a ey ay “Vy . ee ee ee ek) 4,0 8d lw ee aoe 4 ate, ”, Aa] we, . Ny AW ell ie We ieee ertie te Me baked OLR a eke eee ewer ath, Pe ech Yop er WAL Ink BPR wey Pd We ee ce a ee ee ay oy miata) ‘ ws oy i 4 7 ee atk tk ae bc We Gane avd Gare uit: va eee a tees ig aoe AS Iaitat ay eas § ““ ppl ih a ik MA Oe tg fe i mae te deed gede ‘eae “a tad tie, aed PRAY ‘iy! ty 5 iene aera Ses rina, ar odiber ilies IA drt ‘ i be. ht Ae frtheneines 4 A Meh ate q ryt . f 4 2: ie > ty Hee KY ta wh Ow me idares war if ae Pus moat ativan ey * ‘ aha arate wae 7 oe eyo mi R we ie ten «matt h ee © a A NE UROL REET tat ied aR Cy ) i Le oe fh ah Arp uy yl ee adivta av gle BAR reall 4 TN age ‘ie aa ¢ fe i’ ‘A . g *. T 14 as ie 1 * ; Yee DA aes Vel enewaegas aw. LYE A eo A a? oI « Were e +044 oe NEY a vei re A TTR eee ee ke: “ae 7) a Pay ae “fe ism 2 SS He ‘ ) ier uee a ae ead aad ae ; vd 4; ‘ POOR RCC LET cnet Om tea dat Py pRas eye MALE ‘ anh ae CRC Rae , Tian9, HAR a YE a aay tole A Ue) aad Ce ‘ @ i DR UU KD Rist EIN 4s * “4 te) te res , hea ie ie Re ton : < : ‘a ee Seat hed ge re eae 4 Ash Oe ae. Fah aR: eA mae oF ARG Fs PARNER} Pee Pes yeas a eH a CNA te Lape waged “f Week, ty) a a % be ie Bo a ey Ran sera THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Knrv. LL.D. F.RB.S. &e. AND 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. XLVI.—FOURTH SERIES. JULY—DECEMBER 1873. LONDON. TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the Unwersity of London ; SOLD BY LONGMANS, GREEN, READER, AND DYER; KENT AND CO.; SIMPKIN, MARSUALL, AND CO.; AND WHITTAKER AND CO. ;—-AND BY ADAM AND CHARLES BLACK, AND THOMAS CLARK, EDINBURGH; SMITH AND SON, GLASGOW :— HODGES, FOSTER, AND CO, DUBLIN‘:—-PUTNAM, NEW YORK ‘:—AND ASHER AND CO., BERLIN, “‘Meditationis est perscrutari occulta; contemplationis est admirari perspicua..... Admiratio generat questionem, questio investigationem, investigatio inventionem.”—Hugo de S. Victore. —‘* Cur spirent venti, cur terra dehiseat, -Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugme condat, Quid toties diros cogat flagrare cometas ; Quid pariat nubes, veniant eur fulmma ceelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” : J.B. Pinelli ad Mazonium. CONTENTS OF VOL. XLVI. (FOURTH SERIES.) NUMBER CCCIII.—JULY 1873. Prof. R. Clausius on the Relations between the characteristic Quantities occurring in Central Motions................ Mr. J. A. Phillips on the Composition and Origin of the Waters of a Salt Spring in Huel Seton Mine, with a Che- mical and Microscopical Examination of certain Rocks in euysettabge ( With’a Plate.) 0... oi oe war nye o's ons wien Mr. W. H. Walenn on Negative and Fractional Unitates Prof. J. D. Dana on some Results of the Earth’s Contraction from Cooling, including a discussion of the Origin of Moun- mM he Gk sie ee, sc og eco lveci ceed ae tin . M. L. Lorenz on the Determination of Degrees of Heat in mpa@iine Measure 2... ee ChAT a Notices respecting New Books :— Mr. R. A. Proctor’s Light Science for Leisure Hours. ReeaS NC Se a. occ labasdvadaiale « soe a Ns Galata s aes Selections from the Portfolios of the Editor of the Lunar Empat WALAIOOUG ioe cb. oe eda cee wt ene ees Proceedings of the Royal Society :— Dr. J. Jago on Visible Direction: being an Elementary Contribution to the Study of Monocular and Binocular © UEEETUL | ug cvdehat lel alin gil lettin a, ag On Induced Currents and Derived Circuits, by John Trow- SUMS SU ci We stays secs 36 eos sade ems On Electrical Figures on Conductors, by H. Schneebeli Note on Gaseous Pressure, by Robert Moon, M.A., Honorary Fellow of Queen’s College, Cambridge ................ Note on the use of a Diffraction-“ grating” as a substitute for the Train of Prisms in a Solar Beocbadcants by Prof. oe Racy ce CAUILDG Petar eli 4 la NUMBER CCCIV.—AUGUST. Dr. H. Morton on the Fluorescent Relations of certain solid Hydrocarbons found in Petroleum Distillates............ Page lv CONTENTS OF VOL. XLVI.—FOURTH SERIES. Page Mr. J. W. L. Glaisher on the Form of the Cells of Bees .... 103 Mr. R. Moon on the Integration of the Accurate Equation representing the Transmission in one direction of Sound through Air, deduced on the Ordinary Theory .......... 122 Prof. J. D. Dana on some Results of the Earth’s Contraction from Cooling, including a discussion of the Origin of Moun- AMES © vases se egies sri esmnesh ig ae Ss tet oy ete +: bane 131 Mr. H. A. Rowland on Magnetic Permeability, and the Maxi- mum of Magnetism of Iron, Steel, and Nickel (With Two Palates:)), 5. <3 a; pseyepibesys Se aereay tae Spies Bee ee 140 Prof. Challis on Objections recently made to the received principles of Hydrodynamics .......5....0.0045 aise ee ¢ MLO Lord Rayleigh on the Nodal Lines of a Square Plate ...... 166 Notices respecting New Books :— Astronomical and Meteorological Observations made du- ring the year 1870, at the United States Naval Obser- VACOLY cw ee wos sees ea ta eee ate 174 Procéedings of the Geological Society :— $e Mr. C. J. A. Meyer on the Punfield Section .......... 173 Mr. W. J. Sollas on the Coprolites of the Upper Green- sand, Formation, and.on Plints.. (a.en- ]—_. 5U Sarl). PEC OO AY Se ¢ (6) In this equation the distinction whether the path 1s closed or not is of no consequence. For its applicability it is merely ne- cessary that the motion be stationary, so that the quantities v? and rF’(r) shall not continually change in the same direction, but only oscillate within certain limits and hence have definite mean values. It is not so with my second equation ; in this occurs the period i of the motion under consideration. If, then, the motion takes place in a closed path and therefore regularly repeats itself in exactly the same manner, we can confine our attention to a single run through this path, and take the time required for it as the quantity i. I have treated of this case in my previous memoirs. But when the motion takes place in a path which is not closed, and therefore does not present any periods repeating themselves in the same manner, the contemplation cannot thus be limited simply to one definite period; and a further investigation is re- quired in order to ascertain whether and in what way my second equation can be applied to such a case. 4. For this purpose we will carry a little further the already ~ above intimated division of the total motion into two—the an- characteristic Quantities occurring in Central Motions. 9 gular motion of the radius vector, and the to-and-fro motion of the point within the radius vector. The angular motion of the radius vector we will name motion of rotation, and understand by period of rotation the time during which the radius vector runs through the entire angular space 27. The motion of the point within the radius vector we will name radial motion of vibration, or, briefly, motion of vibration, and choose the name period of vibration for the time during which a vibration to and fro takes place. The period of a rotation may be denoted by 2, and the period of a vibration by 2. The motion of vibration can be treated as quite independent of the motion of rotation, if we introduce the centrifugal as a special force. Let @ denote the angle which the radius vector forms, at the time /, with a fixed right line in the plane of rota- tion, so that eo will denote the angular velocity of the radius vector; then the centrifugal force to which the rotation gives rise will be represented by the product Now, as for the motion of a point about a fixed centre of attraction the proposition is valid that the radius vector describes equal spaces in equal times, we have the equation dé ry? —=¢ oe EA erent in which ¢ is a constant ; and from this we immediately obtain, further, de? 1 mr (Fe) = me". Shas | sees dete cal /AeD) The centrifugal force represented by this expression we will now regard as a force of repulsion exerted from the centre, and to be added to the force represented by F’(r), which is actually exerted from the centre. Then we obtain for the motion of vibration the following differential equation, d*r 1 m Fa =— Ff" (r) + me*s, 2 HigMO ee e888) with the aid of which we can treat the vibration as a motion subsisting by itself. ‘To this motion thus regarded, both my equations are found at once applicable. Equation (2) gives, if we substitute r for z, and —F’ (7) + mc? Hs re 10 Prof. R. Clausius on the Relations between the for X, m (dr\? ET pe I EEN eee lay eee 2 ; =) =ErP)— gee + se The second equation reads, in the form given under (5c) :— 6,U= e Sv? + mv log i. In order to apply this equation, we have first to form the ex- pression of the ergal U for the vibration-motion. In accord- ance with equation (8), we may put v= (FW — me =) dr, from which by integration, writing F(r) for the integral of F’(r), we get m , | U=Fi(r) +- 9 c? Ae _ This is such a function as was mentioned above, containing a quantity ¢ which is constant during each motion, but may change its value on passing from one motion toanother. This quantity must, when we form the variation 6,U, be regarded as constant ; and thus we obtain BUSSEY) + Fe = By introducing this expression into equation (5c), at the same time replacing v? by ey and using instead of 2 the symbol chosen for the period of a vibration, 7,, we transform that equation into G+ 204” eae: m(2Y 810g i, Rigs From the two equations (9) and (10) we can eliminate the 2 quantity = . We will, however, for the present, only employ ye ty Nee Haiti, in the variation of (-) the expression given in (9). At the same time it is to be noticed that ¢his is a complete variation, in which the change of the quantity c must also be considered. We thus get : 660.1 2 5 GX) il — — nt —_ 9 a mo (dt? . 7 Mg mea =t6rk'(r) 5 OO characteristic Quantities occurring in Central Motions. 11 This being put in (10) gives — a m1 a DRA re, ig i dr\2 SF (r) + 9 o°8 = 36rF(r) —% c°} 3M coc-+m (F) 5 log z,, or, differently arranged, OF it SF(r) —8rF"(r) = —me*S ee oN +m (5) tees 2 r2 72 dt fot |e for which we may write 4 / dyp\2 b[ F(r ~47I"7)] =—me8(c-)+m a) Blog i. seach} 5. We will now turn to the motion of rotation. In such a motion, in which the movable point need not have the same distance from the centre at the end as at the commence- ment of a rotation, the period of a rotation of the radius vector also need not be exactly the same for several successive rotations ; yet at all events for a greater number of rotations we shall obtain a definite mean value of the period of a rotation. To this we will refer the symbolz. Now, pursuant to equation (7), we can write L and when we integrate this equation for a whole number n of rotations, consequently between the limits 0=0 and 0=n. 27, there comes ee i n.2m=e( — dt = c= ni, Nghia as r and consequently ee NA ty. dg) Putting this value of cm in equation (12), we obtain 2 é[F (r) —$rF (7) = — 2nmed = +m i Slog, . (14) To this equation we can give a more symmetrical form; for the first term on the right-hand side can, in consideration of equa- tion (13), be transformed thus :— 1 Dre. Bee) 42 — 2armcd a mes id =e 6 log i. Thereby the preceding equation is changed into 7 D b[ F(r) —Srk'(r)] =me? “ 6 log i+m(Z) Slogi,. . (15) 12 Prof. R. Clausius on the Relations between the — The half of the factor mc? ~. is the mean vis viva of the motion of rotation ; for the component of velocity originated by the ro- seeenle) aay ; tation is r——, and the part of the vis viva corresponding to dt this component is oa ee for which, according to (7), we dr\? .. can even put = ee = Just so the half of the factor m7) is the mean vis viva of the motion of vibration. Accordingly the equation is symmetric in relation to the motions of rotation and vibration*. Since, according to (9), the sum of the two factors ENE me and m(7) is equal to rI"(r), we can even give to the preceding equation the following forms, more convenient for many applications :— Lsseen hist shel VFO ; SF) —47F@)] =rF"(V)8 log i—m(Z) Slog;. (16) 1 6[ P(r) —$rF'(r)] =rF'(7)6 log 7, + me? ] a 72 ) log i ° ( 7) This equation, given in various forms under (14), (15), (16), and (17), is the expression of a new relation, universally valid for motions about a fixed centre of attraction. When the central motion is of such a kind that a constant ratio subsists between the period of a rotation and the period of See: ne a vibration, the fraction 71s invariable, and therefore 6 log--=0. 1 4) Thereby the two preceding equations become accordant and are * Pursuant to equation (13), we can also form the following equation :— m ool _m T i i 7 Oe (ce ) + me? + Slog. r 1 : Now, as the expression mc*—3 represents a force of attraction equal to the ‘ ; m 1 centrifugal force, we may regard the quantity — 9 ©'>3, arising from the integration of that expression, as the ergal relative to the motion of rota- . m ] tion. Remembering further that oy c? —> represents the vis viva of the 72 motion of rotation, we see that the preceding equation has precisely the same meaning for the motion of rotation as (10) has for the motion of vi- bration. The sum of the two equations, together with the consideration of (9), gives the preceding equation (15). characteristic Quantities occurring in Central Motions. 18 changed into 8[F(r) —4rF’(r)] =rF'(r)8 logz, for which, as rE" (r) =mv?, we can write SF (r) = 5 Sv? + mv log i. This is the equation which holds for central motions in closed paths, and here appears as a special case of more general equations. 6. Having put the equations in such a manner that they are valid for any conceivable law of force, we will apply them to a special group of such laws, viz. to those according to which the force is proportional to any power of the distance. At the same time, however, we will exclude the minus first power, because in the integration it leads to logarithms, and consequently demands separate discussions, which would detract from the compendious- ness of the analysis. Accordingly, k and n denoting two constants, the latter of which is different from —1, we will put Bae we oe ee a (1) whence results k Fae These formule we have to substitute for F(r) and F'(r) in the above equations. Equation (16) may be selected, which by the substitution is changed into Tah: Weho\. nae <7 MELO) kor") = kr*+18 log i—m 8 log a (20) dt zy l—n 2(n+1) For the sake of a more convenient expression, the quantity p shall now be introduced, with the signification (GIF iA lily te Pipettes ERE ed This quantity can be immediately determined when the energy (sum of ergal and vis viva) is known, consequently when we know, for any position of the movable point, its velocity. That is to say, since the mean vis viva is equal to the virial, we have gene- rally, if K denotes the energy, K=F(r)+4rF(r), and for our special law of force :— k —— k — n+3 —— iat m-+-1 } — n+] — n+] Meera ay Fouaye : 14 Prof. R. Clausius on the Relations Bete the and consequently, employing the quantity p, — n+1 1) erat from which it follows that 1 Ear [SS - ee a eee After substituting, with the aid of this quantity p, for the mean value of a power, represented by r”*!, a simple power p”t!, we can forthwith carry out the variation of it, and write or? +1 = (n+ 1)p"8p. Accordingly, by the introduction of p, equation (20) changes into 1 —N dr 2 1 n pon n+1 i ies (Ore Tra kp ) Np ) log i) n(Z) 6 log i, 5 - (23) Into this equation we will introduce a second simplifying quantity, p; for as the mean vis viva of the rotatory motion and the mean vis viva of the radial vibratory motion together make up the total mean vis viva, we can represent the two former as fractions of the latter, which fractions shall be denoted by p and l-—-p. Thus a : (24) 2(az) = 0-2) ge The value of p may vary between O and 1; and on it depends which out of all the forms possible with a given value of n the path takes. When p=0, the point moves in a right line to and from the centre ; and when p=1, it moves in acircle round the centre. Between these two limits lie all the other possible forms. By introducing p into equation (23) we obtain first a5" php = kp 3 logi— (1—p) kp" +36 log = 3 ] and this equation, divided by kp”*?, gives 1—n 2 As two of the terms of this equation are complete variations, the third term, Slog p= logi—(1—p)dlog >. ee) (1—p)6é log 3 1 characteristic Quantities occurring in Central Motions. 15 must likewise be such, whence it follows that p is a function of — alone, or vice versé — is a function of p alone. Regarding a D a I 1 . . . as a function of p, we can from this function derive others; and we will introduce one, denoted by J, which shall be determined by the following equation :— i dlog— o ——= == I e ° ° e ° log J fa Dp) Zz dp 26) Then is (1—p)6é log = =O lor Ji; it and therefore equation (25) changes into +=" Slog p=Slogi—Slog J. ‘nadie Geattey (274 By transposition and integration of this equation we obtain l—n 2 log i= log p + log J + const. It is immaterial which value we attribute to the integration- constant, since, in accordance with (26), we can suppose any additive constant we please to be likewise contained in log J. The value most suitable for what follows is log ana / = If we put this quantity in the place of the constant, and then combine the three logarithms of the right-hand side, we get ~~ 1” . log 7= log (2na/ p74); and from this we obtain, for the rotation-period i, the following simple expression :— ~, 1—n imora [Mp ed. Bh ct wid shen 2S) We can deduce a corresponding expression for the oscillation- period 7, Equation (25), namely, can also be written in the following form :— l—n 2 8 log p=5 log i, + p8 log = Introducing into this the function J,, which is determined by 16 Prof. R. Clausius on the Relations between the the following equation, d log ogh=—{p a tdp, ww ee the result is similar to the preceding :— : ie, Ol — 97 traf MT). . +. ee Between the functions J and J,, occurring in these two ex- pressions, there subsists, according to equations (26) and (29), the following relation :— ave sei lee ip dp As, with the aid of this equation, one of the two functions can be deduced from the other, we can say that, in the two expres- sions of 7 and 2,, only one undetermined function of p occurs. 7. In equations (28) and (30), the periods z and 7, are ex- pressed by the quantities p and p. According to equation (22), p is a simple function of the energy EH, which remains invariable during the whole motion, and hence can be taken as known. It is otherwise with the quantity p. It is true this has a simple signification (the mean ws viva of the motion of rotation as a fraction of the total mean vis viva); but its value cannot be stated so simply, because for the calculation of the mean value of a variable quantity the whole course of the motion must be taken into consideration. Hence it is advisable to introduce ~ instead of p another quantity the value of which is obtained im- mediately from the data usually employed for the determination of the motion. These are the energy E and the already discussed quantity c, the half of which represents the area described by the radius vector in the unit of time, and which, as well as the energy, remains constant during the whole motion. We will now bring in a quantity q determined by the following equation, aon 72(n+1) assy Le ae 2(m-+1) ian e[ na | ee and which, consequently, can be calculated in a very simple manner from E and ec. In order to find the connexion of this new quantity q with p, we can first, with the aid of equation (22), transform the expres- sion of g into the following :— Eee Aare g=a [Se Oy Ae tis nr ps . eR 588) characteristic Quantities occurring in Central Motions. 17 Further, equations (13) and (24) hold good— results from which, by elimination of -5 Z Te 6 = ae aS oe ° ° . e ° . 34: 1=277 k pp (34) If herein for 7 we put its value from (28), we obtain m e pert ° ° ° e e (35) 2 and the combination of this with equation (33) gives mien, eee ee the .* “(G6) Consequently q stands in a very simple relation to p. Its behaviour is also very similar to that of p. It can like- wise vary only between the limits O and 1, and takes these boundary values simultaneously with p. When c=0, then, ac- cording to (32), is g also =0; and consequently the vis viva of the rotation-motion also, and therefore the quantity p, has the value zero. If, now, ¢ is increasing, p and q increase at the same time. When p has reached the value 1 the path has become circular. For this case we have, in the differential equation d*r i awl m 73 = — kr” + mc 3 2 for the oscillatory motion, to put the differential coefficient = equal to zero; and the equation thereby arising can be brought into the following form :— ONG eae Further, where 7 is constant, we may regard r and p as sig- nifying the same thing, and hence the preceding equation can also be written a?) C? gers? and this gives, in accordance with (33), for g the value 1. Since, according to (36), g is represented by the product pJ, in which J is a function of p only, ¢ itself is likewise a function of palone, and accordingly p can reciprocally be regarded as a func- tion of g only. Thence it follows, further, that J and J,, which Phil. Mag.8. 4. Vol. 46. No. 303. July 1873. C 18 Prof. R. Clausius on the Relations between the we have hitherto written as functions of p, can just as well be regarded as functions of g; and for this we have only to trans- form the relation between J and J, expressed in (31) so that it shall contain g in the place of p. Equation (31) can be written in the following form :— ae = 5. log). ee Differentiation of the logarithms gives 1 dJ, J ad (J, a ap =P A alt Here J, can be taken away from both denominators; and, ac- cording to (36), g can be substituted for pJ. Further, we can transform the two differential coefficients according to p into such according to g by employing the general equation dZ_ dZ dq. dp dq dp wherein the differential coefficient a which occurs on both sides, can be omitted. We thus obtain ds d (J, ‘), na (38) This is the relation sought between J and J,. It is seen that the new equation, in relation to J and g, has the same form J, 1) J =e as (37) in relation to log J,, log >}, and p. 8. In the preceding, for central motions in which the attrac- tive force is proportional to any power of the distance, a series of formule is given which represent the times corresponding to the motion-periods, and various mean values, as functions of two © easily determinable quantities. As these formule are scattered — among the equations applied to their derivation, it will be advi- — sable, for the sake of a more convenient review of them, to briefly recapitulate them in juxtaposition. E denoting the energy of the moving point, and ¢ twice the — value of the area described by the radius vector during the unit — of time, we first form the following two quantities :— 2(n+1) z] a k(n + 3) 1. [2(n+1) Seay m Cc g=m7knti (| 8] ee a : n+ ki pas a a ae characteristic Quantities occurring in Central Motions. 19 We next introduce two functions of g, denoted by J and J,, which are connected by the following equation :— CAR d {J, a dq 1dg\J ‘Then for the undermentioned quantities the equations written after them are valid :— (1) The mean ergal: k — k n+l n+1° (2) The mean vis viva: (3) The mean vs viva of the rotatory motion (according to equation (24), replacing p therein by +) pee pe amy ale (4) The mean vis viva of the radial oscillatory motion : 2 a(t) =5 pen i) (5) The period of a rotation : ~— l—n j==2 ay nee J (276 an (6) The period of a vibration : aera /M pe Jy. Besides the above quantities, others can easily be expressed after the above developments—for example, the mean ergal of the rotatory motion and of the vibratory motion ; meanwhile the _ preceding expressions may suffice. 9. In all these expressions, only one undetermined function of g occurs, since the two denoted by J and J, can, through the relation subsisting between them, be reduced to one. To deter- mine this function also was not originally included in the plan of my investigation, as I only wished to’deduce those conse- quences which result immediately from my new mechanical equations ; but after I had produced the above formule it seemed to me advisable, for the sake of completeness, to undertake at C2 20 Prof. R. Clausius on the Relations between the least an approximative determination of that function. I have therefore developed the function J, in a series, and calculated some of the terms of that series. From the above-mentioned differential equation dr ] m a — kr” + mc? 3 we obtain by the first integration :— m (dr 2 k ml PE (plese) ata SE” Ua Meir en oa se 2 7) Pa Boe wherein EH, as before, denotes the energy of the motion. This gives, for the determination of the time, the differential equation dr Wry ate cee N/a Ne ee m me pte Il or, multiplying both numerator and denominator by 7, zd (r*) dt= 7 aaa ae fat ee) a) =e ++ “Bye —— Into this we will introduce the constants p and q instead of E and ¢, putting, according to equations (22) and (83), i= os n+3 nm+1 PJ ce k 2.n+3 | me aes and c*= — g"p ; We then get L Mp2 es k k — k 5 ee pe OP @ iL On mirey n+3 al m CaS ac mn+ mnt+l : k : If we take away the factor - p”*? from the root-sign, we obtain dt = pil, Vie m Pay ) n+1 or, otherwise written, 72 mae a(S) Ag) [eee ee a), V tt uaanck | p =i dt= bol characteristic Quantities occurring in Central Motions. 21 Herein, for convenience we will put, instead of the fraction se dit=1 Fe als, sont) n+3 4 2 pnts 5 a ay ee This equation must be integrated in order to obtain the vibra- tion-period. Therein, as limits, two values of x are to be taken for which the expression under the root-sign, and accordingly the radial velocity becomes =0. These values may be de- noted by z and z,. The integral from one limit to the other gives the time needed by the movable point in order to arrive at the highest from the lowest value; but as we understand by the vibration-period the time employed by the point in attaining from the lowest to the highest value and then again to the low- est, the double of the above-mentioned must be taken. We thus obtain L=2Xo a —g?+ ea eyes : 2 grrs3 n+1 n+1 Comparing this expression for 2, with that given in (30), we obtain for the function J, the equation oc d(x) I= =, | es Giod (43) L=2 q? JL 2, #2%. ynt3 n+] +] 10. In order to effect this integration, we will first write the equation thus :— we i i d(x?) NEO a af N+3 Be =2%9 thi Oi eke x n+3 nae fu pe ae ) Into this we will introduce a new variable, z, determined by the following equation :— n+3 2 2 (Ar — Ps x OMA eee meee tate ey 3 OAD) If we then imagine the quantity 2? developed in a series ac- cording to ascending powers of z, putting =O 0,2-+-4,2* +a +&e., . 9) 5. (46 and so determine the coefficients of this series that they satisfy the preceding equation, we obtain the following values, in which, - (44) | es 22 Prof. R. Clausius on the Relations between the further, for abbreviation, » with the signification _ (+2) (n—1) Gers (47) is introduced :— a=, | 2 ae aa 2 } —~ /n+8 (ie | 2 n+3 3 | i neue edt, “s= = 78 2.8? | ae n+ 5 1 (48) ee ag AS i ie ee ee ae ee ae | nt+5 2.3?—p La Ta pdee Sa eae 24,89. 5728, 3’ — 1389p? bien ES 26 Babee 7 By the employment of the new variable, z, equation (44) is changed into the following, in which the limits of the integra- tion are definitely given :— fee ae z= NI-@ A(a+ayz+a92? + age? + &e.) | . (49) 27 ak oes iS Peg —¢ 2__ ~2 z=— N1I—-@ The integral herein signified falls, according to the terms of the series, into an infinite number of integrals, the values of which can easily be given. Every term that contains an even power of z gives as an integral the value zero. For the terms with odd powers the following general equation (in which y is to be an uneven integer) holds good :— = Nig | die”) Na ey ai = ¢ 5 (1—gq?) 2° i) NiI=z6 —V1-9-2# q 2__ p2 Creat 2>— If we apply this formula to the odd terms of the preceding equa- tion, we obtain first up es 3.5 J=5 [a+ 5a0—@)4 5-4 501-9) +&e. |. . (50) In this equation, for the coefficients a , a3, &c. we have to put characteristic Quantities occurring in Central Motions. 23 their values derived from (48), taking into account only, the upper of the two signs which stand before the roots, as the lower sign would give a negative period. Thereby we obtain ae Lid Q 2°. 23+ Q st a. 3 (1 q)+pe 3832 (iso5) 24,33. 5?—2°%. 32,139 ‘ Mena 3 ss. = C “(1 g)8-+ &e. |. - (51) Hereby the quantity J, as a function of g is so far determined that, for values of g not deviating too much from unity, it can be calculated with tolerable approximateness. From this series, with the aid of (38), the corresponding series for J can be derived. 1]. This derivation and other calculations become somewhat easier when the series is developed according to ascending powers of 1—g. We will represent the latter difference by a special letter, putting sea ene ee shied fects O2) Then 1—g?= — (1—s)?=2s—s?; and the insertion of this value changes the above series into meta | Aas L= Faall+ gr gst ogee 2+, 39.5 +27. 37: dlu+ 1389p ] oo s+ &e.}. (53) In order from this to calculate J, we can write equation (38) in the following form :— 5 (3)=15 4 18} Lea laash aes Putting herein for J, the preceding expression, we obtain first the Be ential coefficient of os and then, by integration, a itself. The added integration-constants can be readily deter- mined, because for s=0, consequently for the circular motion, the rotation-period 7, and accordingly the value of the function J, can be directly determined. It oa namely, that for this ae ease J is to be put = 1, whence + s Taking into ac- 24, Prof. R. Clausius on the Relations between the J, count this value gives for —| the following series :— i} Ura [1+ mn 2 .O+E 5 Pyne ee 24. 34.5 —2?.3%. 7w—139 py? 2 pe oe a 8 + &e.|. (55) As the fraction = is equal to the fraction 4, the preceding ex- pression represents the ratio between the vibration-period and the rotation-period. We might now, in order to determine J, simply divide equa- tion (53) by equation (55); but then we should only obtain J developed as far as the third power, while the term containing the fourth power is obtainable ; for if we write equation (54) in the form S(p-n)=5(G) . . . 68) we can from this, on account of the factor s on the right-hand side, determine to the fourth power of s the difference es : (which does not contain a constant term, but begins at once with the second power of s), although = is known only to the third power. If we then form the identical equation and employ, on the right-hand side of it, instead of the differ- ence which forms the numerator of the second term, the expres- sion developed to the fourth power, we get —2?.34+ py Jal— seg Pte — orgs 8 — 27, 37.5 +22.3:57.29%+89 +e 910 34 5 c i s¢+ &e. (57) 12. We have therefore-obtained for the functions J and J, expressions from which their values can be approximately deter- mined, and indeed with an accuracy proportional to the small- ness of s, or inversely as the deviation of the path from the cir- cular form. They afford, in many a relation, a ready insight into the behaviour of these functions. characteristic Quantities occurring in Central Motions. — 25 The factor preceding the series in the expression for J,, viz. ca which for n= —8 is infinitely large, and for values of N- n below —3 becomes imaginary, shows very clearly that, for attractive forces proportional to a negative power of the distance, the minus third power constitutes the limit to which stationary motions are in general possible. Further, it is characteristic of both expressions that all the terms which contain s have the common factor w. From this it follows that, when 4»=0, both expressions become independent of the quantity s, equations (53) and (57) changing into J,;= and J=1. ] Jn +3 Now, since according to (47) _ (n+2) (2-1) a n+3 ; this simple behaviour occurs in the two cases in which x has the values —2 and l. These two values of n are the only ones with which the mo- tions universally (that is, for all values of s) take place in closed paths. That is to say, this can only be the case when the ratio between the vibration-period and the rotation-period is invari- Wt hectasat: eel = able, and hence “1, which is identical with —-, must be indepen- dent of s. Thence it follows further that in the series under (55) the coefficients of all the powers of s, from the first onward, must be =O, so that the constant part alone remains—which only happens when «=O and consequently n is either = —2 or = 1. 1 /n+ 3° which, according as n= —2 or n=], takes the value 1 or t. By this is expressed that, in the former case, during a rotation one radial vibration takes place, so that the radius vector has one maximum and one minimum—while in the latter case there are two radial vibrations, so that the radius vector has two maxima and two minima. All the preceding considerations relate to the motions of a material point about a fixed centre. Considerations altogether similar might be instituted in relation to the motions of two material points about each other, and would lead to correspond- ing results. In my previous memoirs I have carried out this extension for the case in which the motions take place in closed paths; and with motions in paths not closed the extension can be made in substantially the same manner. For w=0, the fraction ‘is represented bytheformula be ; p y [ 26 | II. On the Composition and Origin of the Waters of a Salt Spring in Huel Seton Mine, with a Chemical and Microscopical Examination of certain Rocks in tts vicinity. By J. ArtHUR Paiturrs, MInst.C.H., F.GS., F.CS., &c.* [With a Plate. | UEL SETON Copper-mine is situated about one mile north-east of the town of Camborne, Cornwall, and is distant from the sea, on the north coast, alittle more than three miles. Its position will be readily understood by the aid of the accompanying skeleton map (Plate I.) of the district, traced from that of the Geological Survey. The workings of Huel Seton are entirely in “ killas,” or clay- slate ; and the saline waters issue at the rate of 50 gallons per minute, and at a temperature of 92° F., from the eastern fore- breast of the 160-fathom level+. This has intersected a fault or cross-course, which can be traced in a northerly direction to the sea. The temperature of the level from the end of which the water issues, like that of the water itself, is 92° F. The lode ab,cd, fig. 1, Fig. 1. which is not well defined, and is frequently a mere narrow fissure in the clay-slate, has been driven on to its point of intersection 6 with the cross- courseef, andis believed to have been thrown in a southerly di- rection fromd toc. A dyke of porphyry, GH, 40 feet in width, courses parallel with the lode at a distance of a few fathoms to the north ; but its intersection with the cross- course not having been seen, it is not known whether any throw or dislocation actually takes place at this point, as * Communicated by the Author, having been read before the Royal Society, January 30, 1873. + My attention was first directed to the discovery of this sprig by Mr. W. J. Henwood, F.R.S., of Penzance, who forwarded me in June last a cutting from a local newspaper headed ‘A Salt Sprmg in Huel Seton Mine.” This notice states that the water had been sent to Mr. S. T. Rowe, analyst to the Truro Agricultural Association, and that an analysis had been returned * showing it to be highly impregnated with salt, salts of lime, and other chemical matter to the extent of 1072 grains to the impe- rial gallon.” It then goes on to say, *‘ very little iron, no copper, and no r ‘ ; a On the Waters of a Salt Spring in Huel Seton Mine. = 27 shown in the sketch; the direction of the dip is in each case indicated by an arrow. The water which issues from the point w was collected and brought to the surface in carefully cleaned stoneware jars. The following results, in grammes per litre and grains per gallon, were obtained by analysis. Mineral Water from Huel Seton. Solid matter 14°3658 grammes per litre, or 1005°61 grains per gallon. Sp. gr. =1:0123. Analytical Results. | | Grammes per litre. Grains per gallon. I. he | I. Il. Carbonic acid...... "0795 0786 5-56 5:50 Sulphuric acid ... 0178 0177 1:25 1:24 fie aes -0270 ‘0280 1:89 1:96 Chierine .....:...:. 91728 9°1662 642-10 641:63 Bromme:.........-- trace trace trace trace Mle 66.665... °3456 *3460 24°19 | 24°22 Ferric oxide ...... “0031 "0033 ‘22 -23 Manganese......... trace trace trace trace WGOGEE otis 2h. minute trace | minute trace || minute trace | minute trace i 3°4795 3°4963 243°56 244-74 Magnesia ......... 0721 ‘0710 5:05 4:97 Alkaline chlorides.| 6°4920 6°4626 454°44 452-38 Potassium ......... 0832 0835 5-82 5:84 Cresinm =, ......00 trace trace trace trace SOU 2:2977 2:2885 160-84 160-19 LA ee 0805 0794 5°63 5:56 Ammonia’ *..'...... trace trace trace trace Nitrie acid ......... trace trace trace trace The foregoing results may be thus tabulated + :— gas, beyond carbonic acid, was found by the analyst.” The presence of hthium is not mentioned. A few days after the receipt of the cutting above referred to, another copy was received from Mr. R. Hunt, F.R.S., and a third from Mr. J. H. Collins, F.G.S., of Falmouth. I have also much pleasure in acknowledging my obligations to Captain R. Williams, the Manager of the Mines, for the facilities afforded by him for the collec- tion of the water for analysis. * The amount of czsium appears to be very small. On adding chloride of platinum to a rather dilute solution of the alkaline chlorides obtained from this water, a slight yellow precipitate was deposited; this, after re- solution and the removal of the platinum by sulphuretted hydrogen, afforded by the spectroscope indications of the presence of cesium. f¢ As the state of combination in which the various substances present in mineral waters exist cannot be accurately determined, the system of group- ing adopted in the Table must to some extent be regarded as arbitrary. 28 Mr. J. A. Phillips on the Composition and Origin of Grammes per litre. Grains per gallon. I. II. I; II. Calcium carbonate............ 0921 ‘1011 6:45 7°08 Ferrous carbonate ............ 0045 0047 31 33 Manganous carbonate ...... trace trace trace trace Calcium sulphate ............ 0303 0201 2:12 2-11 Cupric chloride ....<.......-«- minute trace minute trace |minute trace minute trace Calcium chloride ............ 6:7697 6°7934 473°88 475-54 Magnesium chloride ......... ‘I712 1686 11-98 11-80 Aluminium chloride ......... 9003 ‘9013 63:02 63:09 Potassium chloride ......... "0919 -0900 6:43 6°30 Ceesium chloride ............ trace trace trace trace Sodium chloride ............ 5:8442 58210 409-09 407°47 isi¢hiumpchloriders sen. 20 4888 ‘4820 34:22 33°74 Potassium bromide ......... trace trace trace trace Potassium silicate (K* SiO®).| -0693 0719 4°85 5:03 IAMMIMONIA eas cokes sean cee trace trace trace trace IND GRICT ACI Creer ean sas eee ore trace trace trace trace Total found by addition 14°4623 14-4641 1012-35 1012°49 Total found directly* ...... 14°3658 | ...... 1005-61 Free carbonic acid............ 0373 0323 2°61 2:26 The nature and amount of the various substances in solution in the saline waters having been determined, it was considered desirable to ascertain by analysis the composition of the principal rocks occurring in the neighbourhood of the spring. It was hoped that in this way information might be obtained respecting the sources from which some of the substances taken up by the water had been derived. It was further thought that, by com- paring the composition of the rock in the immediate vicinity of the cross-course through which the heated waters issue with that of the clay-slate further removed from its influences, it might be possible to ascertain some of the effects produced by their action. In the case of each of the rocks analyzed, numerous thin sec- tions were cut and subjected to careful microscopical examination. “ Elvan,” sp. gr. = 2°64.—The rock constituting the dyke GH, fig. 1, is exceedingly hard and compact, presenting the appearance of a crystalline greyish matrix, enclosing numerous well-defined crystals of flesh-coloured orthoclase ; a specimen of this rock afforded by analysis the following results :— * The difference between the amount of total solid contents found directly and that obtained by the addition of constituents, is doubtless partly due to the partial decomposition of aluminium and magnesium chlorides at the temperature (160° ©.) at which the drying of the residue was effected. the Waters of a Salt Spring in Huel Seton Mine. 29 1# TI. ET etl te diebre. asa) Mtoe 1:56 Me, oi ar 2 FOP76 70°85 menmunal. 20o8s 2 1678 16°86 Ferrous oxide . . . 244 2:50 Manganous oxide . . 1°24 1:18 Smphurss. «fk «|. , ace trace Mamet Se e128 1°21 Meena, iif... , 1d 1:52 cee) 8! ss . 8°08 3°20 eS ST sana 0 19 "92 99°46 99°80 Under the microscope this rock is seen to consist of a felsitic base containing crystals of orthoclase. The base is composed of highly altered felspar, pseudomorphs, apparently after horn- blende, and numerous spherulites exhibiting a radial structure. These spherulitic bodies are not terminated by sharp outlines, but become gradually blended with the surrounding base; their radial structure, however, is perfectly defined, particularly when examined by polarized light. There is a green flocculent sub- stance disseminated throughout the base; and many small patches of quartz are observed, which, by polarized light, appear to break up into granules. There are also prisms of a yreen colour, which are apparently altered hornblende; in a few cases one portion of a crystal is seen to be composed of some hornblendic mineral, while the remainder has been replaced by felspar. In some of the sections examined minute spots and microscopic crystals of iron pyrites were observed. This rock would be generally described as a porphyry; but Mr. 8. Allport, who at my request had the kindness to cnt and examine a section of it, considers its composition would be better indicated by the name Porphyritic Felsite. It has, however, undergone a considerable amount of alteration; and although the larger crystals of orthoclase are for the most part unchanged, the smaller ones are almost without exception pseudomorphs. Gramte from Carn Brea, sp. gr.=2°64.—The Carn Brea Hill, about a mile south-east of Huel Seton, is composed of a rather coarse-grained granite, in which the proportion of quartz is gene- rally large; the felspar sometimes occurs in crystals of consi- derable size. It contains two varieties of mica, the one black (lepidomelane ?), and the other white or slightly tmged with pink ; the latter appears to be a variety of lepidolite. The chemical composition of this granite was found to be as follows :— * Of which ‘19 was lost in the water-bath. 30 Mr. J. A. Phillips on the Composition and Origin of I. Ii. Mater ® co-ie tie beeen 20 1:26 Dileay es. Pye ey APO? 74°76 Mbamina) . 9F 12+.) 16:29 16°18 Ferrous oxide . . . 1:18 1:15 Ferric oxide . . . trace trace Manganous oxide. . ‘55 "62 Sine) OV eee ae ea °26 Mignesia...x. Ge 4b 0 "46 Potassa eaten pe Shee BA 3°74 Seda 2) ete lee 1:13 TANG bial) a) Sia Page ese eral "09 99:53 99:60 A microscopical examination of this rock does not afford much information not to be obtained by a close inspection of hand-specimens. A large proportion of the felspar is seen to be monoclinic ; but triclinic felspar is also present in considerable quantity. The outlines of the crystals are not in all cases sharply defined, and they are sometimes rendered slightly cloudy by some flocculent chloritic mineral. Two varieties of mica are distinctly visible, and occur in both quartz and felspar, together with a little tourmaline. The quartz is much fissured, the sides of the cracks being apparently coated by ferric oxide; it con- tains numerous fluid-cavities enclosing bubbles, which in some of the smaller ones are observed to be in constant motion. Clay-slate &c.—In those portions of the mine situated at a distance from the cross-course, the “ killas” is a very hard clay- slate of a grey colour. Cleavage is in the majority of cases to some extent obliterated; no trace of crystalline structure can be detected ; and the rock, in addition to being traversed by nume- rous strings of white quartz, is thickly studded with minute spots and erystals of iron pyrites. Sp. gr. =2°73. In the immediate vicinity of the fault, which appears to fur- nish a channel for the passage of the saline waters, the slate has become much altered, is of a dark green colour, consists to a great extent of minute acicular crystals, with their longer axes parallel to the planes of cleavage, and in many cases closely re- sembles some varieties of serpentine. Crystals of chlorite are found in the joints of cleavage. It also exhibits many of those highly polished surfaces so frequently met with im serpenti- nous rocks. Sp. gr. = 2°69. By analysis these rocks were respectively found to have the following compositions :— * Of which °34 was lost in the water-bath. the Waters of a Salt Spring in Huel Seton Mine. dl Rock in vicinity of cross- | Unaltered clay-slate. ened: I | Il. I I oo 3134 310 \| 6°87 5 6°84 BTM e eo ceeet yaccss 67°78 67°87 45°85 45:97 a 9-60 9°52 16°60 16°78 Ferrous oxide...... 5:09 4:96 10°59 10:72 Ferric oxide ......) trace trace trace trace Manganous oxide.| 1°27 1-14 1-16 112 Penh Cot acick ae. 2-62 2°54 2-68 2°68 Magnesia .........| 3°48 3:37 6:94 6°87 uo ae 2°45 2:30 ‘92 78 aS. ES eS ee | trace trace ER eetic an whiddd aes 4-46 | 4:32 || 5°64 5-53 SMEPOMY ....00....5. 36] ='68 “a2 | =60), -78} =:146| -80:), =:150 eee “32 { FeS? 28 [ FeS? || -68 { FeS? “70 f{ FeS* 2 Sb Cees | ees “76 74 ELS a ee trace trace 100-56 99-72 /99 47 99:53 Thin sections of the clay-slate situated at a distance from the cross-course are seen under the microscope to consist of bands of transparent granular quartz alternating with layers of similar quartz, through which a transparent, dichroic, pinkish-brown mineral is thickly disseminated in the form of imperfectly de- fined elongated crystals. The outline of these, of which the di- mensions of the largest are 1,35 X pogo Of an inch, is so irre- gular, and they are so crowded and interlaced, that it is impos- sible to determine their crystalline form; they are, however, believed to be hornblende. When examined with an inch objective, the mass, in addition to numerous crystalline bodies, appears to be full of a brown dust, arranged in approximately parallel bands, which much diminish the transparency of those portions of the sections in which it most plentifully oceurs. By the aid of a power mag- nifying 510 diameters, this dust is resolved into crystalline tufts of a dark colour and hornblendic appearance. Dendritic patches and erystals of iron pyrites are disseminated throughout the rock ; and some of the veins by which it is traversed enclose well- defined crystals of both chlorite and hornblende. The altered rock in the immediate vicinity of the cross-course is seen to be composed of closely matted prisms of brown horn- blende enclosing pale green crystals of actinolite. It also con- tains a few crystals of quartz, and iron pyrites in the form of minute cubes. : * a lost 94 per cent. in the water-bath, and 6 1°55 per cent. 32 Mr. J. A. Phillips on the Composition and Origin of Source whence the mineral waters of Huel Seton are probably derived.