Pee at's Ee OR Cee vw OS «} - of hte i. ih NE VO Pet 8 DM oe Bou Ts MIS er Beate Ae a a te - Ca WAAR: the Men ity Bb Wy: _ Seager e eu Ci PLC as SC eet ane easaia wares rit 1 ; ) a ae , $a 8 he x ¥ ais ; mk rr aoe ar Satie ; a TD) PAT vb Cd ou righ vie z i ae Ua eee eo ee ‘ 4 : f a bhedee ee A K a © Ya: sare ae ea be te ‘ uf 26 s ar ya ‘i ¢ xe ih fi Pee dor, fete AA) “yu ( Lat ee “es hk HO es he ROC AIRIE te se " ¥e A RA ta Ry eae i : , ies LAA -_- on le THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE JOURNAL OF SCIENCE. CONDUCTED BY SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & EH. &c. SIR ROBERT KANE, M.D. F.R.S. M.R.LA. ~ WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S. ‘‘ Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not. VOL. XXXIII.— FOURTH SERIES. JANUARY—JUNE, 1867. (With Plate.) (2.2. 03:5 eee 99 The Rev. -S. Haughton on the Wave-lengths of the Transmis- sionsof Museular and Nervous-Action):.... 2 2. .2ceee 118 Mr. J. Croll on the Excentricity of the Earth’s Orbit, and its Physica] Relations to the Glacial Epoch .. 2... .....¢-peme 119 Mr. D. Forbes’s Researches on the Mineralogy of South Ame- TECA shin: sWoicse'd Bip peta rele lout Rn Setal RATS Mieeaclainee i ee err 131 M.P. Schiitzenberger on the Substitution of the Metal in a Salt by Blectro-negative Elements) 2.45.4 50 Ge) 47. - ag eee 140 Archdeacon Pratt’s Comparison of the Anglo-Gallic, Russian, and Indian Arcs, with a view to deduce from them the Mean Figurejof the Harth (eels... iso. G2) aie ee eee 145 Proceedings of the Geological Society :— Prof. Huxley on a new specimen of Telerpeton Elginense.. 152 Mr.S.V.Wood on a section at Litcham affording evidence of Land-glaciation during the earlier part of the Glacial period im' Fmaland ic 5 cei etl espa eee 153 Mr. F. W. Harmer on the evidence ofa third Boulder-clay in’ Norfolk.c 3c ce an ee ee ee ee ee 153 Experimental Demonstration of the Elongation of a Conductor traversed by a Current, ee ae of Elongation by Heat, by Ho Edlund)... . 154 On the Meteoric Shower of 1866, “November 1 14, vy ‘Sir J. Pe W Elenschel, Bart...-2:.94-52 156 Inference from the observed movement of the Meteors in the < ap- pearance of 1866, November 13-14, by G. B. Airy, Esq., Astronomer Royal .... 157 On an arrangement for the Graphical Representation of Curves of Vibration by means of Mechanism, by Ernst Mach .... 159 NUMBER CCXXII.—MARCH. Mr. W. R. Grove on Aplanatic Telescopes ...............- 161 Mr. D. D. Heath on the Dynamical Theory of Deep-sea Tides, andthe Eifectiof- Tidal: Friction: i") 23 4s. 2 oe See 165 Dr. Atkinson’s Chemical Notices from Foreign Journals .... 187 Mr. C. Brooke on Negative Fluid Pressure on a given Surface. 207 Prof. Hennessy on the Physical Properties of Water in relation to Terrestrial Climate, os 300)5 ce 211 Mr. J. Croll on the Reason why the Difference of reading be- tween a Thermometer exposed to direct Sunshine and’ one Shaded Diminishes as we ascend in the Atmosphere ...... 213 Mr. W. F. Barrett on ‘‘Sensitive Flames” ...........0.+-%- 216 CONTENTS OF VOL. XXXIII.—FOURTH SERIES. _ Vv Notices respecting New Books :—The Rev. J. Hunter’s Modern ' Arithmetic, and an Easy Introduction to Conic Sections .. 223 Proceedings of the Royal Society :— Messrs. B. Stewart and P. G. Tait on the Heating of a Mietbysrapid Rotation % vacuo... oe eee 224 Proceedings of the Geological Society :— Mr. W. B. Dawkins on the Age of the Lower Brick Earths Hmiembnames Valleys. 22a OLS ba 233 On the Spectra of the Meteors of November 13— 14, 1866, by Pam Ss! FPG I Pe hee eek | ae 234 Experiments on the Expansion of Superheated Steam, a MM. G. A. Hirn and A. Cazin. a 236 Induction-currents on twisting Tron Wires through which ¢ a Gal- vanic Current is passed, by G. Wiedemann .............. 238 On the Application of the pei aie to ahaa eth a NY ea Niaudet-Breguet at .... 240 NUMBER CCXXIII.—APRIL. Prof. A. de la Rive on the Propagation of Electricity in highly Rarefied Elastic Fluids, and in particular on the Stratifica- tions of the Electric Light in very rare media ...... 241 Archdeacon Pratt: What changes can be made in the arrange- ment of the materials of the mass of a Body, its external form remaining the same, without Err its attraction on an external particle? ........ 961 Mr. B. A. Murray on a rigorous , Demonstration, ‘by elementary Geometry, of the ee Soe usually classed as the Twelfth Axiom of Euclid .... 264 M. G. van der Mensbrugghe on the Tension of Liquid Films. 270 Mr. G. Forbes on the Meteoric Shower of November 1866 .. 282 Mr. J. P. Harrison on Radiation and Vapour .. SA a icieen aC AS) Mr. W. F. Barrett on Sensitive Flames ..... 287 Sir David Brewster’s Additional Observations on a the Paleviza: tion of the Atmosphere, made at St. Andrews in 1841, 1842, G3.) LUC eIA AGI Wi os Pe it Seon ee ae ae 290 Proceedings of the Royal Society :— The Rev. G. C. Hodgkinson’s ae Observations among the Alps, with the Description of a New Actino- (SIVEINEIE ES MER, ROAM EU etfeg Uetha e Lae ge Dt Se 304 Proceedings of the Geological Society :— Mr. G. Maw on the occurrence of Consolidated Blocks in the Drift of Suffolk, and on some Chemical Analyses of "TIT STRAH UGC LSI REG a UA Aiea ig eg VAAL er ah ft aay ce ER 314 On the Thermal Radiation produced by Fluorescence, by Pro- fessor Victor Pierre of Prague ... . 316 On the Dynamic Theory of Deep-sea Tides, by ete Scare ‘Esq. 318 On the Direction of Vibrations in Polarized Light, by M. Mascart. 319 vl CONTENTS OF VOL. XXXIII.—FOURTH SERIES, NUMBER CCKXIV.—MAY. Page Mr. F. C. Webb on one of Ohm’s Laws relating to an Insu- lated Mires ee Th Ge. We eee ea ae ste ae ee ee 321 DrESW..-von Bezold on' Binocular Vision s.-)3¢ 2s os eae 326 Archdeacon Pratt: To find what changes may be made in the arrangement of the mass of a Body, without altering its out- ward form, so as not to affect the attraction of the whole upon anvextermal pout) hvigar wah. te) ela ce ide ka ine pe 332 Dr. How’s Contributions to the Mineralogy of Nova Scotia .. 336 Mr. C. W. Heaton on the Function of the Blood in Muscular Work. fk repeal Sir David Brewster’s s “Additional Observations o on 1 the Polonia: tion of the Atmosphere, made at St. Andrews in 1841, 1842, 1843,°1844, and 1845... 2.002 8k wk one Oe eee 346 Mr. A. Ransome on some of the Conditions of Molecular Action. 360 Prof. Tyndall on the Action of Sonorous Vibrations on Gaseous and Liquid Jets sion Fie. je sek see es 379 Proceedings of the Royal Society :-— Mr. J. Park Harrison on the Relation of Insolation to At- mosphere Hmaidity,,, yikes ges tel weiaten es eee 391 Proceedings of the Geological Society :— . Mr. R. Tate on the Jurassic Fauna and Flora of South ALViICa 2k cide SRS Hele ie ete eee 396 The Rev. O. Fisher on the Relation of the Chillesford Beds to the Fluviomarme: Crag %: 2 0) eee aoe 396 On the British-Association Unit for Electrical Measurements, by AW PLsBreéce ile. ie a cise ee 397 On the Velocity with which a disturbance, produced in a Ga- seous Mass contained in a cylindrical tube, is propagated, by NM Pe due Row a % veoh. cahs at ee ee 398 Note on the Theory of Tidal Pee by D. D. Heath, M.A.. 400 NUMBER CCXXV.—JUNE. - Mr. C. Tomlinson on some Phenomena connected with the Ad- hesion of Liquids to Liquids (With aPlate.) .. . 401 Prof. Magnus on the Influence of the Adhesion of Vapour i in Experiments on the Absorption of Heat ...............2 4138 Prof. Tyndall’s Note on the preceding Paper .............. 425 Mr. J. Croll on the Change in the Obliquity of the Ecliptic, its Influence on the Climate of the Polar Regions and on the eveltorthe Seay, tc Sere ee er ee ieee i , Philosophical Magazine of May 1866 contains an article on the above subject, in which I showed that the maxi- mum magnetic effect upon the needle is obtained when _ (ata) (+0) 55 ee oe re g being the galvanometer resistance, and a, b, c, and d the four branch resistances ; and I have there already mentioned that the above expression for g is only correct under the following three conditions :— 1. The resistance in the battery branch must be small, as compared with the parallel resistance of the two double branches which ,re opposite the galvanometer-branch, 7. e. small in propor- (ad) (b-+0) at+b+e+d 2. Balance must be almost established, and 3. The sectional area of the insulating covering must be small in proportion to that of the conductor; or, to express this more generally, the proportion of the non-conducting to the conducting sectional area must be a constant value for wires of various dia- meters. The first and second conditions are fulfilled in all cases of practical interest ; but not so the third, as the thickness of silk covering is always the same for thin as for thick wires. Thus a tion to * Communicated by the Author. 30 Mr. L. Schwendler on the Galvanometer Resistance correction appears necessary in the expression for g. To find this correction, and to inquire whether its influence be really so great as to necessitate its application in practice, is the chief purpose of the present paper. This inquiry is not only of in- terest in the special case of Wheatstone’s diagram ; it enters, as insulating covering for coiled wires is always necessary, into all cases where the resistance is to be found for any instrument in any circuit, to produce the maximum magnetic effect. We will consequently conduct the following investigation in such a manner as to make the result of it generally applicable. Calling g the unknown resistance which is to produce the maximum magnetic effect for a given space, k the external resistance in any circuit, which resistance is always a certain function of the given resistances of the different branches with the exception of g*, q the sectional conducting area of each convolution, A the sectional non-conducting area, consisting of the insulating covering and the empty space due to each convolution, » the specific conductivity of the wire, U the number of convolutions necessary for fillmg the given space with wire, we then have A U= ’ gq+A and SUB g rg 3 thus ater q A and B are two constants for a constant space; 7. e. A is the area of a gross section of the convolutions through one side, and B the length of an average convolution in the given space. B =. ; Pens Ay represents, therefore, an electrical resistance which is constant for a given space and constant conductivity, and which may be * For instance, in Wheatstone’s diagram, poe SOOT a. at+b+ctd to be employed in testing with Wheatstone’s Diagram. 31 called v'; thus “i i Ue Ay i \/ oe v! A fee q In case A=0 or = =constant, we again have U= Vg const., our former substitution ; in consequence of which, to produce the maximum magnetic effect, we always have g=k, or The resistance of the wire filling the given space must be equal to the external resistance. But as the radial thickness of the insulating covering is always ; Non the same for wires of various diameters, i will be variable with g, i. e. with g; and consequently I=f (A), to produce the maximum magnetic effect for a given space; or, considering the insulating covering of wires, The resistance of the space must be not equal to the external resistance. In order to find this function f(k), we will suppose the space equally filled up with wire; and taking 6 as the radial thickness of the insulating covering, we can put = 2 a oe (4/4 +8) es ea” in which c¢ is a constant, expressing the arrangement of the convolutions in equally filling the space with wire*. This value of - substituted in the expression for U, and put- ting g= ug * Supposing we divide the sectional area A, by filling the space with wire, into squares, we have c=4; or into hexagons, C= 3A, ce: 32 Mr. L. Schwendler on the Galvanometer Resistance As 6 is to be constant for all wires, seo expresses for a given space and constant conductivity a constant electrical resistance, which may be w; and putting 1 L ve v we have g = v /U= — i) and U developed, we arrive at sgt a/b s/2a/bs fy But as U, the number of convolutions in a given definite space, cannot increase indefinitely with g, because 6,*the radial thickness of the insulating covering, is always larger ‘than zero, we have here to adopt the minus sign of the square ro u=Z44/2-,/8 Vinee Ow t v w v a 4a If we now call Y the magnetic moment of the branch, of which g is the resistance and U the number of convolutions, we have r Y = const. +h? or by substituting for U its value, and putting / g=x, &e., we obtain wee Pr pele 2w W/V / Any? Y= const. sce i > ve+k and the question now is, which value of x raises Y to its maxi- mum? It is 3a aE sg) op ay w / 7 ] vo | os 2 ee i es eh Sy to be employed in Testing with Wheatstone’s Diagram. 33 or after some simple reductions we arrive at last at the equation PS Ade) oo | rr) w * The above equation of the fourth degree has only two real roots, which are both positive. One of these two roots is always larger than 4, and the other smaller than k; but as only v= Vk adY? : : makes —; negative, only this one corresponds to a maximum of dx? Y and answers our question*. Thus . e=g =k; or Considering the insulating covering of wires, the resistance of the space, which shall produce the maximum magnetic effect, must be always smaller than the external resistance, and may be calcu- lated numerically by equation (3). If we substitute in equation (38) vv =). 1. é. 5=0 w (no insulating covering), we have again our former expression, =o i; and therefore the difference between & and g depends in every case on the coefficient a vv 3 w 2. e. increasing with this coefficient. An inquiry into the nature of this coefficient will therefore be of interest. We had before prayoeuy. (ine Seige. ANor + and Nei ae * The other root, > Vk or2z?= g>k, gives the maximum for Y, if the positive sign of the square root in Y is adopted ; and the reason that equa- tion (3) contains both these maxima is, that == is identical for both the Y, we may adopt the — or the + sign of the square root. Phil. Mag. 8. 4. Vol. 33. No. 220. Jan. 1867. D 34: M. L. Schwendler on the Galvanometer Resistance thus Sv Wee —_"* =6? 3 e e e e e e 4, és w AB (4) as may be calculated. If we express electrical resistances in Siemens’s units, we have “ to measure 6? and A in square millims., B in metres, and X is the specific conductivity of the wire when the conductivity of pure mercury at 0° is equal to unity. Now, the external resistance being given, and m known by formula (4), we may calculate numerically (Pi) by equation (3). But as such acalculation, especially for prac- tical use, is inconvenient, it will be better to give an approximate algebraical expression for g, which we may obtain in the follow- ing manner. If we put in equation (3) r= V9, _we have g?—kmg Vg —2kg +k? =0, or (kg)? aking V9, or (k—g)4= m2? Substituting on the right hand g=k—p, where p is an unknown positive quantity, 2. e. a certain function of and increasing with & and m, we have (k—g)* = Km? (k—p)? ; and expanding the right-hand term, we have (A—g)*= hem? (ke — Bk"p + Bkp* —p*) 3 or neglecting all terms with powers of p against 4°, we have ap- proximately (k—g)$= Bn? or, g developed, gHh(L—W/ km?) sae This formula gives g a little too small, but near enough for practical use, as the following Table will show :— to be employed in Testing with Wheatstone’s Diagram. 35 k, g=z" 4/7..2 ea af in Siemens’s units.| by equation (3). g' =k 1—y/ km*).| 9—9- 100 85°56 83°90 + 1°66 200 164:00 162-00 + 2:00 300 <2 236°40 == 500 ee 379°50 + 700 sadied 516-60 == 900 as 648°90 + 1000 762:00 714-00 +48:00 m in this Table =0:0026; i. e. 6 =0:03 millim., » =55 (pure copper at 0°), B=0:2 metre, A=200 square millims. and c=4, supposing the area A divided into squares. The above Table shows that when m=0-0026, which it may sometimes exceed, the corrected value for g differs between 14-44: per cent. and 23°8 per cent. from the corresponding external resistance k, a difference which is evidently too great to be neg- lected where we have to deal with weak electrical currents, for instance in measuring resistances with Wheatstone’s diagram. Now we will suppose we have to determine the best resistance of the galvanometer in Wheatstone’s diagram, then (at+d)(6+e) at+d | Peg ce od meee ea atd J 24 vont a aag i e{1 .cm gene aiel (iT) the insulating covering of the wire being considered in this ex- pression for g. If we put in formula (6) m=O (no insulating covering), we have again our former expression (2), __(a+d)(6+c) atd : Bede Gee din et ds, I may mention here that, where the external resistance varies between wide limits, it will be better to divide the given space into two equal parts and fill each of them with wires of different diameters, so as to use them either successively or in peepee connexion. D2 C= thus 36 Dr. E.C. O. Neumann on an Apparatus for directly Let X' be the average external resistance between two given highest limits, x” the average external resistance between two given lowest limits; then we have ety =k, saan at+y é x and y being the resistances of the two equal parts of the space ; thus For example, in’ the bridges usually used in cable-testing we have, according to formula (2), k' =1009 Siemens’s units, and k= 109 - therefore x= 1244 y = 8846 2 which values may be each corrected, as regards msulating cover- ing, either by equation (8) or by formula (4). VI. On an Apparatus for directly measuring the Velocity of Sound in the Atmosphere. By Dr. KH. C. O. Neumann*. [With a Plate. | VERY sound-wave which starts from any point in the atmo- sphere exerts an impact on any body opposed to it ; so that if the body is a stretched membrane, it is agitated in such a man- ner that the first and strongest displacement must ensue in the direction of the motion of the wave of sound. A second mem- brane stretched in the same manner, but at a different distance, will be agitated in the same manner, but after an interval of time whose magnitude depends on the difference in the distances of the two membranes from the source of sound. By the aid of the apparatus I am about to describe, it is possible to fix the in- stants of the first displacements of those membranes, and thus determine the velocity of sound in the air. . The velocity of sound is the same in tubes as in the open air. On this principle a box was constructed about 82 centims. in length, 66 centims. in breadth, and 7 centims. in height, of whose * Translated from Poggendortt’s Annalen, vol. cxxviil. p. 307. measuring the Velocity of Sound in the Atmosphere. 37 internal arrangement fig. 5, Plate I., gives a ground-plan. On one of the ends are the two embouchures A and B; on the bottom, partitions 7 centims. in height and 7 centims. distant from each other are glued, as represented in fig. 1. The box was closed by a cover which fitted tightly the sides and ends, as also the partitions. It is readily seen that the box thus represents a coiled square tube, the two ends of which, A and B, are close to each other. On the cover there is, moreover, a rectangularly bent tube of square sec- tion, C D, fig. 6, open at D, and also a pair of shallow fillets. The former serve for receiving the sound which starts from the mouth of a small pistol EK which acts as source of sound, the latter to give this pistol a firmer bearing. The tube CD takes up the sound at D, conducts it to the opening in the cover C, through this down to the lower space at F, fig. 1, where its course divides into two, opposite in direction,—one in the direction of the arrow m, the short wayto A ; and the other in the direction of the arrows N, 0, p, 9,7, s the path to B, which is exactly 6 metres longer. Hence the sound will reach B at an interval of time after A, the magni- tude of which interval depends on the length, 6 metres, of the path of the sound between the points FandG. To determine this interval, a disk 383 centims. in diameter, moveable by a wheel O P, fig. 7, was used, along with an additional piece of appa- ratus, K I, consisting of a board M N and the short tubes H and I, K and L, fastened on it. The latter part, with the additions H and J, was inserted in the openings A and B, and fastened by means of screws. The metal tubes K and L, 65 millims. in width, are exactly in the directions of A and B in the perforated hoard ; so that the sound can pass unaltered from A and B to the caoutchouc membranes stretched on K and L, and can excite them. Exactly in the centres of the external surfaces of the latter, wooden blocks are fastened, supporting the iron rods f and g, which are 5 millims. long and 1 millim. in thickness. To obtain an approximate idea of the mode in which a dis- charge from the gun E acts, it was charged with 3 décigrammes of powder and fired, after a board 25 millims. in thickness and about two pounds weight had been so placed that it touched the rods fand g without pressing them inwards. The board was projected at once with a violent shock. In a second experiment the same board was coated with white paper, and the ends of the rods, which were quite smooth, coated with printers’ ink. The board, which was at a distance of 15 millims: from the rods, was not hit after a second equally strong shot; but the membrane d, in consequence of too violent agitation, was burst, so that a new and less tight one than e had to be stretched. As the charge of 3 décigr. was obviously too strong, it was reduced to 2 décigr.; and by continued trials,the board being gradually brought nearer to 38 On direct Measurement of the Velocity of Sound. the rods fand g, it was found that f (answering to d) struck out ex- actly 10 millims., d, on the contrary, 8 millims. After the termi- nation of these preliminary trials, the first object was to determine the distance of the stroke of the two rods fand g. With this view the disk O P, whose anterior surface was covered with white paper, was brought within 6 millims. of the blackened rods, and in such a manner that they must strike the periphery of a circle 80 centims. in diameter drawn on the disk OP. As long as the disk was not rotated, after each discharge two black points were formed at the same distance on the same periphery, which was to be accepted as the normal difference of stroke. But when the disk was rotated, the distance was greater or less, ac- cording to the direction of the rotation. When the rotation had a definite velocity of one turn in a second, the difference between the distance of the marks in that case and in the normal case was constant and amounted to 16} millims. It follows thence that with the given velocity of rotation of the disk a point of the periphery of the above circle of 80 centims. diameter passes through 161 millims. in the time which sound requires to tra- verse 6 metres. If we put the velocity of a point of the peri- phery =a, and call b the length of the path of a point of the periphery in the time which sound requires for its path in the apparatus, the length of which shall be /, the velocity c of sound is obviously determined from the equation a ee As al was previously known, it is only necessary in each expe- riment to divide by 4 to find ¢ at once. The above values substituted gave c=346:217 metres at 22° C. Of course in such apparatus it is necessary that there be— (1) Perfect unalterability of the position of the plane PO during the rotation of the disk. (2) Perfectly uniform rotation. (3) An accurate determination of the path of the sound in the tube. In the present apparatus the rotation of the disk is effected by hand, the time being taken by a seconds-pendulum, which is sufficient for instruction in schools. But considering that this rotation might be made more certain and more rapid by a good clockwork, that the dimensions of the tube might then be consi- derably smaller, and the source of sound feebler, it will be seen that this apparatus is capable of an amount of improvement sufficient for obtaining the most accurate results. Dresden, April 1866. | VII. Experimental and Theoretical Researches into the Figures of Equilibrium of a Liquid Mass without Weight.—Seventh Series*. By Professor J. Phateaut. Further examination of the glycerine-solution ; methods of prepa- ring it, which are much more certain and effectual than those first given.— Theory of the production of liquid films (continued) ; applications of the theory.—Various kinds of liquid films.— Theory of the production of liquid veins.—General principle re- lating to the actual formation, by means of liquid films, of sur- faces whose mean curvature is zero. 7. the date of the publication of the Fifth Series of these re- searches, I had made numerous trials in order to tind the best way of preparing the glycerine-solution, and I believed that J had succeeded. In fact, on the one hand, a bubble of 1 decimetre diameter, blown with the solution as I was in the habit of pre- paring it at that time, lasted for three hours when supported on a ring of iron wire in the open air, a duration which necessarily seemed enormous in comparison with the couple of minutes which is the longest time that a bubble of the same size, blown with a mere solution of soap, will last under the same circum- stances ; and, on the other hand, several successive preparations made in the same way had given me the same result, so that I considered my method of preparation sure. But on prepa- ring fresh quantities of the solution during the following summer, although I still used English glycerine and Marseilles soap bought at the same shop, I no longer met with the same success. I therefore felt it needful to take up again the examination of the glycerine-solution, with a view to finding surer and more generally applicable processes of preparing it. I have thus arrived at a simple theory of the solution in question, an exposition of which may be found in my complete memoir, and which has led me to adopt methods of preparation whose success I can now, I think, guarantee as almost perfectly certain, inasmuch as I have em- ployed them a great many times with glycerine obtained from two different sources and with two different kinds of soap. These new processes, moreover, give a degree of permanence to the films which is greatly superior to the most successful results formerly obtained. I still consider the English glycerine (Price’s), recommended * For translations of the previous 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, and vol. xxiv. p. 128. + Translated from the author’s abstract (published in the Annales de Chimie et de Physique, S. 4. vol. vil. p. 362, August 1866) of the original memoir contained in the Mémoires de Académie de Bruxelles, vol. xxxvi. 40 Prof. J. Plateau on the Figures of Equilibrium in my Fifth Series, the best. Other kinds of glycerine, how- ever, which are much less expensive, are now manufactured in France by the same processes, and might perhaps be used if needful in place of Price’s glycerine; but it would be necessary to employ them in different proportions. I have always got the best results in summer; I shall therefore confine myself here to describing the new process as I practise it at that season. It is desirable to choose a period of warm weather, in order that the temperature of the room, at least during the day-time, may not fall below 20° C. during any part of the whole process. Marseilles soap which has been recently bought, and therefore still contains its full quantity of moisture, is the best; this is to be cut up into very small pieces and dissolved at a moderate heat in forty times its weight of water. When the solution has returned nearly to the temperature of the room, it must be fil- tered, and 8 measures of this solution and 2°2 measures of Price’s glycerine are to be poured into a bottle; the bottle must be well shaken, long enough to ensure a thorough mixture of the liquids, and then left to itself for seven days. On the morning of the eighth day, the bottle is to be put mto water cooled by stirring pieces of ice in it, so as to lower its tempe- rature to about 3° C., and this temperature must be kept con- stant for six hours by adding fresh ice as it may be required. The liquid next requires to be filtered through very permeable paper ; but the liquid in the filter must be prevented from getting warm again, otherwise the precipitate which has been caused by the cooling might partially redissolve. For this purpose, before pouring any of it on the filter, a small wide-mouthed stoppered bottle of an elongated shape is filled with bits of ice, the stopper put in in order to make it heavier, and laid in the filter so that one side of it rests upon the filter; the bottom of the bottle in which the funnel is supported should lkewise be surrounded with ice. ‘The solution is now to be taken out of its cold bath and immediately poured upon the filter; the first portions which pass are turbid; but it ts only necessary to pour them back into the filter two or three times in order that the liquid subsequently collected may be perfectly limpid. There is no need for me to add that, if the filtration lasts rather long, the ice in the small bottle must be renewed every now and then. The ice placed round the lower part of the bottle in which the filtrate is collected is simply for the purpose of preventing the turbid portions which pass through at first from getting warm. If there is a large quantity of the liquid, it is necessary to dis- tribute it upon several separate filters all acting at-once. After filtering, the liquid must be allowed to stand for ten days; and the preparation is then complete. of a Liquid Mass without Weight. 4] ~ Under the best circumstances, films of the liquid prepared as above possess an extraordinary degree of permanence : a bubble of 1 decimetre diameter, deposited on a ring of iron wire 4 centims. in diameter which has been previously wetted with the same solution, may last for eighteen hours when freely exposed to the air of the room—that is to say, six times as long as a bubble made with the solution prepared as described in my Fifth Series. The sub- stances used in making the liquid being manufacturing products, vary in quality more or less in different specimens, so that I have obtained a result like that just mentioned only exceptionally; from what follows, however, an opinion may be formed of the superiority of my new process, and of the degree of reliance which may be placed upon it. Out of twenty-one successive preparations made during the summers of the four years last past, and with different specimens of Price’s glycerine and of Marseilles soap, only two, in which the soap and the glycerine employed were the same, were unsuc- cessful; but I have some reasons for suspecting an error in the weighing of the soap. All these liquids were tested by means of a bubble of 1 decimetre in diameter deposited on a ring, as I have already said. Deducting the two cases of failure, nineteen specimens remain: for three of these the longest time that a bubble lasted was five hours; for three others it was seven hours; for two it was eight hours; for four it was nine hours ; for four others, ten hours; for one, eleven hours; for one, twelve hours ; and for one, eighteen hours. A very remarkable thing is, that, when a bubble lasts for a tolerably long time, the film acquires after an hour or two sen- sibly the same thickness over the whole extent of the bubble, excepting, of course, the small part at the bottom intercepted by the metallic rmg. This uniformity of thickness is apparent from the disposition of the interference-tints. Another thing which is not of less interest is, that these tints advance at first towards those of the first order, but afterwards retrograde as far as the red or green of the last order, and sometimes even as far as white. This degradation of the tints arises, as I have shown in my Fifth Series, from the absorp- tion of moisture from the surrounding air by the glycerine- solution. The theory which I have formed of the glycerine-solution leads to the further consequence that the substitution of pure oleate of soda for Marseilles soap ought to yield, by a much simpler process, a liquid far superior to even the best of those prepared with soap. This anticipation is fully borne out by ex- periment. In fact all that I found necessary was to dissolve the oleate of soda in distilled water at a gentle heat, and then to 42 Prof. J. Plateau on the Figures of Equilibrium mix glycerine with this solution ina proportion not much differ- ent from that required when soap is employed. The solutions thus prepared were ready for use by the next day, or the next but one, and they yielded bubbles of 1 decimetre diameter, whose maximum persistence in the air exceeded twenty-four hours. Oleate of soda is therefore the substance with which the glyce- rine solution ought properly to be prepared; it is the substance indicated by theory ; and the preparation by means of it becomes a matter of the greatest ease. Unfortunately, pure oleate of soda is not an article of commerce, and it can therefore be pro- cured only by appealing to the kindness of a chemist. In a closed vessel, bubbles formed of the glycerine-solution show a degree of persistence which is very much greater still, especially if'a substance like chloride of calcium, capable of ab- sorbing moisture, is put at the bottom of the vessel. For ex- ample, with a solution prepared with oleate of soda, but which was not particularly good, and gave bubbles which did not last more than twelve hours in the air, I obtained without drying the air in the vessel a maximum persistence of forty-one hours, and, when the air was dried, a persistence of more than fifty-four hours. In the complete memoir I have pointed out some pre- cautions that ought to be taken. I return from this discussion of the glycerine-solution to the generation of films. In my Second and Sixth Series I have ex- amined the generation and all the peculiarities (1) of the films formed by filling up with oil a solid framework immersed in the alcoholic liquid, and then gradually removing oil from it, (2) of the films raised by air-bubbles on the surface of a liquid, and (3) of those which start from the wires of a solid skeleton figure which is immersed in the glycerine-solution and then lifted out. In the present series I extend this examination to other kinds of liquid films. I begin with complete bubbles obtained by blowing through a tube widened out at the further end. When, for example, the opening of the bowl of a tobacco-pipe is dipped into soap and water or into the glycerine-solution and then withdrawn, a small film extends at first from the liquid to the mouth of the bowl; and I show that on continuing to raise the latter, the equilibrium of the figure of the film soon becomes unstable ; the film then contracts, closes up rapidly below, separates from the liquid, and comes to fill the mouth of the pipe as a plane film. In this state of things, on blowing down the stem of the pipe, this film being now subject to an excess of pressure upon one surface, must either burst or bulge outwards ; now, unless it is execedingly thin, its cohesion will be more than sufficient to prevent it breaking; consequently it will begin to bulge and : : of a Liquid Mass without Weight. 43 swell; and since the viscosity of the liquid will at the same time greatly retard the descent of the molecules towards the lowest point of the curvature, the film will go on bulging and swelling ; and, lastly, inasmuch as it is supported by a circular periphery and is continuous throughout its whole extent, starting from this periphery, it must, in accordance with a principle established in my Fourth Series, constitute a portion of a sphere. As we continue to blow into the bubble, the portion of a sphere thus formed must evidently increase continually in diameter until the film becomes at last so thin that it breaks. If we stop blowing before getting near the point at which the bubble would burst, and give the pipe a rather rapid upward movement, the bubble lags behind to a greater or less extent, on account of its inertia and the resistance of the air; but in con- sequence of its cohesion and its adherence to the solid edge, the film in most cases does not break, and the bubble remains for an instant united to the edge by a hollow stem formed by an up- ward extension of the film. Now if, for greater simplicity, we suppose the rapid motion of the pipe to take place in a direc- tion exactly perpendicular to the plane of the opening, the form of the film must still constitute a figure of revolution ; and I have shown in my Fourth Series that the sphere is the only equilibrated figure of revolution closed upon the axis; this stemmed figure therefore cannot, since it is closed below upon the axis, constitute a figure of equilibrium ; consequently it must undergo a spontaneous modification ; and it is evident that the hollow stem will contract so as to separate into two portions, of which the upper one will go to fill the mouth of the pipe as a plane film, while the lower one will close the bubble, which thus becomes isolated in the air and forms a complete sphere. liverybody knows that it is possible to blow bubbles in this way at the end of a narrow tube that is not widened out. In this case, when the end of the tube has been plunged into the liquid and withdrawn again, capillary action retains a short column of liquid in the tube, and on afterwards blowing in at the other end, this column comes to form a small liquid mass over the open end, and the air entering into it expands it and converts it into a bubble. I next recall a well-known but curious process for the pro- duction of plane, or nearly plane, films of liquid. A bottle con- taming a small quantity of the glycerine-solution is taken in both hands, by the neck and by the bottom, and, being held horizontally, a movement is given to it which obliges the liquid to sweep over the whole internal concave surface. As soon as the motion is stopped, one or more plane films are found to be arranged across the bottle, which can then be set upright on a Ad. Prof. J. Plateau on the Figures of Equilibrium table, when the films become horizontal. In the detailed me- moir | likewise explain the production of such films as these by the cohesion and viscosity of the liquid. These films present some remarkable properties: they last for an astonishing length of time, and their interference-tints even reach blackness; a film of this kind, formed in a bottle of about 7 centims. diameter, lasted for eighteen days, and had become black all over. There is a special class of liquid films upon which I dwell longer, namely those due to the spreading out into a sheet of a liquid in motion. Attention was called to these films by two beautiful papers by Savart, published in the Annales de Chimie et de Physique for 1838. In the first paper this distinguished physicist imvestigates more particularly the phenomena which arise when the continu- ous portion of a liquid vein, projected vertically downwards, strikes perpendicularly against the centre of a small solid disk. Under these circumstances the liquid spreads out into a sheet or film, which, when everything else remains the same, takes dif- ferent forms, according to the velocity with which it flows: with a moderate head of liquid, the vein on striking the disk spreads out all round into a perfectly unbroken film, shaped lke a large inverted capsule, whose free slightly serrated edge throws out a great number of small drops, which start from ‘the salient angles of the teeth; with a smaller head, the film becomes more and more curved, and at last closes up completely below. In his second paper Savart investigates the effects produced by the mutual impact of the continuous parts of two liquid veins projected from circular openings, in directions which are exactly opposite to each other at the point where the veins meet. With equal heads and openings of the same size, the liquid spreads out into a disk whose plane is perpendicular to the common tangent to the axes of the two veins. Under a common head of mode- rate amount, the liquid disk is surrounded by a small thick- ened border, from which a multitude of little drops are thrown out. Savart’s observations led him, for moderate heads of liquid, to the two following laws :—with the same-sized openings, the diameter of the sheet is sensibly proportional to the head simply ; and with the same head, it is sensibly proportional to the area of the openings. He further shows that, with openings of different sizes, and a common head of considerable amount, the film is conical; and that if the head is sufficiently diminished, the base of the conical film contracts, and at last closes completely. Savart attributes the closing up of these films, as well as of Se ee a ee of a Liquid Mass without Weight. 45 those described in his first paper, to the attraction of the mole- cules ; but he confines himself to this simple general view of the matter. I explain the facts more precisely by help of the fol- lowing consideration: when a liquid film is curved and its two principal flexures are not in opposite directions, each element of the film exerts, as I have shown in my Fifth Series, a pressure perpendicular to the surface and directed from the concave side. The pressure thus arising, when the velocity of projection of the Jiquid is sufficiently diminished, increases the meridional cur- vature of the films in question so far as to close them com- pletely. In order to complete the theory of these phenomena, it still re- mained to account for the limitation of the films when not closed, _ as well as for the formation of the drops which escape from their margins. M. Hagen, who repeated and varied the principal experiments contained in Savart’s second paper, has proposed what appears to be a correct theory of the limitation of the films, and one which leads to the two laws pointed out above. As to the ge- neration of drops, M. Hagen avows that he has not been able to find any satisfactory explanation: and this is just what might have been expected; for this phenomenon depends upon a prin- ciple propounded in my Second Series, with which it was impos- sible for M. Hagen at that time to have been acquainted. The following is, | am convinced, the exact explanation of the matter. Let us call to mind what happens immediately after the two orifices are opened, and while the disk of liquid is still increas- ing in diameter. This disk evidently constitutes a figure of re- volution whose meridional section presents a very high curva- ture at the equator—that is to say, precisely at the margin of the sheet ; now this high curvature necessarily gives rise to a strong capillary pressure directed along the radius of the disk, but in the opposite direction to the motion of the liquid. Hence at the edges of the disk the liquid is subject to two opposing forces, one of which tends to move it away from the centre, and the other to make it approach the centre, and consequently a lateral motion of the liquid must ensue; in other words, during the growth of the disk, the liquid that is thrown back must form a thickened border all round its circumference. This border, however, having the shape of a sort of cylinder that has been bent round into a ring, forms, as I have shown in my Second Series, an unstable figure, and must as an absolute necessity break up during its development into isolated masses; on the other hand, the border, by virtue of the inertia of its total mass, cannot completely lose its velocity at the same time as the por- tion of the film to which it immediately adheres; the small 46 Prof. J. Plateau on the Figures of Equilibrium masses into which it has been transformed will therefore sepa- rate themselves from the circumference of the film, and will be projected with the slight excess of acquired velocity which they retain. At the same moment the capillary pressure must ra- pidly give rise to a new border, which soon resolves itself, like the first, into isolated masses; and so the action will go on. I have shown in my memoir that this theory agrees with all the details observed by Savart and by MM. Hagen and Magnus ; and it applies equally to the drops projected from the margin of the open films described in Savart’s first paper. To the class of films of which we have just been speaking, belong also those which M. Maguus obtained by the collision of two liquid veins whose axes form a certain angle with each other. These films exhibit some remarkable peculiarities that are easily accounted for. We have seen above that Savart’s films, when they assume curved shapes and the velocity of the liquid is sufficiently dimin- ished, close up in consequence of the capillary pressures exerted by all the points of their two surfaces by virtue of their curva- ture. The singular mode of formation of bubbles observed by my son belongs to the same class of phenomena. ‘The experi- ment consists in projecting obliquely into the air soap-water contained in a capsule, so as to spread out the hquid into a thin sheet or film; this film generally breaks into several pieces, each of which immediately closes so as to form a complete hollow bubble, which descends more or less slowly. The phenomenon is due to the margin of each partial film acquiring a thickened border or hem; this falls more quickly than the central part, which is opposed by the resistance of the air, so that the film assumes a highly dome-shaped form with its convex side turned upwards; the rest is done by capillary pressure. . I mention, in conclusion, a last species of films: they are like- wise formed by a liquid in motion ; but cohesion and viscosity play ouly a secondary part in their production, since the mole- cular veins of which they may be considered to be made up have no tendency to separate from one another. A film of this kind is formed by a jet of liquid projected downwards from an orifice having the form of a rectilinear slit—a jet whose singular ap- pearance is well known. I made known a long time ago an experiment which seems to me curious, inasmuch as it exhibits visibly a large vertical film of liquid, one of the free edges of which has a thickened border, and has the form of a straight line inclined to the horizon. The experiment consists in making water issue from a vertical and rectilinear slit extending up one side of the vessel from near the bottom to above the surface of the liquid. It is the free upper surface of the film which exhi- of a Liquid Mass without Weight. 47 bits the form just mentioned. In my memoir I have given the theory of the phencmenon, and have indicated the conditions requisite for its successful realization. * It may be seen from my preceding Series that, when an un- stable liquid figure breaks up spontaneously into two or more masses or partial figures, these remain united together two and two, before their complete separation, by a liquid vein more or less cylindrical in shape, which afterwards resolves itself into separate spherules. 1 show that the phenomenon of the gene- ration of these veins is analogous to the generation of films, and that it also depends upon the cohesion and viscosity of the liquid. I conclude with announcing a general principle concerning the production, in the form of films, of surfaces whose mean curvature is zero. This principle, to which I attach great im- portance, is as follows :— A surface whose mean curvature is zero being given, imagine that there is traced out upon it any closed outline whatever, subject only to these conditions—(1) that it circumscribes a finite portion of the surface, and (2) that this portion does not exceed the limits of stability of the given surface has such limits ; bend an iron wire so that it has exactly the shape of the closed outline in question, oxi- dize it slightly with dilute nitric acid, plunge it completely into the glycerine-solution and take tt out again; it will be found occupied ‘by a film representing the portion of a surface that has been sup- posed. This outline must, of course, be provided with a projection by which it can be held. For example, a plane is a surface whose mean curvature is zero, and any closed figure traced upon a plane encloses a finite por- tion of it; now a slightly oxidized iron wire bent into the shape of any arbitrary but closed plane figure, and immersed in the glycerine-solution and then withdrawn, always brings with it a plane film. Similarly, if on a catenoid contained between two circular bases, we imagine an outline formed of two opposite mer- diona! arcs and of the halves of the circumferences of the two bases, these two halves being taken on the same side of the plane containing the meridional arcs, this outline, when constructed in iron wire, gives with the glycerine-solution a film representing the corresponding portion of the catenoid. Surfaces which for the most part are very curious, can be thus realized, as if by enchantment. The only difficulty consists in choosing the closed outline and exactly determining its form ; but this can always be done when we know either the equation or the geometrical generation of the surface. In a subsequent Series [ will make known some new examples of such realizations. pas a VIII. On the Multiplication of Partial Differential Operators. By Professor SYLVESTER *. : the last Number of the Magazine I explained the sense in which I employ the term operator as distinguished from an operant, the distinction being somewhat analogous to the gram- matical one between a verb and a noun; for as a combination of the predicate and copula gives rise to a verb which has independent laws of inflexion and regimen, so an operator is a new species of quantity which, springing from the union of an operant and the symbol of operation, becomes amenable to its own proper laws of functional action and subjection+. I found it convenient also to refer to an operator as an energized operant t. At the outset of the paper a proposition was stated inadvertently, regarding any energized function of a set of variables and their corresponding elementary operators, in too general terms. Such function remaining unrestricted in regard to the principal letters x,y, Z,... should have been limited to be a Jinear quantic im re- gard to the elementary operators 6,, 6,,6,,... If @ be any such function, the proposition in question, thanks to the happy intro- duction of the star symbol, may without any auxiliary definition of the derivatives dg, ds, ... employed in the preceding paper, be stated as follows, with perfect freedom from any shade of am- biguity, ef = [eltePr-1) 8] x, which theorem (¢ being an arbitrary parameter) contains the general rule for expanding (¢x)” in terms of the quantities [pxpl*s [papudlx; [paprprd]*, &e.§ * Communicated by the Author. + Thus an operator forms a new part of speech in algebra. It may be well to notice in this place, in order to prevent error arising hereafter, that the process of energization must in general be indicated, not by the mere apposition of an asterisk, but of brackets and asterisk. Thus, although P turned into an operator may be correctly designated by Px, PxP similarly energized will be represented by [PxP]x, and not by P«Px. Conversely, denergization will consist im the abstraction of an asterisk and brackets, and not of the former merely. Thus PxPx denergized is not PxP but P?+ P*P, because PxPx is [P?+P«P]«; whereas PxPx di- vided by *, a term employed in the sequel in a footnote, is simply PxP, so that star division, or destellation as it may be termed, is not to be con- founded with denergization. t+ OrI might have used the word vitalized to convey the same idea,—the operator being the operant endued with power of action, but none the less for that capable of being acted upon, calling to mind the relation between dead and living matter. So denergization might be termed amortizatzon, a word which exists in the language. § Thus, ex. gr., when p=bbat+ 20c65+3dbe+ eoes ee ee a PR eS ee ee ee ap te 4 On the Multiplication of Partial Differential Operators. 49 In like manner, the statement concerning the commutable Operators @* and yx, made in a footnote, should have been the theorem in the text easily enables us to see that pe UY ea(a, b,c. dc...) = F(a, b+ax, c+ 2br+a27, d+3cx+3ba?+ az’,...); which, as remarked by Mr. G. De Morgan and others at the Mathematical Society, may be regarded asa transformation and generalization of the fun- damental law of development in Arbogast’s theory, sometimes called by the name of Arbogast’s first or unreduced method. The identification with the method im question merely requires the supposition that F(a, b,c,d,...) should become a function exclusively of a single one of the letters within the parentheses ; but of course we must write the left-hand side of the equation under the unreduced form e"F* F(a, b,c, d...). The proof, as noticed by my distinguished mathematical friend Mr. Sa- muel Roberts, of the generalized theorem is virtually implied in the method by which I established long ago the partial differential equations of the inva riants to any system of forms; 2. e. it follows from the observation that the effect upon F of altering v into x+ dz and leaving a, b, ¢ unaltered is the same as the effect of leaving x unaltered and altering a, b,c, d,... into b+abz, c+2bdx, d+8céz,... Consequently er ai UCD iy tree acai aes sa. be | ae Be and therefore, by Maclaurin’s theorem, F(a, b+ az, c+bx+2ax,...)=ex6* F(a, 6, c,...). In memory of the author who appears to have been the first to employ the form which I have called a Protractant, it may hereafter with propriety be termed also an Arbogastiant. ; : O* The equivalence of e*®* with fe —% *, when @ represents an Ar- q p bogastiant, or rather aform slightly more general, had been previously stated, but in a much less commodious manner, by Professor Cayley in a memoir contained in Crelle’s Journal, vol. xlvii.p.110. An inspection of this me- moir will satisfy the reader how inarticulate was the language of algebra at the not remote epoch when Mr. Cayley’s paper was written, and how, for want of a distinctive abstract symbol of operativeness, she strove like one lame of speech and tongue-tied, to give intelligible expression to her ideas. With the star sign the restraining ligament has been cut, and henceforth algebra, as far as yet developed, may revel in unbounded freedom of utter- ance. The rise of this star above the mathematical horizon marks one of ° the epochs of algebra. It is worth remarking how already it is be- ginning in its turn to assume the attributes of quantity (vide the con- cluding footnote of this paper, where it is used as a divisor); so that appa- reutly it is destined to run the same course as Newton’s fluxional symbol, which is, and of fatal necessity must have been, superseded by the let- tered symbols of Leibnitz, which have now long ago, to all intents and pur- poses, become converted into a new species of algebraical quantity. As Phil. Mag. 8. 4. Vol. 33. No. 220. Jan. 1867. K 50 Prof. Sylvester on the Multiplication of limited to the case where those two operants, @, ~, are each of them linear quantics in regard of 8,, 8,, 6:,... The proposition advanced guardedly in the Postscript concerning any lineo-linear functions of 2, y, z,...62, Sy, d2,-.. (“there can be little or no doubt, &c.’’) I now also wish to be understood as affirming ab- solutely. I proceed to give a universal theorem for the mul- tiplication of any number of operators, energized functions Of 2; Y,.Z, 2... §: 0. 10y; Os; freed from all restrictionyas linearity of form in respect to the latter set. The method by which I arrived at this very general theorem was in substance identical with that embodied in the demonstra- tion spontaneously furnished me by my ever ready correspondent Professor Cayley ; and as I cannot improve upon his statement, it would be a waste of time to substitute my own words for his. Accordingly, after enunciating the theorem, I shall give the proof of it in the very words of our unrivalled Cambridge Professor, from which it will be seen that in essence this theorem consists soon as it becomes necessary (as will probably before long be the case) to express the specific relation of the star to something which limits and dis- criminates its mode of application, it must in its turn develope into a third species of symbolical quantity; and so there may be im store for the future of algebra an endless procession of more and more abstract symbols of operation, each successively developing into a more and more subtle species of quantity, suggesting the analogy of successive stages of so-called impon- derability in the material world. A propos of Arbogastiants, it is worthy of a passing notice that if I be any invariant to the form (a, 0, c,...h, k), and we write A for the Arbo- Ax)” gastiant (/0,+2kd;+...), then = expresses the effect of the substi- WpGxscntska t ie : h | performed upon I. This theorem is an easy conse- quence of the conjunction of the three circumstances, (1) that if Iz, y is what I becomes when for a, 0, c,...k we substitute respectively ax+ by, be+cey,...kx+ly, Ix, y will be a covariant to the form (a, b, c,...h,k, l), : 5A be Ax)” and that consequently the last coefficient in Ix, y will be = I; (2) that this coefficient must bear the same relation to /,k,...e,b as the first does to a, 6, c,...k; and (3) that an invariant to the form (J, k,...c, b)is iden- tical with the same invariant to the form (0, ¢,..., /). I think I have been informed that Leibnitz was the first to employ the method of the so-called separation of symbols: in his tract on the Calculus of Differences, the poet sage of Collingwood contributed powerfully to its further development; if he should chance to cast his eyes over these pages he will, I fear, stand aghast at the Frankensteim he has thus (it may be unwittingly) played no unimportant part in bringing into existence ; or, rather, I should fear, did not all the world know his perfect candour and un- stinted sympathy with every form of manifestation of human intelligence. Partial Differential Operators. 5] in applying the symbolical form of Taylor’s theorem to the ex- pansion which, in itself symbolical, contains the generalization of Leibnitz’s theorem, thus giving rise to a symbolism of the second order, a phenomenon which, it is believed, here for the first time makes its appearance in analysis. Let $,,$5,63,...6r be any functions of x,y,2...3 52,dy,59-+- capable of being developed in a series of integer powers of the latter set of variables, where it is of course understood that d d d : 6,= ee = f oe ie eooy in like manner let d d ——) =! a ee ee =a oa so that in fact 6!,, d',, d',,... are abbreviated expressions for 83,, 93 Mw 65,, ... or, if we please so to say, for Bad yd LE SE ee a 4, ‘g Let 6,,;; 6; signify the operants 6,; &', restricted to operate exclusively on ¢;; finally, let Ay j= 5'p, 5 82,5 +5 y, ¢ Sy, 34+ 545, ¢. 8, 5+ oes then giving to 7, 7 all possible values subject io the imequalities t1 | O°OOgbO- 1.) i... 0°46298 |0°44872 (I--K) £30552, 65750 40°30 §| 4 074.6462 4°6220 Wats) aie. 0°9996 | 1°3776 | 9°35 Be OPIS E OTs Rieveye 2°46298 |0°83075 |Vv.V seveee/1°9434 2°7319 | 4°39 | I | 0'71138 F is computed with a correction for the place of the helix on the primary, and with a resistance which includes that of the Weber =(0:00779. The Weber must havea considerable Il of its own; but as I did not know its constants, and as this II must vary with the deflection, I did not compute it. Possibly some of the discrepancies may be owing to this. ‘The sparks show the difference of tension ; they were taken with platinum points, and when the machine was excited by four Groves. ‘The column, sum of components, gives for the coliateral combinations the values which arise from adding the ® of each helix, taking into account the Weber’s resistance. 1. It will be observed that G+ H with twice as many spires, and V+ V' with thrice as many as G, give the same current; so also that of [+ K is near that of I. 2. On the other hand, G.H is twice G, and V. V! twice V+ V!. 3. It is also manifest that the effect of I is not proportional to its diminished resistance: its F is 4°4 times greater than that of G, but its actual current is only 2°5. This is at once explained by its 4 being so much less. So also the ratio of the theoretic to the effec- tive current is nearly unity in G+H, while it is only 0°73 in V+ V’, and for the samereason. InG.H.(I+K) the ratio is still smaller ; but I shall recur to this. -I now used the four primaries I+K= L on P”, single helices on the others. I had some doubt whether the difference of the * These values of F should be multiplied by a factor representing the F of G, which must be greater than its ®, here assumed as unity. As, however, it belongs to all, its omission does not affect the comparison. 70 Royal Society :—Rev. T. R. Robinson on increasing cores might not influence the results, and tried this with P’, P'’, and one P*, ose core =1:90 inch in diameter and 15:5 inches long. It has 349 spires of No. 15 in two layers. G was put on each of them, and cur rents transmitted, which made their ¥’s nearly equal. Taste II. Name pa eh ®. Sets. | Spark. Y. PM es GSES I'00 ros14* | gts 2°22,5 1169 1 i ee 2°04, 10000 2° g°2)27 1168 PY rane cies 3°00 1'0054. Be 2662, 1156 It follows from this that the least of these cores is large enough for the excitation produced by four cells: the size does seem to in- crease the spark, though this increase may be owing to better insula- tion of the core-wires in P!!! and P’+. The following results were obtained with the ciiéeaniogl rheotome worked at a uniform speed of 13 discharges per second, TasBxe IV.’ ®, F. Sets. = nee II. b. components. Geen aicswes 1°0000 || 1°0000 | ... | 1:000C0 I'000C0 =|: 1'00779 L=I4+k T'SSa2) | WAT STOO. IM TONKOA TwiGo ola ee. | 0°64. 0°34624.— Cte Rican pb see SUD wl OLA |) 2 KORO ARE Ml Wescnhes 16+ 0°7 5002 — Ema Beet aa B°One2 1) eo" Broo. | st teL Org 7059 2°38 324 ET Peet sicait ta sice EATS. (0578 he VmPOdmnn le Tae 1'7o00co =|: 0°8 5385 C=A+B EOS S2i it A ORTZ We ¥2 Oto S ss Nea vane 0°56286+| 0°92704 IN. aiaarg eu att 2 K's 5°4100 Tl OPL7 ZOD Tien oasis 0°31646 | 0°27756 AL Biase penne: BVEESO ian gOR ib! se OG SOS S.1 ik ivan 0°23149 | 0'46542 A Rec wigs 2 OAOS |W ABORT SO GOOG ho naar. 023149 | 0°46542 RHEE, sasha 375558 | 5°2464 | 1 | 067776 3°8504 Lai Biel: Rare 4°3179 | 675756 | 3 |.0°65666 4°1799 Gases... 5°1460 | 6'9400 | 3 |0°74153 4°6932 GeO.) 0°O758> | S°208T | ae) .o'7AiGg0 60488 M-+N......... 2 5207 5°4536 Zi! CAO Noa” piesa nar 0°63292 | 0°26862 =O pheas 1*7616 RA ROO dl are O° Geer | ewe nena 0°73130 - | 0°23248 S=M+N T6087). | GASH a) BT |(orgg Gia Sly arias. 065810 | 0°28543 LOW ORS aaene B50 © || LONG 7 7A. cide Org0mae 3°4.996 MNIK 8°1939 | 15°7398 1 |. 0°52058 $°2736 1. As before, two helices in series give no increase ef quantity ; - M-+N is the same as N, G+L nearly the mean of G and L. 2. The quantity of collateral helices is seen in column 6 (asin Table II.) to be the sum of the separate actions of each. cies are not greater than what can be explained by the uncertainties inherent in these measures, which I have already described, The discrepan- One * 2-5 sets taken on the first day were very unsteady. The one taken on the second was close, and gave 1:0267. + At the same time I tried two helices similar to A and B, except that their wire is varnished zon, which were given to me by Dr. Callan. 0:6887, and their spark only 0:524 in. great, a difference caused solely by the greater resistance of the iron, Their ® is The © of A+B is 2'9138 times as the Electricity given by Induction- Machines. 71 apparent exception is a strong confirmation of this rule—the case of G.H(I+K). Its observed 6=3-0552, while the sum =—4-6220. G and I being on the same primary are excited together; but in. measuring either, as there is no current in the other (but merely a state of tension), their [1 is not changed. When, however, they are connected collaterally, the currents react on each other, their IT’s are increased: the ®’s are thus diminished, and therefore their re- sultant is the sum of quantities less than those used in the computa- tion. The d's in this case become—for G 0°94289, for H 0°79885, and for I+ K 0°34588, which are quite sufficient to account for the difference. 3. As with I in Table II., so here it will be observed that N has less relative power than either I or K ; its actual power is even less, though its theoretical force exceeds theirs in the proportion of 5: 4. This is explained by its 6 being so much smaller; but it gives this important information, that, at least in helices of these dimensions, nothing is gained by using wire thicker than that of I, or = inch*. 4. The effect of L is far less than that of I+ K. In the first the helices are on the same primary, in the other onseparate ones. In the former case the II is larger, for it is the sum of the I of each on itself, and those of each on the other; 6 therefore is less. Besides, the potential of the core on the helices is less than when each of them is central on it. The difference is even more remarkable in O as compared to its elements M+N, its effect being only 0°7 of the other, and 0°3 of the theoretic power. ‘The same disparity of course prevails in their combinations; O. L giving only 3:46, while the same four helices arranged on separate primaries give 8°19. The combinations G.H(1+K) and G.L.H have the same helices ; but in the first two were on the same primaries. As, however, they were 1°5 inch instead of 0°5 apart, the II was not so much increased as in the other cases, and therefore there is not quite so great a decrease of power. The following practical maxims may be deduced from the expe- riments and reasoning which I have related. The attention of instrument-makers has been chiefly directed towards increasing the length of spark given by these machines, and in this they have succeeded to a surprising degree; but in doing so they have not added to the quantity of electricity which is pro- duced by them. This, however, is by far the most important object ; for in most applications of the inductorium all tension above what is necessary to force the necessary quantity of current through the cir- cuit is useless, nay sometimes injurioust. Iam inclined to think ~ that a tension which gives sparks of 4 inches will be found quite sufficient in ordinary cases, and this will be given by about 20,000 spires; all beyond only adding to the weight of the instrument, its cost, and the difficulty of insuring its msulation. It must be kept in mind that the mere quantity is independent of the length * This is between 27 and 28 of the Birmingham wire-gauge. I believe Ruhm. korff uses 28. + It has often been remarked that intense discharges will not show strata well jn an exhausted tube, ' 72 ~ Royal Society. of wire: I actually found it the same for a flat: spiral of 21 spires and for a helix of 13,655. It is not, I believe, ascertained what is the best proportion of height and diameter for a secondary helix of a given number of spires. It is generally made as long as its primary, though perhaps not on any definite principle. The magnetic potential P is in this form a little greater thanin that which I used, but so also is IT: the length of wire is less, which increases F, but also decreases 0; and a priori it is not easy to decide which way the balance inclines. The II is something less if the spires be in separate sections than if they be in one continuous coil. The dimensions of the core do not seem to be of importance as to quantity within the limits which I tried; their length seems to in- crease the tension. The quantity is greatly diminished when the rheotome works rapidly ; and in spectral work the probable limit of its slowness is that the impression on the eye shall be continuous. _ The quantity increases with the diameter of the wire up to a maxi- mum, which is attained when this is about the sixty-fifth of an inch. Helices may be combined either for tension or quantity without much loss of these respective powers*. If for the first, they are combined in series; the genera] tension is the sum of the individual ones, and in this way we can obtain sparks of a length limited only by the strength of the insulator which is interposed between the primary and secondary helices. If the latter be all of the same wire, the quantity remains unchanged ; if they differ in this respect, it will be intermediate between the weakest and strongest. If they are combined for quantity, they must be set collaterally, z. e. all their positive terminals connected, and all their negative. The resulting current will be the sum of all the separate ones, but the tension is not increased ; the sparks seem even a few hundredths of © an inch shorter, but are much denser, and in the higher combi- nations approach to the character of a jar discharge. Hence there is no risk to the apparatus by extending this mode of combination to any extent. It deserves notice that the helices need not be equal in tension or resistance; thus the arrangement G. K gives little less than the sum of its components, though K has only half as many spires as G and but a tenth of its resistance. _ In combining these instruments, the primaries should not be con- secutive if of large numbers, for so the action of their extra-current ‘would be very destructive to the rheotome; with Pi ey containing 726 spires in series the spark in the mercurial one is almost explo- sive, but when they are collateral it works quietly. Were, however, ten or twelve to be so combined, it would require a battery of very large cells to maintain the current, and it is better to have a separate battery for each pair of primaries. In this I find no difficulty; the negativet poles of all the batteries are connected with the mer- * The connectors add some resistance and some counter-induction. t If the mercury be made positive, each discharge makes a sharp report and blows about the metal and alcohol in most unpleasant profusion. e Geological Society. 73 cury of the rheotome; from its platinum point, separate wires go to the entering bind-screw of each primary, other wires go from their exit bind-screws to the positive poles of their respective batteries, and thus their action is perfectly simultaneous. Of course, if many bat- teries were used, the current in the rheotome might be too power- ful, but then there would be no difficulty in having separate rheo- tomes worked by one electromagnet, and (at least with the mercurial form) adjusting them by a revolving mirror to pertect synchronism. In this way I feel sure that we can attain an amount of electric power which has not yet been approached by the inductorium, and which may be expected to be a most powerful means of research in those inquiries to which I referred at the commencement of this paper. At the head of these stands the palmary discovery of Mr. Huggins, that there are nebulee and comets whose. matter possesses spectral attributes not corresponding to that of the sun, the stars, or our own earthly elements. Is that difference an indication of some body suz generis, oY a mere result of peculiar temperature or other molecular conditions? Is, for instance, the bright line, cor- responding to one of nitrogen, which occurs, we may say, normally, produced by nitrogen as such? If so, what has blotted out the other bright lines of that magnificent spectrum? Is it due to an element of nitrogen, dissociated by some enormous temperature from other elements, perhaps from hydrogen, one line of which is also present? And the third line, elsewhere unknown—is it the herald of a new body, or merely a derivative from another spectrum? We cannot even hope for an answer to these questions till the spectra of at least those elements which seem cosmical have been examined through a range of temperature extending from the lowest that developes in them luminous lines, to the highest that is excited by the most potent electric discharges which we can produce and control. Now, to obtain such a graduated range, the plan of combination which I have been describing seems well fitted. It, ofcourse, cannot be expected to equal, under any extension, the wonderful voltaic bat- tery of Mr. Gassiot (at least its arc-discharge) ; but how few can avail themselves of such an instrumentas that! Butif, as seems probable, we can without much difficulty increase the heating-power of the induction-discharge an hundredfold, we shall have made a very great step, and by means which are everywhere accessible. Inductoria are common; there are few situations where a physicist cannot obtain access to several, and combine them as Despretz did the voltaic batteries of Paris to make the experiments which have thrown such splendour on his name. as GEOLOGICAL SOCIETY. [Continued from vol. xxxu. p. 545. ] December 5, 1866.—Warington W. Smyth, Esq., M.A., F.R.S., President, in the Chair. The following communications were read :— 1. “A Description of some Echinodermata from the Cretaceous rocks of Sinai.” By P. Martin Duncan, M.B., Sec. GS. The existence of Cretaceous rocks in the district of Sinai has been 74 Geological Society. surmised for several years ; but, owing to the scarcity of fossils, they have not been correlated with any of the Asiatic formations. An examination of the Echinodermata collected by the Rev. F. W. Hol- land from the limestones of Wady Mokatteb and Wady Badera has enabled Dr. Duncan to show their parallelism with the red lime- stones in South-eastern Arabia, the fossils from which he described in a former paper. All the species now determined are well-known forms, characteristic of the typical Upper Greensand of Europe; but those formerly described from Sinai by MM. Desor and D’Or- bigny seem to be peculiar to that region. ‘The author observed that by adding the Echinodermata from Sinai to these from South-east Arabia, we obtain a fauna eminently characteristic of the Middle Cretaceous period; and in conclusion he drew attention to the interesting fact that the majority of the wide-wandering Echinoderms had a tendency to vary from their types: both in Europe and in Arabia, while the rest remained persistent in form. 2. ‘* Geological Description of the First Cataract, Upper Egypt.” By J. C. Hawkshaw, Esq., F.G.S. _ At the First Cataract the Nile flows over crystalline rocks consist- ing principally of quartz, felspar, and hornblende, combined in | various proportions, and there appearing under the forms of syenite, greenstone, hornblende, and mica-schists, or else occurring in sepa- rate masses. In the bed of the river the surface of the harder por- tions of these rocks is beautifully polished. The whole district is traversed by dykes of greenstone, of which the prevailing direction is EK. and W. The crystalline rocks forming the bed of the river are overlain by a sandstone, sometimes coarse and gritty, and at other times fine- grained and compact. ‘The prevailing colour is light yellow; but in places +t is dark purple, and even black, owing to the presence of iron. As yet no organic remains have been discovered in it. ‘This sandstone rests on the uneven surface of the syenite in slightly inclined strata, dipping N.N.E. It is nowhere altered at its junction with the syenite, nor is it anywhere penetrated by dykes. To the eastward of the First Cataract is a wide valley, commencing opposite the Island of Philee, and joining the Nile valley again about three miles below Assouan. ‘Through this valley the Nile may have formerly flowed, as freshwater shells and deposits of Nile-mud are found at a considerable height above the present level of the river. To the westward of the First Cataract the crystalline rocks dis- appear below the sandstone, and the country is almost entirely covered with sand of a rich yellow colour, composed of fine rounded grains of quartz. 3. “On the Drift of the North of England.” By J. Curry, Esq. Having first given a general sketch of the district under considera- tion, and noticed the various rock-formations occurring therein, the author described in detail the distribution of the drift, showing that the prevailing direction in which it had been carried was from north- west to south-east, with certain variations, dependent upon the con- Intelligence and Miscellaneous Articles. 75 figuration of the land. He then described the wide distribution of Shap-Fell granite, especially referring to its occurrence in radial lines from the granitic mass, and called attention to the fact that detritus of various rocks in the vicinity of the lakes has been carried over the Stainmore ridge into the valley of the Tees. Mr. Curry then described the occurrence of drift along the western slope of the Pennine chain, and from Castle Carrock across the northern end of that chain, as well as in the valleys of the Tyne and the ‘lees, pointing out also the absence of drift from Alston Moor and Upper Teesdale, and down the valley of the Wear to the city of Durham. In conclusion the author discussed the manner in which the drift- materials had been transported, referring it chiefly to marine opera- tions on ancient shore-lines at various altitudes; and in explanation of the fact that the upper limit of the drift is not at a uniform ele- vation, he suggested that it may in great measure be due to a varia- tion in the volume of the ocean, instead of to elevations and depres- sions of the earth’s crust. XI. Intelligence and Miscellaneous Articles. OBSERVATIONS BY A NEW OPTICAL METHOD. BY A. TOPLER. HE want in practical optics of some method of detecting ete hand the existence in glass intended for lenses of places of vary- ing densities, so-called tears (Schliere), led the author to construct an apparatus, which not only achieves the object in question, but has also been found applicable to determining differences of density in all possible transparent media. The light proceeding from a bright lamp through the aperture of a small shade falls upon a system of lenses of large aperture as apla- natic and achromatic as possible (the head of a photographic appa- ratus). The transmitted light concentrates in a focus at a distance of from 10 to 25 feet on the other side. A simple Keplerian telescope consisting of two lenses is so set up that its optical axis coincides with the axis of the system of lenses in question, and that the focus of the rays issuing from the system of lenses lies in front of the object-glass of the telescope. ‘The telescope, moreover, is so drawn out that the rays issuing from the eyepiece have their point of junc- tion in the pupil of the eye, and hence project on the retina the image of a uniformly illuminated field of view. If a screen be laterally pushed in front of the object-glass of the telescope, as soon as its edge passes by the place of the focus the field of view will at once become dark. If either in the glass of the system of lenses In question, or in media which are interposed before or behind it, there are places of different densities, some rays will thereby be de- flected from their path, not pass through the focus, and hence not disappear when the screen is pushed across; these rays give then ~ in the dark field of view an image of the tear, by which name the author designates in general places of different densities in a trans- parent medium. . The apparatus constructed by this method served, at first, only 76 Intelligence and Miscellaneous Articles. to detect tears in glass in the proper sense of the word; and the result was, that in thick plates of glass, such as are used for making ordinary spectacle-glasses, a square inch of perfectly homogeneous glass was sought in vain. ‘Those tears were found most injurious which in the apparatus presented the appearance of a surface covered with fine pencil-marks. Irregularities in density in the air which were produced by ascend- ing warm air could be recognized even if the difference in tempera- ture of the warm body and of the surrounding air only amounted to 0°-6. Unequally warmed or pressed glass also exhibited distinct tears. For a study of the issue of different gases into the air the apparatus was also used ; and it was observed that a jet of coal-gas ascending vertically preserved a coherent cylinder for a longer time than carbonic acid which descended vertically. The evaporation of alcohol, even at the temperature of 0° C., could be detected by means of the apparatus. The investigation of flame showed that, besides the different envelopes which are visible to the naked eye, there is an external one which surrounds the entire flame and obviously arises from the heated air. To the observation of the electric spark the author devoted espe- cial attention, and the view was confirmed that the spark in jumping across rarefies the air. It is of especial interest to observe how the sound-waves become visible in the apparatus when the sound is produced by the jumping spark; the author by the naked eye could even observe the diffraction, refraction, and reflection of sound. Un- fortunately he did not succeed in contriving an objective representa- tion of these phenomena.—From a Review in the Hortschritte der Physik, vol. xx. of a pamphlet published by the author at Bonn in1864. OBSERVATIONS ON CERTAIN LINES OF THE SOLAR SPECTRUM. BY M. ANGSTROM. I have read with great interest a note by M. Janssen on the telluric rays of the solar spectrum, in which the author points out a mode of experimentally obtaining these. Having been occupied for more than three years with the determination of the wave-lengths of a great number of Fraunhofer’s lines, I have frequently had occa- sion to observe the telluric rays, and that under circumstances rarely offered to observers who are placed in a lower latitude than that of Upsala. M. Janssen says, in his note, that aqueous vapour produces in the solar spectrum five groups of obscure lines, extending from D to A, and among which would be found the group A and a great part of B. I also think that A and B are telluric lines; but they are not due to aqueous vapour. The following are the facts on which I rely. During the great colds of January 1864, I several times ob- served the solar spectrum at Upsala, and once at a temperature of —27°C. The telluric lines near D, C, and a, as well as those from a to B, had almost entirely disappeared; while the groups A and B, and a third, situated near the middle between B and C, and which Sir D. Brewster designates by the letter C, were very intense, more so even than they were in summer for the same height of the sun. Intelligence and Miscellaneous Articles. 77 These three groups all present the same aspect: they consist of a very marked line, and of a series of very fine ones, almost equally distant; the intensity alone increases in going from C towards A. The constant appearance of these three groups, and their similarity of aspect, lead us to attribute them to a common origin; but, as I have said, this is not to be sought in the action of aqueous vapour, but rather in that of a permanent gas, carbonic acid for instance. The spectra of the compound gases, and more especially those of metallic oxides, present great: similarity to the groups in question ; and this leads me to suppose that they are due to the absorption exerted by a compound gas. That they belong to our atmosphere, and not to that of the sun, follows from the change of intensity of 5, and especially of C, with the height of the sun, and also from their general appearance; for they have not, like all others which possess a certain intensity, a direct relation with the spectrum of a simple body. The hypothesis of the solar origin of Fraunhofer’s lines has this consequence, that the spectrum formed by rays emanating from the edge of the star ought to show these lines more strongly than does the spectrum of the rays from the centre. Yet this prevision of the theory is not confirmed; at all events the result has not corre- sponded to the expectation of physicists. ‘The experiments of Mr. Forbes and myself have given a negative result. Yet a differ- ence has been established ; the light in the centre has only furnished in the middle of the spectrum the strongest of Fraunhofer’s lines, but with a very pronounced intensity : the contrary would have been expected. In the course of last year, in common with M. Thalen, I under- took a comparison of the solar spectrum with that given by the iron electrodes of a battery of 50 elements. We discovered more than 460 lines corresponding to the iron lines. ‘These experiments led me to view the phenomena of absorption under a new point of view, which ought, I think, to dispel the contradiction which I have indi- cated between theory and observation. If, for instance, we observe the iron lines by the aid of a powerful Ruhmkorff’s coil, three very brilliant and some other feebler lines are observed between G and the strongest calcium lines. But if the inductorium is replaced by a battery of fifty elements, not only does the number of lines very materially increase, but their relative intensity undergoes great changes. Among the fifty lines which we then counted in this limited region of the spectrum, we could only with difficulty identify the three intense lines observed with the inductorium. Applying this result to the sun, we may suppose that the rays on the edge will not give a spectrum in which the most intense rays will have a relatively greater intensity, but a spectrum in which, on the contrary, the feeblest will be the most pronounced ; the result will be a feebler spectrum—that is, one without very pronounced rays. This is exactly what I have observed, although the difference of the two spectra be not considerable. It is easy to produce in the solar spectrum changes which have been ascertained in the iron spectrum. 78 Intelligence and Miscelianeous Articles. It is enough to pass the solar image in front of the aperture of the collimator, so that at length the telescope only receives diffused light. Most of Fraunhofer’s lines appear then in acertain sense to become effaced, while the others are strengthened ; these lines, which then gain in intensity, are in general the intense lines of iron obtained with the aid of the inductorium. Among the results arrived at in the research already cited, there are two which appear worthy of attention. The first is, the certain presence of manganese in the sun; we have observed the coin- cidence of at least thirty lines. The other is, the discovery of a- new hydrogen-line. The spectrum of hydrogen presents, as 1s well known, three lines—two of which coincide with C and F, and the third with a line near G. The fourth line which we have ob- served is near the middle of the interval between G and H;; it coin- cides with a very intense solar line which we have designated by h. With Geissler’s tube this line is very distinctly seen, although itis much less feeble than the three others. This result is the more satisfactory, as the line A was the only one among those of a cer- tain intensity whose origin still appeared mysterious. ‘The explana- tion of it which we have found in the spectrum of hydrogen acquires an additional interest from the fact that the line / occurs several times in the stellar spectra drawn by Mr. Huggins. As the relative in- tensity of the spectral lines of hydrogen greatly depends on the den- sity and elastic force of the gas, we may probably draw some con- clusions in this respect from the intensity of the corresponding absorption-lines which exist in the solar spectrum. This is a sub- ject to which I shall recur.—Comptes Rendus, Oct. 15, 1866. REMARKS ON THE ABOVE COMMUNICATION. BY M. JANSSEN. The above observations of M. Angstrém refer to points of science with which I have closely occupied myself, and I propose shortly to discuss the results with the author. But among M. Angstrom’s results is one which, according to him, disaccords with the results I have recently published on the spectrum of aqueous vapour. On this point [ shall reply at once. M. Angstrom, in measuring the wave-lengths of the solar spec- trum, had occasion to observe telluric rays; and having observed that some of them continued even during very cold weather (when the air, therefore, was extremely dry), he concludes that all the tel- luric rays should not be attributed to the vapour of water. M. Ang- strém especially cites A, B and a group between B and C. I will venture to remark that M. Angstrom is here combating me with my own ideas. Ihave never thought or enounced that the spectrum of aqueous vapour would represent the totality of the telluric spectrum. My investigations on the terrestrial atmosphere have had for their object to show that gases and vapours have at all temperatures the power of elective absorption, and that spectrum analysis might be applied to the study of the atmosphere of the planets as well as to that of the sun. ' Thus, having observed that Sir David Brewster's bands were re« Intelligence and Miscellaneous Articles. 79 solved into fine lines, I found analogous results for hyponitrous acid, the vapour of iodine, bromine, &c. These facts were announced to the Philomathic Society of Paris in December 1864; they are contained in the Comptes Rendus and in various scientific journals. Since then my communications have always been to the same effect. Thus in 1864 I said, summing up my observations in the Alps, ‘‘ All these observations have shown me that aqueous vapour in the shape cf cloud or of atmospheric vapour did not appear to act, but that it is aqueous vapour as elastic fluid which plays an important part in the production of the telluric rays of the solar spectrum.” (Comptes Rendus, Jan. 30, 1865.) It is thus seen that I am far from attributing to aqueous vapour all the telluric rays of the solar spectrum; I have, on the contrary, always thought that all the gases of the atmosphere had their part in the phenomenon—a part which for some would be very difficult to ascertain, but which must in principle exist. In the course of my investigations I have frequently been able to observe in very cold weather differences between the relative in- tensities of the telluric rays, those of aqueous origin becoming feebler than the others*. These distinctions are met with on my maps; but I think it would be premature, before publishing the spectrum of aqueous vapour, which Iam now obtaining by a sure experiment, to discuss the origin of any special line.—Comptes Rendus, Oct. 29,1866. NOTE, BY MESSRS. DE LA RUE, STEWART, AND LOEWY, ON THE DISTRIBUTION OF SOLAR SPOTTED AREAS IN HELIOGRAPHIC LATITUDE. In a paper which is now being printed, and which forms the second series of our Researches on Solar Physics, we have investi- gated the relation between solar activity and the ecliptical longitude of the planets; and as a result we believe that we have discovered a connexion between the behaviour of sun-spots and the longitudes of Venus and Jupiter. We have under consideration another branch of this research, which, however, cannot be completed for some time; but as the results already obtained seem to be of interest at the present moment, we venture to lay them before the Royal Astronomical Society. Mr. Carrington, it is well known, has given in his most interest- ing volume onthe sun a diagram exhibiting the distribution in helio- graphic latitude of sun-spots from time to time. Now, if Venus and Jupiter have an influence on solar activity, it might reasonably be conjectured that when these planets crossed the solar equator * But I have never found any spectral line more pronounced in winter than in summer, which would be opposed to the general principle that the elective absorption of gases dimmishes with the temperature. It is pro- bable that M. Angstrom has committed an error of estimation, which is very difficult to avoid (as I have convinced myself) when the spectra compared cannot be made to have the same luminous intensity. 80 Intelligence and Miscellaneous Articles. the solar activity would be more confined to the equatorial regions of the sun, and that when they were furthest removed from the solar equator this activity would extend outwards towards the solar poles. It appears to us that in Carrington’s diagram there is probably evidence of an action of this kind, due to both of these planets ; and in the Table which accompanies this note, and which has been de- rived in a general manner from Carrington’s diagram, it will be seen how closely the minor epochs of solar activity in their approach to the equator agree with the epochs at which Venus crosses the solar equator, and how the solar activity spreads out towards the poles at those times when Venus is furthest removed from the solar equator*. The influence of J upiter and a more searching investigation into that of Venus will occupy our earliest attention. It will be seen from a late circular of M. Chacornac, that he has drawn attention to Carrington’s curve of latitude and to the minor sinuosities, without, however, giving the above explanation. Lastly, we may state that we are led by our investigations to the conclusion that solar activity, as shown in the phenomena of sun- spots, would not exist but for planetary motion, any more than cer- tain physical phenomena of the planets would be produced without solar influence. Times of Nearest Approach of Venus to the Solar Equator, and of crossing it. 1 1854 Between January 5 and January 10 2 a April 26° 6) May 1 3 August 17,45 Aueust 7233 4 3 December 6. ,, December 12 5 1855 as March 30 ,, April 4 6 hg July 204 G2 4daly: 24 Z me November 10 ,, November 14 8 1856 3 February .29 .,, March 5 9 5 June 2? on, lie 26 10 - October 11 _,, October 16 11 1857 - February ~ 1. ,,° February ~7@ 12 Aa May 24 ,, May 28 13 - September 14 ,, September 19 14 1858 > January 4 ,, January 8 15 . April 27 5 May 1 16 re August 16 ,, August an {7 = December 7 ,, December JB 18 1859 ee March 29 gy Setoryl 1] 19 i July 20) sy July 25 20 - November 8 ,, November 13 Pi 1860 5 March 1 ,, Mareh 5) 29 . dune 26 ,, June 25 23 33 October 11 ,, October 16 24 1861 rs January 31 ,, February 4 Monthly Notices of the Royal Astronomical Society, Nov. 9, 1866. * A chart accompanied this notice, which will be printed in the series of papers in course of publication by the Authors. THE LONDON, EDINBURGH, anv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] FEBRUARY 1867. XII. On the Meteoric Shower of the 14th of November, 1866. By Guorce Forsss, Esq.* [ With a Plate. | i attempting to investigate the causes of any phenomenon in nature, the first object to be aimed at is the accumula- tion of facts. This is more especially the case in a science, such as Meteoric Astronomy, which is still in itsinfancy. Hence it is that observations like those to be detailed in this paper, of however slight importance they may be when considered by themselves, yet when placed side by side with observations of a like nature, by other observers in other places, may help in arriving at the true theory of the nature and motions of those interesting ob- jects called meteors or shooting-stars. It may be mentioned that the night on which the late meteoric shower took place was much clearer and less stormy in St. An- drews than in many other places in Great Britain. It may also be well to state that the whole of my observations were noted down before I read any account of the meteors in the newspapers or elsewhere. In the first place, I shall proceed to give the results of the observations made by me at St. Andrews on the numbers, direc- tion of flight, and general characteristics of the shooting-stars ; and also of observations on particular meteors. I shall then proceed to compare my observations with those which have been * Communicated by the Author, having been read before the Philoso phical Society of St. Andrews on the loth of December, 1866. Phil. Mag. 8. 4. Vol. 83. No. 221. Feb. 1867. G 82 Mr. G. Forbes on the Meteoric Shower published by other observers within the last month, and finally make a few remarks on the conclusions to be derived from all these observations. As there was some doubt whether the November shower, if it should take place at all, would do so on the morning of the 13th or 14th, I looked out for a few minutes at about 12 o’clock on the night common to the 12th and 13th, but not seeing any meteors I did not watch any more. On the evening of the 13th I kept a constant look-out from my window, and saw several fall between 112 and 11545™. At 115 45™ they began to be more numerous, and I then went outside, where there was a good point of view from which the whole heavens could be very well seen. I stood looking eastwards in the direction of the constellation Leo, and began to count at 12 o’clock. This was done by pricking holes in rows on a card, which were afterwards counted at leisure. I stopped counting at 1 o’clock, by which time I had marked down 883 meteors, which is on an average about fifteen per minute. The greater number of these fell in the last 20 mi- nutes; and at about 1 o’clock I could not mark them all; for they were then falling at the rate of five or six in the second, sometimes even faster. ‘The maximum seemed to take place at about 1) 15™, On the following night I looked out for about three-quarters of an hour, beginning at 12 30™, but did not see any me- teors. At the first glance it was obvious that the meteors were coming all from one direction, in the east; and on attentive observation the point from which they all appeared to radiate could be seen to lie within the sickle in Leo. During the whole night I only saw three or four going in the opposite di- rection, or any that did not seem to be directed to the general radiant-point. The appearances presented by these bodies will now occupy our attention. Hach meteor had a distinctly defined head or nucleus, whose course was marked by a train left by it. The nucleus was generally red or orange-coloured. It appeared suddenly, and as suddenly disappeared. The prevailing colour of the trains was greenish white, those nearest the horizon being usually most coloured. The colour of the train seemed in general to be complementary to that of the nucleus. The train consisted of a bright line, formed with enormous rapidity when near the zenith. The line was not uniform in breadth, but was broadest in the middle and pointed at the ends. The widening in the middle seemed to be caused by a falling down- wards of the matter composing the train. After lasting usually of the 14th of November, 1866. 83 only for a few seconds, the train then faded away. I fre- quently noticed that the head of the meteor was visible for a short distance beyond the extremity of the train. The nearer a meteor was to the radiant-point, the shorter was the apparent distance traversed. This was the case to a re- markable extent. Likewise the luminosity of a meteor and that of its train was much less the nearer it was to the radiant-point. The time, however, during which a meteor was visible seemed to remain pretty constant in whatever part of the heavens it was seen. So much fore-shortened did their paths become, that in the constellation Leo one frequently saw merely a point of light bursting forth, and then fading away. The longest trains ex- tended over nearly 40°; but the general distance traversed by those near the zenith was about 20°. The next observations to be noticed are those on particular meteors. At about half-past twelve I saw a meteor larger than Venus at her brightest, which burst in all directions: it was blue in colour. It was first visible in the head of Hydra, and then shot down nearly to the horizon in an inclined direction, which pointed towards the general radiant-point. I only saw two or _ three bursting meteors during the whole night. At 125 41™ the most brilliant and remarkable meteor that I saw during the whole night appeared. This was a triple me- teor, in which each of the three components was fully as bright as Venus. They shot through the zenith with enormous ra- pidity, following one another in quick succession almost ex- actly in the same line, and leaving a train extending over a distance rather exceeding that between the bright stars Alde- baran and Betelgeux. This train lasted till 125 49™. It was at first lance-shaped, like those of the other meteors. It then gradually shortened, thickened, and at the same time became of a serpent-lke form. It continued to get thicker and shorter till it was of an oval shape, having a spiral appearance. After continuing to contract for a short time longer, it remained for some time with a diameter of 15 minutes, when, after growing fainter, it slowly disappeared 8 minutes after its appearance. During the whole time that these changes were proceeding, the impression given was that they were produced by the action of currents in the air. Its position, shortly before its disap- pearance, was in the Milky Way, close to the star @ Persei. I noticed that stars were visible through this nebulous mass. At 15 20™ I was standing close to the house with my face turned towards it. I suddenly saw the wall of the house close to me illuminated by a crimson flash. At the same time I heard a shout from a friend, but on turning round was too late to see anything. He, however, told me afterwards that at 84 Mr. G. Forbes on the Meteoric Shower that moment he had seen a very large fireball, of a green colour, passing through the zenith, and had seen it bursting. At 2h 138™ I saw a large meteor which left a distinct train, which, after passing through the serpentine and oval forms already described with relation to another meteor, disappeared after having been visible for two minutes. Its position was a little north of the bright star Menkar im the constellation Cetus. The next thing to be done is to compare the observations which have now been mentioned with those which have been published in the newspapers and elsewhere. First, as to the numbers of the meteors. The numbers counted have varied very much under different circumstances. This is owing in some instances to a greater or less number of ob- servers having been employed, in others apparently to differences in the skill of the observers, and in many cases, doubtless, to the state of the atmosphere. Thus while, by myself, I counted between the hours of 12 and 1 only 883, Mr. Hind, along with three friends, counted 1120. The trained staff of observers, again, under Mr. Glaisher at the Greenwich Observatory, counted be- tween the same hours 2032. At Malta the meteors were sup-— posed to be falling at the rate of 500 or 600 per minute. It was there impossible to count them, and the scene was com- pared to a shower of hail. Some observers at the time of maximum display counted only about 40 per minute, while others counted three times that number in the same time. I have heard from only one observer an account of meteors being seen on the morning of the 13th. Between the hours of 11 and 3 he had counted 50. This was in Fife. No one n Britain seems to have seen any on the night following that of the great display. An account from Saragossa, in the ‘ Times,’ states that the great shower took place on the morning of the 15th. This, however, is most probably a misprint. Accounts also from Penzance say vaguely that they were visible on that night. Every one seems to agree in fixing the time of maximum dis- play at between 12 minutes and 15 minutes past 1 on the morning of the 14th. The curves (Plate III.) show the gradual increase in numbers up to about 1 12™, and the decrease in numbers after that time. The first is deduced from the observations of Mr. Alexander Herschel at Glasgow. Here the ordinates measure propor- tionally the number of meteors seen in periods of one minute, each counted at unequal intervals. In the second, the ordinates also measure proportionally the numbers seen in periods of one minute, counted at intervals of of the 14th of November, 1866. 85 10 minutes. This curve is drawn from the observations of Mr. Glaisher’s observers at Greenwich. In the third and fourth curves the numbers were counted during periods of 5 minuteseach. The third one is from the ob- servations of Mr. G. J. Symons in London, which were counted every quarter of an hour; the fourth from those of Mr. C. G. Talmage in Hssex, by whom the numbers were counted every successive five minutes, from 12552™ to 247™, This last curve shows most minutely the changes at the time of the maximum display. On looking at these curves, the first thing that strikes us is the suddenness of the rise and fall in the numbers. Thus be- tween 125 45™ and 125 50™ eighty-seven were visible, and between 15 0™ and 12 5™, that is in the same length of time, and but one quarter of an hour later, the number seen was 264. The next thing to strike us is the similarity in the curves on each side of the maximum ordinate. Next, as to the direction of the flights of the meteors. Every one noticed that they all came from an easterly direction. The point was accurately fixed from careful observations, and was found to lie a little south by east from y Leonis. Mr. J. P. H. Boileau, however, writing from Malta, states that the radiant-point lay at nearly equal distances from Regulus in Leo, Alpharet in Hydra, and Procyon in Canis Major; which is in a point considerably to the south-east of that mentioned above. The colours of the heads or nuclei of the meteors were gene- rally stated to be red or orange-coloured. The Rev. Robert Main describes them as being ‘in general whitish or yel- lowish, while some were red or orange-coloured, and one was bluish.” | The greatest difference of opinion exists as to the colours of the trains of the meteors. Some say that they were blue; others bluish white or pale bluish; others greenish or greenish white; while in Malta they are reported to have been white, sometimes tinted with red and blue. As to the time of duration of the trains, most observers agree in assigning two or three seconds as the usual time. An ob- server in Penzance, however, states, as a remarkable fact, that one meteor left a train which was visible for several seconds. Short as this time appears, it was yet sufficient for two ob- servers to use spectroscopes ; but they did not succeed in ob- taining any results either with regard to the meteors or their trains. They did not even find the sodium line noticed by Mr. Alexander Herschel in some of the August meteors. Of the observations of particular meteors, those described by £6 Mr. G. Forbes on the Meteoric Shower Mr. Alexander Herschel, in a letter to the ‘ Times,’ as made by him at Glasgow, are the only ones I have read of anywhere that seem to agree with those noted by me. He says, “ Large meteors appeared at 124 33m, 12> 41™, 2h 14m, 2842", These meteors left streaks which endured from five to fourteen mui- nutes.” The first of these agrees in time with a large bursting meteor observed by me, which, however, I did not notice to leave any long-lasting train. The second is undoubtedly the remarkable triple meteor which I saw, and whose position I noted carefully shortly before its disappearance. Mr. Herschel does not give, in the letter referred to, any particulars of the position of this object from which its height might be calcu- lated. The third one he mentions must be the same meteor as that described above, which I saw at the same time. Im this case, however, as in the last, he gives no particulars. Many observers noticed long-lasting trains like those already described. The serpentine form was also remarked by several observers. Mr. J. M. Heath noticed one train, after assuming the serpentine form, to contract into the form of the section of a lens, and at the same time to revolve about an axis. Messrs. Thompson, who observed at Cardiff on behalf of the British Association, saw similar changes going on in the train of a me- teor which remained visible for 12 minutes. They also noticed that this train was transported some distance im a westerly direction, The Rev. Robert Main noticed the same phenomenon in a different meteor*. Very few fireballs seem to have been observed anywhere. Besides the one already mentioned, a large one was seen at Edin- burgh at 3551™, of a deep blue colour, leaving behind it a golden-coloured train, not pointed as in the case of the ordinary meteors. This fireball shot from east to west not far from the zenith. Very few meteors were seen by any observer to burst. The great fact proved by this extraordinary shower is the periodicity of the returns of these displays of meteors. This be- lief 1s grounded on the observations of similar showers since the year 902, and was first suspected by Humboldt. The general direction of flight from a radiant-point shows that these bodies come in parallel directions. That the ra- diating appearancei s merely the result of perspective is clearly shown by the arc traversed being greater, and also by the speed and brilliancy being greater, the further the meteors were from the radiant-point. * M. Schmidt, in writing to the Astronomische Nachrichten, states that at Athens he observed a train which lasted foran hour. He also fixed the time of maximum display at about 2h 15m Athens time. of the 14th of November, 1866. 