiarity, statistics are given of the light-curve of R Sagitte and of § Lyre, two variable stars which present peculiarities similar to the sun. Finally, the results are tested to see whether they exhibit any trace of planetary influence; and fer this purpose the conjunctions of Jupiter and Venus, of Venus and Mercury, of Jupiter and Mer- cury, as well as the varying distances of Mercury alone in its ellip- tical orbit, have been made use of; and the united effect is exhibited in the following Table, the unit of spotted area being one-millionth of the sun’s visible hemisphere :— Excess or Deficiency. A. FS Angular Jupiter and Venus and Mercury alone Mercury and separation, Venus. Mercury. (Perihelion=0). Jupiter. 0 to 30 + 881 +1675 — 380 — 227 30 to 60 — 60 — 139 —1188 —317 60 to 90 — 452 — 1665 — 1287 —994 90 to 120 — 5/9 — 2355 — 1262 —714 120 to 150 — 709 —2318 — 1208 —508 150 to 180 — 759 — 1604 —1027 —49] 180 to 210 — 893 — 481 — 519 —416 210 to 240 — foe + 547 + 430 —189 240 to 270 — 263 + 431 +1082 — 25 270 to 500 + .70 + 228 +1436 +154 300 to 330 480 +1318 +1282 +164 330 to 0 +1134 + 2283 + 586 — 45 March 17.—Captain Richards, R.N., Vice-President, in the Chair. The following communication was read :— “On the Estimation of Ammonia in Atmospheric Air.” By Horace T. Brown, Esq. In the attempts that have been hitherto made to estimate the ammonia present in atmospheric air, the results arrived at by the various experimenters have differed so widely that it is still a matter of uncertainty what the quantity really is. That it is a very small amount all agree, but the extreme results on record vary as much as from 13:5 to ‘01 part of carbonate of ammonium per 100,000 of air. It may therefore not be without interest to give an account of a simple method affording very concordant and, I believe, accurate results, at the same time being easy of performance and requiring but little time for an experiment, The apparatus used consists cf two glass tubes, each of about 1 of Ammonia in Atmospherte Arr. 55 metre in length and 12 millims. bore. These are connected air-tight by means of a smaller glass tube, and inclined at an angle of 5° or 6° with the horizon. Into each of the larger tubes are introduced 100 cub. centims. of a mixture of perfectly pure water and two drops of dilute sulphuric acid (sp. gr. 1°18). Through this acidulated water a measured quantity of the air under examination is slowly drawn, in small bubbles, by means of an aspirator.. No porous substance must be used to filter the air, for reasons to be stated hereafter.. The air is conducted into the absorption liquid through a small piece of quill tubing drawn out to a small aperture at the end immersed. This tube must be kept quite dry throughout the experiment. Great care must be taken to cleanse perfectly every part of the apparatus with water free from ammonia, -and the caontchoue plugs, or corks, used must be boiled for a short time in a dilute solution of caustic soda. The stream of air is so regulated as to allow about 1 litre to pass through the apparatus in an hour. By directing the point of the delivery-tube laterally, each bubble has imparted to it on rising an oscillatory movement which facilitates complete absorption of the ammonia. When from 10 to 20 litres of air have passed, the liquid is emptied from the tubes into upright glass cylinders, an excess of a perfectly pure solution of potash added, and then 3 cub. centims. of a Nessler solution. The standard of comparison is made in the ordinary way, only using acidulated in place of pure water, and neutralizing with potash after adding the standard solution of ammonium salt. Beyond somewhat retarding the point of maximum coloration, a little potas- sium sulphate does not interfere with the delicacy of Nessler’s reaction. If the experiment has been conducted with proper care, at least 4 of the total ammonia ought to be found in the first tube. Four or five litres of air are generally quite sufficient to give a decided reaction, but it is better to use not less than 10 litres, as before mentioned*. Very many experiments have been made by this method, both on air from the town of Burton-on-Trent, and that of the adjoining country. The air from the town, as might be expected, varies some- what in composition; much more so than that taken from the open country, as may be seen from the following Tables, in which are given some of the numerous results obtained. The ammonia is calculated in every case as carbonate ( (NH,), CO,) ; for although nitric acid is sometimes found in air, yet its presence must be looked upon as accidental. In the immediate vicinity of towns some of the ammonia must also be in the form of sulphate, sulphite, or ammonium chloride. * When the air to be examined is highly charged with ammonia, as that from stables &c., a perfectly dry bottle of 3 or 4 litres capacity should be carefully filled with a pair of bellows, 100 cub. centims. of acidulated water introduced, and, after closing securely, the whole well agitated at intervals for three or four hours. The liquid is then poured out, and the NH, estimated by the Nessler solution as usual, 56 Royal Society :—Messrs. Roscoe and Thorpe on the (1) Air taken from town, (Taken at a height of 2 metres from ground, ) (NH,), CO, as grammes (NH), CO, in parts Date of Experiment. per 100,000 litres of air by weight per at 0° C. and 760 mm. barom. 100,000 of air. 1869. September 30.4 soc. si 161204) cae. a 8732 October 4) Wheiiiowas we "62107 99) estas "4801 ry) © AE: wh: fe O20) (te Bethea "4059 BG eral 1621.1 Akl sie ‘ °4801 November Dir ates L30729: >is Basten °8293 “a 28 Part, PRs W000) awa ae °8503 (2) dir from country. (Taken at a height of 2 metres.) (NH,), CO, as grammes (NH,), CO, in parts Date of Experiment. per 109, 000 litres of air per 100,000 of at 0° C. and 760 mm. barom. air. 1869. December 6 . sania as Ua ss sien 3890 ” Oo a he with oh aaah e+ *7826 venie e "6085 9 D ie stdin tas Stee ioe 6601 oie ae "9102 L de secre ee icons 3s - OOGO ac eee “O121 1870. February 12 . siiad dake ad EO. TT sea : “9904 The direction of the wind does not seem to have any influence on the ammonia found ; immediately after heavy rain, however, the quantity falls somewhat below the average, but the air is again re- stored to its normal condition after a lapse of two or three hours. Attempts were made to make the method more delicate still by ab- sorbing the ammonia in pure water and then distilling, but the nitro- genous organic matter suspended in the air was found to interfere with the results. When the air is passed through cotton-wool before entering the absorption-tubes, it is found to be entirely deprived of its ammonia by the filter. This is also the case with air artificially charged with ainmonia to a large extent. This absorption is not due to the pre- sence of hygroscopic moisture, since cotton-wool, when absolutely dry, is capable of taking up 115 ¢2mes its own bulk of dry ammonia (confined over mereury) at 10°°5 C. and 755°7 millims. barom., the gas being again slowly evolved when the ia is left in contact with the air at 100°C. All other porous substances that were tried for filtermg agents were found to possess this property more or less; even freshly ignited pumice-stone is not entirely without absorptive effect upon the gas. March 31.—-Lieut.-General Sir Edward Sabine, K.C.B., President, in the Chair. The following communication was read :— “On the Relation between the Sun’s Altitude and the Chemical Intensity of Total Daylight in a Cloudless Sky.” By Henry E. Roscoe, F.R.S., and 7. E. Thorpe, Ph.D. In this communication the authors give the results of a series of Relation between the Sun’s Altitude and Chemical Intensity. 57 determinations of the chemical intensity of total daylight made in the autumn of i867 on the flat tableland on the southern side of the Tagus, about 83 miles to the south-east of Lisbon, under a cloud- less sky, with the object of ascertaining the relation existing between the solar altitude and the chemical intensity. The method of measurement adopted was that described in a previous communi- cation to the Society*, founded upon the exact estimation of the tint which standard sensitive paper assumes when exposed for a given time to the action of daylight. The experiments were made as fol- lows :— 1. The chemical action of total daylight was observed in the ordinary manner. . 2. The chemical action of the diffused daylight was then observed by throwing on to the exposed paper the shadow of a small blackened brass ball, placed at such a distance that its apparent diameter, seen from the position of the paper, was slightly larger than that of the sun’s disk. 3. Observation No. 1 was repeated. 4 Observation No. 2 was repeated. The means of observations 1 and 3 and of 2 and 4 were then taken. The sun’s altitude was determined by a sextant and artificial horizon, immediately before and immediately after the observations of che- mical intensity, the altitude at the time of observation being ascer- tained by interpolation. It was first shown that an accidental variation in the position of the brass ball within limits of distance from the paper, varying from 140 millims. to 230 millims., was without any appreciable effect on the results. One of the 134 sets of observations was made as nearly as possible every hour, and they thus naturally fall into seven groups, viz. :— (1) Six hours from noon, (2) five hours from noon, (3) four hours from noon, (4) three hours from noon, (5) two hours from noon, (6) one hour from noon, (7) noon. Each of the first six of these groups contains two separate sets of observations,—(1) those made before noon, (2) those made after noon. It has already been pointed out+, from experiments made at Kew, that the mean chemical intensity of total daylight for hours equidistant from noon is the same. The results of the present series of experiments prove that this conclusion holds good generally ; and a Table is given showing the close approximation of the numbers obtained at hours equidistant from noon. Curves are given showing the daily march of chemical intensity at Lisbon in August, compared with that at Kew for the preceding August, and at Pard for the preceding April. The value of the mean chemical intensity at Kew is represented by the number 94:5, that at Lisbon by 110, and that at Pard by 313°3, light of the in- tensity 1 acting for 24 hours being taken as 1000. * Roscoe, Bakerian Lecture, 1865, [Phil. Mag. S. 4. vol. xxix, p. 233. | ¥ Phil. Trans. 1867, p. 558. 58 Royal Society :— ‘The following Table gives the results of the observations arranged according to the sun’s ailitude. Chemical Intensity. No. of observations. Mean altitude. Sun. Sky. Total. ieee ss ee 9 51 0:000 0°038 0:038 ere oe ae 19 4] 0-023 0:068 0°085 oe ee wee 31 14 0°052 0:100 0°152 in at te aie 42 13 0:100 O-115 0°215 SOR Sy Gael 03 09 0-136 0°126 0:262 ee eee cc. 61 08 0°195 0°132 0°327 1 Ge ii ang A Ae 64 14 0-221 0°138 0°359 Curves are given showing the relation between the direct sunlight (column 3) and diffuse daylight (column 4) in terms of the altitude. The curve of direct sunlight cuts the base line at 16°, showing that the conclusion formerly arrived at by one of the authors is correct, and that at altitudes below 10° the direct sunlight.is robbed of almost all its chemically active rays. The relation between the total chemical intensity and the solar altitude is shown to be represented graphically by a straight line for altitudes above 10°, the position of the experi- mentally determined points lying closely on to the straight line. _ A similar relation has already* been shown to exist (by a far less complete series of experiments than the present) for Kew, Heidel- berg, and Para; so that although the chemical intensity for the same altitude at different places and at different times of the year varies according to the varying transparency of the atmosphere, yet the relation at the same place between altitude and intensity is always represented by a straight line. This variation in the direction of the straight line is due to the opalescence of the atmosphere; and the authors show that, for equal altitudes, the higher intensity is always found where the mean temperature of the air is greater, asin summer, when observations at the same place at different seasons are compared, or as the equator is approached, when the actions at different places are examined. The differences in the observed actions for equal altitudes, which may amount to more than 100 per cent. at different places, and to nearly as much at the same place at different times of the year, serve as exact measurements of the transparency of the atmosphere. The authors conclude by calling attention to the close agreement between the curve of daily intensity obtained by the above-mentioned method at Lisbon, and that calculated for Naples by a totally different method. April 7.—Dr. William Allen Miller, Treasurer and Vice- President, in the Chair. _ The following communications were read :— “On Supra- annual Cycles of Temperature in the Earth’s Surface- crust.” By Professor C. Piazzi Smyth, F.R.S. The author presents and discusses the completely reduced obser- * Phil. Trans, 1867, p. 555. The Rev. Samuel Haughton on the Granites of Scotland. 59 vations, from 1837 to 1869 inclusive, of the four great earth-ther- mometers sunk into the rock of the Calton Hill, at the Royal Ob- servatory, Hdinburgh, by the late Principal Forbes, pursuant to a vote by the British Association for the Advancement of Science. Leaving on one side the several natural-philosophy data which have been investigated from smaller portions of the same series of observations both by Principal Forbes and Sir ‘William Thomson, the author applies himself solely to trace the existence of other cycles than the ordinary annual one, in the rise and fall of the dif- ferent thermometers. Of such cycles, and of more than one year’s duration, he considers that he has discovered three; and of these the most marked has a period of 11:1 years, or practically the same as Schwabe’s numbers for new groups of solar spots. Several numerical circumstances, however, which the author details, show that the sun-spots cannot be the actual cause of the observed waves of terrestrial temperature, and he suggests what may be, concluding with two examples of the practical use to which a knowledge of the temperature cycles as ob- served may at once be turned, no matter to what cosmical origin their existence may be owing. “On the Constituent Minerals of the Granites of Scotland, as compared with those of Donegal.” By the Rev. Samuel Haughton, F.R.S., M.D. Dubl., D.C.L. Oxon. | During the past summer (1869) I completed my investigation of the constituent minerals of the Scotch Granites, and secured spe- cimens, from the analysis of which I obtained the following results :— I. Orthoclase. No, E. No. 2. No. 3. No. 4. Ge 65°40 64°44 64°48 64°48 PUI... . sy 19°04 18°64 20°00 20:00 Peroxide of iron.... trace. 0°80 none. none. emer Or22 0°66 1:01 0°78 Digemesia .... 0... trace. trace. trace. none. i i raciran a05 2°73 E72 DAS oo ae ee 11°26 iy Ie 12:81 12°10 oo 0°20 0°80 0°64 0°08 99°75 100°22 100°66 99°63 No. 1. Stirling Hill, Peterhead. Occurs in an eruptive Granite, in veins, in well-developed reddish-pink opaque crystals, encrusted with erystals of Albite. No.2. Rubislaw, Aberdeen. Large beautiful reddish-pink opaque erystals, in veins, associated with white Mica. The Granite of Rubislaw is of metamorphic origin, and different in character from the eruptive Granite of Peterhead. No Albite has been found in it. No. 3. Peterculter, Aberdeen. In metamorphic Granite ; white, translucent, large crystals. | 60 Royal Society :— No. 4. Callernish, extreme west of Lewis. In metamorphic Gra- nite ; in large grey crystals, with a slight shade of pink, translucent. The oxygen ratio of these felspars is as follows :— No: 1. No. 2. No. 3. No. 4. poh {ols ae a 33°956 33°456 Ba 4/5 aoAs/ Alumina&c. .. 8°898 8°950 9°348 9:348 Tame ys. ses 0°061 0°187 0:286 0:221 OUR. ercrere core 0°929 0°699 0°440 0'561 Potash... 3... 1:908 2°059 2 TL sb 2°051 45°752 45°351 45°723 45°658 No, Ic No. 2. No.3: No. 4. SHIMLA Gene wv aaeae Less 11°35 Lisa 11°82 Peroxides...... 3°06 3°04 3°22 3°30 Protoxides .... 1°00 1:00 1:00 1:00 The Granites of central and western Scotland are metamorphic rocks, like those of Donegal and Norway, with which they are geo- logically identical; and truly eruptive Granite occurs at only a few localities, as, for example, near Peterhead. The second felspar associated with Orthoclase in the Metamorphic Granites is Oligoclase, asin Donegal; while the second felspar asso- ciated with Orthoclase in the eruptive Granites is Albite, as in Mourne, Leinster, and Cornwall. The fact thus indicated by the Scotch Granites is completely in accordance with the mode of occurrence of Oligoclase and Albite in the Irish Granites. II. Oligoclase. No. 1. No. 2. Silica. sais CObiwa alas ee 62°00 61°88 Px nur nial hss oie na teas |: roe 23°20 24:80 Magnesia ..... Leet cee OGRE tren —— trace. aie 0's jaye ds SOMA ee We 4°71 4:93 Side rae ben ce oem 920 $12 ecasliger a ites etic’. ott cs see 0°43 0:98 99°54 100°71 No. 1. This Oligoclase occurs in the Granite of Craigie-Buckler, near Aberdeen; it is white and opaque, and so much resembles Cleavelandite in appearance as to have been mistaken for that variety of Albite; its analysis proves it to be Oligoclase. The crystals do not exhibit striation. No. 2. From the Granite of Rhiconich, in the west of Sutherland- shire; it is greyish white, semitranslucent, in large striated crystals, and resembles the Oligoclase of Ytterby, in Sweden. The Rev. Samuel Haughton on the Granites of Scotland. The oxygen ratios of the Oligoclase are as follow :— No. 1 ee Ne oo Lor Alumina , merited igo te ee eS Se 1:339 “opal lea saa hapa 2°360 weet ee! Oe 0:072 46°805 Hence we obtain :— No. 1 Ried eek ts Aa ENE aa 8°54 Cie CS ee a em 2°88 PPOHOMINES, 5c nh esaseis fo OO These oxygen ratios prove the felspars to be Oligoclase. III. Albdite. urea a eee he ri, weaves 68°00 Acberenman 9 Oe OP TS QOHOG apres 22 PE BOT, PAS VSG tA SULwOQESH ini deavestan so) OSE AL -. -trace: RU remieee Casita! daeare Lc sie Fae 10°88 LEOUE SLA Gene nee One een 0°68 99°91 61 This Albite occurs at Stirling Hill, near Peterhead, in eruptive Granite, and is found associated with red Orthoclase in veins; it encrusts the large crystals of Orthcclase, and is semitranslucent, and is generally stained on the surface by peroxide of iron. Oxygen Ratios. ME ee I UO coc 5. sess MI hae os 5 we ves eA css a: ie Lime .. 0°099 Es as 2°790 SL Sasi 0-114 This mineral is cvidently a typical Albite. There are two kinds of Mica found in the Scotch Granites, and both Micas resemble very closely the corresponding minerals of the Donegal Granites. 62 ~ Royal Society :— IV. White Mica. Silica . sag) pie. 44°40 Fluosilicon (Si F ) Se Alumina ..... at 37°36 Peraxade‘obiton.. 0c S ses 2°04 Me ae ati ctw otis teen tle Oe 0°78 MISS CSIS wens. ys oes 0 + Bias see 0°57 Oe Mares ic's 1d d where serene ‘esa | OM em Potash Fee aipiaues< ser oi aie! oe 9°87 Protoxide of manganese a OA NV AGI Rate Hemi se w) Steels os Uoaiead 1°84 98°19 The specimen of Mica here analyzed came from veins in the Granite quarry of Rubislaw, near Aberdeen, and occurs in large plates, associated with red Orthoclase. It was carefully examined for lithia, but no trace of this alkali could be found in it. The angles of the rhombic plates were 60° and 120° exactly, and the angle between its optic axes was found to be 72° 30!. The black Mica in large crystals is very rare, but it seems abun- dantly disseminated in minute scales through most of the Scotch Granites. The following analysis was made on specimens found near Aberdeen by Prof. Nicol, and kindly forwarded to me by him, for the purposes of this paper :— V. Black Mica. TUT cs uO = 69°() 14:6 13°8 SVC i weesere athe ae 9 8) 10°86 10°86 O, eH ge ROE aR = 64°0 13°56 — 16H, O hat ee at = 288:°0 60°97 60°44 A72°3 oo oe The sodium in this and in the following compounds was separated from the vanadium by precipitating the vanadic acid as the perfectly insoluble basic lead salt hereafter described. This was dried at 100° and weighed, then dissolved in nitric acid and decomposed by sul- phuric acid, and the solution of V, O, in excess of this acid gave on evaporation a finely crystalline mass. The filtrate from the lead pre- cipitate freed from lead yielded on evaporation sodium sulphate. Full — analytical details of this method, as well as of the other by precipi- ~ tation as the insoluble ammonium metavanadate, are given in the memoir. By frequent crystallizations the trisodium vanadate is slowly decomposed into the tetrasodium salt, caustic soda being formed. This singular reaction was most carefully examined and the amount of sodium hydroxide liberated determined volumetrically. 2. Tetrasodium Vanadate, Na, V,O,+ 18H, O.—This salt crystal- lizes in beautiful six-sided tables ; it is easily soluble in water, inso- - luble in aleohol, and is precipitated by the latter liquid from aqueous solution in white scales of a silky lustre. As long as the salt contains free alkali or tribasic salt, it forms, on precipitation with alcohol, oily drops which solidify after some time. The tetrasodium vanadate is always formed by the first fusion of vanadic acid with excess of car- bonate of soda, and can be easily prepared in the pure state by re- crystallization. Found (mean of many Calculated. determinations). Na, te Bae = 92:0 14°58 14°61 dA EE == 102°6 16°27 15°97 Oia a ae =' 112°0 17°27 os 18H, O = 324:0 51°38 51°80 630°6 99°99 The salt loses 17 molecules of water at 100°. The corresponding Calcium and Barium Vanadates, Ca, V, O,, and Ba, V, O,, are white precipitates obtained by adding the chlo- rides to a solution of tetrasodium vanadate. If calcium chloride be added to a solution of the trisodium salt, dicalcium vanadate is pre- cipitated, the solution becoming strongly alkaline from formation of calcium hydroxide and absorbing carbonic acid from the air. Com- plete analysis showed that the calcium salt contains 2} molecules of water of crystallization, whilst the barium salt is anhydrous. Lead Vanadates. 1. Tribasie or Ortho-Lead Vanadate, Pb, 2(VO,).—Obtained as Prof. Roscoe on Vanadium. 67 a light yellow insoluble powder on precipitating the tribasic sodium salt with a soluble lead salt ; it yielded on analysis 11°75 per cent. of vanadium, the calculated quantity being 12°04 per cent. 2. Vanadinite, the Double Orthovanadate and Chloride of Lead, 3Pb, VO,+Pb Cl,, can be artificially prepared by fusing for a few hours a mixture of vanadic acid, oxide of lead, and chloride of lead, in the above proportions, together with an excess of sodium chloride. After cooling, a greyish crystalline mass is left, containing cavities filled with long crystals having the same colour as the mass, which -under the microscope could be distinguished as six-sided prisms. The crystalline powder is then boiled with water until no further traces of soluble chlorides are extracted. The following analysis shows that this substance has the same composition as the vanadinites from Zimapan and Windischkappel, analyzed by Berzelius and Rammelsberg* :— Natural vanadinite. Calculated. Zimapan, Windischkappel, Artificial 3 (Pb, VO4) Pb Cl,. Berzelius. Rammelsberg. — vanadinite. | 73°08 70°4 71°20 71:96 Vanadium.... 10°86 — 9°77 EL‘ bs Chlorine .... 2°50 2°54 2:23 2-3] Orysen:.. <5: 13°55 —= —-- —— The specific gravity of the artificial vanadinite at 12° C. is 6°707, that of the natural being 6°886. 3. Basie Di-Lead Vanadate, 2(Pb, V,O,)+ Pb O.—This salt is precipitated as a pale yellow powder when acetate of lead is added to a solution of disodium vanadate, the liquid acquiring an acid reac- tion. It is completely insoluble in water and in dilute acetic acid, but dissolves readily in nitric acid. Calculated. Mean found. Pb, .- =. 10385°0 69:92 70°18 V, ae = 200° 2 13°86 b°3 O =, 2400 16°22 ——. 1480°2 Silver Vanadates. 1. The Ortho-Silver Vanadate, Ag, VO,, is obtained as an orange- coloured precipitate by mixing a freshly prepared solution of the tri- sodium salt with a solution of silver nitrate, in which every trace of free acid has been neutralized; unless these precautions are at- tended to, the precipitate consists of a mixture of the ortho- and pyro-salt. The trisilver vanadate is insoluble in water, but readily dissolves in ammonia and nitric acid. Analysis gave the following results :— I ete * Pyromorphite and apatite have already been artificially prepared by Deville and Caron, and also by Debray, whilst mimetesite has been obtained artificially by Lechartier. F2 68 Geological Society :— Calculated. Found (mean). Ag, PAOR ca = 324°0 73°75 73°83 Mee ane: = Oto 11°67 11°76 EP ps: = 64:0 14°58 — 439°3 100-00 2. The Tetrabasice Silver Vanadate, Ag, P,O,, is prepared by mixing a solution of the corresponding sodium salt with a neutral solution of nitrate of silver. It falls as a yellow dense crystalline precipitate, resembling in colour the ordinary phosphate of silver. On dissolving the salt in nitric acid, the silver is precipitated as chlo- ride, and the vanadium determined as V, O.. Analysis gave :— Calculated. Found. Ag, oe eaenees = 4352 66°81 66°45 7. baste adie = 10256 15°87 15°97 Se ee = 112) 17°32 ——— ‘ ews 646°6 100:00 The reactions of the tri- and tetrabasic vanadates of the other metals are then described. The author has to thank Messrs. Oelhofer and Finkelstein for the valuable assistance which they have given him in the above investi- gation. GEOLOGICAL SOCIETY. (Continued from vol. xxxix. p. 463.] November 10th, 1869.—Prof. T. H. Huxley, LL.D., F.R.S., President, in the Chair. The following communications were read :— 3. On Hypsilophodon, a new Genus of Dinosauria.” By Pro- fessor Huxley, F.R.S., President. The author described the characters presented by the skull of a small Dinosaurian reptile obtained by the Rev. W. Fox from a Wealden bed at Cowleaze Chine in the Isle of Wight. One of the most striking peculiarities of this skull was presented by the pre- maxillary bone, which seems to have been produced downwards and forwards into a short edentulous beak-like process, the outer surface of which is rugose and pitted. The author remarked upon the known form of the symphysial portion of the lower jaw in the Dinosauria, and indicated that its peculiar emargination was pro- bably destined to receive this beak-like process of the preemaxillaries, which may have been covered either by fleshy lips or by a horny beak. The dentigerous portion of the premaxilla bears five small conical teeth. The alveolar margin of the maxilla bears ten teeth, On the Affinity between the Dinosaurian Reptiles and Birds. 69 which are imbedded by single fangs, and apparently lodged in distinct alveoh. The summit of the crown, when unworn, is sharp and pre- sents no trace of the serrations characteristic of Jguanodon ; but it is sinuated by the terminations of the strong ridges of enamel which traverse the outer surface of the crown. The teeth thus present some resemblance to those of Jguanodon; but the author regarded the two forms as perfectly distinct, and named the species under con- sideration Hypsilophodon Foawit. Of the lower jaw the right ramus is present; but its distal extremity is broken off, and its teeth are concealed. On the outer surface of the lower jaw the centrum of a vertebra is preserved. | The author then referred to a fossil skeleton in the British Mu- seum, which has been regarded as that of a young Jyuanodun ; it is from the same bed as the skull previously described. The author remarked that, in form and proportions, the vertebrae were quite different from those of Jguanodon, and apparently identical with those of his new genus, as shown by the centrum preserved with the skull: the animal had at least four well-developed toes; and other peculiarities were indicated, which seem to prove that it was quite distinct from Jguanodon. This skeleton the author identified with his Hypsilophodon Fowii, and described its characters in: detail, dwelling especially upon the peculiarities of the pelvic bones, which are singularly avian in their structure. 4, “ Further Evidence of the Affinity between the Dinosaurian Reptiles and Birds.” By Professor Huxley, F.R.S., President. In this paper the author reviewed the evidence already cited by himself and others (especially Professor EK. D. Cope) in favour of the ornithic affinities presented by the Dinosauria, and discussed at length the recently ascertained facts which bear upon this question, some of the most important of which are derived from the spccies described by him in the preceding paper under the name cf Hyp- silophodon Foxit. He summed up his paper by a comparison of the different elements of the pelvic arch and hind limb in the ordinary reptiles, the Dinosauria and Birds, and maintained that the structure of the pelvic bones (especially the form and arrangement of the ischium and pubis), the relation between the distal ends of the tibia and the astragalus (which is perfectly ornithic), and the strong cnemial crest of the tibia and the direction of its twist furnish additional and im- portant evidence of the affinities between the Dinosauria and Birds. Mr. Seetry doubted whether these animals should be called Reptiles at all, as they seemed to him to form a group distinct alike. from reptiles, birds, and mammals, but occupying an intermediate position. In the hinder limbs of Pterodactylus the analogies were closer with mammals than with birds. He thought it possible that the peculiar structure of the hinder limbs of the Dinosauria was due to the functions they performed rather than to any actual affinity with birds. The Presipent, in reply, stated that Hypsilophodon, from the 70 Geological Society :— character of its teeth, probably subsisted on hard vegetable food. He expressed a hope that Mr. Fox would allow a closer examination of his specimens to be made. Hewas unable to agree with Mr. Seeley’s views. He was inclined to think that the progress of know- ledge tended rather to break down the lines of demarcation between groups supposed to be distinct than to authorize the creation of fresh divisions. November 24th, 1869.—Prof. T. H. Huxley, LL.D., F.R.S., President, in the Chair, The following communications were read :— 1. “On the Dinosauria of the Trias, with observations on the Classification of the Dinosauria.” By Prof. Huxley, LL.D., F.R.S., President. The author commenced by referring to the bibliographical history of the Dinosauria, which were first recognized as a distinct group by Hermann von Meyer in 1830. He then indicated the general cha- racters of the group, which he proposed to divide into three families, v1Z, :— I, The Mucanosavrip#, with the genera Teratosaurus, Paleosaurus, Megalosaurus, Poikilopleuron, Lelaps, and probably Huskelo- SUULUS ; II. The Scerrposaurip#, with the genera T'hecodontosaurus, Hyle- osaurus, Pholacanthus, and Acanthopholis ; and Ill. The Ievanopontipm, with the genera Cetrosaurus, Iguanodon, Hypsilophodon, Hadrosaurus, and probably Stenopelys. Compsognathus was said to have many points of affinity with the Dinosauria, especially in the ornithic character of its hind limbs, but at the same time to differ from them in several important par- ticulars. Hence the author proposed to regard Compsognathus as the representative of a group (Compsognatha) equivalent to the true Dinosauria, and forming, with them, an order to which he gave the name of ORNITHOSCELIDA. The author then treated of the relations of the Ornithoscelida to other Reptiles. He indicated certain peculiarities in the structure of the vertebree which serve to characterize four great groups of Reptiles, and showed that his Ornithoscelida belong to a group in which, as in existing Crocodiles, the thoracic vertebre have distinct capitular and tubercular processes springing from the arch of the vertebra. This group was said to include also the Crocodilia, the Anomodontia, and the Pterosauria, to the second'of which the author was inclined to approximate the Ornithoscelida. Asa near ally of these reptiles, the author cited the Permian Parasaurus, the struc- ture of which he discussed, and stated that it seemed to be a terres- trial reptile leading back to some older and less specialized reptilian form. With regard to the relation of the Ornithoscelida to birds, the Mr. Duncan on the Physical Geography of Western Europe. 71 author stated that he knew of no character by which the structure of birds as a class differs from that of reptiles which is not fore- shadowed in the Ornithoscelida, and he briefly discussed the ques- tion of the relationship of Pterodactyles to birds. He did not con- sider that the majority of the Dinosauria stood so habitually upon their hind feet as to account for the resemblance of the hind limbs to those of birds by simple similarity of function. The author then proceeded to notice the Dinosauria of the Trias, commencing with an historical account of our knowledge of the occur- rence of such reptilian forms in beds of that age. He identified the following Triassic reptilian forms as belonging to the Dinosauria :— Teratosaurus, Plateosaurus, and Zanclodon from the German Trias ; Thecodontosaurus and Palwosaurus from the Bristol conglomerate (the second of these genera he restricted to P. cylindrodon of Riley and Stutchbury, their P. platyodon being referred to T'hecodonto- saurus); Cladyodon from Warwickshire; Deuterosaurus from the Ural; Ankistrodon from Central India; Clepsysawrus and Bathygna- thus from North America; and probably the South-African Prote- rosaurus. 2. “The Physical Geography of Western Europe during the Mesozoic and Cainozoic periods, elucidated by their Coral-faunas.” By P. Martin Duncan, M.B.Lond., F.R.S., Secretary. The author commenced with a notice of the typical species of the coral-fauna of the deep seas which bound continents remote from coral-reefs, and then made some remarks upon the littoral corals. The peculiarities of reef, lagoon, and shallow-water species were then explained, with the relations of the two faunas to one another. The author then referred to certain exceptional species, imdicated the genera the species of which constitute the existing reefs and contributed to form those of the past, and noticed the representa- tives of some modern genera in old reefs. He pointed out that a correspondency of physical conditions during the deposition of cer- tain strata was indicated by their containing analogous forms-—the presence of compound ccenenchymal species indicating neighbouring reefs, and their absence in places where simple or non-ccenenchymal Madreporaria are found being characteristic of deep-sea areas remote from the Coral-seas. By applying the principles thus elaborated to the evidence as to the condition of the seas of the European area from the Triassic period to the present time, the author then showed what must probably have been the physical condition of this part of the world at different periods. December 8th, 1869.—Prof. T. H. Huxley, LL.D., F.R.S., President, in the Chair. The following communications were read :— 1. “ Notes on the Brachiopoda hitherto obtained from the Pebble- bed at Budleigh-Salterton, near Exmouth, in Devonshire.” By Thomas Davidson, Esq., F.R.S., F.G.S., &e. The author first described the general characters, and discussed FO 24 Geological Society: — the opinions that have been put forward as to the origin, of the pebbles forming this bed. Nearly 40 species of Brachiopoda have been obtained from them. The fossils contained in the pebbles have been regarded as of Lower-Silurian age; the author considered the great majority of the Brachiopoda to be Devonian. The species identified with Silurian fossils are:—Lingula Lesuewre (Rouault), Z. Rouaulti (Salter), and LZ. Hawket (Rouault). The species regarded by the author as undoubtedly Devonian (2. e. either pre- viously described from Devonian deposits or associated with such species in the same pebble) are 12 in number, namely :—ASpirifer Vernewilit (Murch.), S. macroptera (Goldf.), Athyris budleighensis (sp. n.), Atrypa (reticularis ?), Rhynchonella inaurita (Sandb.), R. el- liptica (Schnurr), &. Vicaryi (sp. n.), and 2 undetermined species of Rhynchonella, Streptorhynchus crenistria (Phil.), Productus Vi- - caryt (Salt.), and an undetermined Chonetes. Eight species occur- ring in the same rock, three of which have been doubtfully identified, are considered by the author to be probably Devonian. The species supposed to be determined are :—Orthis redux (Barr.) and O. Ber- thos. (Rouault), Silurian; and Spirifer octoplicatus (Sow.), Devo- nian and Carboniferous, but possibly identical with the Silurian S. elevatus (Dalm.). The others are 2 new species of Orthis, and a new Rhynchonella (?), and an undetermined species of Terebratula(?) and Strophomena (?). Finally the author noticed 14 species (all new, ex- cept Orthis pulvinata, Salt.) only known from these pebbles, but which were stated to possess a Devonian facies. 2. “ On the relation of the Boulder-clay without Chalk of the North of England to the Great Chalky Boulder-clay of the South.” ~ By Searles V. Wood, Jun., Esq., F.G.S. The author described the Yorkshire glacial clays as of two kinds:— the lower, contaiing chalk débris, and belonging to the uppermost member of the glacial series in Eastern and East-central England ; the upper, containing chalk sparingly in its lower part, and gradually losing this upwards. On the coast only the latter occurs north of Flambro’. He stated that, paleontologically, the Lower and Middle glacial deposits closely agree with the Crag, and are quite distinct from the deposit at Bridlington, which he placed immediately above the “ Great Chalky Clay.” The absence of chalk débris in the deposit north of Flambro’ has been regarded as evidence of a drift from north to south; but the author stated that the purple clay without chalk extends over much of the north-eastern part of the Wolds, from the sea-level to an ele- vation of 450 feet, and that outliers of it occur at intervals along the Holderness coast-section as far as Dimlington, 42 miles south of the northern limit of the Wolds. In the direction of Flambro’ and York the clay was said to be destitute of chalk, which would not be the case had the Wolds formed a sea-shore causing a drift from the north to pass either to south-east or south-west. The author described the characters of the Great Chalky Boulder- clay in the eastern and central counties of England, and maintained On the Iron-ores and the Basalts of the North-east of Ireland. 73 that the chalk found in it (equal, according to him, to a layer of at least 200 feet over the entire Wold) could only have been detached by the agency of moving ice, which he believed to have covered nearly the whole Wold for a long period. The author stated that boulders of Shap Fell granite are confined to the deposit of clay without chalk, and discussed the means by which they could have been distributed. He ascribed their disper- sion to the agency of floating ice during an adequate submergence of the district. He supposed them to have passed from Shap Fell by what is now the pass of Stainmoor. Thus he ascribed the formation of the ‘“ Great Chalky Clay” to the extrusion from the sea-foot of a great sheet of ice, of mate- rials abraded by the latter, the land being depressed 600—700 feet below its present level; and that of the clay without chalk and with boulders of Shap-Fell granite to deposition during a period of much greater depression (about 1500 feet), throughout which the sea bore much floating ice. He considered that the “ Great Chalky Clay” indicated a long period during which the land, with its enveloping ice, remained stationary, and that during this period, when intense cold prevailed, the arctic fauna of Bridlington be- came established. He thought that the recommencement of sub- sidence was indicated by the reddish-brown or brownish-purple sediments of Holderness, in which some chalk occurs. He then indicated the species of Mollusca which have occurred in the purple clay without chalk about Scarbro’ and Whitby, all of which were said to belong to existing forms, and thus to be in accordance with the date assigned’ by him to that deposit. The molluscan fauna of Moel Tryfane was referred to by the author, who stated that he regarded it as belonging to the period of emergence from the deepest depression, during which the clay without chalk was as- sumed to have been deposited, 7. e. to the earliest part of the post- glacial period, to which the stratified drifts of Scotland are referred by Mr. A. Geikie. December 22, 1869.—Professor Huxley, LL.D., F.R.S., President, in the Chair. The following communications were read :— 1. “On the Iron-ores associated with the Basalts of the North- east of Ireland.” By Ralph Tate, Esq., Assoc. Linn. Soc., F.G.S., and John 8. Holden, M.D., F.G.S. The authors introduced their account of the iron-ores of the Antrim basalts by stating that since 1790 an iron band had been known in the midst of the basalt of the Giant’s Causeway, but that only within the last few years have further discoveries been made, which have developed a new branch of industry in the north-east of Ireland. The iron-ore of the numerous exposures was considered to repre- ‘sent portions of one sheet extending uniformly throughout the basalt and over a very large area, Indeed everywhere the iron band and 74: Geological Society :— its associated rock-masses present identical features, from which the authors deduced the following generalized section :— The underlying basalt gradually passes upwards into a variegated lithomarge of about 30 feet thick, graduating insensibly into a red or yellow ochre or bole of about 5-6 feet in thickness, which passes into a dense red ochreous mass of about 2 feet, charged with ferru- ginous spheroids consisting chiefly of a protoxide and peroxide. The spheroids are of the average size of peas; they increase in number and size towards the upper part of the band, and not unfrequently constitute that portion of it. The line of junction between the iron band and the overlying and usually more or less columnar basalt is in all cases well defined, and in a few instances exhibits decided unconformability. : The authors discussed the several theories that may be sug- gested to account for the origin of the present condition of the piso- litic ore, and proceeded to point out what appeared to have been the several stages of metamorphic action by which the pisolitic ore had been elaborated out of basalt. From field observations and chemical analyses, they have been led to consider the bole and lithomarge to be the resultants of aqueous action in combination with acidulated gases, which, dissolving out certain mineral substances, has effected the decomposition of the basalts,—and to assume that the bole underlying the iron band was a wet terrestrial surface, and that the subsequent outflow of basalt effected, by its heat, pressure, and evolved gases, a reduction cf the contained oxides of iron into the more concentrated form in which they occur in the pisolite, the aggregation of the ferruginous particles being a result of the same actions. The ferruginous series, with interstratified plant-beds, at Bally- palidy was next described, and demonstrated to be of sedimentary origin—the ferruginous conglomerate resulting from the degrada- tion of the pisolitic ore, of which it is chiefly reconstructed, and of the underlying ochres. Many additions were made to the list of plant-remains from these beds; and priority of discovery of plants in the Antrim basalts was accorded to Dr. Bryce, F.G.8. ” 2. “Notes on the Structure of Sigillaria.” By Principal Dawson, F.R.S., F.G.8., Montreal. In this paper the author criticised the statements of Mr. Car- ruthers on the structure of Sigillaria (see Q. J. G. 8. xxv. p. 248). He remarked that Sigillaria, as evidenced by his specimens, is not coniferous; that the coniferous trunks found in the Coal-formation of Nova Scotia do not present discigerous tissue of the same type as that of Sigillaria; that no Conifer has a slender woody axis sur- rounded by an enormonsly thick bark; that Calamodendron was probably a Gymnosperm, and allied to Sigillaria; that although Stigmaria may not always show medullary rays, the distinct sepa- ration of the wood into wedges is an evidence of their having ex- Af a On a Crocodilan Skull from Kimmeridge Bay, Dorset. 75 _isted; that the difference in minute structure between Sigillaria and Stigmaria involves no serious difficulty if the former be regarded as allied to Cycadacee ; and, further, that we do not know how many of the Stigmarie belong to Sigillaria proper, or Favularia, or to such forms as Clathraria and Lewoderma, which may have been more nearly allied to Lepidophloios ; that the fruit figured by Golden- berg as that of Sigillaria is more probably that of Lepidophloios, or may be a male catkin with pollen; and that he has found T'rigono- carpa scattered around the trunks of Sigillaria, and on the surface of the soil in which they grew. He agreed with Mr. Carruthers in regarding Mr. Binney’s Sigillaria vascularis as allied to Lepido- dendron. Prof. Morris thought that Clathraria and Lepidophloios ought to be discriminated from the Sigillariw, as being rather more nearly allied with cycadaceous plants, especially the former. He pointed out the manner in which certain vascular bundles communicating between the centre of the stem of Stgillaria and allied genera and their bark might be mistaken for medullary rays. 3. “Note on some new Animal Remains from the Carboniferous and Devonian of Canada.” By Principal Dawson, F.R.S., F.G.S., Montreal. The author described the characters presented by the lower jaw of an Amphibian, of which a cast had occurred in the coarse sandstone of the Coal-formation between Ragged Reef and the Joggins Coal- mine. It measured 6 inches in length; its surface was marked on the lower and posterior part with a network of ridges enclosing rounded depressions. ‘The anterior part of the jaw had contained about 16 teeth, some of which remained in the matrix. These were stout, conical, and blunt, with large pulp-cavities, and about 32 longi- tudinal striz, corresponding to the same number of folds of dentine. The author stated that this jaw resembled most closely those of Baphetes and Dendrerpeton, but more especially the former. He regarded it as distinct from Baphetes planiceps, and proposed for it the name of B. ininor. If distinct, this raises the number of species of Amphibia from the Coal-measures of Nova Scotia to nine. The author also noticed some insect-remains found by him in slabs containing Sphenophyllum. They were referred by Mr. Scudder to the Blattarize. From the Devonian beds of Gaspé the author stated that he had obtained a small species of Cephalaspis, the first yet detected in America. With it were spines of Machairacanthus and remains of some other fishes. At Gaspé he had also obtained a new species of Psilophyton, several trunks of Prototaaites, and a species of Cyclo- stigma. 4, “Note on a Crocodilian Skull from Kimmeridge Bay, Dorset.” By J. W. Hulke, F.R.S., F.G.S. The author described a large Steneosaurian skull in the British 76 Intelligence and Miscellancous Articles. Museum, from Kimmeridge Bay, which had been previously re- garded as Pliosaurian, and was recently identified with Dakosaurus by Mr. Davies, Sen. From the agreement of their dimensions, and their occurrence near together, the author thought it probable that this skull and the lower jaw described by him last session belonged to the same individual. It differs from the Stencosaurus rostro-mmor in the greater stoutness of its snout, in the presence of an anterior pair of nasal bones prolonged into the nostril, and in the number of its teeth. The author proposed to name it Stencosaurus Manseli, after its discoverer. 5. “ Note on some Teeth associated with two fragments of a Jaw, from Kimmeridge Bay.” By J. W. Hulke, F.R.S., F.G.S. The author described some small teeth associated with fragments of a long slender snout not unlike that of an Ichthyosaur, but too incomplete to be certainly identified. The teeth are peculiar in the great development of the cementum, which gives the base of the tooth the form of a small bulb. The exserted crowns are slightly curved, smooth, cylindrical, and pointed. The attachment to the dentary bone was probably by means of the soft tissues; and the teeth seem to have been seated in an open groove in the surface of the jaw-bone. Until additional material reveal the true nature of this fossil, the author proposes to place it alone, and to call it pro- visionally Huthekiodon, , X. Intelligence and Miscellaneous Articles. EXPERIMENTS ON THE VELOCITY OF THE PROPAGATION OF SOUND IN WATER IN A CAST-IRON CONDUIT 8 DECIMETRES IN DIAME= TER. BY M. FR. ANDRE. Hos been commissioned by the Ecole des Ponts et Chaussées to superintend the supply-works of the canal from the Aisne to the Marne, I had occasion to assist at the laying down of a tubular conduit intended to conduct the water from the pumping-works to the head of the supply reservoir. This conduit consisted of cast-iron tubes of 0°8 metre internal diameter and 0:02 metre thick, joined together by sockets and bands, and formed altogether a straight line of about 600 metres. ‘The difference of level between the two ends of the conduit was 17°23 metres. In order to test the joints of the tubes, the conduit had to be filled with water and the latter subjected to a pressure of 8 atmospheres. It occurred to me that this experiment afforded a good opportunity of making some fresh measurements of the velocity of the propaga- tion of sound in water. The conditions under which I operated were as follows. To record the motions of the liquid, instead of using electric re- gisters, the fixing of which is always difficult and costly, I made use of a pneumatic register, which physiologists, and particularly M. Intelligence and Miscellaneous Articles. 7% Marey, have of late frequently used. The disturbance communi- cated itself to the air confined in a small caoutchouc tube, and thence to a membrane of goldheater’s skin. A very delicate lever fastened to this membrane indicated by its oscillations the slightest movements of the liquid. The time was calculated by help of a tuning-fork, which inscribed its vibrations on the blackened sheet of a registering cylinder. This tuning-fork, which was verified several times, gave, for a tempera- ture of 20°, 256 vibrations in a second. Before experimenting on the conduit filled with water, I performeda series of experiments on the velocity of the propagation of sound im air, in order to ascertain the degree of correctness this method admits of. The apparatus, except some slight modifications, remained the same. ‘The sound was produced by a pistol charged with about one gramme of powder. The shock communicated to the air of the conduit was propagated through the whole length of the tubes, and thenreturned, after reflection. At each successive departure and return the small style of the membrane gave very distinct indications on the registering cylinder. As the initial shock and the reflected shocks were observed, the causes of error due to the inertia of the register were eliminated. The greatest difficulty consisted in determining the temperature of the air enclosed in the conduit. The tubes were laid in an open trench ; and whilst their upper part, heated by the sun’s rays, had a temperature of 40°, the part in contact with the ground had one of 20° only. Taking these two numbers as extreme limits of the temperature of the air confined in the conduit, I found for the velocity of sound, reduced to zero, V,=326'60 metres (supposing the temperature 40°), V,=337°50 metres (supposing the temperature 20°). It is certain that the first number must be nearer the truth than the second; for the part of the tubes exposed to the sun was con- siderably greater than that in contact with the ground. I now come to the experiments made on the velocity of sound in the conduit filled with water. After first assuring myself that the in- terior was absolutely void of air (which is easily done by examining the joints), I fitted an hydraulic-press pump to the upper part of the conduit. ‘The shock in the water was caused by forcing-in the piston suddenly. With whatever rapidity the lever of the pump was lowered, no shock, properly so called, was produced, but a gradual compres- sion; thus the indication of the style upon the register, instead of being a well-defined zigzag, as in the case of air, traced an elongated curve, of which the point of coincidence with the spiral inscribed by the style at rest was difficult to determine. However, four succes- sive experiments gave a mean of 345 vibrations of the tuning-fork between the initial andthe return shocks. ‘The length of the conduit between the two plates which closed its extremities was 603°25 metres; hence the distance travelled by the compression, between 78 Intelligence and Miscellaneous Articles. departure and return, was 1206°5 metres. ‘The temperature of the water at the top of the conduit was 20°, and 13° at the bottom. The temperature of the surrounding air was 18°. Under these con- ditions the velocity of the propagation of the compression was found to be 897°80 metres per second. The second and the third return shocks were too feeble to enable us to deduce any accurate measure. Wertheim deduced, from the sound given by brass organ-pipes dipping in water, 1173 metres per second as the velocity of sound in water. ‘This number is much less than 1485 metres per second, found by MM. Colladon and Sturm in direct experiments made on the Lake of Geneva. The value which I found is still further from the number observed in an indefinite mass of water. Notwithstanding this divergence, which I do not pretend to explain, I think it useful to give my re- sults, which subsequent studies may confirm. I confine myself to calling the attention of physicists and geome- ters to the influence which the elasticity and friction of the con- taining sides may have on the propagation of a shock in the midst of an almost incompressible fluid. Probably the difference between the propagation of a shock in an indefinite medium and that which we observed in a cast-iron cylinder is due to this circumstance. — Comptes Rendus, March 14, 1870. EXPERIMENTAL RESEARCHES ON THE DURATION OF THE ELEC- TRIC SPARK. BY MM. LUCAS AND CAZIN. The apparatus which we use to measure with accuracy the dura- tions of electric sparks depends essentially on an application of the vernier. A mica disk, 15 centims. in diameter, blackened on one face by a photographic process, and divided near its edge into 180 equal parts by means of transparent marks, is mounted on a horizontal axis, which may be made to rotate with a velocity varying from 100 to 300 revolutions in a second. A crank and gear govern this rapid motion. For one turn of the handle the mica disk makes 664 turns. Another disk, of the same radius and centred on the same hori- zontal axis, is fixed vertically, as near as possible to the moveable disk. It consists of silvered glass, and has, towards the summit of its vertical diameter, six transparent marks, which form a vernier, in order to estimate the sixth of the interval between two consecutive marks on the mica disk. The two disks are enclosed in a circular box of blackened copper. The vernier forms the bottom of it, on the side of the source of light. The mica disk turns in the interior. On the side of the observer there is a metal plate for a cover; a small aperture, provided with a plate of glass, is arranged opposite to the vernier in order to admit of observations. In this manner the moveable disk is preserved from dust, protected against shocks, and sheltered from currents of air. The general appearance of this chronoscope, which has been very Intelligence and Miscellaneous Articles. 79 cleverly constructed by M. Duboseq, recalls the apparatus devised and used by M. E. Becquerel for his important investigations on the phosphorescence of bodies. Instead of the handle, a wooden pulley of several grooves is sub- stituted, over which a catgut cord passes, which also passes round another pulley of a much larger diameter fixed on the fly-wheel of a gas-engine. ‘This machine, which was very obligingly lent by its inventor, M. Hugon, is of half a horse-power. It works with great regularity ; it may be started and stopped almost instantaneously ; and unlike steam-engines, the pressure need not be maintained during the times of stoppage. Thus it is of excellent service. To charge the Leyden battery in which the electricity is con- densed, one of Holtz’s machines is used, the plate of which is put in motion by the gas-engine. The sparks pass between two metal knobs 11 millims.in diameter. At exactly half the distance between these two knobs is formed the principal focus of the lens of a colli- mator, so that the luminous rays fall perpendicularly on the vernier. The aperture of the chronoscope is viewed through a magnifying- lass. ¢ Suppose that the electric spark occurs periodically under precisely the same conditions, whilst the mica disk turns almost uniformly. An observer looks through the eyeglass of the telescope and calls out the number of marks which he observes simultaneously with each spark. Another observer registers these numbers, and counts the number of turns which the handle of the chronoscope makes per minute. Let N be the number of sparks observed, S the total number of marks read, x the number of turns of the handle. The duration y of the spark, in millionths of a second, is given by the formula __ 10000 S 12n Tor Two 1) e ° ® ° ° ° (1) in which p is a constant parameter, equal to 0°70 for our apparatus. If e denote the angular breadth of the marks on the mica disk, w the angle between the axes of two consecutive marks, and : the angular breadth of the marks of the vernier, then _ 6(e+e!) a (2) Formula (1) assumes N to be a large number; thus, we usually observe series of a hundred sparks. Other things being equal, the duration of the electric spark is a function of the surface of the Leyden battery, or, in other words, of the number of jars which compose it. By varying this number 2 by units from 1 to 9, we found that the duration y may be expressed by the formula y=h(1—a’). Sie Sgn f see See ese (3) 80 Intelligence and Miscellaneous Articles. With two zinc knobs, 2°292 millims. apart, the following results were obtained :— log a=1:9050453 } (4) log A=1°5192181 or a= 0°80361 } tee ores k=33:°05355 . Diff —_——_—_——_|Differ- —41 millims.; then it rises at first parallel to the preceding, attains A= + 30 millims., and further on coincides with the curve A. The separation of these curves evidently depends on the liquid | in the manometer not instantly indicating the pressure of the gas, and on the level being more or less behind according as it must run a greater or less length before reaching the position of equilibrium. Let us suppose the variation of the real pressure of the gas to be represented by the line g Az (fig. 5). When the valve of the manometer is opened the liquid would indicate h= —fog if it could move instantly, and if the pressure of the gas remained invariable. But whilst the liquid moves, the pressure of the gas increases ; and when the level indicates h= —ké, the pressure corresponds to the poimt 7. The point 0 is evidently higher than the point g, and it is also lower than the point / on account of the impulse the liquid receives. The level afterwards rises until the manometric column and the pressure of the gas are in equi- librium, which can only take place after a certain time. Let the valve be opened after a time o f’>o/f. Instead of instantly indicating h= —f' g', it only indicatesh=—k'b'; and the distance of the point J! from g! and J’ is less than before, because the impulse and the initial rarefaction f!g' have been less; moreover the duration /!k’ of the depression is also less than fk, because k'b'=0°54 atmosphere. ‘Temperature between 19° and 20°. O= 0°15 |t=... 29 77-\ 129 23 53 | 90 h=—2mm| +98 | —62 | —15 a +8 EB lees. 0 9=0:17 aR ens 7 | 144 | 186 54 | 90 hae. a8? 256 at +8 |} +11 al a J 9= 0-20 eee) 129 6-3 98 | 151 54 | 90° [eset A Pole BFC 625.1) 9 23 +7 42 | 0 9= 0-23 cl es 2a 62 | 109 | 17:9 53 | 90 V3") t49'| 2 et 0 48 ive Pade The coordinates of the minimum of the curves are h=—65 millims., ¢=4°5 seconds, in Series IV., and h= —62 millims., =2-9 seconds, in Series V. Hence a result of the increase of the dimensions of the mano- meter, as might be foreseen, is to lessen the variation of the levels, without changing materially the values of 4. We also see that the curves of Series IV. rise more slowly from the minimum than those of Series V. The differences which the curves present at their point of de- parture are due to the presence of the tube aa! in Series V., as we shall see in the following paragraph. It may be observed that, the effect of this tube being to raise for an instant the curve at its point of departure, it attains its minimum a little later; so that our conclusion cannot be doubted. § VIL. Influence of the position of the tube which connects the re- servoirs with the manometer. We shall see in what this influence consists in the following series, which may be compared with Series I. These two series only differ in that the manometer Q is put in communication with the tube S (fig. 2) in Series I., and with the tube H! in Series VI. Thus the tube of communication passes into the middle of the side of the reservoir B in Series I., and very near to the large stopcock, on the side of the reservoir A, in Series VI. f ; OSS CLL, eC es ee 7 (see, oe ee ee a ew M. Achille Cazin on Internal Work in Gases. 97 Series VI. (September 1867). Dry air. Manometer communicating with the tube H! (fig. 2). p,=3'86 atmospheres, p,=0°22 atmosphere. Temperature19°. e=0-10 f=... | 37] 89] 136] 203/ 24] 54 | 120 h=—3mm| 192] —40 | +10] +18 | +16] +14] +3 0 f = 0-21 Pode awee | 1 Sle | Pare iy oak ye s., | 1 hey | oe eee oe |) 275.) 17) eel eit 44 6= 0:30 9| 66| 97] 142] 24] 54 | 120 Av4 888) S25) eGalreblD oS (0) 6 0 0= 0°38 2-9 6| $2] 113] 153] 24 | 120 h=0 Bigg ae" 10 | Pig | +8.) 14 0 @= 0-92 32] 71] 105] 161} 25 | 55 | 120 M2 288/51 SBR | ob 9e)--BDZaled2oh! s-E1 0 It will be seen, in tracing the curves of this series, that when the valve of the manometer is opened after a time 0 < 0°30 second, the exterior level of the manometric liquid rises at first very ra- pidly higher the lower @ is, and afterwards redescends and com- ports itself as before. The form of the first two curves of Series VI. is that of the line a! b! b" ¢! of fig. 1. It is easy to explain this peculiarity. Before the expansion commences, the tube D H’R and the reservoir A are filled with compressed gas. When the expansion commences, and before the valve R is opened, the gas in the tube D H! R escapes into the reservoir A; and it may happen that the valve opens before the tube is emptied. Then the manometer indicates a momentary increase of pressure, until equilibrium is again established throughout the tube. An analogous effect may be produced in Series I. on account of rarefaction in the tube SR: the de- pression of the level will be increased by this effect for small values of 8. But the difference of pressure between the reser- voir B and the tube S R is much less than between the reservoir A and the tube DH'’R. Moreover I used for S R a wide and short lead tube. This kind of influence is therefore altogether insignificant in experiments arranged like those of Series I. It must be observed that if > 0-30 second, the results are the same in the two series; so that it is a matter of indifference whether the manometer communicates with the tubulures S, H!, or even H (as was the case with the glass reservoir B), on con- dition that we do not take @ too small. Comparisons analogous to those I have just mentioned have been frequently repeated ; and they all lead to the conclusion that equality of pressure establishes itself very quickly in the reservoirs, and that it afterwards maintains itself, as is repre- sented by the line ghie, fig. 5, whilst the various portions of the gas exchange among themselves motion and heat, Phil. Mag. S. 4. Vol. 40. No. 265. Aug. 1870. H 98 M. Achille Cazin on Internal Work in Gases. It will be remembered that I have mentioned in § V. two ex- periments on hydrogen not given in Series III. They show that the influence only manifests itself for @< 0-1 second. Continuation of Series III. A@= Us:08 a 22 6:2 ll 16 24 60 h=0 +19 —1l13 —34 —13 —6 —l1 0 @= 0:09 eee 2°3 6-9 10°8 18-4 na | OO h=—6 +13 —112 —24 —14 —3 siake 0 § VIII. Influence of the arrangement of the channel which joins the two reservotrs. Wishing to investigate at the outset of these researches the influence of the mode of communication of the manometer with the copper reservoir A and the glass one B, I had fitted inte- riorly to the tubes D, E (fig. 2) some copper tubes, aa’, a, a’, open at a’, a’,, so that the interior pressure might be transmitted to the manometer Q, either by the pipe a’a D H'R, or by the similar one a’!,a, HH R. These tubes grazed the sides of the tu- bulures of the reservoirs, and did not seem likely to obstruct the jet of gas when it rushed from A towards B. I was very much astonished, in making some experiments. like the preceding, to see the curve take the form of the line me (fig. 1); & attained the maximum value +250 millims. (water), the difference of pressure p,—, being about four atmospheres. This effect was always produced, whatever the value of 0. It underwent no change when an opening was made at the point a, of the tube, when the extremity a’, was closed, and, finally, when both a, and a', were closed. In this latter case the internal pressure was transmitted to the manometer only by the passage a'aD H'R, whilst in the other cases we used either this passage or the other, The tube a, a’, was suppressed, and then the effects of series V. observed, which are described in § VI. and represented by the line a! b! b" c, fig. 1. It is evident that the anomaly observed was due to the action of the tube a, a’, on the gaseous jet, and that the tube aa! exer- cised an analogous action, but not so great. Hence this is the explanation of the anomaly :— 7 Let us distinguish three parts in the gas of the reservoirs :— (1) that which remains in the reservoir A after the expansion ; (2) that which remains in the reservoir B before the expansion ; (3) that which passes from the reservoir A into the reservoir B. When the expansion has taken place, there is equality of pres- sure between these three parts; the magnitude p of this pressure depends on the state in which each is found. It afterwards varies, in proportion as these parts mix together and exchange heat, either with one another or with the sides; and when these exchanges have ended, the pressure attains the final value p’. 7 M. Achille Cazin on Internal Work in Gases. 99 At the moment equality of pressure commences, the first part is cold, the second is warm, and the third is in a condition which depends on the friction which it has produced during the expansion. Let us suppose that this friction is greater in one experiment than in another; then there is a greater heating in the third part of the gas; consequently the pressure p is greater, If we notice a value pp! (p' having, moreover, the same value in both cases). This is what occurred in my experiments: the portion of gas which passed from reservoir A glided along the tubes a! a, a, a’, and produced great friction, especially along the part a, a',, because the molecules in this place had the greatest velocity. As to the first two parts of the gas, their velocity was inconsiderable, and they behaved almost as if the tubes aa’, a,a', had not existed. By suppressing the tube a, a',, the friction was considerably di- minished, and the increase of pressure was much less than before. These observations clearly demonstrate that the sides of the canal X Y which join the two reservoirs exert an influence on the curve of excesses of pressure 2; this influence consists in raising the minimum 0 of this curve (fig. 1). It ought to be appreciable with the glass vessel (the neck of which was 12 cen- tims. long), but is lessened as much as possible with the zinc reservoir which was used in the actual experiments. The neck of this reservoir was, in fact, very wide and very short (dia- meter 5 centims., length 4 centims.). This influence was considerable in an experiment I made with a stone vessel: the neck consisted of a wide glass tube; it formed an ajutage 15 centims. long and 4 centims. thick, and there was a little cement on the edges of the tube. The curves obtained by means of this reservoir were generally of the form a b'b"c' (fig. 1). I was compelled to give up the use of it. I onght to remark that it must not be concluded, from the curve mnp, that friction occasions the creation of a quantity of heat different from that which results from the destruction of the velocities of the gaseous molecules under ordinary circumstances. The final thermal effect is always the same in every case—such, for example, as would be observed in a body of water surround- ing the reservoirs. That which changes with the intensity of the friction is the law of the pressures during the expansion, because the succession of thermal and partial mechanical effects itself changes. The conversion of work into heat is effected the more quickly the more intense the friction. [To be continued. | H 2 [ 100 ] XII. On the Spectra of Carbon. By W. Marsnaru Watts, D.Sc.. Physical-Science Master in the Manchester Grammar School*. 1 a paper published in the Philosophical Magazine for Octo- ber 1869, I showed that carbon, like hydrogen and nitrogen, is capable of giving two or more distinct spectra, and I endea- voured to explain these differences as dependent solely on differ- ences in the temperature to which the carbon-vapour was heated. Leaving the spectrum of the Bessemer flame out of consideration, the following estimations of temperature were given for the car- bon spectra I., II., and LV. :— Cif... . . Below 1500° C. CE SN Se LIAB QO MG Eta 10,000" C. CIV 2" SP VAbove 10000" C: The spectrum No. II. is that obtained by the electric discharge in carbonic oxide or olefiant gas at a few millimetres pressure. The only evidence for the temperature assigned to it was the fact that the electric spark in either carbonic oxide or olefiant gas at the ordinary pressure gives the spectrum No. I., that on increasing the density of the gas the temperature rises, as 1s shown by the addition of new lines (groups € and @), but on di- minishing the pressure the spectrum No. I. gives place to spec- trum No. II. The lowest temperature at which the spectrum No. I. is produced having been shown to be about 1500° C., it was concluded that spectrum No. II. belonged to temperatures below 1500° C. It appeared probable that more decisive evidence as to the temperature of the discharge in a Geissler’s tube might be ob- tained by means of certain sodium- and lithium-lines, which become visible only at a high temperature. Ifa bead of sodium chlorate be brought into a Bunsen-flame, the spectroscope shows during the final deflagration of the salt, besides the D lines, four other groups of lines, whose wave-lengths are given in Ang- strém’s map as follows :— Naess ¢ + 687 ten-millionths of a millimetre. 51524 Ney ees sera ts My 4.982 Nad : 5 nee oy) a9 6160 Nae, ae; aie 43 %, * Communicated by the Author. Mr. W. M. Watts on the Spectra of Carbon. 101 The readings of these lines on the scale of my spectroscope are NaB,56; Nay,75°5; Nad, 83:2; Nae, 43; the Fraunhofer lines C, D, and F reading 34:5, 50, and 90 re- spectively. The same lines were observed by Huggins* in the spark taken between sodium poles, and were shown to be due to sodium itself, since they were obtained by the use of pure sodium-amalgam. Diacon + obtained them from the flame of hydrogen which had been passed through an iron tube in which sodium was volatilized. The sodium-spectrum obtained by means of a Bunsen burner gives only the D lines; but if the temperature of the flame be increased, these other lines become visible and in the order given above. I find that Na becomes visible almost precisely at the tem- perature at which platinum melts. This, according to the ex- periments of Deville, is 2000° C. The flame of hydrogen in air (of which the temperature, ac- cording to the experiments of Bunsen, is 2024° C.) gives the D lines only. The flame is incapable of fusing platinum except at one point. The Bunsen flame of coal-gas and air gives only D. The flame is incapable of melting platinum. The flame of coal-gas fed by a jet of air gives a spectrum in which, besides D, the line Na is faintly visible. This flame is just capable of fusing a fine platinum wire. The flame of coal-gas fed by a mixture of oxygen and air (con- taining about 30 per cent. oxygen and 70 per cent. nitrogen) gives Na f distinctly and Naé faintly. Navy and ¢ are not seen. The flame fused platinum tolerably easily. The flame of coal-gas fed by pure oxygen gives a spectrum containing Na, +, 6, and e, but eis only faint. The flame fuses platinum easily. The flame of carbonic oxide in air (temperature 1997°, Bun- sen) gives only the D line. It is incapable of melting platinum. Carbonic oxide fed by a jet of air still gives only D. The flame just melts platinum. Carbonic oxide fed by oxygen (temperature of flame 3033° C., Bunsen) gives Na and y brilliantly. Na6 and e were not seen. The flame melts platinum easily. The flame of sulphur in air (calculated temperature 1900° C.) gives the D lines only. It melts gold, but not platinum. The flame of sulphuretted hydrogen in air (calculated tempe- * Pogg. Ann. vol. exxiv. p. 275. [Phil. Mag. 1864, vol. xxvii. p. 542.] t+ Comptes Rendus, vol. ly. p. 334. 102 Mr. W. M. Watts on the Spectra of Carbon. rature 2250° C.) gives the D lines only. It melts gold but not platinum. We may therefore employ the line Na B as a test of tempera- ture indicating a temperature at least 2000° C. Certain lines of the lithium. -spectrum may be employed for the same purpose. In the Bunsen burner, a bead of hthium- chloride gives a spectrum of one red line whose wave-length is about 6684. The flame of coal-gas fed by a jet of air shows, besides the red line, an orange line whose wave-length is about 6107. In the flame of coal- -gas and oxygen a blue line (4605) is added; and in the electric arc a fourth line (4921) becomes visible. "All these lines can be obtained by means of lithium- ehlorate in the Bunsen-flame. A vacuum-tube containing coal-gas gives the same spectrum as if carbonic oxide or olefiant gas were employed, viz. the spec- trum CII. This experiment was repeated with a coal-gas tube containing pieces of metallic sodium. At first the spectrum was that of carbon, as previously described; but as the tube became heated by the continued discharge, the hne Naf came out fol- lowed by the lines y, 6, and e, and the carbon-lines faded away till ultimately the sodium-spectrum of five lines alone remained. During this change the carbon-lines and the sodium-lines were seen together; and as the temperature to which the sodium-vapour was heated cannot be supposed to be different from that to which the carbon-vapour was heated, it follows that the spectrum C IT. may be produced by carbon heated above 2000° C. It is to be observed also that this spectrum may be produced by carbon heated not much above 2000° C., since it was obtained together with C8 and without Cry, which comes out under 3000° C. Carbon-spectrum No. I. is given by the blue cone of the Bunsen flame, the temperature of which cannot be much above 1500° C., and is certainly less than 2000° C.; and the same spectrum (with the addition of two new groups of lines, €and 6) is obtained at all temperatures up to that of the cyanogen-flame in oxygen, or probably 10,000° C. We have thus two quite dif- ferent spectra, each of which has been shown to be due to carbon. itself, and not to any compound of carbon, which are proved to be obtainable at the same temperature. In the case of the six dif- ferent spectra of hydrogen described by Wiillner*, which are all obtained by the electric discharge in gas at different pressures, we may suppose the differences to be due to difference of tempe- rature ; but in the case of the carbon-spectra we are forced to some other explanation. It is worthy of remark that, while the spectrum CII. is obtained only by the use of electricity, the * Pogg. Ann. vol. cxxxvil. p. 337. [Phil. Mag. May 1870, p. 366.] Dr. W. J. M. Rankine on Thermodynamics. 103 spectrum CI. can be obtained both from flame and by the use of the electric spark. The sodium-lines £, y, 5, and ¢ are seen in the spectrum of the electric light, of the spark of an induction-coil between sodium poles in air, both with and without the Leyden jar, and are ob- tained simultaneously with the hydrogen-lines e, 8, and y in a hydrogen vacuum-tube. The simplest mode of obtaining them is to heat the narrow part of the vacuum-tube with a Bunsen flame; the discharge inside the hot part of the tube becomes yellow and exhibits the sodium-lines brilliantly. I have confirmed the results obtained by Willner in his expe- riments on hydrogen under pressure, and have pushed the pres- sure to nine atmospheres. ‘The spectrum of the spark of an in- duction-coil (without condenser) in the gas at nine atmospheres’ pressure is still far from being continuous. H «@ is still a very bright and distinct lime; H 6 and y are merely maxima of light. XIII. On Thermodynamics. By W.J. Macquorn Rankine, Cb ED:, FOR. SS Tch Ey Se To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, [ I rightly understand the paper of the Rev. J. M. Heath, published in the Philosophical Magazine for July 1870, p. 51, he lays down a principle which may be virtually expressed by saying that the work done by a force in overcoming attrac- tions or repulsions cannot take effect in producing heat, —that is, in accelerating molecular motions. That principle is perfectly correct, and is an obvious consequence of the laws of motion; and every one who knows those laws must agree with Mr. Heath when he states it. But from the remarks with which his state- ment is accompanied, he seems not to be aware that this very principle has been most carefully kept in view by every author of original researches in thermodynamics, and by every writer on the subject who has understood those researches. In fact the problem which is solved by the general equation of thermody- namics may be stated as follows:—A certain quantity of work being done by the action of external forces on a body in a cer- tain way, to distinguish that quantity of work into two parts, one of which is expended in overcoming molecular attractions and repulsions, and the other in accelerating molecular motions. A system of particles contained within a vessel and in,a state of rest, being kept 7n equilibrio by their mutual attractions and repulsions, exerts a pressure or a tension against the internal sur- face of that vessel according as repulsions or attractions predo- 104 Dr. W. J. M. Rankine on Thermodynamics. minate; and work done in altering the capacity or the figure of the vessel does not produce heat, but only stored up energy, like that possessed by a bent spring. A system of particles confined within a vessel, and not sen- sibly attracting or repelling each other, but in a state of motion, exerts outward pressure against the internal surface of that vessel through the reactions of the particles that tend to escape, but are prevented by the vessel from doing so; and work done in diminishing the capacity of this vessel wholly takes effect in ac- celerating the motions of the confined particles,—that is, in the language of thermodynamics, producing heat. The condition of actual bodies is compounded of those two ; and it is by means of an equation deduced from what has been called the “Second Law” of thermodynamics, that the force ex- erted by a substance against the internal surface of a vessel con- taining it (in other words, the elastic force of the substance) is distinguished into two components, due respectively to mole- cular attractions and repulsions, and to the reactions of moving” particles (of the nature of centrifugal force). It is the latter component of the force only that 1s taken into account in calcu- lating how much heat is produced by a given alteration of the dimensions or figure of the containing vessel. It has been proved by experiment that very nearly the whole of the work done in compressing a gas takes effect in producing heat; and hence it has been concluded that the elasticity of gases is almost wholly due to the motion of their particles, the compo- nent due to attractions and repulsions being small in comparison. The detailed exposition of the principles to which I have briefly referred, and the comparison of their results with those of expe- riment, have been made so often, by so many authors, and in so many ways, that it would be a waste of time and space for me to explain them further here; and I shall therefore, in conclusion, merely refer to Professor Tait’s work on Thermodynamics as the best source of information regarding the history and present condition of that science; for he gives a summary, in very mo- derate compass, of the different methods of demonstration fol- lowed by the various original authors. In most of the popular writings on the subject, the second law of thermodynamics, together with its proofs and consequences, is omitted, as requi- ring too much mental exertion for its comprehension. I am, Gentlemen, Your most obedient Servant, W. J. Macquorn RankINeE. Glasgow, July 5, 1870. _p. 161. [105 ] XIV. On the Refractive Indices and the Dispersion of Opaque Bodies. By W. WERNICKE*, MPSBIOUS indirect methods have been employed for the de- termination of the refractive indices of bodies which appear opaque when they are of such thickness as is requisite for direct determination by means of prismatic deflection. The one mostly used is the determination of the angle of the greatest polariza- tion (or of the nearly identical principal angle of incidencet) of the substance, the tangent of which is assumed to be equal to the refractive index. But, apart from the contradictions to which we are led by a comparison of the refractive indices of metals deter- mined by this method with those obtained by another method of determination, the observation of the angle of polarization is very uncertain: even with transparent substanccs of great refractive power, results are at times obtained which differ even in the first decimal { from those correctly determined by means of prismatic deflection. The same uncertainty occurs ina still higher degree with Wollaston’s method for the determination of refraction by, means of the total reflection: most opaque bodies of great refrac- tive power, when placed in contact with an hypothenuse-surface of the prism, afford no definite limiting angle of total reflection. Still less applicable is Arago’s method, who, by means of Poisson’s formule, determined the refractive index of mercury to be 5°829, from the ratio of the quantity of perpendicularly incident light reflected to that which is transmitted. If this method is applied to silver, which reflects 95 per cent. of light, the refractive index is found to be 71°8, whilst the method by the angle of polariza-. tion only gives 4-8. A fourth method, more recently applied by Quincke§, according to which the velocity of light in the metal is determined by means of the displacement of fringes which is produced by two interfering pencils of light, one direct and the other passing through a thin lamina of the metal, has given the refractive indices of a few metals less than 1, which is in agree- ment with Cauchy’s formula, but in contradiction to the results of the method by the angle of polarization. All these methods can at most give, in the most favourable case, an approximate idea of the magnitude of the mean refraction ; not one is suitable even for an approximate determination of the dispersion. In the present research I describe a method which admits the - determination of the refractive indices and of the dispersion of a * Translated from Poggendorff’s Annalen, 1870, No. 1. + Haughton, Phil. Trans. vol. cli. pp. 81-125. t Cf. de Sénarmont, Ann. de Chim. S. 2. vol. Ixviii. p. 337. § Monatsber. d. Berl, Akad. 1863, p. 125. Phil. Mag. S. 4. vol. xxvii. 