—Before attempting to account for the presence of the mineral constituents found in these waters, it will be neces- sary to consider the bearing and importance of the following facts :— (a) The average elevation of the surface of the mine is about 300 ft. above the sea; and the 160-fathom level, being 960 feet below the adit or drainage-tunnel and 1080 feet from the sur- face, is consequently much beneath low-water mark. (6) The cross-course, shown in the accompanying geological map, may, as has been already stated, be traced for a distance of three miles to the coast, and apparently forms the channel through which the saline waters effect an entrance into the workings. . (c) The water contains a very large proportion of chloride of sodium. (d) Similar springs of hot saline water were met with, below the level of the sea, in the neighbouring mines of North Roskear and North Crofty, both situated on the same cross-course. These waters have not been analyzed. (e) A hot spring yielding waters possessing the same general characteristics as those from Huel Seton, formerly issued at the Huel Clifford Mines in the 230-fathom level, or at a depth of 1320 feet below the sea. It will be seen, by referring to the Map, that in this case a well-defined cross-course can be conti- nuously traced in a north-westerly direction from the immediate vicinity of the spring to the sea at Tobban Cove*. * These mines are now abandoned and consequently flooded. The waters issued at a temperature of 125° F., and at the rate of 150 gailons per minute. The late Dr. W. A. Miller, who analyzed them in 1864, ob- tamed the following results :— Sp. gr. =1:007. The saline constituents were found by evaporation to amount to 646°1 grains per imperial gallon, consisting of :— Chiorideofshitiniuim: 5. 4es Hosen eee 26°05 Chloride of potassium with a little chloride 14°84 OL CHSIUNM Be ise ee ec eee misters Chloride of sodimim= 07 se ens cee 363°61 Chloride of magnesium: 5). 4.5.5.4. +. 8°86 Chloridevoncal cium) aa see eee 216717 Sulphate olvealemmn 270-7 eee cace seit WZ NSUINCH aus ae Ween aie eo ane eae Se ee Ren eRe Pe are 3°65 Oxides of iron, alumina, and manganese. minute quantity 645°45 (‘‘ Chemical Examination of a Hot Spring in Huel Clifford, Cornwall, by Professor W. A. Miller, M.D. &c.,” Report of the Thirty-fourth Meet- ing of the British Association &c., held at Bath, September 1864.) the Waters of a Salt Spring in Huel Seton Mine. 33 My friend, Mr. W. J. Henwood, has called my attention to the fact that so long ago as 1827 waters rich in chloride of sodium had been found in some of the Cornish mines by Mr. R. W. Fox. This gentleman says*, “In some instances I have de- tected common salt, particularly in the water from the bottom of the United Mines, the Consolidated Mines+, Hue] Unity, and Poldice. Out of the 92 grains of residuum from the latter}, 24 grains proved to be the muriate of soda, 52 grains the muriates of lime and magnesia, and the remainder muriatic acid with iron and sulphate of lime. The water from another part of the same mine contained 54 grains of common salt. All these mines are in ‘ killas’ or primitive slate, and several miles from the sea. It may be inferred from such facts as these that the sea- water must in some places penetrate into the fissures of the earth.” Previously to discussing whether the water in question is or is not the result of infiltrations from the sea, it will be instruc- tive to compare, by calculation, its composition with that of sea- water so diluted with distilled water as to contain the same amount of fixed constituents as that found in the Huel Seton spring§. Analyses of the waters of the German, Atlantic, and Pacific oceans agree so closely with one another as to justify the conclusion that the waters of the entire ocean have an essen- tially similar composition ; but for the purpose of this compa- rison, an analysis of the waters of the Irish Sea by Messrs. T. E. Thorpe and E. H. Morton has been selected ||. This analysis has been chosen, both from the circumstance of its recent date, and also because, from the geographical position of the locality whence the water was obtained, it may be regarded as fairly representing the waters of the Atlantic Ocean which wash this portion of the Cornish coast. * Transactions of the Royal Geological Society of Cornwall, vol. iii. (1827) p. 324. J Lately part of the Clifford Consolidated Mines. { From the evaporation of a pint of water. § The error consequent on the assumption of the dilution being made with distilled water is not great. Four deep-mine waters recently ana- lyzed gave an average of ‘42 gramme of solid matter per litre, or less than 3 per cent. of the solid contents of the water in question. _ || Ann. Chem. Pharm. clviii. pp. 122-131. Phil. Mag. S. 4. Vol. 46. No. 303. July 1873. D 34 Mr. J. A. Phillips on the Composition and Origin of Water from the Irish Sea so diluted Mineral water from as to contain the same amount of Huel Seton. solid matter per litre as the water from Huel Seton. Grammes per litre Grammes per litre (calculated). found (mean). Ghiorme yy ee e070 9°1695 iBrommes . 2 ae OOO trace Sulpiuric acids. 6. olne 0178 iliteaee eee slemihes > nis bls sweet gih "0275 TAU LUH Oa Da PP ndihtata ntti el dpa Mine R08 0458 Ferric oxide . : . . ‘0019 "C029 IMiaicantese nt or ae ee trace Copper te ve een ee minute trace Rimes SS ee etal 3°4829 Magnesia. fe OO TE ‘0715 Alaline Bhionides . 11-5398 6:°4773 Rotasstumr © 2) 6 5. sae OGD "0834, resin ae 5 ea ae ete e trace GUN ce, wee aes "0800 Sodium os tee, 2°29338 Ammonia. . . . .. trace trace Carbonic acid . . . ‘0096 ‘0790 Nitric acid . . . . ‘0006 trace If the Huel Seton spring be regarded as only yielding modi- fied and diluted sea-water, it will be found, on comparing the | two columus of the foregoing Table, that the percentage of chlo- rine in the second has been considerably augmented, that the sulphuric acid has almost entirely disappeared, silica and alu- mina have been taken up, and the amount of calcium has been greatly increased, whilst magnesium has, on the contrary, been | abstracted. The amount of alkaline chlorides has thereby been - ] much reduced; but a considerable quantity of lithium has entered into solution. It would at first appear that the presence of a much larger amount of chlorine in the waters of the saline spring than should be found in dilute sea-water holding an equal quantity of solid constituents in solution affords an argument against the proba- bility of the Huel Seton waters having had such an origin. If, however, neglecting the smaller differences, the chlorides of cal- cium and aluminium in the spring-water be, on the one hand, replaced by an equal weight of chloride of sodium, and, on the other, the excess of sulphuric acid in the dilute sea-water be re- placed by chlorine, making a correction for the resulting slight difference in the total weight, the amount of chlorine in the two columns will be found very nearly the same. This objection is consequently disposed of. the Waters of a Salt Spring in Huel Seton Mine. 35 The analyses of the different rocks in the vicinity of the spring have shown that the granite only could have furnished the lithium, of which the waters have taken up a notable amount. A consideration of the various phenomena connected with the occurrence of this and other apparently similar springs which have at different times been discovered in the district, would seem to lead to the inference that they all have some more or less direct communication with the sea, and that they are either the result of infiltration of sea-water through faults, or are true and independent sources, which, before being tapped below the sea-leve], had found their way to the ocean through the faults or channels before alluded to. It would be impossible to ascertain the precise conditions under which springs of this description have been produced ; but the accompanying ideal sketch may perhaps assist in ren- dering intelligible what would appear, in the present state of our knowledge, a not improbable explanation of their origin. The plane ABC D (fig. 2), being that of the cross-course, is Fig. 2. a RSS Sie eT Or : NA DAPI SAY 7 SES yoo: BY, WSF INT RR SEP TTT ELISA OO #, y < \ SN / ps pak y & = ~ mad y A y aa (% J 4 seen to extend through both granite and clay-slate to the sea. From the close contact of its surfaces, the presence of clay, and from other causes, this fault is supposed not to be uniformly permeable by water, which can only follow the circuitous pas- sage, abcd. In this way it penetrates to depths where reactions take place, which, although not entirely in accordance with the results of daily experience in our laboratories, can, after the in- vestigations of M. Daubrée, M. de Sénarmont, and others, be readily understood. : By the action of sea-water on silicates of calcium, silicates of sodium and chloride of calcium may be produced. The sulphate of sodium of the sea-water will be decomposed by the chloride of calcium, with the production of sulphate of calcium and chloride of sodium. The decomposition of clayey matter by common salt I) 2 36 Mr. W. H. Walenn on Negative and Fractional Unitates. may produce chloride of aluminium and silicates of sodium, while the magnesium of the chloride of magnesium may be replaced by calcium ; lastly, a portion of the potassium in the sea-water appears to have been replaced by the lithiwm of the granite. The alteration which has taken place in slates in the vicinity of the cross-course has evidently been attended with the loss of a large percentage of its silica. In fact this appears to have been the chief chemical change effected, since, if we calculate what would be the composition of the clay-slate after the reduc- tion of its percentage of silica to the amount contained in the altered rock, the calculated results will be found to agree very closely with the analysis of the latter. One per cent. of lime, however, has been exchanged for alumina, and about the same amount of magnesia has been substituted for an equivalent quantity of potassa and soda. III. On Negative and Fractional Unitates. By W. H. Warenn*. Rages definition of a unitate, as originally given im the year 18687, 1s :-—The remainder to any given divisor (usually a digit), determined by a certain theorem, without the know- ledge of any multiple of that divisor. The theorem was stated to be :—“‘If ¢ be the tens’ and wu the units’ digit of a two-figure number, and 6 be any integer less than 10, then (10O—d)t+u has the same remainder to 6 as 10¢+ 4; ples of its use were given. In a paper read to the British Association at Liverpool in 1870t, the expression (10O—6)¢+w was expanded to (10—6)”-!a + (10—6)"—2b + (10—6)"-8e + ... + (10 —8)?s +(10—6d)t+u, n being the number of digits in the given number—so as to adapt it to other than two-figure numbers; and further examples of its use were given. The examples showed that this theorem is useful, especially when 6=9, in checking calculations and verifying Tables; when other values of 6 are used, it is applicable to quickly ascertaining the remainders to divisors. In his address to the Mathematical Section at the British ” and numerous exam- * Communicated by the Author. + Phil. Mag. S. 4. vol. xxxvi. p. 346. t Report of the British Association for the Advancement of Science for 1870, Transactions of the Sections, p. 16. Mr. W. H. Walenn on Negative and Fractional Unitates. 37 Association Meeting of 1869 at Exeter, Professor J. J. Sylvester laid much stress upon the employment of inductive philosophy in mathematics. He said that he was aware that many who had not gone deeply into the principles of mathematical science be- heved that inductive philosophy, or the method of evolving new truths by induction, was reserved for the experimental sciences, and that the methods of investigation in mathematical science might all be classified as deductive. He went on to say that this opinion is not a correct one, and that many valuable results are obtained in mathematical science by induction, or reasoning from particulars to generals, which could not otherwise be ob- tained so easily. Although making a distinction between ma- thematical induction and the induction used in natural philo- sophy, De Morgan, in his article in the ‘ Penny Cyclopedia’ on this subject, states that an instance of mathematical induction occurs in every equation of differences and in every recurring series. Taking the definition of mduction as given by Dr. Whateley, namely, “a kind of argument which infers respecting a whole class what has been ascertained respecting one or more individuals of that class,” it will be evident to any experimenter in chemical or physical science who is also acquainted with the use of induction in mathematical science, that mathematical in- duction is of a higher and more perfect kind than the induction used in the physical sciences, especially when it assumes the form of successive induction as De Morgan ealls it, and as it is em- ployed in recurring series. It is this high class of reasoning, which is involved in the con- struction of series that recur according to a given law, that makes the use of recurring series so valuable in unitation. Neverthe- less, in addition to the policy of investigating every general result by the use of a more general application of inductive phi- losophy, namely by the calculation or examination of particular examples (and so, having by one train of reasoning obtained a general result, proving or illustrating the use of that general result by particular applications), it 1s especially necessary to study examples of every possible type in unitation. It 1s more- over necessary to have other means than the principles of recur- ring series, and of verification by examples, to ascertain the truth of certain results, in consequence of the number of anoma- lies that present themselves for explanation. These anomalies occur not only at the ordinary singular values that the theory of numbers affords, such as 0 and 1, but the base of the system of unitation—take 9 for mstance—together with the submultiples of that base, namely six and three, also furnish singular or anomalous values. In respect of operations, as might be expected, inverse opera- 38 Mr. W. H. Walenn on Negative and Fractional Unitates. tions, such as subtraction and division, when regarded as opera- tions upon unitates, involve mathematical mvestigation and a rigid comparison of results. These results used for comparison, may either consist of the separate determination of unitates by totally distinct processes, or of individual examples obtamed by the application of unitation to checking calculations that are known to be correct. Applying the principles and modes of thought sketched out above to the examination of the meaning of a negative unitate, the following results are arrived at. It is important to bear in mind certain properties of unitates. Ist. By definition, the unitate of a given number to a given base, say 9, is the remainder obtained by dividing the given number by the base, 9; it must therefore always be a plus or positive quantity, equal to or less than 9. 2nd. Nought (or QO) never occurs in unitation; when there is no remainder the unitate of the number is 9. The three cases into which subtraction of unitates resolves itself are :— (I.) When the unitate of the subtrahend, or number to be sub- tracted, is Jess than the unitate of the minuend or quantity to be diminished. In this case the subtraction of the former uni- tate from the latter leads to a plus or positive unitate, which is the unitate of the remainder. (II.) When the unitate of the sub- trahend is equal to that of the minuend. The subtraction leads to Oasa unitate; this may at once be written 9. (III.) When the unitate of the subtrahend is greater than that of the mimuend. Regarded algebraically, this subtraction leads to a negative uni- tate, and, to obtain its real value, it must be subtracted from 9. Thus when, in unitation, the expression 6—8 occurs, it may be written —2, but should be at once reduced to a positive quantity by adding 9 to it, thus 9—2=7, 7 is the unitate required ; if it be desired to give the —2 a name, it may be called the co-uni- tate of 7. For arithmeticians only, it may in practice be the best plan to add 9 to the unitate of the minuend in the last two cases before performing the subtraction of the unitate of the sub- trahend therefrom. The performance of the operation of division upon unitates is derived from the performance of the same operation upon ordi- nary numbers; but, unlike that operation upon ordinary num- bers of which it is the analogue, it always has a remainder, or may be presumed to have one. This is a consequence of no Rd unitate being equal to 0; for instance, in = 5, the unitate 5 i iaiad 9 of = Be the unitate of the quotient 5 may be written 5+ 5? which is (for the purpose of checking the division of 25 by 5) Mr. W. H. Walenn on Negative and Fractional Unitates. 39 25+9 34. equal to ee 7 OF or Therefore unitates of all quotients ie. may be obtained by preserving them in the fractional form which they originally have—neither neglecting the remainder, nor re- ducing any fraction which may thence arise to lower terms, but preserving the exact unitate of the divisor to the very end of the process, either in reducing the unitate of the fraction which ex- presses the division to be checked, or in reducing the unitate of the quotient (or answer), including the unitate of the remainder. If there be no remainder, the unitated remainder must be a frac- tion which has 9 for its numerator. Division of unitates, there- fore, renders the investigation of fractional unitates necessary. ay, I Since all divisions can be written under the form a. 7 and. Bae] : since 7 =b-1, it follows that the question of fractional unitates is identical with that of the unitates of the (—1)th power of numbers, and also with that of the unitates of reciprocals decimally expressed. In the annexed Table of unitates of the powers of numbers, it is observable that the unitates of UniUni. Uni. Uni. Oni. {Uni Uni Uni. Uni nin. Oni. emia iae™ lh? --a%. 1a*) | a®) a8] a? 4 a8. | a. | a. Ae [1 eG a a ae ae Slilelal(si7islilelals|7z Flilsiolslol9lelgle/alo Palla yale paypal elite ae 637.18 4lafils|7isla MP elo lolslelololslols .. J Se Ea eae ieee emis ais) i181) si1ai\si i Pa olalolslolo\9lo9l9\9 ee 1 Hd Pe a itt the same power of different numbers (the vertical columns) repeat themselves after every nine consecutive numbers; also that (with some exceptions presently to be noticed) the unitates of different powers of the same number (the horizontal columns) 40. Mr. W. H. Walenn on Negative and Fractional Unitates. repeat themselves after every six consecutive powers. In this Uni. way the column for reciprocals, headed a—! is obtained, so far as the numbers 1, 5, 7, 2, 4, 8 are concerned; for these are also the unitates of the corresponding decimals to the reciprocals, the unitate of 7-1 or of 1 being obtained from the unitate of the de- cimal value of 74,=:0625. *To test the correctness of these uni- tates, the principle that every number is the reciprocal of its own reciprocal may be applied ; accordingly the following equa- tions are true in unitates, bearing in mind that, in the case of unitates, the signs +, —, x, +, and = have not the same signification as in ordinary arithmetic. The words “ the unitate of ”’ are understood to be placed before every numerical value set down. I=i=l b= | =1x6=6. a= i=? tt uo, 7a a EXOT Bay, B= [=1x3=8 ga = CRT 8. aa 5 EXO Ft aa, 9= 7 =1x9=9 Another property of reciprocals that will test these results is, that the product of any number multiplied by its reciprocal is always equal to unity. This is found to be true in carrying out Uni. the column headed a7! in the above square Table according to this principle; and it is clear that neither 3, 6, nor 9 multiplied by any other whole number can give a product whose unitate is 1. The operation of multiplying the unitates by their reciprocals is Ixl=1. AX 7 =2o—l0=f. 7 x4—23— 10 29x5=10=1. oer Ole 8 x 8=64=10=1. oxs=3=1. 6xi{=£=1., ox. — ae It is to be remarked that the discontinuity of the series in the case of the unitates of the powers of 3, 6, and 9 respectively, which is evident from the second and higher powers not follow- ing the same law of recurrence as the first and powers below the first follow, is an indication of departure from a general rule, On some Results of the Earth’s Contraction from Cooling. 41 which is borne out by the Table of reciprocals calculated by means that are totally independent of series. From the values that have been thus obtained and verified for the unitates of the reciprocals of 1, 2, 4, 5, 7, 8, it follows that, in any division sum which has these unitates in the divisor, the corresponding unitates of their reciprocals may be written as multipliers to find the unitate of the quotient. For instance, in 5 gi ie : —=5, as above given, the following is the readiest process of 5 unitation—the unitate of =7 xX2=14=5, and the unitate of 5=5. This substitution of multiplication for division cannot be made in the case of the unitates of the reciprocals of 3, 6, or 9; therefore in the cases in which 3, 6, or 9 is in the denomi- nator, and in these cases only, it is necessary to preserve the fractional form of the unitate during the whole of the process of unitation. Thus, considered zn extenso, subtraction gives birth to co-uni- tates or negative unitates, and inverse powers, or the operation of division, to fractional unitates, or unitates that are irreducible to the whole number form. 74 Brecknock Road, N., June 1873. IV. On some Results of the Earth’s Contraction from Cooling, in- cluding a discussion of the Origin of Mountains. By James D. Dana*. Part I. REPARATORY to a discussion of some questions connected with the earth’s contraction, I here present a statement of the views which I have entertained with regard to the prominent results of this agency. They first appeared in 1846 and 1847, in volumes ii., 1i1., and iv. of the Second Series of the American Journal of Science, and were somewhat extended in 1856 in vol. xxi.t Full credit is given to earlier writers in connexion with the articles referred to. The views are as follows} :— * From the American Journal of Science and Arts, vol. v. June 1873. Communicated by the Author, with additional notes. + Vol. ii. p. 385, ili. pp. 94, 176, 380, iv. p. 88, xxii. pp. 305, 335. { I may add in this place that a sight of Madler’s chart of the moon in 1846, six years after my visit to the crater of Kilauea, in the Wilkes Exploring Expedition, prompted to the first of the articles on the subject (that on the Volcanoes of the Moon, vol. ii. pp. 335, 1846), in which the origin of continents and oceanic basins is considered. The most important 42 Prof. J. D. Dana on some Results of 1. The defining of the continental and oceanic areas began with the commencement of the earth’s solidification at surface, as proved by the system of progress afterward. 2. The continental areas are the areas of least contraction, and the oceanic basins those of greatest, the former having earliest had a solid crust. After the continental part was thus stiffened and rendered comparatively unyielding, the oceanic part went on cooling, solidifying, and contracting throughout ; consequently it became depressed, with the sides of the depres- sion somewhat abrupt. The formation of the oceanic basins and continental areas was thus due to “ unequal radial contraction”. 3. The principal mountain-chains are portions of the earth’s crust which have been pushed up, and often crumpled or pli- cated, by the lateral pressure resulting from the earth’s con- traction. 4. (a) Owing to the lateral pressure+ from contraction over of Prevost’s papers on the origin of mountains had been published six years before, but I knew nothing of his views until after my paper was ready for publication, as I remark in a paragraph near its close. * The principle thus expressed by Professor LeConte in volume iv. of the same journal (1872) does not differ essentially from my old view, ex- cept that it is connected with the idea of a solid globe. Professor LeConte, on p. 466 of his article, attributes to me the opinion that the “sinking of sea-bottoms, determined by interior contraction, is the [source of the] force by which continents are elevated.” But I have never referred the origin of continents to such a cause, or to any other than that stated above. Moreover the elevation of mountains on the borders of continents I have attributed, not to “sinking sea-bottoms ” merely, but to lateral pressure produced by contraction over continental as well as oceanic areas, that on the oceanic being made much the greatest, as stated beyond. My language is frequently ambiguous on this last point, because I speak of the oceanic as the “‘ subsiding” areas. But the term is used relatively. In volume 1. on p. 179 (1847) I observe that mountain elevations occur “ near the limit between the great contracting and the non-contracting (comparatively non- contracting) areas;”’ and in various places I describe the contraction as general. In my ‘Manual of Geology,’ on page 732, I remark that the elevating “‘force acted most strongly from the oceanic direction,” which was the idea throughout. I do not deny, however, that I have supposed too large a part of the lateral force to have come from the special contrac- tion and consequent subsidence of the oceanic part of the globe. Professor N.S. Shaler, im 1866 (Proc. Boston N. H. Soc. vol. x. p. 237, vol. xi. p. 8, and Geol. Mag. vol. v. p. 511), presented, as original, the idea that “‘mountain-chains are only folds of the outer portion of the crust caused by the contraction of the lower regions of the outer shell,” and that ‘the subsidence of ocean-floors would, by producing fractions and dislocations along shore-lines, tend to originate mountain-chains along sea-borders and approximately parallel to them,”’ which is essentially the view that LeConte attributes to me. These ideas are coupled with others respecting limita- tions of the action of contraction due to denudation and deposition, in which I have no share. + In my papers in 1847 I used the terms lateral pressure, lateral force, the Earth’s Contraction from Cooling. 43 both the continental and oceanic areas, and to the fact that the latter are the regions of greatest contraction and subsidence, and that their sides pushed, like the ends of an arch, against the borders of the continents, therefore, along these borders, within 300 to 1000 miles of the coast, a continent experienced its pro- foundest oscillations of level, had accumulated its thickest depo- sits of rocks, underwent the most numerous uplifts, fractures, and plications, had raised its highest and longest mountain- chains, and became the scene of the most extensive metamorphic operations, and the most abundant outflows of liquid rock. And (b) since the most numerous and closest plications, the greatest ranges of volcanoes, the largest regions of igneous erup- tion and metamorphic action exist on the oceanic slope of the border mountain-chains instead of the continental, therefore the lateral pressure acted most effectively in a direction from the ocean. (c) Since these border features are vastly grander along that border of a continent which faces the largest ocean, therefore the lateral pressure against the sides of a continent was most effective on the border of the largest oceanic basin, and for the two (the Pacific and Atlantic) was approximately proportioned to the extent of the basins,—this being due to the fact that the oceanic were the subsiding areas (that is, those which contracted most); and that the larger area became the most depressed. 5. The oscillations of level that have taken place over the in- terior of North America, through the geological ages, have in some degree conformed in direction of axis to those of the border regions, all being parts fundamentally of two systems of move- ments—one dominantly in a direction northwestward or from the Atlantic, the other northeastward or from the Pacific. 6. Owing to the approximate uniformity of direction in the lateral thrust under these two systems through the successive ages (a consequence of the isolated position of the continent be- tween two oceanic basins, transverse to one another in axial direction), mountains of different ages on the same border, or part of a border, have approximateiy the same trend, and those of the same age on the opposite border (Pacific and Atlantic) have in general a different and nearly transverse trend. Hence “one dial plate for the mountains of the world, such as Elie de _ Beaumont deduced mainly from European geology, will not tension, horizontal force, force acting tangentially, as synonyms. “ Lateral pressure ” was the term oftenest employed, and it was explained by refer- ence to a Prince Rupert’s drop. (See Amer. Journ. Sci. 2nd ser. vol. iii. p-96 &e.) The action appealed to was not in any way different from the ‘*tangential thrust’ of Mallet. A Prof. J. D. Dana on some Results of mark time for America” (Amer. Journ. Sci., 2nd ser. vol. iil. p- 3898, 1847; vol. xxu. p. 846, 1856). 7. The features of the North-American continent were to a great extent defined in pre-Silurian time, the course of the Azoic, from the Great Lakes to Labrador, being that of the Appala- chians, and various ridges in the Rocky Mountains foreshadow- ings of this great chain, and so on in many lines over the conti- nental surface; and thus its adult characteristics were as plainly manifested m its beginnings as are those of a vertebrate in a half-developed embryo. 8. Metamorphism of regions of strata has taken place aay during periods of disturbance, or when plication and faults were in progress—all metamorphic regions being regions of disturbed and generally of plicated rocks. The heat required for alteration came up from the earth’s liquid interior. (This part of the view requires modification, while the other part, I believe, remains good.) 9. The volcanoes of the continental areas are mostly confined to the sea-borders, or the oceanic slope of the border mountain- chains—not because of the vicinity of salt water, but because these were the regions of greatest disturbance and fractures through lateral pressure. Volcanoes are indexes of danger, never “ safety-valves.” | 10. Earthquakes were a result of sudden fracturings and dis- locations proceeding from lateral pressure. In vol. i. p. 181 (1847) occurs the remark :—“ We see that the lateral pressure exerted would be likely to dislocate ;” and in the next line, ‘such fissurings, whether internal or external, would cause sha- kings of the earth (earthquakes) of great viclence, and in all periods of the earth’s history, and it might be over a hemisphere at once.” Another important subject (that of the systems in the trends of feature-lines over the globe) is discussed in the articles re- ferred to; but I pass it by for the present. I propose to bring the above principles under consideration with reference to making such changes as may now be necessary. I take up, first, the question as to whether oscillations of level (that is, subsidences and elevations) have been made by the lateral pressure resulting from contraction, as is assumed in my writings on the subject and those of most other authors; and how was the lateral thrust from the direction of the oceanic areas made to differ in its results from that from the opposite direction ? After which I shall pass to the subjects of meta- morphism, igneous eruptions, volcanoes, the earth’s interior, and the origin of oceanic basins. P i” —e”DUlUh LC lee a eee ee eae the Earth’s Contraction from Cooling. 45 1. Have subsidences been produced by lateral pressure ? The theory of Professor James Hall, that the great subsidences of the globe have been made by the gravity of accumulating sediments, has been shown elsewhere* to be wholly at variance with physical law. Another theory is presented by Professor LeConte in his recent paper in the last volume of the American Journal of Science, to which the reader is referred. Admitting, with Pro- fessor Hall, that the mean thickness of the accumulations in the Appalachian region of Pennsylvania is 40,000 feet, and therefore that this is the measure of the gradual subsidence that attended their deposition, he shows that the temperature in the bottom deposits would have been, supposing the usual rate of imcrease downward (1° F. for 58 feet of descent) 800° F., and at 10,000 feet 230° F.; and he argues that hence there would have re- sulted below, first, “lithification and therefore increasing den- sity, and therefore contraction and subsidence pari passu with the deposit ;” next, or at a greater depth, ‘‘ aqueo-igneous softening ” or “melting,” the temperature of 800° F. being “ certainly suf- ficient to produce this result as well as metamorphism, and during this process the subsidence would probably continue ;” and, in addition, the underlying strata on which the sediments were deposited would have participated in the “ aqueo-igneous fusion ” and thus have added to the result+. * Amer. Journ. Sci. 2nd ser. vol. xlu. p. 210 (1866); 3rd ser. vol. v. p. 347 (1873); LeConte, ib. 3rd ser. vol. iv. p. 461 (1872). ? The principal points in Professor Hall’s theory of mountains, pub- lished in 1359 (Amer. Journ. Sci. 2rd ser. vol. v. p. 347), are :— 1. Coast regions the courses of marine currents, and hence of deposited sediments. 2. The accumulation of sediments by their gravity gradually sink the crust, and thus a great thickness is attained; the rocks become solidified and sometimes crystallized below. 3. The continents afterward somehow raised—not the mountain-regions separately. 4, Shaping of the mountains out of other sediments by denudation. oO. Metamorphism due to “motion,” “fermentation,” and a little heat ; the heat coming up from below (the isogeothermal planes rising) in conse- quence of the increasing accumulations at surface. In Professor LeConte’s theory (Amer. Journ. Sci. 3rd ser. vol. iv. pp. 345, 460 (1872) :— 1. The same as in Professor Hall’s. 2. As explained in the text above. 3. After an aqueo-igneous softening of the beds below, the lateral thrust from the earth’s contraction pressed together the region of sedimentary accumulation, plicating and crushing the beds. 4. The elevation of mountains due solely to crushing and plication. 5. Metamorphism consequent on the heating derived by the rise of the isogeothermal planes. A6 Prof. J. D. Dana on some Results of No other cause of the gradual subsidence than that here cited is appealed to. Now the whole of this contraction took place, if any occurred, in the underlying Archean rocks (Azoic, or Laurentian and Hu- ronian) ; for in obtaining by measurement this thickness (40,000 feet) the contracted rocks were measured. The 40,000 feet of subsidence required was therefore wholly independent of contraction in the stratified sediments. But these underlying Archean rocks were probably crystallized before the Paleozoic era began; for in New York and New Jersey they are in this condition, and they underlie the Silurian rocks unconformably ; and the New-Jersey Archean or High- land region is but a northern part of that of Pennsylvania and Virginia. They would consequently have expanded with the heat instead of contracting. Even if not crystallized, they would have been well compacted under the enormous weight of 40,000 feet of strata; and no experiments on rocks that I have met with authorize the assumption that the ordinary law of ex- pansion from heat would have been set aside. For further argument on this point | refer to the subsidence in the Connecticut valley during the era of the Connecticut river sandstone (supposed to be Triassico-Jurassic). The thick- ness of rock produced in the era was probably about 4000 feet ; and this is the extent, therefore, of the registered subsidence. The sandstone strata, as 1s apparent in many places, rest on the upturned metamorphic rocks (gneiss, mica-schist, &c.) of Paleeozoic or earlier age. As shown in the preceding para- graph, the contraction, under Professor LeConte’s pr inciple, must have been confined to the underlying rocks; and since these are crystallme metamorphie schists, and the depth of sand- stone was not sufficient to raise much the temperature within them (the rocks are in general little compacted and often feebly solidified), the heat ascending from below as accumulation went on above would have produced expansion imstead of contraction. Without further reference to facts, it is, I think, clear that the subsidence required could not be obtained by the method - appealed to by Professor LeConte. Whatever cause, in either of the above cases, occasioned the subsidence, it must have been one that could do its work in spite of opposition on the part of the heat in the rocks themselves or those below. Another cause of local subsidence 1s local cooling beneath, ac- companying the increasing accumulation of sediments. But this idea 1s too obviously absurd to require remark. | In the present state of science, then, no adequate cause of subsidence has been suggested apart from the old one of lateral pressure in the contracting material of the globe. ee ee Se a ee the Earth’s Contraction from Cooling. A7 2. Have elevations been produced directly by lateral pressure ? The theory of Professor Hall denies that mountains are a result of local elevations, or of any elevation apart from a general continental. This hypothesis I have elsewhere discussed*. Professor LeConte makes the elevation of mountains real ; but after explaining that the crushing effects of lateral thrust would necessarily cause a lengthening upward of the compressed strata (as in the compression of slate rocks attending the pro- duction of slaty cleavage), and thereby produce a large amount of actual elevation, arrives at the view that there is no perma- nent elevation beyond what results from crushing. With crush- ing, in this action, plication is associated; but it should have a larger place than his words seem to give it (in all plication the rocks over a region being pressed into a narrower space, which could be done only by adding to the height), as it has performed tenfold more work of this kind than crushing. But are plication and crushing the only methods of produ- cing, under lateral pressure, the actual elevations of mountain- regions? Is there not real elevation besides? In the later part of the Posttertiary or Quaternary era the region about Montreal was raised nearly 500 feet, as shown by the existence of sea-beaches at that height; and similar evidence proves that the region about Lake Champlain was raised at the same time at least 300 feet, and the coast of Maine 150 to 200 feet. Hence the region raised was large. No crushing or pli- cation of the upper rocks occurred ; and none in the under rocks could well have taken place without exhibitions at the surface ; and this cause, therefore, cannot account forthe elevation. The elevated sea-border deposits of the region are in general hori- zontal. This example is to the point as much as if a mountain had been made by the elevation. But we have another example on a mountain-scale, and one of many. Fossiliferous beds over the higher regions of the Rocky Mountains are unquestioned evidence that a large part of this chain has been raised 8000 to 10,000 feet above the ocean-level since the Cretaceous erat. The Cretaceous rocks, to which these fossiliferous beds belong, were upturned in the course of the slowly progressing elevation ; and so also were part of the Tertiary beds ; for the elevation went forward through the * Amer. Journ. Sci. 2nd ser. vol. xli. pp. 205, 252 (1866), and 3rd sev. vol. v. p. 347 (1873). + The height of the Cretaceous (stratum No. 2 of the Upper Missouri Cretaceous) at Aspen, in Wyoming, is full 8000 feet above tide-level (Meek). Beds occur also in South Park, Colorado, the height of which is 8500 feet; and, according to Hayden, in the region of the Wind-River Mountains the beds have a height of 10,000 to 11,000 feet aliove the sea. 48 Prof. J. D. Dana on some Results of larger part, or all, of the Tertiary era. But the local crushing or plication of these beds cannot account for the elevation; and no other crushing among the surface-rocks of the mountains can be referred to this era. There may have been a crushing and crumpling of the nether rocks of the mountain. But it must also be admitted that there might have been, under tan- gential pressure, a bending of the strata without crushing, espe- cially if there is beneath the earth’s rind along the continental borders a region or layer of “aqueo-igneous fusion,” such as Professor LeConte recognizes. In the course of the geological history of the North-American continent, there were many oscillations of level in the land. Portions that were raised above the sea-level in one era, in another subsided again and sank beneath it; and Professor LeConte, in the course of his discussion, admits the existence of an elevated region along the Atlantic border which afterward disappeared. Had the elevation in the case of such oscillations been dependent on plication and crushing beneath, so complete a disappearance afterward would have been very improbable. Such facts as the above appear to prove that elevatory move- ments have often been, like those of subsidence, among the direct results of lateral pressure. The facts are so well known and the demonstration so generally accepted as complete, that I have suspected that there is here an unintentional omission or over- sight in Professor LeConte’s paper. 3. Kinds and Structure of Mountains. While mountains and mountain-chains all over the world, and low lands also, have undergone uplifts in the course of their long history that are not explained on the idea that all moun- tain-elevating is simply what may come from plication or crush- ing, the component parts of mountain-chains, or those simple mountains or mountain-ranges that are the product of one process of making, may have received, at the time of their original making, no elevation beyond that resulting from plication. This leads us to a grand distinction in orography hitherto neglected, which is fundamental and of the highest interest in dynamical geology—a distinction between :— 1. A simple or individual mountain-mass or range, which is the result of one process of making, ike an individual in any pro- cess of evolution, and which may be distinguished as a monoge- netic range, being one in genesis ; and 2. A composite or polygenetic range or chain made up of two or more monogenetic ranges combined. The Appalachian chain (the mountain-region along the Atlantic border of North America) is a polygenetic chain; it the Earth’s Contraction from Cooling. 49 consists, like the Rocky and other mountain-chains, of several monogenetic ranges, the more important of which are :—(1) The Highland range (including the Blue Ridge or parts of it, and the Adirondacks also, if these belong to the same process of making) pre-Silurian in formation. (2) The Green-Mountain range, in western New England and eastern New York, com- pleted essentially after the Lower Silurian era or during its closing period. (3) The Alleghany range, extending from southern New York southwestward to Alabama, and completed immediately after the Carboniferous age. | The making of the Alleghany range was carried forward at first through a long-continued subsidence—a geosynclinal* (not a true synclinal, since the rocks of the bending crust may have had in them many true or simple synclinals as well as anticli- nals), and a consequent accumulation of sediments which occu- pied the whole of Paleozoic time; and it was completed finally in great breakings, faultings, and foldings or plications of the strata along with other results of disturbance. The folds are in several parallel limes, and rise in succession along the chain, one and another dying out after a course each of 10 to 150 miles; and some of them, if the position of the parts which remain after long denudation be taken as evidence, must have had, it has been stated, an altitude of many thousand feet ; and there were also faultings of 8000 to 10,000 feet, or, accord- ing to Lesley, of 20,000 feet+. This is one example of a mono- genetic range. The Green Mountains are another example, in which the his- tory was of the same kind :—first, a slow subsidence or geosyn- clinal, carried forward in this case during the Lower Silurian era or the larger part of it, and, accompanying it, the deposition of sediments to a thickness equal to the depth of the subsidence ; finally, as a result of the subsidence and as the climax in the effects of the pressure producing it, an epoch of plication, crush- ing, &c. between the sides of the trough. _ In the Alleghany range the effects of heat were mostly con- fined to solidification, the reddening of such sandstones and shaly sandstones as contained a little iron in some form, the * From the Greek y7 earth, and synclinal, it being a bend in the earth’s crust. t See an admirable paper on these mountains by Professors W. B. and H. D. Rogers in the Trans. Assoc. Amer. Geol. and Nat. 1840-42. J. P. Lesley gives other facts in his ‘Manual of Coal and its Topography,’ and in many memoirs in the ‘Proceedings of the American Philosophical Society.’ A brief account is contained in the author’s ‘ Manual of Geology.’ { Oxide of iron produced by a wet process at a temperature even as low as 212° F. is the red oxide, Fe? O*, or at least has a red powder. (Am. Journ. Sci. 2nd ser. vol. xliv. p. 292.) Phil. Mag. S. 4. Vol. 46. No. 3038. July 1873. 1D 50 Prof. J. D. Dana on some Results of coking of the mineral coal, and probably, on the western out- skirts where the movements were small, the distillation of mineral oil, through the heating of shales or limestones contain- ing carbohydrogen material, and its condensation in cavities among overlying strata, with also some metamorphism to the eastward; while in the making of the Green Mountaims there was metamorphism over the eastern, middle, and southern por- tions, and imperfect metamorphism over most of the western side to almost none in some western parts. Another example is offered by the Triassico-Jurassic region of the Connecticut valley. The process included the same stages in kind as in the preceding cases. It began in a geosyn- clinal of probably 4000 feet,-this much being registered by the thickness of the deposits; but it stopped short of metamorphism, the sandstones being only reddened and partially solidified—and short of plication or crushing, the strata being only tilted im a monoclinal manner 15° to 25°; it ended in numerous great longitudinal fractures asa final catastrophe from the subsidence, out of which issued the trap (Dolerite) that now makes Mount Holyoke, Mount Tom, and many other ridges along a range of 100 miles*. : These examples exhibit the characteristics of a large class of mountain-masses or ranges. A geosynclinal accompanied by sedimentary depositions, and ending in a catastrophe of plica- tions and solidification, are the essential steps, while metamor- phism and igneous ejections are incidental results. The process is one that produces final stability im the mass and its annexa- tion generally to the more stable part of the continent, though not stable against future oscillations of level of wider range, nor against denudation. It is apparent that in such a process of formation elevation by direct uplift of the underlying crust has no necessary place. The attending plications may make elevations on a vast scale; — and so also may the shoves upward along the lines of fracture; — and crushing may sometimes add to the effect; but elevation — from an upward movement of the downward-bent crust is only an incidental concomitant, if it occurs at all. 7 We perceive thus where the truth lies in Professor LeConte’s important principle. It should have in view alone monogenetic — mountains, and these only at the time of their making. It will © then read (plication and shovings along fractures being made ~ more prominent than crushing) :— | Plication, shoving along fractures, and crushing are the true * This history is precisely that which I have given in my ‘ Manual of Geology,’ though without reeognizing the parallelism in stages with the history of the Alleghanies. the Earth’s Contraction from Cooling. 