87 The increase in numbers, and the subsequent decrease, as we passed through the group, show that the meteoric bodies are more abundant in the middle than near the outside ; ; yet the very sudden increase and as sudden decrease in numbers seem very inexplicable. It is supposed that the meteors, on coming in contact with our atmosphere, become luminous by the arresting of their mo- tion. The height of meteors has been found to average ninety- five miles at first appearance, and sixty miles at extinction. Now it seems wonderful that our atmosphere at a height of ninety-five miles can have such an effect. Another curious fact is, that we have not yet heard of any me- teoric matter having been found on the earth’s surface since the late shower. Now, where do they go to? It is exceedingly improbable that they 2 get free from our atmosphere; and that they should be aed into meteoric dust seems unlikely, since they did not appear to be diminished in size during their progress; and, as has been already stated, the nucleus was seen in many cases after it had ceased leaving a train. These and other questions must be settled by the accumula- tion of observations; and all who are interested in this depart- ment of astronomy must look forward with expectation to the Report of the Committee on this subject to the British Asso- ciation at their next Meeting. These reports have for some years past contained the fullest accounts of meteors and me- teoric showers. The progress which has been made from the observations of the last thirty years fully warrants the expecta- tion that much information will now be gained in this branch of science from the observations which have been made, in many different parts of the world, of the late remarkable shower. Note on the Curves. (Pl. III.) In each of the curves the time marked is the mean of the period during which the observations were made. In the curve deduced from Mr. Talmage’s observations, the num- bers visible in five minutes were first counted at 125 52m, from which time, till 128 57™, he counted 127. In the preceding four minutes (from 125 48™ to 125 52™) he had counted 107, and between 125 47™ and 125 47™ 30s he had counted 39. Hence, whatever number was visible between 125 47™ 308 and 12» 48™, the number in the five minutes preceding 122 52m must have considerably exceeded that in the five minutes fol- lowing. This is mentioned merely to show the remarkable coincidence in the three lowest curves in marking this increase in the numbers at 12° 40™. And it should be noticed that 88 Dr. Rankine on the Phrase “ Potential Energy,” the first curve is no exception, since the times at which the numbers were counted could not show this increase. Other slight differences in the details of the different curves are doubtless due to the differences in the intervals, and in the periods during which the numbers were counted. XIII. On the Phrase “ Potential Energy,” and on the Defini- tions of Physical Quantities. By W. J. Macquorn RANKINE, C.E., LLD., F.R.SS. Lond. & Edinb., &c.* : 1. [* the course of an essay by Sir John Herschel “‘ On the Origin of Force,” which appeared some time ago in the Fortnightly Review, and has lately been republished in a volume entitled ‘‘ Familiar Lectures on Scientific Subjects,” the opinion is expressed that the phrase ‘ potential energy” is “ unfortunate, inasmuch as it goes to substitute a truism for the announce- ment of a great dynamical fact” (Familiar Lectures, p. 469). 2. There is here no question as to the reality of the class of relations amongst bodies to which that phrase is applied, nor as to any matter of fact concerning those relations, but as to the convenient and appropriate use of language. This is a sort of question in the decision of which authority has much weight ; and when an objection to the appropriateness of a term is made by an author who is not less eminent as a philosopher than as a man of science, and whose skill in the art of expressing scientific truth in clear language is almost unparalleled, it becomes the duty of those who use that term to examine carefully their grounds for doing so. : 8. As the phrase “potential energy,” now so generally used by writers on physical subjects, was first proposed by myself, in a paper “On theGeneral Law of the Transformation of Energy” +, read to the Philosophical Society of Glasgow on the 5th of Janu- ary, 1853, I feel that the remark of Sir John Herschel makes it incumbent upon me to explain the reasons which led me, after much consideration, to adopt that phrase for the purpose of de- noting all those relations amongst bodies, or the parts of bodies, which consist in a power of doing work dependent on mutual configurations. , 4. The kind of quantity now in question forms part of the subject of the thirty-nimth proposition of Newton’s Principia; * Communicated by the Author, having been read to the Philosophical Society of Glasgow. t Viz. that the effect of the presence of a quantity of actual energy, in causing transformation of energy between the actual and the potential forms, is the sum of the effects of all the parts of that quantity. and on the Definitions of Physical Quantities. 89 but it is there represented by the area of a figure or by symbols only, and not designated by a name; and such is also the case in many subsequent mathematical writings. 5. The application of the word “force” to that kind of quan- tity is open to the objection, that when ‘ force” is taken in the sense in which Newton defines ‘‘ vis motriz,” the power of per- forming work is not simply force, but force multiplied by space. To make such an application of the word “force,” therefore, would have been to designate a product by the name properly belonging to one of its factors, and would have added to the con- fusion which has already arisen from the ambiguous employment of that word. 6. The word “ power,” though at first sight it might seem very appropriate, was already used in mechanics in at least three differ- ent senses, viz.: first, the power of an engine—meaning the rate at which it performs work, and being the product of force and space divided by time; secondly, the power, in the sense of effort or pressure, which drives a machine; and thirdly, ‘“ mechanical powers,” meaning certain elementary machines. Thus “ power” was open tu the same sort of objection with “force.” 7. About the beginning of the present century, the word “energy” had been substituted by Dr. Thomas Young for “ vis viva,” to denote the capacity for performing work due to velocity ; and the application of the same word had at a more recent time been extended by Sir William Thomson to capacity of any sort for performing work. There can be no doubt that the word ‘energy ”’ is specially suited for that purpose; for not only does the meaning to be expressed harmonize perfectly with the ety- mology of évepyeva, but the word “ energy ”’ has never been used in precise scientific writings in a different sense; and thus the risk of ambiguity is avoided. 8. It appeared to me, therefore, that what remained to be done was to qualify the noun “energy” by appropriate adjec- tives, so as to distinguish between energy of activity and energy of configuration. The well-known pair of antithetical adjectives “actual” and “potential” seemed exactly suited for that pur- pose; and I accordingly proposed the phrases “ actual energy ” and “ potential energy,” in the paper to which I have referred*. 9. I was encouraged to persevere in the use of those phrases by the fact of their bemmg immediately approved of and adopted by Sir William Thomson—a fact to which J am disposed to as- cribe in a great measure the rapid extension of ,their use in the course of a period so short in the history of science as fourteen * Green’s “ Potential,” or “ Potential Function,” is a quantity homoge- neous with one form of potential energy, but of opposite algebraical sign. 90 Dr. Rankine on the Phrase “ Potential Energy,” years*. I had also the satisfaction of receiving a very strong expression of approval from the late Professor Baden Powell. 10. Until some years afterwards I was not aware of the fact that the idea of a phrase equivalent to “ potential energy ” in its purely mechanical sense had been anticipated by Carnot, who, in an essay on machines in general, employed the term “ force vive virtuelle,”’ of which “ potential energy ” might be supposed to be almost a literal translation. That coincidence shows how na- turally the phrase “‘ potential energy,” or something equivalent, occurs to one in search of words appropriate to denote that power of performing work which is due to configuration and not to activity. 1]. Having explained the reasons which led me to propose the use of the phrase “ potential energy,” I have next to make some observations on the objection made by Sir John Herschel to that phrase, that ‘‘it goes to substitute a truism for a great dynamical fact.” 12. It must be admitted that the use of the term “ potential energy ” tends to make the statement of the law of the conser- vation of energy wear to a certain extent the appearance of a truism. » It seems to me, however, that such must always be the effect of denoting physical relations by words that are specially adapted to express the properties of those relations, or, what amounts virtually to the same thing, of drawing up precise and complete definitions of physical terms. Let A and B denote certain conceivable relations, and let them be precisely and com- pletely defined; then from the definitions follows the proposition that A and B are related to each other in a certain way; and that proposition wears the appearance of a truism, and is virtu- ally comprehended in the definitions. But it isnot a bare truism ; for when with the definitions are conjoined the two facts ascer- tained by experiment and observation—that there are relations amongst real bodies corresponding to the definition of A, and that there are also relations amongst real bodies corresponding to the definition of B—the proposition as to relation between A and B becomes not a bare truism, but a physical fact. In the present case, for example, “actual energy” and “ potential energy ” are defined in such a way that from the definitions it follows that what a body or a system of bodies gains m one form of energy through mutual actions it loses in the other form—in other words, that the sum of actual and potential energies is “conserved; and this sounds like a truism; but when it is proved by experiment and observation that there are relations amongst real bodies agreeing with the definitions of “ actual * Sir William Thomson and Professor Tait have lately substituted the | word “kinetic ” for “ actual.” and on the Definitions of Physical Quantities. 91 energy ” and “ potential energy,” that which otherwise would be a truism becomes a fact. 13. A definition can neither be true nor false ; for it makes no assertion, but says, “let such a word or phrase be used in such a sense;” but it may be real or fantastic, according as the descrip- tion contained in it corresponds or not to real objects and phe- nomena; and when by the aid of experiment and observation a set of definitions have been framed which possess reality, preci- sion, and completeness, the investing of a physical fact with the appearance of a truism is often an unavoidable consequence of the use of the terms so defined. 14. In the case of physical quantities in particular, the defini- tion involves a rule for measuring the quantity ; and the proof of the reality of the definition is the fact that the application of the rule to the same quantity under different circumstances gives consistent results, which it would not do if the definition were fantastic ; and hence the definitions of a set of physical quantities necessarily involve mathematical relations amongst those quanti- ties, which, when expressed as propositions and compared with the definitions, wear the appearance of truisms and are at the same time statements of fact. 15. In illustration of the foregoing principles, it may be pointed out that there is a certain set of definitions of the mea- surement of time, force, and mass which reduces the laws of mo- tion to the form of truisms: thus— I. Let “ equal times’ mean the times in which a moving body under the influence of no force describes equal spaces. This defi- nition is proved to be real by the fact that times which are equal when compared by means of the free motion of one body, are equal when compared by means of the free motion of any other body. If the definition were fantastic, times might be equal as measured by the free motion of one body, and unequal as mea- sured by that of another. Il. Let “force ” mean a relation between a pair of bodies such that their relative velocity changes or tends to change in magnitude or direction, or both; and let “ equal furces” mean those which act when equal changes of the relative velocity of a given pair of bodies occur in equal times. This definition is proved to be real by the fact that the comparative measurements of forces made in different intervals of time are consistent with each other, which would not be the case if the definition were fantastic. III. Let the “mass” of a body mean a quantity inversely proportional to the change of velocity impressed on that body in a given time by a given force. This definition is proved to be real by the fact that the ratio of the masses of two given bodies 92 Prof. Tyndall on Sounding and Sensitive Flames. is found experimentally to be always the same when those masses are compared by means of the velocities impressed on them by different forces and in different times, and is also the same whether each of the masses is measured as a whole or as the sum of a set of parts. Assuming those definitions as merely verbal, without refer- ence to their reality, the laws of motion take the form of verbal truisms ; but when experiment and observation inform us that permanent relations exist among real bodies and real events corresponding to the definitions, those apparent truisms become statements of fact. 16. One of the chief objects of mathematical physics is to ascertain, by the help of experiment and observation, what phy- sical quantities or functions are “conserved.” Such quantities or functions are, for example, I. The mass of every particle of matter—conserved at all times and under all circumstances. II. The resultant momentum of a body or system of bodies —conserved so long as internal forces act alone. Ill. The resultant angular momentum of a body or system of bodies—conserved so long as internal forces act alone. IV. The total energy of a body or system of bodies—con- served so long as internal forces act alone. V. The thermodynamic function—conserved in a body while it neither receives nor gives out heat. In defining such physical quantities as those, it is almost, if not quite, impossible to avoid making the definition imply the property of conservation ; so that when the fact of conservation is stated, it has the form of a truism. 17. In conclusion, it appears to me that the making of a phy- sical law wear the appearance of a truism, so far from being a ground of objection to the definition of a physical term, is rather a proof that such definition has been framed in strict accordance with reality. Glasgow University, January 9, 1867, XIV. On Sounding and Sensitive Flames. By Joun Tynpatt, LL.D., F.R.S., Professor of Natural Philosophy R.I., &c.* HE sounding of a hydrogen-flame when enclosed within a glass tube was, I believe, first noticed by Dr. Higgins in 1777. The subject ‘has been since investigated by Chladni, De la Rive, Faraday, Wheatstone, Rijke, Sondhauss, and Kundt. The action of unisonant sounds on flames enclosed in tubes has been * Abstract of a lecture delivered at the Royal Institution of Great Britain, on Friday, January 18, 1867 Prof. Tyndall on Sounding and Sensitive Flames. 93 investigated by Count Schaffgotsch and myself. The jumping of a naked fish-tail flame, in response to musical sounds, was first noticed by Professor Leconte at a musical party in the United States. He made the important observation that the flame did not jump until it was near flaring. That his discovery was not further followed up by this learned investigator was probably due to too great a stretch of courtesy on his part towards myself *. Last year, while preparing the experiments for one of my “Juve- nile Lectures,” my late assistant, Mr. Barrett, observed the effect independently; and he afterwards succeeded in illustrating it by some very striking experiments. With a view to the present discourse, and also to the requirements of a forthcoming work on scund, the subject of sounding and sensitive flames has been re- cently submitted to examination in the laboratory of the Royal Institution. The principal results of the inquiry are embodied in the following abstract. Pass a steadily-burning candle rapidly through the air, you obtain an indented band of light, while an almost musical sound heard at the same time announces the rhythmic character of the motion. If, on the other hand, you blow against a candle-flame, the fluttering noise produced indicates a rhythmic action. When a fluttering of the air is produced at the embouchure of an organ-pipe, the resonance of the pipe reinforces that par- ticular pulse of the flutter whose period of vibration coincides with its own, and raises it to a musical sound. When a gas-flame is introduced into an open tube of suitable * The observation of Professor Leconte is thus graphicaily described :— ** Soon after the music commenced, I observed that the flame of the burner exhibited pulsations in height which were exactly synchronous with the audible beats. This phenomenon was very striking to every one in the room, and especially so when the strong notes of the violoncello came in. It was exceedingly interesting to observe how perfectly even the frills of this instrument were reflected on the sheet of flame. A deaf man might have seen the harmony. As the evening advanced, and the diminished con- sumption of gas in the city increased the pressure, the phenomenon became more conspicuous. The jumping of the flame gradually increased, became somewhat irregular, and finally it began to flare continuously, emitting the characteristic sound indicating the escape of a greater amount of gas than could be properly consumed. I then ascertained, by experiment, that the phenomenon did not take place unless the discharge of gas was so re- gulated that the flame approximated to flaring. I likewise determined that the effects were not produced by jarring or shaking the floor and walls of the room by means of repeated concussions. Hence it is obvious that the pulsations of the flame were not owing to indirect vibrations propagated through the medium of the walls of the room to the burning apparatus, but must have been produced by the direct influence of aérial sonorous pulses on the burning jet.”—Silliman’s American Journal for January 1858 ; Phil. Mag. for March 1858. 94 Prof. Tyndall on Sounding and Sensitive Flames. length and width, the current of air passing over the flame pro- duces such a flutter, which the resonance of the tube exalts to a musical sound. Introducing a gas-flame into this tin tube three feet long, we obtain a rich musical note; introducing it into a tube six feet long, we obtain a note an octave deeper—the pitch of the note depending on the length of the tube. Introducing the flame into this third tube, which is fifteen feet long, the sound as- sumes extraordinary intensity. The vibrations which produce it are sufficiently powerful to shake the pillars, floor, seats, gal- lery, and the five or six hundred people who occupy the seats and gallery. The flame is sometimes extinguished by its own violence, and ends its peal by an explosion as loud as a pistol- shot. The roar of a flame in a chimney is of this character: it is a rude attempt at music. By varying the size of the flame, these tubes may be caused to emit their harmonic sounds. Passing from large pipes to small ones, we obtain a series of musical notes, which rise in pitch as the tube diminishes in length. This flame, surrounded by a tube 17% inches long, vibrates 459 times in a second, while that contained in this tube, 102 inches long, vibrates 717 times in a second. Owing to the intense heat of the sounding column, these numbers are greater than those corresponding to organ-pipes of the same lengths sounding in air. The vibrations of the flame consist of a series of partial ex- tinctions and revivals of the flame. The singing flame appears continuous; but if the head be moved to and fro, or if an opera-glass, directed to the flame, be caused to move to and fro, or if, after the method of Wheat- stone, the flame be regarded in a mirror which is caused to rotate, the images due to the revivals of the flame are separated from each other, and form a chain of flames of great beauty. With a ‘longer tube and larger flame, by means of a concave mirror, I can project this chain of flames upon a screen. I first clasp my hand round the end of the tube so as to prevent the cur- rent of air which causes the flutter from passing over the flame ; the image of the flame is now steady upon the screen before ou. I move the mirror, and you have this continuous luminous band: I withdraw my hand ; the current of air passes over the flame, and instantly the band breaks up into a chain of images. A position can be chosen in the tube at which the flame bursts spontaneously into song. A position may also be chosen where the flame is silent, but at which, if it could only be started, it would continue to sound. It is possible to start Prof. Tyndall on Sounding and Sensitive Flames. 95 such a silent flame by a pitch-pipe, by the siren, or by the human voice. It is also possible to cause one flame to effect the mu- sical ignition of another. The sound which starts the flame must be nearly in unison with its own. Both flames must be so near unison as to pro- duce distinct beats. A flame may be employed to detect sonorous vibrations in air. Thus, in front of this resonant case, which supports a large and powerful tuning-fork, I move this bright gas-flame to and fro. A continuous band of light is produced, slightly indented through the friction of the air. The fork is now sounded, and instantly this band breaks up into a series of distinct images of the flame. . Approaching the same flame towards either end of one of our tin tubes with the sounding flame within it, and causing it to move to and fro, the sonorous vibrations also effect the breaking up of the band of light into a chain of images. In this glass tube, 14 inches long, a flame is sounding: I bring the flat flame of a fish-tail burner over the tube, the broad side of the flame being at right angles to the axis of the tube. ‘The fish-tail flame imstantly emits a musical note of the same pitch as that of the singing flame, but of different quality. Its sound is, in fact, that of a membrane, the part of which it here plays. . Against a broad bat’s-wing flame I allow a sheet of air, issuing from a thin slit, to impinge. A musical note is the consequence. ‘The note can be produced by air or by carbonic acid ; but it is produced with greater force and purity by oxygen. The pitch of the note depends on the distance of the slit from the flame. Before you burns a bright candle-flame: I may shout, clap my hands, sound this whistle, strike this anvil with a hammer, or explode a mixture of oxygen and hydrogen; though so- norous waves pass in each case through the air, the candle is absolutely insensible to the sound; there is no motion of the flame. I now urge from this small blowpipe a narrow stream of air through the flame of the candle, producing thereby an incipient flutter, and reducing the brightness of the flame. I now sound the whistle; the flame jumps visibly. Matters may be so ar- ranged that when the whistle sounds the flame shall be either almost restored to its pristine brightness, or the amount of light it still possesses shall disappear. Before you now burns a bright flame from a fish-tail burner. I may, as before, shout, clap my hands, sound a whistle, or 96 Prof. Tyndall on Sounding and Sensitive Flames. strike an anvil; the flame remains steady and without response. I urge against the broad face of the flame a stream of air from the blowpipe just employed. The flame is cut in two by the stream of air; it flutters slightly; and now when the whistle is sounded the flame instantly starts. A knock on the table causes the two half-flames to unite and form for an instant a flame of the ordinary shape. By a slight variation of the ex- periment, the two side flames disappear when the whistle is sounded, and a central tongue of flame is thrust forth in their stead. . Passing from a fish-tail to a bat’s-wing burner, I obtain this broad steady flame. It is quite: insensible to the loudest sound which would be tolerable here. The flame is fed from this gas- holder, which places a power of pressure at my disposal unattaim- able from the gas-pipes of the Institution. I turn on more gas ; the flame enlarges, but it is still sensible to sound. I enlarge it still more, and now a slight flutter of its edge answers to the sound of the whistle. Turning on a little more gas, and sound- ing again, the jumping of the flame is still more distinct. Finally I turn on gas until the flame is on the point of roaring, as flames do when the pressure is too great. I now sound my whistle; the flame roars and thrusts suddenly upwards eight long quivering tongues. 1 strike this distant anvil with a hammer, the flame instantly responds by thrusting forth its tongues. Another flame is now before you. It issues from a burner formed of ordinary gas-tubing by my assistant. The flame is 18 inches long, and smokes copiously. I sound the whistle ; the flame falls to a height of 9 inches, the smoke disappears, and the brilliancy of the flame is augmented *. Here are two other flames, also issuing from burners formed by my assistant. The one of them 1s long, straight, and smoky; the other is short, forked, and brilliant. I sound the whistle ; the long flame becomes short, forked, and brilliant ; the forked flame becomes long and smoky. As regards, there- fore, their response to the sonorous waves, the one of these flames is the exact complement of the other. Here are various flat flames, 10 mches high, and about 3 inches across at their widest part. They are purposely made forked flames. When the whistle sounds, the plane of each flame turns ninety degrees round, and continues in its new. po- sition as long as the whistle continues to sound. Here, again, is a flame of admirable steadiness and brilliancy, * Mr. Barrett also observed the imcrease of light on the shortening of a flame by a musical sound ; nor did the superior effect of high notes escape the attention of this acute and skilful young experimenter. Prof. Tyndall on Sounding and Sensitive Flames. 97 issuing from a single circular orifice in a common iron nipple. I whistle, clap my hand, strike the anvil, and produce other sounds; the flame is perfectly steady. Observe the gradual change from this apathy to sensitiveness. The flame is now A incheshigh. I make its height 6 inches; it is still indifferent. I make it 10 inches; a barely perceptible quiver responds to the whistle. I make it 14 inches high, and now it jumps briskly the moment the anvil is tapped or the whistle sounded. I aug- ment the pressure; the flame is now 16 inches long, and you observe a quivering which announces that the flame is near roaring. I increase the pressure; it now roars, and shortens at the same time to a height of 8 inches. I diminish the pressure a little; the flame is again 16 inches long, but it is on the point of roaring. It stands, as it were, on the brink of a pre- cipice. The whistle pushes it over. Observe it shortens when the whistle sounds, exactly as it did when the pressure was in excess. The sonorous pulses, in fact, furnish the supplement of energy necessary to produce the roar and shorten the flame. This is the simple philosophy of all these sensitive flames. The pitch of the note chosen to push the flame over the brink is not a matter of indifference. I have here a tuning- fork which vibrates 256 times in a second, emitting a clear and forcible note. It has noeffect upon this flame. Here are three other forks, vibrating respectively 320, 384, and 512 times in a second. Not one of them produces the slightest impression upon the flame. But, besides their fundamental: notes, these forks can be caused to sound a series of overnotes of very high itch. I sound this series of notes: the vibrations are now 1600, 2000, 2400, and 8200 per second respectively. The flame jumps in response to each of these notes, the response to the highest note of the series being the most prompt and ener- getic of all. To the tap of a hammer upon a board the flame responds; but to the tap of the same hammer upon an anvil the response is much more brisk and animated. The reason is, that the clang of the anvil is rich in the higher tones to which the flame is most sensitive. Here again is an inverted bell, which I cause to sound by means of a fiddle-bow, producing a powerful tone. The flame is unmoved. I bring a halfpenny into contact with the sur- face of the bell: the consequent rattle contains the high notes to which the flame is sensitive. It instantly shortens, flutters, and roars when the coin touches the bell. Here is another flame, 20 inches long. I take this fiddle in my hand, and pass a bow over the three strings which emit the deepest notes. There is no response on the part of the flame. Phil. Mag. 8S. 4. Vol. 33. No. 221. Feb. 1867. H 98 Prof. Tyndall on Sounding and Sensitive Flames. I sound the highest string: the jet instantly squats down to a tumultuous bushy flame, 8 inches long. I have here a small bell, the hammer of which is caused to descend by clock-work. I hold it at a distance of 20 yards from the flame. The strokes follow each other in rhythmic succession, and at every stroke the flame falls from a height of 20 to a height of 8 inches. The rapidity with which sound is propagated through air is well illustrated by these experiments. There is no sensible inter- val between the stroke of the bell and the shortening of the flame. Some of these flames are of marvellous sensibility ; one such is at present burning before you. It is nearly 20 inches long; but the slightest tap on a distant anvil knocks it down to 8. I shake this bunch of keys or these few copper coms in my hand: the flame responds to every tinkle. I may stand at a distance . of 20 yards from this flame: the dropping of a sixpence from a height of a couple of inches into a hand already containing coin knocks the flame down. I cannot walk across the floor without affecting the flame. The creaking of my boots sets it m vio- lent commotion. The crumpling of a bit of paper, or the rustle of a silk dress, does the same. It is startled by the plashing of a raindrop. I speak to the flame, repeating a few lines of poetry; the flame jumps at intervals, apparently picking certain sounds from my utterance to which it can respond, while it is unaffected by others. In our experiments downstairs we have called this the vowel flame, because the different vowel sounds affect it differently. Vowel sounds of the same pitch are known to be readily distin- guishable. Their qualities or clang-tints are different, though they have a common fundamental tone. They differ from eack other through the admixture of higher tones with the funda- mental. It is the presence of these higher tones im different proportions that characterizes the vowel sounds ; and it is to these same tones, and not to the fundamental one, that our flame is sensitive. J utter a loud and sonorous U, the flame remains steady ; I change the sound to O, the flame quivers ; [ sound E, and now the flame is affected strongly. I utter the words boot, boat, and beat in succession. To the first there is no response ; to the second, the fiame starts; but by the third it is thrown into violent commotion; the sound AA! is still more powerful. When the vowel sounds are analyzed, their constituents are found to vary in accordance with the foregoing experiments, those characterized by the sharpest overtones being the most powerful excitants of the flame. (See Helmholtz in Pogg, Annalen, vol. evi. p. 286.) The flame is peculiarly sensitive to the utterance of the letter S. Ifthe most distant person in the room were to favour me with a “hiss,” the flame would be instantly shivered into tu- On some Effects produced by a Fluid in Motion. 99 mult. The utterance of the word “hush,” or “ puss,” pro- duces the same effect. This hissmg sound contains the precise elements that most forcibly affect the flame. The gas issues from its burner with a hiss, and an external sound of this cha- racter added to that of a gas-jet already on the point of roaring is equivalent to an augmentation of pressure on the issuing stream of gas. I hold in my hand a metal box containing com- pressed air. I turn the cock for a moment, so as to allow a puff to escape—the flame instantly ducks down, not by any transfer of air from the box to the flame, for I stand at a distance which utterly excludes this idea; it is the sound of the issuing air that affects the flame. The hiss produced in one orifice precipitates the tumult at the other. Note.—Those who wish to repeat these experiments would do well to bear in mind, as an essential condition of complete success, that a free way should be open for the transmission of the vibrations from the flame, backwards, through the gas-pipe which feeds it. The orifices of the stopcocks near the flame ought to be as wide as possible. XV. On some Effects produced by a Fluid in Motion. By Grorce Farrer Ropwet1, F.C.S.* [ With a Plate. | No. III. 1. Effects produced by a stream of liquid, (a) entering, and (8) issuing from a liquid mass at right angles to its surface.—2. Amount of lateral action exercised by (a) a jet of water, and (() a jet of steam of known. pressure.—3. Note on the constitution of a de- scending liquid jet. 1{* the first and second of these paperst I have considered the various modes by which air is carried down by a stream of water; in the present I propose to treat chiefly of some effects more or less directly attributable to the so-called “lateral action ” of Venturi{, which Professor Magnus§ has proved to result from the well-ascertained fact (also demonstrated theoretically by Daniel Bernouilli and by Poisson) that the pressure exerted by a fluid in motion is less than its pressure when at rest. Asa consequence of this action, a fluid entering or issuing from a fluid mass at rest tends to produce various effects, some of which have been described below. * Communicated by the Author. + Phil. Mag. for January and September 1864. { Recherches expérimentales sur le principe de la communication latérale du mouvement dans les fluides. § “On the Motion of Fluids,”’ Transactions of the Royal Academy of Sciences of Berlin, 1848. Translated im the Philosophical Magazine for Jauuary 1851. H 2 100 Mr. G. F. Rodwell on some Effects 1. Effects produced by a stream of liquid, (a) entering, and (8) issuing from a liquid mass at right angles to its surface. A stream of water flowing at the rate of 12 cubic centimetres per minute, was allowed to run down the side of a beaker con- taining water, upon the surface of which lycopodium had been sprinkled; the adhesion of the glass flattened the stream into a thin ribbon of water 6 millims. broad by 1 millim. thick. At the point where the stream entered (A, fig. 1, Plate II.) the particles of lycopodium were driven forward in a straight line to the opposite side of the beaker; they then returned in the direc- tion of the arrows, and entered the central current immediately beneath the descending stream. At the junctures of the re- turning currents with the central current the lycopodium re- volved with great rapidity in circles moving in epposite direc- tions, as shown in the figure, which represents the water-sur- face. Particles of lycopodium were found to collect together on ~ each side of the descending stream; when these were dislodged from their position, the circular currents disappeared, and lyco- podium was observed to rise a short distance into the descend- ing stream, and to revolve in ellipses moving in opposite direc- tions. One ellipse was apparent on each side of the descending stream; and the major axis of each was four or five times as great as the minor. By colourimg the descending stream, the main body of liquid entering the beaker was seen to pass between the ellipses, although the space was not more than one tenth of the breadth of the whole stream. In fig. 2 (in which the eye is supposed to be on a level with the water-surface) A represents the descending stream, B the water-surface, and C the stream as it enters the water after passing between the ellipses. In the first experiment a central current is produced by the entering stream, which flows across the beaker until it reaches the opposite side, when it divides into two currents, returning by the sides of the vessel. Immediately before the coalescence it is obvious that the side currents move at right angles to the central current; circular currents at the points of juncture are the result. The motions which produce these circular currents are, {#) the motion possessed by the returning currents, directly derived from the motion of the central current, but of less mag- nitude on account of the friction of the sides of the vessel, plus (8) the motion caused by the lateral action of the central current when the side currents approach it, acting together in one di- rection ; and (y) the motion of the central current acting in a direction at right angles to this. In the second experiment the particles of water of the return- ing currents, when they are compelled by the central current to produced by a Fluid in Motion. 101 discontmue to move in their original direction, are influenced by the adhesion of the glass, which tends to draw them upwards; they are no longer prevented from rising by the accumulation of lycopodium on each side of the descendimg stream, and they meet with less resistance thanif they moved forward at once with the central current, they consequently ascend. To the motions producing the circular currents in the first experiment, we have to add that produced by the adhesion of the glass, acting in a different direction ; as a consequence, the circular motion of the water-particles is changed into an elliptic motion, the major axis of the ellipse being os the direction of the newly edged force, as we should expect. A jet of water issuing from an orifice 1°5 millim. in diameter with sufficient force to rise to the height of a metre, was caused to enter water at right angles to its surface. A cylindrical copper vessel, *3 metre in diameter by :17 metre deep, was used for the purpose ; and the water-surface (upon which lycopodium was sprinkled) stood at a height of 75 millims. from the bottom of the vessel. The orifice of the delivery-tube was placed 3 mil- lims. above the water-surface, and the jet was allowed to enter near the side of the vessel. The particles of lyeopodium beneath the influent jet immediately began to revolve around it in con- centric circles, having the jet for their centre, and currents were produced similar to those shown in fig. 1, but moving mm a re- verse direction ; that is to say, the side currents moved from the jet, and the central current into which they united moved towards the jet. When the influent jet was placed in the centre of the vessel instead of near its side, the lycopodium moved radially to the sides of the vessel, and returned ; after which the course of the currents could not be traced, because they met each other in various positions, producing spiral and circular eddies. If in- stead of allowing the jet to enter the water by its clear portion, that is to say, above the vena contracta, it was caused to enter by its opake and agitated portion, the particles of lycopodium, in- stead of revolving around the jet, were drawn towards it by a spiral current and carried beneath the water-surface. A jet of water, similar in all respects to that employed in the last experiment, was allowed to escape 1 millim. beneath the surface of water; it issued from the water at right angles to its surface, and in contact with the side of the containing vessel. After ascending to the height of about 100 millims. the jet divided and returned in two parabolas, one on each side of the- ascending jet. Lycopodium entered the ascending jet with great velocity, followed the path of the parabolas, and reentered the jet by currents moving in a parabola, which started from 102 Mr. G. F. Rodwell on some Effects the returning streams, and ended at the ascending jet; within these parabolic currents the particles of lycopodium were ob- served to revolve in ellipses moving in contrary directions. Par- ticles of lycopodium rose into that portion of the two descending streams most remote from the ascending jet, and revolved in ellipses moving in opposite directions, the major axis of each ellipse being parallel to the descending stream. ‘The particles in each elliptic current revolved in a direction opposite to that of those which revolved in the ellipse (within the parabolic current) nearest to it. In fig. 3, A represents the ascending jet, B B the returning streams, CC the parabolic currents on the water- surface immediately beneath them, and D the central surface- current induced by the lateral action of the ascending jet. The jet A ascends until it is stopped by the adhesion of the substance of the vessel, it then returns by the two parabolic streams BB. Now these returning streams tend, on entering the liquid mass beneath them, to produce the same currents which we have seen (from the first experiment) to be produced when a stream of liquid enters a liquid mass at right angles to its surface. But particles of water are hurrying towards D to supply the place of those which are perpetually dragged from the vessel by the lateral action of A; hence the currents which would otherwise proceed in straight lines from the points at which B B enter the fluid are caused to curve round to the point from which A issues. Many very beautiful effects may be produced by allowing a jet of water, capable of rising to the height of about a metre, to impinge upon the edge of a vessel. The jet, more or less re- strained by adhesion, breaks up into numberless globules of water following a great variety of curved paths. When a jet of water is allowed to escape just beneath the surface of water upon which lycopodium has been scattered, the currents produced at right angles to the axis of the jet are rendered very apparent by the rapid rush of lycopodium into the ascending jet. The particles are carried away by the jet, and in this manner a large surface of water may be entirely freed from lycopodium in the course of a few minutes. One of Venturi’s first experiments on lateral action was that in which he caused a stream of water to flow through a vessel containing water, and to escape above its level, by which means the water speedily sank to the level of the stream. A Jet of water delivering, say, 100 cub. centims. per minute may be caused (by allowing it to escape nearly vertically several millimetres be- neath a water-surface) to remove far more than its own volume of water from the vessel. The quantity removed obviously de- pends entirely upon the velocity of the issumg Jet: currents are produced by a Fluid in Motion. 103 established which convey particles of water to it ; and the latter are removed from the vessel, in virtue of their cohesion to the water of the jet, from which they receive a direct communica- tion of motion. The jet escaping in air rises to a height of, say, a metre; but when it escapes beneath a water-surface it rises only to one-third or one-fourth of that height, because it has given up a great deal of its motion to the particles of water which leave the vessel in company with it. The action of the so-called “hydraulic belt” is perfectly ana- logous to that of a jet escaping upwards from beneath a water- surface; indeed the revolving band may be viewed as such an ascending jet. The hydraulic belt is employed to raise water from deep wells, and consists of'an endless band of felt passing over two rollers, one placed at the top and the other at the bot- tom of the well; rapid motion is communicated to the band by the revolution of the upper roller, and water adheres to it, and rises with it until in passing over the upper roller it is thrown off at a tangent. Now water is forcibly dragged from the well in virtue of its adhesion to the band ; currents are thus established in the mass of liquid in the well at right angles to the direction of the issuing water, and by these water is perpetually conveyed to the band. The adhering particles of water share the motion of the band; and they do not descend, because, although gravity could readily overcome their adhesion, it has in this instance to stop a certain amount of motion associated with each particle, before it can begin to act against their adhesive force. The quantity of liquid raised by such a process depends upon the velocity of the band and the viscosity of the liquid (which is only another term for expressing the amount of cohesion possessed by its particles). Thus, the rate of revolution of the band being constant, if we take ether, water, and treacle as the liquids, we should be able to raise a larger quantity of treacle than of water, and of water than of ether ; or, again, to raise equal quan- tities of these liquids, we should require the band to be driven with the greatest velocity for ether, less for water, and least for treacle. But, on the other hand, the denser the liquid, the greater would be the amount of force necessary to produce a given rate of revolution. 2. Amount of lateral action exercised by (a) a jet of water, and (B) a jet of steam of known pressure. a. Water-jet.—In order to gain some idea of the amount of liquid entering a current laterally, I took a graduated tube (A, fig. 4) 15 millims. in diameter, filled it with water, and placed within it a tube B, 4°5 millims. in diameter, and drawn out at C to an orifice 1‘5 millim. in diameter. B was 5 metre long; and 104 Mr. G. F. Rodwell on some Effects when the water in A was level with the orifice of C, it dipped ‘4 metre beneath the water-surface m A. The tube B was filled with water before introducing it into A (the orifice C bemg closed by the finger); on opening C, water flowed from A and came to rest about 20 millims. above the orifice of C; but when a substance capable of being wetted by water was placed at ©, the water in A immediately sank to the level of C. The cause of this is obvious: when the water in A had fallen nearly to the level of C, the adhesion of the glass of B for the water within it was sufficient to counterbalance the weight of a small column of water in A; but so soon as the water in B was allowed to come in contact with another body outside B, the adhesion within the tube was counterbalanced by adhesion outside, and water consequently flowed from C until a perfect level had been estab- lished. The tube D, 4°5 millims. in diameter, was placed above the orifice C in such a manner that its centre was 6 millims. from the centre of C, and it was caused to deliver a stream of water (flow- ing from a cistern with a water-head of ‘66 metre) exactly at aright angle to a line passing through the centre of C. The apparatus being thus arranged, and the water in A standing on a level with the orifice C, it is obvious that any force tending to remove water from A has to overcome the downward pressure of a column of water in the longer limb of B, and also that, the greater the amount of water removed from A, the greater is the pressure to be overcome. When water was allowed to flow from D at the rate of 1575 cub. centims. per minute, the following quantities of water were removed from A by the lateral action of the stream :— First half minute . . . 21 cub. centims. Second _,, aa tales raya )3) a ithird:\-) . . . No water removed. The flow from D was now diminished one-half (viz. to 787-5 cub. centims. per minute), the level of the water in A with C being first attamed. The flow from A was as follows :— First half minute . . . 5 cub. centims. Second _,, MR eg Peta se Third.’ , . . . No water removed. When the flow of water from D was diminished to one-fourth its original quantity (viz. to 393°75 cub. centims. per minute), no water was removed from A. When water flowing from D at the rate of 1575 cub. centims. per minute was allowed to flow for half a minute (so that 21 cub. centims. were removed from A), and was then diminished produced by a Fluid in Motion. 105 to a flow of 300 cub. centims. per minute, water passed from the descending stream through B to the tube A, and quickly restored the level which the more rapid current had rendered unequal. At the commencement of the experiment the particles of water in B are at rest; as soon as water flows from D, the par- ticles exposed at C pass into the descending stream, and par- ticles immediately behind these rush forward to fill the vacated places; but the greater the number of particles removed, the greater is the force tending to draw them back into A; for the pressures become more and more unequal, and more and more force is stored up in each of the particles of water in B above the water-level in A. Thus there is a strain upon the particles which acts against the lateral force of the stream from D, and the amount of water removed from A gradually becomes less, until a point is reached at which the pressure of the column of water in the longer limb of B exactly balances the force exercised by the descending stream; water then ceases to be removed from A. In the last experiment, as long as the water flowed with a certain velocity, the weight of the column of water in B, tend- ing to equalize the levels, was incompetent to draw water from the current, because it would have to stop a certain amount of motion before it could do so; but when the velocity of the cur- rent was diminished, the weight of the column of water in B became competent to stop the motion of the particles of water, and therefore to equalize the pressures by drawing water from the descending stream. 8. Steam~jet.—The first experiments with a jet of steam were made to determine the variation produced in the lateral-action effect by changing the angle at which the jet impinged upon the orifice of a discharge tube; and the effect was measured in the same manner as that employed to measure the lateral effect of a jet of water. The steam was allowed to attain a pressure of 304 millims. of mercury*, and to escape through an orifice 4°5 millims. diameter placed 6 millims. from the orifice C of the tube B (fig. 4) ; the same tubes were used, and the experiments were conducted in the same way as with the water-jet experiments described above. The rush of steam lasted about ten seconds at the above pressure, during which time the various amounts of water given below were removed from the tube A (fig. 4). The tube B was first filled with water, and afterwards left empty ; so that in the one case the steam impinged against a surface of water, and in the other against a surface of air. In fig. 5 the _ * Equal to ‘4217 kilopramime on a square centimetre, or to 6 lb. on a square inch. 106 Mr. G. F. Rodwell on some Effects various positions of the tube D are shown; S represents the horizontal limb of the tube B. 1. Tube delivering the steam-jet inclined to the tube S at an angle of 22°-5, (A, fig. 5.) Tube full of water. (Steam impinging on water-surface.) . Mean of twenty-one determinations, eight of which gave 3°5 cub. centims., and seven of the remainder 3°25 cub. centims., =3'34 cub. centims. Tube empty. (Steam impinging on air-surface.) No water was removed. P4p Angle of 45°. (Ess fig. 5.) E cub. centims. Tube full. Mean of fifteen determinations = 9°73 Tube empty. pe Se “a = oulek 3. Angle of 67°°5. (C, fig. 5.) Tube full. Mean of nine determinations 12°52 Tube empty. ,, eight 33 8°66 4. Angle of 90°. (D, fig. 5.) Tube full. Mean of nine determinations varying between 13 and 13°75 cub. centims. Tube empty. Mean of eight determinations = 10:09 5. Angle of 112°°5. (H, fig. 5.) Tube full. The water was forced back into A (fig. 4). Tube empty. ‘The air in B was depressed below the water- surface in A (fig. 4). 6. When the tube delivering the jet of steam was placed at angles of 135° and 157°°5 (F and G, fig. 5), air was forced violently through the tube B (fig. 4), and escaped by its lower orifice into the graduated tube. ll Tl 13°32 The above experiments do not represent the lateral-action effect of a jet of steam sustained at an unvarying pressure, because (from the fact of the boiler being small), the maximum pressure could only be sustained for ten seconds when the steam was escaping from a tube 4°5 millims. in diameter: these experiments are thus capable of being strictly compared among themselves, but they must be considered to show the effect of varymg the impinging angle rather than the absolute effect of steam of the pressure employed. The following experiments were made in order to determine the absolute lateral-action effect of a jet of steam sus- tained at an unvarying pressure. A stopcock having an internal diameter of 4°5 millims. was connected with a tube proceeding direct from a large steam- boiler the pressure of steam in which varied from 1013 to 1520 produced by a Fluid in Motion. 107 millims. of mercury*. A glass tube, A, fig. 6, °3 fhetialonte by 4 millims. internal diameter, was drawn out at one end to an orifice 1°5 millim. in diameter, and was placed in the position shown in the figure, the lower end dipping into a vessel of mer- cury, B; C represents the end of the stopcock. A scale was attached to A to indicate the amount of diminution of pressure (and consequent ascent of mercury in A) caused by the lateral action of the jet of steam proceeding from U. ‘The upper orifice of A was placed exactly in the axis of the effluent jet. By looking through a jet of effluent steam of high pressure a small inner cone (shown in the figure) is observed, to the apex of which the greater number of particles of steam converge; around and beyond thisc one there is steam of less density ; and it will be seen below that, beyond the apex of the cone, the amount of lateral action diminishes considerably. The following results were obtained with a pressure of steam equal to 1216 millims. of mercury + :— Atmospheric pres- | Distance of the orifice of A from the | Height to which sure (barometer orifice of C in millimetres. ¥ aS- | =760 millims.) ceuded in A. | Sf ieutelet. Sin aot a reduced to | | | millims. millims. 1 millim. (within the ne ae teaaideat 196 564 | 3 B milims. yy ceeeennce 228 532 ae the apex of the cone).. 180 580 »» beyond the cone) .......... 126 634 = 3 ” 23) hee to 38 722 5 aE BERT 27 | 733 745 When the orifice of A was 1 millim. distant from the orifice of C (a plane parallel to the one being at right angles to a plane parallel to the other), and the centre of the orifice of A coinci- dent with the centre of a cross section of the effluent jet, as in a, fig. 6, the mercury, as stated above, rose in A to a height of 196 millims. When the centre of the orifice of A was placed in a position midway between the centre and circumference of a cross section of the effluent jet, as in 8, the mercury ascended to a height of 105 millims. Finally, when the centre of the orifice of A was placed very near the circumference of a cross section of the effluent jet, as in y, the mercury ascended only to a height * That is to say, from 14062 to 2°1094 kilogrammes on a square centi- metre, or from 20 to 30 Ib. ona square inch. + Equal to 1°6874 kilogramme on a square centimetre, or to 24 Ib. on a square inch. 108 Mr. G. F. Rodwell on some Effects of 52 millims., the distance of the orifice of A from that of C being the same throughout. Itis thus seen that the lateral action is nearly four times as great in the axis of the jet as at its circumference; and we should naturally expect the particles in the axis to move with far greater velocity than those at the circumference, for the same reason that the water in the centre of a river moves faster than that near the banks. ‘The same effect must obviously also ob- tain with solid particles such as sand, and even with large masses of matter. Who has not observed the passage of a crowd through a narrow channel (the corridor of a theatre for instance), and the rapid movement of the centre stream compared with that of the side streams? The individuals composing the centre stream make use of those at the sides as friction rollers; moreover the latter are impeded by friction against the walls of the corridor. The passage of water or steam through a resisting medium is perfectly analogous ; hence the results mentioned above. A tube A, fig. 7, was fitted with a brass cap B, capable of being screwed steam- tight upon the stopcock. A was 450 mil- lims. longand 5 millims. in internal diameter ; ; the length of the crosspiece C was 150 millims. Within C a brass tube 3°25 mil- lims. in diameter was introduced, so that the steam issuing from the stopcock passed through it instead of entering C. The lower end of A dipped into a vessel of mercury D, and a scale was attached to A to show the height to which mercury ascended in virtue of the lateral action of the steam-jet issuing from the brass tube within C. The greatest effect was found to be produced when the orifice of the brass tube was about 45 millims. from the orifice of C. The following results were obtained :— Pressure of steam, | Height to which he es a in millimetres of | the mercury as- = 760 4 aie es mercury. cended in A. em maillims:) reduced to millims. millims. millims. 1013 330 430 1165 380 380 1292 407 353 It is thus seen that, by an arrangement of this kind, the lateral action of a jet of steam having a pressure = 1165 millims. of mercury* is competent to reduce the atmospheric pressure to one-half. * Equal to 1:6171 kilogramme on a square centimetre, or ' to 23 Ib. on a square inch. produced by a Fluid in Motion. 109 It is usual to employ a gaseous body (air or steam) in motion for lecture illustrations of lateral action. As examples take, («) the suspension of a thin glass bulb in a vertically effluent jet of steam ; (@) the approach of two disks facing each other by direct- mg a jet of air through the centre of one of them so that it strikes the other; and (ry) the collapse of a partially open sheet of paper by blowing a current of air between the opposite leaves. But the lateral action of a liquid may be quite as readily shown as a lecture experiment. Thus, if a tube A, fig. 8,3 millims. in internal diameter, be caused to deliver a stream of water (flow- ing from a cistern with a waterhead of at least a metre), parallel to, and immediately beneath the surface of water, air will force itself through the water, as shown at B, and will be carried along by the jet until it finally escapes from the water some distance from the point at which it entered. Or construct a small mer- cury gauge of the form shown in fig. 9, and let the extremity A, drawn out toa fine point, be introduced into a liquid mass, while a magnified image of the limb B is thrown upon a screen by means of the electric lamp: on now causing a jet of water to impinge upon A at right angles to it, the diminution of pressure will be very apparent in the magnified image. Or, once again, let a jet be allowed to flow near a sphere of oil floating in static equilibrium in a medium of its own density, and the sphere will be observed to lengthen itself into an ellipsoid, with the major axis at right angles to the direction of the influent jet. 3. Note on the constitution of a descending liquid jet. It is well known that a descending liquid jet presents a per- fectly smooth continuous appearance above the vena contracta ; whereas below it a series of swellings and contractions appear, and the previously transparent jet becomes opake. By looking at a descending jet placed in front of a rapidly rotating strap furnished with alternate light and dark bands, Savart* found that its opake portion was composed of detached masses of liquid ; moreover he observed that the swellings of the jet were produced by drops extended horizontally, and the con- tractions by drops extended vertically —each drop passing through a series of osciliations, being alternately extended vertically and horizontally, and (of necessity) midway between the two posi- tions assuming the form of a perfect sphere. He further detected very Small spherical drops between the larger drops. Plateau, in a series of admirable and elegant researches (“ Sur les figures d’équilibre d’une masse liquide sans pesanteur”’), examined with * “Mémoire sur la constitution des veines liquides, lancées par des orifices circulaires en mince paroi,” Annales de Chimie et de Physique, vol. lin. (1833). 110 Mr. G. F. Rodwell on some Effects great accuracy the transformation of a liquid cylinder into iso- lated spheres, and clearly explained the cause of the phenomena observed by Savart. One of the modes of examination adopted by Plateau was to lessen the velocity of a descending liquid jet, so that its resolution into spheres could be watched with greater ease and without the employment of Savart’s strap or a revol- ving mirror. He effected this by causing a stream of oil to flow from a small funnel, through a column of liquid of slightly less density than the oil; it was then observed that when nearly all the oil had flowed from the funnel (that is to say, when the ve- locity of the effluent stream was least), the stream did not pre- serve its cylindrical form, but was resolved into spheres. Imme- diately before the separation of a sphere, a fine thread of liquid was seen to be extended between the sphere and the liquid from which it separated; and on the separation of the sphere this thread suddenly contracted into one or two minute spheres. The cause of the small intermediate drops observed by Savart was thus ex- plained. Their formation was afterwards observed by Magnus* in the case of a descending stream of water, his observations being made with a revolving mirror, and also by means of a rapidly rotating disk furnished with a narrow slit through which the stream was viewed. Professor Guthrie, in a recent paper “On Drops”y+, seems to ignore the existence of the fact that these drops were observed by Savart, Magnus, and Plateau, and accurately investigated by the last-named physicist. “When water,” he writes, “falls from glass through air, immediately after the drop separates, a very minute drop is frequently projected up- wards from the upper surface of the drop. 1 have not traced the conditions under which this supplementary drop is formed,” &c. From the above mode of expression one is led to infer that he was unaware of the previous detection of these supplementary drops. The particles of liquid of a descending stream must obviously acquire avery high velocity by the acceleration of gravity ; and it consequently follows that the struggle between cohesion and gravity which takes place below the vena contracta of a descend- ing stream cannot, from the shortness of its duration, be ob- served except by means of a rotating mirror, or by some other appliance for causing a body in motion to appear to the eye to be at rest. Plateau’s column of oil can be readily observed to transform itself into isolated spheres; but the production of the thread and its subsequent contraction into a small sphere can * “ Hydraulic Researches,” part 2, Poggendorff’s Annalen, vol. evi. Translated in the Philosophical Magazine for September 1859. ft Proceedings of the Royal Society for July 1864. : | produced by a Fluid in Motion. 111 only be observed by very close watching with the eye a short distance fromthe column. Experiments of this nature are there- fore unsuited for the lecture table. I have, by modifying Pla- teau’s experiment, reduced the velocity of a descending fluid to a minimum, so that the separation of a sphere, together with the intermediate thread and the sphere which it produces, can be readily shown as a lecture experiment. The mode of effecting this is, to cause the cohesion acting upon the particles of a fluid mass floating in a medium of nearly its own density to slightly preponderate over the gravitating force of the mass, and then, by slowly reducing the density of the medium, to allow gravity to act upon one portion of the mass. A tall beaker was filled with a mixture of alcohol and water of the same density as oil: a quantity of oil was then introduced suf- ficient to form a sphere about 35 millimetres in diameter. When the sphere floated perfectly at rest in the centre of the medium, a small quantity of water was added so as to render the medium shghtly denser than the oil; the sphere now rose slowly to the surface, and assumed the form of a hemisphere with its plane surface in contact with the surface of the liquid. On gently warming the alcohol-and-water mixture, the hemisphere length- ened itself until it became a thick cylinder, hemispherical below, and with its upper end in contact with the liquid surface. Then it began to narrow at a point nearly midway between its opposite ends; and this continued until the cylinder was resolved into two masses of oil, separated by a narrow thread. A moment later the two masses suddenly contracted,—the upper one to a very convex plano-convex lens with its plane surface in contact with the liquid surface, the lower one to a nearly perfect sphere, which during its descent to the bottom of the beaker be- came slightly extended, alternately, at right angles to and parallel with the water-surface. The thread of oil which had been drawn out by the weight of the lower mass, being no longer thus re- strained, contracted into a small sphere floating midway between the separated masses of oil. Perhaps a more effective mode of showing the experiment is the following. Prepare, as before, a mixture of alcohol, and water ; introduce a quantity of oil sufficient to form a sphere from 40 to 50 millims. in diameter, and let the density of the mix- ture be such that the sphere floats 20 or 30 millims. below the surface, the entire depth of the liquid being from 175 to 200 millims. On heating the mixture the sphere extends itself into an ellipsoid with its major axis at right angles to the liquid sur- face ; it then gradually contracts at a pomt midway between the ends, until, as in the previous experiment, only a fine thread separates the two larger masses of oil; rupture then ensues, and 112 Mr. G. F. Rodwell on some Effects the thread gathers itself into a sphere. The lower mass com- mences its descent as an ellipsoid having its major axis at right angles to the liquid surface, next becoming a sphere, then an ellipsoid with its major axis parallel with the liquid surface, once more a sphere, and so on until it reaches the bottom of the vessel, while the upper mass of oil ascends to the surface, and comes to rest as a hemisphere with its plane surface in contact with the surface of the liquid. Let us consider the rationale of this experiment. It is universally stated that when a mass of liquid is heated from beneath, the heat is conveyed to different parts by cur- rents (a central ascending current of warm liquid, and descend- ing side currents of cold liquid), by which means the whole mass of liquid soon becomes of a uniform temperature. Now, if the liquid in the above experiment rapidly acquired a uniform temperature, it is obvious that the lengthening of the oil-sphere into an ellipsoid and the transformation of the ellipsoid into isolated masses could not take place. For if the density of the liquid were uniformly lessened, the oil-sphere would descend en masse, and rupture could not ensue between its particles, be- cause before the occurrence of rupture gravity must act unequally upon the sphere; that is to say, the upper part must be com- petent, while the lower part is incompetent, to resist the action of the force. I was hence led to examine whether, under the conditions of the above experiment, the liquid does rapidly acquire a uniform temperature. In the case of a homogeneous liquid, or of a uniform mix- ture, I found that the same temperature was rapidly acquired by all parts during heating from beneath. An _ oil-sphere placed in a perfectly uniform mixture, did not lengthen itself into an ellipsoid, but descended without change of form to the bottom of the beaker. The manner of trying the experiment described above was, to mix alcohol and water until the mixture possessed nearly the specific gravity of oil, then to imtroduce the oil, and to bring the oil-sphere to its desired position by pouring in alcohol. Now alcohol and water do not very readily mix, hence the upper layers of the liquid contained more alcohol than the lower layers ; and this accounts at once for the different temperatures observed, because the capacities for heat of alco- hol and water differ considerably. It will be seen by the fol- lowing results that, under the conditions of the above experi- ment, the alcohol-and-water mixture does not rapidly acquire a uniform temperature. The mixture was placed in a beaker, and it occupied a depth of 175 millims. therein ; the beaker was piaced upon a flat piece of copper heated by hot water. In order to measure the temperature - produced by a Fluid in Motion. 113 two thermometers, reading accurately together, were employed, and they were read by means of a lens. I was unable to detect any difference of temperature between the liquid near the sides of the vessel and that (in the same horizontal plane) in the cen- tre; neither did I find that the liquid soon acquired a uniform temperature. Thus, after heating for some time, the liquid near the top had a temperature of 19° C., that midway between the top and bottom of 23° C., and the liquid at the bottom of 40°°5 C. In another experiment, in which the heating had been continued for a longer time, the temperature was taken in successive in- tervals of space—the entire depth of the liquid (175 millims.) being divided into seven layers (as we may call them), each 25 millims. thick. The following were the temperatures, begin- ning at 25 millims. below the surface :— First (uppermost) layer . = 30C Second layer an = 30 : sar. | 555 spat Fourth _,, =a 2 EDA = 46 Sixth (lowermost) layer . = 46 It is thus seen that a uniform temperature was by no means rapidly acquired throughout the liquid mass. Now, at the commencement of the experiment described above (p.111), the oil-sphere floats in static equilibrium ; that is to say, it displaces a quantity of liquid precisely equal to its own weight, in a medium of uniform temperature. On heating the liquid, it soon happens that the layer in contact with the under surface of the oil-sphere becomes hotter, and consequently less dense, than the layer m which. the upper part of the sphere floats; a part of the sphere is now surrounded by a medium of its own density, while the other part is surrounded by a medium of less than its own density. The densities, of the alcohol-and-water mixture and of the oil, do not decrease pari passu for equal imcrements of heat; and the oil does not receive heat so readily as the mixture, for it was sometimes found to be as much as 6° C. lower than the layer of liquid in which it floated. Gravity can now act upon the lower portion of the oil; and the con- sequence is that the sphere becomes an ellipsoid with its major axis in the direction of the force which has produced the change— that is to say, parallel to a plumbline. The upper part of the ellipsoid is still unacted upon by gravity, while the lower part has now reached a deeper and consequently warmer and less dense layer; hence gravity exercises greater force upon it; and there is nothing to resist this but the cohesion of the oil-particles. Contraction now commences at the point of greatest strain; and Phil. Mag. 8. 4. Vol. 33. No, 221. Feb. 1867. f 114 Mr. G. F. Rodwell on some Effects as gravity continues to predominate, rupture becomes more and . more imminent. When this occurs, the lower mass, no longer restrained by the cohesion of the upper mass, and being now in a medium of less than its own density, sinks to the bottom ; while the upper mass, having suffered a slight decrease of den- sity by being dragged into a warmer layer by the lower mass, and being now liberated from that weight, is in a medium of greater density than its own, and consequently ascends to the surface. It is obvious that the portion of this explanation which relates to the separation of the lower oil-mass applies equally to the. experiment first described, in which the oil-mass, mstead of floating in the medium, had its upper (plane) surface in contact with the liquid surface. I may remark, in conclusion, that while the former experiment takes about four minutes (from the com- mencement of heating), the experiment last described does not require more than one or two minutes. The latter experiment is most effective, and best suited for the lecture-table. 14 Denbigh Place, S.W. January 11, 1867. Addendum. The following experiments (which were rot finished in time for insertion in the body of the text) would seem to prove the correctness of the explanation given above as to the cause of the lengthening of the oil-sphere into an ellipsoid, and its subsequent resolution into detached masses, under the conditions of the de- scribed experiment. In order to ascertain the comparative rate at which the hquids employed in that experiment acquire a uniform temperature, a litre of each was heated for an hour, under precisely the same conditions, and the temperatures were observed at intervals of ten minutes. The beaker containing the liquid was placed upon a surface of sand (so that all parts of the bottom of the beaker might be uniformly heated) spread in a thin layer upon a copper plate heated by hot water. The temperatures were taken by means of two thermometers reading accurately together, one placed with the:lower part of its bulb 3 millims. from the bottom of the beaker, and the other with the upper part of its bulb 3 millims. from the water-surface. The depth of the hquid column was 130 millims. Distilled water and methylated alcohol were first tried sepa- rately. The temperature of the water was 6° C., and of the alcohol 6°°5 C., the specific gravity of the latter at that tempe- rature being 0°830. The following results were obtained :— ~ produced by a Fluid in Motion. 115 pace — Water at 6° C. Methylated alcohol at 6°-5 C. ture from the | err ae Upper ther- | Lower ther- | Upper ther- | Lower ther- ing. mometer. mometer. mometer. mometer. minutes. 9 10 11-75 C. | 12-000. 16-25. | 16500. 20 17:00 17:50 23°25 23°50 30 21:25 22°50 28°50 29:00 40 25-00 | 2625 32-00 32°50 50 =| 2850 30:00 34-75 35-25 | 60 | 31-25 32°50 ~ 36°50 37°25 | It is seen from the above that a uniform temperature was very rapidly acquired by both liquids, the greatest difference in tem- perature between the uppermost and lowermost layers of water amounting to only 1°50 C., and in the case of the alcohol to only 0°75 C.- In making the experiment with the sphere of oil, it will be borne in mind that a mixture of alcohol and water was employed, and that the oil-sphere floating therein was’ brought to its de- sired position by pouring a small quantity of alcohol into the mixture as soon as the sphere had come to rest. It was there- fore thought to be advisable to ascertain the rapidity with which the mixture acquires a uniform temperature, and to what extent this result is retarded by the addition of a known quantity of alcohol. ‘ In order to determine this, a mixture was made of 500 cub. centims. of water at 4°°5 C. with 500 cub. centims. of methyl- ated alcohol at 6°C. The resulting mixture (care being taken to make it perfectly uniform) was found to occupy a volume of 980 cub. centims., and to possess a temperature of 14°:25 C. It was allowed to cool down to 7° C., and then heated for an hour, under the same conditions which obtained when each liquid was heated separately, the temperatures being noted at similar intervals. At the end of the hour it was cooled to 7° C., and 50 cub. centims. of alcohol at 8° C. were poured in, and the heating recommenced. The added alcohol was coloured by means of a minute quantity of roseine, in order that the depth to which it penetrated might be observed. (It is need- less to remark that the tinctorial power of roseine is so great that the amount added could not affect the accuracy of the ex- periment.) Although the alcohol was poured into the mixture (already containing half its bulk of that fluid) from a height of 40 or 50 millims., it showed no tendency to mix readily: the great bulk of it (as shown by the amount of colour) remained [2 : 116 Mr. G. F. Rodwell on some Effects within 20 millims. of the surface, and the colour was observed to gradually shade off till at a depth of 55 millims. it disap- peared; so that the 50 cub. centims. of added alcohol were entirely in the uppermost 55 millims. of liquid. The entire quantity of liquid now exceeded 1000 cub. centims., and its depth was 140 millims. The following results were obtained :— Time of taking . Alcohol-and-water mixture the tempera- ga eats Tee. at 7° C., with 50 cubic ture from the centims. of alcohol added. COUMMMIENCE., | be ee ee ment of heat-| Upper ther- | Lower ther- | Upper ther- | Lower ther- mg: mometer. mometer. mometer. mometer. minutes. 3 S es é 10 15:00 C. 15°75 C. 9:25 C. 19-50 C. 20 20:50 21:25 12:60 26°75 30 25°75 26:50 20-00 32°00 40 30:00 31:00 26-00 35°00 50 33°75 34:50 30°25 39-00 60 36:00 36°75 34:50 41:00 It will be observed that the alcohol-and-water mixture acquired a uniform temperature as rapidly as either of its components heated alone, the greatest difference between the uppermost and lowermost layers of liquid amounting to only 1°C. But after the addition of the alcohol (although its quantity was less than one-twentieth of the total amount of liquid heated) a very dif- ferent result is observed ; for we find no less than 14°:75 C. dif- ference of temperature *between the uppermost and lowermost layers of liquid. The amount of heat, however, associated with the entire mass of each liquid at any given time during the heat- ing is nearly the same, but it is differently distributed. If we take mean temperatures, we find that the greatest difference amounts to 1°35 C.; but the approach is often much nearer, and in one case we have coincidence. Thus at the end of forty mi- nutes’ heating, the temperatures of the uppermost and lowermost layers of the alcohol-and-water mixture were respectively 30° C. and 31° C.; and of the same mixture after the addition of the alcohol, 26° C. and 35° C.: we thus obtain the following means . 30+ 31 26 +385 — 29°. 5} 5} = 30°50 C. —30°50 C., The following Table shows the means for each time of obser- vation :— | produced by a Fluid in Motion. 117 Alcohol-and-water Time of taking the} Alcohol-and-water ARE oe ERE temperature from mixture. the commencement. added alcohol. exhorting. Mean temperature.| Mean temperature. minutes, - a 10 15°375 C. 14°375 C. 20 20-875 19:375 30 26°125 26:000 40 30:500 30°500 50 34:125 34-625 60 36°375 37°750 On continuing to heat the mixture containing the added alcohol, the upper layer in which it was present suddenly coalesced with the liquid beneath it, and the entire mass of liquid became at once of a uniform temperature. The lower thermometer stood at 42° C., and the upper one at 36° C., im- mediately before the coalescence. It is seen from the above experiments that the addition of a small quantity of alcohol to a mixture of alcohol and water deter- termines a very unequal acquirement of heat throughout the mass of that mixture during the process of slow heating from beneath. For, on account of the tardiness with which the added liquid mixes with the liquid to which it is added, the mass be- comes divided into two distinct layers, the upper one containing more alcohol than the lower; and this latter receives almost all the heat communicated to the liquid, until, when a certain tem- perature has been attained, the two layers coalesce, uniformity of mixture and uniformity of temperature being simultaneously established throughout the mass. We have, I conceive, in the above results the explanation of the cause of the change of the oil-sphere into an ellipsoid, and its subsequent transformations ; for (as mentioned in the text) it is a necessary condition of this experiment that the fluid medium shall not during heating rapidly acquire a uniform temperature. 14 Denbigh Place, 8.W., January 23, 1867. [ 11s 24 XVI. On the Wave-Lengths of the Transmission of Muscular and Nervous Action. By the Rev. Samue, Haveuton, M.D., Fellow of Trinity College, Dublin. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, eo following result may prove of some interest to those physiologists who are capable of applying it so as to draw from it the consequences it seems capable of affording. (1) The rate of the muscular susurrus, first observed by Wol- laston, and estimated by him at “from 20 to 30 in a second,” has been fixed by Dr. Collongues of Paris, by means of tuning- forks, at 35 in a second, and by myself, by means of organ- pipes, at 82 in a second. (2) The rate of the tinnitus aurtum, which is eaused by the action of the nerves, has been fixed by me at 1024 in a second. From these data, 1t follows that the rate of nerve action 1s from 29 to 32 times as fast as the rate of muscular action. (3) The experiments of Dr. Schelske have shown that the velocity of wave-transmission of sensation in the living body of man is 97 feet per second. And, lastly, (4) The experiments of Professor Aebe, of Berne, prove that the velocity of wave-transmission of muscular contraction in frogs is 3 feet per second. The wave-transmission in the nerves is therefore 52 times as fast as the wave-transmission in the muscles—or 29 times as great if we adopt Helmholtz’s determination of the rate of trans- mission im the motor nerves of the legs of a frog, viz. 88 feet per second. Now in any kind of wave-propagation, whether due to mecha- nical or chemical changes, we have N= s where X is the wave-length, v is the wave-velocity, t is the rate of vibration, or period of the change. It appears from the preceding physiological experiments, taken together, that v varies inversely as ¢ when muscles a nerves are compared ; and consequently that % is constant: The wave-length of the transmission of muscular wl nervous action is constant, and lies between 1°125 and 1:225 inch. If this conclusion be correct, important consequences ought to follow from it; for the nerves and muscles are so connected in Mr. J. Croll on the Excentricity of the Earth’s Orbit. 119 their distribution, that many advantages would flow from having their wave-lengths the same, and consequently the positions of the nodes identical, notwithstanding the very different velocities with which waye-pulses are propagated along them. I am, Gentlemen, Your obedient Servant, SaMUEL HavcGurTon. Trinity College, Dublin, _ January 18, 1867. XVII. On the Excentricity of the Earth's Orbit, and its Physi- cal Relations to the Glacial Epoch. By James Crouu*. i igo Philosophical Magazine for January 1866 contains a Table of the values of the excentricity of the earth’s orbit for one million of years before and after the epoch a.p. 1800. From that Table it is seen that between 1,000,000 and 700,000 years ago there were three periods when the excen- tricity reached a very high value. It appears highly probable that if the glacial epoch resulted from an extreme condition of excentricity, these three periods might be those of the boulder- clay, when the country was completely covered with ice, an opinion in which I am happy to find Sir Charles Lyell concurs fF. As the Table referred to gives the values only at epochs 50,000 years apart, in order to arrive at a more accurate knowledge of the condition of the earth’s orbit during those periods, I have calculated the excentricity at epochs 10,000 years apart from 1,000,000 to 700,000 years ago. Mr. Stone found that about 210,000 years ago there was a period when the excentricity reached the value of 0:0575 {. In order to include this period, I have also given the excentricities from the present time back for 250,000 years at periods 10,000 years apart. ~ Column IV. gives the number of days that the length of the winter exceeds that of the summer when the winter occurs in aphelion. At present our winter is about eight days shorter than our summer, but 850,000 years ago, when it occurred in aphelion, it would be actually about thirty-five days longer than the summer. Column V. gives the number of degrees Fahrenheit that the midwinter temperature of our island would be lower than at present. This column has been calculated by a method de- scribed in the ‘ Reader’ for December 9th, 1865, and which * Communicated by the Author. Tf Principles of Geology, new edition, vol. i, p. 296. tT Phil. Mag. for June 1865 (Supplement). 120 Mr. J. Croll on the Hacentricity of the Earth’s Orbit, was proved to hold approximately true. (See also Sir Charles Lyell’s ‘ Principles,’ new edition, vol. i. p. 29-4.) | | | | em em or TER | Iv. V. VI. VI. | | Midwinter cane | Number | | Number | Number of perature of the, of years | of days by | degrees by Midwinter! centre of Scot- | before” | py centri- | Longitude | which the | which the | tempcra- [land, on the sup-| epoch | ‘city. of perihe- [winter was|midwinter | ture of the position that ie 1800. | : hon. longer tempera- | centre of | Gulf-stream was than the | ture was | Scotland. | affected by | | summer. | lowered. | change of ex- | | centricity. | 1,100,000| 0-0303 | 5412 | 1414 | 248F.| 1429F, 6 F. 1,050,000) 0:0326 4 8 15°16 26:0 13 4-4 1,000,000, 0-0151 |248 22 | | 990,000, 0-0224 | 313 50 | 980,000) 0°0329 | 358 2 15°34 261 12-9 | 43 979,000| 00441 | 32 40 20°55 | 31:5 75 |) —2°6 960,000) 0:0491 | 66 49 22°87 | 338 5:2 —5'6 950,000) 0-0517 | 97 51 24:08 | 35:0 4 —7F) 940,000) 0-0495.|127 42 | 23:06 | 34:0 5 —5:9 930,000, (0425 | 156 11 19-71 30°6 8:4 —1°5 920,000; 0:0305 | 181 40 14:23 | 25:0 14 a7 910,000) 0-0156 | 194 15 900,000, 60-0102 |185 2+ 890,000) 0:0285 | 127 1+ $80,000) 0:0456 | 152 33 22°97 | 32-2 6°8 — 35 870,000) 90-6607 | 180 23 28:97 | 389°0. =. 0 —12°3 850,000 0:0708 | 209 41 32°90 | 436 —4°6 —18 850,000) 00747 | 2389 28 34:70 | 45:3 —6:3 —20 840,060, 0-0698 | 269 14 32:43 | 48°2 —42 —17°6 830,000) 0:0623 | 298 28 29:00 | 40-0 --1 ; —138 820,000 0:0476 |326 4 22°13 | 33-1 5:9 — 47 $10,006) 0:0296 | 348 30 800,000; 0:0132 | 343 49+ 790,000, 0-0171 | 293 19+ 780,000) 0:0325 | 803 38 15°16 | 26:0 13 4-4 779,000) 00455 | 328 38 21:20 | 326 7 — 33 760,000, 0-0540 | 357 12 25:10 | 360 3 — 84 790,000, 0:0575 | 27 18 | 27:00 | 37:7 13 —10°6 740,000, 0-0561 | 58 30 26:12 379 2 — 97 730,000) 00507 | $0 55 23°61 34°6 4-4 — 66 720,000; 0-0422 | 125 14 19°62 | 3806 8-4 — 15 710,000) 0:0307 | 177 26 14:32 | 25:0 14 a7 700,000) 0:0220 | 208 13 | . 650,000) 0:0226 | 141 29 600,000; 00417 | 32 34 550,600) O-OL66 | 251 50 | 500,000) 0-0388 | 1938 56 | | | | 450,000) 0:0308 | 356 52 | 400,000; 0:0170 | 290 7 | 350,000! 0-0195 | 182 50 | | 300,000) 0-0424 | 23 29 | and its Physical Relations to the Glacial Epoch. 121 TABLE (continued). Ibe WHE III. IV. Wie VI. VII. Midwinter tem- | SS eee ot Schiaplo dents of days egrees jaw ay sn Longitude | by wich eae ihe ee ve A nes on the soy before | Excentri- | of perihe- | the winter | midwinter | ture of the aes aac ae epoch city. lion. was longer | tempera- | centre of a macted Wo 1800. : than the | ture was | Seotland. y summer, | lowered. change of ex- centricity. 250,000 0-:0258 | 59 39 f . i 240,000 0°03874 | 74 58 17°41 28:'3 107 1°5 230,000) 0-0477 | 102 49 22:22 32°0 7 — 33 ¥220,000, 0:0497 | 124 33 23°15 34°1 4-9 — 6 ¥210,000, 0°0575 | 144 55 26°77 377 13 —10°6 200,000 0:0569 | 168 18 26°49 37°4 16 —10-2 ¥190,000, 0°0532 |190 4 24-73 35°7 3°3 = 6 ¥180,000, 0:-0476 | 209 22 22°13 33°1 59 — AZ ¥170,000) 0:0437 |228 7 20°36 31°3 77 — 2-4 160,000 0:0364 | 236 38 16:92 27°3 11:2 2°1 150,000, 0:03382 | 242 56 15°44 26-2 12°38 42 140,000) 0:0346 | 246 29 1609 | .26:9 12:1 3°3 130,000; 0°0384 | 259 34 17°80 28°8 10:2 0:8 120,000, 0:0431 | 274 47 20:09 31:0 8 = 2 1110,000| 0.0460 | 293 48 21°38 32°4 6°6 — 3 100,000, 0:0473 | 316 18 22-03 33:0 6 — 46 + 90,000; 0:0452 |340 2 21:01 32°0 7 — 32 t 80,000) 0-0398 4 13 18°45 29°4 9°6 0 t 70,000; 0:03816 | 27 22 14-69 25°5 13°5 51 + 60,000; 0°0218 | 46 8 50,000; 00131 | 50 3 t 40,000; 0:0109 | 28 36t + 30,000) 0-0151 | 5 50} + 20,000, 00188 | 44 0 + 10,000' 0:0187 | 78 28 0} 0:0168 | 99 30 The excentricity and longitude of the perihelion at the periods marked thus (x) were calculated by Mr. Stone of Greenwich Observatory, and those marked (T) were calculated by M. Leverrier. It will be seen that at the periods marked thus (tf) the perihelion has a retrograde motion. It will also be observed that at those periods the excentricity was at a minimum. Column VI. gives the midwinter temperature of our island. It is found by subtracting the numbers in column V. from 39°, the present midwinter temperature. It has been shown (see Phil. Mag. for August 1864, and ‘Reader,’ December 2nd and 9th, 1865) that when the excen- tricity reaches a high value, and one of the solstice-points is in perihelion, the difference between the temperature of the two hemispheres must be very great. The hemisphere which has its winter in aphelion and under a condition of glaciation, is much 122 Mr. J. Croll on the Kexcentricity of the Earth's Orbit, colder than the opposite hemisphere which has its winter in perihelion and enjoying an equable climate; and the conse- quence is, the aérial currents from the pole to the equator must be much stronger on the colder hemisphere than on the warmer because the difference between the temperature of the pole and the equator is greater on the former hemisphere than on the latter. When the northern hemisphere, for example, is under glaciation, the north-east trade-winds will be much stronger than the south-east. The medial line between the trades will consequently lie a considerable distance to the south of the equator. The effect of the northern trades blowing across the equator to a great distance will be to impel the warm water of the tropics over into the Southern Ocean. And this, to an enormous extent, will tend to exaggerate the difference be- tween the temperature of the two hemispheres. But it is worthy of notice that a strong undercurrent of air flowmg from the north pole to the equator implies an equally strong upper current flowing from the equator to the pole. Now, if the effect of the undercurrent be to impel the warm water of the tropics into the Southern Ocean, and thus raise the temperature and melt the ice in the southern hemisphere, the effect of the upper current will be to carry moisture raised by evaporation in tropical regions away to the north, there to be deposited in the form of snow on reaching the great ice- sheet covering the arctic and temperate regions. The general effect of the whole will be to produce an accumulation of snow and ice in the northern hemisphere, and a diminution of these in the southern. - The effect of the aérial currents on the Gulf-stream during the glacial epoch must have been peculiarly marked. It hasbeen shown * that if the equatorial current of the Atlantic, the feeder of the Gulf-stream, were removed merely a few degrees to the south of its present position, the entire current would be turned into the Brazilian branch and flow into the Southern Ocean, and thus probably stop the Gulf-stream: altogether. But during the glacial epoch, on the northern hemisphere, when the medial line lay at a considerable distance to the south of the equator, the greater portion of the equatorial current, if not the entire current, must have flown into the Southern Ocean. But let us assume, what will certainly be admitted to be a mo- derate estimate, that 850,000 years ago, when the excentricity was near its superior limit, that the Gulf-stream was reduced to one-half its present volume, when the northern hemisphere was under glaciation. The midwinter temperature in the centre of Scotland, as is well known, is about 28° higher than * Phil. Mag. for August 1864. and its Physical Relations to the Glacial Epoch. 123 it would otherwise be were it not for the influence of the Gulf- stream *. A reduction of the Gulf-stream to one-half its pre- sent volume would lower the temperature of the centre of Scot- land about 14°. According to column VY. the temperature of this country 850,000 years ago, owing to the greater distance of the sun at midwinter, would be lowered 45°°3. Now add 14° for the di- minution of the Gulf-stream, and we have 59°:3 below the pre- sent midwinter temperature, or—20°3 as the midwinter tem- perature of the centre of Scotland at that period. Assuming, then, that the diminution of the Gulf-stream was propor- tionate to the extent of the excentricity, column VII. gives the actual midwinter temperature of the centre of Scotland at the corresponding periods. The difference between the midwinter temperature of Scot- land at some of those periods and its present is certainly great. But there is, however, nothing extravagant or unlikely in sup- posing the existence of so low a temperature during the glacial epoch when we reflect that at the present day there are places on the same parallel of latitude as Scotland which have a mid- winter temperature nearly as low as any indicated in the Table: for example, at the Cumberland House in North America, situated in a lower latitude than the south of Scotland, the present midwinter temperature is upwards of 13° below zero. That the cold of the glacial epoch in Scotland was to a con- siderable extent due to a stoppage, or at least great diminution, of the Gulf-stream, is attested, I think, by the fact pointed out by the Rev. Mr. Crosskey from a comparison of the fossils of the glacial beds of Canada with those of the Clyde, that the change of climate in Canada since the glacial epoch has been far less complete than in Scotland+. The American continent was no doubt, during the glacial epoch, as cold as, if not colder than the continent of Europe; but then, if the Gulf-stream was stopped during the glacial epoch, the rise of temperature which would follow on the return of the stream at the close of that epoch would be greater in Scotland and all over the western shores of Hurope than in America. It might be thought that if the winters had been so much colder at the periods in question than at present, owing to the sun’s greater distance during that season, the summers, on the other hand, ought to have been so much warmer, owing to the sun’s greater proximity. About 850,000 years ago the winters, according to the Table, were 45° colder than at present; and * See Dove ‘On the Distribution of Heat over the Surface of the Globe,’ Map V. 7 Transactions of the Glasgow Geological Society for 1866. 124 Mr. J. Croll on the Excentricity of the Earth’s Orbit, were the sun’s distance the only element that determined the temperature, the summers would have been at least 45° warmer than at present. But had such been the case, there could have been no glacial epoch. For a summer so warm, notwith- standing its shortness, would have been sufficient to melt the snows of winter. In this case, the theory which attributes the glacial epoch to an extreme condition of excentricity must be abandoned. It was, no doubt, this which had led to the gene- ral, if not universal, belief that the glacial epoch could not have resulted from an augmentation in the excentricity of the earth’s orbit. And it is perfectly true that were it not for physical agencies which are brought into operation by the change of ex- centricity, and thus to a great extent alter the condition of things, the astronomical causes would wholly fail in producing a glacial epoch ; for the purely astronomical effects of excentri- city, as has been clearly shown by Sir John Herschel*, Aragoy, Humboldt{, and others, are compensated by others of an oppo- site character; so that excentricity, viewed from an astronomical stand-point, does not appear capable of accounting for the gla- cial epoch. In short, without having taken into consideration the physical causes to which we refer, it was impossible that any relation could ever have been perceived between a high condi- tion of excentricity and the glacial epoch. There is one astronomical effect however, which is, not com- pensated by an astronomical effect of an opposite character. The total quantity of heat received from the sun per annum is inversely proportional to the minor axis of the earth’s orbit. And this has been stated by Sir John Herschel to be an astro- nomical vera causa of change of climate during geological epochs§. But as the excentricity increases, the total quantity of heat re- ceived from the sun increases also. Hence astronomy would lead us to conclude with Prof. Haughton ||, that a glacial epoch ought to occur, not when the excentricity is at the superior, but at the inferior limit. In a former paper I endeavoured to show that this astronomical effect, which is but trifling, is far more than neutralized by causes of a physical nature, and that, instead of an increase of excentricity producing an increase of temperature, as had been generally considered, the very reverse is the case. One of the physical causes to which I refer is the presence of * Outlines of Astronomy, article 368. + Edinburgh New Philosophical Journal for April 1834, p. 224. An- nuaire for 1834, pp. 199, 201. { Cosmos, i lv. p. 459. § Discourse on the Study of Natural Philosophy, article 140. | Phil. Mag. for May 1866. 4] The variation in the quantity of heat received from the sun per annum can never exceed one three-hundredth part of the total amount. and its Physical Relations to the Glacial Epoch. 125 snow and ice. While the ground remains covered with snow and ice, as was shown at considerable length on a former occa- sion*, dense fogs prevail, which cut off a great portion of the sun’s rays and thus lower the summer temperature. But even supposing the sun’s rays were to reach the earth with their full intensity, they would, no doubt, melt the snow accumulated during the long winter, but they would fail to raise the summer temperature so long as the snow remained unmelted. In Green- land, a country covered with snow and ice, the pitch has been seen to melt on the side of a ship exposed to the direct rays of the sun, while at the same time the surrounding air was far below the freezing-point ; a thermometer exposed to the direct radiation of the sun has been observed to stand above 100°, while the air surrounding the instrument was actually 12° below the freezing- pomt+. A similar experience has been recorded by travellers on the snow-fields of the Alpsf. These results, surprising as they no doubt appear, are what we ought to expect under the circumstances. The diathermancy of air has been well established by the researches of Professor Tyndall on radiant heat. Perfectly dry air seems to be nearly incapable of absorbing radiant heat. The entire radiation passes through it almost without any sensible absorption. Consequently the pitch on the side of the ship may be melted, or the bulb of the thermometer raised to a high temperature by the direct rays of the sun, while the surrounding air remains intensely cold. “A joint of meat,” says Professor Tyndall, ‘‘ might be roasted before a fire, the air around the joint being cold as ice” §. The air is cooled by contact with the snow-covered ground, but is not heated by the radiation from the sun. When the air is humid and charged with aqueous vapour, a similar cooling effect also takes place, but in a slightly different way. Air charged with aqueous vapour is a good absorber of radiant heat, but it can only absorb those rays which agree with it in period. It so happens that rays from snow and ice are, of all others, those which it absorbs best. The humid air will ab- sorb the total radiation from the snow and ice, but it will allow the greater part of, if not nearly all, the sun’s rays to pass unab- sorbed. But during the day, when the sun is shining, the ra- diation from the snow and ice to the air is negative; that is, the snow and ice cool the air by radiation. The result is, the _- air is cooled by radiation from the snow and ice (or rather, we should say, ¢o the snow and ice) more rapidly than it is heated by * Phil. Mag. for August 1864. T Scoresby’s ‘ Arctic Regions,’ vol. ii. p.379. Daniell’s ‘ Meteorology,’ vol. u. p. 123. t Tyndall, ‘On Heat,’ article 364. § Ibid. 126 Mr. J. Croll on the Excentricity of the Earth’s Orbit, the sun; and, as a consequence, in a country like Greenland, covered with an icy mantle, the temperature of the air, even during summer, seldom rises above the freezing-point. Were it not for the ice, the summers of North Greenland, owing to the continuance of the sun above the horizon, would be as warm as those of England; but, instead of this, the Greenland summers are colder than our winters. Cover India with an ice- sheet, and its summers would be colder than those of England. If at the glacial epoch the heat of the sun during the short summer in perihelion, for reasons already stated, would fail to melt the total quantity of snow accumulated during the long and intensely cold winter—which no doubt it would—then the snow and ice would accumulate year by year till the surface of the entire country would be covered. After this the mean temperature of the summers, no matter what the intensity of the sun’s rays might be, could not rise far above the freezing- point. The rays which fell upon the ice-covered ground would have no tendency whatever to raise the temperature ; they would simply melt the ice; and as the ice-covered surface would cool the air more rapidly than the sun would heat it, the summers could not possibly be warm. “At those periods of extreme excentricity when the winter oc- curred in perihelion, there would be a short and warm winter and a long and moderately cold summer. The winters would pro- bably be about as warm as the summers, and an equable and uniform condition of climate would prevail over the whole year. The midsummer temperature 850,000 years ago, did the winter occur in perihelion, would be about 75°, according to the mode of calculation adopted. At the periods 950,000 and 750,000 years ago the temperature would be 60° and 63° respectively. But there are certain modifying circumstances which might pro- bably prevent the temperature of the winters from risimg much above perhaps 50° or 60°. In the arctic regions there would be an absence of the sun for several months during winter, and the cold from stellar space would no doubt be intense. This would tend to lower the tem- perature of the winters in temperate and subarctic regions to a certain extent. But, on the other hand, there is one powerful agent which would now come into play, that would prevent the possibility of a low temperature in arctic regions even in the absence of the sun. I refer to the enormous quantity of warm water which at this period would be flowing into those regions. The midsummer temperature determined according to the sun’s distance at the periods 950,000, 850,000, and 750,000 years ago, were the winter then in perihelion, would be 39°, 27°-4, and 36° respectively. But, again, there are here also mo- and its Physical Relations to the Glacial Epoch. 127 difying causes which would prevent the possibility of the sum- mer temperature ever falling so low as 27° or even 36°; for sur- rounded by awarm sea our summers could at this time no more have been cold than during the glacial epoch they could have been warm when the land was covered with celd ice. I feel satisfied that it will yet turn out, when the subject has been better investigated, that the influence of ocean-currents in modifying the climate of the polar regions of the globe has not been duly estimated. Were there no ocean-currents, and the polar regions to depend alone upon the direct heat of the sun, the temperature of those regions would be enormously below what it actually is. The difference of temperature between the equatorial and polar regions of the globe is far less than it would otherwise be, did the temperature of each zone depend alone upon the quantity of heat received directly from the sun. A very considerable amount of the temperature of+polar regions is due to the heat absorbed by the ocean in equatorial regions, and couveyed there by ocean-currents. This process tends to lower the temperature of the equatorial regions and raise the tempera- ture of the polar, and thus reduce the difference between the two. The truth of what has just been stated will be obvious if we simply reflect on the quantity of heat transferred from the equa- torial to the northern regions by one stream alone, namely the Gulf-stream. I have not been able to find any trustworthy estimate of the actual quantity of water conveyed by the Gulf- stream. From a rough estimate made after an examination of the Charts of the United States Coast Survey, I believe that the total quantity of water transferred is at least equal to a stream fifty miles broad and 1000 feet deep, flowing at the rate of four miles an hour; and the mean temperature of the entire mass of moving water is not under 65° at the moment of leaving the Gulf. Captain Maury considers the Gulf-stream equal to a stream 32 miles broad and 1200 feet deep, flowing at the rate of five knots an hour*. ‘This is a somewhat higher estimate. Now the density of air to that of water is as 1 to 770, and its specific heat to that of water is as 1 to 4°2. Consequently the same amount of heat that would raise 1 cubic foot of water 1°, would raise 770 cubic feet of air 4°°2, or 3234 cubic feet 1°. The quantity of heat conveyed by the Gulf-stream is there- fore equal to that which would be conveyed by a current of air 3234 times the volume of the Gulf-stream and at the same temperature and moving with the same velocity. In order to convey an equal amount of heat from the tropics by means of an aérial current, it would be necessary to have a current about 14 mile deep and at the temperature of 65° blowing at the rate of * Physical Geography of the Sea, § 24. 