106 M. W. Wernicke on the Refractive Indices great number of that group of bodies which stand next to the metals in degree of opacity, as the protoxides, oxides, peroxides and chlorides, bromides, iodides, and sulphides of the heavy me- tals. The method depends on the fact that these substances admit of being prepared as uniformly thin layers, which show interfe- rence- colours varying with the thickness of the layer. When these colours are examined by the spectroscope, we see spectra of alter- nate bright and dark bands, from the number and position of which the wave-length of light in the substance, and therefore the refractive index, not only en bloc, but also for the different colours. or Fraunhofer’s lines, may be deduced. From the comparative perfection of the methods of preparing the thin layers, the accu- racy of the results which this method furnishes depends almost entirely on the delicacy of the balance, which is preferable to any indirect method of determining the thickness of the layers. i, To determine the wave-length from the position of the maxima or minima in the spectrum, it is first of all necessary to deduce the equations subsisting between these magnitudes with regard to elliptical polarization and absorption. As the interference- bands in the spectrum are best observed in reflected hght with perpendicular incidence, I give the complete formule for this case only. If e denotes the thickness of a thin layer of the substance to be investigated, attached to a metal, then, according to the theory of the colours of thin plates, the intensity of reflected light with perpendicular incidence is L= (r+ p)?—4rp sin? D \ “ake po — apeiron (1) In this expression 7 and p denote the amplitudes of the light reflected from the layer into the air and from the metal into the layer, when the amount of incident light is put equal tol. r is always positive, p only when the refractive index of the layer lies between the indices of the two bounding media, usually air and metal ; p is negative when it is greater or less than each of the other two. The magnitude D is equal to (c+ 61 5 mae in which X is the wave-length of light in the substance, and 6,, 6, denote the retardations which the light undergoes by reflection at the metal surface—that is, the reflection and refraction at the limit of the substance and the air. Formula (1) presupposes that the material of the thin layer is perfectly transparent; in order to apply it to bodies which, although thin, exert an appreciable absorption on light, the | | | and the Dispersion of Opaque Bodies. 107 coefficient of absorption must be introduced. If & denotes the quantity of light passing through a layer whose thickness is le then, according to the law of absorption given by Herschel and Brewster, and afterwards confirmed by Bunsen, Roscoe, and others, the quantity of light which emerges from a layer of the thickness ¢ is =A*. If in deducing the formula (1) we re- member that the amplitude of light in each passage through a layer is diminished to ke, then we obtain for the intensity of the reflected light the expression _ (r+pk*)?—4rpk sin? D (2) inh Rl pk) ark? sin? Dt The first differential of this magnitude for ¢ gives as common condition for the maxima and minima of the intensity of light the equation =sint D | : | 16r?2r(1 — p?k?*)? + 7(] pk) {r(1 + p?k*) + (1 +7r°)k*t nr? log?k 161s? (1 — p?k?*)? + 7? (1 + p%hk?*)?. 2. log? k cre ir(1 + p°k**) + p(] pi et 2. r?. log? k ¥ 16r?7?(1 — pk)? 4 72() + p’k*)?. log?. k out of which, for the minima, -___O Beep (hte Alogi sees Mi slanl t eta) 1l+y.A*. log?k results, in which the sign of the square root is positive, and the coefficients a, 8, y are as follows: @ + p?k?e) @ aL : +pr-+ pth?) io ‘sda l6r*(1— pee 2 1— i —r° pk + pth - + (5) B= oe (1 + p?k«)? ' YT V6n2(1 — p2k*)2 Equations (4) and (5) show that the influence of the absorp- tion is only perceptible when the natural logarithm of the coeffi- cient of absorption & has a value equivalent to the reciprocal value of the wave-length XA. For all bodies which, with the thickness of 4X, are still perceptibly transparent to light of the wave- length 2, from the smallness of the coefficients a, 8, y the terms multiplied by X? almost entirely disappear in equation (4), and sin? D »(3) 108 M. W. Wernicke on the Refractive Indices sin D acquires the values + 1 and —1 for the minima of intensity —) Qa 2 x becomes equal to an indefinitely large multiple of 7; conse- quently of the light; that is to say, the argument D or ( e+ 6,—6 rn : 9 2—m . 9? 465.00). ee ees (6) in which m may be any positive whole number. The magnitudes 6, and 6, cannot be experimentally determined with sufficient accuracy by,means of the formula which the theory of elliptical polarization gives ; but even if they could, in order to obtain the most correct value of X possible we should nevertheless have to proceed according to the following reasoning. Let e, and e, be two values of «, and m, and m, the values of m, which satisfy equation (6); then by subtraction, since 6, and 6, in both cases remain the same, e+ —eé Nek eat eee ae eal According to this formula, the differences of the thicknesses ¢, and e, of the layer for which the minima of the intensity of light occur are proportional to the wave-length, which may be veri- fied by observation. The observations are now conducted in the following manner. If by any of the following methods a thin layer of the body to be examined is prepared and then observed in reflected light through the spectroscope, the solar spectrum is at first seen un- changed in the field of view; when the layer has reached a cer- tain thickness, a dark band appears at the more refrangible end, which, with mereasing thickness of the layer, moves through the spectrum, and after a definite period again appears in the original place. If the thickness of the layer is still further increased, then two, three, and more dark bands gradually appear in differ- ent places of the spectrum. The bands increase in sharpness, and, when more than three are together at the same time, are sometimes so dark that direct sunlight is needed in order to re- cognize Fraunhofer’s lines: generally cloud-light is sufficient to fix their position in the spectrum. If we wish to determine the wave-length of the lhght in the substance for any particular Fraunhofer’s line, then the layer must be made so thick that a dark least band appears in this place; the layer with its support is placed in a balance which is very delicate for small weights, and is then strengthened until the bands appear for the second, third, or fourth time in the same place of the spectrum. The increases in weight give the magnitudes €,— €,, €,—€,, €,—€, and and the Dispersion of Opaque Bodies. 109 so forth’; and the differences m,—m, have for those cases the values 1, 2,3. With a little practice it is not difficult to deter- mine by time the increase of the layer, and in this way to obtain beforehand the moment in which the minima reappear in the same place of the spectrum. If p denotes the increase in weight of the layer determined by the balance after a minimum has passed m times a given Fraun- hofer’s line, s the specific weight, o the surface of the layer, then the refractive index of the substance for the line in question is __M.8.0. ue ser en mE RET (8) when /, denotes the wave-length of the light in air for that line. Lae For the production of thin layers, with various substances several methods often present themselves; they cannot, however, always be used for the production of good interference-layers. By heating iron in air, for instance, very thin layers of protosesqui- oxide of iron are obtained, a body which, prepared electrolytically, gives distinct interference-spectra and beautiful colours. If it be attempted, however, to strengthen by further heating the thin layers which only show the first dull colours, we get neither the beautiful colours of the second series, nor generally any interference-bands in the spectroscope. The reason of this can be easily shown: the layers obtained by heating are only pure protosesquioxide on the surface; within they get less oxygen ; and from a body which from the outside to the inside is continu- ally changing its refractive index the interference-phenomena cannot be expected. The best interference-layers are obtained by suitable action of chemical agents on thin metal layers, or by electrolysis. I have prepared numerous interference-layers by both methods; but at present I confine myself to the latter, which is especially fitted for oxygen compounds of the heavy metals. Nobili (Pogg. Ann. vol. x.) described a great number of liquids the electrolysis of which gives coloured rings on plates of gold, platinum, and other metals ; but they are of no value for the pro- duction of interference-layers. It is easy to prove, for instance, that the rings which he obtained on the positive electrodes of silver, copper, zinc, and bismuth consisted of the oxygen com- pounds of these metals, and were produced by oxidation of the plates by means of the electrolyzed oxygen, but contained nothing whatever of the substance of the electrolytes used. If Nobili had used dilute sulphuric acid or an alkaline solution instead of those different solutions, he would with a corresponding intensity a= 110 M. W. Wernicke on the Refractive Indices of the current have obtained the same rings, The only excep- tions to this are the few precipitates which he obtained on gold or platinum. In the following paragraphs I explain the methods by which serviceable interference-layers are best obtained for optical examination, and how their optical constants and specific weight are determined. 1. Suboxide of Copper. In the preparation of the interference-layers of this body two different ways are available. In both cases a solution consisting of 30 grs. hydrate .of soda, 60 grs. seignette salts, and 25 ars. blue vitriol in 500 cubic centims. of water, serves as a decompo- sing liquid. Using as cathode a thin platinum plate about 1 deci- metre square, and, as anode, two* copper points at a distance of 2 centims. on each side of the middle point of the plate (each pre- senting a surface of a few square millimetres), by means of the current of a smallt Bunsen’s element only so much hydrogen is condensed on the platinum plate as will reduce the oxide of copper to suboxide. The surface of the anode may at first be taken a little larger, for the first precipitate is formed slowly ; the anode may afterwards be lessened to the prescribed size, to be certain that no metallic copper is reduced along with the prot- oxide. Ifthe anode be too large, then at first pure protoxide is obtained ; but afterwards the hydrogen, which is developed more abundantly, reduces the oxide either wholly or partially to metal, The limit between the two processes, however, is tolerably wide; and the smallest traces of metallic copper can be recognized by placing iodine on it, which leaves the suboxide perfectly un- changed, whilst it immediately changes the metal into subiodide. If the surface of the platinum was sufficiently clean (the cleansing is best done by rubbing the plate with linen cloth soaked with a solution of soda, and by placing the plate for some time as a cathode in an alkaline solution so that it becomes electrolytically covered with hydrogen), the colours soon appear in the following order—gold, brown, purple, blue, &c.{, and re- peat themselves within a few hours three or four times almost un- changed; as the thickness increases, only pale green and pale red * I must here observe that the laws of divided currents in fixed conduc- tors for this and similar fluids are by no means applicable; the influence of polarization so preponderates that, even by using one point, both sides of the cathode almost equally colour themselves. This is so much more the case the weaker the current and the slower the decomposition. + The resistance of alkalie copper solution is so considerable that a small piece of copper or zinc wire accomplishes the same effect as a large Daniell’s element, if in both cases equal exciting fluids are applied. { All the substances investigated show at first Newton’s rings in the transmitted light when the reflection takes place from a metal. ——— ee a. ee ee OO ge a ee and the Dispersion of Opaque Bodies. 111 alternate, which after about five or six hours blend into one another and form a pale brownish red closely resembling metallic copper. If the layer be then observed with the spectroscope, four dark bands will show themselves between Fraunhofer’s lines F and B. The layer can be made more than double as thick, and then in the interval named eight or vine minimum-bands obtained. Such a spectrum is, in consequence of the bounding of the dark bands by the high intensities of light of the maxima, far more brilliant than an ordinary absorption-spectrum. The spectrum and also the colours are most splendid when the reflection takes place from silver; for this purpose a thin silvered glass forms the best support for the layer, which moreover conducts sufficiently well and makes possible the examination of the layers in transmitted light. | | Pigincine the surface of the platinum from impurities, which are particularly obstructive to the formation of a uniform layer, is most easily accomplished if it is first covered with copper by means of an alkaline solution of copper. Instead of platinum, ordinary tinfoil may be applied with advantage, which, before _ the plating, is cleaned by breathing on it and polishing it with a linen pad sprinkled with prepared chalk. The tinfoil is coppered by the current of a weak Bunsen’s element in an alkaline copper solution ; the tinfoil covers itself uniformly with a bright copper _ coating and with condensed hydrogen, which, precipitated simul- _ taneously with the copper, adheres far better to the plate than it would without this—that is, better than if the tinfoil in a soda so- _ lution were to be covered with hydrogen. After from ten to fifteen _ minutes the current is broken, and the copper-covered tinfoil, with- _ out being washed, is instantly suspended in the above-mentioned solution of copper. The reduction by the hydrogen adhering to the plate soon begins; the copper is gradually coloured golden- yellow, red, blue, whitish, greenish yellow, and again golden yellow. It takes about fifty minutes for these colours to deve- lope themselves ; the development afterwards proceeds slowly ; _ but it is best to interrupt it at the second golden-yellow, where a ‘minimum near the line F appears in the spectroscope, and to cover the plate afresh with hydrogen if stronger layers are wanted immediately. For this purpose a soda solution of 1-035 specific gravity is used, which is first diluted with an equal quan- _tity of water; ifthe lye or the current be too strong, the suboxide of copper may be reduced to metallic copper. With the pre- scribed data, in ten minutes the layer of suboxide of copper will _be covered with a layer of hydrogen, which within an hour re- duces from the solution of copper a layer of suboxide of the thick- ness of half a wave-length. This method may also be used as a convenient lecture experiment, to make visible the hydrogen 112 M. W. Wernicke on the Refractive Indices condensed on the surface of a metal, and to determine its amount quantitatively. To ascertain the specific gravity of the suboxide of copper, the absolute weight and also the loss of weight of a platinum plate in water were determined by several experiments, and it was then coated with a thicker layer of suboxide (being exposed twelve, and from that to thirty-six hours to the action of the current). When the layer becomes opaque, the copper colour changes to a dark violet ; the least traces of metallic copper, which in the event of a too strong current might be mixed, would change the beautiful violet into an ugly dark brown. When the layer has reached the desired thickness, the absolute weight and the loss of weight of the whole plate are determined. | From four experiments with layers of different thicknesses and almost perfectly agreeing in their results, the density of the suboxide of copper (at 15° C.) was found to be s=5:975. To determine the refractive indices, a rectangular sheet of tin- foil, 10°72 by 7:76 centims., was copper-plated, and then a uni- form layer of suboxide of copper deposited on it. The increase of weight after the minimum-bands had passed eleven times through the line F amounted to 0°08975 gr., and after seven passages of the band through the line C to 008970 gr, From these numbers and equations (8) and (9), together with Fraunhofer’s numbers for the wave-lengths of these lines in air, we calculate the refractive exponents for F and C to be 2°963 and 2°558. A second rectangular sheet of tinfoil, whose surface was 18230 square millims., gave for the refractive indices of the lines E and D, after nine and six passages of the minimum-band, the num- bers 2°816 and 2°705 respectively. A third plate, 21946 square millims. in surface, gave for B the value 2°534; so that the refractive indices of suboxide of copper (Cu? QO) are as follows :— Fraunhofer’s line Refractive index C ata re: D S70 US The refraction, like the dispersion, of suboxide of copper is therefore, apart from the doubtful determinations, the greatest which has hitherto been observed for a solid body. and the Dispersion of Opaque Bodies. 1138 2. Hydrated Peroxide of Lead. By the electrolytic decomposition of a solution of oxide of lead in potash at the positive pole, a series of colours is obtained which is commonly used to represent Nobili’s rmgs. The solu- tion for this purpose is prepared by boiling litharge with a strong alkaline lye. As, however, comparatively little lead goes into so- lution, and operations with strong alkaline fluids are attended with inconvenience, it is more judicious to prepare the solution in the following manner:—5O germs. of acetate of lead dissolved in water are poured, whilst being stirred, into a solution of 50 grms. of tartar and 35 grms. of hydrate of soda, and after the precipi- tate has disappeared is diluted with water to 500 cubic centims. This liquid still gives good results when three-fourths of the lead have been precipitated by the electrolytic process. As a positive electrode I have always used a platinum plate about 1 decimetre square, which is preferable for the measure- ments, as other metals might become oxidized by the active oxygen; the negative pole consists of two small plates of lead or platinum, arranged on both sides of the platinum plate at equal distances from the edges and bent sharply downwards. This system, after insulation of the conducting-wires, it is easy to regulate so that the positive platinum plate shall be uniformly coloured. With these dimensions of the apparatus a small weak Bunsen’s element is sufficient to produce the layers. It appears to be generally considered that the body which gives the interference-colours is peroxide of lead; but the far lower specific gravity (the statements of the density of PbO? vary between 8-903 and 8-933) which | found as the result of nume- rous concordant experiments induced me to investigate it more closely. It followed that the coloured layers on the positive-pole plate, whatever solutions were applied, are never PbO?, but a hydrated oxide of definite composition, which only with difficulty entirely loses its water at a higher temperature, without at the Same time any oxygen disappearing. In athicker layer it forms a compact, bright, blue-black body, which adheres firmly to the platinum, and is by no means hygroscopic, so that its specitic gravity is easily determined. Three determinations, which dif- fered very little in their results, gave, as the mean, for the den- sity of hydrated peroxide of lead s==6°169; a number which is very different from the specific gravity of the dry hydrated peroxide of lead. For the investigation of the refraction and dispersion, it is pru- dent to place the spectroscope in front of the decomposition-appa- ratus with glass sides; in this way, since the liquid is colourless, Phil. Mag. 8. 4. Vol. 40. No. 265. Aug. 1870. I 114 M. W. Wernicke on the Refractive Indices the passage of the interference-bands in the spectrum can be ob- served and the current broken at the proper moment. The colours form far more quickly than with suboxide of copper; the strength of the current 1s so regulated that the layers increase half a wave- length within from seven to ten minutes or a little longer. If the increase takes place too quickly, the layers as they thicken become brittle, and the colours are not perfectly pure. Whilst with suboxide of copper, for ight having the refraction of Fraunhofer’s line F, the minimum-bands can be plainly ob- served, yet with hydrated peroxide of lead this is no longer the case for line E; in the whole of the more refrangible portion of the spectrum no trace of interference-bands is observable, whilst in the yellow, and still more in the red part, they occur with great sharpness. From this it must be inferred that the body, even in layers of the thickness of one or a few wave-lengths, is only transparent for yellow and red rays. To determine the refractive index for the line D, a thin plati- num plate 18570 square millims. in surface was introduced into the decomposition-apparatus, and after it had been tared the pas- sage of a minimum-band was observed fifteen times through that line. The increase in weight of this layer, fifteen half wave- lengths thick, amounted to 0°166 milligrm.; therefore the re- fractive index, according to formula (8), is sya 15 x 18570 x 6°169 x 0°:0005888 mh 2 x 0'1660 For the line C a similar inspection gave the value n(C)=2°010, When the layer reaches a thickness of twenty-four half wave- lengths (D), then from D downwards in the red part of the spec- trum six minimum-bands appear, of which the last is almost coin- cident with line B. Whilst a minimum travels from D to B, the thickness of the layer increases about 1% (D); so that nineteen wave-lengths \(B)=23°5A(D). From this it follows that n(B) =1'802. The latter consideration may therefore serve as con- trol for the direct determination by weighing. The numbers n(D) =2:229 | n(C) =2-010 n(B) =1:802 show that the refraction by hydrated peroxide of lead is less, but the dispersion somewhat greater than that by suboxide of copper. 3. Hydrated Peroxide of Manganese. The interference-layers of this body are best obtained by elec- trolysis of very dilute neutral solutions of salts of protoxide of manganese ; 12 grms. chlorate of manganese and 8 grms. ace- and the Dispersion of Opaque Bodies. 115 tate, dissolved in 500 cubic centims. of water, form a liquid which gives good results even when a great portion of the manganese is separated by the electrolytic process. Concentrated solutions are by no means applicable; even the liquids which Nobili (Pogg. Ann. vol. x.) and Bottger (vol. 1.) used for the preparation of the coloured rings are too concentrated. A weakly-charged element is used along with the decomposition-apparatus described for hydrated peroxide of lead; as the liquid is colourless, the progress of the interference-bands during the operation can be observed through the spectroscope. The strength of the cur- rent is best directed so that the layer grows half a wave-length within from fifteen to thirty minutes; if the growth goes on too quickly, the thicker bright blue-black layer becomes brittle, and with a change of temperature, especially by a wash of cold water, easily cracks. To determine the specific gravity, layers of more than 100 wave-lengths in thickness and of the absolute weight of about 0-5 grm. were prepared; from two concordant experiments the density at 13° C. was s=2°542. The body is not MnO?, but, like all bodies of this group, a hydrate which does not lose its water under the air-pump. It is transparent to green and blue rays in quite thin layers only, of from 1 to 2 wave-lengths, so that minimum-bands can be ob- served in E and F'; with greater thicknesses the same only appear in the yellow and red. The minimum in F, however, is so broad and faint that the wave-length cannot be determined from it by the simple spectroscope without the application of photometrical means. For the lines EH, D, C, I have obtained according to the foregoing methods the values n(E) = 1:944, n(D) = 1-862, n(C) = 1°801. III. General Conclusions. Besides the bodies already described, I also prepared a num- ber of interference-layers im electrolytic and chemical ways, which, like those described, are distinguished by an unusually strong dispersion. The examination of these bodies has led to the conclusion that all bodies of strong dispersion have optical pro- perties in common which appear of interest for the theory of light. It is known from experience that dispersion and absorption are related to one another ; and Cauchy, in his “ Mémoire sur la dispersion de la Lumiére,” has given an equation in which this I2 116 Onthe Refractive Indices and the Dispersion of Opaque Bodies. relation is implicitly contained. The discussion of this equation, of which one side is an infinite series, presents some difficulties ; it has been thought* sufticient to retain the first two terms of this series and neglect the rest. This would be permissible, as M. Christoffel has shown, if in every case the sphere of action were infinitely small in comparison with the wave-length. That the last assumption is not admissible, however, the discussion of the incomplete equation shows ; for it yields the result that every spectrum is bounded at the violet end by a visible beam of defi- nite refraction. This inference is a physical absurdity, since it presupposes the existence of bodies which, under any arbitrary angle of incidence, totally reflect a visible beam, or completely absorb it on the surface. The dispersion-formula derived from the imperfect series, even if correct for large wave-lengths, can offer no explanation as to what really occurs at that limit at the more refrangible end of the spectrum. Whilst this limit with substances of weak dispersion would lie very far in the ultra-violet, it sometimes appeared in the green in the bodies which I investigated. With no single body of this group were even traces of interference observed in the violet. The reason of this phenomenon might be sought in a strong re- flection of these rays at the surface, or in a strong absorption in the interior; it has been shown that the latter is the preponde- rating cause of the absence of interference-bands. Then they always vanish gradually with increasing thickness from the violet to the red end of the spectrum, and are very soon only present in the yellow and red. Hence the absorption increases with decreasing wave-lengths, and indeed continuously so for a cer- tain position in the spectrum which is special to each substance, and so quickly that on the other side of it no ray can pass through a layer of the thickness of half a wave-length. Hence in transmitted light sufficiently thick layers of bodies of preeminent dispersion always appear yellow-red or red. I have sought in vain for a substance of this kind which would be trans- parent with green, blue, or violet light. To meet any objections to these matters of fact arismg from the mention of apparent exceptions, I must make the following remarks. Thin layers can be prepared in different ways which strongly absorb the light and are transparent to other than yellow or red light ; such layers, however, like glass coated with soot, are not to be regarded as bodies, but as loosely connected apparatus of in- dividual particles, and can only be quoted as exceptions if it be proved generally that they possess refractive and dispersive * Cauchy, “ Mém. sur la Disp.,” and Christoffel, Pogg. Ann. vol. cxvil. pp. 27-45. Is the Corona a Solar or a Terrestrial Phenomenon 2 117 properties. For example, let chlorine, bromine, iodine, sul- phur-vapour, or sulphuretted hydrogen act on thin layers of silver; then layers of chloride, iodide, and sulphide of silver are obtained, which in comparison with the metals and the metallic oxides described are very transparent, and show in the spectro- scope beautiful interference-bands. If, however, the intensity or duration of the action of those agents exceeds a certain limit, the structure of the layers is destroyed; the same are then to be regarded as aggregates of many particles (in several cases microscopic crystals), although they appear to the eye as coherent masses; they are more opaque than the metal itself, and show no trace of interference-bands in the spectroscope. In reference to the chemical combination of the oxygen-com- pounds of the heavy metals prepared by electrolysis, the follow- ing result has been found :—Those compounds separated by the current at the positive pole are not, as has hitherto been commonly assumed*, peroxides, but definite hydrates of the same, which do not lose their moisture under the air-pump. I believe I am able to lay this down as a general proposition, as I have proved it for the most different metals, namely lead, manganese, cobalt, bis- muth, and antimony. The o«ides and suboxides separated at the negative pole are, on the contrary, always free from water, as must be inferred from the examination of the electrolytic sub- oxides of copper, bismuth, antimony, and oxide of iron. Berlin, October 1869. XV. On the Determination whether the Corcna is a Solar or Ter- restrial Phenomenon. By Grorce M. Suasroxke, Hsq.t ee is my intention in this paper to attempt to show that, with the existmg state of our knowledge of the corona, the theory set forth by Mr. Lockyer, that the corona is a terrestrial pheno- menon, is quite possible, rather than to show that other theories are wrong ; and further to demonstrate how the question may be set at rest by observations on future eclipses. The points which present themselves are as follows :— 1. What are the facts with respect to the spectra of the corona seen in past eclipses ? 2. What spectra ought we to obtain from the corona on the terrestrial theory during totality ? 3. Are the spectra obtained from the corona in past eclipses reconcilable with those we ought to get on the above hypothesis ? * Vergl. Wohler, ‘ Ueber das Verhalten einiger Metalle im el. Strom,” Nachr. der Kgl. Ges. d. Wiss. u. der G. Univ. zu Gott. 1868, No. 8. + From the Monthly Notices of the Royal Astronomical Society, June 10, 1870. 118 Mr. G. M. Seabroke on the Determination whether 4. What spectrumought wetoget fromthe corona after totality ? 5. What spectrum ought we to get before totality on the fol- lowing side of the moon ? 6. What difference will there be between the spectrum of the central portions of the corona and that of the distant parts during totality ? . With regard to 1. During the Indian eclipse, Major Tennant writes :— Directly I saw the whole moon in the finder I set the cross-wires immediately outside its upper limb. By the time I got to the spectroscope the cloudy range seen in the photographs had vanished from the slit, and I saw a faint continuous spectrum. Thinking that want of light prevented my seeing the bright lines which I had fully expected to see in the lower strata of the co- rona, I opened the jaws of the slit and repeatedly adjusted by the finder, but without effect. What I saw was undoubtedly a conti- nuous spectrum, and I saw no bright lines. There may have been dark lines, of course ; but with so faint a spectrum and the jaws of the slit wide apart they might escape notice.” With respect to the American eclipse, Professor Pickering, with an ordinary chemical spectroscope directed to the sun’s place during totality, saw a continuous spectrum with two or three brright lines, one “near HK” anda second ‘‘ near C.”” Professor Young, while ex- amining a part of the prominence at + 146°, saw C, near D, a line at 1250420, and another at 1850+20, and the 1474 K line very bright, but not equal to C and D,; but he observed that the 1474 K line, unlike C and Dg, extended across the spec- trum ; and on moving the slit away from the prominence it per- sisted, while D, disappeared. He also believes that the two faint lines between it and D, behaved in hke manner. On ex- amining a prominence on the other side of the sun, he observed nine lines and a faint continuous spectrum without any traces of dark lines in it. As to the second point, let us find what spectrum we ought to obtain from a corona at a point on the earth where the limbs of the sun and moon are in line,—that is, where the eclipse is total exactly. the Corona is a Solar or Terrestrial Phenomenon. 119 Let A be a point on the earth where the sun is eclipsed ; BC, limit of earth’s atmosphere ; D, the moon ; H E, photosphere of sun ; E F, the apparent corona. Now, if the corona be terrestrial, the light producing it must be reflected or separated from the atmosphere within the triangle ABC. Join BD and produce to G. Then G is the most distant point from the limb on the sun’s disk from which light is reflected to A by the atmosphere; and if the triangle HAF or angular extent of the corona from the sun is given, wecan find Z HAG. ZHEAG GH The angles being small, -——- ZEAF mes EF approximately. GE:CB::ED:DO, therefore an=c3®?, svadinla) and EA EF:CB::EA:CA, therefore EF = CBG: «» {2) and H D=HA—AD; and AD being small in proportion to EA, ED may without great error be taken as equal to EA. Dividing (1) by (2), ED orEA Pee e 5 CA... height of atmosphere BMP) hone BA ~ DC” dist. of moon—height of atm. ’ CA ZAuAG height of atmosphere * ZEAF ~ dist. of moon— —height of atmosphere’ height of atmosphere | dist. of moon—height of atmosphere EAG=EAF If, for example, we now take eerrete i ahe AN MR ES: EBON and Height of atmosphere . . . . =100 miles, and Dist. of moon—height of atmosphere =240,000 miles, then LEAG=30 7 _=0"75, 240,000 120 Mr. G. M. Seabroke on the Determination whether Therefore the only part of the photosphere available in this case for illuminating the atmosphere is a ring of photosphere O"-75 in width ; and from the figure it will be seen that only that part of the corona most distant from the centre (as at B) will receive even the whole of this ight; and it is manifest from the figure that the nearer any part of the corona is to the centre (nearer C) the less light will it receive from the photosphere, so that the mean illumination of the corona by the photosphere is only equal to that which would be given by a ring } x 0""75 =0"-375 wide. Now, since the chromosphere extends from E towards F, the whole of the atmosphere producing the corona is illuminated equally by the chromosphere; and since the mean height of the chromosphere is much more than 0-375, or other height deduced from the foregoing formula, it is quite possible that the dark lines of the spectrum coming from so small an area of photosphere may be blotted out, as Mr. Lockyer observes, by the light from a greater area of chromosphere wherever the chromosphere contains the proper substances ; and it is probable that the vapours of a number of substances from the photosphere are carried up into the chromosphere in small quantities sufficient to obliterate the dark lines, since we find the vapours of magnesium, sodium, ba- rium, and iron sometimes in the chromosphere. Although the total amount of light of all kinds given by an equal area of chromosphere is small compared with that givenbyan equal area of photosphere, still each particular kind of ight from the chromosphere is as intense, or nearly so, as that particular kind of light from the photosphere; so that if equal areas of chromosphere and photosphere be illuminating a part of our atmosphere, that part would give a spectrum having its dark lines erased by the chromosphere, or a continuous spectrum. When the area of the photosphere is much less than that of the chromo- sphere, the bright lnes given by the chromosphere would be much more visible than the remaiming dark lines of the photo- spheric spectrum. From this it appears that during totality we ought to get from the corona a nearly continuous spectrum, with bright lines given by the substances in the chromosphere. Some of the dark lines of the photospheric spectrum ought to remain, where the chro- mosphere does not contain substances giving bright lines in their place. Where the illuminating areas of the photosphere and chromosphere are equal, which is possible where the chromo- sphere is unusually low, we ought to obtain a spectrum as above, but without bright lines, the chromospheric lines being then only just able to obliterate the dark ones. 3. In the Indian eclipse Major Tennant saw a continuous the Corona is a Solar or Terrestrial Phenomenon. 121 spectrum without bright lines, which is that we should obtain on the above hypothesis when the areas of chromosphere and photosphere illuminating our atmosphere are equal; but it is Shown above that during totality with the ordinary height of chromosphere the illuminating area of chromosphere is much greater than that of the photosphere, so that the part of the chromosphere illuminating that part of the corona under exami- nation must have been unusually low, or, as was probably the case, there were bright lines; for, as he says the spectrum was very faint, they may have been missed. There ought on this hypothesis to have been dark lines ; but Major Tennant says that with so wide a slit he might have missed them. Professor Pickering saw a continuous spectrum with bright lines, which is what we ought to obtain when the atmosphere is illuminated by a greater area of chromosphere than photosphere, as has been shown to be the case when the chromosphere is at its normal height. The dark lines which ought to have been visible on Mr. Lockyer’s theory might possibly have been too faint to be noticed, since, as stated above, the area of photosphere in this case would be small in proportion to that of the chromosphere, so that the bright lines would appear very plainly when the photospheric spectrum was too faint to render the dark lines visible. As to the 1474 K line observed by Professor Young to extend across the spectrum beyond the other lines of the chromosphere, Mr. Lockyer observes that he often sees this line and often does not, which appears fatal to this being a real corona line, as, if so, it ought always to be visible. Professor Young also seems, in the note to his observations, to be doubtful how far this line ex- tended from the prominence; and it is very probable that this line is either iron or hydrogen. There seems to be no evidence that the other lines seen in the corona spectrum are not chromo- spheric lines. 4. With regard to this point, an inspection of the figure will show that, as the moon passes over the sun, more photospheric light becomes available for illuminating the corona; but so long as the available area of the photosphere is less than that of the chromosphere, the dark lines of the spectrum, due to the photo- sphere, will be erased by the chromospheric lines (wherever the chromosphere contains the proper substances) ; and as the moon moves forward the spectrum should on this hypothesis change ; and when the illuminating area of the photosphere becomes greater than the area of the chromosphere, the dark lines of the photospheric spectrum should appear. It will also be seen that the larger the illuminating area of the photosphere becomes, the smaller will be the difference between the spectrum of the interior part of the corona and that of the exterior part, since, whatever 122 Prof. R. Clausius on a Mechanical Theorem be the extent of the illuminating surface of the photosphere, the exterior parts of the corona will only receive an excess of light over that received by the interior part equal to the amount of photospheric light received by those parts during totality, or, as in the case above taken, the excess will be equal to that given by a ring of light from the photosphere 0-75 wide (or GE in the figure), so that, when a few seconds of photosphere are visible to the observer, the difference between the spectra of the exterior and interior parts of the corona would be inappreciable. 5. What spectrum ought the corona to give before totality on the following side of the moon? In this case, when the angular distance of the limits of the sun and moon is some seconds, the difference between the spectra of the exterior and interior parts © of the corona is small, since no part of the atmosphere in this case will be illuminated by the photosphere ; so we ought to ob- tain a chromospheric spectrum, together with a faint photospheric one caused by a small amount of photospheric light reflected from the photosphere by the chromosphere. 6. On the foregoing hypothesis, during totality the parts of the corona nearest the centre should give a different spectrum from the more distant portions, since the portions nearer the centre receive less photospheric light than the more distant parts, and the same amount of light from the chromosphere. In order to test the correctness of this theory, advantage may be taken of the following facts:—I1st. At that period of the eclipse when the limb of the sun and moon are in line with the observer, there will be a difference between the central and dis- tant parts of the corona; and this difference will decrease as the moon passes on, whereas, by the other theory, there should be the same difference as long as the corona is visible. 2nd. Ifthe corona be terrestrial, the spectrum of any portion of it ought to be continually changing during the passage of the moon; but if solar, the spectrum should remain unchanged. XVI. On a Mechanical Theorem applicable to Heat. By RK. Ciavstus*, N a treatise which appeared in 1862, on the mechanical theory of heat+, I advanced a theorem which, in its sim- plest form, may be thus expressed :— The effective force of heat is * Translated from a separate impression communicated by the Author, having been read before the Niederrheinischen Gesellschaft fiir Natur- und Heilkunde, on June 13, 1870. + Phil. Mag. S. 4. vol. xxiv. pp. 81, 20] ; The Mechanical Theory of Heat, p. 215. applicable to Heat. 123 proportional to the absolute temperature. From this theorem, in conjunction with that of the equivalence of heat and work, I have, in the subsequent portion of that treatise, deduced various con- clusions concerning the deportment of bodies towards heat. As the theorem of the equivalence of heat and work may be reduced to a simple mechanical one, namely that of the equivalence of vis viva and mechanical work, I was convinced @ priori that there must be a mechanical theorem which would explain that of the increase of the effective force of heat with the temperature. This theorem I think I shall be able to communicate in what follows. Let there be any system whatever of material points in sta- tionary motion. By stationary motion I mean one in which the points do not continually remove further and further from their original position, and the velocities do not alter continuously in the same direction, but the points move within a limited space, and the velocities only fluctuate within certain limits. Of this nature are all periodic motions—such as those of the planets about the sun, and the vibrations of elastic bodies,—further, such irregular motions as are attributed to the atoms and mole- cules of a body in order to explain its heat. Now let m, m’, m'', &c. be the given material points, 2, y, Z, z', y', z', x", y", 2", &c. their rectangular coordinates at the time z¢, and X, Y, Z, X', Y', Z’, X", Y", Z", &c. the components, taken in the directions of the coordinates, of the forces acting upon them. Then we form first the sum ml (dx\? aah ay = aL (a) +z) +(@) | for which, v, v/, v", &c. being the velocities of the points, we may write, more briefly, > 5 vw, which sum is known under the name of the vis viva of the system. Further, we will form the following expression :— —42>(Xe+ Yy+ Zz). The magnitude represented by this expression depends, as is evident, essentially upon the forces acting in the system, and, if with given coordinates all the forces varied in equal ratio, would be proportional to the forces. We will therefore give to the mean value which this magnitude has during the stationary motion of the system the name of Virial of the system, from the Latin word vis (force). 124 Prof. R. Clausius on a Mechanical Theorem In relation to these two magnitudes the following theorem may now be advanced :— The mean vis viva of the system is equal to its virial. Distinguishing the mean value of a magnitude from its vari- able value by drawing a horizontal line over the formula which represents the latter, we can express our theorem by the follow- ing equation :— 25 es —43(Xxv+ Yy+ Zz): As regards the value of the virial, in the most important of the cases occurring in nature it takes a very simple form. For example, the forces which act upon the points of the mass may be attractions or repulsions which those points exert upon one another, and which are governed by some law of the distance. Let us denote, then, the reciprocal force between two points of the mass, m and m’, at the distance r from each other, by ¢(7), in which an attraction will reckon as a positive, and a repulsion as a negative force; we thus have, for the reciprocal action :— = 2+ $ 0)" a= $07) And since for the two other coordinates corresponding equations may be formed, there results —1(Xet Yy+Zz+ Xa! + Y'y! + Zz!) = ird(r). xtending this result to the whole system of points, we obtain — 32 (Xv+ Yy+ Zz)=32rd(r), in which the sign of summation on the right-hand side of the equation relates to all combinations of the points of the mass in pairs. Thence comes for the virial the expression 42 rg(r) ; and we immediately recognize the analogy between this expres- sion and that which serves to determine the work accomplished in the motion. Introducing the function ®(r) with the signi- fication = | d(r)dr, we obtain the familiar equation —>(Xdzx + Ydy + Zdz)=d> P(r). The sum {(r) is that which, in the case of attractions and re- (a! — x)? r Xe+Xl2'=$(r)” applicable to Heat. 125 pulsions, which act inversely as the square of the distance, is named, irrespective of the sign, the reciprocal potential of the system of points. As it is advisable to have a convenient name* for the case in which the attractions and repulsions are governed by any law whatever, or, more generally still, for every case in which the work accomplished in an infinitely small motion of the system may be represented by the differential of any magnitude dependent only on the space-coordinates of the points, I propose to name the magnitude whose differential represents the negative value of the work, from the Greek word épryov (work), the ergal of the system. The theorem of the equivalence of vis viva and work can then be expressed very simply; and in order to exhibit distinctly the analogy between this theorem and that respecting the virial, I will place the two in juxtaposition :-— (1) The sum of the vis viva and the ergal is constant. (2) The mean vis viva is equal to the virial. In order to apply our theorem to heat, let us consider a body as a system of material points in motion. With respect to the forces which act upon these points we have a distinction to make: in the first place, the elements of the body exert upon one another attractive or repulsive forces; and, secondly, forces may act upon the body from without. Accordingly we can divide the virial into two parts, which refer respectively to the internal and the external forces, and which we will call the internal and the external virial. Provided that the whole of the internal forces can be reduced to central forces, the internal virial is represented by the formula above given for asystem of points acting by way of attraction or repulsion upon one another. It is further to be remarked that, with a body in which innumerable atoms move irregularly but in essentially like circumstances, so that all possible phases of mo- tion occur simultaneously, it 1s not necessary to take the mean value of rd(r) for each pair of atoms, but the values of rd(r) may be taken for the precise position of the atoms at a certain moment, as the sum formed therefrom does not importantly differ from their total value throughout the course of the individual motions. Consequently we have for the internal virial the expression 22rg(r). As to the external forces, the case most frequently to be con- sidered is where the body is acted upon by a uniform pressure normal tothe surface. ‘The virial relative to this can be expressed * The term force-function, besides some inconvenience, has the disad- vantage of having been already used for another magnitude, which stands to the one in question in a relation similar to that in which the potential- function stands to the potential. 126 Prof. R. Clausius on a Mechanical Theorem very simply; for, p signifying the pressure, and v the volume of the body, it is represented by Sp. Denoting, further, by h the vis viva of the internal motions (which we call heat), we can form the following equation :— = $2rh(r) +3pv. We have still to adduce the proof of our theorem of the rela- tion between the ws viva and the virial, which can he done very easily. The equations of the motion of a material point are :— d*x mee d*y d*z m WP =X 3 ae TY ih a San Z But we have d* (x) ames 0) = uF r) +2 oe or, differently Bias dx d*x — d?(a?) 2G) = Noe” aida Multiplying this equation by 7 and putting the magnitude X for ae we obtain di?’ tn)" = : m d?(x?) CNdeR oY Adee The terms of this equation may now be integrated for the time from 0 to ¢, and the Tae divided by ¢; we thereby obtain 5A, (ae) = ae | e+ Ge Ca) in which (— 2) denotes the initial value of fe. t 1 aN ( a) dt and 7 {eat occurring in the above equation, represent, if the duration of time ¢ The pie? 2 is properly chosen, the mean values of ( =) and Xwz, which were dx \* << WEY denoted above by ie and Xx. For a periodic motion the applicable to Heat. 127 duration of a period may be taken as the time ¢; but for irregular motions (and, if we please, also for periodic ones) we have only to consider that the time ¢, in proportion to the times during which the point moves in the same direction in respect of any one of the directions of coordinates is very great, so that in the course of the time ¢ many changes of motion have taken place, and the above expressions of the mean values have become suffi- ciently constant. The last term of the equation, which has its factor included in the square brackets, becomes, when the motion is periodic, 2 =O at the end of each period, as at the end of the period a 2 resumes the initial value (3 ) ) . When the motion is not 0 periodic, but irregularly varying, the factor in brackets does not so regularly become =0; yet its value cannot continually in- crease with the time, but can only fluctuate within certain limits ; and the divisor ¢, by which the term is affected, must accord- ingly cause the term to become vanishingly small with very great values of ¢. Hence, omitting it, we may write m (dx\? iz Dy =) = —iXe. As the same equation is valid also for the remaining coordi- nates, we have da\? _ (dy? , (dz? Xa+Yy+4Zz), sted +(w ie =) |=— ker y+ Ze), ‘or, more briefly, 5o= —1(Xe+Yy+Za), and for a system of any number of points we have the perfectly corresponding one m— 2g P= — 42> (Xa + Vy Zz). Hence our theorem is demonstrated ; and at the same time it is evident that it is not merely valid for the whole system of mate- rial pomts, and for the three directions of coordinates together, but also for each material point and for each direction separately. rit Bes. XVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 68.] April 28.—Dr. William Allen Miller, Treasurer and Vice- President, in the Chair. HE following communication was read :— “ On a Cause of Error in Electroscopic Experiments.” By Sir Charles Wheatstone, F.R.S. To arrive at accurate conclusions from the indications of an elec- troscope or electrometer, it is necessary to be aware of all the sources of error which may occasion these indications to be misinterpreted. In the course of some experiments on electrical conduction and in- duction which I have recently resumed, I was frequently delayed by what at first appeared to be very puzzling results. Occasionally I found that I could not discharge the electrometer with my finger, or only to a certain degree, and that it was necessary, before commen- cing another experiment, to place myself in communication with a gas-pipe which entered the room. How I became charged I could not at that time explain ; the following chain of observations and ex- periments, however, soon led me to the true solution. I was sitting at a table not far from the fireplace, with the electro- meter (one of Peltier’s construction) before me, and was engaged in experimenting with disks of various substances. To ensure that the one I had in hand, which was of tortoiseshell, should be perfectly dry, I rose and held it for a minute before the fire; returning and placing it on the plate of the electrometer, I was surprised to find that it had apparently acquired a strong charge, deflecting the index of the electrometer beyond 90°. I found that the same thing took place with every disk [ thus presented to the fire, whether of metal or any other substance. My first impression was that the disk had been rendered electrical by heat, though it would have been extra- ordinary that, if so, such a result had not been observed before; but on placing it in contact with a vessel of boiling water, or heating it by a gas-lamp, no such effect was produced. I next conjectured that the phenomenon might arise from a difference in the electrical state of the air in the room and that at the top of the chimney ; and to put this to the proof, I adjourned to the adjacent room, where there was no fire, and bringing my disk to the fireplace I obtained precisely the same result. That this conjecture, however, was not tenable was soon evident, because I was able to produce the same deviation of the needle of the electrometer by bringing my disk near any part of the wall ofthe room. This seemed to indicate that different parts of the room were in different electrical states; but this again was disproved by finding that when the position of the electrometer and the place where the disk was supposed to be charged were interchanged, the charge of the electrometer was still always negative. ‘The last resource was to assume that my body had become charged by walking across the carpeted room, though the effect was produced eveu by the most ES LP rl a ee hh hl ate aa Tae. Royal Society. 129 careful treading. This ultimately proved to be the case; for resu- ming my seat at the table and scraping my foot on the rug, I was able at will to move the index to its greatest extent. Before I proceed further I may state that a gold-leaf electrometer shows the phenomena as readily. When I first observed these effects the weather was frosty ; but they present themselves, as I have subsequently found, almost equally well in all states of the weather, provided the room be perfectly dry. I will now proceed to state the conditions which are necessary for the complete success of the experiments, and the absence of which has prevented them from being hitherto observed in the striking manner in which they have appeared to me. The most essential condition appears to be that the boot or shoe of the experimenter must have a thin sole and be perfectly dry; a surface polished by wear seems to augment the effect. By rubbing the sole of the boot against the carpet or rug, the electricities are separated, the carpet assumes the positive state and the sole the ne- gative state; the former being a tolerable insulator prevents the po- sitive electricity from running away to the earth, while the sole of the foot, being a much better conductor, readily allows the charge of ne- gative electricity to pass into the body. So effective is the excitation, that if three persons hold each other by the hands, and the first rubs the carpet with his foot while the third touches the plate of the electrometer with his finger, a strong charge is communicated to the instrument. Even approaching the electrometer by the hand or body, it be- comes charged by induction at some distance. A stronger effect is produced on the index of the instrument if, after rubbing the foot against the carpet, it be immediately raised from it. When the two are in contact, the electricities are in some degree coerced or dissimulated ; but when they are separated, the whole of the negative electricity becomes free and expands itself in the body. A single stamp on the carpet followed by an immediate removal of the foot causes the index of the electrometer to advance several degrees ; and by a reiteration of such stamps the index ad- vances 30° or 40°. The opposite electrical states of the carpet and the sole of the boot were thus shown: after rubbing, I removed the boot from the carpet, and placed on the latter a proof-plate (¢. e. a small disk of metal with an insulating handle), and then transferred it to the plate of the electrometer; strong positive electricity was manifested. Performing _ the same operation with the sole of the boot, a very small charge was carried, by reason of its ready escape into the body. The negative charge assumed by sole-leather when rubbed with animal hair was thus rendered evident. I placed on the plate of the electrometer a disk of sole-leather and brushed it lightly with a thick camel’s-hair pencil; a negative charge was communicated to the elec- trometer, which charge was principally one of conduction, on account of the very imperfect insulating-power of the leather. Various materials, as India-rubber, gutta percha, &c., were sub- Phil, Mag. 8. 4. Vol. 40. No, 265, Aug. 1870. 130 Royal Society :— stituted for the sole of the boot; metal plates were also tried: all communicated negative electricity to the body. Woollen stockings are a great impediment to the transmission of electricity from the boot ; when these experiments were made I wore cotton ones. When I substituted for the electrometer a long wire galvanometer, such as is usually employed in physiological experiments, the needle was made to advance several degrees. At the Meeting of the British Association at Dublin in 1857, Professor Loomis, of New York, attracted great attention by his ac- count of some remarkable electrical phenomena observed in certain houses in that city. It appears that in unusually cold and dry win- ters, in rooms provided with thick carpets and heated by stoves or hot-air apparatus to 70°, electrical phenomena of great intensity are sometimes produced. A lady walking along a carpeted floor drew a spark one quarter of an inch in length between two metal balls, one attached toa gas-pipe, the other touched by her hand ; she also fired ether, ignited a gaslight, charged a Leyden jar, and repelled and at- tracted pith-balls similarly or dissimilarly electrified. Some of these statements were received with great incredulity at the time both here and abroad; but they have since been abundantly confirmed by the Professor himself and by others. (See Silliman’s American Journal of Science, July 1858.) . My experiments show that these phenomena are exceptional only in degree, The striking effects observed by Professor Loomis were feeble unless the thermometer was below the freezing-point, and most energetic when near zero, the thermometer in the room stand- ing at 70°. Those observed by myself succeed in almost any weather when all the necessary conditions are fulfilled. Some of these condi- tions must frequently be present ; and experimentalists cannot be too much on their guard against the occurrence of these abnormal effects. I think I have done a service to them, especially to those engaged in the delicate investigations of animal electricity, by drawing their at- tention to the subject. May 19.—General Sir Edward Sabine, K.C.B., President, in the Chair. The following communications were read :— “On the Cause and Theoretic Value of the Resistance of Flexure in Beams.” By W. H. Barlow, F.R.S. The author refers to his previous papers, read in 1855 and 1857, wherein he described experiments showing the existence of an ele- ment of strength in beams, which varied with the degree of flexure, and acts in addition to the resistance of tension and compression of the longitudinal fibres. It was pointed out that the ratio of the actual strength of solid rectangular beams to the strength as computed by the theory of Liebnitz is, In cast iron, as about 21 to 1. In wrought iron as 13 and 1? to 1. And in steel,:as 12 and 12 to 1. Mr. W. H. Barlow on the Resistance of Flexure in Beams. 131 The theory of Liebnitz assumes a beam to be composed of longi- tudinal fibres only, contiguous, but unconnected, and exercising no * mutual lateral action. But it is remarked that a beam so constituted would possess no power to resist transverse stress, and would only have the properties of a rope. Cast iron and steel contain no actual fibre; and wrought iron (although some qualities are fibrous) is able to resist strain nearly equally in any direction. The idea of fibre is convenient as facilitating investigation ; but the word fibre, as applied to a homogeneous elastic solid, must not be understood as meaning filaments of the material. In effect it repre- sents lines of direction, in which the action of forces can be ascer- tained and measured ; for in torsion-shearing and “ angular defor- mation’? the fibres are treated by former writers as being at the angle of 45°, because it has been shown that the diagonal resistances have their greatest manifestation at that angle. 3 Elastic solids being admitted. to possess powers of resistance in the direction of the diagonals, attention is called to omission of the effect of resistance in the theory of beams. The author then states, as the result of his investigation, that com- pression and extension of the diagonal fibres constitute an element of strength equal to that of the longitudinal fibres, and that flexure is the consequence of the relative extensions and compressions in the direct and diagonal fibres, arising out-of the amount, position, and direction of applied forces. Pursuing the subject, it is shown that certain normal relations subsist between the strains of direct fibres and their relative diago- nals, evenly distributed strain being that in which the strain in the direct fibres is accompanied by half the amount of strain in the rela- tive diagonal fibres. Any disturbance of this relation indicates the presence of another force. Thus tensile forces applied at r2ght angles to compressive forces of equal amount, produce no strain in the diagonals. But if forces applied at right angles to each other are both tensile, or both com- pressive, the strain in the diagonal is as great as that in the direct fibres. It is also pointed out that in a given fibre a 6c, the point 6 may be moved with regard ‘to @ and c, thus producing plus and minus strains in the same fibre. ‘Treating a solid as being made up of aseries of laminz, and showing that every change of figure can be represented by the variation in length of the diagonals, taken in connexion with those of the direct fibres, the author proceeds to trace the effects of the application of tensile and compressive forces acting longitudinally on either side of the neutral plane, and shows that curvature is the result of the relation between the strains in direct fibres and those.in the diagonals. The operation of a single tensile force applied along one side of the plate and a transverse stress are likewise traced out, and the ‘conditions of “ elastic equilibrium’’ referred to. K 2 1382 Royal Society :— The amount of resistance offered by the diagonal fibres is shown as follows :— Le abcd represents a portion of a beam strained by transverse forces into the circular curve a e. Two resistances arise. 1. That due to the extension and compression of the longitudinal | fibres produced by the rotation of 6 d about the neutral axis, which is the resistance considered in the theory of Leibnitz. 2. That due to the extension and compression of the diagonal fibres, caused by the deformation of the square a 6 ¢ d into the figure : ahoc, which is the resistance of flexure. | It is then shown that, in a solid rectangular beam, the second resistance is equal to the first, and that both resistances act indepen- | dently, and consequently that the true theoretic resistance of a solid rectangular beam is exactly twice that arrived at by the theory of : Leibnitz, The strength so computed is in general accordance with the results of experiments in cast iron, wrought iron, steel, and other materials, the maximum strength being found in cast iron, which is one- eighth above, and the minimum in glass, which is one-fourth below the calculated strength. The author considers this treatment of the subject as arising ne- cessarily out of Dr. Hook’s law ‘‘ut tensio sic vis,’’ and that it is in effect completing the application of those principles which were only partially applied by Leibnitz. The paper concludes with some practical illustrations (accompa- nied by photographs) of the effect of diagonal action. . The appendix contains the results of experiments on the tensile, _ compressive, and transverse resistances of steel. ; ‘On Deep-sea Thermometers.” By Staff-Commander John E. Davis, R.N. | The results of thermometric observations at great depths in the _ ocean not being of a satisfactory nature, the attention of the Hy- drographer of the Navy was directed to the defects in the construc- tion of the Six’s self-registering thermometers then in use, and also to the want of knowledge of the effects of compression on the bulb ; _— Staff-Commander J. E. Davis on Deep-sea Thermometers. 1383 and as it was known that a delicate thermometer was affected in vacuo, it was natural to suppose that an opposite effect would be had by placing them under pressure, and particularly such as they would be subjected to at great depths. Several thermometers, of a superior construction, were made by different makers, and permission was granted to make experiments by pressure in an hydraulic press; but much delay was caused by not being able to obtain a press suitable to the requirements, until Mr. Casella, the optician, had a testing-apparatus constructed at his own expense, and the experiments were commenced. Previously to the experiments being made, Dr. W. A. Miller, V.P.R.S., proposed, or rather revived, a mode of protecting the bulb from compression by encasing the full bulb in glass, the space between the case and the bulb being nearly filled with alcohol*. A wrought-iron bottle had been made to contain a thermometer, for the purpose of comparison with those subjected to compression ; but it failed, and finally burst under great compression; it proved, however, of but little consequence, as those designed by Dr. Miller showed so little difference under pressure that they were at once ac- cepted as standards. Two series of experiments were then most carefully made, at pres- sures equal to depths of 250, 500, 750, &c. to 2500 fathoms, the results of which satisfactorily proved that the strongest-made unpro- tected thermometers were liable to considerable error, and therefore that all previous observations made with such instruments were in- correct. Experiments were also made in the testing-apparatus with Sir Wm. Thomson’s enclosed thermometers, to ascertain the calorific effect produced by the sudden compression of water, in order to find what error, if any, was due to compression in the Miller pattern: an error was proved to exist, but small, amounting to no more than 1°4 under a pressure of 3 tons to the square inch. The dredging-cruise of the ‘ Porcupine’ afforded an opportunity of comparing the results of the experiments made in the hydraulic test- ing-apparatus with actual observation in the ocean, and a most careful series of observations were obtained by Staff-Commander E. K. Calver at depths corresponding to the pressure applied in the testing-apparatus ; the result was, that although there was a differ- ence in the curves drawn from the two modes of observation, still the general effect was the same, and the means of the two were identical. From these experiments and observations a scale has been made by which observations made by thermometers of similar construction to those with unprotected bulbs can be corrected and utilized, while it is proposed that by means of observations made with the Miller pattern in the positions and at the same depths at which observa- tions have been made with instruments not now procurable for actual * Phil. Mag. November 1869, 134 Royal Society :— éxperiment, to form a scale for correcting all observations made with that particular type. In conclusion, it is suggested that to avoid error from the unsatis- factory working of the steel indices, which, from mechanical diffi- culties in their construction, cannot always be depended on, two instruments should be sent down for every observation ; and although their occasional disagreement of record may raise a doubt, a little experience will enable the observer to detect the faulty indicator, while their agreement will create confidence. A description of sach deep-sea metallic thermometers as have been invented is appended. _ On the Chemical Activity of Nitrates.” By Edmund J. Mills, D.Sc. In the course of his researches upon nitro-compounds, the author found it extremely desirable to submit the genetic relations of those bodies to a detailed examination ; in other words, to trace the modifi- cations undergone by nitryl as it is transmitted (from the chloride, hydrate, or free radical) through an adequate succession of combi- nations. One of the first steps in this direction is the preparation of nitrylic chloride, which can be most easily effected, according to a statement in Watts’s ‘ Dictionary of Chemistry’ *, by the action of phosphoric oxychloride on plumbic nitrate— 3 Pb (NO,),+.2 PO Cl,= Pb,(PO,), +6 NO, CL. Among other modes of verifying this equation, the examination of the residue left behind when excess of the oxychloride is heated with plumbic nitrate, and then distilled off in a current of dry: air, appeared the most simple and obvious. The results were found not to agree with the equation; and after three nitrates had been tried, a law of chemical activity became evident, rendering the reaction worthy of pursuit for its own sake, although, as an available source of nitrylic chloride, it had failed entirely. The nature and mode of establishment of this law constitute the subjects of the author’s memoir. When a nitrate is treated with phosphoric oxychloride, as has just been mentioned, the residue contains phosphoric oxide and a metallic chloride. Within the limits of experimental error, or subject to other satisfactory explanation, the ratio between these two products is constant for each nitrate; and trom that ratio a quotient a can be found as follows :— weight of chlorine AEE Cl al weight of chlorine % 4:06 weight of phosphoric oxide weight of phosphoric oxide P.O, This quotient, which is different for each nitrate, is termed the “coefficient of chemical activity ”’ of nitrates, and the method of ob- taining it is designated the ‘“‘ method of ratios.’’ The data from which OViols iver id. : : 7 Dr. H. J. Mills on the Chemical Activity of Nitrates. 1385 a is deduced, namely, certain weights of argentic chloride and magnesic pyrophosphate, are, if singly considered, new with each experiment ; they depend on time, rate of heating, the state of divi- sion of the nitrate, and other conditions. But, assuming the results to have been brought about under a law of chemical action, the values of a must be independent of those circumstances, by which the pri- mitive numerator and denominator could have been only pari passu affected ; they are related only to the actual occurrence of the re- action. This property, in a chemical ratio, has not, it is believed, been previously observed. After describing the means employed for obtaining a current of dry air, the apparatus required for the reaction, and the individual ex- periments which were severally made, the following Table of results ae : : ‘ x is given, & being the symbolic value of a nitrate, and Q= =e a = Q Thallous nitrate ........ 8:76 265°30 30°29 Argentic nitrate ........ 5°48 169°94 31:01 Plumbic nitrate ........ 5:17 165°56 82°02 Rubidic nitrate ........ 2°38 147°40 61:93 O(eesic nitrate ......55.. 2-21 195:01 88°24 ‘Potassic nitrate ........ 1:99 101°14 50°82 Sodic mitrate’.. 0...) s 02. 1°70 85°05 50:03 Pore nitrate ok) oe. 1°61 69-00 42°86 The above list probably contains all the metallic nitrates that can be completely dried, excepting nitrates derived from amines and amides, which, in the present state of our knowledge of the phos- phamides, it was evidently advisable to exclude. In the silver group, the mean value of Q is 31°11; and the fol- lowing equation may be accepted therefor :— Pe Fee dll In the potassium group we have likewise | x 0 50°42" Hence, within each set of nitrates, chemical activity is in direct proportion to symbolic yalue. It is further sufficiently apparent that (excepting rubidic nitrate) « and increase and diminish in the same general order. Within the limits of error, the Q column is an in- complete arithmetical series, the most probable value of whose first term is 6°258, so that Q=m 6°258, m being integral. Reasons are then adduced for identifying the number 6°25 with Dulong and Petit’s constant of specific heat. Moreoyer, since the product of specific heat and symbolic value is, 136 Geological Society :— generally, x 6°25, and m is greater than n, taking m=wn and s=the specific heat of a nitrate, we have Q= 27 6°25 : but DS=710: 25.5 1 Qc ads, and D532) SSR ~ Q «ds as the expression for chemical activity in terms of specific heat. Compa- ring the coefficients (a, a'} for any two nitrates, the following relations are obtained :— and it is shown that these formule agree sufficiently well with expe- riment. Where m=m! and «=w', we have the simple expression The values of Q are strictly equivalent to each other in pomt of activity. The author believes that a is commensurate with the elec- tive function of chemical attraction, first discovered by Bergman. He terminates the memoir with a reference to some well-known in- stances of chemical action (such as that of argentic nitrate on a mixture of aqueous potassic chloride, bromide, and iodide) as serving to bestow a presumptive generality on his principal conclusions. GEOLOGICAL SOCIETY. [Continued from p. 76. ] January 12th, 1870.—Prof. Huxley, LL.D., F.R.S., President, in the Chair. The following communications were read :— 1. “On the Geological Position and Geographical Distribution of the Reptilian or Dolomitic Conglomerate of the Bristol Area.” By R. Etheridge, Esq., F.G.S., Palzontologist to the Geological Survey of Great Britain. The author noticed the history of our knowledge of the Dolomitic Conglomerates of the Bristol area from which the remains of Dino- saurian Reptiles have been obtained, and then described their mode of occurrence and distribution over the district near Bristol. He regarded these deposits as due to the action of the sea-waves of the later or Middle Triassic periods upon the rocks of older Triassic (Bunter) or Permian age during the gradual elevation of the land, and as the probable representatives in point of time of the Muschelkalk, otherwise deficient in Britain. The author then noticed the influence of the conglomerate upon the production of certain minerals, such as calamine and hematitic iron-ores, and discussed at some length the probable course of the phenomena of Mr. J. Prestwich on the Crag of Norfolk and associated Beds. 137 denudation which furnished the materials for the formation of the conglomerate at different levels, in which he recognized two great periods of oscillation, the first witnessing a downward movement of the Paleozoic lands and lasting throughout the deposition of the New Red marl and sands, and the second, during which the accu- mulations of the former were again, at least partly, denuded. With regard to the time at which the remains of Thecodont Reptiles were imbedded in the conglomerate, the author inferred from the evidence that this took place late in the period of the Keuper. 2. “ On the Superficial Deposits of portions of the Avon and Severn Valleys and adjoining Districts.” By T. G. B. Lloyd, Esq., C.E., F.G.S. The author, after describing the general characters of what he termed the Drifts of the Upper and Lower series, and the fresh- water gravels of the Lower Avon, comprised within the district of the Avon valley between Tewkesbury and Rugby, and of the Severn valley above and below the town of Worcester, endeavoured to show that there was a balance of evidence in favour of the existence of an upper and lower platform of drift in the main valley of the Lower Avon, the upper one being of marine origin, and probably belonging to the same epoch as the stratified beds of gravel in the neighbourhood of Worcester, which contain marine shells and mam- malian remains, whilst the lower one, of freshwater origin, had been derived from the former by fluviatile action, as supposed by the late Prof. Strickland. Further, that there was no evidence to warrant the supposition of the existence of high- and low-level river-gravels in those portions of the Severn and Avon valleys under review, and that the apparent absence of any freshwater shells in the gravels of the Severn valley between Bridgnorth and Tewkesbury led to the inference that the freshwater gravels of the Avon were not repre- sented in the adjoining portions of the Severn valley, although re- mains of some of the same species of Mammalia occurred in both localities. After stating his opinion that the time had not yet ar- rived for indulging in theoretical speculations concerning the pheno- mena of the Drifts of the Upper and Lower series exhibited in so small an area as the one under consideration, the author concluded by expressing hopes that the facts which he had brought forward would contribute their share of help to the further elucidation of the question. 