51 sources of the elevation that takes place during the making of geosynclinal monogenetic mountains. And the statement of Professor Hall may be made right if we recognize the same distinction, and also reverse the order and causal relation of the two events, accumulation and subsidence ; and so make it read :— Regions of monogenetic mountains were, previously and pre- paratory to the making of the mountains, areas each of a slowly progressing geosynclinal, and consequently of thick accumula- tions of sediments. The prominence and importance in orography of the moun- tain individualities described above as originating through a geosynclinal make it desirable that they should have a distine- tive name ; and [ therefore propose to call a mountain-range of this kind a synclinorium, from synclinal and the Greek épos, mountain. This brings us to another important distinction in orographic geology, that of a second kind of monogenetic mountain. The synclinoria were made through a progressing geosynclinal. Those of the second kind, here referred to, were produced by a progress- ing geanticlinal. They are simply the upward bendings in the oscillations of the earth’s crust, the geanticlinal waves, and hardly require a special name. Yet, if one is desired, the term anticlinorium, the correlate of synclinorium, would be appro- priate. Many of them have disappeared in the course of the oscillations ; and yet some may have been for a time, perhaps millions of years, respectable mountains. The ‘ Cincinnati uplift,” extending southwestward from southern Ohio (about Cincinnati) mto Tennessee, and referred by Newberry and others to the close of the Lower Silurian, was made at the same time, or nearly, with the Green Mountains; but while the latter range is a synclinorium, the former is a geanticlinal or an anti- clinorium, and it is one of the few (probably few) permanent monogenetic elevations of this kind over the earth’s surface. There may possibly have been crumpling or crushing in the deep-seated rocks below, which determined its permanence. As far as the Paleozoic rocks constituting it go, it is a simple syn- clinal ; but it is really a synclinal of the earth’s crust, and hence wholly distinct from ordinary synclinals, or those subordinate among the plications in a synclinorium, like the synclinals of the Alleghanies. The geosynclinal ranges or synclinoria have experienced in almost all cases since their completion true elevation through great geanticlmal movements, but movements that embraced a wider range of crust than that concerned in the preceding gevo- synclinal movements, indeed a range of crust that comes strictly K 2 52 Prof. J. D. Dana on some Results of under the designation of a polygenetic mass. Thus the Con- necticut-valley sandstone beds, which must have been but little raised by the slight upturning they underwent at the epoch of their disturbance (since there was then neither plication nor crushing), are now 700 feet higher above the sea-level in Mas- sachusetts than near New Haven, Connecticut; and this is owing, not to denudation, but toa subsequent elevation in which much of New England participated—a true geanticlinal uplift. So it has been the world over. The great uplift of the Roeky- Mountain region of more than 8000 feet, which began after the Cretaceous, had nothing to do, as I have said, with crushing or plication, although there was disturbance of the beds in certain local Cretaceous and Tertiary areas; it appears to have been a true geanticlinal elevation of the Rocky-Mountain mass, itself mainly, if not wholly, a combination of synclinoria. Geosynclinals and geanticlinals of low angle, like those of the present day, graduate msensibly into horizontal surfaces. The later oscillations in the world’s history have taken in a vastly wider range of crust than those of early time. We cannot point to any geosynclinal in progress that is probably on the way to become the site of a new synclinorium. This comes from the fact already stated, that the completion of a synclinorium has generally consisted im tie solidification as well as plication of the rocks, and the addition of the whole mountain-region to the more stable portion of the earth’s crust; and the further fact that this process has been often repeated in past time, until the crust has been so stiffened above, as well as below, that only feeble flexures of vast span are possible, even if the lateral pres- sure from contraction had not also declined in force. 4, How was the lateral thrust from the direction of the ocean made to differ in its action or results from that from the opposite di- rection ? The fact of a difference in the effects of the lateral thrust from the opposite directions, the oceanic and continental, is beyond question. The evidence may here be repeated. The greatest of elevations, as well as subsidences, and also of plications and igneous eruptions, have taken place on the conti- nental borders or in their vicinity ; they thus show that there is something peculiar along such regions. Again, the border mountains in North America are parallel to the axes of the ad- joining oceans, and thereby at right angles, instead of parallel, to one another. Again, the folds in the Appalachians are not symmetrical folds, but, instead, have one slope much steeper than the other, proving inequality in the action of lateral pres- sure from the continental and oceanic directions. Further, the the Earth’s Contraction from Cooling. 53 larger ranges of uplifts and effects of heat occur on the oceanic slope of the principal border mountaiu-chain instead of the con- tinental slope, favouring the view that this lateral thrust was more effective in the direction from the ocean against the con- tinents than in the opposite. Finally, there is the fact that the disturbances or effects of lateral thrust have been very much the greatest on the border of the /argest oceans. But has this greater effectiveness of lateral thrust from the direction of the ocean been due to a proportionally greater con- traction and subsidence of the oceanic crust than the continental ? —the sinking causing the oceanic arch to press against the sides of the basin. I formerly made this the chief means of moun- tain-lifting ; and now, while not giving it so great prominence, I believe it to be a true cause. It is certain that the depressing of the ocean’s bed, like the raising of the continental areas, has been in progress through the ages. The great principal rise of the continent and continental mountaims took place after the Cretaceous period or during the Tertiary, and some of it even in the Quaternary ; and this is almost positive demonstration that the bottoms of the oceans were tending downward contem- poraneously. It is not possible in the nature of contraction that it should have been all accomplished in these basins at the beginning of their existence—a point I shall further illustrate when discussing the nature of the earth’s interior. Moreover the mobile waters that occupy the oceanic depressions would have given important aid in the cooling of the underlying crust. It is to be noted also that the distance between the axis of the Appalachians in North America and the opposite (African) side of the Atlantic is 4000 miles, and that between the axis of the Rocky Mountaims and the opposite (Australian) coast of the Pacific is over 7000 miles ; while between the axis of the Appa- lachians in Virginia and that of the Rocky Mountains in the same latitude the distance is hardly 1500 miles. Hence the contraction was absolutely greatest over the oceanic areas inde- pendently of any result from special causes ; and if the generated pressure was not expended in uplifts over the oceanic areas themselves, it would be in uplifts on its borders. In addition to the above advantage which the oceanic areas have had in the making of border oscillations, the lower position of the oceanic crust, and the abruptness with which the sides fall off, give it an opportunity to push beneath the sides of the continents; and this would determine the production of such mountains and just such other effects of pressure on the conti- nental borders as actually exist, even if contraction were equable over the globe—that is, were alike in rate over the oceanic and continental areas. It puts the oscillations over the continents 54 On some Results of the Earth’s Contraction from Cooling. inevitably under the direction of the adjoining oceanic crust. The angle of slope of the deep-water sides of the oceanic basin is generally above five degrees*. This conclusion is further sustained by the known univer- sality of oscillations over the oceanic basin. The central Pacific area of coral islands (“registers of subsidence”) stretches from the eastern Paumotus to the western Carolines, 90 degrees in longitude, and it indicates that the comparatively recent coral- island subsidence involved a region stretching over more than one fourth the circumference of the globe. The fact teaches that the movements of the globe, which have been in progress through all time in obedience to the irresistible energy generated by contraction, have been world-wide, and so world- deyelapines even down to the last era of geological history. The above considerations sustain me in the opinion expressed in 1856 (Amer. Journ. Sci. 2nd ser. vol. xxii. p. 335), that the relation in size between the mountains and the bordering oceans is not merely “ formal,’ as pronounced by my friend Professor LeConte, but has a dynamical significance. In view of the considerations here presented, I believe there is no occasion to reject the fourth proposition, 4: (a) on page 42, but only to modify it as follows :— 4. (a) Owing to the general contraction of the globe, the greater size of the oceanic than the continental areas, and the greater subsidence from continued contraction over the former than over the latter, and also to the fact that the oceanic crust had the advantage of /everage, or, more strictly, of obliquely upward thrust against the borders of the continents because of its lower position, therefore along these borders, within 300 to 1000 miles of the coast, &c. [To be continued. | * The angle of slope on the sides of the oceanic basin has not yet been properly investigated. ‘The margin of the basin on the Atlantic border is now in about 100 fathoms water (600 feet). According to soundings by the Coast Survey, as lam informed by Mr. A. Lidenkohl of the Coast- Survey Office, through J. E. Hilgard, Esq., Assistant-in-Charge, the slope between 100 and 200 fathoms off Cape Hatteras is 2° 31’, off New York entrance 2° 02', off George’s Shoal 1° 35’. - But for the region beyond 200 fathoms the data are not sufficient for any certain conclusion. Mr. Liden- kohl observes :—“‘ If the soundings by Lieutenant Murray off Cape Look-out can be trusted, the slope between the 100- and 2000-fathom line must be over / degrees. Berryman’s soundings off St. George’s Bank indicate a slope of about 33 degrees. From this it may be inferred that the slope rather increases than decreases beyond the 200-fathom line.” Ey By J V. On Thermodiffusion of Gases. By W. Feppersen, of Leipzig*. eee PTICAL considerations have opportunely been ap- plied by Carl Neumanny to the proposition that if a limited portion of a gas enclosed in a tube of unlimited length (or one that returns into itself) be different in density from the rest of the gas, an artificially produced difference of tempera- ture at the two ends of this portion must occasion a continuous motion throughout the endless cylinder of gas in a determined direction—and, indeed, from the cooler to the warmer end through the limited portion in question, if the gas in this be in the state of condensation. By experiment I have answered, in a simple manner, to the requirements of the theory. Already in the beginning of this year (1872) I found that experiment confirmed that theory, in that without exception the expected direction of the motion could be recognized. My experiments, however, did not per- mit the deduction of definite laws—partly because they were in reality only qualitative, in order to prove the fact generally, and partly on account, as it appears, of manifold disturbing influ- ences which were not further ascertained. I therefore thought I must defer their publication until i should have an opportu- nity of furnishing more exact data. Meanwhile the publication _ of the results of an investigation by M. Louis Dufourt has in- duced me already, although I have only a few, properly speak- ing, qualitative results, to publish what I have hitherto disco- vered, because my observations are the converse of Dufour’s and in harmony with them. My experiments were performed in this manner :—A substance in the form of powder was stuffed tight into a glass tube so as to form therein an immovable plug. ‘This tube was fixed in a horizontal position; and the two ends which projected on each side of the plug were each connected air-tight, by means of caoutchouc, with another horizontal glass tube, which was stopped bya drop of liquid at any place in its interior. In this manner, every displacement of the air cylinder contained in the middle portion of the tubes must displace the two drops of liquid at its extremities in the same direction. One end of the plug was now exposed to a constant source of heat, the other being left cold or artificially cooled. Then, without exception, * Translated from a separate impression, communicated by the Author, from Poggendorff’s Annalen, vol. cxlviii. pp. 302-311. t Berichte der Koénigl. Sdchsischen Gesellschaft der Wissenschaften, Feb. 15, 1872. { Archives de Geneve, Sept. 1872, pp. 10, 11. 56 M. W. Feddersen on Thermodiffusion of Gases. there appeared a slow displacement of the air column in a di- rection through the plug, from the cold to the heated end, sometimes quicker, sometimes slower, sometimes stronger on one side and sometimes on the other. Spongy platinum was the first substance with which I experi- mented, in the expectation that, in consequence of its great ab- sorptive capacity, especially for oxygen, with it rather than any other substance an action would be perceptible. Into a tube of about 34 millims. diameter, a length of about 60 millims. of spongy platinum was pressed, which had been heated to redness two days previously. When I inserted a drop of mercury in the accessory tube, applied preliminarily to the heated side only, there was indeed a displacement backwards of the drop, but to a considerable degree with strong heating only. In presence of the minuteness of the pressure-force set free, the drop of mercury was evidently too heavy. I substituted for it sulphuric hydrate ; and immediately, with the difference of temperatures 10° (that of the room) and 100°, the expected movement began in a striking manner. As an example, out of various experi- ments I will only mention that, in the eight hours period of observation, the drop once. moved 195 millims. away from the heated end. Within this entire interval, however, the speed of the motion varied. In another instance, the platmum being fresh from incandescence, a brisker movement took place. — Nevertheless the displacement of the drop was always slow; so that changes in the temperature of the apartment (of course not heated) may have exerted a sensible influence. I therefore took a shorter tube about 125 millims. in diameter, inserted therein a plug of recently incandescent spongy plati- num of 31 millims. length, and placed at each end a long tube of glass 34 millims. in diameter, stopped by a drop of sulphuric acid. One end of the plug was exposed to a temperature of about 200°*, while the other end was left to cool freely down to the temperature (8°) of the unwarmed room. On account of the great heat-conducting capacity of the platinum, this end was also not inconsiderably heated. The following were the ascer- tained displacements in the accessory tubes, all in the direction from the cool, through the plug, to the hotter side :— * Compare what is said further on, under “Gypsum.” M. W. Feddersen on Thermodiffusion of Gases. 57 Cold side. Hot side. Time. Calculated for Caleulated for Observed. 10 minutes. Observed. 10 minutes. h m hm millims. millims. millims. 12 Oto 12 10 225 225 tube wanting | _millims. 12 10 ,, 12 15 94 188 95 190 1] 15 ,, 12 25 |tube wanting | ...... 241 241 12 25 ,, 12 30 105 210 95 190 12 30 ,, 12 35 110 220 tube wanting Accessory tubes removed, and, after an hour and a half, replaced. 2 Oto 2 5 73 146 49 98 25, 220 205 137 153 102 220,, 230 151 151 112 112 230 ,, 235 76 152 58 116 After the last observation the bent end of the tube on the cold side was immersed in sulphuricacid. The displacements ceased as soon as the acid had risen about 6 millims. in the -tube, in which position it remained until, at the end of an hour and a half, I dismounted the apparatus. The capillary rising of the acid in the tube did not amount to one millimetre; so that the difference of pressure produced by the difference of temperature on the two sides of the plug corresponded to a column of sul- phuric hydrate of at least 5 millims. height. Spongy palladium.—In most of my ‘experiments with this lL introduced it into an atmosphere of oxygen; but the results ob- tained were the least regular of any. I had contrived a special arrangement of straight and T-tubes to bring oxygen into the plug-tube as well as into the accessory pieces. In the experi- ments a movement always showed itself in the expected direc- tion, but with extraordinary variability. The singular irregu- larities appeared to be provoked chiefly by the variability of the absorption by the palladium with oscillations of temperature ; but probably the aqueous vapour, which always formed when the atmospheric air was expelled from the tube by oxygen, was a further cause of the irregularities. Nevertheless the direction of the phenomenon was by all this not reversed. As an example of the movement the following numbers of one observation may serve: the tubes had from 34 to 4 millims. internal diameter, and on both sides were stopped by a drop of oil. Time. Cold side. Hot side. h m h m millims. millims. 9 5 to 9 25 130 ian 9) 25))',, 9 35 155 190 945 ,, 9 50 45 Aperture touching oil sur- face raises slight bubbles. 58 M. W. Feddersen on Thermodiffusion of Gases. In this example, therefore, between 95 25™ and 95 35™ the oil drop on the hot side removed 190 millims. from the heated part; while that on the cold side moved 155 millims. nearer to the cold end of the palladium. Gypsum.—In a tube of 124 muillims. internal diameter was a plug of gypsum 70 millims. in length, which, after its pourmg- in, had remained some time and become air-dry. The glass tube was encased in sheet copper over one end of the plug; and by a feebly burning spirit-lamp placed beneath, that part was heated to about 200°*, while it was protected from draughts as much as possible by pasteboard walls. The other end of the plug was exposed to the temperature of the room (8°), and mani- fested, when touched, a very slight warming. On stopping the accessory tubes, 34 millims. in diameter, with mercury, no movement made its appearance even after fifteen hours. When afterwards sulphuric hydrate was taken for the liquid stop, I ob- tained the following dispiacements in the direction from the cold to the hot side :— Cold side. Hot side. Time. Calculated for Calculated for Observed. 10 minutes. Observed. 10 minutes. hm h m millims. moillims. millims. millims. 10 15 to 10 45 | tube wanting.| ...... 60 20°0 10 45 ,, 11 30 Ei as a ids IM Naa bb 87 19-3 11 30 ,, 12 J5 5 11°5 45 10-0 1215 ,, 115 52 8:7 32 53 130,, 2 0 20 6:7 23 hod. The aqueous vapour developed from the gypsum, at first in large quantity, and at last only sparingly, did not disturb the direction of the phenomenon. Charcoal.—Instead of gypsum the tube had, under otherwise like conditions, a plug, 90 millims. in length, of coarsely pow- dered and recently heated fir charcoal. After the setting-up the drop of sulphuric acid did not at first move at all on the heated side, while on the cold side it moved briskly toward the charcoal. * The temperature was measured, as the bulb of a thermometer rested ‘on the copper sheath ; above, 1t was somewhat protected from radiation by a loose-lying piece of pasteboard. As is seen, the determination is very closely approximative. The temperature, however, was preserved pretty constant. M. W. Feddersen on Thermodiffusion of Gases. 59 Cold side. Hot side. Time. Calculated for Calculated for Observed. 10 minutes. Observed. 10 minutes. h m h m millims. millims. millims. millims. p.M. 2 50to 3 40 250 50 20 4-0 3 40 ,, 4 20\ tube wanting.| _...... 125 31°2 A D5. 5..4 45 200 100 65 32°5 5 0,, 5 30 200 67°7 30 10:0 5 30 ,, 6 10 130 32°5 50 12°5 630, 7 O 220 738° 60 20-0 Pa Gin 715 73 48°7 23 15-3 During the night the lamp went out, and cooling took place. a.M. 6 50 to 7 50 285 47°5 tube wanting. | we O85) 9:9 265 44-2 immovable. 9 0 ,,12 Oj tube wanting.) *...... 415 23°1 m2'o,, F “0 225 375 10 | 1-7* 1 0,, 1 30 40 13:3 immovable. We see here that in every instance the motion observed in the drop followed the direction through the plug from the cold to the hot end. From the fact that the drop on the cold side always moved quicker than that on the hot side, it must be concluded that, besides the phenomenon of gas-displacement, there was also a special absorption with the charcoal, greater than that which appeared in like manner to take place with the spongy platinum. : _ Stheic acid.—The arrangement of the experiment was the same as with the two last-named substances. The length of the plug (of silicic acid in powder fresh from incandescence) in the tube of 124 millims. diameter amounted to 110 millims. After the acticn of the difference of the temperatures (about 200° and 8°) had lasted continuously some 34 hours, the follow- ing observations were made :— Cold side. Hot side. Time. Calculated for Calculated for Observed. 10. minutes. Observed. 10 minutes. Bem bh) m millims. millims. millims. millims. p.m. 5 10to6 O 65 13:0 60 12:0 6 10 ,, 6 30 90 45:0 75 375 ~ 6 380,,7 10 125 31433 140 39°0 710,,7 30 56 28-0 59 29:5 7 30,8 0 64 21:3 79 25-0 * From 12 o’clock the end of the tube on the hot side was closed by a drop; the difference of pressure produced by the process was not sufficient to overcome the capillary attraction at that place. 60 M. W. Feddersen on Thermodiffusion of Gases. The accessory tubes were taken away at night; yet the difference of temperatures was maintained. Cold side. Hot side. Time. Calculated for Calculated for Observed. 10 minutes. Observed. 10 minutes. hm hm millims. millims. millims. millims, a.m. 6 40to7 10 103 34:3 116 38°7 7 10,,7 40 75 25:0 80 26:7 7 40 ,,8 10 74 24:7 82 27°3 8 10 ,, 8 40 50 16°7 59 19:7 8 40 ,, 9 10 \tube wanting.| —_....... 83 27°7 9 10 ,, 9 40 5 OEY Le as eo cae 76 25°3 Of absorption, such as took place with charcoal and spongy platinum, there is here no trace perceptible. Calcined magnesia.—The experiment was made with freshly heated magnesia under the same conditions as the last-mentioned substances. In the tube of about 124 mullims. diameter the length of the plug was at first 100 millims. Cold side. Hot side. Time. Calculated for Calculated for Observed. 10 siantee’ Observed. 10 dainutes’ hm hm millims. millims. millims. millims. 5 30to5 40 145 145 tube wanting. 5 40 ,, 5 50 140 140 3 tae 5 50, 6 0 132 132 95 95 6 0,, 6 15 214 143 135 90 615 ,, 6 30 |tube wanting.| ...... 134 89 6 30 ,, 6 35 5 SA vehi Wake adse 43 86 6 35 ,, 6 50 205 137 154 103 6 50,7 O 142 142 tube wanting. For the following experiments a part of the magnesia was ex- tracted from the tube, in consequence of which the length of the plug was reduced to 40 millims. Cold side. Hot side. Time. Calculated for Calculated for Observed. 10 minutes. Observed. 10 minutes. hm hm millims. millims. miilims. millims. 7 30 to7 35 142 284 114 228* 7 35 ,, 7 40 140 280 106 912 * In support of the quantity of gas supposed to have passed through the cross section of the plug in the unit of time, let it be remarked that a cylin- der of about 13 millims. length in the accessory tubes represents a volume equal to that of a cylinder of | millim. length in the diaphragm-tube. M. W. Feddersen on Thermodiffusion of Gases. 61 After this, the bent end of the tube on the cold side was im- mersed in sulphuric hydrate. The sulphuric acid rose quickly to 53 millims. height, while the drop received a displacement corresponding to the dimensions of the closed spaces. The po- sition remained unchanged during the first hour; but after the lapse of the second hour the acid had risen to 62 millims.,and after another 14 hour to about 80 millims., where the bend of the tube commenced ; and so any further diminution of pressure in the tube could not be observed. Sustained blowing with the mouth into the open end on the warm side very soon reduced (as was to be expected) the column to zero. The numbers observed with magnesia, again, point to an ab- sorption of the gas by the substance in the form of powder. From the preceding experiments with the most heterogeneous substances it appears to follow that it is a universal property of porous bodies, when in the form of diaphragms, to draw gases through them in the direction from the cold to the hot side. We have thus a phenomenon of diffusion which, contrary to ordinary diffusion, occurs even when the same gas under the same pressure is found on both sides of the diaphragm. This is a singular, hitherto unknown phenomenon; and we are there- fore justified in giving it the name of Thermodiffusion. Whether this kind of diffusion depends also on the nature of the gas, so that with mixed gases a selective diffusion might take place (that is, a mechanical separation of the gases), analogous to that which occurs in the diffusion of liquids, I have not yet been able to discover; it appears at all events probable when Dufour’s experiments are taken into consideration. Further, it may be an argument in favour of this view, that I often observed a progressive diminution in the velocity of the motion in the en- closed space, starting from the attachment of the tubes, such as must necessarily occur if, on the cooler side, one of the consti- tuents of atmospheric air diffuses through to the warmer end more quickly than the other ; for the closed space on the former side would be sooner exhausted of the more easily diffusing gas than of the other. Dufour, /. c., states that when gases are caused to diffuse, there Is a rise of temperature on the side where the more quickly dif- fusing gas enters the porous diaphragm, anda fall of temperature on the opposite side ; so that in his experiments diffusion pro- duces a change of temperature; in mine a change of tempera- ture causes diffusion, and the latter in a direction such that the 62 Prof. L. Lorenz on the Determination of artificially produced difference of temperatures, if we apply the laws discovered by Dufour, is diminished by the process of dif- fusion itself. Accordingly we find between thermodiffusion and Dufour’s discovery a reciprocity analogous to that between heat and electricity in the ordinary thermo-current and Peltier’s phe- nomenon. If the forces set free by thermodiffusion appear mostly to be trifling, yet it cannot be forthwith maintained that this pheno- menon plays only a quite subordinate part in the economy of nature; for the conditions of its occurrence may at least be widely spread. Davos, 26th December, 1872. VI. Determination of Degrees of Heat in Absolute Measure. By L. Lorenz, of Copenhagen*. ee of the most important means of modern times, for elu- cidating the connexion between various forces indepen- dently of all physical hypotheses, is the determination of the magnitudes dependent on these forces by the same absolute units. While the system of absolute measures has been carried out in the sciences of magnetism and of electricity, the degree of heat has only been determined arbitrarily ; and thus, so to speak, the thread has been broken which connects heat with the other physical forces. The object of the present investigation is to establish a definition of the absolute degree of heat in a purely empirical manner, and by introducing it into science to illustrate more clearly the relation in which heat and electricity stand to each other. The absolute units introduced by Gauss and Weber, which we shall use in the sequel, are the millimetre as unit of length, the second as unit of time, and the milligramme as unit of mass. By means of these units the electromagnetic unit of current-intensity is defined as being the intensity of that current which, travers- ing the unit of surface, acts upon a magnetic pole as an infi- nitely small magnet whose moment is unity. Weber has further | defined the unit of the quantity of electricity as being that quan- tity of positive electricity which in the unit of time moves, in the direction of positive electricity, in a current whose intensity is unity, it being presumed that the same quantity of negative electricity is simultaneously transferred in the opposite direction. In what follows we shall, in common with many other authors, define the unit of electricity as being the sum of the quantities of positive and negative electricity which, moving in opposite directions through a circuit, produce the unit intensity of current. * Translated from Poggendorfft’s Annalen, No. 11, 1872. Degrees of Heat in Absolute Measure. 63 The absolute unit of heat is defined as being the quantity of heat equivalent to the absolute unit of work. If, now, the degree of heat be defined as the increase of temperature which produces an absolute unit of heat in being imparted to the unit of mass of water, the degree of heat is arbitrarily determined, since it depends on the physical nature of the substance chosen, namely water. If instead of a certain quantity of water we select a cer- tain number of atoms of an element, then, in accordance with Dulong and Petit’s law, the heatmmg which a given quantity of heat produces in these atoms is independent of the nature of the substance, and it only remains to settle more precisely the number of atoms to be chosen. The law in question does not hold quite accurately with re- ference to the solid elements; yet the deviations are explained by the fact that heat is not only used for heating, but also for performing internal work. On the contrary, the law certainly holds for all those gases in reference to which it can be assumed that none of the heat is consumed in internal work. The loss of heat in external work can be avoided by heating the air under constant volume. According to Regnault, we have for constant pressure the spe- cific heats Nitrogen. Oxygen. Hydrogen. 0°24380 0:21751 3°40900 Hence, to heat under constant pressure 14 mgrms. nitrogen, 16 mgrms. oxygen, 1 mgrm. hydrogen, there are required 3°41320 3°48016 3°40900 relative units of heat (1 mgrm. water through 1° C.). These three numbers, of which especially the first and last are very near each other, show, in accordance with Dulong and Petit’s law, that the same quantity of heat is required to raise the same volume at the same pressure, and therefore also, as we assume, the same number of atoms of the gases in question, through one degree. Under constant volume the specific heat of these gases is in the ratio 1°40: 1 less (1°41 on the old, and 1:3945 from Regnault’s determinations of the velocity of sound in air); if of the above three numbers we take the mean value of the two which most closely agree with each other (for nitrogen and hydrogen)—that is, 3°4111, we obtain 2°436 thermal units (1 mgrm. of water through 1° C.) as the quantity of heat required for heating under constant volume as many atoms of a permanent gas as are contained in 1 mgrm. of hydrogen. 64. Prof. L. Lorenz on the Determination of The relative unit of heat used here may be readily expressed in absolute units of work; defined in this measure we will ex- press it by A. The unit of heat is equivalent to a work of 433 milligrammetres; and as the weight of a milligramme is 9806 absolute units (that is, the acceleration of gravity expressed in millimetres), we have A=425 x 10” absolute units. But to heat 1 mgrm. hydrogen at constant volume through IC. 2'436 A =1035 x 10” absolute units are necessary. Just as a definite quantity of heat is necessary to raise the same number of atoms of various elements through one degree, so, according to Faraday’s electrolytical law, equal quantities of electricity are required to separate equivalent quantities from an electrolyte. But as equivalent quantities do not always corre- spond to the same number of atoms, it is necessary to choose a definite type for electrolysis. As such a type I prefer the electrolysis of bodies constructed on the formula RC] (Br, $)—partly because an equal number of atoms of the element are separated at each electrode, and partly because we have here the greatest number of atoms which can be separated from an electrolyte by the same quantity of electri- city. All deviations from the type taken must then be regarded as arising from secondary actions of the chemical forces. Thus, while we regard the electrolysis of strong hydrochloric acid as normal, the decomposition of water must be regarded as a de- viation, which may perhaps be explained by assuming that two atoms of oxygen unite to form a double atom. In tbe unit of time an electrical current of unit imtensity hberates in a voltameter 545 mgrm. hydrogen*. The same cur- rent will liberate from strong hydrochloric acid the same weight of hydrogen and as many atoms of chlorine—that is, will separate at both electrodes as many atoms as are contained in 7}, mgrm. hydrogen. To raise the same number of atoms through 1° C. under constant volume, we require, in accordance with what has been said above, = A=0:005075 A =216 x 10° absolute units. We may now define a degree of heat in absolute measure as that increase of temperature which the unit of work produces, in being completely and exclusively changed into heat, zn the same number of atoms of the element which the unit of electricity lbe- rates from an electrolyte under normal circumstances. * Conf. Wiedemann, Die Lehre vom Galvanismus, second part, p. 917. Degrees of Heat in Absolute Measure. 65 From what has been said, this increase of temperature is ee 105 of a Centigrade degree ; and in accordance with the definition given, 1 degree Centigrade =0:005075 A=216 x 10° absolute units. Besides the connexion between heat and electricity which is expressed by Dulong and Petit’s law, and by Faraday’s electro- lytical law, and which we have used in establishing a definition of the absolute degree of heat, there is another connexion, which found its first expression in Wiedemann and Franz’s law, that the conductivity of the various metals for heat and for electricity are in the same ratio. Subsequent investigations have shown, however, that this ratio changes with the temperature, and therefore that the law in its original form cannot be completely valid, but requires a modification. The influence of heat upon electrical conductivity has been in- vestigated by several physicists, as Lenz, Becquerel, Arendtsen, and especially by Matthiessen and von Bose*. These physicists investigated the conductivity of ten different pure metals, namely silver, copper, gold, zinc, cadmium, tin, lead, arsenic, antimony, and bismuth. From their investigations the remarkable result was obtained, that the diminution of electrical conductivity for an increase from 0° to 100° C. is the same for all these metals, namely 29-307 per cent. The resistance increases, therefore, for the same increase of temperature by 41-46 per cent —that is, In a somewhat greater ratio than the increase of temperature (36: 6 per cent.) if we calculate the temperature from the abso- lute zero (—273° C.). Matthiessen and Vogt+ found subse- quently that among the pure metals iron forms an exception, inasmuch as its conductivity may decrease by more than 38 per cent. But few experiments have been made as to the influence of temperature on conductivity for heat. It must, however, be remarked that all the older experiments on thermal conduction agree with the former assumption, that the conductivity is inde- pendent of the temperature. Angstrémt found with reference to two bars of copper, which, however, were probably not quite pure, that between O° and 100° there was a decrease of con- Bae Power of from 15 to 21 per cent., and for iron of 28°7 per cent.; while Forbes$ found for bar iron a decrease of 15°7 and 23°3. per cent. * Phil. Mag. S. 4. vol. xxiv. p. 405. Tt Phil. Mag. S. 4. vol. xxvi. p. 542. -{ Gfvers. af K.Vetensk. Forhandl. 1862. Pogg. Ann. yol. exviii. p. 423. § Trans. oe Royal Soc. 1862-64. Phil. Mag. S. 4. Vol. 46. No. 308. July 1873. F 66 Prof. L. Lorenz on the Determination of If we now observe that electrical conductivity for the various pure metals is nearly inversely proportional to the temperature calculated from absolute zero, while their thermal conductivity approaches more to constancy, and further that in the case of iron the deviations for both kinds of conductivity are in the same direction, then we may say that the preceding facts esta- blish, with as great closeness as can be expected, the law that the conducting-power of a pure metal for heat and for electricity is proportional to the temperature calculated from absolute zero. This ratio must obviously more or less vary in several cases. If, for instance, the metal is not homogeneous, or contains ad- mixtures of foreign metals, and, generally speaking, im cases in which, owing to unequal heating in the interior, thermo-electric currents may be formed, then the thermal conducting-power will probably be increased, or at all events the relation between the two kinds of conductivity will be altered. This is doubtless the ease when heat can be transmitted as radiant heat in the interior of bodies. In this kind of transmission we must seek the reason why thermal conductivity for all transparent and translucent media, and generally for all non-metallic bodies, is apparently far greater than that which would correspond to their electrical conductivity. Lastly, if the body is liquid, the ratio must alter, owing to the mobility of the parts. If, for instance, a column of liquid is heated from below, this mobility will, of course, in- crease the observed conductivity. If it is heated from above, currents in the imterior cannot be entirely avoided; for every part of the liquid in the same horizontal section cannot have quite the same temperature; the colder parts will then sink, and the warmer ones rise toward the source of heat; and the conducting-power must therefore be diminished in consequence of the motion of the parts. We must hold, then, that the law, if it is at all valid, is pro- bably only absolutely so for pure homogeneous and solid metals. In fact even an unequal heating will make the metals heteroge- neous and will give rise to thermo-electrical currents. From the foregoing observations I shall now attempt to de- duce the ratio between the conducting-power of metals for heat and for electricity in absolute units. We shall obtain from this the remarkable result, that for a pure homogeneous solid metal this ratio ts equal to the temperature calculated Jrom the absolute zero eapressed in the above-defined absolute units. To determine thermal conductivity in absolute measure, we must know how great is the quantity of heat which traverses each unit of surface of a plate of given thickness and with a given difference of temperature at the two sides. The older expe- riments on this subject have, for very intelligible reasons, led to Degrees of Heat in Absolute Measure. 67 results which are not concordant and which, are far too low; hence we can only use the experiments of Angstrom, Forbes, and Neumann, which agree pretty closely with each other, although these observers made their experiments independently of each other and in very different, manners. We will for the present use the units chosen by Angstrom, the centimetre, the minute, the Centigrade scale, and as thermal unit 1 grm. of water 1° C. Angstrém* found for the thermal conductivity of Wopper’ ... .)», 0894 at 0° C. OB ir ofc, 2 ous) hE OOS, yy Mepis pe ys wie fo LOB PEM his a OO), The last determination was made with a mercury column en- closed in a glass tube, which was heated from the top. Forbes found, in the above-mentioned experiments, for Renin eke en.) L236 iat. OF -C, LTP OE ONE RNG Re 5712 Re Pease iol oo OL a i Neumanny determined the thermal conductivity of five differ- ent metal bars, and at the same time made a comparative deter- mination of their relative electrical conductivity. While this was taken at 100 for silver, that of copper was assumed to be equal to 73°3. These results were, with the above units :— Thermal Electrical conductivity. conductivity. q Copper... 66°48 73°3 0:907 ess... S12 17-9 1:012 MamGes hs}. 1843 Ziel 0:873 German silver . 6°566 6:45 1:018 remo) 2 2) Br824. 10°20 0-963 The ratio between the thermal and the electrical conductivity (which is designated by q) 1s greatest for brass and German silver. This is not accidental, but probably a consequence of the fact that they are not pure metals. In like manner we obtain, in agreement with what has been said above, a discordant and ob- viously too low value for mercury; we find for this metal, from Angstrom’s experiments, g=0°617, taking as the electrical con- ductivity of mercury 1°72. The mean value of the quotients g for copper, zine, -and iron is 0°914 according to Neumann’s experiments. Whether, in * Pogg. Ann. vol. exviii. p. 423, and vol. exxili. p. 628. Ann. de Chim. et de Phys. 1862, vol. Ixvi. p. 183. F2 68 Prof. L. Lorenz on the Determination of accordance with other experiments, this number should be made greater or less is difficult to decide; but as the thermal conduc- tivity in Neumann’s experiments was not reduced to 0°, g must be taken as a little less for this reason. Hence, then, we may take g=0-90 at 0° C. as the result which may be deduced from the present experi- ments with the greatest degree of probability. The value of g thus determined is, in Angstr6m’s units, the thermal conductivity of a metal whose electrical conductivity is 1, that of silver beg taken as equal to 100. Through each square millimetre of a surface with the thermal conductivity gq, whose thickness is 1 millim., there pass in each second 1 ll g 7700 * 1° 60 = 600 relative units of heat (1 grm. water 1° C.), with a difference in temperature of 1° C. at the two sides. As the thermal unit used here is equal to 1000 A, and as we have found that 1° C. expressed in absolute units is equal to 0005075 A, the absolute thermal conductivity corresponding to q, which we will call x, is defined by q 1000 A “= 600 * 00050750 7 ee From this we see that the factor by which the thermal conducti- — vity is reduced from AngstroOm’s units to absolute measure is independent of A. With the value we have assumed above for gq, If we designate the corresponding absolute electrical conduc- tivity by 4,, we should have, in accordance with the above law, =D Eas ki, where T is the temperature calculated from the absolute zero. _ For the freezing-point of water T is equal to 273 x 1° C., and, if a degree Centigrade is expressed in absolute units, T=1°385 A=589 x 107, from which | _9.00468 A ==1-99 x 107. kK If, now, we wish to calculate the absolute resistance of a Sie- mens’s unit (a column of mercury a metre in length and a square millimetre in section at O° C.), we must know the ratio between | Degrees of Heat in Absolute Measure. 69 the specific conductivities of silver and mercury. This ratio alters materially with the physical condition of silver; even if, as is most usual, the silver be used in the form of hard-drawn wire, no great accuracy is attainable in the determination of the ratio. In Wiedemann’s Lehre von Galvanismus (Part I. page 181) we find the numbers 1°739 (E. Becquerel), 17 (Lamy), 1°63 (Mat- thiessen) for the conductivity of mercury, that of silver being taken as 100. Matthiessen subsequently* gave the number 1-65 ; and Siemens’s determinations} gave 1: Ee and 1:78. These numbers hold for 0° C. We may thus take the conductivity of mercury at 0° C. as approximately equal to 1°72; so that, in accordance with the above calculation, the resistance in absolute measure would be 1 1-72k Hence Siemens’s unit of resistance denoted by S is, in absolute measure, = 000272 A=1°16 x 107. S=—2°72A=1:16.x 101. We will compare this result with the direct absolute measure- ments of Siemens’s unit of resistance, which have been made partly with the aid of induced currents, and partly by measuring the quantity of heat developed in a conductor by a constant current. By the first method Webert found Si= 1502571 x.102% while the Committee of the British Association$ found as a mean S=0°964 x 10!°: A small correction introduced by Matthiessen, by which both values are reduced 0:3 per cent., is in the present case without significance. These determinations do not, therefore, materially deviate from the values of S calculated from the thermal conductivity ; they are both, however, somewhat lower. The reason for this differ- ence might be sought in the less accurate determination of the thermal conductivity as compared with the electrical conducti- vity ; I think, however, that the reason for this discrepancy is to be sought elsewhere. The great difference, considering the accuracy with which the experiments were made, between Weber’s results and those of * Phil. Mag. S. 4. vol. xxi. p. 195, + Phil. Mag. S, 4. vol. xxi. p. 25. { Abh. d. k. Gesellsch. d. Wissensch. Gottingen, 1862. § British Association Report, 1863, Jenkin. 70 Prof. L. Lorenz on the Determination of the British Association Committee, a difference which actually amounts to 8 per cent., points to errors which cannot be ascribed to accidental faults of observation, but must rather be ascribed to animperfect theory. It is here to be observed that the experiments were made with induction-currents of varying intensity ; yet we may at present undoubtedly state, both from theoretical and ex- perimental investigations, that we know only the elements of the theory of variable induction-currents, and that the results can only be regarded as a first approximation. Hence, notwith- standing the great care with which these measurements have been made, we must not ascribe too great a weight to them. The determination of the electrical resistance by means of the disengagement of heat which a constant current produces in a conductor is theoretically far simpler and more certain than the induction method in the manner in which this has hitherto been applied. Fortunately we possess a large series of experiments earefully executed and calculated by Quintus Icilius*. This physicist determined the heat which a given intensity of cur- rent disengages in a second in various copper and platinum wires, the electrical resistance of which was determined by means of a standard measured by Weber in absolute units. If V de- notes the number of relative units of heat (1 mgrm. water 1° C.) which are developed in a second in a Siemens’s unit of resistance by the current-intensity S, we obtain by these experiments a determination of the constant e in the equation V=as* x 1:0257 x 10", if with Quintus Icilius we use Weber’s determination of electrical resistance; while with the former signification of A as the abso- lute equivalent of work for the relative unit of heat (1 mgrm. water 1° C.), and of s as the absolute value of Siemens’s unit of resistance, we have AV =—s?S. From the two equations we have S=aA x 1:0257 x 1019, » In the experiments in question three several liquids were used in the calorimeter, namely water, alcohol, and oil of turpentine. The former liquid had the advantage over the two others, that it gave the quantity of heat directly in the units chosen; on the other hand, a small error cannot be avoided, owing to the greater conductivity of water for electricity, by which the disengagement of heat, and therewith also the constant «, must be found rather too sinall. Owing to its volatility, the experiments with alcohol * Pogg. Ann. vol. ci. p. 69. Degrees of Heat in Absolute Measure. on showed such small agreement among each other that they must be left out of consideration. As the average of twenty-eight experiments with water, we obtain a= 2'543 x 10-!