128 Mr. J. Croll on the Excentricity of the Earth's Orbit, four miles an hour from every part of the equator over the northern hemisphere towards the pole. Ifits velocity were equal to that of a good sailing-breeze, which Sir John Herschel states to be about twenty-one miles an hour, the current would require to be above 1200 feet deep. The Gulf-stream, before it returns from its northern journey, is cooled down to about 40°. Hach cubic foot of water therefore carries from the tropics upwards of 1500 units of heat. A greater quantity of heat is probably conveyed by the Gulf-stream alone from the tropical to the tem- perate and arctic regions than by all the aérial currents which flow from the equator. During the warm periods of the glacial epoch (that is, when the glaciation prevailed in the southern hemisphere), the quan- tity of warm water flowing from the tropical to the arctic re- gions would, as we have already seen, far exceed that which is being transferred at present. ‘The effect that this would have along with the short and warm winter in melting the polar ice would be enormous. At that period Greenland, in all probability, would be free of ice. We are apt, on the other hand, to overestimate the amount of heat conveyed from tropical regions to us by means of aérial currents. The only currents which flow from the equatorial regions are the upper currents or anti-trades, as they are called. But it is not possible that much heat can be conveyed to us directly by them. The upper currents of the trade-winds, even at the equator, are nowhere below the snow-line. They must therefore lie in a region actually below the freezing-point. In fact, if those currents were warm, they would elevate the snow- line above themselves. The heated air rising off the hot burn- ing ground at the equator, after ascending for a few miles, becomes exposed to the intense cold of the upper regions of the atmosphere. It then very soon loses all its heat, and returns from the equator much colder than it came. It is impossible that we can receive any heat directly from the equatorial re- gions by means of aérial currents. It is perfectly true that the south-west wind, to which we owe so much of our warmth in this country, is a continuation of the anti-trade. But the heat which this wind brings to us is not derived from the equa- torial regions. ‘This will appear evident, if we but reflect that, before the upper current descends to the snow-line after leaving the equator, it must traverse a space of at least 2000 miles; and to perform this long journey several days will be required. During all this time the air is im a region below the freezing- point ; and it is perfectly obvious that by the time it begins to descend it must have acquired the temperature of the region in which it has been travelling. and its Physical Relations to the Glacial Epoch. — 129 If such be the case, it is evident that a wind whose tempera- ture is below 32° could never warm a country such as ours, whose temperature does not fall below 38° or 39°. The heat of our south-west winds is derived, not from the equator but from the warm water of the Atlantic—in fact, from the Gulf-stream. The upper current derives its heat after it descends to the earth. There is one way, however, whereby heat is indirectly conveyed from the equator by that current ; that is, in the form of aque- ous vapour. In the formation of one pound of water from aqueous vapour, as Professor Tyndall strikingly remarks, a quantity of heat is given out sufficient to melt five pounds of cast iron*, It must, however, be borne in mind that the greater part of the moisture of the south-west and west winds is de- rived from the ocean in temperate regions. The upper current receives the greater part of its moisture after it descends to the earth. The greater part of the moisture received at the equa- tor is condensed and falls as rain in those regions. These, as well as many other considerations which might be ‘stated, seem to lead to the conclusion that, in order to raise the mean temperature of the whole earth, water should be placed along the equator—and not land, as is generally believed. For if land is placed at the equator, we prevent the possibility of conveying the sun’s heat from the equatorial regions by means of ocean-currents. The transference of heat could only then be effected by means of the upper currents of the trades ; for the heat conveyed by conduction along the solid coast, if any, can have no sensible effect on climate. But these currents, as we have just seen, are ill adapted for conveying heat. The surface of the ground at the equator becomes intensely heated by the sun’s rays. This causes it to radiate off its heat more rapidly into space than a surface of water heated under the same conditions. Again, the air in contact with the hot ground becomes also more rapidly heated than in contact with water; and consequently the ascending current of air carries off a greater amount of heat. But if the heat thus carried away were transferred by means of the upper currents to high latitudes and there employed to warm the earth, then the heat thus con- veyed might to a considerable extent compensate for the absence of ocean-currents, and land at the equator might in this case be nearly as well adapted as water for raising the temperature of the whole earth. But such is not the case ; for the heat carried up by the ascending current at the equator is not employed in warming the earth, but is thrown off into cold stellar space above. This ascending current, instead of bemg employed in warming the globe, is in reality one of the most effectual means that the * Heat as a Mode of Motion, article 240. Phil. Mag. 8. 4. Vol. 83. No. 221. Feb. 1867. K 130 Mr. J. Croll on the Excentricity of the Earth’s Orbit. earth has of getting quit of the heat received from the sun, and of thus retaining itself at a much lower temperature than it would otherwise be. It is in the equatorial regions that the earth loses as well as gains the greater part of its heat. So of all places it 1s here that we ought to place the substance best adapted for pre- venting the dissipation of the earth’s heat into space, if we wish to raise the general temperature of the earth. Water, of all sub- stances in nature, seems to possess this quality to the greatest extent; and, besides, it is a fluid, and therefore adapted by means of currents to carry the heat which it receives from the sun to every corner of the globe. In assuming those three periods of great excentricity between 1,000,000 and 700,000 years ago to be those of the true unstra- tified boulder-clay (Lower Till), there is one slight difficulty that meets us. It seems to place the glacial epoch too far back. Can it be really 700,000 years since the close of the period of the boulder-clay ? When we look at a gorge several thousand feet in depth that has been cut out of the solid rock since the period of the boulder- clay by a small streamlet, and reflect that this streamlet will run for centuries without producing any perceptible effect on its rocky bed, our first impression would be that 700,000 years 1s but a short period for such a feeble agent to perform such an enor- mous amount of work. But we are deceived. ‘Time, as repre- sented by geological phenomena, is deeply impressive ; and when we attempt to express it in figures we are apt to be misled; for we can form but a very inadequate conception of immense dura- tion represented in numbers. If a stream were to deepen its channel only one-tenth of an inch in a year, it would in 700,000 years cut a gorge nearly 6000 feet deep. It would deepen its channel nearly 600 feet were it to scoop out only an inch in a century. The quantity of sediment discharged into the sea annually by the Mississippi river is 28,188,083,892 cubic feet. The area of drainage 1s 39,029,760, 000, 000 square feet*. Consequently 1 foot is being removed off the face of the country every 1388 years and carried into the sea. If the rate of denudation be as great in this country as in America, then 500 feet must have been removed off the face of the country and carried by our rivers into the sea since the period of the boulder-clay, if we place that . period 700,000 years back. Uumboldt thinks that the mean elevation of all the land is less than 1000 feet. According to the rate at which the rivers are carrying the land into the sea, if there be no more elevations of the land, our continents will * See “ Report on the Sediment of the Mississippi River,” Proceedings of the American Association for the Advancement of Science, 1849. Researches on the Mineralogy of South America. 13l not remain over one million and a half years above the sea- level. | 3 It may therefore yet turn out that between 240,000 and 80,000 years ago might be the period of the glacial epoch, and that those glacial epochs between 1,000,000 and 700,000 years ago may belong to the Miocene period. With the view of ascertaining if the superior limit of excentri- city was reached about 850,000 years ago, I determined the values for one or two periods closely before and after this period, but cannot find a higher value than that which has been assigned to it. 851,000 0°07454 850,000 0:074664 849,500 0:07466 849,000 0:07466 There is another phenomenon necessarily connected with the changes of the excentricity, viz. the submergence and emergence of the land resulting from the displacement of the earth’s centre of gravity occasioned by the transference of the ice-cap from the one hemisphere to the other, to which I shall at present simply allude. Abouta year ago I stated, as an objection to this theory, that the lowering of the ocean by the removal of the water to form the cap would exceed the rise occasioned by the displace- ment of the centre. Since then this objection has been re- peatedly urged. There are, however, several considerations which appear to have been overlooked by those who have discussed the submergence question. When these are taken into account, it will be found that the objection referred to is rather premature, and that, even assuming the earth to be a rigid mass throughout, a submergence to the extent of 100 or 200 feet is not only a possible but a necessary effect. But the discussion of this point must be deferred till another occasion. XVIII. Researches on the Mineralogy of South America. By Davip Forsus, F.R.S., &c.* V. General Mineralogy of Chile. “LY AVING been enabled to devote much more time to the exploration of Chile than to that of any of the other countries of South America which I visited, I was occupied some four years in traversing that country im all directions, from con- * Communicated by the Author. 132 Mr. D. Forbes’s Researches on the siderably south of Santiago northwards up to the frontiers of Bolivia in the desert of Atacama, and in inspecting all the prin- cipal, anda great number of the lesser, mining districts scattered © along the range of the Cordilleras. These explorations enabled me not only to visit, with but very few exceptions, all the mineral, localities mentioned in Do- meyko’s ‘ Mineralogy’*, then the only work upon the subject, - but also to more than double the number of species therein de- scribed as occurring in Chile. Such an investigation, as might be expected, gave me not only the opportunity of forming an extensive and valuable col- lection of minerals, but also of specially studying the occurrence of the minerals themselves, with reference to the geological position of the rock-matrix in which they were imbedded; and it was soon evident, upon comparing the data obtained, that, so far from the appearance of minerals (using the word mineral more especially to designate such compounds as differ from the bulk of the rock-matrix) being, as is generally considered, acci- dental, on the contrary, if we except only a small number of more usually occurrimg compounds which are common to a variety of circumstances, the others invariably presented themselves under similar conditions, had the same associated minerals along with them, and, when the geological age of the eruptions in which they occurred could be satisfactorily as- certained, frequently, if not always, corresponded in geological age. In Chile, as elsewhere, the intrusive rocks, with their accom- panying metallic lodes, furnish the greater number of mineral species, and it was everywhere found that similar minerals, or classes of minerals, accompanied the eruption of similar rocks. In the present communication, therefore, it 1s intended to bring forward a statement of the mineral species met with in Chile, and then to attempt a classification or grouping of the same in accordance with the mode of what might be termed their geological occurrence. The following enumeration represents probably as correct a list of the Chihan mineral species, together with their chemical formule +}, as can at present be attempted. * Domeyko has since published a second edition of his work, with con- siderable additions; but the list of Chilian mmeral species here brought for- ward will be found still more extensive. + The formule are all arranged according to the old notation, as the new has as yet not been generally adopted by mineralogists. Mineralogy of South America. Adamite, 2ZnO, AsO°+ HO. Agate, Si0?+ HO. » Akanthite, AgS. Albite, NaO SiO’ + Al? 0? 3 Si0*. Algadonite, Cu’ As. Alisonite, 3Cu2S+3PbS. Almandine, 3 RO, SiO? + R? 0%, SiO®. Alum, manganese, MnO SO*; Al?0°3S0°, +24H0. Alum, soda, NaO SO?+ Al? 0? 380? +24HO. Alumina, cupreous silico-phosphate, _ (CuO Fe0)?, PO? +2(3 Al? 0? PO’) +2(3 Al? 03, SiO*) +26 HO. Alunogen, Al? 0’, 3S0?+18 HO. Amalgams, Ag? Hg*; Ag Hg; Ag’ Hg’; Ag’ Hg’. Ammiolite(3HgS, SbS*)+ (3Hg0O,SbO?). Anglesite, PbO SO. Anhydrite, CaO SO?. Annabergite, 3 NiO, AsO°+8 HO. Antimony, Sb. Antimonial silver, Ag? Sb, Ag?® Sb. Apatite(chlorapatite),12CaO,PO°+CaCl. Apatite, cupreous (do.). Arquerite, Ag® Hg. Arragonite, CaO CO”. Arsenic, As. Arsenolite, AsO®. Arsenide of silver, Ag® As. Arsenide of silver, iron, and cobalt, (Ag, Fe, Co)® As. Arsenide, bibasic, of nickel and cobalt, (NiO, CoO)? AsO’ +8 HO. Arsenide, tribasic, of nickel, NiO AsO°. Arsenio-autimonide of silver (Ag Fe)* (AsSb)*. Asbestus, 3RO, 2Si0?+ RO Si0°, Asbolan, CoO MnO?+ HO. Astrakanite, MgO SO? + NaOSO?+4HO. Atakamite, 3CuO, CuCl1+5 HO. Augite, 3RO, 2 SiQ°. Axinite, (3 RO, R? 0*)(Si, B)O°, Azurite, 2(CuO HO) CO”. Barytes sulphate, BaO SO°. Barnhardite (Homichline), 2Cu?S + FeS?. Bieberite, (Co, Mg) O SO?+7HO. Bismuth, Bi. Bismuthic silver, Ag’? Bi. Bismuthine, BiS. Blakeite, Fe? O?, 3S0°+9HO., 133 Botryogene,3FeO,2S0? + 3Fe20? + 36HO Bournonite, 3(Cu” Pb)S+Sb? 8°, Brochantite, 4 CuO, SO?+3HO. Bromyrite, AgBr. Calamine, ZnO CO?. Calcite, CaO CO?. Cerusite, PbO CO?. Chabasite, (3 RO®, R? 0*) 2Si0°. Chalcopyrite, Cu S+Fe? 8°. Chalcotrichite, Cu? O. Chalybdite, FeO CO?. Chanaralite, (NiO CoO)? AsO? +8 HO. Chiastolite, 2 Al? 0%, 3 Si0?. Chileite, Fe? O? HO. Chloanthite (Co Fe Ni) As’. Chrysocolla, 3CuO, 2Si0®+6HO. Cinnabar, HgS. Cobalt bloom, 3 CoO, AsO°+8 HO. Earthy do. Cobaltine, CoS?-++CoAs?. Colophonite, 3CaO, SiO? + Fe? 0?, SiO®. Condurrite, 6CuO, AsO?. Copiapite, 2 Fe? 0?, 5S0°+18HO. Copperas, FeO SO?+-7 HO. Copper nickel, NiAs. Copper, Cu. Copper glance, Cu?S. Copper sulpharsenite, 3Cu?S, AsS°. Coquimbite, Fe? 0?, 3S0°+9 HO. Covelline, CuS. Cuban, CuS+ Fe? 8’. Cuprite, Cu? O. Cuproplumbite, (Cu? Pb)S. Danaite, (Fe CO) (AsS)?. Darwinite, Cu?® As. Descloizite, 2 PbO, VO*. Discrasite, Ag® Sb. Dolomite, CaO CO?+Mg0 CO?. Domeykite, Cu® As. Embolites, AgCl+AgBr. Enargite, 3Cu” S+AsS?. Epidote, 3 RO, Si0® +2 R? O°, Si0®. Epsomite, MgO SO®+7 HO. Erinite, 5CuO, AsO°+2 HO. Erubescite, FeS+-2Cu?S. Erythrine, 3000, AsO°+8HO. Eucairite, (Cu? Ag) Se. Fahlerz, 4(Cu* Zn Fe Ag)S+-(Sb, As)? S°. Fahlerz,mercurial,(Cu?Hg)S + (SbAs)?S°. Fibroferrite, Fe? O?, 2SO?+10HO. Fieldite, 4(Cu? Zn Fe Ag)S+(Sb As)? 8°, 134 Fluor-spar, CaF. Galena, PbS. Garnet, 3FeO, Si0?+ Al? 0%, SiO*. Gibbsite, Al? 0? +3 HO. Glauberite, (NaO CaO) SO?. Glauber-salt, NaO SO?+ 10HO. Glaukodote, (CoFe) (S As)’. Gold, Au. Gothite, Fe? 0?+ HO. Graphite, C. Grossular, 3CaO, SiO? + Al? 0%, Si0®. Guayacanite, 3Cu?, S+As 8’. Gypsum, CaO SO?+2HO. Hematite, Fe? O°. Hayesine, CaO, 4 BO*. Homocline, 2 Cu? S+ FeS?. Hornblende, 3 RO, 2Si0?+ RO, SiO®. Todyrite, AgI. Iron, meteoric. Iron-pyrites, FeS?. fron, magnetic, Fe? S*. Iron glance, Fe? O*. Tron magnetic oxide, Fe’ O*. Tron protosulphide, FeS. Kerargyrite, AgCl. Kermesite, SbO?+2SbS?. Labradorite, RO Si0?+ Al? G? Si0%. Lapis lazuli *. Laumonite, 3CaO, 28i0?+3Al? O°, Si0® +12 HO. Lead oxychloriodide, 2Pb (CI? I) -+3Pb0. Leucopyrite, FeAs”. Libethenite, 5Cu0, PO®?+HO. Limonite, Fe? 0?+3 HO. Linarite, PbO SO’+Cu0 HO. Magnetite, Fe® O*. Malachite, CuO CO?+- HO. Marmatite, (Zn Fe) 8. Marcasite, Fe S?. Melanite, 3 CaO, SiO? + Fe? 03, Si0®. Mercury, Hg. Miargyrite, AgS + Sb? S*. Mimetene, 9 PbO (AsP) 0°+ PbOl. Minium, Pb? O+. Mispickel, FeAs?+ FeS?. Molybdenite, MoS. Muscovite, (3 RO, R? 0%) SiO®, Mr. D. Forbes’s Researches on the Natron, Na0 CO?+10 HO. Nitratine, NaO, NO°. Nitre, KO, NO®. Olivine, 3 RO, Si0*. Olivinite, 4 CuO, AsO°+HO. Oligoclase, RO, Si0®+ Al? 0, 2 SiO*. Orthoclase, KO, Si0?+ Al? 02,3 Si0%. Pearlspar, CaO CO?+ MgO CO?. Pelokonite, RO Mn0O?+HO. Pharmacolite, 2CaO, AsO’+6 HO. Phosphochalcite, 5CuO, PO®+3 HO. Phosphate of lime and copper. Pickeringite, MgO, SO?+ Al? 0°, 3 SO? +24H0O., Polybasite, 9(AgCu?) $+ (SbAs)? S*. Prehnite, 2CaO Si0?+ Al? O% SiO? + HO, Proustite, 3AgS+As S?. Psilomelane, RO, MnO?+ HO. Pyrargyrite, 3AgS+Sb 83. Pyrrhotine, Fe’ S°. Quartz, SiO?. Rammelsbergite, NiAs*. Resin (fossil). Realgar, AsS. Rutile, TiO”. Sal-ammoniac, NH? Cl. Salt, NaCl. Sassolin, BO?. Scapolite, 3RO, 2Si0?+2Al? 0, Si0®. Scheelite, cupreous, (CaO CuO) WO*. Schreibersite, (Ni? Fe*)P. Scolezite, CaO Si0*?-+ Al? 0? Si0?+3HO., Silver, Ag. Silver glance, AgS. Smaltine, (Co Fe Ni) As®. Spherosiderite, FeO CO?, argillaceous. Stephanite, 6AgS +Sb?8°. Stibnite, Sb? S*. Stilbite, CaO, Si0*+ Al? 0%, 3Si03, Stromeyerite (Cu? Ag) S. Stypticite, 2Fe? O?, 2S03, Sulphur, S. Sulphide of zinc and lead, 3 ZaS +2PbS. Tagilite, 4Cu0, PO®+-3 HO. Talc, 6 MgO, 5 Si0?+2 HO. Taltalite,6CuO,Si0? + 2(Al20?Fe?0%) SiG? Tannenite, Cu? S+ Bi? S*, “ Ihave not visited the locality of this mineral near Ovalle, but I have been informed that it is found at the point of contact of a limestone rock with a diorite or granite. Mineralogy of South America. 135 Tennantite, 4(Cu*® Fe) S+As?S*. Vivianite, 3FeO, PO°+8HO. Tetrahedrite,4(Cu?AgFeZn)S+(AsSb)?S*] Wad, MnO?2+H9, Thenardite, NaO SO°. Wulfenite, PhO MO®. Trona, 2NaO, 3CO2. Zincblende, ZnS. Tourmaline, (3RO, R? 0%) (B Si) 0°. Zincblende (auriferous). Uralite, 3 RO, 2Si0*+ RO, Si0®. Zincblende (cupriferous). Vanadinite, 9 PbO, VdO®+ PbCl. Zincblende (plumbiferous),3ZnS+2PbS. Vanadinite (cupreous). In the classification of these minerals the following arrange- ment will be employed as fulfilling all necessary conditions :— 1. Minerals of meteorie origin. 2. Minerals the products of active volcanoes. 3. Minerals of the recent or unconsolidated surface-deposits. 4 Minerals of the tertiary formations. 5. Minerals of the post-cretaceous basaltic dykes. 6. Minerals of the post-oolitic diorite eruptions, and their accompanying metallic veins. (a) Minerals resulting from the mutual reactions and alte- ration of the above under the influence of air, fresh and sea-water. 7. Minerals of the great oolitic porphyrite eruptions with their interstratified tuffs, and other contemporaneous beds. (a) Mineral products of the decomposition and alteration of do. (0) Minerals specially developed in these rocks at the points of contact with the intrusion of the before-mentioned Diorite and basalt. 8. Minerals of the post-Silurian auriferous granite eruptions and accompanying metallic veins. (a) Mineral products of the alteration of above. 9. Minerals of the metamorphic rocks of pre-Devonian age. (a) Minerals specially developed in these rocks at the point of contact with the granite intrusions. It may here be remarked that the greater part of Chile seems to have been above water from the Silurian to the Liassic period*, and again from the Neocomian to the period of the deposition of the older tertiary formations on that coast. (1) Minerals of Meteorite Origin. In the aérolites known to have fallen in Chile are found only Peridote. | Schreibersite. Nickel iron. Protosulphide of iron. * Traces of apparently Triassic rocks are, however, found, especially in the north of Chile, which become more strongly developed still further northwards in Bolivia and Peru. 136 Mr. D. Forbes’s Researches on the And it may be remarked that a microscopic examination of the peridote found in aérolites reveals a very distinct structure, altogether characteristic of the same, and differing from that of the olivine found in other rocks. (2) Mineral Products of Volcanic Action. As what may be called primary minerals are found :— Pyroxene. Sulphur. Olivine. Chloride of iron. Anorthite*. Sulphurous acid. Quartz. Sulphuric acid. Pumice. Boracic acid (sassolin). Obsidian. Hydrochlorle acid. And as secondary minerals :— Alum. Gibbsite. Tron glance. Soda alum. Hayesine. Hematite. Copperas. Gypsum. (3) Minerals of the recent or Unconsolidated Surface-deposits. Soda alum. Gypsum. Quartz. Astrakanite. Iron-pyrites. Fossil resin. Calcite. Limonite. Sal-ammoniac. Copperas. Natron. Salt. Epsomite. Nitratine. Thenardite. Glauberite. Nitre. Trona. Glauber-salt. Pickeringite. Vivianite. Manyof which, as it will be perceived, occur as saline effervescences on soils at one time covered by the sea. (4) Minerals composing the Beds of the Tertiary Formations. In these formations, besides lignite, spherosiderite, calcite, and iron-pyrites, few mineral substances are found in a suffi- ciently pure state to be considered true species ; and the whole mass can only be regarded as the result of the wearing down of rocks of a previous age. (5) Minerals of the Post-Cretaceous Basaltic Dykes. These rocks have a strong general resemblance to the basalts of the Giant’s Causeway in Ireland, and, like that, are generally so compact as only to allow of their components being distin- guishable by the assistance of the microscope. It is there- fore uncertain what exact felspars they may contain; but in ~ some cases Labradorite has been made out with certainty, along with augite or hypersthene, and a magnetic mineral the character *.The felspars occurrimg in these volcanic rocks have not yet been studied. Mineralogy of South America. 137 of which is not yet examined into, and which may be metallic iron (stated by Andrews to be present in the rock of the Giant’s Causeway), or possibly magnetite or magnetic titanoferrite. The zeolites, Chabazite, Laumonite, Prehnite, scolezite, and stilbite also occur, either in this basalt or at its junction with the oolitic porphyrites. (6) Minerals of the Post-Oolitic Diorite Eruptions, with their 3 accompanying Metallic Veins. The diorites themselves are composed only of felspar and hornblende when normal, and never contain quartz, unless in localities where they have broken through quartzose strata, and in so doing may have taken up some quartz at points close to the junction. I cannot state what exact felspar or felspars are to be regarded as normal constituents ; but albite appears to be frequently present : the hornblende varies from dark green-black to light green; and occasionally even white (asbestos) appears as a constituent. These eruptions are far the richest in associated minerals; and we find the following species of primary mine- rals :— 3 Akanthite. Copper glance. Marmatite. Algadonite. Copper (sulpharseni-| Marcasite. Alisonite. ate). Mercury. Amalgams. Cuban. Miargyrite. Antimonial silver. Cuproplumbite. Mispickel. Antimony. Danaite. Molybdenite. Apatite (chlor-). Darwinite. Polybasite. Arquerite. Discrasite. Proustite. Arsenic. Domeykite. ' Pyrargyrite. Arsenide of silver. Enargite. _ Rammelsbergite. Arsenide of silver, Erubescite. Realgar. _ iron, and cobalt. Fahlerz. Silver. Arsenio-antimonide Fahlerz (mercurial). Silver (bismuthic). of silver. Fieldite. Silver glance. Barnhardite. Fluor-spar (traces). Smaltine. Barytes sulphate. Galena. Stephanite. Bismuth. Glaucodote. Stibnite. Bismuthine. Gold. Stromeyrite. Bournonite. Graphite. Taltalite. Chaleopyrite. Guayacanite. Tannenite. Chloanthite. Hematite. Tennantite. Cinnabar. Homocline. Tetrahedrite. Cobaltine. Tron-pyrites. Zineblende. Colophonite. Tron glance. Zincblende (plumbi- Copper nickel. Leucopyrite. ferous). Copper (native). Magnetite. And from the subsequent alteration and mutual reactions of the above under the influence of air, fresh and salt water, we find them associated with the following secondary minerals :— 138 Mr. D. Forbes’s Researches on the Adamite. Chalcotrichite. Kermesite. Manganese alum. Chalybdite. Lead (oxyiodochlo- Alumina (cupreous Chanaralite. ride). silicophosphate). Chileite. Limonite. Alunogen. Chrysocolla. Libethenite. Ammiolite. Cobalt bloom. Linarite. Anglesite. Earthy bloom. Malachite. Annabergite. Condurrite. Mimetene. Apatite (cupreous). Copiapite. Minium. Arragonite. Copperas. Olivinite. Arsenolite. Copper (native). Pearlspar. Arseniate of nickel Coquimbite. Pelokonite. and cobalt (tribasic).| Covelline. Pharmacolite. Arseniate of nickel Cuprite. Psilomelane. (hydrous bibasic). Descloizite. Quartz. Asbolan. Dolomite. Stypticite. Atacamite. Embolites. Sulphur. Azurite. Erinite. Tagilite. Bieberite. Erythrine. Vanadinite. Blakeite. Fibroferrite. Vanadiate of lead Brochantite. Gothite. and copper. Browyrite. Gypsum. Wad. Calamine. Todyrite. Wulfenite. Cerusite. Kerargyrite. Zincblende. (7) Minerals pertaining to the great Porphyrite Eruptions of the Oolitic Period, with their interstratified tuffs and other contem- poraneous beds. These porphyries are seen both in the form of dykes break- ing through the strata, and as immense beds of crystalline rock interstratified with ashes, tuffs, and breccias, the two latter of which apparently have been poured out under and more or less broken up and stratified by the action of the ocean. These rocks are true porphyries, being composed of crystals of felspar in a felspathic base; when occasionally some crystals of Uralite are found in them, they become true Uralite porphyries; but quartz is never met with as a constituent, except in such circum- stances as indicate that it has been produced as the result of subsequent alteration, or of more or less complete decomposition of the felspar in the rock itself. It is to be regretted that as yet no study of the felspar species constituting these rocks has been made ; but triclinic felspars are present, whilst oligoclase is noted as having been met with along with soda-lime felspars. Thin beds of impure limestone and lig- nite are occasionally met with amongst the stratified tuffs; and in some of the porphyries the following zeolites have been spa- ringly encountered :—Chabazite, Laumonite, Prehnite, scolezite, and stilbite, as well as agate, common opal, and calcite, the latter three minerals evidently formed from the decomposition of lime- felspar. Mineralogy of South America. 139 At the points of contact with the diorite rocks we find fre- quent development of the following minerals, evidently formed by a recombining and recrystallizing action on the components of the strata themselves, viz. axinite, epidote, melanite, lapis lazuli, scapolite, and tourmaline; and we also find beds of limestone converted into anhydrite and gypsum, apparently from the sul- phurous fumes which have accompanied the diorite eruptions, and which also appear to have been a main agent in the production of much kaolin and hydrosilicate of alumina produced from de- composition of felspars; whilst the hgnite beds encountered near dioritic eruptions are frequently converted into true mineral carbon, retaining the burnt woody structure, or ito anthracite. (8) Minerals of the Post-Silurian Auriferous Granite Erup- tions, and their accompanying metallic veins. This granite here, as well as all over the world where I have studied it, is invariably composed of orthoclase, Muscovite, and quartz, with particles of gold and iron pyrites disseminated oc- casionally throughout it; at its points of contact with other rocks through which it has forced its way it often contains tour- maline and hornblende, as well as occasionally scapolite; and when the granite is in greatly preponderating mass in relation to the metamorphic strata, we sometimes find it appearing as hornblendic granite for some considerable area, apparently from the absorption of more or less of the strata in question; normally, however, it is a compound of only orthoclase, Musco- vite, and quartz. The minerals which it carries along with it in Chile are almandine, chalcopyrite, gold, graphite, iron pyrites, magnetite, iron-glance, traces of pyrrhotine or magnetic pyrites, marcasite, and to which possibly we may add eucairite, and traces of rutile and cupriferous Scheelite*. As secondary minerals, we find calcite, chalybdite, Chilcite, dolomite, Gothite, Limonite, and quartz. (9) Minerals of the Metamorphic Rocks of Pre-Devonian Age. These are but few, and are almandine, common garnet, hornblende, graphite, phlogophite, Muscovite (?), quartz and tale; and at the points of contact with the granitic eruptions, we find tourmaline, epidote, and chiastolite. ; * A selenite (eucairite?) is reported from Port Flamenco, where granite occurs, and also from a locality in the back Cordilleras of Coquimbo. [I have placed it in this group, as I found the selenides of Cacheonta near Mendoza pertained thereto. Rutile is found, but in mere traces, in the granite of the coast; and the cupriferous Scheelite was discovered by Do- meyko in small quantity in the Llamuco copper vein which cuts through the granite of Illapel. 140 +#M.z. P. Schiitzenberger on the Substitution of the From the above résumé of the mineralogy of Chile, it will be seen that there is an evident tendency of the various minerals, or groups of minerals, to show definite relations of association not only with one another, but with the appearance of certain | eruptions of crystalline rocks, and that the appearance of a mineral under more than one condition is the exception, and not the rule, and is only the case with some of the more common species, as quartz, calcite, iron-pyrites, and some few others. It can also be noted that frequently, when the same crystal- lographic species appears under more than one condition of oc- currence, the mineral is found in each case to be marked by distinctive crystallographical or chemical characters: thus, for example, garnet, when found in the metamorphic or granitic rocks, appears as almandine or common garnet (an iron-alu- mina garnet), but when in the dioritic rocks, or in contact with the same, it appears as colophonite or melanite (an iron- lime garnet); and although as yet not found in Chile, we know that garnet, when occurring in trappean rocks, presents itself as pyrope. Similar relations can be traced in the case of mica, olivine, hornblende, apatite, and various other minerals. Again, on perusal of our Chilean list, it will be found that many minerals, usually so abundant and characteristic of mi- neral deposits in other parts of the world, are here present in but extremely minute quantities, as magnetic pyrites, fluor- spar, rutile, &c.; whilst many others, as Cassiterite, Wolfram, strontianite, celestine, Witherite, chrome iron, beryl, are totally wanting. When we examine the mineral list, we observe therein com- pounds of thirty-six of the chemical elements, but find that tin, titanium, strontium, fluorine, glucinum, lithium, tung- sten, tantalum, columbium, platinum, yttrium, cerium, lan- thanum, didymium, uranium, selenium, tellurium, and several others are either undiscovered as yet or only found in minute traces. XIX. On the Substitution of the Metal in a Salt by Electro- negative Elements. By P. SCHUTZENBERGER *, 1. Acetate of Chlorine, C?H?O 0 Cli REPARATION.—The only method applicable to the pre- paration of acetate of chlorine, and of the salts of chlorine in general, is direct synthesis—the combination of anhydrous * This article is an abridgment of a very interesting paper of Dr. Schiitzenberger’s bearing date 1863. Owing to the circumstance of its Metal in a Salt by Electro-negative Elements. 141 acetic acid with oxide of chlorine. 20°02 grms. of anhydrous acetic acid in a state of purity, and cooled by means of a mixture of salt and ice, were treated with 17:08 grms. of liquid hypochlorous acid. The mixture of the two substances in equivalent propor- tions has the colour of blood at first, and shows no signs of im- mediate action, but soon begins to lose colour, even when kept in the freezing-mixture, and does not disengage gas, nor lose weight. From this disappearance of colour, it is reasonable to infer that combination, or at any rate some kind of chemical action, has taken place. To make sure that the acetic acid had been saturated with hypochlorous acid, a portion of the product was mixed with an excess of hypochlorous acid, which commu- nicated to it a persistent red tint. On subsequent heating in the water-bath to 30° C., the excess of hypochlorous acid was driven off, and the liquid became colourless as before. The same result may be arrived at more conveniently by leading a stream of dry hypochlorous acid at once into anhy- drous acetic acid surrounded with-cold water, until the liquid ac- quires a decidedly yellow colour. The gas is readily absorbed and combines immediately; afterwards the excess of hypo- chlorous acid is expelled by heating to 30° C. The resulting acetate of chlorine is a liquid of a very pale bright yellow, with a powerful and irritating smell, calling to mind that of its two constituents. It explodes violently when heated to a temperature bordering on 100° C., sometimes with production of light, if the quantity of substance operated upon is sufficient. It keeps very well in the dark and at a low temperature ; but in direct or diffused daylight and at ordinary temperatures it undergoes gradual decomposition, evolving oxygen and chlorine, and leaving acetic acid. Under these conditions the stoppers of the bottles containing it are thrown out with violence. It dissolves instantly and in all proportions in water, giving a mixture of hydrated acetic and hypochlorous acids which de- colorizes solution of sulphate of indigo, disengages oxygen when heated, and in fact presents all the characteristic re- actions of the two acids. This result shows that in the original compound both anhydrides exist combined without any com- plex change. having been published as a “ Thesis,” it has not received the attention which it merits. The last-named reaction puts mto the hands of the che- mist a convenient method of making a regular descent of the fatty alcohol series. Any given normal alcohol being taken, it may be oxidized to its corresponding fatty acid. The fatty acid then, by means of Schiitzenber- ger’s reaction, gives off carbonic acid and leaves an ether of the alcohol immediately below the one started with ; and so the series may be regu- larly descended.—J. A. WANKLYN. 142 M. P. Schtitzenberger on the Substitution of the The following experiments exhibit the constitution of acetate of oxide of chlorine. | Action of Metals.—Platinum, iridium, gold, silver, and pal- ladium, unless finely divided, are without action in the cold. Platinum-black or sponge effects the decomposition of the acetate of chlorine, even at ordinary temperatures, into chlorine, oxygen, and anhydrous acetic acid. Heated to 50° or 60° C., a similar decomposition is effected by the other metals, even when they are not finely divided. There is no formation of chloride or acetate of the metal employed; and, in fact, the action is purely one of contact. A second class of metals react at ordinary temperatures or at 50°, with formation of acetate of the metal and disengagement of chlorine, a small quantity of chloride of the metal resulting as a product of a secondary action. Sodium, potassium, and magne- sium, which act with great energy, and aluminium, manganese, iron, nickel, zinc, bismuth, copper, lead, cadmium, mercury, tin, and antimony, which act with varying degrees of energy; belong to this class. The third class contains the metals which do not act in any way under any circumstances. Only chromium and platinum which has been fused belong to this class. Peroxide of manganese does not act at all on acetate of chlo- rine. Peroxide of lead acts when heated, behaving like plati- num-sponge, only less energetically. The metalloids act powerfully. Sulphur is very violent, sul- phurous acid and chlorine being disengaged :— 4.( (C? H?O Cl)O) +S=S80?+ Cl + 2¢ (C? HO}? 0). Iodine dissolves instantly and is decolorized. There escapes chlorine. No chloride of iodine results. Bromine behaves hike iodine. Phosphorus acts violently, giving phosphoric acid, there being disengagement of chlorine. Arsenic acts with violence, evolving chlorine and forming ap- parently an acetate of arsenic. ; Amorphous silicon is without action, even when heated. Wood-charcoal and graphite act when heated, producing chlo- rine and carbonic acid. Binary compounds of active elements behave as if the two elements were separate. ‘Thusicdide of potassium evolves chlo- rine, giving acetate of potash and acetate of iodine. Chloride of iodine disengages chlorine and gives acetate of iodine. The sulphurets of copper and bismuth, &c., give off chlorine, sulphurous acid, and leave an acetate of the metal. Arseniuret of iron evolves chlorine, giving acetate of per- oxide of iron and apparently acetate of arsenic. Metal in a Salt by Electro-negative Elements. 143 Organic matters, such as sugar, alcohol, &c., are oxidized at the expense of the acetate of chlorine, and disengage the chlorine. In general, nearly all substances of a more electro-positive character than chlorine drive chlorine out of acetate of chlorine. The acetate of chlorine was analyzed thus :— 0°370 grm. of acetate of chlorine was dissolved in water and treated with sulphurous acid, and then precipitated with nitrate of silver. It gave 0°580 grm. of chloride of silver, correspond- ing to 38°77 per cent. of chlorine. _ The formula (C? H? O Cl)O requires 37°566 per cent. of chlo- rine. The reaction by which acetate of chlorine is formed is this, - (C2 H80)?0+Cl20= (C2 H3 0 Cl) 0 + (C2? H30 ClO, being a double decomposition, chlorine and acetyle exchanging against one another. The reaction between acetate of chlorine and water is (C? H3O0 Cl)\O+ H? O= (C? H3O0 H)O0+Cl1H O. Acetate of bromine has not been obtained pure. It presents many points of resemblance to the corresponding chlorine-com- pound. It is very unstable and difficult to deal with. 2. Acetate of Iodine. The most convenient way of preparing acetate of iodine is the following :— 30 grms. of anhydrous acetic acid, to which 15 grms. of iodine have been added, are submitted to the action of a current of well- dried hypochlorous acid.- The apparatus must be kept cool by being surrounded with cold water. The hypochlorous acid may be made with great ease and facility by passing a mi«ture of chlorine and carbonic acid over peroxide of mercury prepared by precipitation and dried at 100° C. The object of using the carbonic acid to dilute’ the chlorine is to regulate the action. During the absorption of the hypochlorous acid by the anhydrous acetic acid and iodine, several changes in the appearance of the substances will be noted. The iodine will disappear by degrees, and then an abundant crop of yellowish-white acicular crystals will be formed. If the transmission of the hypochlorous acid be continued, these acicular crystals will gradually dissolve, and at the same time there will be an abundant evolution of chlorine. The liquid will next become quite colourless. This stage of the operation being reached, it 1s well to stop the transmission of the hypochlorous acid. In afew minutes there will be an abun- dant deposit of small crystallie grains, colourless at first, but 144 On the Substitution of the Metal in a Salt. becoming rose-coloured, and ultimately brown on exposure to the light. Thus, according to the stage at which we stop the addi- tion of hypochlorous acid, we obtain acicular or granular erys- tals sensitive to the light. The granular crystals are separated from the mother-liquor, washed with anhydrous acetic acid, and finally dissolved in anhydrous acetic acid at 60° C. The so- lution, which should be colourless, is separated from a small residue of iodic acid and then allowed to cool, when it de- posits prismatic crystals with very brilliant facets. The greatest care must be taken to avoid the action of the light. Even a strong gas-light is sufficient to yellow the crystals. Finally, the adherent anhydrous acetic acid must be removed from the crystals by warming them to 50°C. in a current of dry air. When exposed to moist air, the crystals deliquesce very rapidly, iodine being set free. Water or absolute alcohol decom- poses them instantly, giving iodine, iodic acid, and hydrated acetic acid. In the case of alcohol there is also production of acetic ether. At 100° C., even in dry air, the crystals evolve a little iodine. At temperatures above 100° C. they decompose rapidly, sometimes with a slight explosion, setting free much iodine. Analyses of the crystals purified by three crystalliza- tions and dried in a current of dry air were made as follows :— It was proved that chlorine was absent. 0°675 grm. of the silver-salt was prepared by calcining the crystals with pure hme and then dissolving in dilute nitric acid and precipitating with nitrate of silver. This silver-salt, which should be iodide of silver, was then heated in a current of chlorine: loss in weight 0°260 erm. ‘Theory, supposing chlorine absent, 0°262 grm. It was furthermore shown that the whole of the iodine exists in a pecu- liar state, treatment of the crystals with water giving all the iodine as free iodine and iodic acid. Found. Calculated. §——————__——_ lw 2 See ee II. SL ee DVS iV. VI. WEL. et J 2) 2368.4 22:2 ot coal ok CELL. Man MO Dae ie aa Mee Oe 90 |. 2° So. a.cicarrneiaei bk cil pee eee 2°83 Me AD ANT fs Se ANAT, FAT Od AO OB re. eos ore 016, 3159 304 100-00 It will thus be seen that iodine is triatomic in acetate of iodine, C? H?O)3 ( ye f08, being the rational formula of the substance in question. A very interesting reaction takes place when the product of the action of chloride of iodine on acetate of soda is heated above Comparison of the Anglo-Gallic, Russian, and Indian Arcs. 145 100° C. Carbonic acid is evolved, chloride, iodide, and acetate of methyle being formed, whilst the residual solid is common salt. A similar reaction has also been observed in the case of buty- rate of soda, and also with benzoate of soda, iodide of phenyle and biniodide of phenylene being formed in the latter case. XX. Comparison of the Anglo-Gallic, Russian, and Indian Ares, with a view to deduce from them the Mean Figure of the Earth. By Archdeacon Pratt, M.A., F.R.S. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, HROUGH the kindness of Lieut.-~Colonel Gastrell, officia- ting Surveyor-General of India, the formulz for the semi- axes of the Mean Figure of the Earth, which I demonstrated in my last communication to you, have been reduced to numbers for the three long arcs—the Anglo-Gallic, the Russian, and the Indian, which stretch over more than 22, 25, and 21 degrees of latitude respectively. Three forms of the meridian are thus deduced, corresponding to these three long arcs, involving re- spectively the three unknown quantities (¢;), (¢g), (¢;)—that is, the sums of the unknown local attractions at all the stations in the three separate arcs. which make the three meridians Tae “ee the same ; and these values of (¢,), (¢,), (¢,) are all very small; so that no ex- travagant hypothesis has to be resorted to, regar rding the amount of local attraction, to produce this identity of form. The average of the three values of the semiaxes thus deduced gives a=20926184, 6=20855304 feet, e=1—295'3 ; and none of the six values of a and b depart from these average values by so much as 300 feet; generally the departure is far less. These, therefore, I consider to be the true values of the semiaxes of the mean figure of the earth. They agree, as I said. they would, with the values deduced from my first method of correcting Bessel’s process, differing in fact by only the infinite- simal quantities 5 and 12 feet (see No. 64, Proceedings of Royal Society, p.270; or my ‘Figure of the Harth,’ third edition, p. 134). The mean figure has never before been determined, taking into consideration the effect of local attraction. The forced hypothesis of an elliptic equator and an ellipsoidal figure, which General de Schubert first suggested, and afterwards Phil, Mag. 8. 4. Vol, 33. No, 221. Feb, 1867. L 146 . Archdeacon Pratt on the Anglo-Gallic, Russian, | virtually abandoned (see Monthly Notices of the Royal Astrono- mical Society, vol. xx. p. 265), is thus proved to be unnecessary and without any foundation. In a future communication I will consider the effect of the revision of my method of treating this subject upon the esti- mated amount of local attraction in India, and upon my specu- lations regarding the constitution of the earth’s crust. 2. I will now give the calculations above referred to for finding the Mean Figure. The data given in the following ‘Table are gathered from the British Ordnance Survey Volume, pp. 766-768, and the Monthly Notices of the Royal Astronomical Society, vol. xix. p. 35, and the values of n are calculated from the formula n=13°75 sin2/. The meaning of brackets en- closing an algebraical symbol, thus (¢,), has been already ex- plained to be, that the sum of all quantities like that within the brackets is to be taken for all the stations of the arc under con- sideration. The meaning of brackets when a logarithm is en- closed within them is this, that the number is to be taken of which the number within the brackets is the logarithm; thus 58°6109= (1°7679784). Ares, — (ma). | (mB). (a), (aG). (Bye Ul Sanaa n. Anglo-Gallic.|+ 118-9267 |— 45-3653 |+155-0671 |— 35-5339 |+-11°1906| ...... 135500 Russian ...... +386:°3623 |— 126-4488 |4-335°5318 | —112-1421 |+389-9745 | ...... 13°7491 Indian ...s6< _ 12-7516 — 10°4936 |+ 46°5750|+ 36°6984 |+29-3612| ...... 81031 _@a@), |_@™@) | _@ |_ @@) | | @ | @ 2 2 a — Anglo-Gallic.|— 60-3098 |4+. 24-3352 Russian ...... —291°4511)+ 85-4950 Indian ......;+ 0:3492/+ 0°5757 — 27-7474 |4 111962 |— 4:5177|+0-9034|— 0:3645 — 228-4246 |4+ 67-0066 |— 19-6559 |+4-1918 |— 1-2296 — 0:3185|— 0:5168 |— 08521 |—0-1979 |— 0-3264 The sums of the above quantities. - Anglo-Gallic.|+ 58°6109 |— 21:03801 |+-127:3197 |— 24:3377 |+ 66729 | +0:9034 | +13°1855 Russian ...... + 94:9112|)— 40-9538 |+-107-1072 |— 45-1855 | +20-3186 4-4-1918 |4+ 12-5195 | Tndian cea _ 12-4024 | — 9:9179 |4+- 46-2615 |+ 386°1816 |+4+28°5091 |—0°1979 |+ 7:7767 I. Lhe Anglo-Gallic Arc. _ The equations of my last paper for finding the values of U, and V, become, when the numbers are substituted from the Table, 58-6109 + 127-3197 U, —24:3377V,-+ 0:9034(¢,) =0, —21:0301— 24°3377U,+ 6:6729V,+13-1855(¢,)=0, a ey ae and Indian Arcs, and the Figure of the Earth. 147 or | (1:7679784) + (2°1048957) U, — (1°3862795) V, + 1:9558801) (¢,) =0, — (1°3228414) — (1:3862795) U, + (0°8243146) V, + (1:1200966) (7,) =0. Mirinating V, by multiplying crosswise by its coefficient and adding, (2°59229380) + (2: 9292103) | U,+ (0° eta uae — (2°7091209) — (2°7725590) + (2°5063761) or 901104 81059) Us + 0 —511:82—592:32 f +320-90 —120°72-+257:27U, +326-93(¢,) =0, or — (20817792) + (2:4.103891) U, + (2°5144548) (¢,) =0; -, U,=(1'6713901)— (0'1040657) (¢,). From the first of the equations in V, we have V, = (0°3816989) + (0-7186162)U, + (2:5696006)(¢,) | = (0°3816989) — (0:8226819) | (¢;)=2'4082 —6-6479 | (4) + (0°3900063) + (2°5696006) + 2°4547 +0:0371 = 48629 —6°6108(¢,) = (0°6868953) — (0°8202540) (7,). je by the formule of my last paper, ni ae “1 20890000— —2089U,; 2089=(3:3199384) ; = 20890000 — (2°9918285) + (3°4240041) (¢,) = 20890000 —980°2 + 2654-6 (¢,) = 20889020 + 2654°6(4,) = (7°3199180) + (3°4240041) (¢,), qb 1 fa,+6,. Vig ene 12 = 00 ae ey 600 = (2°7781513) > ke fit (7:3199180) + (34240041) \ ayy = 600 L + (6:3078637) — (6:4412224) = (45417667) + (0°6458528) a) + (3°5297124) —(3:6630711) = 34815 + 4:4 (¢,) =38201 —4599(¢ ); 3386 — 4603°3 a, = 20927221 —1944(t,), b, = 20850819 +7254 (t,), L2 148 Archdeacon Pratt on the Anglo-Gallic, Russian, II. The Russian Are. Following a similar process, we have 94-9112 +107:1072U,—45:1855V,+ 4°1918(¢,)=0, —40°95388— 45°1355 U,+ 20°3186 V, + 12:5195(¢,) =0, or : (1:9773174) + (2°0298187) U,— (16545183) V, + (0°6224006) (¢,) =0, — (1°6122942) —(1:6545183) U, + (1:3078938) V, + (1:0975870) (¢,) =0, (3°2852112) + (3:3377125) | U.+ (19302944) } ed Sy esacsinhy (atone +(2: 7521053) J or 1928°46 + 2176°27 | U,+ 85:17 1 (4) — 1848°47 —2037°21 + 565:07 7999+ 189:06 U,+650-24 (4,)=0, (1-90380357) + (2°1432022)U, + (2°8130737)(t,)=0 ; (C) and to the horizontal force, and therefore will not affect ne general form or position of the wave. The friction on the bottom, on the other hand, varies directly with v, and so alters the form of the effective force, and necessitates a reconsideration of the problem. If a simple wave-form be compatible with the existence of this friction, the ridge must necessarily lie to the eastward of the moon ; for (3) the velocity at that point must be forward and a maximum, and the effective force must therefore vanish. Now at the ridge the pressure-force (- g =, and the force of friction is eastward; therefore the moon’s foree must there be westward and equal to it. Similar reasoning shows that the lowest point must be westward; but it does not seem to be pos- sible to adjust the general relations of forces and velocities every- where to our conditions, except on the assumptions, Ist, that fric- tion is proportional to the velocity, which is known to be ap- proximately true in slow motions, and, 2ndly, that the effect is to check equally all the water in each vertical column as if it were all directly subject to the action of the sea-bottom—which can _ hardly be true, though probably the resulting calculation ex- hibits something closely resembling the case of nature; for it is the average forward velocity on which the form of the wave depends. On this assumption, taking our origin at an indeterminate distance 6 to the eastward of the moon, and putting, as before, y =cCcos 2a, we have (C) »= =e cos2q@; and if f be the coeffi- se eient of friction, its accelerating force at w is —’— cos 20. On the other hand, the moon’s force is now — ogHl sin2(w—6), or — 29H } iz _ The second term of this force may be made everywhere to neutralize the force of friction by making 2gH sin 26= ite —, which at once shows that c will now never become infinite. ‘AG then we have left an extraneous force, which differs from our former one only by being multiplied by cos26. The conditions will therefore be fulfilled by making c= a Combining these two equations, squaring their terms, and observing. that Deep-sea Tides, and the Effect of Tidal Friction. 173 m®*=gK, we get 2 2 re { (=) a [5 beads, or c= 2V/ yell 3 K 4gk S4q(e—K)?+f2K}4 and by division, a eee eo moe K) 9, /g(e— K) With shallow seas tan 26 is negative, and 6> 7 or the pas- sage of the moon over the meridian is nearer to the time of low water which has preceded it than to that of high water which follows it. With seas deeper than K, the reverse would be the ease. When «=K, c= and the passage is at midtide or slack water. In this case c= ove H, or = H. m is here supposed to be expressed in angular measure, and is about ie om = therefore cannot be large, unless f is extremely minute. | : 7. If there be two bodies moving over the equator at differ- ent rates (m,, m,) and exerting different forces, the conditions will be fulfilled by superposing the wave suited to one body upon that which suits the other; 7. e., if y, be the elevation at w due to one body (and therefore, by what precedes, = y, the velocity d and A—“1 the form of the corresponding force), then, with the Ane dw 2 two bodies, y=y,+y, and v= muh et wil satisfy the equa- tions, whether taking account of friction or not. _ This gives us the rule for combining the lunar and solar tides. But it also enables us to deal with the fact that neither lumi- nary maintains a constant equatorial force on the canal. We are only concerned with the force estimated in the direction of that canal ; and whether the luminary slowly alters its declina- tion or its distance from the earth, the result is a periodical change in the intensity, but not in the form of the force; and the change may be represented by substituting for the constant H an expression H + A cos 7#, or, if necessary, by adding a series of terms similar to the second with different values of 7. H then corresponds to the mean disturbing force, and H+A to the maximum and minimum, and the time ¢ is reckoned from the time of maximum force, 174 Mr. D. D. Heath on the Dynamical Theory of The actual force at the time fis then represented by the preés- sure of a wave whose height at @ is (H+ A cos it) cos 20= H cos 2 +b oua(o-f) voa(or)} =i; + pe or, putting H cos 2a +h cos2(o-5) +hoos2(o+: 3): _ The first term is the one we have dealt with, representing the: effect of the mean moon moving at therate m. The other terms represent two waves of the same form as the principal one, but. whose ridges are at. any time ¢ at distances st to the cast and west of it, 7. e, which are propagated so as to ‘lps or gain ¢ on if at the rate 5- - They may be conceived as dite to two imaginary 5 moons smaller than ne ‘mean moon in the ratio of 4.to H, and moving with rates m+ 5 ; and the actual tide at any time will be found by the superposition of the waves due to these three imaginary bodies. If there were no friction, these three waves would each 15 with their ridges at right angles to their respective luminaries, and the highest tides would be when these bovies all coincide, or when the force is a maximum. At other times, as the height of the tidal wave in a shallow sea is greater the smaller its rate. of progress (i. e. the nearer K is to x), the eastern luminary dis- turbs the main tide more than the western, and the time of high’ water is slightly retarded after the time of maximum, with a re- verse effect after the minimum. But when we take account of friction, the ridges are at un- equal distances east of their respective luminaries, and the time of greatest tides, which is when the ridges coincide, is not the time of greatest force. When zis small, or the change of force slow, the interval may be thus found, taking account only of the first powers or differentials in the changes :— m and m-+ = 9 being the rates of progress of the mean and sub- sidiary moons, i" K and K+AK, 6 and 6+e be the | ing quantities in our formulas, we have approximately (m+ 5) i + mis st AK), or ak=™a4/Ki. | _— and the Effect of Tidal Friction. 175 And | ee JK tan 28= Vi pail wh ence I¢ d. tan 26 or (cos 287 = 27 NENA =Eees ibe Fin oc SK eft K+K- ~ 2/9 L2/K(e—K) * (e—K)? ~ 4g («—K)* Now, when the ridges coincide, the distance will be equal to that by which the luminaries have separated in the time ¢; or =e. Whence, ee we obtain 2 aos etK. Ag (K— («—K)? This is independent of both h andi; so that for small and slow changes of force, the lagging of the maximum tide behind the time of maximum force depends only on the mean rate m, a more rapid change of force being counterbalanced by a greater value of e. For numerical calculation we may make our equations for 6 and for ¢ homogeneous by reintroducing the radius (a) of the earth, observing that ¢ and fare numbers ; whence we sce that = (cos 26) generally ¢ is of the order of magnitude of i , and may be very gK sensible. ’ And this completes our éhéoiy of the tide in an equatorial canal, 8. If we suppose a canal drawn in any way along the earth’s surface, the problem becomes very complicated in its details, and I do not here propose to work it out; but the principles of the past imvestigation are generally applicable—unless, in- deed, we have to deal with a case where the length of wave necessary to keep pace with the changes in any part of the moon’s force ceases to be much larger than the depth of the sea (as in a small circie close to the pole, for instance), and so have to take account of vertical effective forces. - ay For, first, with the motions restrained to be lonettaditnad only, the variations in the centrifugal force (mentioned in 4 (a)), although they are not vertical as on the equator, have no effect: - Referring any point in the canal to its polar distance (@) and longitude ols if ds be an element of the canal, the velocity rela- tively to it of a particle of water and the components in and 176 Mr. D. D. Heath on the Dynamical Theory of : ls dé transverse to the meridian will be respectively es ae : dt’ , have both waves of that character coex- isting ; otherwise the semidiurnal wave wil! be of an unknown, or at best approximately known form. The general remarks as to the connexion of equatorial depth and position of wave hold equally here as in the other case— though the only case we shall treat of forms one of the exceptions. ‘Deep-sea Tides, and the Effect of Tidal Friction. 188 But the equations reducing themselves in this case to 2(B—ge) cos 20=2n sin 8 cos Ov, — mu, —2(B—gc) cos a =m sin 6v,—2n cos Ou,, —me sin 20 = = 4 {i fap de —1 be sin 0 ‘the equations for determining w, and v, become | - SB —ge) {m.cos 20+ 2n cos? 6 = {4n? cos? 9—m?} ieude a (B —gc) {2n cos 20 + mi cos 0 = {4n? cos? @—m?| sin On, ; and the right-hand coefficients vanish when cos 0= + 5 and our approximations fail whenever m < 2n, unless the left-hand coefficients vanish at the same ie Now, giving cos? @ the value 3 these coefficients will be found tahp.. etn Qn2k a fais 4 Qn? On2 m noe es. n*¢, an Fa m* + mn— Kn ¢, -both of which vanish when m=n. This case, therefore, of which alone Laplace has treated, is no longer, as before, at the boun- dary between possible and impossible conditions, but a Spee possible casein the midst of impossible ones. And it is smgular in its algebraical no less than in its physi- cal character ; for the differential equation determining « loses its general form, and consequently the position of the wave no longer depends on the equatorial depth. For making m=n, we find 4:cos? @—1 is a common factor of each of the equations for wu, and v,, and they become du | 2(B—ge) = ao (whence a 0) ; and 3 | 2(B—ge) cos 0=nv, sin 6 ; whence the coefficient of « in the equation of continuity vanishes : and it becomes : dk nc do 2(B—ge) the integral of which may be written sin 20, ge ee COs” Ue Root in 2(B—ge) =I{l—q pase a 184 | Mr. D. D. Heath on the epmannoa” Theory of where / is arbitrary, and 2 F n?ec q=- 2(B—ge)l Solving this, 3 Qq1B Qqlg—n® the sign of which varies with the sign of g, and with the mag- nitude of gl. Ifg be positive, or the depth diminish with 0, 2 there will be low water under the moon, unless g/ > ay" If g be negative, c is positive, or there is high water under the moon whatever the depth. To have the diurnal and semidiurnal tides both of the form we have been considering, we must have g=1. If g=0, c=0; that is, with a sea of uniform depth, and the moon stationary in her orbit, we should have no visible di- urnal tide ; only small oscillatory motions corresponding to the values of u and v. In the case we have been considering, where m=n, the angular velocity v=v, cos@ is of the form a is cos w, which becomes infinite at the pole. But the linear velocity v sin =a cos 0 cos @; and if we combine this with u=a sin w, we get the whole linear velocity =a\/1—sin? 6 cos? w; and the tangent of the inclina- cos 6 cosa sin @ Hence at the pole the actual velocity is a, directed westward along the meridian perpendicular to the moon’s meridian — (Airy, 103). I am not aware that the extremely special character given to these theorems of Laplace, and particularly as regards the diurnal wave, by making m=n, has been before remarked upon. 11. The friction, which makes the wave take an oblique posi- tion with reference to the moon, necessarily implies a reaction on. the solid earth ; and it is now admitted on all hands that one effect is a retardation of the earth’s rotation. But the mode and the measure of this action seems not yet quite settled upon. Mayer, in a paper translated in this Journal (1863), argues (on false grounds I think) that there must be, and states that in fact there is a perceptible westward current in spite of causes which tend to eastward motion ; and he assigns to this prepon- derant motzon the effect of diminishing the rotation. But then he goes on to assign another cause, viz. the form of the wave, as presented to the attracting force of the moon; and proceeds to calculate the amount “in the same manner as that employed in computing precession,”—a process which is based on tion of its direction to that of the moon’s meridian = Deep-sea Tides, and the Effect of Tidal Friction. 185 the fact that the mass of the solid earth must move with the protuberances without sliding*. The Astronomer Royal having (by an oversight, I venture to think) convinced himself that no effect on the earth’s rotation can be produced by those forces of the first order, with friction, of which his own canal theory took account, seeks for such an effect entirely in a current produced by forces of the second or higher orders. In an extract from the ‘ Rede Lecture’ (May 1866) given in this Journal, Sir W. Thomson calculates the effect in the mode which Mayer also proposes, as if the water were merely a machine for conveying the whole force of the moon to the solid earth ; but this extract contains no discussion of the principle. I proceed to give my own present view of the matter. The only case in which the tide with friction has been inves- tigated is in a canal. For the purpose of facilitating the calcu- lation, we have assumed that the friction at the bottom of each vertical column acts as an equable accelerating force on every particle of water in that column, 7. e. that it is equivalent to a set of moving forces whose resultant is proportional to the mass of the column, or («+y)dw, acting at a height ho above the bottom. If this be physically true, the reaction on the solid earth is equal and opposite to this. The accelerating force is fv, or (C), and the moment to turn the earth westward is LY ety) (1+ = + 2) ae and as changing the sign of y changes the numerical value of this expression, the sum of the moments all round the equator is not zero as Mr. Airy has madeit. Putting y=c cos 2, and integrating from @ to 277+ a, the only term which does not vanish is that arising from (cos 2)?, 2 and it gives we (1+x). Now, treating the question as if the protuberances were adhe- rent to the solid earth, the moon’s horizontal moving force on the elevation (y) above the mean level is, by our formulas, —2gH sin 2(w—58)ydo ; and its moment round the centre of the earth is 1+«+ - Putting its value for y and integrating, the only term which does not vanish is that arising from sin 2(@—54) cos 2a, and it is ine? 2gHe sin 26(1+4«)7, which (by 6) ae a (1+ «)7, the same * IT made some very crude and blundering remarks on‘ extracts from this paper, which alone I had seen. 186 © On the Dynamical Theory of Deep-sea Tides. as we obtained from friction. That is, friction without perma- nent current does act, as Sir W. ‘Thomson’s calculations iar pose, simply as a conductor of the external force*. I do not suppose friction really acts as here supposed, or that the theory of the equatorial tide with friction is perfect. But it does seem clear to me that the moving force of friction at the bottom, if its accelerating force there be proportional to the velo- city, must be in proportion to the mass above (as it is in solid friction) ; it produces the retardation at the bottom against the opposing friction of the faster-moving layers of water above it, and must be greater in proportion to the greater number of those layers. I think, therefore, there must be some effect of what one may call clinging friction, whether there be any current fric- tion or not. But any argument tending to show a predominating current tends to show that it is subject to a force which is increasing it; so that Mayer is quite right in looking out for visible effects, however infinitesimally small the cause. And then, taking the existence of a preponderance of eastward protuberances of ascer- tained magnitude and position as a datum, the more the current the less the total effect on the rotation of the solid earth. | For the law of the conservation of areas cannot be affected by inter- nal friction ; and the moon’s motion round the centre of gravity of the system depends solely on the shape, in nowise on the cur- rents, of the earth’s surface. Therefore, if the water is slacken- ing in its eastward motion, the solid earth is not slackening so much as the calculation founded on the shape would bring out. There still remains a question which I wish some astrono- mer would work out. Will this action go on at such a rate as ever to reach the limit of a coincidence of the day and the side- | real month? or will it, with whatever fluctuations, on the whole get less and less, so as never to reach some definite limit? If one might assume that the moon’s orbit would remain (looking only to the luni-terrestrial system) nearly circular, a relative esti- mate of the various changes in the whole system (moon’s dis- tance, length of day, magnitude of tide, and change of figure of the earth) might be made, though perhaps not of the time it would take to arrive at any given “stage. * He has obtained a numerical result assuming aie elevation (c) to be 1 foot, which is about what the formula (K) would give for a sea between 3 and 4 miles deep at the equator. But he assumes 6= = which is the greatest purchase the moon’s force can have, and which, by analogy, pro- bably belongs to a sea in which /=L, or about 7 miles. But we seem a long way from the state of knowledge i in which numerical estimates can be of much value, [187+] XXV. Chemical Notices from Foreign Journals. By X. Arxinson, Ph.D., FCS. [Continued from p. 62. ] yy 1860 Stas published an important memoir on the deter- ‘mination of the atomic weights of some of the elements, a brief abstract of which appeared in this Journal*. From his experi- ments he drew the conclusion that Prout’s law is invalid,—that is, that the atomic weights of the elements are not multiples by a whole number of a fundamental unit—an idea which is at the basis of the hypothesis of the identity of matter. The conclu- sions derived by Stas from his experiments were contested by: Marignac+, who upheld the validity of Prout’s law. Since 1860 Stas has been engaged in continuing his investi- gations, and has recently published the results in a large quarto volume of 800 pages, illustrated by numerous engravings of the apparatus he used. Besides making fresh determinations, Stas has incidentally investigated the question whether the cireum- stances under which a body is formed have any influence on its composition ; and he has found that, in the case of chloride of. ammonium, neither different modes of preparation nor differ- ences in temperature and pressure at the time of its formation have the slightest influence. 3 ; | - He has also treated the question of the invariability of the relations in weight of the elements forming chemical compounds.. Thus, if there are two bodies, a binary compound A B and a: ternary compound A B C, which have the two elements in com- mon A and B, is the ratio of A to B in each case the same? For imstance, in iodide of silver and in iodate of silver, is the ratio of iodine to silver in each case the same? » ie The following abstract of Stas’s researches is taken from the Zeitschrift der Chemie, and will, though inadequately, give an idea of their value. From the scale on which they were undertaken, the knowledge and judgment displayed in devising and selecting the methods, and the skill and conscientious care with which all’ possible sources of error are either corrected or allowed for, these researches are certainly without example in this kind of inves- tigation. I, The research is divided into three parts, in the first of which the author treats of the constancy of composition of chemical substances. To the preparation of the materials used he devoted the greatest possible care. _* Phil. Mag. S. 4. vol. xxii. p. 138, T Ibid. p. 142. 188 Chemical Notices :—M. Stas on the Silver was prepared partly by the reduction of chloride of silver by milk-sugar, and potash, but more advantageously by precipitation with sulphite of ammonia. For this purpose silver coin was dissolved in nitric acid and the solution evaporated to dryness, the residue fused in order to decompose any admixture of platmum salts, then dissolved inammoniacal water, and mixed with the requisite quantity of sulphite of ammonia. The reduction takes place slowly in the cold, more rapidly when heated to 60-76°. The solution of silver must be so dilute that it does not contain more than 2 per cent. of silver. The precipitated silver is washed with ammoniacal water, and then concentrated ammonia poured upon it. On standing in the air the liquid ought not to become blue; if it does, some silver is dissolved. As much as five pounds of silver were worked up at once. In order to test the purity of the silver, it was heated on a lime support in the oxyhydrogen blowpipe. It fused without being covered with any spots, began to boil with evolution of a bright b/we vapour (a greenish vapour indicates the presence of copper), and finally distilled without leaving a residue. Distillation is probably the best means of obtaining perfectly pure silver. . Large. burettes were used for estimating the silver solution, and were kept in a reservoir of water always at the same tempe- rature. The normal solutions were placed in a perfectly dark- ened room, which was lighted by a gas-lamp with a yellow screen. Determinations of silver by diffused daylight, according to the author, never gave perfectly accurate results. The estimation was effected in a black box provided with a slide, lighted by a lamp whose light passed first through a round flask filled with a solution of neutral chromate of potash. Only a thin column of the solution to be tested was thus lighted. But by this ar- rangement it was possible to detect 4, of a milligramme of silver in a litre of solution, and, by waiting a suitable time (fifteen minutes, for instance), as little as =>-7}5 of a milligramme. Ten grms. of the pure silver were dissolved at a time and mixed with normal solution of chloride of sodium (containing 5°42 grms.), and the excess of the silver dissolved determined by means of the normal solution of chloride of sodium. The percen- tage of pure silver was found =99-994—100-00 per cent., mean 99:997. The Sal-ammoniac was purified in different ways. (1) Hot sa- turated boiling solution of sal-ammoniac was boiled with nitric acid of 1°4 spec. grav. as long as chlorine was given off. Hy- drate of lime was then added, and the disengaged ammonia col- lected in water and saturated with hydrochloric acid gas.. The sal-ammoniac thus obtained was dried at 100° in a current of ammoniacal gas, and then sublimed at as low a temperature as Determination of Atomic Weights. 189 possible in glass flasks specially constructed. This sal-ammoniac sublimed without leaving a black residue. (2) Sulphate of am- monium was heated with concentrated sulphuric acid until decom- position commenced, nitric acid added so as to decolorize it, and it was then treated with hydrate of lime in a bath of common salt. The subsequent treatment was the same as the above, (3) Nitrate of potassium prepared by Stromeyer’s method was heated with zinc and iron wire. The zinc had been freed from charcoal by fusion with soda and saltpetre, or with litharge. The iron wire had been heated in a current of air and then re- duced with hydrogen. This ammonia, as well as that prepared by methods (1) and (2), has simply a penetrating smell, and not an unpleasant one, like the ammonia of commerce. The sal-am- moniac prepared from the ammonia obtained by method (3) was sublimed in vacuo in a long glass tube at as low a temperature as possible. The sal-ammoniac used in the rest of the experi- ments was always freed from an admixture of ammonia by being heated until vapour began to form. , Of all these kinds of sal-ammoniac definite weights were mixed with silver solution at the ordinary temperature or at 100°. For 100 parts of silver there were always 49°592-49-602 parts of NH*Cl, the mean being 49°597. If sal-ammoniac and silver were weighed in atomic weights (in round numbers 14 and 108), there was always an excess of silver in the solution, which frequently amounted to one hundred times as much as the sources of error in the method. Hence neither temperature nor pressure have any influence on the composition of sal-ammoniac. To prove the unchangeability of the relative weights of the elements which form chemical combinations, the author reduced chlorate, bromate, and iodate of silver by sulphurous acid. In the chloride obtained, chlorine and silver were present in exactly the same ratio as in chlorate of silver. Iodate of silver prepared by precipitating iodate of potassium with nitrate of silver is impure. It always contains an admix- ture of nitrate of silver which is not to be removed by washing. Only in case of precipitation with sulphate or hyposulphate of silver is a chemically pure preparation obtained. Reduction with sulphurous acid was effected under complete exclusion of air, and only with freshly prepared acid. Pure sulphurous acid produces in a solution of nitrate or sulphate of silver a white precipitate of sulphite of silver. But if an acid be used which has been exposed to the light, the precipitate is grey, owing to the admixture of sulphide of silver. Such an acid is totally un- fitted for reducing iodate of silver. Bromate of silver must not be prepared with nitrate of silver. Bromate of potassium is precipitated with sulphate or hyposal- 190 M. Stas on the Determination of Atomic Weights. phate of silver. The precipitate is completely washed out, and twice recrystallized from water. In order to avoid liberation of bromine during the reduction, the decomposition ‘must a _ effected at O°. Chlorate of silver cannot be obtained pure by dissolving oxide or carbonate of silver in chloric acid; chlorine must be made to act directly on oxide or on carbonate of silver. If oxide or car- bonate of silver be diffused in excess of saturated chlorine-water, ull the silver is changed into chloride of silver, and the liquid contains, along with chlorine, free hypochlorous acid without a trace of chlorie or perchloric acids, If during constant agitation chlorine be passed into water in which excess “of oxide of silver is diffused, hypochlorite of silver is formed, which is very easily soluble in water, and in the presence of oxide or carbonate of silver can be kept several days without change. But without this admix- ture it is extremely unstable; it decomposes into chloride and ‘perchlorate of silver. Perchloric acid is not formed in this case. Eight pounds of pure nitrate of silver were precipitated with carbonate of potassium (prepared from cream of tartar), washed with water by decantation for fourteen days, diffused in water, and treated with chlorine for 14 hour in a flask which was kept in constant agitation. (The manganese used for the chlorine was freed from nitrates by being boiled with dilute sulphuric acid.) The agitation was continued until the cessation of the smell of hypochlorous acid, and the carbonate of silver was now washed completely pure. Only in this way could the car- bonate of silver be gradually freed from alkali. It was then dif- fused in water, again treated with chlorine, whereby a solution of hypochlorite of silver was obtained by decantation, which was then left in the dark to spontaneous decomposition. By evapo- ‘ation, pure chlorate of silver was obtained. As the action was only carried so far that not more than two-fifths of the theore- tical quantity of chlorate of silver was obtained, the formation of perchlorate of silver was excluded. It was only after the third treatment of carbonate of silver with chlorine that the chlorate of silver obtained was perfectly free from potassium. Pure chlorate of silver is quite permanent in the air. It only attracts moisture in case it contains some hygroscopic perchlorate of silver. The reduction must be effected by a solution of sulphu- rous acid at 0°. The Reagents.—The distilled water was freed from organic substances by being distilled with manganate of potassium. The ‘first portions of the distillate were removed. If rain-water was used, a considerable quantity of ammonia passed over. In that ‘ease the water had to be distilled a second time, with the addition of some acid sulphate of potassium or sodium. For very accu- .M. Stas on the Determination of Atomic Weights. 191 rate experiments the condensing-tube of the still was made of platinum. : | - Lodaie of potassium was prepared by heating iodide of potas- sium with chlorate of potassium. In order not to exceed the temperature of the decomposition of iodate of potassium, a retort containing chlorate of potassium alone was simultaneously heated in the same sand-bath. The chloride of potassium was removed by lixiviation, the iodate three times recrystallized, and each time again lixiviated. The pure salt did not become yellow in the air. Pure iodate of potassium can also be obtained by treating iodine with caustic potash, but not by the action of chlorate of potassium on iodine. | - In order easily to purify codate of silver, it must only be pre- cipitated from dilute solutions (containing 2 to 23 per cent. of the salt). The precipitate is shaken up with the wash-water. It-is washed twelve to fifteen times with cold, and then several times with hot water. The precipitate is placed upon a funnel which is closed by fine silver wire and some linen. By means of the air-pump most of the water is removed. It is then dried ina current of hot air.freed from organic matter. Drying under the air-pump is inadmissible; there is always so much organic matter from the grease of the plate that the silver-salt scon be- comes coloured, and even blackened. The behaviour of other silver-salts (for instance, the nitrate, bromate, and chlorate of silver) is similar. Sulphurous acid was prepared by heating copper with sulphuric acid which had been diluted with one-half to two-fifths of its volume of water. The iodic acid was prepared by oxidizing iodine with nitric acid. In this case, however, only about one- fourth of the iodine used is obtained in the form of iodic acid. It is evaporated to dryness, dissolved in water, again evaporated, and the residue heated to 200°. But, from the operations in the pies vessels, the acid always contains an admixture of soda and ime. igi Hyposulphate of silver was prepared by precipitating a manga- nese salt with sulphide of barium. ‘The filtrate is evaporated, the residue dissolved in cold water, and the salt obtained recrys- tallized three times. It is then precipitated by sulphuric acid, and at once saturated with oxide or carbonate of silver. Neutral and colourless hyposulphate of silver is thus obtained. . The solu- tion of hyposulphurie acid has little stability. After some time it contains sulphurous acid. eH Pure sulphate of silver must be perfectly indifferent to test- paper. ‘The solution of fused nitrate of silver is poured into a boiling solution of pure double sulphate of potassium. The precipitate is washed with cold and then with boiling water. 192 M. Stas on the Determination of Atomic Weighis. The boiling solution of this body gives, with bromate of potas- sium, a bromate of silver which is unchangeable in the light, and can be boiled with water without decomposition. It soon undergoes decomposition in contact with organic matter (under the air-pump, for example). Hence all the water used for the decomposition had to be twice distilled over manganate of po- tassium, ) Eb The second part of the research contains new determinations of the atomic weights of silver, iodine, bromine, and chlorine. Iodide of silver.—1. A weighed quantity of silver (97 and 43 grms.) was dissolved in nitric acid of 1°21 to 1°25 spec. grav. The long-necked flask was provided with a bulb apparatus which contained some water, and the other end of which dipped in a small flask also containing water. The bulb apparatus was ground in the neck of the flask; and all parts of the apparatus were separately weighed. The heating was effected in a gas- furnace, in which the heat was made as uniform as possible by several superimposed layers of wire gauze. When all the silver was dissolved, the contents of the bulb apparatus and of the little flask were added to the principal quantity of the liquid, and the liquid distilled off at as low a temperature as possible. The residue was treated with concentrated pure sulphuric acid, and the sulphate of silver formed again heated with sulphuric acid and with sulphate of ammonia. The acid distillate obtained from the evaporation of the solution of silver was evaporated in a porcelain dish, and the solution also treated with sulphuric acid. All the sulphate of silver is now dissolved in water and precipitated by a solution of hydriodic acid. The latter is prepared by the addition of a very dilute solution of sulphurous acid to iodine diffused in ice-cold water. if the solution is not kept cool, or if too much sulphurous acid is used, sulphur is separated in the reaction. The precipitate is well shaken and washed by decan- tation with hot water. After the wash-water has been allowed to stand, it is filtered through a small filter, and the filtrate first concentrated in a glass retort, then ina platinum one, and after- wards in a platinum dish. There remained a residue of only 0-6 milligramme, from which 0°6 milligramme of AgI were separated. The iodide of silver is introduced into a glass bulb provided on two opposite sides with tubulures, one of which is closed with fine platinum wire. The iodide of silver is dried in this bulb in the air-bath and weighed. In order that while the agueous vapour is escaping no iodide be lost, both tubulures of the glass bulb are provided with weighed flasks. The condensed aqueous _M. Stas on the Determination of Atomic Weights. 193 vapour is expelled and the flasks again weighed. The iodide of silver is first weighed at 100°, then at 200°, and is finally fused. The weight remained unaltered. During the whole operation the iodide of silver remained in the dark. Pure iodide of silver is of a dirty bright yellow, and is unaltered in the light. It is only altered by light in the presence of sulphurousacid. Fused iodide of silver varies from yellow to dark reddish brown. It attacks glass more slowly than chloride or iodide of silver. Treated in this manner, 100 parts of silver gave in the mean 21775325 parts of iodide of silver; the mean difference was +0:0035. The iodine - used for the determinations of the atomic weights was purified in two ways. Light pounds of iodine were dissolved in a con- centrated solution of two pounds of iodide of potassium, and then not more than three-fourths of the iodine precipitated by water. The washed precipitate was distilled off in a current of aqueous vapour, the distillate dried over nitrate of calcium (this being the only substance that can be used), and, in order to remove all water and HI, distilled twice over anhydrous caustic baryta. Or one pound of iodine is agitated with highly concentrated am- monia, and the almost colourless liquid separated by a drawn-out funnel from the iodide of nitrogen formed. It is washed by de- cantation with concentrated ammonia, and at length upon the filter with cold water. The iodide of nitrogen, while still moist, can be rubbed in a mortar without danger. Diffused in much water, it slowly decomposes at the ordinary temperature, and ra- pidly and without danger between 60° and 65°, pure iodine being separated. lodide of ammonium remains in solution along with another salt, which is white and explosive and very little soluble in cold, but more easily so in hot water (iodate of ammo- nium). The washed iodine is distilled with aqueous vapour, in which the admixed salt remains behind. The latter decomposes at a little over 100° witha slight explosion, and separates iodine and gases. The separated iodine is purified as above. The quantity of iodine obtained from the iodide of nitrogen was always less than it ought to be from theory, if iodide of nitrogen had to decompose into iodide of ammonium, iodine, and ni- trogen. Pure iodine differs in appearance from commercial. Fused, it is fluid, and almost entirely black. At ordinary temperatures it emits no vapours. The saturated vapour is intensely blue, and violet in the diffused state. Iodine does not melt at 113°, but is liquid at 115°. The boiling-point is above 200°. Ordinarily the fusing-point is stated to be 107°, and the boiling-point 175°-180°. ~ 2. The complete synthesis of iodide of silver was effected in two ways. (a) Pure iodine was sublimed in a glass bulb, rubbed while Phil. Mag. 8. 4. Vol. 33. No. 222. March 1867. 0 194 M. Stas on the Determination of Atomic Weights. still hot, and weighed* in a glass tube which was closed by a stopper. The equivalent weight of silver was then changed by method 1 into metallic bilver, and the cold solution of silver mixed with so much sulphuric acid that sulphurous acid pro- duced no precipitate. The iodine was changed into hydriodie acid by the addition of solution of sulphurous acid, and the latter then added to the solution of silver. (0) Solution of ammonia was saturated with sulphurous acid at 0°, and the solution mixed with three times its volume of ammonia. "The iodide was changed into hydriodic acid; the rest of the process was the same as in (a) ihe deposition of iodide of silver is promoted by lengthened agitation and then by warming. [Iodine and silver were always weighed out in the ratios of the old atomic weights (127 and 108). it was found that there was each time an excess of un- combined iodine, which was estimated by standard solution of silver. The whole of the iodide of silver was now collected, as described above, and weighed. Six experiments, made with the ereatest care and with varying quantities of material (23-160 grms. of silver), showed that 100 parts of silver gave 217:5371 parts of iodide of silver, starting from the weight: of the iodine and the silver used,—or 2175335 parts, taking into account the weight of the iodide of silver used. The numbers varied between 217°529 and 217:543. From the experiments in I, 100 parts of silver yield 217°5825 iodide of silver, i: a 217°5371 = | aS 217°5835 i. ” Marignac found 217:5335 Bromide of silver was prepared by precipitating sulphate of silver with hydrobromic acid. To prepare the latter, bromide of potassium free from iodine is precipitated to the extent of three- fifths by means of nitrate of silver, and agitated for some time with the liquid. In order to remove chlorine, the bromide of silver 1s again shaken and finally heated with a solution of bro- mide of potassium. Thereupon it is diffused in water and treated with sulphuretted hydrogen. The solution of hydro- bromic acid is freed from excess of sulphuretted hydrogen by means of pure bromide of silver, and is then carefully distilled. The concentrated hydrobromic acid thus obtained is colourless and permanent in the air. It is only the acid which contains iodine that thus becomes coloured. Jor precipitating the silver astandard quantity of hydrobromic acid was used ; for an excess of hydrobromic acid might dissolve some bromide of silver. Bromide of silver precipitated in the cold is white. It was washed with cold water, and then a current of aqueous vapour was passed into the liquid to promote the deposition of bro- ~* All weighings are of course reduced to weights ¢n vacuo. 33 M. Stas on the Determination of Atomic Weights. 195 mide of silver. By this means bromide of silver becomes yellow, as also when bromide of potassium is poured upon it. By cold water it again becomes white with a very feeble tinge of yellow. White bromide of silver rapidly becomes violet in the light, yellow more slowly ; fused bromide of silver is quite permanent in the light. In the presence of traces of free bromine, white bromide of silver is also permanent in the light. The bromide of silver obtained, like the iodide of silver, was weighed ina glass bulb. It can be fused without loss of weight, provided no gases or vapours enter the apparatus. For the complete synthesis of bromide of silver, pure bromine had to be weighed. The latter was prepared by distilling bromide of potassium and bromate of potassium, or bromide of barium and bromate of barium, with sulphuric acid. The bromide of potassium of commerce was freed from admixed iodine by add- ing to a quarter of the solution bromine-water until the brown colour at first formed passed into a very bright orange-yellow colour. The other three-fourths of the bromide-of-potassium solution were then added, and all the iodine removed by shaking with CS*. The solution, which had been freed from CS? by boiling, was mixed with not quite six equivalents of hydrate of potash for one of KBr, and chlorine passed in. By evaporating the liquid, at first only half the bromate of potassium formed was utilized, the mother-liquors served for the preparation of bro- mate of barium. The bromate of potassium was recrystallized three times, and suitably lixiviated each time. The pure salt ought neither to render turbid nor colour a boiling and perfectly neutral solution of sulphate of silver. By heating in porcelain vessels (platinum vessels are attacked by it), the bromate is con- verted into bromide of potassium. Towards the end there is a little explosion and separation of bromine. Five equivalents of this bromide of potassium are mixed with one equivalent of the unchanged bromate of potassium, and distilled with sulphuric -acid. ‘The bromine which separates in the cold is collected in a retort containing a solution of bromide and bromate of potas- sium, from which it is distilled off in the water-bath. ‘To free it from every trace of chlorine, it is dissolved in concentrated solution of bromide of calcium, and precipitated therefrom by water. Bromide of calcium was prepared by dissolving purified bromine in caustic lime mixed with ammonia and then concen- trating the solution. The precipitated bromine is repeatedly dried over bromide of calcium and distilled off anhydrous phos- phoric acid. The latter was sublimed in a current of air. The bromine is finally agitated with finely powdered caustic baryta, and distilled after being poured off. | The mother-liquors from the preparation of bromate of potas- sium were diluted with five times as much water, heated to 80°, 02 196 M. Stas on the Determination of Atomic Weights. and freed from sulphuric acid by a dilute solution of chloride of barium. The decanted liquid was heated to boiling, and chlo- ride of barium added so long as the precipitate formed was re-dis- solved. The solution was poured into porcelain dishes, and by rapid cooling the bromate of potassium deposited in as fine powder as possible ; for only by this means could all admixed chloride of potassium be washed away. From the filtrate more barium-salt is obtained by a repetition of the same treatment. It is purified by threefold recrystallization, and by heating partly changed into bromide of barium. The subsequent separation of bromine is effected as above. Pure bromine boils at 63° under a pressure of 759°7 millims. When solid, it looks like iodine, with more of a steel-grey colour, however. A dilute aqueous so- lution is intense and of a pure yellow. The bromide of potas- sium prepared from this bromine was identical with that pre- pared from bromate of potassium or barium.’ The weighing of the bromine was effected in a closed glass tube provided with capillary tubulures. One end of this tube dipped in a flask filled with standard solution of sulphurous acid; in the bottom of this flask an S-tube was fused. The flask was also connected with a potash-apparatus, also contaiming sulphurous acid. The S-tube is closed by a caoutchouc stopper, and the flask cooled to 0°. Before one end of the bromine-tube is broken off, the bromine itself is made to freeze, The bromine is now gradually allowed to enter the sulphurous acid, which is always kept cool, and the bromine is finally heated. On cooling, sulphurous acid ascends into the bromine-tube. The other point of the latter is then broken off, all parts of the apparatus washed out, and the whole liquid poured into the solution cf sulphate of silver which in the mean time has been prepared. If bromine and silver are taken in the ratios of the atomic weights 80 and 108, there is only a very slight excess of silver. The bromide of silver pre- cipitated in the absence of Ag Br is pale yellow, but becomes dark yellow on being heated, or by treatment with bromide of potassium. If white and dark yellow bromide of silver be treated with zinc and sulphuric acid, in the first case a blackish grey and sometimes purple, butin the latter a purewAitesilver is precipitated. The results of all the experiments were as follows :-— 100 parts of silver yield 174°083 parts Ag Br* Four experiments. Com- plete synthesis. bg coe Marignac found (1843) 174-077 parts Ag Br From the ratio of the ato- | 174-077 parts Ag Br mic weights we have * One experiment, in which only Ag and Ag Br were weighed, + From the ratio of the Ag and Br weighed. M. Stas on the Determination of Atomic Welghts. . 197 The observations varied between 174079 and 174:097. Complete analysis of todate of silver—aA weighed quantity of the salt is decomposed by ignition, and the iodide of silver weighed, as well as the oxygen which escapes. The decompo- sition was effected in a current of nitrogen, in an apparatus in which iodine that had become free, or particles mechanically carried away, could be held back. The icdate of silver was con- tained im a glass bulb, provided on each side with long tubulures, on which metallic tubules with cocks were placed. In one of these tubulures, which was somewhat narrower, there was first of all a stopper of silver wire, then some asbestos treated with aqua regia and ignited, thereupon a layer (15 to 18 centimetres in length) of finely divided silver, prepared by precipitating in the cold solution of silver with sulphite of ammonium. Then there was again asbestos, fine silver wire, and finally a spring of silver wire which held all the parts together. For the absorption of the oxygen a tube was used 75 to 80 centims. in length, provided with metallic cocks, which first of all contained a stopper of metallic wire, then a layer 10 to 12 centims. in length of copper turnings, 10 centims. of copper reduced from oxide of copper at a high temperature by carbonic oxide, 20 centims. of copper reduced at a low temperature, and then slightly oxidized copper turnings, to burn any hydrogen that might have been formed. It was then closed, first, with a fine copper wire, then asbestos, and lastly a spring of copper wire, which prevents the removal of the mixture by a current of air. The oxide of copper used was prepared by the ignition of nitrate of copper, and was boiled with caustic potash until it was free from sulphur. : | The iodate of silver retains persistently some water ; and hence the tube containing the copper was connected with three U-tubes, 40 centims. in length and 24 centims. internal diameter. The tubes were filled with pieces of pumice, which were twice mois- tened with sulphuric acid, then ignited, filled in while still hot, and while at a temperature of 300° so much sulphuric acid added that the latter was at a height of 14 centim. in the bend of the tube. After filling, the tubes were drawn out and joined by caoutchouc tubes, which were then bound round with silver foil. A fourth, smaller U-tube served as a control, and, lastly, a fifth as a protection of the four against the atmosphere. The nitrogen, prepared by passing air over copper, was con- tained in a large gas-holder, to the water of which a solution of hydrated protoxide of tin in potash was added, to absorb O and CO*. The nitrogen is first passed through a tube containmg sulphuric acid, then through two CaCl tubes, then over a layer of ignited copper 90 centims. in length (reduced from oxide of 1938 M. Stas on the Determination of Atomic Weights. copper by carbonic oxide), and lastly through five U-tubes filled with pumice and sulphuric acid. ‘These U-tubes are jomed by tubes made of unvulcanized caoutchouc. The last U-tube is provided with a metallic stopcock. Between the copper tube and the five U-tubes there is a T-piece, which is provided with stopcocks at its three ends, the lowest of which is connected with an air-pump. To get rid of all the air from the nitrogen- purifying apparatus, the gas is passed.through, the apparatus exhausted, again filled with nitrogen, and this process is fre- quently repeated. The apparatus for the analysis was now tested. It was filled with nitrogen, connected with the air-pump by a tube 25-30 centims.in length, and 1-3 millim. inbreadth, pumped free from air, and weighed. Heated to redness in the current of nitrogen, again exhausted and weighed, the weight was not found to change. It did not change even on remaining five days on the balance, being thus exposed to considerable variations m the temperature and in the barometer. With loads of 100 grms. the variation did not amount to half a milligramme. A system of apparatus constructed in exactly the same manner served as a counterpoise. The balance had to be enclosed in a double layer of white lien, on account of the delicacy of the swing. The substance was now introduced into the glass bulb, everything exhausted, weighed, and the decomposition set up in the current of nitrogen. Two experiments were made, with 98 and with 159 grms. of iodate of silver. The glass bulb in a dish coated with magnesia was heated with the greatest care, and more strongly only towards the end of the experiment, which in one case lasted six, and in the other eleven hours. The silver. does not then attack the glass. It is well known that by heating silver in glass, yellow spots are often formed. By heating weighed quantities of glass and silver in a current of dry air to the tem- perature of bright redness, the weight remains unchanged. It is only when the heating is continued until the glass softens that there is a considerable absorption of oxygen and formation of silicate of silver. The substance which had spirted on the upper part of the glass bulb during the heating of the iodate of silver was decomposed by some burning charcoal. At the end of the experiment the parts of the glass with which the silver had been in contact were coloured yellow, or brownish yellow. Direct expe-. riments had shown that the glass increases considerably in weight, though the total weight of the apparatus remains unchanged ; silicate of silver is formed and an alkaline iodide. As in the de- composition of the iodate of silver all the oxygen is combined, at the end of the experiment the total weight of the apparatus ought not to have changed, which was found to be exactly the case. M. Stas on the Determination of Atomic Weights. 199 ~ Aviother portion of iodate of silver was reduced by sulphurous acid, and only the iodide of silver weighed. The iodate of silver, after being dried at 180°, was weighed i in exhausted flasks, then lieated to fasion, and freed from the last traces of water in a current of air above 100°. It was then dissolved in dilute am- monia and decomposed by sulphurous acid at 0°. From this the cottipesition of iodate of silver was calculated as follows :— Mean. Ae! ~ . 83:024 83°028 83-0239 83°0253 ere 5, + 16976 16:972 169761 16:9747 100-000 100:000 100°0000 100-0000 Hence the atomic weight of iodide of silver is in the mean 234-779, and the atomic weight of silver 107:928, and that of iodine 126°857 (Q@=16), according to the synthesis of iodide of silver. A complete synthesis of bromate of silver did not succeed ; for on heating the salt there was finally and quite unexpectedly a most violent explosion. Hence the salt, dried at 150°-160°, was weighed in a glass bulb closed by a doubly perforated glass stopper, in which delivery-tubes were ground. The salt was fused in a current of dry air, which had been freed from organic matter by being passed over heated oxide of copper ; it was then fused, and after condensation of all aqueous vapour transferred into weighed U-tubes containing pumice and sulphuric acid. The salt was then reduced in the usual manner with sulphurous acid. 100 parts of bromate of silver contain, Mean. Ag Br .. 79°649 79°653 79651 The atomic weight of Ag Br is therefore=187°87. Taking into account the results of the synthesis of Ag Br, the atomic weight of silver is=107°921, and of bromine 79°91. Chlorate of silver was also reduced by sulphurous acid.. This salt 1s always rendered impure by traces of Ag Cl, which arise from the organic constituents of the atmosphere. Like the iodate and bromate, it persistently retains some water. It was there- fore put ito a large weighed glass flask, which was carefully heated on the air-bath. At 243°-24.5° chlorate of silver fused, and through it was passed a continuous current of pure dry air. After cooling and weighing, the silver-salt was dissolved in water, and the clear solution poured into another flask. In the first one there remained only small traces of admixed chloride of. silver, which were weighed with the flask and allowed for. The solu- tion of chlorate of silver was reduced by sulphurous acid. An accurate investigation of the wash-waters showed that they con- tained not a trace of silver dissolved. The chloride of silver 200 M. Stas on the Determination of Atomic W eights. persistently retains some sulphuric acid, and is much more difficult to wash, especially if it cakes together. It is intro- duced into a flask closed by a stopper, which by a suitable arrangement is set in a circular and wavy motion. The clearing of the liquid was effected by passing steam into it and not into the chloride, by which caking is prevented. The complete washing out lasted seven days, the flask being kept warm day and night. All the wash-waters, after being allowed to stand, were filtered through a fine filter; all the “vessels were rinsed out with solution of cyanide of ammonium, and the latter evaporated with the addition of hydrochloric acid. In one ex- periment the chloride of silver obtained was fused in a current of hydrochloric acid gas. No liberation of sulphuric acid could be perceived, nor was there any alteration in the weight of the chloride of silver. In one experiment 138 grms., and in another 259 grms. of chlorate of silver were used. The experiments gave, in 100 parts of chlorate of silver, Mean. Ag Cl . 74°919 74.922 74°9205 O Bo ered OOS L 25:078 25:0795 100-000 100-000 100-0000 Hence the atomic weight of Ag Cl=143°395, that of silver =107:937, and that of chlorinc=5-458, from the synthesis of chloride of silver. The final result of this set of determinations of the atomic weights is as follows (O@=16) :— Silver. From the composition of AgI and AgI ©? = 107:928 ” ” Ag Br ” Ag Br 68 = 107°921 a5 a AgCl ,, Ag€l 0% = 107-937 Mean . = 107-9229 Stas sicarlier experiments 2092. 1. ) 6h aks ahh 5 mvib) oy wei eyiek: i) LeGBbye RE esl Kn 0a ne jie eS eS dole | ee LO O40 PES Sila! (hay) sj Guan So) syle lee py = 1b eOB47 126°848 ' These experiments of Stas, made with the most extreme care, agree in a surprising manner with the numbers obtained by Marignac by simpler methods. Fil. The last part of the paper contains new determinations of the atomic weights of nitrogen, potassium, sodium, and lithium. They were effected by the conversion of the chlorides into nitrates. The glass vessels used in this, as in the earlier parts of the in- vestigation, were made from a special glass. Bohemian glass alone resists, in the most powerful manner, the action of concen- trated acids. By experiments at a glass manufactory, the author was convinced that a lime-soda glass possessed the requisite properties, provided it contained an adequate excess of silicic acid. The following mixture was used: mitted sta he he? 21 FO PONE 1 Pees On Mic ea Sai. Soda Cosas ERR OC) (mies ise Ae C9 22 AOS in which equal atoms of Ca, K and Naare present, and which con- sisted of the purest materials. On evaporating in a flask made from this glass a pound of the most concentrated nitric acid, the flask, after washing out the small residue, was only found to have lost a milligramme in weight. -Melting nitre caused no loss of weight. Nitve, twice evaporated with concentrated nitric acid and fused, diminished the weight of the flask by 2°5 milligrammes, Pure nitric acid was prepared from commercial (spec. grav.= 1:5) by boiling and by two rectifications. The chlorides were heated in a platinum crucible, and while still hot filled into hot glass tubes provided with glass stoppers. It was established by special experiments that, for the complete change of the chlorides, three parts of nitric acid were required for the conversion of 1K Cl, four parts for the conversion of 1Na Cl, and 5:5 for one part of Ii Cl. : The weighed salt was introduced into a long-necked flask, which, by means of a glass stopper, was connected with a bulb-tube that dipped into a flask with water. When the liquid was heated to 40-50°, decomposition took place without effer- 202 M. Stas on the Determination of Atomic Weights. — vescence. When all the gas was expelled, the flask was inclined, and the nitric acid distilled off at as low a temperature as possible. To prevent the salt from creeping; the flask was surrounded by a cylinder of tin plate, so that: only part of the bottom covered with liquid was directly heated. The dry residue was now slowly heated to melting m a current of dry air, and by rapid cooling suddenly made to solidify. The flask was now weighed and treated a second time in the same manner. A careful examination of the water in the flask, as well as of the nitric acid distilled: off, showed that no appreciable particles had been carried over. Chloride of potassium.—The salt investigated was prepared in three ways :— (a) Nitre was recrystallized ten times, and decomposed by hydrochloric acid. 100 parts of this chloride of potassium gave 135°643 parts of nitrate of potass. (5) Chlorate of potassium was decomposed by ignition in a platinum retort. As the chloride of potassium contained traces of platinum and of silica, it was ignited with sal-ammoniac, dis- solved, and the evaporated residue fused. 100 parts of chloride of potassium gave 135°638 of nitrate of potass. In another preparation the fused salt was twice dissolved, again evaporated and fused. 100 parts of chloride of potassium then furnished 135°647 of nitrate of potass, (c) Chloride of potassium was prepared from platino-chloride of potassium. Five pounds of platinum were dissolved in aqua regia and mixed in the dark with lime, then, after being acidified, precipitated by chloride of potassium, and the fully washed pre- cipitate ignited with carbonate of potassium and sodium. The washed platinum was a second time dissolved, and again pre- cipitated by chloride of potassium. The precipitate, washed and boiled with water, was divided into three parts by partial solution. At first one-third of the whole mass was dissolved, then one half of the residue, while, finally, an undissolved residue remained. All three portions, dried at 200°, were reduced in a current of hydrogen, whereby water was given off, which thus only com- pletely escapes when the salt is decomposed. Hence this salt is not suited for determining the atomic weight of platinum. The chloride of potassium washed out was evaporated in a platinum retort and fused. Of the three portions of chloride of potassium 100 parts gave, 135°649, 1385°645, 185°640, and 135-655 parts of nitrate of potassium. Chloride of potassium (a) examined in the spectrum- apparatus gave a very distinct sodium reaction. A direct analysis made with 4 grammes of the salt, showed, ay ce the quantity of so- dium did not amount to more than from 315 tO zy of a milligramme. Chloride of potassium (0) gave also the sodium-line, as also did M. Stas on the Determination of Atomic Weights. 208 chloride of potassium (c), though this least of all. In these cases the sodium comes in from the atmosphere. Ten grammes of each chloride of potassium were weighed in a platinum boat and volatilized m a current of nitrogen in a porcelain tube. (a) left 0‘0056—0°006 per cent. of residue (silica); (6)=0°0045 —0°015 per cent.; (c)=0°025 and 0:0048 per cent. The mean of all experiments is, 100 parts of KCl give 135°6423 parts of nitrate of potassium. Chloride of sodium.—(a) Finely pulverized bicarbonate of so- dium was lixiviated, ignited, dissolved in hot water, the solution rapidly cooled, and the fine salt deposited well washed out. It was then thrice recrystallized, saturated with hydrochloric acid gas, the solution evaporated in a platinum retort after the addition of some sal-ammoniac, and ignited. The salt was then’ again dissolved, poured off from the separated silica and alumina, evaporated with the addition of ammonio-chloride of platinum and fused. It was, finally, again dissolved with the addition of sal-ammoniac, and, at length to expel all sal-ammoniac, kept in a state of fusion for a long time. 100 parts of chloride of sodium gave 145°453 parts Na NG®. (6) The chloride of sodium (a) was dissolved, mixed with bi- chloride of platinum, by which no precipitate was formed, evapo- rated and heated until decomposition set in. Only 3% of the residue was dissolved ; the solution, evaporated till a crust began to form, was then rapidly cooled, and the salt deposited washed with ice-cold water. From the mother-liquor two crystallizations of sodio-chloride of platinum were obtained by similar treatment. Thesolutionof the three portions was precipitated with chemically pure sal-ammoniac, and the solution evaporated after the addi- tion of some ammonio-chloride of platinum, and ignited. The residue, again dissolved, was evaporated and fused. 100 parts of chloride of sodium furnished 145°468, 145°465, 145°459, and 145:443 of nitrate of sodium. The mean of the whole=145-4526. The chloride of sodium (a), volatilized in a current of nitrogen, left 00047 per cent. of silica, with lime and soda; (d) left 0:0085— 0:0045 silica, with lime and soda. Lithium.