3. On the Surface-deposits in the neighbourhood of Rugby.” By J. M. Wilson, Esq., F.G.S. January 26th, 1870.—Prof. T. H. Huxley, LL.D,, F.R.S., President, in the Chair. The following communication was read :— “On the Crag of Norfolk and associated Beds.” By Joseph Prestwich, Esq., F.R.S., F.G.S. The author commenced by referring to his last paper, in which 138 Geological Society :— he divided the Red Crag into two divisions—a lower one, of variable oblique-bedded strata, and an upper one, of sands passing up into the clay known as the Chillesford clay. In 1849 he had alluded to the possibility of this clay being synchronous with the Norwich Crag, He has since traced this upper or Chillesford division of the Red Crag northwards, with a view to determine its relation to the Nor- wich Crag. He has found it at various places inland; but the best exhibition of it occurs in the Easton-Bavant Cliff. He there found in it a group of shells similar to those at Chillesford, and under it the well-known bed of mammaliferous or Norwich Crag, with the usual shells. The author also showed that in this cliff and the one nearer Lowestoft traces of the Forest-bed clearly set in upon the Chillesford clay. He traced these beds at the base of Hor- ton Cliff, and then passed on to the well-known cliffs of Happis- burgh and Mundesley. He considered the Chillesford clay to pass beneath the Elephant bed, and to represent some part of the Forest- bed. The same clay may be traced to near Weybourne. The Crag under these beds he referred to the Chillesford sands. Mention was then made of the sands and shingle above the Chillesford, for which the author proposed the names of ‘“ Southwold Sands and Shingle.” These, usually, are very unfossiliferous ; but at two or three places near Southwold the author found indications of an abundance of shells (Mytilus &c.) and Foraminifera in some iron- sandstones intercalated in this series. In the Norfolk cliffs these beds contain alternating seams of marine and freshwater shells. The inland range of the beds to Aldeby, Norwich, and Coltishall was next traced, and the Chillesford clay shown to be present in each section, and the sands beneath to be referable to the Chilles- ford sands, as already shown by other geologists, on the evidence of the organic remains. Mr. Gwyn Jeffreys, who had carefully examined the shells of the Norwich Crag for the author, stated that a consi- derable number of arctic species were found in the Norfolk Crag which did not occur in Suffolk. While, therefore, the Norwich Crag seems to be synchronous with a portion of the Suffolk Crag, that portion is the upper division ; and therefore the triple arrangement proposed by Mr. Charlesworth and advocated by Sir C. Lyell, together with the fact of the setting in of a gradually more severe climate, pointed out by the late Dr. Woodward and by Sir C. Lyell, are con- firmed. Mr. Prestwich then referred to the origin of the materials of the Southwold shingle, and showed that, with few exceptions, they came from the south. In it he had found a considerable number of worn fragments of chert and ragstone from the Lower Greensand of Kent. He considered this a convenient base-line for the Quaternary period, as then commenced the spread of the marine gravels over the south of England, and soon after commenced the great denudations which have given the great features to the country. On the Fossil Corals of the Australian Tertiary Deposits. 139 February 9th, 1870.—Prof. Huxley, LL.D., F.R.S., President, in the Chair. The following communications were read :— 1. “On the Fossil Corals (Madreporaria) of the Australian Tertiary Deposits.” By P. Martin Duncan, M.B. Lond., F.R.S., Sec. Geol. Soc., Professor of Geology in King’s College, London. The author noticed the history of our knowledge of the South- Australian Tertiary Deposits, and indicated the general distribution | of the fossiliferous beds from which the corals forming the subject of his communication were derived. ‘These were said to be con- fmed to the region west of Cape Howe, prevailing especially in the province of Victoria, where they had been admirably surveyed by Mr. Selwyn and the officers under him, and to consist chiefly of limestones covered, and in some cases underlain, by great outflows of basalt. The author then gave a list and descriptions of the species (31 in number) of fossil Madreporaria obtained from these South- Australian Tertiary beds, followed by remarks on the characters and relations of the more remarkable forms, and on the localities where they have occurred. From his examination of these fossils, he objected to the application of the divisions adopted in European geo- logy to the deposits in which they are found. He then compared the assemblage of corals obtained from the South-Australian Tertiaries with those found in various deposits elsewhere, or living in the existing seas. The species were stated not to belong to reef-building forms, but to such as now occupy the sea-bottom from low spring- tide mark to the depth where Polyzoa abound. Of these, 20 genera were said to be now represented in the Australian seas; but only three of them to have species in the Tertiaries, viz. the cosmopolite Trochocyathus, Flabellum, and Amphihelia. The fossil species of these were stated to be quite distinct from those now living in the neighbouring sea. Two species, viz. Flabellum Condeanum and F. distinctum, are living in the Chinese, Japanese, and Red Seas; the - author’s Plecotrochus elongatus is very nearly allied to the Chinese : P. Condeanus ; and a Deltocyathus is regarded by the author as only a varietal form of a living West-Indian and European Miocene species (D. italicus). Three species are common to the Australian and European cainozoic deposits. Several of the species were said to present curious anomalies of structure, such as so frequently appear in Australian forms, and those of the different beds to exhibit so close a general resemblance, that they offer no evidence of great changes _ haying taken place during the deposition of the whole series of sedi- _ments. The evidence afforded by the fossil corals led the author to _ conclude :—that, at the time of the formation of these deposits, the _ central area of Australia was occupied by sea, having open water to the north with reefs in the region of Java, and with openings into _ the Mediterranean and Sahara to the north-west ; that Continental India did not form part of a great continent; that the greater part _ of America was submerged, and the Caribbean sea a coral-area; that _ the bulk of the lend was situated in the north and south; and that 140 Geological Society:— the upheaval of Australia and New Zealand was approximately syn- chronous with that of the great mountain-chains of the Old World, with the closure of the Panama area, and the depression of the areas on either side of the American continent. 2. “Note on a new and undescribed Wealden Vertebra.” By J. W. Hulke, F.R.S., F.G.S. The author in this note describes a very large Wealden vertebra which he obtained last autumn at Brook, Isle of Wight, remarkable for its great size, its extremely light structure, and the extraordinary de- velopment of the processes connected with the neural arch. It con- sists of a thin outer shell, enclosing a very open cancellated tissue, having extremely large spaces, comparable with those of Ptero- sauria, and surpassing those of the cancellous tissue in any of the known larger Dinosaurs. A wedge and notch, similar in principle to the ophidian zygosphene and zygantrum, but differently placed, are superadded to the ordinary articular processes. A broad hori- zontal platform stretches along the side of the arch from the trans- verse process to the postzygapophysis. The neural spine is com- posite ; all the outstanding parts are supported and strengthened by thin bony plates. Only a small part of the centrum is preserved, so that the form of this, and in particular of its articular faces, is not determinable. The author notices, in conclusion, certain tex- tural resemblances between the vertebra and a peculiar Strepto- spondylian vertebra in the British Museum, from the Weald of the south-east of England. 3. ‘* Note on the Middle Lias in the North-east of Ireland.” By Ralph Tate, Esq., A.L.S., F.G.S. The author remarked that hitherto no higher member of the Jurassic series than the Lower Lias has been detected in Ireland. He stated that he had received from near Ballintoy some blocks of a grey, marly, micaceous sandstone, containing an assemblage of fossil forms, indicating that the rock from which they were derived belonged to the lowest part of the Middle Lias. The origin of these specimens, which were obtained ‘‘ from cultivated fields and patches of drift,” was said to be still unknown: and the occurrence of Hip- popodium ponderosum, associated with Middle-Lias species, as in the Island of Skye, coupled with the agreement in lithological composi- tion between the Irish blocks and the Pabba shales, led him to suggest the possibility that the former may have been transported from the Hebrides by glacial action. February 23rd, 1870.—Joseph Prestwich, Esq., F.R.S., President, in the Chair. The following communications were read :— 1. ‘¢ Additional observations on the Neocomian Strata in York- shire and Lincolnshire, with notes on their Relations to the Beds of the same age throughout Northern Europe.” By J. W. Judd, Esq., E.G.8. This paper embodied the results of the author’s further study of Mr. J.W. Judd on the Neocomian Strata in Yorkshire &c. 141 the Neocomian beds of the north of England, in connexion with those of North-western Germany. The inland development of these strata in the Vale of Pickering was described as being greatly obscured by superficial deposits. The beds, however, exposed at Reighton, West Heslerton, and Knapton were shown to agree, both in physical and paleontological characters, with several of those before described in the cliff section at Speeton. The Neocomian ironstones of Lincolnshire have, since the date of the former paper on the subject (1867), been extensively opened out by mining-operations; and the valuable and instructive sections thus afforded were described in detail. A general sketch was then given of the range and characteristics of the Neocomian strata in Yorkshire and Lincolnshire. Evidence was next adduced to show that strata of the same age, and remarkably similar in character, had been deposited over a very wide area in Northern Europe. Throughout the whole of these districts, however, the Neocomian strata were very inadequately ex- posed, and afforded no good general sections ; and the Speeton Cliff thus acquired an additional interest from the fact that it forms a valuable, and almost the ony key whereby we can correlate the beds over this vast area. Studying the continental deposits in this manner, by the aid of the Speeton section the fossiliferous clays of the island of Heligo- land were shown to belong to the “zone of Ammonites Speetonensis,” 7. e. the upper part of the Lower Neocomian. The boulders found in the drift deposits of Holland were referred to as evidence of the former wide extension of limestones similar to those of Tealby in Lincolnshire. In Westphalia the sandstones, limestones, ironstones, and clays, so extensively developed in the hills of Bentheim and the Teutoburger Wald, were shown to be of Middle Neocomian age, while certain beds of clay in the same district were referable to the Upper Neocomian. In Hanover the? “ Hilsthon” of M. Fr. Ad. Romer was shown to be in its upper part Upper Neocomian, and in its lower part Middle Neocomian, the latter passing locally into beds of oolitic ironstone, sandstones, and limestones precisely similar to those of the same agein Lincolnshire. The narrow strip of highly inclined Neocomian strata along the northern foot of the Hartz was shown to belong to the same two subdivisions. In Brunswick, how- ever, the Neocomian series was more complete; for underneath some 400. feet of clays, which on paleontological evidence clearly belong to the Upper and Middle divisions, there were certain marly lime- stones, in places becoming ferruginous, containing an abundant and interesting fauna which was most unmistakably that of the Lower Neocomian. It was then pointed out that in northern Germany there was evidence, as in this country, of an unconformity existing between the Upper Cretaceous and the Neocomian, as well as between this last and the Jurassic. Attention was also drawn to the fact that while the Neocomian series was complete in Yorkshire and Brunswick, its lowest member was absent in the intermediate districts, being 142 Intelligence and Miscellaneous Articles. apparently replaced by the freshwater deposits of the German Wealden. 2. “ On Deep-mining with relation to the Physical Structure and Mineral-bearing Strata of the S.W. of Ireland.” By Samuel Hyde, Esq. ocniiinieaed by R. Etheridge, Esq., F.G.S. XVIII. Intelligence and Miscellaneous Articles. ON THE USE OF THE ELECTRIC CURRENT IN CALORIMETRY. BY M. J. JAMIN. OULE’S law gives the heat which is developed in conductors when traversed by currents. A metal wire may be regarded as a focus. It may have any possible form and be placed where we please, in the midst of liquids or gases; a quantity of heat will be given off proportional to the time, to its resistance, and tothe square of the intensity of the current,; it will heat those bodies by a quan- tity which can be measured, and which is inversely proportional to their mass and to their specific heat. Hence results a new process to determine this specific heat. After numerons trials I fixed upon the following arrangements. I. Case of Solids and of Liquids.—In dealing with a aphid or a liquid, I use as a calorimeter an elongated eylindzical vessel of thin copper, on which is coiled 8 metres of German-silver wire 0:2 millim. in dia- meter, and covered with silk. ‘This spiral commences at the bottom of the vessel, and ascends to one-third of its height; it is connected with the circuit by thick copper wires; its resistance is measured for all the temperatures of the experiment. I envelope it witha thin silk ribbon to keep it in its place, some swan’s down to insulate it, and I enclose the whole in:an envelope of thin copper polished. When the calorimeter contains a liquid and a current. is caused to pass through the spiral, nearly all the heat will be transmitted to the sides, then to the liquid ; ; ascarcely appreciable portion will be transmitted to the swan’s down. With this view,.fresh liquid must be continually brought into.con- tact with the sides by uniform agitation. For this purpose a. basket of metal gauze, formed of two concentric tubes, is immersed in the calorimeter. A small machine raises and lowers it at equal intervals; a thermometer marking the hundredth of a degree is immersed in the central tube; itis fixed, and is read witha telescope. When the specific heat of solids is to be measured, they are placed in.the basket in the water. This constitutes the entire apparatus; the operation is one of ex- treme simplicity. After pouring into the calorimeter the weight .of liquid which is to be investigated and agitating it some time, the variation (if any) of the thermometer is observed for five minutes. Generally it does not vary. A current of a measured intensity is then made to pass during one, two, &c. minutes, until an elevation Intelligence and Miscellaneous Articles. 143 of 3 or 4 degrees is produced ; this is noted, after which the cooling of the thermometer is observed during five minutes. The quantity of heat given off is known, the effect it has produced is calculated, and from the known formule of calorimetry the desired capacity is deduced *. The old method required two operations, which were :—the first, to heat in a stove for a long time the body to be studied, and to pour it with minute precautions into the calorimeter; the second, to ob- serve the thermometer immersed in the calorimeter. In the method which I propose the first operation is omitted, and the second suffices such as it was before. ‘lhe corrections remain the same, but are simplified. They are simplified because a lower temperature is sufficient, and because, the heat given off being proportional to the time, the me- thod known as Rumford’s is applicable. We may even dispense with all correction, as I shall show. I provided the external envelope of the apparatus with a spiral twenty times as long as the first, and immersed the whole into a vessel containing twenty times as much liquid as the calorimeter, and forming a medium in which the latter is immersed. The current passes simultaneously into the two spirals; it produces there heats proportional to the quantities of liquid, and consequently equal heatings. At each moment the temperatures of the calorimeter and its surroundings are in equilibrium, and the first, neither gaining nor losing any thing by radiation, is subject only to the action of the current. It is impossible to maintain this equilibrium strictly during the whole time of the experiments if they are prolonged; but it is very easy to establish it within a few tenths; and that is sufficient to obviate all necessity for correction. Thus we can measure for each degree the specific heat of a liquid (water or alcohol for example) ‘from the lowest temperatures to its boiling-point. Ihave verified this method by determining the capacities of iron and of copper, which are the most difficult to obtain exactly, because they’are very small. 1 found 0:098, 0-093. M. Regnault obtained the numbers 0°113, 0°095, which are a little larger; but he operated with a higher temperature. II. Of Gases and Vapours.—The advantages of this method are ‘especially apparent when treating of aériform fluids. A gaseous cur- ‘rent passes through a glass tube to the middle of a cork of badly ‘conducting material; a thermometer there measures its tempera- ture. It immediately enters a second tube through the folds of a ‘metal spiral or a bundle of twisted wires traversed by electricity— that is'to'say, through a focus; it becomes heated and meets a second thermometer, which measures its increase of temperature. Before * ‘Suppose two experiments to be made with the same current during the ‘same time, with the weights P and P’ of water and of the liquid to be stu- died. The quantities of heat are the same; they have heated the liquids 6and @’ degrees. Denoting the weight of the calorimeter reduced to water by 7, and the capacity sought by 2, we have (P+7)O=(P'a+7)6'. 144 Intelligence and Miscellaneous Articles. emerging, the gas is led round the first tube to prevent any loss by radiation and conductibility ; and when the temperature has become stationary, we may say that all the heat of the focus, which is known, is taken by the gas, the temperature of which is increased by a mea- sured quantity; hence the specific heat can be deduced. There are two advantages in this method. The first is, that the greatest cause of error which Delaroche and Bérard, and afterwards M. Regnault, met with is suppressed. In their experiments the gas reached 100° in a calorimeter at 10°; and the greatest difficulty. was felt in appreciating the heat which passes by conductibility from the hot tube to the cold calorimeter. In my method the gas reaches at the ordinary temperature (say, 10°), it passes from the spiral at about 20°: the difference is 10°; it was 90° before; the present error is at most one-ninth of the former. Here is the second improvement. The whole of my apparatus is the size of a finger, it is of thin glass; it might be of mica, even of goldbeater’s skin ; it weighs no more than a litre of gas, and expends no more heat in reaching the final temperature. ‘Ten litres of gas are sufficient to make one measurement; thus the difficulties which for a long time had to be overcome in order to obtain a uniform cur- rent disappear, ordinary gasometers suffice, and the method is appli- cable even to vapours. A first determination gave the number 0°242 for air, instead of 0°237, which M. Regnault found. Thermometers, even, may be dispensed with, and the temperature measured by the increase of resistance in the wires. It is known that a resistance 7 at zero becomes r(1+at) at ¢ degrees. That being the case, let two equal bundles of wires be placed one after the other in a tube; then, having decomposed the total circuit into two equal derived circuits, let us make each of them pass, first through one of the two bundles of wires, then into a differential galvano- meter; the latter remainsat zero. But ifacurrent of gas at ¢ degrees be sent through this tube, it will pass at ¢+6 in the first spiral, at t+ 20 in the second; they take a difference of temperature 6, a different resistance, and the galvanometer is deflected. It is reduced to zero on introducing, by means of a special rheostat, a platinum wire into one of the circuits. The length of this wire is proportional to the increase of temperature 0; it admits of measurement. The same apparatus is applicable to vapours. The liquid to be examined is distilled as regularly as possible; the current of vapour is at first superheated by the first bundle of wires, it afterwards tra- verses the second, becomes heated by a quantity 0, which is measured as before ; the vapour is condensed, and afterwards weighed. In order to take into account the irregularities of the distillation, it is neces- sary to observe the apparatus from minute to minute. III. Latent Heat.—In order to measure latent heats, a double alembic is employed, of which one part is exterior; the liquid in it is caused to boil, and the vapour is brought there after having been condensed by a refrigerator: the effect of this is simply to raise to the boiling temperature the interior alembic, which contains the same liquid, and in which is immersed the spiral, the resistance , : 7 1 j Intelligence and Miscellaneous Articles. 145 of which is known for every temperature. ‘The vapour which forms in the second apparatus is collected during ten minutes, before the passing of the current; there is scarcely any; the circuit is then closed, which determines a rapid boiling. The heat supplied is known; the vapour which it has formed without change of tempera- ture is weighed, and the latent heat is deduced. IV. The two Specific Heats.—A third application of the same prin- ciple can be made. In a large bell-glass filled with air a metal wire is stretched ; an intense current is passed for a short time through it, which developes a determined quantity of heat; a fraction of this disappears by radiation; the remainder, which is constant, gives heat to the gas, which can be measured in two ways—either by in- crease of the volume at constant pressure, or by increase of the pressure at constant volume. From these two effects the ratio of the two specific heats can easily be deduced; and the number found is about 1°42, a number indicated by the velocity of sound. These experiments are now in full operation. I wished by this communication to make my own the general method which will be applicable to all questions of calorimetry. I have associated with me in this work four distinguished pupils of the Laboratoire de Recherches de la Sorbonne, MM. Richard, Amaury, Champagneur, and A. Thenard. We shall presently publish the results of our work. — Comptes Rendus, March 28, 1870. ON THE FIXED NOTES CHARACTERISTIC OF THE VARIOUS VOWELS. BY M. R. K@NIG. According to the researches of MM. Donders and Helmholtz, the mouth, arranged for the emission of a vowel, has a note of stronger resonance, which is fixed for each vowel, whatever may be the fundamental note on which it is given. A slight change in the pronunciation modifies the vocal notes so sensibly that M. Helm- holtz has been able to propose to linguists to define by these notes the vowels belonging to the different idioms and dialects. Hence it is of great interest to know exactly the pitch of these notes for the different vowels. M. Donders sought to arrive at this by observing the rustling or whistling which the current of air produces in the mouth when the different vowels are whispered ; the notes which he has found differ considerably from those given by M. Helmholtz. The latter used a set of tuning-forks, which he made to vibrate in front of the mouth when it was arranged to articulate a vowel. Every time the sound was strengthened by the air enclosed in the cavity of the mouth, this mass of air was evidently in unison with the tuning-fork. By this method, which is more correct than the first, M. Helmholtz found that the vowel A was characterized by the fixed note (siD),, O by (siD),, E by (sib),; and these results really appear incontestable. As none of the tuning-forks arranged was sufficiently acute for the vowel I, M. Helmholtz tried to determine the characteristic note by the means already employed Phil, Mag. 8. 4. Vol. 40. No. 265, Aug. 1870. L 146 Intelligence and Miscellaneous Articles. by M. Donders, and he found it to be re,. If a tuning-fork be tuned for this note, we ascertain, in fact, that it is increased whilst the mouth passes from E toI; atleast I have been able to assure my- self that the increase occurs before the mouth is exactly arranged for the I. Hence the true characteristic of I must be higher. By | constructing tuning-forks more and more acute, I ascertained that this note was approached ; it was finally found to be si?,; with tuning- forks still higher, it isimmediately felt that the limit has been passed. For OU M. Donders had given fa,. Thisnote can undoubtedly be strengthened by the mouth, but it is only in departing very little from the position O; and one feels that the note of OU must be much more grave. M. Helmholtz assigns fa,toOQU. However, a tuning- fork fa, does not resound before the mouth arranged for OU, which M. Helmholtz accounts for by the smallness of the opening of the mouth; but it seemed to me that this smallness of the opening, while rendering a very energetic increase impossible, must still admit an appreciable increase in the intensity of the sound. Having more- over ascertained the simple ratios which exist between the notes of the vowels O, A, E, I, ascending by octaves, I thought that this law would extend to the vowel OU. I verified this hypothesis circumstantially by means of a tuning-fork, the pitch of which could be raised by means of slides; I was thus able to assure myself that the characteristic note of OU (such as I ordinarily pronounce it) was really (si)),; for the maximum of resonance always occurred between 440 and 460 simple vibrations. For the pronunciation of the Germans of the North (to which the experiments of M. Helmholtz also refer), the vowels are then cha- racterized as follows :— ou O A E I (sib). (sd), Gide E Gd)» — (sid),; or, in round numbers of simple vibrations, 450, 900, 1800, 3600, 7200. It seems to me more than probable that we must seek, in the sim- plicity of these ratios, the physiological cause which makes us find nearly always the same five vowels in the different languages, although the human voice can produce an indefinite number, as the simple ratios between the numbers of vibrations explain the existence of the same musical intervals among most nations. It is some time since I obtained these results; but I wished to have them verified by several eminent physiologists, whose approba tion has encouraged me to publish them.—Comptes Rendus, April 25, 1870. COMPRESSIBILITY OF GASES UNDER HIGH PRESSURES. BY M. L. CAILLETET. ; In ‘order to obtain very high pressures applicable to the experi- ments in which I am engaged, after numerous trials I fixed upon an apparatus which consisted of a hollow steel cylinder firmly eee ee a Intelligence and Miscellaneous Articles. 147 fastened on a cast-iron stand. A piston, also of steel, is moved in this cylinder by a sqnare-threaded screw, which works in a female screw of bronze, wedged in the axis of a fly, also of cast iron. When this fly is turned by means of the pegs on its circumference (as the screw cannot follow it in its rotation, owing to a catch secured by two slide bars), the piston traverses the vacuum of the cylinder in a direc- tion determined by the direction of the motion of the fly. The water which the cylinder contains cannot escape; a leather is fitted so per- fectly that, even under pressures of more than 800 atmospheres, scarcely a drop of liquid escapes. To the cylinder in which the compression is effected a steel laboratory-tube can be united by a capillary tube of copper—which, leaving that part of the apparatus quite free, allows the majority of the experiments to be made here. The pressure is estimated by two mutually controlling processes: (1) by a lever which rests on a very moveable valve; (2) by a Des- goffe’s modified manometer, which I will briefly describe. This instrument consists of a cylindrical cast-iron vessel, filled with mercury, upon which rests a metallic disk. A thin membrane of caoutchouc separates the disk from the mercury, which con- sequently cannot escape. A metal rod penetrates to the centre of the disk, passing through a leather fixed in a bronze cylinder con- nected with the pressure-machine. When the compressed water acts on the small piston, the pressure is transmitted to the mercury, which rises in a vertical glass tube, communicating with the reser- voir. If the ratio of the surface of the small piston to that of the disk is =1: 100, then for a pressure of 100 atmospheres the mercury will only rise in the manometric tube 1 atmosphere, or 0°76 metre. A grave a@ priort objection might be made to this apparatus; in fact, it is not known what resistance the leather exercises on the piston. In the apparatus employed by me, the ratio of the surfaces is =1: 212, and it is sufficient to lower the piston + of a millimetre in order to raise the mercury 4°30 metres, the height of my manometric tube. The path traversed being very small, the resistance will be nearly none. To overcome the inertia, the mercury is caused to oscil- late about its position of equilibrium in the glass tube by means of a small lever, which acts on the compressing disk. The manometer thus constructed has been verified up to 80 atmospheres by the help of a very Jarge manometer, in which the compressed air was replaced by hydrogen. ‘The graduation was based on the numbers published by M. Regnault. The apparatus for pressure, such as I have just described it, easily gives pressures from 8 to 900 atmospheres, which can be maintained for a considerable time. Danger from the burst- ing of any part of the machine, there is almost none: steel tubes filled with liquid have frequently split without any of their parts being projected. In an experiment, in which I subjected to about 850 atmospheres pressure 60 cubic centimetres of hydrogen, the laboratory-tube was broken, the compressed gas suddenly expanded and exploded with L2 148 Intelligence and Miscellaneous Articles. the sound ofa pistol-shot; but the splinters of broken glass were not thrown about, owing to the metal cover. {n order to investigate Mariotte’s law under high pressures, I employ a cylindrical glass tube capable of containing 40 to 50 cubic centims. of gas; a capillary glass tube is welded to this reservoir, in which the compressed gases will be measured. The other extremity of the reservoir is open and tapered. This apparatus is filled with the gas to be examined pure and dry, the extremity of the capillary tube is welded, and to the lower point a kind of small inverted gauge filled with mercury is fitted, which admits of the apparatus being placed in the laboratory-tube filled with mercury. At the moment when the pressure is exerted by the machine, the mercury, pressed by the water, will penetrate into the reservoir through the tapered part, will drive back the gases in the capillary tube, and will just stop ata point of its height. In order to determine this point exactly (which cannot be done during the experiment, because the apparatus is enclosed in the steel tube), I had recourse to an artifice which gives extremely correct results. With this object I slightly gilded the interior of the capillary tube by M. Bottger’s process. The mercury, rising in contact with the sides, dissolves the gold; and the height of the bright metal corresponds exactly with the height attained by the mercury. This is noted on a coat of varnish applied to the surface of the glass. It can be un- derstood how a great number of heights, corresponding to the vo- lumes occupied by the gas at pressures determined by the manometer, may thus be found. The correctness of the determinations which I have obtained de- pend especially (1) on the marking of the heights attained by the mercury in the capillary tube, (2) on the weights of this mercury, (3) on the correctness of the manometer. I have assured myself by numerous experiments that the volume of the mercury could be ob- tained very correctly ; the weight taken has always been the mean of four operations. I have already discussed the correctness of the manometer; I have moreover compressed at the same time, in the same tube, two different gases. I thus proved that the volumes occu- pied by the two gases under identical pressures corresponded well to the numbers found in my experiments. ‘The numbers obtained have not undergone the correction due to the compressibility of the glass apparatus; I did not know this contraction; I made all my de- terminations for the different gases under the same pressures, in such a manner that, if a cause of error not recognized should vitiate my results by the same quantity, the experiments, made under identical conditions, will still remain comparable. As M. Regnault has done in his memorable researches on the com- pressibility of gases, I have calculated the departures from Mariotte’s vipi the numbers thus obtained were taken as lengths of the ordinates for the construction of the curves, which cannot be given here :— law by employing the formula Intelligence and Miscellaneous Articles. 149 Atmospheres. Hydrogen. Air. BOwieties oO. urs 0°9810 10131 1 SEA Pe sreegeae aici oe 1:0118 BONE ei. oi! dre later a 1:0106 TS sts a Noe 0:9552 1:0098 Bae eS te ee BE 0°9442 1:0062 BI HEP BOE fete O9372 1:0047 MCL SMS, OO RE i 1:0027 PROVE AS Ped Oe! ODESS 0°9990 Beane a 1.215 Sta isencers sss 0:9078 0°9862 vo SPS a BRO. 275 0:9001 0:9792 Smo IB. AE OBL 48 at 0°9399 BRINE ates olele Sete attte a's 0°8761 0°9465 peer OF AO Be! 0°8670 0°9230 Se S Siete. 62s 0°8537 0°9047 SCS Ue BBR A ag On se 1 0°8929 peemeet tere ee SUE EY) Oe 0°8347 0°8672 Ue OE a Se 0°8136 0°8265 memes A! NA OA, 229073893 0:7927 2 Se 0°7701 0°7502 Beeimrtrsts SABI 88 a, 0°7580 0°7215 eS SIO EN HH 0°6895 BPD. FRE PEG DF 0°6660 The above results were obtained me operating on 43°638 cubic centims. at +15°. It appears, according to these numbers, that Mariotte’s law is not verified for high pressures; each gas in contracting seems to follow a special course. Hydrogen decreases regularly; air, on the con- trary, very curiously, reaches a maximum at 80 atmospheres, and afterwards decreases more rapidly than hydrogen. In presenting these still very incomplete experiments to the Aca- demy, I simply wished to record them, reserving to myself the time necessary for their execution. I am at present occupied in pursuing my determinations with much higher pressures, and extending them to other gases.— Comptes Rendus, May 23, 1870. NOTE TO MR. MOON’S PAPER ON THE SOLUTION OF LINEAR PAR- TIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER, IN THE PHILOSOPHICAL MAGAZINE FOR JULY. I desire to point out that when the coefficient U in the equation O=Rr+S8s+Tt+Pp+Qq+ Uz is finite, the assumptions c=1, ¢,=c,= &c. =0 materially cripple the generality of the result; as a glance at the mode in which each of the coefficients A,, A,, &e. is formed from its immediate predecessor will readily show. July 23, 1870. 150 Intelligence and Miscellaneous Articles. ON THE RAPIDITY OF THE ABSORPTION OF CARBONIC OXIDE BY THE LUNGS. BY M. N. GREHANT. “. In the researches which I made in 1864 on the renewal of air in the lungs of man, I proved that in a man the volume of whose lungs is equal to 2°93 litres after an inspiration, and to half a litre of air after an expiration, 100 cub. centims. of gaseous mixture, taken at any point of the air-vessels, have received 11 cub. centims. of pure air. From this measurement, obtained by experiment, I drew this con- clusion—that if a man be placed in an atmosphere containing poisonous gas, from the first inspiration this gas is distributed throughout all the air-vessels, to be given up to absorption by the blood. To establish more completely this consequence, and to study the successive phases of poisoning by the medium of the lungs, I made several experiments in the physiological laboratory at the Museum of Natural History, under the direction of my illustrious teacher, M. Claude Bernard. As a poisonous gas I used carbonic oxide; and I chose this gas for several reasons. M. Claude Bernard was the first to make out that carbonic oxide kills animals because it fixes itself on the red blood-globules and displaces the oxygen combined with these globules, that in an animal which succumbs to poisoning by carbonic oxide the arterial blood contains much less oxygen than the normal arterial blood and the globules are combined with a large proportion of carbonic oxide. We know that the crystalline combination of carbonic oxide with hemoglobine has been investigated and isolated by M. Hoppe- Seyler, and that the spectroscope supplies a qualitative test for this combination of oxygen with hzemoglobine. But in the research which I have undertaken I had another object. I proposed to determine quantitatively the proportion of carbonic oxide combined with the red globules at the different periods of poisoning: this is why I have employed, in order to extract the carbonic oxide from blood, the following method, which offers every certitude. After having extracted the gases from some normal blood in a vacuum at 40°, by means of a mercury pump, a volume of sulphuric acid double that of the blood was introduced into the extraction-appa- ratus, the bath was heated to 100°, and boiling was maintained for half an hour; under these conditions we still obtained carbonic acid, a trace of oxygen, and a little nitrogen, but no trace of carbonic oxide. But if the blood of an animal poisoned with carbonic oxide is operated on in the same manner, the vacuum alone at 40° gives carbonic acid, oxygen, and nitrogen, but no trace of carbonic oxide; whilst sulphuric acid at 100° in the vacuum destroys the globules, and completely drives away the carbonic oxide combined with the hzemoglobine. To verify the correctness of this method, I caused blood to absorb a i | Intelligence and Miscellaneous Articles. 151 known volume of carbonic oxide, and by the action of sulphuric acid at 100° I disengaged the same volume of gas. I must here make an important remark. If, instead of heating to 100° the mixture of blood and sulphuric acid in an empty globe communicating with the mercury pump, this mixture is heated in a retort furnished with a delivery-tube, the temperature increases, and then under the ordinary pressure a very considerable voluine of carbonic oxide is furnished by the decomposition of the albuminous matter and of the hemoglobine ; hence this more simple method must be completely rejected. Having thus established a method by which the disengagement of the carbonic oxide combined with hemoglobine in the poisoned blood is effected, I have been able to study the first phases of poisoning. In a large bell-glass provided with a tubulure, a mixture of 9 litres of air and 1 litre of pure carbonic oxide was made; the tubulure of the bell-glass is closed by a three-way stopcock, which I used in measuring the volume of the lungs. The carotid artery of a dog was exposed, and a glass tube inserted which is joined to a caout- chouc tube closed by a pinch-cock; a muzzle well fitted to the head of the animal is united by a caoutchouc tube to the stopcock of the bell. ‘The animal at first breathes the air; at the commence- ment of a minute noted on a seconds’ watch, I open the stopcock of the bell; the animal immediately inhales the poisonous gas ;_be- tween the 55th and 80th second after the commencement, I collect in a syringe, fixed in the vent-pipe of the carotid, 50 cubic centime- tres of arterial blood, which is immediately injected into the appa- ratus for extracting the gas; the gases of the blood are extracted at 40°; then, by sulphuric acid at 100°, the carbonic oxide is ex- tracted. The following are the results which have been furnished by the poisoned blood, and also those given by a sample of normal blood of the carotid submitted to exactly the same processes. Dry gases at zero and under a pressure of 760 millimetres. Carbonic Nitro- Carbonic acid, gen. Oxygen. oxide. 100 cubic centimetres of poi- ; ; : : soned arterial blood...... } oa a a oa 100 cubic centimetres of nor- j ; ‘ : mal arterial blood ...... } rae Me ange hd I repeated this experiment on another dog, but after having arranged two apparatus for the extraction of the gases from the blood, in which an absolute vacuum had first been made. The ani- mal was connected in the same manner with the bell contain- ing the mixture rendered poisonous by ,), of carbonic oxide; but some arterial blood was collected twice; the first was taken from the 10th to the 25th second, the second from the 75th to the 90th 152 Intelligence and Miscellaneous Articles. second ; then the animal was restored by air; afterwards the gases were extracted simultaneously. Carbonic Nitro- Carbonic acid. gen. Oxygen. oxide. 100 cubic centimetres of the : : ; ; arterial blood first taken si tie iinet oh ee 100 cubic centimetres of the arterial blood teva} 44:3 .22 46 4:01 18°41 Other experiments, made under the same conditions, give analo- gous results. Hence we see that in an animal breathing air con- taining +1, of carbonic oxide (a mixture highly poisonous), the arterial blood, between the 10th and 25th second, contains already 4 per cent. of carbonic oxide and less oxygen than the normal blood (14°6 per cent.) ; and between 1 minute 15 seconds and 1 minute 30 seconds, 18°4 per cent. and oxygen in very diminished quantity (4 per cent.). At that time the animal was in great dan- ger; and had the experiment lasted a minute longer, it would have died. These indisputable results are directly applicable to man; and we may assert that if a man enters a highly deleterious atmosphere, the gaseous poison is dissolved in the arterial blood from the first mi- nute, and brought into contact with the anatomical elements, which kills him. Every day we have too numerous examples of sudden death hap- pening to workmen whose occupations compel them to expose them- selves to deleterious gases or vapours, either in descending wells or entering the galleries of mines, the air of which is poisoned, or more or less deprived of oxygen. But physiologists have certainly given advice which might in future free the life of man from all such dan- gers ; and this advice ought to be carried out by law. Before descending a well, ditch, or gallery, of which the air has not been renewed for a long time, the workman ought to lower a cage containing a bird or a small mammal, as a rat or a guinea-pig : if the animal, left in the confined atmosphere fcr ten to fifteen minutes, can stand this test, a man may descend without fear; if the animal succumb, ventilation must be energetically established, until another animal can resist a new proof. The employment of an animal in this manner would preserve man from accidents too frequently mortal, as the Davy lamp, in coal- mines, has saved the lives of so many miners.—Comptes Rendus, May 30, 1870, THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] SEPTEMBER 1870. XIX. On the Cause of the Motion of Glaciers. By Jams Crott, of the Geological Survey of Scotland*. The generally accepted theory proved by the Rev. Canon Moseley : to be incorrect. NCE the time that Professor Tyndall had shown that all the phenomena formerly attributed by Professor Forbes to plas- ticity could be explained upon the principle of regelation, disco- vered by Faraday, the viscous theory of glacier-motion has been pretty generally given up. The ice of a glacier is now almost universally believed to be, not a soft plastic substance, but a sub- stance hard, brittle,and unyielding. The power that the glacier has of accommodating itself to the inequalities of its bed without losing its apparent continuity is referred to the property of rege- lation possessed by ice. All this is now plain; but what is it that impels the glacier forward is still a question under discus- sion. Various theories have been propounded regarding the cause of the descent of glaciers, all of which have been abandoned with the exception of that which attributes their descent to gra- vitation. But as the ice of tie glacier descends with a differen- tial motion, we have not only to explain what causes the glacier to slide on its bed, but also what displaces the particles of the ice over One another and alongside one another. What, then, is the force which shears the ice? The answer generally given is that gravitation alone is the force which does this; or, in other words, the mere weight of the ice is sufficient to overcome its cohesive force and to displace the particles over one another. The * Communicated by the Author. Phil, Mag. 8. 4, Vol. 40, No, 266, Sept. 1870. M 154 Mr. J. Croll on the Cause of the Motion of Glaciers. Rev. Canon Moseley has lately investigated this point, and has found that the amount of work performed on a glacier (assu- ming, of course, that the ice shears in the solid state) during its descent through a given space is enormously greater than the work of the weight of the glacier descending through that space. He has determined the amount of work performed by gravitation in the descent of a glacier, and the amount of internal work performed on the ice during the descent; and has found that, in respect to a glacier of the same uniform rectangular section and slope as the Mer de Glace at Les Ponts, and moving with the same uniform velocity, the aggregate work of the resistances which oppose themselves to its descent in a given time is about thirty-four times the work of the weight in the same time; consequently it is physically impossible that the mere weight alone of the glacier can be the cause of its descent. The impression left on my mind after reading Canon Moseley’s memoir in the Proceedings of the Royal Society for January 1869 was that, unless some very serious error could be pointed out in the mathematical part of his investigation, it would be hopeless to attempt to overturn his general conclusion as re- gards the received theory of the cause of the descent of glaciers, by searching for errors in the experimental data on which the conclusion rests. Had the result been that the actual shearing- force of ice is by twice, thrice, four times, or even five times too great to allow of aglacier shearing by its own weight, one might then hope that, by some more accurate method of determining the unit of shear than that adopted by Canon Moseley, his ob- jection to the received theory of glacier-motion might be met; but when the unit of shear is found to be not simply bythree times, four times, or even five times, but actually by thirty, forty, or fifty times too great, all our hopes of overturning his conclusion by searching for errors in this direction vanish, even although there are some points connected with his unit of shear that are not very satisfactory. The ice of a glacier is in the hard, solid, and crystalline state. This is now generally admitted. Then, if the particles of the ice shear in this state, Canon Moseley’s calculations show that the glacier cannot possibly descend by its weight only, as is generally supposed; and the generally received theory of glacier-motion must therefore be abandoned. I can perceive no way of escape from this conclusion. I presume that few who have given much thought to the subject of glacier-motion have not had some slight misgivings in regard to the commonly received theory. There are some facts which I never could harmonize with this theory. For example, boulder-clay is a far looser substance than ice; its Mr: J. Croll on the Cause of the Motion of Glaciers. 155 shearing-force must be very much less than that of ice; yet im- mense masses of boulder-clay will lie immoveable for ages on the slope of a hill so steep that one can hardly venture to climb it, while a glacier will come crawling down a valley which by the eye we could hardly detect to be actually offthe level. Again, a glacier. moves faster during the day than during the night, and about twice as fast durmg summer as during winter. Pro- fessor Forbes, for example, found that the Glacier des Bos near its lower extremity moved sometimes in December only 11°5 inches daily, while during the month of July its rate of motion sometimes reached 521 inches per day. Why such a difference in the rate of motion between day and night, summer and winter ? The glacier is not heavier during the day than it is during the night, or during the summer than it is during the winter; neither is the shearing-force of the great mass of the ice ofa glacier sensibly less during the day than during the night, or during the summer than during the winter; for the temperature of the great mass of the ice does not sensibly vary with the seasons. Then, if this is the case, gravitation ought to be as able to move a glacier during the night as during the day, or during the winter as duringthe summer. At any rate, if there should be any difference it ought to be but trifling. It is true that, owing to the melting of the ice, the crevices of the glacier are more gorged with water during summer than during winter ; and this, as Professor Forbes maintains*, may tend to make the glacier move faster during the former season than during the latter. But the advocates of the regelation theory cannot con- clude, with Professor Forbes, that the water favours the motion of the glacier by making the ice more soft and plastic. The melting of the ice, according to the regelation theory, cannot yery materially aid the motion of the glacier. The fact that the rate of motion of a glacier depends upon the amount of heat that the ice is receiving shows that heat in some way or other stands related as a cause to the motion of the glacier. But the point under consideration is, If the ice of a glacier shears in the solid state, as is generally supposed, has Canon Moseley proved that a glacier cannot descend by its weight only ? I have carefully read the interesting memoirs by Mr. Mathews and Mr. Ball in reply to Canon Moseley; and although I agree with the most of their remarks regarding the unsatisfactory nature of Mr. Moseley’s own theory of glacier-motion, yet I am unable to perceive that any thing which they have advanced materially affects his general conclusion as regards the commonly received theory. If the ice of a glacier shears, nothing which I have yet * Occasional Papers, pp. 166, 223. M2 156 Mr. J. Croll on the Cause of the Motion of Glaciers. seen advanced to the contrary can, so far as I perceive, overturn Mr. Moseley’s conclusion, that the glacier cannot descend by its weight only. The interesting experiment described by Mr. Ma- thews*, of a plank of ice supported horizontally at each end being deflected in the middle without any weight being applied to the ice, does not appear to me to prove any thing either in favour of the generally received theory or against Canon Moseley’s conclusion, —for this very simple reason, that whatever theory we may adopt as to the cause of the motion of glaciers, the deflection of the plank in the way described by Mr. Mathews follows as a neces- sary consequence. Although no weight was placed upon the plank, it does not necessarily follow that the deflection was caused by the weight of the ice alone ; for, according to Canon Moseley’s own theory of the motion of glaciers by heat, the plank ought to be deflected in the middle, just as it was in Mr, Mathews’s experiment. A solid body, when exposed to variations of temperature, will expand and contract transversely as well as lon- gitudinally. Ice, according to Canon Moseley’s theory, expands and contracts by heat. Then if the plank expands transversely, the upper half of the plank must rise and the lower half descend. But the side which rises has to perform work against gravity, whereas the side which descends has work performed upon it by gravity ; consequently more of the plank will descend than rise, and this will, of course, tend to lower or deflect the plank in the middle. Again, when the plank contracts, the lower half will rise and the upper half will descend; but as gravitation, in this case also, favours the descending part and opposes the rising part, more of the plank will descend than rise, and consequently the plank will be lowered in the middle by contraction as well as by expansion. Thus, as the plank changes its temperature, it must, according to Mr. Moseley’s theory, descend or be de- flected in the middle, step by step—and this not by gravitation alone, but chiefly by the motive power of heat. I do not, of course, mean to assert that the descent of the plank was thus actually caused by heat; but I assert that Mr. Mathews’s expe- riment does not necessarily prove (and this is all that is required in the mean time) that gravitation alone was the cause of the deflection of the plank. Neither does this experiment prove that the ice was deflected without shearing; for although the weight of the plank was not sufficient to shear the ice, as Mr. Mathews, T presume, admits, yet Mr. Moseley would reply that the weight of the ice, assisted by the motive power of heat, was perfectly sufficient. Had Mr. Mathews laid his plank horizontally across an inclined plane and fixed the two ends of the plank so as to prevent them * Alpine Journal for February 1870; ‘ Nature’ for March 24, 1870. Mr. J. Croll on the Cause of the Motion of Glaciers. 157 moving, everybody (whatever might be his theory as to the cause of the motion of glaciers) would at once admit that the middle of the plank (which, of course, was not fixed) would begin slowly to descend the incline in the manner that the ice of a glacier actually does, and that the plank, not being permitted to move at its ends, would become bent or deflected in the middle. Then, if everybody would admit that the plank would be deflected in the middle notwithstanding the friction of the ice on the in- clined plane, and the diminished pressure of the weight of the ice in consequence of its resting on the slope, surely no one could conclude that, were the inclined plane removed and the plank sus- pended in the air by its two extremities, as in Mr. Mathews’s experiment, it would not descend in the middle. I shall now briefly refer to Mr. Ball’s principal objections to Canon Moseley’s proof that a glacier cannot shear by its weight alone. One of his chief objections is that Mr. Moseley has as- sumed the ice to be homogeneous in structure, and that pres- - sures and tensions acting within it are not modified by the vary- ing constitution of the mass. Although there is, no doubt, some force in this objection (for we have probably good reason to be- lieve that ice will shear, for example, more easily along certain planes than along others), still I can hardly think that Canon Moseley’s main conclusion can ever be materially affected by this objection. The main question is this, Can the ice of the glacier shear by its own weight in the way generally supposed? Now the shearing-force of ice, take 1t mm whatever direction we may, so enormously exceeds that required by Mr. Moseley in order to allow a glacier to descend by its weight only, that it is a matter of indifference whether ice be regarded as homogeneous in struc- ture or not. Mr. Ball objects also to Mr. Moseley’s imaginary gla- cier lying on an even slope and ina uniform rectangular channel. Surely Mr. Ball does not suppose that a glacier would descend more easily in an irregular and broken channel having a variable slope and direction than it would do in a straight channel uni- form in width and slope. And if he does not, why advance such an objection? Canon Moseley assumed, as he had a perfect right to do, that if the glacier could not descend by its weight in his Imaginary channel, it could much less do so in its actual one. That a relative displacement of the particles of the ice is in- volved in the motion of a glacier, is admitted, of course, by Mr. Ball; but he states that the amount of this displacement is but small, and that it is effected with extreme slowness. This may be the case; but if the weight of the ice be not able to overcome the mutual cohesion of the particles, then the weight of the ice cannot produce the required displacement, however small it may be. Mr. Ball then objects to Mr. Moseley’s method of determin- 158 Mr. J. Croll on the Cause of the Motion of Glaciers. ing the unit of shear on this ground :—The shearing of the ice in a glacier is effected with extreme slowness; but the shear- ing in Canon Moseley’s experiment was effected with rapidity ; and although it required 75 lbs. to shear one square inch of sur- face in his experiment, it does not follow that 75 lbs. would be required to shear the ice if done in the slow manner in which it is effected inthe glacier. “In short,’ says Mr. Ball, “ to ascer- tain the resistance opposed to very slow changes in the relative positions of the particles, so slight as to be insensible at short distances, Mr. Moseley measures the resistance opposed to rapid disruption between contiguous portions of the same substance.” There is force in this objection; and here we arrive at a really weak point in Canon Moseley’s reasoning. His experiments show that if we want to shear ice quickly a weight of nearly 120 lbs. is required; but if the thing is to be done more slowly, 75 lbs. will suffice*. In short, the number of pounds required to shear the ice depends to a large extent on the length of time that the weight is allowed to act; the longer it 1s allowed to act, the less will be the weight required to perform the work. “Tam curious to know,” says Mr. Mathews when referring to this point, “ what weight would have sheared the ice if a day had heen allowed for its operation.”” I do not know what would have been the weight required to shear theice in Mr. Moseley’s experiments had a day been allowed; but I feel pretty confi- dent that, should the ice remain unmelted, and sufficient time be allowed, shearing would be produced without the application of any weight whatever. There are no weights placed upon a glacier to make it move, and yet the ice of the glacier shears. If the shearing is effected by weight, the only weight applied is the weight of the ice; and if the weight of the ice makes the ice shear in the glacier, why may it not do the same thing in the experiment? Whatever may be the cause which displaces the particles of the ice in a glacier, they, as a matter of fact, are dis- placed without any weight being applied beyond that of the ice itself; andif so, why may not the particles of the ice in the ex- periment be also displaced without the application of weights ? Allow the ice of the glacier to take its own time and its own way, aud the particles will move over each other without the aid of external weights, whatever may be the cause of this; well, then, allow the ice in the experiment to take its own time and its own way, and it will probably do the same thing. There is something here unsatisfactory. If, by the unit of shear, be meant the pressure in pounds that must be applied to the ice to break the connexion of one square inch of two surfaces frozen together and * Philosophical Magazine for January 1870, p. 8; Proceedings of the Royal Society for January 1869, Mr. J. Croll on the Cause of the Motion of Glaciers. 159 cause the one to slip over the other, then the amount of pressure required to do this will depend upon the time you allow for the thing being done. If the thing is to be done rapidly, as in some of Mr. Moseley’s experiments, it will take, as he has shown, a pressure of about 120 lbs.; but ifthe thing has to be done more slowly, as in some other of his experiments, 75 lbs. will suffice. And if sufficient time be allowed, as in the case of glaciers, the thing may be done without any weight whatever being applied to the ice, and, of course, Mr. Moseley’s argument, that a glacier cannot descend by its weight alone, falls to the ground. But if, by the unit of shear, be meant not the weight or pressure necessary to shear the ice, but the amount of work required to shear a square inch of surface in a given time or at a given rate, then he might be able to show that in the case of a glacier (say the Mer de Glace) the work of all the resistances which are opposed to its descent at the rate at which it is descending is greater than the work of its weight, and that consequently there must be some cause, in ad- dition to the weight, urging the glacier forward. But then he would have no right to affirm that the glacier would not de- scend by its weight only; all that he could affirm would simply be that it could not descend by its weight alone at the rate at which it is descending. Mr. Moseley’s unit of shear, however, is not the amount of work performed in shearing a square inch of ice in a given time, but the amount of weight or pressure requiring to be applied to the ice to shear a square inch. But this amount of pres- sure depends upon the length of time that the pressure is applied. Here lies the difficulty in determining what amount of pressure is to be taken as the real unit. And here also lies the radical defect in Canon Moseley’s result. Time as well as pressure enters as an element into the process. The key to the explana- tion of this curious circumstance will, I think, be found in the fact to which reference has already been made, viz. that the rate at which a glacier descends depends in some way or other upon the amount of heat that the ice is receiving. This fact shows that heat has something to do in the shearing of the ice of the glacier. But in the communication of heat to the ice time necessarily enters as an element. There are two different ways in which heat may be conceived to aid in shearing the ice: (1) we may conceive that heat acts as a force along with gravitation in producing displacement of the particles of the ice; or (2) we may conceive that heat does not act as a force in pushing the particles over each other, but that it assists the shearing processes by di- minishing the cohesion of the particles of the ice, and thus allow- ing gravitation to produce displacement. The former is the function attributed to heat in Canon Moseley’s theory of glacier- 160 Mr. J. Croll on the Cause of the Motion of Glaciers. motion ; the latter is the function attributed to heat in the theory of glacier-motion which I ventured to advance some time ago*. It results, therefore, from Canon Moseley’s own theory, that the longer the time that is allowed for the pressure to shear the ice, the less will be the pressure required; for, according to his theory, a very large proportion of the displacement is produced by the motive power of heat entering the ice; and, as it follows of course, other things being equal, the longer the time during which the heat is allowed toact, the greater will be the proportionate amount of displacement produced by the heat; consequently the less will require to be done by the weight applied. In the case of the glacier, Mr. Moseley concludes that at least thirty orforty times as much work is done by the motive power of heat in the way of shearing the ice as is done by mere pressure or weight. Then, if sufficient time be allowed, why may not far more be done by heat in shearing the ice in his experiment than by the weight applied? In this case how is he to know how much of the shear- ing is effected by the heat and how much by the weight. If the ereater part of the shearing of the ice in the case of a glacier is produced, not by pressure, but by the heat which necessarily enters the ice, it would be inconceivable that in his experiments the heat entering the ice should not produce, at least to some extent, a similar effect. And if a portion of the displacement of the particles is produced by heat, then the weight which is applied cannot be regarded as the measure of the force employed in the displacement, any more than it could be inferred that the weight of the glacier is the measure of the force employed in the shearing of it. Ifthe weight is not the entire force employed in shearing, but only a part of the force, then the weight cannot, as in Mr. Moseley’s experiment, be taken as the measure of the force. How, then, are we to determine what is the amount of force required to shear ice? in other words, how is the unit of shear to be determined? If we are to measure the unit of shear by the weight required to produce displacement of the particles of the ice, we must make sure that the displacement is wholly effected by the weight. We must be certain that heat does not enter as an element in the process. But if time be allowed to elapse during the experiment, we can never be certain that heat has not been at work. It is impossible to prevent heat entering the ice. We may keep the ice at a constant temperature, but this would not prevent heat from entering the ice and producing molecular work. ‘True that, according to Moseley’s theory of glacier-motion, if the temperature of the ice be not permitted to vary, then no displacement of the particles can take place from * Philosophical Magazine for March 1869, Mr. J. Croll on the Cause of the Motion of Glaciers. 161 the influence of heat; but according to the molecular theory of glacier-motion which I have adopted, heat will aid the displace- ment of the particles whether the temperature be kept constant or not. In short, it is absolutely impossible in our experiments to be certain that heat 1s not in some way or other concerned in the displacement of the particles of the ice. But we can shorten the time, and thus make sure that the amount of heat entering the ice during the experiments is too small to affect materially the result. We cannot in this case say that all the displacement has been effected by the weight applied to the ice, but we can say that so little has been done by heat that, practically, we may regard it as all done by the weight. This consideration, I trust, shows that the unit of shear adopted by Canon Moseley in his calculations is not too large. For if in half an hour, after all the work that may have been done by heat, a pressure of 75 Ibs. is still required to displace the particles of one square inch, it is perfectly evident that if no work had been done by heat during that time, the force required to produce the displacement could not have been less than 75 lbs. It might have been more than that; but it could not have been less. Be this, however, as it may, in determining the unit of shear we cannot be permitted to prolong the experiment for any consider- able length of time, because the weight under which the ice might then shear could not be taken as the measure of the force which is required to shear ice. By prolonging the experiment we might possibly get a unit smaller than that required by Canon Moseley for a glacier to descend by its own weight. But it would be just as much begging the whole question at issue, to assume that, because the ice sheared under such a weight, a glacier might descend by its weight alone, as it would be to assume that, because a glacier shears without a weight being placed upon it, the glacier descends by its weight alone. But why not determine the unit of shear of ice in the same way as we would the unit of shear of any other solid substance, such as iron, stone, or wood? If the shearing-force of ice be determined in this manner, it will be found to be by far too great to allow of the ice shearing by its weight alone. We shall be obliged to admit either that the ice of the glacier does not shear (in the ordinary sense of the term), or if it does shear, that there must, as Canon Moseley concludes, be some other force in addition to the weight of the ice urging the glacier forward. Physical objections to the Rev. Canon Moseley’s own theory. Although Canon Moseley has thus so ably and so successfully shown the insufficiency of the generally received theory of the cause of the descent of glaciers, he has, however, I ventureto think, 162 Mr. J. Croll-on the Cause of the Motion of Glaciers. not been so fortunate in his attempt to establish a theory of his own. And I cannot help thinking that the influence which his remarkable communication to the Royal Society, on the impossi- bility of the descent of glaciers by their weight alone, would have had on the minds of physicists, has been much impaired by the prominence which he has since been giving to a theory which few, I fear, will ever be able to accept. Whatever may be the fate which awaits the generally accepted theory of the cause of glacier- motion, his own theory seems to be beset by difficulties of a phy- sical nature which will require to be removed before he can expect that it will be received by physicists in general. Most of these difficulties have already been noticed and dis- cussed by Professor Forbes, Mr. Mathews, Mr. Ball, and others. I shall therefore only briefly allude to a few of those that more particularly bear on some points which have not already been sufficiently discussed. Canon Moseley has shown that the mere weight of the ice is wholly insufficient to overcome the cohesion of the crystalline particles, so as to break their connexion and cause them to be displaced one over the other. This point I regard as fully esta- blished. It is implied in the generally received theory, that, in the descent of a glacier, owing to differential motion the cohe- sion of the particles of the iceis broken, and that these solid par- ticles are forced over one another and alongside one another. Mr. Moseley then concludes that it follows, as a necessary consequence, that there must be some other force, in addition to the weight of the ice, pushing the glacier forward. Here lies the fundamental error. He has not proved that in the descent of the glacier the connexion of the solid particles of the ice has to be broken. True, the ice moves with a differential motion, and, as a necessary consequence, the particles are displaced over each other. ‘Two particles separate, and the one moves past the other; but the point to be determined is this :—were the two particles at the moment when separation took place both in the hard crystalline and solid state? Canon Moseley does not prove this; he merely assumes it to be the case; but it must be proved to be the case, not assumed to be so, before he can conclude that it necessarily follows that in the descent of the glacier some force in addition to the weight of the ice is required to push the glacier forward. Certainly he is warranted in concluding that it necessarily follows that the generally received theory 1s incorrect, becatise — in this theory it is assumed that the particles shear in the solid state. He would be warranted in saying to those who believe in the generally received theory, “‘ You assume with me that in the descent of a glacier the cohesion of the solid particles of the ice has to be overceme and the one particle forced past the other, Then Mr. J. Croll on the Cause of the Motion of Glaciers. 163 you must be wrong when you assert that the glacier descends by its weight only; for, as I have demonstrated, the mere weight of the glacier alone is not sufficient to do this.” Canon Moseley has not, however, proved that the glacier cannot absolutely descend by its weight alone; he has only proved that if the glacier shears in the way that it is generally supposed to do, it cannot de- scend by its weight alone. Had it been established that the ice of the glacier shears in the way that it is generally supposed to do, Mr. Moseley’s results would leave us no other alternative than to conclude that there must actually be some other cause in addition to the weight of the glacier impelling it forward ; and we should be obliged to seek in heat or in something else for this additional impelling power. I presume that Canon Moseley has not duly considered this point, and that consequently he has been led to the conclusion that, if his late remarkable results be received (which no doubt they will ere long), we shall then be obliged to adopt his own theory of glacier-motion, or some other similar theory which calls in the aid of forces more powerful than that of gravitation to impel the glacier downwards. That he supposes that we are forced to this alternative is, I think, apparent from the way in which he has lately introduced his theory. ‘The ice of a gla- cier,” he says, “ behaves itself in its descent exactly as the lead did in my experiment. The Mer de Glace moves faster by day than by night. Its mean daily motion is twice as great during the six summer as during the six winter months. The con- nexion between its rate of motion and the external temperature is most remarkable. It has been carefully observed, and the results, as recorded by Professor Forbes, leave no doubt of the fact, that no change of external mean temperature is unaccompanied by a corresponding change of glacier-motion. From this it fol- lows that the two are either dependent on some common cause, or that the one set of changes stands in the relation of a cause to the other. That both sets of phenomena (the changes of the sun’s heat and the changes of glacier-motion) should be due to some common independent cause seems impossible. We are forced, therefore, on the conclusion that one is caused by the other. And as the changes in the glacier-motion cannot cause the changes of solar heat, it must be the changes of solar heat which cause the changes of glacier-motion’’*. It is certainly true that the fact that the glacier moves more rapidly during the day than during the night, and during sum- mer than during winter, proves that there must be some physical connexion between the heat of the sun and the motion of the * Proceedings of the Bristol Naturalists’ Society, vol. iv. p. 38 (new series). 164 Mr. J. Croll on the Cause of the Motion of Glaciers. glacier. It is also true that the changes of the sun’s heat and the changes of glacier-motion cannot be due to a common cause. And it is admitted that the changes in the glacier-motion must in some way or other be dependent upon the changes in the sun’s heat. Further, it is admitted that the changes in the sun’s heat are the cause of the changes in glacier-motion ; but it entirely depends upon the meaning which we attach to the term “ cause” whether it will be admitted that the sun’s heat is the cause of the motion of the glacier. If by cause of the motion of the gla- cier be meant every thing without which the glacier would not descend, then it is admitted that heat is a cause of the motion of the glacier. But if by cause of the motion of the glacier be meant the energy or power that impels the glacier forward (and this is the meaning which Mr. Moseley seems to attach to the term), then we are not compelled logically to admit that heat is the cause of the motion of the glacier; for it may only be a ne- cessary condition to the operation of the cause, whatever that cause may be, which impels the glacier forward. The absence of a necessary condition will as effectually prevent the occurrence of an effect as the absence of the cause itself. It does not follow that, because a glacier will not move without heat, heat is ne- cessarily the cause of its motion. Gravitation may be the cause, and heat only a condition. The fundamental condition in Mr. Moseley’s theory of the de- scent of solid bodies on an incline is, not that heat should main- tain these bodies ata high temperature, but that the temperature should vary. The rate of descent is proportionate, not simply to the amount of heat received, but to the extent and frequency of the variations of temperature. As a proof that glaciers are subjected to great variations of temperature, he adduces the fol- lowing :—“ All alpine travellers,” he says, “from De Saussure to Forbes and Tyndall, have borne testimony to the intensity of the solar radiation on the surfaces of glaciers. ‘I scarcely ever,’ says Forbes, ‘remember to have found the sun more piercing than at the Jardin? This heat passes abruptly into a state of intense cold when any part of the glacier falls into shadow by an altera- tion of the position of the sun, or even by the passing over it of acloud” *, | Mr. Moseley is here narrating simply what the traveller feels, and not what the glacier experiences. The traveller is subjected to great variations of temperature; but there is no proof from this that the glacier experiences any changes of temperature. It is rather because the temperature of the glacier is not affected by the sun’s heat that the traveller is so much chilled when the * Proceedings of the Bristol Naturalists’ Society, vol. iv. p. 37 (new series). Mr. J. Croll on the Cause of the Motion of Glaciers. 165 sun’s rays are cut off. The sun shines down with piercing rays and the traveller is scorched ; the glacier melts on the surface, but it still remains “cold as ice.” The sun passes behind a cloud or disappears behind a neighbouring hill; the scorching rays are then withdrawn, and the traveller is now subjected to radia- tion on every side from surfaces at the freezing-point.’ It is also a necessary condition in Mr. Moseley’s theory that the heat should pass easily into and out of the glacier; for unless this were the case sudden changes of temperature could produce little or no effect on the great mass of the glacier. How, then, is it possible that during the heat of summer the temperature of the glacier could vary much? During that season, in the lower valleys at least, every thing, with the exception of the glacier, is above the freezing-point ; consequently when the glacier goes into the shade there is nothing to lower the ice below the freezing- point; and as the sun’s rays do not raise the temperature of the ice above the freezing-point, the temperature of the glacier must therefore remain unaltered during that season. It therefore follows that, instead of a glacier moving more rapidly during the middle of summer than during the middle of winter, it should, according to Moseley’s theory, have no motion whatever during summer. The following, written fifteen years ago by Professor Forbes on this very point, is most conclusive :— But how stands the fact? Mr. Moseley quotes from De Saussure the following daily ranges of the temperature of the air in the month of July at the Col du Géant and at Chamouni, between which points the gla- cier lies: bs At the Col du Géant . . 4°257 Reaumur. mrPeramount ““.° .° .. + 10-092 Hy And he assumes ‘the same mean daily variation of temperature to obtain throughout the length ’ [and depth ?] ‘ofthe Glacier du Géant which De Saussure observed in July at the Col du Géant.’ But between what limits does the temperature of the air oscil- late? We find, by referring to the third volume of De Saussure’s Travels, that the mean temperature of the coldest hour (4 a.m.) during his stay at the Col du Géant was 33°'03 Fahrenheit, and of the warmest (2 p.m.) 42°61 F. So that even upon that ex- posed ridge, between 2000 and 3000 feet above where the glacier can be properly said to commence, the air does not, on an ave- rage of the month of July, reach the freezing-point at any hour of the night. Consequently the range of temperature attributed to the glacier 1s between limits absolutely incapable of effecting the expansion of the ice in the smallest degree’’*., * Phil. Mag. S. 4, vol. x. p. 303, 166 Mr. J. Croll on the Cause of the Motion of Glaciers. Again, during winter, as Mr, Ball remarks, the glacier is com- pletely covered with snow and thus protected both from the in- fluence of cold and of heat, so that there can be nothing either to raise the temperature of the ice above the freezing-point, or to bring it below that point; and consequently the glacier ought to remain immoyeable during that season also. There can be no doubt, therefore,” Mr. Moseley states, ‘that the rays of the sun, which in those alpine regions are of such remarkable intensity, find their way into the depths of the glacier. They are a power, and there is no such thing as the loss of power. The mechanical work which is their equivalent, and into which they are converted when received into the sub- stance of a solid body, accumulates and stores itself up in the ice under the form of what we call elastic force or tendency to di- late, until it becomes sufficient to produce actual. dilatation of | the ice in the direction in which the resistance is weakest, and by its withdrawal to produce contraction. From this expansion and contraction follows of necessity the descent of the glacier ”’*, When the temperature of the ice is below the freezing-point, the rays which are absorbed will, no doubt, produce dilatation; but during summer, when the ice is not below the freezing-point, no dilatation can possibly take place. All physicists, so far as 1am aware, agree that the rays that are then absorbed go to melt the ice and not to expand it. But to this Mr. Moseley replies as follows :—‘ To this there is the obvious answer that radiant heat does find its way into ice as a matter of common observation, and that it does not melt it except at its surface. Blocks of ice may be seen in the windows of ice-shops with the sun shining full upon them, and melting nowhere but on their surfaces. And the experiment of the ice-lens shows that heat may stream through ice in abundance (of which a portion is necessarily — stopped in the passage) without melting it, except on its sur- face.” But what evidence has Mr. Moseley to conclude that if there is no melting of the ice in the interior of the lens there is a portion of the rays ‘‘ necessarily stopped” in the interior? It will not do to assume a point so much opposed to all that we know of the physical properties of ice as this really is. Has Mr. Moseley, after accurately determining the amount of work performed in melting the ice of his lens during any given time, found it to fall short of the amount of work which ought to have been performed by the heat absorbed during that given time? If he has done this in a manner that can be relied upon, then he has some warrant to conclude that there is a portion of the rays stopped which goes to perform work different from that of melting * Proceedings of the Bristol Naturalists’ Society, vol. iv. p. 39 (new series). Mr. J, Croll on the Cause of the Motion of Glaciers. 167 the ice, and that this work in all probability is the expansion of the ice, Or has he determined directly that his lens, after reach- ing the temperature which is considered to be the melting-point of ice, actually continued to expand as the rays passed into it? It is absolutely essential to Mr. Moseley’s theory of the motion of glaciers, during summer at least, that ice should continue to expand after it reaches the melting-point; and it is therefore in- cumbent upon him to afford us some evidence that such is the case; or he need not wonder that we cannot accept his theory, because it demands of us the adoption of a conclusion so con- trary to all our previous conceptions. But, as a matter of fact, it is not strictly true that when rays pass through a piece of ice there is no melting of the ice in the interior. Experiments made by Professor Tyndall show the contrary*. There is, however, one fortunate circumstance connected with Canon Moseley’s theory. It is this; its truth can be easily tested by direct experiment. ‘The ice, according to this theory, descends not simply in virtue of heat, but in virtue of change of temperature. ‘Try, then, Hopkins’s famous experiment, but keep the ice at a constant temperature; then, according to Moseley’s theory, the ice will not descend. Or try Mr. Mathews’s experi- ment, but keep the ice-plank at a constant temperature, and the plank ought not to sink in the middle. But let it be observed that although the ice under this condition should descend (as there is little doubt but it would), it would show that Mr. Mose- ley’s theory of the descent of glaciers is incorrect, but it would not in the least degree affect the conclusions which he has lately arrived at in regard to the generally received theory of glacier- motion. It would not prove that the ice sheared, in the way generally supposed, by its weight only. It might be the heat, after all, entering the ice, whichaccounted for its descent, although gravitation (the weight of the ice) might be the impelling cause, The present state of the question. The condition which the perplexing question of the cause of the descent of glaciers has now reached seems to be something like the following. The ice of a glacier is not in a soft and plastic state, but is solid, hard, brittle, and unyielding. It ne- vertheless behaves in some respects in a manner very like what a soft and plastic substance would do if placed in similar cir- cumstances, inasmuch as it accommodates itself to all the inequa- lities of the channel in which it moves. ‘The ice of the glacier, though hard and solid, moves with a differential motion ; the particles of the ice are displaced over each other, or, in other words, the ice shears as it descends. It had been concluded that * See Philosophical Transactions, December 1857. 168 Mr. J. Croll on the Cause of the Motion of Glaciers. the mere weight of the glacier was sufficient to shear the ice. Canon Moseley has investigated this point, and shown that it is not. He has found that for a glacier to shear in the way that it is supposed to do, it would require a force some thirty or forty times as great as the weight of the glacier. Consequently, for the glacier to descend, a force in addition to that of gravitation isrequired. What, then, isthis force? It is found that the rate at which the glacier descends depends upon the amount of heat which it is receiving. This shows that the motion of the glacier is in some way or other dependent upon heat. Is heat, then, the force we are in search of ? The answer to this, of course, is, since heat is a force necessarily required, we have no right to assume any other till we see whether or not heat will suffice. In what way, then, does heat aid gravitation in the descent of the glacier? In what way does heat assist gravitation in the shear- ing of theice? There are two ways whereby we may conceive the thing to be done: the heat may assist gravitation to shear, by pressing the ice forward, or it may assist gravitation by diminish- ing the cohesion of the particles, and thus allowing gravitation to’ produce motion which it otherwise could not produce. Every at- tempt which has yet been made to explain how heat can act as a force in pushing the ice forward, has failed. The fact that heat can- not expand the ice of the glacier may be regarded as a sufficient proof that it does not act as a force impelling the glacier forward ; and we are thus obliged to turn our attention to the other conception, viz. that heat assists gravitation to shear the ice, not by direct pressure, but by diminishing the cohesive force of the particles, so as to enable gravitation to push the one past the other. But how is this done? Does heat diminish the cohesion by acting as an expansive force in separating the particles? Heat cannot do this, because it cannot expand the ice of a glacier; and besides, were it to do this, it would destroy the solid and firm character of the ice, and the ice of the glacier would not then, as a mass, possess the great amount of shearing-force which ob- servation and experiment show that it does. In short it is because the particles of the ice are so firmly fixed together at the time that the glacier is descending, that we are obliged to call in the aid of some other force in addition to the weight of the yvla- cier to shear the ice. Heat does not cause displacement of the particles by making the ice soft and plastic; for we know that the ice of the glacier is not soft and plastic, but hard and brittle. © The shearing-force of the ice of the moving glacier is found to be by at least from thirty to forty times too great to permit of the © ice being sheared by the mere force of gravitation ; how, then, is it that gravitation, without the direct assistance of any other force, can manage to shear the ice? Or to put the question Mr. J. Croll on the Cause of the Motion of Glaciers. 169 under another form: heat does not reduce the shearing-force of the ice of a glacier to something like 1:3193 lb. per square inch of surface, the unit required by Mr. Moseley to enable a glacier to shear by its weight ; the shearing-force of the ice, notwith- standing all the heat received, still remains at about 75 lbs. ; how, then, can the glacier shear without any other force than its own weight pushing it forward? This is the fundamental ques- tion ; and the true answer to it must reveal the mystery of gla- cier-motion. We are compelled in the present state of the pro- blem to admit that glaciers do descend with a differential motion without any other force than their own weight pushing them forward ; and yet the shearing-force of the ice is actually found to be thirty or forty times the maximum that would permit of the glacier shearing by its weight only. The explanation of this apparent paradox will remove all our difficulties in reference to the cause of the descent of glaciers. There seems to be but one explanation (and it is a very obvious one), viz. that the motion of the glacier is molecular. The ice descends molecule by molecule. The ice of a glacier is in the hard crystalline state, but it does not descend in this state. Gravitation is a constantly acting force; if a particle of the ice lose its shearing-force, though but for the moment, it will de- scend by its weight alone. But a particle of the ice will lose its shearing-force for a moment if the particle loses its crystalline state forthe moment. The passage of heat through ice, whether by conduction or by radiation, in all probability is a molecular pro- cess ; that is, the form of energy termed heat is transmitted from molecule to molecule of the ice. G . 28547 480:88 50 37 52 430°68 1:64384 430°83 2969:7 42990 508847 .. 1:64852 - In this case the error in the wave-length of the middle line (2854°7) is —O°20, as determined from the angular deviations, and —0-05 as determined from the indices. It must be borne in mind that, in this part of the spectrum, the determination _ * Bestimmung der Wellenlingen der Fraunhoferschen Linien des Sennen spectrums, p. 43. ) Mr.A.S. Davis on the Probable Character of Cometary Orbits. 183. both of wave-lengths and of indices of refraction is difficult, on account of the feeble intensity of the light. Since only the differences between the angular deviations of the spectral lines are employed in the formule above given, it follows that, in determining wave-lengths by the method in ques- tion, it is not necessary to employ a spectrometer with a divided circle and appliances for the measurement of large angles. 0 We bat: .. | 66]... | 11/142! 17/21-2) 24-1) 30] 39) 120 ‘Vaated i. [=24l ... | +5]4+20)/+25/4+28/4+-25/420/4-13] 0 gf 0=51 we | 67] ve | LL)... |17-5| 24-4) 29-2] 84) 40/120 | es 10 a» |—13} es [+10] ... |+-30/4-25/4-20/4+-15)410) 0 Eee 52 ee ieggr se ine Viper ete ts 40 Fae Ana 49 pb BS) ad PEAS? HeOalevole. fai [ela The curves of this series have been traced in fig. 7; and the line X X was obtained by following the general rule given in § IV. It represents the actual variable pressure deduced from the observed variation of the manometric level. It cuts the axis of the abscissee in the point =9 seconds ; and its maximum cor- responds to y= +30 millims., z=18 seconds. The greatest depression of h, for the curve C, occurs where = —1386 millims. (sulphuric acid). We must notice the first curve, A, which remains below X X. It represents an experiment in which the level of the manometer was very low at the moment the valve was opened. We see that P2 204: M. Achille Cazin on Internal Work in Gases. at the end of 0:18 second the actual pressure was less than the final pressure p! by a quantity smaller than 221 millims. (sul- phuric acid). | From curve B, at the end of 1:4 second, the difference was ereater than 136 millims. Thecurve X X satisfies these various conditions. Series X. (December 1867). Dry carbonic acid. Metal reservoir B. p,=2'42 atmospheres, p,=0°60 atmosphere. Temperature between 5° and 8°. 6=0"11 j=235 | wl). os) 123 | as 4 22 27 33 | 120 h=—23™ | —43/} —10) +10 | +25 | +28 | +25 | +20) +15 0 @=0:12 26) 5:3) 7:9) 103) 165 20 26 31 | 120 p= 9 —32| —8)| +12) +22) +380) +27 | +22 | +18 0 g— 2 42 7| 99} 11°8 14 | 17°5 23 35 | 120 h=—3 —25| —5|+15| +25! +30 | +32 | +28 | +19 0 b=19 S72 | 69) 984 4 4 | oma 32 | 120 k= —24 —26 0 | +20 +31} ... | +25 | +20 0 9= 38 5] 7:5 11 Pee al /e> 24 31 | 120 h=—5 —10 0 | +20 .. | +29 | +25 | +20 0 6= 3'8 52) 7:8 12 ; 19 25 34 | 120 h=—4 —9| +1] +20 .. | #26 | +29 | +21 0 o— 4:5 7:2 13 18-2 26 3l 37 | 120 h=-—5 +3] ... | +20) ... | +28) +383 | +28 | 423 0 6= 5-4 (fe ae eee ame 17 15| 19-6 30 42 46 | 120 h=-—9 +5} ... | +20) +380) +383 | +25 | +15 | +12 0 6= 74 aes 9:4 i ae 20 31 44 47 | 120 h=—9 +8 | +28 +31 | +23 | +13] +11 0 The results of this series are collected in fig. 7, where the line X! X! of the real pressure is traced in order to compare it with the preceding. It cuts the axis of the abscisse at the pot x=6 seconds; and its maximum is approximately at the point y=380 millims., 2=18 seconds. The greatest depression of h occurs when for the first curve 2 1s = — 43 (sulphuric acid). Let us first remark that the maximum is nearly at the same place in the two series, so that the elevation of the lime X X above the axis of the abscissee cannot be attributed to the motion of the gaseous mass, since in Series X. the excess of pressure p,—pg is half that of Series [X. This confirms the opinion advanced in the preceding Section ; for the fall of temperature in reservoir A diminishes with p,, and consequently the heat given off by the sides also diminishes. The heating also diminishes in reservoir B, and with it the heat withdrawn by the sides: as in Series IX. the quantity of gas contained in reservoir B is greater than im the other series, the heat withdrawn by reservoir B may have diminished as much as the heat given up by reservoir A; whence M. Achille Cazin on Internal Work in Gases. 205 it would follow that there would be nearly the same excess of heat given off by the sides. As to the depression, it seems to diminish more rapidly than the pressure y,, which also confirms the opinion advanced with respect to one of its causes. By diminishing p, we diminish the velocities acquired during the expansion, and with them the tem- porary diminution of pressure which the gas undergoes. The same results have been obtained by the comparison of several other series observed at various times and under different arrangements. I shall mention a few of them. Series XI. (September 1867). Dry hydrogen. Metal reservoir B. P,=2'70 atmospheres, p,=0°52 atmosphere. Temperature 20°. (é=0"10 | #=21! 56| 84] 113!) 162] 25/... | ...| 60 eat 63 4 ig 19 | ET) ea 9=0-19 23) 54| 7:7) IW) 172!) 25] 50| ...| 60 are’ AGO Oe hOB IF |) EDO) Ire ed eekly | ciel 0 9=0-20 23! 48) 62) 85) 106) 151/196! 25 | 60 po 9 Soe) ae 8 Peis Rare Ph pig te 8) gto othe PSP Bb ho FE cece 10d (19-70. 25: 60 h= —5 Say hoo eels nape eOb ein noch ed le 0 @—1-07 29) 58! 85] ... | 10-7! 12:9|202] 24 | 60 \h= —4 age Teele | | eg | alg ee 4 | This series must be compared with Series VII., in which the excess of pressure was nearly double ; the maximum of depression was also nearly double; finally the line X X cuts the 2-axis nearer the origin in the series where the value of p, is the least. I shall mention also a series on air, with the glass reservoir and a water-manometer with a spherical enlargement; we shall be able to compare it with Series IV. performed under the same conditions, but with an excess of pressure p,—pg nearly double, Series XIT. (May 1867). Dry air. Glass reservoir B. Water-manometer with a sphe- rical enlargement. P\=2'76 atmospheres, p,=0°73atmosphere. Temperature = 14°. g=o-12|¢=.. | 46 | 93] 124] 21 | ... | 120 | | aes GO iia tet ha3icl eres he +2) pa) 0 §=0°12 sis 4:6 8 12:3 LS hi ZO he 12 =o of Salad Neti ya tee ve Ae Wl age v 6=0°16 re 5:2 1-4 19-2 wie te | ta eee ees +11 | —14 —3 ay Re pore +8 00>] §=0°20 re 4) 11 20 ne ee 120 | {noo CelGe ae St he eee | 0 206 M. Achille Cazin on Internal Work in Gases. The maximum depression is about one-third of that in Series IV., and the curves rise considerably above the axis of the ab- scisse. We must remark that the curves of this latter series affect the form a! b' 6" c! (fig. 1), although the water-manometer communicated with the tubulure H of the rarefied reservoir. This denotes friction in the tube which joined the two reservoirs. Without this disturbing influence the depression would have been greater in Series XII. In mentioning these experiments (which were made at the outset of this research) I wished to con- vey some notion of the difficulties which present themselves in researches of this kind, and of the progressive course which has led me to adopt the present apparatus, the results of which pre- sent no uncertainty. § XII. Influence of the nature of the gas. We are now going to compare with one another Series I. (air), IX. (carbonic acid), and VIII. (hydrogen). All these series were made with the apparatus ultimately adopted, and under the same circumstances. Their curves are traced in figs. 4, 7,6. The curves X X present considerable differences, which we will examine. Let us consider the gases in the following order—hydrogen, air, and carbonic acid. We see from figs. 6, 4, and 7 that the maximum of / is nearly the same for the three gases; but it is reached more or less rapidly, so that the abscissz of this maxi- mum go on increasing; the abscissz of the point where the line X X cuts the axis of the 2’s also increase; finally this line in- clines more and more to the axis of the 2s. I conclude from these observations that the point g (fig. 5) is lowest for hydrogen and highest for carbonic acid. In fact, let us suppose the point g to be at the same height for hydrogen and carbonic acid, and that the valve is opened at the end of the time of (fig. 5) which corresponds to the point g. Whilst the level of the manometer descends, the more rapidly the pressure of the gas increases, the more quickly will the mi- nimum 6b be reached, but the less will it have receded from the axis of the 2’s. The ordinate kb would thus be smaller for hy- drogen than for carbonic acid, which is contrary to observation. The point g cannot have the same abscissa for the three gases ; this abscissa must increase from hydrogen to sulphuric acid, in the same way as the abscissa o k of the point b. Thus when the stopcock which separates the two reservoirs 1s opened, equality of pressure is established soonest with hydrogen, latest with carbonic acid; and, moreover, the instant this equality of pressure begins to take place, the pressure is smallest for hy- drogen, and greatest for carbonic acid. M. Achille Cazin on Internal Work in Gases. 207 If these effects be compared with what is known of the velocity of the efflux of these gases, it will be found that the gr xater the - velocity the smaller the abscissa of; hence the idea of a rela- tion of cause and effect between this velocity and the depression observed in my experiments. We have thus a confirmation of the opinion advanced in Sections X. and XI. The depression is due to the velocities acquired during the expansion. [If it is due to this cause alone, it must disappear simultaneously with the velocities; and the prompter the extinction of these velocities, the closer the point / will be to the origin of coordinates, o. The mobility of hydrogen is certainly greater than that of carbonic acid. The molecules of hydrogen are to those of car- bonic acid as a very elastic ball is to one which is but slightly so. Consequently the agitation, the whirlings, which gradually destroy the motion in reservoir B, must continue longer with hydrogen than with other gases. On the other hand, the velo- cities acquired at the moment when the expansion ceases are greater for the former gas. This tends to increase the duration of the agitation. Since, according to my experiments, the du- ration of the depression is, on the contrary, for this gas less than half of that for carbonic acid, it must be admitted that some other cause influences this effect. We cannot find it in the action of the sides, because the line X X rises less above the axis of the abscissz for hydrogen than for the other two gases ; so that the excess of heat given out over that withdrawn by the sides is the least for hydrogen. Now a diminution of this excess can only cause the pomt / to recede. But this effect is explained very well by aspontaneous cooling which is greater for carbonic acid than for air, and independent of the velocities acquired during the expansion, because the sides must take so much more time to let the cooling disappear the more considerable it is. Hence the question is resolved in the same way as that which has occupied Messrs. Joule and Thomson; but the method which I have employed enables us to distinguish the influence of each of the circumstances which play a part in the phenomenon; and it is that which must be done when it is impossible to eliminate them. I think the same circumstances must present themselves in the experiments of the English physicists, and that their method, more simple in appearance than mine, cannot give exact quantities. The experiments which I have described do not prove that there is a spontaneous cooling in hydrogen ; but they demonstrate that there is in air and carbonic acid. As to the numerical values, they can only be obtained approximately, as we shall presently see. We have now to examine the differences which the parts of the 208 M. Achille Cazin on Internal Work in Gases. curve X X above the axis of the abscisse present. They may be due to several causes—such as the difference of temperature ac- quired during the expansion by the various parts of the gaseous mass, the difference of the specific heats, that of the conducti- bility, and, finally, that of the emissive and absorbent powers. Let us first compare hydrogen and air. Both must un- dergo almost the same thermometric effects; for we have ap- proximately, for the gas expanded in A and the gas compressed in B, the usual formula K~1 Cae L+at! \p! : with K— 1-41; Besides, these two gases have the same specific heat for a con- stant volume, and also the same emissive or absorbing-power ; but they have not the same conductivity. That of hydrogen is the greatest. Hence the less the conductivity the higher the curve X X rises. What can be the effect of conductivity? The variations of temperature due to the action of the sides will be more rapid for hydrogen than for air. If the temperature of the total mass is greater than the temperature of the sides when the mixture is effected, it will descend more rapidly; hence the maximum of / must be less for hydrogen, and the curve must — reach the axis of the abscissee more quickly. Let us now compare air and carbonic acid. The thermome- tric effects are less for the latter, and the specific heat is greater ; it is the same with regard to its emissive or absorbing-power. As to the conductivity, it cannot differ much. The first cause acts in a direction contrary to the other two: it tends to dimi- nish the quantities of heat taken up or given off by the sides, and consequently to lower the maximum of the curve X X; the other two causes tend to raise it. There may be compensation; and we cannot foresee the direction of the resulting effect. But experiment has given the same maximum, so that we can admit the compensation. | These various considerations appear sufficient to enable me to give a complete explanation of all the particular points which my experiments present. We can ‘calculate approximately the temperatures which cor- respond to the various stages of an experiment. The mixture is completely effected at the moment the curve X X reaches its maximum ; the greatest value observed is 36 mil- lims. of sulphuric acid, which represents 4 millims. of mercury. The excess of temperature of the gaseous mass being 6¢, we have, for £=10°, p=760, dp=4, M. Achille Cazin on Internal Work in Gases. 209 l+a(t+6t) pt Op l+at p whence 6¢= 283 ap == gee B Until the gaseous mass has reached this state, its various parts are not of the same temperature, and consequently it is impos- sible to deduce from the pressure observed the thermometric state of the gas. We can only estimate what must have been the temperature of the whole mass for its pressure to be that which we observed at a certain period. For example, as h=0 for 5 seconds with hydrogen, we may admit that all the velocities are extinguished after 5 seconds, and we then see in fig. 7 that h=—40 millims. with carbonic acid, equivalent to p= —5 mil- lims. of mercury. The preceding formula gives d¢=—1°8. The excess of pressure p,—p! was 2°85 atmospheres. This estimation is evidently uncertain, and can only give a notion of the order of magnitude of the effects produced. I have made a series of experiments on protoxide of nitrogen with the glass reservoir. This series should be compared with Series II. (hydrogen). Series XIII. (August 1867). Protoxide of nitrogen. Glass reservoir B. p,=3'95 atmospheres, p,=0°49 atmosphere. Temperature between 20° and 238°. a f9=0-4 |t=5-9 | 11-7| 15-8] 195] 24] 54] 84| 120 ge gun. | = aae | 9a) ag | 7 | er ts | es p, £9=0-49 63 | 106 139| 17-2| 221] 24] 39/120 ely Hag Pigg phage 1eh sale obs (0 g pesos 69 | 122) 17/ 211/241] 54] 84} 120 = ie OG IO Ol te | 7 | Pe p,{ 9=052 69 121/155! 20) 26| 41/ 86/120 h= +6 Wigs 82 0s eile Leh o%6 bee lode no nf 9=0°64 7-| 1 | 167] 21) 25) 41 120 | tia 19 ag? og Poh os) oF Pd |e oO yf 8=097 73 | 126/166 |°21-2) 237!) 54] 84] 120 Gud yt) per era 9il cinco} eed es lace Q=1-4 FB iV Bel 16-9 ley BB) lish, BS elel soaysfh cneari 420 Pee | 904) —91.| 10-0; 45) | oe le uf 0=29 9-1 | 142) 191! 292| 52] 2) | 821120 pees iatl) (op ape yi gdicpe|! Les) sone! meso 1 [0=63 9-1 | 125 | 172/221} 27) 57] ... | 120 ae | -19 | -10| 0] +5] +7] +5) | 0 The curves X X of Series II. (hydrogen) and XIII. (protoxide of nitrogen) are traced in fig. 8. They meet the axis of the abscissee in the pomts #=6 seconds and x=16 seconds, or 210 M. Achille Cazin on Internal Work in Gases. thereabouts, Hence the difference is still more marked than in the preceding series. We also see from the Table of Series II. that the initial depression is greater for hydrogen—which con- firms a conclusion already given, because for this gas the velocities of efflux are greatest. It is certainly convenient to make reser- voir B of greater capacity than the zinc reservoir ; but the neces- sity of keeping up a current of water around it makes me prefer the latter in final experiments. § XIII. Summary and conclusions of the experiments. All the observations above given may be summed up in the following statement :— When a reservoir containing compressed gas is placed in com- munication, by a large orifice, with a reservoir containing the same gas rarefied, equality of pressure establishes itself very quickly in the two reservoirs (0-1 second). When equality of pressure commences, the velocities acquired have not completely disappeared. At this instant there is a mechanical work pro- duced in the first reservoir and a certain quantity of heat has disappeared. ‘There is, on the contrary, mechanical work ex-. pended m compression and heat created in the second reservoir ; but a part only of the vires vive produced during the efflux has been transformed into heat. Whilst the velocities acquired con- tinue to disappear in creating more heat, the pressure increases. When all agitation has ceased, the heat which has disappeared from the gas of the first reservoir remains greater than that which has been created in the gas of the second reservoir. If the sides were impermeable to heat, equilibrium of temperature would re- establish itself by exchanges of heat between the cold and hot parts, and the final temperature would be less than the initial. As the sides are not impermeable to heat, those of the first reser- voir give heat, those of the second take heat from the gas, and finally there is an introduction of exterior heat, so that the ex- changes between the cold and hot parts bring about a tempera- ture greater than the initial temperature. One part of the heat introduced remains in the gas and re- places the heat which has disappeared in the operation ; the rest is retaken by the sides during the very slow cooling which re- establishes the initial temperature. Hence, during the entire operation, there is at the same time, change of distribution of heat between the various portions of the sides, and destruction of a certain quantity of heat, which is so much greater the more the gas diverges from the laws of Mariotte and Gay-Lussac. It is this latter quantity which is converted into internal work in the gas. [To be continued. | oes ay XXV. Remarks on a Paper by Dr. Sondhauss. By the Hon. J. W. Strutt, Fellow of Trinity College, Cambridge*. > fia Nos. 5 and 6 of Poggendorff’s Annalen for this year there is a paper by Dr. Sondhauss “On the Tones of Heated Tubes and Aérial Vibrations in Pipes of various forms,” in which are given formule of considerable generality embodying the results of original and other experiments. Many years agot Dr. Sondhauss had investigated the influence of the size and form of flask- or bottle-shaped vessels on the pitch of the sounds pro- duced when a stream of air is blown across their mouth, and had obtained as an empirical formula for flasks with rather long cy- lindrical necks, C = I A ie sere gy where z is the number of vibrations per second, o the area of the section of the neck whose length is L, and S the volume of the body of the flask. C is a constant determined by the expe- riments. Qn the other hand, when L is very small compared with the diameter of the neck, which then becomes a mere hole, Be eae! Ooty hac ee In the paper now under discussion it is sought to fill up the gap, as it were, and the following formula is arrived at as appli- cable for all proportions of L and o%, a o n= 2A bene aiy orcad cea or, as I prefer to write it, a o es (s+ meV vey in which a= velocity of sound. c is a constant, of which Dr. Sondhauss says that it relates to the change in the velocity of sound in closed spaces from which the sound-waves have only a restricted exit ; and its value, as found from the experiments, is approximately 2°3247. In (VII.), if o be small, =e o V Gi WE LS’ e e e e ( LTE) If, on the contrary, L be very small, a of n = ca @ « ° . e e ° IX. A/c §3 ue) * Communicated by the Author. + Poge. Aan, vol. Ixxxi. 212 The Hon. J. W. Strutt’s Remarks on Ifin (VII.) we further put S=O, a 1 | =iV note’ og a result which Dr. Sondhauss applies to cylindrical tubes closed at one end. This being admitted, it readily follows that for a pipe open at both ends, — ——__—_—__—______— 6 ° e e XI. o/ L(L+2,/c) a An extension is next made to the case of more than one neck, but it will not be necessary for my purpose to repeat the for- mule. 166-6 | 166-6 166°8 The foregoing Table shows that although (X.) represents Wertheim’s observations with considerable accuracy, yet, Helm- holtz’s rational formula (D) is on all grounds to be preferred. 215 Dr. Sondhauss expresses himself strongly as to the difficulty which exists in determining accurately the pitch of the very un- certain sound produced by tubes whose diameter is not small compared with their length, an opinion which I entirely share. It is indeed difficult to understand how Wertheim obtained results of such precision. But I cannot agree with Dr. Sondhauss when he goes on to say that resonance is not a sure guide in de- termining accurately the pitch of a pipe; for it was by this me- thod exclusively that the determinations recorded in my paper were made. I have there given at length my reasons for adopt- ing it, and for doubting the results of the method of blowing, although such experiments as those of Wertheim go to show a pos- teriort that in his hands at least it was not unworthy of dependence. Other experiments of Wertheim are calculated from formula ([X.) and show a tolerable agreement. The difference between (IX.) and Helmholtz’s theoretical formula (C) relates only to a constant multiplier, and corresponds to a difference of pitch of about a quarter of a semitone. The discordances are attributed (no doubt correctly) to the unsuitable form of some of the vessels, and consequent imperfect fulfilment of the theoretical condition to which (C) is subject. We come next to vessels in the form of flasks with a cylindrical neck of sensible length. Dr. Sondhauss gives a Table contain- ing the results of a comparison of (VII.) with some experiments of his own. The average discordance amounts to about a semi- tone. Although it was evident beforehand that in most cases the limitations on formula (A) were grossly violated, I thought it worth while to calculate in accordance with (A) the theoretical pitch, and have given the results in the form of a Table :— a Paper by Dr. Sondhauss. | qe, nm, cal- | n, cal- No. of Shape of ae L,in |Diam., in| 2, ob- | culated | culated exp. vessel. hia eon millims. | millims. |served. from from i (VII.).} (A). 1. '341260)Sphere. 17-1 60 5S 241°6 | 246-°9 | 251-3 ia ceckses Cylinder. 60°9 19 12°5 430°5 | 454:°5 | 453°6 ce eae ee 10°7 15 10 966-5 | 959 970 aaa Bee 97:7 13 9 287:3 | 311°2 | 309-2 eae eee 66:2 175 11°6 143-7 | 155-2 | 158°8 Bae scvto.| evasas 117°8 183 18 170°9| 170°4 | 1785 BA Pec sicweisss Octagon.| 654°5 193 26°5 114 | 1067 | 107°6 | Sphere. 763 118 20°5 256°0 | 285°6 | 306-1 >: Cylinder.| 117°8 15 25°3 5747 | 589°5 | 600-2 SS ee 132°4 44 27 362 | 429-2 | 441-4 ll. |342740/Sphere. 923 205 25 85°4| 83:2x| 83-7 12. 844210 Cylinder. 8920 30 36 761) 766 76°6 13. |341260)Sphere. 178 160 18°5 152-2} 155°8 | 159-1 14, 344210) ...... 1:09 il 2 812°7| 842-6 | 825-4 |S RSSAS Sieereree “30 2-2 | 2:2 (1933 |1926-2 | 1902 * The result of the formula (VII.) ought evidently here to be greater than that of ( A). On a recalculation I find 85°8 instead of 83°2, 216 The Hon. J. W. Strutt’s Remarks. All the columns except the last are copied from Dr. Sond- hauss’s paper. It will be found that the observations are better represented by (VII.) than by (A) ; but it must be remembered that (VII.) contains an arbitrary constant, c, which acts nearly as a constant multiplier, although, if I understand Dr. Sondhauss aright, its value was not determined from this series of experi- ments. However this may be, it is certain that nearly all the values of n calculated from (A) are too great. The fact is that (A) is scarcely applicable to the experiments at all. In only five cases is the ratio of the diameter of the neck to the dimension of the vessel even tolerably small. These are 1, 4, 11, 12, 14; but in 1, on account of the extremely small diameter of the neck and its considerable length, the influence of friction is probably sensible ; and its effect would be to lower the pitch. The body in 4 is cylindrical, and perhaps too long in proportion to the quarter wave-length. In 11, 12, and 14 the agreement is suffi- ciently good. I consider accordingly that there is no evidence in the Table unfavourable to formula (A), supposed to be stated - with the proper restrictions. In my own experiments, made by the method of resonance, I found a very good agreement between the directly observed and the calculated pitch, the average error being under a quarter of a semitone. Even with formula (VII.) as the basis of calculation there would be a fair agreement, cer- tainly better than is the case with Dr. Sondhauss’s own experi- ments. The difference between (VII.) and (A) is, as I have already remarked, comparatively small, and could only be cer- tainly distinguished under favourable circumstances. Not find- ing the necessary data in Dr. Sondhauss’s paper, I venture to quote some experiments from the paper on Resonance. There are seven observations in which the necks were sufficiently long to bring out the difference between the formule, being more than four times the diameter. It willbe seen that the alteration is in every case for the worse if the formula (VII.) is substituted for (A). n, calculated mn, calculated m, observed. from (A). ara 126 127°7 131 108°7 107-7 110 180 179°7 184 228 233°7 259 204 201°9 207 182 186°3 190 384 391°6 400 These experiments seem to decide the question ; but it would be interesting to see if Dr. Sondhauss obtained a similar result a Paper by Dr. Sondhauss. pag by the method of blowing. The difference, amounting in (VIII.) and (8B) to half a semitone, is far greater than any error to be feared in the measurement of pitch or of the dimensions of the vessel, and ought therefore to give a sufficient handle to decide between the formule, if proper attention is given to the choice of a suitable resonator. In the foregoing remarks I have natu- rally dwelt most on my differences with Dr. Sondhauss; but | should be sorry to have it supposed that I write in a hostile spirit, or do not recognize the claims of one to whom the science of acoustics is so largely indebted. Terling Place, Witham, August 12, 1870. Postscript, August 19. I have since calculated the results of the experiments of Wertheim on pipes open at both ends, and find that in this case a 4(41 a =) also the rational formula (n= agrees best with the observations :-— - . D n, observed | n, calculated | 2, calculated ; y * by Wertheim. |by Sondhauss.| by myself. 3371 785 80 202:0 197°6 203'4 3395 500 wna ~ 806-9 299'6 301°5 3413 355 “se 4183 4063 408-4 3371 280 aes 5120 490°4 491°7 3418 157 ney 836°6 789:2 7773 3413 1000 60 164°3 162-2 163-0 3418 640 ace 251:0 247°3 248°5 Raeane 340 ae 450°7 438°8 441°5 3413 1000 48 165°6 163°8 164:5 3427 350 2 452°3 439°1 442-0 3413 1000 25 167°5 167:0 167°4 “eee 20 168-2 1677 168:0 aiden aici 11 169-1 169°0 169-2 gi le) Ba are 5 170-0 169°3 169-9 3390 906 30 182-5 181°8 182°3 ees 307 21 526-7 521-2 524:0 a 541-5 20 306:2 303-2 304°3 aa a 392 ane 419-6 A4ld‘1 415-7 ee 676 aor) | 240-6 239°1 240°1 eke 343 Pee 458°8 4518 454°6 Phil. Mag. S.4. Vol. 40. No. 266. Sept. 1870. Q r 218 4 XXVI. On the Principles of Thermodynamics. By the Rey. J. M. Hearu*. | HAVE for some time past been challenging the attention of scientific men to the consideration of a very important ques- tion :—whether some of the most elementary principles in dyna- mics have not been overlooked by those who originally framed the language of thermodynamics; and whether their successors have not indolently adopted that language, and the notions which it was formed to embody, without using sufficient care to purify it of those errors which the prepossessions and imperfect know- ledge of the first investigators had made almost unavoidable in them. Mr. Rankine has replied to me, in the August Number of this Journal, to the effect that the principles I contend for are (as far as he understands me) right; and I think he must be taken as admitting, by his silence, that they were in fact ignored by the earliest original investigators in the science. But he tells me that the more modern writers, at least the best among them, had long ago perceived all that I have been pointing out, and have so altered their creed and their language as to be free from the reproach which I appear to make against them. In support of this statement, Mr. Rankine has given us two propositions embodying the creed which is considered orthodox at the present moment. Mr. Rankine’s name is so high an authority upon this point, that there can be no question that we have from him an authentic statement of what the present doctrine is, which it is said is in strict harmony with all that I have called for, If, therefore, I myself can make a similar statement of my own opinions, we shall at once be enabled to judge both whether the two doctrines are essentially one and the same, as is alleged, or, if different, which of them has the best claim to be accepted as representing the truth of the matter. I understand Mr. Rankine’s first proposition to be, that if the elasticity of a body results from the mutual attraction or repul- sion of its particles acting upon one another, any forcible com- pression of such a body would result in “ stored-up energy,” but would be wholly incapable of producing (molecular motion or) heat. And I think he imagines that this is the doctrine which I have only just now come to perceive for myself and am bring- ing forward as somewhat of a novelty; whereas it has long ago been perceived by the best writers of the present time, and they are one and all careful in all cases to separate the amount of energy expended in this “ storing-up of energy” by “ overcoming the resistance of repulsive forces ” from the total amount, before they estimate the remainder, which alone can produce heat. * Communicated by the Author. The Rev. J. M. Heath on the Principles of Thermodynamics. 219 Mr. Rankine’s second proposition is, that if the body’s elasti- city is the result of the mere motion of particles having imertia but not acting upon each other by forces of attraction and repul- sion, then in the compression of such a body by external force all the force employed imparts motion to the particles of the gas, and that the addition so made to the previous vis viva of those particles is the same as the ws viva which the same force acting through the same space would have generated supposing the par- ticles had been previously at rest,—or, in other words, that the compressing force will descend through the same space whether there be any resistance to its motion or none. These two propositions (if indeed I have rightly understood them) appear to me to involve a conclusion completely subversive of the whole doctrine of thermodynamics, viz. that the production of heat in different bodies by compression depends upon their molecular constitution—and, furthermore, that upon no hypo- thesis as to the constitution of a body will the production of heat be in accordance with the true mechanical laws of the production of wis viva. If the body consists of particles which mutually repel each other, Mr. Rankine thinks no heat can ever be generated by impact or compression in such a body, although it is certain that vis viva can be generated among its particles. If the body consists of only moving and impinging particles without repulsive forces, Mr. Rankine thinks that the new heat generated by con- densation in such a body will be equal to what a merely mecha- nical solution of the question teaches us would be the ¢otal vis viva—1z. e. the sum of what there was at first, added to the addi- tion made by the work done by the force. I believe my own analysis of what is objectionably called the “overcoming of resistance by a force”? to be true in mechanics, and to be free from each of the objections above stated. If the area of the piston by which a volume of gas is com- pressed is unity, and P is the external load put upon it, and p is the internal pressure of the gas opposing its descent, then P may, at every point of the descent, be considered as consisting of two parts, one =p which we will call p’, and the remainder, which therefore will be P—p’. p and p! constantly increase as the piston descends and the volume of the gas diminishes; and P—p! consequently is dimi- nishing during the whole descent. Let P—p!=0, or P=p!, when v has become v'. The whole amount of deduction, there- fore,which has to be made from the action of P through the space v—v is {> dv. The question is, What has been the employ- Ou ment of this force? My answer is, that it is the sum of all the pressures which, atevery point of the descent, have held the elasti- 220 The Rev. J. M. Heath on the Principles of Thermodynamics city of the gas below in statical equilibrium. It has generated no motion whatever, although it is a force exercised by a moving body; but it has neutralized the resistance; so that they might both of them be at once entirely struck out of the equations of solution, and the problem so converted into a more simple one of the condensation of a gas possessing no elasticity by the action of the force (P—p, de. The corrections which this solution supplies to the twoproposi- tions of Mr. Rankine respectively are, that, in the first, it admits the generation of heat by the force (Pe p, dv, which Mr, Ran- kine denies ; and in the second it denies the generation of heat by the force | pdv, which Mr. Rankine asserts. I believe my so- v lution to be right in both instances; but it is upon the latter point that I anticipate there will be the greatest difficulty of agreement between us, as the appeal is tacitly to a proposition which [ think Mr. Rankine will at first sight consider imad- missible. In speaking of a gas whose elasticity results from the motion of its particles, Mr. Rankine says, “work done in diminishing the capacity of this vessel wholly takes effect in accelerating the motions-of the confined particles.” I believe that a gas of this nature may be condensed and its pressure increased (as is re- quired by the law of Mariotte) without increasing the vis viva of the particles, and therefore without altering the heat. The pressure at any given point on the surface depends upon the number and frequency of the impacts of the particles, and the vis viva of each of them. We may confine our attention to the impacts of one particle only of a given force. This particle will repeat its impact upon a given spot the more frequently, the shorter the path is which it traverses between two successive im- pulses; in other words, it will return the more frequently, the more the volume of the gas is contracted. If, therefore, imme- diately after any one appulse of the particle the piston is made to take a new position (still one of rest) immediately below its former position, or to descend through the infinitesimal space dv and there remain stationary, the particle will return to it sooner than it would do in its former position. It will strike it and will be reflected by it without any increase of its motion; in other words, the Pressure may be increased and the Volume contracted without evolution of Heat. Liphook, August 11, 1870. [ 221 ] XXVII. Proceedings of Learned Societies. : ROYAL SOCIETY. [Continued from p. 136.] June 16, 1870.—General Sir Edward Sabine, K.C.B., President, in the Chair. (THE following communication was read :— “ On Supersaturated Saline Solutions.’—Part II. By Charles Tomlinson, F.R.S. The object of this paper is to develope more fully the principles attempted to be established in Part I.*, not only by clearer defini- tions of terms, but also by new facts and conclusions. ‘The paper is divided into two sections; in the first of which are stated the con- ditions under which nuclei act in separating salt or gas or vapour from their supersaturated solutions, while in the second section is shown the action of low temperatures on supersaturated saline solu- tions. The first section opens with definitions of the terms used. A nucleus is a body that has a stronger attraction for the gas or vapour or salt of a solution than for the liquid that holds it in solution. A body is chemically clean the surface of which is entirely free from any substance foreign to its own composition. Oils and other liquids are chemically clean if chemically pure, and contain no sub- stance, mixed or dissolved, that is foreign to their composition. But with respect to the nuclear action of oils &c., the behaviour is different when such bodies exist in the mass, such as a lens or globule, as compared with the same bodies in the form of films. Catharization is the act of clearing the surface of bodies from all alien matter; and the substance is said to be eatharized when its surface is so cleared. As every thing exposed to the air or to the touch takes more or less a deposit or film of foreign matter, substances are classed as catharized or uncatharized accordingly as they have or have not been so freed from foreign matter. Referring to the definition of a nucleus, substances are divided into nuclear or non-nuclear. The nuclear are those that may, per se, become nuclei. The non- nuclear are those that have not that quality. The nuclear substances would seem to be comparatively few, the larger number of natural substances ranking under the other division. Under nuclear substances are those vapours and oily and other liquids that form thin films on the surfaces of liquids and solids ; and generally all substances in the form of films, and only in that form. Thus a stick of tallow, chemically clean, will not act, but a film of it will act powerfully ; and, again, a globule of castor-oil will not act, if chemically clean; but in the form of a film, whether chemically clean or not, it will act powerfully. If a drop of a liquid be placed on the surface of another liquid, it * Phil, Mag. September 1868. 222 Royal Society :— will do one of three things (apart from chemical action): (1) it will diffuse through the liquid, and in general, under such circum- stances, not act as a nucleus; or (2) it will spread out into a film, or (3) remain in a lenticular shape. It becomes a film or a lens ac- cording to the general proposition that, if on the surface of the liquid A, whose surface-tension is a, we deposit a drop of the liquid B, whose surface-tension, 4, is less than a, the drop will spread into a film; but if, on the contrary, 6 be greater than a, or only a little less, the drop will remain in the form of a lens. Hence if B spread on A, A will not spread on the surface of B. This general proposition may not always apply in the case of supersaturated saline solutions, on account of the superficial viscosity, es) 8 greater or less difficulty of the superficial molecules to be dis- placed. A glass rod drawn through the hand becomes covered with a thin film ; or the same rod by exposure to the air contracts a film by the condensation of floating vapours, dust, &c. ; and in either case it is brought into the nuclear condition. A second class of nuclear bodies are permanently porous sub- stances, such as charcoal, coke, pumice, &c. The action of these is chiefly confined to vaporous solutions ; and if catharized they have no power of separating salts from their supersaturated solutions. | Under the non-nuclear, forming by far the larger class of sub- Hotta are glass, the metals, &c., while their surfaces are chemically clean. Among the non-nuclear substances will be found air; for its as- cribed nuclear character is due, not to itself, but to the nuclear par- ticles of which it is the vehicle. Thus, as stated in Part I., if air be filtered through cotton-wool it loses its apparent nuclear character ; so also if heated. When a catharized body is placed in a supersaturated solution, such solution, as explained in Part I., adheres to it as a whole; but if such body be non-catharized, the gas or vapour or salt of the so- lution adheres to it more strongly than the liquid portion, and hence there is a separation. In the present paper it is shown that an active or non-catharized surface is one contaminated with a film of foreign matter, which filmy condition is necessary to that close ad- hesion which brings about the nuclear action; for it can be shown that an oil, for example, is non-nuclear in the form of a lens or glo- bule, but powerfully nuclear in the form of a film. Some liquids (absolute alcohol for example) form films, and act as nuclei by separating water instead of salt from supersaturated so- lutions. Other liquids (glycerine for example) diffuse through the solutions without acting as nuclei. Fatty oils may slowly saponify, or oil of bitter almonds form benzoic acid in contact with supersaturated solutions of Glauber’s salt without acting as nuclei. The solutions (say of Glauber’s salt) are prepared with 1, 2, or 3 parts of the salt to 1 part of, water; they are boiled, filtered imto Mr. C. Tomlinson on Supersaturated Saline Solutions. 228 clean flasks, and covered with watch-glasses. When cold, the watch- glass being lifted off, a drop of oil is deposited on the surface of the supersaturated solution. In an experiment described, a drop of pale seal-oil formed a well-shaped film, with a display of iridescent rings ; and immediately from the lower surface of the film there fell large flat prisms with dihedral summits of the 10-atom sodic sulphate. The prisms were an inch or an inch and a half in length, and three eighths of an inch across. The crystallization proceeded from every part of the lower surface of the film, and as one set of crystals fell off, another set was formed, until the whole solution became a mass of fine crystals in a small quantity of liquid, an effect quite different from the usual crystallization which takes place when a supersaturated solution of Glauber’s salt is subjected to the action of a nucleus at oie or two points in its surface, as when motes of dust enter from the air, or the surface is touched witha nuclear point. In such case small crystalline needles diverge from the point and proceed rapidly in well-packed lines to the bottom, the whole being too crowded and too rapid to allow of the formation of regular crystals. Similar experiments were made on solutions of Glauber’s salt of different strengths, with drops of ether, absolute alcohol, naphtha, benzole, the oils of turpentine, cajeput, and other volatile oils, sperm, herring, olive, linseed, castor, and other fixed oils of animal and vegetable origin, with this general result, that, whenever the liquid drop spread out into a film, it acted as a powerful nucleus; but when the oil formed a lens there was no separation of salt, even when the flasks were shaken so as to break up the lens into small globules. If, however, a sudden jerk were given to the flask so as to flatten some of the globules against its sides into films, the whole solution instantly became solid. A similar effect was produced by introducing a clean inactive solid, for the purpose of flattenmg a portion of oil against the side of the flask. Stearine from sheep’s tallow that had been exposed to the air pro- duced immediate crystallization ; but by boiling the solution and covering the flasks, the stearine, now catharized, had lost its nuclear character on the cold solution. Similar observations were made with the fixed oils that form lenses or globules in the solution. So also volatile oils containing products of oxidation, dust, &c. are nuclear ; but when catharized by being redistilled, they are inactive in the glo- bular state, active in the form of films. Supersaturated solutions of potash alum, ammonia alum, sodic acetate, and magnesia sulphate were also operated on, with results similar to those obtained with solutions of Glauber’s salt. When a liquid forms a film on the surface of a supersaturated so- lution, the surface-tension of the solution is so far diminished as to bring the film into contact with the solution, when that differential kind of action takes place whereby, the salt of the solution adhering more strongly to the film than the water of the solution, the action of separation and crystallization, thus once begun, is propagated throughout. A similar action takes place with solid bodies that have contracted filmy nuclei qy being touched or drawn through 224 Royal Society. the hand, or merely exposed to the air; they are active or nuclear by virtue of the films of matter which more or less cover them. On the other hand, when a drop of oil (or many drops) is placed on the surface of a supersaturated saline solution, and it assumes the lenticular form, or even flattens into a disk, such lens or disk is separated from actual contact with the solution by surface-tension. That the adhesion is very different from that of a film may be shown by pouring a quantity of recently distilled turpentine, for example, on the surface of chemically clean water, and scraping upon it some fragments of camphor; these will be immediately covered with a solution of camphor in the oil, which solution will form iridescent films, and sail about with the camphor, vigorously displacing the turpentine, and cutting it up into smaller disks and lenses. So in the case of supersaturated saline solutions ; the oil-lens is not suffi- ciently in contact with the surface of the solution to allow of the exertion of that differential kind of action whereby salt is separated. Even when, by shaking, the oil is broken up into globules, and these are submerged, they are still so far separated from the solution by surface-tension as to prevent actual contact. In the second section it is shown that solutions of certain salts which remain liquid and supersaturated at and about the freezing- point of water, by a further reduction in temperature, to from 0° F. to —10° and in the absence of a nucleus, rather solidify than crystal- lize, but on being restored to 32° recover their liquid state without any separation of salt. . A solution of ferrous sulphate, for example, at 0° Fahr. formed tetrahedral crystals at the surface, which spread downwards until the contents of the tube became solid. In snow-water at 32° the frozen mass shrank from the sides of the tube, formed into asmooth rounded mass, and gradually melted, leaving the solution clear and bright without any deposit. On removing the cotton-wool from the mouth of the tube, small but well-shaped rhomboidal crystals soon filled the solution. A similar experiment was tried with the double salt formed by mixing in atomic proportions solutions of the zincic and magnesic sulphates. A supersaturated solution of this salt at about —8°F. became solid, and it melted quickly at 32°. Such a solution may be solidified and melted a number of times, provided it be protected from the action of nuclei; but if the cotton-wool be removed from the tube, even when the contents are solid, and be immediately re- inserted, there will be’a separation of the salt during the melting, in consequence of the entrance of nuclear particles from the air. Solutions of such a-strength as to be only saturated at ordinary emperatures, and therefore not sensitive to the action of nuclei, become very much so by reduction of the temperature below 32° Fahr. Salts that contain a large amount of water of crystallization, such as the zincic and magnesic sulphates, require only a small portion of added water in order to form supersaturated solutions, and they be- eome more sensitive to the action of nuclei as the temperature falls, ~ Geological Society. 225 or, in other words, as they become more highly supersaturated. Thus a very strong solution of calcichloride, which is not sensitive te nuclei at 40° or 45°, becomes very much so at 24° or 34°, The sodio-zincic sulphate contains only 4 proportionals of water of crystallization; and hence its supersaturated solutions are not stable at low temperatures. When freshly made, they may be re- duced to 10° Fahr. without separation of the salt; but by repose, even in clean tubes and in the absence of nuclei, long crystals of the separated salts occupy the length of the tube, but they are in- visible on account of having the same refractive index as that of the solution in which they are immersed. In the course of time, pro- bably from the escape of vapour of water through the porous plug, they become visible. A solution of the ammonia zincic sulphate at 4° Fahr. formed beautiful large feathery crystals of an opaque white, which gradually filled the tube. They melted rapidly at 32°. A supersaturated solution of nickel sulphate resisted a tempera- ture of 6° Fahr. Mixed with an equivalent weight of cupric sulphate, the two salts separate if the solution is exposed to the air; but in closed tubes the solution at 0° Fahr. forms beautiful feathery crys- tals, which melt rapidly at 32°, without any separation of salt. Similar phenomena are produced by a supersaturated solution of zinc sulphate and potash alum in equivalent proportions exposed to a temperature of 4° Fahr. A similar solution of the cupric and magnesic sulphates at —4° also became solid, and melted rapidly at 32°. Experiments were also made with the sodic and magnesic sulphates, cadmic, and some other sulphates. The addition of potassic sulphate to other sulphates, in atomic proportions, forms double salts, which, so far as they were examined, do not form supersaturated solutions. The effect of low temperatures was in some cases to throw down a portion “of the salts in the anhydrous form, upon which were formed by repose crystals of a lower degree of hydration than the normal salt. Some cases of this kind are described in the paper. em GEOLOGICAL SOCIETY. [Continued from p. 142.] March 9th, 1870.—Warington W. Smyth, Esq., F.R.S., Vice-President, in the Chair. The following communications were read :— 1. “On the Structure of a Fern-stem from the Lower Eocene of Herne Bay, and on its allies, recent and fossil.” By W. Carruthers, Esq:, F.L.S., F.G.S. The author described the characters of the fossil stem of a Fern obtained by George Dowker, Esq., F.G.8., from the beach at Herne Bay, and stated that in its structure it agreed most closely with the living Osmunda regalis, and certainly belonged to the Osmundacee, 226 Geological Society. The broken petioles show a single crescentic vascular bundle. The section of the true stem shows a white parenchymatous medulla, a narrow vascular cylinder interrupted by long slender meshes from which the vascular bundles of the petioles spring, and a parenchy- matous cortical layer. ‘The author described the arrangement of these parts in detail, and indicated their agreement with the same parts in Osmunda regalis. He did not venture to refer the Fern, to which this stem had belonged, positively to the genus Osmunda, but preferred describing it as an Osmundites, under the name of O. Dowkeri. The specimen was silicified ; and the author stated that even the starch-grains contained in its cells, and the mycelium of a parasitic Fungus traversing some of them, were perfectly represented. Its precise origin was unknown; it was said to be probably derived from the London Clay, or from the beds immediately below. 2. “On the Oolites of Northamptonshire.” By Samuel Sharp, Esq., F.G.8. The author stated that his ultimate purpose was to describe seve- rally the Oolitic beds occurring in the Northampton district, in the more northerly parts of the county, and in the neighbourhood of Stamford, to exhibit fossils gathered from each locality, and to correlate the several series and thus to endeavour to establish the character and sequence of the Oolites of this Midland district. He anticipated, however, that the publication by the Geological Survey of their maps and memoir of North Northamptonshire (the work of Mr. Judd) would intervene and might render superfluous the carry- ing out this work in its entirety ; but in the meantime he submitted his first part, “The Oolites of Northampton and Neighbourhood.” The author stated that there were four areas within a compara- tively small space in which the whole of the beds occurring in each, from the Great Oolite down to the Upper Lias (inclusive), were accessible. These were situated at or about:—1, Kingsthorpe; 2, Northampton; 3, Duston; 4, Blisworth. The Oolitic beds in these several areas were described in detail, the beds of the North- ampton Sand (as comparatively little known) being those to which the greatest interest attached. These he proposes to class in three divisions—the “‘ Upper,” the “ Middle,” and the “ Lower ” North- ampton Sand. The individual beds of the several localities were shown to vary considerably ; but collectively they would present the following ge- neral section, the maximum thicknesses being given in feet :-— feet. A. White Limestone, disposed in beds of from a few inches to about 3 feet in thickness, much fissured, and vary- < 2 ing in character, and containing characteristic Great- _ mR Dotto SOSBIIR: Re. 565 theucvacelss wR PE Pe ees. Ree: 25 To | Blue and grey clay, dug for brick-making, with a fer- ruginous band at base, and Great-Oolite fossils...... 16 [Line of unconformity. ] Intelligence and Miscellaneous Articles. 227 : feet. ae C. White or grey sand, more or less coherent, and with ey occasional ferruginous stains, sometimes quarried for 5 building-stone. A plant-bed is usually found in this OLESEN ae rrr ae Pee eae a 12 (D. A series of very variable beds, composed sometimes of ferruginous sandstone in thin layers, which overlie cal- careous beds containing shelly zones, false bedding being frequent. Sometimes the whole section consists of cal- careous rock with false bedding ; sometimes it presents a series of beds of compact ferruginous sandstone with no fossils. In one instance the entire section consists of white sand and sandstone, with no fossils ........ 30 Coarse Oolitic or subcrystalline Limestone, with fossils, overlying a calcareo-arenaceous slate, like Colleyweston RUC te es oR ee re ee ES 2 Bao 4. InFerror Oorire.—Northampton Sand. 5 |. Beds chiefly consisting of Ironstone, containing Rhyn- E chonella variabilis and R. cynocephala, and Ammonites LS Oyrons at tHe base sti ak ead aoe siia 85 This general section, the author stated, might be nepaptl as typical section of a considerable portion of the county of North. ampton. In his concluding remarks the author referred to the great lime- stone which marked the country about Stamford and, traversing ‘Rutland, attained its greatest thickness in Lincolnshire. ‘This limestone was proved by its paleontological contents to be Inferior Oolite; and its place, with reference to the beds described in the paper, was shown to be in the interval (marking the line of uncon- formity) between B and C of the general section. It thus tended to confirm the statement of the author that the line of division between the Great and the Inferior Oolite in the neighbourhood of Northampton occurred at that point. The paper was illustrated by the exhibition of a large collection of fossils from the several areas, including some new species, promi- nent among which was a new Starfish, named, in compliment to the author, “ Stellaster Sharpit,” by Dr. Wright, F.R.S.E., F.G.S., and described by him in a Note appended to this paper. XXVIII. Intelligence and Miscellaneous Articles. ON THE EXTENSION OF OHM’sS LAWS TO ELECTROLYTES, AND ON THE NUMERICAL DETERMINATION OF THE RESISTANCE OF DI- LUTE SULPHURIC ACID BY MEANS OF ALTERNATE CURRENTS, BY MM. F. KOHLRAUSCH AND A. NIPPOLDT. ‘HE special resistance of electrolytes is complicated with the pheno- mena of polarization which most frequently accompany electrolysis. To determine the first element it must be freed from the influence of the second, which presents great difficulties. The authors think they have removed these difficulties by causing induction-currents to pass through the liquids alternately in opposite directions. This method is not new; it has already been employed by MM. De la 228 Intelligence and Miscellaneous Articles. Rive, Lenz, Poggendorff, and Vorsselmann de Heer* ; and it has been proved that the polarization was not completely destroyed by this means. But it may be hoped that it can be completely annulled by diminishing the duration of the alternate currents, which diminishes the perturbing electrolytic effect—and by increasing the size of the electrodes, which diminishes the intensity of the currents, and con- sequently the polarization, which is nearly proportional to it. It will be acknowledged that this object is attained when the resistance of the liquid follows Ohm’s law—that is to say, when this resist- ance could be replaced by that of the wire of a metallic rheostat, whatever the intensity. In order to apply this method, three apparatus are indispensable— an induction-apparatus which gives currents alternately in opposite directions, an apparatus for their measurement which admits of these currents being compared, and also a rheostat. For the induction-apparatus the szren by Weber and R. Kohl. rausch was chosen’. . It is an ordinary siren having the moveable disk of magnetized steel. ‘This magnet rotates inside a rectangular multiplier similar to those of ordinary galvanometers; and its rotation produces in the wire of the multiplier induced currents which change their direction at each half-revolution. There is no better instrument with which to measure these alter- nate currents than Weber’s bifilar dynamometer. Its deviation, 4, is proportional to the square of the intensity of the induced currents which traverse it; and these latter vary with the velocity of the rota- tion of the disk of the siren, a velocity which may be measured from the sound produced. When, for all velocities of the siren, the resistance of the column of liquid cculd be replaced by that of the same length of wire of the rheostat, it was clear that the polari- zation had disappeared, and that the rheostat measured the special resistance of the liquid. Now this is what always occurred when the electrodes had the greatest dimensions (2900 square millims.). In these experiments the velocity of the disk varied from 2°3 to 76°9 turns per second; the electromotive force of the induced cur- rent varied consequently from ;; to 3 of that of a Grove’s element. The authors wished to operate on weaker currents. ‘They used the thermoelectric currents produced by an iron-copper element, which gives for 1° of difference of temperature an electromotive force equal to zasgo7 Of that of Grove, this difference not having in their expe- riments exceeded 4°. ‘This current passed through a solution of sulphate of zinc 83 millims. in length and having a section of 2400 square millimetres; in order to measure it the dynamometer had to be replaced by a very sensitive galvanometer. In these experiments the electromotive force descends to 755/57, of Grove’s, and the liquid follows Ohm’s laws in all cases. The memoir ends with a determination of the resistance of water acidulated by sulphuric acid at different degrees of concentration. By collecting all the experiments at the same temperature, the fol- * Poge. Ann. vols. xlv., xlviii., lii., lui. + Mémotres de la Société Royale de Saxe, vol. vi. p. 699. Intelligence and Miscellaneous Articles. 229 lowing Table has been drawn up, in which the resistances are ex- pressed in Siemens’s units—that is, compared to a column of mercury at zero, 1 metre in length and having a section of 1 square metre :— Density at |Volume of SO*H|Resistance at 22°,). «tion for 1°, 18°°5. per cent. He — J). 0:9985 0:0 744807 0°47 per 100 1:0000 0:2 464170 0°47 “: 1:0504 8:3 34461 0°65 - 1:0989 14-2 18909 0°65 11431 20:2 14961 0:80 . 1-2045 28:0 13107 1°32 i 1:2631 35:2 13106 1:26 - 13163 415 14258 1-41 . 1:3597 46-0 15731 1°57 rf 1:3994 50-4 17691 1:58 - 14482 55:2 20755 1:42 é 1:5026 60°3 255238 iio 18380 100:0 78742 2°66 ” The resistances in the above Table have been corrected by a dimi- nution of 0:2 per cent., in accordance with a note, at the end of the memoir. They can be represented by a very regular curve, which has a minimum ordinate when the density of the solution is 1°233. Hence acidulated water which contains 31°6 per cent. of monohydrated acid offers the least resistance to the passage of the current. ‘The coefficient of reduction with the temperature is supposed constant, although this constancy has only been demonstrated directly for so- lutions of sulphate of zinc ; hence this coefficient must not be ap- plied to great variations of temperature.—Poggendorff’s Annalen, vol. exxxvili.; Annales de Chimie et de Physique, April 1870. ON LIQUIDS OF HIGH DISPERSIVE POWER. BY WOLCOTT GIBBS, M.D., RUMFORD PROFESSOR IN HARVARD UNIVERSITY. Of the liquids which haye hitherto been proposed for the construc- tion of prisms, bisulphide of carbon unquestionably presents the greatest advantages. It is cheap, colourless, and unites a moderately high mean refractive to a very high dispersive power. By tacit con- sent a prism of 60° filled with this liquid: has come to be adopted as a sort of standard. The disadvantages of the bisulphide are equally well known; and I have spent no little time and labour in the en- deavour to find a liquid with a still higher dispersive power, less volatile, less sensitive optically to changes of temperature, and less offensive in odour. In these efforts I have not been altogether suc- cessful, no one liquid examined possessing all the qualities desired. Many organic liquids with high dispersive powers are difficult to prepare in a state of purity, and speedily become discoloured by absorption of oxygen from the air. Such are oil of cassia, the colour- less oil obtainable from balsam of Peru, and others. The thallic al- 230 Intelligence and Miscellaneous Articles. cohol of Lamy* is far too costly. The solution of silico-tungstate of sodium‘, of metatungstate of sodium ¢, and of soluble tungstic acid§ as obtained by dialysis, all promised good results from their extra- ordinary densities ; but all proved difficult to prepare in a state of purity, and extremely easy of decomposition. A solution of phosphorus in bisulphide of carbon has, according to Messrs. Dale and Gladstone ||, a dispersion of 0:2254, or nearly one and a half times as great as bisulphide of carbon alone, but becomes turbid on exposure to sunlight from the formation of amorphous phosphorus. It occurred to me that, by dissolving sulphur with the phosphorus, the formation of amorphous phosphorus might be pre- vented ; and experiment proved that this was the case. The solution, as thus obtained, has a pale yellow colour, but is perfectly clear and undergoes no change by the action of light even when long continued. I have been in the habit of preparing it by dissolving one part of dry flowers of sulphur and two parts of phosphorus in four or five parts of bisulphide of carbon, and filtering the liquid through a well-dried ribbed paper filter, which is easily done. The refractive and disper- sive power of the solution will of course vary with the quantity of phosphorus and sulphur dissolved. By a gentle heat the whole, or nearly the whole, of the bisulphide of carbon may be driven off, a liquid compound of sulphur and phosphorus remaining, which has so high a mean refractive power that it cannot be employed with prisms having a refractive angle of more than 45°-50°. The same end may, however, also be attained by continually adding phosphorus to a saturated solution of sulphur in bisulphide of carbon, in which phos- phorus appears to be soluble without limit. With a strong and probably saturated solution of sulphur in CS, the angle between Li and D was 0° 50’ 10". When phosphorus was added the angle was 2° 25' 30", the refracting angle of the prism being 60°. In this last case the angle between Na, and Na, was 0° 2' 20". The spectrum was perfectly clear, the definition of the dark lines leaving nothing to be desired. In consequence, however, of the yellow colour of the liquid, there is always a marked absorption of the violet end of the spectrum. In working with the above described solution I have employed hollow glass prisms with refracting plates cemented on with a mix- ture of glue and molasses. These were found to be perfectly tight and to last for months without change. The great disadvantage in the use of a solution of sulphur and phosphorus consists in the danger of breaking the prisms, the liquid taking fire spontaneously when it has been a few seconds in contact with any porous material like wood or paper. On the other hand, however, the large quantity of sulphur * Ann. de Ghee et de Physique, 4th series, vol. iii. p. 373. + Ibid. p. 5 i Scheibler in Journal fiir Prakt. Chinue, vol. Ixxxiii. p. 273, § Graham in Journal of the Chemical Society, vol. ii. p. 318, || Phil. Mag. S. 4. vol. xviii. p. 30. §| The number 0°225 is the aifes erence between the indices for the extreme red and yiolet rays, = Intelligence and Miscellaneous Articles. 231 present prevents the fire from spreading, a drop placed upon a piece of wood leaving after combustion only a charred spot. When not in use, the prisms should be kept in an iron pot with atight cover. In this manner I have employed and preserved two during a long and hot summer. The viscid or, rather oily nature of the solution serves to prevent, to a great extent, the formation of ascending and descending currents from slight changes of temperature; and when the prisms are well shaken before use, the definition remains perfect for a long time. In my spectroscope the prisms rest upon a plate of glass instead of upon one of metal.—Suliman’s American Journal, July 1870. ON THE PROPAGATION OF SOUND IN TUBES. BY M. AD. SEEBECK. It is admitted that the velocity of sound propagated in a tube is less than in the open air, and the smaller the tube the less the velo- city*. Kirchhoff has given the following formula for the velocity of sound :— K V=A( ae —), or V az in which A is the velocity in air, r the radius of the tube, the num- ber of vibrations, K a constant dependent on the calorific conduc- tivity and on friction. ‘This formula is the same as the one given by Helmholtz, except the meaning of the constant K. The method employed by Seebeck does not differ materially from that which Schneebeli adopted in order to verify Helmholtz’s for- mula, and of which he has already given an accountf. The apparatus used was constructed of a horizontal tube, closed near one end by a moveable piston; near the other a very narrow lateral tube was soldered, to which a caoutchouc tube was fitted which com- municated with the ear. A sound was produced in front of the open- ing of the tube by means ofa tuning-fork fixed horizontally to a piece of wood insulated by some caoutchouc supports. That the ear may hear distinctly the sound produced by the tuning-fork, at the junc- tion of the large tube closed by the piston and the small tube com- municating with the ear there must be a node, due to the coexist- ence of direct and reflected waves against the piston. If a loop is produced, the sound perceived by the ear will have its minimum in- tensity ; it is this character which is to be appreciated; and it is then known whether the distance from the piston to the opening of the ‘small tube is equal to 2 or in general to (2n+1)* A being the wave-length of the sound produced; from this we get the velocity of sound by the formula V=ni, 2 being the number of vibrations of ‘the corresponding sound. ‘The whole section of the tube was agi- tated, which Kirchhoff’s formula presupposes, except for the largest * Annales de Chimie et de Physique, 8. 4. vol. xv. pp. 487, 492, 7 Ibid. vol. xvi. p. 512. 232 Intelligence and Miscellaneous Articles. tubes used. ‘The observations were reduced to zero by means of the formula A,= end of each series of observations a thermometer placed close at hand: the air in the tube was first dried by chloride of calcium. Seebeck used Konig’s four tuning-forks, which give the notes uwt,, sol,, mi,, ut,, of which the numbers of vibrations were 512, 384, 320, 256. He found the following results :— Tuning-forks. Diameter. a = or. uts=256. miz= 320. sol,=384. uts=512. millims. millims. millims. millims. millims. 3°4 ee 317°26 318°86 322°98 9 325°63 327°22 327°68 328°44 17%5 327°82 329°24 329°86 330°92 29 3824°54 325°36 326°72 326°10 The velocity of the sound diminishes with the diameter of the tube, except for the largest (27= 29 millims.), which Seebeck attributes to the whole of the section not having been agitated; it may also be that in the large tubes the motion of the gaseous molecules is not parallel to their axis. By adopting for the velocity of sound in air a the number 332'77 millims., a result obtained from the determina- tions by Moll and Van Beek, Seebeck has calculated the difference A—V. According to the formula by Kirchhoff, we must have K A—V=A Son ek and consequently, for the same sound and various tubes, (A—V,) x 27, =(A—V,) x 27, an equation which the determinations of Seebeck satisfy, except for the largest tube (27=29 millims.). But it was also found that (A—V) 2, for the same value of 7, isno longer constant. Seebeck recognized, on the contrary, that the product (A—V)n2 was ob- viously constant; and consequently the diminution of velocity of sound in a tube varies in inverse ratio with the power 3 of the num- ber of vibrations of the corresponding sound. Seebeck also made some investigations when the interior of his tubes was covered with leather or flannel: he proved that there was a considerable diminution in the velocity of sound; in the latter case it fell to281°7 millims. These experiments, however, leave some- thing to be desired, because the interior of the tube was not com- pletely covered. A small slit was made that the position of the piston might be observed: would it not be possible to determine the position of the piston exactly by means of the rod by which it is re- gulated ?—Poggendorff’s Annalen, vol. cxxxix. p. 104; Annales de Chimie, April 1870. Tank LONDON, EDINBURGH, saxo DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] OCTOBER 1870. XXIX. On Ocean-currents.—Part III. On the Physical Cause of Ocean-currents. By JaMEs Crout, of the Geological Survey of Scotland. [Continued from vol. xxxix. p. 194.] > heel is no point connected with ocean-currents on which more diversity of opinion has existed than in regard to their origin. At present, however, there may be said to be only two theories held on the subject, viz. that which attributes the currents to the influence of the trade and other winds, and that which attributes them to differences in specific gravity be- tween the waters of intertropical and polar regions. The latter theory appears at present to be the more prevalent of the two, although, perhaps, not so among scientific men. It is difficult to conceive how a theory so manifestly erroneous should have gained such general acceptance. Its popularity is no doubt chiefly owing to the very great prominence given to it by Lieut. Maury in his interesting and popular work ‘ The Physical Geo- graphy of the Sea.’ Another cause which must have favoured the reception of this theory is the ease with which it is per- ceived how, according to it, circulation of the waters of the Ocean is supposed to follow. One has no difficulty, for ex- ample, in perceiving that if the intertropical waters of the ocean are expanded by heat, and the waters around the poles contracted by cold, the surface of the ocean will stand at a higher level at the equator than at the poles. Mquilibrium being thus disturbed, the water at the equator will tend to flow towards the poles as a surface-current, and the water at the poles towards the equator as an undercurrent. ‘This, at first sight, looks well, especially to those who take but a superficial view of the matter. Phil, Mag. 8. 4, Vol. 40. No. 267. Oct. 1870. R 234 Mr. J. Croll on the Physical Cause of Ocean-currents. We shall examine this theory at some length, for two reasons: 1, because it lies at the root of a great deal of the confusion and misconception which have prevailed in regard to the whole subject of ocean-currents ; 2, because, if the theory is correct, it militates strongly against the physical theory of secular changes of climate advanced in the preceding part of this paper. We have already seen that when the excentricity of the earth’s orbit reaches a high value, a combination of physical circum- stances tends to lower the temperature of the hemisphere which has its winter solstice in aphelion, and to raise the temperature of the opposite hemisphere, whose winter solstice will, of course, be in perihelion. The direct result of this state of things, as was shown, is to strengthen the force of the trade-winds on the cold hemisphere, and to weaken their strength on the warm hemisphere ; and this, in turn, we also saw tends to impel the warm water of the intertropical region over on the warm hemi- sphere, and to prevent it, in a very large degree, from passing into the cold hemisphere. This deflection of the ocean-currents tends to an enormous extent to increase the difference of tem- perature previously existing between the two hemispheres. In other words, the warm and equable condition of the one hemi- sphere, and the cold and glacial condition of the other, are, toa great extent, due to this deflection of ocean-currents. Butif the theory be correct which attributes the motion of ocean-currents to a difference in density between the sea in intertropical and polar regions, then it follows that these currents (other things being equal) ought to be stronger on the cold hemisphere than on the warm, because there is a greater difference of tempera- ture and, consequently, a greater differenee of density between the polar seas of the cold hemisphere and the equatorial seas, than between the polar seas of the warm hemisphere and the equatorial seas. And this being the case, notwithstanding the influence of the trade-winds of the cold hemisphere blowing over upon the warm, the currents will, in all probability, be stronger on the cold hemisphere than on the warm. In other words, the influence of the powerful trade-winds of the cold hemisphere to impel the warm water of the equator over upon the warm hemisphere will probably be more than counterba- lanced by the tendency of the warm and buoyant waters of the equator to flow towards the dense and cold waters around the pole of the cold hemisphere. But if ocean-currents are due not to difference in specific gravity, but to the influence of the trade- winds, then it is evident that the waters at the equator will be impelled, not into the cold hemisphere, but into the warm. As Lieut. Maury appears to be the acknowledged exponent of the theory which attributes ocean-currents to the difference of Mr. J. Croll on the Physical Cause of Ocean-currenits. 235 specific gravity between the waters at the equator and the poles, I shall now proceed to consider at some length his views on the subject, the more especially as we find in his work on the phy- sical geography of the sea almost every argument that can be advanced in favour of the theory which he advocates. Although considerable diversity of opinion has prevailed in regard to the cause of ocean-currents, yet it is remarkable how little is to be found of a purely scientific character bearing directly on the dynamics of the subject. Another reason which has induced me to select Maury’s work is, that it not only contains a much fuller discussion on the cause of the motion of ocean-currents than is to be found any- where else, but also that it has probably passed through a greater number of editions than any other book of a scientific character in the English language in the same length of time. lieut. Maury on the Cause of the Motion of Ocean-currents. Although Lieut. Maury has expounded his views on the cause of ocean-currents at great length in the various editions of his work, yet it is somewhat difficult to discover what they really are. This arises chiefly from the generally confused and some= times contradictory nature of his hydrodynamical conceptions. After a repeated perusal of several editions of his book, the fol- Jowing, I trust; will be found to be a pretty accurate representa- tion of his theory :— Ocean-currents, according to Maury, due to difference of spe- cific gravity.—Although Maury alludes to a number of causes which, he thinks, tend to produce currents, yet he deems their inflience so small that, practically, all currents may be referred to difference of specific gravity. | “ If we except,” he says, “the tides, and the partial currents of the sea, such as those that may be created by the wind, we may lay it down as a rule that all the currents of the ocean owe their origin to the differences of specific gravity between sea- water at one place and sea-water at another; for wherever there is such a difference, whether it be owing to difference of tempe- rature or to difference of saltness, &c., it is a difference that disturbs equilibrium, and currents are the consequence” (§ 467) *, To the same effect see §§ 896, 37, 512, 520, and 537. Notwithstanding the fact that Maury is continually referring to difference of specific gravity as the great cause of currerits, it is difficult to understand in what way he conceives this differ- ence to act as a cause. Difference of specific gravity between the waters of the ocean | * The edition from which I quote, unless stated to the contrary, is the _ one published by Messrs. ‘T, Nelson and Sons, 1870, | R2 236 Mr. J. Croll on the Physical Cause of Ocean-currents. at one place and another can give rise to currents only through the influence of the earth’s gravity. All currents resulting from difference of specific gravity can be ultimately resolved into the general principle that the molecules that are specifically heavier descend and displace those that are specifically lighter. Tf, for example, the ocean at the equator be expanded by heat or by any other cause, it will be forced by the denser waters in temperate and polar regions to rise so that its surface shall stand at a higher level than the surface of the ocean in these regions. The surface of the ocean will become an inclined plane, sloping from the equator to the poles. Hydrostatically, the ocean, considered as a mass, will then be in a state of equili- brium; but the individual molecules will not be in equilibrium, The molecules at the surface in this case may be regarded as lying on an inclined plane sloping from the equator down to the poles, and as these molecules are at liberty to move they will not remain at rest, but will descend the incline towards the poles. When the waters at the equator are expanded, or the waters at the poles contracted, gravitation makes, as it were, a twofold effort to restore equilibrium. It in the first place sinks the waters at the poles, and raises the waters at the equator, in order that the two masses may balance each other; but this very effort of gravitation to restore equilibrium to the mass destroys the equilibrium of the molecules by disturbing the level of the ocean. It then, in the second place, endeavours to restore equi- librium to the molecules by pulling the lighter surface-water at the equator down the incline towards the poles. This tends not only to restore the level of the ocean, but to bring the lighter water to occupy the surface and the denser water the bottom of the ocean; and when this is done, complete equilibrium is re- stored, both to the mass of the ocean and to its individual mole- cules, and all further motion ceases. But if heat be constantly applied to the waters of the equatorial regions, and cold to those of the polar regions, anda permanent disturbance of equilibrium maintained, then the continual effort of gravitation to restore equilibrium will give rise to a constant current. In this case, the heat and the cold (the agents which disturb the equilibrium of the ocean) may be regarded as causes of the current, inas- much as without them the current would not exist; but the real efficient cause, that which impels the water forward, is the force of gravity. But the force of gravity, as has already been noticed, cannot produce motion (perform work) unless the thing acted upon descend. Descent is implied in the very conception of a current produced by difference of specific gravity. But Maury speaks as if difference of specific gravity could give rise to a current without any descent, Mr. J. Croll on the Physical Cause of Ocean-currents. 237 “Tt is not necessary,” he says, “to associate with oceanic currents the idea that they must of necessity, as on land, run from a higher to a lower level. So far from this being the case, some currents of the sea actually run up hill, while others run on a level. The Gulf-stream is of the first class” ($ 403). “The top of the Gulf-stream runs on a level with the ocean ; therefore we know it is not a descending current ” (§ 18). And in § 9 he says that between the Straits of Florida and Cape Hatteras the waters of the Gulf-stream “are actually forced up an inclined plane, whose submarine ascent is not less than 10 inches to the mile.” To the same effect see $$ 25, 59. It is perfectly true that “it is not necessary to associate with ocean-currents the idea that they must of necessity, as on land, run from a higher to a lower level.” But the reason of this is that ocean-currents do not, like the currents on land, owe their motion to the force of gravitation. If ocean-currents result from difference of specific gravity between the waters in tropical and polar regions, as Maury maintains, then it is necessary to assume that they are descending currents. Whatever be the cause which may give rise to a difference of specific gravity, the motion which results from this difference is due wholly to the force of gravity ; but gravity can produce no motion unless the water descend. This fact must be particularly borne in mind while we are con- sidering Maury’s theory that currents are the result of differ- ence of specific gravity. Ocean-currents, then, according to Maury, owe their existence to the difference of specific gravity between the waters of inter- tropical and polar regions. This difference of specific gravity he attributes to two causes—(1) to difference as to temperature, (2) to difference as to saltness. ‘There are one or two causes of a minor nature affecting the specific gravity of the sea, to which Maury alludes ; but these two determine the general result. Let us begin with ‘the consideration of the first of these two causes, Viz. :— Difference of specific gravity resulting from difference of tempe- rature—Maury explains his views on this point by means of an illustration. ‘ Let us now suppose,” he says, “ that all the water within the tropics, to the depth of one hundred fathoms, sud- denly becomes oil. The aqueous equilibrium of the planet would thereby be disturbed, and a general system of currents and counter currents would be immediately commenced—the oil, in an unbroken sheet on the surface, running toward the poles, and the water, in an undercurrent, toward the equator. The oil is supposed, as it reaches the polar basin, to be recon- _ verted into water, and the water to become oil as it crosses _ Cancer and Capricorn, rising to the surface in intertropical 238 Mr. J. Croll on the Physical Cause of Ocean-currents. regions, and returning as before” (§20). ‘ Now,” he says (§22), “do not the cold waters of the north, and the warm waters o the Gulf, made specifically lighter by tropical heat, and which we see actually preserving such a system of countercurrents, hold, at least in some degree, the relation of the supposed water and oil ? ”” In § 24 he calculates that at the Narrows of Bemini the difference in weight between the volume of the Gulf-water that crosses a section of the stream in one second, and an equal volume of water at the ocean temperature of the latitude, sup- posing the two volumes to be equally salt, 1s fifteen millions of pounds. Consequently the force per second operating to pro- pel the waters of the Gulf towards the pole would in this case, he concludes, be the ‘‘ equilibrating tendency due to fifteen mil- lions of pounds of waterin the latitude of Bemim.” In §§ 511 and 512 he states that the effect of expanding the waters at the torrid zone by heat, and of contracting the waters at the frigid zone by cold, is to produce a set of surface-currents of warm and light water from the equator towards the poles, and another set of undercurrents of cooler and heavy water from the poles towards the equator. See also to the same effect §§ 513, 514, 896. | There can be no doubt that Maury concludes that the waters in intertropical regions are expanded by heat, and those in polar regions. are contracted by cold, and that this tends to produce a surface-current from the equator to the poles, and an undercur- rent from the poles to the equator. We shall now consider his second great cause of ocean-cur- rents, viz. :— Difference of specific gravity resulting from difference in degree of saltness—Maury maintains, and that correctly, that saltness that, other things being equal, the saltest water is the densest. He suggests “that one of the pur- poses which, in the grand design, it was probably intended to accomplish by having the sea salt and not fresh, was to impart to its waters the forces and powers necessary to make their circu- lation complete” (¢ 495). Now itis perfectly obvious that if difference in saltness is to cooperate with difference in temperature im the production of ocean-currents, the saltest waters, and consequently the densest, must be in the polar regions, and the waters least salt, and con- sequently lightest, must be in equatorial and intertropical re- gions. Were the saltest waters at the equator, and the freshest at the poles, it would tend to neutralize the effect due to heat, and, instead of producing a current, would simply tend to pre- vent the existence of the currents which otherwise would result from difference of temperature, Mr. J. Croll on the Physical Cause of Ocean-currents. 239 A very considerable portion of Maury’s book, however, is devoted to proving that the waters of equatorial and intertropical regions are salter and heavier than those of the polar regions; and yet, notwithstanding this, he endeavours to show that this difference in respect to saltness between the waters of the equato- rial and the polar regions is one of the chief causes, if not the chief cause, of ocean-currents. In fact, it is for this special end that so much labour is bestowed in proving that the saltest water is in the equatorial and intertropical regions, and the freshest in the polar. f “In the present state of our knowledge,” he says, “ concern- ing this wonderful phenomenon (for the Gulf-stream is one of the most marvellous things in the ocean) we can do little more than conjecture. But we have two causes in operation which we may safely assume are among those concerned in producing the Gulf- stream. One of these is the increased saltness of its water after the trade-winds have been supplied with vapour from it, be it much or little ; and the other is the diminished quantum of salt which the Baltic and the Northern Seas contain” (§ 37). “ Now here we have, on one side, the Caribbean Sea and Gulf of Mexico, with their waters of brine; on the other, the great Polar basin, the Baltic, and the North Sea, the two latter with waters that are but little more than brackish. In one set of these sea-basins the water is heavy, in the other it is light. Between them the ocean intervenes; but water is bound to seek and to maintain its level ; and here, therefore, we unmask one of the agents con- cerned in causing the Gulf-stream”’ ($ 38). To the same effect see §§ 52, 522, 528, 524, 525, 526, 528, 580, 554, 556. Lieut. Maury’s two causes neutralize each other. Here we have two theories put forth regarding the cause of ocean-cur- rents, the one in direct opposition to the other. According to the one theory, ocean-currents exist because the waters of equa- torial regions, in consequence of their higher temperature, are less’ dense than the waters of the polar regions; but according to the other theory, ocean-currents exist because the waters of equatorial regions, in consequence of their greater saltness, are more dense than the waters of the polar regions. If the one cause be assigned as a reason why ocean-currents exist, then the other can be equally assigned as a reason why they do not exist. According to both theories it is the difference of density between the equatorial and polar waters that gives rise to currents; but according to the one theory the equatorial waters are lighter than the polar, whilst according to the other theory they are heavier than the polar. Hither the one theory or the other may betrue, or neither; but it is logically impossible that both of them can, for the simple reason that the waters of the equator cannot 240 Mr. J. Croll on the Physical Cause of Ocean-currents. at the same time be both lighter and heavier than the water at the poles. They may be either the one or the other, but they cannot be both. Let it be observed that it is not two currents, the one contrary to the other, with which we have at present to do; it is not temperature producing currents in one direction, and saltness producing currents in the contrary direction. We have two theories regarding the origin of currents, the one diametrically opposed to the other. The tendency of the one cause assigned is to prevent the action of the other cause. If temperature is allowed to act, it will make the intertropical waters lighter than the polar, and then, according to theory, a current will result. But if we bring saltness into play (the other cause) it will do the reverse: it will increase the den- sity of the intertropical waters and diminish the density of the polar; and so far as it acts it will diminish the currents pro- duced by temperature, because it will diminish the difference of specific gravity between the intertropical and polar regions which had been previously caused by temperature. And when the effects of saltness are as powerful as those of temperature, the difference of specific gravity produced by temperature will be completely effaced, or, in other words, the waters of the equato- rial and polar seas will be of the same density, and consequently ~ no current wili exist. And so long as the two causes continue in action, no current can arise, unless the energy of the one cause should happen to exceed that of the other; and even then a current will only exist to the extent by which the strength of the one exceeds that of the other. The contrary nature of the two theories will be better seen by considering the way in which he supposes difference in saltness is produced and acts as a cause. If there is a constant current resulting from the difference in saltness between the equatorial and polar waters, then there must be a cause which maintains this difference in saltness. The current is simply the effort to restore the equilibrium lost by this difference ; and the current would very soon do this, and then all motion would cease, were there not a constantly operating cause maintaining this disturbance. What, then, according to Maury, is the cause of this disturbance, or, in other words, what is it that keeps the equatorial waters salter than the polar? The agencies in operation which keep the waters in equatorial regions salter than the polar are stated by him to be heat, radia- tion, evaporation, precipitation, and secretion of solid matter in the form of shells, &. The two most important, however, are evaporation and precipitation. The trade-winds enter the equatorial regions as relatively dry winds thirsting for vapour; consequently they absorb far miore i . . : Mr. J. Croll on the Physical Cause of Ocean-currents. 241 moisture than they give out; and the result is that, in intertro- pical regions, evaporation is much in excess of precipitation; and as fresh water only is taken up, the salt being left behind, the process, of course, tends to increase the saltness of the inter- tropical seas. Again, in polar and extratropical regions the re- verse is the case ; precipitation is in excess of evaporation. This tends in turn to diminish the saltness of the waters of those regions. See on these points $$ 31, 33, 34,37, 179, 517, 526, and 552. In the system of circulation produced by difference of tempe- rature, as we have already seen, the surface-currents flow from the equator to the poles, and the under or return currents from the poles to the equator; but in the system produced by differ- ence of saltness, the surface-currents flow from the poles to the equator, and the return undercurrents from the equator to the poles. That the surface-currents produced by difference of salt- ness flow from the poles to the equator, Maury thinks is evident for the two following reasons :— (1) As evaporation is in excess of precipitation in intertropical regions, more water is taken off the surface of the ocean in those regions, than falls upon it in the form of rain. This excess of water falls in the form of rain on temperate and polar regions, where, consequently, precipitation is in excess of evaporation. The lifting of the water off the equatorial regions and its deposit on the polar tend to lower the level of the ocean in equatorial regions and to raise the level in polar; consequently, in order to restore the level of the ocean, the surface-water at the polar regions flows towards the equatorial regions. (2) As the water taken up at the equator is fresh, and the salt is left behind, the ocean, in intertropical regions, is thus made salter and consequently denser. ‘This dense water, therefore, sinks and passes away as an undercurrent. Thiswater, evaporated from intertropical regions, falls as fresh and lighter water in temperate and polar regions ; and therefore not only is the level of the ocean raised, but the waters are made lighter. Hence, in order to restore equilibrium, the waters in temperate and polar regions will flow as a surface-current towards the equator. Undercurrents will flow from the equator to the poles, and sur- face or upper currents from the poles to the equator. Difference in temperature and difference in saltness, therefore, in every re- spect tend to produce opposite effects. That the above is a fair representation of the way in which Maury supposes difference im saltness to act as a cause in the production of ocean-currents will appear from the following quotations :— “In those regions, as in the trade-wind region, where evapo- ae 242 Mr. J. Croll on the Physical Cause of Ocean-currents. ration is in excess of precipitation, the general level of this sup- posed sea would be altered, and immediately as much water as is carried off by evaporation would commence to flow in from north and south toward the trade-wind or evaporation region, to restore the level”? ($509). “‘ Onthe other hand, the winds have taken this vapour, borne it off to the extratropical regions, and precipitated it, we will suppose, where precipitation is in excess of evaporation. Here is another alteration of sea-level, by elevation instead of by depression ; and hence we have the motive power for a surface-current from each pole towards the equator, the object of which is only to supply the demand for evaporation in the trade-wind regions” (§ 510). _ The above result “would follow, supposing the ocean to be fresh. He then proceeds to consider an additional result that follows in consequence of the saltness of the ocean. “‘ Let evaporation now commence in the trade-wind region, as it was supposed to do in the case of the fresh-water seas, and as it actually goes on in nature—and what takes place? Why, a lowering of the sea-level as before. But as the vapour of salt water is fresh, or nearly so, fresh water only is taken up from the ocean; that which remains behind is therefore more salt. Thus, while the level is lowered in the salt sea, the equilibrium is destroyed because of the saltness of the water; for the water that remains after evaporation takes place is, on account of the solid matter held in solution, specifically heavier than it was before any portion of it was converted into vapour” (§ 517). “The vapour is taken from the surface-water; the surface- water thereby becomes more salt, and, under certain conditions, heavier. When it becomes heavier, it sinks; and hence we have, due to the salts of the sea, a vertical circulation, namely, a descent of heavier—because salter and cooler—water from the surface, and an ascent of water that is Jighter—because it is not so salt—from the depths below” (§ 518). In section 519 he goes on to show that this vapour removed from the intertropical region is precipitated in the polar regions, where precipitation is in excess of evaporation. “ In the preci- pitating regions, therefore, the level is destroyed, as before ex- plained, by elevation, and in the evaporating regions by depres- sion ; which, as already. stated, gives rise to a system of surface- currents, moved by gravity alone, from the poles towards the equator”’ ($520). “This fresh water bemg emptied into the Polar Sea and agi- tated by the winds, becomes mixed with the salt; but as the agita- tion of the sea by the winds is supposed to extend to no great depth, it is only the upper layer of salt water, and that to a mo- derate depth, which becomes mixed with the ie The specific Mr. J. Croll on the Physical Cause of Ocean-currents. 243 pravity of this upper layer, therefore, is diminished just as much as the specific gravity of the sea- water inthe evaporating regions was increased, And thus we have a surface-current of saltish water from the poles towards the equator, and an undercurrent of water salter and heavier from the equator to the poles”? (§ 522). ‘This property of saltness imparts to the waters of the ocean another peculiarity, by which the sea is still better adapted for the regulation of climates, and it is this: by evaporating fresh water from the salt in the tropics, the surface-water becomes heavier than the average of sea-water. This heavy water is also warm water; it sinks, and being a good retainer, but a bad conductor of heat, this water is employed in transporting through under- currents heat for the mitigation of climates in far distant regions” (§ 526). “ For instance, let us suppose the waters in a certain part of the torrid zone to be 90°, but, by reason of the fresh water which has been taken asensy oan in a state of vapour, and con- sequently, by reason of the proportionate increase of salts, these waters are heavier than waters that may be cooler, but not so salt. This being the case, the tendency would be for this warm but salt and heavy water to flow off as an undercurrent towards the polar or some other regions of lighter water’? (§ 554). That Maury supposes the warm water at the equator to flow to the polar regions as an undercurrent is further evident from the fact that he maintains that the climate of the arctic regions is mitigated by a warm undercurrent, which comes from the equa- torial regions, and passes up through Davis Straits. See $§ 534-544. The question now suggests itself: to which of these two an- tagonistic causes does Maury really suppose ocean-currents must be referred ? Whether does he suppose, difference in tempera- ture or difference in saltness, to be the real cause? I have been unable to find any thing from which we can reasonably conclude that he prefers the one cause to the other. It would seem that he regards both as real causes, and that he has failed to perceive that the one is destructive of the other. But it is difficult to conceive how he could believe that the sea in equatorial regions, by virtue of its higher temperature, zs lighter than the sea in polar regions, while at the same time it zs not lighter but heavier, in consequence of its greater saltness—how he could be- lieve that the warm water at the equator flows to the poles as an upper current, and the cold water at the poles to the equator as an undercurrent, while at the same time the warm water at the equator does not flow to the poles as a surface-current, nor the cold water at the poles to the equator as an undercurrent, ‘but the reverse. But, unless these absolute impossibilities be 244 Mr. J. Croll on the Physical Cause of Ocean-currents. possible, how then can an ocean-current be the result of both causes ? The only explanation of the matter appears to be that Maury has failed to perceive the contradictory nature of his two theories. This fact is particularly seen when he comes to apply his two theories to the case of the Gulf-stream. He maintains, as has already been stated, that the waters of the Gulf-stream are salter than the waters of the sea through which they flow (see §§ 3, 28, 29, 80, 34, and several other places). And he states that one of the chief causes of the Gulf-stream is this, that “ we have on one side the Caribbean Sea and Gulf of Mexico, with their waters of brine; on the other the great Polar Basin, the Baltic, and the North Sea, the two latter with waters that are but little more than brackish. In one set of these sea-basins the water is heavy, in the other it is hght. Between them the ocean intervenes; but water is bound to seek and to maintain its level; and here, therefore, we unmask one of the agents concerned in causing the Gulf-stream” (§ 38). There can be no doubt whatever that it 1s the density of the waters of the Gulf- stream at its fountain-head, the Gulf of Mexico, resulting from its superior saltness, and the deficiency of density of the waters in polar regions and the North Sea &c., that is here considered to be unmasked as one of the agents. If this be a cause of the motion of the Gulf-stream, how then can the difference of temperature between the waters of intertropical and polar regions assist as a cause? ‘This difference of temperature will simply tend to undo all that has been done by difference of saltness; for it will tend to make the waters of the Gulf of Mexico hghter, and the waters of the polar regions heavier. But Maury maintains, as we have seen, that this difference of temperature is also a cause, which shows that he does not per- ceive the contradiction. This is still further apparent. Maury maintains, as stated, that “‘ the waters of the Gulf-stream are salter than the waters of the sea through which they flow,” and that this excess in saltness, by making the water heavier, is a cause of the motion of the stream. But he maintains that, notwithstanding the effect which greater saltness has in increasing the density of the waters of the Gulf-stream, yet, owing to their higher tempera- ture, they are actually lighter than the water through which they flow ; and as a proof that this is the case, he adduces the fact that the surface of the Gulf-stream is roof-shaped ($$ 39-41), which it could not be were its waters not actually lighter than the waters through which the streams flow. So it turns out, in contradiction to what he had already stated, that it is the lesser density of the waters of the Gulf-stream that is the real cause of Mr. J. Croll on the Physical Cause of Ocean-currents, 245 their motion. The greater saltness of the waters, to which he attributes so much, can in no way be regarded as a cause of motion. Its effect, so far as it goes, is to stop the motion of the stream rather than to assist it. But, again, although Maury maintains that difference of salt- ness and difference of temperature are both causes of ocean- currents, yet he appears actually to admit that temperature and saltness neutralize each other so as to prevent change in the specific gravity of the ocean, as will be seen from the following quotation :— “Tt is the trade-winds, then, which prevent the thermal and specific-gravity curves from conforming with each other in intertropical seas. The water they suck up is fresh water; and the salt it contained, being left behind, is just sufficient to coun- terbalance, by its weight, the effect of thermal dilatation upon the specific gravity of sea-water between the parallels of 34° north and south. As we go from 34° to the equator, the water grows warmer and expands. It would become lighter; but the trade- winds, by taking up vapour without salt, make the water salter, and therefore heavier. The conclusion is, the proportion of salt in sea-water, its expansibility between 62° and 82°, and the thirst of the trade-winds for vapour are, where they blow, so balanced as to produce perfect compensation ; and a more beau- tiful compensation cannot, it appears to me, be found in the mechanism of the universe than that which we have here stum- bled upon. It is a triple adjustment: the power of the sun to expand, the power of the winds to evaporate, and the quantity of salts in the sea—these are so proportioned and adjusted that when both the wind and the sun have each played with its forces upon the intertropical waters of the ocean, the residuum of heat and of salt should be just such as to balance each other in their effects; and so the aqueous equilibrium of the torrid zone is preserved” (§ 436, eleventh edition). “ Between 35° or 40° and the equator evaporation is in excess of precipitation; and though, as we approach the equator on either side from these parallels, the solar ray warms and expands the surface-water of the sea, the winds, by the vapour they carry off, and the salt they leave behind, prevent it from making that water lighter’? (§ 437, eleventh edition). * Philosophers have admired the relations between the size of the earth, the force of gravity, and the strength of fibre in the flower-stalks of plants ; but how much more exquisite is the system of counterpoises and adjustments here presented between the sea and its salts, the winds and the heat of the sun!” ($ 438, eleventh edition). How can this be reconciled with all that precedes regarding 246 Mr. J. Croll on the Physical Cause of Ocean=currents. ocean-currents being the result of difference of specific gravity caused by a difference of temperature and difference of saltness ? Here is a distinct recognition of the fact that difference in salt- ness, instead of producing currents, tends rather to prevent the existence of currents, by counteracting the effects of difference in temperature. And so effectually does it do this, that for 40°, or nearly 3000 miles, on each side of the equator there is abso- lutely no difference in the specific gravity of the ocean, and consequently nothing, either as regards difference of tempera- ture or difference of saltness, that can possibly give rise to a current. But it is evident that, if between the equator and latitude 40° the two effects completely neutralize each other, it is not at all likely that between latitude 40° and the poles they will not to a very large extent do the same thing. And if so, how can ocean-currents be due either to difference in temperature or to difference in saltness, far less to both. If there be any differ- ence of specific gravity of the ocean between latitude 40° and the poles, it must be only to the extent by which the one cause has failed to neutralize the other. If, for example, the waters in latitude 40°, by virtue of higher temperature, are less densé than the waters in the polar regions, they can be so only to the extent that difference in saltness has failed to neutralize the effect of difference in temperature. And if currents result, they can do so only to the extent that difference in saltness has thus fallen short of being able to produce complete compensation. Maury, after stating his views on compensation, seems to become aware of this; but, strangely, he does not appear to perceive, or, at least, he does not make any allusion to the fact, that all this is fatal to the theories he had been advancing about ocean-cur- rents being the combined result of differences of temperature and difference of saltness. For, in opposition to all that he had previously advanced regarding the difficulty of finding a causé sufficiently powerful to account for such currents as the Gulf- stream, and the great importance that difference in saltness had in the production of currents, he now begins to maintain that so great is the influence of difference in temperature in causing currents that difference in saltness, and a number of other compensating causes are actually necessary to prevent the ocean-currents from becoming too powerful. “Tf all the intertropical heat of the sun,” he says, “ were to pass into the seas upon which it falls, simply raising the tem- perature of their waters, it would create a thermo-dynamical force in the ocean capable of transporting water scalding hot from the torrid zone, and spreading it while still in the tepid state around the poles .... Now, suppose there were no ~ Mr, J. Croll on the Physical Cause of Ocean-currents. 247 trade-winds to evaporate and to counteract the dynamical force of the sun, this hot and light water, by becoming hotter and lighter, would flow off in currents with almost mill-tail ve- locity towards the poles, covering the intervening sea with a mantle of warmth as a garment. The cool and heavy water of the polar basin, coming out as undercurrents, would flow equa- torially with equal velocity.” : “Thus two antagonistic forces are unmasked, and, being un- masked, we discover in them a most exquisite adjustment—a com- pensation—by which the dynamical forces that reside in the sun- beam and the trade-wind are made to counterbalance each other, by which the climates of intertropical seas are regulated, and by which the set, force, and volume of oceanic currents are mea- sured” ($$ 437 and 438, eleventh edition). The force resulting from difference of specific gravity not suffi- cient to produce motion.—I shall now consider whether the forces to which Maury appeals have the potency that he attributes to them. Is the force derived from the difference of specific gravity between the waters of the ocean in intertropical and polar regions sufficient to account for the motion of ocean-currents ? The utter inadequacy of this cause has been so clearly shown by Sir John Herschel, that one might expect that little else would be required than simply to quote his words on the sub- ject, which are as follows :— | _ First, then, if there were no atmosphere, there would be no Gulf-stream, or any other considerable ocean-current (as distin- guished from a mere surface-drift) whateyer. By the action of the sun’s rays, the surface of the ocean becomes most heated, and the heated water will, therefore, neither directly tend to ascend (which it could not do without leaving the sea) nor to descend, which it cannot do, being rendered buoyant, nor to move late- Yally, no lateral impulse being given, and which it could only do by reason of a general declivity of surface, the dilated por- tion occupying ‘a higher level. Let us see what this declivity would amount to. The equatorial surface-water has a tempe- rature of 84°. At 7200 feet deep the temperature is 39°, the level of which temperature rises to the surface in latitude 56°, Taking the dilatability of sea-water the same as that of fresh, a uniformly progressive increase of temperature, from 39° to 84° Fahr., would dilate a column of 7200 feet by 10 feet, to which height, therefore, above the spheroid of equilibrium (or above the sea-level in lat. 56°), the equatorial surface is actually raised by dilatation. An arc of 56° on the earth’s surface measures 3360 geographical miles; so that we have a slope of 1-28th of an inch per geographical mile, or 1-32nd of an inch per statute tile for the water so raised to run down. As the accelerating 248 Mr. J. Croll on the Physical Cause of Ocean-currents. force corresponding to such a slope (of 1-10th of a second, 0"-1) is less than one two-millionth part of gravity, we may dismiss this as a cause capable of creating only a very trifling surface-drift, and not worth considering, even were it in the proper direction to form, by concentration, a current from east to west, which it would not be, but the very reverse.”’—Physical Geography, ar- ticle 57.) It is singular how any one, even though he regarded this conclusion as but a rough approximation to the truth, could entertain the idea that ocean-currents can be the result of dif- ference in specific gravity. There are, however, one or two reasons which may be assigned why the above has not been generally received as conclusive. These calculations refer to the difference of gravity resulting from difference of tempera- ture; but this is only one of the causes to which Maury ap- peals, and even not the one to which he most frequently alludes. Maury insists so strongly on the effects of difference of saltness, that many would no doubt suppose that, although Herschel may have shown that difference in specific gravity arising from dif- ference of temperature could not account for the motion of ocean-currents, yet nevertheless this, combined with the effects resulting from difference in saltness, might account for their motion. This, of course, would not be the case with those who perceived the contradictory nature of Maury’s two causes ; but most people probably read the ‘ Physical Geography of the Sea’ without being aware that the one cause is destructive of the other. Another reason is, a few very plausible-looking objections have been strongly urged by Maury and others against the theory that ocean-currents can be caused by the impulses of the trade-winds, which have not been duly con- sidered ; and probably these objections appear to many as for- midable against this theory as Herschel’s arguments appear against Maury’s theories. There is one slight objection to Herschel’s result: he takes 39° as the temperature of maximum density. This, however, as we shall see, does not materially affect his conclusicns. Observations on the temperature of the maximum density of sea-water have been made by Erman, Despretz, Rossetti, Neu- mann, Marcet, Hubbard, Horner, and others. No two of them have arrived at exactly the same conclusion. This probably results from the fact that the temperature of maximum density depends upon the amount of salt held in solution. No two seas, unless they are equal as to saltness, have the same temperature of maximum density. The following Table of Despretz will show how rapidly the temperature of both the freezing-point and of maximum density is lowered by additional amounts of'salt, Mr. J. Croll on the Physical Cause of Ocean-currents. 249 ar Ne toe of Temperature of reezing-point. Maximum density. 9-000123 —T21 ¢. + 1190. 00246 — 2:24 — 1:69 0:0371 —2-77 — 475 0-0741 —5:28 — 16:00 He found the temperature of maximum density of sea-water, whose density at 20°C. was 102738, to be —3°°67 C. (25°4F.), and the temperature of freezing-point — 2°55 (27°°4F.)*. Some- where between 25° and 26° I’. may therefore be regarded as the temperature of maximum density of sea-water of average saltness. We have no reason to believe that the ocean, from the surface to the bottom, even at the poles, is at 27°-4 F., the freezing-point. An error to the extent of a degree or two, however, will not materially affect the conclusion at which we may arrive. Let us therefore assume the temperature of the ocean at the poles to be 32°, and the surface-temperature at the equator to be 80°. Maury states that at the depth of 7200 feet at the equator the temperature is about 36° (§ 440, eleventh edi- tion). Although this agrees pretty nearly with the results arrived at by several observers who have attempted to deter- mine the temperature of the ocean at great depths in equatorial regions, still 36°, the temperature assigned at 7200 feet below the surface, is probably too high; for these observations were made with thermometers unprotected from the pressure of the water on their bulbs, which at so great a depth would equal more than 200 atmospheres; 32°, at a depth of 7200 feet, may probably be nearer the truth than 36°. But we shall assume that we must descend to a depth of, say, 10,000 feet, before the temperature of 32°, that of the poles, is reached. Let us also assume that the temperature decreases at a uniform rate from the surface downwards to that depth. Calculating, then, from Muncke’s Table of the Expansion of Sea-water, we have about 18 feet as the height at which the water at the equator stands above the level of the ocean at the poles. The distance from the equator to the poles is about 6200 miles. The force im- pelling the water down this slope of 18 feet in 6200 miles would therefore be equal to about z3sh555 that of gravity. For ex- ample, the force impelling a cubic foot (64 lbs.) of water at the surface of the ocean would scarcely be equal to the weight of one- fourth of a grain. But in reality it would not nearly equal this; for we have been assuming in our calculations that the temperature of the * Philosophical Magazine, vol. xii. p. 1 (1888), Phil. Mag. 8. 4, Vol. 40, No. 267, Oct. 1870. S 250 Mr. J. Croll on the Physical Cause of Ocean-currents.; ocean at the equator decreases at a uniform rate from the sur- face downwards, which is far from being the case. The rate of decrease is most rapid at the surface, and decreases as we de- scend. The principal part of the decrease of temperature takes place within no very great depth from the surface ; consequently the greater part of the excess of temperature at the equator over that at the poles affects the sea to no great depth. But there is another reason why the expansion of the waters at the equator cannot amount to near 18 feet. It is this: the rate at which water expands as its temperature rises is not uniform, but increases with the temperature. Sea-water, according to Muncke’s Table, in rising for example from 32° to 42° expands (00047, whereas in rising from 70° to 80° it expands no less than ‘00152. But these higher temperatures affect only a small quantity of water near the surface; the great depth of water below is affected by the lower temperatures, which do not pro- duce much expansion. As no reliable observations, so far as I am aware, have been made to ascertain the rate at which the temperature of the waters at the equator decreases from the surface downwards to great depths, it is impossible to determine with any thing like accuracy the height at which the ocean, in virtue of higher temperature, should stand above the level of the ocean at the poles. But one thing we are certain of is that it must be very much under 18 feet, and that the force acting on the waters of the ocean to impel them forward as a current resulting from the difference of specific gravity between the sea in intertropical and polar regions, is very much under one- fourth of a grain per cubic foot. And if the sea in intertropical regions 1s much salter than the sea in polar regions, as Maury strongly insists, then this will make the force still less; for this will go so far to neutralize the effects due to difference of temperature between the waters of equatorial and polar regions. It is perfectly evident that a pressure of one-fourth of a grain on the cubic foot of water, were it even so great as that, would be totally inadequate to overcome the mere molecular resistance of the water to go into motion, far less to produce the great currents of the ocean. It is therefore certain that ocean-cur- rents are in no way whatever due to differences of specific gravity. But it must be observed that this force of one-fourth of a grain per cubic foot would affect only the water at the surface; a very short distance below the surface the force would be abso- lutely insensible. If water were perfectly fluid, and offered no resistance to mo- tion, it would not only flow down an incline, however small it might be, but would flow down with an accelerated motion. Mr, J. Croll on the Physical Cause of Ocean-currents. 251 But water is not a perfect fluid, and its molecules do offer con- siderable resistance to motion. Water flowing down an incline, however steep it may be, soon acquires a uniform motion. There must therefore be a certain’ inclination below which no motion ean take place. Experiments were made by M. Dubuat, with the view of determining this limit*. He found that when the inclination was 1 in 500,000, the motion of the water was barely perceptible; and he came to the conclusion that when the inclination is reduced to 1 in 1,000,000, all motion ceases. But the inclination afforded by the difference of temperature between the sea in equatorial and polar regions does not ex- ceed the half of this, and consequently it can have absolutely no effect whatever in producing currents, no, not even the “trifling surface-drift”? which Sir John Herschel is willing to attribute to it. There is an error into which some writers appear to fall to which I may here refer. Suppose that at the equator we have to descend 10,000 feet before water equal in density to that at the poles is reached. We have in this case a plain with a slope of 10,000 feet in 6200 miles, forming the upper surface of the water of maximum density. Now this slope exercises no influ- ence in the way of producing a current, as some seem to sup- pose; for this is not a case of disturbed equilibrium, but the reverse. This slope is the condition of static equilibrium when there is a difference between the temperature of the water at the equator and the poles. The only slope that has any tendency to produce motion of the water is the slope formed by the surface of the ocean in the equatorial regions being higher than the surface at the poles; but this is a slope of only 18 feet in 6200 miles. Objections to Dr. Carpenter’s theory of a general interchange of equatorial and polar waters. Lieut, Maury’s theory of a general interchange of water between the equator and the poles resulting from a difference of specific gravity, caused by difference of temperature, has lately been advocated by Dr. Carpenter+. He considers that the great masses of warm water found by him and his col- leagues in their late important dredging-expeditions in the depths of the North Atlantic must be referred, not to the Gulf-stream, but to a general movement of water from the equatorial regions. ‘‘ The inference seems inevitable,” he says, * Dubuat’s ‘ Hydraulique,’ tome i. p. 64 (1816), See also British As- sociation Report for 1834, pp. 422, 451. Tt See Proceedings of the Royal Society for Dec. 1868, Nov. 1869, Lecture delivered at the Royal Institution: ‘Nature,’ vol, i. p. 490. 252 Mr. J. Croll on the Physical Cause of Ocean-currents. that the bulk of the water in the warm area must have come thither from the south-west. The influence of the Gulf-stream proper (meaning by this the body of superheated water which issues through the ‘ Narrows’ from the Gulf of Mexico), if it reaches this locality at all (which is very doubtful), could only affect the most superficial stratum ; and the same may be said of the surface-drift caused by the prevalence of south-westerly winds, to which some have attributed the phenomena usually accounted for by the extension of the Gulf-stream to these regions. And the presence of the body of water which lies between 100 and 600 fathoms deep, and the range of whose temperature is from 48° to 42°, can scarcely be accounted for on any other hypothesis than that of a great general movement of equatorial water towards the Polar area, of which movement the Gulf-stream constitutes a peculiar case modified by local condi- tions. In like manner the Arctic stream which underlies the warm superficial stratum in our cold area constitutes a peculiar case, modified by the local conditions to be presently explained, of a great general movement of polar water towards the equatorial area, which depresses the temperature of the deepest parts of the great oceanic basins nearly to the freezing-point.” In support of this theory of a general movement of water between equatorial and polar regions, Dr. Carpenter adduces the authority of Humboldt and of Prof. Buff*. I have been unable to find any thing in the writings of either from which it can be inferred that they have given this matter special con- sideration. Humboldt merely allades to the theory, and that in the most casual manner; and that Prof. Buff has not carefully investigated the subject is apparent from the very illustration quoted by Dr. Carpenter from the ‘ Physics of the Earth.’ “The water of the ocean at great depths,” says Prof. Buff, “ has a temperature, even under the equator, nearly approaching to the freezing-point. This low temperature cannot depend on any influence of the sea-bottom. . ... The fact, however, is explained by a continual current of cold water flowing from the polar regions towards the equator. The following well-known experiment clearly illustrates the manner of this movement. A glass vessel is to be filled with water with which some powder has been mixed, and is then to be heated at bottom. It will soon be seen, from the motion of the particles of powder, that currents are set up in opposite directions through the water. Warm water rises from the bottom up through the middle of the vessel, and spreads over the surface, while the colder and therefore heavier liquid falls down at the sides of the glass.” This illustration is evidently intended to show not merely the * Proceedings of the Royal Society, vol. xvii. p. 187, xviii. p. 463. Mr. J. Croll on the Physical Cause of Ocean-currents. 253 form and direction of the great system of oceanic circulation, but also the way that the circulation is caused by heat. It is no doubt true that if we apply heat (say that of a spirit- lamp) to the bottom of a vessel filled with water, the water at the bottom of the vessel will become heated and rise to the surface; and if the heat be continued an ascending current of warm water will be generated; and this, of course, will give rise to a compensating under current of colder water from all sides. In like manner it is also true that, if heat were applied to the bottom of the ocean in equatorial regions, an ascending current of hot water would be also generated, giving rise to an undercurrent of cold water from the polar regions. But all this is the diametrically opposite of what actually takes place in nature. The heat is not applied to the bottom of the ocean, so as to make the water there lighter than the water at the surface, and thus to generate an ascending current; but the heat is applied to the surface of the ocean, and the effect of this is to prevent an ascending current rather than to produce one, for it tends to keep the water at the surface lighter than the water at the bottom. In order to show how the heat of the sun pro- duces currents in the ocean, Prof. Buff should have applied the heat, not to the bottom of his vessel, but to the upper surface of the water. But this is not all, the form of the vessel has some- thing to do with the matter. The wider we make the vessel in proportion to its depth, the more difficult is it to produce currents by means of heat. But in order to represent what takes place in nature, we ought to have the same proportion between the depth and the superficial area of the water in our vessel as there is between the depth and the superficial area of the sea. The mean depth of the sea, according to Sir John Herschel, may be taken at about four miles*. It may be somewhat more, or it may be somewhat less, than this; but that will not materially affect our result. The distance between pole and pole we shall take in round numbers as 12,000 miles. The sun may therefore be regarded as shining upon a circular sea 12,000 miles in diameter and four miles deep. The depth of the sea to its diameter is therefore as 1 to 3000. Suppose, now, that in our experiment we make the depth of our vessel 1 inch, we shall require to make its diameter 3000 inches, or 250 feet. Let us, then, take a pool of water 250 feet in dia- meter, and 1 inch deep. Suppose the water to be at 32°. Apply heat to the upper surface of the pool, so as to raise the tempe- rature of the surface of the water to 80° at the centre of the pool, the temperature diminishing towards the edge, where it 1s at 32°. It is found that at a depth of two miles the tempera- * Physical Geography, article 17. 254 Mr. J. Croll on the Physical Cause of Ocean-currents. ture of the water at the equator is about as low as that of the poles. We must therefore suppose the water at the centre of our pool to diminish in temperature from the surface down- wards, so that at a depth of half an inch the water is at 32°. We have in this case a thin layer of warm water half an inch thick at the centre, and gradually thinning off to nothing at the edge of the pool. The lightest water, be it observed, is at the surface, so that an ascending or a descending current is impossible. The only way whereby the heat applied can have any tendency to produce motion is this:—The heating of the water expands it, consequently the surface of the pool must stand at a little higher level at its centre than at its edge, where no expansion takes place; and therefore, in order to restore the level of the pool, the water at the centre will tend to flow towards the sides. But what is the amount of this tendency ? Is it sufficient to overcome the molecular resistance of the water to go into motion? The amount of this tendency depends upon the amount of the slope. We have already seen that unless the slope exceeds 1 in 1,000,000, no motion can take place; but the slope in the case under consideration amounts to only 1 in 1,820,000 ; consequently motion is absolutely impossible. That the great masses of warm water found by Dr. Carpenter in the North Atlantic cannot be due to currents produced by difference of temperature, as he supposes, can be proved in an other way. According to his theory there ought to be as much warm water flowing from intertropical regions towards the Antarctic regions as towards the Arctic. We may therefore, in our calcu- lations, consider that the heat which is received in tropical regions to the south of the equator goes to warm the southern hemisphere, and the heat which it receives on the north side of the equator goes to warm the northern hemisphere. The warm currents found in the North Atlantic in temperate regions we may conclude came from the regions lying to the north of the equator—or, in other words, from that part of the Atlantic lying between the equator and the tropic of Cancer. At least, accord- ing to Dr. Carpenter’s theory, we have no reason to believe that the quantity of warm water flowing from the tropical re- gions to the temperate and polar in the Atlantic is greater than the area between the equator and the tropic of Cancer can sup- ply—because he maintains that a very large proportion of the cold water found in the North Atlantic came, not from the Arctic, but from the Antarctic regions. But if the North At- lantic is cooled bya cold stream from the southern hemisphere, the southern hemisphere in turn must be heated by a warm cur- rent from the North Atiantic—unless we assume, which is very Mr. J. Croll on the Physical Cause of Ocean-currents. 255 improbable, that the compensating current flowing from the Atlantic into the southern hemisphere is as cold as the Ant- arctic current. But Dr. Carpenter admits that the quantity of warm water flowing from the Atlantic in equatorial regions to- wards the south is even greater than towards the north. “The unrestricted communication,” he says, “ which exists between the Antarctic area and the great Southern Ocean-basins would involve, if the doctrine of a general oceanic circulation be ad- mitted, a much more considerable interchange of waters between the Antarctic and the Equatorial areas than is possible in the northern hemisphere” *. And as a proof that this is actually the case, he adduces the fact known to navigators that in the Southern Ocean there is a perceptible “ set”’ of warm surface- water towards the Antarctic Pole. We have already seen that, were it not for the great mass of warm water which finds its way to the polar regions, the tem- perature of these regions would be enormously lower than they really are. It was seen also that the comparatively high tempe- rature of North-eastern Europe was due also to the same cause. But if it is doubtful whether the Gulf-stream reaches our shores, and if it is true that, even supposing it did, it “ could only affect the most superficial stratum,” and that the great mass of warm water found by Dr. Carpenter in his dredging-expeditions came di- rectly from the equatorial regions, and not from the Gulf-stream, then the principal part of the heating-effect must be attributed, not to the Gulf-stream, but to the general flow of water from the equatorial regions. It surely would not, then, be too much to assume that the quantity of heat conveyed from equatorial re- gions by this general flow of water into the North Atlantic is at least equal to that conveyed by the Gulf-stream. Let us, then, assume that the total quantity of heat conveyed from equatorial regions into the North Atlantic and Arctic Ocean by all the various processes, the Gulf-stream included, is equal to twice that conveyed by the Gulf-stream. We shall now consider whether the area of the Atlantic to the north of the equator is sufficient to supply the amount of heat demanded by Dr. Carpenter’s theory. | The entire area of the Atlantic, extending from the equator to the tropic of Cancer, including the Caribbean Sea and the Gulf of Mexico, is about 7,700,000 square miles. In a former part of this papery} it was shown that, even assuming the volume of the Gulf-stream to be considerably less than one half what either Sir John Herschel or Lieut. Maury estimates it to be, the quantity of heat conveyed by the stream through the Straits * ‘Nature,’ vol. ip. 541. Proce. Roy, Soe. vol, xviii. p, 473. T Phil, Mag. S, 4. vol, xxxix. p. 89. 256 Mr. J. Croll on the Physical Cause of Ocean-currents. of Florida is equal to all the heat received from the sun by 1,560,935 square miles at theequator. The annual quantity of heat received from the sun by the torrid zone per unit surface, taking the mean of the whole zone, is to that received by the equator as 39 to 40, consequently the quantity of heat conveyed by the Gulf-stream is equal to all the heat received by 1,600,960 square miles of the Atlantic in the torrid zone. Dr. Carpenter is mistaken in supposing that “all the calcu- lations which have been made as to the quantity of water which issues from the Narrows, and the amount of heat which it con- veys, are based upon the assumption that both its temperature and its rate of movement are the same throughout its depths as they are at its surface””*. The surface-temperature of the stream at the Narrows is somewhat about 85°; but I have taken the mean temperature of the water at this place as only 65°. The cold return current, according to Dr. Carpenter, has a temperature as low as 30° or 82°; but, not to overestimate the quantity of heat derived from the Gulf-stream, I have taken the return current at 40°. In this case the quantity of heat conveyed through the Narrows I estimate to be 25 thermal units per pound of water. But had I taken the surface-temperature of the stream and Dr. Carpenter’s estimate as to the temperature of the cold return current, I should have had 538 or 55 thermal units per pound as the amount conveyed. My data were de- rived, not from popular treatises on physical geography, but from a careful analysis of the sections and charts of the United- States Coast Survey ; and any one who will be at the trouble to examine these will easily satisfy himself that I have underesti- mated both the temperature and volume of the stream. But if, according to Dr. Carpenter’s views, the quantity of heat conveyed from the tropical regions is double that conveyed by the Gulf-stream, the amount of heat im this case conveyed into the Atlantic in temperate regions will be equal to all the heat received from the sun by 8,201,920 square miles of the Atlantic between the equator and the tropic of Cancer. This is 32 of all the heat received from the sun by that area. ‘Taking the annual quantity received per unit surface at the equator at 1000, the quantities received by the three zones would be respectively as follows :— iguatdie:: figs we EE TA oe ORR TPoprigZ0ne yy!s9 Te yee) este wth ROS Dewipenate Zone ol) hd es eh a AP ee Hpipiplganety. is sey it ee eee! ae Now, if we remove from the Atlantic in tropical regions 34 * ‘Nature,’ vol, ii, p. 334, | | | | | | | | | } Mr. J. Croll_on the Physical Cause of Ocean-currents. 257 of the heat received from the sun, we remove 405 parts from every 975 received from the sun, and consequently only 570 parts per unit surface remain. It has been already shown that the quantity of heat conveyed by the Gulf-stream from the equatorial regions into the tempe- rate regions is equal to 1°° of all the heat received by the At- lantic in temperate regions*. But according to the theory under consideration the quantity removed is double this, or equal to 100 of all the heat received from the sun. But the quantity received from the sun is equal to 757 parts per unit surface ; add then to this }°° of 757, or 367, and we have 1124 parts of heat per unit surface as the amount possessed by the At- lantic in temperate regions. The Atlantic should in this case be much warmer in temperate regions than in tropical; for in temperate regions it possesses 1124 parts of heat per unit sur- face, whereas in tropical regions it possesses only 570 parts per unit surface. Of course the heat conveyed from tropical regions does not all remain in temperate regions; a very considerable portion of it must pass into the arctic regions. Let us, then, as- sume that one half goes to warm the Arctic Ocean, and the other half remains in the temperate regions. In this case 183°5 parts would remain, and consequently 757+183°5=940°5 parts would be the quantity possessed by the Atlantic in temperate regions, a quantity which still exceeds by no less than 370°5 parts the heat possessed by the Atlantic in tropical regions. As one half of the amount of heat conveyed from the tropical regions is assumed to go into the Arctic Ocean, the quantity passing into that ocean would therefore be equal to what passes through the Straits of Florida, which amount we have already found to be equal to all the heat received from the sun by 6,873,800 square miles of the arctic regionst. But taking the volume of the Gulf-stream, as already stated, at one half our original estimate, the quantity of heat passing into the Arctic Ocean would therefore be equal to all the heat received by 3,436,900 square miles of the Arctic Ocean. The entire area covered by sea beyond the arctic circle is under 5,000,000 square miles; but taking the Arctic Ocean in round numbers at 5,000,000 square miles, the quantity of heat conveyed into it by currents to that received from the sun would therefore be as 3,436,900 to 5,000,000. The amount received on the unit surface of the arctic regions we have seen to be 454: parts. The amount received from the currents would therefore be 312 parts. This gives 766 parts of heat per unit surface as the quantity possessed by the Arctic * Phil. Mag. S. 4,vol, xxxix. p. 90, + Ibid. p. 84. 258 Mr. J. Croll on the Physical Cause of Ocean-currents. Ocean. Then the Arctic Ocean also would possess more heat than the Atlantic in tropical regions ; for the Atlantic in these regions possesses only 570 parts, whereas the Arctic Ocean pos- sesses 766 parts. It is true that more rays are cut off in arctic regions than in tropical; but still, after making due allowance for this, the Arctic Ocean, if Dr. Carpenter’s theory be correct, ought to be as warm as, if not warmer than, the Atlantic in tropi- cal regions. We may therefore conclude that there can be no such large quantity of warm water, in addition to that of the Gulf-stream, as Dr. Carpenter supposes, flowing into the North Atlantic from the equatorial regions ; for there is not heat in those regions suf- ficient to supply such a current. We may also conclude that, at least in respect of the Atlantic, it is not correct that there is more warm water flowing from the equatorial regions into the southern hemisphere than into the northern ; for a very large proportion of the heat conveyed by the Gulf-stream is derived from the southern hemisphere. In fact the great equatorial current, the feeder of the Gulf-stream, comes from the southern hemisphere. The entire area of 7,700,000 square miles of sea in equatorial regions lying to the north of the equator would not be sufficient to supply the current passing through the Narrows of Bahama. Were the heat of the Gulf-stream all derived from the northern hemisphere, the following would then represent the relative quantities of heat per unit surface possessed by the Atlantic in the three zones, assuming that one half of the heat of the Gulf- stream passes into the arctic regions, and the other half remains to warm the temperate regions :— From the Equator to the Tropic of Cancer . . 773 From the Tropic of Cancer to the Arctic Circle 848 From the Arctic Circle to the North Pole . . 610 These figures show that, were it not that a very large propor- tion of the heat possessed by the Gulf-stream is derived from the southern hemisphere, the Atlantic, from the equator to the tropic of Cancer, would be as cold as from the tropic of Cancer to the North Pole. The comparatively high temperature which prevails in the northern parts of the Atlantic and in the Arctic seas is there- fore to a considerable extent due to heat derived from the south- ern hemisphere. And no doubt this transference of heat from the southern hemisphere to the northern by means of ocean- currents, as was mentioned on a former occasion *, is the cause * Phil, Mag. vol. xxxix. p. 103, Dr. E. J. Mills on Chemical Substance and Chemical Functions. 259 why the mean temperature of the southern hemisphere is so mtich lower than that of the northern. We shall now proceed to consider the objections which have been urged against the theory that ocean-currents are due to the impulse of the trade-winds. ! (To be continued. | Erratum. In Part I. of this paper, vol. xxxix. p. 89, 8th line from bottom, for 9°83 read 9-08. XXX. On Statical and Dynamical Ideas in Chemistry.—Part IT. Chemical Substance and Chemical Functions. By Eymunp J. Mitts, D.Sc.* 7 the preceding Part the history of the ideas connected with acid, allcali (base), and salt was concisely stated, and it was shown that while, on the one hand, those ideas are erroneous and self-contradictory when they designate something particular, so, on the other hand, the most consistent and general theory that has been stated with respect to them is that of Avogadro, who is their modern expounder in the sense of chemical polarity. These results were in harmony with the idea of motion, the criterion adopted in these papers. The practical result is that. there is no such thing as an acid, base, or salt, though the use of the adjec- tives and qualitative nouns derived from these terms might pro- bably be successfully defended. If any one deny this conclusion he is bound to give a satisfactory definition of an acid, for ex- ample—a task in which, as history clearly shows, success is un- likely to accrue. Having thus pointed out the value of the idea of motion in the conerete sphere of external chemistry, I may now penetrate, or perhaps ascend, to the remoter regions of Chemical Substance and Chemical Functions, where the service of the same idea will prove available. 1. Chemical Substance. We are accustomed, in the language of everyday chemistry, to say that such and such bodies or substances undergo certain operations ; sulphur, hydric nitrate, aniline, &c. are spoken of as bodies or substances indifferently. In recording the facts of an analysis (even of a mechanical mixture), it is customary to say that so much substance contained or furnished so much of a pro- duct ; and this product may be volatile macter or organic matter, which, in its turn, may become substance for analysis. A che- * Communicated by the Author. For Part I. see Phil. Mag. 1869, vol, xxxvii. p. 461, 260 Dr. E. J. Mills on Chemical Substance mical substance, however, is always understood to mean an object that is chemically homogeneous in its own class. But the name is refused to a mechanical mixture; and I have often heard it stated, in that sense, “this is not a chemical substance,’ or, more curtly, “this is not a substance.” Chemical body and chemical matter are phrases that seldom occur, even in a parti- cular signification. On the whole it appears that ‘‘ substance,” considered as a chemical term, ‘is used in two ways :—(1) asa loose expression*, synonymous with “ body” or “ matter,” them- selves being then loose expressions; but more especially (2) as indicating a specific scientific distinction. This latter employ- ment is worthy of attentive examination. The elder chemistry, possessing few known obiects for expe- riment, had regarded more their fundamental unity than thei! individual diverseness. Then, as at the present day, but few chemists were cultivators of philosophy, so that the general pre- valence of that philosophical regard was rather an accident than amerit. Indeed it can often he traced, almost with certainty, to a belief in the primitive unity of human races, and the tree of life in the midst of the garden, doctrines whose origin is known not to have been philosophical. In modern times more definiteness has permeated the idea of substance. (Qualitative analytical me- thods, gradually increasing in precaution and refinement, were able to demonstrate when a substance was pure; quantitative processes followed with tardy corroboration. From the latter sprang the law of definite proportions discovered by Higgins and Dalton, with its immediate consequence—the theory of che- mical composition. In this manner an @ priort control was ac- quired over quantitative analysist. Constancy in composition was regarded as a proof of purity, and purity was imevitably attended with constancy in composition. Such was the first precise notion of a chemical substance. “ Peculiar earths” might be discovered, and “ peculiar elements” afterwards pre- pared from them; and so long as the latter were accounted as being merely means to an end (composition, namely), the no- tion of constancy could be universally maintained. But what of the means themselves? Were the elements com- pound or absolutely simple? The prevalent tendency has been to affirm the latter alternative. Mercuric sulphide, for example, can be made by the direct addition of mercury to sulphur; but it did not appear that any two substances, on being placed in contact, produce sulphur. The polar theory, it is true, has re- presented sulphur and other elements as intrinsically dual, like * Thus Naquet, Principes de Chimie, first edition, p. 1, says, “Ce qui constitue les corps s’appelle matiére ou substance.” t+ Compare Dalton, ‘ New System,’ p. 213, and Chemical Functions. 261 mercuric sulphide; but inasmuch as it has excluded, by its own fundamental condition, the existence in the free state of what (in sulphur) would correspond to the mercury and sulphur of the experiment, no chemist, probably, has ever considered the ele- ments compound in the same sense as he has entertained that consideration in respect of other bodies. Hence it is that con- stancy of composition has been insensibly supplemented, perhaps supplanted, by another idea of universal applicability, namely that of homogeneousness. The definition that a chemical substance is that which is che- mically homogeneous in its own class may become more intelli- gible on illustration. Each element is, as has been stated, esteemed homogeneous; that is, the whole list of elementic dis- criminants fails to show that it consists of more than one thing, or that it can be made by putting two or more things together. Each amine is homogeneous; because the varied application of aminic discriminants, such as potassic hydrate, hydric chloride, platinic chloride, reveals one thing only. [An elementic discri- minant such as an extremely high temperature, would of course remove any amine from its own class.| The definition is evi- dently in the main analytical. It moreover proves to be not unjust when tested by the idea of motion. For im the idea of homogeneousness there is no limit reserved; while the process and result of classification, depending partly on experiment, partly on convenience, are confessedly destitute of finality and absoluteness—indeed of any statical property. Whatever theory may have been proposed as to the nature of substance in general, there does not appear to be any real ob- stacle in adding thereto the idea of homogeneousness. Spinosa, who defined substance as “ that whose conception needs not the conception of another thing as necessary to its formation,” Hobbes and Berkeley, whose subjective doctrine is well known, and Leibnitz, who stated substance to be “a being capable of action,” have more in common than at first appears. I cannot find on examination any thing in their views or tendency excluding homogeneousness or even inconsistent with it. On the other hand, the idea of homogeneousness is preeminently chemical, no other science offering it so frequently, and none on so especially inductive a basis. When, therefore, to our idea of substance in general we add that of homogeneousness, we know what is che- mical substance ; and no further supplement is necessary. The substantial in chemistry is, consequently, wholly unre- lated to indivisibles; and it cannot be known or determined by theories of constitution or the canons of formule. For many _ years past chemists have been in the habit of using methods of symbolic representation which, while they undoubtedly express 262 Dr. E. J. Mills:on Chemical Substance numerical relations of the highest value and merit, are usually understood to mean much more than any experimenter has yet been able to adduce. Consider, for instance, the formula i Tease I pass over the assertions that H, H, and O stand for atoms fixed in space or elsewhere*, one H being above the other, and the O being outside the two, and so forth. Almost every one takes that formula to mean, among other things, that water contains hy- drogen and oxyg -er—probably because hydrogen and oxygen are obtainable from water. Yet when the hydrogen and oxygen united they underwent loss, and are consequently no more the antecedent hydrogen and oxygen than liquid chlorine is gaseous chlorine. Our symbolic system does not guard against this error, It is an evident and not an uncommon statement that we can only judge of a substance by its reactions—that is, by motion, But if so, the statical argument is abandoned, and we can neither continue to ascribe discrete parts to chemical substance nor im- plicate them in its formule. The result of the preceding investigation may perhaps surprise the reader. It is now evident that, side by side with the great theory of limits, has been running a confluent stream, never mixing therewith and for the most part unnoticed, How long they may continue to flow together is a question of the greatest moment to theoretical chemistr y- When the inconsistency be- tween the atomic and homogeneous theory is more generally realized, fewer minds will be aa to admit them both simul- taneously. 2. Chemical Functions. It has been shown that chemical substance cannot be —* and is not practically regarded, statically. Our contemplation of it is an act, the result of ferent experimental acts ; beyond this we know nothing ; and the precise idea of it, as above arrived at, is therefore commensurate with a mode of motion. When from chemical substance we descend to groups of che- mical substances, modes of motion of subordinate generality require to be contemplated; and these are chemical functions. An inquiry into the nature of these is not without its value, and, as in the previous paper, turns at first upon the use of words. The term alcohol, just like “ acid,” first implied a specific sub- stance ; but its meaning has grown generic with the advance of chemical discovery. The word is now applied to bodies gene- * The atoms being regarded by all atomists as in some way fixed, though not by all as fixed in space, an extraspatial region becomes a necessity, and Chemical Functions. 