°; and of ten experiments with oil of turpentine, a=2°652 x 10-1, There is no greater difference between these two values of « than might have been expected from the greater conductivity of water ; hence the latter number must be taken as that which follows with the greatest probability from Quintus Icilius’s experiments. With this value of « we obtain S=2°720A=1:16x 10"; that is, exactly the same value for Siemens’s unit of resistance in absolute measure which we have deduced above from the thermal conductivity of the metals. That it is exactly the same value ~ must, of course, be regarded as accidental. In another way also we obtain a confirmation of the accuracy of the law here propounded, since we shall find that in this law there is the closest agreement between the laws for the propa- gation of energy in metals, no matter whether this transmission is effected by the motion of heat or of electricity. . By energy we understand any magnitude which can be mea- sured by units of work. We will consider only the propaga- tion of heat and of electricity so far as it is effected in both cases by conduction; so that we may waive any considerations as to the propagation of heat in the interior of a body by radiation and by thermoelectric currents, just as in the case of electricity we neglect the propagation by induction and by thermoelectrical currents. If by Q we denote the energy present in a body in the unit of volume, the increase ay ut which Q experiences by ther- mal conduction in the form of heat in the element of time df, is expressed by Pe mese) idk a thd) ta So aT at ei) ade de” ALi ce ate where T is the temperature and « the thermal conductivity, which may in general be regarded as a function of the tempe- rature. If we substitute in this, in accordance with the law propounded above, aI 72 Prof. L. Lorenz on the Determination of where k is the electrical conductivity, we obtain QQ) d ped aa de coll aed a Aah Sudo eae se qe ae pee in which equation all the magnitudes may be considered to be expressed in absolute units. As the increase of energy here only occurs in the form of heat, it stands in a known relation to the increase of temperature, dependent on the specific gravity and the specific heat ; and the equation gives therefore completely the law for the propagation of heat by conduction. If in any point 2, y, z of a body the components of the inten- sity of the current are u, v, w, and if k is the electrical conduc- tivity, the quantity of heat received by the element of volume dx dy dz in the element of time df is, according to Joule’s law, u?+v? +? k If this element of volume contains at the same time the quantity of electricity ¢dx dy dz, and if the electrical tension (potential) there is P, the element acquires at the same time the energy da dy dz dt. de P a dx dy dz dt in the form of electricity. If, then, as before, Q denotes the energy present in the unit of volume, the increase arising from the motion of electricity, and which occurs both as heat and as electricity, is dQ, a de u?+v?+w? ie =i Ete ee ee In like manner, if we disregard the electricity which results from induction, from Ohm/’s law we have dP dP dP Ugh 2 ria dp 1 So ope a Mile (4) in addition to which we have Kirchhoff’s equation de du dv dw i= -\atate) 5) Thus AQ du dv dw aoe act pan =i ee +@)= uf, tog, tH Gre from which there follows dQ duP dvP dwP rele ae aon Degrees of Heat in Absolute Measure. 73 If, owing to the transference of energy, electromotor forces are formed in the interior (thermoelectricity), for no element in which they arise does either Joule’s or Ohm’s law hold. Yet even in this case the latter equation seems to retain its validity ; for it agrees with the observation that a constant current which passes through one section of a conductor from a less to a greater tension produces an absorption of heat which is propor- tional to the intensity of the current and to the increase of tension. Yet im this case we disregard any possible thermoelectric currents in the interior of the body, and we obtain from the last equation, by means of equations (4), 2 2 2 os DR eS ae Marie ans dy dy 4 de... dz Comparing this equation with equation (2), we see that the laws for the propagation of electricity by electrical conduction and by thermal conduction have quite the same form; the po- sitive or negative electrical tension and the absolute temperature calculated from absolute zero will correspond to each other, and, if we choose the absolute measure for the degree Centigrade which has here been proposed, may be measured with the same units. In accordance with these equations a body will receive in each element of its volume the same increase in energy, whether it be unelectrical and have in various places a different absolute tem- perature T’, or whether it be uniformly warmed and have an electrical tension +P whose numerical value in each point is equal to T. It is, however, here presupposed that & has in both cases invariably the same value, which is only approximately true. In the next moment the ratio will be materially altered, since the increase of energy in the electrical body occurs in the form of heat, not of electrical tension. Hence the law for the propagation of electricity cannot be determined by equation (7), which can only serve to define the increase of energy, whereas, as we have seen, the laws for the propagation of heat are defined by equation (2). If electricity continuously moves without change through a body (and this is the cenly case we can here deal with, as we do not take induced currents into consideration), the quantity of electricity is in each moment the same, and the equation then becomes du ia dv | dw ee PC? ae This equation, combined with equations (4), gives / B) “ oY pee ae eee Newer ic) emer Mane tap. azz The electrical tension will therefore have to be determined from = 74: Prof. L. Lorenz on the Determination of this equation in combination with the given limiting con- ditions. The motion of electricity is here looked on as permanent ; that this may completely be the case, the heat developed (which in this case represents the total mcrease in energy) must be conducted away. In order now to develop further the ana- logy between electrical tension and temperature, we will amagine the corresponding suppositions applied to the motion of heat in a body; that these suppositions cannot in fact be fulfilled may in this case be disregarded. We consider a body in which the motion of heat is kept per- manent, and in which the entire energy which heat can produce in the form of work in passing from a higher to a lower tempe- rature is conducted away from every point of the body. If, now, the quantity of heat W at the absolute temperature T is added to a body in every second, and simultaneously and con- tinuously therewith the quantity of heat W, at a lower tempe- rature T, passes away by conduction, the condition remains un- changed if the entire difference W—W, is converted into work ; and, in accordance with the mechanical theory of heat, the entire amount of work which the quantity of heat W can produce in the change of temperature T to T, is obtained if we have UN i I If we put for the three-coincident surfaces of an infinitely small rectangular parallelepiped = = & dy dz+n dx dz+Cdz dy, we have for the other three surfaces Wake dé ) 2 =) 7. =(£+ dnt dy dz+ (n+ di dx dz +(é+ a dx dy ; and equation (9) will then give Biryaa ae ane + Tr ==(()), ° ° e ° e (10) In this case TEdydz is the quantity of heat transmitted through the surface dy dz in the unit of time; but this is also defined by ae dy dz if « is the thermal conductivity ; then oe te k aT PUT Wee yee and in the same manner dT dT n=—k = —_—_ dy’ dz Degrees of Heat in Absolute Measure. 75 In combination with equation (10) these equations give dk cs dk 7 dk ue dx dy dz J ie dy ¥ dz We see, therefore, that in the motion of heat which we have here imagined, in which the suppositions are quite analogous to the conditions which actually obtaim for the permanent motion of electricity, the temperature would be determinable by the same differential equation as the electrical tension. By the permanent motion of electricity through a body heat results, which ultimately acquires a permanent motion when it is continuously conducted away in the same manner. The in- crease of energy which owes its origin both to the motion of elec- tricity and to that of heat is now ni/ in each element of the body ; and from the equations (2) and (7) we shall obtain d , ee +T") d k d(P? a A d k (BIE T3\ic; Se iae dy Bere da ae By this equation, in combination with equation (8), both the electrical tension P and the absolute temperature T are to be determined when both the motion of electricity and that of heat are become permanent. If, for instance, we pass electricity through a body, keep- _ Ing in a small part oy of its surface a constant electrical tension P,, and in another part o, ofits surface the tension P,, and if at the same time we maintain both surfaces at the same constant temperature T,, while the other part of its surface is kept sur- rounded by perfectly bad conductors of heat and electricity, a permanent motion of electricity and of heat will ultimately result, and the electricity will develop the same heat as is conducted away by the surfaces oy and oj. If we put =O aiaitkac tu ala =0. (12) Paste? BAP B= hy ois ew ip haco GB} in which A and B are two arbitrary constants, we shall obtain by the equations (12) and (8), Gi ac hee | a gl atetg a dz ee 4 Both constants A and B will then be so determined that for both surfaces cy and o, $=0, by putting pe+T?+AP)+B=0, p?+T2+AP,4+B=0. With the values of A and B which result from these, namely A (eee andin—eogb —i?,-, -.. (15) (14) 76 Determination of Degrees of Heat in Absolute Measure. we shall have for all points of the body o=0,> Tae... oo Le since here both the differential equation (14) and the limit- ing conditions in the surfaces a, and o, are satisfied, while the hmits for the rest of the surface of the body, where & is nid, are satisfied by any given value of ¢, and therefore as well as by that here taken. From equations (13), (15), and (16) we have T?_T2=(P,—P)(P—P.).. .- «a ela If, then, a constant electrical current be passed for some time through a conductor of any shape which is surrounded by bad conductors, and if the temperature at the two surfaces be kept constant and equal, it will be possible by equation (17) to calcu- late the temperature at each point of the conductor from the two differences of electrical tension at the given point and the con- ducting surfaces. The result found will, conversely, serve for an experimental determination of the Centigrade degree in absolute units. The increase of temperature which depends on the electrical current is T—T,. Now T?—T? > (T—T,)?; and in accordance with the last equation, (Eo) es Bom) ae As the right-hand side acquires its greatest value for2P=P,+P,, if Pp is taken as greater than P,, we have also TT soma 0 Ge ead 6 I'rom this we see that the greatest increase of temperature which can result in any point of the circuit is always numerically smaller than half the difference of the electrical tensions in the two conductor-surfaces. It would be equal to just half this difference if the conductor-surfaces could be cooled to the ab- solute zero—that is, for Ty>=0. Thus the differences of elec- trical tension, and the greatest increase of temperature which can be obtained by them, stand in the closest connexion with each other. Hence it is not without interest to calculate the difference of electrical tension in the poles of a voltaic element for instance, the electromotive force of the element, in Centigrade degrees. Thus theelectromotive force ofa Daniell’selementis about 12 x 10!° absolute units; half the difference of tension of the elements, or, as it is commonly expressed, the positive tension of the element (the negative taken at. the same amount), is therefore 6 x 10'° Notices respecting New Books. 77 absolute units, or (since 1° C. is equal to 216 x 10°) 2780° C. This would thus be the greatest increase of temperature which the element could produce with a constant current in a circuit if the element itself were kept at a constant temperature. This increase of temperature would in fact only take place if the ele- ment or its poles could be cvoled down to absolute zero; if, on the other hand, we assume for this the temperature of 20° C. above the freezing-point of water, we shall obtain from equa- tion (17) 2502° C. as the greatest increase of temperature. In a thermoelectric element of copper-pyrites and copper inves- tigated by Bunsen*, the electromotive force was about equal to one tenth of a Daniell’s element; the positive tension therefore was about equal to 278° C. when one junction was heated to the melting-point of tin, and the other to about 60° C. above the freezing-point of water. In fact the greatest increase of tempe- rature, if it were calculated as above, would be about 111° C. Yet it cannot be concluded from this that, for instance, the last-named element could not produce a spark (and consequently a far greater heating) through the interruption of the circuit; | am convinced, on the contrary, that this is possible. To show with what extraordinary facility the electrical spark can result from a break in the circuit, I will adduce the following experi- ment. An electrical current, whose intensity in absolute mea- sure was 20, was passed through a copper wire 1 millim. in thickness. ‘This was connected with a sharp kuife-edge, with which another part of the wire was scraped with rapid strokes. It was then seen that in complete darkness there was still a bright space between the steel knife-edge and the copper wire when the distance between the two points of the copper wire which were placed by the knife-edge in conducting communica- tion was only 400 millims. This facility with which a spark results from the interruption of the current, however, shows only that induction here plays an important part. VII. Notices respecting New Books. Light Science for Leisure Hours. Second Series. By Ricwarp A. Procror, B.A. London: Longmans and Co. R. PROCTOR tells us in his titlepage, quoting from Tenny- son, “the truths of science [are] waiting to be caught;” and numerous at the present day are the fishers for these truths. In the work before us the author performs the office of urging scientific facts combined with his own and others’ opinions into the nets pre- pared and spread for their reception, these nets being the minds of his readers. In the short notice which we propose to give of this * Pogg. Ann. vol. cxxill. p. 505. 78 Notices respecting New Books. second series, it will be our object to draw the attention of the reader to the mental process which he ought to perform while perusing the familiar essays presented to him: he must gather of every kind of opinion; indeed he cannot fail to do so; but it is incumbent on him to store up that which is good and to cast the bad away. These thoughts have been suggested by the controversial spirit which generally pervades the essays. So important is it to present the truths which science seeks in a familiar form to the uninitiated, that, after carefully perusing the volume, we pondered for some interval of time over the title itself, “ Light Science” for “ Leisure Hours,” and were almost inclined to come to the conclusion that it partook of the nature ofa misnomer. ‘Turning to the essays entitled “The ever-widening World of Stars” and “Movements in the Star-depths,” we could not find in either the characteristic of lightness. With so masterly a hand have they been written that every step the author takes to establish the poimt he aims at (that of the unity of the sidereal universe) is of the most sterling cha- racter. To regard either of them as light is doing injustice to the sublime science of which they form a part; and we feel certain that if our leisure hours are to be occupied by that which is “ light ” (we cannot help adding the concluding part of the sentence, ‘and trifling ”), then Mr. Proctor’s Essays are not the pabulum for minds that seek for light reading in their leisure hours; for there is not one essay in the volume but requires thought, and deep thought too, ere the reader can gather up the good and cast the bad away. Perhaps Mr. Proctor adopted the title from a desire to catch the nets that they might catch the truths. In the author’s sketch of the life and works of Mrs. Somerville, we find him giving expression to his conviction that, as respects the main purpose of her great work, ‘The Mechanism of the Heavens,’ Mrs. Somerville failed entirely ; and as explanatory of so remark- able a conclusion, one, be it remembered, opposed to the opinion of the late Sir John Herschel, which is quoted by Mr. Proctor, the author alleges that in his opinion success was altogether impossible, and also that ‘the thorough training, the scholarly discipline which can alone give to the mind the power of advancing beyond the point up to which it had followed the guidance of others, had un- fortunately been denied to her.” Otherwise, and under happier auspices, our author intimates that Mrs. Somerville might have done original work. Mr. Proctor, we apprehend, has had the advantage of this thorough training, and has experienced this scholarly discipline, and therefore is on the road for executing much original work; but has he ever heard of men or women bemg beyond the age in which they lived and worked? Have all who occupy niches in the great temple of Science had their names enrolled in the records of universities ? or have the pioneers in the perpetual siege which has been for ages and is still carried on with the view of acquiring a knowledge of the great forces operating in the Natural World, always been men who have first distinguished Notices respecting New Books. 79 themselves by their proficiency in their academical studies? Where are the self-taught men who have even left behind them in the race others who have had the advantages of which Mr. Proctor speaks ? We cannot agree with the author even in the slightest manner depreciating the work of so gifted a woman as Mary Somerville ; and it might have been that, had she undergone the discipline of which he speaks, she might have found herself hampered, even as when she endeavoured to please Mr. Murray she considered that she departed from clearness and simplicity. We fully agree with her own estimate, that the truths of science are in themselves not so formidable as most persons imagine; and, as regards the popular- izing of science, so dear to Mr. Proctor, we much question whether the course adopted and greatly patronized in the present day is one calculated to extend the basis of the pyramid of knowledge. Is it not rather aiming at increasing its height? and do we not find in our ordinary intercourse with mankind that the knowledge is in the books and but seldom in the minds of men? There are many passages in the Essays to which we should like particularly to direct the attention of the reader, both for their excellence and also for the controversial aspects which they bear ; but our space reminds us that to the reader himself we must leave them, simply advising him to use his own judgment, and to read the work not as ome which he would take up to while away a leisure hour, but one requiring patient and steady thought, and especially to weigh the author’s opinions, which in some cases we think he will find far from being “light.” The Essays are calcu- lated to advance science, not so much by the author’s endeavour to present it in an attractive form, as by leading the thoughtful reader to test every opinion presented in them. Selections from the Portfolios of the Editor of the Lunar Map and Catalogue. London: Taylor and Francis. This Selection, in which it is mtended to place on permanent record observations of the physical aspects of lunar objects, contains papers by the Rev. T. W. Webb, Edmund Neison, Henry Pratt, and the Editor, which treat more or less on changes on the moon’s surface, a knowledge of which is increasing in interest. These are followed by illustrated notices of recent observations, and compari- sons of these with older observations. We hope this attempt to bring observers of the moon into communication with each other will meet with the support it deserves. From the great heat which the moon’s surface attains under its long day it is likely Bal change is continually occurring upon it. [80x] VIII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from vol. xlv. p. 391.] March 13, 1873.— William Spottiswoode, M.A., Treasurer and Vice-President, in the Chair. ene following communication was read :— “Visible Direction: being an Elementary Contribution to the Study of Monocular and Binocular Vision.” By James Jago, M.D. Oxon., A.B. Cantab., F.R.S. It is a well-known fact that when the eye has been displaced in its socket, as, for instance, by the tip of the finger applied to the eyeball through the eyelid, all objects seen by it deviate from their true directions; and the author’s mode of proceeding m this paper is to inquire whether visual deviations that may be observed in arbitrary, but methodically devised, displacements of the eyeball in its socket follow any law, and then to consider how far the results thus derived are conformable with other monocular and binocular experiences, and how far they may be available in the explanation of certain phenomena that have been deemed ano- malous in physiological optics. Having pointed out means by which the ball may be easily dis- placed in any direction, he draws attention to the fact that, when by such means the apparent directions of objects seen by the eye are made to deviate from their true directions through fully 30°, the orbital muscles so fully retain their command over the movements of the eyeball, that that point in the visual field which was painted on the point of direct sight in the centre of the foramen centrale retine still continues to be there painted. He shows this to happen ~ whatever be the direction in which the eyeball is displaced in its orbit. This fact being a fundamental one in the inquiry he has in hand, he puts it to nicer tests still. He adjusts the two eyes, when equally displaced so as to cause objects to deviate greatly from their true directions, to look awhile at the top of a high object in the open air, and having obtained a strong spectrum of this object in the retine, he, with the released eyes, looks at an appropriate mark on a grey wall, and finds that the spectrum really has its margin across the point of direct sight ; and he tries other experiments in corroboration. Also by agitating a pin-hole in a card across the eye when look- ing at such a high object, he brings the retina into view, and sees that the point of direct sight is visibly within the foramen centrale retine, as made visible by the shadow of the wall that bounds the foramen. He indicates other means of proving the same fact. He gathers from a series of experiments that the mastery of the orbital muscles over such movements of the eyeball as are requisite for pointing the optic axis to its objective point, is practically Royal Society. 81 unimpaired by such shiftings of the eyeball in its socket as have been described. He then proceeds to show that the regulating duties of the orbital muscles, when the eyeball is displaced in its orbit, are not: only fulfilled as to the rotation of the optic axis about a central point, but as to the rotation of the eyeball about this axis. To make experiments to this end, we must have another subjectively visible retinal spot besides the foramen centrale; and this we nega- tively have in the punctum cecum, or at the base of the optic nerve. A diagram is devised by which we may manage that one point of it shall be seen by the direct sight of both eyes, whilst another point is found to fall in the middle of the blind spot of one eye; and the diagram is examined by this eye when this has been pushed from its orbital place upwards, downwards, inwards, and outwards, and in various oblique directions, besides when more or less twisted on its axis; and thus it is demonstrated that what happened with the point of direct sight in the retina happens equally surely for every other retinal pomt—that under all these displacements the orbital muscles do not forfeit their control of the eyeball, but so regulate its movements that the different points of the field of vision remain constantly painted on the same retinal points. From these and other methodically continued experiments, he draws the general inference, that if the centre of the foramen cen- trale retine be forced at any instant from its position by any sort of manipulation, and then made to describe a circle round its first position of ease whilst the optic axis has never ceased to remain parallel to its first direction (that is, has generated a cylinder in revolving), the axis of the seeming field of vision will have so re- volved as to have generated a cone, whose apex is posterior to the retina in the first or undisturbed direction of the optic axis. The like might have been said of any other normal to the retina, the axis of the base of the optic nerve, for instance, were it accessible to light, whilst a twisting retinal movement about a fixed axis twists the seeming field of vision. ___ If the optic axis revolve so as to generate a cone whose apex is in front of the eye, the axis of the seeming field may, according to circumstances, generate a cylinder, or a more acute cone enclosing the other. Conversely, the parallax of the visual field being noted, we can assign the retinal displacements that have produced them. Should undue contraction of any orbital muscle, or discordant contractions of the orbital muscles, engender visual parallaxes, we may as safely judge from these parallaxes of the retinal displace- ments that must have been induced, as if they had been due to manipulation of the eyeball. In these summarized conclusions we have the means of solving highly important problems in physiological optics. Tt is found that sensation, or the function of responding to ob- jective light, is exclusively resident in the retinal elements of the bacillar layer, but that the visual functions of the retina extend no Phil. Mag. 8. 4. Vol. 46. No. 303. July 1873. G 82 Royal Society :— further; for it has been evinced in manifold experiments that when the axes of all the pencils of objective light which concur in imaging a picture upon the retina are normals to its surface, any point m the picture may be perceived as lying in successive directions, form- ing very variable angles with and round about its normal. The retina cannot inform us of the visible direction of any point painted on its surface. This being so, there is no alternative but to seek for a solution of the mystery in the structure out of which the retina proceeds, for the property in question is plainly inherent in the visual ner- vous apparatus. The author recalls that he had long ago pointed out that, though the optic nerve in its orbital course and its fibres in their retinal course are obnoxious to mechanical pressure, no visual sensation can be immediately produced by such pressure on nerve-trunks or branches. Sensation can only be produced by pressure through the sclerotic by affecting the rods and cones of the bacillar layer, and then only when the flexure of the retina crowds together the internal (as to the eye) ends of the bacillar elements. He cites his former words :—‘‘ When we turn in the dark the eyeballs sharply, or even mildly, a couple of white circular rings, brighter at one margin than the other, enclosing a paler area with a central dark spot, flash forth, the diameter extending an angle of several degrees. ..... The phenomenon is plainly the result of flexure of the retina where the nerve runs into it, as the eye is pulled round in its socket until it drags upon the nerve; and it is to be noted that it is agai where the inner retinal elements are squeezed laterally that the pheno- menon is disclosed.” The absence of the tough and dense sclerotic where the nerve penetrates it, as well as of the choroid, indicates how readily the nerve must yield to the slightest traction. In these previously recorded facts the author feels assured that he had, unwittingly, provided himself with a key to the secret of visible direction. For it has been shown by diversified experiments that whenever there is a parallax in visible direction it is accompanied by a dis- placement of the base of the optic nerve in the same direction—that is to say, by traction upon the nerve-stem, tending to carry its distal extremity that way. The “ white circular rings, brighter at one margin than the other,” have been instanced as proclaiming © that such traction cannot occur without flexure between the nerve- -stem and the eye-apple, which displays itself at the junction of the optic disk with the surrounding retinal expansion. In other words, under the concordant action of the orbital muscles, all the move- ments of the globe are so equably coordinated that the nerve-stem is never subjected to unwonted traction, and consequently always emerges through the ocular tissues to open out into the retina as a normal to their surfaces, in which case no visual parallax appears. But no sooner is there lateral traction than the axis of the emergent nerve-stem, or of the optic disk, deviates from the said normality ; and were that disk impressible by objective light, its central point Dr. J. Jago on Visible Direction. 83 would deviate in the same direction, and an equal deviation in visible direction would be associated with every other point in the visual field. Hence we are fairly landed upon the conclusion that visible di- rection, which has already been tracked backwards to the optic nerve, is a function of its terminal direction, bemg identical with it at the centre of the optic disk, both in the equable use of the eye and in the unequable. Finally, it is clear that if the eyeball be twisted round the axis of the optic disk the terminal portion of the nerve will be twisted in the same direction; and thus the opposite twisting of the visible field in certain experiments related are explicable by the same hy- pothesis—an hypothesis that accounts for all the phenomena of visible direction, whether regular or irregular. Whenever the inverted retinal: image, by means of nervous arrange- ment, is reinverted, an erect image is seemingly projected, if not from, by means of the base of the optic nerve. The principles here arrived at, when applied to binocular vision, lead to the observation of phenomena that have not been before put on record. Wheatstone, in his classic paper in the Philosophical Transac- tions, wherein he announces his discovery of the stereoscope and expounds its theory, only speaks of stereoscopic vision from two perspectives, an appropriate one for each eye, when (no instrument being used) the optic axes meet each other beyond them, or have pre- viously intersected, so that each eye sees the other’s perspective ; that is, in all experiments by him and other subsequent writers on the subject the optic axes have always been supposed to intersect or to lie in one plane. But as it has been demonstrated that the axes of visible direction need not be coincident with the optic axes, it ought to follow that we may continue to see bodies in relief from a pair of stereoscopic perspectives, though these are not placed transversely to each other. Two perspectives of a pyramid are drawn, such as, when placed laterally apart as is usual im stereoscopic slides, and looked at by concourse of the optic axes beyond them, yield a hollow pyramid, and when looked at by a previous decussation of these axes yield a solid pyramid. But these perspectives are placed so that the one which was at the left has the one that was at the right im- mediately underneath it, with about half an inch of plain paper between them. Then it comes to pass that by properly displacing the right eye- ball upwards, by means of the tip of the finger placed underneath it, we can put the under perspective immediately upon the upper one seen with the other eye, and thus realize the hollow pyramid ; or by placing the finger upon the top of the left eye, we can de- press the upper perspective to cover the under one, and thus realize the solid pyramid. The first pyramid depends from the plane of the paper, the second stands upon it. By means of a finger under one eye and another upon the other, 84 Intelligence and Miscellaneous Articles. we can obtain either hollow or solid pyramids anywhere between the two perspectives; or by a finger on both eyes, or under both, we can obtain the pyramid and its “ converse” below or above both perspective outlines. In all these cases the optic axes do not intercept each other, but the axes of visible direction (functional of the final directions of the optic nerves) do meet on the paper; that is, the first pair of axes are not, and the second pair are, in such a realization as is herein planned, in one plane. In all these cases the perspectives fall on similar parts of the two retine, as in the modes originally mentioned by Wheatstone. The author goes on to consider in what way the sensorium refers the sensations it receives notice of from the optic nerves into space, so as to fix the place, size, and form of an object. The theory of vision in retinal normals beg proved to be un- tenable, it is admitted that there is some such association of the two retin as to have fairly suggested the theory of “identical” or “eovering” points; but this relation he believes to be subordinate to a law by which the sensorium projects or emits its perceptions into space, as 1t were in two imaginary cones of sight-rays, which, though not issuing from the ends of the optic nerves, have apices whose positions are functional of the directions of these ends for the instant in question—and that it is by the intersection of the sight-rays in these cones, limited by the law of similar retinal parts, that the places, sizes, and forms of objects are determined. Hence, if we conceive that a pair of stereoscopic perspectives, one being imaged on one retina and one on the other, exist as sight-affections in miniature in the substance of the optic nerves, the size of the resultant solid form will be greater the greater is the distance from the nerves at which the axes of visible direction intersect, or the optic axes when they are coincident respectively with them. The paper concludes by exemplifying in sundry ways the modes in which the conclusions in it may be applied im investigating seem- ingly anomalous phenomena in physiological optics. IX. Intelligence and Miscellaneous Articles. INDUCED CURRENTS AND DERIVED CIRCUITS. BY JOHN TROWBRIDGE. pene expression for the intensity of an induced current, deduced by Neumann and Sir William Thomson, is as follows :—i= - cae in which & is a coefficient depending upon the resistance of the complete wire in the secondary circuit, and U is a certain “ force- function” which depends solely upon the form and position of the wire at any instant, and on the magnetism of the influencing body. The expression, in general language, is as follows :— ‘‘When a current is induced in a closed wire by a magnet in relative motion, the intensity of the current produced is proportional Intelligence and Miscellaneous Articles. 85 to the actual rate of variation of the ‘force-function’ by the dif- ferential coefficients of which the mutual action between the magnet and the wire would be represented if the intensity of the current in the wire were unity.” This investigation was undertaken to ascertain if the laws of derived circuits apply to the currents of induction, which are re- presented by equations of which the above is a type. A reflecting galyanometer of large resistance was included in the secondary circuit, and connected by copper wires of very small resistance with the coil in which the secondary currents were produced: the re- sistance of these wires was infinitesimal in comparison with the resistance of the galvanometer. The galvanometer- was then shunted. ‘The first two columns of the following Table show that, with an inappreciable resistance outside of the galvanometer coils, the shunts made no difference in the deflection of the galvanometer- needle when the shunts were not less than three ohms. Below this the current divided. The resistance of the galvanometer was 5880 chms ; and the last numbers in the second and third columns show that an equal impulse was transmitted through both the shunt and Exterior Shanta Exterior Resistances, zt Sea Defiections.| Resistances, | Deflections. | in ohms. ; in ohms. 0 3 210 10 210 0 + 210 20 210 O 5 210 30 210 0 6 210 40 210 0 5880 210 100 190 .the galvanometer ; for no reason can be assigned why it should take one course in preference to the other. ‘Two galvanometers, there- fore, of the same resistance, one forming the shunt to the other, will give the same deflection, which is equal to that given by the undivided circuit. Resistances were then introduced into the circuit exterior to the galvanometer-coils, and a shunt of 588 ohms was used. The fifth column shows that no effect was produced by the- shunt until the exterior resistance was appreciable in comparison with that of the galvanometer. The following Table exhibits the effect of resistances which were appreciable in comparison with the galvanometer-resistance. The same shunt of 588 ohms was used. The second column is calcu- lated on the assumption that 2 =" (where £' is a coefficient) is Hs and that the laws of Kirchhoff hold. The third column is obtained from the experimental data. The fourth equivalent to 7,= oad fifth columns are also calculated on the assumption that i=z 86 Intelligence and Miscellaneous Articles. =tangent of the deflection. Columns second and third are ex- pressed in arbitrary scale-divisions. gem Calculated | Experimental] Ratio of | Ratio of eee te value of 7. | value of z. | Intensities.| Tangents. 1500 1242 1375 2000 1033 1055 1-06 1:03 2600 954 990 1-06 1:04 3000 767 825 1-06 1-04 3500 673 770 ila | 1:05 4000 613 660 1:05 1:03 4500 558 649 1:05 1:07 5000 514 550 1:04 1:03 It will be seen by comparison that, with large resistances exte- rior to the galvanometer-resistance and appreciable in connexion with it, the laws of the division of currents practically hold, and as the exterior resistance approaches that of the galvanometer the coincidence with the laws is more marked. From the above it appears that, under certain conditions, an in- duced current does not divide according to the laws of divided circuits, but approximates to these laws when there is a resistance exterior to the galvanometer which is appreciable in comparison with that of the galvanometer.—Silliman’s American Journal, May 1873. ELECTRICAL FIGURES ON CONDUCTORS. BY H. SCHNEEBELI. M. Schneebeli has investigated the conditions on which depend the dimensions of Kundt’s electrical figures, which result from the adhesion of a fine insulating powder upon a metallic conductor from ° which a discharge has just issued*. In his experiments, the dis- charge of a Leyden jar took place between a horizontal metal plate, sprinkled with Lycopodium-powder (for the production of the elec- trical figures), and an electrode in the form of a knob, cone, or point surmounting it. The author has found, like M. Kundt, that, ceteris paribus, the diameter of the figure increases with the distance of the electrode from the plate, but not in a constant ratio; the line which represents the ratios is not straight, but an undulated curve. Also the size of the figure augments with the quantity of electricity which produces it. When the electrode is composed of a certain number of points, a circular figure is formed beneath each of them. If a small disk of glass is interposed in the path of the discharge, there is produced * Kundt’s figures are produced with great neatness on the positive electrode, but are only obtained with difficulty upon a plate serving as the negative electrode. That physicist found that the diameter of the figures increases with the length of the discharge, and in proportion as the dia- meter of the opposite electrode to the plate diminishes (Archives des Sci- ences, 1869, vol. xxxv. p. 212). Intelligence and Miscellaneous Articles. 87 on the plate a space void of powder and having exactly the shape of the disk. With electrodes of a conical form with an angle of 60° or of 30°, or in the shape of a tapering needle, M. Schneebeli ascertained that the electrical figure is as much larger as the angle at the summit of the cone is smaller. Lastly, the diameter of the figure is greater when the discharge is effected in a rarefied gas than at the ordinary pressure.—Archives des Sciences Physiques et Natur elles, vol. xlvi. p. 269. NOTE ON GASEOUS PRESSURE. BY ROBERT MOON, M.A., HONO- RARY FELLOW OF QUEEN’S COLLEGE, CAMBRIDGE. As Mr. Strutt appears indisposed to continue the controversy between us*, it may perhaps be permitted me to recapitulate its results. Mr. Strutt impugned my views as to gaseous pressure on two grounds tT :— 1. That an expression for the pressure involving both sale a density leads to absurd results. . That the analytical argument upon which I based such an ex- Bec. fails, “‘the question at issue” being ‘“‘a purely physical one ”—the pressure prevailing 1 in a fluid in motion being, as he con- sidered, settled by Boyle’s law, which he assumed to hold in that case. How far the first part of this criticism was justified I remit to the judgment of those who may think it worth while to refer to my papers in the Philosophical Magazine for August and February last how far the second part is consistent with fact appears from the second paragraph of Mr. Strutt’s recent paper. 6 New Square, Lincoln’s Inn, June 2, 1873. NOTE ON THE USE OF A DIFFRACTION-“ GRATING” AS A SUBSTI- TUTE FOR THE TRAIN OF PRISMS IN A SOLAR SPECTROSCOPE. BY PROF. C. A. YOUNG. Since the diffraction-spectrum differs from a prismatic spectrum of the same length in having the less-refrangible rays more widely dispersed, it some time ago suggested itself that a so-called “ Gutter- platte,” or “grating” of fine lines, might advantageously replace the prisms in spectroscopes designed for the observation of the solar prominences through the C line. In this idea I was strongly con- firmed on seeing last winter some of the beautiful gratings ruled upon speculum-metal by Mr. Chapman, Mr. Rutherford’s mechani- cian. ‘The spectra furnished by these plates far exceed in brilliance and definition any thing of the kind ever before obtained. * See paper “On the Law of Gaseous Pressure” in the Philosophical Magazine for June 1873. + See paper “ On Mr. Moon’s Views on Gaseous Pressure ” in the Num- ber of the Magazine for July last. 88 Intelligence and Miscellaneous Articles. Through the kindness of Mr. Rutherford I have recently come into possession of one of them, having a ruled surface of something more than a square inch, the lines being spaced at intervals of -45 of an inch. Combining this with the collimator and telescope of a common chemical spectroscope, we get an instrument furnishing a spectrum of the first order, in which the D lines are about twice as widely separated as by the flint-glass prism of 60° belonging to the original instrument. In the neighbourhood of C the dispersion is nearly the same as would be given by four prisms. The spectra of the higher orders are generally not so well seen, on account of their overlapping each other; but fortunately with one particular adjustment of the angle between the collimator and telescope, the C line in the spectrum of the third order can be made to fallin the vacant space between the spectra of the second and fourth orders, and we thus obtain an available dispersion near ly the same as that of the instrument I am accustomed to use. On applyimg the new instrument to the equatorial, [ found (under atmospheric conditions by no means favourable, though the best that have presented themselves as yet) that in the first-order spec- trum: I could easily see the bright chromosphere-lines C, D,, and I’; I could also, though with great difficulty, make out Hy, (2796 K). On opening the slit the outline of the chromosphere and the forms of the prominences were well seen in the spectra of both the first and third orders, quite as well, I think, as with my ordinary instru- ment in the same state of the air. The spectra are, of course, fainter ; but as this loss of light affects the background upon which the prominences are projected as well as the objects themselves, it does not materially injure their appearance. The grating is much lighter and easier to manage than a train of prisms ; and if similar ruled plates can be furnished by the opticians at reasonable prices and of satisfactory quality, it would seem that for observations upon the chromosphere and prominences they might well supersede prisms.—Silliman’s American Journal, June 1873. DUPLEX TELEGRAPHY. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, It may be as well to say that the plan of duplex telegraphy by means of two batteries, working together on the receiving instru- ment, but counteracting one another on the instrument at the send- ing end, was patented by me some months since. It is one of the many instances in which a plan occurs to two different people nearly at the same time. Yours obediently, H. Hieron, _ Putney, June 11, 1873. . Mag. J. 4. Vol. 46. PLT. ‘ ” . . “ . . at . . i . ~ ‘ : eS . . . 3 . . ‘ : = = . ry . : - 7 ‘ . . . . bal t . D5 : 5 . = ‘ . 4 . ~ x - . = ; . . . . he a . . ‘ 2 Faults Thermal Spriags i a. ® Mintera Bros. hth + the D lines are about twice gg ; ° belongi ai nt-glass prism of 60° belonging to the eighbourhood of © the dispersion js ven by four prisms. : Pers are generally not so well seen h other; but fortunately with fe angle between the collimator and setum of the third order can pp etween the spectra of the second ‘nan available dispersion nearly Tam accustomed to use. i fothe equatorial, T found (under = favourable, though the best that in the first-order spec. osphere-lines C, D,, and 1; fy, make out Hy, (2796 K), romosphere and the forms B spectra of both the first ith my ordinary instru- : Mhe spectra are, of course, ig Prone atrects the backeround upon which ae are projected as well as the objects themselves, it bes not materially injure their appearance. in The grating is much lighter and easier to manage than a train of i prisms ; and if similar ruled plates can be furnished by the opticians | at reasonable prices and of satisfactory quality, it would seem that | for observations upon the chromosphere and prominences they might well supersede prisms. —Silliman’s American Journal, June om enc 1873. ie DUPLEX TELEGRAPHY. } : To the Bditors of the Philosophical Magazine and Journal. ! GENTLEMEN, ee Tt may be as well to say that the plan of duplex telegraphy by y means of two batteries, working together on the receiving instru- 2} ment, but counteracting one another on the instrument at the send- ® ing end, was patented by me some months since. It is one of the ial many instances in which a plan occurs to two different people nearly at the same time, Yours obediently, H. Hienton, Putney, June 11, 1873. 