—Purified carbonate of hthium was dissolved in hydro- chloric acid, and freed from lime and magnesia by sulphuretted hydrogen, oxalate of ammonium, and baryta-water. The baryta was removed by sulphate of ammonium, the filtrate evaporated, and the ammonia-salts expelled. The fused residue was dissolved in absolute alcohol, mixed with its volume of ether, and the solution treated by a freezing-mixture. The chloride of lithium deposited still contained much sodium. Nor from nitrate of lithium can all sodium be removed by ether-alcohol. The Li Cl was now dis- solved, mixed with neutral carbonate of ammonium, and the mix- 204 M. Stas on the Determination of Atomic Weights. ture warmed with continual agitation as long as the precipitate increased. The salt was put into a cylinder which stood on a flask in connexion with the air-pump. By this means all the mother-liquor could be drained away. It was washed in the same way with ammoniacal water. From the wash- waters, by eva- poration and ignition and treatment in a similar manner, a fresh portion of carbonate of lithium was obtained. The salt was now dissolved in nitric acid, again precipitated with carbonate of am- monium, and the same operations repeated five times. In this manner 55 grammes of pure salt were obtained from 1200 grammes of crude carbonate of lithium. The salt obtained from the mother-liquor was diffused in water and brought into solu- tion by means of carbonic acid gas (prepared by igniting bicar- bonate of sodium). The clear solution boiled in platinum vessels separated a pure carbonate of Jithium, which was cnce more sub- jected to a similar treatment. The salt was dissolved in a platinum boat heated to 160°-175°, and a current of dry hydrochloric acid passed over it, whereby all spirting was avoided. When the decomposition was finished, the chloride of lithium formed was fused in the atmosphere of hydrochloric acid gas, and cooled in a current of nitrogen. The platinum boats were directly put into cylindrical vessels, which were provided with metal caps and stopcocks. The apparatus were pumped empty and weighed. To dry these cylinders, the author introduces small iron boats con- taining oxide of copper and soda. For this purpose the author ig- nites in a porcelain tube the iron boats, which are half-filled with a mixture of 1 part of saltpetre and 24 finely divided copper. This mass dehydrates more rapidly than anhydrous phosphoric acid. For the purpose of an accurate investigation of the chloride of lithium, the contents of one of the boats was dissolved in water, The solution slowly but distinctly turned htmus-paper blue. The alkaline reaction remained even after part of the chloride of lithium had been volatilized in a current of hydrochloric acid, it being allowed to cool in a current of nitrogen. Entirely vola- tilized in a current of hydrochloric acid, chloride of lithium left no trace of a residue. If this chloride of lithium was mixed with solution of silver in the ratios of the atomic weights Cl=35'5, Li=7, Ag=108, the liquid always contained an appreciable trace of silver, which could be estimated by means of normal solution of sal-ammoniac. Here, as well as in the case of Na Cl and K Cl, the phenomenon was observed that an almost precipitated solution of silver, which still contains 1-2 milligrammes of silver in solution, is precipi- tated both by chloride of sodium and by solution of silver. The more acid the solution of silver, the more marked is the phenomenon, M. Stas on the Determination of Atomic Weights. 205 100 parts of silver correspond to 39:356-39-361, mean= 39°358 parts of chloride of lithium. Hence if Cl=35-457, Li is=7:022. Chloride of lithium was converted into nitrate by evaporation with nitric acid. Owing to the hygroscopic character of the latter salt, the flask for weighing the residue was provided with a chloride-of-calcium tube. The nitrate of lithium, evaporated in the platinum retort with excess of nitric acid, had a feebly al- kaline reaction after being fused in the platinum vessel. The nitrates of potassium and sodium exhibit a similar deportment. 100 parts Ji Cl gave 162°588-162°600, mean 162°595 parts of nitrate of lithium. Synthesis of nitrate of silver—A weighed quantity of the purest silver was dissolved in nitric acid, the solution evaporated, the residue heated almost to fusion in a current of air and again weighed. A repetition of the entire operation, by evaporation with nitric acid, &c., no longer altered the weight of the nitrate of silver. 100 parts of silver gave 157:494-157°4964 (mean 157°4952), and sharply heated (mean) 157-484 parts of fused nitrate of silver. On fusion, nitrate of silver loses a trace of nitricacid. Hence its real weight is between those given above. The atomic weight of nitrogen is thus found to be (Cl= 35°457) from the ratio eC Ke NG? er a ke 14-048 Na @ls Na NO*® « 0). os. == M048 rer li NOt. sos ee fw = 146046 mere Ae NO a ss Se 4044 Mllegiy sad eo Ais 14-045 From the synthesis of Ag NO? , = 14-041 »” ” 9 = 14-042 Asa supplement, the author adduces some older and some newer experiments on the relative proportions between bromide of potassium and silver. Bromide of potassium was prepared by igniting bromate of potassium. As ultimately bromine is always given off, the salt was dissolved in water mixed with pure bromide of ammonium, the dry mass heated until all ammonia was expelled, and then fused. Silver was then weighed out in the ratio of the atomic weights Br=80, Ag=108, K=89, precipitated with bromide of potassium, and the excess of silver estimated by a standard solution. 100 parts of silver correspond to 110°361 and 110°360 parts of bromide of potassium. . 206 M. Stas on the Determination of Atomic Weights. After solution in water the bromide of potassium from the pre- vious experiment left traces of silica. Filtered through spongy platinum, the filtrate decanted, after standing a day, was par- tially evaporated and the residue fused in a current of nitrogen. 100 parts correspond to 110°360 parts K Br. The rest of the solution of K Br was evaporated to crystallization, and the se- parated salt divided into three portions. Hach crystallization obtained was fused in a platinum boat and in a current of ni- trogen. Only in the presence of bromate of potassium does fusing bromide of potassium attack platinum vessels. From bromide of potassium once crystallized 110°342 parts were obtained for 100 parts silver; from ¢wice crystallized, 110°346; and from the salt which had been three times crystallized, 110°338 parts K Br. A fresh portion of bromate of potassium which had been five times recrystallized was changed into K Br. 100 parts of silver corresponded to 110°360 of this bromide of potassium. The same salt, recrystallized in the manner just described, showed the relation 100 Ag: 110°336 K Br. The mother-liquor and wash-water from it evaporated, and a part of the residue ignited in a current of bromine-vapour, gave a bromide of potassium which exhibited the relation 100 Ag : 110°344 K Br. Another part of the residue was changed into chloride by ignition in chlorine gas, and this volatilized in a current of nitrogen. A residue of 0°005 per cent. silica was left. Bromide of potassium from bromine and caustic potash.—In order to prepare pure potash, pure cream of tartar was lixiviated, heated almost to decomposition, then crystallized seven times, and carbonized in a silver crucible. The carbonate of potassium still contained silica, alumina, and traces of iron. It was de- composed in a silver crucible by hydrate of lime prepared from precipitated carbonate of lime. The lye was added to the bro- mine, evaporated, and the residue exhausted with absolute alcohol. The bromide of potassium was washed away by ice-cold water, and the residue, bromate of potassium, repeatedly recrystallized and at length ignited. After the separation of the bromate of potassium, bromide of potassium was prepared from the mother- liquor, which was heated to fusion. It was dissolved in bromine- water, evaporated, and smartly dried. The salt then dissolved completely in water. In the spectrum-apparatus this salt ex- hibited no stronger reaction than other salts. 100 parts of silver correspond to 110°332 and 110°343 parts of bromate of potassium, Bromide of potassium from bromide of barium.—Bromate of barium which had been four times recrystallized was precipi- tated with carbonate of potassium. ‘The filtrate evaporated, dis- On Negative Fluid Pressure on a given Surface. 207 ‘solved, and, after standing, rapidly cooled, gave a bromate of potassium, which was washed out with cold water, thrice crystal- lized, and then fused. For 100 parts of silver, 110°357 parts of this bromide of potassium were obtained. The same salt was dissolved in bromine-water, evaporated, the residue heated to about 400°, again dissolved, and the solution, which was not perfectly clear, filtered through spongy platinum and evaporated to crystallization. Of this salt there were 110°334 parts for 100 parts of silver. The bromide of potassium in the residue from ‘this salt exhibited the ratio 100 Ag : 110°335 parts IX Br. As the general mean, 100 parts Ag correspond to 110345 parts K Br. Marignac found that 100 parts correspond to 110°343 parts K Br. We give in conclusion the average numbers for the atomic weights determined by the author :— 6 =16. J ea Silver . ... =107°930 107°660 Nitrogen... 14044 14-009 Bromine Sie: 79:952 79°750 Chlorine an” 35°457 35°368 Jodine . . . 126°:850 126:583 Lithium... . 7°022 7001 Potassium . . 39°137 39°040 Sodium... °".« 23°043 22-980 Oren Sis 16-000 15-960 XXVI. On Negative Fluid Pressure on a given Surface. By Cuarres Brooxn, M.A., F.RS. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, 3 aia perusal of two papers in the last Number of your valu- able Journal, containing some highly interesting experi- ments on fluid motion, but in which I have sought in vain for any definite exposition of their physical causes, has induced me to send you a brief (unpublished) paragraph from my chapter on Hydrodynamics, which will, I think, help to place the origin = mee and other analogous phenomena in a somewhat clearer ight. In the well-known experiment of Bernouilli, in which a current of fluid passing through a diverging conical tube draws in addi- tional fluid through a lateral branch, and also in that of De- .sormes, in which a stream of air issuing from an orifice ina plane surface virtually attracts a circular disk placed parallel to and in front of it (which I have found to hold good equally with a jet of water), and in other similar phenomena, the cause has 208 Mr. C. Brooke on Negative Fluid been ascribed to “lateral action ;”’ which in reality does no more towards their elucidation, than did of old the “ principle of suc- tion” for the explanation of the lifting-pump. In reference to Bernouilli’s experiment, I proceed to observe :— “This physical fact may probably be best explained thus :—Each moving particle has acquired a certain amount of energy, by which it exerts a pressure in the direction of the axis of the tube through which it is passing. If flowing towards the smaller end of a conical tube, Ain the figure, this pressure, ab, may be resolved into ac perpendicular, and cb parallel to the side of the tube; of these dc is wholly effective against the side of the tube, and if an aperture or lateral branch exists the fluid will escape thence, If, on the contrary, the fluid flow towards the /arger end, as in B, then c b, the por- tion of the pressure a 0 resolved perpendi- cularly to the side of the tube, acts en- tirely from its surface; and if a lateral branch, entering the tube at a right angle, be immersed in a small vessel of fluid, atmospheric pressure on the fluid in the vessel being transmitted through the branch-tube, and unopposed at its point of junction, will cause the fluid to enter the conical tube at that point. And it is evident that the greater the value of c 6, that is, the greater the velocity in the conical tube, the greater will be the lateral influx; this result is confirmed by experi- ment; for as the velocity of the fluid in B increases, that in the lateral branch may be raised through a higher vertical column.” In this case it is clear that the pressure of the fluid against the interior of the diverging tube is, according to ordinary geome- trical language, negative. Precisely the same reasoning will apply to Desormes’s experiment, because the space between the parallel plane surfaces may be conceived to be made up of a number of radial wedge-shaped diverging tubes. In the experiments, however, which have induced these remarks, the negative or diminished pressure on certain orifices 1s due, not to the resolution of a statical pressure, but to very different causes. In the experiments of Mr. Rodwell (and in analogous experi- ments by Professor Magnus, published in your Number for Ja- nuary 1851), the existing negative pressure appears to me to be fully explained by cohesion existing between similar, or adhesion between dissimilar molecules; and that these forces are sufficient may, I think, be inferred from the fact that a column of water _ about two feet high, and of sulphuric acid nearly four feet high, may be sustained in a very nearly exhausted and sealed vertical glass tube merely by the cohesion of the fluids themselves, and their adhesion to the surface of the glass. Pressure on a given Surface. 209 In the experiment of Mr. Rodwell (p. 105), in which a stream of water descending freely from the orifice of a vertical pipe withdraws water from the orifice of a horizontal pipe placed in contact with the stream near the point of issue, the “lateral action ” is explained by “a strain upon the particles which acts acainst the lateral force of the stream ;” but surely this is only removing the difficulty one step further, for what causes the “strain.” To this I would simply reply, “Cohesion: as soon as the velocity of the issuing molecules exceeds that at which they will slide freely over each other, the pressure at the orifice of the horizontal pipe becomes negative, and fluid escapes until the negative pressure is balanced by the weight of the column vir- tually raised.” Precisely the same remarks will apply to the steam-jet, except that when the lateral tube contained air only, the force in action was adhesion of the molecules of air to those of vapour. The “inner cone” mentioned in p. 107 I presume to be the space occupied by “ dry” steam. _ Before quitting this part of the subject, permit me to notice a remark of Professor Magnus in the paper alluded to. After de- scribing the water-bellows (in which water descending by its own gravity in a large vertical pipe about 13 feet long draws in air through a number of orifices, which being carried down by the stream into a water-closed chamber, produces a stream of air sufficient for blowing a furnace), he observes that ‘the real phy- sical cause of the descent of the air is still totally unknown.” Surely in this case the negative pressure of the water against any given point of the tube arises from the antagonism between the cohesion of the molecules above to the fluid at rest, and the downward pressure of the molecules below, due to their acquired energy. ‘These opposite forces acting on any two vertically con- tiguous molecules will tend to separate them, and thus to pro- duce a negative pressure on the horizontally adjacent molecules, which is transferred to the inner surface of the pipe; and any air-bubbles that enter the orifices near the top of the pipe enable the molecules below them to acquire more vis viva than those above, and thus the negative pressure becomes augmented as the fluid descends. _ In regard to Mr. Rodwell’s first experiment, there is a remark- able resemblance between his lycopodium-figure and those ob- served by Strehlke* when a drop of fluid covered with lycopo- dium is deposited on a vibrating plate near a nodal line; he also observed that when drops were similarly placed on opposite sides of the line, the gyratory motion was (as might be expected) in opposite directions. The second memoir to which I proposed to allude is that of * Poggendorff’s Annalen, vol. xl. p. 146. Phil. Mag. 8. 4. Vol. 88. No. 222. March 1867. B 210 On Negative Fluid Pressure on a gwen Surface. Professor Tyndall. In his “ sensitive flames” the pressure of the issuing gas is so adjusted that the slightest augmentation of pressure makes the flame roar, the roaring being always accom- panied by elongation in bat-wing and fish-tail burners, and by considerable shortening in a jet from a single orifice. The pressure at the orifice of the jet is of course the difference of the external and internal pressures, and may be equally aug- mented by the diminution of the former, or the increase of the latter: and the pressure is momentarily augmented by external diminution each time that the phase of rarefaction of a progres- sive sound-wave reaches the orifice ; and, within wide limits, the more rapid the vibrations, the more decided will be the effect. I apprehend that there is not the slightest alteration of the mean pressure (measured by the quantity of gas issued in a given time), whether the sensibility of the flame be brought into action or not. With all due respect for the author’s acknowledged experi- mental ability, I must demur to the inferences arising from his concluding note. I cannot conceive that the vis viva, or energy, of the few molecules at the orifice can be sufficient to impart sen- sible vibration to the contents of the gas-pipe. Could, for ex- ample, a flute or an organ-pipe be made to speak with an em- bouchure no larger than the orifice of a gas-burner? “I guess” not: and the continuous gas-pipe would not even have the advan- tage of these, in reinforcing by reciprocation the impressed wave- motion. And moreover, in one at least of the forms of burner (the fish-tail), the supposed. in-flowing wave-motion would be in pe- culiarly disadvantageous circumstances ; for the waves in similar phases entering by the two orifices would, after reflexion from the opposite sides, of necessity interfere ; and would be in much the same condition as light-waves diffracted at the sides of a small object, as a pin, the resultant motion being nil, and, there- fore, the effect darkness. But even granting the vibrations in the gas-pipe, I do not see how they can affect the phenomena in question ; because, from the progressive motion of the column of gas, they would not be synchronous with those propagated in the surrounding stationary atmosphere. Is the final injunction respecting ample gas-ways the result of experiment, or of infer- ence only? I remain, Yours faithfully, CHARLES BROOKE. 16 Fitzroy Square, February 13, 1867. p<2ir J XXVII. On the Physical Properties of Water in relation to Ter- restrial Climate. By Professor Hennessy, F.R.S. &c. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, Pe aha me to express my satisfaction at seeing that conclu- sions to which I have been led several years since, and which have appeared in the pages of your Magazine as well as in other publications, have been reproduced in your last Number by Mr. James Croll. _Your able contributor has already done me the honour of sanctioning or adopting other results which I had previously published, and I may therefore be excused for briefly referring to them in the course of the present communication. In your Number for March 1859, S. 4. vol. xvi. p. 181, a paper is printed im which the properties of water in their rela- tion to terrestrial climate during different geological epochs is the principal subject under discussion. After establishing, as I venture to think, the superiority of water as a heat-distributor over the earth’s surface compared with the other materials of the earth’s coating, I applied the results to explain the operation of the Gulf-stream, and afterwards to the question of geological chmate. After a short discussion of Sir Charles Lyell’s theory, of the calorific influence of a belt of equatorial land combined with circumpolar oceans, I made the following statement, which I place side by side witha passage from Mr. Croll’s paper :— Mr. Croll (1867). *« These, as well as many other considerations which might be stated, seem to lead to the con- ’ clusion that, in order to raise the mean temperature of the whole earth, water should be placed along the equator—and not land, as is generally believed”’ (p.129). Professor Hennessy (1859). ** Not only are there physical grounds for adopting a somewhat different conclusion [from Sir Charles Lyell’s] (namely, that the most favourable condition for a generally high terrestrial tem- perature would be in a compa- ratively equable distribution of land and water over equatorial and extra-tropical regions, in- stead of a concentration of land in the former), but the study of the present relations of ‘sea and land seems to strongly verify the views on which this conclusion is based” (p. 189). At p. 180 Mr. Croll refers to the equatorial regions as the most important with reference to gains and losses of solar heat. This I had already pointed out in section 6 of my paper, and in a still more explicit manner in a paper read before the British . P2 212 Onthe Properties of Water in relation to Terrestrial Climate. Association in 1862. From the abstract of the latter I may give a parallel passage :— Mr. Croll (1867). “ Tt is in the equatorial regions that the earth loses as well as gains the greater part of its heat. So of all places it is here that we ought to place the substance best adapted for preventing the dissi- pation of the earth’s heat into space, if we wish to raise the ge- neral temperature of the earth” - (p. 130), Again :— Mr. Croll (1867). ‘‘ Water, of all substances in nature, seems to possess this quality to the greatest extent ; and, besides, it is a fluid, and therefore adapted by means of currents to carry the heat which it receives from the sun to every corner of the globe” (p. 130). Professor Hennessy (1862). «The torrid zone of the earth must be far more effective than all the rest of the earth’s surface as a recipient of heat. It follows, therefore, that the distribution of the absorbing and radiating sur- faces within the torrid zone must upon the whole exercise a pre- dominating influence in modify- Ing general terrestrial climate ” (Report of the British Associa- tion, 1862, Transactions of the Sections, pp. 31, 32). Professor Hennessy (1859). ‘‘The physical properties of water appear upon the whole more favourable than those of the land, to the accumulation, re- tention, and distribution of solar heat throughout the matter com- posing the external coating of the earth” (p. 192). Another conclusion which I drew from this, namely that a state of high mean temperature over the earth, such as seems to have existed during some geological epochs, would be brought about by the absence of continents or large islands and the pre- valence of oceans, Mr. Croll in a former paper (Phil. Mag. August 1864, p. 128) attributes to Professor Phillips, although Professor Phillips himself in a note cites my publication where the conclusion was first enunciated. Inthe same paper (p. 128) Mr. Croll refers to the Astronomer Royal and “ others” as hay- ing proved in 1860 the inadequacy of geological causes to dis- turb the earth’s axis of rotation. Having written to the ‘Athe- neum’ at the same time as the Astronomer Royal in 1860, it is possible that I am meant among the “others.” The prin- cipal object of my letter was to call attention to the fact that my proof of the stability of the earth’s axis, contained in a letter addressed to the late Sir John Lubbock, was published eight years before, in the Proceedings of the Royal Society (see also Phil. Mag. May 1852, S. 4. vol. i. p. 386). In his paper of August 1864, Mr. Croll criticises Poisson’s * * Diminished Difference of Thermometers in upper Air. 2138 theory of geological climate, and shows that the approach of our solar system to other systems which that theory implies would seriously and permanently disturb the orbits of the planets. Such a result had been pointed out by Mr. Hopkins in 1852 ; but at the Meeting of the British Association at Manchester in 1861, in the course of a discussion on a paper by Sir W. Thom- son, I showed that our system could not approach another system so as to increase terrestrial temperature to the extent of time required by geological phenomena, without the production of a double star group of which our sun would thenceforth be a member. Mr. Croll was probably not acquainted with this cir- eumstance, as my speech appeared (as far as I am aware) only in the local press and in a volume subsequently printed at Man- chester. | I am, Gentlemen, Your faithful Servant, Henry Hennessy. Dublin, February 5, 1867. XXVIII. On the Reason why the Difference of reading between a Thermometer exposed to direct Sunshine and one Shaded Dimi- nishes as we ascend in the Atmosphere. By JaMEs Crouu*. oe remarkable fact was observed by Mr. Glaisher, that the - difference of reading between a black-bulb thermometer exposed to the direct rays of the sun and one shaded diminishes as we ascend in the atmosphere. On viewing the matter under the light of Professor Tyndall’s important discovery regarding the influence of aqueous vapour on radiant heat, the fact stated by Mr. Glaisher appears to be in perfect harmony with theory. The following considerations will perhaps make this plain. The shaded thermometer marks the temperature of the sur- rounding air; but the exposed thermometer marks not the tem- perature of the air, but that of the bulb heated by the direct rays of the sun. ‘The temperature of the bulb depends upon two elements: (1) the rate at which it receives heat by direct radiation from the sun above the earth beneath and all sur- rounding objects, and by contact with the air; (2) the rate at which it loses heat by radiation and by contact with the air. As regards the heat gained and lost by contact with the surrounding air, both thermometers are under the same conditions, or nearly so. We therefore require only to consider the element of radiation. We begin by comparing the two thermometers at the earth’s * Communicated by the Author. 214 Mr. J. Croll on the Diminution of Difference between + surface, and we find that they differ by a very considerable num- ber of degrees. We now ascend some miles into the air, and on again comparing the thermometers we find that the difference between them has greatly diminished. It has been often proved, by direct observation, that the intensity of the sun’s rays increases as we rise in the atmosphere. How then does the exposed ther- | mometer sink more rapidly than the shaded one as.we ascend? The reason is obviously this. The temperature of the thermo- meters depends as much upon the rate at which they are losing their heat as upon the rate at which they are gaining it. The higher temperature of the exposed thermometer is the result of direct radiation from the sun. Now, although this thermometer receives by radiation more heat from the sun at the upper posi- tion than at the lower, it does not necessarily follow on this ac- count that its temperature ought to be higher. Suppose that at the upper position it should receive one-fourth more heat from the sun than at the lower, yet if the rate at which it loses its heat by radiation into space be, say, one-third greater at the upper position than at the lower, the temperature of the bulb would sink toa considerable extent, notwithstanding the extra amount of heat received. Let us now reflect on how matters stand in this respect im regard to the actual case under our - consideration. When the exposed thermometer is at the higher position, it receives more heat from the sun than at the lower, but it receives less from the earth; for a considerable part of the radiation from the earth is cut off by the screen of aqueous vapour intervening between the thermometer and the earth, But, on the whole, it is probable that the total quantity of radiant heat reaching the thermometer is greater in the higher position than in the lower. Compare now the two positions in regard to the rate at which the thermometer loses its heat by radiation. When the thermometer is at the lower position, it has the warm surface of the ground against which to radiate its heat down- wards. The high temperature of the ground thus tends to di- minish the rate of radiation. Above, there is a screen of aqueous vapour throwing back upon the thermometer a very considerable part of the heat which the instrument is radiating. upwards. This, of course, tends greatly to diminish the loss from radiation. But at the upper position this very screen, which prevented the thermometer from throwing off its heat ito the cold space above, now affects the instrument in an opposite manner ; for the ther- mometer has now to radiate its heat downwards, not upon the warm surface of the ground as before, but upon the cold upper surface of the aqueous screen intervening between the instru- ment and the earth. This of course tends to lower the mercury. We are now in a great measure above the aqueous screen, with exposed and shaded Thermometers in upper Air. 215 nothing to protect the thermometer from the influence of cold stellar space. It is true that the air above is at a temperature little below that of the thermometer itself; but then the air is dry, and, owing to its diathermancy, it does not absorb the heat radiated from the thermometer, and consequently the instru- ment radiates its heat directly into the cold stellar space above, some hundreds of degrees below zero, almost the same as it would do were the.air entirely removed. The enormous loss of heat which the thermometer now sustains causes it to fall in tempe- rature to a great extent. The molecules of the comparatively dry air at this elevation, being very bad radiators, do not throw off their heat into space so rapidly as the bulb of the exposed thermometer ; consequently their temperature does not (for this reason) tend to sink so rapidly as that of the bulb. Hence the shaded thermometer, which indicates the temperature of those molecules, is not affected to such an extent as the exposed one. Hence also the difference of reading between the two instruments must diminish as we rise in the atmosphere. This difference between the temperature of thé two thermo- meters evidently does not go on diminishing to an indefinite extent. Were we able to continue our ascent in the atmosphere, we should certainly find that a point would be reached beyond which the difference of reading would begin to increase, and would continue to do so till the outer limits of the atmosphere was reached. The difference between the temperatures of the two thermometers beyond the limits of the atmosphere would certainly be enormous. The thermometer exposed to the direct rays of the sun would no doubt be much colder than it had been when at the earth’s surface; but the shaded thermometer would now indicate the temperature of space, which, according to Sir John Herschel and M. Pouillet, is more than 200° Fahrenheit below. zero. It follows also, from what has been ‘stated, that even under direct sunshine the removal of the earth’s atmosphere would tend to lower the temperature of the earth’s surface to a great extent. This conclusion also follows as an immediate inference from the fact that the earth’s atmosphere, as it exists at present charged with aqueous vapour, affects terrestrial radiation more than it does radiation from the sun; for the removal of the atmosphere would increase the rate at which the earth throws off its heat into space more than it would increase the rate at which it receives heat from the sun; therefore its tempera- ture would necessarily fall until the rate of radiation from the earth’s surface exactly equalled the rate of radiation fo the surface. Let the atmosphere again envelope the earth, and ter- restrial radiation would instantly be diminished ; the tempera- 216 Mr. F. W. Barrett on Sensitive Flames. ture of the earth’s surface would therefore necessarily begin to rise, and would continue to do so till the rate of radiation from the surface would equal the rate of radiation received by the surface. Equilibrium being thus restored, the temperature would remain stationary. It is perfectly obvious that if we envelope the earth with a substance such as our atmosphere, that offers more resistance to terrestrial radiation than to solar, the temperature of the earth’s surface must necessarily rise until the heat which is being radiated off equals that which is being received from the sun. Remove the air and thus get quit of the resistance, and the temperature of the surface would fall, because in this case a lower temperature would maintain equilibrium. It follows, therefore, that the moon, which has no atmosphere, must be much colder than our earth, even on the side exposed to the sun. Were our earth with its atmosphere as it exists at present removed to the orbit of Venus or Mars, for example, it certainly would not be habitable, owing to the great change of temperature that would result. But a change in the- physical constitution of the atmospheric envelope is really all that would be necessary to retain the earth’s surface at its present tempera- ture in either position, as has been clearly shown by Professor Tyndall*. Erratum in No. 221. Page 130, line 18 from top, for thousand read hundred. XXIX. Note on “Sensitive Flames.” By W.F. Barrett, Teacher of Experimental Science at the London College of the Interna- tional Education Society, late Assistant in the Physical Labo- ratory of the Royal Institution. Le the last Number of the Philosophical Magazine Professor Tyndall has published the abstract of his Friday evening lecture at the Royal Institution, “On Sounding and Sensitive Flames.” In the historical note prefixed to that abstract, Pro- fessor Tyndall has stated my relationship to the latter subject. It is briefly this. In 1865, while preparing the experiments for one of the Christmas lectures at the Royal Institution, I noticed that the higher harmonics of a brass plate (which I was sounding with a violin-bow in order to obtain Chladni’s figures) had a remark- able effect on a tall and slender gas-flame that happened to be burning near. At the sound of any shrill note the flame shrank * Heut as a Mode of Motion, article 546 (second edition). The “ Rede” Lecture on Radiation, pp. 45 & 47. + Communicated by the Author. Mr. F. W. Barrett on Sensitive Flames. 217 down several inches, at the same time spreading out sideways into a flat flame, which gave an increased amount of light from the more perfect combustion of the gas. Having drawn Pro- fessor Tyndall’s attention to this influence of certain notes on a naked gas-flame, with his consent I followed up the observation by a short investigation, of the results of which he was unaware, with a view to ascertain the cause and exalt the action of this singular phenomenon. | I subsequently heard that a somewhat similar but reverse effect to that which I had observed had been noticed in America, and for the first time read the details of these experiments in the lecture to which I have referred. I was then made aware that Professor Leconte had noticed (in 1858) that musical sounds caused the spasmodic jumping of a fish-fail gas-flame, and had made the happy observation that the flame did not jump until the pressure of the gas caused it to be near flaring. Having submitted Professor Leconte’s discovery and my own simple ob- servation to a careful examination, Professor Tyndall incorpo- rated the results in his elegant lecture demonstration of January the 18th last. As, however, that lecture dwelt almost entirely upon the action of sounds on gas-flames rendered sensitive by increasing the usual gas-pressure, which, with many, imtroduces a difficulty in the repetition of the experiments, I have thought it worth while to publish the following brief record of my experiments, made with gas burnt direct from the main. The experiments for the most part were executed at my own home, during the months of June and July 1866. They will be found to add but little, if any- thing, to the comprehensive paper published by Professor Tyndall. The general effect noticed is as follows. A gas-flame burning from the tapering jet, B, fig. 1, gives the appearance represented in that figure. It is a dull quivering flame, throwing off clouds ef unconsumed carbon. When a shrill note is uttered or played, this flame at once shrinks in height and spreads out in width, taking the shape shown in fig. 2. In the first figure the flame has a loose and ill-defined shape; in the second it has, as it were, acertain degree of tension, with a flat divergent appearance, thick at the edges. To naked flames capable of responding by their motion to certain sounds Professor Tyndall has given the name of sensitive flames; by this expressive word they will in future, I trust, be designated. When a sensitive flame is spread out under the mfluence of sound, I will term it in this paper a divergent flame. It was noticeable that the divergence of the flame did not reach to the burner, but under the main flat- tening, a, fig. 2, was a small swelling, b, at right angles to, and 218 Mr. F. W. Barrett on Sensitive Flames. clasping the root of a. This small lower divergence appeared to be due to the shape of the burner, and its presence will be neg- lected. The plane of the divergent flame is uninfluenced by Fig. 1. Fig. 2. the direction of the sound, but depends entirely on the position of the burner, and moves with it. I now sought to find how far the effect was influenced by the size and shape of the burner whence the gas issued. Burners were formed of glass tubing drawn out and the points broken off so as to obtain orifices of various sizes. Flames of different length and volume were thus produced. Sensitiveness was only Mr. F. W. Barrett on Sensitive Flames. 219 obtained with the longest and most voluminous flames. Having found the best size for the burner, I now altered its shape by carefully snipping and filing the orifice. It was at once noticed that the shape as well as the size of the burner was an important element in the production of the phenomenon. Metal burners with circular orifices, after adjusting by repeated trials their size and shape, answered equally as well as glass ones. The stem of a tobacco-pipe does not answer for a burner; the bore is too small; but a gas-fitter’s brass blowpipe, if straightened and filed to a rather larger aperture, makes a very fair burner. On ac- count, however, of the ease with which they can be reproduced, I preferred in general to use burners formed of glass tubing. By care a burner was obtained which gave a remarkably sensi- tive flame ; this burner is represented in fig. 3. It is formed of glass tubing about 2 of an inch in diameter, contracted to an_ orifice +4 of an inch in diameter. It is very essential that this orifice should be slightly V-shaped, as shown in the figure*. When this burner was connected by a length of india-rubber tubing to the gas-pipes, the stopcock being fully open, a tapering flame about 15 inches long was obtained (fig. 1). With this flame the following experiments were made. A noise of any kind—walking on the ground, shutting a book, or stamping a chair, for example—caused the flame to shrink down more or less. Its action was like that of a sensitive, ner- vous person uneasily starting and twitching at every little noise. These noises consisting of a mixture of notes, the experiment was purified by trying a series of tuning-forks of different pitch, ranging from 256 to 512 vibrations per second, It was found that none of the fundamental notes of these forks caused the flame to shrink; but a fork of higher pitch, or the higher notes of the series of large forks, instantly caused a divergence of the flamet. A large inverted bell was sounded by a violin-bow and caused to yield one of its higher harmonics. The flame was intensely influ- enced; and avery pretty effect was here observed: the beats (due to the interference of the vibrations of the bell), which were faintly audible, were rendered more apparent by the movements of the flame; at every beat the momentary silence allowed the flame partially to regain its original height, from which, however, it was almost immediately thrown down by the sound which fol- * Nothing is easier than to form such a burner ; it is only necessary to draw out a piece of glass tubing in a gas-flame, and with a pair of scissors snip the contraction into the shape indicated. + This and the next experiment I made at the Royal Institution in June 1866. The influence of pitch on the flame is well illustrated by running up the scale of a pianoforte: when the high notes are approached the flame becomes uneasy, and at last diverges strongly when the note equals about 1500 vibrations per second. 220 Mr. F. W. Barrett on Sensitive Flames. lowed, erecting itself again at the next beat, only to be thrust’ back as the sound again welled up; thus a sort of breathing flame was produced, the aspirations of which were strictly timed to the sighing of the bell*. I next tried the action of a large brass plate fixed at its centre to a stand. Throwing the plate into vibration by means of a fiddle-bow, an energetic and large divergence of the flame was obtained when the higher notes of the plate were sounded. Holding the plate thus sounding close to and parallel with the flame, a more strained and intense diver- gence took place; the flame was in fact almost split in two, the edges becoming denser and the central part a mere film of flame ; but the divergence never reached down to the burner. Slowly moving the plate so as to bring different parts in succession op- posite the flame, the principal nodal lines could be traced as easily as with sand. The intervals of rest in the vibrating plate allowed the flame to raise itself up, and in its sluggish combus- tion to stand, as it were, at ease, whilst the ventral segments dragged it down to active burning and apparent attention. As a lecture-illustration, this method of showing the higher vibra- tions of a plate will be found useful where an audience is unable to look down upon the plate to see the arrangement of sand on the nodal lines. In this, as in all other experiments, the sur- prising change in the brilliancy of the flame 1 is a most striking part of the phenomenon. The divergence of the flame is not due to the impact of trans- lated puffs of air, but is an effect caused by sonorous vibrations. This can be easily proved. For instance, standing a few yards from the flame and bringing the hands forcibly together as.if to clap them, but stopping short of doing so, the flame remains undivergent, the slightest clap, however, at once produces a strong divergence. It is astonishing how far off a sound affects the flame, notwithstanding the intervention of solid obstacles ; one experiment will illustrate this. Whistling has a powerful effect on the flame, especially so the shrill whistle obtained by blowing into a key. Whilst I observed the flame, a friend whistling in this way left the room wherein was the flame, and, closing the door after him, slowly retreated upstairs; though its action was enfeebled by closing the door, the flame still continued to shrink at every whistle, and was visibly affected even when the whistle was sounded where it could barely be heard, in a closed apartment three stories away t. It-certainly is * TI observe that Professor Leconte has previously noticed that his fish- tail gas-flame exhibited pulsations im height exactly synchronous with the audible beats of a musical instrument. + Professor Tyndall, in his lecture, has shown that by slightly increasmg the pressure of the gas the fiame 1s susceptible of even greater sensitiveness than is shown in this experiment. Mr. F. W. Barrett on Sensitive Flames. 22 a most wonderful thing to consider, how almost infinitely small is the amount of vibratory motion sufficient to alter so com- pletely the aspect of a large flame of gas: and this sensitiveness of such a gas-flame to certain sounds would lead one to hope that it might be put to some use for experimental or prac- tical purposes. The chirp of a cricket would, I have no doubt, have an energetic action upon the flame. Speaking to the flame in an ordinary voice at a distance of 30 or 40 feet away caused a very marked divergence. It was noticed that the letter s had a very strong effect on the flame; and it was very curious to watch the flame as it apparently mocked any person who happened to be speaking*. Whilst making some of the foregoing experiments last summer, I was led to observe that the pressure of the gas had an important influence upon the divergence of the flame, and remarked that an increased pressure acted like a shrill sound in spreading out the flame, which gave at the same time a roaring noise. Pro- fessor Leconte has, however, decidedly the prior claim to this observation, which Professor Tyndall has raised to an expla- nation of the phenomenon. Professor Tyndall remarks, “The gas issues from its burner with a hiss, and an external sound * In the last Number of the Philosophical Magazine, Professor Tyndall has already remarked on the striking effect upon the flame produced by the letter s, or by the hiss given when compressed air issues from an orifice. Associated with this observation there are some other remarkable pecu- liarities connected with the sound of the letter s. When listening from some elevated point to the singing of a large assemblage of people, I have frequently noticed that when a word contaming any sibilant was sung, the sound of the peoples’ voices united itself into a sharp, loud and somewhat prolonged hiss, like the escape of high-pressure steam from a small nozzle, and quite unlike anything produced by any other letter. In a paper pub- lished in the Philosophical Magazine for June 1849, the Astronomer Royal has stated his belief that the sound of s or z is produced by “ an interrup- tion of the continuity of the particles of air’’—that it is in fact a broken wave, in its progress resembling the rush of a bore on a river; and has compared it to a broken-headed sea which, meeting an embankment, is not regularly reflected as the larger waves would be, but runs along the side to a far distance. In support of this analogy, Mr. Airy mentions the fact that a sibilant sound is not returned by an ordinary echo, and that in whispering-galleries the buzzing sound of a whisper is carried along close to and never quits the surface of the dome, being only beard at the oppo- site side by applying the ear close to that surface, while an ordinary sound is not. transmitted along the surface, and is not so strikingly heard at the opposite side. From theoretic considerations, Mr. Airy remarks that any clear musical sound would have a tendency to degenerate into a hiss by mere distance of transmission, and that this conversion would soonest take place with loud sounds on ahigh key. That emiment philosopher is, how- ever, unaware whether there exists any mstance of such a conversion: might not a sensitive flame be applied to the determination of this interest- ing point ? 222 Mr. F. W. Barrett on Sensitive Flames. of this character added to that of a gas-jet already on the point of roaring is equivalent to an augmentation of pressure on the issuing stream of gas.” This explanation is, I believe, the only distinct one that has yet been given; and I think the follow- ing observations confirm and supplement it. I noticed that if a sensitive flame be gently blown on through a glass tube, while blowing on the flame it shrinks and diverges exactly as if it were under the influence of sonorous vibration, and it diverges the more strongly the nearer one blows to the root of the flame. The flame also very forcibly diverges when a fiddle-bow is drawn across or a wetted finger drawn down the metal or glass tube which conveys the gas to the burner; if the tube be of india- rubber, giving it the slightest shake causes the flame to diverge, a rapid fluttering of the flame being produced when the tube oscillates. Professor Leconte has compared the movement of the flame to that of a liquid vein under the influence of sonorous vibrations, and has shown the striking resemblance between his observa- tions on a gas-flame and Savart’s experiments on jets of water. The latter physicist has proved that certain notes cause a liquid vein to emit a musical sound, and at the same time break up into drops the portion of the jet which was previously conti- nuous. ‘The flame behaves in a precisely similar manner. I have often noticed that, when rendered divergent by a sound, it yields, more or less clearly, a musical note of slightly different pitch. And I have lately ascertained, by examining the image of the flame in a moving mirror (it is best to diminish the brightness by smoking the glass), that, whilst the flame shown in fig. 1 is continuous, the continuity is broken when the flame is diverging under sonorous vibrations or flickermg or roarmg under increased pressure. In this state fig. 2 becomes nothing more than a succession of flames, resembling a singing flame ora troubled liquid vein. To obtain perfect success in repeating these experiments, the observations of Professor Leconte, Professor Tyndall, and the few - I have here detailed would show that regard must be had (a) to the pressure of the gas, (b) the freedom of the gas-passages, (c) the shape of the burner, (d) the size of the orifice. Atten- tion to all of these cannot fail to give a flame sensitive to the minutest noises: but, as I have endeavoured to show in the fore- going note, success may be obtained by using gas direct from the main, and merely attending to the shape of the burner— choosing also the dusk of the evening as the best time for making the experiments; for then the pressure on the main ap- pears to be at its maximum. [223 XXX. Notices respecting New Books. Modern Arithmetic, a Treatise adapted for School Work and Private Study. By the Rev. Joun Hunter, M.A. Pp. 246. London: Longmans and Co. peers the chief difficulty of drawing up a good practical book on arithmetic arises from the fact that the order in which the parts of the subject have to be taught is not that in which they would be systematically arranged. For purposes of systematic arrangement the parts of the subject would follow each other thus:—First, the rules of addition, &c. for integers, vulgar and decimal fractions ; next, the same rules and subsidiary processes for concrete or mixed num- bers; and, lastly, the application of the rules to questions of com- mercial arithmetic. A book so arranged may be very proper for boys or young men already instructed, who merely wish to revise and ex- tend their knowledge of the subject, but is quite unfit as a manual even for intelligent boys. If the reader doubt this, let him 1 imagine an arrangement by which.a boy is taught to ‘‘find the sum of 0° 125, 4°163, and 9° 457 correct to five places of decimals,’”’ before he has been taught to ‘‘ find the value of 11 lbs. of beef at 103d. a pound.” Yet this is the order adopted in perhaps the majority of madern books upon arithmetic, and certainly in some written with conspicuous ability. And it must be allowed that a completely satisfactory alter- native arrangement is not easily suggested—though there can be little doubt that the right order for teaching is to divide the subject into two courses, so as to introduce the learner to concrete numbers as soon as possible. This is in fact what Mr. Hunter has done in the treatise before us. His first course consists of the four rules for integers, one or two processes in vulgar fractions in anticipation of the distinct treatment of that subject in the second course, mixed numbers, miscellaneous examples, and rule of three. The arrange- ment, though causing a want of symmetry in the book, is doubtless substantially right; but we think it might be es in detail ; e.g. such examples as “multiply £76 19s. 8,3,d. by 58” (p. 49) should hardly be introduced before the formal freneicu of vulgar fractions. The remainder of the work takes in the whole of the subjects ge- nerally contained in the best modern treatises, and seems to us, so far as we have examined it, to be very well done. On the whole, we can cordially recommend it to any one in want of a good practical treatise on arithmetic, illustrated by a large number of well-chosen examples. Easy Introduction to Conic Sections. By the Rev. Joun Hunter, M.A. london: Longmans, Green, and Co. 1866. Pp. 87. This work consists of a selection of the most elementary proposi- tions in coordinate geometry, illustrated by a considerable number of very elementary examples. How limited is the selection will be gathered from the fact that, in the case of each conic section, nothing 224. Royal Society :—Messrs. Balfour Stewart and Tait on more is given than its equation in its simplest form, and those of its tangent and normal, together with a few properties that follow directly from those equations. The object of the work is to put the merest elements of the subject in a very simple form, with a view to en- abling a beginner to obtain some knowledge of it before proceeding to more elaborate works. The simplification is mainly effected by inserting steps of algebraical processes which are commonly sup- pressed or curtailed. The author tells us, in his preface, that in writing the book he has had an eye to what, from long experience in tuition, he has found needful. We therefore infer that there are mathematical students who find ‘An Kasy Introduction to Conic Sections’ necessary. ‘To ourselves, unenlightened by the author’s experience, it would have seemed better that a student who found insuperable difficulties in such a book as Mr. Todhunter’s “‘ masterly work”? would do well to spend a little more time over the lower branches of mathematics before proceeding to the higher. XXXI. Proceedings of Learned Becteues: ROYAL SOCIETY. [Continued from p. 73. | Dec. 6, 1866.—Lieutenant-General Sabine, President, in theChair. - Te following communication was read :— “On the Heating of a Disk by rapid Rotation zm vacuo.’ By Balfour Stewart, M.A., F.R.S., and PB. G. Tait, M.A. (Continued.) 16. The apparatus ard certain preliminary experiments having been described in the previous paper *, the authors now proceed to: relate what further experiments have been made. In the preliminary experiments it was conclusively shown (art. 8) that the effect on the pile caused by rotation of the disk was due to radiant heat, and also (art. 9) that this effect was not due to the heating of the rock-salt which, in most of the experiments, was placed before the mouth of the cone. It was also rendered probable that the effect was not due to ra- diation from heated air, by the two following considerations :-— (1) Because in order that nearly dry air of such a tenuity might give such a radiation it would require to be heated enormously. (2) Because when the lampblack was removed from the aluminium - disk, leaving it a rough metallic surface, the indication afforded by the galvanometer was reduced to about one-fourth of the amount with the blackened disk. The following observations tend to strengthen this proof :. = (3) The heating effect is the same in hydrogen or in coal- -2aS ag in air, although there is no question that the absorptive, and there- fore the radiative power of coal-gas is much greater than that of air. This is shown by the following sets of experiments, which were made with the blackened aluminium disk insulated with ebonite, and ~ with rock-salt in the cone. * Phil. Mag. vol. xxx. p. 314. the Heating of a Disk by rapid Rotation in vacuo. 225 - 6A | #4 8, a Ze a Heat indication. 52 o eee & q E 3 aa & Soe |e = Nature | Tension |@ — 3, - Ste S43lumpgs « of gas. | of gas, in |S ¢ bo eee es ea |. fas | De inches, |2.. 2 = £ Ss 3 - XS oa =| sions, | Fahr. Zz BSE l yin. 2 30 22 22°5 ... |bydrogen| 0:6 95 VIII. 3 30 22 23°3 ote air 0-7 Ex | 2 30 20 a 0°-95 |hydrogen| 0°5 97 X. 2 30 20 - 0°:87 air 1-1 XI. 3 30 20 sas 0°°85 |hydrogen| 0:25 98:5 IY: 3 30 20 ie 0°86 | coal-gas| 0°25 95 (4) It may be objected to (2) that the greater heating effect from a blackened aluminium disk than from an unblackened one does not prove that this heating effect may not be due to air, since the blackened surface may be imagined to lay hold of the air more than the metallic one. But the following sets of experiments prove that the heating effect of the aluminium disk with both sides black- ened is the same as when only one side is blackened. 2 1 eat “3 = fas} = {cD} s 4 = He) 5 a cS a ES : | . a O-n 4 Ses) ||) etr—til— qo s (= (es a Hee] Sog ja, sao| aie ome oS |SESs 238 O88) 2 go ‘a's Ss \Sea| Bee soak Sox | Ss x 2 30 20 0:9, 1:1 | Disk blackened on one side. XIE, 3 30 20 0-8 0-4 | Disk blackened on both sides. It would therefore appear to be proved that in these experiments the heating effect is due to the increased temperature of the disk. 17. Before proceeding further it may be advisable to detail some experiments made with an ebonite disk 5 inch thick. In these experiments care was taken that the ebonite should have the same temperature throughcut its thickness, so that there might be no flow of heat from the interior to the surface, or vice versd. The experi- ments were made with rock-salt in the cone. ' 1 wie 2 Bg a @ jae. ab ai 2 é = De * oS “= = ae S = oS esieee ans Si Tension eo 2rs ‘3 Bec Sri wily & ho ‘2° a |Nature off of gas, in eH = ll S ss sl4 3.3 aa e568 gas. | inches. 3 a a 7, pea ey Oe pe ag Bay ee 6.3 30 20 32 air ita. RVs 1 30 20 30 air 0:26 XVI. 1 30 20 31 air Teer XVII. 2 30 20 28°5 air 0:26 - XVIII 2 30 20 28°5 air 0:25 XIX. | 3 30 20 29. |hydrogen| 0-25 90 Phil, Mag. S. 4, Vol. 33, No. 222. March 1867. Q 226 Royal Society :—Messrs. Balfour Stewart and Tait on From these experiments it may be taken for granted that the heat indication given by an ebonite disk is, like that from an aluminium disk, independent both of the density and chemical constitution of the residual gas. It is also highly probable that the unknown cause of the heating effect is the same for both disks. 18. To return now to the aluminium disk, it may be shown that the heating of this disk is not caused by revolution under the earth’s magnetic force ; for (1) the following calculation, kindly furnished by Professor Maxwell, shows that the heating effect due to this cause would, for the aluminium disk 45 of an inch in thickness, amount, under the circumstances of rotation, only to z,4,, of a degree Fahr., whereas the observed effect is more than half a degree. An ellipsoid, semiaxes a, 8, c, revolves about the axis c with velo- city w, in a uniform magnetic field. To find its electrical state at a given instant. At the given instant let the axes of 2, y, 2 coin- cide with a, 6, ¢; then using the notation in the paper on the Elec- tromagnetic field *, ay dy | dy Pe poya— 7 =Pps VW pwyy— 7 = 9sR—= —pe (Bybee) — gq =" P QR electromotive force, « y magnetic intensity, W electric ten- | sion, »=coefficient of magnetic induction=1 for everything but iron, ~ P, %7 electric currents, p=resistance of cubic unit of volume. — The condition of the currents being confined to the ellipsoid, is x te at ete Solving, we get Hw wa po OG ge ee By )e ig @ee% | ig bee aax Ob By p= puoy(2’+y’) — pore atgrea) +C. _ This is the complete solution. The heat (measured as energy) produced in unit of volume in unit of time is p(p’+q°+7"). The whole heat produced in the ellipsoid in unit of time is ae \aeate} 15 p a+e' +c) i dae ae pen ee If a=, this is 15 a) pee +3). If ¢ is small compared with a, it becomes , BA iG “w'a'e'(a +B"). If the axis is horizontal, a +(3°= HH’ sin* 0+ V*, * Phil. Trans, 1865, p. 459. the Heating of a Disk by rapid Rotation in vacuo. 2277 where H=horizontal magnetic force, and V=vertical magnetic force, and @=angle between the axis of rotation and the magnetic meridian, a=radius and ¢ half the thickness, w=2mn, where n denotes the revolutions per second; »p=1; p is the resistance of unit length and unit section. Now, the resistance of 1 metre long and 1 millimetre diameter 4 === 10°=0'0575 x 107 ° e . . e . 5) for aluminium in metrical units by Matthiessen, or ao 3 p is the same for metrical and for British measure. At Kew horizontal foree=3°'81, dip 68°°10; @=90° in the experi- ‘ments, .*. a°-+(°=104'8 British measure. The revolving body is not an ellipsoid but a cylinder, equally thick 15 throughout ; to correct for this we shall put oF ce for c’. _ We get for the energy converted into heat by electrical action per second 12°91 in grain-foot-second measure. _ Now 772g=energy required to raise 1 grain of water 1° Fahr. heats yo: 70,000 ‘The disk = 16 X ‘22 grain of water, .*. energy corresponding to 1° 32°2 =/72X = x 15400, 16 ° 12°91 12°91 or rise of temperature per second= 154015400 23716000 degree 1 : Fahr. or about 61276 degree in 30 seconds. This is when the heat is uniformly distributed through the thick- mess of the disk, which it will be in less than thirty seconds. If ‘there were no conduction, the rise of temperature at the surface would ‘be about twice the value found above. '. (2) It would appear from the above formula that the heating effect ‘due to this cause should increase with the thickness of the disk. ~The following experiments show that, on the contrary, the heating effect, as regards temperature, diminishes as the thickness of the disk increases. ; 22 5) ao 1 oe BS eee) =. edo a,c = renin os eee 2S! OR Ver cs es x [HBS] Sry SERFS S188 g SPE S| 28 [OSs Sla.osia 6. |S 3.5| . Bs Sue BS 3 g.a s Sanaa \ or eee sa i fale oS GEE |) 30 20 08 | O04 | Aluminium disk 3; inch thick. XX.| 38 30 21 17 | O4 | Aluminium disk 3, inch thick. ’ (3) The heat indication afforded by an ebonite disk is against the Q 2 ee 228 Royal Society :—Messrs. Balfour Stewart and Tait on conclusion that this effect is due to rotation under the earth’s mag- netic force. It would therefore appear to be proved that in these experiments the increased temperature of the aluminium disk is not due to rota- tion under the earth’s magnetic force. 19. It might perhaps be said that the heating of the disk may be due to heat conducted from the bearings into the disk and then distributed outwards ; and this conjecture “will require to be examined, since the bearings are, no doubt, heated by friction during the mo- tion. ‘This heating effect on the bearings was measured “by means of a very delicate thermometer, which was inserted into a small hole in the bush through which oil is supplied to the spindle, and made to be in metallic contact with the sides of this hole; the mean of three observations made the heating effect at the spindle due to ro- tation to be 4° Fahr. In the next place, the aluminium disk, separated from its metallic spindle by the ebonite washer, and in every respect the same as when made to rotate, had its spindle heated artificially by a mercury bath, generally at least 40° Fahr. above the previous temperature. After the lapse cf two minutes the effect upon the pile -was hardly perceptible—not more than five divisions. (1) It would appear from this experiment that the heating effect observed in rotation cannot be due to heat conducted from the bearings through the ebonite washer, since a temperature difference between the bearings and the disk ten times greater than that pro- duced by rotation causes a heating effect at least six times less than that caused by rotation in a somewhat less time. (2) The ebonite washer used to prevent the heat of the bearings from reaching the aluminium disk, is a.cylindrical disk, its thickness being imo tenths of an inch, alt the area of one of its faces 3°15 square inches. It is shielded behind by a brass disk, of similar size, which brass disk being near the bearings, and metallically connected with them, we may suppose to have the same temperature as the bearings. Thus one face of the ebonite washer is in contact with brass, having the temperature of the bearings, while the other is in contact with the aluminium disk. Supposing that this washer, used’ to protect the aluminium disk from the heat of the bearings, was of iron instead of being of ebonite, we can calculate approximately from Principal Forbes’s determinations of the absolute conductivity of this metal, how much heat would be conducted across. the washer during the experiment. According to these observations, if a cube of iron — whose side is one foot, have one of its faces kept permanently at | a temperature 1° C. higher than the opposite face, the quantity of — heat conducted across in one minute will be °011 unit nearly, a unit denoting the amount of heat required to raise a cubic foot of water 1°C. Since in these observations both the temperature difference and the unit are expressed in the same thermometric degrees, we may, if we choose, substitute degrees Fahr. for degrees Centigrade in the above expression for conductivity. Now, if we assume as an approximation that during the whole experiment of rotation the heat the Heating of a Disk by rapid Rotation in vacuo. 229 conducted across such a washer is the same as if for one minute the temperature difference between both sides of the washer were kept at 2° Fahr., andif we make allowance for the surface and for the thick- ness of the washer, we obtain the following expression as approxi- mately representing the heat conducted across the washer during the experiment, MA ent eer. Pas we | Heat="011 x 2x 144 * 79 028 unit nearly, where the first factor is on account of the double temperature differ- ence, the second on account of the surface, and the third on ac- count of the thickness. | But a unit of heat in the above expression denotes the amount ne- cessary to raise a cubic foot of water (or nearly 1000 ounces) 1° F. Now the weight of the disk is 10°5 ounces, and its specific heat is 0°22. Hence the above amount of heat will raise the disk *028 x a x a= 12° Fahr. in temperature. Hence we see that if the material of the washer had been of the metal bismuth, of which the conductivity is 7 times less than that of iron, and if we suppose the circumstances of the experiment to be equivalent to a temperature difference of 2° Fahr. between the two sides of the washer lasting for one minute, then the quantity of heat conducted across the washer will be a little greater than that observed. But the conductivity of ebonite is no doubt very much less than that of bismuth, and therefore on this account we cannot suppose that the heating effect observed is due to conduction. ; (3) In this investigation no account has been taken of the unequal distribution of temperature from the centre to the circumference of the disk, the tendency of which would be to diminish the effect upon the pile (which was directed to the circumference of the disk) of the heat passing through the washer; and indeed, when this element is taken into account, it is not surprising to find, as was actually the case, that im some preliminary experiments, where the disk was me- tallically connected with the spindle, the effect was not greater than with the ebonite washer. (4) The short time in which the effect attains its maximum value is against the supposition that it is caused by conduction from the bearings. (5) The fact that (as we shall afterwards see) the temperature effect in three aluminium disks of different thicknesses is inversely proportional to the thickness, is also against this supposition. (6) And so is the fact that a heat-effect obeyimg apparently the same laws, holds for an ebonite disk im which there is but a very feeble conduction. On the whole, therefore, we cannot suppose this effect to be due to conduction, or at least we must conclude that the effect of conduc- tion constitutes only an exceedingly small fraction of that observed. 230 Royal Society:—Messrs. Balfour Stewart and Tait on 20. It was suggested to the authors by Professor Stokes and by Mr. Grove, that the effect might be due to vibrations of the disk, the energy of which, owing to the viscosity of the disk for such vibra- tions, might ultimately become converted into heat; and it is neces- sary to examine this question. 3 ‘{ (1) The thickest aluminium disk was found to be out of truth not more than ‘015 inch on each side. Hence, the thickness of this disk being °05 inch, when turned with moderate rapidity, its apparent thickness should be ‘015 +°05-+4+°015="08 ; and experiment showed that when turned very fast, its apparent thickness was no greater. ‘The greatest possible range of vibrations o ithe disk at its circumference could not, therefore, be more than ‘015 inch on either side of the position of rest. Again, it was ascertained by means of the note given by this disk,. that it vibrates about 250 times per second. Let us suppose the whole mass to have the same range of ex- cursion (this will of course increase the result), the equation of vibration (not allowing for loss by viscosity) is w='015 cos nt, and also time of vibration land tlie a nm 250° Hence n=500 x 3:14=1570, say, Sakai in. in, sa = 015 x 1570 sin nt, .*. greatest velocity =23°55, or say 2 feet per second. Hence the energy of this motion in foot pounds, Q =weieht of disk i dsx weight of disk 1n pounds X Dy =weight of disk in pounds through ;4, of a foot. But an approximate experiment performed by causing the disk to ring, and noticing how long the sound lasted, would seem to show that probably the energy of vibration of the disk diminishes at first, and therefore constantly (if it is maintained) at the rate of the whole in 3 seconds. Ilence in 30 seconds it loses 10 times as much as the whole ; that is to say, in 30 seconds the heat produced cannot be greater than that due to the energy produced by the disk falling under gravity through 4% of a foot. Reducing this to its heat-equi- valent, the greatest possible heat-effect due to vibration during 30 seconds rapid turning will be less than 3 10.24 1 if sei oo Seer sy li 7 29 070 which is a very small fraction of the effect observed. ———— ” the Heating of a Disk by rapid Rotation in vacuo. 231 (2) The thin aluminium disk was out of truth about ‘02 inch on each side. Its note of vibration was as nearly as possible one octaye lower than that of the thick disk, while its coefficient of viscosity was somewhat greater, say in the proportion of 3 to 2, than that of the thick disk. On the supposition that the heat generated is due to vibration, if we call the heat generated during 30 seconds in the thick disk =1, then that generated during the same time in the thin disk ought to be © | 1 02 \? ‘ ta 2* (ars) XEXG=h where the first factor is on account of difference of time of vibration, the second on account of difference of range, the third on account of difference of mass, and the fourth on account of difference of viscosity. - But the heating effect (as far as quantity of heat is concerned) pro- duced in the thin disk is as nearly ag possible the same as that pro- duced in the thick disk. This fact is therefore against the hypothesis that the heating effect is due to vibration. (3) In order to estimate the effect (if any) of want of truth in the disk, the thick aluminium disk was purposely put out of truth about 33 times its usual amount; but the heating effect was as nearly as possible the same in both cases, being 32 divisions of the scale in both. On all these grounds it would appear that the heating effect cannot be due to vibration of the disk. 21. It is hardly necessary to mention that the heating effect cannot be due to radiation and convection from the wheelwork, which is no doubt slightly heated during the experiment, for the mass of this metallic matter is so great, that we cannot imagine it to be heated more than 1° Fahr. Now the radiation from this against the back of the disk may certainly be neglected, while the convection must be very small, since in the experiments the pressure of the air was very small. Besides, the heating effect, as will be seen shortly, was found to be independent of the pressure. 22. It has thus been shown that the disk is heated during the experiment, and that this heating effect— (1) Is not due to rotation under the earth’s magnetic force ; (2) Is not due to conduction of heat from the bearings ; (3) Nor to radiation or convection from the wheelwork (4) Nor to vibrations of the disk. And in view of the large and constant nature of this heating effect it may be asserted that it cannot be sensibly due, either to one of these causes singly, or to their combined effect. 23. It will now be shown that the heating effect is independent both of the density and chemical constitution of the residual air and vapour around the disk. In art. 16, if we compare together the 7th, 8th, 9th, 10th, 11th, and 12th sets of experiments, we shall see that the heating effect was sensibly the same, whether the residual gas was atmospheric air, or hydrogen or coal-gas. . 282 : | Royal Society. As hydrogen diffuses very quickly, it might perhaps be supposed that when heated by rotation it might find access to the pile through the rock-salt cover more easily than heated atmospheric air, so that while the whole effect might appear the same in hydrogen as in air, yet only part of that in hydrogen might be due to radiant heat, the remainder being due to heated gas which had obtained access to the pile. This was, however, disproved by an experiment, which showed that by blackening the interior of the cone, the effect upon the pile was just as much diminished in a hydrogen vacuum as in an air vacuum; and hence in both cases the whole effect is due to radiant heat. : But, besides the residual gas, it may with truth be supposed that there is always more or less of aqueous vapour, and also a little of the vapour of oil, and perhaps of the vapour of mercury in the receiver. As regards the hygrometric state of the residual air and its influence on the disk, this would appear to be of the following nature :— (1) When the vacuum has just been made, there is generally a’ hygrometric difference between the air and the surface of the disk, on account of which there is a strictly temporary effect, either im the direction of heat or cold, at the surface of the disk, owing probably to condensation or evaporation of small quantities of aqueous vapourt ; but this effect disappears the moment the motion is stopped, leaving behind the permanent effect apparently unaltered. (2) This temporary effect disappears when the disk has been left for some hours in the vacuum. Next, with regard to. vapour of oil, we cannot suppose its effect to be so large or so different in character and constancy from that of aqueous vapour as to account for the effect observed. Add to this that the effect takes place with an uncoated metallic disk probably to the same extent as with a coated one. The same remark may be made with regard to vapour of mercury. The effect would therefore appear to be independent of the chemical nature of the residual gas and vapour around the disk. In order to prove that this effect is also independent of the pres- sure of the residual gas, it is only necessary to refer to the whole body of experiments which have been described, to see that between 4 inches and 0°25 inch there is no perceptible variation in the effect observed. 24. The following generalization may now be made :— (1) If a perfectly true aluminium disk (without vibrations) be made to rotate in a vertical plane at the earth’s surface, after the manner herein described, there will be an increase of the tempera- ture of the disk, which is not due to communication of heat from the bearings or machinery, nor to the earth’s magnetic force. (2) This heating effect is independent of the density and chemical constitution of the residual air and vapour which surround the disk. (3) It is probable that the quantity of heat developed in disks of similar extent of surface and similar circumstances of motion is the same. For, in the first place, the quantity of heat developed in three aluminium disks, ‘05, ‘0375, ‘025 of an inch in thickness respect- Geological Society. 233 a would appear to be the same, the relative thermometric effect for these disks varying inversely as their thickness, and being in the following proportions, 30, 43, 60, as determined by one complete set of experiments. Again, the quantity of heat developed in the thick aluminium disk, with its surfaces both uncoated, was probably the same as when one surface was coated and one left bare, or as when both surfaces were coated. 25. The authors will not attempt here a further pence aaah but they would desire to make one remark. In absence of definite knowledge of the nature of that medium which transmits radiant light and heat, it might be supposed possible that when a radiant body is in rapid motion, the intensity of its radiation is somewhat increased. But if we bear in mind that in these experiments the effect was observed after bringing the disk to rest, and that the temporary effect during rotation sometimes observed can probably be otherwise accounted for, we are forced to conclude that, as far as we may judge from these experiments (and they are of a very delicate nature), there is no perceptible effect of motion upon radi- ation. In conclusion the authors desire to say that they are much in- debted to Mr. Beckley, who not only invented the apparatus, but assisted at all the experiments, and without whom they could not have been performed in a manner so satisfactory. They are also in- debted to Mr. Atkinson for his kindness in lending them a large gasometer, and to Mr. Browning and Mr. Ladd for exceedingly true aluminium and ebonite disks. ee GEOLOGICAL SOCIETY. [Continued from p. 154.] _ January 9, 1867.—Warington W. Smyth, Esq., M.A., F.R.S., President, in the Chair. The following communication was read :— ‘“¢On the age of the Lower Brick-earths of the Thames Valley.” By W. Boyd Dawkins, M.A. (Oxon.), F.G.S. - The Lower Brick-earths of the Thames Valley have been a fertile source cf discussion since the year 1836,—Dr. Falconer considering them to be anterior in age to the Boulder-clay, Mr. Prestwich be- lieving them to belong to the Low-level series of Quaternary de- posits. ‘The author divides the evidence upon this question into two heads—Physical and Paleontological. The sections at Ilford, Grays, Thurrock, Crayford, and Erith evince the same sequence of deposits. At the bottom of all are the fluviatile Brick-earths and Gravels, whence the Mollusca and Mammalia are derived, and which are remarkable for the horizontality of their bedding and the even sorting of the component parts. Lying on the eroded top of these is a deposit (the trail of Mr. Fisher) of a highly confused nature, 234: Intelligence and Miscellaneous Articles. containing stones, often with their long axes arched, and never sorted by the action of water. It contains also many stones and boulders that could only have been floated to their present situation by ice. It is as remarkable for the contortion of its bedding as the deposits below are for their horizontality. On its uneven summit rests the surface-soil, which is the mere rain-wash of the neighbour-- hood. These three deposits indicate three epochs :—first, that of the. Brick-earths, in which the water was unencountered by floating ice; then that of the trail, which is probably a mere ice-wash formed under a glacial climate; and lastly, the rain-wash, formed under temperate conditions. The date of the excavation of the Thames Valley being uncertain, and also the fact of the Boulder-clay sea having extended into it being non-proven, it is possible that the trail, or ice-wash, may be the subaérial equivalent of the Boulder- clay, and that consequently the Brick-earths may be preglacial. The palzontological evidence is also very important in deciding their age. The presence of Klephas priscus and Rhinoceros megarhinus indicates the affinity of this group of deposits to those of Preglacial age on the Norfolk shore, and to the foreign Pliocenes. The tichorhine and leptorhine Rhinoceros, on the other hand, point towards de-: posits of clearly defined Postglacial age. The beds under considera- tion are also as remarkable for the absence of some as for the presence of others of the Pleistocene mammals. The preglacial Trogonthere, Rhinoceros etruscus, Elephas meridionalis, Sorex mos- chatus, and Cervus dicranios are absent on the one hand, the entire group of Postglacial Arctic Mammalia on the other—and especially, among these latter, the Reindeer. From these premises it follows that the beds in question, as affording remains in part peculiar to the forest-bed of Norfolk and the Pliocenes of France and Italy, and in part to the postglacial deposits, occupy a middle point in time between the two, being more modern than the former and more ancient than the latter. or these reasons the author suggests the insertion of the group of deposits in the classified list of Pleistocene deposits as follows :—(1) Forest-bed of Norfolk—climate temperate ; (2) Lower Brick-earths of the Thames Valley—climate temperate ; (3) Glacial deposit—climate severe; Postglacial deposits—climate severe, but gradually becoming temperate. XXXIT. Intelligence and Miscellaneous Articles. ON THE SPECTRA OF THE METEORS OF NOVEMBER 138-14, 1866. BY JOHN BROWNING, ESQ. NO view the shower If chose the observatory of Mr. H. Barnes, at Upper Holloway. The situation was good, the observatory being built on high ground and so placed that the radiant-point rose in the contrary direction to the lights of London. I devoted my attention exclusively to attempting to obtain the spectra of as many meteors as possible, Intelligence and Miscellaneous Articles. 235° - After catching a few spectra in different directions, I at length decided on keeping the direct-vision prism pointed a little to the west of Leo Major, with the axis of the prism parallel to the horizon. The spectra which I saw were those of meteors which started from the radiant-point and passed through the belt of Orion. Of course the number of meteors which came into my field was comparatively limited ; but the whole of them travelled in a direction parallel to the axis of the prism, a condition essential in the observation of the spectra. From the rapid flight of the meteors rendering the spectra very -difficult to catch, I cannot pretend to speak with confidence of the appearance of the spectra shown by the prism; but I saw a great: difference between the spectra. I believe that I saw spectra of the following kinds :— A. Continuous spectra, or those in which the whole of the colours of the solar spectrum were visible excepting the violet rays. B. Spectra in which the yellow greatly preponderated, but which in every other respect resembled those above described. C. Spectra of almost purely homogeneous yellow light, but with- a faint continuous spectrum—that is, a faint trace of red on oneside . and green on the opposite side of the yellow portion of the spectrum. D. Spectra of purely homogeneous green light; of this kind I only saw two. - I observed through the prism spectra of several trains. The light, which was mostly blue, green, or steel-grey, generally appeared ho- mogeneous; but this may have arisen from the light having been too faint to produce a visible spectrum. Stars below the second or third magnitude, although visible through the prism, fail from this cause to give spectra in which blue and red are perceptible. _ 1t will probably be remarked that I have not spoken of having observed any lines in the spectra. All the nuclei seemed to give continuous spectra which contained the whole of the colours of the spectrum; what I should term the tails, not the trains, of the nuclei presented the appearances I have described, In every instance I remarked that orange-yellow appeared to preponderate over the other colours in the continuous spectra. When a prism only is used, it seems to me impossible that any sharply-defined lines should be shown. Still, from differences in the colours of spectra, some infor- mation may, I think, be obtained. As is well known, chemists and mineralogists infer the presence of certain elements in the substance under analysis from the colour communicated by the substance to the blowpipe-flame. ‘Thus, if the flame become yellow, they suspect the presence of sodium ; red, strontium; green, barium or thallium ; lavender, potassium. The prism will do more than this; it will show if the flame contains even a faint trace of any other colour, while without the prism the faint colour would be completely masked by the colour which predominates. From: the difficulty of catching meteors within such a narrow space, I fear it will be found impossible to use a prism provided with a slit formed by a pair of knife-edges so as to define any lines. But I think it may be possible to use a 236 Intelligence and Miscellaneous Articles. prism in connexion with a cylindrical lens. Such an arrangement would be capable of showing well-defined lines if the observed me- teors contained any elements which would give bright lines in an ordinary spectroscope.—Monthly Notices of the Royal Astronomical Society, January 11, 1867. ~ EXPERIMENTS ON THE EXPANSION OF SUPERHEATED STEAM. BY MM. G. A. HIRN AND A. CAZIN. We have proposed to ourselves to treat experimentally the follow- ing question :—Steam being superheated (that is, brought to a cer- tain tension, and at a pressure less than the maximum tension cor- responding to this temperature), it is made to undergo a certain expansion, during which it neither gains nor loses heat, it remains superheated and overcomes a pressure equal at each moment to its elastic force; required to determine under these conditions the final temperature and pressure. The following is the principle of our method. | The vapour being contained in a reservoir under a pressure greater than that of the atmosphere, a large orifice is opened, by which a jet suddenly rushes out. We may suppose a certain surface which separates the vapour into two parts ; one of these parts is completely expelled, the other exactly fills the reservoir at the end of the flow; and its elastic force has, during the expansion, always held in equi- librium the external pressure on its surface, so that this part of the surface is under the given conditions. It is enough to ascertain the final temperature and pressure of this part. When the flow ceases, the pressure sought is equal to that of the atmosphere, and the tem- perature has to be found. For this purpose it is to be observed that three cases may present themselves: the vapour remaining in the re- servoir may (1) be still superheated, (2) have exactly attained the state of saturation, (3) be supersaturated. In the first case the final pressure is less than the maximum tension corresponding to the final temperature; in the second the final pressure is equal to this tension; in the third the final pressure is the same, but part of the vapour condenses, forming a visible mist in the reservoir if it is provided with parallel glass plates. By varying either the. initial pressure or the initial temperature, so that the mist gradually dimi- nishes, it ultimately disappears; and then we have the expansion under conditions very nearly corresponding to the second case. Taking the pressure of the atmosphere as the maximum tension of the vapour, the corresponding temperature is found from Regnault’s Tables, and is thus obtained with a certain approximation. Thus there is no thermometer: the vapour in expanding indicates to us its own temperature when it becomes cloudy, and we have only to observe under what circumstances this cloudiness ceases to be pro- duced. This new method is sufficiently delicate; by its means we have been enabled to resolve the question proposed with an unlooked- for success, Intelligence and Miscellaneous Articles. 237 The reservoir with parallel glass plates is that of the Scientific Association of France, which one of us had constructed for another research at the Paris Observatory, made under the auspices of M. Le Verrier. It consists essentially of a horizontal copper cylinder, of a capacity of about 7 litres, with glass plates at its extremities, and heated by an oil bath. ‘To this cyclinder we fitted a large stop- cock, of 4 square centimetres aperture, for the escape of the steam. The duration of the flow was so small that the heating-action of the sides during the expansion could be neglected. To this apparatus we connected a steam-boiler, of a capacity of 1&0 litres, so large that it was easy to maintain a constant pressure, and, lastly, a manometer arranged so that all the measurements were accurate. The experiments were made last September, in the manufactory of Haussman, Jordan, Hirn, and Co., at Logelbach, near Colmar. The oil bath being at a given temperature, and the water in the boiler at a lower one, a quantity of vapour was driven through the cylinder sufficient to expel all the air. The escape stopcock was closed, the pressure kept constant, and the tube from the boiler to the cylinder heated so that the vapour of the latter was well dried. Both the pressure and the temperature of the oil bath were noted. Closing the communication, and opening the large stopcock, a screen of paper brightly illuminated, or a mirror reflecting the day- light, was looked at through the glass plates. The experiment was repeated at the same temperature, but with different initial pressures. Supposing that we start from a pretty strong pressure, we observe a thick mist. Working then at decreasing pressures, the mist diminishes, passes through a series of stages, and ultimately appears no more; the limit sought has then been exceeded. Increasing the pressure, the mist is again found; and by repeating the observa- tions under pressures alternately increasing and decreasing, we can ultimately estimate the original he pa corresponding to the limit sought with an absolute error of ='; of an atmosphere. We give in a Table the results "of ten series of observations ; 7 the temperature is given by the air-thermometer :— Initial Initial Final Final pressure. temperature. pressure. temperature, atm, 6 atm, 6 1°597 131°5 0°984 99°6 1685 151°8 0:984 99°6 2°115 174:°0 0:981 99°5 2°219 179-0 0°98] 99°5 2°451 189-2 0:979 Meio aed: 2°528 192°2 0:981 99°5 2°636 197°8 - 0°975 99°3 3°231 219°4 0:975 99°3 3°743 239°0 0°967 99°1 4°275 254°7 oh) O:967 99°] From our experiments, the law of the expansion of superheated steam cannot be represented by the known formula of Laplace and 238 .Intelhgence and Miscellaneous Articles. Poisson, to which we are led, admitting alone Mariotte’s and Gay- Lussac’s law and the equivalence of sensible heat, which disap- peared in the expansion, to the external work. But assuming that heat is consumed not merely by external work but by a certain in- .ternal work, we arrive at a theoretical solution agreeing very well with observed facts. It is sufficient to add to the equation express- ing the equivalence_between the heat which disappeared and the work produced, another equation which replaces Mariotte’s and Gay- Lussac’s law, and of which this is only a particular case. The general formula applicable to.all bodies may be rationally demon- strated from the principles of thermodynamics (G. A. Hirn, Exposi- tion analytique et expérimeniale de ia Théorie Mécanique de la Chaleur, 2nd edit. p. 207). Not merely do our experiments prove the existence of internal work in the expansion of vapour, but they also confirm one of the consequences of the new theory, and give a means of measuring internal work.—Comptes Kendus, Dec. 31, 1866. . -INDUCTION-CURRENTS ON TWISTING IRON WIRES THROUGH WHICH A GALVANIC CURRENT IS PASSED. BY G. WIEDEMANN. The twistings of the molecular magnets in magnetic bars effected by torsion may give rise to induction-currents which traverse the ‘bars in the direction of their axis, or circulate ina spiral in the axis of which the bar is fastened. Both these phenomena have been used by Wertheim and by Matteucci to determine the changes in the temporary and permanent magnetic moment of iron and steel bars in torsion—which may, however, be more accurately and completely ‘effected by direct measurement of the magnetism of the bars by the deflection of a steel mirror suspended in front. of them. In the same manner induction-currents are formed if an iron wire is twisted through which a galvanic current is either passing or has been passed. Asa supplement to my earlier experiments on similar matters, I beg to communicate a few experiments made in. this direction. 1. Between a brass clamp fastened ona board, and a second clamp provided with a divided circle, which could turn ina bearing screwed on the table, a well-annealed iron wire of 1°3 millim. diameter and 400 millims. in length was stretched. The wire was surrounded by a spiral of copper wire, the ends of which were connected with the multiplier of a reflecting galvanometer at a distance of 3 millims. from the torsion-apparatus. A galvanic current was next passed through the iron wire, which was twisted by turning tbe rotating clamp. The deflection of the mirror of the galvanometer indicated in this the formation of an induction-current. After its occurrence, the mirror recurred to its former position of rest, proving that the de- flection could not have been directly produced by the magnetization _of the twisted iron wire. BY If the current passed through the iron wire traverses it from the rotating.to the fixed clamp (“from back to front.’’), the current pro- Intelligence and Miscellaneous Articles. 239 -duced in the coils of the spiral is in the same direction as that of the rotating clamp=that is, in the direction of the torsion, and this whatever the direction of the rotation. On untwisting the wire there is am induced current in the opposite direction. If the direc- tion of the current passed through the wire be reversed, the direction of the currents produced by torsion and detorsion is changed also. If even after opening the current the wire is twisted and untwisted, induction-currents occur in the surrounding spiral which have the same direction as the induction-currents on twisting and untwisting the wire during the passage of the current. By the assumption of rotating molecular magnets these phenomena may be sufficiently explained. Ifa current is passed, for instance, from the rotating to the fixed clamp, the molecular magnets arrange themselves in such a manner that their north poles are turned towards the left of a man swimming in the current on the axis of the wire, and even after the cessation of the current they retain this position. If now the wire is twisted in the direction of the hands of a watch, for instance, for an observer standing in front of the clamp, according to earlier observations the molecular magnets will turn their south poles to the posterior end of the wire at the clamp, by which the wire also acquires asouth pole. Hence an induction-current must _be formed in the induction-spiral, which would impart to the wire an opposite polarity, and must traverse the wire therefore in the same direction as that in which the rotation of the clamp has taken place; in untwisting, the molecular magnets return to their original posi- tion, and a current in the opposite direction is produced, which would of itself prevent them from doing this. Inverting the direction of the current passed through the wire, or of the torsion, an ignited wire was clamped, as before, in the torsion-apparatus, and a galvanic current passed through it. After opening the latter, the fixed and _the rotating clamp between which the wire was stretched were con- nected with the multiplier of a mirror galvanometer. If the wire was now twisted either in one direction or the other, the deviation of the magnetic mirror again indicated the occurrence of. induction- currents. The direction of these currents is always the same as the direction of the current previously passed through the wire, whatever be the direction of the torsion. Hence in a certain sense the cur- rent which had been passed through the wire occurred again on twisting. If now the wire was untwisted, a new apducHoucgprrent was formed in the opposite direction. The formation of these induction-currents also can be deduced without difficulty. By the current which is passed through the iron wire its molecular magnets are placed transversely, with “their axes at right angles to the axis of the wire. If now the wire is twisted, _the molecular magnets are deflected on one side or the other from their transversal position, and at the same time an induction-current must be formed which of itself would bring them back into that po- sition—that is, having the same direction as the current previously passed through the wire. As, on untwisting, the molecular magnets 240 Intelligence and Miscellaneous Articles. return more or less completely to their transversal position, the induc- tion-current thereby formed must have such a direction that it opposes this motion, and must thus be in an opposite direction to the cur- rent passed through the wire.—Poggendorff’s Annalen, Dec. 1866. APPLICATION OF THE TUNING-FORK TO HOROLOGY. BY M. NIAUDET-BREGUET. M. Duhamel, and several physicists after him, have used the luning-fork for measuring small intervals of time. Following their steps, I have proposed to myself to prolong indefinitely the vibra- tions of a tuning-fork by clockwork. The apparatus I have constructed consists, like an ordinary clock, of two parts, a clockwork and an apparatus for isochronous oscilla- tions, acting on each other by the intervention of an escapement. The tuning-fork regulates the rate of the clockwork, which in turn gives at each vibration a small impulse to the tuning-fork, necessary for prolonging its oscillatory motion. ‘The clockwork, by means of needles on the axes and turning in front of dials, renders it possible to count the vibrations of the fork. The most accurate method of controlling the regularity of an in- strument of this kind consists in comparing the regulating tuning- fork with a free one, by M. Lissajous’s optical methods. I have thus been able to confirm the agreement of the two forks once set going, the free tuning-fork being put in vibration by the hand each time the comparison is to be renewed. ‘The accord is retained even if the motive-weight of the apparatus is doubled or tripled. The tuning-fork which I used made about 100 single vibrations (50 double) in a second. I have tried another which made about 200 single vibrations in a second; and the apparatus worked with- out necessitating any change. I think it certain that much more acute tuning-forks might be used, provided the dimensions of the escapement were suitably diminished. It is easily understood that by placing on the limbs of the tuning- fork two eyual symmetrical masses, the rapidity of the vibrations will be diminished; and it is easy to conceive arrangements by which all velocities between two extreme limits can be obtained. I think the principle of the instrument might be very useful in chronoscopic experiments—that is to say, those destined to measure small intervals of time. It might also be used for giving a uniform motion to various apparatus of registration or observation which are employed in the sciences. Lastly, it gives synchronism to two rapid clockwork movements, which has not yet been realized, and which is frequently wanted in telegraphic and other applications.— Comptes Rendus, December 10, 1866. THE LONDON, EDINBURGH, axyp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. ‘FOURTH SERIES.] APRIL 1867. XXXIII. O12 the Propagation of Electricity in highly Rarefied Elastic Fluids, and in particular on the Stratifications of the Electric Light in very rare media*, By Professor A. DE LA Rive ft. § 1. General Considerations. T was long supposed that whereas gases oppose a greater or less resistance to the passage of electricity, a vacuum con- ducts it very well. The use of Ruhmkorff’s induction-coil, by supplying a better and more certain means of studying the pro- pagation of electricity im rarefied gases, has shown that the pre- sence in a space of the smallest quantity of ponderable matter in the shape of an elastic fluid is sufficient to enable this propa- gation to take place, but that an absolute vacuum prevents it entirely. The demonstrative proof of this important principle is due essentially to the conclusive experiments of Mr. Gassiot ; although previously, if not completely admitted, it was at least foreseen as an indirect consequence of earlier investigations f. * These researches form part of a more extended investigation into the propagation of electricity by highly rarefied elastic fluids, which has ap- peared in the Mémoires dela Société de Physique et d’ Histoire Naturelle de Geneve, vol. xvu. p. 59, and an abstract of which has been published in the Comptes Rendus de I’ Académie des Sciences de Paris for April 13, 1863. I now publish them with some additions; and I shall also publish in an early Number of the Archives another part of the same investigation, which I have completed since the first publication, and which relates to the action of magnetism on electric discharges which are traversing highly rare- fied gaseous media.—A. DE LA RIVE. + Translated from the Archives des Sciences Physiques et Naturelles, vol. xxvi. p. 177 (July 1866). j t See Traité de [ Hlectricité, par A. de la Rive, vol. ii. p. 112, Phil, Mag. §.-4, Vol. 83. No. 223. April 1867. R 242 Prof. De la Rive on the Propagation of Electricity Mr. Gassiot has succeeded in giving a direct and rigorous proof of this principle, by producing an almost absolute vacuum in tubes previously filled with rarefied carbonic acid, by intro- ducing into them a fragment of potash which was allowed to cool after having been heated. The talented English physicist has since obtained a confirma- tion of his first results by using a water-battery of high tension instead of the induced current of Ruhmkorff’s apparatus*. It may therefore be regarded as completely proved that an abso- lute vacuum does not permit the passage of electricity, and that this passage can only take place through the agency of a ponde- rable medium. This medium may be of extreme tenuity, it 1s true; but its presence is not therefore the less essential for the transmission of electr icity. Thus elastic fluids, which had long been considered such unperfect conductors ah electricity that they were classed among insulators along with glass or resin, are capable, when reduced to a sufficient degree of ra refaction, of transmitting electric dis- charges of sufficient force to affect a magnetized needle, and to be acted upon in their turn by magnets in the same way as vol- taic currents. The transmission of electricity through elastic fluids presents certain special characteristics which render it one of the most important physical phenomena. In the first place, the fact that gases do not conduct electri- city until they are reduced to a certain degree of rarefaction, ap- pears at first sight incompatible with the principle that an abso- lute vacuum is a non-conductor ; for if electricity 1s propagated by matter, it scems as if the propagation ought to take place so tauch the more easily in proportion as the matter is in larger quantity. It is not so, however; and experiment shows that between a vacuous space and a space filled with gas at the atmospheric pressure, there is a degree of rarefaction of the gas (for exam ple 2-5 millims. for hy ydrogen) at which it possesses a maximum of conductivity or a minimuin of resistance; and this appears to prove that the mutual disposition of the particles, in- a , of their particular nature, exerts great infiuence on the conducting-power of the gaseous medium. Another not less important characteristic of the propagation of electricity through elastic fluids is the preduction of strie, or the stratification of the electric enh which occurs when ‘elie gaseous medium is brought to such a degree of rarefaction that the discharge or current passes easily. “This stratification was attributed at first to the employment ‘of induced curr ents, and to the opposition of the currents succeeding each other in contrary * Proc. Roy. Soe. vol. xii. p. 329, December 18, 1862. in highly Rarefied Elastic Fluids. 