263 rally which are susceptible of easy oxidation in two or more de- finite stages, with the successive production of derivatives resem- bling acetylic hydride and hydrate; and with these prominent attributes a number of others of minor importance are usually associated. Such are, for instance, the power of yielding pecu- liar classes of oxides (ethers, mixed ethers, compound ethers, &c.). In order to render the name specific, a specific designation, as methylic or amylic, is prefixed to it. But what is the logical result when we examine this operation? The word “alcohol” proves to be not the name of a thing, but the name of what a thing will do—to wit, yield a peculiar kind of derivatives. Hence it is the name of a function. In like manner, aldehyde, ketone, glycol, amine, amide, acid, base, salt, and similar designa- tions may be shown to be pure designations of chemical functions. It must be borne in mind that I am here making an analysis of a practical use of part of chemical nomenclature as actually re- ceived by every one, just as in 1, the current ideas on chemical substances were accepted as a groundwork; and the result is exclusively dynamical in both cases. ‘There are no parts in sub- stance. The material image of an alcohol becomes more than ever an illusion. There is another class of names* whose use is rapidly extend- ing, and whose character is especially dualistic. Such are hydric sulphate, sodic chloride, &c. They fulfil the double duty of giving a specific and generic designation, and of indicating a certain mode of chemical decomposition. Their chemical mean- ing, therefore, is as assuredly dynamical as that of the names whose signification has been above investigated. [Although not writing on the subject of nomenclature, I wish to express my decided opinion in favour of the Berzelian method. In the first place, it follows the immemorial usage of the Greek, Latin, and English languages to make it a rule to qualify by means of an adjective ; secondly, it proceeds upon the plan universally adopted in botany ; thirdly, it is available throughout descriptive chemistry, and is sufficiently supple for any legitimate inflexion. These are great advantages. Onthe other hand, such names as “notassium nitrate,” ‘ disodium tartrate,” ‘hydrogen and so- dium tartrate” (a rather ambiguous expression), &c. offend against systematic grammatical usage, have no counterpart in any other science, are excessively awkward to compound, and often are very inharmonious. Chemistry might profitably lose many of her oldest acquirements, but she ought not to give up her adjectives without a struggle. | * Berzelius, Journ. de Phys, vol. lxxiii. p. 263, [ 264 ] XXXI. On the Magnetism of Electrodynamic Spirals. By GeorcE Gore, F.R.S.* } HAVE made some experiments on the influence of high temperatures upon the magnetic condition of electrody- namic spirals formed of iron, copper, and platinum, the heat being obtained by means of a voltaic battery. Experiment 1.—Two horizontal spirals of wire, A and B, fig. 1, Fig. 1. were employed. A was composed of a platinum wire 34°% cen- tims. long and 1°42 millim. thick, and B of a copper wire 34°9 centims. long and 2°59 millims. thick—each being coiled into a cylindrical helix about 3°8 centims. long and 1°6 centim. in dia- meter, with exactly the same number of turns in each; they were united by means of binding-screws, C. A magnetized steel needle, D, about 8 centims. long, was suspended in the di- rection of north and south (by means of a fibre about 35 or 40 centims. long), with its south pole between and equidistant from the ends of the two coils, which were about 3 centims. asunder; the needle was weighted at its centre by a little piece of lead. One of the wires was coiled in the direction of a right-handed, and the other of a left-handed screw, so that on passing the cur- rent through them the magnetism excited in their ends nearest to the needle was of the same kind; and the direction of the current was such that the poles of the wires were of the same kind as that of the nearest end of the needle. With ten Grove’s cells as one series, the platinum plates of which were 16°5 cen- tims. long and 7°7 centims. wide, the platinum wire became very hot, but not red-hot, whilst the copper wire remained cold; the needle remained equidistant between the two wire poles, being equally repelled by the hot platinum and cold copper. * Communicated by the Author. Mr. G. Gore on the Magnetism of Electrodynamic Spirals. 265 Experiment 2.—In this experiment the spirals were 1:5 cen- tim. in diameter and 2°9 centims. long, Fig. 2. and were placed parallel to each other, as in fig. 2, and were formed of platinum wire °82 millim. thick, and copper wire 2°05 millims. thick; but in other re- spects the arrangements were similar to those of No. 1 experiment. With the ten Grove’s cells as one series the pla- tinum wire was quite red-hot through- out, and the copper wire cold, and the pole of the needle remained equally re- pelled by each spiral as before; and with the cells as a double series of five, the platinum wire was bright red-hot, and the needle remained in the centre the same as if no current was passing. A bright red heat, therefore, did not sensibly increase or decrease the mag- netizing influence of the platinum spiral; and the magnetism of that spiral was independent of change of temperature, and of the molecular state produced by change of temperature. Experiment 3.—The arrangements were the same as in the last experiment, except that an iron wire was substituted for the platinum one, and ten large Smee’s cells, 12 inches x 8 inches, substituted for the Grove’s battery. With an iron wire 1:42 millim. thick the iron wire became heated to about 200° C., and repelled the needle much more powerfully than did the cold copper spiral. With an iron wire ‘95 millim. thick the iron spiral, though much hotter, still repelled the needle more strongly than the copper one; and also repelled it strongly after the cur- rent was stopped and both the wires were quite cold, evidently because it retained much of its induced magnetism. With a “No. 23” iron wire, *68 millim. thick, the iron spiral became red-hot, and repelled the pole of the needle with but little greater force than that of the copper spiral ; on shifting the copper spiral to a distant part of the circuit and renewing the current, the iron spiral repelled the needle strongly. This experiment shows :— first, that an electric current of a given strength passing simulta- neously through two similar spirals of wire, one of iron and one of copper, produces at moderate temperatures a greater degree of magnetism in the former than in the latter; secondly, that when the iron wire attains a red heat its total magnetic power is not much greater than that of the copper; thirdly, that the iron Phil. Mag. 8.4. Vol. 40. No. 267. Oct. 1870. fi N 266 Mr. G. Gore on the Magnetism of Electrodyname Spirals. at moderate temperatures possessed both the magnetism due to the current itself and that zmduced by the current upon the mole- cules of the iron, whilst the copper possessed only that which belonged to the current itself; and, fourthly, that by a rise of the temperature of the iron to redness the induced portion of the magnetism in it decreased, whilst the magnetism due to the cur- rent alone remained equal to that in the copper. Experiment 4.—I now tried flat spirals of wire facing each other abont 4 centims. apart, with their axes in one horizontal line (see fig. 3); the spirals were about 2:5 centims. in diameter, and each contained four turns of wire. With 20 centims. length of iron wire ‘95 millim. in diameter, and 20 centims. of copper wire 2°07 millims. in diameter, and the ten large Smee’s elements, the iron spiral became nearly red-hot; at the first in- stant of passage of the current the iron repelled the similar pole of the needle somewhat more strongly than the cold copper; but as it became hot its excess of repulsion became less. I now sub- stituted twelve Grove’s cells (of the size already mentioned) as a double series of five for the Smee’s battery: the iron wire be- came red-hot, whilst the copper one remained cold, and the needle remained about equidistant between the two helixes. With a flat helix of thin platinum wire substituted for the one of iron the platinum one became nearly white-hot, and appeared to repel the needle a little more than the copper ; it is difficult, however, to make the spirals perfectly uniform, and to exactly determine the middle point between them. Experiment 5.—In this experiment no needle was employed. Two flat spirals (A and B, fig. 4), about 1:8 centim. in diameter, | ' 15 centims. long, and each of Mr. G. Gore on the Magnetism of Electrodynamic Spirals, 267 composed of thin iron wire Fig. 4. thesamethickness,were taken, and one of them freely sus- pended (by means of the two fibres C, C) vertically and facing the other at a distance of about 2 or 3 millims. apart. The lower ends of the spirals dipped into two small cups of mercury to enable the con- nexions to be made with free- dom of motion to the sus- pended one; and the similar poles of the spirals faced each other. Thecurrent from the twelve Grove’s cells in single series was passed through them; they immediately re- pelled each other and then melted. The same current was now passed through two similar ones 1:6 centim. in diameter, com- posed of thicker iron wires, each 12 centims. long and ‘95 mil- lim. thick; they repelled each other most distinctly and strongly whilst warm, and also whilst quite red-hot, and the moveable one instantly fell back on disconnecting the battery. As general results of these experiments on electro-spirals, it is shown, first, that a red heat diminishes only the induced magne- tism in an electro-spiral of iron, and does not increase or decrease that due to the current alone; secondly, that a red-hot electro- spiral of iron is capable of inducing magnetism, but not of having magnetism induced in it; thirdly, that the production of heat by electricity in a wire of great resistance, whether of iron, cop- per, or platinum, is not attended by a diminished production of the magnetism due to the current in the heated part of that wire. These results also support the view that the magnetism of an electro-spiral of copper or other non-magnetic or slightly mag- netic metal is not due to a particular position or mode of motion of the particles of the metal, but is a direct result of, and inse- parable from, the electric current itself; whilst that of a similar spiral of iron is partly due to the same cause, and is partly de- pendent upon a molecular condition which is destroyed by a high temperature. The induced magnetism of iron is a much more complex phe- nomenon than the magnetism of an electric current, because it depends both upon temperature and upon the molecular struc- ture of the iron; whereas the magnetism of an electric current T2 268 M. Achille Cazin on Internal Work in Gases. is entirely independent of temperature, and of molecular struc- ture, and cohesive strength, except so far as they affect the quantity of the current, as is also shown by the magnetic cha- racter of an electric current circulating through an electrolyte, and also of the electric discharge in rarefied gases. XXXII. Memoir on Internal Work in Gases. By M. Acuitie Cazin. [Concluded from p. 210.] Part IJ.—AprricaTion oF THE THERMODYNAMICAL FoRMULA TO THE INVESTIGATION OF THE INTERNAL WoRK IN GASES. § I. On the internal work performed in a gaseous mass when the reservoir which contains it 1s connected with a second, empty reservoir. bs pias the problems which can be treated by means of the thermodynamical formule, and which relate to the ex- periments described in the first part, the following is the most simple :— Problem 1.—In a reservoir whose sides are impermeable to heat, there is 1 kilogramme of gas of which the volume and tem- perature are v,, ¢, respectively ; this reservoir is connected with a second, empty reservoir, with sides impermeable to heat, of v, capacity: to calculate the temperature ?' and the pressure p! which are established when the exchanges of heat and motion have en- tirely ceased, and the internal work effected. Whilst the efflux is going on, heat disappears in the first reservoir, with production of mechanical work; in the second reservoir vires vive are created which are equivalent to this work, and which are finally transformed into heat. No external work is either produced or spent; no amount of heat is either taken from or given to external bodies. If there were no attraction between the molecules of the gas, no internal work would be put in operation; the heat created would be equal to the heat which had disappeared, and finally the temperature would again become ¢,. But if there is molecular attraction, it has at length been overcome, and the quantity of heat which disappeared ex- ceeds that which has been created; the difference is equivalent to the internal work produced, and the state of the gas is SE A Oe eT The thermodynamical formulz enable us to calculate this final state. M. Achiile Cazin on Iniernul Work in Gases. 269 I shall denote by dQ the heat supplied to the body when it undergoes an elementary modification ; KdT the increase of its sensible heat, K being its true spe- cific heat, and T=273+7° its absolute temperature (¢ in Centigrade degrees) ; A the calorific equivalent of the unit of work ; dl1 the elementary internal work produced ; dK the elementary external work produced. The general relation is AQ= Kad + Adi + Adu. 50:16 05s 1 (L) The sum KdT + Ad] is the differential of a function U which has been called total internal heat by M. Zeuner, virtual energy by M. Hirn. It is remarkable in this one thing, that its varia- tions only depend on the initial condition and final condition of the body, and not at all on the manner in which the change of condition is effected. Its mechanical equivalent is still called internal energy. For each body, there exists a certain relation, Oper ee hs a ee he) in which it is sufficient to have two of the three quantities p, v, T in order that the condition of the body may be determined. It is this relation which is expressed approximately, for the gases called permanent, by the laws of Mariotte and Gay-Lussac, pv gre te pissed: let a IB) M being a constant which depends on the units adopted and on the nature of the gas. Thus the quantity dU will be a function of two of the three variables p, v, T (of v, T for example, considered as indepen- dents) ; and when the body undergoes any final change we shall have U-U,>= b(v,, T)) —(%, To), whatever may be the law of the change between the initial con- dition vp, To, and the final condition v,, T,. It follows from this that the variation of virtual energy U— Uy remains the same between the same limits, whether the mode of change be reversible or non-reversible. Consequently from the two fundamental theorems of thermo- dynamics, and from the experimental fact that for air a condition exists in which relation (8) is verified, the following relation, ap- 270 M. Achille Cazin on Internal Work in Gases. plicable to changes of every kind, can be demonstrated*, au=Kat+aa((7%, —p)d, 2. . where oi is the partial derivative of p with respect to T, as de- duced from equation (2). In the present problem, dQ=0 and dE=0. Hence dU=0; and the integration between the conditions v,, T,; »!, T’ gives K(T,—T’) = af ae. —p)o. (a) gee Rem Such is the formula from which T’ may be known when the relation (2) is known. Hach member of that equation expresses in calories the internal work effected in the operation. It may be easily seen that, if formula (3) be taken for that relation, we shall find T,—T'=0, which is not justified by experiment. I am going to apply for- mula (5) to carbonic acid, for which formula (2) may be cal- culated empirically within certain limits by means of the expe- rimental data of M. Regnault. Mr. Rankine has calculated, following M. Regnault’s experi- ments on the heating of carbonic acid under a constant volume, an empirical formula which is very convenient for the calculation, and of which Messrs. Joule and Thomson have made use in their researches on the efflux of gases through narrow orifices t. This is the formula :— _ Pool _ apr . Jo Den ae Po Y» To are relative to one kilogramme of gas at the tempera- ture of melting ice and under the pressure of one atmosphere. From this formula may be derived dp _ 2apor . at ae * P. de Saint-Robert, Principes de Thermodynamique, p. 82 (1865). + Philosophical Transactions of the Royal Society of Loudon! vol. exliv. part 2, p. 337 (1854). M. Achille Cazin on Internal Work in Gases. QF 1 ‘and by introducing this value in equation (5), we obtain T,-T= eco pe oh at ey whence T 2 > po Ns / (h-N) +N’, Aapyv? N= 2 af ya ve KT, | (7) Nie PAAP ro Ko! J The calculation is, as may be seen, very easy. Before applying formula (7) numerically, it is important to see how formula (6) satisfies the various experiments of M. Reg- nault on the compressibility and dilatation of carbonic acid. Mr. Rankine took a=1°9; but I found, when all the experi- mental data of M. Regnault were taken into consideration, that the value a=1-'6 was more suitable. The reader will be able to decide the question from the following reasoning. In his memoir on the density of gases*, M. Regnault says that a glass globe of 9°881086 litres at zero contained 19°539 grms. (mean of five experiments) of carbonic acid gas at zero and under the pressure of one atmosphere; from this may be deduced the volume of one kilogramme of gas under normal circum- stances, Vy =0°50571 cub. m. By means of the Table on page 236 of vol. xxvi. of the Mé- motres de I’ Académie des Sciences de Paris, we obtain v =0°38307 cub. m. at zero, under the pressure of 1000 millims. of mercury. The specific volume at zero and under various pressures may after- wards be calculated by means of the formula on page 426, vol. xxl. of the same Mémoires, which gives the results of experi- ments made on carbonic acid at about 8°; at zero the same for- mula is admitted. Finally, in the memoir on the dilatation of gas}, we find (p. 112) that, under the pressure of 3589 millims. of mercury, the binomial of dilatation at constant volume from 0° to 100° is 1+100 «=1°'38598, * Mem. de l Acad. des Sciences de Paris, vol. xxi. pp. 147 & 155. + Mém. de Acad. des Sciences de Paris, vol. xxi. 272 M. Achille Cazin on Internal Work in Gases. and (p. 117) that the binomial of dilatation at constant pressure 1s __ §£1:37099 under the pressure of 760 millims. 1: 1002 Nites Vere oe ae By means of these data I calculated the following Table, in which column p (1) gives the observed pressures, column p (2) gives the pressures calculated from formula (6), taking a=1°6; column p (8) gives the pressures calculated according to the same formula, taking a=1:9. It may be seen that the numbers of column p(8) all diverge in the same direction from the numbers of column p (1), whilst those of column p(2) diverge at first in one direction, then in the opposite; which justifies the use of a= 1:6 :-— v T. | pl). | p(@). |p)—p(2).) » (3). |p(1)—p@). cub. met. & millims. | millims. | millims. | millims.| millims. 0°69333 | 373 760 756 ame! 755 + 5 0-38307 | 273 1000 996 + 4 0:20779| 373 2520 2508 + 12 2504 + 16 0:15008| 273 2520 2510 + 10 0:10437| 273 3589 3578 + 1] 0°10437} 373 4974 4955 + 19 4950 + 24 0:03831} 273 9226 9257 — 3l 0°01915| 273 16705 | 16961 — 256 16380 +325 Between zero and 100°, one atmosphere and twelve atmospheres, the values of p (2) are sufficiently near ; but at twenty-two atmo- spheres the difference p (1)—p (2) is large enough to make the formula of Mr. Rankine not very exact; but I thought it neces- sary to use it provisionally, with the modification relative to a which I have indicated. In order to establish a more satisfac- tory empirical formula, some data relative to high temperatures would be necessary, which are totally wanting. Numerical application of formula (7) :— v, =0°10871 cub. m., vl =0'52056__,, The ratio of these two numbers is that of the reservoirs of my ultimate apparatus. I consider one kilogramme of carbonic acid at 10°, passing from volume v, to volume v’, in the conditions of the problem already enunciated :— ] A= 795? a =1'6, Po = 1038384, M. Achille Cazin on Internal Work in Gases. 273 V =0°50571 cub. m., T= 278°, T, = 283°, K=0°17. This value of K is the specific heat at a constant volume and a high temperature. According to M. Regnault, the specific heat at constant pressure is 0°2396 towards 200°. If the ratio of the two specific heats were 1:29, as it seems to be at the ordi- nary temperature *, K would be equal to 0°18. But it is not proved that this ratio does not increase with the temperature. M. Hirn took 0164 for the value of K. By taking 0:17 I do not think a very large error is made. With these various data the formula (7) leads to T’= 280°, whence T,-—T’'=3°. Having T’ and v’, the pressure p’ in millimetres of mercury can be calculated by means of the formula (6), in which py>=760 millims. It is found that p'=753°'15 millims. In the same manner, by introducing into this formula the values of T,, v, we shall have, for the initial pressure, p,= 8572 millims. (4°7 atmospheres). Suppose that after the expansion the heat of the sides reesta- blishes the temperature T, in the gaseous mass. Then the pres- sure, which was p’, will become p; and this value may be cal- culated by introducing T,, v’ into formula (6) ; we obtain p=761°30 millims. Thus one kilogramme of carbonic acid at 10° and under a pressure of 4°7 atmospheres expanding, without external work and without transmission of heat, to the pressure of about one atmosphere (753°15 millims.), undergoes a spontancous fall of temperature of 3°. When it afterwards resumes its primitive temperature by the action of the sides, its pressure rises p—p'=815 millims. The example just given furnishes some numbers quite compa- rable with those given by my experiments. _* A. Cazin, “ Essai sur la détente et la compression des gaz sans varia- tion de chaleur,” Annales de Chimie et de Physique, S. 3. vol. Ixvi. p. 206 (1862). 274 M. Achille Cazin on Internal Work in Gases. It may be observed that py, =388'31, pl vo! =3892-06, p v' =396:30. Now the first and last of these products refer to the same temperature T,; and we have ! Pp? =1-0206, PY; a number which accords very well with the experiments of M. Regnault on the compressibility of carbonic acid. By comparing the initial condition and the final condition before the calorific action of the sides, we get I,,! pv > Pr); § IL. On the internal work which is accomplished in a gaseous mass when it flows into the atmosphere under a constant pressure. Problem I1.—A gas maintained under the constant pressure p,, and at the constant temperature T,, flows into a space the sides of which are impermeable to heat, where it is maintained at the constant pressure p’: to calculate the final temperature T’ which establishes itself beyond the orifice when the gaseous molecules have lost their velocities in producing heat. This simple case refers to the experiments of Messrs. Joule and Thomson and to those of M. Hirn. Conceive the gas to be contained in an indefinite cylinder (fig. 9) divided into two parts by the partition HE in which is the orifice. In the permanent efflux there is on each side of the par- tition a certain space in which the molecules of the gas acquire velocity,and afterwards lose it in again forming heat. Let CandD be the two planes which bound this space, and yw the gaseous mass contained in it. Suppose the cylinders to have a section equal to the unit of surface, and consider one kilogramme of gas under the pressure p, and at the temperature T, ; 1t will occupy a cer- tain volume v,=AC. During the efflux the mass of gas 1+y passes from the condition AD to the condition CB, and the part BD=v' contains one kilogramme of gas at the temperature T’ and under the pressure p'. As in the two positions of the mass 1+ the part contained in the space CD remains in the same’ condition, we may say that one kilogramme of gas has passed from the volume AC to the volume CB, and apply to this change the fundamental formula of thermodynamics (1). We suppose that the sides of the cylinder are impermeable to heat; then dQ=0; consequently if external work has been M. Achille Cazin on Internal Work in Gases. 275 effected, there must have been a variation of the virtual ener sy equivalent to this work and of contrary sign. Let us examine whether there is external work. The motion of the plane A to the position C represents a work p,v,; that of ite plane D passing in the same time to B represents a work p'v', taken with the opposite sign to that of the preceding. The work Py, 1s expended ; the work pv! is, on the contrary, produced ; finally our gas has flowed out, produ- cing the work p'v'—p,v,, if the value of this expression is posi- tive; if it is negative, the gas has, on the contrary, expended this quantity of work. Without foreseeing the sign of this quantity, we shall only say that v'p! i} dE= p'v! —pyvy. 171 As to the variation of the virtual energy, we shall have the same expression as in the preceding section, so that the equation of the problem is Kt — T)+a(" ae —p)do+A( pie! —p,r,)=0, (8) v1Ty from which we can deduce T’ when we have the function (2). The second term of equation (8) represents internal work esti- mated in calories. Iam now going to apply this equation to carbonic acid. By combining equations (8) and (6) we obtain T’—T, K (T’/—T,)+ Aporo| T. Ay Bare a5 — i aa) |= =i, whence may be deduced T, —N+ Ace ia dAapvylo i, 20 2, (KT) +Apo%) N= SAapvely vo (KT 5+ Apovo) J formulz analogous to formule (7). When T’ is calculated, its value and that of vo! may be intro- duced into formula (6) and thus p’ may be deduced ; we shall then obtain the quantity p'o'—p,v,. _ Numerical application.—By employing the same data as in 276 . M. Achille Cazin on Internal Work in Gases. the preceding section, it is found that T! =279°44, T,—T'=3°'56, p'=751°63 millims., pl =391°27. We have already had py, = 88831. Hence p'v!=p,v, is positive, and there is a production of ex- ternal work during the efflux. This work has been produced at the expense of the virtual energy of the gas ; and by that may be explained why the fall of temperature T,—T! is greater than in the first problem. Discussion of the eaperiments of Messrs. Joule and Thomson and of M. Harn. Messrs. Joule and Thomson have made their experiments under conditions in which the gas on leaving the orifice resumed the initial temperature T,. From that moment the sides fur- nished to each unit of weight of the gas the heat C,(T,—T"), Cp being the specific heat at constant pressure. We shall easily pass from the preceding case to this latter. The gas was in the condition p', v’, T’; it passes to the tem- perature T, and to the volume v' under the constant pressure p’ ; hence it expands in producing external work p'(v!'—v') ; its vir- tual energy experiences an increase v'T Key ok { 1: ae pe. v'T! al The fundamental equation (1) gives therefore v!Ty C,(T,—T) =K(T,—T) + { (7 dp p)do-+ Ap!(o!—0/), v'T! av This equation may give v’. But by adding equations (10) and (8) together we get C I Ny Ep III o(1,—-T)=A : (Tip —P dot A( pe —py,). - (11) vj+1 This formula reveals the final condition of the gas passing from the condition p, v, T, to the condition p! vo” T,, with transmission of the external heat C,(T,—T'). Moreover it is immediately obtained by means of the fundamental equation (1). In calculating it as I have done, there is the advantage of fol- lowing gradually the operation under its two phases. In order to apply these formule to carbonic acid, it is only M. Achille Cazin on Internal Work in Gases. 277 necessary to combine equation (11) with formula (6), and the following simple formula is obtained :— BAapyvz/1 1 C,(T,—T) = re e ie i 2 4 CE) from which we can deduce v". I shall use equation (12) in order to verify the calculation made of T’ by means of equations (9). To this end I introduce in formula (6) the values T,=283° and p'=751°63 millims., and from it deduce v!'=0°527296 cub. m., p'v =396'33. Having vw’, we introduce its value into equation (12); and putting C,=0°216, I find T,—T'=38°56, which is just the value deduced from formule (9). The identity of the numbers evidently depends on the value of C,; but the value which I have chosen is rather too great, so that it leads us to take 3°56 as aminimum. ‘The smallest value of C, observed by M. Regnault is 0°187; this number leads to T,—T'=4°11, and we must regard this value as a maximum. Messrs. Joule and Thomson have made use of the formula (12) by expressing vy, and v" as functions of p, and p! by means of the law of Ma- riotte. In fact putting v P= TAT v pil =Tyy we have 3Aav,T T,-T= 9 -9(n, —p'), . «4 « (18) 1 C,T (pi p’) In this formula the pressures are expressed in units of weight on the unit of surface; if we wish to express them in atmo- spheres, we shall take SAavgT, . 10334: pay o+o 'Gpheie fel Such is the formula employed by the English physicists, p- 337 of their memoir*, Let us examine if it agrees with (n,—n') atmosphere. (14) * Philosophical Transactions of the Royal Society of London, vol. exliv. part 2. There is a mistake in the printing of the last formula of page 337; the P, a P, . P factor is omitted. 0 278 M. Achille Cazin on Internal Work in Gases. formula (12). Making, in this latter as in the preceding cal- culation, n;=4°7 atmospheres and x! =0-989, we find © T,—T'=3"-46, which number is a little less than that deduced from formula (12); but the difference is so trifling that the approximation of formula (14) is justified. All the preceding formule follow the course of the phenomena; but they can never give very exact numbers, on account of the uncertainty which prevails as to the value of some of the con- stants, such as a, A, K, and C,. ‘Thus Messrs. Joule and Thomson have taken, from Mr. Rankine, 3AAav, . 1038384 Cp instead of 2°4365685 and 278, which I have adopted. Consequently formula (14) gives with these numbers T,—T'=4°:09. On page 336 of the memoir just quoted may be read that the cooling observed with a difference of pressure of 60-601 pounds on a square inch was 5°:049 at the temperature of 12°844. This excess of pressure is equivalent to n,—n'=4°216 atmo- spheres, if we assume for one atmosphere a pressure of 14°373 pounds per square inch. Formula (14) gives the preceding number with the constants of Mr. Rankine véry well; but with those which have been used in the preceding calculations we obtain under the same circum- stances 4°°65, a smaller number. It is possible that in the experiments of Messrs. Joule and Thomson the thermometer may have been placed at too small a distance from the orifice for the vis viva of the jet to be com- pletely converted into heat. Let us see what in fact was the mode of operating. In the large apparatus described in volumes exlin. and exliy. of the Transactions of the Royal Society, the gas contained in a gasometer 1s withdrawn by a pump and forced into a long ser- pentine tube surrounded by water. At the end of this serpen- tine tube is a wooden cylinder into which cotton is pressed, 2°72 inches in length and 1°5 inch in diameter; and beyond, a tube is adjusted which reconducts the gas to the gasometer. The pump maintains the regular circulation, and keeps the pressures p,and p! constant on each side of the porous partition. The able physicists took the most minute precautions in order to obtain regular effects. A thermometer placed very near the partition received the gas after its expansion in the form of a multitude log =2°5111438 and T,=274, : | | | | { M. Achille Cazin on Internal Work in Gases. 279 of small jets, having certainly very little ws viva; and when the pressures were perfectly constant, this thermometer indicated a constant temperature considerably less than the external tem- perature. The general effects correspond to the theory; but I do not think that the method is susceptible of very great accuracy. The influence of the sides and the porous partition on the thermometer was very great (as the experimenters observed) when there were variations of the pressure p,. Besides, the gas was not com- pletely dry, and the correction of the effect due to moisture not very accurate. Finally the position of the thermometer must have had an enormous influence. Very close to the partition the jets were still animated by a certain velocity, and the temperature must have increased very rapidly from the partition to a certain distance, from which it again became equal to the external tem- perature. It appears evident to me that the effect observed on the thermometer does not indicate the temperature which the gas would have if it returned to rest after the expansion without external calorific action. I think that the thermometer indicated too low a temperature, and that hydrogen would have been able to produce analogous effects to those of air under the same cir- cumstances, as occurred in my own experiments. Unfortunately, particulars of the observations made on this gas are not given. Neither is the method employed by M. Hirn* free from all objection. Aqueous vapour on leaving the boiler passes through a tube of 5 centims. diameter, where it is superheated; it passes through an orifice of 4 millims. into a cubical wooden box, which is enveloped by two other boxes. Thus the expanded vapour circulates in the spaces between the boxes before issu- ing into the atmosphere; and consequently the central cavity is conveniently sheltered from the cooling action of external bodies. In this cavity the thermometer is placed ; it is perfectly sheltered by a partition against the direct shock of the jet of vapour, so that the molecules of vapour only impinge upon it after they have lost their velocities. But, on account of the mag- nitude of the orifice, the molecules of vapour have a great velocity on each side of the orifice, and there is a great fall in the tem- perature, due to the velocity, between the orifice and the parti- tion. Hence the radiation of the sides is considerable, and the jet only returns to rest after having received heat from without ; and therefore the final temperature observed on the thermometer is too high. This objection was made by M. Combest. * Exposition analytique et expérimentale de la Théorie mécanique de la chaleur, second edition, p. 177 (1865). | Exposé des principes de la Théorie mécanique de la chaleur, par M. Combs, p. 238 (1867). 280 M. Achille Cazin on Internal Work in Gases. I do not think that the thermal effects at present in question can be studied very exactly by means of the thermometer. The inevitable action of the sides, alone, prevents entire exactness. M. Hirn has given in one of his last memoirs some very simple formulz, by means of which we can solve the problems before us*. I tried to apply them; but the results to which they lead differ from those which I have given. Following the method invented by M. Hirn, and which is applied in the memoir quoted to the vapours of water, of bichlo- ride of carbon, of sulphide of carbon, of alcohol, and of ether, I calculated a formula for carbonic acid, pa (2), / apeaghidg SoReal But I have not found for the constants a, 6, 8 values which made the formula agree sufficiently with the Table on page 272. If an agreement between them were established, that formula would take the place of the formula of Mr. Rankine, and, intro- duced into the preceding equations, would solve our problems. For example, in the problem of § I., formula (5) would give Abv® 1 1 — _— 0 —= ———— }, aha sees y=) The calculations which I have made in the second problem indicate that it is very distinct from the first. In order that the mechanical and thermal effects might be the same in these two problems, it would be necessary that pv=pyr; and this equality seems to me impossible. The contradiction may very likely be only apparent between the results at which I have arrived and those of M. Hirn. It is not in the spirit of criticism that I refer to it here. Seeking to resolve those ques- tions which have been already treated by my excellent friend, by means of a method differing from his, I meet with differences which may be explained by the inexactness of the numerical data. The importance of formula (15), which M. Hirn has used with advantage in the study of vapours, imposed on me the comparison of the two methods; and I have made it in the hope that it may contribute to the elucidation of a delicate ques- tion of thermodynamics. * G. A. Hirn, “ Mémoire sur la Thermodynamique,” Ann. de Chim. et de Phys. May 1867, p. 91. _M. Achille Cazin on Internal Work in Gases. 281 “§ UL. On the internal work in a gas which undergoes expansion or compression without external calorific action, and of which the elastic force at each moment balances the pressure exerted on ats surface. Problem U1I.—A kilogramme of gas at temperature T, passes from volume v, to volume V2 while overcoming external pressure equal at each moment to its elastic force, without there being either addition or loss of external heat: knowing v,, T,, and v,, to calculate the final temperature T, and the internal work effected. This operation belongs to the kind which are termed rever- sibles. It cannot be realized in practice; but a gaseous mass which pushes a piston in a cylinder, or which is compressed by the piston so quickly that the external heat may be neglected, comports itself very nearly as in the problem enunciated. The quantity of external heat which the gas takes in changing its condition may be represented by Q= | Tig, @ being a function (of two of the variables p,v, T) which Mr. Rankine has called the thermodynamic function. If v and T be taken as the variables, we have* ‘b=KLT+A Dae, a being the partial derivative of p deduced from relation (2). In the present problem Q=0; hence ¢= constant, and con- sequently VT 9 Keg taf Cae A ane lg) 1 v This equation being combined with relation (2), T, may be calculated when T,, v,, vo are known. The initial and final pres- sures Pj, P. may be calculated by means of relation (2). A relation between p and v may afterwards be established, which will serve to calculate the external work v2 { pdv. V1 Finally, the internal will i v To d) 7 —p)do. foes aT Hence the problem is solved. * P. de Saint-Robert, Principes de Thermodynamique, p. 69 (1865). Phil. Mag. 8.4. Vol. 40. No. 267, Oct. 1870. 282 M. Achille Cazin on Internal Work in Gases. For carbonic acid in particular, formula (6) must be used, and equation (16) will become i Aapor eae Apo V2 Aapyry. ‘0 eI T, | Kot? KY, “2, * Ry Whence T, may be deduced by tentative methods. The internal work effected will be 1 1 2 ea ae ot a e 2apors a Tv, If there were no external work (as in $1.) between the same volumes, initial and final, we should evidently have a final tem- perature T’> T,; and we have seen in this section that the in- ternal work was 1 1 2 oe Se eee e april; Tv, Hence it would be greater than the preceding. According to this, the internal work would not be a function of the volume alone, and there would be internal work expended during the cooling at constant volume, which ought to reduce the gas from the condition v,I’ to v,T,. In other terms, the mo- lecular forces ought to create heat during the cooling. Conversely, during the heating at constant volume there would be internal work produced. It is probable that the apparent specific heat at constant vo- lume decreases when the temperature rises. Let C, be that spe- cific heat; C, the specific heat at constant pressure (determined. by M. Regnault), then v2 =o The quantity C, increases considerably with the temperature ; hence it seems probable that y increases rather rapidly with the temperature. It is for experiment to confirm these previsions. By the method described by me in these Annales in 1862, y might be investigated up to 100°. The apparatus described in the first part of this memoir would be very suitable. I hope to be able to make some trials in this direction. The calculations indicated in this section would be of no utility at the present time, because I know of no experiments on the expansion and compression of carbonic acid. I content my- self at the present moment with indicating them, reserving the application of them for a special study, and remark that my method permits us to find the relation which exists between the pressure and the volume of a gas which is compressed or expanded under the conditions stated in the enunciation of the problem. —— M. Achille Cazin on Internal Work in Gases. 283 Up to the present time a relation get Ce ee ew appears to be admitted, such as was established by Laplace and Poisson before the appearance of the thermodynamic theory. In the recent experiments which M. Hirn and myself have made on the expansion of aqueous vapour, the value of @ varied very little, so that we could accept it as constant by attributing the variations to experimental errors. Such is, I believe, the opinion of M. Hirn and M. Zeuner*. I have undertaken some new researches on carbonic acid which may throw some light on this matter. . | | § IV. On the passage of a gas from a reservoirwhere it is com- pressed, into a reservoir which contains a certain quantity of the same gas rarefied. The following problem, which relates to the experiments de-. scribed in the first part of this memoir, can be solved by means of the relations established in the preceding sections.. - Problem 1V.—In a reservoir A, of volume V,, is a certain weight of gas under the pressure p, and at the temperature T’,. In a second reservoir B, of volume V,,-is another weight of the same gas, under the pressure p, =LZPTK, normal latitude, N= 4POK, central latitude, 7" =ZQOK, parametric latitude ; viz. isthe parameter most convenient for the expression of the values of the coordinates a, y (v7=A cos XV, y=C sin X’) of a point. P on the ellipse. The relations between the three latitudes are C C? tan AY = q tan = 2 so that X”, X/, X are in the order of increasing magnitude. I use in like manner /, /', / in regard to the vertex V. The course of a geodesic line is determined by the equation tan A, cos A! sin a= const., where X/ is the reduced latitude of any point P on the geodesic line, and «@ is at this point the azimuth of the geodesic line, or its inclination to the meridian. Hence, if /' be the parametric latitude of the vertex V, the equation is cos WV’ sin a= cos 1! (whence also, when \)=0, «=90°—/'; that is, the geodesic line cuts the equator at an angle =/’, the parametric latitude of the vertex). The equation in question, cos! sina=cos/', leads at once to Legendre’s other equations: viz. taking, as above, A, C for the equatorial and polar semiaxes respectively, and 6 for the - Patel 5.) excentricity, 6= \/ |— a ; and to determine the position of P Z2 337%; Prof. Cayley on the Geodesic Lines on the meridian, using (instead of the parametric latitude 0’) the angle @ determined by the equation cos d and writing, moreover, s to denote the geodesic distance Vv Ps and A to denote the longitude of P measured from the meridian C A which passes through the vertex V, these are ds=dp VC + AS sin’! cod, py cos I! dd V/ C0? + A?6? sin? l' cos* F A 1—sin? /' cos? ‘ which differential expressions are to be integrated from ¢=0; and the equations then determine 2, s, and A, all in terms of the angle ¢,—that is, virtually s and A, the length and longitude, in terms of the parametric latitude X/. Writing, with Legendre, sin x! — = ET sin /! A?6? sin? J! | C= Aen? TO sinh C? Bap Waeonts C? + Ad? sin?/!? za SoSnte also n= tan? I, © 2 = GK cost! = Acos? then the formule become oreo C ST OTE 2 ht ieee hia V1—c? sin? ¢, db V1—c®sin? d 1+nsin? a) d\ =M. Hence integrating from ¢=90, and using the notations F, E, TI of elliptic functions, we have C s= 5 Ble, p), A= * {(n402)I(n, ¢, $) — °F (6, $)}5 viz. these belong to any point P whatever on the geodesic line, parametric latitude of vertex =/’; and if we write herein 6=90°, then they will refer to the node N, or point of intersection with the equator, on an Oblate Spheroid. 333 The position of the point @ is at once obtained by writing =0: viz. this gives c=0, d=1, M= ze n=O: the differential expressions are ds=Cdd¢, dA= = dp. Or integrating from 6=0 C C to d= a we have s=A. woe ark. 5? agreeing with each 7 other, and giving longitude of a= or, what is the same i ag thing, £«0B=(1— a8 Writing in the formule //=90°, we have c=6, b= - x =0; whence dA=0, or A= const., =5 since the geodesie line here coincides with the meridian CB; and moreover s=AK(6, ¢); viz. this is merely the expression of the distance from C of a point P on the meridian CB. But we do not thus obtain the position of the point y. To 22 it we must consider a position of V consecutive to C, say, l!/= 56 where ¢ is indefinitely small; » is thus indefi- nitely te ‘ge, and the integral II (n, c, h) 1s not conveniently dealt with. But it may be replaced by an expression depending on 2 2 3 n(<, ¢, ¢), where — is indefinitely small; viz. (Legendre, Fonct, Ellip. vol. i. p. 69) we have = F'/ ae ein va tan n(’ II(n, c, 6) =F (c, 6) + 9 1H oT Hee es (a9) where 2 ae n)(a + “) We thus have Bef AF (c es VnV +n wait Vatand _ ia : V1l+n /1—c* sin? d — (+n) (S, Ne 2 e.. . where, ~ being small, B04 Prof. Cayley on the Geodesic Lines dg | II (=, C; ) =\i ie “sin *6) V1—c? sin? h 2 ; | 2 . (1— Sin? ¢) dp ‘ : = (-—2 = (1--) Fe, 4) + Ble 9): § V7 1—c*sin® ( n (¢ es, (¢, $) And expanding also the tan! term, we thus have A= U4 aF(c. + ee ie Re V1+n tan V (1+2) (c? +n) cial eee ae =o ( ae (¢, b )-(1+< “\ He, ee ee n ager J1+n oe which, in the term in {} neglecting negative powers of n, becomes M — 7 /} —2 sin? d A= TV ad +086, $) Ele, @)— cot p/m ae We may moreover write c=6, b= 2 p=90°—N, n= aM=e and therefore = =e, so that the formula is A=e4 — — 5 +O (c,90°—A!) — E(c, 90°—X’) — tan N/T aoa b = oY osc —c? cos’ + K(e, sale b°F(c, 90°—N)}, where I retain c¢, 0 as standing for iG Meee 1— Ae ae respectively. Writing herein \/=0, we have 7 i\ i 5 —e(H,c—b?F \c), where the coefficient Ejc—6°F ec is Tv 2 Tew | =| # (vI=e sin? 9 — ee 2 cos*Od0 _ >» Vl—c? sin? 6 | =? 335 consequently positive; that is, A, the longitude of the node, is less than 90°, as it should be. Hence in order that A may be = 90°, we must have 2! negative, say, A’ = —y', where p! is po- sitive; and, observing that we may under the signs H, F write 90°—p' instead of 90°+y', we thus have %, TT a 3 = 5 te 4/1 —c?cos?y/tan py! —H(c,90°— pw) + BF (c,90°—p!)! ; on an Oblate Spheroid. that is, we must have tan p!/1—c? cos? pl = H(c, 90°— pv!) —b?F (c, 90°—p’) ; viz. w/ is here the parametric latitude (south) of the intersection of the meridian C B with the consecutive geodesic line—that is, of the point y. As pw! increases from 0 to 90°, the left-hand side increases from 0 to oo; and the right-hand side, beginning from a positive value and either attaining a maximum or not, ulti- mately decreases to 0; there is consequently a real root, which is easily found by trial. Thus a C=4/3 (the angle of modulus =60°), b=; or the equation is tan pls/1—F cos? p= 5 (90°— p!) — 1 F90°—p). Using Legendre’s Table IX., we have este — in" E. F, E- o z 13 Sy SB % [sy ag ae ve 08 5 =. 9 a> S = & oh ie | | | ee ue | “alee | al eal. ee : at D D iS 2 ms S Q | x2 | ~ lols f Ww & bo og => a = D tx Y = 4 aes a a S116 a 2 & ‘ig l aN an & fs ye a Sas ss = Sd a 2 = ~ II IN ct B of cS a S s : ar 2 S ct : : . iy : ¥ on an Oblate Spheroid. 339 where the columns marked with an + show respectively the longitude of the node, and the length (or distance of node from vertex), for the geodesic lines belonging to the different values of the argument J’, The remarks which follow have reference to the stereographic projection of the figure on the plane of the equator, the centre of projection being the pole (say the Sonth Pole) of the spheroid. It is to be remarked that if a point P of the spheroid is projected as above, by means of an ordinate into the point Q of the sphere radius OK(= OA), then projecting stereographicallyas to the sphe- roid and the sphere from the south poles thereof respectively, the points P and Q have the same projection. And it is hence easy to show that an azimuth at a point of the meridian (parametric latitude ’, normal latitude A, and therefore tan \! = San r) is A projected into an angle (a) such that sin \/ tan (a) = aE tan a. In fact in fig. 3, if we take therein OK, OC for the axes of x, z respectively, and the axis of y at right angles to the plane of the paper, and if we have at P on the surface of the spheroid an element of length PR at the inclination « to the meridian PK, then if zy, z are the coordinates of P, and x+o2, y + dy, e+éz those of R, we have d= pcosasinn, oz = —p COs a COSA, sy= psina, and thence oy tan a= r/ ba? + 82? Now, if the meridian and the points P, R are referred by lines parallel to O z to the surface of the sphere radius O A, the only difference is that the ordinates z are increased in the ratio C:A; so that if the projected angle be («), we have tan («)= hatha 0: eo and then projecting the sphere stereographically from its south pole, the angle in the projection is =(a). And according to the foregoing remark, the angle («) thus obtained is also the projec- 340 Mr. J.C. Douglas’s Reply to My. Templeton’s tion of « from the south pole of the spheroid. We have thus tan (a) _ / ba? +822 __ / sin? X + cos? AX tan a 4 CB. Indeed, assuming that the prong remains unbent and swings as a pendulum about C, then mean velocity of A CA mean velocity of B© CB’ or in the case of fork A, which has the dimensions given in § 4, mean velocity of A 3256 —1:0003. mean velocity of B’ 38255 The result is that the prevailing tendency to disturbance de- pends upon the interference of two currents, pand q (fig. 8), which are set up alternately. As before, the space v between p and g willbe a spot of comparative calm, but not a spot for accumulation. § 18. If the face c be horizontal but turned upwards, and if the powder be sprinkled upon the upturned face, it is set in vio- lent agitation. Each particle moves to and fro with great velocity in the plane of vibration. Those nearest the edge are pretty sure to be presently thrown off. Those which are so situated as to be 350 Mr. F. Guthrie on Approach caused by Vibration. thrown across the middle line parallel tof, remain on the fork for a longer time. The apparent effect produced is assisted by the retention of images on the retina; and the appearance is as though a nebulous band of powder rested along the middle of the ¢ face parallel to f. On account of the greater amplitude of the vibrations at the edges of the prong, a particle there will be hurled forward with greater force than one nearer to the central line. Ifthe particle projected happen to ahght upon the fork when the latter is moving in the same direction as the particle, it will be hurled forwards again, and perhaps be precipitated over the edge parallel tof If it alight when the fork is moving in the opposite direction it will be thrown back again. § 19. It appears, then, from §§ 11-18 that when the fork is vibrating in a plane parallel to b, it is only on face a that any appreciable air-circuits are formed, and that there such circuits do not extend sensibly beyond at most 0°006 metre. § 20. Weshall see that the existence of such air-circuits, con- fined as they are to the immediate vicinity of the fork, are quite insufficient to account for the class of phenomena which have to be described, and which are similar to the fundamental fact men- tioned in § 1. § 21. Haperiment 7.—To one end of a splinter of wood, 0°5 metre long, a card 0:08 metre square was fastened in such a wa that the plane of the card was vertical, and contained the line of the splinter. The whole was hung from a fibre of unspun silk (fig. 9) and counterpoised. The tuning-fork A was set in vibra- tion as before, and was brought towards the card in the three re- lative positions corresponding to those of § 6; namely :— (1) (H,). The face a parallel to the card. (2) (H,). The face 5 parallel to the card. (3) (H, or Hz). The face ¢ parallel to the card. In all three cases the card moved towards the fork. The rate at which the card moved was greatest when the fork was sounding loudest. In all three cases it was possible to draw the card from a distance of 0-05 metre at least,—a distance quite beyond the direct influence of the superficial whirls which exist in position (1) (on face a). § 22. There is perhaps nothing essentially contrary to reason in the conception of two bodies in space free to move, so related to one another that while the first has no tendency to move to- wards the second, the second has a tendency to move towards the first. But if the tendency of the one to move is caused by the condition of the medium between the two, it seems inevitable that the tendency shall be mutual. Thus, if that tendency result from a general diminution in the tension of an elastic medium Mr. F. Guthrie on Approach caused by Vibration. 351 between the two, they will be urged towards one another. To test the reciprocity of the motive tendency in the case under con- sideration, the following experiment was tried. § 23: Hxperiment 8.—The tuning-fork A was fastened to the end of arod 1 metre long; the other end of the rod was counter- poised, and the whole was hung from a silk tape. If the ver- tical plane passing through the rod be called V, then the rod and fork received in succession the three relative positions :— (1) (H,), V parallel to a. (2) (H,), V parallel to 5. (3) (HH, or H,), V parallel to ec. In (1) and (2) the fork was simply hung from the suspended rod; in (8) it was fastened to an iron rod in the direction of its axis, and the two were then attached to the suspended rod at their common centre of gravity. The fork was sounded by the bow as before, and a piece of card 0:05 metre square was brought near the face a in (1), b in (2), and ¢ in (8). In all cases the sus- pended fork approached the card; but, owing to the great inertia of the suspended fork and counterpoise, the motion was much slower and léss striking than was the case when the card was hung. § 24. Experiment 9.—Further, instead of a card, a second fork B (sounding A) was set in vibration, and brought into the neighbourhood of the vibrating suspended fork A. The three faces a!, b', c! of the fork B were held in succession parallel to the three faces a, b, c of the fork A—that is, parallel to V when the faces a, b, c were in each of the three positions described in § 23. There were thus nine combinations effected. In every case the suspended fork approached the stationary one. Hence, to whatever cause the approach is due, the action is mutual. § 25. The next question, the solution of which promised to throw light upon our problem, was this :—What is the general or mean condition as to tension of a medium in which undula- tions are generated? Though this question has received very great attention from theoretical physicists, it has not been ap- proached, as far as I am aware, from the side of experiment in the manner to be described. § 26. Experiment 10.—The fork A was fixed in an upright position in its sounding-box. One of its prongs was closed ina glass tube T, 0°4 metre long and 0:042 metre internal diameter, carrying a cork through which the prong passed. The upper end of T (fig. 10) also carried a cork through which passed a narrow tube ¢, bent twice at right angles and dipping into water. The mternal diameter of ¢ was 0°0035 metre. The corks of the tube T were made tight with wax, and a little air was expelled 352 Mr. F. Guthrie on Approach caused by Vibration. from the tube T by warming it with the hand, so that, when the atmospheric temperature was regained, the water stood at some distance up the tube ¢. The tube ¢ was firmly clamped in several places to prevent vibration, and consequent centrifugal effect. On passing the bow across f, the enclosed prong was also set in vibration. When the amplitude of the vibration was as great as possible, the water had sunk in the tube ¢ to the amount of 0003 metre. The moment both prongs were suddenly stopped the level of the water in ¢ was restored. The depression of the level in ¢ cannot be due to increased temperature ; for, if it were so, the increase of volume would be gradual and accumulative, and on stopping the vibration the contraction due to cooling would be also gradual, whereas the attainment of maximum ° depression and the restoration to normal volume are practically instantaneous. § 27. We have here accordingly an experimental proof that the rapid motion (in this instance vibration) of a body in a me- dium produces on the whole an effect similar to that which would be produced by the expansion of the body, namely, a dis- placement of the medium. [If air were perfectly elastic and had no inertia, no such total displacement could ensue; and I think I may safely predict that the apparent expansion of the medium will be found, in the case of hydrogen less, and in the case of carbonic acid greater, than in that of air*. § 28. Though we know the dimensions of the fork and its rate of vibration, and though we can measure with tolerable ac- curacy the amplitude of its vibrations, we can only calculate from this the mean velocity of any given point, because in the middle of a vibration the fork is moving very much faster than towards the commencement or termination. Hence this vibratory dis- placement cannot, with our present data, be connected with the known rate at which air enters a vacuum. § 29. The fundamental experiment of §§ 1 and 21 next sug- gested for its explanation the following question. Let there be two equal and opposite forces, P and Q, producing equilibrium upon a body having inertia; let one of them, P, be increased and diminished by a series of equal increments and decrements fol- - lowing one another in rapid succession. Will the continually varying force, whose mean is P, maintain average equilibrium with the unaltered force Q? The plane of the cardboard in §$ 1 and 2] is the seat of two opposing forces, namely the pressure of the atmosphere on both sides. When the sounding-fork is held on one side, the pressure on that side undergoes successive and equal increments and decrements. Accordingly, if the ques- tion just proposed be answered in the negative, a sufficient ground * Compare the sighing of an organ-pipe after it has been sounded. —<-_-—_ — — Mr. F. Guthrie on Approach caused by Vibration. 353 will be at hand for the approach of the cardboard to the fork. _ § 30. Experiment 11.—A “Cartesian diver” was made out of a test-tube, a bubble of air, and a beaker-glass of water. This was so nicely adjusted that it rose when near the surface of the water, and sank when the top of the tube was 0-05 metre below the surface. When resting on the bottom of the beaker, the top of the test-tube was below the surface of the water. When the diver was resting on the bottom of the beaker, the tuning-fork A in a state of vibration was presented to the glass in various directions with regard tothe tube. The fork was placed some- times in contact with the water, sometimes in the neighbouring air, and sometimes in contact (towards the base of the fork) with the glass. Although the vibration of the bottom of the beaker caused the diver to leap up, it variably sank again and showed no sign of undergoing any alteration in specific gravity. If, now, the question in § 29 were answerable in the negative, the equilibrium would have been destroyed, because the atmospheric pressure on the one hand, and the elasticity of the contined air on the other being equal and opposite forces, an alteration in one, caused by its subjection to successive sonorous waves, would have altered the volume of the confined air and so destroyed the equilibrium. § 31. I hoped to throw light upon the fundamental experi- ments of §$ 1 and 21 by varying the nature of the surface of the body which received the vibrations, with the view on the one hand of preserving them, and on the other of dispersing them ‘as much as possible. With this view Experiments 12 to 15 were undertaken. § 32. Experiment 12 (fig. 11).—Upon one end of a splinter of wood 0°5 metre long, a cylinder of cardboard 0:03 metre in diameter and 0:04 metre deep, closed at the bottom, was fastened in such a manner that its axis was horizontal and its bottom in the plane V. The cylinder was counterpoised, and the whole was hung from an unspun silk thread. The vibrating fork A was brought near the open end of the cylinder in the three po- sitions already described, and also with one prong inserted into and nearly touching the bottom of the cylinder. In all cases motion towards the fork ensued. § 33. Experiment 13.—A handful of cotton-wool was hung upon the splinter in place of the cylinder of Experiment 12. The cotton moved towards the fork from a distance of at least 0:05 metre, when the latter was presented to it in either of the three positions, § 6. Muslin and washleather behaved in a similar manner, § 34. Haperiment 14.—A paper circular drum, 0°25 metre in 354 Mr. F. Guthrie on Approach caused by Vibration. diameter, having a rim 0°025 deep, was hung by a silk tape in the same manner as the cylinder of § 32. Parchment was stretched across the wide end of a funnel 0°20 metre in diameter. The neck of the funnel was placed in the mouth, and the drum of the funnel was brought opposite and parallel to the edged face of the paper drum. Air was rapidly forced into and drawn out — of the funnel. The paper drum moved towards the funnel even from a distance of 0-1 metre. § 35. Experiment 15.—A sbeet of cardboard 0°4 metre square was hung in the plane V from a rod | metre long. The card- board was counterpoised and hung from a silk tape. The paper drum of § 34 was placed 0-05 from the cardboard and parallel to it, and was then tipped. The cardboard moved towards the drum. § 36. Experiment 16.—A rod of brass 1:2 metre long, pro- vided at the ends with disks of brass perpendicular to the rod 0:26 metre in diameter, was set in longitudinal vibration by means of resined leather. One of the disks was held during the vibration near to the cardboard of § 35, also near the cotton- wool and muslin of § 33. Im all cases the suspended body moved towards the disk. By this means it was easy to cause motion when the two were at the distance of 0:2 metre. § 37. I have in the preceding paragraphs sought to eliminate systematically secondary and disturbing influences from the fun- damental experiment. The experimental results appear to me to point to the following conclusions. Whenever an elastic medium is between two vibrating bodies, or between a vibrating body and one at rest, and when the vibra- tions are dispersed in consequence of their impact on one or both of the bodies, the bodies will be urged together. The dispersion of a vibration produces a similar effect to that produced by the dispersion of the air-current in Clément’s expe- riment; and, like the latter, the effect is due to the pressure exerted by the medium, whichis in a state of higher mean ten- sion on the side of the body furthest from the origin of vibration than on the side towards it. In mechanics—in nature there is no such thing as a pulling force. Though the term attraction may have been occasionally used in the above to denote the tendency of bodies to approach, the line of conclusions here indicated tends to argue that there is no such thing as attraction in the sense of a pulling force, and that two utterly isolated bodies cannot influence one another. If the etherial vibrations which are supposed to constitute ra- diant heat resemble the aérial vibrations which constitute radiant sound, the heat which all bodies possess, and which they are all supposed to radiate in exchange, will cause all bodies to be urged towards one another. [ 355 ] XLVI. Experimental and Theoretical Researches into the Figures of Equilibrium of a Liquid Mass without Weight.—Ninth, Tenth, Eleventh and last Series. By Professor PLatTEAU*. Ninta Series.—Secondary causes which affect the persistence of liquid films.—Film-figures of great permanence.—Historical survey of observations relating to liquid films.—Capillary ascen- sion to great heights in tubes of large diameter.—Constitution of a current of gas passing through a liquid. 'N the last Series I endeavoured to show that, although cohe- sion and internal viscosity play the chief part in the deve- lopment of all liquid films, these causes are not sufficient when we have to do with films which are both large and durable, like those formed by soap-water, and that in such cases other and entirely distinct conditions must concur—namely, great superfi- cial viscosity and a comparatively weak tension. But when such films have been actually produced, their duration is affected by a certain number of secondary causes, which I pass in review in this Series. The first of these causes consists in the small disturbances communicated to the films by the movement of the surrounding air and by the vibrations conducted by the ground. These small disturbances no doubt act by overcoming the inertia and fric- tional resistance of the molecules; they thus hasten the descent of the molecules, and consequently the attenuation of the film ; and besides this, they cause the breakage of the parts that are very thin. It is partly on this account that the films generally last longer in closed vessels; for then one of the causes of disturb- | ance (namely the movement of the air) is got rid of. A second cause is evaporation (when the liquid constituting the film is susceptible of it). From the experiments described in the last Series, I conclude that in the case of liquids which do not admit of being blown into bubbles, evaporation is favourable rather than hurtful to the permanence of the films. I try to account for this singular fact, and I show that the contrary is true in regard to liquids that are easily blown out into bubbles ; that is to say, in the case of these the persistence of the films is dimi- nished by evaporation. For instance, hemispherical bubbles about a centimetre in diameter, formed at the surface of a solu- tion of Marseilles soap, last for several hours in an atmosphere * Translated from the Author’s abstract, in the Annales de Chimie et de Physique, S. 4. vol. xix. p. 369 (March 1870), of the complete memoir published in the Mémoires de ? Académie de Bruzelles, vol. xxxvil. For abstracts of the preceding Series see Taylor’s Scientific Memoirs, vol. iv. p- 16, vol. v. p. 584; and Phil. Mag. (S. 4.) vol. xiv. p. 1, vol. xvi. p. 23, vol. xxii. p. 286, vol. xxiv. p. 128, vol. xxxii. p. 39, and vol. xxxvii. p. 445, 356 Prof. J. Plateau on the Figures of Equilibrium saturated with aqueous vapour, but only for a few minutes when they are freely exposed to the air. The glycerine-solution not only does not emit vapour, but, on the contrary, absorbs the moisture of the surrounding air; and it is partly because of this that films of this liquid last so long even when exposed to the air. In the third place, since gravity constantly causes the liquid to descend towards the base of the films, it is plain that, by get- ting rid of or lessening the action of this force, the duration of the film must be increased. Hence it evidently follows that, other things being equal, a horizontal film will last longer than one which is inclined or vertical. I have made this comparison in the case of films of soap-water formed upon rings of iron wire 7 centims. in diameter and exposed to the air, one being horizontal and the other vertical. The average persistence of the first was 25 seconds, and that of the latter 13 seconds. Hence the position, or, more accurately, the greater or less degree of in- clination, of the film must be reckoned as one of the secondary causes that we are considering. In the fourth place, combinations of films always last a much shorter time than figures formed ofa single film. This is because the highly concave surfaces of the small masses of liquid which form the liquid edges, and especially those which exist at the points of junction of these edges, produce a continual drain upon the liquid of the films and thus tend powerfully to make them thinner. The combination of films into systems is therefore likewise one of the secondary causes which modify their per- manence. In the fifth place, films generally last longer in proportion as they are of smaller size. For instance, if systems of films are produced upon two skeletons of similar shape but of different sizes, the one on the smaller skeleton lasts the longest. If the persistence generally diminishes when the size of the films is increased, this is, [ think, simply because the greater a film is, the greater is the chance that one point or another will yield to some cause of rupture. Under certain circumstances this effect of size does not show itself; for mstance, films of soap- water formed upon rings 10, 7, 2, and 1 centim. in diameter lasted on the average for the same length of time. This last fact may be explained by the consideration that the drain of liquid caused by the great concave curvature of the small quan- tity of liquid which connects the film with the whole of the mner circumference of the ring, tends to make the smaller films last a shorter time, and thus the effects of size and curvature may neu- tralize each other. | Lastly, it is needful, in the sixth place, to take account of the nature of the solid to which the film adheres, and of the condi- of a Liquid Mass without Weight. 357 tion of its surface. For instance, we know that films formed upon rings or frames made of iron wire that has not been oxi- dized break immediately, or last only for a very short time; and according to the Abbé Florimond, soap-bubbles of a much larger size can be blown with a glass pipe than with a clay one &c. From this examination of all the accessory circumstances, it follows that a film of given size will last longest if it is a plane horizontal film, attached all round to the side of a glass vessel, entirely shielded from evaporation, and protected from the mo- tion of the surrounding air, and, as much as possible, from the tremors conducted along the ground. Now all these conditions were fulfilled in the case of a film 7 centims. in diameter men- tioned in my Seventh Series, formed of the glycerine solution and placed inside a bottle: accordingly this film lasted eighteen days. I next pass to another subject. The beauty of the film-figures of the glycerine-solution naturally gives rise to the wish to have them entirely permanent. In the case of one of them (the sphere) this object is attained, as every one knows, by means of molten glass; but the production of other figures in this mate- rial, especially of such as are formed by an assemblage of films, would present difficulties, and in any case it would not be con- venient. The first idea that suggests itself is to employ a liquid which produces films that become solid by simple evaporation in the cold, such as collodion, solution of albumen, &c.; but with a liquid of this kind no result can be obtained except by limiting our attempts to figures of very small size. Hence, in order to succeed in producing figures of tolerable size, we are obliged to have recourse to substances which, like glass, are liquid only at high temperatures, and to seek for one which fulfils the double condition of not requiring a very high temperature to melt it, and of being capable of extension, in the molten state, into films of sufficient size. I succeeded almost completely with a mixture of one part of pure gutta percha and five parts of resin, kept at a temperature of about 150° C.; the frame employed was a cube measuring 5 centims. along the edge. The system of films that was produced was very firm, and lasted, I think, more than two years, when a slight blow reduced it to fragments—from which we must conclude that the constitution of the films had undergone a gradual change. I think one would succeed still better, and that the gradual alteration would be less, if a somewhat larger proportion of resin were employed. I conclude the part of my work which is specially devoted to liquid films by a succinct account of every thing that, as far as my knowledge goes, has been published in relation to such films independently of my own researches. 358 Prof. J. Plateau on the Figures of Equilibrium According to figures represented on an Etruscan vase preserved in the Museum of the Louvre, it appears that even in ancient times children amused themselves with blowing complete bubbles. With regard to modern times, I will content myself in this ex- tract with saying that the colours, tension, pressure, average thickness, persistence, constitution, and different modes of pro- duction of the films, the phenomena of endosmose exhibited by them, a few special facts and applications, the form of certain films, and, subsequently to my investigations, of systems of films have been made the subject of these observations. Before returning to the general questions connected with the figures of equilibrium, I discuss in the present Series two phe- nomena, the discussion of which could not well be brought in elsewhere. As every one knows, the ascent of liquids in tubes, the sides of which they are able to wet, does not take place to any consi- derable extent except when the internal diameters of the tubes are very small, whence has arisen the expression capillary pheno- mena ; and gravity always puts a limit to the height of the column that is raised. But if the action of gravity were neutralized, these limitations ought to disappear, and a liquid ought to be able to rise to any height in a tube of any diameter. It appeared to me to be interesting to try this application of my processes, by using either oil surrounded by the alcoholic liquid, or the alcoholic Jiquid surrounded by oil. The tubes that I employed were both of them 42 centims. long, and one 14 and the other 15 centims. in internal diameter. I describe in the me- moir a series of indispensable precautions, which it would occupy too much space to mention here, and by means of which the ex- periments completely succeeded. The oilin one of the tubes and the alcoholic mixture in the other rose gradually to the top; the motion of the oil, however, was retarded, while that of the alco- holic mixture was accelerated. ‘he oil required 21 minutes 1 second in order to rise 4 decims.; the first decimetre was traversed in 1 minute 47 seconds, and the fourth in 9 minutes. To rise in hike manner 4 decimetres, the alcoholic mixture took only 5 minutes 55 seconds; it accomplished the first decimetre in 1 minute 42 seconds, and the fourth in 1 minute 16 seconds. The second fact that I discuss here is the constitution of a current of gas traversing a liquid. A current of air issuing from a round hole and rising through a liquid may be considered as the converse of a liquid vein projected downwards through the air from a similar round hole. I prove that, apart from mole- cular figurative forces, the forms of the current of gas would be completely analogous to that of the liquid vein, also considered as not subject to figurative forces. In both cases the form would of a Liquid Mass without Weight. 359 approach to a cylinder, or rather to a very elongated cone; only one of the figures would exhibit as depressions what the other exhibited in relief. Now, considered with regard to molecular forces, the conditions of equilibrium and stability are exactly the same for hollow figures as they are for figures in relief. Hence, just as the liquid vein changes into isolated masses under the action of the molecular forces, so the current of gas ought to transform itself into separate bubbles—which, as every one knows, is conformable to experiment. But I point out that there is this difference between them ; that the liquid vein always presents a continuous portion of greater or less length, while with the current of gas, unless it has quite an enormous velocity of translation, the bubbles ought to be formed very near the opening, and hence the current can- not have acontinuous part. I verified this deduction by means of air escaping under a pressure of 130 centims. of water from an opening 5 millims. in diameter, below a stratum of water only 20 millims. in thickness: this current, notwithstanding its great rapidity and its having to pass through a very shallow layer of water, caused a bubbling at the surface, thus proving that it had been already changed into bubbles. TentH Series.—Results arrived at by Geometricians, and expe- rimental verifications. Beer discussed analytically in a first memoir the rotation- experiments of my First Series; in a second memoir he came back to the same subject, treating it more precisely by the aid of elliptic functions ; and he also gave by the same means the in- tegral equation to the meridian lines of the equilibrium-figures of revolution for the case of rest. M. Delaunay, considering surfaces of revolution with a constant mean curvature from a purely mathematical point of view, arrived at an elegant method of generating their meridian lines. M. Lamarle has applied his geometrical methods to the same subject. M. Mannheim has pointed out a simple rectification of the meridian lines in question. In relation to the surfaces generated by these same lines, M. Lindelof has arrived at a series of remarkable results, relating particularly to the measurement of areas and volumes. Goldschmidt, and more recently MM. Lindelof and Moigno, have discussed the catenoid analytically. In conclusion, as the last result bearing specially upon equilibrium-figures of revolu- tion, M. Lamarle has shown that, among ruled surfaces, the cy- linder is the only one that has a finite and constant mean cur- vature. Poisson was, I believe, the first to investigate the general dif- ferential equation of the figures of equilibrium of a liquid mass 360 Prof. J. Plateau on the Figures of Equilibrium without weight ; and he accordingly thus obtained the equation to surfaces of constant mean curvature. Meusnier had pointed out the skew helicoid with directing plane as a surface whose mean curvature was nothing; M. Catalan has proved that this helicoid and the plane are the only ruled surfaces of the mean curvature zero. M. Lamarle has integrated the general equation in the case of helicoids, and has thus found four other surfaces besides the skew helicoid with directing plane. Mr. Jellett has indicated a simple condition which every closed surface of constant mean curvature, except the sphere, must satisfy. The general case of surfaces whose mean curvature is zero was first treated by Monge and Legendre; M. Scherk has deduced, from the integral which they gave, the equations in finite coor- dinates of five particular surfaces. M. Ossian Bonnet has made known another more convenient integral, and has applied his method to the investigation of surfaces of the kind in question which pass through a determinate continuous contour. M. Ser- ret has shown how they can be made to pass through a series of straight lines not situated in the same plane; and M. Mathet, by a method different from that of M. Bonnet, how they can be made to pass through a given plane curve. M. Catalan has published another integral still of the general equation, and has deduced from it several surfaces. I also recall the researches of Dupré, Rennes, and M. Van der Mensbrugghe relating especially to the tension of liquid sur- faces, researches of which I have spoken already in the Highth Series. Now let us see what are the experimental verifications. I have measured the limit of stability of the catenoid by means of a laminar catenoid formed between two equal rings, whose dis- tance could be gradually varied and exactly measured; and the result was found to agree perfectly with that deduced from Gold- schmidt’s calculation. I have applied the general principle which concludes my Seventh Series to the realization of the skew helicoid with direct- ing plane, by employing a closed outline of iron wire composed of two spires of a regular helix, of a part of the axis, and of two straight lines connecting this part with the extremities of the helix. When this outline is taken out of the glycerine-liquid, it is found to be occupied by a beautiful curved film which repre- sents exactly the helicoid in question. I have realized in the same way in the laminar form, upon an appropriate framework, a portion of a remarkable surface first discovered by M. Scherk, and since discussed by M. Catalan. M.Van der Mensbrugghe, by applying still the same principle, has also realized another of M. Scherk’s surfaces. of a Liquid Mass without Weight. 