4 ie alice any t CORNWALL | | orth | Ni Tobban aK Sheep Rock | Hayle UUg Gull R S " ONancekuke- = © BNancehie . - ¢\ Y, Dregea ~<* . Treloweth | q 3 Hap 5; 2, HERR een Sppilllo sain ey Tihidy = Cai Se Doleoaty aN: “Camborne eh a OTTLE Devonian Altered. Devonian Cranite | a So oq ‘ = . os cant greene wtih of Chega nla deat a — nen A ag a nam pipes a a at dew y Se atten an Rp oe Sethe artpee. S . ! ’ * > ‘ > ~, - . bi - * , : = % r : - ; ; . r, . ' . Ly ‘ x ) \ ae ss . - y . ‘ y od é . a al ee . ’ ‘ i ¥ > > , y ? . . ’ ‘ 4 . : s - 2 * ey j rey x : J ‘ + Foe ‘oe =) = 5 i Ks { ss , \ : ~ = v Ps E . i : j 2 , , * eh ’ \ : ae oe wf “he ¥ . ho ve ae 7 ‘ . y ‘ js Tae ‘ . i ' . ‘ " 2 a “ ' ‘eS 4 : + i * - 3 as ‘ Py = . t : THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] AUGUST 1873. X. Fluorescent Relations of certain solid Hydrocarbons found in Petroleum Distillates. By Henry Morton, Ph.D., Pre- sident of the Stevens Institute of Technology *. N ‘a previous paper embodying the results of some observa- tions upon the fluorescent relations of commercial anthra- cenet, | have alluded to the existence of an analogous body among the final products of some petroleum-distillations ; and I now propose to relate more fully the facts developed in a study of these bodies. Nearly a year since, Professor EK. N. Horsford placed in my hands a small specimen of petroleum-distillate, from which [ succeeded in separating a crystalline solid, fluorescing in a re- markable manner with a bright green colour. The amount of material at my command was too small (being in fact but a few grains, extracted from less than an ounce of the substance sent me) to admit of more than a preliminary ex- amination. I succeeded, however, in establishing its optical (fluorescent and absorptive) relations to commercial anthracene, and its difference from that substance in fusing-point and solu- bilities. After encountering some difficulty in tracing up the supply to its source, I was introduced by Professor G. F, Barker to Mr. * Communicated by the Author. T See this Journal, 1872, vol. xliv. p. 345. Phil. Mag. S. 4. Vol. 46. No. 304. Aug. 1873. H 90 Dr. H. Morton on the Fluorescent Relations of certain John Truax, of Pittsburgh, who has been most obliging in fur- nishing me with every facility that could be wished. The preliminary history of the material with which we have to work is as follows :— ; When the residues left in the distillation of petroleum for the manufacture of illuminating-oils are redistilled to obtain lubri- cating-oils and paraffine, there passes over near the end of the operation, and when the still is at the bottom almost or even ~ quite red-hot, a thick resinous matter of a dark honey- or light sepia-colour, which is used as a lubricant for the necks of “rolls” in iron mills. This is the material from which the new body is extracted by the following process. The tarry matter above described is mixed with about its own volume of benzine (petroleum-naphtha), and is thrown ona stout filter, where it is well washed with the same solvent. This leaves a dark olive-green flaky powder, constituting about 3 per cent. of the original mass, and very similar in ap-. pearance to crude commercial anthracene. We now wash this with alcohol, and even digest it in this liquid, by which means a brown material, whose solution in alcohol bas a decided blue fluorescence, is removed. The substance is then dissolved in hot benzole (coal-tar naphtha) and filtered in a jacketed funnel (by which operation a quantity of black powder is removed), and is allowed to crystal- lize on cooling. It then deposits in very small acicular crystals collecting in tufts; andthe purification is carried on by re-solution and crys- tallization from fresh benzole. The substance then has the colour of potassium chromate. The following Table of solubilities will indicate the motive for the above treatment. Benzine, hot (160° F.), dissolves 1 part in 1155 om cola (70 8.) a4 i 2900 Alcohol, hot (160° F.) Pietyen ib. 4172 ee cold (70° F.) ie » | 16625 Benzole, hot (160° F.) Me i 95 33 cold (70° F’.) 93 29 152 This substance dissolves in turpentine pretty freely, and yet more so in carbon-bisulphide and chloroform. In ether and olive-oil and carbon-bichloride it is hardly as — soluble as in benzine. Methods of Examination. For the study of the spectrum of the fluorescent light, the solid Hydrocarbons found in Petroleum Distillates. 91 following arrangement was made. The porte-lumiére A being at- tached to the shutter of a win- dow facing towards the south, a beam of sunlight was thrown by it horizontally into the room and concentrated by a lens of 12-inch focus placed at B. At C was placed an apparatus (fig. 2) con- sisting of a circular horizontal table adjustable up and down on Ca a vertical rod and turning with a Qs “click.” Around the circumfer- ence of this table were eight little “stalls” capable of holding test-tubes or specimen-bottles. Fig. 2. By this means eight different | specimens could be rapidly com- | pared, each in succession, being brought by the action of the click into an identical position with re- ference to the exciting light and the spectroscope. This whole ap- paratus was so placed that an image of the sun was formed on the tube or bottle nearest to the lens B. A glass tank filled with a strong solution of ammonio- cupric sulphate was placed, as in- dicated, between B and C; and to this was sometimes added a plate of violet glass. The spectroscope D employed in these observations was generally one of Browning’s with a single prism of very high dispersion, giving a range of 3° 54! between C and S of the solar spectrum; but a spectro- scope with two similar prisms by the same maker and one by Desaga of less dispersive power were also used occasionally. A small direct-vision aie Acarued = : z ] . . Cc Ss or bands of absorption. For examining absorption-bands, every thing else remained the 92 Dr. H. Morton on the Fluorescent Relations of certain same, except that the spectroscope was turned round into the posi- tion indicated in fig. 8, and the stand for specimens was replaced Fig. 3. Sy by a plane table D, on which the substance to be studied was supported either in a cell of glass or in a bottle. White glass bottles of about one-ounce capacity formed cylindrical lenses of a very convenient character for this purpose. To examine the relative exciting-power of the various colours of the spectrum, an arrangement, nearly identical with that described by Professor Stokes as his “ Third Method ”*, was - employed. Fig. 4. In this case the hght thrown in by the porte-lumiére A passed through a narrow adjustable slit at B, then encountered a prism at C, and after this a lens of about 12-inches focus at D, by which an image of the spectrum was thrown on a screen or tank at E. A spectroscope placed behind this screen was employed, in a manner presently to be described, to measure the refran- gibility of certain rays. Thus, suppose a pure spectrum showing the Fraunhofer lines clearly to be thrown on a screen coated with some fluorescent body placed at H, and that a point of maximum or minimum fluorescence were observed, and we wished to determine accu- rately the refrangibility of the rays to which this effect was due. A fine needle was made to pierce the paper at this pomt; and the light thus allowed to pass through the screen was then mea- sured by the spectroscope. Of course the hole, once made, could, by movement of the screen, be brought into coincidence with any point in the spectrum. * Philosophical Transactions, 1852, Part II. p 470. solid Hydrocarbons found in Petroleum Distillates. 93 With solutions in tanks the same plan was followed, a small piece of card with a needle-hole being moved into the required position and the transmitted light then measured. OBSERVATIONS. Spectrum of Fluorescent Light from Solid Thallene. When a portion of the yellow crystalline substance above de- scribed, and which, to avoid circumlocution, I shall hereafter call thallene, in allusion to the brilliant green colour of its fluores- cence, is examined in the manner first described and represented in fig. 1, we obtain a spectrum such as is indicated in fig. 5. Fig. 5. This begins with a very broad bright space in the orange and yellow ; then, separated by shades or bands of less brilliancy, follow two green spaces, and lastly one of blue, much less bril- liant than the others, and best seen when the violet glass 1s added to the blue tank (see fig. 1). The scale employed in the above and subsequent drawings of spectra is that with milli- metre-divisions introduced by Bunsen. This spectrum, it will be seen, differs from that of impure an- thracene, or chrysogen as found in commercial anthracene, in two respects. First, there is no decided separation of the orange and yellow rays from the red by a dark space in this thallene- spectrum as in the other. Second, there is found in this spec- trum a strong bright band in the blue under circumstances in which it cannot be recognized in the spectrum given by the former substance. Absorption-spectrum of Solid Thallene. At a temperature of about 460° F., thallene fuses without de- composition ; and we may thus obtain a translucent plate of it between slips of mica or on glass in a condition convenient for the study of its absorption in the manner shown in fig. 38. But we may also dissolve it in melted paraffine, or spread it by rub- bing on filter-paper, or mix it with varnish and so coat paper with it. In any of these shapes, when examined by transmitted light, as in fig. 2, it shows an absorption-spectrum such as 1s represented in fig. 6. 94 Dr. H. Morton on the Fluorescent Relations of certain Fig. 6. 8 I ie ff 13 “f sae o i a i In this we find a very strong narrow i, having the line F in its centre, then a less-defined double band at 100 and 110 of the scale; another, yet less sharply defined, from 120 to 130 connected by a shade with the point about 140, where the ab- sorption becomes total. The marked difference between this and the absorption-spectrum of commercial anthracene consists in the double character of the second band, and in the much lower position of the third band, which ends, above, about where that of the anthracene begins. We will now pass to the method of observation indicated already in fig. 4. The screen upon which the pure solar spectrum was thrown, located at E (see fig. 4), was prepared as follows :—A piece of filter-paper was coated with pure thallene by rubbing it on in powder with the finger. It adheres very well to the paper, and produces in this way a very regular and beautiful surface. A strip of this is attached with gum to a piece of white card ; and this slides in horizontal grooves in a frame E (fig. 3), which is pierced by a large opening. The spectrum is so adjusted as to fall on the fluorescent strip, and also on the adjacent part of the card; and we have the ap- Pige 7. sduludatuutul a | 3 t pearance indicated in fig. 7, where S T represents the part of the spectrum which falls on the thallene-covered paper, and RV that portion which falls on the card. The spectrum upon the card runs, of course, from red to violet, but even below the fixed line G becomes very dim, and between G and H. ceases to show any decided light. Where these higher. rays fall upon the solid Hydrocarbons found in Petroleum Distillates. 95 thallene, however, in place of becoming less brilliant towards the upper end, they glow with remarkable intensity; and all about 14 we find a brilliant green ground on which the lines H, H’ and others appear with beautiful distinctness. Below this the colour is a bluish white as far as a little below F, beyond which there is no fluorescent action, and the spec- trum looks alike whether it fall on the thallene or on the card. The brightness of the spectrum on the thallene, however, is not uniform between 8 and 14, but presents a series of gradu- ated maxima and minima, which are represented in the woodcut (fig. 7). To measure the positions of these maxima, the simple device already alluded to was employed. A pinhole was pierced in the fluorescent paper at some convenient point, as at a (fig. 7); and by sliding the entire card or screen in the grooves which sup- ported it, this pmhole was brought to the part of the spec- trum whose location it was desired to fix (for example, as in the figure, at the middle of the broad maximum a); and then, the spectroscope being placed behind E, the refrangibility of the light passing through the pinhole is directly measured. A comparison of fig. 7 with fig. 6, bearing in mind that the scale of the latter is double that of the former in actual dimen- sions, though the numbers correspond, will show that the maxima in fig. 7 exactly correspond with the absorption-bands of fig. 6. This indicates that the absorption in this case is in very close relations with the fluorescence of the substance ; and to this con- clusion many phenomena to be presently noticed give confirma- tion. That such a connexion should exist is eminently natural, since those rays which expend their force in fluorescence, 7. e. in producing vibrations of a less rate, ust evidently disappear ; but it does not follow that all rays which are absorbed develop fluor- escence ; and so, as in the uranium salts, we may expect to - find absorption-bands which have no immediate relation to fluor- escence, although here also there will always be aspecial absorp- tion corresponding to the maximum of fluorescence-exciting power. This was observed by Stokes at the outset. What we have to notice here is that this body thallene has no appreciable absorption other than that due to its fluorescence—or, in other words, that nearly all the rays absorbed by it are converted into fluorescent motions and not into those of heat. I have spoken only of the rays as high as H! when referring to the fluorescence excited by.a pure spectrum on a screen of thallene; but it must not be supposed that this is the upper limit of the effect. With lenses and prisms of quartz, I have 96 Dr. H. Morton on the Fluorescent Relations of certain projected on such a screen a solar spectrum shen the fixed lines for a great distance above H. The fluorescence excited by rays about and arene H does not, however, seem to suffer any change in intensity, but yields a uniform and brilliant green light, on which the solar lines are seen with admirable distinctness. Indeed this substance seems to me to surpass any heretofore known as a screen for the study of the violet and extra-violet rays. Thallene in Solution. As had been already noticed, thallene is soluble in a number of liquids; and in all cases it communicates a strong blue fluor- escence to the solvent, or, more strictly, fluoresces strongly with a blue colour in solution. When this blue fluorescent light is examined with the spec- troscope, it is found, like the green fluorescence of the solid, to break up into bands; but in the solution these are found in all eases to be displaced strongly towards the upper end of the spec- trum, which at once explains the change of general tint in the light from green to blue. Fig. 8, which represents the spectrum of the solution in ben- zole, will, by comparison with fig. 5, indicate this change ; and we shall see that the three most distinct bright bands at 6°8, 3-4, and 9°8 in the spectrum of the solid are moved to 7:2, 8°9, and 10-7 respectively in the spectrum of the solution. Fig. 8. 5 6 7 8 10 . il 12 ii ei If in place of benzole we employ siteeiiea as a solvent, we find that the bands occupy sensibly the same positions; but if sulpuric ether is used, the bands are somewhat more displaced. With turpentine the displacement seems to be a little less than with ether, and with alcohol about the same, while with olive- oil an intermediate position is occupied, and with carbon-bisul- phide the displacement is least of all. The following Table will give some measurements of the po- sitions of corresponding bands in various solutions :— Carbon- Benzole and : ; ; bisulphide. chloroform. Olive-oil. Turpentine. Ether. 68-0 71:6 2 ae 9-9 73.8 87:6 88°5 89°6 89:8 90:1 106°6 107°8 109°2 1081 solid Hydrocarbons found in Petroleum Distillates. 97 If now we observe the absorptive action of these solutions in the manner indicated in fig. 3, we shall find that the absorp- tion-bands, like those of fluorescence, are displaced upwards in the spectra of the solutions as compared with their position in that of the solid. This will be illustrated by comparing fig. 9, which represents Fig. 9. the absorption-spectrum of thallene dissolved in benzole, with fig. 6, which is the absorption-spectrum of solid thallene. The absorption-bands of the solutions in benzole, chloroform, and olive-oil do not appear to differ in any important degree ; but in the etherial solution the bands are higher than in the others. In the solution in turpentine the lower band especially is exceedingly faint, so as to escape recognition entirely in the method of observation employed in the other cases, even when a pint bottle of solution was used; but when the tube of a Duboseq saccharimeter was filled with this solution, this line could be detected with a direct-vision spectroscope. In carbon-bisulphide solution a similar difficulty was encoun- tered, so that in a preliminary publication J spoke of these bands as not appearing; but renewed observation has enabled me to assure myself that in this solution all the bands exist, and at lower points in the spectrum than in any of the other solutions yet examined, the lowest one in particular occupying a point even below that of the corresponding band in solid thallene. There is also in this solution a decided general absorption of all rays above EF, which causes some special difficulty in measuring the bands. In such cases as this the mode of observation to be next no- ticed is specially efficient as a guide, indicating what we must look for in each case. A similar dispiacement of bands by change of solvent has been noticed by Hagenbach in the case of soot, amide of phthalic acid, chlorophyl, purpurine, &c. (Pog- gendorfi’s Annalen, 1872, vol. cxlvi. p. 533) ; and I have also found it in a number of the uranium salts. When a pure spectrum is thrown on the side of a tank of glass or quartz filled with the benzole solution, by the arrange- ment of prism &c. indicated in fig. 4 we see, on looking down 98 Dr. H. Morton on the Fluorescent Relations of certain into it from above, long trails of light running through the so- lution, as shown in fig. 10. Fig. 10. TE i | eee Po etadu ae? ofa ae ey eee ae as ne These trails are variously coloured as follows: a is very faint and olive-green ; 0 is very bright and of a vivid green; ¢c is bright sky-blue; and d is of an indigo tintrunning into violet towards H. The appearance is indeed exceedingly beautiful, from the rich- ness of the colours and the delicate manner in which they fade off and blend. The brightest bands or trails (b and c) are each penetrated, as it were, from the further side of the tank by a long blade of darkness, the result undoubtedly of the absorptive action of the fluid for the corresponding rays, which causes them to be more rapidly exhausted ; while those at either side, being less energe- tically active and acted upon, penetrate further before their mo- tion is converted into fluorescence. Near H, where the actions of absorption and fluorescence are most intense, the light hardly seems to pass beyond the actual surface of the liquid. Exact parallels to all these actions were observed by Stokes in chlorophyl (Phil. Trans. 1852, Part II. p. 489) ; but though I have examined all the substances enumerated by him, I have in no case found so beautiful an exhibition of the phenomena as this solution furnishes. When the light from these trails is examined with a hand- spectroscope, it is seen that the bright green one 4 wants the solid Hydrocarbons found in Petroleum Distillates. 99 upper blue band 10:7, which is present in ¢ and d, This was a necessary result from Stokes’s law, that fluorescent light never contained rays of higher refrangibility than that by which it was excited ; for the exciting light of b was only a little above F, or 9 to 9°15 of the scale. Turpentine dissolves only a small portion of thallene, which, however, communicates to it a blue fluorescence. When examined in the manner just described, its appearance resembles in many respects that of a similarly weak solution in benzole; but there are certain points of distinction. Thus the first band above F is at some distance from it; the second band is decidedly double, with its upper half of a paler colour; and the band above G is likewise evidently divided (see fig. 11). Fig: 11. The dark blades of absorption are not seen in this or in a dilute benzole solution. A solution of thallene in carbon-bisulphide having, as we have seen, its absorption-bands very low in the spectrum, pro- duces also in this last method of examination a very characteristic appearance. The first trail of light is entirely below F, and is pierced by a dark blade; its colour is bright green. The next is midway be- tween F and G, is bright blue, but does not penetrate very far into the solution, and does not show a black blade. The upper 100 Dr. H. Morton on the Fluorescent Relations of certain trail is of a faint indigo tint, penetrates but little into the hquid, and begins decidedly below G. In a former paper attention was drawn to the effect which an exposure to sunlight produced upon the bands of absorption exhibited by commercial anthracene. A cold solution of that substance, showing its bands with great distinctness, loses them eutirely by an exposure of ten minutes to the direct rays of the sun. ‘Thallene similarly treated loses its lower band in five mi- nutes, but its upper one (@. e. the broad double band) only after thirty minutes’ exposure. A saturated hot solution under like conditions loses its lower band in thirty minutes, and its upper one in about two hours. By placing it, however, near the focus of a large burning-glass of 15 inches diameter, ten minutes sufficed for this effect. When a solution of anthracene so exposed for one minute is allowed to cool, it deposits white pearly scales (of pure anthracene), which show no trace of a banded spectrum by fluorescence. When a solution of the yellow anthracene (obtained by wash- ing the crude material with benzime, dissolving in hot benzole, filtering, and crystallizing by cooling), which contains much chrysogen, is similarly treated, after ten minutes’ exposure in the focus of the lens, it deposits on cooling crystals of anthracene nearly white, but still showing a banded spectrum; the bands are weaker than before, but occupy exactly the same positions ; the general fluorescence of the substance is also greatly reduced. Thallene, however, under similar conditions (that is to say, exposed in hot solution in a 4-ounce flask for ten minutes near the focus of the large lens and allowed to cool) deposits crystals almost white but having a slight grey shade; and these show a distinctly banded spectrum, whose bands are located in almost the same positions as those of an etherial solution, but are a little more elevated. Their centres are in fact located as follows: —7°34, 9°18, 11°17, omitting the lowest band, which is too broad to be well indi- cated in this way. The general colour of the fluorescent light emitted by this substance is light blue; and to distinguish it I would propese the name Petrollucene. A solution of this in benzole shows a slight further elevation of bands, as 7°38, 9°2, and 11:24; and when a pure spectrum is thrown on this solution only two trails of ight are seen—one about four fifths of the way from I’ to G, and the other above G. These are blue and indigo in colour respectively. As illustrations of the action of fluorescence, these substances (thallene and petrollucene) surpass, I think, any bodies hereto- fore known. solid Hydrocarbons found in Petroleum Distillates. 101 The green light emitted by thallene surpasses in intensity that furnished by any other substance, the only one which approaches it being platinocyanide of barium in a peculiar condition, which, however, is by no means under control. There are in the collections of the Stevens Institute of Tech- nology some screens and words painted with this salt on cards of a few inches area, prepared by Albert Sohn, of Frankfort-on- the- Maine, which approach thallene in brilhancy ; but the pure salt, even when forming fine crystals, is very inferior in the energy of its fluorescence. Anthracene forms, as is well known, acompound with chlorine (bichloranthracene), whose solutions in alcohol and benzole fluoresce brightly and give a spectrum (banded in the upper regions) which has been studied by Hagenbach (Poggendorff’s Annalen, vol. cxlvi. p. 385. This led me to attempt the preparation of a like compound with thallene. A quantity of bichloranthracene having been first made, to ensure accuracy in the method of working, thallene was sub- mitted to the same treatment, 7. e. was mixed with benzole and subjected to a current of chlorine for about an hour, and was again exposed in the dry state to the action of chlorine. A strong reaction was shown, considerable heat being developed, and the entire substance acquiring a chocolate colour. The pro- duct, however, showed no tendency to crystallize. In its tarry state and in solution its fluorescence is moderately strong, hut yields a continuous spectrum from about C to E. Having next prepared some bibromanthracene and examined its fluorescence, I submitted thallene to an identical treatment. But here also, though a compound was formed crystallizing in very minute needles from its hot benzole solution, neither the solid nor the solution showed any indications of fluorescence. I found moreover that, while anthracene combines with about twice its weight of picric acid to form the picrate, which crystal- lizes in long needles of a rich strawberry colour, thallene requires fully four times its weight of picric acid to saturate it. On cooling from hot solution, a granular mass of minute crystals is ‘formed, having a rich orange-red colour. Examined under the microscope, these crystals are seen to be short prisms with well- defined pyramidal terminations. Sulphuric acid of density 60° B., which rapidly blackens an- thracene even at the ordinary temperature, gives thallene a rich grass-green colour, which remains unchanged even after stand- ing for weeks and exposure to a temperature of 60° C. In this condition it continues to give a bright fluorescence, 102 On the Fluorescent Relations of certain solid Hydrocarbons. yielding a banded spectrum identical with that characterizing it in its normal state. I should therefore conclude that no true combination had occurred, and that the change from a yellow to a green colour resulted from the presence of minute black particles produced -by the action of the sulphuric acid upon some small portion of an adherent impurity. This view is confirmed by the fact that with petrollucene, which is almost colourless, sulphuric acid: pro- duces a dark green colour, approaching to black. Continued application of heat causes thallene, treated as above, to dissolve, forming a compound perfectly soluble in water. The picric-acid compounds, both of anthracene and thallene, show no fluorescence ; so that this gives us a convenient method of determining the point of saturation. Examined with Becquerel’s phosphoroscope, the duration of fluorescence in solid thallene was found to be about =), of a second ; but that of its solution was too brief to be appreciable even at the highest velocity which could be given to the in- strument. To exhibit the fluorescence of thallene, I have found the fol- lowing methods most effective :— Ist. The electric light, without any lenses, is allowed to fall directly on it through a plate of blue or violet glass. In this way one can show various devices, filling an entire stage without difficulty. Allowing the light to pass through the condensing- lenses of a lantern greatly reduces the effect. 2nd. Burning magnesium wire behind a blue glass. The effect here also is very powerful. 3rd. Connecting im series a number of nitrogen-spectrum tubes and exciting them with a powerful coil. The great lack of general illuminating-power in the hight so produced makes the effect in this case very striking. A lime-light behind a blue glass will exhibit the fluorescence of thallene fairly well, but not that of petrollucene. The violet end of a projected spectrum might be regarded as a good source of exciting light, but is, as a matter of fact, infe- rior to any of those before mentioned. Nevertheless the other- - wise invisible bands of metallic spectra, up to the position of the group O, may be exhibited to the largest audiences by the use of ascreen covered with thallene. In painting designs and screens with thallene, it is best to grind it with damar varnish and ben- zole. A glass goblet coated with thallene is well suited for Gassiot’s electric cascade. ‘ee ce XI. On the Form of the Cells of Bees. By J. W. lL. GuaisuEr, B.A., Fellow of Trinity College, Cambridge*. ees following account of the history of the problem of the bee-cell is extracted from pp. 428-430 of ‘ Homes with- out Hands,’ by the Rev. J. G. Wood (London, 1869) :— “Tf a single cell be isolated, it will be seen that the sides rise from the outer edges of the three lozenges above mentioned ; so that there are, of course, six sides, the transverse section of which gives a perfect hexagon. Many years ago Maraldi, being struck with the fact that the lozenge-shaped plates always had the same angles, took the trouble to measure them, and found that in each lozenge the large angles measured 109° 28’, and the smaller 70° 32’, the two together making 180°, the equivalent of two right angles. He also noted the fact that the apex of the three- sided cup was formed by the union of three of the greater angles. “Some time afterwards, Réaumur, thinking that this remark- able uniformity of angle might have some connexion with the wonderful economy of space which is observable in the bee-comb, hit upon a very ingenious plan. Without mentioning his rea- sons for the question, he asked Kcenig, the mathematician, to make the following calculation:—Given a hexagonal vessel terminated by three lozenge-shaped plates, what are the angles which would give the greatest amount of space with the least amount of material? Koenig made his calculations, and found that the angles were 109° 26’ and 70° 34’, almost precisely agreeing with the measurements of Maraldi. The reader is re- quested to remember these angles. Réaumur, on receiving the answer, concluded that the bee had very nearly solved the diffi- cult mathematical problem, the difference between the measure- ment and the calculation being so small as to be practically negatived in the actual construction of so small an object as the bee-cell. “‘ Mathematicians were naturally delighted with the result of the investigation ; for it showed how beautifully practical science could be aided by theoretical knowledge; and the construction . of the bee-cell became a famous problem in the economy of nature. In comparison with the honey which the cell is in- tended to contain, the wax is a rare and costly substance, secreted in very small quantities, and requiring much time for its pro- duction ; it is therefore essential that the quantity of wax em- ployed in making the comb should be as little, and that of the honey contained in it as great as possible. “ For a long time these statements remained uncontroverted. * Communicated by the Author. 104 Mr. J. W. L. Glaisher on the Form of the Cells of Bees. Any one with the proper instruments could measure the angles for himself; and the calculations of a mathematician like Koenig would hardly be questioned. However, Maclaurin, the well- known Scotch mathematician, was not satisfied. The two results very nearly tallied with each other, but not quite; and he felt that in a mathematical question precision was a necessity. So he tried the whole question himself, and found Maraldi’s mea- surements correct, namely 109° 28! and 70° 32’. “He then set to work at the problem which was worked out by Koenig, and found that the true theoretical angles were 109° 28! and 70° 32’, precisely corresponding with the actual measurement of the bee-cell. “ Another question now arose. How did this discrepancy occur? How could so excellent a mathematician as Keenig make so grave a mistake? On investigation it was found that no blame attached to Koenig, but that the error lay in the book of logarithms which he used. Thus a mistake in a mathema- tical work was accidentally discovered by measuring the angles of a bee-céll—a mistake sufficiently great to have caused the loss of a ship whose captain happened to use a copy of the same loga- rithmic tables for calculating his longitude.” It is proper to add that Mr. Wood prefaces the above narra- tive with the words, “I must acknowledge my thanks to the Rev. Walter Mitchell, Vicar and Hospitaller of St. Bartholo- mew’s Hospital, who has long exercised his well-known mathe- matical powers on this subject, and has kindly supplied me with the outline of the present history.” The last sentence in the first extract, viz. that about the loga- rithms (in which the italics are Mr. Wood’s), induced me to ex- amine the original memoirs that relate to the history of the problem of the form of the bee-cell; and although the story as given above is on the face of it erroneous, as the determination of the angles that occur in a bee-cell by measurement to the nearest minute is clearly impossible, still I was not prepared to find that the whole story narrowly escapes the verdict tot sen- tentie, quot mendacia*, As, however, the manner in which so elaborate and romantic a fable has gradually grown up out of simple and even common- place facts possesses interest, and as moreover most of the mis- statements have received the sanction of previous writers, I think * Jt is only fair so far to anticipate matters as to remark at once that Mr. Wood (or Mr. Mitchell) is not chargeable with the origination of the false statements that occur in the narrative quoted, for most of which in the above shape Lord Brougham seems to be chiefly responsible ; but the con- cluding paragraph about the logarithms (which will be seen to be totally without foundation), as far as I know, first makes its appearance in ‘Homes without Hands.’ Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 105 it will be found that the history of the matter is well deserving of attention, although the account quoted, occurring in a work of a popular character, would not, however glaring its inaccu- racies, per se require refutation in a scientific journal. It is convenient to give at the outset, before entering into any details, a brief account of the facts that did occur, for comparison with that quoted above. Maraldi measured the angles of the rhombs and also those of the trapeziums*, and found that, as nearly as he could determine them, the larger angles in both cases were about 110°, and the smaller the supplement of this angle, viz. 70°; it naturally occurred to him to investigate ma- thematically what the angles must be on the supposition that those of the rhombs and trapeziums were exactly equal, and he found as a consequence of this hypothesis that the values in question were 109° 28! and 70° 32'. These angles were not, therefore, the results of direct measurement, but were derived from the solution of a mathematical problem suggested by the actual measurements. Réaumur, suspecting that economy of wax was the reason for the angles being such as they were, ex- plained the form of the cell to Keenig, and (without mentioning what had been done by Maraldi) asked him to determine ma- thematically what the angles of the rhombs would be if for a given capacity the surface of the cell were made a minimum. Keeni solved the problem, and gave as his result 109° 26! and 70° 34’, differing by only 2’ from what Réaumur (erroneously) regarded as the angles absolutely measured by Maraldi. Koenig accom- panied his solution by some remarks to the effect that the ques- tion was one that required the methods of Newton and Leibnitz, so that the bees had solved a problem that was beyond the reach of the old geometry. Maclaurin showed that this was inaccurate, by giving a solution depending only on ordinary geometry ; and he found the angles to be 199° 28! and 70° 32!, agreeing with Maraldi’s theoretical values. Maclaurin read Maraldi’s memoir correctly, and understood the angles by measurement to be 110° and 70°; and he merely just notices the trifling error made by Keenig in his calculation, regarding it as quite an unimportant matter. These are all the facts on which Mr. Wood’s narrative is founded ; and it therefore follows (1) that Maraldi did not find the angles by measurement to be 109° 28! and 70° 32', (2) that Maclaurin was not led to consider the matter by observing the discrepancy between Maraldi’s and Keenig’s values, (3) that he did not make any measurements himself, and (4) that the dis- * By the angles of the trapeziums in this paper are invariably meant the two angles where the sides of the cell are intersected by the rhombs; the angles at the mouth of the cell are, of course, right angles. Phil. Mag. 8. 4. Vol. 46. No. 304, Aug. 1873. I 106 Mr J. W. L. Glaisher on the Form of the Cells of Bees. covery of the error in the logarithmic table is a fiction, the method Koenig employed never having transpired, so that it 1s quite as likely as not that he never used logarithms at all. | The sentence about the pleasure of the mathematicians 1s no doubt merelyrhetorical; but few personswho have any knowledge at all of the history of science will be able to read without a smile the grave statement that, more than halfa century after the pub- lication of the Principia, mathematicians were delighted at their science having given a proof of its utility by the solution of a simple geometrical question. Before entering into further detail with regard to the history of the problem of the bee-cell, which presents several other points besides those already mentioned, it is proper to state that the subject was treated, in very much the same way as in this paper, by the late Robert Leslie Ellis, in a short memoir which was first published after his death in the volume of his collected writings (edited by Walton, Cambridge, 1863), pp. 353-857. Ellis’s remarks were called forth by Lord Brougham’s essay on the subject (which will be noticed further on and seen to be very inaccurate); and he has pointed out that the values 109° 28! and 70° 32! were not the result of measurement; he has also corrected Lord Brougham on another point (viz. about Bosco- vich), which will be referred to presently. The former miscon- ception Hillis speaks of as being “still current and repeated by every writer or nearly so on the subject;” and he refers to a further accuracy occurring in Dr. Carpenter’s ‘ Physiology ’*. As, however, Ellis’s paper occupies only a small portion of the ground covered by the present communication, it will be conve- nient for the sake of completeness to give the whole account here as if it had not been written; but it must be understood that the portion relating to Maraldi is exhaustively treated by himt+. Maraldi’s memoir is entitled ‘Observations sur les Abeilles,” and occupies pp. 299-834 of the Memoirs of the French Academy for 1712 (Paris, 1714)¢. The result of the measurements is given on p. 309 in the following words :— — * The passage in question (‘ Human Physiology,’ 3rd edit. 1856, p. 251) concludes with the words, “‘ the bees being thus proved to be right and the mathematician wrong.” Dr. Carpenter refers to Lord Brougham (vide infra), from whose essay he takes the account, and who is responsible for all except the statement that he (Lord Brougham) took into account cer- tain small quantities that had been previously neglected, and thus showed that the agreement of theory with observation was perfect. + It should be mentioned that Ellis adds some remarks on the construc- tion of the cells which are not connected with the subject of the present papers ie Me {t But there are different editions; in another edition (Paris, 1731 before me the memoir occupies pp. 297-331, and the spelling. and accen- tuation are more modernized ; the quotations are from pp. 307 and 309. Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 107 ““Chaque base d’Alveole est formée par trois rombes presque toujours égaux et semblables, qui suivant les mesures que nous avons prises, ont les deux angles obtus chacun de 110 degrés, et par consequent les deux aigus chacun de 70 degrés ;” and on p. 312 the result of the equality of the angles of the rhombs and trapeziums is given: ‘ Outre ces avantages qui viennent du cdté de la figure de la base, il y en a encore qui dépendent de la quantité des angles des rombes; c’est de leur grandeur que dépend celle des angles dez trapezes, qui forment les six cotéz de l’Alveole; or on trouve que les angles aigus des rombes, étant de 70 degrés 32 minutes et les obtus de 109° 28 minutes, ceux des trapezes qui leur sont contigus, doivent étre aussi de la méme grandeur.” The étant, as Ellis remarks, being the prothesis of a hypothetical proposition, 7f they are &c. then so and so; and in this way the mathematicians Maclaurin, Bosco- vich, and Lhuillier have read it. Maraldi was an able mathe- matician; and no doubt, after his previous statement of what his measurements gave, it no more occurred to him that a non- mathematical reader might imagine these angles were the result of more accurate measurements, than it did that there was any necessity to give the details of the solution of the geometrical problem involved. Réaumut’s researches are to be found on pp. 389-391 of t.v. of his Mémoires pour servir & V’histoire des Insectes (Paris, 1740). The following is the account of the proposition of the question to Koenig :—“Convaincu que les abeilles employent le fond pyramidal qui mérite d’étre préféré, j’ai soupgonné que la raison, ou une des raisons qui les avoit décidées, étoit ’épargne de la cire ; quentre les cellules de méme capacité et a fond pyramidal, celle qui pouvoit étre faite avec moins de matiére ou de cire, étoit celle dont chaque rhombe avoit deux angles, chacun d’en- viron 110 degrés, et deux chacun d’environ 79. Sans parler de la grandeur de ces angles, aprés avoir fait admirer la disposition des rhombes &4 M. Koenig .... je lui proposai de résoudre le probleme suivant. Entre toutes les cellules exagonales a fond pyramidal, composé de trois rhombes semblables et égaux, dé- terminer celle qui peut étre construite avec le moins de matiére.”’ Koenig gave 109° 26! and 70° 34! as the angles of the rhombs ; and then Réaumur sent him the ‘ Memoirs of the Academy ’ for 1712, and he (Keenig) “ was agreeably surprised” to find there- from that his results only differed by 2’ from Maraldi’s 109° 28! and 70° 32/, which Réaumur speaks of as “les mesures les plus précises de ces angles.” Réaumur unfortunately does not give Keenig’s investigation ; but he mentions that it was presented to the Academy in 1739. The volume for this year contains no memoir by Keenig (so that, if he presented one, it was not con- 108 Mr. J. W. L. Glaisher on the Form of the Cells of Bees. sidered deserving of publication in extenso) ; but the matter is noticed at length in pp. 30-35 of the Histoire at the beginning, where, however, only a general account of the matter is given, and no further information about Koenig’s solution is added*. The historian of the Academy states that Réaumur also proposed the question to other mathematicians, from whom, however, he did not receive solutions; he speaks of the bees being only in error to the trifling amount of 2’, and adds that the “ grande merveille ” is their solution of a problem belonging to the higher geometry. Maraldi proposed to himself the problem, Supposing the rhombs and trapeziums have equal angles, what are they? and Réaumur proposed to Keenig the problem, What must the angles of the rhombs be, if the surface is a minimum? The answer to the latter question is, “‘ Equal to the angles of the tra- peziums ;” so that both problems give the same values for the angles; only Maraldi worked his numerical calculation correctly, Keenig incorrectly. What happened was that one mathematician was right and another wrong, not that the bees were right and the mathematicians wrong. How Koenig, who had himself just been considering the. mathematical problem of the bee-cell, could on reading Maraldi’s memoir have failed to see that the latter’s values were the result of a geometrical investigation of the same nature as that which he had just completed, and that they ought to have agreed exactly with his own, is perfectly un- accountable; but it seems to have been the fact. Réaumur (t. v. p. 390) gives, on Koenig’s authority, the amount of wax saved as equal to the whole quantity that would be required for a hexagonal bottom (‘‘M. Keenig a pourtant démontré que les abeilles ceconomisent la cire, en préférant les fonds pyramidaux aux fonds plats, qu’elles ménagent en entier la quantité de cire qui seroit nécessaire pour un fond plat”). This is incorrect ; it will appear further on that the saving is between one fifth and one sixth of the amount here stated. Maclaurin’s paper, “Of the Bases of the Cells wherein the * Réaumur’s words (t. v. p. 390) are: “Si je ne craignois qu’on se lassat de m’entendre parler géométrie, je rapporterois volontiers les démon- strations de M. Koenig; mais ceux qui sont curieux de les voir, n’y per- dront rien pour ne les pas trouver ici. Le mémoire qui les donne, a été lu a l’Académie en 1739, ii en sera fait mention dans-l’Histoire de cette méme année; elles y seront exposées plus nettement, et mises dans un plus grand jour, par notre Célébre Historien, que je ne le pourrois faire.” This implies that Koenig’s solution was presented in extenso to the Aca- demy, and that Réaumur expected it would be so published. In point of fact, however, as already mentioned, not one word of the solution itself was printed ; and all that can be inferred about it from Réaumur’s and the histo- rian’s remarks (which latter are not remarkable for their profundity) is, that it depended on the differential calculus. Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 109 Bees deposit their Honey,” appears in the Philosophical Transac- tions for 1743, pp.565-571*. After an accuratet history of the question, he gives a geometrical proof of Keenig’s proposition to disprove the assertion that any “higher geometry than was known to the Antients’’ was necessary, and correctly finds the angles to be 109° 28! 16” and 72° 31! 44”. He proceeds, “Though Monsieur Maraldi had found by his mensuration these obtuse angles to be of about 110 degrees, the small difference between this and the 109° 28! 16", just found by calculation, seems to have been either accidental, or owing to the difficulty of measuring such angles with exactness. Besides that he seems to admit the real equality of the several plane angles, that form as well the apex, as the other solid ones we have been treat- ing of. And, as to the small difference between our angle and that determined by Mr. Koénig, who first considered this pro- blem, but has not yet published his demonstration of it, that can only be owing to his not carrying on his computation so far, and would scarcely have been worth the mentioning, were it not yet in favour of the practice of these industrious little insects.” The whole of the above passage has been quoted, because other- wise the concluding words “ were it not in favour &c.” might give an erroneous impression of Maclaurin’s meaning, which from the context is seen to be that the correct answer is 2! 