248 directions, which occurs under these circumstances. But several physicists, and particularly Mr. Gassiot, have obtained this phe- nomenon by means of the electricity of the ordinary electrical machine, and still better with that of a battery of high tension, in which cases there could be discharges and currents in one di- _ rection only. Mr. Gassiot has found, by studying these strie in a great number of tubes containing vapours or gases more or less rare- fied, that their number, colour, form, and mutual position depend upon the degyvee of rarefaction of the elastic fluid and upon the ay of the battery. Ifa column of distilled water, the length of which can be varied by bringing closer together or separating to a greater distance two platinum wires which dip into it, is in- troduced into the circuit of the battery, all the above- mentioned variations in the stratification of the electric light can be pro- duced in one and the same Geissler’s tube, by altering in this way the total resistance of the cirewit. These appearances vary so regularly with the amount of tension, that they may serve to indicate the degree of tension in a closed circuit, just as the di- vergence of the gold-leaves connected with the poles of the bat- tery indicates the tension when the circuit is open. Before passing to the more particular examination of this stra- tification of the electric ght which is the special object of this investigation, | will add a few words more about the general phenomenon of the propagation of electricity by gaseous fhedia: In 1863 I made some preliminary researches upon the con- ducting-power of some of the gases, and more particularly of hydrogen, nitrogen, and atmospheric air; I perceived the great superiority.1n this respect of hydrogen to the other Qases ; "and I showed that, when brought to such a degree of rarefetion that their conductivity was near its maximum, columns of these three gases obeyed the same laws as the bes t conduetor s, with reference to the influence of their length and diamnet ter upon the intensity of the electricity transmit ited. Since then, M. Morren has pub- lished* the evades of a careful examination of this question, and has given for several gases the pressure at which each of them possesses its maximum conductivity. But, in order to complete this investigation, there are still some determinations wanting, and some points which call for further examination, partic Shag the influence of temperature, and that of the presence of d hfe erent vapours in the rarefied ioe This is a subject with which i am at present occupied, and I will make known the results when the new researches which I hore to take in hand immediately are ras For the present, I will “confine myself to stating here some * Ann. de Chim. et de a sere 4. vol. iv. p. 325; 2 244 Prof. De la Rive on the Propagation of Electricity results which I have succeeded in obtaining while studying the propagation of electricity in metallic vapours, and which, although still far from complete, are not without interest. But previously it is necessary that I should shortly indicate the process which I have employed in my experiments for generating and for mea- suring the electricity. The electricity is produced by means of a Ruhmkorff’s appa- ratus of moderate power, worked by two Grove’s cells of large surface, and a contact-breaker of the ordinary construction. It is true that the electricity thus produced consists of two dis- charges successively in opposite directions; hence, if the cireuit which the discharges have to traverse is composed of good con- ductors only, such as metallic wires, or even distilled water, no deflection is produced by them on a galvanometer, since, the cur- rents being alternately of equal intensity in opposite directions, and succeeding each other very rapidly, the effect of their joint action is that they neutralize one another. But if the cireuit contains an elastic fluid, even very much rarefied, the resistance which this fluid opposes to the passage of the two successive discharges causes one of them to predominate, so that the result- ing phenomena are such as would be produced by a series of discharges all taking place in the same direction. This differ- ence arises from the mode of construction of the ‘apparatus, which causes the two induced currents, though equal to each other in quantity, to be. of unequal tension; so that when an imperfect conductor, such as a gas more or less rarefied, is placed in the circuit, only one of the currents is transmitted (or at least it is transmitted in much greater force than the other), and hence the series of currents have all one and the same direction. In order to measure the intensity of the transmitted currents, a glass trough, 20 centims. long by 5 wide and 3 deep, contain- ing distilled water, is placed in the circuit which they are required to traverse; two platinum plates, fixed one at each end of the trough and having a surface exactly equal to the transverse sec- tion of the water, serve to establish a connexion between this water and the rest of the circuit. Two platinum wires inserted into glass tubes are held vertically by firm supports, so that their lower ends dip into the distilled water—these ends projecting _ only a millimetre beyond the glass, so as to form a pair of ‘ Wol- laston’s points,’—while the upper ends are connected with the two terminals of a galvanometer the wire of which is well insu- lated. The supports which hold the platinum wires are moveable along a divided scale; so that the ends which dip into the water can be brought as near together as possible, or can be separated by nearly the whole length of the trough. ‘The distance between the platinum-points is reeulated by a micrometer-screw, and is in highly Rarefied Elastic Fluids. : 245 thus known within a tenth of a millimetre. These two points lead off an almost inappreciable proportion of the current which traverses the distilled water, but a quantity which is nevertheless sufficient to act very distinctly on the magnetic needle. Fora constant strength of the principal current, the intensity of the derived current depends on the distance between the two points ; and hence, if the intensity of the principal current varies, the dis- tance to which it is at any time needful to separate the two points in order that the indication of the galvanometer may remain con- stant 1s a measure of the proportionate strength of the corre- sponding derived current, and therefore gives, by a relation which is easily found, the intensity of the total current. The apparatus that I have employed to study the propagation of electricity by metallic vapours consists of a large glass globe provided with four tubulures and supported on a foot. The two tubulures which are at the extremities of the horizontal diameter are provided with stuffing-boxes, through which pass metallic rods fitted with points of metal or of carbon, between which the voltaic arc cau be produced by means of a battery of sixty or eighty Bunsen’s cells. The two tubulures situated at the extre- mities of the vertical diameter allow of the passage of two brass rods terminated by metallic balls, between which the discharge of the Ruhmkorff’s apparatus passes at the same time. After exhausting the globe, it is filled with weil-dried nitrogen, and this is rarefied till its pressure becomes from 2 to 3 millims. ; the electric discharge is then allowed to pass, and its intensity is measured by the process of derivation that I have just described. After having ascertained that this intensity is constant, the horizontal metallic points are brought near each other, so as to set up the voltaic arc, which acts here simply as a source of heat, and is kept going for some minutes. At a certain moment the intensity of the electric discharge, which is in action at the same time as the voltaic arc, is observed to increase very considerably. At the same instant the colour of the discharge, which in the nitrogen was a dark rose-colour, changes completely, and it assumes a hue which depends upon the nature of the points between which the voltaic arc is passing. This new appearance lasts for some instants after the are has ceased; and in fact it is then that it is most remarkable, for it is no longer affected by its contrast with the light of the are. The voltaic are was produced successively between points of silver, copper, aluminium, zinc, cadmium, and megnesium, and be- tween points of gas-carbon, all these substances being capable of being volatilized at the high temperature to which they were subjected. With points of silyer and zinc, the elcctric discharge assumes 246 Prof. De la Rive on the Propagation of Hlectricity a very decided blue colour, but darker with zine than with silver With points of copper, cadmium, aluminium, and magnesium the tint is green, very dark with copper, apple-green with cad- mium, very lioht eveen with magnesium, and a whitish green with aluminium. With poms of gas-carbon, the colour of the discharge is light blue, and changes to bluish when the are ceases; this is owing to the production of a small quantity of earburetted hy drogen eas. . The effects are most distinct at the upper part of the globe, where the vapours resulting from the voltaic are collect. The strize or stratifications of the electric light are even more marked in these vapours than they are in rarefied gases. The intensity of the electric discharge is increased in conse- quence of the presence of metallic vapours within the globe; this increase depends on the nature of the vapour: with séver and copper it is very considerable, the galvanometer going suddenly from 80° to 60° at the moment when the change of colour of the discharge shows that it has begun to be transmitted by the me- tallic vapour. The increase; though smaller, is still distinct with aluminiwm- -vapour; W ith the vapours of zinc, cadmium, and mag- nesium it is mueh smaller, namely from 10° to 20° only. Its very large in the case of the are produced by means of poimts of gas-carbon, perhaps in consequence of the presences of small quantities of carburetied } che ae £as, | [have also tried points of iran - Fiabe with the former I observed certainly a change of colour in the electric discharge and a slight increase of ‘te mene but with the latter I ob- tained nothing more than a very st mall increase in the intensity of the di scharge, which might be due to the influence of the enormous elevation of temperature on the conductivity of the rarefied nitrogen ffect, however, which is too slight to exert any sensible Bak enee upon ‘the foregoing e} ASU (Lem.), FP > TU (Cor. 2, first principal proposition) ; F U is common to TU and FP; .. UP>TF. The right-angled triangles ARP, A WZ, A V K have the hy- pothenuses equal; the angle AVK>AWZ>ARP (Lem.) ; | therefore in the right-angled triangles S Re, OWd, X Ve (the hypothenuses SR, OW, XV being equal), the side X e> Od>Se; therefore the segment YK>PZ> UP (Cor. 2, first principal proposition) ; and as we have shown UP>TF,.. YK>TF; that is, the perpendicular G K in the quadrangle ABGH cuts off the side A B a quantity Y K similar to, but greater than and in advance of TF cut off by the homologous perpendicular C F in the quadrangle ABCD. Now, supposing the sides A B, CD to be not more than m times as long as TF, by constructing m triangles with the conditions of construction of ACF, AGK, &c., a perpendicular of one of them, homologous to C F or GK, will fall on the prolongation of the side, Fig. 11. AB (or CD, as may be) ; and if , the angles ABD, BDC were right angles, there would be two perpendiculars drawn from one point to a straight line, which is impossible. The angles ABD, BDC therefore cannot be right angles. Suppose them to be acute, and AC, BD to be equal; from the middle point of AC to the middle point of B D (fig. 11) draw a line EF; it will be perpendicular to both (a), and you would have a construction (two right angles and two equal and acute) just de- monstrated impossible. Suppose A Clongerthan BD. Take EA’, Fr. Cc A! EB ‘ i 1 1 ! ' 1 1 1 t t ! 1 ! 1 1 t 1 a] 1 { 1 270. M. .G. Van der Mensbrugghe on the EC'=FB, FD; you would have the same impossibility. It follows, therefore, that as the angles A BD, BDC cannot be =e or acute, they must be obtuse. Therefore &c. Cor.—In a quadrangle, if two opposite sides are equal, and two adjacent angles comprised by them and a third side are right angles, the other two angles also are right angles. : XXXVI. On the Tension of Liquid Films. By M. G. Van per MENsBRUGGHE *. FORCE of contraction or tension has long been attributed to the surface-layer of films. If this conception is in conformity with fact, liquid films are in all respects similar to stretched membranes ; it was by starting from this idea that M. Plateau arrived at the enunciation of a general principle, accord- ing to which, in every laminar system constituting a polyhedral structure, the sum of the areas of all the plates is a minimum. Yet the tension of liquid surfaces was still a simple hypothesis ; but M. Lamarle, in a memoir in which he has brilliantly turned to account the above principle, has shown that in the case of a liquid mass submitted solely to the action of its own parts, the known phenomena of molecular attraction are necessarily accom- panied by a superficial tension{. It merely remained to render manifest this force which had so long remained mysterious. This has been recently effected by Professor Dupré of Rennes: in the second part of his Cinquiéme Mémoire sur la Théorie Mécanique de la Chaleur he gives several ingenious methods of demonstra- ting the contractile effects produced on the surface of liquids. I may be permitted to adduce here one of the experiments which this able physicist describes in regard to a laminar surface. He uses ‘a ee simple apparatus, consisting of a vertical metallic plate (fig. 1) cut out at G F EH, and of Fig. 1. another very light one (K L) applied against the first at K and L. The faces opposite each other are moistened with solution of soap ; and when the moveable plate, at first placed at F K, is made to descend, a liquid film fills the interval. The rapid ascent of KL when left to itself is enough to prove the existence of * Coen nein ge oi by the Author, from the Bulletin de ? Académie Royale de Belgique, ser. 2. vol. xxii. + “ Recher ches expérimentales et théoriques sur les figures de l’équilibre d’une.masse liquide sans pesanteur,” 6th series, Mém, de ? Acad. Roy. de Belgique, vol. xxxiil. t “Sur la stabilité des systémes liquides en lames minces; notions préliminaires, art 1,” Mém. de Acad. Roy. de Belgique, vol. xxxv. - Tension of Liquid Films... _ 271 the force of contraction ; a fall, on the contrary, is observed if the liquid film has been burst. The friction is less and. the success more certain if K L is replaced by a wire, one bent end of which fits at F in a small hole, while the other end moves on a circular edge replacing HK H’’*, - Reflecting on these experiments, I have devised some others, which, at the same time that they show very neatly the force of contraction, acquire a special interest in this respeet—that they can be used for certain exact verifications of the theory. Hence I have no hesitation in submitting to the judgment of the Aca- demy these new methods of studying the tension of liquid films. i. Equilibrium of a Flexible Thread submitted to the Tension ts a Liquid Film. Given a plane or curved film produced, for instance, by Pla- teau’s glycerine liquid ; it follows clearly from the principle of tension that, by giving to this film a contour one portion of which is perfectly flexible, it will at once be seen to assume the figure corresponding to the least possible extent of the laminar surface. Now this is confirmed by facts in a decisive manner. Let us first investigate the pheno- _- Fig. 2. mena in the case of plane films. Let EH abcd (fig. 2) bea horizontal square +t of iron wire, in any two points of which (m and 7) in one of its sides (ad) are fixed the ends of a perfectly flex- ible and very fine silk or cotton thread; let this arrangement, sup- ported by a hook f, also of iron wire, be immersed in the glycerine liquid; as soon. as we withdraw it we obtain a plane film in which the thread mon “~ ™ TOTS floats without affecting any regular shape. That being the case, if by means of a point of filter-paper the laminar portion monm be broken, the flexible contour soon assumes the form of a per- fect arc of a circle. It is obvious that the experiment would still succeed even if the portion mn of the solid wire ab were first suppressed. This result proves that the residual flr: amonbe d @ occupies in fact the least surface possible ; in fact the calculus of varia- tions teaches us that the area comprised: between a straight line mn, and acurve mon of given length, is a maximum when this curve is an are of a circle; this condition clearly necessitates * Ann. de Chim. et de Phys. e Paris, ser. 4. vol. vii. + The shape of the plane solid contour is completely arbitrary. 272 M. G. Van der Mensbrugghe on the that of a minimum of the laminar surface which remains. We shall see further on how statics lead to the same law. If the silk thread has a length equal to or greater than the perimeter of the solid skeleton diminished by mn, the whole of the liquid film should be destroyed at the moment that the part between mv and the flexible thread is burst. This is confirmed by the following observation: when the contour is circular or oval, the entire film disappears, and the thread lies along the solid skeleton; when this is polygonal, the adherence between the flexible thread and the solid wire sometimes leaves little films in the angles. The experiment described may be modified so as to be still more striking. A fine silk thread of suitable length is chosen, and its two ends tied, so as to form a closed contour; it is then moistened with the glycerine liquid; the horizontal film is then formed, and the moistened thread carefully placed in it; this remains on the surface, assuming an irregular figure; but the moment the portion within its contour is burst, this assumes suddenly the shape of a perfect circumference, which is retained even if the film is placed in a vertical po- Fig. 3. sition. Fig. 3 represents the hquid film perforated by its circular aperture. I come now to the case where we work with curved films. We are not concerned here with surfaces of equilibrium whose mean curvature is not zero—for example, the sphere, the cylinder, the unduloid of M. Plateau, &c.; for when surfaces are obtained in the laminar state, they always exert a pressure on the air they contain; but if any portion of their figure were burst, this would quickly disappear completely. Hence I have been obliged only to operate on minima surfaces, or on those whose mean curva- ture was zero; produced in the form of lamine, they exert no pres- sure on the air in contact with them; hence it is that I have been able partly to burst these films without destroying them in their entire extent. I first made some experiments on the catenoid, that is, the surface produced by the revolution of a chain about the right line perpendicular to its axis of symmetry. ‘To obtain this figure I employed M. Plateau’s method*, which consists in using two rings 70 millims. in diameter, for instance : one of these rests on a tripod; the other is provided with a fork by which it can be held in the hand, or attached to a support if necessary. The * “ Recherches expérimentales et théoriques sur les figures d’équilibre @une masse liquide sans pesanteur,” ser. 6, § 15, Bull. de ? Acad. Roy. de Belgique, vol. xxxm. Tension of Liquid Films. 273 two rings are first placed almost in contact, and the. small inter- val which separates them is filled with the glycerine liquid by ineans of a pencil; the upper ring is then raised, and the desired surface is formed between them: the distance between the two rings should be less than two-thirds of their diameter, as otherwise the equilibrium would become unstable. Having thus obtained the catenoid, I carefully applied to the film a closed thread 14 centims. long ; in virtue of its weight, it sank to the base of the figure, leaving generally a narrow lamina within its contour. When I burst this, the tension of the liquid was exerted in all directions ; the form of the residual film did not appear altered, and the thread was arranged in the form of a perfectly stable and symmetrical skew surface. Holding in the hand the upper ring,and thus successively giving to the catenoid different heights, I could procure variations in the shape of the curve described by the thread. When the height was only 1 or 2 centims., I ob- served two symmetrical arcs placed on each side of a vertical plane passing through the axis of the catenoid ; the rest of the thread adhered to the two metallic rings. In proportion as these were more separated, the parts adhering were gradually detached ; and the two symmetrical arcs, coming closer, became longer, while their curvature diminished. When I continued to raise the upper ring, I observed the skew curve become continuous and touch the lower ring. It is scarcely necessary to add that the experiment may also be made by fixing two points of the flexible thread to the upper ring and then bursting the portion of the film between this ring and the thread. I then repeated the same operations on the surface having the equation | 4 sin mz = (e™*— e—™*) (emy — e—™Y) , the mode of obtaining which, in the form of film, I have recently described *, I have previously said that these experiments may be used for certain accurate verifications of theory. In fact, let it be pro- posed to obtain a mathematical solution of the following general problem :— Given a laminar surface in equilibrium, to ascertain the curve produced by a very flexible inextensible thread, without weight and at its exterior contour solely acted on by the contractile furce of the liquid film ; this thread may, moreover, form a closed contour, or it may have two points fixed on the solid skeleton, serving as sup- port for the surface in question. * “ Discussion et réalisation expérimentale d’une surface particuliére a oo moyenne nulle,” Bull. de ? Acad. Roy. de Belgique, ser. 2. vol. xxi. Pp. edu. Phil. Mag. 8. 4. Vol. 33. No. 223. April 1867. T 274 M. G. Van der Mensbrugghe on the It is clear, in the first place, that the force which acts on each point of the thread is a normal to the curve, and comprised within the tangent plane led from this point to the lamellar sur- face; I assume, further, that this tension has everywhere the same intensity. That beimg granted, let S be the constant force of contraction of the liquid film, A, w, v the angles it makes with three rectangular axes at any point of the thread which has the coordinates x, y, z; let ¢ be the tension of the thread at this point, and s the arc of the curve sought. We shail ob- tain the following three equations, which express the conditions necessary and sufficient for the equilibrium of the thread : d (2 =) 4 S cosrX+ : 0, ds d: d ( = Ni (1) S cos B + S —0O ds d a(é =) S cos y+ 2 —0 ds a) If we multiply these three equations respectively ee We 2 = reduce and add the three first members, we shall obtain in this manner, dx dy =| S[ cosa + cos wot + cosy 5 | +(@)+G)+Q lea da a7. ady “dy saz 5), Ws deen aa ds? " ds ds? Now the trinomial dx dy dz CONE + Ce as + cos Vis is evidently zero, for the tension of the liquid film is normal to the curve ; we further know that da\? (wy (a (=) + is =e Gail = and that consequently dx d*x | dy d*y | dz dz ide "as de ae Tension of Liquid Films. 279 The above equation reduces itself to dt le whence t= constant, a formula which is the expression of this general law :— 1. Whatever be the laminar surface on which is placed the flexible thread, the tension of the latter is everywhere the same. This result permits us to write the equations (1) under the fol- lowing simple form :— | | d?x tae = —S cosa, d*y ds? SS = S cos FB, d?z 73 =—Scosp. These three relations, squared, and then added together, give AG ia) + oe (Ga) J=s Now if p represents the radius of curvature at any point of a curve, we have always, by a theorem of the differential calculus, VG) aay hence we have also t? F whence, disregarding the sign, — C2. =§?, —=S. p From this follow two other laws, which are very simple and completely general :— 2. The curve assumed by a flexible inextensible thread without weight, subjected to the action of the force of contraction of a liquid film in equilibrium, has everywhere the same radius of curvature. 3. The ratio between the tension of the thread and the radius of curvature is constant and equal to the force of contraction of the liquid film. db 276 M. G. Van der Mensbrugghe on the The laws we have deduced from the principles of statics are in complete accordance with the consequences drawn from the calculus of variations in regard to the present question ; 3; in fact, if the following question be proposed—to find on a given surface a curve closed or passing through two given points on a fixed curve, and such that it contains in itself, or makes with the fixed curve, the greatest possible area,—we arrive at this result, that if @ be the angle made at any point by the radius of curva- ture p of the desired curve with the normal to ‘the surface, we have always* in @ send = constant. p But if, asin the present case, the radius of curvature is every- where in the tangent plane to the surface, we have clearly sing =) whence p= constant, as has been shown above. We will now examine how far the theory just laid down is confirmed by experiment. We have seen, in the first place, that on a plane film the silk thread is arranged either as an arc of a circle or as a complete circumference, according asits extremities are fixed to two points of the solid skeleton or to each other : in this case, therefore, the law of the constancy of the radius of curvature is satisfied. On the other hand, it is clear @ priori that the tension of the thread , is the same in each of its points, considering that perfect sym- metry prevails all along the curve. Moreover it is clear that this tension is independent of the length of the part immersed, pro- vided the radius of curvature of the arc remains unchanged ; for the equilibrium existing in any entire circumference will neces- sarily exist in any are of the latter, if at the extremities of the arc a force be allowed to act equal and opposite to the tension of the circular thread. As to the third law, which expresses the equality between the force of traction of the liquid and the ratio of the tension of the thread to its radius of curvature, the following is the mode in which we have been able to verity ibe Let us take a large square of iron wire abcd (fig. 4), having sides 20 centims. in length, and supported by a fork; attach at any point (m) of the skeleton one of the ends of a silk thread, while a small weight (a wax pellet for instance) is fixed to the other; this being done, and the horizontal liquid film having been constructed, let us moisten a small portion of the thread, * Vide Legons de Calcul des Variations, par MM. Lindeléf et Moigno. Paris, pp. 292-296; or l’ Exposé géométrique du Calcul Différentiel et In- tégral, par M. Lamarle, part 3, pp, ooh: 570. Rese of Linuid Bins. 277 starting from the point m, Fig. 4. and lay it on the liquid surface, holding inthe hand the wax pellet and keeping the free end of the silk in a vertical position. Burst- ing thenthe film formed be- tween the silk and the solid skeleton, the thread will be immediately stretched, and if we raise the weight a little we shall see the part immersed gradually increase. The parts of the thread which are in this manner gradually added to those already submitted to the tension of the liquid should be previously moistened, otherwise the film will burst. When equilibrium is judged to have been established between the tension of the thread and the weight it supports, the skeleton is gently raised, being turned about the side ab, which during this movement of rotation remains horizontal: when the film is nearly vertical, the weight is let go, and the direction ob- served in which it tends to move; if it descends, it is clearly because the traction exerted by the liquid is too small; and accord- ing to theory the radius of the circle ought to be increased, which is effected by increasing the distance of the fixed point m from the last part immersed, n, and submitting at the same time a fresh portion of silk tothe action of the Itquid ; we can thus re- tain the curve in its form of a semicircumference. If, on the contrary, the weight is raised, we ought to diminish the radius of the are. Weendeavour in this manner to attain equilibrium ; and we ascertain whether the curve produced is semicircular by ex- amining, with the aid of compasses, whether the maximum height eois equal to the semidistance of mm. When the weight remains immoveable, if the film be made perfectly vertical, in general equi- librium will still be maintained ; yet it 1s only due to the friction exerted at the point n, where the thread quits the film. In fact, disregarding this friction, we see that as the weight sinks, the radius of the arc decreases. But in this case the tension of the thread also diminishes, and the motion should continue in the same direction ; if the weight ascends, on the contrary, the radius of curvature, and hence also the tension of the thread, increases more and more, which imparts to the motion commenced a gra- dually increasing velocity. This being the case, as long as equilibrium continues, due ® “AU | 278 M. G. Van der Mensbrugghe on the to the small resistance previously mentioned, let us note the dia- meter mn of the curve, cut the thread near the point n, and weigh the end of the thread along with the pellet which it supports. If the theory previously given be correct, the ratios between the weights and the corresponding radii should be equal. I have made by this method a series of experiments, and I have ob- tained the numbers in the following Table (the first column contains in the order of decreasing magnitude the weights ¢ in milligrammes, the second the radii p in millimetres, and the third the corresponding values of the ratio #: p) :— t. p- tip. 531 95:0 5°59 419 75:0 5°59 202 35°5 572 1538 28:0 5:46 140 22:0 6°36 120 18:0 6°67 118 18°75 6:29 102 17°4 5°86 101 15:7 6°43 60 9°5 6:32 Mean value . . . 6:029 The values of ¢:p are thus seen to be so near as to show the constancy of the ratio between the tension of the thread and the corresponding radius of curvature ; the deviations (which, more- over, are very irregularly distributed) ought to be attributed especially to the nature of the equilibrium to be realized before effecting the measures, and to the varying action of the friction, which exerts more influence in either direction when the radius of curvature is less. There still remains, however, a slight cause of error, arising from the weight of the part of the thread im- mersed, and the small liquid mass which adheres to it. This dis- turbing cause, which clearly imcreases with the length of the part immersed, has always the effect of diminishing the ten- sion ¢, and therefore the ratio ¢:p; this effect seems to be shown, in fact, by the numbers in the third column of the preceding Table. _ We have seen above that the theoretical ratio ¢: p expresses the tension of the liquid film; in the special case of the gly- cerine liquid I used, I obtained for the intensity of this force the approximate value 6°029, being the mean of ten numbers in the last column of the Table, which amounts to saying that the tension of a liquid film is about 6:03 milligrammes for a millimetre in length. This refers to the double force exerted by the two faces of the film; hence the superficial tension of the glycerine Tension of Liquid Films. 279 liquid employed would always be about 3 milligrammes per millimetre. In fine, as regards plane films, the experiments seem to me to exhibit a sufficient agreement with the three laws deduced from statical principles. An exact and direct verification of these laws in the case of curved films presents serious difficulties. In all the attempts I have made from this point of view, the skew curves which the thread assumed always appeared to have the same radius; but in order to be quite sure, I must have had recourse to very long and complex calculations. Yet in this case, as in that of plane curves, everything leads to the suppo- sition that observation would confirm theory. Il. Equilibrium of a Metal Ring suspended to a Liquid Film. I have observed, in experiments on the catenoid, that when I moved the upper ring on either side of its normal position, the film would often raise the lower ring—an effect evidently due to the tension of the liquid. I concluded from this fact that, by making the lower ring sufficiently light, I might be able to obtain it suspended to the liquid plate and kept in equilibrium by the force of contraction of the latter. Tio determine this, I had a ring made of iron wire 53°30 millims. in diameter, and 0°6 mil- lim. in thickness; it rested on three feet, also of iron wire, 25 millims. in length, and 0:25 millim. in thickness. This ring, previously well moistened with the glycerine liquid, being placed with its feet on a table, I approached to it the large ring (at- tached to a fork), on which was already a liquid film ; as soon as the two rings had stuck together, I gently raised the forked ring. The portion of the film in the lower ring remained plane; but the annular part was Fic. 5 curved, as was to be expected, in ope the shape of a portion of a catenoid. Raising then the higher ring, a mo- ment was soon reached at which the lower system was also raised,and was ET TRE Ts OR ERD ON then suspended to the liquid film. [ van a Fig. 5 represents on a scale of one- ae ee half the system in equilibrium; the | =~ | portion of a catenoid is shaded. I found that the stability of the equilibrium was perfect; for by blow- ing on the circular film with suffi- cient force to make the system de- SS scend, I saw the portion of a ca- Wit tenoid elongate without breaking ; as soon as I -ceased to blow, the small ring quickly ascended. eae wa 280 M. G. Van der Mensbrugghe on the This experiment not only demonstrates in an elegant man- ner the tension of liquid films, but renders it possible to find approximately the imtensity of this force. In fact, knowing the mean diameters* and the vertical distance of the rings, the portion of a catenary can be found which would, by its revolu- tion round the line of the ‘centres of the two circumferences, produce the surface obtained; from this the angle e can be calculated, which the tangent to the lowest point of the genera- ting curve makes with the vertical. Now this tangent gives exactly the direction in which the tension S of the film acts on the suspended ring to keep it at rest. This being granted, it is clear that the sum of the vertical components of this tension along the lower ring holds in equilibrium the weight of the system sup- ported. Hence, calling this weight p, andr the mean radius of the lower ring, we have 9477S cosa =p - Para tt} whence Ga siPiney 27 COS & This formula shows us now why the equilibrium of the ring is very stable. In fact, as the system is made to descend the angle @ diminishes, cosa increases, as well as the resulting action 27S cosa directed upwards; the ring ascends therefore, and passes its position of equilibrium, to return quickly to it, for the weight p then preponderates. The investigation of the angle « gives rise to pretty long cal- culations; to avoid them I attempt to make a as little differ- ent from 0 as possible; with this view, I load the lower ring until the tangent at the lowest point is almost, if not exactly, vertical. By this means an approximate value of S may be ob- tained by dividing the weight of the system suspended by the circumference of the smaller rmg. The experiment is made in the following manner. I take for the upper contour, not a forked ring, but a ring supported by three legs of about 5 cen- tims. in length (fig. 6); tothe legs Fig. 6. of the smaller ring is attached a disk of paper intended to receive the load. A liquid film having been formed with the upper ring, I place it horizontally on its supports, and carefully raise the lower ring so as to effect its contact with the film; I then carefully let go the lower system, which remains suspended to the laminar surface. That being done, the circular film is burst, and I wait five minutes, at the’ * By mean diameter of a ring I intend half the sum of the external and internal diameters. Tension of Liquid Films. 28] end of which L absorb, by means of a piece of filtering-paper, the small mass of liquid which adheres to the lower ring. Placing then sand on the paper disk, I load the system until the tan- gent at the lowest point of the generating curve is but little removed from the vertical, after which I wait five minutes, and remove as soon as possible the fresh quantity of liquid which surrounds the small ring. ‘Taking care, then, always to keep this horizontal, I gradually increase the burden, but by gradually smaller amounts, in proportion as I more closely approach the point at which the tangent to the base of the curve will become vertical. Let us suppose this point attained; the weight suspended is then at its maximum value, and equilibrium should cease to be stable. ‘To understand this, it must be ob- served that when the tangent is exactly vertical, the lower ring passes by the summit of the meridional chain; if then,’ for any reason, the ring descends by the smallest amount, it passes beyond the summit in question, and hence the tangent should be inclined in a contrary direction. But from this moment @ increases, and therefore the action 2778S cos « of the tension diminishes, so that the weight ought to continue to descend. ‘This is just what ob- servation confirms. As soon as the ring is low enough to rest on the table, I can burst the film without fearing to derange the load and thus alter its weight. In this manner I have made a series of ten experiments; the following numbers give in milli- grammes the greatest weights successively obtained :— 1012 1005 1001 1008 1027 1021 1050 1001 1011 1068 These values are sufficiently close to one another, excepting two, which exceed the least by 49 and 67 milligrammes respect- ively. These deviations are probably due to a cause of error which escaped me,—for instance, to a drop of liquid which was added to the load at the time the film was broken. In any case, taking the mean of the ten values, and dividing by 2rr = 167:45, we get : 1020-4 ~ 167°45 Excluding the two greatest values and taking the mean of the other eight, we should have 1010 S= 167-45 =6:031. These numbers, which give the tension for each millimetre of length of a catenoidal film, differ, as will be seen, but little from the values obtained for S in my experiments on the equilibrium of =6°095. 282 Mr. G. Forbes on the Mctcoric Shower of November 1866. a flexible thread on a plane film. By direct observation I thus succeed in supporting the accuracy of the proposition previ- ously admitted, which expresses the complete independence be- tween the tension and the curvature of a liquid film. XXXVII. Additional Note on the Meteoric Shower of November 1866. By Grorce Forsss, Esq. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, re ee addressing my last communication to you, the ob- servations made by Mr. Maclear at the Cape of Good Hope, on the late meteoric shower, have been published in the Monthly Notices of the Astronomical Society. The observations of the numbers I collected in successive periods of five minutes each, and projected them on the plate of curves I had before de- duced from British observations. A most curious fact immedi- ately became apparent. In the first place the time of maximum frequency reduced to Greenwich time was fourteen or fifteen minutes earlier than the time of maximum frequency 1 in Britain. And also, as may be seen in the annexed woodcut, in which both curves are esti- mated by Greenwich time, every point on the Cape Town curve is about a quar- ter of an hour earlier than the corresponding point on the British curve. Of the four curves that were compared in the February Number of the Philosophical Magazine, I chose forcompa- rison that deduced from the observations of Mr.Talmage, who observed at Leyton, in Essex, because in this case the numbers were also coun- ted m successive periods of five minutes. The similarity of the two curves is certainly more remarkable than any one could have expected ; in fact every irregularity in the one is brought out most Cape Town 12-30 1-0 1-30 z-o 2-30 * Philosophical Magazine and Journal, February 1867. Mr. J. P. Harrison on Radiation and Vapour. 283 clearly in the other. The curves in the woodcut are both drawn on the same scale, $ an inch representing 100 meteors per five minutes. In looking at the curves, we see that they are extremely like, except that every point on the Cape Town one is about a quarter of an hour earlier than the corresponding point on the British one. Now this appears to me to be easily explained thus. If the earth in its orbit cut that of the meteors at right angles, there would be little difference in the times. But since these orbits cut each other at an angle of about 19°*, the case is very much altered ; and if we take p to represent the perpendi- cular distance between two planes passing through Essex and Cape Town, both parallel to the ecliptic, then the: distance passed over between the times that Cape Town and Essex touch the middle of the meteoric band =p cot 19°. Now, from arough approximation, I find that p = about 5000 miles. Hence, since cot 19°=2-90421, and the velocity of the earth in its orbit is 1134 miles per minute, we have _ s__ 5000 x 2:90421 eat 1134 from which the time ¢ is about 13 minutes. So close an ac- cordance between the calculated and observed times is very re- markable. And what has been said with respect to the time of maximum applies equally well to each point of time. I should like to take this opportunity of mentioning an error which I made in drawing the curves in Plate III. in the February Number of the Philosophical Magazine. I by accident made every point of the lowest curve (that of Mr. Talmage) five minutes earlier than it should have been. I am, Gentlemen, | Your obedient Servant, St. Leonard’s Hall, St. Andrews, GEORGE ForBEs. March 15, 1867. 3 XXXVIII. On Radiation and Vapour. By J. Park Harrison, M.A.+ i ecb lately shown that the intensity of insolation near the surface of the ground is increased by the presence of a certain quantity of vapour and cloud {, I wish to submit one or two reasons for hesitation in accepting, at any rate to their full extent, the conclusions at which Mr. Croll has arrived on the subject in the higher regions of the air. * As deduced separately by the Astronomer Royal and Sir J. Herschel. + Communicated by the Author. { Proceedings of the Royal Society, No. 90, p. 356. 284: Mr. J. P. Harrison on Radiation and Vapour. There can be no doubt that the apparent variations in solar radiation at the same altitudes of the sun is due to heat re- ceived by our instruments from the counterradiation of cloud and other matter. Precisely the same laws are in operation as regards this secondary radiation by day, as Dr. Wells proved so conclusively are at work by night, though the action m the case of the solar-radiation thermometer is masked by a continuous supply of heat from the direct rays of the sun. On the occasion above alluded to, it was assumed as an axiom that transparent vapour absorbs less heat than cloud, or:even fog, and consequently exercises less influence over temperature. Now Dr. Wells, whilst perfectly aware of the fact that radiation from the air itself was very slight, had found that it nevertheless occurred, though he attributed it, in the absence of experiment, to the presence of particles of solid matter suspended in the at- mosphere. Professor Tyndall’s discovery of the absorptive pro- perties of aqueous vapour shows the sagacity and accuracy of Wells’s conclusions, but in nowise alters the results of his inves- tigation. It was found by both Prevost and Wells that on clear nights the slightest cloud passing across the zenith at once caused a considerable rise in the mercury of an exposed ther- mometer, and stopped the deposit of dew. The question has recently been submitted by Colonel Strachey to the test of numbers in the pages of this Magazine*; but his Tables afford materials for showing that the fall in temperature by night at Madras, which was considered to be owing to the decrease in vapour-tension, is to be ascribed, according to Dr. Wells’s law, to the absence of cloud. As regards the effects of vapour or cloud in the higher regions of the air, it may be gathered from somewhat conflicting evidence that bodies of vapour, of more or less tenuity and extent, float about in the drier atmosphere, and affect the temperature of the air in much the same way relatively as m the case of clouds’ nearer the earth. If this be so, however, it may be asked, how isit that so little difference is found four or five miles high in the readings of the exposed and shaded thermometers? It appears to follow as a matter of necessity that less difference would be found, provided no floating cloud (however light) overshadowed the instruments. But here we are met at once with the fact that a sufficient shelter is supplied by the balloon itself. | May it not be that in the recent balloon ascents there were special circumstances which rendered it difficult to obtain high readings of insolation ? * Phil. Mag. July 1866. Mr. J. P. Harrison on Radiation and Vapour. 285 1. If the sun was in even moderately high altitude, the rays could not reach the instruments. 2. Most of the ascents took place early or late in the day, when the sun was in very low elevation; or if nearer midday, at seasons when from its altitude the sun has also little power. 3. A balloon is constantly “gyrating ;” so that the instru- ments were more frequently in the shade of the several persons who occupied the car than in sunshine; in addition to which there were shadows from the numerous ropes. 4. Under these circumstances, even when moved into the sun, the few seconds allowed for taking observations with the solar thermometer would not suffice for heat to be absorbed and con- ducted through the mercury. 5. The solar thermometer was not placed in a box so as to be protected from the wind. 6. And the delicate blackened-bulb thermometer, which is most frequently alluded to, does not appear to have been enclosed in a glass sphere. 3 That the cause of the slight differences between the readings of the shaded and exposed thermometers must be sought for within the car of the balloon itself and the circumstances at- tending the several ascents, would further appear to be evident from the fact that the readings of the solar thermometer ob- tained under half a mile (2640 feet) above the sea-level also differ very little from those which were taken in shade. The parti- culars of each case, which are exhibited in the following Table, are extracted from the several reports which were presented to the British Association in 1864 and 1865*, Table of Thermometric Observations taken during Mr. Glaisher’s balloon ascents. - Thermometers. Dat-. Hour. i R ks. Me Height. : : Delicate aa Dry- | Wet- hace bulb. | bulb. Hnlb hm s feet i fh Feb. 27, 1865.| 159 Ovm.| 474 |49:5F.| 42-0F.| 51:5 F. Dec. 1, 1864. | 2 39 0 ,, 890 [47-2 | 433 | 47-0 |Sun shining brightly. June 27, 1864.|;7 4 0.,, 1578 |54:0 | 47:8 | 53°5 | Sun at edge of cloud. Wee, . 1) (864_,|.2.41 0. ,, 1618 |45°0 |41-2 | 44:5 Sun shining brightly. ' Aug. 29, 1864. | 4 8 30 ,,, 1883 |68:2 |55°5 | 70:0 | Aug. 31, 1863. | 6 15 40 ,, 1963 {51:5 {49:0 | 52:0 | Sun shining. | Sept. 29, 1863. |10 19 Oam.| 2039 |47:0 | 37:5 | 53-0 | June 13, 1864.| 7 11 30 p.m.) 2380 |52°8 | 45-9 | 55:5 Sun bright. * No observations of black-bulb thermometers were published in 1862 and 1863. 286 Mr. J. P. Harrison on Radiation and Vapour. On comparing these observations with the mean results ob- tained under similar circumstances at higher elevations, the dif- ferences are found slightly to increase with height. Still it would appear that the excessive readings of solar thermometers in dry regions, mountainous, or otherwise, must be in a great measure due to reflexion and secondary radiation, and not (at Jeast to the extent supposed) to increased force in the solar rays in consequence of the absence of vapour, or their passage through a less depth of atmosphere*.. The conclusion arrived at by Mr. Croll, that the moon, if sur- rounded by ether, would be colder than the earth, is neither in accordance with the laws of radiant heat nor, if correctly under- stood, to be gathered from the remarks on the subject by Pro- fessor Tyndall. Indeed I was not long ago informed by. this eminent physicist and experimenter, that the question had been set at rest by the exhaustive researches of Dulong and Petit. The law, as laid down by them, is very simple and easy to be understood. ‘* When a body cools in a vacuum its heat is en- tirely dissipated by radiation; when it is placed in air, or in any other fluid, its cooling becomes more rapid, the heat carried off by the fluid being in that case added to that which is dissipated by radiation” +. Count Rumford also subjected the question to experiment, and found that a thermometer half an inch in diameter in the centre of a hollow globe of glass void of air and hermetically sealed, after having been transferred from a bath of boiling water to one of water mixed with pounded ice, on the mean of two experiments, cooled down from 80° to 10° (R.) in 16™ 105, whilst the same thermometer under similar treatment in a globe filled with air, cooled down from 80° to 10° in 9™ 45s . It appeared well that the fact should be made more widely known that, whilst the sun’s rays may pass through dry air as freely as through a vacuum, heat from a secondary source, or from a surface heated by the sun, passes with more difficulty through a vacuum than through dry air§. * Under a vertical sun and clear atmosphere no doubt maximum insola- , tion is obtained independently of radiation from cloud or other matter. + Encyclop. Met. art. “ Heat” (172). See also Balfour Stewart’s work ‘On Heat,’ 1866, p. 260. + Lobtained similar results last summer in the receiver of an air-pump, with a thermometer heated by the sun’s rays admitted through a hole in a shutter, and directed on the black bulb of the instrument by means of a lens. The mercury cooled down to the temperature of the room more ra- pidly im air than zm vacuo. § Leslie ascertained that the greatest intensity of the sun’s rays at noon in the winter solstice, at Edinburgh, was 4°°5 F. in the height of sum- mer, when the sun was 3° above the horizon, the intensity was 1° F. [ 287 ] XXXIX. On Sensitive Flames. By W. F. Barrert, Lecturer on Physical Science at the International College*. Sis CE the publication of my “ Note on Sensitive Flames ” J in the last Number of the Philosophical Magazine, I have arrived at what I believe to be the cause of the phe- nomena there described. In that paper I showed that a tall and voluminous flame of coal-gas, burning in the ordinary way, under the influence of a shrill sound sank nearly half its height and changed its shape, at the same time entering into a state of rapid isochronous vibration which continued so long as the sound was sustained. Hitherto the only explanation to this effect is that given by Dr. Tyndall in his exposition of the sub- ject at the Royal Institution, which is based on the fact that an increased pressure similarly changes a sensitive flame. The ex- planation given in the abstract of that lecture is, that “an external sound added to that of a gas-jet already on the point of roaring is equivalent to an augmentation of pressure on the issuing stream of gas”’+. But I venture to think that this statement does not show how sonorous vibrations can effect an increase in the pressure of the gas, nor does it explain the many perplexing facts that have been observed. These perplexities are removed and the whole phenomena, it appears to me, made very simple by the following considerations. A sensitive flame is one which, on the slightest mechanical in- crease in the pressure or, what here comes to the same thing, in the velocity of the gas as it issues from the burner, will change its shape and take very much the appearance it has when influenced by sound. Now the sonorous pulses excited by a sound throw, among other things, the pipe which conveys the gas to the burner into vibration, the flow of gas is thereby driven from the sides and urged more towards the centre of the tube; and the current, thus confined within narrower limits, must issue from the burner with an increased velocity so long as the sound continues. It is the greater rapidity thus induced in the issuing stream of eas which causes the flame to shorten and diverge; the lowering of the flame being an analogous effect to that noticed and ex- plained by Dr. Thomas Young in his well-known experiments on streams of smoke escaping into the air at different velocitiest. If the above explanation be correct, then certain facts should be observed. For example, under the influence of sound the gas, as it passes through the pipe leading to the burner, will partake of the vibratory motion impressed on that pipe, the * Communicated by the Author. + Phil. Mag. February 1867, p. 99. + Phil. Trans. 1800, p. 112; Miller’s ‘Chemical Physies,’ p. 304. 288 Mr. W. F. Barrett on Sensitive Flames. flame ought therefore to be in a state of vibration: this is the case. Moreover the gas will ripple through the burner with a rhythmic flow timed to the pitch of the exciting sound; and therefore the rate of this vibration of the flame should vary with the pitch of the note: I have found this also to be the case. The louder and more sustained the exciting sound, the greater the amplitude and the more continuous the vibrations of the gas- pipe; and hence the greater should be the effect on the current of gas and thus on the flame: thisis so. The higher the pitch of the sound, the more rapid the vibrations of the pipe and the greater the disturbance of the gas within ; hence there should be a more marked effect with such notes: and this is well known to be the case. A sound excited contiguous to the pipe, even if far distant from the flame, should have more effect than away from the pipe at the same distance: this is so. A contraction of the gas-pipe near the burner should cause a greater velo- city of the gas, and ought, therefore, to produce a somewhat similar action to a sound: it does so, as is easily proved by pinching a flexible tube near the burner; the flame at once shrinks and roars ; and if a Bunsen’s screw-clip be used to pinch the tubing, it will be seen how wonderfully small a pressure on the screw is sufficient to cause the shrinking and roaring of the flame when near its sensitive pomt. Hence, mechanically checking the flow of gas near the point where it issues from the burner should disguise the effect produced by the sonorous vi- brations, and the more effectually if the gas pass through an oblique as well as a contracted channel: this is the case, a par- tially turned stopcock at all near the burner being fatal to a sensitive flame. Many feet of free tubing should thus be neces- sary, after the stopcock, in order to abolish the ricochetting of the current of the gas from side to side of the pipe, and allow the stream to resume its tranquil fow*: and this is found to be the case, Professor Tyndall having remarked, as an essential | condition of success, ‘that a free way should be open for the transmission of the vibrations from the flame, backwards, through the gas-pipe which feeds it,’”—not, however, for this reason, I believe, but that a current of gas filling the tube and of equal density throughout is necessary, in order that the feeble vibra- tions of the pipe may be impressed on and retained by the stream of gas. The material and thickness, as well as the length of the gas-pipe, should cause a difference in the result; and I believe such a difference can be detected with various kinds of tubing. Although the foregoing observations strongly support, if they * T am indebted to Mr. Sugg, the eminent gas engineer, for information on this among other pomts, he having ascertained that such a ricochet- ting of a current of gas can be produced. Mr. W. IF. Barrett on Sensitive Flames. 289 do not establish, the theoretical explanation I have offered, yet I sought directly to determine its truth by examining the state of the current of gas in the pipe. For this purpose a burner was attached to a long length of glass tubing and the stream of gas rendered visible by passing it through two bulbed tubes, the first containing hydrochloric acid, the second ammonia. The dense fumes of ammonic chloride thus formed tracked the passage of the gas through its conduit, and clearly marked the unignited column of gas rising from the burner. Owing per- haps to the narrow diameter of my tube I could not detect any change in the appearance of the smoke passing through it whilst a sound was being made. A new and most instructive effect was, however, observed. The column of unignited gas was as sensitive to the influence of sound as the flame itself, shrinking and diverging at a whistle, a clap of the hands, &c., just as did the flame. Substituting air for the coal-gas, I forced a stream of the former through the same apparatus, employing as the nipple from which the air issued a steatite burner having a circular ori- fice ‘046 inch in diameter, a burner which with coal-gas under an increased pressure (about 34 inches of water) gives a most sensitive flame. Gently urging the air from the bag, a slender stream of smoke was obtained which, when undisturbed, rose to a height of 14 inches before it broke and scattered into a divergent head. The sound of a whistle instantly brought this head down to a height of only an inch above the nipple: so swift and large a fall astonished me greatly ; for it exceeded anything I had ob- tained with flames. So wonderfully sensitive was this column of smoky air that, although the pressure was kept constant, yet it was rarely still for long together, the recurrence of little noises, and inaudible vibrations communicated to the room, con- stantly disturbed and shivered the fragile thing. In fact, to certain notes this stream of air was far more sensitive than the most sensitive flame | have ever obtained. This greater sensitiveness of the air might be expected, as it is unattended with the upward draught of the long column of heated air which ac- companies the flame. But not to the same notes were the air and the flame equally sensitive ; for comparatively low notes influ- enced the stream of air, whilst the sound of a hiss, so energetic in its action on the flame given by this burner, had but little effect on the column of smoky air. This is accounted for by the fact that the velocity of the stream of air was much less than that of the stream of gas; and, as a general rule, the less the velocity of the stream of gas the graver the note which affects the flame. When a sound, as of a whistle, was sustained and loud, it could be seen that the brush-like head of the column was broken Phil, Mag. 8. 4. Vol, 83. No, 223, April 1867, U 290 Sir David Brewster on the Polarization into two separate diverging streams, the size of the enclosed angle varying with the intensity of the sound*. Just as with the flame, an increase in the velocity of the current diminished the length of the unbroken stream of air; and at a great velocity the head did not split, but was brought down close to the nipple, after the manner of the experiments of Dr. Young, to which re- ference has been made. Having thus, I think, proved that the main agent which pro- duces the change im a sensitive flame is the vibration imparted to the gas-pipes, it must not be forgotten that the character of the orifice in the burner is a very essential part of the pheno- menon, not only determining the shape into which the shrinking flame is thrown, but also influencing the pitch of the note which most powerfully affects the fame. A small orifice yields a flame affected by higher notes than the flame from a larger orifice, where the velocity of the issuing gas is less,—another expression of a fact already stated. There are other phenomena connected with this part of the subject, which may be worthy of future consi- deration. 7 XL. Additional Observations on the Polarization of the Atmo- sphere, made at St. Andrews in 1841, 1842, 18438, 1844, and 1845. By Sir Davip Brewster, K.H., D.C_L., FRS., &e.F heen the publication of my “ Observations on the Polari- zation of the Atmosphere,”’ t a long and elaborate memoir on the same subject, by Dr. R. Rubenson, has appeared in the Acts of the Royal Society of Sciences of Upsal§. The observa- tions which it contains were made with the finest instruments, and with a degree of accuracy which had not been attempted by previous observers. They were begun at Upsal in 1859, and carried on at Rome between the 6th of June and the 5th of August, 1861, at Segni in the Campagna between the 6th and the 27th of August, 1861, and at Rome from the 5th of October, 1861, to the 27th of July, 1862. Although Dr. Rubenson has devoted a section of his work to ascertain the cause of atmospherical polarization, another section ' * This observation at once brought to my recollection the result of an experiment I had made, at the request of Dr. Tyndall, some time ago when at the Royal Institution : it was aprecisely similar splitting up of a column of smoke under the influence of the energetic vibrations of a large tuning- fork. Whatever merit, therefore, may attach to the priority of this observa- tion does not belong to myself. + From the Transactions of the Royal Society of Edinburgh, vol. xxiv. Communicated by the Author. + [See Phil. Mag. vol. xxx. p. 118, &c., 1865.] _ § Ser. in. vol. v. This memoir has been published as a separate work in 4to, pp. 238, Upsal, 1864. : of the Atmosphere. 291 to the determination of the place of maximum polarization, and a third to the causes which disturb the polarization of the atmo- sphere, yet the chief object of his labours was to study the daily variation of the polarization of the maximum point; and so fully has he treated this important branch of his subject, that the description of his polarimeter, of his method of using it, and the discussion of his observations, with the observations them- selves, occupy three-fourths of his memoir. In his section on the Cause of Atmospherical Polarization, Dr. Rubenson is led to the same conclusion which I had de- duced from my earliest observations—namely, that the light of the blue sky is polarized by refiexion from the molecules of air, and not from vesicles of water with parallel sides, as maintained by Clausius, nor, as conjectured by others, from extremely minute drops of water, nor from molecules of aqueovs vapour in an intermediate state between that of gas and that of vesicles. According to Arago, the distance of the place of maximum polarization from the sun was 89° 6/, the mean of six observa- tions. I found 89° to be the mean of a great number of obser- vations, but, like Arago, I considered 90° to be the nearest ap- proximation to the place of maximum polarization. Dr. Ruben- son found it to undergo, as I did, great variations, chiefly from 88° to 92°, the general mean of which, from his observations, was 90° 2’, half of which is so near to the polarizing angle of air, which is 45° 0! 32", as to place it beyond a doubt’ that the light of the blue sky is polarized by refiexion from its particles. Tn his section on the Causes which disturb the Polarization of the Atmosphere, Dr. Rubenson found, as I did, that clouds and fogs and smoke were the cause of the greatest perturbations ; and he also found, as I had done*, that the intensity of the po- larization was reduced by the crystals of ice floating in the atmo- sphere which form the kalo of 238°. Dr. Rubenson has not observed the secondary neutral point which I found sometimes accompanying the neutral point of Arago when it rises above the horizon, or is setting beneath it ; and he has never been able to see, even under the fine sky of Italy, the neutral point which I discovered under the sun, and which, I believe, has not been seen by any other observer than M. Babinet. In 1854 M. Félix Bernard+ made several observations at Bordeaux in order to determine the intensity of the maximum polarization at different hours of the day. Though made onl on four days of the month of October (from the 16th to the 19th inclusive), he found “that in proportion as the sun ap- * Treatise on Optics, p. 394, and Edinb. Trans. vol. xxiii. p. 226. + Comptes Rendus, vol. xxxix. p. 779, October 1854. U2 292 Sir David Brewster on the Polarization proaches the meridian, the value of the maximum polarization diminishes, that this value increases, on the contrary, in a con- tinuous manner as the sun recedes from the meridian, and that it reaches its maximum when the sun is very near the horizon, the amplitude of this variation being ahout 0°09.” On the 16th of October, 1854, the maximum polarization 1 in- creased gradually after midday from 25° to 0° of the sun’s alti- tude, from 0°6286 to 0°7051 ; and on the 19th of October, from 5° to 85° of the sun’s altitude, it diminished from 0: 7083 to 0:6106. On these two days the maximum polarization, at an altitude of 20°, was 0°6582 and 06464 respectively, the mean of which 1s 0°6523, differing only 0:12 from 0°64, as computed from Fresnel’s formula by M. Bernard, from my observation in 1842, that, when the sun’s altitude was 20°, the intensity of the maxi- mum polarization at 90° from the sun was equivalent to that which would be produced by reflexion from the surface of glass whose index of refraction was 1:486, at an angle of 65° 30/*, Before he became acquainted with the memoir of M. Bernard, Dr. Rubenson had completed his observations on the same sub- ject; and though they lead to a similar result, yet they possess a peculiar value from their having been made with the finest m- struments, in different localities, at almost all the seasons of the year, and under various states of the atmosphere. From a careful examination of his observations, Dr. Rubenson arrives at the general conclusion “ that the atmospheric polariza- tion is subject to a diminution during the morning, and to an in- crease during the evening, without one’s being able to assign with certainty the precise hour of the minimum polarization.” These changes Dr. Rubenson found to be often influenced by pertur- bations, commonly of short duration, and taking place indiffer- ently at all hours of the day. They frequently arise from clouds or smoke, and probably often from cirrus too faint to be seen. According to Dr. Rubenson, the blue colour of the sky, na normal state of the atmosphere, and 90° from the sun, is feeble at sunrise, increases rapidly in intensity, and attains to its maxi- mum some hours before noon, the number of hours being differ- ent at different seasons. The intensity of the colour diminishes towards noon. It then increases, reaches a second maximum after some hours, and then diminishes quickly towards sunset. The relation between the blue colour of the sky and the inten- sity of its polarization is a problem which remains to be solved. In 1859 M. Liais made observations on the polarization of the atmosphere during his voyage from France to Brazil, and at San Domingo in the bay of Rio Janeiro. Tis observations * Johnston’s ‘Physical Atlas,’ ‘‘ Meteorology,” p. 10; or Phil, Mag. 8. 3. vol. xxiv. p. 453, December 1847. of the Atmosphere. | 293 were made at the beginning of dawn and at the end of twilight, with the view of determining the height of the atmosphere. From the observations made at sea he obtained 320, and from the observations made on land 540 kilometres, or 212 miles, as the height of the atmosphere *. The most recent observations on the polarization of the atmo- sphere were made by M. Andrés Poey, between 1862 and 1864, under the tropical sky of the Havannah. The observations them- selves have not been published; but he states, as one of the most important of their results, that “at sunrise and sunset the system of atmospherical polarization ought necessarily to present two planes of rectangular polarization—one vertical, passing through the eye of the observer and the sun, and the other hori- zontal, with four inversions of the signs, and four neutral points 90° from each other.” M. Poey adopts my theory of atmospherical polarization, and the analogy which I poimted out between the lines of equal po- larization and the isochromatic lines of biaxal crystals, and be- tween the same lines and those of uniaxal crystals when the sun is in the zenith, the neutral points now meeting the suny. It will be seen from the preceding details that the subject of atmospherical polarization has become one of the most important branches of optical meteorology. It has already thrown much light on the constitution of the atmosphere; and when it has been studied in different climates and at different altitudes above the sea by Alpine travellers and scientific aéronauts, it will doubt- less have still more valuable applications. Under this impression I have been induced to submit to the Society the rest of four years’ observations which I made at St. Andrews, and which, along with those already published, will exhibit the optical condition of the atmosphere on many days during every month of the year. 1841, April 28.—Wind west; fine day. Mean time. 3h 0 p.m. Polarization a maximum in the plane passing through the sun and the zenith, and at 88° 16’ from the sun. 2 He. Ve When the sun, or the anti- solar point, rose or set, the neutral line of the polariscope bands, held and moved ver- tically, was an hyperbola, as shown in fig. 1. * Comptes Rendus, &c. vol. xlviii. pp. 109-112. T Ibid. vol. Ix. p. 781, April 17, 1865. 294: Sir David Brewster on the Polarization 1841, April 30. Mean time. h m y ae) Polarization a maximum in plane of zenith and sun, and at 78° 25’ from sun. 1841, May 6. 3 30 Polarization, when a maximum, greater in plane of zenith and sun than im any other plane. At sunset the difference small. The polarization was greater in the S. horizon than at the same point in the N. horizon, probably from the sky being there freer from haze. 1841, May 8. 10 10 Polarization, or R, =253°, and a maximum in plane of zenith and sun. In the N.E., ‘at an altitude of 40°, R=142°, and also much less in 8.W. horizon. 1841, May 9. 12 noon. Sky greenish blue. In plane of zenith and sun R=133°. At4® R=243°and 222° in different places, and always greatest where the sky was bluest. 1841, May 11. 3 45 P.M. R=243°, and a maximum in plane of zenith and sun. In other planes R=223°. 1841, May 12. 10 15 a.m. The sky blue and unusually clear throughout the day. Barom. 30°] m.; therm., 9» p.m. 48°. =26}° in plane of zenith and sun and a maximum. Tn other planes 221°. 11 40 ,, R=283° in plane of zenith and sun. 213° in lower planes. White clouds; cumuli in motion. ie) 12 0 ,, R=273 in plane of zenith and sun. R=203 near horizon. R=253 at mtermediate points. 1] 20 p.m. R= 263 in plane of zenith and sun. R=213 near E. horizon. Near the large white cumuli R diminishes. 4 30 R= 302 in plane of zenith and sun. R=253 in horizon. 6 O R=273 in plane of zenith and sun. R=24? in horizon. 710 R= 303 j in plane of zenith and sun. R= 282 j in horizon. fe ao b= 302 in plane of zenith and sun. R= 292 in horizon. 7 45 R=283 in plane of zenith and sun. R= 283 in horizon. , See Phil. Mag. vol. xxx. pp. 120, 162 for the places of the “neutral points on this day. of the Atmosphere. 295 1841, May 14.—The sky in the forenocn has very little blue in it, being in its colour a French grey. RB less than 144°. Meantime. ¢ _ en R= 142, and R=183 in a bluer part of the sky. According as the thin white haze which masked the blue colour of the sky was removed or returned, the places of the neutral points constantly varied in thew position. In the evening the sky became clear, and R became 245° and 263°. 184], May 16.—See Phil. Mag. vol. xxx. p. 162. 1841, May 16.—Barom. 29:4in. Windy. Considerably above the horizon R varied from 175° to 145°, as the blue sky was more or less distant from the white moving clouds. At 75, when the blue was purer, R=224° at 45° of altitude in the S. At 7242" R= = 941° at 20° altitude in the N. 1841, May 17.—Barom. 29°5 in. 1 20 R=1/2, the maximum polarization at 99° from sun in the plane of zenith and sun. 2 0 R=174, and 154° at lower altitudes. The following observations from May 24:to June 3 were made in Edinburgh :— 1841, May 24. 11 10 i ve maximum in plane of zenith and sun. R= 141 j in horizon. After a cloud had passed the polarization was diminished. 3.15 R= 291 maximum in plane of zenith and sun. R= 144 elsewhere. 5 0 R=261 maximum in plane of zenith and sun. R= 24+ in horizon. Babinet’s neutral point near the sun. 2 -O R= 221 in zenith and horizon. Height. © Ones br9 Arago’s neutral pomt* . 2 is 22. 5 sO Do. do. Bi is 17 48 9 0 Do. do. Bie ed Ts, 56 R=20 in zenith. R= 22+ in horizon. - 1841, May 25. 6 0 Arago’s neutral point in iiaicaw and the hyperbolic neutral line distinct. * The height of Arago’s neutral point is to be understood as above the antisolar point, and that of Babinet as above the sun. £96 Sir David Brewster on the Polarization 1841, May 27.—Slightly hazy. Mean time. 4 45 R=202° in zenith. R=194° in horizon. Babinet’s neutral point not seen. 1841, May 28. Li 70 R=153°., Hazy bands, ill-defined and ragged. Observations resumed at St. Andrews. 1841, June 3.—In the morning, R=144° and ree 6 Op.m. R=253° in zenith and horizon. 6 27 ,, Arago’s neutral point not above horizon. 6 386 ,, Do. do. very near the horizon. 643 ,, Do. do. above and close to horizon. See Phil. Mag. vol. xxx. p. 121 for the height of Arago’s neutral pot. 1841, June 6.—Barom. 29°9 in. 4 45p.m. R= 143° through zenith. R=233%° 45° above S. horizon. R=223° in S. horizon. In and near the horizon the white bands of the polariscope are bluish on the side of the neutral line from the sun. Maxi- mum polarization more than 90° from sun, and diminished by clouds coming on. Arago*. 6.40 18 36 8 20 Sky very clear .. ve 19 28 8 30 21 20 8 36 Sun set. Haze in S8.E. 8 45 R=284° through zenith, and 264° in horizon. 9 10 R=28° through zenith, and in 8. 17320 Om, and N. horizon. Fy 39 9 30 Haze continued. {22 12 1841, June 8.—Barom. 380 in. Fine day. 11 40 R=211° through zenith. R=19° in W. horizon. 1 80 R= 2921 ° through zenith. ! 4 10 R=261° through zenith. R=27° 30' from N.E. horizon. 4 30 R=284° 45° above N.E. horizon. 4 45 Babinet’s neutral point and the neutral hyperbolic line clearly seen. D DOT = 20° to 24° as the sky was more or less clear. * The numbers under Arago and Babinet are the heights of their neutral points above the antisolar point and the sun. tT See Edinb. Trans, vol. xxii. p. 221. of the Atmosphere. 297 At this hour the curious phenomenon shown in the annexed figure was seen, two hyperbolic neutral lines mecting in the sun. Fig. 2. lly Y =swe lee Babinet’s neutral point Mean time. . above sun. m ° i 6 42 wis le +s ee SE P.+ so bd dende —1¢0 As the total mass of the imaginary body equals zero, the first term of this integral vanishes of itself. That the external attrac- tion may be zero, the remainder of the integral must be zero, aud this for all values of c. Hence 1 am ("r { { { prt? P; du dw dr=0 eo a0 for all positive and integral values of 2. As p is a function of r, and must be independent of all parti- cular standards of measure of 7, it must be the same function of rr. Letr+r=v. The above condition then becomes 1 27 (1 ’ { { (pi? de dv=0. —1e/0 0 By successive integration, pits pit Ae 2 dy = —j p—- —>——_. — +... fe Pi peak ESE Ea) do Or, if p, p®, p®, ... represent the values of p and its differen- tial coefficients when v=1, ‘a ‘2g p®) po p® ara = G4 3)G 44) G43) AG See . |i (° prt? P; du dw dr —id0 20 an yit3P, po) —it3 po — a ‘ea er ee — 304 Archdeacon Pratt on a Problem in When 7 is taken indefinitely great, the expression within the brackets ultimately becomes p, and this is independent of 2. For those parts of the body which are outside the sphere (of radius a) w is greater than 1, and the quantity outside the brackets (as I show below) beonals infinite, and therefore the whole expression under the signs of integration is infinite when 2 is indefinitely increased, unless u=1. As the integral must not become infinite, I come to the conclusion that w=1 or r=a, and the surface of the imaginary body is a sphere = can have no other form. 2. But I have to show (what I have assumed abana that the quantity outside the brackets becomes infinite when 7 is infinitely increased. at P,= coefiicient of ai in {1 +a?—2ap\—:, or in iy a\ —2 1 i (1—aey+(1—*) /P=5 (2+ >) = cos ¢, or in 13 22 ¢ La), akira? : (145 geet g Geert. lt gota gat--) ello e (esl) s = Rt 0d ets) ley gee | | ay 8, (e+; + 3a. (=3) 2 5(= ae =2A;cosih+2A;_2 cos (t—2)h+ . Put ip= 7, then - P,=2A, cos ope: _ =) APP oe Now A, is less than 1 and greater than = lead Aj—2 99 if oP) 93-2 i 9” bus atijerr a deem A, (Gfzis odd) 1 ih ply ease A, (ifziseven) 1 5 =) - Choose yf less than 90°, and increase 7 indefinitely ; then @ is indefinitely small, or p nearly 1, or the attracted point c, p!, o! (which may be anywhere outside the body) is always taken im- mediately above the point 7, w, w on thesurface. All the terms of the series for P; are positive, and therefore P; 1s greater than relation to the Figure of the Earth. 3395 any one of them. Thus, taking the first, cos a 3 a EO, ut? cos awe: P. is ultimately greater than +3 and is therefore infinitely great for values of wu greater than 1 when z becomes infinite. This is what was to be proved. 3. Having shown that the surface of the imaginary body is a sphere, I have to find the law of itsdensity. The original equa- tion of condition now becomes 1 2m (‘a ( { ‘| prit? P. dudw dr=0. —l~v/0 0 “rit? dr= Fa, [t, @) 0 Se cig east Hach = <5 a series of Laplace’s functions. Then 1 2m { \ Be dai 0) —lev/0 ee EDP + Kd sail | 4143 Ta ae )P+ .. Bi dudo=0. The first side of this equals 47’; by a property of Laplace’s functions, FE’; being the same function of yw! and o! that F; is of pe and a, P. is ultimately greater than ’ Suppose 7 fc. t'—O; hence also f;=0 for all positive values of 2, (on i 0 This is independent of w and w; and therefore p is independent of w and a, and is a function of r only. 4. I-come then to this conclusion, that the imaginary body can be only a sphere, with its density (positive and negative) varying as any function of the distance from ‘the centre of the sphere. Hence (as I showed in my paper in your Number for August 1866) no changes in the arrangement of the materials of a body can be made so as to preserve the external attraction unaltered, except uniform and complete spherical concentration or disper- sion of matter to or from one or more fixed centres in the body. | J. H. Prarr. Jutog, March 7, 1867. [9886] XLVI. Contributions to the Mineralogy of Nova Scotia. By Professor How, D.C.L., University of King’s College, Windsor, Nova Scotia. [Continued from vol. xxxi. p. 170.] if. by ICHTYNE.—A mineral which I refer to this species was brought to me by a farmer from Cornwallis, King’s co., where it had attracted attention as something possibly valuable, and was known as “little pebbles,” a name which, in the absence of information upon the geological situation of the mineral, gives some clue as to the mode of its occurrence. What I received consisted of several small pieces, either rounded and bean-like with smooth dull surfaces, or irregular in form with angular prismatoidal outline and of lustre somewhat glassy. This lustre was much more distinctly seen on breaking the pieces ; these were brittle, and had a conchoidal fracture. The greatest hardness observed was about 7:5; the specific gravity in three experiments was respectively 2°775, 2°815, and 2°881, the mean of which numbers is 2°823. In colour it was indigo-blue, blue-black, and greenish black with a grey tint in some parts; the streak and powder were white. Before the blowpipe, fragments frothed and fused to a dark enamel. As might be expected from the differ- ences in colour and the varying specific gravity, the composition of the “ pebbles” is not uniform: the constituents appear to be the same; but their relative proportions are not constant, as is shown by the following analyses which were made by fusion with carbonated alkalies for the constituents other than potash and soda, these being estimated after treatment with fluor-spar and sulphuric acid. The iron was found to exist both as peroxide and protoxide, the latter being by far the more abundant; no attempt, however, was made to ascertain the exact relative pro- portions on the small amount of mineral in my possession. The nature of the alkalies present was made out by fusion with car- bonate and chloride of barium and subsequent testing with bi- chloride of platinum dissolved in strong alcohol. The results obtained were— IL. Il. IIL. CA Roc ea at Ieee ale OOOO 57°47 Houle NUTINI Gs, 1 Picts) ent. ye, 11°53 lo Rrotoxude-omimon* (a5 pn. 14°79 16°62 Protoxide of manganese . .. 0:57 0-19 Nia aio ct ca ip a ay 2°01 5:12 MACE SIA gio earn Meath el dials 721 3°33 Mater. iii, 2c amen Bes eee Potash and traces of soda. .. me 3°03 98°58 * Tron really found in small part as Fe? O°. Dr. How on the Mineralogy of Nova Scotia. 337 Since the iron exists in small proportion as peroxide, there is a close general accordance between the numbers found, especi- ally in the third analysis, and those given for Wichtyne by Lau- rent (Dana’s ‘ Mineralogy,’ 4th edit. p. 177), viz. :— RCE et tet aT Font tt Oe etermttren FL8 eee kr Peroxide of iron. .. .- . 40 Protoxide of iron’... . | 13°38 Marnie eyes t 8 te BE NEY 76 @) Magnesza Sa SE OO Potash and a little soda . 3:5 99-4, The physical characters of Wichtyne, as stated by Laurent, agree upon the whole tolerably well with those given above ; they are—specific gravity 3:03, hardness sufficient to scratch glass, colour black, lustre dull. There is therefore little doubt that the Nova Scotian mineral now described is rightly referred to the species Wichtyne, which, taking all its characters and its composition into consideration, it resembles more closely than it does any of the allied minerals, glaucophane, violan, Sordawalite, and tachylite. The whole group is of extremely rare occurrence, none of the members of it apparently being found at more than one or two localities. The only locality given for Wichtyne is Wichtis in Finland, whence Hausmann changes Laurent’s de- signation to Wichtisite, which seems preferable. The matrix of the mineral at Cornwallis, N.S., 1s, as I found on examination of small adherent portions, a soft yellowish mineral containing peroxide of iron and carbonate of lime, the latter being appa~ rently most abundant ; it is possibly a limestone. Pencil-stone.—A mineral with this local designation is found in a thin bed extending for a considerable distance through rocks ; considered to be of the age of the Hudson-River group, about Merigomish in the eastern part of the province. It is of an ash- grey colour, a somewhat schistose structure and close texture, adheres slightly to the tongue, and feels rather soapy on smooth surfaces; it has a glimmering lustre, and is most readily cut with a knife; its hardness is 1-5, its powder and streak are grey- ish white. From the circumstance of excellent soft but firm pencils, much prized for writing on slates, being made from it, it receives its local name. Analysis shows it to belong to the clay-slate family ; it was at first taken for pyrophyllite, the com- pact variety of which, used in the United States for making pen- cils, it much resembles. It also in some respects agrees with agalmatolite, with which the compact pyrophyllite had been con- founded before Brush pointed out that they were really distinct (Silliman’s Journal, July 1858, p. 69). Its specific gravity is Phil. Mag. 8. 4. Vol. 33. No. 224. May 1867. Z 338 ‘Dr. How on the Mineralogy of Nova Scotia. 2°71. In the following analysis, although the finely powdered mineral was fused with about four times its weight of the mixed alkaline carbonates, the alumina was not perfectly separated from the silica, but the quantity retained was not large enough to be material. The presence of potash and soda was proved by fusion with chloride and carbonate of barium, and subsequent testing with bichloride of platinum in alcohol. The iron is given as protoxide, because it was found that after fusion an exceedingly small amount of peroxide was present, which might have been formed in the process. The results obtained were— Silica (retaining a very little Al? 0) 60°53 Alama 0 0) Se oie 5 A RS SOM Protoxide of ion) 5,2 GA ees tee Potash and trace of soda. . . . 4°39 Magnestan io yin uw a\ iy Gi) ak ay ee Wat ex) boas Wii al ele PV, CN Sea say 100-00 which have a general accordance with those found in the analyses of clay-slate given by Dana (Mineralogy, 4th edit. p. 510), one of which is as follows, the specimen examined being a bluish- black clay-slate from Rothwaltersdorf :-— Sihieas: Aye a ae ene OL eZe Alwmmitia tye o hace he eee Lo Protoxide of iron . . . 8:54 PME oy hoa i ho A ee Oe Potashe ie ek aye ey a eee Nlapnesia! (ish 04 cho enn Oe Water re ket iae Nie ag ie 99-99 They do not tally with those given as calculated from the for- mula assigned to agalmatolite by Nicol (Mineralogy, p. 227), ViZ.— Dibica 0) st) Gr beeOe Alamina 22000" OU SROs DSS OU Potashe 0) 2082) ie OU eG Wiater 2) 5) hk. 8h P82 AeA@ 100-00 with which mineral, however, the Merigomish pencil-stone agrees in its softness, texture, and colour. It is decidedly differ- ent from the “pencil-slate” of Von Cotta (Rocks Classified, p- 264), which he describes as separated or separable into pen- cils. Very characteristic specimens of this were found some years ago by Dr. Dawson and myself in lower carboniferous rocks at Horton Bluff, at the mouth of the Avon, N.S.,ina Dr. How on the Mineralogy of Nova Scotia. 339 thin bed: the mineral or rock was of a blue-black colour, and separated into pencils in our hands in the most perfect manner. Variegated Soft Slate——Among the Devonian rocks at Beech Hill near Kentville, King’s co., is found a very soft mineral which somewhat resembles the pencil-stone just described; it is ex- ceedingly easily cut with a knife, writes well on a slate, adheres slightly to the tongue, and has the same elements, as shown by a qualitative analysis, the peroxide of iron, however, being much more abundant (the alkalies were not tested for). It glistens on a fresh surface as if from the presence of minute scales of mica. Its characteristic quality is that of showing, when cut to a smooth surface, sets of concentric bands of different colours (which may be described as white, grey, yellow, and red, and tints made up of mixtures of these) and varying thicknesses about a centre of a long oval shape. The colours arise of course from variations in the amount and state of oxidation of the iron present. The material is very much admired, and would form handsome inlaid work not subject to friction. Indian Pipe-stone.—I1 mention here as probably in composition analogous to the preceding, a dark-coloured nearly black mi- neral, found on the Montengan shore in the district of Clare, Digby co., in the extreme west of the province, which was used by the Micmac Indians for making their stone pipes. The rocks at Montengan Cave, Poole describes (Report on Gold Fields, Nova Scotia, 1862) as slates of varying hardness: he could not find the seam from which the specimen of pipe-stone given him, to - which I am now referring, was obtained. The pipe-stone of Dana (Mineralogy, p. 252) is clay-slate, a greyish-coloured _ variety from Oregon having been analyzed by Thomson, and is mentioned in connexion with Catlinite, described as a reddish claystone. Bitumen in Calcite.—This interesting addition to the minerals of the province was made by W. Barnes, Esq., Mining Engineer of Halifax, who kindly furnished me with specimens, and gave me some details as to its mode of occurrence. It is found in Inverness co., Cape Breton, in an elevated range of altered rocks im which the lower carboniferous strata are apparent. Limestone is abundant but very muck altered, and rests at a high angle of inclination on altered black shales containing much pyrites ; gypsum also occurs in the neighbourhood. The mineral is dull black externally; it breaks with a con- choidal fracture, giving a very brilliant jet-black surface. It is scattered in separate masses on the surface of a highly siliceous rock, containing pyrites among calcite in six-sided prisms and in dog-tooth crystals. Some of these masses are an inch or more in length, of rounded outline, and lie free; others, smaller, Z 2 340 Dr. How on the Mineralogy of Nova Scotia. . are nearly surrounded by groups of crystals; in one case a mass is imbedded in a nearly transparent crystal; and sometimes the calcite when broken exposes a brilliant surface of enclosed mi- neral. These masses look occasionally like a drop of black wax melted on to a crystal of calcite, and are sometimes perfectly globular. It is brittle and affords a black powder. In a closed tube it softens, swells, gives a bituminous odour and a little oil. On platinum it swells up and burns with a smoky flame to a bulky black porous residue, not having the coherence of coke, and finally leaves a very small ash. It sinks im benzine and floats in bisulphide of carbon ; so that its specific gravity is pro- bably about 1:1: it dissolves to a small extent only in these menstrua, and after being boiled in them is readily powdered under a glass rod. It cannot be distinguished im appearance from the Albertite of New Brunswick, the mineral which has been called Albert coal and New-Brunswick asphalt. It resem- bles this mineral also in being slightly affected by benzine; but it dissolves somewhat less freely in bisulphide of carbon, which I find to become rapidly coloured on Albertite, especially when heated (this property does not seem to have been noticed in the discussion as to the character of this mineral). Side by side with Albertite on an iron plate on which tin had been melted for a short time, it smelt of bitumen, became tough and some- what elastic, and finally rubbed down to a brownish-black powder, while the Albertite scarcely smelt, but also became tough and somewhat elastic under a glass rod, and rubbed down to a black powder. I regret not being able to compare the composition of these minerals: Professor Anderson of Glasgow was kind enough to undertake an ultimate analysis of the Cape-Breton bitumen, but at the close of the combustion an unfortunate accident de- prived him of the results. There appears unquestionably to be a close relationship between this mineral and Albertite; and the occurrence of the former imbedded in a globular form in calcite is absolute proof that it 1s not coal. This mode of oc- currence. is precisely similar to that given for some bitumen by Andrews, in a very interesting paper on Petroleum in its Geo- logical Relations (Silliman’s Journal, July 1866, p. 40), who found ‘‘ among the crystals of calc-spar globular masses of pure bitumen, showing that the bitumen was at least in a semifluid state. This bitumen originated in the shales.” With regard to the origin of the Cape-Breton bitumen now under consideration, since it is altered by strong heat, and is found underlying and overlying calcite as well as imbedded in the same, the formation of both must have resulted from alter- nating action other than distillation, and it was probably of a chemical nature and took place at an elevated temperature. [341 J XLVII. On the Function of the Blood in Muscular Work. By C. W. Heaton, F.C.S., Lecturer on Chemistry to Charing Cross Hospital Medical School*. ht Ma of the recent writers on the origin and nature of muscular power seem to have assumed that the oxidation from which it is derived is effected in the tissue itself, outside the walls of the capillaries. Those who, with Liebig, Voit, Ranke, and Playfair, derive the whole of the power from the oxidation of the tissue, find this assumption a necessity ; but it appears to have been adopted also by Fick and Wislicenus, who follow Traubey in assigning the office to the fats and so-called carbohydrates, and by Donders, who attributes it to both classes of compounds. Mayer, however, in his now celebrated treatiset, adopted a different view, and argued with extreme ability that all oxidation took place in the blood. Since his time this theory has received some occasional isolated support ; but upon the whole it appears to have been neglected. This is the more curious, since its truth would not only destroy the hypothesis of Liebig, but also the opposite and not less extreme one of Traube. For if force ge- nerated inside a capillary is capable, under the influence of the nerves, of producing muscular contraction outside it, it is ob- viously impossible to assign the origin of that force to either nitrogenous or non-nitrogenous compounds exclusively. Fick and Wislicenus have shown, as Donders had before, that the oxidation of the latter class of compounds contributes something, perhaps the greater part, to muscular work; but, on the other hand, it cannot be doubted, after Savory’s experiments on rats and Voit’s upon a dog, that muscular work may be performed as usual in an animal body, even when non-nitrogenous articles are entirely excluded from the food. The beautiful experiments of Stokes§ have illustrated very re- markably the mode in which oxidation 1s effected in the blood. He showed that the colouring-matter of the corpuscles, to which he applied the name of cruorine, was capable of acting as a car- rier of free oxygen between the air and the oxidizable materials of the blood. He illustrated this function not only by the action of reducing agents on a solution of the corpuscles, but also by the more striking experiment of allowing the blood-solution to * Communicated by the Author. + Virchow’s Archiv, vol. xxi. p. 386 (1861). t Die organische Bewegung in ihrem Zusammenhange mit dem Stoff- wechsel, 1845. § Proc. Roy. Soe. vol. xui. p. 355. 342 Mr.C. W. Heaton on the Function of reduce itself by remaining for a few days in a tube out of contact with air. The cruorine was again oxidized instantaneously by agitation with air. This last experiment proves that the corpus- cles have the faculty of oxidizing nitrogenous materials, either their own substance or else some portion of the serum with which they are in contact. Hoppe-Seyler has since found* that, in a rabbit killed by drowning, the blood exhibits the spectrum of reduced cruorine. That the oxygen is held in combination in the corpuscle by the weak force termed by Frankland “ mole- cular combination,” is evident from the well-known fact that carbonic oxide displaces from it its own volume of oxygen. Now, if the oxidation of muscle is effected in the tissue itself, it is clearly necessary to suppose either that the oxygen, upon the stimulus of the motor nerves, leaves its combination in the cor- puscle, traverses the walls of the capillary m company with the outgoing stream of nutrient fluid, and only enters into new com- binations when it has passed to some comparatively distant muscle-fibre, or else that the corpuscle itself liquefies and passes out bodily through the thin membrane with its loosely combined oxygen. Both suppositions seem to me very improbable ; for, as Stokes’s experiment proves that the absorbed oxygen of the corpuscle is capable, without any nerve-influence, of entering into direct combination with the materials of the blood itself, it is difficult to understand why such combination should be de- ferred until the oxygen has traversed the walls of the capillary. Moreover, as muscle-fibre is now known to be at any rate not | the only substance oxidized to produce muscular work, it is plain that much of that muscular work must, upon the current theory, be produced by the oxidation outside the capillary of the very same substances, fat &c., which are present abundantly in- side it. Why oxygen should reject fat mside the capillary and oxidize it outside it is hard to imagine. But evidence of a more direct kind is, I think, accessible to us. The tissues are undoubtedly nourished by a stream of fluid which exudes from the walls of the capillaries in virtue of the pressure to which the blood is subject. As the tissues disinte- grate they liquefy and are carried, together with the excess of the nutritive fluid, back to the blood by means of the lymphatics, which take their origin in the intervascular spaces of the tissue. Hence Mayer suggested that the lymph was a measure of the amount of fluid exuded from the walls of the capillaries. Taking the quantity of lymph from Majendie’s calculation, he inferred that not 1 per cent. of the blood left the blood-vessels in the course of the circulation, and consequently, as all the blood re- * Zeitschrift fiir Chem. New Series, vol. i. p. 214. the Blood in Muscular Work. 343 quired renewal on its return to the heart, that 99 per cent. of the total oxidation of the body was effected in the blood-vessels. In this form, however, the proof is not quite complete. It may be argued that a large proportion of oxygen leaves the blood-vessels in the exudate, and that, small as is the total quantity of the latter, it may yet contain enough oxygen to do the work of the muscles. + I have therefore made a calculation of the quantity of oxygen which can possibly be supposed to pass out of the blood. I pur- posely exaggerate every figure employed, in order if possible to avoid cavil. The first point is to ascertain the extreme quantity of fluid exuded in twenty-four hours. Bidder and Schmidt estimate the lymph at 22 lb. I will take it at 30 lb. A large proportion of this arises of course from glands and other organs which do no muscular work; but this I neglect. It may be suggested that some part of the fluid exuded may return direct to the ca- pillaries without passing through the lymphatic system. No doubt this is the case; but the quantity so returned is probably small, as the pressure in the vessels would naturally tend to prevent it. The pressure, indeed, probably acts in forcing the fluid onwards into the lymphatics. Nevertheless, to avoid ques- ‘tion, I will assume that the quantity returned in this way is twice as great as the lymph, and I thus get 90 lb., or about 40 litres, as the daily amount of exudate; and I think every one will admit that this is an extreme overstatement. Any oxygen which passes out into the tissue must obviously pass in solution in this 40 litres ; and the next point 1s to ascer- tain the quantity of oxygen which it can possibly be supposed to carry with it. Lymph resembles diluted liquor sanguinis in composition, and is destitute of colour. The exudate is therefore in all probability derived mainly from the liquor sanguinis, which, as Berzelius showed, will hardly dissolve more oxygen than water. Moreover, its dilution proves that, as might have been anticipated from the colloidal character of blood, a considerable part of the exudate actually consists of water. But, to put the case in the strongest possible light, I will assume that the whole of the exudate consists of liquefied corpuscles—of scarlet cruorine, in fact, charged to its utmost with oxygen. Again exaggera- ting, I assume that the corpuscles of arterial blood contain 40 per cent. by volume of oxygen. This gives as the quantity of oxygen in the 40 litres of exudate 16 litres, or 22°88 grammes. Ts this sufficient to do the muscular work actually accomplished in the twenty-four hours? The following is an extremely low estimate of the daily work of the muscles : — | 344 Mr. C. W. Heaton on the Function of Metrekilogrammes. Hearts) .iieumentiey amin. «an, 000 LES ah ie eeleg sera Br yaieep AEOAOWO Voluntary muscles . . 20,000 100,060 To do even this small amount of work, double the quantity, or 200,000 metrekilogammes of force, must be developed (Hei- denhain). Now 22°88 grammes of oxygen would oxidize-— 7°89 grms. of fat, taken as having average composition of oleine, margarine, and stearine (Lawes and Gilbert), or 15°39 grms. of muscle, taken as equal in composition to albumen. Multiplying these quantities by the force-values obtained by Frankland*, we obtain these figures :— Metrekilogrammes. Bat ee BOR a S4le er ee SOUS Muscle 15°39x1848 . . =28,440 So that, even upon this extravagant calculation, we see that whether it oxidized fat or muscle, the oxygen exuded could not account for one-sixth of the work done by the muscles. To give even the 200,000 metrekilogrammes of force there must be a daily exudate of 264 litres, or more than a quarter of a ton of arterial corpuscles ! I think it is therefore certain that all, or nearly all, the force of the body is generated in the blood, and that Mayer was per- fectly right in saying that “the muscle produces mechanical effect at the expense of the chemical action expended in its eapil- lary vessels.” Hence it is natural to inquire what modification this view compels us to make in our ideas of muscular disinte- gration. In the first place, it forces us to admit that this disintegra- tion is a simple decomposition, and not an immediate oxidation. When a muscle suffers disintegration, either by uatural change or during muscular work, two classes of compounds are known to be produced. The members of one class are ternary and contain the residue of watér, while those of the other are quaternary and contain directly or indirectly the residue of ammonia. To the former class belong the fatty acids, lactic acid, sugar, &c., and to the latter such bodies as leucin, creatin, creatinin, uric acid, and urea. The greater portion of these products of de- composition are probably carried to the blood by the lymphatics ; and some of them, notably sugar, leucin, and urea, have been discovered in the lymph. The oxidation in the blood of such of * Phil. Mag. September 1866. the Blood in Muscular Work. 345 these compounds as are capable of it contributes to the heat, and probably to the work also of the body. Professor Haughton, in his well-known papers on Diabetes mellitus*, while he as- sumes that the normal disintegration of tissue is an oxidation, suggests that in the diseased state a large portion of the tissue is not oxidized, but is simply decomposed into urea and sugar. Mayer’s view compels us to believe that this, or something like this, is the normal process, and consequently that the pheno- mena of diabetes, as far as they are independent of the nature of the food, must be due either to increased disintegration or to diminished oxidation, or possibly to the conjunction of both causes. He found that increased excretion of urea went hand in hand with the presence of sugar in the urine; but as the food of the patients was increased from two- to four-fold, the observa- tion does not prove much. The great bulk of the nitrogen of the food must be excreted as urea. I will not speculate on the mode in which force developed in the blood is capable of producing contraction in the tissue. The process is subject to the control of the nerves, and is probably connected with the production of electricity; but one conclusion seems so probable that I cannot help suggesting it. It has long been known that muscular contraction is invariably attended with increased muscle-metamorphosis. Liebig, Helmholtz, Du Bois Reymond, Ranke, and others have left no doubt upon this point ; and it may even be considered to be proved that in- creased work is attended with a slight though irregular increase in the excretion of nitrogen; for though in Fick and Wislice- nus’s experiment, as well as in many previous ones, this result was not observed, its absence has been shown to be due to the shortness of the time during which the observation was made, and in the recent careful experiments of Dr. Parkest+, in which this source of error was eliminated, the increase was clearly shown. What, then, is the cause of this increase? It is obviously absurd to attribute it to mere mechanical friction of the muscle- fibres, to ordinary wear and tear; and it therefore seems natural to ascribe it to the excess of force which remains after the per- formance of the work. That an excess of force is always deve- loped is certain ; and though much of it may afterwards assume the form of heat, it seems not improbable that some part may be spent in producing chemical decomposition, and so be once more stored up as potential energy. It appears indeed possible that all normal muscular disintegration, inasmuch as it is sub- ject to the influence of the nerves and attended with electrical * Dublin Quarterly Journal of Medical Science, vols. xxxi. xxxii. xxxv. T Proc. Roy. Soe. vol. xv. p. 339. 346 Sir David Brewster on the Polarization currents, may be effected in this way. If this view be accepted, muscular disintegration, so far from being the cause of muscular work, must rather be regarded as an effect contingent upon it. Ranke’s beautiful experiments upon the effect of the products of muscle-metamorphosis in checking muscular contraction by increasing the conductivity of the tissue, are in perfect accord- ance with Mayer’s theory. XLVIII. Additional Observations on the Polarization of the Atmo- sphere, made at St. Andrews in 1841, 1842, 1843, 1844, and 1845. By Sir Davip Brewster, KH, D.C.L. FR. Soe: [Continued from p. 304. | 1842, January 6.—Fine day. = Apparent tire. Arago. h m O ; 2 34 5. > “5 55 ig .6 Babinet. 2 38 ae 16 18 R= 24° in zenith pianes “ggie se 30° aoiye E. horizon. 1842, January 7. ae fine oe with haze. 9°18 A.M. .. ea 15 51 12 Onoon. Ke me tals 13 &3 Argo. PPL A Nie ae. ail ge By 20 34 IZ 4pm. .: a By a 22,0 12 9 ,, R=222° mzenith .. i's Oy DDD: sack ot Zs at ta 20. 40 Abe Me ad itier, net aM atte 19 49 At 95 18™ R=24°, a maximum, in horizon. The neutral line was convex to the sun. Sky clear, without clouds. 1842, January 16.—Ground everywhere covered with snow. Babinet. ra ic Wop Toba N: 19 25 1842, January 17. =e Hirie clear Fats ; therm. 36°. 8 37 a.m. R=243° at 35° alt., 202° in horizon. 16 55 3 47 P.M. R=25° in zenith; 244° in horizon. Neutral line concave towards the sun. 1842, January 21.—Barom. 29°77 in. ; dry, frosty day. 972° in zenith plane, and 242°] 00 ‘ =275° in zenith plane, and 243° eae near horizon i at Babinet. 3 31 er ah ae af ae 1SF3 of the Atmosphere. 347 1842, January 25.—Snow covers the ground. Barom. 29:4in. Apparent time. hm Arago’s neutral point in horizon. 1 12 p.m. ee in zenith plane, and +15° in horizon. 2715) 5, : 16 45 Bie... R=182° i in ea. se 15° in Leave 19 21 340 ,, R=182° inzenith, and at 50° alt. 15°. 16 20 Arago. Babinet, Bla Ue s di is as 17 20 a Sa 5, a A 18 30 1842, ona 27.—Barom. 29:2 in.; therm. 36° at 85 30™. Arago, Pay oe R=243° near horizon; neutral line concave to sun. Ca) RS ae 4c Er as 11 50 a) : 20 40 Boe sy R=25° in zenith plane and S. horizon. Thin clouds, al bl hie in clouds, almost invisible every- ee where but above the sun ee 1842, January 28.—Barom. 22°69 in. Fine day; fresh. Arago. 2 7 p.m. R=22%° zenith; 253° in E. horizon. 13° 5 R= 264° in eae 273° in S.E,, = 23 2 and 263° in S.W. horizon. : =e 2 eS) ee os ki are 20 25 _ | i tap ale as ae 19 41 Babinet. Sool ep Me ie 18 48 Meh s ss es — ot 18 10 AO Te \'55 a 16 52 1842, January 29. See Phil. Mog. vol. xxx. pp. 123, 163. 1842, February 2.—Very fine day, and clear sky till 24, 1} 30 a.m. Arago’s neutral point not risen. R=25° m zenith plane, 202° in horizon. s #3 Arago. 2 Op.m. A thick, impure sky. 1842, February 3.—Fine day. 443 p.m. -. irs - La 20 20 Babinet. 3 fags 23 Shiai a pita | 1842, February 4. clade bay 30°1 15 in. Fine day; cloudy. Arago. 3 14 R=202° in zenith, 243° at 50° alt. W. hor. 18 40 R=25° in zenith, thin whitish clouds, 4 0 242° in E. enon 10° alt., 223° in 20 37 alt., 20° W. horizon a 4 44 & x re 20 14 348 Sir David Brewster on the Polarization 1842, February 5.—Barom. 30°05 in. Fime day; sky per- fectly clear. Apparent time. Arago. h m 7 ° 1 Tl =f ay Hi tea 17 25 1 44 a .o Lit oS 23 10 3 48 ae a By aS 225 4 9 se +5 e a 20 50 4 31 be She ie Ne 20 30 35] eee in zenith, 263° to 183° on E. horizon, neutral line convex to sun. Babinet. A ae At 17 20 4 33 R=282° in “renee oe : 19 ‘42, 9 5am. R=222° at 30° alt. S.W. bom. 20 38 12 34p.m. R=272° in zenith, 202° in horizon. Dark haze in horizon from E. to W. by N. 2 6 ,, R=272° in zenith, to 143° in horizon. 1842, February 10.—Fine day, but cloudy. Arago. 27 R=242° at 25° above W. horizon. 16 45 3 58 S is oe ae 19 20 4 45 R=262° in north .. Exe 17 43 Babinet. By a) R= 29° in zenith, and at alt. 30° E. hor. 18 38 A Bis y. 19 “4 4 41 Pie My oe HT PX Wes Clouds came on, followed by great rain and wind, at 10" p.m. 1842, February 1].—Rain in the forenoon and till 25 30™ p.m. Arago. Dell) R=243° at 30° above S.E horizon. 17 33 3 55 R=293° in zenith. Sky quite clear. 21 8 420 R=295° in zenith. Sky quite clear. 19 45 4 38 ae 4 at si 20)" Babinet. 3 22 R=281° in zenith, andin N. horizon. 3.53 ay re se he 16 19 4 23 a) 4 36 ue ¢ ye bi 19 34 a oe ibe in zenith. Neutral line con-| j¢ 3¢ vex tosun. R=283° at 15° alt. { 1842, February 12.—Barom. 29°3 m. Rainy, with wind. Cleared up at 45. Arago 4 18 17 “98 Clouds passed away. oe Babinet. 4 20 17 12 3 Do R=241°, but reduced to 203° when watery clouds passed-over the sky from W. to S. of the Atmosphere. 349 1842, February 15.—Rain in morning, then fine day. Wind west *. ppp time. Babinet. : m ° 1 425 R=272° inzenithto 223°mS.E. hor. 21 58 4 44 “iS ee 20 24 4 55 Barom. 30°05 in., therm. 43° ; wind west. 20 30 Clouds came into S. horizon at 46 55™, and the whole of the N. and N.E. horizon, especially above the sea, was covered 6° or 8° high with a dark band of distant haze. N.B.—At 35 48™, when the Fig. 3. neutral point was 1° 57! high, there was just above the sea-hori- zon, HH, a portion mn of + bands, a continuation of those on the sea, so that there were two neutral points here. These were more fully developed at 35 58”, as shown in a former papert. 1842, February 16.—Barom. 30°16 in. t At noon, sun’s alt. 21°, there Fig. 4. is clearly a faint neutral point a little above the horizon, and 19° below the sun. At 24 48™, though the bands at Arago’s neutral point are all +, as in fig. 4, they are most weak- ened at mn, which is the effect of the secondary cause. R=195°in zenith, and in both horizons at 25° alt. At 35 10™, the weak polarization at mn now extends down to HH. R=222L° in zenith, and in horizon at 25° alt. At 35 44™ the two neutral points are developed as in the annexed figure, the — bands aa being just 3 distinctly visible. == 1842, February 18.—See Phil. — ~ Mag. vol. xxx. pp. 123, 167, = * See Phil. Mag. vol. xxx. pp. 123, 163. + Tbid. vol. xxx. p. 128. t Ibid. vol. xxx. pp. 123, 167. ——__ = SE 350 Sir David Brewster on the Polarization 1842, February 19.—Fine day, with wind. Apparent time. h m Arago. 258 R=261° in S.E. horizon, alt. 30°. pam of] Neutral wibink 2° alt. 13 38 3 20 Secondary neutral point seen. 14 42 Fleeey clouds over neutral point. Ne 1 Ren OARS ee 7 2B. 8 440 R=245° inzenith plane. me 19 28 1842, February 21.—From 4" 52™ to 4 57™ a secondary neutral point to that of es was aa but imperfectly de- veloped*. 1842, February 22.—Dull cold morning, which cleared up about 1 25™, when R=214° in clear sky, from which clouds had passed. 3 94 eae in zenith, 223° near W. and 15 40 . horizon. 5 56 3) aoa ess we cf st 17 29 Negative bands do not touch the sea- | 3 44 horizon. Secondary neutral point > 20 26 in the horizon. AD ik 54 sé 5: 20 50 ADR as oe ss as 23 8 SS Mak. ue ae A 12 Babinet. 4 6 Pol. of moon, R=3°; R=273°inzenith.17 15 Ca SE ses B. 16 19 Di Gn en ee <5 <5 a 19 5 1842, February 24.—Barom. 29 in. Arago. oe Ye eran 17-20 232) R26, in zenith ; 27a in S.E. hor. 3 51 R=232° in zenith, and 253° at 35° alt. N.W. horizon. 1842, February 25.—Dull day; frost in morning; cleared up at 4h 2m, Babinet. 5 9 R=28° in zen.; 263° in E. and W. hor. 17 50 Arago. 5 12 ee ye 4) a TSi'5 1842, March 2.—A wet day, the place of the sun being seen as a white spot. 2 20 The polarization everywhere extremely feeble. Babi- net’s neutral pomt was nearly 75° above the ho- rizon, or about 54° above the sea! See March 16. * See Phil. Mag. vol. xxx. pp. 124, 163, 167. of the Atmosphere. 351 1842, March 4.—Cloudy and sunshine. PyEeeat time. Arago. 1 18 R=252° in zenith, and 223° at 30° alt. W. horizon. 1 48 One plate of glass at 60° incidence compensates the po- larization on the sea-horizon opposite the sun. 3 53 ; 3 58 ae = a z. ll 13 9 23 a ae sik ee 12 22 5 26 He wie 43 ae 17 55 Babinet. 5 38 R=272° in zenith, and 223° im horizon. 17 22 1842, March 7.—115 80™ R=282° in zenith, to 184° in horizon ; but at 14 30™, after showers of hail and rain, R=224° in zenith. 1842, March 10.