361 I have verified a consequence of M. Bonnet’s researches— namely, that an infinity of surfaces having the mean curvature zero can always pass through a closed outline, either plane or not plane, of absolutely any form. I have had the strangest and most complicated closed outlines made of iron wire, and on issuing from the glycerine-solution each of them was found to be occupied by a single film: this experiment proves, in the first place, that, given any closed outline whatever, there is always at least one surface of mean curvature zero a finite portion of which can fillit. I next show how to make the film undergo as many changes of shape as may be wished without its equilibrium being destroyed, and without its ceasing to rest upon the whole of the closed outline; but I show that it is no longer a finite portion of each of these new surfaces that occupies the given outline. I had found by calculation that the volume of the limiting ca- tenoid is half that of the cylinder on the same base and of the same height; and I have verified this result by means of a full catenoid of oil, formed between two disks within the alcoholic solution, and having the limiting height; the disks were then brought nearer until the liquid mass formed a cylinder ; and the height of this cylinder was found to be half that of the catenoid. Lastly, by the use of suitable solid frameworks, I have realized @ portion of one of M. Lamarle’s helicoids, likewise by means of oil surrounded by the alcoholic solution. Exevenru Serres.—Limits of stability of figures of equilibrium. —General theory of the stability of these figures—Stability of systems of films.—Stability in cases when gravity comes into play. As might be seen from the preceding Series, the sphere is very probably the only closed figure of equilibrium, all the rest having infinite dimensions in certain directions. When the attempt is made to realize partially one of these last, either by means of oil surrounded by the alcoholic solution, or with a film of the gly- cerine-solution in air, it is generally found that, if the solid ter- minations to which the mass or the film adheres are placed so as to comprise too great a portion of the figure, the latter will not form; whence we must conclude that, with the terminations separated to this extent, it would be unstable. In the present Series I investigate, in the first place, by aid of experiment, cal- culation, and reasoning, the limits of stability of most of the figures of equilibrium that I have studied, and especially of the figures of revolution contained between two equal bases perpen- dicular to the axis. When a sphere of oil is freely suspended in the alcoholic mix- ture, it always exhibits perfect stability of form. If this form is altered by movements imparted to the surrounding liquid,themass Phil. Mag. 8. 4. Vol. 40. No. 268. Nov. 1870. 2B 362 Prof. J. Plateau on the Figures of Equilibrium always resumes exactly its previous shape. A soap-bubble isolated in the air exhibits equally a permanent and stable form. ‘The sphere, then, has no limit of stability; that is to say, whatever may be the extent, relatively to a complete sphere, of the portion of a sphere actually produced, this portion is necessarily im a state of stable equilibrium. Thus, for instance, a perfectly per- manent double convex lens of oil can be produced in the alcoholic mixture upon a ring of iron wire. This result, being independent of the radius, and consequently of the curvature of the sphere, is equally true when the radius becomes infinite, or, in other terms, when the surface of the sphere becomes a plane. Accordingly the plane also has no limit of stability ; that is, it can be produced within a solid outline of any extent without ceasing to be stable, as can be verified by the formation, for instance, of a film of the glycerine-solution within a plane outline of iron wire of any shape and of any size. My first experiments upon liquid cylinders proved that such a cylinder is unstable when the ratio of its length to its diameter exceeds a value comprised between 3 and 3:6, which I have called the limit of stability of the cylinder. I had arrived at this result by means of cylinders of oil formed within the alcoholic mixture between two solid rings or disks. In the present Series I attack the theoretical investigation of the precise value of the limit in. question. Suppose one of our cylinders of oil to have been pro- duced between two disks, and short enough to be stable. Ii, by gently pushing the oil towards one of the disks with a glass rod, we cause the artificial formation of a bulging anda constric- tion, and if this modification of the figure does not go beyond a certain limit, the mass, when afterwards left to itself, resumes spontaneously the original cylindrical form; but if the change of shape exceeds this limit, it increases spontaneously, and the transformation becomes complete—that is to say, the mass sepa- rates into two unequal portions. Now, if we were to produce the precise degree of alteration which separates these tendencies to two opposite effects, it is evident that the mass would be indifferent to either one or the other; there would therefore in that case result a condition of equilibrium, although of unstable equilibrium. And since the figure would still be a figure of revolution, made up of an enlargement and a contrac- tion, it would necessarily form a portion of an undulating surface — or unduloid (ondulotde). In the second place, since this partial unduloid would constitute the degree of alteration at which there would begin a spontaneous tendency to a more profound alteration, it would differ less from the initial form (namely the cylinder) in proportion as the latter was nearer to its limit of stability ; and this is confirmed by experiment. Lastly, when the cylinder is of a Liquid Mass without Weight. 363 actually at this limit, the unduloid would coincide with it, or, if the expression is preferred, it would differ infinitely little from it, since the faintest trace of an enlargement and a contraction would then be sufficient to bring about the spontaneous transformation. Hence, when a cylinder of liquid is precisely at its limit of sta- bility, we can always conceive of a partial unduloid which differs infinitely little from this cylinder, and is made up of exactly one enlargement and one contraction. Now we have the differential equation of the first order of the meridian lines of equilibrium-figures of revolution, and in the case of an unduloid infinitely near to a cylinder, this equation can be integrated by the ordinary methods. It then gives a curve of sines (sinuotde) for the meridian line; and if we try what is the sum of the lengths of the chords of a convex and of a concave are of the curve of sines, we find that, representing this sum by L, and the radius of the cylinder by r, we have the rela- tion L=2-r. But the length L is evidently that of the cylinder at its limit of stability ; and if it is divided by the diameter 2r, it gives what I have called the limit of stability of the cylinder, which it will be seen is exactly equal to the ratio 7. I have verified this result of calculation by new experiments more accurate than my first, and likewise performed upon cylin- ders of oil contained between disks and surrounded by the alco- holic mixture. Before stating their results it 1s necessary to make one remark. When we are not too near the limiting con- dition, there are two characters which clearly indicate stability or instability : if, when a cylinder has been formed approaching the limit, we produce in it artificially a slight enlargement and con- traction by impelling the oil with the pomt of the syringe, and the figure then resumes its previous form, it is evident that it still possesses actual stability ; on the other hand, if while we are trying to produce the cylinder (that is, while there is still an excess of oil and we are withdrawing some so as to arrive at the cylindrical form) the figure begins to change of its own accord before this form is reached, we must conclude that the cylinder which it is wished to produce would be unstable. In the experiments in question, I gave in succession the follow- ing values to the ratio between the distance of the disks to their diameter :— 3°6, 3°3, 3:18, 3:14, 3:09, 3:11, 31s. It will be seen that the first three ratios exceeded the limit 3°14, but that they became successively nearer and nearer to it; now, for these three ratios the above-mentioned character of instability was distinctly shown, bat in a decreasing degree from the first 2B2 ad 364 Prof. J. Plateau on the Figures of Equilibrium to the last. The last three ratios were, on the contrary, below the theoretical limit, but also successively approached it ; and with them the character of stability was recognized, although likewise becoming less and less marked from one to another. Lastly, with the theoretical ratio 3:14 itself neither of these characters was exhibited: in this case, as with the lower ratios, the exact cylinder was arrived at without difficulty; but when this cylinder was left to itself, it began, after remaining appa- rently unaltered for a few seconds, to change, at first with ex- treme slowness, but afterwards gradually more and more quickly. The figure divided itself as usual into a bulging and a constricted portion, and the change of shape continued until complete separa- tion had taken place. The results of experiment accordingly agreed completely with that of calculation. As I proved in my Second Series, a liquid cylinder, of which the length is considerable as compared with its diameter, sepa- rates of its own accord into bulging portions alternating with constricted portions, both becoming more and more distinct until the whole figure is changed into a succession of isolated spheres. I then arrived at the following conclusions,—that a cylinder of indefinite length, with its surface entirely free, and formed of a liquid without weight and completely devoid of viscosity, would im all probability transform itself in such a way that the sum of the lengths of an enlargement and a contraction would be equal to that which corresponds to the limit of stability. But I showed at the same time that the sum of these lengths increases with the resistances, either external or internal, that retard the trans- formation. Now in the present Series, supposing a cylinder of indefinite length, or only of very great length, formed of a real liquid, and therefore one in which the transformation is neces- sarily interfered with, at least by viscosity, and assuming that at the commencement of this transformation the meridian line of the figure is still a curve of sines, I investigate mathematically the difference between the capillary pressures exerted by a con- tracted and those exerted by an expanded portion ; and in this way | find that the excess of the former above the latter increases with the length of the contracted and expanded portions. It will thus be understood how, when there are resistances, the transformation spontaneously adjusts itself so as to overcome them, increasing the difference of the pressures by an increase in the length of the contracted and enlarged portions. Experiment, moreover, confirms the result of the above calcu- lation, leaving out of account any hypothesis as to the nature of the orginal meridian line. I have in fact established that if cy- linders of oil are formed between the same pair of disks, exceed- ing to a greater and greater extent the limit of stability, as can of a Liquid Mass without Weight. 365 be done by help of an appropriate artifice, the transformation becomes more and more rapid. For the limiting ratio 3:14, the duration of the phenomenon was eleven minutes; with the ratio 3°18 it was only four minutes; with the ratio 3°3 it was two minutes; and with the ratio 3°6 one minute. Now it is plain that a more rapid transformation implies forces of greater in- tensity. It follows, besides, from the calculation of which I have spoken, that if the ratio of the distance between the bases to their dia- meter is less than 7, and if we suppose one half of the figure to be slightly increased and the other half to be slightly diminished in width, the capillary pressures of the swollen portion will over- come those of the contracted portion, and so the cylindrical form tends to reproduce itself. Lastly, the same calculation shows that if the ratio is exactly equal to 7, and if the swelling and the contraction are of infinitely small amount, the capillary pressures are the same in both parts. We have accordingly here a second method which gives the precise limit of stability of the cylin- der; only it assumes @ priori that at the commencement of the transformation the meridian line is a curve of sines. I next pass to the unduloid. Here the conditions of stability are different according as the middle of the figure produced is occupied by a constriction or by a bulging portion: in the former case these conditions seem to vary according as the unduloid differs more or less from a cylinder; but in the second case the limit is distinctly recognizable. A partial unduloid with a bulge at the middle is exactly at its limit of stability when its bases coincide with the circular sections of the necks of the two con- strictions between which the bulging portion is contained. I draw this conclusion both from experiment and from a course of reasoning which would take up too much room for insertion here. M. Lindeléf has arrived at the same result mathematically. Hence we get another method still by which we can ngo- rously determine the limit of stability of the cylinder. It is well known that M. Delaunay has proved that the meridian lines of surfaces of revolution of constant mean curvature are generated by one of the foci of a conic section which rolls upon the straight line constituting the axis of revolution. In the case of the un- duloid, the rolling conic section is the ellipse ; and it is plain that the portion of the described line which is comprised between any two consecutive points of minimum distance from the axis, corresponds to one complete rotation of the ellipse. Hence the partial unduloid generated by this portion (that is to say, the unduloid at its limit of stability) has a length equal to the per1- phery of the ellipse in question ; now, when this ellipse becomes a circle, the unduloid becomes a cylinder; and consequently this, 366 Prof. J. Plateau on the Figures of Equilibrium at its limit of stability, has a length equal to the circumference of the rolling circle. But this circumference is evidently equal to that of the cylinder; hence the limiting cylinder has a length equal to its own circumference; and hence, lastly, the ratio of the length to the diameter has the precise value 7. I have already discussed the question of the limit of stability of the catenoid in my Tenth Series, and I then described expe- riments which fully confirm the theoretical result. No general statement can be given of the limit of stability of the nodoid (nodotde), whether the figure be generated by a por- tion of a node of the meridian line, or by an are of this line convex towards the outside. Except in the case of the cylinder, the partial figure of revolu- tion can be contained between unequal circular bases ; and then the conditions of stability are necessarily different. We have a curious instance of this in the case of the catenoid: if the cir- cular section of the neck be taken as one of the bases, the figure has no longer any limit of stability; that is to say, the other base may be taken as far away as we please in the indefinite figure without the portion contained between the two bases ceasing to be stable. I verify this conclusion experimentally upon a catenoid of which the circle at the neck had a diameter of only 3°5 centims., while the diameter of the other base was 20 centims. I next consider from a general point of view the question of the stability of figures of equilibrium. It is admitted by geo- metricians, as a result of analysis, that the surfaces represented by the equation = Ny =C (that is to say, surfaces of constant mean curvature), are also those which, for a given volume, have the smallest superficial area. But if we were to accept this prin- ciple without restriction, it would follow that every partial quid figure of equilibrium terminated by a solid system would be ne- cessarily stable, whatever portion it might represent of the com- plete figure: the cylinder, for instance, would be completely stable however great its length; the unduloid lhkewise would remain perfectly stable whatever the number of bulging and constricted portions contained between its two solid bases, &c. In fact the superficial layer, beg, as is now known, really in a state of tension, makes a constant effort to contract ; hence, if its area were always a minimum in a state of equilibrium, any very small change of form would increase its area, and consequently the superficial layer would tend to resume its former dimensions and to restore the figure of equilibrium. Geometricians have been led to the above principle by the ana- lytical result that the variation of such surfaces is always zero, of a Liquid Mass without Weight. 367 which seems necessarily to imply either a minimum or maximum of extent ; and since it is evident that, with a given volume the surface can always be increased by a proper change of form, it has been concluded that a minimum ought to be chosen. Now there was an equally legitimate intermediate supposition, which has not been made, and which corresponds with the actual fact ; that is, that, beyond definite limits, the surface is a minimum re- latively to certain kinds of small changes of form, while it is a maximum relatively to others. _I prove the truth of this last principle by the study of the cy- linder. Let us consider a liquid cylinder, terminated by two solid bases, of any given length as compared with its diameter. It is obvious, in the first place, that it may be made to undergo small modifications of form which, without changing its volume, increase its surface. This would evidently be the case, for in- stance, if it were to become grooved with fine longitudinal ridges and hollows, such that the sum of the ridges was equal in volume to the sum of the hollows, each being measured relatively to the original surface; and it is probable that it would also be the case for any other modification which should change the figure of re- volution. : But let us suppose that the figure, without ceasing to be a figure of revolution, were to transform itself into a succession of alternately expanded and contracted portions, this change of shape being of finite but excessively small amount. Then, if we suppose the meridian line of the figure thus modified to be a curve of sines, the area of the surface of the portion composed of one expansion and one contraction can be found by calculation, the condition that the volume shall not change being always kept in view, and it is thus found that if the length of the portion in question exceeds the circumference of the original cylinder, the surface is less than that of the corresponding portion of the cy- linder; and since the same result is applicable to each similar portion of the entire figure, it follows that, under these circum- stances, the total surface diminishes. The surface of the cylinder is accordingly a maximum relatively to the kind of alteration we have just indicated, and it is by a change of this kind that, as we know, the spontaneous transformation of the cylinder takes place. Thus a liquid cylinder whose length exceeds its circumference, or, in other words, in which the ratio of the length to the dia- meter exceeds the quantity 7, is necessarily unstable, because the constant tendency of its superficial layer to diminish its area favours the kind of change of shape which we have just been considering. I may notice in passing that the theory of the constitution of liquid veins which I have set forth at the end of my Second Series depends upon this necessity. 3868 On Figures of Equilibrium of a Liquid Mass without Weight. One point still remained to becleared up. According to the calculation I have been speaking of, in order that the surface may be diminished by the kind of transformation here indicated, it is sufficient that the sum of the lengths of an expanded and con- tracted part of the figure should exceed the circumference of the cylinder ; and this allows us to attribute to this sum an infinite number of different values. But nevertheless, as has been shown in the Second Series, in a cylinder that is very long relatively to its diameter, when the transformation takes place quite regularly, the sum in question is always the same for the same cylinder under the same circumstances, whence we must infer that there is some special condition which regulates the choice of the mass. We may add that analogous considerations apply to the other unstable figures. I examine the matter, and arrive at the fol- lowing as a very probable conclusion :—that, among all possible changes of shape which would diminish the surface, the mole- cular forces choose that one which allows the smallest possible departure of the mass from another figure of equilibrium. In the cylinder, for example, the mass will assume at the beginning of the transformation the figure which, considering the resist- ances, makes the nearest possible approach to.the unduloid. The combination of liquid films, which I have studied parti- cularly in my Sixth Series, likewise presents some remarkable phenomena in relation to their stability. I tried to establish ex- perimentally that every equilibrated system of films in which more than three films meet at one liquid edge, or more than four liquid edges at one liquid point, is an unstable system. M. La- marle has since discussed the question in detail in his memoir “On the Stability of Liquid Systems formed of thin Films.” Set- ting out from the general principle that I had laid down at the end of my Sixth Series—namely, that in every permanent assem- blage of films the sum of the areas of the films must be a mini- mum,—he succeeds in giving a strict demonstration of the condi- tions above mentioned relatively to the number of films and of liquid edges ; and he arrives besides at many other interesting results. Lastly, I recall the fact that M. Duprez, in his memoir “ On a particular case of the Equilibrium of Liquids,”’ has investigated a phenomenon in which the stability or instability of a liquid surface depends conjointly on the action of gravity and of mole- cular forces. The phenomenon referred to is the familiar one of the suspension of a liquid in a vertical tube open at the lower end when the diameter of the opening is below a certain limit ; but M. Duprez has shown that this limit is much greater than was generally supposed. He has held up water in this way in a tube the diameter of whose opening was 19°85 millims. ; while Royal Society. 369 the theory founded upon the conditions of stability of a liquid surface gave him 21:13 millims. as the exact value of the limit- ing diameter. I conclude by pointing out that all my Series together, count- ing from the second inclusively, establish the Experimental and Theoretical Statics of Liquids acted on solely by Molecular Forces. The present Series is followed by an analytical index to the contents of the eleven Series. XLVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 308.] June 16, 1870.—General Sir Edward Sabine, K.C.B., President, in the Chair. [HE following communications were read :— ** Note on the Construction of Thermopiles.”” By the Earl of Rosse, F.R.S. Although in the measurement of small quantities of radiant heat by means of the thermopile much may be done towards increasing the sensibility of the apparatus by carefully adjusting the galvano- meter and rendering the needle as nearly astatie as possible, there must necessarily be some limit to this; and it therefore appears de- sirable that the principles on which thermopiles of great sensibility can be constructed should also be carefully attended to. With the view of obtaining a pair of thermopiles of greater sen- sibility and of more equal power than I had been able to procure ready made, I made a few experiments with various forms of that instrument ; and I was led to the conclusion (one which might have been foreseen) that the sensibility of the thermopile is much in- creased by reduction of its mass, and more especially by a diminution of the cross section of the elements. To obtain a clear idea of the problem before us, which is how to construct the thermopile so that, with a given amount of radiant heat falling on its face, the greatest current may be sent through the galvanometer, let us consider the thermopile under two different con- ditions :— 1. With the circuit open. 2. With the circuit complete. In the first case, when radiant heat falls on the face of the pile, the whole mass of metal rises in temperature, the rise being greatest at the anterior face, and less and less as you approach the other end. This rise of temperature will increase till the heat radiated from the anterior face, together with that which traverses the depth of the pile and is radiated from the posterior face, is just equal to that radiated to the anterior face at that moment, or when k(t+t)=kt +7 (t(—t’') = Q, where (¢, t!) are respectively the temperatures of the anterior and 370 Royal Society :— posterior faces, s, / the cross-section and depth of the pile, ¢ pro- portional to the mean conductibility of the material of the pile, Q the quantity of heat falling on the pile in a unit of time, and ka constant. Let us now suppose the circuit completed, and we shall have, in addition to the above, two causes operating to reduce the tempera- ture of the anterior face—the abstraction of heat by the electric cur- rent, and proportional to that current =LI, where I is the intensity of the current and L a constant ; then there will be equilibrium when k(t+t')+ Li=kt+— (t—t)+ LI=Q. It is quite clear therefore that if Q be constant, I will become the larger the smaller the other two terms become ; and therefore as long as the first term continues small compared with the remaining terms, and the resistance in the pile is very small compared with that in the rest of the circuit, we shall increase the intensity of the current by every reduction of the cross section of the elements of the ther- mopile. } There is another point which, though less important, cannot be entirely lost sight of—namely, that the more we reduce the mass of the anterior face and adjacent parts of the pile, the more rapidly will the temperature rise to its state of equilibrium, and therefore the more convenient will it be for use where the needle is liable to disturbances from various causes, and where consequently, the more speedily the needle can be brought to rest, the more accurately will its observed motion be a measure of the radiant heat falling at that moment on the face of the pile. Let us now compare the case of a single pair of small cross section with a metal disk soldered to the junction of the two bars, and of sufficient size to catch all the radiant heat required to be measured, with that of a pile of ” pairs, each of equal dimensions with those of the single pair, the area of face being the same in the two cases. By increasing the number of elements from one to n, we increase the number of solderings in that proportion ; consequently the ave- : bia rvenyid rage amount of heat reaching any soldering is ;, #8 great as that reaching the soldering of the single pair; therefore, if the same percentage of the total heat be lost by conduction, the total electro- motive force is the same in the two cases. But inasmuch as the total cross section of metal to conduct the heat away from the an- terior face is ” times as great in the pile as in the pair, and the resistance of the pile is ~ times as great as that of the pair, the pile will be inferior in power to the pair, unless these two causes of inferiority are counterbalanced by the loss due to the greater average distance to the soldering from the points where the heat reaches the face, in the case of the pair, than that of the pile of pairs. The experiments already referred to were made with three differ- ent thermoelectric pairs. These consisted each of a pair of bars of The Earl of Rosse on the Construction of Thermepiles. 371 bismuth and an alloy of twelve parts of bismuth and one part of tin of different thicknesses, of about equal lengths in each case, and sol- dered about 7 inch apart, upright, on disks of sheet copper of 3 inch diameter. A slip of wood was placed between the two bars, to protect them from injury; and to it they were fixed with thread. ‘The three piles were compared with a pile of four elements, made by Messrs. Elliott ; and, the deviation due to the latter being taken equal to unity, the following deviations were obtained for the three thermo- pairs :— Weight of | Weight of disk face. clog tala Deviation. Metals employed. I. 8 grains | 42 grains ‘676 Bismuth, antimony. Hl. | 43, Gieiiyy 1:35 | Bismuth eet tin Ta: Hl. 1 orai 2 . Bismuth, 2 grain BDAY, 3°23 Bismuth { aid, A heavy and a light pile were also compared, taking the interval between raising and depressing the screen, first = minute, and then =2 minutes ; and it was found that, in the first case, Deviation due to light pair SSS SSS SS 2°6 > Deviation due to heavy pair aud, in the second case, Deviation due to light pair _ 5. 9: soe 3 Deviation due to heavy pair so that the light pair arrived rather more rapidly at the condition of equilibrium than the heavier pair. Although the above experiments are far less complete than I could have wished, they are sufficient to show that the sensibility of thermopiles may be considerably increased by diminution of the section of the bars composing them. Whether they may be with ad- vantage reduced to a greater extent than I have already done I cannot say ; but I am inclined to think that they may. I have ascertained from Messrs. Elliott that the alloys used by them in the construction of thermopiles, at the time when I received mine from them, were 32 parts of bismuth +1 part of antimony, and 14+ of bismuth +1 part of tin. If allowance be made for the substitution of the first of these two alloys for pure bismuth, the difference between Elliott’s pile and the pairs II. & III. will be rather greater. The pile by Messrs. Elliott, if made of the same metals as I employed, would have been reduced in power from 1 to 0°9. The construction of thermo-couples, on the plan I have described, is comparatively easy. In about two hours I was able to make one ; 372 Royal Society :— and in more experienced hands their construction would be still easier. An experiment was made with one of the piles to ascertain whether, when the heat was not directed centrally on the pile, much diminution of power would take place. There was less deviation, in consequence of the increase of the mean distance which the heat had to travel before it reached the soldering; but I believe that this defect might be remedied, probably without diminution of the power of the pile, by increasing the thickness of the face and leaving the dimensions of the bars the same. “On the Radiation of Heat from the Moon.”—No. II. By the Earl of Rosse, F.R.S. In a former communication to the Royal Society I gave a short account of some experiments on the radiation of heat from the moon, made with the three-foot reflector at Parsonstown, during the season of 1868-1869. I then showed :— Ist. That the moon’s heat can be detected with certainty at any time between the first and last quarter, and that, as far as could be ascertained from so imperfect a series of observations, the increase and decrease of her heat with her phases seems to be proportional to the increase and decrease of her light as deduced by calculation*. 2ndly. That a much smaller percentage of lunar than of solar rays is transmitted by a plate of glass ; and we therefore infer that a large portion of the rays of high refrangibility which reach the moon from the sun do not at once leave the moon’s surface, but are first absorbed, raise the temperature of the surface, and afterwards leave it as heat-rays of low refrangibility. 3rdly. That, neglecting the effect of want of transparency in our atmosphere, and assuming, in the absence of any definite informa- tion on the subject, that the radiating-power of the moon’s surface is equal to that of a blackened tin vessel filled with water, the lunar surface passes through a range of 500° F. of temperature ; conse- quently the actual range is probably considerably more. Athly. The proportion between the intensity of sunlight and moon- light, and between the heat which comes from the sun and from the moon, as deduced from those observations, agreed as nearly as could be expected with the values found by independent methods, and for this reason might be considered the more reliable. During the past season these observations have been continued : but much time has been spent in trying various modifications of the ap- paratus ; and a satisfactory comparison of observations made on dif- ferent nights, under different circumstances, has been impossible. However, by more numerous and more complete experiments, made alternately with and without an interposed plate of glass, the second conclusion arrived at during the previous season has been to a great extent confirmed. The following Table gives the values found for the percentage of the moon’s heat which passes through glass :— * See Phil. Mag. vol. xxxviil. p. 317. The Earl of Rosse on Lunar Heat-Radiation. 370 : Percentage Date of ae Altitude of | of moon’s heat observation. opposition. the moon. | transmitted by glass. °o ie) 15 13°3 le April 15th, 1870 5 204 16:5 II. 24. 16°6 Il. ' 15 14°5 if merit r6th .....5..- 15 { 24 14°6 rT ; 194 10°0 I. mori 17th .:....... 31 { A de ik March 13th ...... 50 50 71 February roth ... 66 44 84 February gth...... 77 32 9°3 . 44 II‘ Fr. April gth eacecsens 81 { 16 110 TI. prik Sth .iisi:. 93 30 12°0 March 8th......... 109 27 13°90 Mean = 11°88. The same plate of glass which was used in I. and II. on April 15th, and in the experiments on the two following nights, was tested for the solar rays, and the following values of the percentage of heat transmitted were obtained :— se) 05001 SSG Tens ee, RS = Ee RR Pi PUPIL GU esaa vate. Me crcanet Se cdetveescens 89°3 84°3 87°1 Meanonw April’ r8th.. oo... i cc...ectee es 86°38 The piece of glass used on the other occasions, instead of being placed at six or eight inches from the pile, was laid against the end of the protecting cone, or about half an inch from the face of the pile. When it was placed in this position and tested for solar rays, an increase of deviation in the proportion of 1*1 to 1 was obtained, owing to the “bottling up’ of the sun’s rays as in an ordinary greenhouse, and the keeping off of currents of air. It seems therefore to be clearly proved that there is a remarkable difference between the sun’s and the moon’s heat in regard to their power of passing through glass. The amount transmitted varies from night to night ; and in the later observations the value was generally larger than in the earlier ones. Possibly this may have arisen from the formation of a slight and imperceptible film of moisture on the surface of the glass, which was much more unlikely to form during the much shorter period* of exposure to the night air in the later observations. * About 12 minutes in place of 30 to 60 minutes. 374 Royal Society :— The experiment made during the previous season to determine the ratio between the heating-power of the moon and of the sun was repeated.with more care; and the value found, taking what appeared to be the most probable mean heating-power of full moon, as deter- mined on various nights, was Sun’s total heat et et ee ONLY Moon’s total heat See Taking the percentage of light transmitted by glass* =92 Do. do. of sun’s heat =87 Do. do. of moon’s heat = 12 ms do. of heat from a body at 180° F. = 1:6 0 i >and o4i an 7 ; Tepresent respectively the percentage of dark and luminous rays present in the moon’s radiant heat, and One and ny vor 7 the corresponding quantities for the sun’s radiant heat, we have Ox:016+7x°92 _. ee TEs ey Ee ee | ee +0 and Ros re 0'x °016+7 x 92 _.g7, l’+of tyat Dadet | Se Me = In all the foregoing experiments on lunar radiation the quantity measured by the thermopile was the difference between the radiation from the circle of sky containing the moon’s disk and that from a circle of sky of equal diameter not containing the moon’s disk ; we have obtained no information in reference to the absolute temperature of either the moon or the sky. The following experiment was therefore made with the view of trying to connect the radiation of the sky with that of a body of known temperature. The deviation due toeach degree (Fahrenheit) differ- ence of temperature between a blackened tin vessel containing hot water and subtending a given angle at the pile and a similar vessel containing colder water was first ascertained; then a similar deter- mination of that due to the difference of radiation from one of these vessels, and from a portion of sky of equal diameter, was made. The following was the result :— * All these values, except the first, were determined by experiment for the specimen of glass employed. The Earl of Rosse on Lunar Heat-Radiation. YAS Altitude | Calculated Apparent of part | difference eke ri | tempera- R k of sky of tem- Sides hi ture of piste e examined. | perature. Nasr the sky oe ee 49 23°9 55°5 31°6 Sky hazy. Bey 2ot a ee, be | ae Sky apparently black Bs 53° ze: i see and transparent ; is 2 3 5°°5 occasional light %) 4 so 47 oe clouds “ 64 26'2 44. 17°8 | : If the temperature of space be really as low as is supposed, this result seems to indicate considerable opacity of our atmosphere for heat-rays of low refrangibility. The ever varying transparency of our atmosphere has been found to be a very serious obstacle; but the much greater steadiness of the needle during the later experiments (the mean error of the last few nights’ observations having been from two to three and a half per cent. only of the whole deviation *) encourages us with the hope that, by taking advantage of favourable moments, and measuring the moon’s light simultaneously with her heat, more accurate informa- tion on this subject may soon be acquired. | The observations were examined with the view of ascertaining how far the heating-power of the moon’s rays varies with her altitude. Owing to the interference of clouds, and the limited range of altitude within which the observations were made, it is hardly worth while to give the results in detail; however, I may just say that the heating- power of the moon’s rays appears to diminish with her altitude only about one-third as fast as the intensity of the solar chemical rays as ascertained by Roscoe and Thorpe. An attempt was made to ascertain, by comparing two measure- ments of the moon’s light at different altitudes with two corresponding measurements of her heat, whether our atmosphere intercepts the heat-rays to a greater extent than the luminous rays. It was found that while the light was diminished with the altitude in the propor- tion of about 3 to 1, the heat was diminished in the proportion of about 5 to 1. In consequence, however, of much of the moon’s light and heat being intercepted by hazy clouds or eondensed vapour at the lower altitude, the experiment was inconclusive as to the effect of a transparent atmosphere on the dark rays of heat. The accompanying diagram shows the proportion between the amount of lunar heat found on various nights at various ages of the moon. There appears to be a general accordance between the varia- tion of her radiant heat with her phase and the corresponding amount of her light as deduced by calculation. * During the experiments of the previous season the mean error varied be- tween 27 per cent. and 85 per cent. or more. ts, men ‘fect. exper little after full moon. Royal Society: — | OOF o98L gO9E ORT ; Gm 098 1aege oOck OSL © Qu = ore lis) =| S e & 2) mM SI io) eS oO (0) a2) =; call ae = w 5) ® 5 mM ios) & mM < NOCW MGN WALNVAD 1SVI NOOW TIN4 Wane IMTS Se eee the maximum of heat seems to bea Mr. A. Le Sueur on the Great Melbourne Telescope. 377 Subjoined is a Table giving the dates of the various observations, with the reference numbers corresponding to those on the diagram, and with remarks on the state of the sky. Number Date of di gy observation. Remarks. ijagram. ee) April, 4th 2 32.04. II. | January 8th ..:...) No mention of cloud. PR April Ste. ss.cen- IV. | January 9th ...... No mention of cloud. Vo March’ Sth: 4.7. Extremely clear sky. Neseagril oth. ..)...: No mention of cloud. [night by a halo. __VII. | January oth - ...| Sky not good; thin hazy clouds, followed later in the VIII. | February gth...... IX. | January 11th...... Much wind. X. | February roth ...| No mention of clouds. XI. | January 12th...... Occasional small clouds, and rather hazy: _ XII. | November 19th...) Clouds producing prismatic colours round the moon, PTs) March 13th. | 44532. POE ptil 13th 000: Sky not good; fleecy clouds. [clouds. AV PaApril TAth ,...:.... Bad night ; stopped after 10 minutes, in consequence of ROVE april roth -2:::.7.. Sky very clear. XVII. | January 16th...... XVIII. | September 20th ...} Occasional clouds. XIX: | February 16th...) Sky hazy at sunset ; occasional clouds. [night. Mee | April.r6th .......:. Sky apparently not quite so clear as on the preceding ROE, April 17th... XXII. | November 22nd...| Fog and white frost, afterwards drift. XXIII, | November 23rd...) No remark about cloud. ** Observations with the Great Melbourne Telescope, in a Letter to Professor Stokes.” By A. Le Sueur. Observatory, Feb. 27, Dear Sir,—I have little more definite to tell you with reference to the star » Argis. Thinking that a larger dispersion would be of advantage, I have had a supplementary arrangement added to the spectroscope, by means of which a direct prism may be interposed between the collimator and the usual prism. With this increased dispersion, the red line keeps its place; the yellow one turns out to be slightly more refrangible than D. The green lines, which, with the smaller dispersion, were very difficult, now become almost unmanageable; this would seem to throw some doubt on their reality, as mere extra dispersion should have little effect on real lines. The direct prism being a small one, does not take in the whole of the pencil when condensed to the limits bearable by the collimator ; but as the arrangements at my disposal do not in any case admit of utilizing the full condensation, the smallness of the prism has not had any material effect. On the whole, I am now inclined to think that, with respect to Phil. Mag. 8. 4. Vol. 40. No. 268. Nov. 1870. 2C - 378 Royal Soctety :— the green lines, the appearance of the spectra is due to a character of light somewhat similar to that of a Orionis, &c.,—a spectrum of groups of dark lines, with spaces more or less free between them, producing the effect (when the light is not sufficient to bear a slit fine enough for dark lines) of a spectrum crossed by bright lines. The behaviour of the red line, however (of the blue one, being less conspicuous, I cannot speak with so much confidence), would lead to the already drawn inference that it is a real hydrogen line. I have examined other stars of about the same magnitude as n Argis; in the majority of these there is not even a suspicion of condensation in any part of the spectrum; red stars, R Leporis for instance, give a spectrum not dissimilar to that of » Argis; but the red line on none of the stars examined is so conspicuous as in 7. The weather since the beginning of this year has been more fa- vourable, so that I am able, by degrees, to increase the amount of work done. The routine work is the review of figured nebule; as might be expected, the 4 feet gives views considerably different from the C. G. H. drawings ; but at present I have nothing worthy of spe- cial mention. The light of the nebule, as they are taken up for general exami- nation, is analyzed with the prism; of those which have been exa- mined I have yet found none of which it may be certainly said that the light is not of definite refrangibilities. In irregular nebule, the bright knots even, which are so distinctly mottled as to point to a cluster condition, give out, as far as I have yet seen, light which is monochromatic, or nearly so. Acknowledged clusters, where discrete stars are plainly discernible, are of course excluded. Of the nebulosity mixed up with such clus- ters as 47 Toucan, I cannot speak with certainty ; but if the light were monochromatic, I think that (in the case particularized at least) the brilliancy would be sufficient to afford a definite impression. Would you call Lord Rosse’s attention to 1477-78 (general cata- logue) of which I enclose a diagram from measured positions? The confi- guration differs so widely from that given in the Philosophical Transac- . tions, that, with reference to the ro- tation of the two nebulous stars, it would be interesting to have the evi- » dence of any additional observations made at Parsonstown. From Mr. Huggins’s observations of the nebulee in Orion, I gather that he has seen only the three usual lines ; with a wide slit, I had lately a very strong suspicion of a fourth line, pro- bably G. I have not specially ex- IN Mr. B. Broughton’s Hzperiments on Living Cinchone. 879 amined the nebulz since; but probably Mr. Huggins will be able to give confirmatory evidence. On the night of February Ist we had a pretty brilliant auroral display. Being at work at the time, I missed part of it; but as soon as I became aware of its existence I applied the spectroscope. At moments four lines already known were easily visible, the chief line being remarkably brilliant. A much narrower slit than that used could have been borne at the time of maximum display, which, how- ever, lasted only a few moments. I was intent on measuring the lines, as at the time I had,no published definite information with reference to other than Angstrom’s special line; but at moments light was seen at the red end of the spectrum sufficiently bright to leave a distinct impression of colour; when, however, special atten- tion was devoted to that part of the spectrum the aurora had greatly diminished in brilliancy, so that I was unable to make out whether a red line existed, or whether there was a general spectrum at the red end. I incline to the latter opinion, and put it down to the rose- coloured arc; this arc, however, which seemed pretty brilliant after the streamers had disappeared, did not then give a visible spectrum. Probably this phenomenon has been observed before to better pur- pose ; but I cannot find mention thereof in published accounts. Yours truly, A. Le Sueur. ** Chemical and Physiological Experiments on Living Cinchone.” By J. Broughton, B.Sc., F.C.S., Chemist to the Cinchona Planta- tions of the Madras Government. The memoir describes the principal scientific results which have been obtained during the last three years, in the course of chemical work on the Neilgherry Cinchona Plantations. The chemical characteristics of the various parts of the Cinchona plant are described. The condition in which the alkaloids are met with in the living bark is shown to be that of a slightly soluble tan- nate existing in the parenchymatous cells. The order of formation of the alkaloids is shown to be, Ist, un- crystallizable quinine; 2nd, crystallizable quinine; 3rd, cinchoni- dine and cinchonine. Reasons are adduced for thinking that the alkaloids are really formed in the tissues in which they are found. The effect of the solar rays falling on the bark, either while living on the tree or when separated, is shown to be prejudicial to its con- tained alkaloids. The effect of shielding the bark artificially, and the influence of elevation of the site of growth, are detailed. The question as to whether the alkaloids are substitutes for the ‘mineral bases is discussed, and a series of experiments is described, which combine to show either that such substitution does not take place, or does so only in a very partial degree. 2C2 380 Geological Society :— GEOLOGICAL SOCIETY. [Continued from p. 310. } April 13th, 1870.—Sir P. de Malpas Grey Egerton, Bart., M.P., F.R.S., Vice-President, in the Chair. The following communications were read :— 1. A letter from Dr. Gerard Krefft, dated Sydney, 29th January, 1869, accompanying a model of the left lower incisor of Thylacoleo carnifex, Owen, and the original fragment from which the model was made. Dr. Krefft also referred to the fossil remains of Herbi- vorous Marsupials in the Museum at Sydney, which included, ac- cording to him, besides a great number of Wombats (Phascolomys), many wombat-like Kangaroos or Wallabies (Halmaturus). He pro- posed to divide the Kangaroos into the following groups :— (1) Macropus, dentition as in Macropus major. (2) Halmaturus, with the premolar permanent, divided into two subgroups :— a. True Wallabies, with the premolars long, narrow, and com- pressed, and the rami of the lower jaw but slightly anchy- losed. 6b. Wombat-like Wallabies, with the premolars compact, rounded, and molar-like, and the rami of the lower jaw firmly anchylosed. Illustrative sketches and photographs accompanied this paper. 2. “On the Fossil Remains of Mammals found in China.” By Prof. Owen, LL.D., F.R.S., F.G.S. The specimens of teeth described by the author were obtained by Robert Swinhoe, Esq., late H. M. Consul at Formosa, chiefly by purchase in the apothecary’s shops at Shanghai. They included two new species of Stegodon (named S. sinensis and S. orientalis), a new Hyena (H. sinensis), a new Tapir (Tapirus sinensis), a new Rhino- ceros (fR. sinensis), and a species of Kaup’s genus Chalicotheriwm (C. sinense). The author remarked that the whole of these teeth presented an agreement in colour, chemical condition, and matrix which led to the conclusion that all belonged to the same period. But for the presence of the Chalicotherium, they would have been referred either to the Upper Pliocene or to the Postpliocene period. The author did not consider that the occurrence of one Anoplothe- rioid species need affect the determination of the age of these fossils, especially as Chalicotherium departs in some respects from the type Sia Anoplotherium, and is not known from deposits older than the {iocene. Mr. Busk on the Species of Rhinoceros from a Fissure-cavern. 381 3. “Further discovery of the Fossil Elephants of Malta.” By Dr. A. A. Caruana. Communicated by Dr. A. Leith Adams, F.G.S. The author described a new locality in Malta in which the re- mains of Elephants had been found recently—the Is-Shantiin fissure at the entrance of Micabbiba. It was filled with a compact deposit of red earth containing fragments of limestone, many teeth and fragments of bones of Elephants, associated with bones of large birds. The author found three small shark’s teeth, and a small tooth which he regarded as belonging to Hippopotamus. He indi- cated the nature of the teeth and bones of Elephants found by him in the newly discovered fissure. The whole of the five localities in which ossiferous fissures have been discovered are in the same part of the island ; and the author concluded with some remarks upon the geological conditions under which the remains of mammalia must have been accumulated, and upon the probability that a connexion then existed between Malta and Africa. In a note appended to the paper Dr. A. Leith Adams stated that the supposed tooth of Hippopotamus was a germ true molar of one of the pigmy elephants, and that the Shark’s teeth have probably been derived from the Miocene deposits. April 27th, 1870.—R. A. C. Godwin-Austen, Esq., F.R.S., Vice-President, in the Chair. The following communications were read :— 1. “On the Species of Rhinoceros whose remains were discovered in a Fissure-cavern at Oreston in 1816.” By George Busk, Esq., Ph.5., £.G.S. The object of this paper was to show that the Rhinoceros whose remains were discovered by Mr. Whidbey in a fissure-cavern at Oreston, near Plymouth, in the year 1816, and described by Sir Everard Home in the ‘ Philosophical Transactions ” for 1817, belonged, not as has hitherto been supposed by every one except the late Dr. Falconer, to Rhinoceros tichorhinus, but to Rh. lepto- rhinus, Cuv. (f. megarhinus, Christ.). The remains in question are in the Museum of the Royal College of Surgeons, and consist of between thirty and forty more or less broken portions of the teeth and of numerous bones of the skeleton. The greater number being hardly in a condition to afford satisfactory diagnostic specific characters, the remarks in the paper were limited to the teeth and to a perfect metacarpal bone, which appeared amply sufficient for the purpose. The teeth mainly relied upon were the first or second upper molars (m’ or m’) of the right and left sides. Both the teeth were broken, but what was wanting in one was supplied by the other. The characters exhibited were shown to be unlike those of 2. ticho- rhinus, and quite in accordance with those of LR. leptorhinus. These were the thinness and smoothness of the enamel, the configuration of the dorsal surface, the form and size of the columns, and the dis- 382 Geological Society :— position and relations of the “ uncus” and “ pecten” (“ crochet” and ‘anterior combing-plate,” and the consequent absence of the cha- racteristic ‘‘tichorhine pit” or fossette. The less strongly marked characters by which the teeth could be distinguished from those of R. hemitechus, Fale., and &. etruscus, Fale., were also pointed out: The metacarpal bone selected for the illustration of the diagnosis is 94 inches long, and remarkable for the compression of the shaft and its comparative slenderness, as contrasted with the same bone in R. tichorhinus, specimens of which were exhibited on the table, and which, in no case within the author’s knowledge, ever exceeds 74 or 8 inches in length, and is proportionally much thicker than in ft. leptorhinus or any other extinct species. The size and form of the bone also showed that the species could not be either 2. hem2- techus or RR. etruscus; for although the means of direct comparison with the third metacarpal of those species did not, to the author’s knowledge, exist in London, its probable general dimensions and proportions could be deduced from those of the corresponding meta- tarsal, of which bone numerous specimens were available. It was further shown that the Oreston metacarpal exactly corresponded with those of R. leptorhimus, from Grays Thurrock, in the British Museum. The determination of the species appears to be of considerable interest, inasmuch as it affords an additional instance of the occur- rence in England of the great southern Rhinoceros. This is also the only example of the discovery of that species, except in river or other deposits, either in this country or on the Continent. 2. “On two Gneissoid series in Nova Scotia and New Bruns- wick, supposed to be the equivalents of the Huronian (Cambrian) and Laurentian.” By H. Youle Hind, Esq., M.A. This paper described the relations of two gneissoid series in Nova Scotia and New Brunswick, which have hitherto been regarded as intrusive granites and syenites, and have been thus represented on the published geological maps of those provinces. The author con- sidered that these gneisses were in the main of Laurentian age, the Huronian or Cambrian rocks occurring only in patches over a vast area of Laurentian porphyroid gneiss. The old gneiss was stated to be brought to the surface by three great undulations between the Atlantic coast of Nova Scotia and the Laurentian axis of America north of the St. Lawrence. These axes were rudely parallel to one another; and in the troughs which lay between them the Silurian, Devonian, and Carboniferous series occurred in regular sequence, the New Brunswick Coal-field occu- pying the central trough. On the line of section, in the troughs to the north-west and south-east, the Lower Carboniferous was stated to be the highest rock series which has escaped denudation. The gold-bearing rocks of Nova Scotia are of Lower-Silurian age, and rest either on Huronian strata or, where these had been re- moyed by denudation, on the old Laurentian gneiss. The gold is My. E. Billings ons ome Lower-Silurian Trilobites. 383 found chiefly in beds of auriferous quartz of contemporaneous age with the slates and quartzites composing the mass of the series, which, in Nova Scotia, is 12,000 feet thick; and the auriferous beds are worked, in one district or another, through a vertical space of 6000 feet. Besides auriferous beds of quartz, intercalated beds and true veins are found to yield gold, and are worked. A series of sharp and well-defined anticlinals ridge the province of Nova Scotia from east to west, while another series of low broad anticlinals of much later date have a meridional course. At the intersection of these anticlinals the gold-districts are situated, be- cause there denudation has best exposed the upturned edges of the auriferous beds of quartz, and rendered them accessible, sometimes exposing also the underlying gneiss. Plans of Waverley and She:- brooke gold-districts were exhibited, showing the outcrop of the edzes of the slates and auriferous beds of quartz in semielliptical forms, with the gneiss at the base of the ellipse. On this ground it was suggested that a correct mapping of the gneisses of Nova Scotia would have an important influence on the development of the mineral resources of the province. A plan of some of the lodes in the Waverley gold-district showed the result of operations in 1869, subsequently to the publication of a geological map and sections of the district furnished to the De- partment of Mines by the author in 1868. Citations were made from the annual reports just issued of the Chief Commissioner of Mines and of the Inspector of Mines, confirming the correctness of the author’s plans exhibiting the geolozical structure of Waverley, which is a type of all the Nova Scotian gold-districts. May 11, 1870.—Joseph Prestwich, Esq., F.R.S., President, in the Chair. The following communications were read :— 1. “ Notes on some specimens of Lower-Silurian Trilobites.” By K. Billings, Esq., F.G.S., Palzeontologist of the Geological Survey of Canada. (1) The author first described a specimen of Asaphus platyce- phalus, of which not only was the hypostome preserved i situ, but also the remains were more or less well preserved of eight pairs of legs, corresponding with the eight segments of the thorax, to the under- side of which they had been attached. The appendages take their rise close to the central axis of each segment; and all curve for- wards, and are thus most probably ambulatory rather than natatory feet. They appear to have had four or five articulations in each leg. Three small ovate tubercles on the pygidium may perhaps indi- cate the processes by which the respiratory feet were attached. Mr. Billings referred to the large number of Tribolites which haye been examined, and expressed his belief that only the most perfectly 384 Geological Society :—Dr.J.W. Dawson on the Structure preserved specimens are likely to have the organs on the underside preserved. (2) Mr. Billings next deseribed the doublure or pleura in the Tri- lobites, comparing it to that of Limulus. He then proceeded to describe a row of small scars and tubercles on the underside of the pleure, to which both Dr. Volborth and Dr. Eichwald believed soft swimming feet or hard horny legs had been attached. As these were first seen by Dr. Pander in a Russian Trilobite, Mr. Billings has called them “ Panderian organs.” He thinks, soft natatory appendages may have been attached to these scars. (3) Mr. Billings directed attention to the Protichnites and Ch- mactichnites, which he thinks may now be referred to Crustacea, belonging to the division T'rilobita. (4) Finally, Mr. Billings described a section of a, rolled-up Caly- mene senaria, the interior Eats of which appears to be full of minute ovate podien from J, to ;4, of an inch in diameter. These small ovate bodies the author believes to be eggs. 2. * Note on the palpus and other appendages of Asaphus, from the Trenton Limestone, in the British Museum.” By Henry Wood- ward, Esq., F.G.8., F.Z.S. Mr. Woodward, when comparing the Trilobite sent over by Mr. Billings with specimens in the British Museum, presented by Dr. J. J. Bigsby, F.R.S., discovered, upon the eroded upper surface of one of these, not only the hypostome exposed to view, but also three pairs of appendages, and what he believes to be the palpus of one of the maxille. This furnishes an additional fact to Mr. Billings’s most interesting discovery, besides confirming its correctness. Mr. Woodward considers the so-called “‘ Panderian organs” to be only the fulcral points upon which the pleuree move, and showed that such structures exist in most recent Crustacea. He considered that the evidence tended to place the Trilobita near to, if not in, the Isopoda Normalia. He remarked that the prominence of the hypostome reminded one strongly of that organ in Apus, and suggested that we might fairly expect to find that the Trilobita represented a more generalized type of structure than their representatives at the present day, the mo- dern Isopoda. 3. “On the Structure and Affinities of Stgllaria, Calamites, and Calamodendron.” By J. W. Dawson, LL.D., F.R.S., F.G.S., Prin- cipal and Vice-Chancellor of M‘Gill University, Montreal. The object of this paper was to illustrate the structure and affi- nities of the genera above named, more especially with reference to the author’s previous papers on the “ Structures in Coal” and the “ Conditions of Accumulation of Coal,” and to furnish new facts and conclusions as to the affinities of these plants. Wih reference to Sigillaria, a remarkably perfect specimen of the and Affinities of Sigillaria, Calamites, andCalamodendron. 885 axis of a plant of this genus, from the Coal-field of Nova Scotia, was described as having a transversely laminated pith of the Sternberyia type, a cylinder of woody tissue, scalariform internally and reticu- lated or discigerous externally, the tissues much resembling those of Cycads. Medullary rays were apparent in this cylinder; and it was traversed by obliquely radiating bundles of scalariform vessels or fibres proceeding to the leaves. Other specimens were adduced to show that the species having this kind of axis had a thick outer bark of elongated or prosenchymatous cells. The author stated that Prof. Williamson had enabled him to examine stems found in the Lancashire Coal-field, of the type of Binney’s Stgillaria vascu- laris, which differed in some important points of structure from his specimens, and that another specimen, externally marked like Sigillaria, had been shown by Mr. Carruthers to be more akin to Lepidodendron in structure. These specimens, as well as the Szgz- laria elegans illustrated by Brongniart, probably represented other types of Sigillarioid trees ; and it is not improbable that the genus S?- gillaria, as usually understood, really includes several distinct generic forms. The author had recognized six generic forms in a previous paper and in his “Acadian Geology ;” but the type described in the present paper was that which appeared to predominate in the fossil Sigillarian forests of Nova Scotia, and also in the mineral charcoal of the coal-beds. This was illustrated by descriptions of structures oc- curring in erect and prostrate Stgillaric, on the surface of Sternbergra- casts, and in the coal itself. The erect Calamites of the coal formation of Nova Scotia illus- trate in a remarkable manner the exterior surface of the stems of these plants, their foliage, their rhizomata, their roots, and their habit of growth. Their affinities were evidently with Hquisetacee, as Brongniart and others had maintained, and as Carruthers and Schimper had recently illustrated. The internal structure of these plants, as shown by some specimens collected by Mr. Butterworth, of Manchester, and soon to be published by Prof. Williamson, showed that the stems were more advanced in structure than those of mo- dern Hquiseta, and enabled the author to explain the various ap- pearances presented by these plants when the external surface is preserved, wholly or in part, and when a cast of the internal cavity alone remains. It was further shown that the leaves of the ordinary Calamites are linear, angular, and transversely wrinkled, and differ- ent from those of the Asterophyllites properly so catted, though some species, as A. comosus, Lindley, are leaves of Calamites. The Calamodendra, as described by Cotta, Biyney, and others, and further illustrated by specimens from Nova Scotia and by several interesting and undescribed forms in the collection of Prof, Williamson, are similar in general plan of structure to the Cala- nutes, but,much more woody plants—and if allied to Equisetaces, are greatly more advanced in the structure of the stem than the mo- dern representatives of that order. Specimens in the collection of Prof. Williamson show forms intermediate between Calamites and 386 Geological Society :— Calamodendron, so that possibly both may be included in one family ; but much further information on this subject is required. The tissues of the higher Calamodendra are similar to those of Gymno- spermous plants. The wood or vascular matter of the thin-walled Calamites consists of multiporous cells or vessels, in such species as have been examined. In conclusion, a Table was exhibited showing the affinities of Si- gillariw, on the one hand, through Clathraria and Syringodendron with Lycopodiacee, and, on the other hand, through Calamodendron with Equisetacee ; while in another direction they presented links of connexion with Cycads and Conifers. 4, «Notes on the Geology of Arisaig, Nova Scotia.” By the Rev. D. Honeyman, D.C.L., F.G.S. The author referred to a previous paper on the Upper Silurian rocks of Nova Scotia, which he stated appeared to him now to be generally repetitions of his Arisaig series. He noticed the occur- rence of fossils in one of the beds previously supposed to be almost destitute of organic remains, and described the occurrence, in Arisaig township, of a band of crystalline rocks which appeared to contain Eozoon and were probably of Laurentian age. A note from Prof. Rupert Jones, giving an account of the fossils referred to by Dr. Honeyman, was also read. May 25th, 1870.—Joseph Prestwich, Esq., F.R.S., President, in the Chair. The following communications were read :— 1. “Contributions to a knowledge of the Newer Tertiaries of Suffolk and their Fauna.” By HE. Ray Lankester, Esq., B.A. (1) The Suffolk Bone-bed and the Norfolk Stone-bed.—The author pointed out that the recognition of the distinction of these two de- posits from the overlying shelly crags was an important step in the determination of the history of these beds. He combated the notion that the Bone-bed and Stone-bed were identical in their contents, and especially dwelt on the differences of the mammalian fauna found in the two. The late Dr. Falconer’s views, hitherto prevalent, con- sisting in regarding the fauna of the Suffolk Bone-bed, Norfolk Stone-bed, and Forest-bed as all of one and the same history and extent, he most strongly opposed. thinoceros Schleiermachert, Tapirus priscus, Hipparion, Hyena antiqua, and a well-defined Miocene Mastodon (Fauna 1) had been found in the Bone-bed be- low the Suffolk Crag—the first three in some abundance, but never in the Stone-bed or Forest-bed of Norfolk. They belonged to a different fauna from that indicated by the other mammals common to the Bone-bed and Stone-bed (Fauna 2), viz. Mastodon arvernen- sis, Equus sp., and certain forms of Cervus (studied by Mr. Boyd Dawkins). On the other hand, the Hlephas meridionalis (Fauna 3), occurring in the Norfolk Stone-bed and in the Forest-bed, had never On the Newer Tertiares of Suffolk and their Fauna. 387 been found in the Suffolk Bone-bed. Mr. Lankester suggested that the association of the first two of these three groups of mammals in Suffolk, and of the second two in Norfolk, might be explained by the hypothesis that they succeeded one another in time, the first (late Miocene)being confined to Suffolk, and dating from before the Diestien period, since he had obtained a Mastodon tooth of the M. tapiroides form enclosed in a Diestien box-stone, the third having existed in Norfolk at a period subsequent to the Coralline Crag, but before the Norwich Crag was deposited, chiefly represented in the lower part of the Forest-bed, but also in the Stone-bed, whilst the second group of mammals had existed in both areas at an intermediate period. Mr. Lankester maintained that this was the explanation suited to the facts as they at present stand, and considered that the question was not one to be shirked. All geological inferences from paleontology rest on what is called negative evidence, and hypo- theses must be used ininvestigation. It was shown that the London clay had contributed very little indeed to the number of mammalian remains found in the Suffolk Bone-bed. Six teeth of Coryphodon and four fragments of Hyracotherium were all that could be found in the various collections. (2) The Suffolk Bow-stones.—These nodules the author had pre- viously described as being the remains of a deposit approximately similar to the Diestien or Black Crag of Antwerp, which had pre- ceded the Coralline Crag in Suffolk. An enlarged list of remains of Mollusca from these nodules was given, and a large series of spe- cimens collected by the author was presented to the Society’s Mu- seum. It was from the Diestien beds, containing Conus Dwardinii, Voluta auris-leporis, Isocardia lunulata, &c., that the Cetacean re- mains of the Suffolk Bone-bed were derived. (3) Anew Ziphioid Cetacean from the Bone-bed of Suffolk.—The rostrum (described in detail) was in the collection of the Ipswich Museum. It indicated a Cetacean of the genus Choneziphius, differ- ing from C. planirostris of Cuvier and C. Cuviert (of Prof. Owen’s recent Monograph) in having a solid projecting apex to the rostrum, and no trace of a bifid structure. Mr. Lankester had recently care- fully examined Cuvier’s original specimens in Paris, and suggested that possibly Choneziphius planirostris, C. Cuviert, this, and two other Antwerp specimens are but varieties of one species, according to age and sex. This form, however, was noted as Choneziphius Packard. (4) A new Mastodon from the Suffolk Bone-bed.—A Mastodon tooth, enclosed in Diestien matrix, and indicating a form with open and clear valleys, had been obtained by Mr. Baker of Woodbridge, and noticed by the author a year ago. He had since, in various collections, detected eight other fragments of a Mastodon, very di- stinct from M. arvernensis, and approaching M. tapiroides. Possibly the fragments indicated more than one such distinct species. The condition of these specimens and other evidence tended to associate them with the Rhinoceros Schleiermachert, Hipparion, &c. forming 388 Geological Society. a fauna quite distinct from and older than that which was indicated by Mastodon arvernensis. (5) List of Mammalian Fossils of the Suffolk Bone-bed, with refer- ence to Collections containing them, and Number of Specitmens.—The object of this list.was to furnish an idea of the actual and relative abundance of the various mammalia, and to afford those interested in the matter information as to the much-scattered materials in private collections. 2. * Notes on an Ancient Boulder-clay of Natal.” By Dr. Sutherland, Surveyor-General of the Colony. The author described the extensive occurrence in Natal of a formation which he considered to present the essential characters of Mr. Bain’s “claystone porphyry.” It consisted, of a greyish-blue argillaceous matrix, containing fragments of Granite, Guneiss, Green- stone, Clayslate, &c., often of large size, exhibited ripple-markings in some places, and in others showed a rude approach to wavy stra- tification. It rested generally upon Old Silurian Sandstones, the upper surface of which was often deeply grooved and striated. The author regarded this deposit as an ancient Boulder-clay, perhaps of Permian age. 3. “On the Distribution of Wastdale-Crag Blocks, or ‘ Shap-Fell Granite Boulders, in Westmoreland.” By Prof. Robert Harkness, RS. Gis. The author described the position of Wastdale Crag and the general distribution of the blocks of granite derived from it, and discussed the hypotheses which have been proposed to account for this distribution, and especially to explain how the blocks could have been transported to the eastern side of the elevated ground of Stainmoor. The author considered that neither of the extant hypo- theses, accounting for the transport of these blocks by the agency of a glacier or of icebergs, was tenable ; and he indicated what he re- garded as the chief objections to each of them. He suggested that their transport had been effected by the agency of coast-ice, the land being depressed to the extent of about 1500 feet, which would leave the Wastdale Crag sufficiently exposed to atmospheric action to enable it to furnish the blocks; the icefloes, serving as rafts, would suffice to convey the blocks to other parts of the coast, whilst they would not require any great depth of water to float them. [ 389 ] XLVIII. Intelligence and Miscellaneous Articles. NOTE ON SPIRAL NEBULE. BY T. S. ALDIS, M.A. “Pe following are some points connected with nebule which I have not seen noticed. The spiral structure can, of course, only be seen when we view a nebula nearly perpendicularly to its plane of rotation. The nebulz we see are selected. All those composed of denser substances have long since compacted into stars. Those which are left are of jsmall density; consequently motion in them will be slow. It may be noticed in passing, that to know the density of a nebula of known shape by the period of an outlying mass, the paral- lax of the nebulais not needed. At twice the distance, on twice the scale, with the same density the period is not altered. Now in our own system we have reason to believe* that the pla- nets thrown off the denser nebula (viz. the interior planets) were thrown off in comparatively compact portions; the planets thrown off when the nebula was rare (viz. the exterior planets) were thrown off in crescent-shaped masses or ansze, extending round some consi- derable portion of the interior mass. It is in such crescent shapes that we find the outer portions of the nebule now seen. ‘The cres- cent shape, then, of the detached body is probably a further criterion of their low density, confirming our expectation that the motion will be slow and therefore not easily detected. The spiral formation itself is easily explained. The portion left behind by the contracting nebula is of acrescent shape, the concavity embracing the central mass. As this cools, the interval between the two increases, whilst the outer slowly pursues its now free orbit. If it underwent no further change it would rotate in its periodic time, keeping its concavity constantly towards the central nebula. But it, as well as the nebula, still contracts, and in so doing acquires increased speed of rotation, and thus the foremost cusp will sweep round slowly into the central body, the hinder cusp will sweep out from it. In this way a spiral arrangement of the different detached portions will arise. Of course the foremost cusp, after swinging round a considerable angle, will fall foul of the central mass and be reabsorbed in it, and the hinder cusp, too, will merge in outer masses; so that masses which have rotated considerably will not appear as elongated masses lying across the coils of the spiral, being shorn of their length in the process, and thus the nebula will take its com- plexion from the coils which are in the earlier stages of development. Manchester Free Grammar School, October 11, 1870. * See the paper on the Nebular Hypothesis in the Phil. Mag. Oct. 1869. 390 Intelligence and Miscellaneous Articles. ON THE MOLECULAR THEORY AND LAWS OF ELECTRICITY. BY L. LORENZ OF COPENHAGEN. In a paper on the mechanical theory of heat*, M. A. Dupré has given a lower limit for the number N of molecules contained in a milligramme of water, namely Nis x 10"; that is, that the number is greater than 125 trillions. A similar though somewhat higher limit may, I think, be deduced in an en- tirely different and, as I think, very simple manner. For measuring the intensity of an electrical current I will choose the electromagnetic unit, and as unit of the quantity of electricity that which passes in a second through the section of a conductor when its intensity is equal to unity. I take, as electricity which has passed through, the sum of the positive quantities passing in the direction of the current, and of the negative in the opposite direction. The repulsion, F, of two electrical bodies with the quantities of elec- tricity e and e! and the distance 7 is then expressed in absolute units by in which a=31074 x10". Further, let the electrical tension of a body be that quantity which is required to impart to the body the unit of the quantity of electricity. If p is the electrical tension, e the quantity of electricity, pde is the work required for the communication of the electricity de, and the whole work A of the tension p and the corresponding quantity e is determined by e A= { pde. 0 If, for instance, the quantity e is uniformly distributed upon the sur- face of a sphere whose radius is 7, the tension is ae PR and the work represented by the electricity is Aa=%o= Be 7 | Oe The decomposition of a milligramme of water requires an amount “ Annales de Chimie et de Physique, vol. vii. (1866). Intelligence and Miscellaneous Articles. 391 of work which can be exerted by a certain quantity of electricity ; for the tension is diminished by acertain amount. According to Weber and others, a milligramme of water is decomposed by 107 units of current in a second, and therefore by 107 units of electricity. If we denote by N the number of molecules contained in a milligramme, and by e the quantity of electricity which each must receive and give up in order to be decomposed, then Ne=107. Further, according to Bosscha, the electromotive force of a Da. niell’s element in electromagnetic units (or, what is the same thing, the tension of the positive pole of such an element whose negative pole is connected with the earth) is equal to 10258 x 10’, a number which may also be deduced from Favre and Silbermann’s experiments. ‘The decomposition of water requires a tension 1°46 as great; if thisis denoted by P, we have P=15 x10", Let us suppose that the molecule of water has a tetrahedral arrange- ment, then in which 6 is the distance of two adjacent molecules of water, and the quantity of electricity e which a molecule has received must some- how have spread inside a spherical surface the diameter of which is ¢. The work e corresponding to this quantity of electricity wi// have now its smallest value if the electricity is uniformly diffused over the sur- face of this sphere ; for any other arrangement of the electricity would require an increased work. ‘The tension corresponding to this order will be and this magnitude must therefore be smaller than the actual tension P resulting from another distribution of the same quantity of elec- tricity. ‘Thus we get 2a°e f)