16! nearer to the observed angle (110°) than was Keenig’s angle, a correction favourable to the bees. To a not very careful reader the words might at first sight seem to imply that the writer had vindicated the bees from their supposed error of two minutes. Maclaurin calculates the saving as “almost one fourth part oe V2 of the pains and expense of wax they bestow above what ied was necessary for completing the parallel sides of the cells.” This is quite correct ; the amount mentioned is equal to Said ='183...of the wax required for a plane hexa- V3 gonal floor. It is strange that Maclaurin did not so express it, and thus point out the important error made by Keenig in stating it as equal to the whole floor. Boscovich’s investigations occur in the notes to Stay’s poem {. * The paper appears in full also in the Abridgement by Hutton, Shaw, and Pearson, vol. viii. pp. 709-713 (1809). + “ Monsieur Maraldi had found by mensuration that the obtuse angles of the rhombus’s were of 110 degrees nearly; upon which he observed that if the three obtuse angles which formed the solid angles above mentioned were supposed equal to each other, they must each be 109° 28’; from whence it has been inferred that this last was really the true and just mea- sure of them” (p. 566). t Philosophie recentioris a Benedicto Stay.... versibus tradits 110 Mr. J. W. L. Glaisher on the Form of the Cells of Bees. In the space of six pages and a quarter he has treated the matter very ably and in a manner worthy of his high reputation. He has clearly read with care all that had been previously published on the question, except Maclaurin’smemoir, which he knewof and had in vain endeavoured to procure; he therefore does not know what method Maclaurin used, or whether any of his own remarks had been anticipated by him; but he thinks it likely that such may have happened, “ cum in tanto Geometra nihil desiderari unquam possit, quod aut ad simplicitatem solutionum, aut ad penetra- tionem, et combinationes consectariorum pertineat,” a well- deserved compliment to the Scotch mathematician. 3 Boscovich points out distinctly that Maraldi’s values 109° 28! and 70° 82! were not the result of measurement; and he even goes further and expresses a doubt whether, without the know- ledge of the solution of the mathematical problem, he would even have been able to measure them to the nearest degree. His own words are worth quoting :—‘‘ Mirum sane esset, si Maraldus ex observatione, angulum estimasset intra minuta, quod in tam exigua mole fieri utique non poterat. At isut satis patet ex ipsa ejus dissertatione, affirmat se invenisse angulos circiter graduum 110 et 70, nec minuta eruit ex observatione, sed ex zequalitate angulorum pertinentium ad rhombos, et ad trapezia; ad quam habendam Geometria ipsum docuit requiri illa minuta. Quin immo satis vereor, ne hee ipsa, aut aliqua ejusmodi consideratio dederit ipsum graduum numerum illum tam proximum; nam observatio intra plures gradus incerta esse debuit in mole adeo exigua, nec ita accuraté efformata; cum plures irregularitates, et in hisce rhombis, et in omni reliqua constructione alveolorum observari passim affirmet ipse Reaumurius. “ Verum quidquid sit de graduum numero, certe numerum mi- nutorum Maraldus non proponit tanquam observatione immediata definitum, sed ex illa zqualitatis consideratione, quam diximus, adeoque si Koenigii solutio rite procederet, determmatio minimi non ab angulo observato per illa duo minuta discederet, sed ab angulo requisito ad eyusmodi zqualitatem, cum observato tamen congrueret adhuc intra limites admodum arctos, et qui in ejus- modi argumento omnem superant observatoris industriam.” Réaumur himself (t. v. p. 882) says that some of the rhombs appear square, but that generally they are “ lozanges ou rhombes plus ou moins allongés ;” and any one who remarks how greatly libri x. cum adnotationibus, et supplementis P. Rogerii Josephi Boscovich, S.J. vol. 1. Rome, 1760, 8vo. The note De Apium Cellulis refers to verse 2306 of book vi., and is the last note in the second volume (pp. 498- 504). The first volume was published m 1755, and, according to the Bio- graphie Universelle (Michaud), the third in 1792, the publication having been retarded by Boscovich’s delay im the preparation of the notes. Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 111 they differ from one another will agree with Boscovich in his surprise that Maraldi should have been able to obtain by mea- surement the typical angle correctly to within one ninetieth of aright angle. Of course Boscovich does not impute the slight- est insincerity to Maraldi; he merely points out that the know- ledge of the sclution of the theoretical question may have exer- cised an unconscious bias over his mind, so as to make him announce 110° with more confidence than he might otherwise have felt. Boscovich gives two solutions of Kcenig’s problems, the one by pure geometry, the other by differential calculus. The latter is obtained in exactly the way any one to whom the question was proposed would probably now proceed (at all events it is nearly identical with my own solution undertaken before I had seen any of the investigations on the matter): the correct result is obtained ; and it is suggested that Koenig’s error was produced by his having adopted some complicated method leading to a formula which had to be solved by approximation. With regard to the saving of the wax the process is quite correct; only there is a slip in the course of the work which renders the result inac- curate: the ratio of the amount saved to that required to form a hexagonal base is given as , whereas it should be 2 € malt, —2 pa a The ratio in question is truly found to be PV rales a 208 V3— Vf but in the next line this is by a mistake written TsiighBe aa and the error is retained. This upsets an ingenious suggestion of Boscovich’s, who thought that perhaps Koenig’s error was intro- duced by the accidental substitution of VW 6—2 for ./6—2 in the numerator of the fraction quoted, which would change the ratio into one of equality*. One point of very considerable importance in the form of the cell is first noticed by Boscovich, who observes that by the arrangement adopted every plane cuts every other plane at an angle of 120°: thus the three rhombs forming the apex are in- * Tt is scarcely worth speculating how it was that Koenig did make the error in determining the ratio ; and, of course, the facts can never be known with certainty ; but the following is a guess. Taking the length of a side of : te ORL 2 BOAO Ao the hexagonal base as unity, the amount of the saving is 4 in roe Cg (the first term being the area of the six triangles, the second of the hexa- gonal base, and the third of the three rhombs); if, then, Koenig forgot to a2 by 3, the expression would multiply the area of a single rhomb, viz. reduce to the middle term, viz. the area of the hexagonal base. 112 Mr. J. W. L. Glaisher on the Horm of the Cells of Bees. clined to one another at this angle, and so is each trapezium to the planes it cuts. This leads to the belief that the bees have some means (instrumenta) of constructing planes inclined to one another at this angle. Ellis (who had not seen what Boscovich had written) practically remarked the same thing, and made a guess at what the znstrumenta were a century later (‘ Writings, p- 356). It thus appears that Boscovich discussed the whole subject with completeness, penetration, and (but for the one trivial slip) accuracy. Had his remarks been published in a work better known and more accessible to naturalists, a detailed refu- tation of Réaumur and Keenig a hundred and thirteen years later would have been rendered superfluous. The next memoir* that I know of in which the form of the bee-cell is considered is by Lhuillier, and occupies pp. 277-3800 of the Berlin Memoirs for 1781 (published 1783). The in- troduction (of two pages) and conclusion were written by Cas- tillon, who presented the memoir to the Academy. Lhuillier gives a short account of the history of the subject without ad- verting particularly to Réaumur’s misreading of Maraldi. He argues with Boscovich “que légalité supposée des angles des rhombes du fond et de ceux des trapezes des faces d’un alvéole, est le principe qui a guidé M. Maraldi dans l’estimation de ces angles ;” and adds a new fact, viz. that Cramer, his fellow- citizen (of Geneva) had given some developments on the subject to Koenig which had not been published. After stating that one of Boscovich’s methods is very similar to Maclaurin’s, he begins the next paragraph: “Tous les mathématiciens ont re- gardé cette matiére comme passant les forces de la Géométrie élémentaire,” which is untrue, as the solutions in question are geometrical: the error is a curious one for Lhuilher to have made, as he had certainly read Boscovich’s remarks, and in all probability seen Maclaurin’s paper. He very properly regards the difference of method as of very slight importance im a mathe- matical point of view (and thereby he shows, I think, a truer appreciation of the relations between the modern and ancient methods than either Koenig or the historian of the French Aca- demy) ; and he justifies his own geometrical solution that follows on the ground that it is thus made intelligible to naturalists ; for although it is unlikely that the same person should be both an able mathematician and an able naturalist, still a particular study of the one does not prevent a knowledge of the elements of the other. After his geometrical solution he proceeds to cal- culate the saving of wax; and he finds that the amount used by the bee in the real cell is to the amount that would be required for * “Mémoire sur le minimum de cire des alvéoles des Abeilles et en particulier sur un Minimum minimorum relatif a cette matiére.” Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 118 the prismatic cell with a plane hexagonal floor as 25+ 6 to 28, so that the wax saved is about the one fifth part of that re- quired for the plane floor. Lhuillier merely proves the above value for the ratio; but it is interesting to have the amount of wax required for the different portions of the cells ready for compa- rison. Taking, therefore, a side of the hexagonal section as unity, and assuming with Lhuillier (after Maraldi’s observations) that the ratio of the radius of the inscribed circle of the hexagon to the depth of the prismatic cell of the same capacity as the real cell is as 1} to 5, we have for this depth (viz. the longest side of the trapeziums in the real cell) the value a , and then to three places of decimals— hig Ateaetithesthree rhombs. . 6) «6 = Yada 3°182, (1) six triangles “2 °°). OS ae = 1-061, (ii) 4 six sides of equivalent _ 25/3 ; + prismatic cell i Fi 5 = 21-651, (ii) B Hexagonal base © {))°0> 2! = = = 2°598, (iv) and the surface of the real cell = (1) + (in) — (1) =28°772, while that of the prismatic cell with a flat hexagonal bottom = (iii) + (iv) = 24°249 ; so that the saving is °477, and the ratio is as stated above. It forms no part of my present purpose to give a detailed ac- count of the form of Lhuillier’s minimum minimorum cell; suffice it to say that he extends Réaumur’s problem, and proceeds to inquire what must be the proportion of the depth of the cell to the width of its mouth that it may require the minimum of wax (the shape of the cell, viz. the inclination of the rhombs to the trapeziums and to one another, being supposed as in the bee- cell). A few remarks on this paper will be made further on. Lhuillier refers to Lambert (Beytraége zum Gebrauche der Mathematik, t. i. p. 387 et seg. Berlin, 1772); but I find on reference there is nothing that very closely relates to the subject of this paper. Lambert’s remarks occur in the course of an essay on the Art of Building; and he prefaces chap. v. (on mi- nima in roofs) with the statement that if it were usual to build hexagonal houses we should obtain our model from the bees. In point of fact hexagonal summer-houses, sentry-boxes, towers, &e. are not very uncommon; so that he investigates the condi- tion of roofs of minimum surface both in this case and when the base is square. As the result of the former problem he obtains 114 Mr. J. W. L. Glaisher on the Form of the Cells of Bees. the bee-cell ; and when the base is square the roof is formed of four rhombs, which happen to be of the same form as in the bee- cell (viz. ratio of diagonals = ¥2), with the only difference that when the base is square they are placed with the shorter dia- gonals horizontal, and when the base is hexagonal the longer. He thence concludes that with twelve such rhombs a regular figure of twelve sides could be made exhibiting both the roofs of the 4- and 6-angled buildings, and therefore also of the bee-cell ; after which he adds that this last fact was noted by Kepler in his Harmonice, so that the question Réaumur proposed to Keenig was not so new as he thought (nicht mehr so ganz neu, als es Reaumur geglaubt zu haben scheint). Lhuillier says Lambert’s assertion about the bee-cell is contrary to the contents of his (Lhuillier’s) paper (meaning that certain other forms would be preferable for the house) ; and heisright. In fact Lambert has not at all considered the general problem, what would be the best form for the hexagonal house? but merely the particular case which arises in connexion with the bee-cell, viz., if the base and capacity are given and the roof is to be rhomboidal, what must the angles of the rhombs be ? The next discussion of the form of the bee’s cell that’ I have to notice is by Lord Brougham ; and it occurs in vol. 1. of his ‘Dissertations on subjects of Science connected with Natural Theology, being the concluding volumes of the new edition of Paley’s Works,’ two vols. 1839*. The essay in question occu- pies pp. 218-368; but it is only with the parts of it that relate to the matters already noticed in this communication that we are here concerned, and it must be understood that it is only to these portions that any remarks that may be made have reference, unless otherwise stated. In 1858 Lord Brougham extracted the more salient points from his earlier essay and communicated them to the French Academy}. I cannot find that his memoir has yet been printed by the Academy ; but an abstract appears on p. 1024: e¢ seq. of vol. xlvi. (1858) of the Comptes Rendus; and it is published in extenso by its author as Tract vi. (pp. 103-121) of ‘ Tracts, Ma- thematical and Physical’ (London and Glasgow, 1860). All the statements that will be noticed in this paper appear also in the French memoir, although the wording &c. is sometimes modified * The essay appears in vol. vi. of the collected works of Lord Brougham, by A. and C. Black, Edinburgh; but the Appendix of Demonstrations, con- taining the solutions of the mathematical questions referred to in the text, is left out; and this is done without even an accompanying statement of so important an omission having been made. + It is not, however, stated m the memoir (at all events as printed in the ‘Tracts’ .... 1860) that the facts contained in it had been previously published. Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 115 and the whole contracted. I shall refer to and quote from the original edition of 1839; but wherever the French memoir of 1858 shows any discrepancy it will be pointed out either in the text or a note.. As a résumé of moderate length was given in the Comptes Rendus for 1858, it seemed not unlikely that some one might have anticipated the ensuing remarks; but an examina- tion of the Comptes Rendus from 1858 to 1871 showed that only one communication had in this time been made to the Academy on the subject, viz. by the late Mr. Willich (vol. li. p. 633, 1860), who gives a method of constructing a bee-cell which resembles (and is perhaps identical with) that suggested by Leslie Ellis in his Essay. I may as well mention at once that Lord Brougham’s essay shows that he has read carefully Réaumur and Lhuillier, looked at Maraldi and Maclaurin, and not seen Boscovich; he has, however, written with great confidence, and on him falls the responsibility of perpetuating and stamping with a fresh mark of authority the old fiction that had been exposed three quarters of a century before. His works have been so widely read, and will no doubt continue to beso well known in the future, that he has in all probability given a new and long lease of life to the old and sillv fable: his statements appear on the face of them to be the results of such careful study of the original authorities, and they are presented with such assurance, that few readers will imagine that they can be otherwise than correct. The story, as given by him, is in its facts the same as it appears in the extract from Mr. Wood’s work at the beginning of this paper* (omitting ‘the paragraph about the logarithms); only he does not state that Maclaurin made any measurements; in fact he expressly points out in a note on p. 244 that Dr. Reid, in his Essays+, is wrong in stating that Maclaurin ascertained the angles “ by the most exact mensuration the subject would admit,” or solved the problem “ by a fluxionary calculus.” In reference to Kcenig’s blunder of 2’, Lord Brougham says (p. 244), “ possibly it is in the logarithms that he has, by neg- lecting some decimal places, gone wrong; ” and on p. 345, “ the error into which Mr. Keenig fell. ..... originated most pro- bably in the tables of sines or in the logarithms which he * In a note in the French memoir a more detailed allusion is made to Maraldi’s measures, and the 110° and 70° are regarded as approximate and the 109° 28’ and 70° 32’ as exact: this was Réaumur’s view. + The passage referred to will be found in chap. ii. (Instinct) of Essay IIt. of Dr. Thomas Reid’s ‘ Essays on the Active Powers of Man’ (orig. ed. 1788); but no history of the problem of the bee-cell is there given; in fact the only sentence that has reference to the matter is the one containing the two errors noticed in the text ; and it simply states that the bees have solved the minimum question correctiy. 116 Mr. J. W. L. Glaisher on the Form of the Cells of Bees. used*, Now to both of these suggestions, and to the second espe- cially, there ave great objections. Koenig gave a wrong result as the answer to an arithmetical question; and all that can be said is that he somewhere must have made a mistake in his work: if he neglected too many decimal places, that is of course a blunder as much as if he had written a5 for a3; and, as far as I can see, there is no reason to assume that he made this error rather than any other. The second suggestion, so far being most probable, is possible, but highly improbable. Given that a wrong numerical result is published and nothing further, it 1s 50 to 1 that the blunder was in the computations, not in the tables ; besides, Koenig calculated the saving of wax} (which required no tables or numerical computations) wrongly, so that there is prima facie evidence that he did not use suflicient care. Lord Brougham was especially afraid of any error in the tables, and therefore obtained two solutions of Keenig’s problem, in one of which the dihedral angle between two of the rhombs was the quze- situm ; and he also desired a friend to vestigate the question independently. But all this was quite superfluous; if @ be the smaller angle of the rhombs, the analysis readily gives cos 0=1=:3333333, so that @ can be obtained at once from a table of natural sines; and any one who knows any thing at all about mathematical tables can see at once, by taking a few dif- ferences, whether the table contains an error (particularly so large an error as to produce an alteration of 2'); but even if this is not done, an obvious transformation gives tan 40=,/2=1:4142136, and 46 (@ being here the larger angle) can be found directly either from a natural or a logarithmic canon at once; or any number of similar transformations can be made. Lord Brougham uses (p. 246) the singular phrase “difference introduced by the logarithmic approximations ;”’ perhaps the last two words are merely a euphemism for “ erroneous table,” as it is needless to say that 7-figure logarithms generally give results true to a tenth of a second at least, so that an error of two minutes is out of the question. Whence Mr. Wood or Mr. Mitchell derived the statement that Koenig was not to blame, but that the error really was in in the logarithms, I am unable to say; but [ think it is a fair hypothesis to suggest that Lord Brougham’s, or some similar statement to the effect that the error was most likely in the * This is intensified in the French memoir, “ M’étant assuré .. .. que Keenig était tombé dans l’erreur par les tables de sinus ou des logarithmes &e.,” p. 112. + Lord Brougham does not mention the fact of Koenig having errone- ously calculated the saving. Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 117 tables, has been developed into it by persons not very careful about the truth. ‘The story given by Lord Brougham was suf- ficiently romantic ; but the person who added the climax, and gave it point by the sensational allusion to the ship, certainly deserves to have his services remembered. Maclaurin suggested that Koenig did not carry his approxi- mations far enough; but I imagine that he either felt a delicacy about saying in so many words that Koenig had made a blunder, or that he had in his mind (like Boscovich) the probability of his having obtained a complicated equation and solved it by ap- proximation. But Lord Brougham could not have felt this delicacy a century later; and he certainly did not attach Bos- covich’s meaning to the word approximations. Lord Brougham objects most strongly to the results obtained by Lhuillier ; and his arguments are of so remarkable a charac- ter that I hope I shall be excused for quoting his exact words, and the more so as the reasoning certainly must have appeared to its author to carry weight, as it is reproduced (although somewhat more briefly) in the French memoir. He denies that Lhuillier is right in calculating the saving of wax as only =, ; he writes (p. 291):—“ It is extremely erroneous to represent the saving as only 3; part. ... The proportion ,}, is obtained by comparing the saving upon the base with the whole wax of the cell, including the walls, and supposing the height of the wall to be to the sides as 5 to 1°387. But why is the wax of the wall to be imported into the caleulation, with which it has nothing to do? ‘The question is between two forms of the bottom, not of the whole cell. Suppose two kinds of roof for a house were to be compared in order to choose the one that required least timber ; though the whole house might be made of wood, we should only compare the expense of the roofs, and leave out the walls that would be common to both plans; otherwise the relative amount of the saving would depend on the height of the house as well as the shape of the roof. This becomes the more evident in the case of the cells from the circumstance of their depth varying in the same comb, and forthe same bee, according to many accidental circumstances. .. . [The author then states the great variations that occur in the depth of cells.] The saving therefore is some- where about a ninth, and not somewhat less than a fifty-first part.” “ But there is another consideration which shows still more strikingly the fallacy of the argument derived from taking the whole walls of the cell into calculation. The thickness of the wax is very different in different parts of the cell, bemg much greater in the base, that is, in the rhomboidal plates, and the 118 Mr. J. W. L. Glaisher on the Form of the Cells of Bees. part of the walls adjoining, the six small triangles, which are formed by a line drawn parallel to the base through the points where the rhomboidal plates cut the walls. ‘This is manifest upon inspection ; and I have tried it by weighing equal parts in superficial extent, as far as it was possible, of the base and of the sides, and uniformly found the latter sensibly lighter. It did not seem that the proportion was always the same; but I never found the difference less than in the proportion of 3 to 2. The thickness of the walls varies much more than that of the base in different combs. But any considerable difference be- tween the two portions at once destroys the argument of M. L’Huillier. If it is as 3 to 2, then the saving is nearly an eighth upon the thicker part, and consequently about =, instead of =), of the whole.” The ratio of one ninth is found by comparing the bottoms of the cells, the bottom of the actual cell being taken as the three rhombs and six triangles, and the bottom of the hypothetical prismatic cell as the hexagonal floor and the portions of the sides below a horizontal plane through highest points of the rhombs (supposing the cell placed with its axis vertical and mouth upwards); and the ratio of =4, follows by considering the ratio of the saving to the whole amount of wax, the bottom (defined as above) being supposed half as thick again as the rest of the cell. The above quotations contain, I venture to think, as striking instances of bad reasoning as are often met with in writings relating to mathematical subjects. The comparison is between two kinds of cells; the one requires an amount 7 of wax, the other an amount n+ !5n; and the amount saved is =))n, that is to say, if they built flat-bottomed cells, the bees would have to manufacture ~,; more wax than in reality they do manufac- ture. Ifa house with a V-roof costs £1000, and with a flat roof £1020, the builder who prefers the former saves £20 out of an expenditure of £1000, or =}, of what he spends*; his saving is not a fifth of his expenditure because the walls cost £900, and are the same for both. Lord Brougham says, “ Why is the wax of the wall to be imported into the calculation, with which it has nothing to do ?” and the reply is, ‘‘ Why is the wax of the wall to be left out of the calculation? it is manufactured by the bees in exactly the same way as is the wax for the rhombs and triangles, and is part of the cell built by the bees.” In effect, Lord Brougham replaces “the bees must have walls for their * Or, to state the same thing differently, if m be the wax required for the hypothetical cell, m— ym represents the amount used in the real cell, so.that the saving is ;4, of the amount that would have been needed for the hypothetical cell; it is because Lhuillier so regarded it that he writes TT and not sy: Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 119 cells”’ by “the bees donot manufacturethe wax for thewalls of their cells,” and regards the two assertions as identical. The fact that the depth of the cells is variable is exactly analogous to the fact that the angles of the rhombs vary: none of the cells are per- fect mathematical figures; but we consider merely the figure which we believe to represent the mean or typical cell. In reality Lhuillier’s calculation of the saving is under the mark; for if, as Lord Brougham so strongly insists in reference to the minimum minimorum, the hexagonal plate that closes the mouth of the cell be taken into account also, then the amount of wax in the real cell is 26°370 against 26°847 in the hypothe- tical cell, and the saving is only =~ of the wax used, or even less if we consider a comb, as each cell has its own hexagonal plate, while the sides and rhombs are, except in the outside cells, common to two contiguous cells. With regard to the argument drawn from the increased thick- ness of the rhombs and triangles, it 1s only necessary to remark that, unless we know the reason for this thickening (which we do not), its recognition removes the question of the bee-cell from the province of mathematics (or exact reasoning) entirely. We are comparing the real cell that the bees do make with a hypo- thetical cell which, a priort might have appeared more simple and suitable ; and unless we are sure why the bottom (using the word as above defined) is thicker than the walls, how can we know how much of the hypothetical cell would require to have been thickened if it had been adopted? Ifthe change of thick- ness destroys Lhuillier’s argument, it at the same time destroys all mathematical reasoning as applied to the question. Lord Brougham assumes that what I have called the bottom of the hypothetical cell would have needed thickening had that form been adopted ; but this assumption is purely arbitrary, and how much (if any) of the walls would have required to have been thickened is merely matter of opinion; and the question is thereby removed out of the reach of mathematics, where it is not my object to follow it. I purposely abstain from any remarks on Lhuillier’s minimum mimmorum and Lord Brougham’s objections, partly because I may possibly make the problem there treated of the subject of a separate communication at some future time, and partly because so shallow a cell (whether the hexagonal plate be excluded or not) is clearly unsuitable for the other purposes to which the bees apply their cells besides stormg honey. It is unnecessary here to do more than allude to Lord Brougham’s remarks on Lhuillier and Castillon in reply to the argument marked thirdly in his essay, as any one who has read 1n this paper what Maraldi, Boscovich* &c. * Leslie Kilis corrects Lord Brougham for representing that Bosco- 120 Mr. J. W. L. Glaisher on the Form of the Cells of Bees. did say will see at a glance how much is and how much 1s not correct. I pass over also one or two minor shps. Of course Lhuillier deserves Lord Brougham’s censure for having failed to notice that Maclaurin’s and Boscovich’s proofs were geometrical. I have not hesitated to state plamly the value of Lord Brougham’s arguments in my opinion, as the frankness with which he has expressed his sentiments with regard to the writings of those with whom he did not agree renders any par- ticular display of courtesy towards his own views unnecessary. Even Leslie Ellis writes, “ Hither the habit of an advocate’s mind—for Lord Brougham may be regarded as counsel for the bees—or his not having read Maraldi’s paper must have been the cause of this omission” [viz. of Maraldi’s statement that the angles measured were 110° and 70° :: this is partly supplied, as has been noticed, in the French memoir}; and I must say that the quiet dignity of the mathematical writings on the sub- ject contrasts most favourably with his violent advocacy. The impression any one would receive from reading Lord Brougham’s remarks on Lhuillier and Castillon would be that they had treated the matter ignorantlyand unfairly ; whereas their memoir seems to me (and I believe it would to any one else) an impartial (though not very brilliant) attempt to add to our knowledge and advance truth. As the result of a tolerably careful examination of the whole question, I may be permitted to say that I agree with Lhuillier in believing that the economy of wax has played a very subordinate part in the determination of the form of the cell ; in fact I should not be surprised if it were acknowledged here- after that the form of the cell had been determined by other considerations, into which the saving of wax did not enter (that is to say, did not enter sensibly ; of course I do not mean that the amount of wax required was a matter of absolute indifference to the bees). The fact of all the dihedral angles being 120° is, it is not unlikely, the cause that determined the form of the cell. Whenever a prediction is subsequently verified by experiment, there is always a strong tendency to believe in the truth of the theory whereby the prediction was obtained, even if the course of subsequent research lends no additional support to it, but rather the reverse. And the equality of the angles of the rhombs and trapeziums is no doubt the solution of so many different vich’s remarks imputed dishonesty to Maraldi; and although he had not seen them, he feels no doubt that what Boscovich really did say was merely a reproduction of what Maraldi had himself said. This is so, and Ellis was right; but, curiously enough, although Lord Brougham did not know it and had no ground for supposing it, Boscovich does, as noticed supra, suggest that perhaps Maraldi was helped by theory. Mr. J. W. L. Glaisher on the Form of the Cells of Bees. 121 questions, that the success of Réaumuv’s problem no more proved the economy theory than did the discovery of conical refraction prove Fresnel’s wave theory. No one doubts that the bee-cell is the best that could be contrived for the purposes to which the bees apply it; but the question is, what is the special reason for the three rhombs and their particular form? Lhuillier’s mini- mum minimorum is of little use, as he himself points out ; for no doubt the shape of the insect &c. require a cell of some depth (and perhaps an apex); but his conclusion that economy is not the primary reason is, I think, in accord with the evidence. In an interesting memoir in the Cambridge Transactions%, Whewell has drawn special attention to the manner in which hypotheses may become gradually transformed as new facts are discovered, so as sometimes to become almost the opposite of what they were originally, without their adherents acknow- ledging any defeat. Thus the Cartesians, little by little, modi- fied their vortices by rejecting or altering portions now and then as they were shown to be in opposition to the facts, introducing fresh suppositions, &c., until at length a vortex merely became a complicated piece of machinery for producing a central force, and the Cartesians and Newtonians then ceased to differ, as the vortex, being no longer essential, could be ignored at plea- sure—and this without the former ever yielding or formally confessing defeat. Now the problem of the bee-cell seems very like an hypothesis undergoing transformation. Réaumur (though he only speaks of it as the reason, or one of the reasons) and Maclaurin evidently thought saving of wax paramount; Boscovich gave prominence to other reasons also; and Lhuillier believed economy played only a very subordinate part. Lord Brougham vehemently supports the economy hypothesis, but says it is only one reason among several; and he ridicules Lhuillier for thinking that Réaumur &c. asserted it to be the only reason. This is the first step in the transformation ; and it is quite pos- sible the economy-theorists may in the future, while stili con- tending for their hypothesis, gradually admit that more and more weight is due to the other reasons, till at length they may be contented with an acknowledgment that economy was not ignored—when the transformation will be effected. I think the bee-cell problem is of sufficient importance, as oné of the most remarkable instances of instinct, to merit the space that has been devoted to it. It seems curious that so obvious and easily exposed a story should have been so tenacious of life ; but the explanation no doubt is to be sought in the fact that it hes on the borders of two sciences. In a mathematical point of * “On the Transformation of Hypotheses in the History of Science,” vol. ix. part ii. Phil, Mag. 8. 4, Vol. 46, No, 804, Aug. 1873, K 122 Mr. BR. Moon on the Transmission, in one view the problem is simple, not to say trivial, and possesses but slight interest to a mathematician; and to the naturalist it is £00 mathematical to be pleasing. A mathematician cannot sometimes help feeling some regret that the great discoveries and advances in his science can be only Lawn to the very few who have learnt to read the language that can alone express them; but from the contents of this communication more than one argument might be drawn to show that it is any thing but an unmixed gain to a science to admit of popularization. Cambridge, June 10, 1873. XII. On the Integration of the Accurate Equation representing the Transmission in one Direction of Sound through Air, deduced on the Ordinary Theory. By Rosert Moon, M.A. » Honorary Fellow of Queen’s College, Cambridge*. d hiss following investigation, independently of its bearing on the problem to which it ostensibly relates, I offer as an essay towards a complete theory of the solution of linear partial differential equations of the second order. The transmission of sound through air in one direction may be represented on the ordinary theory by the single equation 0 Fai oe ee (1) where @ and w respectively denote the ordinate of the particle at the time ¢ and in the state of rest, and where e,= - —or by the . pair of equations, dv pte; dé, dt dx’ ® e ® e (2) adv de. J * aa where » and a, “are noe longer to be regarded as the partial dif- ferential coefficients of a, but as independent functions of x and ¢. The solution of this last pair of equations must consist of a pair of relations between the variables ve,@ and ¢, such as Fs (wtvd,) = 0) oR 3 (zive,)=0s a from which it is evident that (1) must be derivable from a pair . of first integrals of the form indicated by equations (3) when we 0= dee substitute in them We = for v and a, respectively. * Communicated by the Author, Direction, of Sound through Air. 123 I. Supposing (1) to be derivable from one only of equations (3)*, as, for instance, the first, the form of F, can readily be determined. For, differentiating F,;=0 with respect to ¢ and « separately, we get i d?c , are 0 =F" (4) + F', (v) at I | (a) ae 7 d*c d*e i 7 O= F(z) + Pie) yt Pile) pe dc dx dt ! ! ! / 9 d*a 2 da O= FY ) BA) — BY (@e) Py (@) + Pi) Poe — Bae)? oe the elimination of between which gives and in order that this may coincide with (1), we must have Pia) !?_a® 3 F', (v) oe P(e) FQ) — Fy(,) FP (2) =0. » + « (5) _ The first of these gives us or O=F2)F OPO; . . . - 6 the auxiliary equations for the integration of which by Lagrange’s method are O=do+ ~ ai DEda,. O= di; whence we have ; v+alog.a,= const., ? =="const, F.== Const. % and therefore F , (txve,)={(v+alog.,), 2, th =o 4o, ee k s suppose, where o=v-+a log. «,. But this value of F, must satisfy (5); hence, since * This is, of course, not a necessary supposition. It will obviously be sufficient if (1) can be derived from any combination of the pair of equa- tions constituting the solution and their derivatives. 124 Mr. R. Moon on the Transmission, in one Me) =#'(@), we must have z.e. we must have either ¢!(w) =0, or i (¢) F a ' (x) =0. The first of these would give us ; EG@ave =o ate which is obviously an inadmissible result. Adopting, therefore, the alternative hypothesis, or o() F—$' (2) =0, and integrating this equation by Lagrange’s method, the auxi- liary equations for which in this case are O=det dh OZ seetO eee A, =$4 (ot = t), v, a be But we have already seen that ¢ is of the form shown by the equation p= h{o, #1} 5 and these forms of @ are incompatible except on the supposition. that ¢! (/) =¢!(v) =O—in other words, unless we have I (¢zvaz) = (a). Therefore the first of equations (8) becomes p(w) =0, or, which amounts to the same thing, we shall get a =0, or Phe valor ¢g=0. 20°, Te Direction, of Sound through Air. 125 which, integrated by Lagrange’s method, gives mV oF Sf. rad ban tre O Equations (7) and (8) together constitute a solution of (1) which, making allowance for the difference of the independent variables employed, is identical with that given by Poisson in the Journal de V Ecole Polytechnique for 1807 * | II. The foregoing result, it will be remembered, has been de- rived on the assumption that (1) is derivable from a single one of the equations (3) and its derivatives. I now propose to inves- tigate the forms which F, and F, must assume in order that (1) may be derivable from a combination of equations (8) and their derivatives. The differentiation of F,=0 gives us da da O=F",(?) +1", (v) We + B (a) ee | dc da i O=F' (a ) +E = tls (4,) ek * When the motions are small the result is altogether different ; for in that case (6) becomes O=F", (4,)+al'(@), which, the auxiliaries for its integration being O=detade,, ~0=dzr,. O=dt, F\=$fo, 2, th, where ©=v-taz,. Hence we have F/@)=¢'(@), F/(@)=¢9'(, Fy'(¢,)=tad'(e), F/(@)=$'(2); and substituting these values, (5) becomes 0=¢'(¢)+ap'(z). The Pe iiries for the integration of this last are - V=driadh Ode: Ss POO meee (eal)y. se 5 w+ (BQ) instead of, as in the case of the accurate equation treated of in the text, p=P(utalog. az). Hence, when the motions are small, we may assign to F,, F, the alternative values of @ given by (8a); or, which is the same thing, we may take for our solution gives us which give us V+ de,g=W (x-+at), V—aa,=W(a—at), which is identical with the or dinary solution given in Aga e case. We cannot, however, adopt the same course in the general case when the motions are not Sail. 126 Mr. R. Moon on the Transmission, in one between the first of equations (4) and the EKhminating = last of (9), and between the last of (4) and the first of (9), we get | ¢\ WW ! ! u 1p, ae pF d?u 0=P,(o)P\() Faw) Fy (@,) + Po) Fu a? ale) F(a) 5-9? ae EQ) aa? 0=F",(4,)P (2) PLP) + Pae,JPy(a,) $4 the addition of which equations gives O=F',(e,) F(x) —F', on (v) + F',(v) F', () —F', (2) F', (as). (10). ~ Again, eliminating —— between the first of each of the pairs © a i (4) and (9), and also between the last of each of the same pairs, we get O= Fo (42) Fy (t) —Pa(d) FY, (2) + { Bo (a2) Fy (v) — Fav) FY (@ ea , O=P, (0) PY (2) — F(a) P,) + {P'a(0) Py (22) —Pro(as)P”, @) } Hence, if (1) holds, we shall have, eliminating ie = 5 between the last two equations and (1), 0= F(a) F'() —PLOP (a) + S (Pa) F's(a) — F(a) P(e) (10) Equations (10) and (11) express the conditions to be satisfied by F,, F, 1m order that (1) may be derivable from a combination of the derivatives of (8). Transform these equations by putting Fy (wives) =f(wto os); Fy (xtve,) =fo(wtoo), @,=v-+alog, ea (12) ®,=v—alog.«,? where then we shall bave BY?) a 1 (,) +fy (@o)» Fd (ve) =fe (@,) +So'(@o), Fya)= 5 {fle A(0)}, | File)= = {flo -A@s)}» M0 =H, OA BY@) =fil@). Bye) =f). Substituting these values in (10) and (11), they become Direction, of Sound through Air. 127 0= S Alle) {Alo)—flo)} + Al () {Aled +£e2)}, “ft (4) A (@:) +A! (2) — Zhe (2) {f'(@1) —f'(@2) $5 O= 4 (41) {fe (1) — fl (@2)} + 5 if (2) {f'(o) +f (@,) | — FF {fled filo} — F Fale) Flloy) +l(ed}, o={ Sf (x) +f, (2 Me (@)) )— 4 HH (v7) —fi'(t ) bac (9) {Ke at) +f (é ) bal @)) Ls a) —fy(t © bAl(on) (2); 0=4 2 Ae) a) +fy (et () bflor) (o, +4 SA (2) fr) (ba a) -{ 2K +£0 }ile)-{Z 40-10 bine. The addition and subtraction of the last two equations give us ig a ; 4 O={ fi (2) +A'(? ) ffllen) -{2h@ +f (é ) ballon) (4), 0=4 = Ae) HO bio) —4 ZA -HO ballers(2) he first of which, when arranged according to the partial differ- ential coefficients of fo, Will stand t a Z 0=4 £ Ae) +0 bile) flo) LO Moll; (4) the auxiliary equations for the integration of which by Lagrange’s method are a | a O= { = fie) +fi(t) hao + nh O=dzr— < hie O0=doa,. Of these equations, the first by means of the second may be put under the form O=f) (z)da+fi (dt +f/ (@;)do,, or, since dw,=0, O=fi(e)de +f (tdé +f (@,) da +fi' (2) do. = ite 128 Mr. R. Moon on the Transinission, in one Hence we may ‘Ben for the auxiliary equations, 0=df,, ee eee" Tb Fe es et Sy (15) O=dw, (since by (12) we have log, ¢,= aie. the integrals of which are 7 A= fu{de— ag 20 dt} = Gn @,=U'. Hence, putting m for the equivalent of C’, we get for the value of f, derived from the integration of (14), fo=feth m; Woh, fo=foim; W.} : On the other hand, equation (13) may be written 0={ = Ala) 0) ffl) —“ flaxys(e) +f'(o.\d(0- 16) 1. at eniee, if this last be a substantive equation between the partial differential coefficients of f,, we shall have for its imte- gration, following a method precisely similar to that already adopted, the auxilary equations or, since, —0, O=d;, O=dutac 2 dt, O=da, ; and, as before, we shall arrive at a solution of the form f= 9 {2 cy}. It is clear, however, that if we have io LUNE, (7510), and also Jo— tunct. (2; @)); we must have m= funct. (n, @,) and ©, = funct. (2, w,). * Note that in the integration of (15) we shall have w, constant; so that by means of the equation f,=C we may express @, in terms of x and t and of quantities which are to be regarded as constant. Thus (15) will always be integrable by means of a factor p. Direction, of Sound through Air. 129 Hence, eliminating 2 between these last, we shall get m== funct. (@,@>), s. f,=Jalmo,) = hinel. {@,0,) : therefore one of the first integrals of (1) will be of the form funct (w,@,) =0, whence it is clear that we must have Vea) (one The substitution of this value of » in equations (2) gives us Adis Gee and a *, v= talog.ar+C, or, since v vanishes when ¢,=1, Dieta LORS ce. 8 from which it is clear that the solution obtainable in this manner must be identical with that already deduced. 2. The only way of escape from this conclusion is to suppose that (16) is illusory, considered as a relation between the partial differential coefficients of f,—or, in other words, that we have file) fi =0, fil(o,)=0. The last of these implies that f, is a function of w,, 2, and ¢ only; hence, writing the former pe) ae 28 f(a) —f,1(d) =0, the auxiliary equations for its integration are ane O=ae % di+dz, O=do,, which give us 1380 On the Transmission, in one direction, of Sound throuyh Air. ; @9-@41 A=h{y de % .t+2)} =f, {1; /} Diem OT ——e @ suppose, where A=ae % .f+2. But W2—-O] Lo ere Si (@e) = ope a Si (4) 3 therefore, since f,!(@,) =0, we must have f,'(k)=0, and there- fore Si=hi (@) 3 that is, one of the equations of our solution must be of the form fi(o;)=9, a conclusion the consequences of which have been already pointed out. On the whole, therefore, it appears that the pair of equations v= +a log. a,, 2a oF “ i} constitute the most general solution of which the equations (2) and (1) are susceptible when the motions are not small. But “,== —, where D denotes the density of equilibrium. Hence, as it is clearly impossible that we shall always have the relation between the velocity and density indicated by the equation v p a oe loBe when the motions are not small, it follows that the equations (2) and (1) must be considered defective in their representa- tion of the motion. 6 New Square, Lincoln’s Inn, March 1873. Paging XIII. On some Results of the Earth's Contraction from Cooling, including a discussion of the Origin of Mountains. By James D. Dana. [Continued from p. 54. | 5. Mountain-making slow work. > obtain an adequate idea of the way in which lateral pres- sure has worked, it is necessary to remember that mountain-elevation has taken place after immensely long periods of quiet and gentle oscillations. After the beginning of the Primordial, the first period of disturbance in North America of special note was that at the close of the Lower Silurian, in which the Green Mountains were finished ; and if time from the beginning of the Silurian to the present included only fifty millions of years—which most geologists of the present day would consider much too small an estimate—the interval be- tween the beginning of the Primordial and the uplifts and metamorphism of the Green Mountains was at least ten mil- lions of years. The next epoch of great disturbance in the same Appalachian region was that at the close of the Carboniferous era, in which the Alleghanies were folded up—by the above estimate of the length of time, thirty-five millions of years * after the commencement of the Silurian; so that the Appala- chians were at least thirty-five millions of years in making, the preparatory subsidence having begun as early as the beginning of the Silurian. The next on the Atlantic border was that of the displacements of the Connecticut-river sandstone, and the accompanying igneous ejections, which occurred before the Cretaceous era—at least seven millions of years, on the above estimate of the length of time, after the Appalachian revolution. Thus the lateral pressure resulting from the earth’s contraction required an exceedingly long era in order to accumulate force sufficiently to produce a general yielding and plication or dis- placement of the beds, and start off a new range of prominent elevations over the earth’s crust. 