—Sky clear, and wind in west. 11 0 R=274° in zenith. 11 15 Neutral point seen below sun. 3 14 R=28° in zenith, 244° in horizon. 4 0 Arago’s neutral point not risen. 4 10 The + bands scarcely seen in horizon. 413 R=28° in zenith. j Arago. 4 15 oe re ae 44 12 55 4 20 As 13 56 4 27 cre secondary neutral point snst touch- 14 54 ing the sea horizon 1842, March 138.—12® 36" R=26$° in zenith. Sky clear. 4 27 The breach inthe + bands not completed. 12 15 4 39 Butat4»39™ the neutral pointisformed. 12 6 Both on the 10th and 13th Arago’s neutral point is above the horizon, though marked by the cause which produces the secon- dary neutral pomt. Over a space of 34° above the sea-horizon, the + bands almost wholly disappear before the — ones are perceptible, and the neutral point is distinct on the sea-horizon. 1842, March 16.—Barom. 22°96 in., the sun occasionally shining through a thickish haze in a 1 sky without blue. Wind slight in south-west. 10 45 Polarization the same as on March 2; Babinet’s neutral point 30° above the sun, or more than 60° above the horizon ! 1842, March 17.—Barom. 29°77 in. Much rain last night. Wind west ; white clouds flying. 10 20 R=2632° mm zenith plane, and soon after 242°. 10 50 R=203° in zenith plane, and in a clear sky over which clouds have passed. 352 Sir David Brewster. on the Polarization 1842, March 18.—Barom. 29:09 in. Wind and rain, day cold, and wind in west. Sng ae time. o/s R25, nee to 20°. ed 9 28 ie 15 48 5 55 oie is bi 55 18 10 6 12 0 bc 55 2 17 48 Babinet. 5 30 R=30° in zenith oe 19 10 5 57 : Be 17 40 6 10 3 20 12 1842, March 19. eee 29 in. 3 54 Polarization of moon, 203°; R=23° in zenith. Arago. 4 39 R=24° in zenith plane; sky very clear. 10 37 5 44 : 19 45 6 4 Polaron Of or 902°; i 991°} inzen.18 47 6 19 a oie ee ate 18 45 Babinet, 5 48 Pen in zenith be 58 19 30 6 12 4 sd 19 45 6 21 ae 17 26 1842, March 24, eekred up [h) Pine day. 2 0 R=223°, 50° above the horizon. 4 0 R=202° j in zenith plane. r 1842, March 26.—Barom. 29:3 in. Cold wind from point north of west. ; Arago. 5 49 oie oi os aie 18 32 6 16 54 35 30 rc 19 25 6 31 ae 5S 30 36 18 4 Babinet. 5D 52 Nae in zenith BAe ae 19 20 6 34 : se 19 40 1842, March 08, Tes ai 4 20 R= 263° m zenith plane, and 18° and 20° in horizon. 1842, March 29. Arago. 6 20 A 4c oe +5 17 55 6 36 a 30 46 35 17 50 Babinet. 6 18 56 50 18 40 1842, March 30. wind quae clouds. Arago. 6 27 R=283° in zenith, to 233°im horizon. 18 13 6 45 Ne Ae se oe 17 55 6 52 ie 5 +3 34 19 37 6 24 Babinet, 6 48 a 20 40 310 R=2l 4° in zenith plane 53 19 54 of the Atmosphere. 353 1842, April 2. Apparent time. Arago. hm ay 6 5 oe a oe re 19 15 ’ 8 ae oe oe 19 42 Babinet. 6 36 a ee 2 ve 18 5 6 38 a -. ee ae 19 8 a : 20 18 1842, April 3. ins a sky ; cae in the afternoon. 11 45 Brewster’s neutral point most aiid: 13 0 seen, Distance from sun 1842, April 5, 6, 8.—See Phil. Mag. vol. xxx. pp. 124, 163, 164 & 168. 1842, April 9.—Barom. 30:16 in. Wind east; bitterly cold. 3 25 R=22}° in zenith plane. The sky clear. Arago. 7 5 46 ws is fe ~e pas 6 55 15 20 7 | Effect of fog oe He 7 2 Babinet. A 49 R=153°inhorizon.. eater Exe 80 6 57 * ; at 19 30 icon 55 49™ and Gn 5 57M a foe came on, and there were no neutral points. 1842, April 10. 4 5 R=182° in zenith, and 143° in horizon. 4 22 R=27° in zenith and 143° in horizon. Babinet’s neutral point very near the sun, and no neutral point seen below the sun. 1842, April 13.—Barom. 30°12sm. Fine day*. Arago. 5 48 a rf Ly, oe 16 20 6 20 ee ee 7 ¥ 17 55 6 54 fe ¥: A +e 19 40 7 10 “a Hs oe ie 19 45 7 19 R=803° in zenith Ae wr 19 4 nee Kh 322° j in zenith : 22 10 R increased from 25° at 44 to 321° at 7h 29m, 1842, April 15.—See Phil. Mag. vol. xxx. p.168. Haze from west, 5 40 ms a: op he 16 25 5 48 18 40 a 57) R= 142° j in zenith ; 182° 20° above N. hor. 18 21 6 28 White nebulosity Se ae 18 50 7-0 Babinet. 5 50 Ly! ware ne were 28 20 * See Phil. Mag. vol. xxx. pp. 124, 164. _ Phil. Mag. S. 4. Vol. 38. No. 224. May 1867. 2A B54 Sir David Brewster on the Polarization 1842, April 16. Apparent time. Arago. hm ° / 5 54 oe ug ae ee 17 25 6 31 22 22 6 59 { R=272 j in renith: 228° in N.,, an eke }19 50 in S. horizon — , 7 peo pe oe 18 55 7 oo ) R= 182° at noon ay: ae 0 45 7 46 oe ve fh 5 23 50 Babinet. 5 58 R=235° in zenith, much less in horizon. 25 40 6 Boat ea in zenith; 21° in W., and 183° hig grt in E. horizon 6 57 He 5 200 3 723 R= 293° 1 im ert, and 24 z 1 in both hor. 17 45 7 37. R=81° in zenith, ond 292° in horizon. 17 35 1842, April 17.—Slight haze. 3 30 Brewster’s neutral point distinctly seen, R=193° in zenith, and 12° in S. horizon. Arago. 5 34 R=173° in zenith, 223° inthor.; clear sky. 20 10 Babinet. 6 3 Babinet’s neutral point just risen 19 30. 7 35 R=283° in zenith plane. 1842, April 18.—Barom. 30 in. 7 14° Pol. moon = 273°, 292° in zenith. 18 45 Arago. 7 23 Pol. moon =28:°, 302° in zenith. 17 45 1842, April 19. fA7 as a ve oF 16 35 Babinet. 7 20. Pol. moon 143° and a maximum .. 18 15 EB s 222°, and maximum 263° 19 10 1842, April 20.—See Phil. Mag. vol. xxx. pp. 125, 168. 1842, April 21.—See Phil. Mag. vol. xxx. p. 173. 11 30 R=233°, maximum at 90° from sun. 110 R=253°, maximum at 90° from sun. Arago. 7 20 se a Se 58 17 55 7 48 A fog came on ee ‘ys 14 24 Babinet. yi22 »f a 20 15 1842, April 22. ins oe 11 10 a.m. R=173°; maximum polarization in zenith 90° from sun. Brewster. 2 0 ,, R=27° at 9C° from sun in zenith plane. 12 10 3 0 ,, R=29°at88° from sun in zenith plane. 11 10 410 ,, R=294° at 90° from sun. Arago. Grae ss 0. oe 55 ae 20 25 Babinet. 6 58 ,, Thin clouds. ra a 22 15 of the Atmosphere. 355 1842, April 24.—Barom. 29°84 in., rising. Apparent time. h m 3 0 Ahaze. Babinet’s neutral point 70° high; Brewster’s not yet risen, After the haze had increased the sky cleared. Babinet. Altitude of Arago’s neutral point 2 un Hah { above horizon .. ee } oe 6 10 ” ” 33 39 13 0 6 10 Secondary neutral point exactly in horizon. 1842, April 25, 26, 27, 28, 29.—See Phil. Mag. vol. xxx. pp. 125, 168, 169. 1842, May 2.—Barom. 29:93 in.; wind east. Arago, REECE relec Ses ys ie a 23 45 7 1 R=225° zenith to 184° in horizon. 24 45 is nA “fe ae 20 15 Babinet. 6 21 R=283° maximum in zenith plane. 16 30 1842, May 3*.—China-ink sky ; wind east. 9 Oa.m. R=19}° maximum polarization in zenith to 143° in horizon. 11 O ,, R=193° maximum polarization in zenith to 144° in horizon; bands ragged. Arago. 11 29 ,, R=20°; maximum at 89° from sun. 10 15 mee, a e909... if; 7: 9 25 1842, May 4. 5 56 6 2 { The — bands of secondary neutral point } 17 34 distinct, and this point commenced 6 13 ae 5 4 a 20 46 The secondary neutral point distinctly : 16 { formed ; ee - Sn 1842, May 9.—Barom. 29°83 in. 5 42 R=221° in zenith plane. 6 7 Bands all positive sk of 19 15 6 18 Positive bands still in horizon. 6 39 fe ps co Ae D547 7 28 v. us i. ae 23 21 Babinet. 6 45 os A Bi : 15 0 7 30 R=192° in zenith plane ui 16 5 1842, May 15, 16, 17.—See Phil. Mag. vol. xxx. pp. 125, 164, 169. 1842, July 16.—At Lacock Abbey, Wiltshire. R= 23° in a singularly fine day, this low polarization indi- cating nebulosity, which collected and produced rain. * See Phil. Mag. vol. xxx. pp. 169, 173. 2A2 356 Sir David Brewster on the Polarization 1842, August 2.—At St. Andrews; Barom. 30 in. - Apparent time, h m 5 9 R=20)° in zenith, and 142° in horizon. 5 27 The bands opposite the sun eeea to weaken, and there is a second neutral point. 6 15 Negative bands distinctly seen. Arago. 6 0 i se 1 20 36 6 26 ath fs o baa 2 ormala! 7129 Sy as fe on PE e | 7 54 eh ee M ig 22 4] 913 Mi Be ai a 33 40! ; Babinet. 6 32 a 13 40 6 39 Arago’ s secondary neutral point distinctly formed. A dark band along the horizon, below Arago’s neutral point. 1842, August 4.—Slight rain in morning; barom. 29°5 in. ; wind west. 5 54 R=25° near horizon. 6 41 Arago’s secondary neutral point in horizon. 7 6 R=293° in clear blue sky. 7 9 Altitude of Arago’s neutral poet abovel 15 49 orizon 1842, August 5.—Rain in forenoon. I observed a singular sky in the west, to the north of the sun and below him. The Fig. 6. whole sky, from A A to the ho- | rizon H H, was clear; but the 4~— (Darwen plug, A part A A was darker than BB, andiof asdeep Chinaamk blue, v0 an ie while B B was much paler. But, 5, Pale blue. i what was singular, these differ- YS ently coloured spaces were se- H-__Whtishy og parated by an irregular line mmm, showing that the whole space mmm HH was a thin sheet of cloud or vapour terminating abruptly at mmm. 5 40 R=173°, max. polarization at alt. oe Arago. 7 9) pret in zenith plane, and 264° a 17 10 alt. 40° 7 25 Acloud approaching the neutral point. 16 35 7 40 R=285°, maximum in zenith plane. 19 30 1842, August 6.—Barom. 29°6 in.; rain at 55 p.m. 7 50 R=283° max. in zenith plane, to 245° im horizon. 7 56 Altitude above horizon of Arago’s neu- } 19 10 ral point ae Clouds around the blue space. of the Atmosphere. 357. 1842, August 11.—Barom. 29°62 in.; rain in morning. Apparent time. h 5 30 R=233° in zen. plane, and203°inS. hor. 5 51 -+ Bands opposite sun almost gone at oar 6 14 above horizon. a 6 40 6 46 14 35 7 20 35 8 4 -Altitude of the two neutral hee above -22 20 the horizon : : Babinet. 7 43 18 25 Sly) R= 297 in zenith... ys : 127 6 1842, August 17.—See Phil. Mag. vol. xxx. p. 169. 1842, August 22.—Warm ; fine day. 9 20 R=24%° maximum polarization in zenith plane, to 194° ur horizon. Arago. iy , ae 18 36 6 37. R= 972° in enieh plane 4 21 16 7 26 R=283° in zenith plane = 19 56 7 49 “ Br ae ae 9D 8 Babinet. E52 iss 1842, August 28, Ble Gi Phil. Mag. ei, xxx. p. 169. 1842, September 9.—Barom. 29:1 in., after rain. 5 53 R==263° maximum polarization in zenith, to 253° in hor. Arago- 6 38 ois 18 57 1842, September 13.—Barom. 29°93 i in. Fine day. 4 39 R=28° maximum polarization in zenith plane. R=273° maximum polarization in 30° alt. 4 50 N.W. horizon, to 244° in horizon. In} 15 35 S. hor. alt. 30°, 262°, to 223° im hor. Deo nt ae ae we 18 35 5 58 R=293° max. pol. Pol. of moon 194°. 20 17 6 36 ¥ ae a oe 20 0 Li2 wis 3 zi ry 16 24 Babinet. 5 31 R=29° maximum polarization in zenith. 14 25 5 56 -e 15 40 6 38 R=293° maximum polarization in zenith. 16 6 i 6 *. 19h. 8 1842, osierie ili ce 29: 45 in., after a rainy day. Arago. 6 48 p.m. ¥ x Madea 3) Babinet. 6 53 ,, R=28%3° max. polarization in zenith. 16 25 1842, September 18.—Fine blue sky. Barom. 29°57 in. 3 0 R=215° im zenith plane, to 193° in horizon. 345 R=223 ie in zenith plane, to 203° in horizon. 4 20 R=25° in zenith plane, to 23° in horizon. 4 46 Fringes all + opposite sun and in horizon. 4 47 Arago. 5 6 " a sf be 15 28 5 36 xs a ae Pe 16 36 5 56 oe rp os 23 20 16 5 21 R=274° max. pol. in zenith, to 24° im hor.19 40 358 Sir David Brewster on the Polarization 1842, September 28.—Fine day. Apparent time. h m Arago. 4 32 R=28° max. eae in zenith plane. , 4 58 1842, September 29. mae Aa ; cold; wind east. 4 37 R=303° maximum Pat oe in zenith. 5 il an $3 17 34 1842, September 30. ee day. 418 R=293°.max. pol. in zenith, to 263° in hor. 4. 24 Neutral point not risen. Bands +. 4 55 bait ne ada 9 4 rs 16 11 5 47 dis aa a Hs 18 18 Babinet. 4 58 : 15 23 5 44 R=293° max. ‘polarization in zenith plane. 17 28 1842, October 15.—Fine day. Barom. 30 in., rising. Arago. 4 32 R=293° max. pol. in zen. to 263° inhor. 18 0 5 11 aie sie 18 11 5 42 "2 So 2c 20 25 30! Babinet. 4 34 bn oi si Ac 15 23 5.9 sh 56 Ay ae 17 26 5 46 ot 20 O 1842, October 19. ee 29: 33 in. Cold. Arago. 4 56 R=274° max. pol. in zenith plane. 19 a 5 5 oe si ah es 20°79 Babinet. Bune she 35 16 39 1842, October 20. Oe ae 29: 62 | in. Fine day; cold. Arago. 415 R=263° nearS. hor. Cloudsin zenith. 14 “46 1842, October 21. 4 49 Neutral point above a cloud oP 18 13 1842, October 24.—Barom. 29°33 in. Rain in the morning; cold. 4 28 55 si We ats 18 46 se Na Babinet. 4 32 R=27° max. polarization in zenith plane. 21 59 1842, November 9.—Barom. 29:06 in., after a storm of wind and rain. Arago. 4 41 Polarization of moon in 8. horizon 253°, 17 "20 1842, November 14.—See Phil. Mag. vol. xxx. pp. 125, 164. 1842, November 15.—Barom. 29°72 in. Hard frost in morning. 2.12 Secondary neutral point im horizon. 17 50 i of the Atmosphere. 359 1842, November 20, 21.—See Phil. Mag. vol. xxx. pp. 125,164. 1842, November 27.—Barom. 29°15 in., rising. A dark band along the horizon. Apparent time. h m 3 57 R=27° in zenith, and 184° in horizon. Arago’s secondary neutral point in horizon, and primary one considerably up. 1842, December 3.—Barom. 29°95 in. Fine day. 12 46 Arago’s neutral point not risen. 12 46 R=27%° max. pol. in zenith, 203° in hor. Atago.. 216 R=283° max. pol. in zen:, 183° nv hor. 19 20: 4 23 sii ve Sy, Pitas 24 22 ae Babinet. 4 28 4s 20 15 1842, Bigeenbor ie sh eat 29: 58 in., rising after rain. Arago. 3 16 ae ye os Se 18 5 Babinet.. 3 19 R=29° maximum polarization in zenith. 17 50 1842, December 18.—Barom. 29°79 in. Raining occasionally. Cito LETS “2 a = a 13. 45 12 23 ae she k4 42: 1842, December 22. thet 99: 38 in., falling. Rain. 2 43 fs ae We 5: 17 50 Babinet. 246 R=29° max. polarization in zenith plane. 16 10 1842, December 23.—Barom. 29°01 in., after rain. Arago. 3 0 re oe o ote 18 16 Babinet. 3 3 R=80° max. pol. in zenith plane. 19 4 1842, December 24.—Barom. 29°33 in. ° Arago. 12, 3. R26 thax, poli, in zenith plane. 15 28 12 44 R=28 93 as : 15 5 bse (R=2/ 35 49 : 17 30 224. R=29 - es 99 18 40 3 8 R=273 PRED toh. fi aD 33/7 R=294 6 $3 as 19 14 : i Wat te A} Babinet. 2 97 Re point of Pui ae 18 98 as the sun’s altitude diminishes. 3.5 ete 25 oe ae CA Wat 3 39 ee fe 17 55! 1842, December 26 nee 98. 88 in. Arago. 1 3 R=263° max. polarization, alt. 30°. 16 25, 3 27 i 17 15 Babinet., 3 30 R=28° max. polarization in zenith plane. 17 40: 360 Dr. A. Ransome on some of the 1842, December 27.—Barom. 29°35 in. Sun shining through a dry haze, which continued all day. The lines in the sun’s spectrum singularly sharp. Apparent time. Arago. h 1] 48 R=263 max. polarization in zenith plane. 15 50 R=234max. polarization in zenith plane, a 143° m horizon. +: oie 1 45 R=24 max. polarization in zenith plane. 20 25 2 3b) R=2/5 5 e fs 21 30 S15 R=29% on os a 19; 0 Babinet. 12 9 oe on Bois y 12 25 1 50 ate Le "> es he 14 40 2 38 = ; 16 5 1842, December 28.—See Phil. Mag. vol. xxx. pp. 126, 164. 1842, December 29.— Barom. 29°50 in. Clear in north. Arago. 11 40 45 = 34 + 15 25 12: 0 a i 45 ae 15 29 Babinet. R= 263° maximum polarization in zenith 1] 44 plane. Slight clouds e 17 49 R=283° alt. 50°. Sky clearer. 1842, December 30.—Boisterous day ; thin white clouds. Arago. 2 0 R=223° max. polarization in zenith plane. 2 24 : 3 1842, December 31.— Windy, and sky cloudy. 11 53 R=273° max. pol.in zen. Sky impure. 16 40 [To be continued. | XLIX. On some of the Conditions of Molecular Action. By Artuur Ransome, M.B., M.A. Cantab.* ANY theories have been broached respecting the ultimate molecular constitution of bodies. The energies of sub- stances have been supposed to depend upon the shape and size of their constituent particles+, their possession of one or more axes of polarity {, their mobility§, and their rotation in various orbits. The phenomena of heat, light, electricity, &c. have also * Communicated by the Author, having been read before the Literary and Philosophical Society of Manchester, March 5, 1867. Tt Dalton, ‘New System of Chemical Philosophy.’ ft Girdlestone, Phil. Mag.S. 4. No. 194, (vol. xxix.) p. 108. § Graham, Phil. Mag. 8.4. No. 177, (vol. xxvi.) p. 409. Conditions of Molecular Action. 361 been referred to the possession by the material particles of im- ponderable atmospheres with various properties*. It is not intended in the present paper to enter upon the dis- cussion of the atomic or molecular constitution of bodies; and although the modes in which matter is related to, or affected by, heat and other physical forces are intimately connected with the subject, and will probably eventually throw much light upon molecular actions, for the present these relations will only be in- cidentally mentioned, and the substance of these remarks will be restricted to more material reactions. It is convenient also to mark off chemical from purely mole- cular actions ; and this may be roughly effected by stating that, whether or not chemical combination results from molecular ac- tions, the peculiar forces of which we shall treat do not take part - in the chemical reactions, nor assist in binding together the ele- ments of the resulting compounds. The force of cohesion also, which binds together the particles of the same substance, will not here be considered. We shall be mainly concerned with the action of different substances upon one another through the in- tervention of certain molecular forces or affinities, or, in other words, with the relations to be observed between the particles of various substances, apart from their chemical activities, when they are brought into close proximity with one another. There are many groups of these actions, and chief amongst them the so-called catalytic or contact actions. Certain of them will now be brought closely under review in an endeavour to ascertain the special circumstances under whick molecular ener- gies come into play. It may be well first, however, to state briefly what is known of the forces in question ; and the following propositions respect- ing them will probably include all that can at present be affirmed about them :— (1) That molecular influence depends essentially upon the elementary nature of bodies. (2) That it acts without regard te mass. (3) That it increases inversely as the distance, at some enor- mous ratio. (4) That its action is in some way affected by calorific, elec- tric, and probably by luminous vibrations, and by chemical affinity. (5) That it does not seem to differ in kind from the attraction of cohesion, which binds together the particles of the same substance. (6) That chemical affinity may be similar in kind, but that it * Norton, Phil. Mag. S. 4. Nos. 188 &c.; and Maxwell, Phil. Mag. S. 4. No. 194, (vol. xxix.) p. 152. 362 Dr. A. Ransome on some of the differs from molecular attraction in the power of producing com- bination. When molecular operations take place between the particles of bodies of dissimilar chemical composition, the following con- ditions are found to favour the production of molecular and che- mical changes :— (1) That two or more of the substances submitted to mole- cular influences have a more or less powerful attraction for one another. (2) That their physical condition is favourable to molecular action. (3) That the molecular agent or catalyte has very low chemical affinities for the substances acted upon. (4) That the molecules of the catalyte are free. Hach of these conditions will be considered separately, and their bearing upon different molecular actions will be noticed somewhat in detail. 1. Of Molecular Affinity. It is a question whether the real molecular force of all sub- stances may not be the same in degree. All substances may possess absolutely the same amount of molecular force; but from their varying chemical affinities, and from the various extent to which they are subject to the different affections of matter, they may not be able equally to exert their molecular power. The molecular force depends so greatly upon the degree of approximation of the particles, and this must be so seriously affected by variations in the above-mentioned conditions, that we cannot affirm that different manifestations of the molecular influence of different substances may not be governed by these conditions, and that the molecular force is not the same in all substances. Until we can appreciate the minute differences 1n the. degrees of approximation of substances to one another during any molecular action, no absolute measure of molecular force can. be applied. Professor Tyndalland M. H. Ste.-Claire Deville, in some of their recent researches, seem to have approached, although they have not as yet effected, the solution of this pro- blem, and no certain means are yet known of testing the dis- tance of atoms from one another. In some minds, indeed, there seems to be doubt as to whether such an influence as we are considering exists apart from chemical affinity. We may therefore be permitted to notice those cases in which molecular force seems to come into play, and to endeavour to point out the mode in which it acts. Attraction of Solids for Liquids.—This heading includes all the cases of so-called capillary attraction, the rise of liquids im Conditions of Molecular Action. 363 capillary tubes, in porous substances, and upon the surfaces of solids, and the formation of drops; probably also many of the phenomena of cementation by means of colloid substances. The simplest case is perhaps that of true capillary attraction. When a fluid rests in a horizontal tube open to the air at both ends, and so small that cohesion of the fluid will prevent it from running into drops, then all the forces acting upon the fluid are equal and antagonistic, except the force of gravitation, which is neutralized by the cohesion of the fluid; the solid and the liquid act and react equaily throughout the whole length of the column of fluid; and at each end of this column the particles of the solid which are just beyond the limits of the fluid act un- perturbedly, and draw it in opposite directions: hence the po- sition is one of equilibrium, and no movement takes place. When, however, the tube is raised into a vertical position, the attraction of gravitation tends to draw the fluid downwards; and if the molecular attraction of the walls of the tube and the cohe- sive power of the fluid are not sufficient to counterbalance the force of gravity, the column of liquid will descend in the tube until it reaches its lower extremity. Here, if the tube be small enough, it will stop, and no portion exude; for the molecular attraction of the lowest part of the tube, which had before been acting in the same direction as gravitation, and in opposition to the same molecular force at the top of the fluid, now changes its direction and tends to draw upwards the lower particles of the fluid (as in the figure) ; and if the weight of the fluid is not too great, equilibrium is again esta- blished, and the column of fluid remains at rest. It will be seen that the molecular attraction now acting up- wards both at the top and bottom of the fluid has no power to eause the column of fluid to ascend; by any upward movement the lower force is at once changed in direction and draws down- wards again. But now let the lower end of the tube be plunged into a vessel containing the same kind of fluid: the particles composing this portion of the tube now draw up successive por- tions of fluid which press upward those already in the tube, and thus act along with the molecular force at the top of the column, and gradually raise it im the tube until its vertical hydraulic pressure equals the united force of these two attractions. It might be supposed that in these cases of capillary attraction we have what we were just now looking for, an actual measure of the molecular force exerted, in the height to which the fluid rises in the tube. If it were possible to learn the exact number 364 Dr. A. Ransome on some of the of particles in any transverse section of the column of liquid and their distance from one another, it might be possible to calculate the force exerted ; but it is needless to say that at present this knowledge is withheld from us. It is interesting to notice the part played by the attraction of cohesion in this case. It has recently been shown by M. Jamin (Comptes Rendus, vol. 1. p. 172) that when successive beads of fluid are contained in a capillary tube, the resistance offered by the cohesive force of these beads may be so multiplied that they will resist considerable pressure, even to 3 or 4 atmospheres. Mercury produces still greater effects; but, on the other hand, alcoho! and oil oppose no resistance to pressure. The same variation, from the varying molecular force of differ- ent substances, is also observed in experiments on capillarity ; and, in relation to this subject, it may be mentioned that the magnitude of drops of fluid distilled from a tube is in proportion to the weight of that fluid raised in that tube by capillary attrac- tion—the chemical composition of the liquid affecting the weight of its drop in a remarkable manner*. Miaxtures.—Mixtures of different fluids afford perhaps the simplest examples of the varying extent to which molecular affi- nity may be manifested. Some fluids will mix in any proportions with one another—for example, alcohol, and glycerine and water. Others, again, as ether and water, at the same temperatures will only mix in cer- tain fixed proportions. In order that two fluids may be entirely miscible, it seems necessary that the particles of each fluid have for those of the other a greater molecular affinity than they have amongst them- selves; in other words, the molecular attraction of one fluid for the other must be sufficient to overcome the cohesive forces of eacht. When fluids are only partially miscible, we can conceive that up to a certain point the particles of one fluid are so separated from one another by those of the other fluid that their cohesive forces cannot draw them together; but as soon as the solution becomes more concentrated and the particles get sufficiently close together, then the cohesive forces gain the ascendant, no further mixation can take place, and saturation is the result. Molecular attractions of Vapours and Gases.—Gases and va- pours also display certain degrees of molecular affinity m their relations to one another, gases being susceptible of mixture with other vapours up to a certain point of saturation. * Phil. Mag. S. 4. No. 181. + The contraction of volume which takes place in some fluids after mix- ture gives considerable probability to this opinion. Condiiions of Molecular Action. 365 Professor Wanklyn* has pointed out the influence of adhesion and of vapour-density upon the distillation of mixtures, by which means a less volatile liquid can be made to distil faster than one more volatile with which it is mixed—as, for instance, in the facilitation of the distillation of oilsin steam; and Dr. Graham + seems to think that nitrogen may diffuse more readily through a platinum plate in company with hydrogen than without its assistance. It seems probable that the rate of diffusion of gases through various porous substances is affected by the molecular affinities of the solids and gases, as well as by the constitution of the gases themselves f. . Solution.—The solution of solids in different solvents, without change of chemical composition, must be similar in its nature to mixture; but in this case a species of liquefaction (or rather dis- integration) must precede mixation. In many instances the action is accompanied by an absorption of heat from surrounding objects, showing that a change of state similar to liquefaction has taken place. If, however, solution involved true liquefaction, the solvent ought to lose exactly that equivalent of heat which is required to melt or liquefy the substance dissolved, which is not the case. But if the particles of the solvent simply come into such close contact with the particles of the solid as to disintegrate and — overcome their cohesion to their fellows, then it is by no means necessary that any heat should disappear from the solution. The action of a most minute portion of alcohol in assisting the pulverization of camphor testifies the probability of this expla- nation. Heat increases the distance from one another of the particles of a solution ; it may also in some instances directly mterfere with molecular attraction, and thus a larger quantity of a solid can be dissolved without bringing its separated particles within the range of their own cohesive or crystallizing forces§. When a substance, such as hydrate of lime, is more readily dissolved in cold than in hot water, it seems probable that its molecular affinity for the solvent is so small that it requires the combined influence of many particles of the solvent condensed upon its molecules to keep them in suspension. When these sol- vent particles are separated from one another by heat, the mole- * Phil. Mag. S. 4. No. 183. + “On the Absorption and Dialytic Separation of Gases by Colloid Septa,”’ Phil. Trans. 1866, p. 420. t+ Dr. Graham, ibid. p. 431. § Mr. Tate has shown that the weight of a drop of fluid is diminished by heat. 366 Dr. A. Ransome on some of the cules of the dissolved substance drop from their grasp and are thrown down. . Catalysis.—The degree to which molecular affinity is exerted upon different substances must play a most important part in de- termining the results of those actions ordinarily termed catalytic, in some cases bringing about decomposition, in others synthesis. When contact with a substance produces decomposition, as when binoxide of manganese facilitates the evolution of oxygen from chlorate of potash, the molecular affinity of the catalyte is probably greatest for one of the constituents of the substance acted upon, and it will attract this to such an extent as to enable it to gain its freedom. When, however, synthesis is the result, as in the action of pla- tinum-black upon alcohol, assisting its oxidation, the catalyte in this case may draw the particles together, or it may be able to concentrate upon itself one of the elements so exclusively that it may appear in an undiluted or liquid form, and hence able to act with greater energy upon the substances presented to it. Osmose.—The phenomena of osmose are probably dependent purely upon molecular affinity. Osmose takes place when a porous but, usually, water-tight septum or membrane separates two mis- cible fluids. In this case the fluids both pass through the mem- brane, but at different rates. The structure and composition of the septum influence the rate of diffusion, and determine which of the two fluids shall pass through most rapidly. Thus, when water and dilute alcohol are separated by an animal membrane, the water will pass through most rapidly ; but when the septum is composed of caoutchouc, the alcohol diffuses at much the greater rate. | The more rapid rate of diffusion of one fluid (A) over that of another fluid (B) may be accounted for by supposing that the sep- tum has a greater molecular affinity for fluid A than for fluid B. The particles of fluid A may perhaps fill the pores of the septum, and if there were no other fluid with which it could mix on the other side of the septum, its attraction for the septum would suffice to keep it from exuding; but since on this other side of the septum there is a fluid with which it is miscible, and since, as we have before seen, miscibi- lity seems to assume that the particles of one of the mixing fluids must have a greater molecular attraction for the particles of the other mixing fluid than they have for one another, it follows that when the particles of fluid B come into contact with those ‘of fluid A they will at once mix with them and drive out some Conditions of Molecular Action. 367 of those particles of fluid A which previously filled the pores of the septum (those particles of fluid A perhaps alone remaining unmixed which were in close contact with and lining the sides of the pores). We may now easily surmise the mode in which the opposite currents are produced. The particles of each fluid at each end of the pores, from their miscibility, will be continually taken up by the opposite fluids (those of fluid A by fluid B, and vice versd), and thus a flow of each fluid one into the other will be started ; and since upon one fluid (A) a double influence is ex- erted, by both fluid B and the septum, its diffusion will proceed at a greater rate. The currents will continue to flow until the affinities of each are satisfied or are in equilibrium. It seems possible that the size of the pores may to a certain extent determine the direction of the current, since upon this circumstance depends the quantity of fiuid in contact with the septum; aud this, if it were true, would assist the solution of many vital problems. In this explanation of osmosis it will be seen that the chief part in the action has been attributed to molecular affinities similar to those which produce solution and mixation—with this difference, that in the septum between the fluids we have certain- mechanical conditions and a rigid insoluble material concerned, instead ofa fluid or a soluble solid*. — Dialysis differs from osmose in the extent to which the current from one fluid (the crystalloid) prevails over that of the other (the colloid) ; it is in fact little more than the diffusion of the crystalloid through the colloid. A colloid possesses all the qualities most favourable to mole- cular (as distinguished from chemical) action. [ts particles have * The account given of endosmosis by M. Lhermite (Annales de Chimie et de Physique, vo}. xlui. p.420) is, m the main, similar to that just stated, except that he scarcely ascribes sufficient importance to the molecular in- fluence exerted by the two fluids one upon the other. Thus he thinks that the passage of the second fluid (B), which is less influenced by the septum than fluid A, is purely passive and due to pressure, and that if the pores of the septum were ever to become entirely lined by fluid A the osmotic action would cease. His experiments, however, give striking evi- dence of the general correctness of the views which I have endeavoured to elucidate. Thus he shows that a kind of osmosis takes place when two miscible fluids, as water and alcohol, are separated by a third fluid (such as essence of turpentine), or ether and chloroform separated by water. And the influence of the mtervening septum is well illustrated by an experi- ment made with alcohol and water separated by a diaphragm of porous earthenware. In this case the chief current is from the water into the spirit; but if the cylinder, after careful drying, be steeped for three or four days in castor oil and then again used, the alcohol will pass over in greatest amount into the water. A 368 Dr. A. Ransome on some of the a feeble cohesive attraction for one another, but they are the more capable on this account of exerting their molecular affini- ties for other bodies; a crystalloid therefore diffuses into a gela- tinous mass as readily as into water. During dialysis the par- ticles of the colloid cling powerfully to the substance of the sep- tum, and thus are unable to pass off into the opposite fluid; but the crystalloid readily traverses the colloid lining the pores of the membrane, and is taken up by the molecular affinities of the so- lution on the opposite side. | Molecular Attraction of Colloids and heated metals for Gases and Vapours.—Dr. Mitchell of New York (in 1830) first noticed the varying rates at which different vapours and gases will diffuse through films of india-rubber and other substances; and Dr. Draper, in his work ‘On Human Physiology’ (p. 152), makes further observations on the subject, and notices its bearing on the physiology of respiration. The same phenomena have recently been more fully investi- gated by Dr. Graham ; and his results were given in an admirable memoir to the Royal Society, and are now published in the Phi- losopbical Magazine. It will not be necessary therefore to review this work ; it will be sufficient to state that his experiments show -that different substances possess very different powers of attract- ing vapours and gases, that the attraction exerted seems to be independent of mass, that the power of attraction which can be exerted by the particles of red-hot or molten metals seems to be sufficiently great in many instances to overcome the dissipating influence of heat, and that certain gases will pass at various rates into and through the substance of these metals when their mo- lecules are so far separated as to allow the passage of liquid or gaseous particles. All these phenomena lead to one general ob- servation, which is most important so far as our present subject is concerned—that in all the actions which have been mentioned powerful molecular influences are at work, and that there is a great diversity in the degree of molecular affinity put forth by different substances. 2. Molecular conditions favourable to Catalysis. It might be anticipated that molecular actions would take place most readily when the substances involved in them are either in a fluid or gaseous condition; but in most so-called ca- talytic actions a powerful influence upon the result is generally exerted by solid substances. The researches of Messrs. Jamin and Bertrand* and Professor Magnust have proved that all solid bodies condense upon their * Phil. Mag. S. 4. vol. vi. p. 156. + Ibid. p. 337. Conditions of Molecular Action. 369 surfaces more or less of any vapour or gas to which they are exposed*, It is not difficult to understand why the mechanical condition of the solid should materially affect the result. Since molecular attraction is independent of the mass, and since its power is only exerted at very small distances, it is evident that molecular at- traction (strictly so called) is only exerted upon foreign sub- stances at the surfaces of the active body (catalyte). The second stratum of molecules will scarcely, if at all, affect substances lying on the surface. It follows, therefore, that a large extent of surface is an important assistance to molecular (catalytic) ac- tions: thus spongy or laminated bodies act more readily than dense solids. Finely divided or pulverulent substances enjoy this advantage to the utmost; but they are under favourable cir- cumstances from another cause—namely, that they present to the substances submitted to their influence an infinite number of points. Action of Points.—When a particle of matter rests upon a surface, it comes within the range of the molecular attractions of several of the particles composing that surface. It is affected not only by the molecule upon which it immediately rests, but also by those closely surrounding it ; and the influence of these last-mentioned molecules perturbs the action of the one support- ing molecule, and prevents it from exerting its full power. When, however, this molecule forms a point protruding from the surrounding surface, it is removed to that extent from the range of the disturbing forces, and its own peculiar energy is brought fully into action. This property of points is well illustrated by their power of fa- cilitating vaporization, or the release of a gas from solution. When a point is placed in a fluid in the act of vaporizing, or giving off gas which had been dissolved in it, by virtue of its undisturbed attraction for the molecules of vapour which are being formed, it soonest collects these molecules into bubbles ; and these collections of gas or vapour, therefore, at this point first attain sufficient magnitude to overcome the resistance of the surrounding medium, and ebullition starts from the pointt. * It is mteresting to observe that, of the gases employed in the researches of Messrs. Jamin and Bertrand, hydrogen was the least absorbed ; thus, in a vessel containing pounded glass and a free space of 590 cubic centims., 595 cubic centims. of hydrogen were taken in, 602 cubic centims. of air, and 645 cubic centims. of CO’. These facts are noticeable in relation to Graham’s observation (Phil. Mag. vol. xxvi. p. 422) that hydrogen can diffuse through graphite 3:8 times as rapidly as air, and Dumas’s state- ment that hydrogen will pass through the pores of a heated iron tube into nitrogen. + It is important to notice, however, that metals with rough surfaces Phil. Mag. 8. 4. Vol. 383. No, 224. May 1867. 2B 370 Dr. A. Ransome on some of the The crystallization of camphor along the striz of matter left by a cloth on a glass rod, or the formation of ice-crystals on a window-pane in the track of the cloth used in cleaning it, are fa- miliar instances of similar influences at work. Most catalytic agents probably owe some part of their power to this influence of points; many of them are employed m the form of powder; and even pounded glass or earthenware have been shown to possess catalytic powers. It is also worthy of notice that the most energetic catalytes are those in which the active element is not only finely divided, but the particles are so separated from one another that they can act alone and without any perturbing influence from others of the same kind. Thus ordinary wood-charcoal, although it will act as a catalyte, is in- ferior in power to animal charcoal, in which the molecules of carbon are separated from one another by earthy matter; and spongy platinum is similarly superior to platinum-black. Bodies also which in the colloidal form are catalytes, from possessing the property of penetrability and allowmg close con- tact, lose their power when by heat or any other agency they are coagulated or pectized, and the molecules are thus brought closer together. It seems probable that in some medicines, as grey, Dover’s, or James’s powders, the activity of the drug is in- creased by the presence of an inert body with which it is incor- porated. The therapeutic value of the fine division of medicine is a subject still requiring investigation. Friction.—It 1s a question how far the coefficient of frietion («) may depend upon the molecular as well as the cohesive at- tractions of the points which form the rough surfaces of the bodies in contact. It may perhaps be permitted to surmise that when these projecting pots are brought together, their mole- cular affinities will have some influence upon the result. 3. The Low Chemical Affinity of a Catalyte. When it is considered that the molecular forces exerted by a catalyte can only be employed when the substances to be acted upon are brought into very close contact with it (so close that if these substances had strong chemical affinities for one another they would certainly combine), and when, further, it is considered that if the catalyte united chemically with other material it would (and probably other substances) radiate more heat than when smooth. But the points which these surfaces present are not the cause of the increase of radiation; this depends rather upon the diminution of density of the sur- faces and their state of greater subdivision. According to Professor Mag- nus, “in consequence of the roughening of the surface, the amplitudes of the heat-oscillations are altered, but not their rate.” (Professor Dana in Silliman’s Journal, vol. iv.) Conditions of Molecular Action. 371 soon cease to exist as such, and would lose its catalytic property, it becomes obvious that catalytes must be chemically indifferent to the substances they act upon. And not only is this the case in fact, but we find that all the substances which have the greatest catalytic energy display chemical indifference, not alone towards those substances which they affect, but also towards or- dinary chemical reagents. Thus, among metalloids, charcoal is at once the most energetic in molecular actions and the least attracted chemically ; pounded glass and sand, compounds of silica, also rank high amongst ca- talytes. Among metals, only those placed at the highest point of the scale, as least subject to the action of oxygen (the most powerful chemical agent)—metals like platinum—these alone act catalytically, without change of chemical constitution. This fact is very clearly shown by some experiments made in the year 1834, by Dr. Charles Henry and my father, “on the Action of Metals in determining gaseous combination”*. They proved that the oxidizable metals, such as copper, cobalt, nickel, lead, iron, silver, even when in a state of minute subdivision (produced by reducing their oxides by hydrogen), did not them- selves act catalytically, but in every case their oxides possessed the power of determining the union of oxygen and hydrogen. The oxides whose power of assisting the combination of oxygen with various substances has been best observed are lime, alumina, binoxide of manganese, sesquioxide of iron, sesquioxide of chro- mium, sesquioxide of nickel, protoxide and sesquioxide of cobalt, protoxide of cadmium, hydrated sesquioxide of uranium, prot- oxide of copper, red oxide of lead, protoxide and binoxide of tin, tungstic acid, and oxide of silver. And amongst these it is in- teresting to mark that Mr. Eyre Ashby, who has most carefully studied this subject, observes that it 1s not those oxides which have an excess of oxygen, nor yet those which most readily part with it, whose influence is most felt, but “it is the sesquioxides which have the strongest tendency to produce and maintain the catalytic glow, and which do produce it in every case in which they are not decomposed by the heat necessary to begin the operation.” In relation to this condition of molecular action, it is worthy of notice that ferments, the most remarkable substances in the organic kingdom for their catalytic power, belong universally to the class of colloid bodies, one of whose chief characteristics 1s that of “ chemical indifference ”’ fF. * A paper on the subject was read before the Literary and Philosophical Society by Dr. Henry, and published in the London and Edinburgh Phi- losophical Magazine and Journal of Science for May 1835. + Even during those fermentations in which certain changes are pro- 2B2 372 Dr. A. Ransome on some of the 4. The Molecules of the Catalyte must be free— That is, must be untainted by any stain of vapour or of any other substance ; otherwise the molecular power of the catalyte will be in some measure neutralized by being exerted upon the substance which soils it. This condition is a very important one. It is probable that upon all bodies, and especially upon detached molecules, there exists a layer of vapour. As I have before stated, Professor Magnus has shown that the most various vapours condense on the surface of solid bodies; and this fre- quently takes place to such an extent that, by careful thermo- electric measurements, he could detect the rise of temperature due to their condensation. The experiments of Messrs. Jamin and Bertrand on the condensation of gases and vapours by pow- dery substances have also been quoted; and the extreme diffi- culty of thoroughly cleansing glass and silver plates from stain is familiar to all photographers. Professor Faraday’s well-known experiment of producing union of oxygen and hydrogen by means of a platinun: plate, requires for its success the most ac- curate cleansing of the plate. When heat quickens a molecular action, as in most catalytic experiments, familiarly in the ordinary platinum lamp, the in- tensity of the subsequent action, when the heat is withdrawn, is probably partly owing to the cleansing-power of the heat, which drives off the layer of vapour with which the catalyte was sur- rounded. The same favouring condition is also probably pre- sent when an acid is assisted in its attack upon a metal for which it has little affinity, by the presence of another more attractive metal alloyed with it. To take one instance, when nitric acid dissolves the platinum in an alloy of platinum with another metal, apart from galvanic action, it seems likely that during the operation the acid is brought into much closer contact with separated particles of the indifferent material than would otherwise be possible, and thus comes within the sphere of chemical combining-forces. duced in, or whichat any rate are accompanied by a decomposition of, the fer- ment, it is probable that the want of chemical energy in the products of the decomposition may permit molecular forces to play their part. Ferments are bodies containing nitrogen, a substance which not only displays very little combining-power, but confers the same indifference upon many of its com- pounds. An observation of the emiment chemist Berthelot gives peculiar point to this remark. He noticed that in fermenting sugars, having the general formula Cen m(HO), by means of animal nitrogenous substances, such as caseine (together with an alkaline carbonate to neutralize any acid as it is formed), decomposition tovk place simultaneously in the sugar (glycerine, mannite, &c.) and in the ferment. The ferment, however, did not rot, but lost the whole of its nitrogen. (Chemist, vol. iv. p. 580.) Conditions of Molecular Action. 373 The nascent state of Bodies.—The great energy of bodies when recently formed, and before their evolution is completed, may be partly due to their greater concentration at this time; but it seems likely that the freedom of their particles, at the moment of their formation, from all taint of other matter may enable them to put forth all the molecular vigour they possess, and assist them to overcome obstacles which would otherwise prevent them from forming a chemical combination*. Catalytic actions.—It will have been noticed that, under the head of each condition of molecular action, allusion has been been made to some form or other of catalytic action. This term has been made to include a very wide range of both physical and chemical reactions ; but strictly its use should be confined to those cases in which a substance (the catalyte) brings about che- mical or physical changes without being itself in any way altered. Thus defined, it would apply to all those actions carried on by means of the catalytes which have already been enumerated—the oxidations of ammonia, of alcohols, ethers, essential oils, and other hydrocarbons, and the decomposition of chlorate of potash by means of binoxide of manganese or the sesquioxide of iron. When these operations are attentively considered, it will be seen that in all of them the conditions we have already examined are fulfilled. Catalytes are substances having little or no che- mical affinity for the materials upon which they act ; their mole- cules are loosely aggregated so as to be able to act independently ; in nearly every case their energy is increased by the cleansing of their surfaces from all taint of other matter. The only re- maining condition, their molecular affinity for the substances acted upon, may be inferred from what has gone before respect- ing the enormous power possessed by several of them of absorb- ing large quantities of certain gases. Upon the hypothesis that catalysis depends purely upon molecular force, it is not difficult to understand why a very small portion of a catalyte is sufficient to produce changes in a large quantity of suitable material: the molecular action once completed upon one part of the substance is not necessarily exhausted. If the substances formed by con- tact with the catalyte have less affinity for it than the original material had, they will readily be given up, the molecular power of the catalyte will be again set free, it will attract fresh portions of the more appropriate material, and the action may go on almost indefinitely. * This observation must have at least equal weight in reference to vital as to purely physical molecular phenomena ; and we can hardly doubt that the power of constantly brmging forth newly formed untainted material in the processes of vital growth must have a most important influence in pro- ducing physiological reactions. 374 On some of the Conditions of Molecular Action. But there is probably more than one influence at work in the case of certain of the oxidations by catalysis which are effected by the aid of metallic oxides and heat. From the accounts of the process given by Mr. Eyre Ashby* and Dr. Henryf, it ap- pears most probable that the heat by which the action is started drives off from the pulverulent oxide all stain or taint of foreign vapour, and leaves its particles free to exercise their molecular energy, and to draw closely to them the vapours freshly sub- mitted to them. In certain cases the approach is so close that the chemical affinity of the organic vapour for oxygen overcomes that of the metal, and reduction of the oxide and oxidation of the vapour take place simultaneously. In the case of silver this accident only increases the energy of the operation, probably from the well-known attraction of silver for oxygen; but with most other metals (e. g. cadmium) the action is not carried on until the nascent metal has attracted fresh oxygen from the air, and nascent oxide is again ready to carry on the catalytic process. It is evident, however, that even in these cases, although che- mical actions are going on in the catalyte, yet the purely mole- cular force plays an important part in producing the result. I have been led to make these few and imperfect observations upon a difficult and obscure subject, chiefly because I believe that it is only by a careful study of molecular physics that we can hope to gain any great advance in our knowledge of the working of organic life. In biology we have to deal for the most part, not with ordinary chemical processes or affinities, but with sub- stances whose chemical reactions are continually modified by va- riations in their molecular conditiont. By the study of the phy- sical relations of these bodies, we may hope, in time, to understand something of the various forms of material which enter into or- ganized structures, and to discover the mode in which, by certain arrangements of their particles, potential energy can be stored up ready to be given out when required. We may also in the same direction learn a little of the, at present, mysterious working of those bodies called ferments, which are so active in the living body. It seems probable at least that amongst the numerous forces at work in the living frame, and coordmated and governed by the principle of life, we must rank the molecular energies of various materials continually supplied in a nascent and active condition ; and thus the study of their physical properties may perhaps be permitted to find a place even in purely physiologica! researches. * Phil. Mag. S. 4. vol. x. p. 52. + Ibid. 8.3. May 1835. { See paper “‘On the Physiological Relations of Colloid Substances, ’ by the author, in the British Medical Journal, February 3, 1866. Bocca L. On the Action of Sonorous Vibrations on Gaseous and Liquid Jets. By Professor Tynpat1, F.R.S. &c. [With the permission of Professor Tyndall we print the fol- lowing extract from the sixth lecture of his work on Sound, now on the point of publication. A portion of the extract has already appeared in an abbreviated form in the Philosophical Magazine. We have also to thank Professor Tyndall for the use of the woodcuts which illustrate the paper.—Eps. | N a former lecture I referred to the oscillations of water in a bottle as revealing the existence of vibrations of a definite period in the general jar of a railway train. The fish-tail flames in some of our metropolitan railway carriages are far more sen- sitive acoustic reagents. If you pay the requisite attention, you will find single flames here and there jumping in synchronism with certain tremors of the tram. A flame, for example, having a horizontal edge when the train is still, will, during the motion, periodically thrust forth a central tongue, and continue to jump as long as a special set of vibrations is present. It will subside when those vibrations disappear, and jump again when they are restored. When the train is at rest, the tapping of the glass shade which surrounds the flame rarely fails, when it is sensitive, to cause it to jump. This action of sound upon a naked fish-tail flame was first ob- served by Professor Leconte at a musical party in the United States. His observation is thus described :—“ Soon after the music commenced, I observed that the flame exhibited pulsations which were exactly synchronous with the audible beats. This phenomenon was very striking to every one in the room, and espe- cially so when the strong notes of the violoncello came in. It was exceedingly interesting to observe how perfectly even the trills of this instrument were reflected on the sheet of flame. A deaf man might have seen the harmony. As the evening advanced, and the diminished consumption of gas in the city increased the pressure, the phenomenon became more conspicuous. The jump- ing of the flame gradually increased, became somewhat irregular, and finally it began to flare continuously, emitting the charac- teristic sound imdicating the escape of a greater amount of gas than could be properly consumed. I then ascertained, by expe- riment, that the phenomenon did not take place unless the dis- charge of gas was so regulated that the flame approximated to the condition of flaring. I likewise determined by experiment that the effects were not produced by jarring or shaking the floor and walls of the room by means of repeated concussions. Hence it is obvious that the pulsations of the flame were not owing to 376 Prof. Tyndall on the Action of Sonorous indirect vibrations propagated through the medium of the walls of the room to the burning apparatus, but must have been pro- duced by the direct influence of aérial sonorous pulses on the burning jet” * The significant remark that the jumping of the flame was not observed until it was near flaring suggests the means of repeat- ing the experiments of Dr. Leconte; while a more intimate knowledge of the conditions of success enables us to vary and exalt them in a striking degree. Before you burns a bright candle-flame: I may shout, clap my hands, sound this whistle, strike this anvil with a hammer, or explode a mixture of oxygen and hydrogen: though sonorous waves pass in each case through the air, the candle is absolutely sensible to the sound; there isno motion of the flame. I now urge from this small blowpipe a narrow stream of air through the flame of the candle, producing thereby an incipient flutter, and reducing at the same time the brightness of the flame. When I now sound a whistle the flame jumps visibly. The experiment may be so arranged that, when the whistle sounds, either the flame shall be restored almost to its pristine brightness, or the amount of light it still possesses shall dis- appear. . The blowpipe-flame of our laboratory is totally unaffected by Fig. 1. fi the sound of the whistle as long as no air is urged through it. By properly tempering the force of the blast, I obtain a flame of the shape shown in fig. 1, the blast not being sufficiently pow- erful to urge the whole of the flame forwards. On sounding the whistle the erect portion of the flame drops down, and while it continues to sound we have a flame of the form shown in fig. 2. Here, moreover, is a fish-tail flame, which burns brightly and * Phil. Mag. March 1858, p. 235. Vibrations on Gaseous and Liquid Jets. 377 steadily, refusing to respond to any sound, musical or unmusical. I urge against the broad face of the flame a stream of air from a blowpipe. The flame is cut in two by the air; and now, when the whistle is sounded, it instantly starts. A knock on the table causes the two half-flames to unite and form for an instant a single flame of the ordinary shape. By a slight variation of the experiment, the two side flames disappear when the whistle is sounded, a central luminous tongue being thrust forth in their stead. Before you now is another thin sheet of flame, also issuing from a common fish-tail burner (fig. 8). You might sing to it, varying the pitch of your voice; no shiver of the flame would be visible. You might employ pitch-pipes, tuning-forks, bells, and trumpets, with a like absence of all effect. A barely perceptible motion of the interior of the flame may be noticed when this shrill whistle is blown close to it. By turning the cock more fully on I bring the flame to the verge of flarmg. And now, when the whistle is blown, you see an extraordinary appearance. The flame thrusts out seven quivering tongues (fig. 4). As long as the sound continues, the tongues jut forth, being violently agi- tated ; the moment the sound ceases, the tongues disappear and the flame reassumes the form of fig. 3. Fig. 3. Fig. 4. Passing from a fish-tail to a bat’s-wing burner, we obtain this broad steady flame (fig. 5). It is quite insensible to the loudest sound which would be tolerable here. The flame is fed from a small gas-holder, which places a greater pressure at my 378 Prof. Tyndall on the Action of Sonorous disposal than that existing in the pipes of the Institution*. I enlarge the flame; and now a slight flutter of its edge answers to Fig. 5. the sound of the whistle. Finally I turn on gas until the flame is on the point of roarimg, as flames do when the pressure is too great. On sounding the whistle, the flame roars, and suddenly assumes the form shown in fig. 6. | When a distant anvil is struck with a hammer, the flame in- stantly responds by thrusting forth its tongues. An essential condition to entire success in these experiments disclosed itself in the following manner. I was in a room illu- minated by two fish-tail flames. One of them jumped to a whistle, the other didnot. The gas of the non-sensitive flame was turned off, additional pressure being thereby thrown upon the other flame; it flared, and its cock was turned so as to lower the flame. It now proved non-sensitive, however close it might be brought to the point of flarmg. The narrow orifice of the half- turned cock appeared to interfere with the action of the sound. When the gas was turned fully on and the flame lowered by opening the cock of the second burner, it became again sensitive. Up to this time a great number of burners had been tried, inclu- ding those with single orifices ; but with many of them the action was nil. Acting, however, upon the hint conveyed in this ob- servation, the pipes which fed the flames were widely opened ; the consequence was that our most refractory burners were thus rendered sensitive. The observation of Dr. Leconte is thus easily and strikingly illustrated ; in our subsequent and far. more delicate experiments the precaution just referred to is still more essential. * A gas-bag properly weighted also answers for these experiments. Vibrations on Gaseous and Liquid Jets. 379 Mr. Barrett, late laboratory assistant in this place, first ob- served the shortening of a tall flame issuing from the single orifice of this burner when the higher notes of a circular plate were sounded ; and, by the selection of more suitable burners, he afterwards succeeded in rendering the flame extremely sen- sitive*. Observing the precaution above adverted to, we can readily obtain in an exalted degree the shortening of the flame. It is now before you, being 18 inches long and smoking copi- ously. When I sound the whistle the flame falls to a height of 9 inches, the smoke disappearing, and the flame increasing in brightness. A long flame may be shortened and a short one lengthened, according to circumstances, by these sonorous vibrations. Here, for example, are two flames issuing from rough burners formed from pewter tubing. The one flame (fig. 7) is long, straight, and smoky; the other (fig. 8) is short, forked, and brilliant. On sounding the whistle, the long flame becomes short, forked and brilliant, as in fig. 9; the forked flame becomes long and smoky, as in fig. 10, As regards, therefore, their response to the sound of the whistle, one of these flames is the complement of the other. Fig. 11. Fig. 12. * For Mr. Barrett’s own account of his experiments I refer the reader to the Philosophical Magazine for March 1867. 380 Prof. Tyndall on the Action of Sonorous In fig. 11 is represented another smoky flame, which, when the whistle sounds, breaks up into the form shown in fig. 12. The foregoing experiments illustrate the lengthenmg and shortening of flames by sonorous vibrations. They are also able to produce rotation. I have here several home-made burners, from which issue flat flames, each about 10 inches high, and 3 inches across at their widest part. The burners are purposely so formed that the flames are dumpy and forked. When the whistle sounds, the plane of each flame turns 90° round, and continues in its new position as long as the sound continues. A flame of admirable steadiness and brilliancy now burns be- fore you. It issues from a single circular orifice in a common iron nipple. This burner, which requires great pressure to make its flame flare, has been specially chosen for the purpose of en- abling you to observe with distinctness the gradual change from apathy to sensitiveness. The flame is now 4 inches high, and is quite indifferent to sound. By increasing the pressure I make its height 6 inches; it is still indifferent. I make it 12 inches; a barely perceptible quiver responds to the whistle. I make it 16 or 17 inches high; and now it jumps briskly the moment the anvil is tapped or the whistle sounded. I augment the pressure ; the flame is now 20 inches long, and you observe a quivering at intervals, which announces that it is near roarmg. A slight increase of pressure causes it to roar, and shorten at the same time to 8 inches. I diminish the pressure a little; the flame is again 20 inches long, but it is on the point of roaring and short- ening. like the singing flames which were started by the voice, it stands on the brink of a precipice. The proper sound pushes it over. It shortens when the whistle sounds, exactly as it did when the pressure was in excess. The action reminds one of the story of the Swiss muleteers, who are said to tie up their bells at certain places lest the tinkle should bring an avalanche down. ‘The snow must be very delicately poised be- fore this could occur. I believe it never did occur; but our flame illustrates the principle. We bring it to the verge of falling, and the sonorous pulses precipitate what was already imminent. This is the simple philosophy of all these sensitive flames. When the flame flares, the gas in the orifice of the burner has been thrown into vibration ; conversely, when the gas in the orifice is thrown into vibration, the flame, if sufficiently near the flarmg point, will flare. Thus the sonorous vibrations, by acting on the gas in the passage of the burner, become equivalent to an aug- mentation of pressure in the holder. In fact we have here re- vealed to us the physical cause of flaring through excess of pres- sure, which, common as it is, has never, I believe, been hitherto explained. In the orifice of the burner the gas encounters Vibrations on Gaseous and Liquid Jets. 381 friction, which, when the force of transfer is sufficiently great, throws the issuing stream into the state of vibration that pro- duces flaring. It is because the flaring is thus caused that an almost infinitely small amount of energy, applied in the form of vibrations of the proper period, can produce an effect equiva- lent to a considerable increase of pressure. Augmentation of pressure is, in fact, a comparatively clumsy means of causing a flame to flare*. All sounds are not equally effective on the,flame; waves of special periods are required to produce the maximum effect. The effectual periods are those which synchronize most nearly with the waves produced by the friction of the gas itself against the sides of its orifice. With some of the flames which you have already seen, a low deep whistle is more effective than a shrill one. With the flame now before you, the exciting tremors must be very rapid, and the sound consequently shrill. I have here a tuning-fork which vibrates 256 times in a second, emitting a clear and forcible note. It has no effect upon this flame. Here also are three other forks, vibrating respectively 320, 384, and 512 times in a second. Not one of them produces the slightest impression upon the flame. But, besides their fundamental tones, these forks, as you know, can be caused to yield a series of overtones of very high pitch. I sound this series: the vibra- tions are now 1600, 2000, 2400, and 3200 per second respect- ively. The flame jumps in response to each of these sounds, the response to the highest sound of the series being the most prompt and energetic of all. To the tap of ahammer upon a board the flame also responds ; but to the tap of the same hammer upon an anvil the response is much more brisk and animated. The reason is, that the clang of the anvil is rich in the higher tones to which the flame is most sensitive. ’ The powerful tone obtained when our inverted bell is reinforced by its resonant tube has no power over this flame. The bell is now sounding, but the flame is unmoved. But when I bring a half- penny into contact with the vibrating surface, the consequent rattle contains the high notes to which the flame is sensitive. It instantly shortens, flutters, and roars when the coin touches the bell. I hold in my hand a smaller bell, the hammer of * As already remarked, a candle-flame is caused to flutter by its rapid motion through the air; and the vertical motion of the flame in the expe- riments just described may help to produce the flaring. The principal cause, however, I believe to be that above assigned. The gas within the burner, and the air outside it, form a continuous medium, through which the effective vibrations are transmitted both to the flame and the orifice that feeds it. 382 Prof. Tyndall on the Action of Sonorous which is worked by clockwork. I send my Fig. 13. assistant to the most distant part of the gal- lery, where he detaches the hammer. The strokes follow each other in rhythmic suc- cession, and at every stroke the flame falls from a height of 20 to a height of 8 inches, roaring as it falls. The rapidity with which sound is propa- gated through air is well illustrated by these experiments: there is no sensible interval between the stroke of the bell and the duck- ing of the flame. When the sound acting on the flame is of very short duration, a curious and instructive effect is observed. The sides of the flame halfway down and lower are seen suddenly fringed by luminous tongues, the central flame remaining apparently undisturbed in both height and thickness. The flame, both in its normal state and with its fringes, is shown in fig. 13. The effect is due tothe retention of the impression upon the retina. The flame actually falls as low as the fringes, but its recovery is so quick that to the eye it does not appear to shorten at all*. The most marvellous flame hitherto discovered is now before you. It issues from the single orifice of a steatite burner, and reaches a height of 24 inches. The slightest tap on a distant anvil reduces its height to 7 inches. When I shake this bunch of keys the flame is violently agitated and emits a loud roar. The dropping of a sixpence into a hand already containing coin knocks the flame down. I cannot walk across the floor without agitating the flame: the creaking of my boots sets it in violent commotion. The crumpling or tearing of a bit of paper, or the rustle of a silk dress, does the same. It is startled by the patter of araindrop. I hold a watch near the flame: nobody hears its ticks; but you all see their effect upon the flame: at every tick it falls. The winding up of the watch also produces tumult. The chirrup of a distant sparrow shakes the flame down; the note of acricket would do the same. From a distance of 30 yards I have chirruped to this flame, and caused it to fall and roar. I repeat a passage from Spenser: the * Numerous modifications of these experiments are possible. Other in- flammable gases than coal-gas may be employed. Mixtures of gases have also been found to yield beautiful and striking results. An infinitesimal amount of mechanical impurity has been found to exert a powerful influence. Vibrations on Gaseous and Liquid Jets. 383 flame picks certain sounds from my utter- Mig. 14. ance ; it notices some by the slighest nod, to others it bows more distinctly ; to some its obeisance is very profound, while to many sounds it turns an entirely deaf ear. In fig. 14 this brilliant flame is shown, tall and ‘straight. On chirruping to it, or on shaking a bunch of keys within a few yards of it, it falls to the size shown in fig. 15, the whole length ab of the flame being suddenly abolished. The hght at the same time is practically destroyed, a pale and almost non- luminous residue of the flame alone remaining. These figures are taken from photographs of the flame. In our experiments down stairs we have called this the “vowel flame,” because the differ- ent vowel-sounds affect it differently. We have already learned how these sounds are formed— that they differ from each other through the admixture of higher tones with the funda- mental one. It is to these tones, and not to the fundamental one, that our flame is sensi- tive. I utter aloud and sonorous v, the flame remains steady; I change the sound to 0, the flame quivers; I sound £, and now the flame is strongly affected. I utter the words boot, boat, and beat in succession. ‘To the first there is no response ; to the second the flame starts; but by the third it is thrown into greater com- motion; the sound Ah! is still more powerful. Did we not know the constitution of vowel- sounds, this deportment would be an insoluble enigma. As it is, however, the flame is a de- monstrator of the theory of vowel-sounds. It is most sensitive to sounds of high pitch; hence we should infer that the sound Ah! contains higher notes than the sound £, that = contains higher notes than o, and o higher notes than uv. I need not say that this agrees perfectly with the analysis of Helmholtz. This flame is peculiarly sensitive to the utterance of the letter s. If the most distant person in the room were to favour me with a “hiss,” the flame would instantly sympathize with him. A hiss contains the elements that most forcibly affect this flame. The gas issues from its burner with a hiss, and an external sound of this character is therefore exceedingly effective. I 384: Prof. Tyndall on the Action of Sonorous hold in my hand a metal box containing compressed air. I turn the cock for a moment, so as to allow a puff to escape: the flame instantly ducks down, not by any transfer of air from the box to the flame; for I stand at a distance which utterly excludes this idea; it is the sound that affects the flame. I send a man to the most distant part of the gallery, where he permits the compressed air to issue in puffs from the box; at every puff the flame suddenly falls. Thus the hiss of the issuing air at the one orifice precipitates the tumult of the flame at the other. , Finally, I place this musical box upon the table, and permit it to play. The flame behaves like a sentient creature ; bowing slightly to some tones, but courtesying deeply to others. I at one time intended to approach this subject of sensitive flames through a series of experiments which, had the flames not been seen, would have appeared more striking than I can expect them to be now. It is not to the flame, as such, that we owe the phenomena which have just been deseribed. Kffects substantially the same are obtained when a jet of unignited gas, of carbonic acid, hydrogen, or even air itself, issues from an orifice under proper pressure. None of these gases, however, can be seen in its passage through air; and therefore we must associate with them some substance which, while sharing their motions, will reveal those motions to the eye. The method which we have from time to time em- ployed in this place, of rendering aérial vortices visible, is well known to many of you. By tapping a membrane which closes the broad mouth of a large funnel filled with smoke, we obtain beautiful smoke-rings, which reveal the motion of the air. By associating smoke with our gas-jets in the present instance, we can also trace their course ; and when this is done, the unignited gas proves as sensitive as the flames. The smoke-jets jump, they shorten, they split into forks, or lengthen into columns when the proper notes are sounded. The experiments are made in this way. Underneath this gasometer are placed two small basins, the one containing hydrochloric acid and the other ammonia. Fumes of sal-ammoniac are thus copiously formed, and mingle with the gas contained in the holder. We may, as already stated, operate with coal-gas, carbonic acid, air, or hydrogen: each of them yields good effects. Here also our ex- cellent steatite burner maintains that supremacy which it exhi- bited with the flames. From it I can cause to issue a thin column of smoke. On sounding the whistle, which was so effective with the flanges, it is found ineffective. When, more- over, the highest notes of a series of Pandean pipes are sounded, they are also ineffective. Nor will the lowest notes answer. Vibrations on Gaseous and Liquid Jets. 385 But when a certain pipe, which stands about the middle of the series, is sounded, the smoke-column drops, forming a short stem with a thick, bushy head. It is also pressed down, as by a vertical wind, by a knock upon the table. At every tap it falls. A stroke on an anvil, on the contrary, produces little or no effect. In fact, the notes here effective are of a much lower pitch than those which were most efficient in the case of the flames. The amount of shrinkage exhibited by some of these smoke- columns, in proportion to their length, is far greater than that of the flames. A tap on the table causes a smoke-jet eighteen inches high to shorten to a bushy bouquet with a stem not more than an inch in height. The smoke-column, moreover, responds to the voice; a cough knocks it down: and it dances to the tune of a musical box. Some notes cause the mere top of the smoke-column to gather itself up into a bouquet; at other notes the bouquet is formed midway down; while notes of more suitable pitch cause the column to contract itself to a cumulus not more than an inch above the end of the burner. As the music continues, the action of the smoke-column consists of a series of rapid leaps from one of these forms to another*. Various forms of the dancing jet are shown in fig. 16. In perfectly still air these Fig. 16. slender smoke-columns rise sometimes to a height of two feet, apparently vanishing ito air at their summits. Even the most sensitive flame then falls far behind them in delicacy; and though less striking, the smoke wreaths are often more graceful than the flames. Every word and every syllable, for example, of the foregoing stanza from Spenser tumbles such a smoke-jet into confusion. To produce such effects a perfectly tranquil atmosphere is necessary. Flame-experi- ments are possible in an atmosphere where smoke-jets are utterly unmanageable. [These experiments on smoke-jets were commenced nearly a year ago. Their execution was entrusted to Mr. Barrett, from * Could the jets of unignited gas be seen without any admixture of smoke, their sensitiveness, I doubt not, might be increased. Phil. Mag. 8. 4. Vol. 83. No. 224. May 1867. 2C 386 Prof. Tyndall on the Action of Sonorous whose notes, written last June, I make the following ex- tract :-— “From many experiments made with care the following fame were obtained :— “1. A jet of air rendered visible by suspended particles of chloride of ammonium, when moving slowly, leaves the orifice from which it is forced as a slender stream of the diameter of the orifice, and of equal thickness throughout a length of from 6 to 12 inches. It then spreads out in an inverted cone. When at a higher velocity the apex of the cone approaches the orifice, but maintains the same angular opening. At the greatest velocity the cone is formed almost immediately as the smoke leaves the orifice. ‘2. The appearances of a jet of air are in all respects the same as those of a jet of steam. “3. When a tuning-fork is held near to this stream it causes the cone to appear where it is held, thus instantly reducing the height of the stream. If held near the orifice the cone is no longer one, but is split mto ¢wo, and each of the two streams issuing from the central stream is seen to possess a kind of involving motion. “4, The splitting of the jet depends on the velocity of the current in relation to the pitch of the fork. “5. With a very low velocity, giving a long parallel line ot ene Ut, will not divide the column, but U¢, will easily do so. Increasing the velocity, the higher notes are all capable of splitting the stream, whilst the lower notes lose their power. “6. At a certain velocity the issuing air often is heard to sound. When this takes place, the column of air is seen to be feebly bifurcated near its root. A tuning-fork in unison with the note (Uf, or Mis) augments the intensity with which the streams diverge. The angle of divergence in all cases re- mains about the same, viz. about 60°. “7. By tapping the table or support of the jet, the cntlee is caused to issue in pulses, giving the smoke as it rolls away a most beautifully crimped appearance. *°8, The jet of smoke can be best seen by reflecting the sun- light on it, and shielding the eyes from the direct glare. “9, The image of the jet, single and bifurcated, can be dis- tinctly seen by its shadow, and can be cast on a screen by a short- focus lens. “10, The bifurcation occurs in the plane of the prongs of the tuning-fork. This is invariably the case. “11. The stream is always easier to split near its root, and sometimes can only be split there. “12, When the jet is sonnding, the stream of smoke is often Vibrations on Gaseous and Liquid Jets. 387 split into three, one of the divisions being subdivided; and generally the subdivision occurs at right angles to the plane of the other” *.] We have thus far confined ourattention to jets of ignited and unignited coal-gas, of carbonic acid, hydrogen, and air. We will now turn to jets of water. And here a series of experi- ments, remarkable for their beauty, have long been known, which claim relationship to those just described. These are the expe- riments of Félix Savart on liquid veins, which have been repeated, verified, and modified in various ways in this place. If the bottom of a vessel containing water be pierced by a circular orifice, the descending liquid vein will exhibit two parts which are unmistakeably distinct. The part of the vein nearest the orifice is steady and limpid, presenting the appearance of a solid glass rod. It decreases in diameter as it descends, reaches a point.of maximum contraction, from which point downwards it appears turbid and unsteady. The course of the vein, more- over, is marked by periodic swellings and contractions. Savart has represented the vein in the manner shown in fig. 17. In this figure a is the orifice end of the vein, the part a n is limpid and steady, while all the part below n is in a state of quivering motion. This lower part of the vem appears continu- ous to the eye; still, when the finger is passed rapidly across it, it is sometimes not wetted. This, of course, could not be the case if the vein were really continuous. The upper portion of the vein, moreover, intercepts vision ; the lower portion, even when the liquid is mercury, does not. In fact, the vein resolves itself at n into liquid spherules, its apparent continuity being due to the retention of the impressions made by the falling drops upon the retina. If the drops succeed each other in in- tervals of a tenth of a second or less, then, before the impres- sion made by any drop vanishes, it is renewed by its successor, and no rupture of continuity can be observed. If, while look- ing at the disturbed portion of the vein, the head be suddenly lowered, the descending column will be resolved for a moment into separate drops. Perhaps the simplest way of reducing the vein to its constituent spherules is one long ago adopted by myself—namely, to illuminate the vein, in a dark room, by a succession of electric flashes. Every flash reveals the drops as if they were perfectly motionless in the air. Could the appearance of the vein illuminated by a single flash be rendered permanent, it would be that represented in fig. 18. And here we find revealed the cause of those swell- ings and contractions which the disturbed portion of the vein * The point of departure of these experiments were those of Dr. Young (Sound and Light,” Phil. Trans. 1800). The experiments with the tall smoke-jets were for the most part executed by Mr. Barrett’s successor, 2C2 388 Prof. Tyndall. on the Action of Sonorous exhibits. The drops, as they Fig. 17. Fig. 18. Fig. 19. descend, are contimually chan- a a a ging their forms. When first detached from the end of the limpid portion of the vein the drop is a prolate spheroid, with its longest axis vertical. Buta liquid cannot retain this shape if abandoned to the forces of its own molecules. The spheroid seeks to become a sphere. The longer diameter therefore short- ens; but, like a pendulum, which seeks to return to its position of rest, the contraction of the verti- cal diameter goes too far, and the drop becomes a transversely ob- late spheroid. Now the con- tractions of the jet are formed at those places where the long- est axis of the drop is vertical, while the swellings appear where the longest axis is horizontal. It will be noticed that between every two of the larger drops is a third of much smaller dimen- sions. Whenever a large drop is detached, by a kind of kick on the part of the retreating vem, a little satellite is shaken after it. According to Savart, their appearance is invariable. 8 This breaking up of a liquid i vein into drops has been a sub-. : ject of much discussion. I hold it to be due to the tremors im- || ® parted to the water by its friction against the boundaries of its ori- fice. To this point Savart traced its pulsations, though he did not think that friction was their cause. Whatever their cause | may be, the pulsations exist, and | they are powerfully influenced by sonorous vibrations, which render the limpid portion of the vein shorter than it would otherwise be. In the midst of a large city it is hardly possible to obtain the requisite aérial tranquillity Vibrations on Gaseous and Liquid Jets. 389 for the full development of the continuous portion of the vein ; still Savart was so far able to withdraw his vein from the influ- ence of such irregular vibrations that its impid portion became elongated to the extent shown in fig. 19. Fig. 17, it will be understood, represents the vein exposed to the irregular vibra- tions of the city of Paris, while fig. 19 represents a vein pro- duced under precisely the same conditions, but withdrawn from those vibrations. The drops into which the vein finally resolves itself are inci- pient even in its limpid portion, announcing themselves there as annular protuberances, which become more and more pronounced, until finally they separate. Their birthplace is the orifice itself; and under even moderate pressure they succeed each other with sufficient rapidity to produce a feeble musical note. By permit- ting the drops to fall upon a membrane, the pitch of this note may be fixed ; and now we’ come to the point which connects the - phenomena of liquid veins with those of sensitive flames and. smoke-jets. If a note in unison with that of the vein be sounded near it, the limpid portion instantly shortens : the pitch may vary to some extent, and still cause a shortening; but the unisonant note is the most effectual. Savart’s beautiful experiments on vertically descending veins have recently been repeated in our laboratory with striking effect. From a distance of 80 yards the limpid portion of a vein has been shortened by the sound of an organ-pipe of moderate intensity but of the proper pitch. The excellent French experimenter also caused his vein to issue horizontally and at various inclinations to the horizon, and found that in certain cases sonorous vibrations were competent to cause a jet to divide into two or three branches. In these ex- periments, the liquid was permitted to issue through an ori- fice in a thin plate. Instead of this, however, we will resort to our favourite steatite burner; for with water also it asserts the same mastery over its fellows that it exhibited with flames and smoke-jets. It will, moreover, reveal to us some entirely novel results. By means of an india-rubber tube the burner is con- nected with the water-pipes of the Institution, and by pointing it obliquely upwards, we obtain a fine parabolic jet, fig. 20. At a certain distance from the orifice, the vein resolves itself into spherules, whose motions are not rapid enough to make the vein appear continuous. At the vertex of the parabola the spray of drops is more than an inch in width, and further on they are still more widely scattered. On sweeping a fiddle-bow across a tuning-fork of the proper pitch, the scattered drops, as if drawn together by their mutual attractions, instantly close up and form an apparently continuous liquid arch some feet in height and span, fig.21. As longas the proper note is maintained the vein looks 390 Action of Sonorous Vibrations on Gaseous and Liquid Jets. like a frozen band, so motionless does it appear. On stopping the fork, the arch is shaken asunder, and we have the same play VA » \ y ~ “N . In the introduction to my memoir I discuss the previous experi- ments on the propagation of sound in the atmosphere; I reduce them to zero by means of Regnault’s coefficient of expansion, and make at the same time the probable correction in each case for the hygrometric state of the air. Of eight numbers representing the results, five are between 332 and 332°44 metres. On the other hand, the number obtained in 1822 by Arago and the Bureau des Longitudes, agrees almost exactly with my estimate. The English astronomer Goldingham’s number(331°1 metres) is very near Arago’s number. Experiments made in the open air on a base of several kilometres can clearly only inspire a very limited degree of confidence, owing to the considerable uncertainty which must prevail as to the true value of the temperature of the air in the path of the sonorous im- pulse. And the error in this respect is the more to be feared, as most of these experiments have been made during the night. Now the researches of modern physicists, such as MM. Babinet, Becquerel, Martens, &c., have proved the existence of a maximum temperature during the night extending to a greater or less height. And Mr. Glaisher’s balloon-ascents during the night have shown that the temperature often continues to increase for considerable heights. The influence of this cause would be to give velocities which are too great ; and it is exactly the smallest of the numbers found for the propagation in free air which is nearest to that I found for the propagation in a cylinder. Hence it is probable that the two velocities of propagation, spherical and cylindrical, are equal; but to obtain a definite solution of this question it would be necessary to work in the atmosphere on a smal] basis, so as to be able completely to study the distribu- tion of temperature in the space. My experimental method is eminently fitted for such an investigation; I had arranged ap- paratus with this view; but the perfect calm of the. atmosphere /which is necessary for the working appears difficult to meet with in our climates.—Comptes Rendus, March 4, 1867. 4.00 Intelligence and Miscellaneous Articles. NOTE ON THE THEORY OF TIDAL FRICTION. BY D. D. HEATH, M.A. To the Editors of the Philosophical Magazine and Journal. Kitlands, Dorking, GENTLEMEN, April 12, 1867. I have only today seen a short criticism on my March paper, by Mr. Stone. I think he will see, on reconsideration, that there is no inconsis- tency in my treatment of the orders of small magnitudes. In the first investigations I am dealing with dinear magnitudes ; and I believe I keep them in due subordination. In (11), which Mr. Stone com- ments upon, I am concerned with a moment, or product of volume, accelerating force, and leverage, and I compare two quantities of this kind together. As this is the part of my paper which is most likely to be gene- rally interesting, I may perhaps be allowed to restate its purport. On the assumptions which I have borrowed from Mr. Airy, the tide-wave, with friction, will lie obliquely at a certain angle 0 to the moon’s position. If we imagine it to become momentarily rigid and attached to the earth, the moon’s action will tend to produce rotation westward, or check the actual eastward rotation; and the moment of this action I calculate as 2gHe sin 26(1-+«)z. If the rigi- dity continued, the obliquity, and consequently the moon’s action, would change. But in fact the oscillatory motion of the water is such as to keep the ridge always in the same relative place. And the question then is, Does the reaction of friction (supposing it to act as required by Mr. Airy’s theory) produce the same effect on the earth as would be produced at each moment by a rigid wave-shape ? And my answer is that the effect of such reaction is a force whose 2 moment is Jme (1+«)z,—a quantity not only of the same order of K magnitude, but identical with the former one, as appears by the pre- vious calculation. In the investigation, v is essentially the oscillatory velocity which produces the wave-shape. Iftherefore there is a permanent current (which I neither affirm nor deny), the force of friction will not be jv, as we have supposed, but /(V +v), where V is the velocity of the current; and I fear the whole matter, when friction is taken account of, may require reexamination. I take this opportunity of requesting the readers of my original paper to strike out the latter part of the paragraph (4, a) as thought- lessly written. ‘The reason for taking the force set free as simply vertical and —2nv is, that we have just before shown that the whole velocity is sensibly horizontal. I will also notice a misprint. In page 167, last line, read __ dv 105 dv dt dw D. D. Hearn. THERE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] JUNE 1867. LILI. Onsome Phenomena connected with the Adhesion of Liquids to Liquids. By Cuarwes Tomurnson, F.C.S., Lecturer on Experimental Science, King’s College School, London*. [ With a Plate. ] HE force of adhesion that exists between liquids and liquids is generally treated of under the heads of diffusion and solution. While, however, there may be little or no adhesion between the respective masses or volumes of two liquids, there may be a powerful adhesion between their surfaces. A drop of creosote, for example, may remain at the bottom of a vessel of water for honrs, or even days, apparently unchanged; but if gently deposited on its surface it will disappear, partly by solu- tion and partly by evaporation, in the course of a few minutes. There exists, im fact, at the surface of liquids a remarkable force of adhesion for other liquids, different from what is commonly understood by diffusion and solution, but rather resembling the attraction that has been recorded and measured between disks of glass or metal and Iiquid surfaces. The remarkable properties of liquid surfaces have attracted the attention of physicists at various times. Not to dwell upon the fact noticed by Pliny, and experimented on by Franklin, that oil, by spreading over the surface of water agitated by the wind, tends to calm it (as we believe, by destroying the ad- hesion between the water and the wind), we may refer to the researches of Carradori, who wrote expressly on the subjectt, * Communicated by the Author. + Dr. G. Carradori, Honorary Professor in the University of Pisa, was, I believe, the first to call attention to some of the remarkable properties of the surfaces of liquids. His first memoir, “ Deil’ Adesione o Attrazione Phil. Mag. 8. 4. Vol. 383. No. 225. June 1867. 2D 402 Mr. C. Tomlinson on some Phenomena connected with and also to those of Volta, Brugnatelli, Prevost, Venturi, and others who noticed it incidentally in their discussions on the cause of the motions of camphor on water. Carradori distinctly showed that oily liquids insoluble in water adhere to its surface with varying degrees of force, and that in general essential oils have a greater adhesion for water than fixed oils. In184.2-43 Dutrochet published an elaborate work* on the surface-action of liquids, in which he endeavoured to account for the phenomena by assu- ming the existence of a peculiar force which he termed the epr- polic, and which according to him is not identical either with heat or electricity, though partaking somewhat of the characters of both those forces. . I have at various times during the last few years published some researches on this surface-action of liquids+. It is pro- bable that most of the facts discovered by the earlier inquirers and the new facts introduced by me are to be explained by re- ference to the forces of adhesion and cohesion; but some of them point apparently to a variation or modification of these forces which does not seem to be well understood. For example, in all my experiments on cohesion-figures I have insisted on the necessity of employing a chemically clean vessel and a chemi- eally clean liquid surface, or there would be no adhesion between the two liquids, and the experiment would fail. But I have often been struck with a failure of adhesion when want of che- mical purity could scarcely have been the cause. I have failed to produce figures in glasses and with glass rods that had been washed in sulphuric acid or caustic potash and well rinsed, until, apparently by exposure to the air, the glasses, the rods, and the liquid surface had assumed an active condition. I will illustrate these and some other phenomena by reference to the motions of creosote on water. When a drop of creosote is gently deposited on the surface of clean water in a chemically clean vessel, it forms a well-defined cohesion-figure. The drop flattens down into a disk about three tenths of an inch in dia- meter ; its edge enters at once into rapid vibratory motion, pro- ducing a quivering of the whole surface of the water; minute di Superficie,” is contained in the Memorie di Matematica e di Fisica della Societa Italiana delle Scienze, vol. xi. (Modena, 1804) p. 75. The second part of this memoir is in vol. xii. part 2. p. 89. There are also various papers on the subject in the Giornale di Fisica Chemica e Storia Naturale di L. Brugnetelli, twenty vols., 1808 to 1827. The numerous references to the discussion on the properties of liquid surfaces with reference to the motions of camphor &c. on water are given in my essay on that subject, published ina small volume entitled ‘‘ Experimental Essays,” 1863. * Recherches Physiques sur la Force Epipolique. kale Philosophical Magazine for 1861-64; and Experimental Essays, the Adhesion of Liquids to Liquids. — 403 globules are shot out from it in radial lines; the figure sails about over the surface of the water, diminishing in size, and vibrating even more rapidly, until at length it disappears. (See Plate LV. fig. 1.) | “T have already explained* that this figure is the resultant of two forees—namely, that of cohesion among the particles of the creosote, which tends to keep the figure towether, and that of adhesion of the surface of the water, ee tends to break it up. The figure from one drop of creosote on the surface of two ounces of distilled water contained in a shallow glass vessel 3 ~ iches in diameter lasts about five minutes. But if the tempe- rature be below about 50°, the cohesion of the figure cannot re- sist the adhesion of the surface. As soon as the drop is placed on the water, the figure is formed for ma instant, but it splits open, forms a kind of brittle arc (figs. 2 & 8), which is shivered into a number of separate disks (fig. 4), each of which is a per- fect cohesion-figure of creosote. These figures perform their evolutions independently of each other, sailing about with rapi- dity, but never clashing with or disturbing each othery. The drop of creosote, stead of forming an active figure, may, under certain conditions, rest on the surface of the water in the form of a well-shaped double-convex lens. These conditions are, (1) want of adhesion, which may result from impurity of surface, and is to be got rid of by a thorough washing; or (2) that un- explained condition of inactivity already referred to. ‘This inac- tivity can be produced by heat. For example, the end of the glass rod used for depositing the drop on the water was held in the flame of a spirit lamp for a short. time and then dipped into the creosote. The drop delivered to the surface of the water was an inactive lens. After about two minutes it became active. The rod was kept in boiling water for some minutes, and after a hasty wiping was used for depositing the drop; an inactive lens was again formed. A few drops of etlcr were poured on the surface of the water and fired ; the surface was rendered in- active for about five minutes; the drop of creosote then flattened down from a lens into a disk with a sharp edge; it began to sway about, then to progress slowly over the surface; in five minutes more the edge began to quiver, and, after various at- tempts, the vibratory motion set in, but not with the vigour dis- played by the figure under its most favourable conditions. It * Phil. Mag. August and October 1861. + In the followi ing experiments (unless otherwise stated) the same vessel of 3 inches in diameter was used with 2 oz. of distilled water. The vessel was Cleaned after every experiment, either with sulphuric acid or caustic potash solution. Morson’s creosote, redistilled at about 418°, was used. The distillate was bright and celourless, and did not become cvlouzed by exposure to light. : 2D2 404 Mr. C. Tomlinson on some Phenomena connected with is remarkable that the flame of pure hydrogen jetted on the glass rod and on the surface of the water had no effect in rendering either inactive. The inactive condition of the rod is exchanged for an active one by exposure to the air. A moderate elevation of the temperature of the water is sufii- cient to produce this inactive surface. At 160° F. there was no adhesion ; the creosote slipped through the surface and formed an inactive sphere at the bottom. At 110° the creosote was in- active at the surface, and remained so during twenty-five minutes. In another experiment an inactive lens on a surface of water at 114° became an active figure on pouring in cold water. If the creosote itself be heated instead of the water or the rod, it forms inactive figures for a few seconds. Creosote raised to 120° was thus inactive. The surface of the water is also rendered more or less inactive by heat for other substances as well as creosote. The well-de- fined but rapid figures of carbolic and cresylic acids are delayed on water at 120°: they first form clear cut disks, and continue many seconds longer than on cold water. Hther becomes sphe- roidal on water at 120°, and rolls about in the form of a sphere ; or if the figure be formed, it is imperfect. ‘The well-defined figures of castor-oil and oil of lavender are either not produced at all, or are greatly injured, on water at 120°. At lower temperatures than the above, the adhesion of the surface is so far diminished as to exert a marked effect on the duration of the creosote figure. With water at 98° the figure was very active, but its duration was eighteen minutes instead of five. In summer weather, when the air is at 70°, the figure does not in general split up. This diminished force of adhesion consequent on a rise of temperature seems to be the commencement of the condition which finally ends in inactivity. There are not only fewer par- ticles within a given area, but their attractive force is diminished and the repulsive force increased. ‘This is not like a case of in- ereased solubility from heat, as when a body dissolves more freely in a hot than in a cold menstruum; for in such case the body is not only expanded by the heat, but currents are excited in the liquid which are constantly bringing fresh particles to act on it. But in the surface-action to which we refer, the cur- rents, if any, are chiefly horizontal, and the first touch of the creosote with the heated surface may saturate the exceedingly thin upper liquid layer, where the adhesive force chiefly resides. It is possible, too, that in some cases, when the disks are mac- tive, the inactivity may be due to a spheroidal condition, although this would not account for all the phenomena above noticed. In another experiment the active creosote figure was sur- the Adhesion of Liquids to Liquids. 405 rounded by atmespheres of hydrogen and carbonic acid. In hy- drogen the vibrations of the fieure were changed into a series of rapid jerks, and the duration was extended fiom five minutes to eleven or twelve; but this may be accounted for by the fact that evaporation was checked and that moisture condensed on the figure. In carbonic acid the action was very energetic, and the duration shortened from five minutes to two or three. A second and a third drop on the same surface also disappeared quickly, very much more so than on water in air, where the first drop lasts five minutes, the second twelve,and the third twenty-five; whereas in a carbonic acid atmosphere the first drop disappeared in two minutes, the second in three, and the third in six; so that car- bonic acid greatly assists the adhesive force of the water-surface for creosote. Other modes of modifying the adhesive force of the water- surface are, (1) by the addition of small portions of liquids or of solids more or less soluble in water, and (2) by covering the surface more or less with a liquid film. A single drop of strong acetic acid was added to the water (below 50°) before the creosote was put on. The figure did not split up; it was very active, but the duration was seventeen minutes instead of five. Now the addition of a body soluble in water partly satisfies, and so far diminishes its adhesive force; that is, the water is occupied with other business and cannot give its undivided at- tention to the creosote. Although water alone has a certain adhesion to creosote, and acetic acid a much stronger adhesion, yet the adhesion of acetic acid to water is stronger than that of water to creosote. The figure does not break up, because the adhesion of the water-surface is actually diminished by the addi- tion of a substance in which creosote is very soluble. In like manner, a drop of ether added to the water before the creosote is put on may prevent the figure from breaking up. The activity of the figure is great; the vibrations are so strong as to increase that quivering of the surface already referred to; and yet in an experiment of this kind the duration was fourteen minutes instead of five. Six drops of alcohol were added to water. The creosote figure did not break up, and its duration was twelve minutes. A drop of bisulphide of carbon forms a lens on the surface of water. The creosote figure did not break up, but played about the lens, and bombarded it with minute globules, which the lens> absorbed. After some time the lens flattened down into a film and broke up, discharging the creosote globules it had swallowed ; and these at once became active. Meanwhile the parent figure continued to vibrate, and its duration was greatly prolonged. 406 Mr. C. Tomlinson on some Phenomena connected with A drop of benzole on the surface flattened out into a disk about an inch in diameter. The moment the creosote touched the water, the benzole reasserted nearly the whole of its cohe- sive force, and shrunk up into adouble-convex lens. The creosote figure played about this lens and drove it about; and the dura- tion of the figure was, as in the other cases, ereatly increased. A drop of Persian naphtha spread out intoa film. The creo- sote figure did not make it collapse as in the case of benzole, but ploughed through it and cut it up im various directions, as camphor does through films of newly distilled essential oils*. Small portions of certain soluble salts greatly diminish, or even destroy the adhesion of the surface of the water. About three-quarters of an ounce of a hot saturated solution of sulphate of magnesia was poured into the glass, which was filled up with about 11 ounce of cold distilled water. A drep of creesote gently delivered to the surface sank to the bottom, and remained apparently without change during twenty-four hours. ue grains of sulphate of magnesia were put into the glass and 2 ounces of cold distilled water poured in. When the salt was dissolved, a drop of creosote was placed on the surface. It formed a large flat circular disk, the edge of which showed minute vibrations. After a few minutes a portion only of the edge vibrated, the other part being rounded and sharp. In this way it made several attempts at vibration and progressive motion; but after about twenty minutes it became inactive, and continued so during twenty-three hours, gradually diminishing in size during that Fine, Tt thus’ appeared that a much less quantity than 20 grains would suffice to lower or destroy the adhesive force of the sur- face. Five grains of Epsom salts to the 2 ounces of water ex- tended the duration of the figure from five to fifteen minutes. Six drops of the saturated solution (cold) added to the water, extended the duration to fourteen minutes and a half, and prevented the quivering of the surface. A second drop of creosote placed on the surface when the first had disappeared, sank to the bottom. Four grains of common salt extended the duration to fifteen minutes; 4 grains of alum rendered the figure inactive in four- teen minutes; 6 grains of acetate of soda in 2 ounces of water at 70° did not seem to disturb the activity of the figure, but changed its character to a shuflling kind of motion. The figure was greatly influenced by the capillanty of the side, sailing round near the edge, and leaving behind it, rather than throw- ing out, numerous small disks, which, usually so active, were in this case mactive. The duration of the figure was thirteen minutes. * See Phil. Mag. for September 1863. ese ee eee the Adheston of Liquids to Liquids. 