that is generated in m when urged through a space dv by the action of a force P against a resistance Q. If P is The Rev. J. M. Heath on the Principles of Thermodynamics. 481 2 Pekin ain : equal to Q, as in the case we are considering, a 3s nothing ; that is, no vis viva is generated in a body by the action of two equal and opposite forces. I do not know how Mr. Ran- kine, and those whose opinions he shares, explain this fact consistently with their belief that it is under these conditions, and these only, that P accelerates molecular motions and there- fore generates heat, and does not store up energy in Q. But, “speaking under all reserve,’ I suppose that they con- trive to continue to attribute the character of a dynamical equation to the equation (P—Q)dv=0 which it had when 2 it retained its full form (P—Q)dv= ae and imagine that P does drive the body m along the length 6v against all the efforts of Q, and that it is in doing this that it generates heat. But if this is the view of any one, I think that person will not see the truth in this matter very clearly until he has discarded it. If P could by any possibility do any one thing which Q could not prevent, then the motion P would communicate to m would be accelerated, not uniform, as it isassumed to be. Those, if there are any, who deliberately maintain such an opinion as this, have not observed that (P—Q)6v is no longer the equation of vis viva at all, but has become the statical equation of virtual velo- cities, and that in that equation the motion of m through dv is not the work of either of the two forces P or Q, but any arbi- trary possible motion derived from an external cause. In the dynamical equation the motion is due to the forces in action. In the statical equation it is independent of and unaffected by those forces; and the supposed case of work done is a case of statics only and not of dynamics. I rely upon this, therefore, for the proof of one half of my assertion, viz. that no acceleration, and therefore no heat, is generated by the action of forces which are in equilibrium, and subject to the equation of virtual velocities, or, in other words, of forces in that condition in which they are said to do work. Mr. Rankine has adduced a mathematical demonstration, de- rived from the theory of the collision of elastic bodies, which he relies on as a positive argument on the other side. What I have just now given is a direct and positive proof that the force above the piston cannot accelerate, so long as it is equilibrated by the resistance below. Mr. Rankine’s argument is, in form, equally direct and positive to prove that it does. I shall simply point out a very important mistake which vitiates the whole of his proof; and unless he can maintain that his reasoning is sound, the pro- position he attempts to support must be taken as disproved. His mistake is this. He represents the piston, in fact, as imparting 432 The Rev. J. M. Heath on the Principles of Thermodynamics: vis viva to the particles without losing any of its own—contrary to the principle which he himself appeals to, that of the conser- vation of force. He finds + (w+v) for the velocity of the particle relatively to the piston after impact; and to get the absolute velocity of the particle, he adds this to u, the velocity of the piston before the impact, forgetting that that velocity has been altered by the impact. The consequence of this oversight is that the velocity of the centre of gravity of the two bodies, and also the sum of their vis viva, are both greater after impact than before it—results impossible according to the true laws of impact. I claim, therefore, at least for the present, to say that Mr. Ran- kine has failed to prove that his proposition is true, and that I. have tendered a proof, as yet uncontroverted, that it is false. I will now pursue the remainder of the main argument, and examine the contrast between my own opinions and those repre- sented by Mr. Rankine, as to cases where the force meets with no resistance, and does, therefore, no work. When Q=0, the 2 general equation of vis viva takes the form Pév= = ; and it is obvious that in this case all the force is employed in producing acceleration, and none of it in “storing up energy.” All the force, to use the ordinary language of mechanics, is employed dynamically, or is doing dynamical work, and none is producing statical work, which is pressure. Ifa gun-barrel is placed ho- rizontally and no friction or atmospheric resistance acts to resist the motion of the ball through its length, the vis viva it has at the muzzle measures the expenditure of the internal energy of the exploded charge, which has become externalized, and is now no longer internal energy in the gas, but actual energy of motion in the bullet. All this, therefore, is energy lost to the gas. But, say the thermodynamists, this gas has met with no resistance, done therefore no work, and can have lost no heat. Have I mis- represented them? Or how do they explain such a monstrous conclusion ? Lastly, I will take the equation in its general form, where forces are employed in both the ways that we have now consi- dered separately, viz. both statically and dynamically, in pro- ducing both pressure and motion. The use of this equation, properly treated, will be to enable us to distinguish these forces into two groups, which, as Mr. Rankine tells us, is the business of thermodynamics, but which I contend has not as yet been properly done. 2 The equation (P—Q)dv =" may be written (P—Q'+ Q'—Q)ov= “on The Rev. J. M. Heath on the Principles of Thermodynamics. 433 And this, again, if we suppose Q'=Q, may be resolved into two separate equations, a statical one, - RO oe a, 3 eee) and a dynamical one, mov? (P—Q’))d0= gy ge eee fa eee (2) Whenever, therefore, P is not equal to (here supposed greater than) Q, we may resolve it into two parts, Q'=Q, which is therefore the reaction of the lower surface of the piston equal and opposite to the pressure of the gas below, and P—Q’, the remaining part of P, which acts upon the particles of the gas as if they were perfectly free. The effect of P—Q! upon the gas is therefore wholly dynamical ; i¢ does not alter the pressure, and its entire effect is the generation of motion. Thermodynamists teach (as far as I may venture to speak of teachings which I can give no mental assent to, and may therefore unintentionally mis- represent in consequence of misunderstanding them) that the whole gain of heat is determined by the first, or statical one, of our two equations. The force Q’ (part of P) presses down the _ piston through dv against the resistance Q, and the work done is Qov, and it is done by Q’,a part only of P; and the remainder, P—QQ’, being an unresisted force, has no effect either on the work done or on the gain of heat. I think this is a true repre- sentation of what they would say, because it appears to me to be what they must say if the case is reversed, and we consider, in- stead of a condensation by piston, the case of expansion, as the discharge of a bullet from a gun-barrel. If P is considered to represent the explosive force of the charge of a gun, and Q the resistance arising from friction, the weight of the bullet, and the pressure downwards of the external air, then Q is a fixed quan- tity, and the whole energy Pov expended can do no more work than Qév; that is to say, that the largest charge that can be put into the gun can do, technically, no more work, and can therefore expend no more heat, than that small charge Q! which is just able to counterbalance Q, so that the ball may move uni- formly along the barrel and fall to the ground when it reaches the muzzle. In this case I apprehend thermodynamists must relegate the excess of gas-force, P—Q’, over the resistance, into that group which we have already discussed, of forces which do no work and exhaust no heat. The truth is, I have never seen anywhere any recognition among writers on this subject of the case of unequal forces acting in this way in condensing or in expanding the gas ; and although the opinion is wholly untenable, I believe that the general con- ception is, at all events when the load on the piston descends 434 Mr. R. Moon on the Equation of Laplace’s Coefficients. and condenses, that the reaction of the gas is always equal to the pressure upon the piston, whatever it may be. That this opi- nion, however, is wrong is evident from this, that if the pressure of the gas were always equal to the external pressure put upon it by the piston, the gas would never yield and be condensed by the descent of the piston, but would continue to sustam it. It appears to me to be certain that the internal pressure of a gas is never avy thing else than that given by Mariotte’s law as de- pending upon the density and the temperature only, and that any additional external force applied to its surface acts dynami- cally, and not statically, upon it. LILI. On the Equation of Laplace’s Coefficients. By RK. Moon, M.A., Honorary Fellow of Queen’s College, Cambridge*. Ss Bat equation of Laplace’s coefficients has attracted the attention of three distinguished English mathematicians, all of whom within a comparatively brief space have passed from the scene—the late Judge Hargreave, Mr. Boole, and Professor Donkin. Having adopted Laplace’s method of transformation and re- duction, Mr. Hargreave gave, in the Philosophical Transactions for 1841, the first solution of the problem im finite terms. One peculiarity of this method is that the equation actually integrated by it is not that which was originally proposed, but a derivative from the latter, the problem solved being in fact vastly more general than that proposed for solution—a circumstance of which the solution obtained by it affords ample proofy. Proceeding by the method of separation of symbols of opera- tion from those of quantity, Mr. Boole, by each of three indepen- dent methods, arrived at an expression for the integral; and one of great elegance, obtained on the same principle, was given by Professor Donkin in the Philosophical Transactions for 1857. In a paper published in the Philosophical Magazine for July last I showed that the equation d?z d*z d*z dz dz Vat gat? aaa +T ap + Pie er Pies axel) where R, 8S, T, P,Q, U are functions of 2 and y only, in the cases which are not amenable to Monge’s method will always have an integral in which z is represented by a series (finite or in- finite according to circumstances) of the form z=Ay(u) +A, | dux(u) +A, | f du®x(u) + &e., * Communicated by the Author. _ For instance, the expression thus obtained for the fiftieth coefficient involves upwards of fifty arbitrary functions. Mr. R. Moon on the Equation of Laplace’s Coefficients. 435 or by a pair of such series; where y is arbitrary, vis determined by the equation ay +84 7 +75 : A seit Nese, Ay= —e JS | da ye Stee, A,= —e—/be { de eyoes ™, O= it &e. &ce., where d*r Uu d? au “ d*u du du A du Se : sc ae d? a4 d?A d?A dA ie du du ? ehT + ay ad?A, a?A, ee dA, dA, 1 dat ee dx dy piles dy? das da Re DA, Ve >= du 5) Rass &e. &e. The equation of Laplace’s coefficients may readily be inte- grated by this general method, some of the peculiarities of which are well illustrated by its application to that equation, of which it probably offers the simplest solution which is obtainable. Retaining the original spherical coordinates, the equation may be written d*w dw = dg? + sin? 0 Te + sin 6 cos 6 jet”: n+1.sin?@.0; and putting @ and ¢ for # and y respectively in the preceding formule, we shall find ~ Inthe paper above referred to, I have stated ‘‘that no constants are to be introduced ”’ in effecting the integrations here indicated. ‘This is true so long as in (1) we have U=0; but where this does not hold, the omission of the constants would greatly curtail the generality of the result, as a glance at the mode in which each of the quantities A,, A,, &c. is derived from its immediate predecessor will at once show, 436 Mr. R. Moon on the Equation of Laplace’s Coefficients. me 0 ‘y= +h V7 —l +log,( tan 5), B=0, n= 4(sin — + cos 0 ee +n.n+l1sin 6. A), a? A, dA ae Y= 4(sin 0a 1e ++ cos 0 7p thentl sin. A), &e. &e., whence we have 1s Waal Ay=— frdo=—4(sin oa +n.nt1fsind.A. dd ), ; Ag=— J yd0= —4(sin oe +n nl {sin 6.A,.d0 : (2) A= — \y,d0= —3(sin gin n+1 {sin 6.A,.d0 ) | &e. &e. ; or, substituting for A and performing the integrations, a : fous Belbsnh 008 +e, } 1 nent (n.nt1— ee 9 n.n+l As= 546 ( = oui Ae0s? 6 4 e¢e i att eosO+ on |, od a (WS) er 1.2)(n.n+1—2.3) 0.89 | (os | ens n.n+1(n.n+1—1.2) Ae “2 ae oo ee r L +t(e.n.n4+l(n. pedb= OT. 2) +e,.n.n+1) cos +e, &e. | &e. If the condition be imposed that the series shall terminate, it may be satisfied by means of the constants introduced in the sub- sidiary integrations. * JTnstead of taking for the base of the arbitrary function the above value of u, we may take e+” for the base where wu has the above value, the form so obtained being identical with that given by Professor Donkin. Its adop- tion, however, adds materially to the complexity of the result. Mr. R. Moon on the Equation of Laplace’s Coefficients. 437 To effect this, let A,, be the coefficient of the last term of the series for w; then from what has preceded it is evident that we may assume A, = Gn, COS OP day 1 COS ae + dm—2 cos O|"~* + &e., where @n, d,_1, &c. are constants; and since by hypothesis A,-1=0, the formule (2) give us 0=sin 9 tn.ml fsinO.A,, dO. The substitution in this equation of the above expression for A,, gives O=man +1 cos O\"*) +m—lan_, cos 6!” + m—2dm_s cos 0" + m—3am_3 cos O|"~" + &e. — May, cos O!"—' —m—1dm_— cos 6" ~" + &e. ws = = Sahel cos 6"*! — cos 6|” cos |” —n.n-+la,, ay n.n+la,_ —2.N+ Ldn» 4 ~~ alm—2 —n. n+ remnea ate &e. 3 whence we derive the equations 0=(m— Ce anes m+ 1 0=(m—1 as _ Dee 0=(m—2— cS 0=(m—3— u _- Am—3— M— lan}, &e. &e., and, ultimately, the following, viz. :— m=n, Om =0, n.n—|] n-2= eS po ; n.n+1—n—1n—2- : ae, oan n.n—ln—2n—3 m—4— ee] (n.n+1—n—1Ln—2)(n.n+1—n—3 n—A4) &e. &e., 438 Mr. R. Moon on the Equation of Laplace’s Coefficients. from which the law of formation of the terms in the series for A, or A, 1s obvious. These being known, A,-; can be deter- mined by means of the equation A,= —4(sin —- +n. n+1 fsin @Ayd8); or O=2A,-+ sin 0 so +n.n+ 1 fsin 6 A,_d0 ; cual Cea) for, from what has preceded, it is evident that we may assume An—1= 5,1 cos 6|"~* +5,_3 cos O"~9 + bn—s—cos0|"° + &e, (where 5,_1, b,-3, &c. are constants) ; and substituting this value n (3), we shall get 0 =2a,,cos 6[” + 2an—2 cos Of”? + 2an_4 cos 6)" * + &e. 4. $,-;'cos cos 6|” +3. bnegic0s Oe pee cos O|"~* + &e. —n—1bn_; cos Ol” *>—n—3by_3 cos Ol" * — &e. cos 6|” cos6|"~ cos cos | as & | —2 =4 whence, equating to zero the coefficients of the different powers of cos 0, we derive the following: —nn+lbz_, —n.n+1b,_3 —Nn. n+ 1 bys - 2Ndn } Se Eee n.n+1—n.n—l bn-1 = 2n—2a _o—n—l n—2 b Dae = n—2 n—1 ; ‘ n.n+l—n—2n—8 ‘ (4) In AG to 3n— n—A by 3, n.n+1—n—4n—5 &c. &e. In like manner, if we assume Bra a= An—2==Cn—2 00s |"? +. ¢,_ 4008 O["-* + 6,6 cos O84 ee we may determine the coefficients Cy», ¢r-4, &c. by means of the equation at ia es ome ere si Ay1=—4(sind 10 2 4+0. n+1 fsin 6A, dO ): or O=2A,-_-1+ sin ef J ee To : 79 +n. n+1 J sin OA,_2d0 ; Mr. R. Moon on the Equation of Laplace’s Coefficients. 439 whence, proceeding as before, we find CU a, ae in ‘7-3 =--coo0lS | Cana Sat Binns, ae n.n+l—n—3n— Cr—-6= 2n— mn —5 Dn ean An 15 ey 4, n.n+1l—n—5 5n—6 &e. &e. 6 Hence, putting T for log. (tan = and yr(u) for / LO dur, x(w)» we have the following expression for w, viz. w =(a,,cos 6)" + a,» cos 0)"""+ &e.) . Wi(T+¢ Yaa ie ane Vv —1) + (bn—1 €08 O\"—' + bn_s cos 6|” *+4 &c.). ee M(T+hdV— =n +',(T—o V —1) + (Cn—» Cos 6”? + c,_4 cos O|"~* 4 &e.) . wi (T+o Vv: ent \ +p(T—d VW —1)4 &e. &e., where, if we choose to put a, =1, as we may do, we shall have a 1, ls aval on n.n+1l—n—1 n—2 : en n.n—ln—2n—3 ivi (n.n+1—n—1n—2)(n.n+1—n—8n—Ay’ an—-6= — ee SSS A ""'"'"'"'"'"— n.n—ln—2n—38n—4n—5 (n.n+1—n—1n—2)(n.n+ 1—n—3n—4)(n.n+1—n—5n—6 &e. &c., and where the constants 0,1, bn-3, &C., Cn—oy Cn—4, &C., taken in order, are determined by equations (4) and (5), &c, in terms of known quantities. 440 Dr.W.J.M. Rankine on the Meteor of Novembar 19, 1870. If n be even, the last two terms of the series will be of the form +(heos?O+k){wo-(T4+6V—l) tv (T—¢ ¥—1)} +1 POT +d V—1)4+y9 (T—d V —1)}. If n be odd, the last two terms will be + (h,cos?0 + k,cos 6) fy" (T +6 VW —1)+~9 %(T-6 V—])} tL(WP(T+¢V—-) +p (T—$V—))}, where h, k, 1; h,, kj, /; are known constants. Lincoln’s Inn, November 12, 1870. LIV. On the Meteor of November 19, 1870. By W. J. Macquorn Ranxine, C.H#., UL.D., F.RSS.L. & E. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, yi Aeataak have appeared in the Scottish newspapers of a very large and bright meteor seen on the 19th instant, about 9 p.m. Greenwich time, from Edinburgh and from Carn- wath (about thirty miles to the south-east of Glasgow). The meteor, as seen from Carnwath, is described as having passed from north-east to south-west, nearly overhead, and as having been followed by a rumbling sound after an interval of ninety seconds. In the immediate neighbourhood of Glasgow there was, on that night, a haze so thick as to conceal the stars; but the glare of light produced by the meteor was distinctly seen at 30 seconds before 9, Greenwich time. It lasted three or four seconds, and, judging by the distinctness with which it illuminated terrestrial objects, was considerably brighter than the light of the full moon. From the appearance of the sky in the quarter in which the light vanished, the luminous object seemed to disappear in a southerly direction, at an altitude less than 30°. A rumbling sound followed, after an interval which was not accurately ascertained, but is believed to have been between three and five minutes, corresponding to a distance of between thirty-six and sixty miles. I am, Gentlemen, Your most obedient Servant, W. J. Macquorn RANKINE. Glasgow, November 23, 1870. fae 7 LV. On a New Method of determining Resistances. By Tuomas T. P. Bruce Warren*. | ee following method of measuring resistances may be of interest to electricians, as it supplies a means of ascertain- ing resistances for a wide range without using a set of resistance- coils, it being necessary to have only one resistance-coil of known value. A condenser, charged from a constant battery, is discharged through a galvanometer of known resistance, shunted with an unknown resistance 2; a known resistance a is then added to the shunt, and the discharge again taken. Assuming the de- flections of the needle to be proportional to the quantities of cur- rent, it is required to determine the value of the resistance x, and also its shunt-power. Resistance of galvanometer . . . =5465 B.A. units. x @ (added toa) e',,, %.. = 3800 a Discharge, aan at shunted with w = 228 divisions. 23 ” ” a+x= 3847 ry) The multiplying-powers of the shunts will be inversely pro- portional to the deflections ; consequently BAGS +e 5465+ (w +300) | a : 71300 : 847 : 228, or 5465 + @ ia c= + (a+ a 1522, «+300 which gives for 2 500 B.A. units, and 11:93 for its shunt-power. The determination of # may be very much simplified if the gal- vanometer be first shunted with the known resistance and after- wards with the unknown resistance, or the two resistances con- jointly. Let a (the known resistance) . = 500B.A.units. Discharge from condenser with 500 unitsshunt= 228 divisions. ” v ” = 347 ” Galvanometer resistance . . . . . . =25465B.A.units. 5465 + 500 =" + #347 500 fish x 228° * Communicated by the Author. Phil. Mag. S. 4. Vol. 40. No. 269. Dec. 1870. 2G 44,2 Mr. T. 't. P. Bruce Warren on a New Method or 5465+a@, 11:93 _ oe aes a =7°'83 shunt-power of x. _ 5465 ~ 683 As this method does not involve direct completion of the bat- tery-circuit, it is adapted to the determination, more especially, of the resistances of liquids which are subject to electrolysis. If the galvanometer-needle be deflected when the terminals are immersed in a liquid, it may be brought to zero in the ordi- nary way. Such acurrent will not interfere with the results, so long as it acts without interruption. In these cases, and also for the measurement of the internal resistance of batteries, a-++# together with the liquid should be inserted as a shunt, and w afterwards varied by a known quantity. When measuring the internal resistance of a battery-cell, it may be necessary to insert a small but known resistance between its poles, so as to diminish the action of its current on the needles. The following illustration will explain this operation :— Resistance of v= = = 800 B.A. units. Resistance of galvanometer . . . . =53884 B.A. units. % battery-celly(shumted) naa ie i a added to battery-cell . = 40 ss 7 interposed between poles of battery 1 B.A. unit. Discharge from condenser, galvanometer shunted with (a+2) Rte ert ” ” ” (a +44 + 2) = 360 ” = 180 divisions. writing & for a+x2, BRA a (Cee) arte Aas + x a=40; «. a—a#7=5'2; ax and by the formula for the derived circuit, 40xxexx1_ HOE iil ae from which we obtain 6°1 B.A. units for the resistance of the cell. This method also supplies a simple means of arriving at the position and resistances of faults in insulated wires or cables. The most accurate results are obtained when the two ends of the cable or core are available for simultaneous operation. With submerged cables it will be more satisfactory to perform the tests from each end; but if this be impossible, the distant end should of determining Resistances. 4.43 be put to earth, when required, by an attendant stationed at that end. The coil or shunt of known value should be, preferably, equal to that of the conductor of the cable. The battery-power re- quired must depend on the resistances of the fault and conductor of the cable. ‘The resistance of the conductor must be carefully ascertained. In the case of iron-covered cables, it will be difficult to connect the ends of the cable to the galvanometer terminals without im- terfering with the zero-position of the needles. The needles may be deflected by a current set up between the copper con- ductor and the iron sheathing of the cable, or even by the tanks themselves. When the resistance of the fault is low, the deflected position of the needie may be taken as zero, or the needle may be set to zero by the aid of other magnets. Care must be taken that the electromotive force of this current shall be insignificant when compared with that of the testing-battery. Supposing the resistances of the galvanometer and conductor to be known, and the two ends of the cable to be led into the testing-room, the connexions will be made alternately as shown in figs. 1 and 2. Galvanometer. Galyanometer. Let R = resistance of conductor A B, o-— ae galvanometer, oS , from end A to 2, including 2, co 25 oF B to 2, including 2, x being the resistance of the fault. If a condenser, first charged from a constant battery, be dis- charged through the galvanometer shunted with R, 7, 7’ conse- cutively, the deflections will be proportional to the shunt-powers of these resistances respectively, or to G+R Gtr Gtr. a ge kg a ae 2G 2 AA On a New Method of determining Resistances. and the value for one being known, the values of the others R may be easily obtained from the observed discharges. The shunt-powers being obtained, the values for 7 and 7’ may be eliminated from the following formula, in which S = shunt- power or multiplying-powers of shunt, G S—l= R? then as r=Ar+a, “=Bet+a, r+r7=Ax+ Be + 22, or =R-+ twice the resistance of the fault. Deducting the resistance of the fault from r or 7’, the distance of the fault from either end will be obtained in units of resistance. Experiment (see figs. 1 and ay Galvanometer resistance . . . . ==5480 Beas units. Resistance of coil . . . =49°39 - Discharge from condenser, aly aaoneren hated with coil (49: 30) i= 1 Discharge from condenser, ealvanometer shunted with Az (B end free) . cae Discharge from condenser, galv aoe es shunted with Ba (A al free) , Ge: = ” Shunt values: AB=—112:0, resist. =49°39 units. Azvz=149:0 Pe ese) Pe Be= 362-0 oo Sako s Av + Br=386'8 + 15°2=52:0 52:0 —49°39=2°6; .. resist. of fault =1°3 unit. =209 7 36°8—1:3=35'5 units = distance of fault from A, 15:2 —1:3=13°9 fc i y B. Tamworth House, Mitcham Common. [ 445 ] LVI. Notices respecting New Books. Text-books of Science.—The Elements of Mechanism. By T. M. Gooveve, M.A., Lecturer on Applied Mechanics at the Royal School of Mines. London: Longmans, Green, and Co. 1870. Pp. 269. a.” is the first published of a series of Text-books designed not merely as school books, but as elementary treatises which, while strictly scientific, shall exhibit the practical applications of the theories they expound. The Series will comprise about sixteen volumes ; and though several are announced as “‘ nearly ready,’’ some time will probably elapse before the whole is completed. Itis rather unfortunate that the first published of the series, how- ever excellent in itself, should be a new edition, and not a completely new work, as we understand the remaining volumes of the series are to be. But though a new edition of a work first published in the year 1860, it is by no meansa mere reprint, but has been rewritten and greatly enlarged. In fact it contains nearly twice as much matter as the first edition. The general arrangement and scope of the two are the same, the enlargement being effected by the expansion of some articles, and the insertion of additional articles here and there. Thus :—The introduction has been expanded from seven to eighteen pages. In the first edition there is an article (156) on Hooke’s joint; this is given almost unchanged in art. 171; but there is added an article of nearly equal length (172) on the effect of interposing a double joint between the axes. The articles on the parallel motion are nearly the same in the two editions; but in the present an additional article (130) gives a brief account of the modification required to adapt the parallel motion to an engine worked by both a high- and a low-pressure cylinder; and so on in other cases. It need scarcely be added that great improvements are hereby in- troduced. ‘The work is written with great clearness and a thorough knowledge of the subject; and though essentially a treatise on a particular branch of Geometry, it will be readily intelligible to a reader possessing no more than a very moderate acquaintance with abstract mathematics. Its purely elementary character has rendered necessary a certain want of system in the arrangement ; but a reader who has mastered its contents will find it an excellent guide for making out the complicated arrangements of machinery actually in use. Should the succeeding volumes of the series preserve the same practical and elementary character, they will be most useful aids to scientific education. [ 446 ] LVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 379.] June 16, 1870.—General Sir Edward Sabine, K.C.B., President, in the Chair. r [HE following communications were read :— “ “Qn the Theory of Continuous Beams.” By John Mortimer Heppel, M. Inst. C.E. In venturing to present to the Royal Society a paper on a subject which has engaged the attention, more especially in France, of some of the most eminent engineers and writers on Mechanical Philosophy, the author feels it to be incumbent on him to state the nature of the claim to their attention which he hopes it may be found to possess in point of originality or improvement on the method of treatment. To do this clearly, however, it will be necessary to advert to the principal steps by which progress in the knowledge of this subject has been made, both in France and in this country. The theory of continuous beams appears to have first attracted at- tention in France about 1825, when a method of determining all the conditions of equilibrium of a straight beam of uniform section throughout, resting on any number of level supports at any dis- tances apart, each span being loaded uniformly, but the uniform loads varying in any manner from one span to another, was inves- tigated and published by M. Navier. This method, although per- fectly exact for the assumed conditions, was objectionable from the great labour and intricacy of the calculations it entailed. Messrs. Molinos and Pronnier, in their work entitled ‘Traité Théorique et Pratique de la construction des Ponts Métalliques,’ describe this process fully, and show that for a bridge of n openings, the solution must be effected of 3n+1 equations, involving as many unknown quantities, these equations being themselves of a complex character ; and they observe, “ Thus, to find the curve of the moments of rup- ture for a bridge of 6 spans, 19 equations must be operated on; such calculations would be repulsive ; and when the number of spans is at all considerable this method must be abandoned.”’ The method of M. Navier, however, remained the only one avail- able till about 1849, when M. Clapeyron, Ingénieur des Mines, and Member of the Academy of Sciences, being charged with the con- struction of the Pont d’Asniéres, a bridge of five continuous spans over the Seine, near Paris, applied himself to seek some more ma- nageable process. He appears to have perceived (and, so far as the writer is informed, to have been the first to perceive) that if the bending-moments over the supports at the ends of any span were known as well as the amount and distribution of the load, the entire mechanical condition of this portion of the beam would become known just as ifit were an independent beam. Upon this M. Clapeyron pro- ceeded to form a set of equations involving as unknown quantities the bending-moments over the supports, with a view to their deter- mination. He found himself, however, obliged to introduce into Royal Society. 4.4.7 these equations a second set of unknown quantities (‘‘ inconnues auat- liaires’’), being the inclinations of the deflection-curve at the points of support, and, not having arrived at a general method of eliminating these latter, was obliged tu operate in each case on a number of equations equal to twice the number of spans. M. Clapeyron does not appear, as yet, to have made any formal publication of his method, but to have used it in his own practice, and communicated it freely to those with whom he came into contact. In 1856, M. Bertot, Ingénieur Civil, appears to have found the means of eliminating this second set of unknown quantities n+ 1 in number for a bridge of m spans, and thus reducing the number of equations to n—1. Each of these equations involved as unknown quantities the bend- ing-moments over three consecutive supports, and was considered, from its remarkable symmetry and simplicity, to merit a distinctive name, that of ‘‘ The Theorem of the three Moments.” The method, however, to which this theorem is the key, is still everywhere called that of M. Clapeyron, and, as it appears to the writer, justly so, as it was an immediate and simple result from his investigations, with which M. Bertot was well acquainted. The next important advance was made in 1861, when M. Bresse, Professeur de Mécanique appliquée a |’ Ecole Impériale des Ponts et Chaussées, completed the matter of the third volume of his course, which is exclusively devoted to this subject*. M. Bresse explains and demonstrates the theorem of the three moments, at the know- ledge of which he had himself arrived from M. Clapeyron’s investi- gations, independently of M. Bertot. He then goes on to the inves- tigation of an equation of much greater generality, in which what is termed by English writers ‘“‘imperfect continuity’ is taken into ac- count, being, however, there replaced by the precisely equivalent notion of original differences of level in the supports, the beam being always supposed primitively straight; besides this the loads, instead of being taken as uniform for each span, are considered as distributed in any given manner. Having obtained this fundamental equation, M. Bresse proceeds to investigate the nature of the curves which are the envelopes of the greatest bending moments produced at each point by the most un- favourable distribution of the load in reference to it, and, finally, gives tables for the ready calculation of results in a great variety of cases, comprising most of those likely to occur in practice. During the time that M. Bresse was engaged in these researches, an Imperial Commission was formed, of which he was a member, for the purpose of devising rules applicable to practice; and the results of his labours have been the basis of legislative enactments equivalent to our Board-of-Trade regulations, prescribing the me- thods to be followed in determining the stresses in the various parts of the structure. About the same time that M. Bresse turned his attention to this * This was communicated to the Academy of Sciences in 1862, though the yolume was not published till 1865. 4.48 Royal Society :— subject, it appears also to have engaged that of M. Bélanger, who in his work entitled ‘Théorie de la Résistance et de la Flexion Plane des Solides &c.,’ Paris, 1862, gives a very complete demonstration— resulting in an equation which in one point of view is slightly more general than that of M. Bresse, as it takes in variation of the moment of inertia of the section from one span to another. In another point of view its generality is slightly less, as it deals only with loads distributed over each separate span uniformly, whereas M. Bresse . replaces the simple algebraical terms expressing these by definite integrals expressing the load as a function of the distance from one of the points of support. As far as the writer is informed, little has been done in France to advance this theory beyond the point to which it was brought by the writers last mentioned, and especially by M. Bresse; but valuable contributions to its development in reference to application to practice are to be found in the work of MM. Molinos and Pronnier above referred to, as well as in various papers by MM. Renaudot, Albaret, Colignon, Piarron de Mondesir, &c. In England little or no attention appears to have been paid to this subject by writers on mechanics till 1843, when the Rev. Henry Moseley, Professor of Natural Philosophy and Astronomy at King’s College, London, published his work on the Mechanical Principles of Engineering and Architecture. In part 5 of this work, which treais of the strength of materials, four cases of continuous beams are fully investigated, and the general case is to a certain extent discussed, the method of M. Navier being perhaps rather indicated than fully developed. Prof. Moseley’s work was altogether a most valuable contribution to engineering science, and, as far as the present subject is con- cerned, no doubt furnished the groundwork of the method applied by Mr. Pole to the solution of other particular but more complex and difficult cases. The first case which engaged the attention of Mr. Pole appears to have been that of the bridge over the Trent at Torksey, consisting of two spans of continuous tubular beams, resting on abutments and a central pier. For special reasons it had become necessary that the real conditions of equilibrium of this bridge should be in- vestigated with more than ordinary precision ; and this Mr. Pole did by a method virtually identical with that of M. Navier, though it does not appear that he had any previous knowledge of that method, except through the medium of Moseley’s work. Throughout Mose- ley’s cases, however, the load on the beam is considered as distributed uniformly over its entire length, whereas Mr. Pole had to deal with the case of different loads on the two spans, and, no doubt, had to devise the method of analysis necessary for its treatment. Mr. Pole’s paper on this subject is published in vol. ix. of the ‘ Minutes of Proceedings of Inst. Civ. En.’ 1849-50. As far as this went, however, it could hardly be considered to have advanced the theory of the subject, as M. Navier’s method included this case, and much more; but about the same time Mr. Mr. J. M. Heppel on the Theory of Continuous Beams. 449 Pole had to investigate the case of a much larger work, the Britan- nia Bridge, where he had to deal with some new conditions, which, as far as the writer is aware, were then for the first time successfully treated. These were that, besides variation of load on the different spans, their cross sections also varied, and there was imperfect continuity over the centre pier—that is to say, the points of support being supposed to range in a straight line, the beam if relieved from all weight would cease to remain in contact with them all, and would consist of two equal straight portions, forming an angle pointing upwards. The process which, for distinction, may be called that of M. Navier was skilfully extended by Mr. Pole so as to include these new circumstances; and by its means results were obtained certainly true within a very small limit, and as near the absolute truth as any existing means of treating the subject would produce. Mr. Pole’s researches on this subject are published in Mr. Edwin Clark’s work on the Britannia and Conway Bridges, 1850. Both from the clear and accurate treatment of the case and the record of the numerous and delicate observations by which the theoretical conclusions were continually verified and kept in check, they are most strongly to be recommended to the attention of engineers having to deal with works of this character. The sequence of events now compels the writer to advert to some studies of his own. In 1858-59, being then Chief Engineer of the Madras Railway, he had occasion to investigate the conditions of a bridge of five continuous spans over the river Palar. Having in India no books to refer to but those of Moseley and Edwin Clark, he found himself unable to extend the treatment of the cases there given to that of a beam with an increased number of openings and varying loads. After many attempts and failures, the same idea occurred to him which appears to have struck M. Clapeyron nine or ten years before—that if the bending-moments over the supports were known, the whole conditions would become known. Following this clue, he was fortunate enough to succeed in at once eliminating the other unknown quantities, which M. Clapeyron had been cbliged to retain in his equations for many years after his original discovery of the method, and thus to arrive at an equation precisely identical with that which had been first published in France by M. Bertot in 1856, and was known as the “Theorem of the three Moments.” This was sufficient for the immediate purpose, as the beams in question were straight and of uniform section throughout, conditions to which this theorem is strictly applicable without any modification whatever. As, however, the writer was at this time under the impression that he was using an entirely new mode of analysis, he was natu- rally anxious to check its results by comparison with those obtained in some well-known case by other means. Fortunately he had at hand that of the Britannia Bridge, perhaps the best that could have been selected ; but for this purpose it became necessary to import into 450 Royal Society :— the fundamental equation the conditions of varying sections in the different spans and imperfect continuity. This, however, presented no great difficulty ; and by means of an equation thus modified, he had the satisfaction of reproducing all Mr. Pole’s results, and thus convincing himself of the trustworthiness of the method in question. The equation thus generalized is absolutely identical with that arrived at by M. Bélanger in the work above referred to*. It would appear, then, that the theory of this subject was indepen- dently advanced to about the same state of perfection in France and in England, though as regards the development of its application to practice no doubt very much the more has been done in the former country. The writer will now advert to some inherent defects of this theory, the cure of which is the principal object of the investigation which follows. The chief one, which is admitted by all writers on the subject, is the necessity for supposing the moment of inertia of the section constant throughout each span; any more general hypothesis, it is said, would render the calculation inextricable. Still it is certain that the conclusions arrived at on the hypothesis of a constant section cease to be true if a variation of section is introduced ; and the amount of error thereby induced, though considered to be probably small, is still a matter of uncertainty. The next defect is the assumption of uniformity of load through- out each span; for although as far as rolling load is concerned no more correct hypothesis could be made, the weight of the bridge itself, if a large one, usually varies considerably in the different parts of the same span. The equation given by M. Bresse, as has been stated, provides for certain kinds of variable loads by the use of integrals ; but the writer is not aware that they have been applied, even by that author him- self, to the purposes of calculation, and it seems to him that in most cases the attempt to make such an application would be beset with difficulties. It will, however, it is hoped, be seen from what follows, that the dealing with variations of the above elements does not in fact pre- sent any very formidable difficulty, though no doubt the labour of calculation is greater; but what the writer regards as most satisfac- tory is the very small difference in the principal results in the case of the Britannia (where these variations greatly exceed in amount those usually occurring), whether obtained by the approximate method hitherto followed, or by the more rigorous one to be explained, afford- ing a strong presumption that in all ordinary cases the former method may be confidently employed without risk of any important error. Should the following treatment of the case be deemed successful, the author would remark that its success is mainly due to the use of an abbreviated functional notation, by which a great degree of clearness and symmetry is preserved in expressions which would otherwise have become inextricably complex. * A paper on this subject by the writer was published in the Minutes of Pro- ceedings of Inst. C. E. vol. xix. 1859-60. Mr. J. M. Heppel on the Theory of Continuous Beams. 451 General Investigation of the Bending-Moments and Deflections of — Continuous Beams. A a b A 1 2 Let 1 2 represent any span of a continuous beam, the length of the span being J, x,y the coordinates of the deflection-curve, the origin being at the point 1. a and 6 particular values of «. €,> €.9 €, Teciprocals of the products of the moments of inertia of the sections in the spaces 1 a, a 6, 6 2, about their neutral axes, by the modulus of elasticity of the material ] (ix) ; Hy» My» #4, loads per unit of length in the same spaces. T tangent of inclination of deflection-curve at 1, to straight line joining | and 2, its positive value beg taken upwards. ¢, >, bending-moments at 1 and 2. P shearing force at 1. Now let the bending-moinent at any point (2. ¥) between | and a be called F,"(2), between a and 6 be called F,(2), between 6 and 2 be called F(z) ; and let the part of this bending-moment which resuits alone from the load on the beam between | and z be called, between 1 and a, f(z), between a and 4, f,'(2), between 6 and 2, f,(zx); and let the first and second integrals of these functions, as of F,'(@), f''(@), be denoted by F,'(x), f'(v), and F(z), f(v), and the value of any one, as F(x), for a particular value of w, as a, by F(a); then Pei ee eee eG) Fi(0)=pa(e-$) +15) Rs te tO) A@)=ma(e—$) +no—9 (eH) +5. @ Also, from equality of moments about the point (wv. y), BG aopere ep a. we F,"(v)=9,—Paetf, (@), : é A : 5 : (5) E"(@o.— Pay, (@) 3 Vo (6) and, from equality of moments about the point 2, Pl=9,—9,+/; (4), rata, pas why - B=H(m- Oth") 452 Royal Society :— Substituting for P in (4), (5) and (6), F,'@)=(1-F) at Fe FFOM'@ - +. F,'@)=(1-F) t+ Fa- h'OAK@ «+ + O) F@=(1-F) ot Fe. —- FA OFK@ — - - (0) equations from which for a given value of w, F,"(«), F,"(2), F,'(#) may be determined if %, and ¢, are known. From the nature of the deflection-curve, from | to a, oo =e F(@); Rr Oe Abe ht, ec Wl MEMES fee 5. (lulls) from a to 6, TY ae,F,'(e) 2g Oe Oi itt aL 2 from 6 to 2, d*y ‘i Fes eke (@) 5 MLS Maa Rae te (( 1S)) *. from 1 to a, oY oF (w)+C; when «=0, F,'(v)=0, a ——T; d 2 =eF,(w)—T; Moet Sythe Seed from a to 6, Ci) ae re Ag ek (M+; siiceligh 4h. Sis pe clenigew -~ Ales eal a eee making #=a in (14) and (15), and transposing, C=e,F(a)—e,F,(6)—T; dy ! T “= F/@)—e,(B@)—F,@))—Ts . ea from 6 to 2 dy _ da making «=6 in (16) and (17), and transposing, C=e,F/(a) +e, (F,(O)—F,(a)) —eF' (2); 2 Y =e F(a) +e, (F(2)—F,(a)) +6, (F)(#)—F,/6)—T; (18) .. from | to a, y=e,F («)—Ta, no constant; forif +=0, F.v=0; y=0; Gs) from a to 6, y=e,F(a)v+e,( F(v)—F(@#)—Ta+C; . . . . . (20) Bene Se Mr. J. M. Heppel on the Theory of Continuous Beams. 458 making v=a in (19) and (20), and transposing, C=e,(F,a— F(a)a) + e,(F,(a)—F’,(a)a) ; ” y=¢,(F\(a)+F,(a)(v—a)) +e,(F,(v)—(F,(@)+F,(@(#—2)) )_Te; (21) from 6 to 2, y=e,F,'(a)x+e,(F, (6)e—F,(a)x) +e,(F,(w)—F',(6)e) -—Tw+C; . . (22) making «=é in (21) and (22), and transposing, y=e(F(a)+F,(a\(w -a)) +e, [( F(6)+ F, (6)(e—4)) —(F,(a)+ F,(a)(w—a)) | +e,[ F(@)—(F,(6)+F,()(~—6))]—-Te. we ee ee. (88) From the way in which this last equation is formed, it is evident that if there were any number of particular values of x to be con- Wake’ sidered, as a, 6, &c., 7, hk, 1, the corresponding values of EI being €1, €,, &C., €,_15 ny It might be written y= e, (F(a) a F,'(@) (@— a)) +e,[ (F,(6) + F,(6)(w—6)) —(F,(a) + F, (a (@—a)) | —Tx; (24) +e,| (F,(c)+F, (e\(w—e)) — (F,(6) + F,(5)(~—8)) | + &c. eal (F(A) +P (A\e—-)) — (EB, af) + Fa (@—J)) | La] if «=/ in (24), y=0; “f ¢[ F(a) + F,(a\(t—a) | +e, (F, (4) +F,'()(0—4)) — (F,(@) + F, (@)(J—a)) | 2 SC) +e,[ (F,(c) +F, (e(U—)) — (F,(6) + F,,(6)(U—8)) | + &e. teal (Ba) + F()U—@) — (Fra) + Fala) ] +e,{ F,)—(F.(A) + F’,.(A)(U—A) | If, now, the formation of the functions F(a), F,'(a) &c. be examined, it is evident that this equation may be written T=Ag, +B9,+C, where A and B are known functions of a, b, c, &c. and e,, €,, €,, &c., and C is a known function of the same and p,, p,, pf, &e. If the adjacent span to the left be now considered, it is evident that a precisely similar equation may be obtained, which may be written T’'=A'¢,+B'¢,+C ; 4.54: | Royal Society :-— adding these, and writing ¢ for T+ T’, which is known, as it is the tangent of the small angle which the neutral lines of the two spans would make at the point 1 if relieved from all load, t=(A+A')p,+B9, +B, +040; which may be written Vi (do Pi» ¢.)=0 > similarly for the other bearing-points in succession, PCbr $x $,)=0, , VCho» ss o)=9, &e., where the number of equations is two less than that of the quantities >» >» &e., so that if two of these are known the rest may be deter- mined. But the first and last are always known, being usually each =(. Therefore they may all be determined. This being so, the bending-moment at any point (w.y) may be found from equations (8), (9), (10) and others of the same form; and the deflection may be found from equations (19), (21), (23), and others of the same form, regard being had to the interval of the beam in which the point under examination lies. If, now, we suppose that a=b=c= &e.=/, equation (25) reduces = AF) ; . * ] similarly, — aa (F\(2)) ; to ] . ot= FO + EF), oe —— pier af c uw? e +5)e4 ght BO age oy Clearing of fractions and transposing, S(U+il')p, +419, +4219, =P til? +24Elt, .. . (26) an equation which was given by the author in his paper afar re- ferred to, and which is nearly identical with the general equation of M. Bresse, and, allowing for difference of notation, precisely so with that of M. Bélanger. If ¢=1 and ¢=0, which is the case of a straight beam of uniform section throughout, 80-+0)p, + 41g, +409, =P yt leu, thee eg) which is the equation generally known as the theorem of the three moments. If in equation (25) we put /=a, it ba T= ae,(S+ 5 oo = “y,); niet a aS (28) and for the central defiection equation (19) becomes se i, a te Y=a'e,(—Fe(6.+6)+ gq) : : (29) Mr. J. M. Heppel on the Theory of Continuous Beams. If we put 6=2a, l=3a, r= ey ee Pee 7 eats (Got Ane (gat rt gem )) Lt fe ] l 11 ee 2 o,+ Sagal ag. (spent qe tht 21643 )) i and central deflection from equation (21), Me (2 yo at 1) Nee 1g ° 144°") fo? ee 5 Bie tbaites 6/25 47 5 $6, (—y58- 16 ~, +a 39 nt att Gos)) l 7 a ee | ] 1] y= If we put 4=2a, c=3a, d=4a, l=5a, al 6] 13 149 9] 13 13 «(He Ta0%” (600t* 300%27 GO MT 37 ee ee pared ee + (Zo rie a a iT agqtet Go het sad 19 19 13 Ess ¢, + — 150 o,—a ir 50) byt = te aie a Lat aa 161 13 =o (+ 150° "and central deflection from equation (23), S{ 9 (-ie- aot? (Geet Gott Tee t ag et gees) | +e ( 70 ay het “ao! i sat Te tt = bat i P te (— Fe ehh (Gait ay tet gaat ay tga res (Gena = ote (Grant ‘ Met a at on iat +5, (—z9?: = wt0( sent 5 Tag fat ae ie Pat Gy Mat th 100 Mat nar 7 Bb dees a his 455 , (30) )) i 500 )) 500! ot) 300") )) e( malts as) pes 50 Mat ptt iggtt ae (31) (32) | (33) 4.56 Royal Society :— As an example of the application of the foregoing method to the purposes of calculation, let the case of the Britannia Bridge be taken, and let the large span be supposed to be divided into five, and the small span into three equal parts, and let the moments of inertia of the sections and loads per unit of length be supposed constant within each part and equal to their mean values. 0 1 A b! a' A a 6 c d We have then the following data :— In spans (1 2) and (1 0), a=972, b=2a, c= 3a, d=A4a, =o a =76°7, b= 2m: = 3g te l ba 1 eS l ee 1 5a 1 L) Wi32n"° °° 1520H . °r 46H: +. P664R Gia oe mh na l Me tee ts SS TOOE 25939608 700m pe, = 2°89, p= 3°31, Hy=3'°57, p,=3°49, p= 3°65, (ene 04S 207, ee ee T+T’=0, E=1440000. In span (2 1), a= 97. 6=2a, C= 3a; d=4a, [= 50; g nl dnd) San, ol Pere pee eel *) 1857R) 71 01664E= = 1746E” 4) ‘TH20E een: Hw, =3°65, == 3°49, p= O7, p,=3'3l, [He 2°89. and, from symmetry of loading, T= ! += —0-002035. _ Applying equations (30) and (32) to spans (1.0) and (1!.2) respec- tively and eliminating T and T’ by adding them, we obtain 0°1888%, + 0°048279, —10481=0; and applying equation 32 to span (2 1), 0°04827¢,+0°08765¢,— 5420=0, $,=46206, 94,=36387. Taking these values of ¢, and ¢,, and applying equation (33) to the calculation of the deflection at the middle of the large span, Y=0°375 ft.=4°5 inches. If, now, the values of ¢,, ¢,, and Y be calculated from equations (26) and (19), on the supposition that the moments of inertia of the section and the loads are constant throughout each span and equal to their mean values, they are ¢,=47030, 9,=35610, Y=4°62, which are almost identical with the values ascertained by Mr. Pole. whence Dr. Rankine on Mr. Heppel’s Theory of Continuous Beams. 457 If the variation of section alone be considered, the load being taken at its mean value, o, =46382, ,=34465, Y=4:52. It therefore appears that the amount of variation in the section and load which occurs in each span of the Britannia Bridge, when taken strictly into account, produces scarcely any effect on the values of the bending-moments and deflections, which are practically the same as those resulting from their mean values considered as - constant; and it may be considered demonstrated that, for most ordinary cases of large bridges, calculations founded on equation _ (26) may be confidently relied on. It need scarcely be remarked that these are much more simple and easy than those founded on the more exact but complex equations above given. In smaller bridges, however, the error of the approximate process will be more considerable, and the process above given may be ap- - plied with advantage to its correction. In concluding this paper, the author desires to record his thanks to his young friend, Mr. Henry Reilly, for the patience and skill with which he made, in detail, all the intricate calculations of the numerical values of the various functions involved in the above de- monstration. « Remarks on Mr. Heppel’s Theory of Continuous Beams.” By W. J. Macquorn Rankine, C.K., LL.D., F.R.S. 1. Condensed form of stating the Theory.—The advantages pos- sessed by Mr. Heppel’s method of treating the mathematical problem of the state of stress in a continuous beam will probably cause it to be used both in practice and in scientific study. The manner in which the theory is set forth in Mr. Heppel’s paper is remarkably clear and satisfactory, especially as the several steps of the algebraical investigation correspond closely with the steps of the arithmetical calculations which will have to be performed in applying the method to practice. Still it appears to me that, for the scientific study of the princi- ples of the method, and for the instruction of students in engineering ‘science, it may be desirable to have those principles expressed in a condensed form; and with that view I have drawn up the following statement of them, which is virtually not a new investigation, but Mr. Heppel’s investigation abridged. Let (#=0, y=0) and (2=/, y=0) be the coordinates of two adjacent points of support of a continuous beam, # being horizontal. Let y and the vertical forces be positive downwards. At a given point xin the span between those points let u be the load per unit of span, and EI the stiffness of the cross section, each of which functions may be uniform or variable, continuous or dis- continuous. In each of the following double and quadruple definite integrals, Phil. Mag.8. 4. Vol. 40. No. 269. Dec. 1870. 2H 458 Royal Society :— let the lower limits be «=0. ((raer—m: ((Sr=s | i aie dees 69 (ries Whee When the integrations extend over the whole span /, that will be denoted by suffixing 1; for example, m,, n,, &c. Let —P be the upward shearing-force exerted close to the point of support (v=0), ®, the bending-moment, and T the tangent of the in- clination, positive downwards, at the same point. Then, by the general theory of deflection, we have, at any point 2 of the span /, the follow- ing equations :— moment, O20 PEs a ae) deflection, y=Tx—PQOFOntF. .. 3. oe ee ae) Let ©, be the moment at the further end of the span /, and sup- pose it given. This gives the following values for the shearing-force P and slope T at the point (v=0) :— P= eM any ea. om aay and because y,=0, __ Pq,—,n =) = qq % 0,9, mg, F, T= j 1 i—_ (2-4 ae P = P a ° ° (5) Consider, now, an adjacent span extending from the point of support (¢=0) toa distance (—#=/') in the opposite direction, and let the definite integrals expressed by the formule (1), with their lower limits still at the same point (v=0), be taken for this new span, being distinguished by the suffix —1 instead of 1. Let —T’ be the slope at the point of support (c=0) Then we have for the value of that slope, bay ae ®_19-1 .m-i19g-1 F _1 —T'=6, —"7)- a + a Tg See (5A) Add together the equations (5) and (5A), and let ¢= T—T"’ denote the tangent of the small angle made by the neutral layers of the two spans with each other in order to give imperfect continuity. Then, after clearing fractions, we have the following equation, which expresses the theorem of the three moments in Mr. Heppel’s theory : 0=0,(9,/? +9q_,P—a Ul? —n_UP)—6,¢,1?—9_,¢_10) ‘ +m,9,l? +m_,qg_,?—F WU? —F_VP—trl”. he That equation gives a linear relation between the bending mo- ments ®_,,®,, ®, at any three consecutive points of support, and certain known functions of known quantities. In a continuous girder of N spans there are N—1 such equations and N—1 unknown moments ; for the moments at the end of most supports are each =0. The moments at the intermediate points of support are to be found by elimination; which having been done, the remaining quantities Dr. Rankine on Mr. Heppel’s Theory of Continuous Beams. 459 required may be computed for any particular span as follows :— The inclination T at a point of support by equation (5); the shear- ing-force P at the same point by equation (4); the deflection y and moment ® at any point in that span by equations (3) and (2). Points of maximum and minimum bending-moment are of course found by making * =0; and points of inflection by making &=0, 2. Case of a uniform girder with an indefinite number of equal spans, uniformly loaded; loads alternately light and heavy.—The supposition just described forms the basis of the formulee given in a treatise called ‘A Manual of Civil Engineering,’ page 288; and it therefore seems to me desirable to test those formulee by means of Mr. Heppel’s method. The cross section of the whole girder and the load on a given span being uniform, the definite integrals of the formule (1) take the following values :— 3 a lS a ie 5 NA ap oo Soo ont oe Gnl” 24S oe The values of those integrals for the complete span are expressed by making «=J, The values of m and qg are the same for every span. In the values of m and F, the load w per unit of span has a greater and a less value alternately. Let w, be the weight per unit of span of the girder with its fixed load, w, that of the travelling load (increased, if necessary, to allow for the additional straining effect of motion) ; then the alternate values of p are pri. s) gd =. ee a! ee (8) The moments at the points of support are all equal; that is, ®,=08,=90_}. Equation (6) now becomes the following (the common factor /? having been cancelled) :— = —20,n, +F,+F_i- tl 3 giving for the bending-moment at each point of support F,+F_,—él 2wi,+w, é =) = = 14 a e ° ° ° ° : = _ EI (9) If ¢ be made =0, so that the continuity is perfect, this equation exactly agrees with the formula at page 289 of the treatise just re- ferred to; and the same is the case with the following formule for the shearing-forces and slopes close to a point of support, and for the moments and deflections at other points :— Shearing-force, light load, pa”, dy be (10) Shearing-force, heavy load, P,=— 3 ib B 460 Intelligence and Miscellaneous Articles. Pg,—®.2,—F, ¢ wP 4 Slope, light load, Dara equ mae arty q8ET? is 7 Slope, heavy load, — = = + ane J Moment, light Joad, Pp | 9 2 b=8, —Pe+-m=—7EI+ top “2 sip be ; | = 12 Moment, heavy load, (12) 5 eee ee w wT a Portas a ye } Central t, light load, ® a - te aoa | entral moment, light load, w=5)=—7 = : | Central moment, heavy load, ®' o=5)=—jEI— — 2 he, Central deflection, light load, y=Tw—Pgt O,n+P( with a5 )= c | J CL 00S a ) gt 3eanr | | c Central deflection, heavy load, y= —Te—Pgt dn +P (with o=—5)= tl wi +3w, 1 9) ..8, 3d4Eiaeel LVIII. Intelligence and Miscellaneous Articles. LECLANCHE’S MANGANESE ELEMENTS. BY J. MULLER. ECLANCHD’S voltaic elements have recently been extensively recommended, although no statements as to their constants have been published. I have thus been led to make a few experiments with them. The arrangement of the elements is as follows :—A plate, or rather a rod of gas-coke is placed in a porous clay cylinder, and the rest of the space filled with a mixture of equal volumes of manganese (pyro- lusite, Braunite) and of gas-coke in pieces the size of a pea. The clay cylinder thus prepared is placed in a wide glass vessel filled with solution of sal-ammoniac,in which is placed an amalgamated zinc rod. To determine the constants of this combination I used Ohm’s method. ‘Three of Leclanché’s cells, connected so as to form one pair of plates, produced a deflection of 13° on a tangent-compass the reduction-factor of which was 74 when this was connected with the rheometer by only short thick copper wires. ‘This deflection was diminished to 5°1 by the insertion of a Siemens’s unit. Hence for the electromotive force of a Leclanché’s element we get the value e= 10°76, and for the essential resistance of one cell Lea O if, according to Waltenhofen’s proposal, we assume as unit that cur- rent which furnishes one cubic centimetre of explosive gas in a minute, and as unit of resistance a Siemens’s unit (the resistance of Intelligence and Miscellaneous Articles. 461 a column of mercury a metre in length and a millimetre square in section). ‘Taking the same unit as a basis, the electromotive force of a Bunsen’s element is equal to 21, and of a Daniell’s equal to 12. Hence the electromotive force of a Leclanché’s element is only 0°896 that of a Daniell’s, while from Leclanché’s determinations * it is said to be 1°38 as great as that of a Daniell’s. This difference (1°38 against 0°896) may he easily explained. With- out galvanic polarization the electromotive force of such an element should be equal to that of a Bunsen’s cell (compare my Lehrbuch der Physik, 7th edit. vol. ii. p. 263). But the degree of polarization de- pends on the strength of the current which the cell furnishes, and therefore on the magnitude of the resistance which is interposed in the circuit. In my experiments the resistance was very small, and hence there was a powerful polarization ; while in Leclanché’s ex- periments the current was not so powerful, and the electromotive force was therefore not so greatly weakened as in my experiments. Leclanché found the mean resistance of a manganese-cell of mean size (porous cell 15 centims. in height and 6 centims. in diameter) to be equal to 550, taking as unit of resistance an iron wire 4 millims. in diameter and a metre in length. Referred to Siemens’s unit, this resistance is 7=N id == 14) ar where 2 is the resistance of ironas compared with mercury (that is, 0°12), and /=550, r=4; while I found r=1°89. The cells with which Leclanché experimented were doubtless somewhat larger than mine. I was concerned to ascertain, if possible, the part which the man- ganese plays inthis. Leclanché’s statements on this point are inade- quate; for he says (Dingler’s Journal) that the manganese rapidly and uniformly absorbs the hydrogen. If by thisit is meant that the hy- drogen liberated at the negative pole is immediately oxidized, the state- ment is manifestly incorrect; for then the galvanic polarization would not exist, and the electromotive force would be 21 (that is, equal to that of a Bunsen’s cell). But whether the manganese does generally exert an influence on the electromotive force can only be decided by investigating a cell which has just the same structure as a Le- clanché’s, but with the difference that the mixture of manganese and carbon is replaced by pieces of carbon (without manganese). For such a cell I found the electromotive force e'=6'16, considerably less, therefore, than the electromotive force of a manga- nese-cell. Hence the voltaic polarization is not entirely removed by the carbon being partly surrounded by manganese, although it is materially lessened. The manganese manifestly gives up some oxygen, although it is not sufficient to oxidize all the liberated hy- drogen. With this agrees the experience, that in Leclanché’s cells which had been for some time in use the manganese had lost its activity.—Poggendorff’s Annalen, June 1870. * Dingler’s Polytechn. Journal, vol. elxxxviil. p. 97. 462 Intelligence and Miscellaneous Articles. ON THE MELTING OF LEADEN PROJECTILES BY THEIR IMPACT UPON AN IRON PLATE. BY EDUARD HAGENBACH. At the commencement of the present year experiments were made at Basle with the view of using targets of iron instead of wood in practice with firearms. Strong plates of iron were, on this oc- casion, fired at from the short distance of 100 paces. Conical bullets by their impact against the iron plate produced a scarcely perceptible indentation, and fell down near the target; at the same time the lead projectile was melted to a very considerable extent. This could be recognized by the fact that, around the point where the ball had struck, the plate was spattered with lead in the form of a white star, that, moreover, the melted lead was found in the vici- nity, and that, of the original bullet, which weighed 40 grammes, only the comparatively small portion of 13 grammes remained. This residual part exhibited a very peculiar kind of deformation and inver- sion, as may be seen in figs. 1 and 2. Fig. 1 gives the section of Fig. 1. Fig. 2. a, a, a ab the original projectile, and fig. 2 the section of the residue; the con- cave surface abcd, in consequence of the pressure resulting from the impact, was transformed into the convex surface a,6,¢,d,. The phenomenon in question is obviously interesting with regard to the mechanical theory of heat, inasmuch as we have here avery distinct example of the transformation of the impetus of the motion of a body into the impetus of molecular motion. We will inquire how far, with the help of this theory, we are in a position to account for the matter in question. According to the statement of a competent military man, the ve- locity of the projectile, under the circumstances in question, may be 2 v assumed to be equal to 320 metres; hence the impetus, eo of the movement of the body is equal to 209 kilogrammetres*. Assuming 424 kilogrammetres as the mechanical equivalent of the heat, this gives us 0°49 thermal unit. Let us now inquire how much heat is neces- sary to produce the melting described. The entire projectile (40 grammes) had to be raised to the temperature of the melting-point of lead, or near it; and then 27 grammes had to be melted. Assuming 100° for the initial temperature of the projectile, which must have been somewhat warmed by the heat of combustion of the powder and by * In this we neglect (what must in any case be very small) the impetus due to the velocity of rotation of the projectile. Intelligence and Miscellaneous Articles. 463 the friction against the barrel, taking the melting-point of lead as 335°, its specific heat as 0°031, and its latent heat of fusion as 5°37, we find necessary For the heating........ 0°29 thermal unit. See flUStOMinan arcana. 0°15 a For both together...... 0°44 +s From this calculation we see :— (1) That the mechanical theory of heat sufficiently accounts for the operation. (2) Almost all the impetus of the motion of the body is trans- formed into heat,—a result which was indeed to be expected, seeing that the iron plate was very slightly deformed, and the projectile rebounded but little. (3) By far the greater part of the heat was used in heating and in melting the lead. ‘This also is readily intelligible ; for the short time within which the entire process was effected could give rise to but little loss by conduction and radiation.—Poggendorff’s Annalen, No. 7, 1870. AN EXPERIMENT ON THE BOILING IN CONJUNCTION OF TWO LIQUIDS WHICH DO NOT MIX. BY AUGUST KUNDT. Magnus *, and after him Regnaultt, have shown that the vapours of liquids which do not mix obey Dalton’s law of diffusion. The common tension of the vapours of two non-miscible liquids (e. g. bi- sulphide of carbon and water) in a state of saturation is equal to the sum of the tensions which would correspond to the state of satura- - tion of the individual vapours for the temperature in question. Two such liquids boil, therefore, when together, at a temperature which is lower than the boiling-point of the most volatile. Magnus, how- ever, in describing his experiments, remarks that the temperature of the boiling liquid is somewhat higher than that of the most volatile when the latter is underneath the less volatile one. Regnault remarks that in the boiling of two liquids which do not mix it is very difficult to preserve constant temperatures in the vapour and in the liquid; the temperature varied materially with the heat- ing and with the formation of bubbles. I have found that the anomaly observed by Magnus (that is, the difference in temperature of the liquid and of the vapour) may be completely avoided, and the experiment be so arranged that the liquid during boiling retains exactly, and without variations, the temperature which corresponds to Dalton’s law. For this purpose I do not heat the liquids, such as bisulphide of carbon and water, together in avessel by direct heat, but heat one by the vapour of the other. Magnus once used this method to show that a concen- trated saline solution can be heated by vapour from pure water to the boiling-point of the solution in question f. The method is applicable both to miscible and to non-miscible liquids. If into a vessel (and best of all a glass cylinder) which is * Poggendorff’s Annalen, vols. xxxviil. and xciil. + Comptes Rendus, vol. xxxix.; Relat. des Expér, vol. ii. { Pogg. Ann. vol. Ixi. p. 250. 464 Intelligence and Miscellaneous Articles. about one-third filled with CS’, steam from a flask with distilled water be passed continuously by means of a tube which goes to the bottom, the liquid (that is, the mixture of bisulphide and water) which is traversed by aqueous vapour has the same temperature as the mixed vapours. Both the liquid and the vapour indicated a tempe- rature of 42°°6, a temperature which of course varies with the purity of the CS* used (boiling-temperature 46°°6) and the barome- tric height. The temperature once obtained is kept perfectly con- stant as long as there is a small quantity of CS* in the cylinder. The same temperature cf 42°°6 is maintained constantly in the liquid and the vapour when the experiment is inverted, and water is poured into the cylinder, and the latter heated by having bisulphide vapour passed in. I made the same experiments with water and benzole, with water and oil of cloves, and several other liquids, and in all cases with the same result. When, for instance, aqueous vapour was passed into oil of cloves, the mixed liquids and also the vapour showed very nearly 99°. More accurate numbers and a few remarks which naturally arise out of them will be published subsequently. For the present it is my purpose to describe an experiment to which I have been led by that above related ; for it elucidates in a very clear manner, and one especially suited for lectures, that two liquids which do not mix boil when together at a lower temperature than the most volatile. As far as I am aware, the experiment has not hitherto been described. If CS* boils when alone at 46°°6, and CS? and water when together at nearly 43°, it is clear that boiling must occur when both liquids are heated separately to a temperature between 43° and 46°°6, about 45°, and are then brought together. Experiment confirms this completely. Into a glass vessel about a foot in height and ? foot in diameter let water be brought whose temperature is not quite 46°°6, let a test-tube about 2 inch in diameter be half filled with CS*and immersed in the water until the temperature of the bisulphide has risen to about 45°. If then the bisulphide be poured into the water, a brisk ebullition is set up, which, with an adequate quantity of water, is maintained for some time. If after a while the ebullition becomes weak or even entirely ceases, stirring with a glass rod starts it again and keeps it in fresh ebullition. By stirring, other particles of water are brought into contact with the CS*, which have not yet been cooled down by parting with the heat necessary for evaporation. Even when the entire mass has already been cooled below 42°, so- litary bubbles rise, though there is no longer a continuous ebullition. The tension of the bisulphide is then only sufficient between the bisulphide and the water, especially if the former does not cover the entire base, but forms detached drops, to form a bubble (as Quincke has also observed *), which, when it attains sufficient magni- tude, can detach itself on shaking or stirring and ascends to the surface. Proper continuous boiling only sets in at a temperature of about 43°.—Poggendorff’s dnnalen, No. 7, 1870. * Pogg. Ann. vol. cxxxix. p. 19. 465 INDEX to VOL. XL. A®RIAL vibrations in pipes of va- rious forms, on the, 211. Aldis (T. 8.) on spiral nebule, 389. Ammonia, on the estimation of, in at- mospheric air, 54. André (F.) on the velocity of the pro- pagation of sound in water, 76. Atmosphere, on the estimation of am- monia in the, 54. Aurora borealis, on a possible cause of the bright line observed by M. Angstrom in the spectrum of the, Ball (J.) on the cause of the descent of glaciers, |. Barlow (W. H.) on the cause and theoretic value of the resistance of flexure in beams, 130. Beams, on the theory of continuous, 446, 457. Bezold (Prof. Von) on the electrical discharge, 42. Bleekrode (Dr. L.) on the influence of heat on electromotive force, 310. Bottger (R.) on the preparation of a liquid for producing Plateau’s figures, 392. Books, new :—Tyndall’s Researches on Diamagnetism, 301; Goodeve’s Elements of Mechanism, 445. Broughton (J.) on the chemical cha- racteristics of the various parts of the Cinchona plant, 379. Brown (H. T.) on the estimation of ammonia in atmospheric air, 54. Cailletet (L.) on the compressibility of gases under high pressures, 146. Calorimetry, on the use of the elec- tric current in, 142. Carbon, on the spectra of, 100. Carbonic oxide, on the rapidity of the absorption of, by the lungs, 150. Cayley (Prof.) on the geodesic lines on an oblate spheroid, 329. Cazin (A.) on the duration of the electric spark, 78; on internal work in gases, 81, 197, 268. Phil. Mag. 8S. 4. Vol. 40. No. 269. Dec, 1870. Chemistry, on statical and dynamical ideas in, 259. Cinchonz, experiments on living, eA Clausius (Prof. R.) on a mechanical theorem applicable to heat, 122. Cometary orbits, on the probable cha- racter of, 183. Comets, on a theory of, 300. Contour-lines, on the forms of, 421. Corona, is the, a solar or terrestrial phenomenon ? 117. Croll (J.) on the cause of the motion of glaciers. 153; on the physical cause of ocean-currents, 233. Davis (A. 8.) on,the bright lime ob- served by M. Angstromin the spec- trum ofthe aurora borealis, 33; on the probable character of cometary orbits, 183; on a theory of nebule and comets, 300. Davis (J. E.) on deep-sea thermome- ters, 132. Dawson (Dr. J. W.) on the structure and affinities of Sigilaria, Cala- mites, and Calamodendron, 384. De la Rive (Prof. A.) on the magnetic rotatory polarization of liquids, 393. De La Rue (Dr. W.) on solar physics, 53. Delaunay (M.) on the late Mr. Hop- kins’s method of determining the thickness of the earth’s crust, 10. Dinosauria, on the classification of the, 70. Douglas (J. C.) on a new optometer, 340. Duncan (Dr. P. M.) on the physical geography of Western Europe during the mesozoic and cainozoic periods, 71. Earth, on the method of determining the thickness of the crust of the, by the precession and nutation of the axis of the, 10; on supra-annual cycles of temperature in the sur- face-crust of the, 58. 2I 466 Earths, on the spectra of some, 302. Edlund (Prof. E.) on the path of electrical induction- and disjunc- tion-currents through gases cf va- rious densities and between poles of different shapes, 14. Electric current, on the use of the, in calorimetry, 142. spark, on the duration of the, Electrical discharge, researches on the, 2 —— induction- and disjunction-cur- rents, on the path of, through gases, 14. —— resistance, on a simple method of constructing high, 4]. Electricity, on the molecular theory and laws of, 390. Electrodynamic spirals, on the mag- netism of, 264. Electrolytes, on the extension of Ohm’s law to, 227. Electromotive force, on the mfluence of heat on, 310. Electroscopic experiments, on a cause of error in, 128. Equations, on the solution of lear partial differential, 35, 149. Equilibrium, experimental and theo- retical researches into the figures of, of a Jiquid mass without weight, 355. Erbia, on the spectrum of, 302. Flexure, on the cause and theoretic value of the resistance of, in beams, 130. Gases, on internal work in, 81, 197, 268; on the compressibility of, under high pressures, 146. Geodesic lines on an oblate spheroid, on the, 329. Geological Society, proceedings of the, 68, 136, 225, 309, 380. Gibbs (Dr. W.) on the measurement of wave-lengths by means of indices of refraction, 177; on liquids of high dispersive power, 229; on tests for the perfection and paral- lelism of plane surfaces of glass, 31]. Glaciers, on the cause of the descent of, 1, 153. Glass, on tests for the perfection and parallelism of plane surfaces of, Sli. Gore (G.) on the molecular move- INDEX, ments and magnetic changesiniron. 170; on the magnetism of electro- dynamic spirals, 264. - Granites of Scotland, on the consti- tuent minerals of the, 59. Gréhant (N.) on the rapidity of the absorption of carbonic oxide by the lungs, 150. Guthrie (Prof. F.) on approach caused by vibration, 345. Hagenbach (E.) on the melting of leaden projectiles by their impact upon an iron plate, 462. Haughton (Rev. 8.) on the constitu- ent minerals of the granites of Scot- land, 59. Heat, on the interchangeability of, and mechanical action, 51, 103, 218, 429; on a mechanical theo- rem applicable to, 122; on the in- fluence of, on electromotive force, 310; on the radiation of, from the moon, 372. Heath (Rev. J. M.) on the inter- changeability of heat and mecha- nical action, 51, 218, 429. Heights, on contour-lines and mea- surement of, 421. Heppel (J. M.) on the theory of con- tinuous beams, 446. Hills and dales, on, 421. Huggins (Dr. W.) on the spectra of erbia and some other earths, 302. Huxley (Prof.) on a new genus of Di- nosauria, 68; on the affinity be- tween the Dinosaurian reptiles and birds, 69 ; on the Dinosauria of the trias, 70. Iron, on the molecular movements and magnetic changes in, 170. Jamin (J.) on the use of the electric current in calorimetry, 142. Koenig (R.) on the fixed notes cha- racteristic of the various vowels, 145. Kohlrausch (F.) on the extension of Ohm’s law to electrolytes, and on the numerical determination of the resistance of dilute sulphuric acid, 227. Kundt (A.) on the boiling in conjunc- tion of two liquids which do not mix, 463. Laplace’s coefficients, on the equa- tion of, 434. Leclanché’s manganese elements, ob- servations on, 460. INDEX. Le Sueur (A.) on the great Melbourne telescope, 377. Light, on the dispersion of, 105. Lime, on the spectrum of, 303. Liquids, on the adhesion between, and solids, 190; of high dispersive power, on, 229; on the magnetic rotatory polarization of, 393; on the boiling in conjunction of two, which do not mix, 463. Loewy (B.) on solar physics, 53. Lorenz (L.) on the molecular theory and laws of electricity, 390. Lucas (M.) on the duration of the electric spark, 78. Lungs, on the rapidity of the absorp- tion of carbonic oxide by the, 150. Luvini (Prof. G.) on the adhesion between solids and liquids, 190. Magnesia, on the spectrum of, 303. Magnetism of electrodynamic spirals, on the, 264. ise gaia elements, on Leclanché’s, 460. Maxwell (Dr. J. C.) on hills and dales, 421. Merz (S.) on an object-glass spectral apparatus, 294. Meteor of Nov. 19, 1870, observations on the, 440. Mills (Dr. E. J.) on the chemical activity of nitrates, 134; on che- mical substance and chemical func- tions, 259. Moon, on the radiation of heat from the, 372. Moon (R.) on the solution of linear partial differential equations, 35, 149 ; on the equation of Laplace’s coefficients, 434. Moseley (Canon) on the cause of the descent of glaciers, 1. Miller (J.) on Leclanché’s manga- nese elements, 460. Nebulz, ona theory of, 300; note on spiral, 389. Nippoldt (A.) on the extension of Ohm’s law to electrolytes, and on the numerical determination of the resistance of dilute sulphuric acid, 22]. Nitrates, on the chemical activity of, 134. Ocean-currents, on the physical cause OF 230. Optometer, remarks on a new, 310. Phillips (S. E.) on a simple method 467 of constructing high electrical re- sistance, 41. Plateau (Prof.) on the figures of equi- librium of a liquid mass without weight, 355. Polarization, on the magnetic rotatory, of liquids, 393. Pratt (Archdeacon) on the method of determining the thickness of the earth’s crust by the precession and nutation of the earth’s axis, 10. Projectiles, on the melting of leaden, Ny their impact upon an iron plate, 462. Rankine (Dr. W. J. M.) on thermody- namics, 103,291 ; on the thermody- namic acceleration and retardation of streams, 288; on the meteor of November 19, 1870, 440; on Mr. Heppel’s theory of continuous beams, 457. Refractive indices and dispersion of opaque bodies, on the, 105. Resistances, on a new method of de- termining, 441. Roscoe (Prof. H. E.) on the relation between the sun’s altitude and che- mical intensity, 56; on vanadium, Rosse (Earl of) on the construction of thermopiles, 569; on the radia- tion of heat from the moon, 372. Royal Society, proceedings of the, 53, 128, 221, 302, 369, 446. Saline solutions, on supersaturated, 221; on the action of low tempera- tures on supersaturated, 295. Seabroke (G. M.) on the nature of the corona, 117. Seebeck (A.) on the propagation of sound in tubes, 231. Smyth (Prof. C. P.) on supra-annual cycles of temperature in the earth’s surface-crust, 58. Solar physics, researches on, 53. protuberances, on, 427. Solids and liquids, on the adhesion between, 190. Sondhauss (Dr.) on the tones of heated tubes and aérial vibrations in pipes of various forms, 211. Sound, on the velocity of the propa- gation of, in water, 76; on the pro- pagation of, in tubes, 231, Spectral apparatus, on anobject-glass, 294, Stewart (Dr. B.) on solar physics, 53, 468 Streams, on the thermodynamic acce- leration and retardation of, 288. Strutt (the Hon. J. W.) on the tones of heated tubes and aérial vibra- tions in pipes of various forms, 211. Sulphuric acid, on the determination of the resistance of dilute, by means of alternate currents, 227. Sun, on the relation between the alti- tude and chemical intensity of the, 56; on the temperature and phy- sical constitution of the, 313. Temperature, on supra-annual cycles of, in the earth’s surface-crust, 58. berg on, 51, 103, 218, 429. Thermometers, on deep-sea, 132. Thermopiles, on the construction of, 369, Thorpe (Prof. T. E.) on the relation between the sun’s altitude and che- mical intensity, 56. Tomlinson (C.) on supersaturated sa- line solutions, 221; on the action of low temperatures on supersatu- rated saline solutions, 295; on a INDEX. salt that is invisible in its mother- liquor, 328. Tones of heated tubes, on-the, 21]. Vanadium, researches on,-62. Vibration, on approach caused by, 345. Vowels, on the fixed notes charac- teristic of the various, 145. Warren (T. T. P. B.) on a new me- Heh of determining resistances, 44]. Watersheds and watercourses, on,425. Watts (Dr. W. M.) on the spectra of carbon, 100. Wave-lengths, on the measurement of, a means of indices of refraction, Lids Wernicke (W.) on the refractive in- dices and the dispersion of opaque bodies, 105. Wheatstone (Sir C.) on a cause of error in electroscopic experiments, 128. Zollner (Prof. F.) on the temperature and physical constitution of the sun, 313; on solar protuberances, 427. END OF THE FORTIETH VOLUME. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STRUT. PLI Phil Mag. S#. Vel £0. | Vig. 9. te [(bydio. Filé. |G Tiicent Brooks, Daye Sti, Phil. Mag. 5.4, Vol 40. PLUL Forms of Eruptions & Cloud -like prominences as cbhserved and drawn by Prof Lollner: F.Zoliner, del. . ‘ Cooper, Clay & C° Lilh, London Geographical Miles 7 8 Ig fig. 1 ISC9. Auupést 29 Fig.2 Posttior 160° The SAIN Protube TANCE Time 10722" lime 11220" Phil. Mag. &. 4. Vol.40. PL, Tl. Hil } \ e \y t ‘ ‘ a + ' ' Ki \, - ? - ‘ 4 ; 1 . - uid 3! Phil. Mag. S. 4. Vol. 40. PU. IV. SW oe Be tae) ee | & Son. Lith — —————— Vincent Brooks Day& S¢ ~ ‘ ' ‘ . ae . a u a aes re . ¢ . . ) - ; ~~ a) bs a : . 5 * q a 4 ; + F i = 4 a " ‘ a la . 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