6. System in the mountain-making movements on the opposite borders of the North American Continent and over the Oceanic areas. A summary of the general system of movements and moun- tain-making on the opposite borders of the continent, and over the oceanic areas, will, I think, render it apparent that the views here sustained have a broad foundation. I omit any special reference to the Archean elevations, and * These estimates of the relative lengths of ages are based on the maxi- mum thickness of their rocks—very uncertain data, but the best we have. 132 Prof. J. D. Dana on some Results of also the local disturbances in the Primordial of Newfoundland, as well as the facts relating to minor changes of level. a. Mountain-making on the Atlantic border. 1. At the close of the Lower Silurian, or a little earlier, a culmination of the great Appalachian geosynelinal resulted in displacements, plications, and metamorphism, and the making of a synclinorium along the Gyeen-Mountain region, these mountains (some summits at present over 4000 feet high above the sea) being the result. The depth to which the region subsided during the Lower Silurian era, and the thickness of the accumulations, are not ascertained ; probably the extent was not less than 20,000 feet. 2. Simultaneously a permanent anticlinorium was made over the Cincinnati region, from Lake Erie into Tennessee, parallel to the Alleghanies of Virginia, 250 miles to the north-west. _ 8. The Acadian region (embracing western Newfoundland, St.-Lawrence Bay, the Bay of Fundy, and part of Nova Scotia and New Brunswick adjoining, and probably the sea south-west between St. George’s Bank and the coast of Maine, with also an area in Rhode Island) was the course of a great geosynclinal, or a series of them, parallel in general direction to that of the Appalachian region; it continued in progress, but with mountain-making interruptions and some shift of position to the eastward, from the Silurian to the close of the. Jurassic. At the close of the Lower Silurian no general disturbances occurred in this Acadian region, so far as is known. In the Anticosti seas, or northern part of St. Lawrence Bay, limestones, as Logan states, were uninterruptedly in formation from the beginning of the Hudson period of the Lower Silurian to the middle of the Upper Silurian, showing that the Acadian geo- synclinal was then in regular progress.. It so continued until the close of the Devonian, when disturbances, plication, and metamorphism took place in eastern Canada, Nova Scotia, and the bordering region of New Brunswick, and the most exten- sive of Acadian Paleozoic synclinoria resulted, according to the observations of Dr. Dawson and others. 4. The close of the Carboniferous age was an epoch of moun- tain-making in the Alleghany region—the Alleghanies from New York to Alabama having been then made, as already explained. 5. At the same time there were disturbances and synclinorian plications in the Acadian region. During the Carboniferous era, according to Logan and Dawson, 16,000 feet of rock had in some parts accumulated; and therefore a geosynclinal of 16,000 feet formed—the rocks in their many coal-beds and root- the Earth's Contraction from Cooling. 138 bearing layers bearing evidence, to the last, of oscillations in- volving an intermittent but progressing subsidence. The syn- clinorium, the resultant, was much less marked than that at the close of the Devonian. 6. Durmg the Paleozoic, along the sea-border, a more or less perfect barrier was made by a geanticlinal uplift (anticlinorium), which was a counterpart to the geosynclinal of the Appalachian region*, 7. The middle or close of the Jurassic period was an epoch of displacements, aud the making of a series of imperfect syn- clinoria along the Triassico-Jurassic areas from Nova Scotia to southern North Carolina, as sufficiently described. 8. During the era of the Connecticut-river sandstone (Tri- assico-Jurassic) a nearly complete sea-border anticlinorium ex- isted, a counterpart to the progressing geosynclinal. Its exist- ence is proved by the absence of all marine fossils from the beds*, — 9. The era closing the Cretaceous, and that of the Tertiary, witnessed but small uplifting and some local displacements of the rocks of these eras on the Atlantic border. The principal movement was geanticlinal; and it involved probably the whole Alleghany region. 10. In the Quaternary there were extended movements of geanticlinal and geosynclinal character, which need not be here described. b. Mountain-making after Archean time on the Pacific border, within the territory of the United States. 1. At the close of the Lower Silurian, none yet known. 2. At the close of the Devonian, none yet knowny. 3. At the close of the Carboniferous age, or the Paleozoic, * In my ‘ Manual of Geology’ the probable existence of such a barrier is recognized, in connexion with the remarks on the geography of the Trenton period in America; and it is particularly dwelt upon and illustrated by a map in the chapter on the Triassic; but it is not spoken of as connected in origin with the geosynclinal that was in progress to the west of it. Evi- dence with regard to this anticlinorium is given in the following part of this memoir. ' { Although no case of unconformability between the Carboniferous and the underlymg Paleozoic is yet distinctly made out in the Sierra Nevada, the Great Basin, or the Wahsatch, such occur further south, according to Mr. J. W. Powell, in the vicinity of the Grand Caiton of the Colorado (see Amer. Journ. Sci. 3rd ser. vol. v. p. 457). The fact that Whitney has found no rocks lower than Carboniferous in the Sierra may be a conse- quence of the same unconformability beneath these mountains. But in the region of the Caiion, the Carboniferous, Triassic, Jurassic, Cretaceous, and Tertiary beds are all conformable. ‘The epochs of mountain-making over the Pacific slope south of the latitudes of the Wahsatch range, and also of that to the north, were different from those within these latitudes. 134: Prof. J. D. Dana on some Results of none yet known; and if none really occurred, then the con- tracting globe at that time, as far as U. S. North America is concerned, must have expended its energies (which it had been gathering during the Paleozoic) in making the Alleghanies, and in some minor plications along the Acadian region. The “ Great Basin,” between the Sierra Nevada on its western border and the Wahsatch range on its eastern (lying along the meridian just east of the Great Salt Lake), contains a number of short ridges parallel to these lofty border ranges, some of which are quite high* ; and they consist, according to King, “ of folds of the infra-Jurassic rocks ;”’ and “it 1s common to find no rocks higher than the Carboniferous,” owing, it is stated, to the erosion that has taken place. It is not clear that part, at least, of the Great Basin plications may not have taken place before the Jurassic era. If not, then the movements must have been in some way involved with those of the Sierra and Wahsatch regions}. 4, At the close of the Jurassic two great geosynclinals, whicn had been in progress through the Paleozoic and until this epoch in the Mesozoic, culmimated each in the making of a lofty synclinorium :—one the Sierra Nevada, some of whose summits are over 14,000 feet high; the other the high Wah- satch, a parallel north and south range. Whitney has proved that the Carboniferous and Jurassic rocks are comformable in the Sierra-Nevada range, and that the close of the Jurassic was the epoch of its origin; but direct proof is not yet found that the Devonian and Silurian forma- * An admirable chart, giving in detail the topography of this whole region and including the Wahsatch, has been prepared by Mr. James T. Gardner, after careful surveys by himself, topographical surveyor of the Exploration of the Fortieth Parallel under Clarence King, and is now ready for the engraver. Mr. King has published thus far only brief chap ters on the geological results of his survey in the volume of J. T. Hague on Mining Industry, vol. ii. He has ready for publication vols. 1. and ii., on Systematic and Descriptive Geology. The Botanical Report of the Survey, vol. v., has been issued; but vol. iv., on Zoology and Palzonto- logy, remains to be completed. . + Mr. James T. Gardner, in a letter of May 8th, informs me that in his opinion all the more important mountain-ranges of the Great Basin (in Nevada) are included ina chain trending about N. 40° E., the whole having a breadth across the trend of 120 miles. Austin, in Nevada, lies near the centre line of the chain. To the west of this elevated region is the great depression where the rivers of Nevada evaporate in Carson, Humboldt, Pyramid, Mud, and other lakes; and to the east isthe great depressed area of Salt Lake. On this view, if these mountains were made at the close of the Jurassic, there were formed at this epoch three lofty synclinoria (the Sierra, the Humboldt, and the Wahsatch) on the western-border, central, and eastern-border chains of the Great Basin. The precise determination of the epoch of origin of the Humboldt chain is therefore of much ims portance. the Earth's Contraction from Cooling. 135 tions are included. The granite axis of the chain probably indicates, as LeConte has suggested, the region of maximum disturbance and metamorphism. | The Wahsatch contains, according to Clarence King, forma- tions of all the ages from the Lower Silurian to the Jurassic; and the whole are throughout conformable; and a great thick- ness of crystalline rocks exists beneath, supposed to be Archean, which he states are conformable also. The plications and mountain-making took place, as King states, contemporaneously with the same in the case of the Sierra, before the Cretaceous era, the Cretaceous beds lying on the Jurassic unconformably. These two synclinoria are 400 iniles apart. The preparatory geosynclinal of the Wahsatch, and probably that of the Sierra, took for its completion, supposing it to have begun with the opening Silurian, a period at least a fifth longer than the whole Paleozoic. : 5. At the close of the Cretaceous another pair of geosyn- clinals, parallel with the coast, but geosynclinals of only Cre- taceous origin, culminated in synclinoria. One of the Cretaceous geosynclinals was in progress east of the Wahsatch, along the whole summit-region of the Rocky Mountains in the United States, Directly east of the Wah- satch, according to King, the beds are 9000 feet thick, or more ; and, as Hayden states, they have a great thickness in the La- ramie Plains, and little less over the upper Missouri region, so that the downward movement was in some parts a profound one, and affected a very wide extent of country. Hayden and King make this disturbance to have taken place after part, or all, of the Eocene period had passed, while Prof. Marsh holds that it occurred at the close of the Cretaceous period*. * Clarence King has very briefly described the Wahsatch region, as well as the country to the west, in the third volume (4to, 1870) of his United- States Geological Exploration of the 40th parallel; and on page 454 he says :—‘‘ Subsequent to the laying down of the old cretaceous system, and of those conformable freshwater beds which close the coal-bearing period, another era of mountain-uplifts occurred, folding the coal series | Creta- ceous and Lower Tertiary] into broad undulating ridges having a general trend north-east.” He then observes that freshwater Tertiary beds of sand and clay, “an immense accumulation,” were laid down unconform- ably over this upturned Cretaceous, and, after the Miocene era, were sub- jected to “ orographic ”’ disturbances and “tilted to an angle of 15° to 20°, or thrown into broad and gentle undulations wherever they lie in the neighbourhood of the older ranges, such as the Wabsatch and Uintah.” These disturbances were confined to within fifteen miles of the Wahsatch. The period in which they occurred witnessed also great outflows of trachytic rocks in this and other parts of the Rocky-Mountain region.’ Mr. King adds, on page 455, that there is no question as to the identity of the beds that overlie unconformably the Cretaceous folds along the eastern flank of the Wahsatch with the horizontal Tertiary deposits of the Green-River 136 Prof. J. D. Dana on some Results of The other geosynclinal belt of the Cretaceous era was to the west of the Sierra Nevada, as described by Whitney. ‘This coast geosynclinal ended in extensive displacements and plications, much metamorphism, and a high synclinorium. 6. The intermediate region, the Great Basin, which had been widened at the close of the Jurassic by the annexation of the plicated and consolidated Sierra and Wahsatch, was the era of a geanticlinal, or at least of absence of subsidence; for King says no Cretaceous rocks occur over it. 7. With the close of the Cretaceous, or when the Cretaceous synclinorian movements of the sea-coast and mountains were ending, a geanticlinal movement of the whole Rocky-Moun- tain region began, which put it above the sea-level, where it has sinceremained. This upward movement continued through the Tertiary. 8. During the Tertiary age, until the close, probably of the Miocene Tertiary, another pair of parallel eeosynelinals, but geosynclinals of Tertiary formation, were in progress. ‘The Cretaceous synclinoria had given still greater breadth and sta- bility to the relatively stable region between them; and one of these new troughs is hence further east on the mountain sis and the other further west on the coast side. In the coast geosynclinal, marine tertiary beds were accumu- lated to a thickness of 4000 to 5000 feet; and then followed the epoch of disturbance ending in another coast synclinorium, a coast range of mountains, in some places metamorphic, and having ridges, many of which are at present 2000 feet or more in height above the sea, and some in the Santa-Cruz range, according to Whitney, over 3500 feet. basin, and that over this basin between‘the Green River and the Wahsatch no single instance of conformity occurs between the coal-beds and the over- lying horizontal freshwater strata. As stated above, he makes the epoch of Cretaceous uplifting to have followed, not the Cretaceous period, but the earliest period of the Tertiary, Eocene beds being, in his view, included with the Cretaceous in the folds referred to. Dr. Hayden has investigated with much detail the Green-River basin and the region east of it, and years since announced that the Lower Ter- tiary beds in some parts of the Rocky-Mountain region were tilted at a high angle. He has held that all the coal-bearing strata were Lower Tertiary, but now agrees with the view expressed by King, and first suggested by . Meek, that part are Cretaceous, while another part are Lower Tertiary, and considers the later Tertiary beds (which lie unconformably on the beds below in the regions of disturbance) Miocene and Pliocene. He states that the thickness of the Cretaceous formation in the Laramie plains is 8000 to 10,000 feet. He observes in a recent letter. to the writer that the coal- bearing strata and Cretaceous are never ;unconformable, but instead are often folded together, and sometimes stand at a high angle, even vertical in many places—as in the Laramie Plains south of Fort Sanders, along the the Earth's Contraction from Cooling. 137 The other is to the east of the Cretaceous axis in the summit region of the Rocky-Mountain chain. A great thickness of freshwater beds was made in the Green-River region and some other places about the Rocky-Mountain summits, and thinner deposits to the eastward. he thickness, in connexion with evidences of shallow-water origin, indicates a progressing geo- synclinal, although the ocean gained no entrance to it. The downward bending ended probably just after the Miocene period, without general displacements; but there were tiltings along the more western border of the Tertiary in the vicinity of the Wahsatch and other mountains. (See note on page 135.) 9. Since the Miocene era, and on through much of the Quaternary, there have been vast fissure-eruptions over the western Rocky-Mountain slopes. They had great extent, espe- cially in the Snake-River region, where the successive outflows made a stratum 700 to 1000 feet thick, over an area 300 miles in breadth. ‘There are other similar regions, but of less area. It is thus seen that along the Pacific side of the continent the crust, under the action of lateral pressure, first bent down- ward profoundly, and then yielded and suffered fracture and plications, directly along a belt, parallel with the coast, either side of the Great Basin (and perhaps over this basin to some extent), the two great lines 400 miles apart. ‘The plicated re- gions thus made, having become firm by the continued pressure and the engendered heat and resultant solidification, the crust next bent, and then yielded, in a similar way, along an axis outside of the former regions of disturbance, the two axes over 600 miles apart; and again all was mended in the same way. Then it bent a third time, just outside of the last range, on each side of the same great area, the lines over 700 miles apart ; and then over the western of the two ranges the beds were displaced, Big-Horn region between Long’s Peak and Pike’s Peak, near Denver in Colorado, &e. Near the mouth of the Big Horn, the Chetish or Wolf Mountains, consist of these upturned strata, and have a height of 1500 to 2000 feet above the Yellowstone. He found the later Tertiary beds some- times tilted at a small angle, never over 10°. The discovery of Dinosaurian remains in some of the coal-beds, announced by Marsh and Cope, and of Inocerami, as ascertained by Meek, is one part of the evidence on which the lower parts of the coal-beds are determined to be Cretaceous. Besides this, there is the fact that the supposed Miocene of the Green-River basin contains remains of mammals that are decidedly Eocene in character; and if these are Eocene, then the coal-beds are some- thing older. Professor Marsh is very strongly of the opinion that all the coal-beds are Cretaceous. On the other side, Lesquereux states that the evidence from fossil plants is totally opposed to making any of the coal-strata Cretaceous. The method of mountain-making, and the principle involved, are the same whatever be the decision as to the exact epoch of the Cretaceous plication. Phil, Mag. 8. 4, Vol, 46, No. 304. dug. 1873. L 138 Prof. J. D. Dana on some Results of solidified, and left in high ridges, but over the eastern the final disturbances were local and slight. There were hence two parallel series, contemporaneous in steps of progress, situated on opposite borders of the Great Basin, a coast series and a mountain series, each having its highest member toward the basim—the coast series the grandest in its three parts and leaving evidences of the profoundest dis- turbance and the greatest amount of metamorphism. The Wahsatch range is nearly as high as the Sierra; but probably a fourth of its height is due to the final elevation of the Rocky- Mountain region. The last bendings were more local than the preceding, be- cause the crust had become stiffened by its plicated and solidified and partly crystallized coatings, as well as by thickening beneath; and, therefore, while the Tertiary movements were in progress the part of the force not expended in producing them carried forward an upward bend, or geanticlinal, of the vast Rocky- Mountain region as a whole. For the same reason profound breakings took place where bending was not possible, and thereby immense floods of liquid rock were poured out over the surface. (Most of the great mountains of the globe were lifted about this time—that is, in the course of the Tertiary era—and many of the great voleanoes were made.) There were irregularities, or exceptional courses, in connexion with this system of movements and their effects. But these show only that in the same area the lateral pressure at work was not alike either in amount or in direction in different lati- tudes, nor was the resistance before it the same. The results correspond with the well-understood effects of lateral pressure. Suppose a long beam, having an even texture, except that a portion toward the middle (say a sixth of the whole length) is stouter than the rest, to be subjected at its extremities to direct pressure. The first yielding ‘and fracture would take place toward the stouter portion on either side. If this break were mended by splicing and’ cementing until firmer than before, the next region of yielding would be just outside of the former. In brief, “the fracturing would be in each case near the stouter portion of the beam. Moreover the extent of the yielding and fracture on each side would have some relation to the amount of pressure against that side. Just so has it been with the earth’s crust under the action of lateral pressure. The facts further illustrate the truth, before announced, that the force from the ocean side had in some way the advantage, and in fact was the greater. But the full difference is not in- dicated by the difference in the results of disturbance, since the shoving force on the side of greatest pressure would not be the Earth's Contraction from Cooling. 139 limited in its action to its own side, unless the intermediate stouter region were wholly immovable. c. Movements over Oceanie areas. The history of the changes of level over the oceanic areas is necessarily a meagre branch of geological science. There are, however, some great truths to be gathered which are of pro- founder import than is generally acknowledged. They show that the oceanic crust has sometimes acted in the capacity of a single area of depression, although of so immense extent. I allude briefly here to only two of the facts, referring the reader to my former articles for a fuller discussion of the subject :— First, the remarkable one that nearly all the ranges of islands over the Pacific ocean, aud even the longer diameters of the particular islands, lie nearly parallel with the great mountain- ranges of the Pacific coast of North America. There is a dyna- mical announcement in this arrangement—which is partly re- cognized, when we refer it, as I have proposed, to the existence of directions of easiest fracture in the very nature of the infra- Archean crust, and regard the courses of these feature-lines of the oceans and continents as having reference to one of these directions. But, besides this, there is a declaration with regard to the direction of the pressure that acted against the continents, and reacted over the oceanic areas. The other fact is that of the coral-island subsidence, already referred to, which affected the tropical ocean for its whole breadth, or more than a quarter of the circumference of the clobe—sinking the sea-bottom at least 3000 feet over a large part of the area, and probably over its axial portions two or three times this amount*. The oceanic basin was evidently one basin in its movement; but the areas of less and greater subsidence, of parallel N.W. by W. trend, so alternate along the southern border of the region of subsidence that we may conclude there were great parallel waves, made by lateral pressure in the crust, as I have elsewhere explained —that is, geosynclinals and gean- ticlinals, such as are the only possible conditions of the crust under the lateral pressure of the contraction. Now this great oceanic subsidence, involving the breadth of the ocean, if begun in the Tertiary era, as is probable, was going forward at the very time when the Rocky Mountains, and other great moun- tains of the globe, were in progress of elevation, as if these were counterpart movements in the earth’s surface; and it continued « Author's Rep. Geol. Wilkes U.S. Expl. Exped. 4to, 1849, p. 399 ; and ‘ Corals and Coral Islands,’ 8vo, 1872, p. 329. + Rep. Geol, Expl. Exped. p. 399. ‘ Corals and Coral Islands,’ p. 328, L2 140 Mr. H. A. Rowland on Magnetic Permeability, on during the Glacial era, when the continental elevations appear. to have reached their highest limit. We gather from these facts how it is that a Serer! submer- Bene, or an emenee mle, gh chanaptenize cotemporaneously s, for example, in the subdieieniteeue Carboniferous, a fii periods, du- ring which the rocks show that there was a eeneral parallelism in the movements. Ifa eeanticlinal were in progress over the middle of the Atlantic crust as a result of the lateral thrust in the continental and oceanic crusts there might also be a reverse movement or general sinking along the continental borders, as well as a rise of water about the continents from the diminution in the ocean’s depth; and when the oceanic geanticlinal flat- tened out again through subsidence, the subsiding crust would naturally produce a reverse movement along one or both con- tinental borders. From the various considerations here presented, derived from both the continental and cceanic areas, it is apparent that the earth has exhibited its oneness of individuality in nothing more fundamentally and completely than in the heavings of its con- tracting crust. The subjects of metamorphism, the earth’s interior, igneous eruptions and volcanoes remain for discussion. In addition I propose to consider the steps in the origination of the conti- nental plateaux and oceanic basins, and also to present some facts bearing on the general nature of the infra-Archzean crust—that is, the part below the earth’s superficial coatings. [To be continued. | XIV. On Magnetic Permeabihity*, and the Maximum of Mag- netism of Iron, Steel, and Nickel. By Henry A. Rowxianp, Instructor in Phy ysics in the Rensselaer Pol ylechnic Institute, Troy, N.Y.+ [With Two Plates. ] Hh ieee than three years ago I commenced the series of ex- periments the results of which [ now publish for the first time. Many of the facts which I now give were obtained then; but, for satisfactory reasons, they were not published at that time. The investigations were commenced with a view to determine the distribution of magnetism on iron bars and steel * The word “permeability *? has been proposed by Thomson, and has the same meaning as ** conductivity ’’ as used by Faraday (‘Papers on Elec- tricity and Magnetism,’ Thomson, p.484; Maxwell’s ‘ Electricity and Mag- netism,’ vol. u. p. 51). + Communicated by Professor J, Clerk Maxwell, M,A., F.R.S, and the Maximum of Magnetism of Tron; Steel, and Nickel. 141 magnets ; but it was soon found that little could be done with- out new experiments on the magnetic permeability of substances. Few observations have been made as yet for determining the magnetic permeability of iron, and none, I believe, of nickel and cobalt, in absolute measure. The subject is important, because in all theories of induced magnetism a quantity is introduced depending upon the magnetic properties of the substance, and without a knowledge of which the problem is of little but theo- retical interest ; this quantity has always been treated as a con- stant, although the experiments on the maximum of magnetism show that it is a variable. However, the form of the function has never been determined, except so far as we may deduce it from the equation of Miiller, i= 220d? 2 tan —~— ae vo which, as will be shown, leads to wrong results. The quantities used by different persons are as follows :-— x, Neumann’s coefficient, or magnetic susceptibility. (Thom- son). k, Poisson’s coefficient. 2, coefficient of magnetization (Maxwell), or magnetic per- meability (Thomson). X, introduced for convenience in the following paper. The relations of these quantities are given by the following equations :— SE iii, P= Lay Aor ~ Aare +8 eae ~ V+ 89 op lei Be She Aeaer ~ "ar ~ 4r(1—k) 167? 1+2kh wi eS cc is 2 The first determination of the value of any of these quantities was made by Thalén. But more important experiments have been made by Weber, Von Quintus Icilius, and more recently by M. Reicke and Dr. A. Stoletow*. The first three of these in their experiments used long cylindrical rods, or ellipsoids of great length; the last, who has made by far the most important experiments on this subject, has used an iron ring. ‘The method of the ring was first used by Dr. Stoletow in September 1871; but more than eight months before that, in January 1871, [had used the same method, but with different apparatus, to measure the magnetism. He plots a a curve showing the va- — *® Phil. Mag. January 1873, 142 Mr. H. A. Rowland on Magnetic Permeability, riation of x; but he plots it with reference to R as abscissa instead of R. x, and thus fails to determine the law. His method of experiment is much more complicated than mine, so that he could only obtain results for one ring; while by my method T have experimented on about a dozen rings and on numerous bars, so that I believe I have been enabled to find the true form of the function according to which yp varies with the magnetism of the bar or the magnetizing-force. Many experimeuts have been made on the magnetism of iron without giving the results in absolute measure. Among these are the experiments of Miller, Joule, Lenz and Jacobi, Dub, and others. The experiments haye been made by the attraction of electromagnets, by the deflection of a compass-needle, or, in one case, by measuring the induced current in a helix extend- ing the whole length of the bar. By the last two methods the change in the distribution of magnetism over. the bar when the magnetism of the bar varies is disregarded, if indeed it was thought of at all: even in a recent memoir of M. Cazin* we have the statement made that the position of the poles is inde- pendent of the strength of the current. He does not give the experiment from which he deduces this result. Now it is very easy to show, from the formula of Green for the distribution of magnetism on a bar-magnet combined with the known variation of x, that this can only be true for short and thick bars ; and it has also been remarked by Thomson that this should be the caset. An experiment made in 1870 places this beyond doubt. A small iron wire (No. 16), 8 inches long, was wound with two layers of fine insulated wire; a small hard steel magnet + inch long suspended. by a fibre of silk was rendered entirely astatic by a large magnet placed about 2 feet distant ; the wire electro- magnet was then placed near it, so that the needle hung 14 inch from it and about 2 inches back from the end. On now exciting the magnet with a weak current, the needle took up a certain definite position, indicating the direction of the line of force at that point. When the current was very much increased, the needle instantly moved into a position more nearly parallel to the magnet, thus showing that the magnetism was now distri- buted more nearly at the ends than before. This shows that nearly all the experiments hitherto made on bar-magnets contain an error; but, owing to its small amount, we can accept the re- sults as approximately true. I believe mine are the first experiments hitherto made on this subject in which the results are expressed and the reasoning carried out in the language of Faraday’s theory of lines of * Annales de Chimie et de Physique, Feb. 1873, p. 171. + Papers on Electricity and Magnetism, p. 512. and the Maximum of Magnetism of Iron, Steel, and Nickel. 148 magnetic force; and the utility of this method of thinking is shown in the method of experimenting adopted for measuring magnetism in absolute measure, for which I claim that it is the simplest and most accurate of any yet devised. Whether Faraday’s theory is correct or not, it is well known that its use will give correct results; at the present time the tendency of the most advanced thought is ¢oward the theory* ; and indeed it has been pointed out by Sir William Thomson that it follows, from dynamical reasoning upon the magnetic rotation of the plane of polarization of lizht, that the medium in which this takes place must itself be in rotation, the axis of rotation being in the direction of the lines of ee Some substances ee of necessity be more capable of assuming this rotary motion than others ; and hence arises the notion of magnetic “conductivity” and ‘ permeability.” Thomson has pointed out several analogies which may be used in calculating the distribution and direction of the lines of force under various circumstances. He has shown that the mathe- matical treatment of magnetism is the same as that of the flow of heat in a solid, as the static induction of electricity, and as the flow of a frictionless incompressible liquid through a porous solid. It is evident that to these analogies we may add that of the conduction of electricityt. We readily see that the reason of the treatment being the same in each ease is that the elemen- tary law of each is similar to Ohm’s law. Mr. Webb§ has shown that this law is useful in electrostatics; and I hope, in a sequel to this paper, to apply it to the distribution of mag- netism: I give two equations derived in this way further on. The absolute units to which I have reduced my results are those in whieh the metre, gramme, and second are the funda- mental units. The unit of magnetizing-force of helix I have taken as that of one turn of wire carryig the unit current per metre of length of helix, and is 47 times the unit magnetic field. This is convenient in practice, and also because in the mathematical solution of problems in electrodynamics the mag- netizing-force of a solenoid naturally comes out in this unit. The magnetizing-force of any helix is reduced to this unit by multiplying the strength of current in absolute units by the number of coils in the helix per metre of length. These remarks * “On Action at a Distance,”” Maxwell, ‘ Nature,’ Feb. 27 and March 6 and 13, 1873. + Thomson’s ‘Papers on Electricity and Magnetism,’ p. 419, note; and Maxwell’s ‘ Treatise on Ee eey and Magnetism,’ vol. 1. chap. xxi. + Maxwell’s ‘Treatise on Electricity and Magnetism,’ arts. 243, 244, and 245. § “Application of Ohm’s Law to Problems in Bi pe enti Phil. Mag. S. 4. vol. xxxv. p. 325 (1868). 144 *, H. A. Rowland on Magnetic Permeability, apply itp to endless sclenoids, and to those which are very lone compared with their diameter. The unit of number of Imes of force I have taken as the number in one square metre of a unit field measured perpendicular to their direction. As my data for reducing my results to these units, [ have taken the hori- zontal force of the earth’s magnetism at Troy as 1°641, and the total force as 6°27. The total force, which will most seriously affect my results, is well known to be nearly constant at any one place for long periods of time. From the analogy of a magnet to a voltaic battery immersed ‘in water I have obtained the following, on the assumption that is constant, and that the resistance to the lines of force passing out into the medium is the same at every point of the bar. Let R = resistance to lines of force of one metre of length of bar. R! = resistance of medium along 1 metre of length of bar. Q! = lines of force in bar at any point. Q.= lines of force passing from bar along small dis- tance I. e = base of Napierian system of logarithms. 2 = distance from one end of helix. 6 = total length of helix. s' = resistance at end of helix of the rest of bar and medium. M= magnetizing-force of helix. We then obtain NTs apelin ox "Oe SRR AS 1) AS See (1) fond M M 1-A LACE Bes ae r re r(b—zx ‘ (AP 1)(/ RRS) > mR Ae © ae in which ae 5 k! aud ye / RR! + 3! / RRs!” for near the eentre of an infinitely long bar, where +0 and * Formule giving the same distribution as this have been obtained by Biot and also by Green. See Biot’s Trailé de Physique, vol. iv. p. 669, and ‘ Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism,’ by Green, 17th section. and the Maximum of Magnetism of Iron, Steel, and Nickel. 143 a. 0) Oe When the section of the ring is thin, equation (6) becomes the same as equation (7), and either of them will give Q! N= 47 p= GRA AO os oct a (8) which is the same as equation (5). In all the rings used the last parenthesis of (6) is so nearly unity that the difference has in most cases been neglected, the slightest change in the quality of the iron producing many times more effect on the permeability than this. Whenever the difference amounted to more than 54, it was not rejected. The apparatus used to measure Q’ was based upon the fact discovered by Faraday, that the current induced in a closed cir- cuit is proportional to the number of lines of force cut by the wire, and that the deflection of the galvanometer-needle is also, for small deflections, proportional to that number. In the ex- periments of 1870-71 an ordinary astatic galvanometer was used ; but in those made this year a galvanometer was specially constructed for the purpose. It was on the principle of Thom- son’s reflecting instrument, but was modified to suit the case by increasing the size of the mirror to 2 of an inch, by adding an astatic needle just above the coil wethout adding another coil, by loading the needle to make it vibrate slowly, and, lastly, by looking at the reflected image of the scale through a telescope instead of observing the reflection of a lamp on the scale. The galvano- ‘meter rested on a firm bracket attached to the wall of the labo- ratory near its foundation. In most of the experiments the needle made about five single vibrations per minute. The astatic needle was added to prevent any external magnetic force from deflecting the needle; and directive force was given by the magnet above. Hach division of the scale was °075 inch long; and the extremities of the scale were reached by a-deflection of ‘7° in the needle from 0. The scale was bent to a radius of 4 feet, and was 3 feet from the instrument. At first a correction was made for the resistance of the air &c.; but it was afterwards found by experiment that the correction was very exactly pro- portional to the deflection, and hence could be dispensed with. This instrument gave almost perfect satisfaction ; and its accu- racy will. be shown presently. | The tangent-galvanometer was also a very fine instrument, and was constructed expressly for this series of experiments. The needle was 1:1 inch long, of hardened steel; and its deflec- and the Maximum of Magnetism of Iron, Steel, and Nickel. 147 tions were read ona circle graduated to half degrees, and 5 inches in diameter. The average diameter of the ring was 164 inches nearly, and was wound with several coils; so that the sensibility could be increased or diminished at pleasure, and so give the instrument a very wide range. The value of each coil in producing deflection was experimentally determined to within at least 4 of 1 per cent. by a method which I shall soon publish. The numbers to multiply the tangent of the deflec- tion by, in order to reduce the current to absolute measure, were as follows :— Number of coils. Multiplier. Pisigirys, Dy wee 805377 SW en, LAO). nr OP8OO Sirre hee iay! 40) C0607 Bei wentiine: Oy YarOo2Ous B6b§ pics 4 Ow! .ncO01I48 By this instrument I had the means of measuring currents which varied in strength several hundred times with the same accuracy for a large as for a small current. For greater accu- racy a correction was applied according to the formula of Blan- chet and De la Prevostaye for the length of the needle, the po- sition of the poles being estimated ; this correction in the de- flections used was always less than 6 per cent. To eliminate any error in the position of the zero-point, two readings were always taken with the currents in opposite directions, each one being estimated with considerable accuracy to +5 of a degree. __ The experiments were carried on in the assay laboratory of the Institute, which was not being used at that time; and pre- cautions were taken that the different parts of the apparatus should not interfere with each other. The disposition of the apparatus is represented in Plate II. The current from the battery A, of from two to six large Chester’s “electropoion ” cells No, 2, joimed according to cir- cumstances, passed to the commutator B, thence to the tangent- galvanometer C, thence to another commutator D, thence around the magnet E (in this case a ring), and then back through the resistance-coils K to the battery. To measure the magnetism excited in H,a small coil of wire F was placed around it *, which connected with the galvanometer H, so that, when the magnet- ism was reversed by the commutator D, the current induced in the coil F, due to twice cutting the lines of force of the ring, produced a sudden swing of the needle of H. As the needle swung very freely and would not of itself come to rest in ten or fifteen minutes, the little apparatus I was added: this consisted of * Tfa bar was used, this coil was placed at its centre. 148 Mr. H. A. Rowland on Magnetic Permeability, a small horseshoe magnet, on one branch of which was a coil of wire; and by sliding this back and forth, induced currents could be sent through the wire, which, when properly timed, soon brought the needle to rest. This arrangement was very efficient ; and without it this form of galvanometer could hardly have been used. To compare the magnetism of the ring with the known magnetism of the earth, and thus reduce it to ab- solute measure, a ring G supported upon a horizontal surface was included in the circuit; when this was suddenly turned over, it produced an induced current, due to twice cutting the lines of magnetic force which pass through the ring from the earth’s magnetism. The induced current in the case of either coil, F or G, is proportional to the number of the lines of force cut by the coils * and to the number of wires in the coil, which latter is self evident, but may be deduced from the law of Gau- gaint. It is evident, then, that if cis the deflection from coil G, and / that from helix F', the number of lines of force passing through the magnet EH, expressed in the unit we have chosen, will be Q'=2n! (6-27 sin 74° 50mRE- Ss . . (9) where 7! is the number of coils in the ring G, the number in the helix F, R the radius of G, 6°27 the total magnetism of the earth, and 74° 50! the dip. The quantity 2n! (6:27sin 74° 50')aR? is constant for the coil, and had the value 14°51. This is the number of square metres of a unit field which, when cut once by a wire from the galvanometer, would produce the same de- flection as the coil when turned over. The experiments being made by reversing the magnetism of the bars, a rough experiment was made to see whether they had time to change in half a single vibration of the needle; it was found that this varied from sensibly 0 to nearly 1 second, so that there was ample time. It was also proved that the sudden im- pulse given to the needle by the change of current produced the same deflection as when the change was more gradual, which has also been remarked by Faraday, though he did not use such sudden induced currents. As a test of the method, the hori- zontal force of the earth’s magnetism was determined by means of a vertical coil; it was found to be 1°634, while the true quan- tity is 1°641. It is sometimes assumed that some of the action in a case like the present is due to the direct induction of the helix around the magnet on the coil F. I think that this is not correct; for when * Faraday’s Experimental Researches, vol. iii. series 29. Tt Daguin’s Tratté de Physique, vol. i. p. 691. and the Maximum of Magnetism of Iron, Steel, and Nickel. 149 the helix is of fine wire closely surrounding the bar or ring, all the lines of force which affect F must pass through the bar, and so no correction should be made. However, the correction is so small that it will hardly affect the result. If it were to be made, = (equation 5) should be diminished by 47M; but, for the above reasons, it has not been subtracted... As a test of the whole arrangement, I have obtained the number of lines of force in a very long solenoid: the mean of two solenoids gave me Q'=12-67M (rR); while from theory we obtain, by equation (7) (u=1), Q’=12-57M (aR), which is within the limits of error in measuring the diameter of the tubes &c. All the rings and bars with which I have experimented have had a circular section. In selecting the iron, care must be used to obtain a homogeneous bar; in the case of a ring I believe it is better to have it welded than forged solid; it should then be well annealed, and afterwards have the outside taken off all round to about + of an inch deep ina lathe. This is necessary, because the iron is “burnt ” toa considerable depth by heating even for a moment to a red heat, and a sort of tail appears on the curve showing the permeability, as seen on plotting Table III. To get the normal curve of permeability, the ring must only be used once; and then no more current must be allowed to pass through the helix than that with which we are experimenting at the time. If by accident a stronger current passes, per- manent magnetism is given to the ring, which entirely changes the first part of the curve, as seen on comparing Table I. with Table II. The areas of the bars and rings were always ob- tained by measuring their length or diameter across, and then calculating the area from the loss of weight in water. The following is a list of a few of the rings and bars used, the dimensions being given in metres and grammes. In the fourth column “annealed” means heated to a red heat and cooled in open air, C annealed” means placed in a large - crucible covered with sand, and placed in a furnace, where, after heing heated to redness, the fire was allowed to die out; “ natural ”? means that its temper was not altered from that it had when bought. 150 Mr. H. A. Rowland on Magnetic Permeability, Results given | Quality of in substance. Table Spec. . Mean , How made.) Temper. pan Weight.) 5.3m, (Area. | State. ——— 0000 ‘“‘Burden’s |Welded and} An- : ne z 1. { best”’iron.| turned. | nealed. ba 63 | 148-61 |-0677 | 916 | Normal. II. Sead Sr Bees tees ep 7°63 | 148-61 |-0677 | 916 | Magnetic. 1 ee eee ees } 7-63 148-01 |-0677| 912 | Burnt. Iv. { Eee Caos ie Natural.| 7:84] 38-34 |-0420| 371 | Normal. vy MORI a } rss 39-78 |-0656| 7695| Magnetic. vi. { Boar seta ee 8:83| 4-806'-0200| 0869| Normal. vit. { See era Natural. | vgs eaten ee 0969| Normal. The first three Tables are from the same ring. Besides these I have used very many other bars and rings; but most of them were made before I had discovered the effect of burning upon the iron, and hence did not give a normal curve for high magnetizing-powers. However, I have collected in Table VIIT. some of the results of these experiments; but I have many more which are not worked we yet. In the following Tables Q= —R? viously described. It is evident that if, instead of reversing the current, we simply break it, we shall obtain a deflection due to the temporary magnetism alone. In this manner the tempo- rary magnetism has been measured; and on subtracting this from Q, we can obtain the permanent magnetism. The following abbreviations are made use of in the Tables, the other quantities being the same as previously described. C.T.G. Number of coils of tangent-galvanometer used. D.T.G. Deflection of tangent-galyanometer. Deflection from coil G. Deflection from helix F on reversing the current. Magnetic field in interior of bar (total). . Deflection from F on breaking current. Magnetic field of bar due to temporary magnetism. Magnetic field of bar due to permanent magnetism, Number of coils in helix F, Q=T+P. has been measured as pre- we EoEe * Almost chemically pure before melting. | rr and the Maximum of Magnetism of Iron, Steel, and Nickel. 