407 The duration varied considerably with several other salts. A curious effect was produced when the creosote was placed on 2 ounces of lime-water. ‘The figure was very active; but, instead of shooting out globules in radial lines, the globules were united into rays, giving the figure the star-like appearance of the cre- sylic-acid figure, with the rays occasionally forked and waving. A film was quickly formed by the union of the creosote and the lime, and strong currents were excited in this film by the vibra- ting figure. Gradually the film gained consistence and closed in on the figure more and more, until it disappeared by solution or combination with the lime. A second drop made its way through the film, cleared out a small space, and was very active. When this was over, a third drop sank thfough the film and was suspended by it just below the surface, where it remained inac- tive until a portion of the film was cleared away; and then it started into life. It appears, then, that the preoccupation of the surface by another film destroys its adhesion for creosote, unless the film or a portion of it be cleared away. In a large variety of cases cre- osote exerts a displacing-power of its own, which is often differ- ently exerted in the case of volatile oils as compared with fixed oils. This difference, which serves as a sort of measure of the adhesive force of the surface for various oils &c., may next be considered. Many of the oils of the turpentine series are spread with great energy by the adhesion of the surface. Thus a drop of the es- sential oil of turpentine no sooner touches the surface than it flashes out into a film which satisfies its adhesion. If now a drop of creosote be placed on this film, it simply slips through and falls to the bottom of the vessel ; but if the drop be carefully delivered to the water near the edge, it will form a convex lens, and, slightly repelling the turpentine film, will make its way into it, so as to be surrounded by it, with a clear intervening space. In the meantime the turpentine becomes thinner by evapora- tion and displays its iridescent colours. The creosote lens flat- tens, widens the clear space around it ; soon the edge begins to quiver ; and all at once, as if at a signal, the vibrations suddenly set in, the figure sails about, everywhere repelling the film, and causing it, or what is left of it, to gather up into disks. When the creosote figure has disappeared, the turpentime disks begin slowly and cautiously to flatten out into films. A second drop of creosote will cause them instantly to collapse. A second drop of turpentine will, in like manner, shut up into a lens the second creosote figure. The film goes through its changes as before ; the second creosote figure in due time becomes active ; and when it has disappeared the disks of turpentine flatten out as before. 408 Mr. C. Tomlinson on some Phenomena connected with Oil of cajeput forms a good film on the surface of water, nearly covering it. A drop of creosote at the side slowly made its way into the film, which retreated from it, waving backwards and forwards as if reluctant to be displaced. The creosote lens gra- dually flattened down, and in ten minutes became active, sailing about and repelling the film, which gathered up into disks. The figure was very active, producing that flashing kind of motion on the surface already alluded to, and clearing a wide circuit of water for its own operations. - Small pellets from the figure fu- riously invaded the film, cutting it up, and rapidly disappearing in the process. The figure continued active during eight minutes, thus making eighteen in all from the first putting on of the creo- sote. The cajeput disks now flattened out into films; a second drop of creosote made them collapse; a second drop ‘of cajeput formed a film which arrested the motions of the second creosote figure; and as the film became thinner by evaporation, it was curious to notice the creosote gradually becoming active. First the edge of the lens became uneasy with nervous twitchings, then it. became a little ragged, and suddenly the whole figure started into life. A third film and a third figure went through their operations on the same surface, the duration of each being, of course, prolonged. The experiment was repeated with water at 75°; and the di- minished adhesion was shown by the cajeput film now occupy- ing less than half the surface instead of the whole. The creo- sote formed a lens as before, which made its way into the film and, gradually flattening, pene active. The film produced by. oil of Myristica also shows shes effects exceedingly well. Oil of savin, oil of juniper, and several others formed films which permanently arrested the motions of the creosote figure ; but on redistilling these oils so as to get rid of oxidized products, smaller films were formed, showing how greatly they had improved in cohesive force by being purified. When the savin film was first on the surface, the creosote figure made it contract into a lens. When the creosote figure was on first, the film arrested its motions for a second or so, but the figure, becoming active, shut up the film. The figure also shut up the juniper film; but, as in some other cases, if the creosote figure first had pos- session of the surface, the drop of juniper formed a small well- ‘shaped lens. Newly distilled oil of coriander forms a beautiful cohesion- figure on the surface of water. The drop spreads rapidly out sas a film of large size; then the edge breaks into a regular and somewhat serrated character, and ve film contracts rapidly, leaving the serrations long and thin, Some of the spaces be- oe ae the Adhesion of Liquids to Liquids. 409 tween the teeth or rays run deeper in than others. Each tooth or ray as it contracts leaves dots of oil regularly placed behind it. In this state it forms fig. 5, the formation of the dots being shown in fig. 5a. Then the deep indentations run more deeply and rapidly in, to branch out into rounded hollows within the disk, as in fig. 6. These ramifications increase and deepen, until they break up the central disk into a number of small disks, which finally remain arranged somewhat symmetrically, as in fig. 7. If the creosote be put first upon the surface, the corian- der instantly arrests its motions. In a recent experiment the creosote split up into a number of active figures, which the co- riander rendered motionless. But in the course of twenty mi- nutes the smallest of the creosote disks became active, cleared a small space in the film for its operations, soon became wildly active, and disappeared with frantic gesticulations. Then the large disks became active. It seemed as if the coriander film had at first closed in all round the creosote figures and stopped them; but as the creosote retained possession of the spots of water on which they actually stood, they waited their time, and as the coriander film became weakened by evaporation and solu- tion the creosote gradually repelled it and soon made a clear space for its own exertions. Having once secured this space, it extended it, and passed over the whole surface, carrying its own clear surrounding space along with it. Indeed the manner in which the creosote figure cuts through some films without touch- ing themisa remarkable sight. As the figure advances, the film recedes, sometimes one, or two, or three tenths of an inch, or more from the figure. It is at the edge of the figure that the chief contest between cohesion and adhesion is going on, and here it is that solution takes place and the figure wastes away: it is always surrounded by a solution which wells away outwards, and which, though invisible, makes its presence felt by its repulsive action. The outward action is also evident by the globules of creosote which are discharged in radial lines from the figure. Oil of lavender, unless recently distilled, permanently arrests the motions of the creosote figure; and even the fresh oil does so for a very long time. A drop of the oil on water makes its beautiful cohesion-figure*, which terminates in a multitude of small lenses connected by a film which easily resinifies by expo- sure to the air. But even in such a case the creosote in the course of an hour or so became active, and repelled the film, its duration being estimated by hours instead of minutes. If further proof were wanting of the remarkable force of ad- hesion that exists between creosote and the surface of water, it is to be found in the fact that creosote displaces many. of the fatty * See Phil. Mag. October 1861, Plate IV.! 410 Mr. C. Tomlinson on some Phenomena connected with oils. For example,.a drop of castor-oil nearly covered the sur- face with its beautiful cohesion-figure. In this case a larger glass was used, 4 inches in diameter instead of 8. A drop. of creosote placed at the side instantly became active, causing the oil to contract into a Jens and chasing it about. When the creo- sote had disappeared, the oil flattened out into a film that occu- pied nearly the whole surface. A second drop of creosote did not shut it up again, but ploughed through it, turning over and thickening the edges of the severed portions. The film was now in long trails, which were swept about by the vibrating figure. When this had disappeared, these trails flattened out and again nearly covered the surface. A third drop of creosote cleared a wide space among the films, like open water in ice. A film of castor-oil on warm water is spun out into threads by the action of the creosote; that is, the film, instead of being cut through, is united by a thread which spins off from one part of the nearly severed portion to the other, until the part which gives the thread is exhausted. The creosote figure also repelled and cut up films of whale-oil, fish-oil, nut-oil, and several! other fatty oils. A -pale seal-oil, very pure and limpid, made a large film. The creosote figure repelled it strongly, but did not shutit up. As the figure moved about it made deep bays in the edge, which yielded as the figure travelled along. ‘The effect was as if a ship were invading the land and carrying its own water, for many feet round it, to sail in. The film formed by balsam of copaiba is at once invaded by the creosote figure, which continues active durmg twenty minutes or more. In the preceding details creosote has been taken as the stand- ard, and the adhesive force of the water judged of with reference to it. Quils of the turpentine series and some other essential oils arrest the motions of the creosote figure only for a short time. As the film of oil becomes thinner the creosote becomes active, and completes its course. Now the time occupied by the figure in doing this may be taken as a sort of measure of the adhesion of the surface for the oil in question. If a film of turpentine extend the duration of the creosote figure to ten minutes, and a film of oil of nutmegs totwenty minutes, it is presumed that the latter oil adheres twice as strongly to the surface as the former. So, when the creosote displaces films, and its duration is scarcely prolonged at all, the adhesion between the water and the film can be but small. Where the duration of the creosote, without losing its activity, is considerably extended, the adhesion of the film must be considerable. It is thought that m this way ‘Tables of the adhesive force of different liquids for each. other may be framed.. —— the Adhesion of Liquids to Liquids. 411 But there are liquids which render creosote permanently in- - active. Such are the oleines of tallow, of fish-oil, of lard, of horse-fat, and of palm-oil, as also oleic acid from beef-tallow. Whether the creosote be first put on the surface, or the oleine, the creosote remains permanently inactive. In such a case we may judge of the adhesive force of the oleines by their power of displacing other films. The following” experiments were tried in a shallow glass 4 inches in diameter, instead of 3 as in nearly all the previous experiments. Castor-oil nearly covered the surface. in hor. 18 25 1848, February 15.—Very cold day; clear only in north. Arago. 2207 me K ee 16 5 1843, February 16.—Barom. 29°18 in., rismg. Fine sky. Babinet. 11 56 R=25° max. polarization, 20° in horizon. 12 57 tic a4 Ae a 9 40 Brewster. 1207, ae 7 Li pi ll 55 Arago. 3 28 R= 291° max. pol.in zenith, 243° inhor. 12 52 4 3 R=294° max. pol. in zenith, 264° inhor. 18 40 » 0 R=30° * 3 » 17 52 eh 4 7 is ot 3S -F 14 52 5 4 2: ve 35 17 26 1843, February 17. —Barom. 29°6 in. Sky not clear in N. horizon. SMG Paget ae ve oe i128 3 30 - se . ae 14 14 1843, March 4.—Barom. 30°08 in. 3.35 R=]4)° max. polarization in zenith plane. 16 45 3 46 17 30 3 54 toe neutral point 50! high. Bary 7 57 in horizon ‘ 4 6 40 oe ee 36 20 30 1843, March 7. 4 40 R=243° maximum polarization inzenith.17 0 1843, March 8.—Barom. 30°13 in. Wind east; hazy. 414 R=245° maximum polarization .. V7 47 1843, March 12.—Barom. 29°34 in., after rain. 4 2. R=25)° max. pol. - Pol..of moon (>. % 13) la) 1843, March 25.—See Phil. Mag. vol. xxx. pp. 126, 165. 1843, March 28.—Barom. 29°84 in. Wind east; dry. Oo i 43 ai “gs 16 45 of the Atmosphere. 457 1843, March 29.—Barom. 29°88 in. Fine day, cold; wind east ; dry. “Apparent time. Arago. 351 R=282°, 253° in S. and 263° in W. hor. 5 58 ae on ue as 18 35 6 26 ws ai es ij 19 33 Babinet. 6 1 R=292° max. pol. inzenith. 28° inhor. 18 22 6 24 R=293° Pf Fe = 18 27 1843, April 7. Arago. 6 54 ks * oe i! 19 0 Babinet. 6 48 ot ar st 16 29 1843, April 10. leet 29°74 in. Very cold wind, north- west. Arago. 6 93 es ee ee ee 20 42 Babinet. 6 95 ee ae 2, 23 1843, April 11 Macs, 29: 80 j in. Very cold. 6 43 R=283° max. a. Sky whitish blue. 17 "30 6 48 ‘ ae e 17 45 1843, April Tay oo 70 im. Babinet. 4 35 as 7 41 35! The sky was covered sit a thick haze, the sun barely seen through it, and showers of hail falling occasionally. The bands a maximum above the sun, but disappeared 9° above horizon. A neutral point was seen at 25° alt. opposite the sun, but the bands below it seemed + ! though extremely faint. 1843, April 17.—See Phil. Mag. vol.ixxx. p. 165. ° Arago. 6 30 R=25} max. pol. in zenith, 203° in hor. 22 32 (jf R= 29 Fe 3 PE 20 44 730 R= 93 9 29 99 20 10 1843, April 19.—Nebulosity in zenith. Clouds round horizon. Arago. 7 30 R=255° max. pol. in zenith plane. 18 35 Babinet. 7 33 vi et 19 0 18438, April 28. set 29°44 in., after rain. Clear sky after clouds had cleared away. Arago. a9 " ~ Me: én 20 23 7 40 oe iN ~ oY 19 37 Babinet. 7 3 R=29° max. pol. in zenith plane. 16 46 7 44 R=29° max. pol. in zenith, 204° inhor. 18 0 458 Sir David Brewster on the Polarization 1843, April 29.—See Phil. Mag. vol. xxx. p. 165. 1843, April 30.—Barom. 30°07 in. Morning, and rising. Not a cloud. Apparent ¢ time. Arago. i 0 R=263° max. pol. in zenith, 232° im hor. |, 4 15 R=264 o A 5 43 Secondary neutral Helnt forming. 6 4 oe 11 20 6 52 R=29° max. pol. in pent 223° in hor. 19 20 1 aa me a max. Pal in ces ae inhor. 19 35 58 : LY A brown haze rising up upon Te blue ee See Phil. Mag. vol. xxx. p. 169. 1843, May 2.—Barom. 30:07 in. Wind east; no sun. Babinet’s neutral poimt near zenith, and polarized bands scarcely seen, excepting at 90° from sun. 1843, May 3.—See Phil. Mag. vol. xxx. p. 165. 6 49 bp ie O10 ne 18 26 ‘ Babinet. 6 53 R=30° max. pol. in zenith, 27° inhor. 14 20 Very clear in zenith, with a whitish sky. 1843, May 6.—Wind east; uniform China-ink clouds over the sky, through which the sun shone brightly, but ill-defined. 4h 43™,—Polarized bands distinct over the face of the sun and above him, but exceedingly feeble opposite the sun. 1843, May 11.—Barom. 30 in. Fine day. 2 30 R=203° max. pol. in zenith plane. 6 0 Neutral point not up .. n6 14 34 6 12 R=234° maximum polarization im zenith. 18 15 Whitish-blue sky. White clouds in horizon. 1843, June 13.—Barom. 30 in. Wind east. ba | Arago. 6 56 aN xs aide ie 19 15 9 10 a4 oe i a 20 25 Babinet. 7 © R=27%° max. polarization in zenith plane. 25 10 913 R=292° in zenith, horizon clear. 18.30 1843, June 14.—Barom. 30:07 in. Splendid day ; wind east. 6 12 R=293° max. pol. in zenith, 214 "in hor. 13 30 se = 2957 an ee 223° in hor. 15 30 . Arago. 7 0 R=295° max. pol. in zenith, 225° in ho- 1] 5 | rizon. Neutral point in horizon. 7 56 as on Sy - 18 20 of the Atmosphere. 459 1843, June 15.—See Phil, Mag. vol. xxx. p. 169. 1843, June 16.—Barom. 30 in. Sky covered with white ne- bulosity. | Apparent time. hm Arago. 12 20 R=253° max. polarization in zenith plane. , , Ze id “5 “A Fila, apn lly 48 7 38 He = ae uA 17 50 Babinet. 7 41 R=293° max. pol. in zenith plane. 15 55 1843, June 21.—See Phil. Mag. vol. xxx. pp. 126, 165. 1843, June 22.—Barom. 29°90 in, Wind east; fine day. Arago. 8 42 Antisolar point in horizon. Clouds in zen. 19 1b 1843, June 23.—Barom. 29°92 in. Fine day. 7 17 R=25° max. pol. in zenith, 183° in hor. 15 35 7 26 ae ae BS AP 17 30 8 58 apa 55 he « Aue 18 30 Babinet. Zot ave ss Se 1518 9 0 R=272° max, pol. in zenith, 22° in hor. 16 50 1843, June 24.—Barom. 29°92 in. Arago. rs eee Fee RPE SRN fo SEES, 5h LER 1843, June 26. 7 25 21 6 : 52 {| Neutral point i in the middle of a ‘bright 17 33 | orange cloud ss 3 1843, July 5.—Barom. 29°57 in., rising. 7 29 R=26° max. pol. in zenith, 203° in S. hor. 16 28 1843, July 6. 6 50 R=283° max. pol. m zenith, ik inhor. 11 45 en eee , 14 15 fai K=18s° polarization of moon .. 17 32 S13, R=29" max, es in zenith plane. 19 30 8 55 Fis 4 es 18 15 Babinet. 7 25 a 13 40 8 15 cael polarization o of moon .. 16 3 8 52 r: 17 11 1843, July 1 1 Basal. 80 in., rising. Pl 6 55 R=293°, max. pol. in zenith ; clear sky. 12 28 7 51 White clouds forming in many places. 21 11! Babinet. 7 54 4 an Wy ceecppuelinie eb 19 10 1843, July 21.—Barom. 29°5; no rain. Arago. 7 34 Thin clouds in zenith and near sun, 20 4 460 Sir David Brewster on the Polarization 1848, July 24.—Barom. 29°87 in., rising; no rain. Abearent game ene 6 58 << sie SA us 17° 52 1843, August 6.—Barom. 29°77 in., after a wet day. 7 27 R=294° max. pol. in zenith: sky clear 18 49 Rabinet. 7 49 we ve 17 39 1843, August 9.—Fine day; rain yesterday. ; Arago. 5 tas jal G00 BEY eee aes 873 ae 18 17 1843, August 10.—Splendid day; haze in zenith; shght white clouds. Barom. 29°97 in.; hot. 11 38. R=24° maximum polarization in zenith plane. 1843, August 19.—Barom.29°6 in., falling ; haze all forenoon. 7 7 ee ee ee ee 18 53 7 51 55 ae 36 ae 18 30 Babinet. 7 23 R=273° maximum polarization .. 17 50 1843, September 6.—Barom. 30:05 in.; splendid, hot day. Arago. fel ve 25 ‘s 55 23 10 Babinet. 7 18 +: ae e = 16 32 1843, September 9.—Barom. 30°05 in.; fine day. Arago. Ofbo? * 3, an 33 56 19 25 Babinet. 7 O a os 46 : 17 23 1843, September 13.—Barom. 29°98 in. ; fine day. : Arago. 5 6 aia point in horizon ; R=25°maxi- l 10 55 mum polarization in 8. horizon. { 6 48 Babinet. 6 53 R=30° max. pol. in zemith, 233° in 8. hor. 16 26 1843, September 20.—Barom. 29°80 in. ; no rain.. Arago. 6 14 oe W., clear E.; R=233° ee 17 42 242° in horizon 1843, September 21.—Barom. 30 in., rising. 5 46) 7 18 59 : A [z= 30° maximum polarization in zee | 17 55 “mith, 253° in horizon; not a cloud ree 5 51 | in the sky oe oe 18 54 6 31) J 18 43 of the Atmosphere. 461 1843, September 22.—Barom. 30°28 in., rising; thick in ho- rizon, with a brownish-red light. i es time. Arago. a1 18 23 By R=292° max. ‘pol. in zenith, 2210 in hor. 19 58 1843, October 31.—Barom. 29°39 in.; fine sunny day. 2. ba Pe a =e 15 40 4 22 we om ne ea 17 56 4 59 LP 20 49 Babinet. 4 24 R=293° max. pol. inzenith, 253°mhor. 17 8 4 45 Polarization of moon 243°. 1843, November 7.—Barom. 29°30 in., rising; fine day. Arago. 4 29 R=293° max. pol. in zen., 263° im S. hor. 18 22 1843, November 14.—Barom. 30°13 in., rising; fine day; wind north-west by west. 4 12 ws ue x -2 18 33 Babinet. 417 R=28°max. pol. in zenith plane .. 18 45 1843, November 20.—Barom. 29°27 in., rising; cold day. Arago. 4 36 =: “4: =5 rs yA asy4 Babinet. 4 37 Zo Bid 18 13 1843, November 29. ee on Arago. 3 31 a aa 14 14 1843, December 1 ee 99 943 in. Fine day. 4 10 ais ar -- “7 18 8 Babinet. 412 ee “s 19 26 1843, December 6. ae he wid west ; clear sky every- where. Arago. 2. 6 ne fi ie i 16 5g Babinet. 3 7 R=283°, 90° from sun - 18 11 1844, January 23.—Barom. 27°8 in., rising ; fine day. Arago. 3 34 ae ae os “i 18 5] Babinet, 3 37 R=27° max. pol. in zenith plane. 17 31 1844, January 25.—Barom. 29°84 in. ; rain till 25 p.m Arago. 4 20 : Se 18 16 426 R=28° maximum polarization i in zenith. Babinet. 4 38 Polarization of moon 173°. a 19 0 462 Sir David Brewster on the Polarization 1844, February 3.—See Phil. Mag. vol. xxx.pp.126, 165. 1844, February 6.—Snow on ground. Apparent time. Arago. h m ie ct ae te 3 13 be ee e% ee 19 1 Babinet. ~ 3.19 R=25° max. pol. in zenith plane. 17 58 4 2 R=27° max. pol. in zenith, 193° im horizon. 1844, February 7.—Clouds over zenith; snow. 9 18 a Arago. ve 18 13 1844, February 16.—Barom. 29°74 in.; wind west; fine day. 12 14 R=263° maximum polarization, to 193° in horizon. i 58 R= 962° 3” 33 a 33 in! R=232° 99 9 1gi9 23 3 14 Neutral point in horizon. 3 20 10 14 3 24 Secondary neutral point : in horizon. . 14 33 3 33 Sky clouded 15 31 4 6 Secondary neutral point disappears. Babinet. 4 32 : 19 49 1844, ee 21.—See Phil. Mag. vol. xxx. p. 127, 1844, February 27.—Barom, 29°12 in., rising. Thaw. , 3 16 Polarization of moon 173°. Arago. 3 44 ay an os os 14 10 1844, March 7.—Barom. 30°03 in., rising. Fine day. 4 48 As nebulosityin zenith; R=13° te 19 90 imum polarization .. 1844, March 27.—Barom. 29-70 in., ue 5 40 Polarization of moon 222° te 20 40 1844, April 11.—Fine day and fine evening ; wind west. 6 a 27 “taax. pele 22%° in horizon. 18 23 qf 53 es ‘is -18 37 Babinet. 6 24 + 5 bh “ 20 50 48 ae setts ai Ae ee 19 19 1844, April 22.—Fine day. Barom. 29°80 in. Arago. 6 29 R=272° max. pol., 223° mS. horizon. 19 31 7 15 Ue at aes ae Silt 20 34 Babinet. 6°37, ae . bs 21) 32 7 18 R=282° max. pol., 223°in S. horizon. 17-28 of the Atmosphere. 463 1844, April 24. —Barom. 29:°87in. Fine day; windy. _ Apparent. time. Arago. 6 1 i i Ma 3 16 55 6 38 - ae 5 es 20 30 Babinet. 6 3 ‘t ‘3 15 58 1844, April 26. ees 29° 84 in., rising. ati: 6 24 * - oe 19 20 1844, April 27—Barom. 30-07 in., rising. P21 R= 14° a ; se 20 50 Babinet. 7 2 A great whiteness inthe sky .. 23 22 1844, May 2.—Barom. 30°25 in. Arago. 5 52 Yeh. s oo) R= 152° max. _ pol. in zenith, 143° "in hor. 22 25 633 R=17 3 5s 14 p23 20 (22: k=20 Ss 6s 144 4, =. 22 25 Babinet: 6 5 :3 13 40 1844, May 3.—See Phil. ae ‘wah xxx: p: 169: 1844, May 7.—Barom. 29°80 in. Whitish sky. : . Arago. 7 3 R=263° max. pol., 203° in horizon. v0 2 Babinet. 7°35 see : 2% 16 30 1844, May 15. ae 30 in,, falling. ~ Fine day. Arago. 6 36 ae e 43 ie 16 50 6 52 23 oa 3% o% 20 6 7 46 3h EY 3% sO D140 Babinet. 6 50 5t ve ae a8 16 10 7 Ol et DY AS 1844, June 3 Bath, 99: 86 i in. Wind west. , 8 46 ss " a . 20 58 Babinet. 8 52 3% Ss 20 35 1844, June 10.—See Phil. Mag. vol. xxx. pp. 127, 165: 1844, June 18.—See Phil. Mag. vol. xxx. p. 127. 1844, August 20.—Barom. 29:77 in., rising. Fine day. Arago. 6 57 R=23° max. pol., 27° in horizon. 4 7 38 R=275° 29 ) 29 20 40. 8 8 ae ce vt 4 21 25 8 46 19 0 8 50 bei i Babine. € | ieee @ ate 17 15 464 On the Polarization of the Atmosphere. 1844, August 26.—Barom. 29°77 in., rising. Fine day. as time. Arago. 6 18 Neut. point among small mottled clouds. 29 0! 1844, August 29.—Barom. 29°92 in., falling. Fineday. A China-ink sky. Brewster’s neutral point distinctly seen. 2 20 R=193° maximum polarization in zenith plane. 1844, September 21.—Barom. 301 in.; cold and clear sky. 6 16 R=283° max. pol. in zen., 253° in hor. 18 55 Babinet. 6 18 Polarization of moon. 173° Aig 17 ut 1845, January 11.—Fine day, cold; wind west. Arago. 210 R=283° max. polarization in zenith. 8 15 1845, January 20.—Barom. 29°48 in. Fine day; frosty. Mean time. Above horizon. 3.10 R=29° maximum polarization in zenith. 3.15 Alt. of Arago’s neutral pomt ... 12 56 317 re of Babinet’s neutral point ; ag 299 0 came on : a 1845, January 24.—Barom. 29°55 in., rising. 3 37 Alt. of Arago’s neutral point oe TLo0 3 59 Alt of Arago’s neutral point - 17 30 4 4 Alt. of Babinet’s neutral pomt .. 19 35 4 39 Alt. of Arago’s neutral point .. 13 35 4 41 Alt. of Babinet’s neutral pomt .. 24 0 1845, January 31.—Therm. 18° at 108 p.m. of the 30th; 84 a.M., therm. 12°. Barom. 29°54 in., rismg. Fine frosty, clear day; ground covered with snow. 12 55 R=262° in zenith and in horizon. 12 55 Arago’s neutral pot in N. hor.; sun’s alt. then 14° 45’. 1 40 Arago’s neutral point still in horizon. 1 40 R=26$° im zenith. 1845, February 1.—Barom. 29°80 in. Frosty day; cloudy till 35, 3 30 Alt. Arago’s neutral point ta 8 15 R=205° max. pol. in zenith to 143° in hor. 3.45 Alt. Arago’s neutral point <4 14 30 R=225° maximum polarization. 1845, April 8.—Barom. 29:06 in. 5 35 Alt. Arago’s neutral point sh 9 10 Gea is Sg pe ei 20 20 5 39 Alt. Babinet’s neutral point .. 25 10 6 4 A BS os a 15 25 M. J.-M. Gaugain on Grove’s Gas Battery. 4.65 1845, April 15.—See Phil. Mag. vol. xxx. p. 127. 1845, July 14.—On the top of Scuirmore, near Glenquoich. Mean time. Above horizon. m ° 1 5 24 Altitude of Arago’s neutral point. 6 40 R=235° max. polarization in zenith plane. 1845, September 6.—Barom. 80°10 in. Fine day; a milky sky. 1 10 R=17° max. pol. in zenith plane. 5 31 R=23°. Arago’s neutral point .. te ¢ 5 41 Arago’s secondary neut. point seen in hor. 13 24 6 36 Arago’s neutral point .. af 4 VOPUG 5 43) Babimet’s. R=283° maximum polariza-} 24 0 6 28 tion, 24° in horizon ee 20 24 ' 1850, July 1, 15, 29.—See Phil. Mag. vol. xxx. p. 176. 1850, July 9.—Barom. 29°79 in., rising. Fine clear sky. 6 56 Bands just visible at the land horizon. 7 95 Bands invisible close to land horizon. 7 21 During the previous 21 minutes no trace of the + bands was seen. At 7" 21™ they were seen, and became ra- pidly brighter. The positive action which here produced the secondary neutral point was not strong enough to produce it by exhibiting the + bands counteracting the — ones at some height above the heri- zon; butit was strong enough to neutralize them for 21 minutes, and to weaken them greatly when they did appear. LIX. On Grove’s Gas Battery. By M. J.-M. Gaueatn*. dae physicists are acquainted with Mr. Grove’s gas-ele- ment, and with the theory of it which he has given. This theory is now generally admitted ; and probably few persons remember the objections which from time to time have been urged against it, especially by M. Schénbein. I have been led by other investigations to return to the subject; and although I was not acquainted beforehand with M. Schénbein’s investi- gation, I have arrived at almost the same conclusions. I used a mode of investigation quite different from those hitherto employed. I only worked with one element at a time ; and instead of measuring the intensity of the current, | mea- sured the, electromotive force directly by the method of opposi- tion. I could thus numerically estimate the influence of the modifications which I -have successively mtroduced into the arrangement of the couple. Mr. Grove thinks it indispensable that each of the platinum | electrodes in his gas-couple should be simultaneously in contact * Translated from the Comptes Rendus, February 25. Phil. Mag. 8. 4. Vol. 83. No. 225, June 1867, 2H 466 M. J.-M. Gaugain on Grove’s Gas Battery. with one of the gases and the liquid beneath. In order to ascertain if this really is so, I made the following determina- tions. I first measured the electromotive force of a couple in which each of the platinums touched at the same time the liquid and the gas, as prescribed by Mr. Grove. I then lowered the platinum wires so as to immerse them completely and to keep the liquid from contact with the gas; and having again mea- sured the electromotive force, J found that it was exactly the same as before. It follows from this observation that the action of the platinum only extends to the dissolved gas, and that the jars containing gas have no other purpose than that of keeping the solutions they cover ma state of saturation. I imagine, moreover, that I can explain why Mr. Grove has arrived at an entirely different result. By my method of ob- servation, the couple I used is only at work for a fraction of a second; in so short a time the gaseous solutions surrounding the platinum wires cannot be appreciably altered. This is no longer the case when the current is allowed to circulate whole days, as by Mr. Grove it was allowed to do: the liquid layers which then surround the platinum wires are continually robbed of the gas they contain, and must take fresh quantities from the reservoirs above; the gases, which thus dissolve solely on the upper surface of the liquid, must reach the platimum wires more easily the nearer these are to the surface. The electromotive force of the gas-couple varies singularly with the condition of the platinum wires used. According to an old observation of Matteucci, the action of platinum wires is increased by heating them in a spirit-lamp-flame some moments before using them as electrodes. Under the most favourable conditions the electromotive force of a gas-couple made with unplatinized platinum wires scarcely exceeds 155. I take as unit the electromotive force of the couple — ,—that is to say, that of a bismuth and copper thermoelectric couple, one of whose junctions is at zero and the other at 100°. As I have some time ago remarked, the electromotive force of the couple Bi—Cu PMR 6° 1900 Varies im different elements even using pure metals ; and therefore the numbers which I shall cite are not comparable with those which M. J. Regnauld obtained when using a differ- ent thermo-electric element from mine. I have found that the electromotive force of the gas-couple is not modified when the oxygen bell-jar is replaced by one con- taining carbonic acid, or even by a jar which only contains boiled water. I have found that the couple formed by join- ing a platinum wire plunged in a solution of oxygen, and a M. J.-M. Gaugain on Grove’s Gas Battery. 4.67 platinum wire immersed in water deprived of gas, developes no current. M. Schonbein had observed these latter facts in the year 1843, and concluded therefrom that in Grove’s gas-couple the oxygen serves to depolarize the positive wire. I entirely assent to this explanation, and think that the function of oxygen in the gas-battery is that of sulphate of copper in Daniell’s battery. The electromotive force of Daniell’s element, Zn— Cu Acidulated—Sulphate water. ofcopper: , is represented by 193; Zo—Cu Acidulated water.’ that of a Volta’s couple, by 178, when the two couples are at rest; but if they are set to work by joining them by a conductor offering very small resistance, it is found, after a few minutes, that the electromotive force of the Volta’s couple falls below 70, while the Daniell’s retains almost all its original force. ‘The explanation of these facts, almost universally admitted, is, that the algebraic sum of the electromotive forces at work is almost the same at starting in each; but, under the influence of the current, the polarization of the copper developes in Volta’s couple a considerable nega- tive force, which diminishes the algebraic sum of the forces of the couple, while in Daniell’s element the sulphate of copper prevents the polarization ; in the same way, in Grove’s element, oxygen serves simply to depolarize the positive wire. it must, however, be remarked that the action of oxygen in the gas-couple is far from being as effective as that of sulphate of copper in Daniell’s element. When a Danicll’s clement is set to work by joining its poles by a short and thick copper wire, the electromotive force rapidly diminishes, even when the couple is arranged as Mr. Grove prescribes. T found in one experiment that this force fell in a few minutes from 152 to 30. ‘To establish this fact, it is necessary to measure the elec- tromotive force of the couple which has been at work the moment contact is broken: a few minutes’ rest restores all its energy I have tried to find im what proportion each electrode contri- buted to the enfeeblement which the couple undergoes under the conditions mentioned. I found that the electromotive force put in play by the wire immersed in hydrogen was lowered simply by 26, and that the antagonistic force developed by the wire plunged in oxygen was 96. In fine, it appears to me established that the electromotive force put in play in Grove’s element is due exclusively, or almost so, to the affinity exerted between the oxygen of the water and the hydrogen condensed by the electrode of platinum. 2H2 [ 468 ] LX. Notices respecting New Books. An Elementary Treatise on Rational Mechanics. By the Rev. Joun Kerr, M.d. Glasgow: William Hamilton [1867], pp. 295. HIS work is designed for the use of those students of natural philosophy ‘“ who have no time for the higher mathematics,” the use of the higher mathematics being avoided” by a free employ- ment of limits and infinitesimals wherever required. Such is the author’s account of the book; and we may add that even when the student has time and inclination to master the higher mathematics, the best introduction to the Calculus is a work in which detached questions are treated by capi a ass as the early sections of the “] dy 0, and the component velocities at every ee in the fluid are therefore alike for both cases. Thus it is only when there is no Seinen ental that some fluid elements can rctate, and that others can move round along a closed curve, in a simply-connected closed space. We may therefore call the motions which have no velocity-potential, gene- rally, vortex-motzons. § 2. We must next determine the variations of the angular veloci- ties €, 7; € durmg the motion, when the only external forces are such as have a potential. Let us note once for all, that if wr be a function of x, y, z, and ¢, and if it increase by dy when these imerease by déz, dy, dz, dé nemaart then aya OE a+ Eon Hay 4 Mae, If we now take ie ae of Pe in the time 6f for the same elementary volume of fluid, we must give dz, dy, dz the values which they have for the moving element—that is, be=usl,. ey=vol, dz wos ; and we obtain sae: ra 4:0 Bi 0, Hae Db » dp dy dz 492 Prof. Helmholtz un Integrals expressing Vortex-motion. We will employ the symbol a in what follows only in the sense that ae dt is the change of yf during dt for that element of the fluid whose coordinates at the commencement of dt were 2, y,2. If we eliminate p by differentiation from (1), and with the help of (2) introduce the new expressions, supposing (1 a) to be true for the forces X, Y, Z,we obtain the following equations:— 6&, du du. .du BF ay Mae én dv dv dv Vinee — —_: — e “e e ® e 3 at ae ae (3) pte, dw , .dw da" "dy dz | or, which amounts to the same, oe du 22 dw ot one 4 7 Oe FOS : dv dw — = — & e e e ® 3 “5 = ( a) aes =E7 +0 - 2 ee, If in a fluid element &, 7, € are simultaneously equal to zero, we have also oF _ on 08 _4 OP ors Hence those elements of the fluid which at any instant have no rotation, remain during the whole motion without rotation. We can apply the method of the parallelogram of forces to rotations. Since &, 7, € are the angular velocities about rect- angular axes, the angular velocity about the instantaneous axis 1s g=V/ 2477+, and the direction-cosines of that axis are Sr If we now take in the direction of this instantaneous axis the indefinitely small portion ge, its projections on the axes are e€, en, and e€. While at x, y, z the components of the velocity are u, v, w, at the other end of ge they are Prof. Helmholtz on Integrals expressing Vortex-motion. 493 au du du OT ue iL dv dv dv v= Ot ee the +7 dw dw dw w= wt ef er +eb a At the end of the time dé, the projections of the distance be- tween the two elements of fluid, which at the beginning of dé limited the line ge, have values which by the aid of (8) may be thus written :— e& + (u,—u)dt=e( E+ e at), \ 6 en + (v, —v)dt=e(n+ i it), eb (ww, —w)dt=e( f+ s at). The left-hand sides of these equations give the projections of the new position of the joining line ge, the right-hand the projec- tions of the new velocity of rotation, multiplied by the constant factor e. It follows from these equations that the joiming line between the elements, which at the commencement of dt limited the portion ge of the instantaneous axis, also after the lapse of — dé coincides with the altered axis of rotation. If we call vortex-line a line whose direction coincides every- where with the instantaneous axis of rotation of the there- situated element of fluid as above described, we can enunciate the above theorem in the following manner :— Lach vortex-line remaims continually composed of the same elements of fluid, and swims forward with them in the fiuid. The rectangular components of the angular velocity vary di- rectly as the projections of the portion qe of the axis of rotation ; it follows from this that the magnitude of the resultant angular velocily in a defined element varies in the same proportion us the distance between this and its neighbour along the axis of rotation. Conceive that vortex-lines are drawn through every point in the circumference of any indefinitely small surface; there will thus be set apart in the fluid a filament of indefinitely small section which we shall call vortex-filament. The volume of a portion of such a filament bounded by two given fluid elements, which (by the preceding propositions) remains filled by the same element of fluid, must in the motion remain constant, and its section must therefore vary inversely as its length. Hence the last theorem may be stated as follows :—The product of the section and the an- 494 Prof. Helmholtz on Integrals expressing Vortex-motion. gular velocity, in a portion of a vortex-filament containing the same element of fluid, remains constant during the motion of that element. From equations (2) it follows directly that dé dy a ay y se oe And, further, from this, sae (V+ iy =) di de BO the integration being i over any given portion 8 of the fluid mass. Integrating partially we have S) Edy dz+ | \\ nda dz+ in) Cdz dy=O0, where the integration extends to the whole surface of 8. Calling dw anelement of this surface, and a, 8, y the three angles made with the axes by the normal to dw drawn outwards, we have dydz=dwcosa, dexdz=dwcusB, dx dy=dw cosy. Hence J) (Ecosa+y cos 8 +€cos y) 6o=0; or if we call g the resultant angular velocity, and @ the angle be- tween its axis and the normal, VV cos 0. da=0, the integration extending to the whole surface of 8. - Now let S be a portion of a vortex-filament bounded by two in- definitely small planes @, and , perpendicular to the axis of the filament; cos @is equal to 1 at one of these, and —1 at the other, and equal to 0 for the rest of the surface ‘of S; hence if g, and q, be the angular velocities in w, and ,, the last equation re- duces itself to ; ei iar whence it follows that the product of the velocity of rotatien and the cross section is constant throughout the whole length of any one vortex-filament. That it does not alter by the motion of the filament itself has been already proved. Tit also follows from this that a vortex-filament can never end within a fluid, but must either return ring-shaped into itself within the fluid, or reach to the boundaries of the fluid, since, if a vortex-filament ended anywhere within a fluid, a closed surface could be constructed for which \¢ cos 8dw would not vanish. § 3. If the motion of the vortex-filaments in a fluid can be deter- Prof. Helmholtz on Integrals expressing Vortex-motion. 495 mined, the preceding theorems enable us to determine &, n, £com- pletely. We shall now consider the problem of finding w, v, w from &, 7, ¢. Thus, let there be given within a mass of fluid which includes the space 8 the values of &, , ¢, which latter satisfy the condition dé a dy , a dx dy ' dz u,v, and w must be found so as to satisfy within the whole space S the conditions SO tee See x! 2d) tate A 0, ea a i @ a 7 22 | We require also the necessary conditions for the bounding surface of S according to the particular problem. According to the given values of &, 7, ¢, we may have some vortex-filaments which are reentrant within the space 8, and also some which reach the boundary of 8 and then break off. If the latter be the case, we can always continue these filaments along the surface of S or without it till they return into themselves, so that a greater space 8S, exists which contains only reentrant vor- tex-filaments. And at the whole of the surface of S, either &, n, € and their resultant g are each =O, or at all events Ecosa +ncosB8+fcosy=qeosO=0, . . (2d) where a, 8, y, 0 have the same values as before. We find values of wu, v, w which satisfy (1), and (2) if we put dP a _ dM 1 = dx | de f | _aP 5 a ey de, dn: r _4@P dM dl, ~ de | da dy” J and determine the functions, L, M, N, and P so as to satisfy within the space 8, the conditions 496 Prof. Helmholtz on Integrals expressing Vortex-motion. di) 95 0 alla 5 dat + aye * ae Pb a°M ) d?M 2M oe ae a tae? | 5 aN, eee a? “et ae ae Cael ek a et at ae er The method of integrating these equations is known. L, M, N are the potential functions of imaginary magnetic matter distri- buted through the space S, with the densities . P the potential of masses external tothe space S. If we denot by v the distance of a point a, b, c from a, y, z, and by £,, 7,, & the values of &, 7, € at that point, we have L=— Th 4 | Esa db ae ; 27r a, , M=— at {((": dadbdc, > + ee ) 27 r Ea fee | nad ({fEanara, | the integration extending to the whole space S,, and P= ({{' da db de, where & is an arbitrary function of a, b, c; and the integration extends through all space exterior to 8. The arbitrary function k must be taken so as to satisfy the conditions at the bounding surface, a problem whose difficulty resembles that of magnetic and electric distribution. That the values of u, v, and w in (4) satisfy the conditions in (1), is proved by differentiation, with attention to the fourth of equations (5). We also find by differentiation of (4), attending to the first three of equations (5), that . dv dw d (du. aM any dw du =i -aees de dz °' dy \dx ' dy de/’ du do _ d ge dM , dN a ENE ae Prof. Helmholtz on Integrals expressing Vortex-motion. 497 Equations (2) are thus satisfied if it can be shown that in the complete space 8, di,’ dM. ~aN Siar tage aes Su eS 5 da **dy * de coi hacaet oe That this is the case is seen from phim (5 a), ce a || [eee a db de, or by is. integration eS a ene Wh ence dx 27 r QT Pewda eat... 1 1, 1 1 dy, iy 4 - dadc— on ({( a da db de, JN cele oat (((2.% = alls da db of | j (} ae da db de. Adding these three equations, and again putting dw for the surface-element of S, we have gt aM dN... “ ee ay et (E cosa+n,cosB+¢ cosy)dw -x((RE + le Os) da dh de. But throughout the entire space Se Oyen aioe ek. (2 a) And over the whole surface, E cosa+n cosB+€ cosy=0. . . (23) Both integrals therefore vanish, and equations (5 b) are satisfied as well as (2). (4) and (5) or (5a) are thus integrals of (1), and (2). The analogy, mentioned in the introduction, between the dis- tance-action of vortex-filaments and the electromagnetic action of current-conducting wires, which gives a very good means of ex- hibiting the form of vortex-motions, is deducible from these theorems. If we put in (4) the values of L, M, N from (5 a), and denote by Au, Av, Aw the indefinitely small elements of u, v, w which in the integrals result from the element dadbdc, also their resultant by Ap, we have 498 Prof. Helmholtz on Integrals expressing Vortex-motion. Age 2 Wh, Serene a ad. 2Q7T re ; Nees ie ep (2—a)o da db de, 27T 73 Dig ela oh ties 27 73 and it follows from these that Au(a—a) + Av(y—b) + Aw(z—c)=0; hence the resultant of Au, Av, Aw is at right angles to r. Further, & Au + 0 Av ae ¢ Aw=0. Hence this resultant is also at right angles to the resultant axis of rotation at a,b,c. Lastly, Ap=/ (Au)? + (Av)? + (Aw)? = ats q sin y, where g is the resultant of €, 7,, €, and v the angle it makes with 7, which is found from qr cosv=(2—ajE + (y—b)n, + (2—0)¢,. iach rotating elemeni of fluid (a) implies in each other element (b) of the same fluid mass a velocity whose direction is perpendi- cular to the plane through (b) and the axis of rotation of (a). The magnitude of this velocity ts directly proportional to the volume of (a), 2ts angular velocity, and the sine of the angle between the line (a) (b) and that axis of rotation, and inversely proportional to the square of the distance between (a) and (b). The same law holds for the force exerted by an element of an electric current at (a), parallel to its axis of rotation, on a particle of magnetism at (0). The mathematical connexion of these phenomena consists in this—that in the fluid vortices, for any element of the fluid which has no rotation, a velocity-potential @ exists satisfying the equation Ob Ep ae © 0. ie Sd 1 ene aaa ie and this holds everywhere but within the vortex-filaments. If we consider the latter as always reentrant cither within or without the fluid, the space for which the above equation for ¢ holds is com- plexly connected, since it remains single if we conceive surfaces of separation through it, each of which is completely bounded by a vortex-filament. In such complexly connected spaces a function Prof. Helmholtz on Integrals expressing Vortex-motion. 499 b which satisfies the above equation can have more than one value; and it must be so if it represent currents reentering, since the velocities of the fluid outside the vortex-filaments are proportional to the differential coefficients of @, and therefore the motion of the fluid must correspond to ever increasing values of d. If the current returns into itself, we come again toa point where it formerly was, and find there a second greater value of @. Since this may occur indefinitely, there must be for every point of such a complexly-connected space an infinite num- ber of distinct values of ¢ differing by equal quantities like those of tan-!—; which is such a many-valued function and satisfies the differential equation. Such also is the case with the electromagnetic effects of a closed electric current. This acts at a distance just as a deter- minate arrangement of magnetic matter on asurface bounded by the conductor. Exterior to the current, therefore, the forces ex- erted on a particle of magnetism may be considered as the dif- ferential coefficients of a function V which satisfies the equation COE OO er —7 + => + =, =0. Bee ys... Oe" But in this case also the space in which this equation holds is complexly connected, and V has more than one value. Thus in the vortex-motion of fluids, as in electromagnetic effects, the velocities or forces external to the vortex-filaments (or electric-current-penetrated space) depend upon potential functions with more values than one, which satisfy the general differential equation of magnetic potential functions; while within the vor- tex-filaments or the space traversed by electric currents, velocities and electromagnetic forces can be expressed (both in an analo- gous manner) by those functions which appear in the equations (4), (5), and (5a). On the other hand, in simply streaming fluid-motion and magnetic forces we have to do with potential functions with only one value, just as in the cases of gravitation, electric attractions, and constant currents of heat and electricity. The latter integrals of the hydrodynamical equations, in which a single-valued velocity-potential exists, we may call integrals of the jirst class; those, on the other hand, where there is rotation of some of the elements of the fluid, and in consequence a yelo- city-potential with more than one value in the non-rotating ele- ments, integrals of the second class. It may occur that in the latter case only such portions of space are to be treated in the example as contain no rotating elements,—for instance, the mo- tion of fluids in ring-shaped vessels, where a vortex-filament may be supposed to hie along the axis of the vessel, and where the pro- 500 Prof. Helmholtz on Integrals expressing Vortea-motion. blem belongs to those which can be solved by the assumption of a velocity- potential. In the hydrodynamic integrals of the first class the velocities of the fluid elements are in the direction of, and proportional to, the forces which a determinate magnetic distribution outside the fluid would exert on a magnetic “particle in the places of the elements. In the hydrodynamic integrals of the second class the veloci- ties of the fluid elements are in the direction of, and proportional to, the forces which would act on a particle of magnetism if closed electric currents passed through the vortex-filaments with a density proportional to the angular velocity in these filaments, combined with magnetic masses outside the fluid. The electric currents inside the fluid must move with their respective vortex- filaments and have constant intensity. The assumed distribution of magnetic matter outside or at the surface of the fluid must be taken so as to satisfy the conditions at the surface. Hach mag- netic mass can also, as we know, be replaced by electric currents. Thus, instead of using for the values of u, v, w the potential- function P of an external mass x, we get quite as general a solu- tion if we give & 7, and € outside of, or at the bounding surface of, the fluid any values such that only closed current-filaments exist; and then the integration in (5a) must be extended to all space in which &, y, and ¢ are different from zero. § 4. In neeetbaerrte integrals of the first class it is sufficient, as I have shown above, to know the motion of the surface. By this the whole motion in the interior isdetermined. In integrals of the second class, on the other hand, the motion of the vortex- filaments in the interior of the fluid must be found with reference to their mutual action, and with attention to the conditions at the surface, by which the problem becomes much more complicated. Even this problem can be solved in certain simple cases—namely, when rotation of the fluid elements takes place only in known surfaces or lines, and the form of these surfaces or lines remains unchanged during the motion. The properties of surfaces bounded by an indefinitely thin sheet of rotating elements can be easily deduced from (5a). If &, 7, ¢ differ from zero only in an indefinitely thin sheet, their potential functions L, M, N will, by known theorems, have equal values on both sides of the sheet; but their differential coeffi- cients, taken in the direction of the normal to the sheet, will be different. Suppose the coordinate axes so placed that at the point of the vortex-sheet we are considering the axis of z is the normal to the sheet, and that of «x the axis of rotation of the _ Prof. Helmholtz on Integrals expressing Vortez-motion. 501 element, so that 7=€=0, the potentials M and N and their differential coefficients have the same value at both sides. Such ; dl dL dl ae: is also the case with L, ohh and oe but 73 has two distinct values, whose difference is 2£c, if e« denote the thickness of the sheet. Consequently equations (4) show that w and w have the same values on both sides of the vortex-surface, but the values of v differ by 2£. “Hence the values of that component of the velocity which is a tangent to the vortex-surface and at right angles to the vortex-lines differ on cpposite sides of the surface. Within the sheet of revolving elements we must take this com- ponent of the velocity as gradually and equably varying from one value to the other. For if & is here constant through the whole thickness of the shell, and « represent a proper fraction, v', v, the values of v at the sides, v, the value in the shell at a distance ae from the first side, we saw that v!/—v,=2£e, while between was a sheet of thickness e and angular velocity &. We have in the same way v! —v,=2£ea=a(v'—v,), which expresses the above result. As we must consider the revolving elements as being themselves moved, and the change of their distribu- tion on the surface depends on their motion, we must assign as their mean velocity along the surface for the whole thickness of the sheet the arithmetical mean of v! and 2. Such a vortex-sheet will be produced if two separate moving masses of fluid come in contact. At the surface of contact the velocity perpendicular to this must be the same for both, but the tangential velocities will in general be different in the two. Thus the surface of contact will have the properties of a vortex-sheet. Hence in general isolated vortex-filaments cannot be supposed indefinitely thin, since otherwise the velocities at opposite sides would be indefinitely great and in opposite directions, and the proper velocity of the filament would remain undetermined. To obtain, therefore, certain general conclusions about the motion of very fine filaments of any section, we must make use of the prin- ciple of the conservation of vis viva. Before we proceed to treat of separate examples, we will first write the expression for the vis viva K of the moving mass of fluid, K=4$A\\\ (u2+e%+w*) dedydz. . . . (8) We now from equations (4) substitute in this integral yee dP a a:) Le ae aan Ey aao(iP 4 db_ aN) ards * ae J? ee dP LE. dM _ di Pome ee tdi: dy ) Phil. Mag. S. 4, No. 226. Suppl. Vol. 33. 21, 502 Prof. Helniholtz on Integrals expressing Vortea-motion. and integrate partially, denoting by a, 6, 7, and @ the angles which the inwardly directed normal of the element dw of the fluid mags makes with the coordinate axes and with the resultant velocity g; we thus obtain, attending to equations (2) and (1)4, K=— th\ de [Pg cos 6 + Livcosy —weosB) + M(w cos a — sae | (6a) + N(ucos B—v cos a) | —h\ {fh (LE+Mn+N6) da dy dz. ‘ihe value of = is found from (1) if we multiply the first by w, the second by v, and the third by w, and add, h( ug +0 ow 4)= — (ut. dp dp it it belle On ay yd a(q*) 9 +h (ue +07 tu We )-5 oy tor twa ° If both sides be multiplied by dx dy dz and integrated through the whole extent of the fluid, noticing that by (1), \\Ve eee Yaw) te dy de=— | pq 0088 do, if yr denote in the interior of the fluid mass a continuous and single-valued function, we obtain dK az = | dolp— —hU+4hq*)\qeos@. . . .« (6d) If the fluid mass be entirely enclosed in a rigid envelope, g cos 0 d must be zero at every point of its surface. Hence —-=9, or dt K = constant. If we consider this rigid envelope as being at an infinite dis- tance from the origin of coordinates, but the vortex-filaments at a finite distance, the potential functions L, M, N, whose masses &, , € are each in sum equal to nothing, are, at an infinite dis- tance R, proportional to R-2, and their differential coefficients as Be but the surface-element dw, if it always correspond to the same solid angle at the origin, is as R®. The first integral in the pepressioti for K (6a), which is extended over the surface of the fluid mass, will vary as R~-%, and therefore vanish for an infinite value of h. The value of K thus becomes K=—h\\\ (LE+My+NQ) dedydz; . . (6)e and this value does not alter during the motion. Prof. Helmholtz on Integrals expressing Vortex-motion. 508 Sb. Straight parallel Vortex-jilaments. We shall first consider the case where only straight vortex- filaments, parallel to the axis of z, exist, whether in an indefinitely extended mass of fluid, or in a similar mass limited by two infi- nite planes perpendicular to the filaments, which comes to the same thing. All the motions are then confined to planes perpendi- cular to the axis of z, and are exactly the same in all such planes. We put therefore du dv _dp_ dV _ Bee de dee Then equations (2) become du dv E=0, 7=0, 2f= Frage (3) become ) oe 0, The vortex-filaments thus retain constant angular velocity, so that they also retain the same section. Hquations (4) become _ dN is dN Sigs Dey ae aN d°N eet eye HE. | aot dy? s By the remark at theend of § 8 we put P=0O. The equation of current lines is thus N = constant. N is in this case the potential function of indefinitely long lines; and is infinitely great, but its differential coefficients are - fimte. Let a and 6b be the coordinates of a vortex-filament whose section is da db, we have aN (dadb. x—a ~ de 1 he dN Gdadb y—b dip 7 3 “= From this it follows that the resultant velocity gis perpendicular to r, which again is perpendicular to the vortex-filament, and that If we havea number of vortex-filaments whose coordinates are 2 2 &/ é 504 Prof. Helmholtz on Integrals expressing Vortex-motion. Li, Yj) Voy Yo, &e. in a fluid mass indefinite in the directions of xz and y, and denote the product of the section and the angular velocity in them by m,, ma, &c., then, forming the sums U=mu, + gu, + mguz &e., V=mMyr, + MWg +My &e., these will be each equal to 0, since the portion of the sum V which arises from the effect of the second vortex-filament on the first, is destroyed by the effect of the first on the second. They are respectively My @,—2 M, Lo—x m,.— +2 and m,.—- 4» a) aan r and so for other pairs in each sum. But U is the velocity of the centre of gravity of the masses m,, m,...in the direction of # multiplied by the sum of these masses; so of V in the di- rection of y. Both velocities are thus zero, unless the sum of the masses be zero, in which case there is no centre of gravity. The centre of gravity of the vortex-filaments remains, therefore, stationary during their motions about one another; and since this is true for any distribution of vortex-filaments, it will also be true of isolated ones of indefinitely small section. From this we derive the following consequences :— 1. Ifthere be a single rectilinear yortex- filament of indefinitely small section in a fluid infinite in all directions perpendicular to it, the motion of an element of the fluid at finite distance from it depends only on the product (da db=m) of the velocity of rotation and the section, not on the form of that section. The elements of the fluid revolve about it with tangential velocity = = where 7 is the distance from the centre of gravity of the filament. The position of the centre of gravity, the angular velo- city, the area of the section, and therefore, of course, the magni- tude m remain unaltered, even if the form of the indefinitely small section may alter. 2. If there be two rectilinear vortex-filaments of indefinitely small section in an unlimited fluid, each will cause the other to move in a direction perpendicular to the line joming them. Thus the length of this joining line will not be altered. They will thus turn about their common centre of gravity at constant distances from it. Ifthe rotation be in the same direction for both (that is, of the same sign) their centre of gravity hes be- tween them. If im opposite directions (that is, of different: signs), _their centre of gravity hes in the line joining them produced. And if, in addition, the product of the velocity and the section be the same for both, so that the centre of gravity is at an infi- Prof. Helmholtz on Integrals expressing Vortex-motion. 505 nite distance, they travel forwards with equal velocity, and in parallel directions perpendicular to the line joining them. To this last case may also be referred that in which a vortex- filament of indefinitely small section moves near an infinite plane to which it is parallel. The condition at the limits (viz. that the fluid must move parallel to the plane) will be fulfilled if in- stead of the plane there be an infinite mass of fluid with another vortex-filament the image (with respect to the plane) of the first. From this it follows that the vortex-filament moves parallel to the plane in the direction in which the elements of the fluid between it and the plane move, and with one-fourth of the velocity which the elements at the foot of a perpendicular from the filament on the plane have. With rectilinear vortex-filaments the assumption of an indefi- nitely small section leads to no inadmissible consequences, since each filament exerts upon itself no displacing action, and is only displaced by the action of other filaments which may be present. It is different with curved filaments. § 6. Circular Vortex-filaments. Let there exist in an infinite mass of fluid only circular vortex- filaments whose planes are parallel to that of xy, and whose centres are in the axis of z, so that all is symmetrical about that axis. Let us change the coordinates by assuming L=YX COS €, a=g Cos e, y=YxX sin €, b=g sine, c=, C=C. The angular velocity o is, by the above assumption, a function of x and z or of g and ¢ only, and the axis of rotation is per- pendicular to y (or g) and axis of z. The rectangular compo- nents of the angular velocity at the point g, e, c are, therefore, &=—osine, n=acose, 6=0. In equations (5 a) we have 7? = (z—c)?+y?+9° —2yg cos (e—e), N=0. From the equations for L and M we obtain, multiplying by cos € 506 Prof. Helmholtz on Integrals expressing Vortex-motion. and sine, and adding and subtracting, Lsin ¢—M cose — 3~ = ( (fee 9 gay alee de Leos e+Msine= + 5 L [(|csete—3 bas (9 gag d(e—<) de In both integrals e and e appear only in the form (e—e); and this may therefore be taken as the variable in the integration. In the second integral the element for e—e=¢ is destroyed by that for e—e=2m7—C; it is therefore zero. If we put o cos e gdg de de : e p= (pee ; Sel (z—c)?+ x? +9°— 29x Cos e we have M cose—Lsin e=, M sin e+Lcose=0; or” L=—wysine, M=YWocose.. . . . . « (Za) Calling 7 the velocity in the direction of the radius y, and no- ticing that on account of the symmetry about the axis of z there can be no velocity in the direction of the circumference, we have u=TCOsée, v=Tsin é; and from equations (4) 2 ay ae ae Lr gh SG ie vi ae, dy From this dlp dp =— =— + — ad. dy 4% OF 3 Ce gy MOL hos The equation of the current-lines is therefore ary = constant. If we perform approximately the miegration for yr for a vortex-filament of indefinitely smail section, putting ody dc=m,, and the corresponding part of xr=,,,, we have an la a ow fe \ ss t Vm, =" /4 mat K)—«x? -, where Sei el ay (g+x) + (e—eP Prof. Helmholtz on Integrals expressing Vortex-motion. 507 and F and E are the complete elliptic integrals of the - st and second orders for the modulus «. If we put, for sake of brevity, U= = (P—E)—«e, where, therefore, U is a function of «, we have m, ,—dU z—c = pS a A a eg Sioa aN 7 «(9g +x)°+ (e—e) If there be a second vortex-filament m at the point xX, 2, and we denote by 7, the velocity in the direction of g which it gives to m,, we shall find this, if we put in the expression for 7 instead of TRF OM, TG ¢.2 Mh. By this process U and « are not changed, and we have ING eT ites ek). ao ste Naw (8) Let us next determine the value of the velocity parallel to the axis of z, which m,, whose coordinates are g and c, produces, and we find ee Pe —dU Kx (z—c)*+9?—¥x? wg 5 ma /LU aN OM de: 2x (9 +x)? + (e—0)? If we call w, the velocity parallel to z which the vortex-ring m, whose coordinates are z and xX produces at the position of m,, we require only to make again the same interchange of letters as before. Hence we find rTyY= 2 2mm, /;— 2mwy? + 2myw 9? —mMTXz —M,T gC= = ./gmw.U. . (8a) Similar sums can be mace for any assumed number of vortex- rings. Denote odgde in the nth ring by m, and the com- ponents of the velocity it receives from the others by 7, and Wn, oniting, however, for the time that which each ring can impart to itself. Call also its radius p,, and ~ its distance from a plane parallel to vy, which magnitudes, no doubt, correspond in direction to what we have called y and z, but as belongmg to a pee ving they are functions of the time, and not independent va riables like vy and z. Finally, let the value of y,-as far as it arises from the other vortex- rings, be wn. We find from (8) and (8a), by writing out and adding these equations for each pair of rings, = (m,,0 Bi = 0, > (2 M,WrPn —MnTnp nn) = PS (nPnWn) . 508 = Prof. Helmholtz on Integrals expressing Vortex-motion. As long as we consider a finite number of separate and indefi- nitely thin vortex-rings in these sums, we can only introduce in w, T, and the portions produced by the other rings. If, how- ever, we suppose the space to be continuously filled with an infi- nite number of such, yf is the potential function of a continuous mass, w and 7 its differential coefficients; and we know that for such a function, as well as for its differential coefficients, the parts due to an indefinitely small portion indefinitely near the point for which the value is sought, are indefinitely small in comparison with those of finite masses at a finite distance*. Let us change the sums into integrals: we may suppose the entire amount of their value at any point to be expressed by w, 7, and vy, and put cas Go age wae a For this purpose we express m as odp dn, dies OF yes 4 : «f 49) 2 foot apn er spin apa 29 Since the ay odp dX is by § 2 constant with respect to the time, (9) can be integrated with respect to ¢, and we have iff op?dp dX= const. Consider the space to be divided by a plane which passes through the axis of z, and therefore cuts all the vortex-rings ; consider o as the density of a slice of the mass, and call Ye the entire mass in the slice made by the plane; M=ffodp dn; and if R? is the mean value of p? for all the elements of mass, Sfp . pap dry = MR? ; and since this integral and the value of ft remain unchanged during the lapse of time, R also remains unchanged during the motion. Therefore if there exist in the unlimited fluid only one circular vortex-filament of indefinitely small section, its radius remains unaltered. The magnitude of the vis viva is in our case, by (6c), * Compare Gauss in the Resultate des magnetischen Vereins, 1839, p. 7. Prof. Helmholtz on Integrals expressing Vortcz-motion. 509 K=—h ff f(LE+Mn)da db de = —hf f fryopdp dr de = —2Q7rh f fyopdp dx. This is also constant as regards time. Again, we remark that, as odp dd is constant with respect to ¢, 5 | | op*ndp r= 2\ font P dp d+ { fooes —dnrdp, hence the equation (9a), if we call / the value of \ for the cen- o) of gravity of the section of the vortex-filament and multiply a it and add, becomes Ke 2 ( cprrap dN+ 5 ( (oot [— ny ip dh=— cae (9 b) If the section of the vortex-filament is ce small and ean indefinitely small magnitude of the same order as /—X and the other linear dimensions of the section, but cdp da finite, then and K are of the same order of indefinitely great quantities as loge. For very small distances v from the vortex-ring we have = V.\(U>y) eC), e=l]— ifn In the value of K, i is rele by p org. Ifg is finite and v of the same order as ¢, K is of the order loge. Only when g is indefinitely great and of the order : does K become indefi- , i) : nitely great, of the order z loge. Then the circle becomes a straight line. But, on the ei hand, = pall hich is equal to s becomes of the order _ the second integral therefore is finite, and for finite values of p is indefinitely small compared with K. In this case we may put in the first integral / instead of A, and we find Pg! K 24 (MR) =— 5°, — omRI= = Since Mt and R are constants, / must vary propor tionally to the time. If Mt is positive, the motion of the elements of fluid on 510 Prof. Helmholtz on Integrals expressing Vortex-motion. the outer side of the ring is in the direction of z positive, on the inner side in the direction of z negative; K, A, and R are from their nature necessarily positive. Hence in a circular vortex-filament of very sinall section in an in- definitely extended fluid, the centre of gravity of the section has, from the commencement, an approximately constant and very great velocity parallel to the axis of the vortex-ring,and this is directed towards the side to which the fluid flows through the ring. Indefinitely thin vortex-filaments of finite radius would have indefinitely great velo- city of translation. But if the radius be indefinitely great, of the order = then R? is indefinitely great compared with K, and / becomes constant. The vortex-filament, which has now become. rectilinear, becomes stationary, as we have already proved for the case of such filaments. We can now see generally how two ring-formed vortex-filaments having the same axis would mutually affect each other, since each, in addition to its proper motion, has that of its elements of fluid as produced by the other. If they have the same direc- tion of rotation, they travel in the same direction; the foremost widens and travels more slowly, the pursuer shrinks and travels faster, till finally, if their velocities are not too different, it over- takes the first and penetrates it. ‘Then the same game goes on- in the opposite order, so that the rmgs pass through each other alternately. If they have equal radii and equal and opposite angular velo- cities, they will approach each other and widen one another ; so that finally, when they are very near each other, their velo- city of approach becomes smaller and smaller, and their rate of widening faster and faster. If they are perfectly symmetrical, the velocity of fluid elements midway between them parallel to ‘the axis is zero. Here, then, we might imagine a rigid plane to be inserted, which would not disturb the motion, and so obtain the case of a vortex-ring which encounters a fixed plane. In addition it may be noticed that it is easy im nature to study these motions of circular vortex-rings, by drawing rapidly for a short space along the surface of a fluid a half-immersed circular disk, or the nearly semicircular point of a spoon, and quickly withdrawing it. .There remain in the fluid half vortex- rings whose axis is in the free surface. The free surface formsa bounding plane of the fluid through the axis, and thus there is no essential change in the motion. These vortex-rings travel on, widen when they come to a wall, and are widened or con- tracted by other vortex-rings, exactly as we have deduced from theory. | Prof. Helmholtz on Integrals expressing Vortex-motion. 511 The above version of one of the most important recent investiga- tions in mathematical physics was made long ago for my own use, and does not pretend to be an exact translation. Professor Helm- holtz has been kind enough to revise it; and it may therefore be ac- cepted as representing the spirit of the original. A portion of the contents of the paper had been anticipated by Professor Stokes in various excellent papers in the Cambridge Philosophical Transac- tions; but the discovery of the nature and motions of vortex-fila- ments is entirely novel, and of great consequence. Sir W. Thomson has recently propounded a very singular speculation as to the ulti- mate nature of matter, mainly founded on the properties of the Helin- holtz ring. I append an extract from a letter I have just received from him, which fills an important gap towards the end of Professor Helmholtz’s work.—P. G. Tarr. ——— _ Following as nearly as may be Helmholtz’s notation, let g be the radius of the circular axis of a uniform vortex-ring, and a@ the radius of the section of its core (which will be approximately circular when a is small in comparison with g), the vortex motion being so instituted that there is no molecular rotation in any part of the fluid exterior to .this core, and that in the core the angular velocity of the molecular rotation is approximately w, or rigorously ox g for any fluid particle at distance y from the straight axis. *“‘T find that the velocity of translation is approximately equal to vt" (IogS2 1), 29 os aE (quantities of the same order as this multiplied by “ being neglected.) g «The velocity of the liquid at the surface of the core is approxi- mately constant and eyual to wa. «At the centre of the ring it is 2 : Twa g «Tf these be denoted by Q and W respectively, and if T be the velocity of translation, we therefore have ‘‘ Hence the velocity of translation is very large in comparison with 512 Prof. De la Rive on the Action of Magnetism upon the fluid velocity along the axis through the centre of the ring, when the section is so small that log 895. large in comparison with 27. a But-the velocity of translation is always small in comparison with the velocity of the fluid at the surface of the core, and the more so the smaller is the diameter of the section in comparison with the diameter of the ring. «These results remove completely the difficulty which has hitherto been felt with reference to the translation of infinitely thin vortex- filaments. I have only succeeded in obtaining them since the com- munication of my mathematical paper (April 29, 1867) to the Royal Society of Edinburgh, but hope to be allowed to adda proof of them to that paper should it be accepted for the Transactions.” May t7e IS86/.3 LXIV. On the Action of Magnetism upon the Electric Discharge in. highly Rarefied Gaseous Media*. By Professor A. DE LA Rivet. N the memoir which I recently published “ On the Propaga- tion of Electricity in Elastic Fluids,” I reserved for a subse- quent publication the vestigation of the manner in which this propagation is-modified by the action of magnetism. I demon- strated the existence of this action as early as 1849, by showing that a magnetic pole causes jets of electricity which escape from it radially to rotate. M. Pliicker subsequently proved by seve- ral remarkable experiments that this action is general. The luminous veins which show themselves in rarefied gases traversed by the discharges of a Ruhmkorfi’s apparatus are in fact attracted and repelled in the same way as electric currents passing along metallic wires would be. In a word, this action is subject to the laws of electrodynamics, with the difference, however, that, all the parts of the moveable conductor being independent of each other instead of being connected together as they are in a rigid wire, they obey perfectly the forces by which they are soli- cited, and take up positions of equilibrium determined by these forces. It follows that each luminous vein assumes the form of a magnetic curve, the only condition under which equilibrium can be produced, since the action of the magnet upon an element of the current is then nothing, the direction of this action be- * Translated from the Archives des Sciences Physiques et Naturelles, vol. xxvii. p. 289 (December 1866). + This paper forms a continuation of the one which I published, on the propagation of electricity in highly rarefied elasticffluids, m the Number of the Archives des Sciences Physiques et Naturelles for July 1866 (vol. xxvi. p- 177). [A translation of the paper here referred to will be found at p, 241 of the present volume of the Philosophical Magazine. | the Electric Discharge in highly Rarefied Gaseous Media. 5138 coming perpendicular to that of an element when the latter is a tangent to the magnetic curve. On the present occasion, my object is to investigate with greater detail the influence exerted by magnetism on electricity when traversing rarefied gases. My researches comprise two series of experiments : :—first, those in which the electromagnet, which is the source of the magnetic action, is placed outside the rarefied gas through which the electric discharge passes; and secondly, those in which the magnetized scft iron is situated within the gas itself. § 1. Haperiments in which the electromagnet is placed outside the rarefied gas. One of the simplest cases is when a glass tube containing the rarefied gas through which the electric discharges are passing is placed either axially or equatorially with regard to the poles of a strong electromagnet. When care has been taken to rarefy highly the gas which transmits the electric discharge, the follow- ing appearances present themselves :—The portions of the dis- charge subject to the magnetic action are squeezed up against the sides of the tube at the parts nearest or furthest from the poles of the magnet, according to the direction of the discharge- and the position of the poles; the striz at the same time become much narrower and more brilliant. Ifthe part of the tube near the electromagnet is that containing the negative electrode, the dark space immediately becomes luminous and presents narrow bright strize, just as the constantly luminous part of the discharge, which seems to advance, would do. At the same time the bluish photosphere surrounding the negative knob diminishes in thickness by at least one-half “and becomes more brillant, and the sort of bluish sheath which surrounded the metallic stem at whose extremity the negative electrode is placed, disappears entirely. The whole of this bluish atmosphere becomes con- centrated about the knob. It seems that all the gaseous veins, which may be regarded as so many conductors of the discharge, instead of radiating from all points of the negative knob and stem and spreading out through the whole gaseous mass as far as the positive electrode, when the magnetic action is exerted upon them radiate only from the negative knob and are con- densed against either one side of the tube or the other, until they arrive at that part of their course where the action becomes in- sensible and they accordingly resume their normal position. This condensation explains why the part of the discharge which was dark, because the gas was there so greatly rarefied, becomes luminous, and why the part which was already luminous becomes narrower and more brilliant, while the striz which it exhibits Prof. De Ja Rive on the Action of Magnetism upon 514. approach closer together. The action of the magnet produces the same effect as would be caused by a local increase in the density of the rarefied gaseous matter. It is not necessary, however, that the action of the magnet should be exerted exactly upon the dark part in order that it may become luminous; it becomes so equally even when the magnetism acts upon a dif- ferent part of the discharge, provided that this is not too far removed from the negative electrode. A consequence of the explanation that we have just given, which is easily verified experimentally, is that the portion of the gas which transmits the discharge must have a lower conduetivity when it is subject to the action of the magnet, and therefore that the electric discharge must encounter a greater total resist- ance In its passage along the inside of the tube, when any part of the tube is brought near the electromagnet, than it did before. Thus a tube, 1 metre long, filled with rarefied hydrogen, gave the following results when the apparatus for producing a derived current * was placed in the circuit :— Pressure. Intensity of the derived current. Miitheut pelea N re eds magnetization, |.°% Me Posi- | at the nega- 8 tive electrode. |tive electrode. millims. 4 33° 30° 20° i} 30 30 10 With a tube 50 centims. long, filled with rarefied nitrogen, _the following results were obtained :— Pressure. Intensity of the derived current. oy Magnetization|Magnetization Lee ies at the posi- | at the nega- Magnenzavon. tive electrode. tive electrode. millims. : | 2 bd” Dee 42° | 4 37 ath 17 Le Fg 25 20 12 | The effects are more marked when the tubes are placed equa- torially between two soft-iron armatures in immediate contact * It should not be forgotten that with this apparatus (a description of which is given in my previous paper) the derived current is nearly propor- tional to the principal current; so that its intensity may be taken as being very approximately a measure of that of the discharge which traverses the tube. \ the Electric Discharge in highly Rarefied Gaseous Media. 515 with the sides of the tube, than when they are placed axially upon the poles themselves. It will be scen that there is a much greater increase of resistance when the magnetism acts on the part of the discharge near the negative electrode, than when it acts on the part near the positive “electrode. This difference is eaused by the fact that, as was shown in my previous paper, the former part has much the higher conductivity, and therefore naturally undergoes a much ereater diminution in conducting- power by the condensation of the gaseous matter caused by the action of the magnet, than it is possible for the second part, where the gas is less rarefied, to undergo. The inversion of the poles of the magnet makes no difference in the foregoing results ; its only effect is to cause an elevation or depression of the dis- charge, which is horizontal when the magnet is not in action. Among the experiments that I have made upon the influence of the external action of magnetism upon rarefied gases enclosed in tubes, I may still mention some in which the tube was coiled up into a flat spiral terminated by two prolongations, perpendi- cular to the plane of the spiral, which serve for the introduction and rarefaction of the gas, as well as for the passage of the elec- tric discharges. The tube of the spiral, and its prolongations, is a little less than a centimetre in diameter, and its entire length is about 80 centims. With nitrogen or atmospheric air, the rare- faction must be carried at least as far as 2 millims. in order that the discharges may pass; with hydrogen, the discharge passes when the pressure is reduced to 5 or 6 millims. Moreover, whatever may he the nature of the gas or its degree of rarefac- tion, the discharge does not begin to pass until several minutes after the gasis put into the circuit. It evidently requires to be charged for a long time with statical electricity before the resist- ance to the establishment of a continuous discharge can be over- come. But when once this resistance has been overcome, the passage of the discharge may be interrupted without its being necessary to wait more than an instant before it begins again when the circuit is completed a second time, provided that the in- terruption does not last for more than one or two hours. The luminous discharge through hydrogen under a pressure or 5 or 6 millims. exhibits very fine and sharp rose-coloured striz ; under a pressure of 2 millims. they become much broader and less sharp, and the colour at the same time becomes paler. The same thing happens with air and nitrogen; but the effects are most distinct with hydrogen. A remarkable appearance is pre- sented by the discharge in the interior of the spiral; it seems to possess a very distinct rotatory motion, the direction of which appears to change with the direction of the discharge: this latter result, however, is not very constant; so that I have been 516 ~=Prof. De la Rive on the Action of Magnetism upon led to conclude that the rotation is only apparent, and is the effect of an optical delusion caused by the discontinuity of the discharge. This point is nevertheless worthy of further inves- tigation. In order to observe the action of magnetism on the spiral dis- charge, I place the glass spiral between the two poles of the electromagnet, so that its plane is parallel to those of the two polar surfaces, the two prolongations of the spiral being thus vertical, one above and the other below this plane. The mag- netization, according to its direction, either causes a condensa- tion of the discharge against the inside walls of the spiral tube, or, on the other hand, repels it towards the outer walls and makes it very diffuse. In the former case the discharge is very brilliant, and the stratifications are strongly marked; in the second case they are hardly visible, and the discharge itself is much broader and very dull. It seems to undergo, even more distinctly than before, the rotatory motion of which we have already spoken. A rather curious fact is, that in the vertical branch-of the tube which is below the spiral, and which is consequently between the two branches of the electromagnet, the discharge divides, under the influence of the magnetism, into two veins, one of which goes to one side of the tube, and the other to the other. One of these veins is very narrow, and of very little brilliance compared with the other. This separation is most likely due to the fact that the induced current of a Ruhmkorff’s apparatus consists in reality, as we have already said, of two induced cur- rents successively in opposite directions, one of which has a much greater tension than the other and passes almost alone through the gas, whereas the other is transmitted with great difficulty, but nevertheless passes (though in very small propor- tion, it is true), since the action of the magnet separates it from the principal discharge, which is in general the only one that we are called upon to consider in phenomena of this kind, in consequence of its much greater strength. I endeavoured to determine, in the case of the spiral tube, as I had done with the large straight tube, the influence of mag- netization upon the resistance of the gas to the passage of the discharge ; and the result that I obtained was rather curious. The two platinum points of the apparatus for obtaining a de- rived current being immersed in distilled water at a distance of 10 millims. from each other, and the spiral tube being filled with hydrogen under a pressure of 2 millims., I obtained a derived current which produced a deflection of 20°. The spiral was placed vertically between the two horizontal armatures of the electromagnet which were exactly in contact with its two faces. As soon as magnetization took place, the derived current was ~ the Electric Discharge in highly Rarefied Gaseous Media. 517 reduced to 15° when the discharge was repelled against the outside walls of the tube, assuming an apparent rotatory motion; while, on the other hand, it rose to 25° when the discharge was con- densed against the inside walls of the spiral. It requires further investigation to decide whether this effect of the direction of the current and of the magnetization depends on the particular form given to the discharge, or on the small diameter of the tube in comparison with its length. § 2. Experiments in which the electromagnet was placed in the middle of the rarefied gas, inside the vessel in which the latter was contained. I now pass on to the case in which the magnetic pole is within the gas which transmits the discharge. In my first experiments I used a glass globe, about 15 centims. in diameter, provided with four tubulures situated respectively at the ends of two diame- ters of the globe perpendicular to each other. Two cylindrical rods of soft iron were fixed, by means of two of these tubulures, inside the globe, and in the direction of the same diameter, so that their imner ends were about 8 or 10 centims. apart, while their outer ends projected nearly.2 centims. from the tubulure. In order to convert the internal ends into two magnetic poles, the outer ends were put in contact with the poles of a strong electromagnet. The other two tubulures served to introduce into the inside of the globe two isolated metallic stems termi- nated by balls, placed at about 10 centims. from each other, which acted as electrodes for the electric discharge, the direction of which was thus equatorial, or perpendicular to the straight line joming the magnetic poles. As long as the soft-iron rods are not magnetized, the electric discharge remains perfectly rec- tilinear ; but as soon as magnetization takes place the discharge, which we will suppose horizontal, takes the form of a semicircle, passing either above or below the line joining the magnetic poles, according to the direction of the magnetization and to that of the current. The form of the luminous arc is that of a half ring, much flattened and widened; the striz are very di- stinctly marked in it, more so than they were in the straight dis- charge; and the outside is greatly indented, especially when the gas contains a small quantity of water- or alcohol-vapour. If the electric discharge, instead of being equatorial, is axial, that is, directed from one of the magnetic poles to the other, the two poles serving as electrodes, it does not undergo any sensible change under the influence of the magnetization. Nevertheless, if the discharge is made to pass between a brass ball and an iron ball placed on the end of an iron rod so that it can be magnetized, the luminous atmosphere surrounding the Phil. Mag. 8. 4. No. 226. Suppl. Vol. 33. 2M 518 - Prof. De la Rive on the Action of Magnetism upon iron ball may be observed to be depressed or elevated at the moment of magnetization: this movement evidently depends on a change of direction on the part of the electric fibres which radiate from the ball. But the best way of studying the action of magnetism in the case of a magnetized bar placed inside the gas, is to use a bell- glass or cylindrical jar, 16 centims. in diameter by 20 centims. in height, in the axis of which is placed a soft-iron rod about 3 centims. in diameter, terminated by a rounded end situated at the middle of the axis of the cylinder. This rod is fixed into a round disk, which serves to close the jar. A metallic ring, about 12 centims. in diameter, made of wire about 3 or.4 millims. in thickness, is situated in a plane perpendicular to the axis of the jar, in such a position that the top of the soft-iron rod is at its centre ; this.ring is soldered to a stem covered with an insula- ting coating, through which it is putin communication with one of the poles of a Ruhmkorff’s apparatus, the other pole of which is connected outside the jar with the end of the soft-iron rod. The whole of that portion of the rod which extends into the jar being covered with an insulating coating, except the extremity, the discharge passes between this extremity and the ring of which it is the centre. In order to magnetize the soft-iron rod, it is only necessary to put it in contact, by its outside end, with one pole of the electromagnet, a thin sheet of idia-rubber beimg put be- tween, so that the whole apparatus may be well insulated. The cylindrical jar is closed at the other end also, where there is no iron rod, and is furnished with two stopcocks, one of which serves for introducing and rarefying the gas, while the other, being constructed in the way devised by Gay-Lussac, allows of the introduction into the jar of a greater or less quantity of any vapour. I made a very large number of experiments with this jar, fill- ing it successively with air, nitrogen, and hydrogen at various degrees of rarefaction, and employing these gases sometimes perfectly dry, and sometimes mixed with larger or smaller pro- portions of water- or alechol-vapour. Dry atmospheric air and nitrogen give almost identical results, the only difference being that the hght is brighter and more distinct with nitrogen. If the soft iron is made the positive electrode and the ring the negative electrode, at acertain degree of rarefaction the luminous discharge is seen to form a sort of peach-red envelope round the top of the soft iron, and a pale violet sheath extends over a greater or less number of degrees of the.ring. Ata very low pressure this sheath surrounds the whole ring, while the top of the soft-iron rod is enveloped by a yose-coloured halo, and a very short jet of the saine colour, the Blectric Discharge in highly Rarefied Gaseous Media. 519 shaped like a large comma, escapes from it. When the soft iron is magnetized, this comma is distinctly seen to revolve, to- gether with the halo from which it proceeds, in one direction or the other, according to the direction of the magnetization. At the same time the violet sheath which surrounds the ring is seen to revolve in the same direction as the rose-coloured halo, although they are separated by a perfectly dark space. On changing the direction of the discharge, a violet envelope appears at the negative electrode, but does not completely cover the summit of the soft-iron rod unless the gas is very much rare- fied ; while at the positive electrode brilliant points may be seen, separated from each other by a rose-coloured glow which sur- rounds the whole of the rmg, and from which there proceed a few regular stratifications concentric internally with the ring. When the gas is not very much rarefied, a luminous jet appears starting from the ring and extending to the top of the central rod of soft iron (from which it is separated only by a narrow dark space), and exhibiting a movement of rotation one way or the other, like the hand of a watch, according to the direction of the magnetization. In this case only part of the top of the soft-iron rod is covered by the violet sheath, and this luminous segment turns with the brillant jet. I made a very great many experiments, under the conditions I have just described, with atmospheric air, nitrogen, and hy- drogen, both dry and more or less charged with vapour. J will now give a summary description of these experiments, remark- ing here, in the first place, that whatever was the nature of the gas and its degree of elasticity, and whether it was dry or im- pregnated with vapour, tie velocity of rotation was always much ereater when the ring was made the positive electrode than when it was negative, and that this rotation, which became more and more rapid as the tension diminished, ceased to be appreciable under a much lower tension in the latter case than in the former. In my first experiments I used a large globe 25 centims. in diameter, the diameter of the rmg being 20 centims., and that of the central rod of soft iron 8 centims. This globe had two tubulures; one of them served for the introduction of the soft« iron rod, the top of which reached to the centre of the globe, while the lower end projected from the tubulure, so that it could be placed on the polar surface of the electromagnet; the other tubulure was closed by a stopcock through which the gas and vapour could be introduced, and which carried an insulated con- ductor that supported the ring and allowed of its being put into the electric circuit. The discharge passed accordingly between the summit of the soft-iron rod and the metallic ring. 2 M2 520 = Prof. De la Rive on the Action of Magnetism upon This globe was filled with air rarefied to 4 millims.; the dis- charge then took place in the form of a jet, which turned at the rate of sixty revolutions per minute when the ring was positive, and of twenty per minute when it was negative. Under a pres- sure of 6 millims. the velocity of rotation was only forty turns per minute in the former case, and twenty turns in the latter. Lastly, with alcohol-vapour, the pressure being 5 millims., the velocities of rotation were respectively twenty-two and eleven turns per minute. These first experiments having put me on the track of re- searches of this, kind, I repeated “this investigation, employing the j jar of 20 centims. by 16 that I have described above. I sive, in the first place, the results obtained with dry atmospheric alr :— Number of turns per minute. Pressure. Ring positive. | Ring negative. millims. 16 55 36 ‘ 12 83 55 9 a9 63 6 eee 100 3 128 2 oon At 9 millims., the ring being the positive electrode, the discharge no longer formed a jet, but was spread out into a sector of 30° to 45°; this sector obeyed the movement of rotation as the jet did previously, but it increased in size in proportion as the pressure diminished, and at 6 millims. it formed a complete circular sheet : the rotation, which up to this point had gone on increas- ing in rapidity, was then no longer perceptible. When the ring forms the negative electrode, it becomes covered with a violet sheath, the extent of which likewise increases as the pressure diminishes, but it still occupies only half the circumference of the ring under a pressure of 4 millims. At this pressure it is seen to revolve very rapidly, but under a pressure of 2 millims. it occupies the whole circumference of the ring, and the rotatory motion is no longer sensible. At the top of the magnetized rod of soft iron there is a rose-coloured halo whence issues a very short point or jet in the shape of a comma, which turns with the violet sheath, and is separated from it by a very considerable dark space. It ought to be mentioned that, under a pressure of 6 or 4 mil- lims. and sometimes under a pressure of 3 millims., it generally happens, when the ring is the positive electrode, that on first ——— the Electric Discharge in highly Rarefied Gaseous Media. 521 completing the circuit, a luminous jet is formed which turns too rapidly for its velocity of rotation to be measured, but which very quickly spreads out so as to form at first for a few moments a sector which continues to revolve, and soon afterwards a com- plete circular sheet which no longer exhibits any perceptible motion. It must not be thought that the action of magnetism ceases when the gas is too far rarefied for there to be any jonget a Vi- sible rotation. The action then shows itself under another form, as is proved by experiments made at pressures of 3 to 2 millims. Thus if the ring is employed as negative electrode, the violet sheath which surrounds it is seen to be depressed at the moment of magnetizing the soft iron, and to rise at the moment of demagnetizing it. If, on the other hand, the ring is made the positive electrode, the rose-coloured sheet, which occupies the space between the ring and the central iron rod, 1s raised, as well as the violet sheet which issues from the summit of the rod, at the moment of magnetization, and uum at the moment of demagnetization. The following more complete experiment with dry nitrogen proves that the rotation begins to show itself at higher pressures when the ring is positive than when it is negative : — Number of turns in one minute. Pressure. Ring positive. | Ring negative. millims. 39 12 29 27 21 495 36 16 67 51 12 99 59 8 115 70 6 “fi 115 5 150 At 4 millims. pressure the rotation is too rapid to be counted, and at 3 millims. it appears to cease completely. The rose- coloured halo is very bright when the top of the soft-iron rod is positive. Moreover, when there is no longer any rotation, a depression or elevation may be observed under the influence of the magnetization, just as with atmospheric air. The pressure of vapour modifies the results obtained ‘ith dry gases In some important respects. In the following experiment with ordinary air reduced to a pressure of 2 millims., aqueous vapour was introduced in successive quantities, so as to increase the pressure solely by the effect of the presence of the vapour. 522 Prof. Dela Rive on the Action of Magnetism upon Number of turns in one minute. Pressure. Ring positive. | Ring negative. millims. 2 4 6 se 92 8 140 70 10 120 52 12 90 50 14 80 48 Tt will be seen that at equal -pressures the rotation is more rapid in presence of aqueous vapour than with dry air,—a fact which is probably connected with the greater facility with which the discharge is transmitted. When the external air is of a me- dium degree of humidity, we have at a pressure of 14 millims. 72 turns instead of 80 with the ring positive, and 44 instead of 48 when the ring is negative. But the most characteristic fact which the presence of aqueous vapour brought out was the division of a single electrical jet under the influence of magnetism into a series of small, distinct, equidistant jets which turn like the spokes of a wheel. This division can be seen only when the ring serves as positive elec- trode. Ata pressure of 6 millims. the single jet begins to ro- tate, and afterwards spreads out and the rotation is no longer sensible; but under pressures of 8, 10, and 12 miilims. the jet di- vides itself under the action of magnetism, as soon as the rotation begins, into five or six jets, which turn, as we have already said, like the spokes of a wheel; whereas when the air is dry the jet never divides itself, but merely spreads out at low pressures into a sector or a circle, the whole of which is continuous throughout. When the ring is negative, it will be observed that, in pre- sence of vapour, the jet which starts from the summit of the soft-iron rod exhibits at the part where it is in contact with the iron, at the moment when the iron is magnetized, instead of a continuous surface, a series of bright points which seem to be the starting-points of an equal number of small jets not sepa- rated from each other far enough to be distinct. It is thus simply an expansion or spreading out which is undergone by the part of the jet which is in contact with the iron, and the jet does not divide itself into several veins. Alcohol-vapour produces exactly the same effect as aqueous vapour. ‘The single jet is much more brilliant in this case than it is with dry air or with aqueous vapour: it exhibits beautiful stratifications which give to it exactly the appearance of a che- nille. Magnetization causes 1t to spread out and to divide into the Electric Discharge in highly Rarefied Gaseous Media. 528 several jets of much greater width than what are seen with aqueous vapour. Nevertheless, if the diameter of the ring 1s too great (more than 15 centims., for example), the subdivision of the jet cannot be obtained except with difficulty, unless the in- tensity of the discharge and that of the magnetization are very considerable. In the following experiment the rarefied gas was hydrogen, and several successive quantities of alcohol-vapour were intro- duced into it. The pressure of the pure and dry gas at the be- ginning was 5 millims. At this pressure, as we shall see imme- diately, hydrogen transmits the discharge solely under the form of aluminous sheet. The pressure was then augmented entirely by the alcohol-vapour, and the following results were obtained :— Number of turns in one minute. Pressure. Ring positive. | Ring negative. millims. 7 Luminous sheet. 92 10 a 52 12 64 48 15 48 38 18 40 32 22 30 25 27 24 18 36 12 10 38 12 10 The division into a greater or less number of separate jet took place when the ring was made the positive electrode. When pure and dry liydrogen 1 is the medium through which the discharges are passed, it is very difficult to obtain the phe- nomena of rotation. At comparatively high pressures, such as 128 millims., jets are certainly obtained, but they are not suffi- ciently continuous for a magnet to be capable of affecting them. At 90 millims. I obtained a small jet in the form of a bluish- ‘white thread, which, when the ring was positive, revolved at the Fate of 85 turns in a minute ; but it soon broke up into a mul- titude of little irregular jets, and the rotation was then no longer perceptible. As far as 40 millims. the action of the magnet was but shghtly marked; at 30 millims. the negative ring became covered with small violet sheaths, separated by uniform intervals, which, at the instant of making the magnet, seemed to exhibit a tendency to motion in one direction or the other, according to the direction of the magnetization. The same thing happens in the case of the small, “uniformly but closely distributed bril- liant points wherewith the ring becomes covered when it is positive. At 5 millims., and still more at 3 and 2, the ring 524 Prof. De la Rive on the Action of Magnetism upon becomes completely covered, when it is negative, with a beautiful violet sheath, which contracts under the influence of the magnet. The top of the iron rod, which is then positive, is surrounded by a beautiful halo of a somewhat rosy-white colour, 3 centims. broad, and very distinctly stratified. Magnetization causes marked contraction in the halo, and causes the striz to approach closer together without diminishing their number; it further causes it to rise up, giving to it the shape of a pear resting with its base upon the magnetic pole. When this pole is the nega- tive electrode, a magnificent violet-coloured tuft, as we have already seen, issues from it, and becomes erect when the mag- net 1s 10 action. All the phenomena that we have here described prove in a striking manner the molecular differences presented by the various elastic fluids, even when greatly rarefied. ‘Thus in the case of hydrogen, although this gas is a very good conductor of electricity, the electric jets obey with difficulty, and only toa slight extent, the action of the magnet, probably on account of the low density of the gas. With air and nitrogen the state of things is just the opposite, especially when these gases are moist. The “singular property possessed by the electric j jet of dividing into several distinct jets, instead of spreading out, under the in- fluence of magnetization, when the medium which it traverses contains a greater or less quantity of vapour, would seem to in- dicate on the part of the vapour greater cohesion than is pos- sessed by the gases properly so called, if it be allowable to talk of cohesion in relation to such highly rarefied elastic fluids. It is also possible that this division into jets is nothing more than the result of an optical illusion due to a very rapid succession of jets starting from different points, but not simultaneous. This is a point for further examination. However this may be, it is evident that the study of the stra- tification of the electric light, and of the action of magnetism on the discharge in different gaseous media, reveals differences among these media which can only be due to differences of mole- cular constitution. Density, in particular, would seem to exert a great influence upon phenomena of this kind, since we find them exhibited to such a small extent by hydrogen, whereas aqueous vapour, and especially the vapours of alcohol and ether, exhibit them in such a marked manner. The special nature of the particular elastic fluids in reference to the greater or less resistance they oppose tothe transmission of electricity must doubtless also come into play. It is therefore not impossible that a more detailed and ‘searching examination of the pheno~ mena we have been considering, and in particular of those con- nected with the action of the magnet on electric currents pro- the Electric Discharge in highly Rarefied Gaseous Media. 525 pagated through highly rarefied elastic fluids, may furnish some new ideas as to the physical constitution of these bodies, and as to the manner in which electricity is transmitted by them. § 3. Supplement to the preceding Researches. The experiments described in §$ 1 and 2 had been already in great part published in the Mémoires de la Société de Physique et d’ Histoire Naturelle de Genéve (vol. xvii. part 1), when I again took up the subject and obtained results which have not hitherto been published, and which appear to me to possess some interest as throwing new light upon the nature of these phenomena. I began by taking two jars, exactly like the one with which I had made my first experiments and which I have “described above (p. 518), and I placed them so that the discharge of the Ruhmkorff’s coil could either be divided between them or be made to traverse them in succession. In the former case, even when care was taken to reduce the air in each as nearly as pos- sible to the same degree of rarefaction, it was very difficult to get the discharge to divide itself equally between them, at least for any length of time. It would cease, after a short time, passing through one of them, and pass wholly through the other ; if then the passage of the discharge was interrupted for a moment and then reestablished, it would often happen that the jar which had previously transmitted the discharge would transmit it no longer, and vice versd. These alternations are very probably due to the difficulty that there is in producing, and in after- wards maintaining, perfect identity between the two gaseous -Inedia, notwitstanding all the pains bestowed upon this matter at the beginning, differences of temperature and of molecular arrangement occurring very quickly. When the discharge traverses the two jars in succession in- stead of dividing itself between them, the rotation takes place with equal rapidity in each, provided that care has been taken to rarefy the air in both to exactly the same extent. A slight difference is apparent only at very low pressures, in consequence of the imperfect identity beimg more sensible at these pressures. For instance :— Number of turns in 15 seconds in both jars alike. Pressure. Ring positive. | Ring negative. millims. 12 14 12 - 10 18 14 8 22, 16 6 29 21 526 Prof. De la Rive on the Action of Magnetism upon _ At 4 millims. pressure, the ring being positive, the number of turns in 15 seconds was 36 in one jar.and 38 in the other. Keeping the two jars in the circuit one after the other, and varying the rarefaction in one of them without changing it in the other, the following results were obtained :— The pressure in one jar being kept constant at 14 millims., the rate of rotation was 14 turns in 15 seconds with the ring posi- tive and 12 with the ring negative. This rate increased a little when the air in the second jar was rarefied as far as 4 millims., but was still only 16 and 13 turns in 15 seconds with the ring respectively positive and negative: this slight increase was evi- dently due to the greater intensity of the electric discharge con- sequent upon the diminution of resistance in the jar in which the pressure of the air was varied. As to this latter jar, the rate of rotation increased in it considerably as the pressure was dimi- nished, as may be seen from the following Table :— Number of turns in 15 secouds. Pressure. Ring positive. Ring negative. millims. 10 16 12 8 20 16 6 24 20 4 33 alae 22 3 Too great to 30 be counted. These two jars being still used, the air in one of them was rarefied as far as possible and aqueous vapour was then intro- duced into it, while the other was filled with very dry air at 10, 12, or 14 millims. pressure. As long as the pressure of the vapour was below that of the air, the rotation in it was the more rapid. It rapidly diminishes when the pressure increases beyond 4 millims., at which point it is 33 turns in 15 seconds with the ring positive, and 20 with the rmg negative. At 6 muillims. pressure the rotations were respectively 26 and 15; at 12 mil- lims. they were 16 and 12; and in the second jar, containing air at 12 millims., they were likewise 16 and 12. It seems to follow from this that, when the elastic force is the same, the rate of rotation is the same in air and in aqueous vapour. In order to make quite sure that this was the case, | replaced both jars parallel to each other in the circuit, so that the discharge was obliged to divide itself between them, and began by trying to what degree of rarefaction it was needful to reduce air in order that its resistance might be equal to that of aqueous vapour of,a certain pressure. I thus found that air at 7 millims. had the the Electric Discharge in highly Rarefied Gaseous Media. 527 same electric conductivity as aqueous vapour at 13 millims. Nevertheless an electric discharge of the same intensity made in the former medium 49 turns (with the ring positive) and 25 (ving negative) in 15 seconds, whereas in the latter it made only | 31 and 17 in the same time. This result proves that the rate of rotation does not depend solely upon the intensity of the electric discharge, but also to a great extent upon the molecular consti- tution of the gaseous medium. On the other hand, if without paying any attention to differ- ences of conductivity, both jars are placed in succession in the same circuit, so that the same discharge necessarily traverses both, the rate of rotation is found to be the same in air and in aqueous vapour when the pressure is the same. Air and Aqueous Vapour at Equal Pressures. | Number of turns in ] minute. Pressure. | Ring positive. Ring negative. | millims. | 10 50 20 | 13 é B2 17 Each of these experiments was made three times, and gave the same result every time. It is therefore equality of elastic force, and not of electrical re- sistance, which determines the equality in the rate of rotation in dry air and aqueous vapour of the same electrical discharge under the influence of two electromagnets of the same strength. Some trials made with alcohol-vapour did not give quite such conclusive results. Thus, at a pressure of 10 millims., the rate of rotation was 17 turns per minute in both media with the ring negative, but with the rmg positive the number of turns was 30 in air and 20 in the alcohol-vapour. At 6 millims. pressure and with the ring negative, the number of turns was 24 in a minute in both air and alcohol-vapour, and with the ring positive it was 30 in both media alike. It therefore seems that, as the pres- sure diminishes, the rates of rotation approach equality. | In the foregoing experiments, the two Jars, exactly similar as to their dimensions and construction, were placed one on each polar surface of a powerful electromagnet, so that it was certain that the intensity of the magnetism of the soft-iron rods in the interior of each was really the same. Subsequently the soft-iron rod in one of the jars was replaced by a rod of brass of like shape and size. ‘The jar thus modified was placed on one of the polar surfaces of the. electromagnet ; and rotation took place as before, 528 Prof. De la Rive on the Action of Magnetism upon solely under the influence of the pole of the electromagnet. In order to examine the effect of this alteration, the two Jars, one containing the brass rod and the other a soft-iron rod as before, were introduced into the circuit one after the other, one being placed on each polar surface of the electromagnet, and both being filled with dry air rarefied to various degrees. Ac- cording to this arrangement of the jars, the air in each was tra- versed by the same discharge. The following are the results obtained :— Number of turns in 15 seconds, Pressure. Tron rod. Brass rod. Ring Ring Ring Ring positive. | negative. positive. | negative. millims. 20 20 12 10 9 18 20 12 11 10 16 24 13 12 11 14 28 14 14 13 12 32 14 16 15 10 38 16 20 19 8 46 19 21 De 7 49 22 225 26 6 56 aif 24 30 5 59 48 26 34 4 a 70 as 40 In another set of experiments the jar with the brass rod gave 25 turns in 15 seconds at a pressure of 8 millims., whichever way the current was sent,—whence we may conclude that the rate of rotation is sensibly the same at this pressure when the ring is negative as when it is positive. The same thing may be said of the higher pressures also, at which the differ- ence, although always on the same side, is too small to be of importance. At lower pressures the rate of rotation is greater when the ring is negative than when it is positive, contrary to what takes place with the jar containing the iron rod; and the difference becomes greater as the pressure diminishes. It may be observed that the absolute rate of rotation is always greatest in the jar with the iron rod, in consequence of the mag- netic pole, which in this case is at the end of the iron rod, bemg much nearer to the electric jet. Moreover the rate of rotation in the jar with the brass rod increases when the iron rod in the other jar is not magnetized and there is consequently no rotation in this jar, notwithstanding that the same discharge passes through it as before. These conditions are easily fulfilled the Electric Discharge in highly Rarefied Gaseous Media. 529 by taking the jar with the iron rod off the pole of the electro- magnet, and placing it at such a distance that it is not affected by it, and leaving everything else as it was. Thus, in thel ast experiment that I have quoted, the two jars being respectively on the two polar surfaces of the electro- magnet, and the air in both being rarefied to 8 millims., we had 25 turns in-a quarter of a minute in the jar with the brass rod, whether the ring was positive or negative; while in the jar with the iron rod there were 46 turns in the same time when the ring was positive, and 22 when it was negative. The jar with the iron rod having been removed from the electromagnet, the numbers of turns in the other jar were 29 and 30 instead of 25 as before, although the discharge still passed through the jar with the iron rod; but the rod not being magnetized, there was no rotation. This effect is sensible only when the pressure is low, as from 8 to 10 millims. or less, and when the ring is positive in the jar with the iron rod. In all probability it is due to the following cause : the soft iron being in this case the negative electrode, its magnetization producing a condensation of that part of the elec- tric jet near to the negative electrode, increases the resistance, and thus diminishes the intensity of the discharge*. This effect is independent of the direction of the magnetiza- tion, and depends only upon the direction of the discharge. Up to a certain point, the rate of rotation of the jet in the jar with the brass rod is independent of the direction of the dis- charge in this jar when there is no magnetization in the other. Nevertheless, when the discharge is weak, I have thought I could detect, at 8 millims. (and even at 6 millims.) pressure, even when the soft-iron rod in the second jar was not magnetized, a difference in the rate of rotation of the jet in the jar with the brass rod, according to whether the ring is positive (in which case the rate of rotation is smaller), or whether it is negative (in which case it is a little greater). It is unnecessary to point out that this is just the contrary of what happens in the jar with the magnetized iron rod. The effect of magnetization can likewise be rendered sensible by putting into the circuit, at the same time as the jar with the brass rod, an electrical egg in place of the jar with the iron rod, One of the rods between which the electric jet passes in the egg is made of soft iron; and as soon as this is magnetized, if it * We have already seen, at the beginning of this memoir (p. 513), the great influence which the neighbourhood of a magnetic pole has upon the electricai resistance of a rarefied gaseous medium, especially when the pole is near the negative electrode, and the discharge is transmitted through a tube. 580 - Mr. S. Roberts on the Order of the Conditions that has been made the negative electrode, the rate of rotation is seen to diminish as before in the jar with the brass rod,—a result which is due in this case also to the magnetization condensing the jet, and so increasing the resistance, whereby the intensity of the electric discharge is lessened. I am fully aware that further study of these phenomena is still required, and I-hope not to be long before I set about it. _ What I now publish is only a first attempt; and my principal object in making it known is to draw the attention of physicists to this interesting subject. LXV. Note on the Order of the Conditions that an Algebraical Equation may have a set of Multiple Roots. By SamMunt Rozerts, Hsg.* 7K may find the order of the conditions, in the coefficients, that an equation may have a set of ¢ multiple roots of the orders 7,, 2, ...m; respectively in the followmg manner. Let dn(w) =0 be the given equation of the degree m; then, in order that it may have m— Xn given roots denoted by 2, @, «+; we must put Pin(#;) =0, Pin (%_) = 90, ee Deed Pin (@m_—sn) = 0, and we can make the remaining 27 roots what we please. Now we may take any ¢ of the roots a, @,... and may as- sume Xn quantities such that 7, of these are approximate (1. e. indefinitely near) to one of the ¢ selected roots, ng, in like man- ner, approximate to another of the selected roots, n, to another of them, and so forth, until the ¢ roots are exhausted. In this manner we obviously get an equation having m—Zn given roots, and having a set of ¢ roots of the orders of multiplicity n,, m4, Nz,...24 by giving to the remaining =” roots the values so as- sumed. But it is plain that these Xn roots may be assumed approxi- mate to the given roots in a variety of ways, the number of which, however, is perfectly definite. For instance, let us consider the n, roots approximate toa given root. Although approximate, these n, roots may be con- sidered as greater or less than the given root by an infinitely small difference. Thus if the given root is x), then 2,+w, 2, —w, where w is indefinitely small, give two different manners of approximating to 2, We may now distinguish the ways in which we can take n, roots approximate to #, as follows :—Let d, mean a root which approaches zx, with a decrement, 2, a root * Communicated by the Author. an Algebraical Equation may have a set of Multiple Roots. 581 which approaches 2, with an increment, then we may have bpmlaginudgs Le: tag ita lat wa Whi Le Ma) Wales ith [a a Wh Ply Degen 2 Opes There are therefore n,+1 ways in which we may constitute z, a multiple root of the order (n,). For a particular set of ¢ given roots, then, the number of ways in which we can form a set of ¢ multiple roots of the orders 7,, 7g, ... 7, respectively is (m, +1) (mg+1)... (m,+1), for which expression we may write P(n+1). Again, the number of ways in which we can take ¢ roots out of m— Xn roots is (m— dn) (m—Zn—1)...(m—Sn—t+1), counting permutations of the ¢ roots, as in the present case we have to count them. Hence the total number of ways in which we can attribute m— Xn given roots and a set of ¢ multiple roots of the orders Hiss Wop ses The 1S P(n+1)(m—Zn)(m—Sn—1)...(m—In—t+l1).. . . (@ But this is the order which we have to obtain; for it is the order of the conditions that the given equation ¢,,(v7) =O may have the stated set of multiple roots, combined with the condi- tions that this equation may have m— Xn given roots. This last set of conditions being linear in the coefficients, the result is simply the order of the conditions for the multiple roots. It has been supposed that n,, m9,...m, are all different ; if p of them have one common value and g of them have another common value, and so on, we must divide the result by ee a feel. 2... 95+; 80.that we have Pia +1) (m—Zn) (m—Zn—1)... (m—2n—t +1) (2) |e SF sel ge mee ees st M. Jonquiéres has given these results as particular deductions from a theorem of great generality, on the multiple contacts of 532 Mr.S. Roberts on the Order of the Conditions that curves (Crelle, 1866, part 4). I have thought it worth while to give a proof apart from geometrical considerations, and to apply the results to some cases in which the coefficients of the equa- tion are supposed to be functions of secondary variables. Let it be supposed that the coefficients of a”, x”—1, a”—?, &c. in the given equation are of the orders A, A+a, A+2a, &c. m the secondary variables. According to a method elsewhere indicated*, I suppose the equation to be broken up into factors of the first degree, the co- : : NX : efficients being of the orders ate ae respectively. The order of the conditions for the stated set of multiple roots must be of the form m.m—1...m—p+1 ree m.m—1 1 MP2 2 ap P leer po — (c) + &e. +mK,, where p is written for Xn+¢, K, is the order of the conditions that p factors of the given equation may constitute a set of ¢ multiple roots of the orders 7, %,... 1”, respectively without the necessary evanescence of any factor; K,_, is the like order rela- tive to p—1 factors of the given equation, the evanescence of a factor being necessarily implied, and so on. It -is important to remark that K,_}, K,-.,.-. ) jawegae affected with the multiplier A, since in each case the identical evanescence of a factor or factors is implied. Now K, is given by (1.2.2.2 +72) ny+1 no+1 N3+1 net Gry Gye) a m m m m SERGE GL AGG Ee 3 a since we have only to apply the general theorem* for the order of the conditions that a given set of linear equations may coexist to the sets of n,+1 factors, n»+1 factors, &c., n+] factors into which 2n-+¢ factors may be divided. But there are 1.2...2+¢ such divisions, which gives the first portion of the expression for K;; and the rule or theorem referred to gives the remaining factors of the expression. _ | This being so, it follows that if NX=0, e=1, the order of which we are treating is (mn »(m—1).(m—2)...m—Yn—t+ 1), * Salmon’s ‘Modern Algebra,’ 2nd edit. p. 281. an Agenaea Equation may have a set of Multiple Roots. 588 M4) No,--- being all different. If p of them have a common value, aad g of ‘them have another common value, and so on, we must take for our result m .(m—1)(m—2) ...(m—Bn—t+1). 1.2...p.1.2...q... Again, if«#=0 and X=1, the order is given by (a) or (4); so that in point of fact the coefficient of A*"+‘—! in the general ex- pression (c) is given by those formule. Now, in order to obtain the complete expression for the order, in some cases the following consideration suffices :—The expres- sion must remain unchanged when for A, &« we substitute X+ma, —a. It is evident that if mstead of beginning with the coefficient of # and proceeding by increments (or decre- ments, as the case may be) of the orders, we commence with the last term of the given equation, and proceed backwards by decrements (or increments, as the case may be) of the orders, we have X-++- am, —« replacing X, a. I take the cases which this consideration enables us to deal with. (1) Three equal roots. The order is of the form m—2)43d2+ Mra -+ m(m—1)a2t, 5 M remaining to be determined. The above expression must be identical with (m—2) {3(X+ am)2—M (A+ am)a+m(m—1)a?}; *, 3m?a?— Mma?=0, M=3m, and the requiredorder is 3(m—2)A(A+ ma) +m (m—1) (m—2). (2) Two equal pairs of roots. The order is of the form (m—2}(m—3) { 2d?+ Mra fs are which must be the same as (m— 2) (m—3) 1 2(X + an)?M (A+ am)a + mn") | Phil, Mag. 8.4, No, 226. Suppl. Vol. 33. 2N 534 Mr. S. Roberts on the Order of the Conditions that Therefore 2a°m?— Mma?=0, M=2m; and the required order is | m(m—1)(m—2)(m—3) 5 2(m—2)(m—8)dA(A-+-ma) + 5 a. (3) Four equal roots. The order is of the form (m—8) {403+ Mra2+Nra2-+m. (m—1)(m—2)a5t which must be the same as : (m—8) 44(.+ am)8—M(rX-+am)a +N(A-+ am) a? —m(m—1)(m—2)a5}. Therefore Ama? — Mma? + Nmai= 2m(m— 1) (m—2)a3, A. 38m?a?—2Mma?=0, giving M=2. 3m, N =2(m—1)(m—2) + 2m?. The order required is consequently A(m—3)\r? + 6m(m—3)rea + 2((m— 1) (m—2) + m?) ro? +m(m—1) (m—2)(m—38)a?. (4) A triple root and a double root. The order is of the form (m— 8) (m—4) {8.208 + MA2a+ Nrw?-+m (m—1) (m—2)a°}, which must be identical with (m—38)(m—4) {3 .2(A+ me)? — M(A-+- am)? + N(A + me) a? - —m(m—1)(m—2)a°}. Therefore 6m? a3 — Mma? + Nina? = 2m(m—1)(m—2)e°, 6 . 38m?a? —2Mme?=0, giving M=9m, . N=2(m—1) (m—2) + 3m?. an Algebraical Equation may have a set of Multiple Roots. 535 The order required is | 6(m — 3) (m— 4)r3 + 9m(m—8) (m—4)rA2a Be (2(m—1)(m—2) +3m?)ra? + m(m—1)(m—2) (m —3) (m4) 28 (5) Three pairs of equal roots. , The order is of the form (m—3) (m—4) (m—5) 45 Ae + MAZe + NXw? + min es ah, which must be identical with (m—3)(m—A4) (m—5) pee pe) ite (A+ ma)?—M(rX+am)?a+N(X+ me)a?— eat Therefore mee —Mm?e2+ Nine = sido aN ura : se a a’, 4in?a?— 2Mma?=0, giving M=2m, (m—1)(m—2) +2m? igs The order required is consequently N= Bie VG 2A Nie BYAF - 2in(m Br —4)(m — Se 3 | 2 (m— =) + 2m? m(m —1) (m—2) (m—3)(m—4)(m—5) 3. te Se The foregoing process, however, is not sufficient to determine all the terms in higher cases. (1) and (2) were given by Dr. Salmon (Quarterly Journal of Mathematics, vol. 1. pp. 255 & 256). (m—3) (m— 4) (m—5)da? 2N2 [ 536 ] LXVI. Note on Mr. Croll’s Paper on the Influence of the Obl- quity of the Eclptic on Climate. By Joun Carrick Moore, TSW el G Sane. N an elaborate memoir in the last Number of the Philoso- phical Magazine, Mr. Croll estimates the annual heat at the poles received from the sun, when the obliquity of the ecliptic was at its maximum (24° 50! 34!), to be greater than at present by 7s of the whole quantity; and as this fraction zs applies to all the subsequent computations, any inaccuracy in it will affect all the numerical results. Mr. Croll deduces this quantity from a paper by Mr. Meech (Smithsonian Contributions to Knowledge, vol. ix.), where Mr. Meech proves the annual amount of heat at the equator, with a maximum of obliquity, to be to that at the poles as 365°51 to 160°04. Mr. Meech, in his very meritorious paper, takes into consideration the variations of heat due to change of obliquity, of Jatitude, of the length of the day, and of the height of the sun above the horizon at each instant; but he makes no allowance for the effects of atmosphere ; and he expressly warns his readers (pages 21 and 44) that his results apply only to the outer limits of the atmosphere, and will not give the resulting terrestrial temperatures. The same warning may be found in Sir Charles Lyell’s last edition of his ‘ Principles of Geology.’ The effects of the increased length of ray and of the increasing density of the lower strata of the atmosphere are considered by the authors of the article “ Climate” in the Encyclopedia Bri- tannica ; and their result is that the heat received at the equator is to that at the poles as more than 8 to 1, instead of less than 24 tol, as Mr. Croll computes. Mr. Croll does indeed allude to the article “ Climate,” but dismisses it rather summarily by saying that the results are “ wholly erroneous.” “The researches of Melloni and Tyndall,” he says, “show that when a ray passes through any substance, the absorption is rapid at first, but the ray is soon sifted, as it is called, and it then passes onwards with but little further obstruction.” But the experiments in the place cited are quite beside this question. They show indeed that ifa ray is made to pass through a number of transparent plates of the same substance and thick- ness, the proportion of the rays transmitted through the first plate is greater than the proportion of those which, having - emerged through the first plate, can pass through the second. But they do not show that, if the successive plates had increased -in thickness or im density, the ray (or rather all that remains of * Communicated by the Author. Chief Justice Cockle on the Conversion of Integrals. 937 it) would pass on with little obstruction. On the contrary, it is proved by a beautiful set of experiments by Prof. Tyndall, that the absorption of heat in passing through a gas varies within certain limits as the density. Now this is the very law of absorption which the authors of “ Climate’ assumed as their data; and, for the correctness of their mathematical results, it is immaterial whether the assumption be that the absorption is due to the at- mosphere, or to the aqueous vapour suspended in the atmosphere. I conclude, therefore, that Mr. Meech’s memoir will not give us the annual terrestrial temperatures, and that I cannot believe the results given in the admirable article “Climate” to be “wholly erroneous” till better reasons are alleged. June 8, 1867. LXVILI. On the Conversion of Integrals. By the Honourable Chief Justice Cocxiz, F.R.S., President of the Queensland Philosophical Society®. 1. Ee: HG ey Ol oe ee es Gh) and supposé that, by means of series or by any other means, we can obtain a solution of (1) in the form y=| (2, DOM eer snot eae. e Mae (2) where the integration signified is either definite or indefinite. 2. The object is to supplant the integration, definite or inde- finite, with respect to v by an indefinite integration with respect to #. This can be done whenever we can find two functions of x only, say e and ¢, such as to satisfy the relation d d d o te cf tht ee =o : @) in which, for brevity, b represents i v) and f(a, v) may be - any function free from integration with respect to » which will satisfy the relation. 3. Taking the variables 2 and v as independent, and integra- ting (3) with respect to v, we have (2 dos cop + (C0) [bao te ON cpp Mains ih o( 2) where X is a function of x only. But, by (1) and (2), this last equation is equivalent to 4 (t—e)y=X—erg la, ) fle, 0)... 6) * Communicated by the Author. 588 Chief Justice Cockle on the Conversion of Integrals. or, if the integration with respect to v in (2) be definite and be- tween limits m and n, to O 4 (6—ey=X—ev{ $e, 2) (0, m)} fle, n) +fle,m). (6) 4, Hither of the last two equations is a linear differential in y, whence y can be expressed by indefinite integrations with re- spect to z only. The function X is to be determined by the conditions of the question*. 5. This process zo be extended. Let ¢ satisfy the relation = fc oe tb + 2 eg) then, co with respect to v, we have a" LNG as $ 1. ie du+ Boz Ay a) (ze dv +evg+ (S—e) fpdv+f=X which is equivalent to | : ay Tht y-B) + C-dy=X— eh —Bo Psi» 9) and, subject to the determination of X, the expression of y by a formula free from integration with respect to v depends upon the solution of a linear differential equation of the second order. In the last three equations f of course represents f(z, v), and throughout this paper it is considered that ¢ and f are free from integration with respect to v; so that our ultimate results in- volve, in the case of equations (5) and (6), no other integrations than those with respect to 2. 6. The process may be further extended and conditions ascer- tained which, when satisfied, enable us to make the expression of the y of (2) depend upon the solution of linear differential equations of an order higher than the second. When (1) isa linear differential equation of the order n, and the y of (2) can be made to depend on a linear differential equation of the order m by the foregoing process, the determination of the function X in general depends upon a linear differential equation of the order n—m. 7. Starting with the equations dV dP : =P 4 =O, ns. Om +09 44 dv $ (8) * When (1) is a linear differential equation of the nth order, X is deter- mined by a linear differential equation of the (z—1)th order, and (5) or (6) gives an internal factor of (1). Chief Justice Cockle on the Conversion of Integrals. 589 I shall apply this process to the equation or integral > xvPdv v= | Sep e . ° ° . ° ° (12) wherein V is any function whatever of v. This integral is in one sense a particular, and in another sense a general case of certain definite integrals used by Boole at page 752 of the Phi- losophical Transactions for 1864. 8. From (12) we obtain vvP b= (2, ane mie e e é ‘ ; : 4 (13) Be oP dx (l—axV)?’ ta dp __ (P+ 0Q) + az? (vP? —VP—vVQ) | 15) dv (l—axV)? ; ee and @ may be put under the form avP —ax?vVP | (1—axzV)? (16) 9. Let v?P So(#,”) = Tayav’ RE ere aie emt a emi ge y/ then we have, availing ourselves of (16), dp _vdb , ad , df, _ (a+2)uP | de dee © ty ~ —axvy? Faihal Ga Se and further, 2 es, aides. @. sav av) Bear) which equation, by putting AL allie ineaaree ie a fatlle. a6] is seen to be of the required form (8). 10. It follows that the differential resolvents of the trinomial algebraic equations used by Boole may be depressed by one order, or by two orders, if we take the form under which Boole exhibited the resolvent. In other words, we may depress by one order the (n—1)-ordinal differential resolvent of a Boolian algebraic trinomial equation of the mth degree. fr=fr (20, 21,22) Brisbane, Queensland, Australia, April 20, 1867. [540-9 LXVIIL. On a Theory proposed by Fresnel, and on a mode of measuring the average size of very fine Particles. By OcpEN N. Roop, Professor of Physics in Columbia College*. | i te the light from a candle-flame be received on a ground glass surface so obliquely that the incident ray makes only a very small angle with the glass surface, the light will be copiously reflected, and a bright uncoloured image of the flame will be seen by reflexion. As the angle made by the incident ray is increased, the reflected image becomes first yellow, then red, and finally disappears altogether. Fresnel has attempted to account} for this fact on the ground that the more refrangible rays, having shorter wave-lengths, are caused to interfere by a difference of path, which is still too small to effect complete interference in the case of the longer waves of red light—the difference in path depending on the depth of the minute scratches on the surface of the glass, and on the angle which the ray makes with this surface. As it is not difficult to measure approximately the angle at which the red ray ceases to be reflected, it would be easy to put this theory to the test of experiment if the average depth of the scratches on the ground surface were known. The impossibility of obtaining such measurements has hitherto prevented this theory of the action of finely roughened surfaces on light from being either confirmed or overthrown. Some time ago, while experimenting on a plane polished sur- face of glass which had been smoked with lampblack to complete opacity, I was surprised to find that the lampblack surface at a great obliquity reflected all the rays of ight with much bril- liancy, so that it resembled in appearance a polished surface of metal or glass. With less degrees of obliquity the reflected light was yellow, red, and finally disappeared altogether. The lampblack surface in this experiment was obtained from burning paraffine, and it was found that the red ray ceased to be reflected at an angle of 18°, reckoning from the glass surface. The source of light was a small gas-flame; and the experiments were made in a darkened room at night, the glass plate with its lampblack surface being attached to the axis of a graduated cir- cle, the lampblack having been removed from the upper half of the plate so as to allow the proper adjustments to be made with the aid of the naked glass surface. I then attempted to mea- . sure with the microscope the average size of the smaller and more numerous particles of lampblack ; the result obtamed was * From Silliman’s American Journal for January 1867. + Poggendorff’s Annalen, vol. xii. p. 210. Prof. Rood on measuring the average size of very fine Particles, 541 that they varied in size from ‘000018 to ‘000012 of an inch, Several months afterwards I made a ealculation to ascertain what the difference in the path of the interfering rays would be, using these data, and what relation this difference bore to the length of a wave of red hight. Assuming the dimensions of the particles of lampblack to be the same in al directions, we have the annexed construction. BD will represent the diameter of a particle of lampblack, the ray AB is refiected from its surface, the ray C B from the layer next below; X is the angle made by the light with the plate; and the difference in path of the two rays will evidently be equal to CB—AB, a quantity readily found by calculation. Taking the size of the lampblack particles to be equal to ‘000018 of an inch, the difference in path of the two rays for an angle of incidence of 18° is ‘000011, while the wave-length of the line C in the red space is nearly ‘000026 of aninch. This shows that the difference in the path is not far from half a wave- length of red light, if the larger of the two estimates of the size of the particles of lampblack is employed. I then made a new set of experiments relative to the angle at which the red ray disappears, using, as before, lampblack from parafiine. This was found to vary somewhat in different por- tions of the same plate, as is seen in the Table below :— le) 208 (ome VSe Zou 20°; 20° mean: 20°'1. New microscopic measurements on the size of the lampblack particles were made with a different microscope, the value of the . micrometer not being known; it was estimated that the Ane of the smaller and more numerous particles varied from 7515, to 90000 Of an inch, but that there were more particles approach- ing the first number than the second—a circumstance of which I have not taken any advantage in the following calculation. Taking the mean of these determinations and combining it with the mean of the 3 st determinations, we obtain for the mean size of the particles -g445 = ‘0000146 of an inch. The average angle of disappearance of the red ray being 20°, - there results a difference of path =:0000098 ; that is, the dif. ference of path is to the wave-length of red light nearly as 10 to 26, 542 Prof. Hood on measuring the average size of very fine Particles. When the difficulty of obtaining an approximate measurement of the size of the particles of lampblack is considered, it is sur- prising to see how nearly the calculated difference in path ap- proximates to half a wave-length of the light in question. I found that a surface of magnesia, produced by smoking a glass plate to opacity with burning magnesium wire, also re- flected light in the same way at very 7 oblique incidences. It was ascertained that the final tint was red, and that the red rays themselves disappeared at 11°. The size of the particles of mag- nesia was estimated at ‘000036. Long after the measurements had been obtained I calculated the difference of path for the interfering rays; this was found.to be °000014., wave-length of C 000026, giving a still nearer approximation to a difference of half a wave- - length. These experiments, then, seem to point out the correctness of Fresnel’s theory ; and we Siena I think, be justified in revers- ing the process, and using the angle of disappearance of the red ray in connexion with the known wave-length of this ray, for the purpose of calculating the average size of small particles or the average depth of fine scratches or furrows. I give below the calculated values of the average size of the particles of Jampblack and magnesia :— Lampblack from parafine. . °*0000188 calculated. 55 . . °0000146 measured. Size of particles of magnesia . *0000338 calculated. 5 e . ‘0000361 measured. Some experiments were made on the angle of disappearance of the red ray with lampblack produced by the burning of dif- ‘ ferent substances: where the figures are connected by a bracket it is intended to indicate that the two angles were obtained from the same portion of the plate. Lampblack from a Lampblaek Lampb! ack solution of spirits of from stearine. from campnor. _ tur pentine in aleghol. (e) @) 18°25 16 22 13°75 15:9 21 16 4 15-1 20 ; ae! 15:4. 17°25 15°6 21 It would appear from these last experiments that the average size of the particles of lampblack from burning camphor is somewhat greater than from paraffine, while in the case of “burning fluid ” the particles are smaller. ee LXIX. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 478.] March 14, 1867.—Lieut.-General Sabine, President, in the Chair. ae following communications were read :— “On certain Points in the Theory of the Magneto-electric Ma- chines of Wilde, Wheatstone, and Siemens.” By C. F. Varley, Esq. In a Letter to Professor Stokes, Sec. B.S. Fleetwood House, Beckenham, S.E. February 23, 1867. My prEAR 81r,—Professor Wheatstone showed that a shunt put into the circuit of the electromagnet increased the power greatly, but the explanation that it increased the power by equalizing the resist- ance of the armature and that of the electromagnet is either wholly incorrect, or very nearly so. Yesterday I had an opportunity afforded me by Mr. C. Siemens of experimenting with his machine, in which the electromagnets have each a resistance of about 250 Ohms = 500 Ohms, the armature 400 Ohms. | On adding a shunt to the electromagnet the flame was greatly in- creased. The two electromagnets when connected in series had a resist- ance of about 500 Ohms. I then connected them in a double cir- cuit, the resistance in this case being about 125 Ohms. By this means the same result as regards resistance could be obtained as by a shunt, with the difference that the power expended in the shunt is lost in heat; while reducing the resistance by the double circuit caused the whole force to be expended on the electromagnet. The results of the experiment were— Ist. The shunt invariably ¢ncreased the power. _ 2ndly. When the magnets were joined in double circuit the power was greatly reduced. The explanation is to me obvious. In a Ruhmkorit’s coil, where the iron core is divided into fine wire, so that the dying magnetism cannot set up currents in the iron core to prolong its existence, the magnetism Is very rapidly lost, and the make-and-break hammer works very rapidly, sometimes as fast as sixty beats per second. if the secondary circuit be closed so that the currents can flow, the make-and-break hammer works very slowly, indeed one or two beats per second; and in 18561 published a description of electromagnets whose action was very slow, and which were rendered sluggish by a copper cylinder around them. Wilde’s armature, when revolving, sends intermittent currents around the electromagnet, whose circuit is broken at every haif re- volution of the armature. Were the magnets composed of fine iron wire, the magnetism would die away rapidly, producing a viclent current by its efforts to main- 544: Royal Society :— tain itself, as in the Ruhmkorff’s coils. (This current is called by foreigners the extra-current. ) : The shunt which Wheatstone inserted carries this current across, and so maintains the magnetism of the electromagnets until the arma- ture gives a second impulse. The current in this shunt will be found to travel in alternate directions; not so that on the electromagnet. When the armature is discharging its current into the electro- magnets, the current in the shunt is in the direction it would have if the shunt were in circuit solely with the armature. When the armature is changing poles and is disconnected, the se- condary current is in full play, and the current in the shunt is in the direction of the current prolonged 1 in the electromagnet, that is, of , the extra current. The force expended in the shunt is wasted in heat ; but a secondary wire on the electromagnet or a copper cylinder would very greatly add to the power by maintaining the magnetism, and not consume uselessly the force now wasted in the shunt. The overlapping of the armature and the solid mass of the elec- tromagnets tends to maintain imperfectly the magnetism during the intervals of xo current from the armature; and but for this the ma- chines, whether they be Wilde’s, Wheatstone’s, or Siemens’s, would none of them work. In 1860 I published a description of two machines I had con- structed, and in 1862, at the Universal Exhibition, I exhibited a ma- chine for adding mechanical force to static electricity without fric- tion. A machine similar in principle, but a little different in construc- tion, has been exhibited recently under the name of Holtz. | Une of my machines bears to the other precisely the same relation that Siemens’s or Wheatstone’s does to Wilde’s. If these be of sufficient interest to the Royal Society, I shall be happy to exhibit them. I am, my dear Sir, Very truly yours, C. F. Variry. “On a Magneto-electric Machine.”’ By William Ladd, F.R.M.S. In June 1864 I received from Mr. Wilde a small magneto-electric machine, consisting of a Siemens’s armature and six magnets. This I endeavoured to improve upon, my object being to get a cheap ma- chine for blasting with Abel’sfusees. This was done by making one of circular magnets, and a Siemens’s armature revolving directly be- tween the poles, the armature forming the circles ; with this I could send a very considerable power into an electro- -magnet, &c. It was then suggested to me by my assistant, that if the armature had two wires instead of one, the current from one being sent through a wire surrounding the magnets, their power would be augmented, and a considerable current might be obtained from the other wire available for external work; or there might be two armatures, one to exalt the power of the magnets, and the other made available for blasting or other purposes. Want of time prevented me carrying this out Mr. F, A. Abel on the Stability of Gun-cotton. 545 until now; but since the interesting papers of C. W. Siemens and Professor Wheatstone were read last month, I have carried out the idea as follows:—Two bars of soft iron, measuring 74 in. X 24 in. xX in., are each wound, round the centre portions, with about thirty yards of No. 10 copper wire; and shoes of soft iron are so attached at each end, that when the bars are placed one above the other there will be a space left between the opposite shoes in which a Siemens’s armature can rotate: on each of the armatures is wound about ten yards of No. 14 copper wire cotton-covered. The current generated in one of the armatures is always in connexion with the electro-magnets; and the current from the second armature, being perfectly free, can be used for any purpose for which it may be required. The machine is altogether rudely constructed, and is only intended to illustrate the principle; but with this small machine three inches of platinum wire *(01 can be made incandescent. April 4.—Lieut.-General Sabine, President, in the Chair. ’ The following communication was read :— ‘‘ Researches on Gun-cotton._-Second Memoir. On the Stability eo: Gun-cotton.” By F. A. Abel, F.R.S., .V.P.C.S. The results of the many observations which had been instituted prior to 1860 upon the behaviour of gun-cotton when exposed to diffused or strong daylight, or to heat, although they agree gene- rally with those of the most recent investigations on the subject, as far as relates to the nature of the products obtained at different stages of its decomposition, cannot be regarded as having a direct bearing upon the question of the stability of gun-cotton produced by strictly pursuing the system of manufacture prescribed by Von Lenk, inas- much as it has been shown that the products formerly experimented upon by different chemists varied very considerably in composition. The investigations recently published by Pélouze and Maury*, into the composition of gun-cotton, and the influence exerted by light and heat upon its stability, are described as having been conducted with gun-cotton prepared according to Von Lenk’s systems The gene- ral conclusion arrived at by those chemists with reference to the latter branch of the subject was to the effect that the material is susceptible of spontaneous decomposition, under conditions which may possibly be fulfilled in its storage and application to technical and warlike purposes ; and the inference is drawn, partly from the results of earlier investigators, and partly from the exceptional behaviour of one or two specimens, that gun-cotton is liable to explode spontaneously at very low temperatures when stored in considerable quantities. It has been shown, in the memoir on the Manufacture and Com- position of Gun-cotton, published last year+, that modifications in the processes of conversion and purification, which appear at first sight of very trifling nature, exert most important influences upon the composition and purity of the product. Gun-cotton of quite ex- ceptional character has been discovered, in several instances, among samples received from Hirtenberg and among the first supplies ob- * Comptes Rendus. } Trans. Royal Society. [For abstract see Phil. Mag. S. 4. vol. xxxii. p. 145.] 546 Royal Society :— tained from Stowmarket ; other exceptional products have also been produced by purposely modifying , in several ways, the system of manufacture as pursued at Waltham Abbey. The very consider- able difference exhibited between some of these and the ordinary products in their behaviour under equal conditions of exposure to heat and light, affords good grounds for the belief that the attain- ment of certain exceptional results, upon which the conclusions of Pélouze and Maury’s report condemnatory of gun-cotton, have been principally founded, are to be ascribed to such variations in the nature of the material operated upon. Very numerous and extensive experiments and observations have been carried on during the last four years at Woolwich, both with small and large quantities of gun-cotten, for the purpose of completely investigating the conditions ‘b y which the stability of this substance, when under the influence of light and heat, may be modified, and with the view of ascertaining whether results recently arrived at in France apply to gun-cotton as manufactured in this country. The principal points which have been established by the results arrived at in these investigations may be summed up as follows :— 1. Gun-cotton produced from properly purified cotton, according to the directions given by Von Lenk, may be exposed to diffused day- light, either im the open air or in closed vessels, for very long periods without undergomg any change. The preservation of the material for 34 years under those conditions has been perfect. 2. “‘Long-continued exposure of the substance in a condition of ordinary dryness to strong daylight and sunlight produces a very eradual change in gun-cotton of the description defined above; and therefore the statements which have been published regarding the very rapid decomposition of gun-cotton when exposed to the sun- light do not apply to the nearly pure trinitrocellulose obtained by strictly following the system of manufacture now adopted. 3. If gun-cotton in closed vessels is left for protracted periods exposed to strong daylight or sunlight in a damp or moist condition, it is affected to a somewhat greater extent; but even under these circumstances the change produced in the gun-cotton by several months’ exposure is of a very triflmg nature. 4. Gun-cotton which is exposed to sunlight until a faint acid reaction has become developed, and is then immediately afterwards packed into boxes which are tightly closed, does not undergo any change during subsequent storage for long periods. (The present experience on this head extends over 34 years.) 5. Gun-cotton prepared and purified according to the prescribed system, and stored in the ordinary dry condition, does not furnish any indication of alteration, beyond the development, shortly after it is first packed, ofa slight peculiar odour and the power of gradually impart- ing to litmus, when packed with it, a pinkish tinge. 6. The influence exercised upon the stability of gun-cotton of average quality, as obtained by strict adherence to Von Lenk’s system of manufacture, by prolonged exposure to temperatures considerably exceeding those which are experienced in tropical climates is very Mr. F. A. Abel on the Stability of Gun-cotton. 547 trifling in comparison with the results recently published by Conti- nental experimenters relating to the effects of heat upon gun-cotton ; and it may be so perfectly counteracted by very simple means which in no way interfere with the essential qualities of the material, that the storage and transport of gun-cotton presents no greater danger, and is, under some circumstances, attended with much less risk of acci- dent than is the case with gunpowder. 7. Perfectly pure guu-cotton, or trinitrocellulose, resists to a re- markable extent the destructive effects of prolonged exposure to tem- peratures even approaching 100° C.; and the lower nitro-products of cellulose (soluble gun-cotton) are at any rate not more prone to alteration when pure. The incomplete conversion of cotton into the most explosive products does, therefore, not of necessity result in the production of a less perfectly permanent compound than that obtained by the most perfect action of the acid mixture. 8. But all ordinary products of manufacture contain small propor- tions of organic (nitrogenized) impurities of comparatively unstable properties which have been formed by the action of nitric acid upon foreign matters retained by the cotton fibre, and which are not com- pletely separated by the ordinary, or even amore searching process of purification. It is the presence of this class of impurity in gun-cotton which first gives rise to the development of free acid when the substance is ex- posed to the action of heat; and it is the acid thus generated which eventually exerts a destructive action upon the cellulose-products, and thus establishes decomposition which heat materially accelerates. If this small quantity of acid developed from the impurity in ques- tion be neutralized as it becomes nascent, no injurious action upon the gun-cotton results, and a great promoting cause of the decom- position of gun-cotton by heat is removed. This result is readily ob- tained by uniformly distributing through gun-cotton a small pro- portion of a carbonate,—the sodic carbonate, applied in the form of solution, being best adapted to this purpose*. 9. The introduction into the finished gun-cotton of 1 per cent. of sodic carbonate affords to the material the power of resisting any serious change, even when exposed to such eleyated temperatures as would induce some decomposition in the perfectly pure cellulose- products. That proportion affords, therefore, security to gun-cotton against any destructive effects of the highest temperatures to which it is likely to be exposed even under very exceptional climatic condi- tions. The only influences which the addition of that amount of carbonate to gun-cotton might exert upon its properties as an ex- plosive would consist in a trifling addition to the small amount of * The deposition of calcic and magnesian carbouates upon the fibre of gun- cotton, either by its long-continued immersion in flowing spring water, or by its subjection to the so-called ‘‘silicating” process adopted by Von Lenk, produces a similar protective effect, which, however, is necessarily very variable in its extent, as the amount of carbonate thus introduced into a mass of gun-cotton is uncertain ; moreover, as it is only loosely deposited between the fibres, the pro- portion is liable to be diminished by any manipulation to which the gun-cotton may be subjected. . 548 Royal Society :— smoke attending its combustion, and ina slight retardation of its ex- plosion, neither of which could be regarded as results detrimental to the probable value of the material. 10. Water acts as a most perfect protection to gun-cotton (except when it is exposed for long periods to sunlight), even under ex- tremely severe conditions of exposure to heat. An atmosphere saturated with aqueous vapour suffices to protect it from change at elevated temperatures ; and wet or damp gun-cotton may be exposed for long periods in confined spaces to 100° C. without sustaining any change. Actual immersion in water is not necessary for the most perfect preservation of gun-cotton; the material, if only damp to the touch, sustains not the smallest change, even if closely packed in large quan- tities. The organic impurities which doubtless give rise to the very slight development of acid observed when gun-cotton is closely packed in the dry condition, appear to be equally protected by the water; for damp or wet gun-cotton, which has been preserved for three years, has not exhibited the faintest acidity. If as much water as possible be expelled from wet gun-cotton by the centrifugal ex- tractor, it is obtained in a condition in which, though only damp to the touch, it is perfectly non-explosive; the water thus left in the material is sufficient to act as a perfect protection, and conse- quently also to guard against all risk of accident. It is therefore in this condition that all reserved stores of the substance should be preserved, or that it should be transported in large quantities to very distant places. Ifthe proper proportion of sodic carbonate be dis- solved in the water with which the gun-cotton is originally saturated for the purpose of obtaining it in this non-explosive form, the material, whenever it is dried for conversion into cartridges, or. em- ployment in other ways, will contain the alkaline matter required for its safe storage and use in the dry condition in all climates. Although some experiments, bearing upon the different branches of inquiry included in this memoir, are still in progress with a view to the attaimment of additional knowledge of the conditions which regulate the stability of gun-cotton, it is confidently believed that the results arrived at amply demonstrate that the objections which have been of late revived, especially in France, against the employment of gun-cotton, on the ground ofits instability, apply only in a comparatively slight degree to the material produced by strictly pursuing the system of manufacture perfected by Von Lenk—that, as far as they do exist, they have been definitely traced to certain difficul- ties in the manufacture of pure gun-cotton which further experi- mental research may, and most probably will, overeome—but that, in the meantime, these objections are entirely set aside by the adop- tion of two very simple measures, against the employment of which no practical difficulties can be raised, and which there is every reason to believe must secure for this material the perfect confidence of those who desire to avail themselves of the special advantages which it presents as an explosive agent. Mr. A. Claudet on Binocular Vision. 549 The nature of the decomposition of gun-cotton when exploded under different conditions is now under investigation by me; and the results arrived at will, I trust, be communicated before long to the Royal Society. April 11.—Lieut.-General Sabine, President, in the Chair. The following communication was read :— «A new fact relating to Binocular Vision.’ By A. Claudet, P-R.S: The persistence of the impression made by light on the retina is demonstrated by many experiments ; but one of the most convincing, which is also very easy to try, is that which is known under the name of the thaumatrope. Let us write the letters composing a word of eight letters, say ‘‘ Vic- toria,’’ on the two sides of a small card, in such a manner that one surface shall contain the Ist, 3rd, 5th, and 7th letters, and the other surface the 2nd, 4th, 6th, and 8th, with a space between them suffi- cient to complete the word on each surface, which blank spaces are in fact to appear filled up during the experiment by an artificial - means to be explained. Fig. 1 shows the arrangement on the two sides of the card (section view). Fig. 2 shows the plan of the card. The white letters are those written on one surface, and the dotted lines those written on the other. Now by means of two strings fixed on the two sides A, B the card may be made to revolve on its axis by turning the string between the thumb and finger of each hand. By this means a very rapid motion may be communicated to the card, and while it is revolving both surfaces are alternately seen in quick succession, and the percep- tion of the two is so simultaneous that the two sets of letters appear as one, and the whole word is read as distinctly as if it were written on one surface only. This is easily explained. It is known that the persisting action of light on the retina has a duration of about one-eighth of a second ; so that if the card makes at least eight revolutions in a second (it Phil, Mag. 8, 4. No. 226, Suppl. Vol. 33. 20 550 Royal Society :— may make considerably more), before one impression has vanished another produces its effect on the next part of the retina, in such a way that they are intermixed and simultaneously visible, producing an uninterrupted sensation. _ The means by which this illusion is produced has been called the oa thaumatrope,” from two Greek words meaning “ wonder” and “turn.” It is difficult to trace the history of this discovery ; but it is certain that it has been the result of a ay old, simple, and well- known experiment. From time immemorial schoolboys have amused themselves by holding a coin between two pins and making it revolve rapidly by blowing upon it, when to their surprise the ‘coin showed the head mixed with the device on the other side. I have been told that as. Sir John Herschel.was one day making this experiment to amuse his children, in the presence of the late Dr. Paris, this gentleman was struck with the idea that if, instead of a coin, a white card was em- ployed on each side of which one part of a design was properly ar- ranged, the two might complete the subject during the revolution. Accordingly he made the experiment, which succeeded perfectly well. If the story is true, certainly Dr. Paris may be regarded as the in- ventor of the thaumatrope, which he has so, well and so fully elu-. eidated in his very interesting and instructive work entitled ‘ Philo- sophy in Sport made Science in earnest.” This philosophical toy may be employed to show another effect of the persistence of the retinal image. If complementary colours are fixed on the two opposite sides of the card, they will become su- perposed during the revolution, and white light will be the result. By the same means, other curious effects of the mixture of various colours might be tried. All these experiments present no difference, whether they are Bak looking with the two eyes or only with a single eye: the effect is the same in both cases. Therefore the illusion is equally monocular and binocular. | But I was not a little surprised to find that the thaumatrope is capable of producing another phenomenon, elucidating very foreibly the principies by which binocular vision is the only real and effective means of showing the distances of objects, which are determined by the degree of the angle of convergence of the optic axes and by one of its corollaries, the sensation of double images for all the points which are not exactly on the plane of vision. The thaumatrope is capable of showing that binocular vision can detect to a degree hardly conceivable the most minute difference in the distances of objects, such as the distance between the planes of the two surfaces of a card, which distance is, nothing more than the aes of the card. Therefore, supposing that the thickness of the card is <1, of an inch and the A from the eyes 15 in., there is _ not a difference greater than the 54, part of the whole distance from the eyes to the two planes of the card; and still the difference of the degree of convergence for two planes so near each other is sufficient to exeite the action of binocular vision, and by it to enable us to de- Mr. A. Claudet on Binocular Vision. 551 tect that infinitesimal difference in their distances. But that such an effect of binocular vision could possibly be displayed while looking at two planes so nearly intermixed as the surfaces of a card revolving upon its axis with such a wonderful velocity is the very extraordinary phenomenon I have discovered, and which I am about to describe and endeavour to explain. If the thickness of the card is A B, fig. 3, and if the two ends of Fig. 3. each string, passing through the holes C and D in the card, are brought together and turned between the thumb and finger, the card will whirl exactly on its axis, and during the revolution the two sur- faces A and B will be at the same distance from the eyes. But if the two strings are drawn,so that one of their knots is asin fic. 4, the surface B will revolve round the plane of the surface A corresponding with the axis cf the string, and, during the revolution, every time that it is made visible to the eyes it will appear as if it were nearer than the surface A. By reversing the position of the knots, as in fig, 5, instead of the Fig. 5. surface B revolving round the plane of A, it will be A that will re- volve round the plane of B. These three different positions of the strings will produce three different effects. In the position of fig. 3 the effect will be normal; that is to say, © the two surfaces coming alternately at the same distance, we shall see the whole word as if the letters were on the same surface. In the position of figs. 4 and 5 we have a very strange illusion. One half of the letters composing the word will appear before or behind the other half, according to the surface upon which they are written and the position of the knots upon that or the other surface. In fig. 4 the letters written on the surface B will appear before the letters on the surface A; and in fig. 5 the letters on the surface A will appear before the letters on the surface B. 202 502 Royal Society :— The cause of the anomaly resulting from the two different experi- ments is entirely and positively due to a sensation of binocular vision ; and we may easily satisfy ourselves that it is so; for, looking with a single eye in both cases, all the letters appear on the same plane, notwithstanding the different distances of the two surfaces given by the position of the knots: and we may add another con- vincing proof, which is that the pseudoscope inverts the distances of the surfaces. At first it is rather difficult to understand how the phenomenon can take place; for asthe perception of the two surfaces is simultaneous, how is it possible that during such a rapid revolution the optic axes ean be made to converge alternately on each surface while it is pass- ing so quickly, and that they should be made suddenly to converge on the other in its turn? 3 However, there cannot be any question that in reality the pheno- menon takes place, and that it is decidedly an effect of binocular vision ; therefore it only remains to be explained how it can be pro- duced. In endeavouring to arrive at the true cause of the pheno- menon, we shall have to bring to mind various physiological sensa- tions which concur in producing the effect. One is the effort we make to obtain distinct vision, and the other the effort we make to obtain single vision. These two efforts act in unison; for it is impossible not to admit that the two muscular processes by which both the angle of convergence is directed to the object and the focus of the eyes is adapted to its distance, for the double purpose of having at once single and distinct vision of every object, are two actions necessarily simultaneous and inseparably connected. They are therefore both, each in its way, criteria of the distances of ob- jects; but they give rise to certain indirect and additional criteria for other distances, in two ways: one, the most important is the double images of the objects situated before and behind the point of. convergence; and the other, but only in a subsidiary way, the degree of confusion of the objects situated before and behind the point of convergence and which are not in focus. The comparison of two points, one of which is in focus and well de- fined, and the other out of focus and confused, helps considerably in forming ajudgment that they are on different planes. But ina ques- tion of binocular vision, perhaps we ought not strictly to take into account this last criterton, which belongs equally to monocular and binocular vision ; and if we allude to it, it is only because, although it does not produce the real stereoscopic effect, still it contributes to give that sort of illusion of relief which by various means may be evinced by monocular vision. Therefore it is particularly the sensation of double images, the degree of their separation, and their respective positions either outside or inside from the centres of the two retinze, which indicate more powerfully the exact distance of the object from the point of single vision either before or behind. When we look fixedly on a point of one surface of the revolving card, that point appears single, and we see at the same time another point on the other surface which appears double, although we hardly Mr. A. Claudet on Binocular Vision. 553 feel that we notice its doubleness ; and from the position or distri- bution of the double images, either on the right or on the left of the central poiut, we have at the same glance the perception of the re- spective distances. Therefore, to judge of the distances of certain objects in the direction of the line of vision, we are not absolutely obliged to alter constantly the angle of convergence. This is proved by our perception of the two distances of the surfaces of the card while it is revolving; for it would be impossible that we should alter the angle of convergence to adapt it alternately to the two surfaces while they are turning so rapidly. The same angle of convergence kept on one or the other surface is no impediment to our seeing both in a sufficiently distinct manner. The whole phenomenon may be better understood by the illus- tration given in fig. 6. When we converge the optic axes on B, this point, being represented on the centre of both retine at B' B", is single, but A being nearer is represented -on the left of the centre of the left retina at A’, and on the right of the centre of the right retina at A"; therefore it appears double. For the same reason, converging on A, this point is single, but B is double, with this difference—that one image is on the right of the left retina, and the other on the left of the right retina; so that the double images of nearer objects situated at A are represented outside the centres of the two retine, and those of further ob- jects situated at B are represented inside the centres of the retinz, and each of these two different sensations brings to our mind the perception of the distance which has produced it. During the revolution of the card we may adapt the convergence either to one or to the other surface and keep it so; but in every case the letters on that surface will appear single and a little better defined ; and this, with the sensation of double images of the letters on the other surface, will be an indication of their respective dis- tances. 2 As I am not aware that the illusion I have described in this paper has ever been noticed before, it has appeared to me that its publica- tion would excite the interest of all those who look for any new fact capable of illustrating the principles of binocular vision, and showing the wonderful property of the angle of convergence, by which the most minute differences in the distances of objects and the slightest relief on their surfaces can be detected, and by which also in the abnormal conversion introduced in its action by the pseudoscope all our sensations are reversed. Therefore the pseudoscope is the great test of the phenomena of binocular vision ; for by reversing certain sensations which by constant habit we may hardly notice, it ren- ders them more conspicuous by the comparison of the abnormal state 554 Geological Society. brought out by its action, and proves the theory of binocular vision in the most effective manner. A truth is never better established than when it can be shown that the same principles are capable of producing contrary effects when they are applied in a contrary way. Professor Wheatstone, by adding the pseudoscope to the stereo- scope, has thus in the most scientific and ingenious manner com- pleted his splendid discovery, and left very little (we might almost venture to say that he has left nothing) for further investigations in the physiology of binocular vision. . GEOLOGICAL SOCIETY. [Continued from p. 397.] February 20, 1867,—Warington W. Smyth, Esq., M.A., F.R.S., President, in the Chair. The following communications were read :— 1, “On the British Fossil Oxen.”—Part II. Bos longifrons, Owen. By W. Boyd Dawkins, Esq., M.A. (Oxon.), F.G.S. The author analyzed the characteristics usually assigned to Bos longifrons, and concluded that there were none of specific value to separate it from the smaller varieties of Bos taurus. The large series of skulls in the Dublin and Oxford Museums show that Bos Srontosus of Nilsson is a mere variation from the more usual type. Professor Owen, on the faith of its occurrence on the Essex shore, along with the remains of extinct animals also washed up by the waves, ascribes to this species a Pleistocene age. This inference, on a rigid examination of the premises, turns out to be faulty; and there is no evidence anywhere in Europe that it coexisted with any of the extinct mammals, the Irish elk being excepted: It is very commonly associated with the remains of man, of a date anterior to the Saxon invasion. It was kept in great herds during the Roman occupation, and supplied the Legionaries with beef. On the Continent, as in Britain, it is found around the dwellings and in the tombs of the Bronze and Stone folk. Nowhere is there evidence of its having a higher antiquity than the Neolithic age of Sir John Lubbock. It, along with its Keltic masters, disappeared before the Saxon invaders, from the more fertile portions of Britain, and took refuge in the Highlands of Scotland and Wales, where it still survives in the smaller domestic races. In no case has it been found in association with Saxon remains. ‘lhe inferences to he drawn about it are :—first, that it has not yet been proved to have existed before the Prehistoric age; and second, that it is the ancestor of the small Highland and Welsh breeds. _ It is essentially the animal with which Archzologists have to deal, and its only claim for insertion in Geological catalogues is the fact of its occur- rence in the most modern of all the stratified deposits. Intelligence and Miscellaneous Articles. 555 2. “ On the Geology of the Upper Part of the Valley of the Teign, Devonshire.” By G. Wareing Ormerod, Esq., M.A., F.G.S. The district noticed in this paper lies to the north of Bovey Tracey. The author described the courses of the Teign and its feeders, and the strata traversed by those streams—namely, Granite and Carboniferous Limestone. Gravels are occasionally found, which the author regarded as having been deposited before the reexcavation of the valley, and he showed that these had been transported by a current from north-west to south-east. From the absence of these gravels in the gorge of the Carboniferous rocks between Hunts Tor, near Chagford, and Clifford Bridge, he con- sidered that that valley had been opened since the time when the boulders and gravels were deposited, and then showed that the stream from the valley of the Teign prior to the opening of that valley would have passed by Moreton Hampstead to Bovey Tracey. The paper contained notices of the Minerals found in the district, and of the Granite veins in the Carboniferous rocks. 3. “ Notes on the Geological features of Mauritius.” By George Clark, Esq. : Mr. Clark described the occurrence of a calcareous formation of at least 30 feet in thickness, with a dip of about 30°, composing many of the islets supported by the coral reefs of the Mauritius, which have been generally regarded as forming an integral part of the islets, but which the author considered to be of greater anti- quity. A soft sandstone was stated to cover in many places the calcareous rock, and to contain imbedded remains of roots, and bases of trunks of trees. LXX. Intelligence and Miscellaneous Articles. ON THE RELATIONS EXISTING BETWEEN THE COMPOSITION, DENSITY, AND REFRACTING-POWER OF SALINE SOLUTIONS. BY M. FOUQUEK. 4) ye research of which the following is a succinct summary was made at the Imperial Observatory of Paris by the aid of instru- ments belonging to that establishment, the use of which was kindly granted to me by the Director. The object of the research was (1) to ascertain whether Biot and Arago’s law for gaseous mixtures also held good for saline solutions, and (2) to study the variation of the refractive index, and of the refracting-power, with the temperature. These investigations required the following operations :—(1) esti- mation of the solutions ; (2) determination of their densities; (38) measurement of their refractive indices. The salts used, forty-three in number, were purified by the ordinary chemical methods, and according to their alterability by 556 Intelligence and Miscellaneous Articles. heat, fused or simply dried at 100° C. before weighing them. The densities were taken by means of a specific-gravity bottle, at tem- peratures between 0° and 100° C., in an apparatus resembling that for determining the boiling-point of thermometers. ‘The determina- tion of the densities was made twice for each solution, at intervals of about six months. The measurement of the refractive indices was effected by receiving a pencil of parallel rays on a prism con- taining the liquid investigated, and determining in each case the two minima of deviation. The prisms employed were constructed of angular flasks, each provided with a‘lateral aperture, on which plane glass was hermetically fixed. Two series of experiments were made, thus :—one at the ordinary temperature, the principal object. of which was to see if Biot and Arago’s law was applicable to solutions ; the second at temperatures increasing from 10° to 95° C., the object of which was to determine the variations of the index and of the refracting-power with the temperatures. In the first series, the necessity of working at constant tempera- tures led me to fit up the apparatus in a cellar at the observatory, where the daily variations are very small, and to avoid as much as possible the other ordinary sources of heat. Hence it was that I used as principal source of light, in determining the indices, the light of a Geissler’s hydrogen-tube ; and I used similar tubes, fur- nishing a bright light and a very feeble heat, to read the ther- mometer and the graduated circle. In the second series of experiments, the prism containing the solutions was placed in an oven closed laterally with parallel glass plates, forming a jacket in which circulated the vapour of water, of alcohol or ether, or vapours of mixtures of these liquids in various proportions. ‘The condensed liquids returned to the boiler in such a manner as to keep upa continual circulation of liquid and vapour, and thus preserve a constant temperature. One hundred and twenty-three solutions of different salts in water, and moreover some simple liquids, such as water, ether, alcohol, benzole, sulphide of carbon, were thus investigated. ‘The numerical results obtained lead to the following conclusions :— (1) The refractive index varies considerably with the temperature. In the interval from 10° to 95° C., the variation of the index for saline solutions always amounts to hundredths. (2) The variation is greater the more concentrated the liquid. (3) The refractive power of saline solutions diminishes as the temperature rises. This diminution is about 0°001 for all the solu- tions I have examined between 10° and 95° C. The mean coefii- cient which represents this variation of the refracting-power most frequently diminishes as the concentration of the solution in- creases ; sometimes it remains stationary; at others, on the contrary, it also increases ; but in all cases it varies much less than the index with the concentration of the liquid. (4) The dispersion diminishes when the temperature increases : the difference between the indices of the rays of aand 6 of the Intelligence and Miscellaneous Articles. D507 hydrogen spectrum diminishes by about 0:0003 between the limits of 10° and 95° C. for water and aqueous solutions. (5) At the same temperature the refracting-power of solutions of the same salt is less the more concentrated the solutions. For each salt dissolved the maximum of the refracting-power is equal to that of distilled water, which is 0°7812 at 4° C. Solutions equally con- centrated of different salts are far from having the same refracting- power. Thus a solution of chloride of calcium the standard of which is 0°326 has a refracting-power higher than that of a solution of nitrate of lime one-seventeenth as strong. There is, however, a singular exception to this rule: solutions of chloride of lithium have a higher refracting-power than that of distilled water ; andthe more concentrated the solution, the higher itis. These solutions are also remarkable for their coefficient of expansion, which is less than that of distilled water, and changes very little for considerable variations in the standard of the liquid. Biot and Arago’s law does not apply rigorously to saline solu- tions; yet in most cases it is sufficiently close, and furnishes for each solution a characteristic number representing its refracting- power. Of a hundred and twenty-three solutions which I investi- gated, there are only sixteen where the observed error exceeds the probable limit of error, and of these sixteen there are fourteen where it is exceeded by only a small quantity. Only in the case of two solutions of chloride of zinc is the discrepance between the calcu- lated and the observed results too great to be attributed to accidental errors: the great affinity of chloride of zinc for water, and the formation of different hydrates in the solution, explain sufficiently this apparent anomaly. Among the salts I have investigated, the solu- tions of two only (chloride and carbonate of lithium) have a refract- ing-power higher than the refracting-power of distilled water.— Comptes Rendus, Jan. 21, 1867. ON THE ESTIMATION OF STAR-COLOURS. BY SIDNEY B. KINCAID, ESQ. The author remarks that, with the exception of the two isolated instances of Sirius and 95 Herculis, the latter of them due to the researches of the late Admiral Smyth and the Astronomer Royal for Scotland, no crucial example of the change of the colour of a star has been determined, although there is every reason to believe that such objects vary as well in their hues as in their apparent brillian- cies. That physical astronomy, which has made such strides in relation to the ‘‘ variables,’”’ has done so little in the matter of side- real chromatics is certainly not owing to any lack of interest on the part of the latter subject of inquiry, but is owing to the difficulties that beset any attempt at accurate chromatic observation. Until the publication of the late Admiral’s last work, which was specially devoted to the ‘‘ Colours of Double Stars,” no general system for reducing such observations to permanent record in connexion with 558 Intelligence and Miscellaneous Articles. perpetual standards of comparison had been introduced; and although a great step was taken by the suggestion to use a universally recog- nized scale of colours as a point of reference (for which aim was given a chromic plate in the book), coupled with the mentioned use by Mr. Huggins of chemical solutions as such standards, many hin- drances were left remaining; and in the great loss by Admiral Smyth’s death shortly afterwards was probably included much fur- ther progress towards their removal. The only instrumental means described by him, the photometrical measurement of the spectrum of the star so as to determine the lucidity of its different sections, is objectionable, as well by reason of its exceeding dependence on the occurrence of opportunities of weather not only “ fine,’ but ‘‘superlatively fine,” as by reason of the great and numerous difficulties which render the application of it almost impracticable. ‘The object of the author is to describe an apparatus for the purpose of determining star-colours, by which the tints of the fixed stars may be exactly recorded relatively to standards easily reproducible by any observer, with any kind of telescope, any number of years hence, and that by a contrivance the manipulation and reading of which is as easy as the plans now usually adopted for photometric estimations. But he first recapitulates the causes of error which particularly belong to this kind of research. These are :— 1st. Personal Equation, including therein three heads, which, although properly so described as belonging entirely to the persona- lity of the observer, are actually distinct, viz.:—(A) That insensibility of the eye to the varieties of colour which in its most extreme form is colour-blindness. (B) Inability of the memory to retain exactly the impression produced by a certain tint, so as to be capable of re- producing and identifying it at a subsequent period. (C) Personal difference in the habit of describing the impression of a particular colour. 2nd, Atmospheric equation. 3rd. Instrumental Equation. Good achromatic refracting tele- scopes are open to little imputation of deceit as regards the exhibi- tion of the colours of celestial objects; but the case is far otherwise with reflectors. The prevalence of excessive redness among Sir W. Herschel’s chronicles of sidereal chromatics has long given rise to the opinion that the speculum-metal misled him in this respect; and in the same way silvered glass mirrors are not (without due correction) reliable in any case where the colour of an object is to be accurately depicted. 4th. Standard of comparison. The requisites in such are that it shall afford the exact shade of colour of the star in connexion with which it is to be used, so that such tint shall be easily reproducible with precision by any observer ata future time from the information transferred by the ordinary use of language, and that it shall be suit- able for comparison with telescopic images. A painted scale like that given in ‘ Sidereal Chromatics,’ by Admiral Smyth, is, on ac- count of its opacity of colour, objectionable, and can scarcely claim to be considered sufficiently reproducible. Precious stones, though Intelligence and Miscellaneous Articles. 559 in many respects suitable, are plainly beyond the reach of most ob- servers ; and the only system which appears to possess the requisite qualification is that of chemical solutions, before referred to. The ‘ Metrochrome,” which it is the author’s object to describe, is shown in side-section and by a face-view in two figures given in the original paper. It consists essentially of three parts: (1) a lan- tern for the production of a constant light; (2) a contrivance for imparting to that light the necessary colour, and so arranged that, the proper tinge once produced, a record of it can be obtained so as to enable it to be reproduced at any time ; (3) apparatus to throw that coloured light into the field of the telescope as an artificial star which can thus be viewed side by side with the image of the real one. - The source of light is a very fine platinum wire, rendered incan- descent by a current of electricity transmitted through it from a Smee’s battery of two cells. The platinum wire is brought into the focus of a lens, so that the rays of light from the lantern issue parallel, _ and therefore come to a focus, after passing through the object-glass - _ of the telescope, at the same distance from it as those emitted by a star. The chromographic part of the apparatus consists of a drum rotating about an axis. ‘The drum has in it six equidistant radial openings—the alternate three of them transmitting the normal light | of the lantern, the other three constructed so as to admit flat-sided stoppered bottles containing chemical solutions of different colours. The outer edge of each of the last-mentioned apertures is graduated into ten parts, and each of them can be wholly or partially closed by means of a radial shutter; the other three apertures can be simulta- neously closed, wholly or partially, by a triune radial shutter: the edge of one of them is divided into ten parts ; and as all are equally affected by the movement of the shutter, the reading applies to the three openings. The drum is made to rotate so as to bring succes- sively the different apertures in front of the lantern; and when the rotation is sufficiently rapid, the impression of colour produced on the retina of the eye will be that of a colour compounded of the co- lours of the solutions in the three alternate apertures, diluted by the white light transmitted through the other three alternate apertures. By a proper selection of the solutions, and adjustment of the magni- tude of the several apertures by means of the shutters, it will be pos- sible to produce the exact colour of a particular star; and then the record of the solutions employed, and of the dimensions of the several apertures, will enable the exact reproduction of such colour at any future period for comparison with the then colour of the star in question. ‘The remaining part of the apparatus is a contrivance for _ throwing the beam of coloured light into the telescope so as to pro- duce, as already mentioned, the image of an artificial coloured star. —Monthly Notices of the Royal Astronomical Society, May 10, 1867. 560 INDEX tro VOL. XXXIITI. ABEL (F. A.) on the stability of gun-cotton, 545. Acetylene, on polymers of, 452. Actinometer, description of a new, 304. Adhesion, on the force of, 401. Airy (G. B.) on the meteoric shower > of 1866, 157. Angstrom (M.) on certain lines of the solar spectrum, 76. Atkinson’s (Dr. E.) chemical notices, 56, 187, 446.. Atmosphere, on the polarization of the, 290, 346, 455. Atmospheric humidity, on the rela- tion of insolation to, 391. Atomic weights, on the determination of some, 187. Baeyer (M.) on neurine, 448; on the constitution of mellitic acid, 449. Barrett (W. F.) on sensitive flames, DlGK23/6 Bauer (M.) on the-chlorinated ethers, 450. Berthelot (M.) on polymers of acety- ' lene, 452. Bezold (Dr. W. von) on binocular vision, 326. | Binocular vision, researches on, 326, 549. Blood, on the function of the, in muscular work, 341 ; on the colour- ing-matter of the, 446. Books, new:— Hunter’s Modern Arithmetic, 223; Hunter’s Intro- duction to Conic Sections, zbd. ; Kerr’s Elementary Treatise on Ra- tional Mechanics, 468. Brewster (Sir D.) on the polarization of the atmosphere, 290, 346, 455. Bromine, on the atomic weight of, 194, Brooke (Ch.) on negative fluid-pres- sure on a given surface, 207. Browning (J.) on the spectra of the meteors of November 1866, 234. Cazin (A.) on the expansion of super- heated steam, 236. Chemical notices from foreign jour- nals, 56, 187, 446. Chlorine, on the atomic weight of, 199; on the acetate of, 140. Circuit, on one of Ohin’s laws rela- ting to an insulated, 321. Claudet (A.) on a new fact relating to binocular vision, 549, Climate, on the physical properties of water in relation to terrestrial, 211 ; on the influence of a change in the obliquity of the ecliptic on, 426. 536. Cockle (Hon. Chief Justice) on the conversion of integrals, 537. Croll (J.) on the excentricity of the earth’s orbit, and its physical rela- tions to the glacial epoch, 119; on the reason why the difference of reading between an exposed and a shaded thermometer diminishes as we ascend in the atmosphere, 213 ; on the change in the obliquity of the ecliptic and its influence on cli- mate, and on the level of the sea, . 426. Cube, on the partition of the, 27. Daniel (L.) on induction experiments, 481; on the transport of a body by the voltaic current and byinduction- currents, 482. De la Rive (Prof. A.) on the propa- gation of electricity in highly rare- fied elastic fluids, 241; on the action of magnetism upon the elec- tric discharge in highly rarefied gaseous media, 512, PNIPE’S. De la Rue (W.) on the distribution of solar spotted areas in heliographic latitude, 79. Dietrich (M.) on the determination of nitrogen, 61. Earth, on the figure of the, 10, 145, 261, 332, 445 ; on the excentricity of the orbit of the, and its phy- a relations to the glacial epoch, Ecliptic, on the change in the obli- quity of the, and its influence on climate, 426, 536. Edlund (E.) on the elongation of a i a traversed by a current, 54 Electric currents, on the elongation of a conductor traversed by, 154; on the theory of the maintenance of, by mechanical work, 474. discharge, on the action of mag- netism upon the, in highly rarefied gaseous media, 512. Electrical force, on the conversion of dynamical into, 469. measurements, on the British- Association unit for, 397. Electricity, on the means of increas- ing the quantity of, in induction- machines, 63;.0n the propagation of, in highly rarefied elastic fluids, 241 Ethers, on the chlorinated, 449. Euclid, on a rigorous demonstration of the 12th axiom of, 264. Figures of equilibrium of a liquid mass without weight, researches on, 39. Films, liquid, on the theory of the production of, 42; on the tension of, 270. Flames, on sounding and sensitive, S216, 25/, 3/0. Fluid in motion, on some effects pro- duced by a, 99. — pressure, on negative, 207. Fluorescence, on the thermal radia- tion produced by, 316. Forbes (D.) on the mineralogy of South America, 131. (G.) on the meteoric shower of the 14th Nov. 1866, 81, 282. Fouqué (M.) on the relations existing between the composition, density, and refracting-power of saline so- lutions, 555, 561 Fresnel, on a theory proposed by, 540. Friedel (M.) on some compounds of silicon, 451. Gases, on the disengagement of, from their saturated solutions, 479. Gaugain (M.) on Grove’s gas-battery, 465. Geological Society, proceedings of the, 73, 152, 233, 314, 396, 544. Gernez (M.) on the disengagement of gases from their saturated solutions, 479. Glacial epoch, on the excentricity of the earth’s orbit, and its physical relations to the, 119. Grove (W. R.) on aplanatic telescopes, 161. Grove’s gas-battery, on, 465. Gun-cotton, researches on, 545. Harrison (J. P.) on radiation and va- pour, 283; on the relation of inso- lation to atmospheric humidity, 391. Haughton (Rev. S.) on the wave- lengths of the transmission of mus- cular and nervous action, 118. Heat, on the evolution of, by the ra- pid rotation of a disk zn vacuo, 224; on the influence of the adhesion of vapour in experiments on the ab- sorption of, 413. , radiant, on the production of, by fluorescence, 316. Heath (D. D.)on the dynamical theory of deep-sea tides and the effect of tidal friction, 165, 400. Heaton (W.) on the function of the blood in muscular work, 341. Helmholtz (H.) on integrals of the hydrodynamical equations which express vortex-motion, 480. Hennessy (Prof.) on the physical pro- perties of water in relation to ter- restrial climate, 211. Herschel (Sir J. F. W.) on the mete- oric shower of 1866, 156. Hirn (G. A.) on the expansion of superheated steam, 236. Hodgkinson (Rev. G. C.), actinome- trical observations among the Aips by, 304. Hovoligy: on the application of the tuning-fork to, 240. How (Prof. ) on the mineralogy of Nova Scotia, 336. 562 Hydrodynamical equations which ex- ‘press vortex-motion, on the inte- grals of the, 485. ee on solid phosphuretted, Induction-currents, on the produc- tion of, by the twisting of the iron wires through which a galvanic cur- rent is passed, 238. experiments, 481. -machines, on the means of in- creasing the quantity of electri- city in, “63. Insolation, on the relation of, to at- mospheric humidity, 391. Integrals, on the conversion of, 537. Todine, on the acetate of, 143; on the atomic weight of, 193. Isomerism, observations on, 1. Janssen (M.) on certain lines of the solar spectrum, 78. Kincaid (S. B.) on the estimation of star-colours, 557. Ladd (W.) on a magneto-electric machine, 544. Ladenburg (M.) on some compounds of silicon, 451. Le Roux (P. F.) on the velocity with which a disturbance, produced in a gaseous mass, is propagated, 398. Lieben (M.) on the chlorimated ethers, 449. Liebreich (ML) on protagon, 448. Light, on the direction of vibrations in polarized, 319. , electric, on the stratifications of the, in very rare media, 241. Liquid films, on the tension of, 270. Liquids, on some phenomena con- nected with the adhesion of liquids to, 401. Lithium, on the atomic weight of, 204. Loewy (M.) on the distribution of solar spotted areas in heliographic latitude, 79. Mach (E.) on an arrangement for the graphical representation of curves ot vibration, 159. Magnet, on the augmentation of the power of a, by reaction, 471. Magnetism, on the action of, upon the electric discharge m rarefied gaseous media, 512. Magneto-electric machines, on certain points in the theory of some, 543. INDEX. Magnus (Prof.) on the influence of the adhesion of vapour in experi- ments on the absorption of heat, 413. Mascart (M.) on the direction of vi- brations in polarized light, 319. Maxwell (J. C.) on the theory of the maintenance of electrical currents by mechanical work, 474. Mellitic acid, on the constitution of, 449, Meteoric shower BS November 14th, 1866, observations on the, 81, 156, 157, 234, 282. Mills (Dr. E. J.) on isomerism, 1. Mineralogy of South America, re- searches on the; 131; of Nova Scotia, contributions to the, 336. Molecular actions, on some of the conditions of, 360. Moore (J. C.) on the influence of the pe uguty, of the ecliptic on climate, 36. Murray (B. A.) on a rigorous demon- stration of the 12th axiom of En- clid, 264. Muscular action, on the waye-lengths of the transmission of, 118. Nervous action, on the wave-lengths of the transmission of, 118. Neumann (Dr. E.C. O.) on an appa- ratus for the direct measurement of the velocity of sound in the atmo- sphere, 36. Neurine, on the preparation and con- stitution of, 449. Niaudet-Breguet (M.) on the applica- tion of the WU to herotaey> 240. Nitrogen, on the determination of, 61; on the atomic weight of, 205. Operators, on the multiplication of partial differential, 48. Particles, on a mode of measuring the average size of very fine, 540. Pencil-stone, analysis of, 337... __ Pfaundler (M.) on the thermal capa- city of various kinds of soils, 56. Physical quantities, on the definitions of, 88. Pierre (Prof. V.) on the thermal ra-_ diation produced by fluorescence, 316, Plateau (Prof. J.) on figures of equi- librium of a liquid mass without weight, 39, INDEX. Potassium, on the atomic weight of, 207. Potential energy, on the phrase, 88. Pratt (Archdeacon) on the figure of the earth, 10, 145, 261, 332, 445. Preece (W. H.) on the British-Asso- ciation unit for electrical measure- ments, 397. Preyer (M.) on a new method of de- termining the amount of colouring- matter in the blood, 446. Protagon, researches on, 448. Radiation and vapour, observations on, 283. Rankine (W. J. M.) on the phrase potential energy, and on the defi- nitions of physical quantities, 88. Ransome (Dr. A.) on some of the conditions of molecular action, 360. Roberts (S.) on the order of the con- ditions that an algebraical equation may have a set of multiple roots, 530. Robinson (Rev. T. R.) on the means of increasing the quantity of elec- tricity im induction-machines, 63. Rodwell (G. F.) on some effects pro- duced by a fluid in motion, 99. Rood (Prof. O. N.) on a theory pro- posed by Fresnel, and ona mode of measuring the size of very fine par- ticles, 540. Royal Society, proceedings of the, 63, 224, 304, 391, 543. Rudorff (M.) on solid phosphuretted hydrogen, 61. Saline solutions, on the relations ex- isting between the composition, density, and refracting-power of, 555. Scheibler (M.) on the constitution of _ mellitie acid, 449. Schtitzenberger (P.) on the substitu- tion of the metal in a salt by elec- tro-negative elements, 140. Schwendler (L.) on the galvanometer resistance to be employed in test- ing with Wheatstone’s diagram, 29. Sea, on the influence of a change in the obliquity of the ecliptic on the level of the, 426. Siemens (C. W.) on the conversion of dynamical into electrical force, 469. Silicon, on some compounds of, 451. Silver, on the atomic weight of, 192. Sodium, on the atomic weight of, 207. 563 Soils, on the thermal capacity of va- rious kinds of, 56. Solar spots, on the distribution of, Sonorous vibrations, on the action of, on gaseous and liquid jets, 375. Sound, on an apparatus for the direct measurement of the velocity of, in the atmosphere, 36. Spectra of the meteors of November 1866, on the, 234. Spectrum, solar, observations on cer- tain lines of the, 76, 78. Stahlschmidt (M.) on the reducing- action of zine, 62. Star-colours, on the estimation of, 557. Stas (M.) on the determination of atomic weights, 187. Steam, on the expansion of super- heated, 256. : Stewart (B.) on the distribution of solar spotted areas in heliographic latitude, 79; on the heating of a disk by rapid rotation in vacuo, 224. Stone (H«J.) on the dynamic theory of deep-sea tides, 318. Stroboscopic disks, on the applica- tion of the principle of, to the opti- cal analysis of vibrating bodies, 16. Sylvester (Prof.) on the multiplica- ae of partial differential operators, Tait (P. G.) on the heating of a disk by rapid rotation in vacuo, 224. Telescopes, aplanatic, on, 161. Thermometers, on the diminution of difference between exposed and shaded, in upper regions of the at- mosphere, 213. Tidal friction, on the theory of, 400. Tides, on the dynamical theory of deep-sea, 165, 318, 400. Topler (Dr. A.) on the application of the principle of stroboscopic disks to the optical analysis of vibrating bodies, 16; on a method of deter- mining differences of density in ' transparent media, 75. Tomlinson (C.) on some phenomena connected with the adhesion of liquids to liquids, 401. Tyndall (Prof. J.) on sounding and sensitive flames, 92; on the action of sonorous vibrations on gaseous and liquid jets, 375; on the action 564 of aqueous vapour on radiant heat, 425. ' Van der Mensbrugghe (G.) on the tension of liquid films, 270. Varley (C. F.) on certain points in the theory of some magneto-elec- tric machines, 543. Vegetation, on the influence of the physical properties of soils on, 60. Veins, liquid, on the theory of the production of, 44. Vibration, on an arrangement for the graphical representation of curves of, 159. Vibrations of sounding bodies, optical analysis of the, 16. Vision, on binocular, 326, 549. Voltaic current, on the transport of a body by the, 482. Water, on the physical properties of, INDEX. in relation to terrestrial climate, lite Webb (F. C.) on one of Ohm’s laws relating to an insulated circuit, 321. Wheatstone (C.) on the augmentation of the power of a magnet by reac- tion, 471. Wheatstone’s diagram, on the galva- nometer resistance to be employed in testing with, 29. Wichtyne, on the composition and physical characters of, 336. Wiedemann (G.) on the production of induction-currents by the twist- ing of the iron wires through which a galvanic current is passed, 238. Willich (C. M.) on the partition of the cube, 27. Zine, on the reducing-action of, 62. END OF THE THIRTY-THIRD VOLUME. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. ALERE FLAMMAMa, AUS Sages. Phil. Mag, Ser. 4,Vol 33, Pt. 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Published the First Day of every Month.—Price 2s. 6d. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE, | AND | JOURNAL OF SCIENCE. | Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson’s * Annals of Philosophy.’ CONDUCTED RY SIR DAVID BREWSTER, K.H. LL.D. F.R.S. L.& E. &e. SIR ROBERT KANE, M.D. F.R.S. M.R.LA. WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S. FOURTH SERIES. N° 222.—MARCH 1867. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and “Co. ; Whittaker and Co.; and H. Bailliére, London :—and by A. and O. Black, and ‘Thomas Clark, Edinburgh; Smith and Son, Glasgow:—Hodges and Smith, Dublin :—and Putnam, New York. CORRELATION AND CONTINUITY. Just published, in 1 vol. 8vo, price 10s. 6d. cloth, THE CORRELATION OF PHYSICAL FORCES. By W. R. Grove, Q.C., F.B.S. A New Edition, being the Fifth, followed by a DISCOURSE ON CONTI- NUITY, delivered by the Author as President of the British Association at Not- tingham, 1866. This DISCOURSE may be had separately, price 2s. 6d. . London: Longmans, Green, and Co., Paternoster Row. Just published, post 8vo, 12s., LECTURE NOTES FOR CHEMICAL STUDENTS. Embracing both Mineral and Organic Chemistry. By E. FRANKLAND, F.R.S., Professor of Chemistry in the Royal Institution of Great Britain and in the Government School of Mines. ‘‘The volume deserves careful study. The novelty of many of its views, coming from so distinguished a chemist, are most suggestive, and cannot fail to exert an impor- tant influence upon theoretical chemistry. All the more important elements and com- pounds, with their modes of preparation, the reaction in each case, their physical of decomposition, are most clearly de- scribed. And thus the object of the work, to furnish names, formule, and reactions, and so to save to the student the time spent in copying these in the lecture-room, is most successfully accomplished.”—Sili- man’s American Journal of Science and Arts, January 1867. and chemical properties, and their modes John Van Voorst, 1 Paternoster Row, E.C. THE ABSTRACTS AND OCCASIONAL PAPERS Published by the ROYAL SOCIETY OF EDINBURGH under the title of ** PROCEEDINGS ” may now be had by Annual Subscription of Four Shillings, or Four Shillings and Sixpence free by post. Edinburgh: R. Grant and Son. London: Williams and Norgate. THE LABORATORY: A WEEKLY RECORD OF SCIENTIFIC RESEARCH. . No. I. on Saturday, April 6. Price 6d. The aim of the projectors of this periodical is to establish a useful medium of intercommunication for workers in the field of Experimental Research. Each Number will contain original communications from eminent chemists and physi- cists, short editorial articles on scientific topics, critical notices of new books, full reports of the proceedings of learned societies, and abstracts of the leading contributions to the Foreign scientific press. Special reports on the chemical products and scientific imstruments of the Paris Exhibition will appear in the early Numbers. All communications for the Editur to be addressed 4 Norman Terrace, Stockwell, S.; and all letters relating to advertisements, subscriptions, and general business to be sent to the Publisher, James Firru, 42a Cannon Street, E.C. [ADVERTISEMENTS continued on 3rd page of Cover. Vol. 33. APRIL 1867. No. 223. Published the First Day of every Month.—Price 2s. 6d. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson’s ‘ Annals of Philosophy.’ ; CONDUCTED BY SIR DAVID BREWSTER, K.H. LL.D. F.R.S. L. & E. &c. SIR ROBERT KANE, M.D. F.R.S. M.R.LA. WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S. FOURTH SERIES. N° 223.—APRIL 1867. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION €OURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co.; Whittaker and Co.; and H. Bailliére, London :—and by A. and C. Black, and Thomas Clark, Edinburgh; Smith and Son, Glasgow:—Hodges and Smith, Dublin :—and Putnam, New York. UNIVERSITY COLLEGE, LONDON. JUNE MATRICULATION EXAMINATION of the University of London. Summer Course of Chemistry, Theoretical and Practical. Professor WILLIAM- son, F.R.S., assisted by Mr. C. H. Ginx, F.C.S. The Course will consist of about Twenty Lessons in Practical Chemistry, and of an equal number of Oral Les- sons, commencing on Wednesday, April 10, at 11 a.m. Fee, including cost of materials and apparatus, £4 4s. SUMMER COURSE of Experimental Physics, including the Elements of Mechanics, Hydrostatics, Pneumatics, Acoustics, and Optics. Professor G. C. Foster, B.A. Lond. This Course will consist of about Thirty Lectures, begin- ning on or about the Ist of April. Fee £3 13s. 6d. A Prospectus of the above and of other courses of instruction adapted for Stu- dents preparing for the Matriculation Examination may be had on application at the Office of the College. CHARLES Cassau, LL.D., Dean of the Faculty of Arts. CHARLES C. ATKINSON, Secretary to the Council. — February 25, 1867. Just published, in post 8vo, price 14s. cloth, ROCKS CLASSIFIED AND DESCRIBED. By BERNHARD Von Corta. An English Edition, by P. H. Lawrence (with English, German, and French ~ Synonyms), revised by the Author. x* Lithology, or a Classified Synopsis of the Names of Rocks and Minerals, also by Mr. LawRENcE, adapted to the above work, may be had, price 5s.; or printed on one side only (interpaged blank) for use in Cabinets, price 7s. London: Longmans, Green, and Co., Paternoster Row. STUDENTS’ CLASS-BOOKS. FRANKLAND’S LECTURE NOTES FOR CHEMICAL STUDENTS. 12s. GREVILLE WILLIAMS’S HANDBOOK OF CHEMICAL MANIPU- LATION. lds. NORTHCOTE and CHURCH’S MANUAL OF CHEMICAL QUALITA- TIVE ANALYSIS. 10s. 6d. | HENFREY’S ELEMENTARY COURSE OF BOTANY. 12s. 6d. BABINGTON’S MANUAL OF BRITISH BOTANY. SIXTH EDITION. Nearly ready. 10s. 6d. ANSTED’S ELEMENTARY COURSE OF GEOLOGY. 12s. , GRIFFITH’S ELEMENTARY TEXT-BOOK OF THE MICROSCOPE. s. 6d. T. RYMER JONES’S GENERAL OUTLINE OF THE ORGANIZATION OF THE ANIMAL KINGDOM. 3ls. 6d. John Van Voorst, 1 Paternoster Row. [ADVERTISEMENTS continued on 3rd page of Cover. ae a MAY 1867. No. 224. Vol. 33. Published the First Day of every Month.—Price 2s. 6d. THE LONDON, EDINBURGH, ano DUBLIN PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. Being @ Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson’s ‘ Annals of Philosophy.’ | | CONDUCTED BY SIR DAVID BREWSTER, K.H. LL.D. F.R.S. L.& E. &c. SIR ROBERT KANE, M.D. F.RS. M.R.I.A. WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S. FOURTH SERIES. 2 N° 224.—MAY 1867. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Sl 0UlUl Agency of Smithsonian Institution. | : . Sold by Longmans, Green | ¢ acai | Co.; Simpkin, Marshall and Co.; WhittakerandCo |) WILLIAM WESLEY, |] -and by A. and C. Black, and | Bookseller and YBublisher, |f sgow :—Hodges and Smith, Thomas Clark, Edinbi }) ©°°** 3 - Dublin :—and Putnam, | 81, Fleet Street, London. | a Printers § Just published, in post 8vo, price 14s. cloth, ROCKS CLASSIFIED AND DESCRIBED. By BERNHARD Von Cotta. An English Edition, by P. H. Lawrence (with English, German, and French Synonyms), revised by the Author. x* Lithology, or a Classified Synopsis of the Names of Rocks and Minerals, also by Mr. LawRENCE, adapted to the above work, may be had, price 5s.; or printed on one side only (interpaged blank) for use in Cabinets, price 7s. London: Longmans, Green, and Co., Paternoster Row. PRACTICAL GEOLOGY.—KING’S COLLEGE, LONDON. PROFESSOR TENNANT, F.G.S., will commence a COURSE of LEC- TURES, on Friday, APRIL 26th, at 9 a.m., having especial reference to the ap- plication of GEOLOGY to ENGINEERING, MINING, ARCHITECTURE, and AGRICULTURE. The Lectures will be continued on each succeeding Fri- day and Wednesday at the same hour. Fee £1 11s. 6d. R. W. JELF, D.D., Principal. UNIVERSITY OF LONDON. Price 4s., THE CALENDAR FOR THE YEAR 1867; Containing the Regulations for each Examination, the Examination Papers set during the past year, and other information. Taylor and Francis, Printers and Publishers to the University, Red Lion Court, Fleet Street. Just published, A New Edition (the Fourth), price 2s. 6d. GLAISHER’S HYGROMETRICAL TABLES. HYGROMETRICAL TABLES to be used with, and Description of, the Dry- and Wet-bulb THERMOMETERS. By JAMES GLAISHER, Esgq., F.R.S., of the Royal Observatory, Greenwich. Taylor and Francis, Red Lion Court, Fleet Street. STAFF COLLEGE EXAMINATIONS. Just published, One Shilling each. REPORT on Tur EXAMINATION FOR ADMISSION ro THE STAFF COLLEGE, held in July 1866; with Copies of the Examination Papers. REPORT on toe FINAL EXAMINATION art roe STAFF COLLEGE in December 1866; with copies of the Examination Papers. Published by direction of the Council of Military Education. Taylor and Francis, Red Lion Court, Fleet Street, E.C. [ADVERTISEMENTS continued on 3rd page of Cover. Vol. 33. JUNE 1867. — No. 2265. Published the First Day of every Month.—Price 2s. 6d. THE LONDON, EDINBURGH, anp DUBLIN . PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosonhical Magazine,’ Nicholson’s ‘Journal,’ and Thomson’s ‘ Annals of Philosophy.’ — CONDUCTED RY SIR DAVID BREWSTER, K.H. LL.D. F.R.S. L.& E. &e. SIR ROBERT KANE, M.D. F.R.S. M.R.LA. WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S. FOURTH SERIES. ; . 3° Ne 295.—JUNE 1867. WITH A PLATE, Illustrative of Mr. C. Tomiinson’s Paper on some Phenomena connected with the Adhesion of Liquids to Liquids. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION €OURT, FLEET STREET. ; Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co. ; Whittaker and Co.; and H. Bailliére, London :—and by A. and C. Black, and Thomas Clark, Edinburgh; Smith and Son, Glasgow:—Hodges and Smith, Dublin :—and Putnam, New York. In a few days, THE MECHANICAL THEORY OF HEAT, With its APPLICATIONS to the STEAM-ENGINE and to the PHYSICAL PROPERTIES OF BODIES. : By R. Cuaustius, Professor of Physics in the University of Zurich. Edited by T. AkcuER Hirst, F.R.S., Professor of Mathematics in University College, London. With an Introduction by Professor TyNDALL. John Van Voorst, 1 Paternoster Row. BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE. The next ANNUAL MEETING of the Association will be held under the Presidency of His Grace the Duke or Buccuevucn, K.B., F.R.S. &c., at Dun- dee, commencing on Wednesday, September 4. Notices of Papers proposed to be read at the Meeting should be sent to the Assistant General Secretary, G. GRirriTH, Esq., Harrow. Members and others who wish to obtain information about the Local arrange- ments are requested to communicate with the Local Secretaries at Dundee. STAFF COLLEGE EXAMINATIONS. Just published, One Shilling each. REPORT on THe EXAMINATION FOR ADMISSION to THE STAFF COLLEGE, held in July 1866; with Copies of the Examination Papers. REPORT on tor FINAL EXAMINATION at tHe STAFF COLLEGE in December 1866; with copies of the Examimation Papers. - Published by direction of the Council of Military Education. Taylor and Francis, Red Lion Court, Fleet Street, E.C. UNIVERSITY OF LONDON. Price 4s., THE CALENDAR FOR THE YEAR 1867; Containing the Regulations for each Examination, the Examination Papers set during the past year, and other information. Price 2s. 6d., THE GENERAL REGISTER OF THE MEMBERS OF THE UNIVERSITY OF LONDON, to January Ist, 1867. Taylor and Francis, Primters and Publishers to the University, Red Lion Court, Fleet Street. [ADVERTISEMENTS continued on 3rd page of Cover. Saya esl SUPPLEMENTARY NUMBER. Vol. 33. No. 226. See \W ES THE are yO DON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE, AND JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson’s ‘ Annals of Philosophy.’ Published the First Day of every Month.—Price 2s. 64d. | CONDUCTED BY SIR DAVID BREWSTER, K.H. LL.D. F.R.S. L.& E. &c. SIR ROBERT KANE, M.D. F.R.S. M.R.I.A. WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S. FOURTH -SERIES. N° 226_SUPPLEMENT. JULY 1867. This SuppLemeEnt to Vol. XXXIII. is published with the regular Number for July, and should be delivered with it to Subscribers. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co. ; Whittaker and Co.; and H. Bailliére, London :—and ‘by A. and C. Black, and | Thomas Clark, Edinburgh; Smith and Son, Glasgow:—Hodges and Smith, fe e | Dublin :—and Putnam, New York. SMITHSONIAN INSTITUTION LIBRARIES 3 9088 01202 3990