151- Each observation given is almost always the mean of several. D.T.G. is the mean of four readings, two before and two after the observations on the magnetism; D.C. is the mean of from four to ten readings; D.F’. mean of three; D.B. mean of two, except in Table I., where the deflection was read only once. In all these Tables the column containing the temporary magnetism T can only be accepted as approximate, the experiments having been made more to determine Q than T. The value of n was generally varied by coiling a wire more or © less around the ring, but leaving its length the same. | The change in the value of D.C. is due to the change in the resistance of the galvanometer from change of temperature, copper wire increasing in resistance about 1 per cent. for every 2°6 C. rise. In Table I. the temperature first increased slowly, and then, after remaining stationary for a while, fell very fast. Tape I, * Burden’s Best” Iron, Normal. | r. C.T.G.|D.T.G.| M. |D.C.} 2.) D.F. ge ae, Q. ir. Cae T, 2n # lated. An 48 4°5 "1456 | 23°4'30} 6-5 | -1083| :08 715| 4910) 5845) 390-7) 528 16-45 5501) ... |...154°6} 910 59} 6005)1092010885| 868-7) 3894 20:2 “Genote. «fe 87°9| 1-465 80} 9667)14180 14074|/ 1129 | 5280 28-6 1-011 | 28°3)10)74°2 | 3-71 1-34 | 24600/24830 24000| 1936 | 8882 ola 1G) 9 hy eats 4 88°2| 4-41 1-48 | 29230 26120 26050) 2078 | 9811 39 {| 1°155 |... |...|92°6 | 4°63 1:53 | 8082026690 26660) 2124 |10)80 APM) t-G25" | 2... | 2129°8. 7-45 2-0 | 4959030570 30740) 2433 |13310 297 «| 28:35 | 1-766 | 28-1).../382°8 | 8-20 25 | 548203103031050| 2470 |16710 29-6 | 1-861 |... |...1384°6| 8°65 2°65 | 578203107031100| 2472 |17710 33°4 2-162 | 23°1)...139-8| 9-95 2°85 | 6651080770 30776) 2448 |19050 af Ade Sole | le 10.1447 ETS 3°05 | 7473029750 29930) 2367 |20390 44°45 | 3-223 |... |...|53°5 |13°38 3°85 | 8948027750 27390) 2208 |25740 52-1 .| 4-225 | ... |...160°3 15-08 4°85 |100800 23860 24730) 1899 |32420 9 |34:65 | 6:744 | ... |.../73°1 /18-28 7:10 122700,18210)18410| 1448 |47680 39°8 8:136 | 23:0).../77-°3 |19-32 7:90 129700)15940/16130 1269 (53040 44°3 9-542 | ... | 1140-6 20°30 9-1 |136300)14280)13920| 1137 |61100 55-1 114-04 SNORE ered 98 14540010360)10760; 824:1,65510 3 | 42-95 |27:18 wee |...[47°4 [23°70 = {11-5 (157700) 5803) 6350) 461-8 76540 51:3 |36°60 wee |. 49°] |24°55 [12-7 (162700) 4445) 4523) 353-8:84180 G0715 51:18 | 23-4)...150°3/25-15 {13-2 |166000) 3243) 3310) 258-087120 © | 175000 0: RR 152 M. 1456 5699 6962 1-080 1-191 1537 1:590 1933 2°377 Q. 426 3346 5700 24350 29280 46150 49070 59680 71660 vA. 2920 5987 $189 22550 24580 30020 30260 30860 30150 TasueE II. pL 232 _ 476 652 1795 1956 2389 2408 24156 2399 M. 2-930 4210 6°769 7273 7626 11:10 13°61 | 22-10 “ Burden’s Best ” Iron, Magnetic. 82720 100900 122800 124300 127100 139500 144700 154600 Mr. H. A. Rowland on Magnetic Permeability, — ooo Q. 1001 9395 16550 37330 42920 48830 59490 59580 90180 98560 104000 108200 Xr. 7039 16980 24240 38780 40130 42340 45180 44450 42400 39400 36310 31330 TasuxeE ITI. * Burden’s Best ”’ Iron, Burnt. 24610 || Tape LY. Bessemer Steel, Normal. 116900 120200) 123900 133100 141200 144400 147500 155500 159400 158400 165800 30730 28060 26240 20270 15140 13120 10970 6642 4870 4864 3250 i M. 1356 2793 5287 | 1726 9398 | 3833 1-421 1-880 1:947 2°300 Q. 327 817 7702 14080 15420 24530 10800 rN. pt. 2412 2995 3264 4079 5421 7487 7920 192 238 260 325 43] 596 630 859 T. | 2-756 | 4469 || 5°698 211-44 ‘120-69 M. 3219 [38-99 Q. 39960 50550 56310 71380 85530 119550 r. pi. 14500 15700 15860 15970 15010 1154 1250 1262 1271 1195 10450) 832 138300) 6685) 532 153700) 3942) 314 T. ——— L. 2446 2233 2088 1613 1200 1045 873 529 387 387 299 30830 \39810 44070 51030 56100 THREE = T. 13080 16350 15980 18340 23610 28020 41360 52930 and the Maximum of Magnetism of Iron, Steel, and Nickel. ’ 158 Tabe V, . , / ay 5 Norway Iron, Magnetic. | _M. | Q | Ce ees ee ne tT Be 865, 6439, 512 | 2-290 10590046240, 3680 | 35240. 2673) 2550, 9910, 759 | 1892 | 4-393 13410030520, 2429 | 54970 ‘5161 13000 25200) 2005 | 5857 || 5-910 14240024090] 1917 | 62810 ‘5572 15310/27480| 2187 | $110 | 7-874 14910018940) 1507 | 68490 ‘6725 3014044820) 3567 | 8921 |13-77 |15680011390| 906 | 77060 ‘9305 5380057820 4602 | 13970 |26-84 165800 6038) 480 | 84710 1-362 7770057110 4545 | 21630 /36-86 |168500 4572! 364 | 87860 1-788 (9300052020 4140 | 28200 | : Tasue VI. Cast Nickel, Normal. SA a 1-433 852 | 595 47-4 | 13-43 | 27100 | 2018 | 160-6 | 11260 2904 | 2377 819 63:1 | 16:53 | 31050 | 1878 | 149°5 | 138530 3°527| 3685 | 1070 | 83:1 ‘| 21-02 | 34950 | 1663 | 132°3| 16480 5555 | 10080 | 1815 | 144-4 ‘| 32:17| 41980 | 1305 | 103°8 | 22300 | 6-783 | 13680 | 2037 | 160:5| 5120 | 33-92) 42650 | 1257 | 100-0 | 23360 7-401 | 15270 | 2063 | 1642) 5614 | 60-91| 50860 | 855 | 66:4 | 29540 9:273| 19600 | 2114 168-2 | 7644 | 82-36) 53650 | 651 |) 51:8) 33460 {11-78 | 24720 | 2098 167-0, 9902 |105:2 | 55230 | 525 | 41:8) 35120 ! Tasie VII. Stubb’s Steel Wire, Normal. Meese | AL | | T cas 1673} 159 | 9538 | 75:9 | 13°65 | 543800) 3978 | 316-6 20900 -6237| 678 | 1087 | 86:5 598 || 19°35 | 77770 | 4020 | 319-9 | 29480 1:084 | 1197 | 1104 | 87:9 | 1101 || 27-483 | 100800) 8676 | 292-6 | 35590 2-043 | 2448 | 1199 | 95-4 | 2257] 33°39 | 111300] 3335 | 265-4 | 45110 2714 | 3446 | 1270 | 101-0 | 3095 |) 85°58 | 115000 | 3228 | 256°9 | 45950 4-221 | 6278 | 1487 | 118-4 | 5145 |) 38-64 | 119400 | 3092 | 246-0 | 48060 10:26 383700 | 3286 | 261-5 | 16170 The best method of studying these Tables is to plot them : one method of doing this is to take the value of the magnetizing- force as the abscissa, and that of the permeability as ‘the ordi- nate; this is the method used by Dr. Stoletow; but, besides making the complete curve infinitely long, it forms a very irre- gular curve, and it is impossible to get the maximum of mag- netism from it. Another method is to employ the same abscissas, but to use the magnetism of the bar as ordinates; this gives a regular curve, but has the other two disadvantages of the first method ; however, it is often employed, and sives a pretty good Phil, Mag. 8. 4. Vol. 46. No, 304, Aug. 1873, M .154 9 Mr. H. A. Rowland on Magnetic Permeability, idea of the action. In Plate II. I have given a plot of Table V. with the addition of the residual or permanent magnetism, which shows the general features of these curves as drawn from any of the Tables. It is observed that the total magnetism of the iron at first increases very fast as the magnetizing-force increases, but afterwards more and more slowly until near the maximum of magnetism, where the curve 1s parallel to the axis of Q. The concavity of the curve at its commencement, which indicates a rapid increase of permeability, has been noticed by several phy- sicists, and was remarked by myself in my experiments of January 1871; it has now been brought most forcibly before the public by Dr. Stoletow, whose paper refers principally to this point*. M. Miller has given an equation of the form 3 ‘ m T=220d2 tan 00005d2 to represent this curve; but it fails to give any concavity to the first part of the curve. A formula of the same form has been used by M. Cazin+; but his experiments carry little weight with them, on account of the small variation of the current which he used, this being only about five times, while I have used a varia- tion in many cases of more than three hundred times. Weber has obtained, from the theory that the particles of the iron are always magnetic and merely turn round when the mag- netizing-force is applied, an equation which would make the first part of the curve coincide with the dotted lmein Plate II.[; and Maxwell, by addition to the theory, has obtained an equation which replaces the first part of the curve by the broken line. 1 believe that I have obtained at the least a very close approximation to the true equation of the curve, and will show further on that Q and M must satisfy the equation Q ; (Otenth) v4 sin Tt eae rae en ees ee 5 (10) It is very probable that Weber’s theory may be so modified as to give a similar equation. Space will not permit me to discuss the curves of temporary * On the Maenetizing-Function of Soft Iron, especially with the weaker decomposing powers. By Dr. A. Stoletow, of the University of Moscow. Translated in the Phil. Mag. January 1873. See particularly . 43. fi + Annales de Chimie et de Physique, February 1873, p. 182. + This is according to Maxwell’s integration of Weber’s equation, Weber having made some mistake in the integration. § Treatise on Electricity and Magnetism, Maxwell, vol. ii, chap. vi. and the Maximum of Magnetism of Iron, Steel, and Nickel. 155 and permanent magnetism ; but I will call attention to the fol- lowing facts which the Tables seem to establish. 1. Nearly or quite all the magnetism of a bar ts, with weak magnetizing-forces, temporary; and this 1s more apparent in steel than in soft iron. 2. The temporary magnetism increases continually with the current. 3. The permanent magnetism at first increases very fast with the current, but afterwards diminishes as the current increases, when the tron is near its maximum of magnetism. I have now described the methods of plotting the Tables hitherto used ; and I will now describe the third, which is, I be- heve, new. This is by using the values of the magnetism of the bar as abscissas, and those of the permeability as ordimates. In this way we obtain a perfectly regular curve, which is of finite dimensions, and from which the maximum of magnetism can be readily obtained. Plate III. shows this method of plotting as applied to Table I. If we draw straight lines across the curve parallel to the axis of Q and mark their centres, we find that they always fall very exactly upon a straight line, which is there- fore a diameter of the curve. The curve of nickel shown upon the same Plate has this property in common with iron. I have made several attempts to get a ring of cobalt; but the button has always been too porous to use. However, I hope soon to obtain one, and thus make the law general for all the magnetic metals. There are two equations which may be used to express the curve: one is the equation of an inclined parabola; but this fails for the two ends of the curve; the other is an equation of the general form +H A=A sin a e ® 2 e (11) in which A, H, D, and a are constants depending upon the kind and quality of the metal used. A is the maximum value of X, and gives the height of the curve ED, Plate III. ; a esta- blishes the inclination of the diameter; H is the line AO; and D depends upon the line AC. The following equation, adapted to degrees and fractions of a degree, is the equation from which the values of % were found, as given in Table I.: Q4-"87%+ an 1000 : The large curve in Plate III. was also drawn i1om this, and the dots added to show the coincidence with observation ; it is seen that this is almost perfect. As A enters both sides of the equation, the calculation can only be made by successive ap- M2 A=31'100 sin 156 © Mr. H. A. Rowland on Magnetic Permeability, proximations. We might indeed solve with reference to Q ; but in this case some values of X as obtained from experiment may be accidentally greater than A, and so give an imaginary value to Q. By plotting any Table in this way and measuring the distance C, we have the maximum of magnetism. T have given in the same Plate the curve drawn from the ob- servations on the nickel ring with Q on the same scale, but X on a scale four times as large as the other. The curve of nickel satisfies the equation dite Neu Qa-b85keenn ANAS) sin (SaaS quite well, but not so exactly as in the case of iron. This ring, when closely examined, was found to be slightly porous, which must have changed the curve slightly, and perhaps made it depart from the equation. In Table VIII. I have collected some of the values of the constants in the formula when it is applied to the different rings and bars, and have also given some columns showing the maxi- mum of magnetism. When any blank occurs, it is caused by the fact that for some reason or other the observations were not sufficient to determine it. The values of a, H, D, and the value of >A, when Q=O, can in most cases only be considered ap- proximate; for as they all vary so much, I did not think it necessary to calculate them ewactly. For comparison, I have plotted Dr. Stoletow’s curve and deduced the results given in the Table, of course reducing them to the same units as mine. It will be observed that the columns headed “ maximum of magnetism” contain, besides the maximum magnetic field, two columns giving the tension of the lines of force per square centi- metre and square inch of section of the lines. These have been deduced from the formula given by Maxwell* for the tension 2 per square metre, which is — absolute units of force. 2 17T This becomes gevUat tay teed 5465500000 kilogrammes per square eentim.| Q? i‘ 173240000 1S Pet square inch, | from which the quantities in the Table were calculated. It is seen that the maximum of magnetism of ordinary bar iron is about 175,000 times the unit field, or 177 lbs. on the (12) “tt * Treatise on Electricity and Magnetism, vol. ii. p. 256. 157 and the Maximum of Magnetism of Iron, Steel, and Nickel. | | “quIng *[RULION 4b "yung bs *[RULION onousu yy *[PULION ‘yung “OIJOUSRIN| *[RULION “c "yung *1eq JO 94845 oIyouse yy | ‘OJ POALOFAI DLOFOG ,, IC} ,, OY} 9INJTYSUOD YOIUPM “STOTIVAIGSYO MOF FSV] OY} qdaoxo ][@ SOUSTIVS SIYT, » EEL OOS |S 2 OOSE.. | F646: 09¢ terse [ores | Qgpy foto OLF €8-8 | O98 0006 | ¢8-¢ OO8P | 9-2 | 0009 | 9¢-— oo¢ce | ¢9-£ | °° | OOOS | GF 0¢6 EL-L | OTOL | OOO0T! 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"IV seeee . eeecce 66 eeeeee 1903S $,qqnyg “AVG g.of1 | 00-21 | OODLE | ‘TemyenN °°" 19938 teuressog: | turd PVA) Geel; NOOO 3 ree eee L68l | 6&EI | OOOIST ; AVANION et *poyvouue ; , ; @0St =| ALGE| GOOLE \\ekansoieg tT oe Suny tt ne 04 66 6“ “Sut 6-9L1 | ZF SL. | OOOSLT FS re 69LE | GFGE | OOUSLT ‘UOIT,,9S9q S Mapang ,, | PULL e@eecee concen s weer sé were ees ecee OTM qJos "ICG ptee* sou ee ‘poyvauuy |"7* oat snorqy Ara A, “ouly “our *W1qU90 aienbs | aaenbs xy) ayy uo jrod [PL UY "Play. aa ° ¢ 3 e Goto | MOT oN] “tedauog, fsourgsqns Jo Amend j10 Fury “UISJOUSVUL JO WINUIIXE] Be regio etn eee a ee a per — ee = A ene ee et ee a ee ee Eee ee SSS + SELL AG SPL 158 Mr, H. A. Rowland on Magnetic Permeability. square inch, and foe nickel 63,000 times, or 22:9 lbs. on the square inch. For pure iron, however, I think it may reach 180,000, or go even above that. It is seen that one of the Norway rings gave avery high result; this is explained by the following considerations. All the iron rings were welded except this one, which was forged solid from a bar 2 inches wide and then turned. Even the purest bar iron is somewhat fibrous ; and between the fibres we often find streaks of scale lying length- wise in the bar and so diminishing the section somewhat if the ring be welded from the bar; when, however, it is forged solid, these streaks are thoroughly disintegrated ; and hence we find a higher maximum of magnetism for a ring of this kind, and one approaching to that of pure iron. But a ring made in this way has to be exposed to so much heating and ‘pounding that the iron is rendered unhomogeneous, and a tail appears to the curve like that in Table III. It 1s evident that this tail must always show itself whenever the section of the ring is not homogeneous throughout. Hence we may conclude that the greatest weight which can be sustained by an electromagnet with an infinite current is, for good but not pure iron, 354 lbs. per square inch of section, and for nickel 46 lbs. ; Joule* has made many experiments on the maximum sustain- ing-power of magnets, and has collected the followmg Table, which I give complete, except that I have replaced the result with his large magnet by one obtained later. TABLE IX. Least area 2 Weight Weight sus- of section, tained + Q. Magnet belong- ng square inch. SUSE: least area ith AD 2775 277 154700 2.) +196 49 250 147000 Map Joules sal 1» -0486 12 275 154100 4.| 0012 202] 162 118300 Mr. Nesbit...... 45 1428 317 165500 Prof. Henry ...| 3:94 750 190 128200 Mr. Sturgeon...| 196 50 255 148500 It is seen that these are all below my estimate, as they should be. For comparison, 1 have added a column giving the values of Q which would give the sustaining-power observed ; some of these are as high as any I have actually obtained, thus giving an experimental proof that my estimate of 354, Ibs. cannot be far from correct, and illustrating the beauty of the absolute * Phil. Mag. 1851. On Objections to the received principles of Hydrodynamics. 159 system of electrical measurement by which, from the simple de- flection of a galvanometer-needle, we are able to predict how much an electromagnet will sustain without actually trying the expe-, riment, In looking over the columns of Table VIII. which contain the values of the constants in the formula, we see how futile it is to attempt to give any fixed value to the permeability of iron or nickel ; and we also see of how little value experiments on any one kind of iron are. Iron differs as much in magnetic permeability as copper does in electric conductivity. It is seen that in the three cases when iron bars have been used, the value of a is negative; we might consider this to be a general law, if I did not possess a ring which also gives this negative. All these bars had a length of at least 120 times their diameter. The mathematical theory of magnetism has always been con- sidered one of the most difficult of subjects, even when, as heretofore, ~ is considered to be a constant; but now, when it must be taken as a function of the magnetism, the diffi- culty is increased many fold. There are certain cases, how- ever, where the magnetism of the body is uniform, which will not be affected. | Troy, June 2, 1873. XV. On Objections recently made to the received principles of Hydrodynamics. By Professor Cuauus, M.A., LL.D., RS, RAS A LARGE proportion of my scientific labours having been devoted to researches respecting the principles and appli- cations of Hydrodynamics, I have naturally taken much interest in the discussion carried on in this Magazine between Mr. Moon and the Hon. J. W. Strutt (Lord Rayleigh) relative to points affecting the very foundations of that department of science. After considering the arguments on both sides, it appears to me that the questions raised demand additional elucidation, to sup- ply which is the purpose of this communication. Mr. Moon’s equation (1) in page 117 of vol, xxxvi. of the Philosophical Magazine, viz. _%y 1 dp bie di * D da includes the principle of constancy of mass, as is shown in the Note in p. 101 of vol. xlv., and for motion in one dimension is perfectly general. Respecting that equation Mr. Moon remarks * Communicated by the Author, 160. Prof. Challis cn Objections recently made to that ‘it holds without reference to any hypothesis as to the law of pressure.” I should rather say that it involves no specifica- tion of a particular fluid, and is therefore applicable to all per- fect fluids. , I see nothing to object to in the argument which follows (in p- 117), from which Mr. Moon comes to the general conclusion that the pressure (p) is a function of the density (p) and velo- city (v). This theorem, which, as far as I know, Mr. Moon has the merit of first demonstrating, is in the same sense general as the equation (1); that is, it contains no specification of the fluid. It shows in fact that, in defining the particular fluid, we are limited to the hypothesis that the pressure is some function of the density and the velocity. Now evidently this general theorem includes the more particular case in which the pressure is a function of the density only. Therefore, by Mr. Moon’s own showing, it is legitimate to make the hypothesis that the pressure of the fluid is always in exact proportion to its density, and by this supposition to define the fluid. This argument proves, since it wholly depends on the fluid being in a state of motion, that the equation p=a?p may be assumed relatively to fluid in motion, and that it is not necessary, if it were possible, to establish its truth for that case by direct experiment. | Mr. Moon is evidently not aware that such an inference is deducible from his argument, inasmuch as he proceeds to employ the equation (1) and the theorem p = funct. (p and v) in all their generality, as if no other course of reasoning were legiti- mate; and in this manner he obtains expressions for the pressure, density, and velocity which satisfy the general equation (1) (see Phil. Mag. vol. xxxvi. p. 124). According to the view I have indicated, these expressions embrace the values of the pressure, density, and velocity for every particular fluid comprehended under the general definition p= funct. (p, v). I have found, in fact, that they are inclusive of the values obtained for air cf given temperature in the ordinary way from the equation p=a’p, But after proving analytically that it is allowable to assume that p=a’p for fluid in motion, the question as to whether this equation is true for a particular fluid (as the air) is, as Lord Rayleigh rightly urges, a physical one, and can only be settled by the aid of experiment. ‘I'he proper process for this purpose is to introduce into the general differential equations applicable to the motion of a fluid the relation p=a’p (already shown to be, pro hac vice, legitimate), and then, after applying the inte- grals of the equations in solying various hydrodynamical pro- blems, to compare numerically the results of the solutions with experiment. Such evidence of the exactness of the equation p=4p is accumulative, increasing with the number and variety the received principles of Hydrodynamics. 161 of the comparisons that admit of being made satisfactorily. One contradictory experiment would be fatal to its truth. As far as my acquaintance with the solutions of hydrodynamical problems extends, I have seen no reason to doubt the exactness of that equation for air of given temperature in motion, within a wide range of density. The legitimacy of the hypothesis that p='p having been proved by an argument for which Mr. Moon is himself respon- sible, it must be under some misapprehension that he contends by other arguments that that equation is not admissible. The fact is, these arguments are vitiated by the circumstance that in- ferences, drawn from an investigation which embraces perfect fluids of all kinds, are treated as “applicable to a particular fluid without previously introducing any condition defining the fluid. To illustrate the foregoing views, I pores to disonss an in- stance of the application of the equation p=a’p which is consi- dered by Mr. Moon to lead to absurd conclusions, viz. that in which ‘‘a vertical cylinder closed at its lower end has an air- tight piston, which is capable of working freely in the upper part of it, and is exactly supported by the air beneath ; and at a given time a given weight is placed upon the piston.” The question is, to determine what motion of the piston is thereby produced. From what has been already said, it will be assumed that the equation o> funct. (p and v) justifies making the hypothesis that p=a’p for air in motion; and the solution of the problem will accordingly proceed as follows. Let the weight of the piston be Mg, and the additional weight mg; and let the distance of the under surface from the bottom of the cylinder be a when the weight is added, and z, after the time ¢. Also let 4%po be the whole pressure of the fluid upon the piston before the weight is put on, and A*p, that at the time t. In general, if p be the pressure at any point of the fluid at the height z above the bottom of the cylinder at any time ¢, we shall have p= funct. (<, ¢), and therefore dp ager dz (Z)=% Pe dt The factor = » expressing the variation of the pressure from point to point at a given time, depends partly on the circum- stance that the impulse immediately g eiven by the bottom of the piston to the contiguous fluid is aegageied, so that for any other position the consequent pressure is a function of z and ¢, and partly on the variation of the pressure at the given time due to the force of gravity. As the total variation of pressure referable to these two causes will always be comparatively very small for 162 Prof. Challis on Objections recently made to a cylinder of moderate dimensions, for the sake of simplicity it will be neglected, and the density of the fluid will be assumed to be at each instant the same throughout, and to vary only with the time. Accordingly for the acceleration of the piston we have Gz) vo Mpa A, di? M-+m J; Rp a pant: | Tema oee KPg % and since by hypothesis k*p)= Mg, and , it follows that as, Mag — =~ —9. dt? (M+m)z, We may now suppose, in order to make the problem more general, that the mass m impinges on the mass M of the piston with a given velocity V, and that the two masses subsequently move on together. Hence their initial common velocity is mV ) M+m fluid as is generated by the impact at the first instant 1s left out of account as being indefinitely small. The same is the case with respect to the impact of one sold body on another, if im- pact be regarded as a short and violent pressure; for the mo- mentum of the impinging body is altered by degrees, beginning with zero, by the reaction of the other, and it is after an interval, however short, that the permanent alteration of its momentum is effected. In the problem before us, the reaction of the fluid is taken account of with sufficient approximation by supposing the density of the air and its pressure on the piston to be af all times inversely proportional to the space which the air occupies. This being admitted, the integration of the above equation gives dz? mV? 2Mga eile cs ey iF (Mim? +29(a—z,)+ Mam °o a In this expression so much of the momentum of the This equation includes the effect of the impact of the momentum mV, and is applicable whether V is positive or negative. The case of V negative might be practically exemplified by suddenly attaching the mass m to M bya string passing over apulley. In that case z, is always greater than a. If M=0, the formula gives for the square of the velocity of m, V?+29(a—z), which is the same as that for motion in free space, as it ought to be. For since k*y>=Mg, if M=0, we should have p>=0, and there would be no pressure to impede the descent of m. If V=0, or the mass m be added to M without impact, the the received principles of Hydrodynamics. 163 expression for the square of the velocity of the piston becomes 2Mga, 2, 29(a—Zz}) + Wo es This expression is still applicable if m be a negative quantity— that is, if the mass M of the piston be supposed to be suddenly diminished by the quantity m. In that case z, is greater than a, and the velocity becomes zero for the value of z, which satis- fies the equation 2Mga, 2 Ca If we suppose that m= —M, which is to suppose that the sur- face of the fluid is exposed to vacuuin by a sudden abstraction of the piston, the above expression for the square of the velo- 2Mga M+m becomes infinite. This case is referred to by Mr. Moon at the end of his article in the Philosophical Magazine for February 1873; and a similar one is adduced in p. 27, vol. xxxvi., where a finite density D is assumed to be immediately contiguous toa density 2D. Such instances of changes of the density, and consequently of the pressure, per saltum, are not embraced by the ordinary principles of analytical hydrodynamics; if suscep- tible of treatment, they would require the application of new principles. I do not profess to be able to indicate what would be the appropriate process; but I regard it as certain that no argument against the validity in general of the equation p=a’p can be drawn from exceptional cases in which the density and pressure vary per saltum. The general expression for the acceleration of the piston downwards being city fails to give any definite result, because the factor Bee ee , (M+m)z,’ M at the first instant, when z,=a, this becomes g— = — OF a M+m for the same reason that a free body begins to descend by the action of gravity; and, as Lord Rayleigh justly maintains, any argument adduced to prove that the descent cannot commence in the former case must equally apply in the other. I think I have sufficiently shown that Mr. Moon’s dissent from this view is attributable to his misunderstanding the character of the equation p= funct. (p and v). I propose to conclude this communication by making some . The piston begins to descend by the action of this force, 164 Prof. Challis on Objections recently made.to remarks on the parts respectively performed by reasoning and by experiment or observation, in establishing the truth of the re- sults obtained in applied mathematics, not having seen in modern scientific productions sufficiently precise information as to the relation between these two parts. (1) The experimental results obtained by Galileo and Atwood respecting the vertical descent of bodies acted upon by gravity, and the experimental proof that the vertical acceleration of a projectile is independent of the motion in a curvilinear path, and and that its horizontal motion is uniform, establish the laws which govern constant accelerating forces. It was absolutely necessary to ascertain these laws by experiment before any abs- tract reasoning respecting accelerating force was possible. But the laws relating to constant accelerating forces having thus. become known, it can be proved by means of Taylor’s theorem, or some equivalent process, that an accelerating force, whether variable or constant, estimated in a given direction, is quantita- tively expressed by the second differential coefficient of the func- tion which gives the distance at any time of the accelerated par- ticle from a fixed plane perpendicular to that direction. Taylor’s theorem is legitimately employed for this purpose on the general principle that abstract calculation is comprehensive of all concrete physical relations. This, in fact, isthe proper @ prior? argument for the truth of that general symbolic expression for accelerative force. On the same expression the whole of Physical Astronomy depends, as well as every department of applied science which requires the calculation of motions produced by accelerative forces. The satisfactory comparison of the results of calculation so made with observed facts constitutes the argument @ poste- riort for the truth of the analytical symbol for accelerative force, and with so much the greater evidence as the number of such comparisons is greater. The analytical proof of Kepler’s laws is a very important part of such evidence, inasmuch as it involves as a corollary the demonstration of the law of gravity, which could not be given by observation alone, nor by calculation alone, but requires that the two processes be combined. In short, the discovery by geometrical or analytical reasoning that a variable force is expressible by the second differential coefficient of space with respect to time, specially characterizes the Newtonian epoch of physical science. (2) A perfect fluid being defined by the properties of mutual pressure, and of easy separability, of contiguous parts, it is pos- sible to demonstrate, for fluid at rest, the ae of equal pressure in all directions from a given point, exclusively by reasoning founded on these properties. (See ‘ Principles of Mathematics the received principles of Hydrodynamics. 165 and Physies,’ pp. 104-107.) In certain cases the law admits of being verified directly by eaperiment; but generally the verifi- cation is effected by comparisons of results obtained mathemati- eally, on the hypothesis of the truth of the law, with observed facts.. Also for the case of fluid in motion an @ priort demon- stration of the same law may be given on principles which are indicated in pp. 172 and 173 of the work just cited. But in this case experiment cannot be directly employed for its verifica- tion; and on this account some mathematicians have thought that the law was not as certainly established for fluid in motion as for fluid in equilibrium. It may, however, be asserted that, although for fluid in motion the demonstration can only be effected by the combination of reasoning with the results of ex- periment, both the @ priori proof of the law, and its verification a& posteriort by comparison of calculated results with observation, are equally valid whether the fluid is in motion or at rest. (3) Assuming that Boyle’s law has been proved by experi- ment to be true for air of given temperature at rest, what evi- dence is there that it is true for air in motion? This question, to which, as far as I am aware, a satisfactory answer has not hitherto been given, I propose to answer as follows :—Since it does not appear practicable to verify the law for fluid in motion by direct experiment, the only course that can be adopted is to justify the assumption of the law for that case by @ priori rea- soning. This having been done, the truth of the assumption has to be confirmed, as in all like instances, by comparison of results mathematically deduced from it with experiment. The chain of the reasoning is therefore incomplete unless it is shown by an @ priori argument that the equation p=F =) ; that at the end of the third interval will be 5 Lie (&) , &c.: and therefore the work done in the first interval e 2 T yill be 4 F24¢; that during the second interval will be > P23; n aie oie [2 that during the third interval will be SEs, &e. It has already been pointed out, however, that the foregoing definition of work implies that the amount of work done in equal intervals of time will be the same. It follows, therefore, that the definition and measure of work above propounded contradict each other in the case we have been considering. 2, Suppose a body whose mass is M to be moving in a certain direction with a velocity V,, and that the force F is applied to the body in the direction of its motion. Professor Maxwell proves ‘that, if during the small time T the body moves through the space s, and has acquired at the end of T the velocity V, we shall have gS (Ue an equation, be it remembered, which holds independently of the magnitude of T, provided F be uniform. If we put V= ay ae we shall have work =Fs=3M(er+2vV,)- 2 eee Now v is the pure product of the force I’ acting on the body M during the time T; whence it appears that, adopting the mea- sure of work above proposed, the work done by the force F on the body M in the time T involves the variable quantity V,, which is entirely independent alike of F, of M, and of T. 3. The right side of the expression (1) will always be positive so long as V, and v have the same sign, 2. e. so long as the direc- tions of the force and the initial velocity conspire. But if the force and initial velocity have opposite directions, and T and V, are both finite, the right-hand side of (1) will first be negative ; as the motion proceeds it will become zero; and it will finally become and continue positive. It results, therefore, from the above measure of work, that the work done in a finite time by a finite force acting upon a body of finite magnitude which is free to move, may be zero. 4, The proper work of force is to generate or destroy mo- mentum*; and the work done by the force. in a given time will * No doubt force has another effect—that, namely, of causing a body to describe, or of preventing its describing, space : but of these two effects, viz. the description of space and the generation of momentum in any in- On the Directive Power of Magnets, &c. 221 be properly measured by the momentum created or destroyed in that time*. The measure thus proposed, in fact, differs from the received measure enunciated by Professor Maxwell less than might at first sight be supposed; for when T is very small, (1) becomes work=Fs= Mv. Vj. Thus, while I contend that the work done in a short interval of time under the above circumstances is properly measured by the momentum generated during the time, according to the views upon the subject which are generally received it is measured by the product of the momentum generated and the initial velocity V,—a position the reasonableness of which, I apprehend, it will be found difficult to establish. 5. If, instead of expressing the work done in terms of the force acting and the time during which it acts, we wish to ex- press it in terms of the force and of the space described under its influence, we have only to replace T in the expression FT by its equivalent in terms of the other variables. This, where the body moves from rest, would give us /2MFs as the measure of the work done by the force F on the body M while moving through the space s. 6 New Square, Lincoln’s Inn, July 29, 1873. XXIV. Hzperiments on the Directive Power of large Steel Magnets, of Bars of magnetized Soft Iron, and of Galvanic Coils, in their Action on external small Magnets. By Groreu Brpprtt Airy, Astronomer Royal, C.B., P.R.S.— With Appendix, containing an Investigation of the Attraction of a Galvanic Coil on a small Magnetic Mass. By JAMES STUART, * Esq., M.A., Fellow of Trinity College, Cambridge t. fa only experiments with which I am acquainted tending to throw light upon the distribution of magnetic power in the different parts of a steel magnet are some very imperfect definitely small interval of time, the former will be ofa lower order of mag- nitude than the latter; while, of the small space actually described in the interval, all but an indefinitely small portion will have been described under the influence of the velocity from time to time generated during the inter- val; the residuum immediately due to the direct action of the force, and in no degeee resulting from acquired velocity, being of the third order of sma! quantities at most. . * From this it follows that the work done by the force F acting during the time T on a body which is free to move will be measured by FT. - + From the Philosophical Transactions for 1872, Part I1., having been read February 8.; ro) 22 The Astronomer Royal’s Heperiments on ones by Coulomb in the French Memoirs for 1789 and other years. It appeared to me that it might be desirable to make experiments of a rather more extensive character, and to add some measures of the magnetic effect of galvanic currents, both directly by their immediate action, and indirectly by the amount of magnetic power which they produce inductively in soft iron. _ For the measure of permanent magnetism I selected a bar magnet 14 inches long, 1°4 inch broad, 0°35 inch thick ; it has not been touched by a magnet for several years, and is likely to be in a state of very permanent magnetism. For the galvanic currents a cylindrical coil was used 13°4 inches long, 1°4 inch in external diameter, and about 0-9 inch in internal diameter ; it has, I believe, four layers of wire, each layer having 160 re- volutions of the wire. The battery used with it consisted of three cells, with sulphuric acid diluted in the proportion of 1 to 6; the plates were of zinc and graphite, each exposing on each side about 8 square inches; the circuit was always completed about half an hour before the experiments were begun; and a delicate galvanometer was placed in circuit, by which the steadi- ness of the current was established. A core of iron 0°8 inch in diameter and of the same length as the coil, removable at plea- sure, fits well in the inside of the coil; the iron is quite soft, and can with ease be entirely freed from any subpermanent magnetism. ‘Lhe first step in the experiment was to neutralize terrestrial magnetism within the area of magnetic experiment. Tor this purpose two powerful 2-feet magnets were placed below the table on which the experiments were made, with their red or north-seeking ends directed to the magnetic north, at a distance (determined by trial) such that the experimental compass was sensibly uninfluenced by terrestrial magnetism. It is possible that some small residual magnetism was perceptible in the com- parison with the feeble galvanic action; but none could be cer- tainly discovered in the other experiments. The compass used for register of the magnetic action is a small and very lively pocket-compass, with needle 1:0 inch Jong, not loaded with a card. The box of this compass is eircular ; and when positions had been selected for the centre of the compass (as will be mentioned), a circle somewhat larger than the compass-boex was described in pencil with each of those positions for centre; and the compass could then be planted with its centre very accurately placed above the intended point. The compass-positions were thus prepared :—Upon a sheet of strong paper the plan ef the magnet, 14 inches by 1:4 inch, was laid down. On each side were drawn two parallel lines, of the Directive Power of Magnets, &e. 223 the same length as the magnet, at distances respectively 1:5 inch and 3°0 inches from the near edge of the magnet; these lines were divided each into ten equal parts; and thus in each line eleven points were obtained at intervals of 1:4 inch. From each of the four angles of the magnet as centre, two quadrants were swept:—one with radius 1:5 inch, at whose extremity and bisection points were taken for the compass-centre; and one with radius 3:0 inches, which was twice bisected, and of which the extreme point and the three bisection-points were taken for the compass-centre. These points were used for the magnet both with its edge and with its flat side towards the compass. of the magnet’s length: but the pole of the galvanic coil is absolutely at its end; indeed some of the experimental directions of force fall a little beyond the end. It is evident, from the remarks of Nos. 6 and 7, that a magnet cannot in any wise be represented as a system of revolving galvanic currents, with an equal number of circuits at every part of its length. With the view of presenting the results in the form which may probably be found most advantageous for comparison with the conclusions from any future theory, I have resolved the forces into rectangular directions, parallel and transversal to the axis of each magnet, by the followimg graphical process. Upon each mean line of direction of force (ascertained as is described above) I have laid down the mean measure of the force (as found above), and upon this measure as hypotenuse I have constructed a right-angled triangle, the lengths of whose sides give the two forces. From the nature of the preceding opera- tions, it is only necessary to form these numbers for one quadrant of each magnet. ‘The results are given in the follow- ing Tables. The Astronomer Royal’s Experiments on Large Bar Magnet. ; Edge towards small Flat side towards LE AEROS (NOL. ‘ magnets. small magnets. Longi- Trans- Longi- Trans- Longi- Trans- tudinal versal tudinal versal tudinal versal ordinate. | ordinate. force. force. force. force. 0-0 2-2 —274 0 —250 0 1-4 2-2 — 283 +161 —260 +137 2°8 2-2 — 262 +315 —236 +276 4:2 2:2 —198 +530 —182 +444 5°6 2-2 — 56 +678 — 36 +540 7:0 2:2 +216 +585 +158 +451 8:08 1-76 +367 +360 +325 +3815 8-5 07 +580 +166 +552 +184 0:0 37 —160 0 — 160 0 1-4 37 — 147 + 73 —149 + 72 2°8 37 —127 + 142 —123 +136 4:2 37 — 88 +205 — 79 +185 56 37 — 19 +235 — 12 +217 70 37 + 49 +205 + 51 +190 8:13 33 + 95 +167 + 92 +154 9°12 2°8 +129 +122 +124 +118 9:79 1:84 +159 + 88 +157 + 82 10:0 0-7 +199 + 42 +190 + 40 the Directive Power of Magnets, &c. 229 Galvanic Coil. an For attracted point. 1 Coil with iron core. || Coil without core. Longi- Traas- Longi- | Traus- || Longi- Trans- tudinal versal || tudinal | versal | tudinal versal 4 ordinate. | ordinate. | forces | 4 fonce. force. force. uaa pe ewsenici sat | De RL AE satiate 2A ae} x20 ee eS ea Gor eter 0 | 1:34 226 || -~286 | +169 || — 240 | + 38 2-68 SL eee a | ees) ee L*.4°02 226 © —193 | 4477 | — 450 | + 825 535 225 | — 42 +632 || — 550 + 848 67 226 || +162 +562 | — 80 +1480 778 170 | +380 +420 +1010 +1630 |} 82 0-74 || +790 +296 || +2480 | +1170 4 0-0 ave All y-oles 0 lew 134 0 1-34 373 || —162 + 82 | = 189 + 4l | 2°68 373 || —124 | +149 | — 200 + 104 | 4-02 373 || — 88 +201 — 217 + 212 | 936 373 || — 19 +226 | — 123 -+ 383 67 373 || =+ 39 +214 | — 57 + 424 7°83 344 | + 94 +176 | + 100 + 436 8°82 2°8 | +134 +149 || + 264 + 410 9-49 1:82 || +1386 + 99 |! + 473 + 338 | 97 073 | +223 + 44 oe 668 + 186 The centre of the large magnet or coil is in every case the origin of coordinates of the external magnetic point on which the action of the large magnet &c. is estimated—the axis of the longitudinal ordinate being the axis of the magnet, and the axis of the transversal ordinate being normal to it. The powers are estimated as those of the red end of the large magnet operating on a small external mass of red magnetism. It will be remembered that, for the galvanic coil without core, all the numbers must be divided by 120. It does not appear possible to infer from these numbers, by any direct analytical process, the law of distribution of magne- tism in the bar. It must be done, I believe, synthetically, by assuming a law, and computing the forces which would result from that law, and then comparing these computed forces with the forces actually observed. The only law which I have tried is the supposition that the intensity of magnetism is propor- tional to the distance from the centre of the magnet, which in- cludes also the law that there is a gradual increase of red magnetism from one end and a gradual increase of blue mag- netism from the other end. Putting / for the half-length of the magnet, a and 6 for the longitudinal and transversal ordi- nates of the attracted point, 2 for the longitudinal ordinate (measured from the centre) of any attracting poimt, and sup- posing the magnet to be a line, it is easily seen that the quanti- 230 The Astronomer Royal’s Experiments on ties to be integrated are :— evil! WAS Transversal eas es le {wa +0} ((a—a)2427}8 and the results of integration are :— 5 rca! ec {(U4+a)? +67}? {(—a)? +67}? +hyp.log {(7+ a)? + 6?\2—/—a} —hyp. log { = b2j2+ [at —al—a?—b? a —ai+a+b? bf (I4a)2+o%? bf (J—a)?+0?}? I have computed these numbers for each of the eighteen stations. For comparison with observation, I have taken the experiments with the flat side towards the small magnets, which represents most nearly the case of a linear large magnet ; and, for facility of comparison, I have multiplied the experi- mental numbers by 6. The following is the comparison :— Longitudinal Longitudinal force = Transversal force = | Experimental. | Theoretical. Longitudinal. Transversal. Longitudinal. | Transversal. — 1500 Or — 1849 0 — 1560 4- 822 —1750 — 1089 —1416 +1656 | —144] —2112 — 1092 +2664 | — 827 — 2528 — 216 +3240 + 155 —3180 + 948 +2706 +1126 — 2283 +1950 +1890 +1589 — 1389 +8312 +1104 |. +2395 — 622 — 960 0 | — 1029 0 — 894 + 482 | — $71 + 517 — 738 + 816 — 776 + 960 | — 474 +1110 — 428 +1267 — 42 +1302 — 2 +1319 + 306 +1140 + 335 + 1066 + 552 + 924 + 409 + 801 + 720 + 708 + 668 + 633 + 942 + 492 -- 805 + 380 +1140 | + 240 + 984 + 251 The agreement is not satisfactory; but I am unable to suggest the nature of the change that ought to be made in the assumed law. I shall add only one remark, of a somewhat practical charac- ter. Ina paper published originally by Dr. Lamont in Pog- gendorff’s Annalen, vol. cxill. p. 239 &c., and of which a translation, by W. T. Lynn, Esq., of the Royal Observatory, is printed in the Philosophical Magazine, 1861, November, the Directive Power of Magnets, &c. 231 Dr. Lamont inferred the proportion of the effects of different steel magnets from the proportion of the effects of different soft-iron bars under the influence of induction. The remark No. 4 (above) goes far, I think, to justify this assumption. Appendix. Remarking the singularity of the experimental result as to the apparent localization of the attractive pole of a galvanic coil at the very extremity of the coil, I commenced an investigation of the theoretical attraction of a coil, on the laws of galvanic attraction usually received. On my mentioning the subject to my friend James Stuart, Hsq., Fellow of Trinity College, Cam- bridge, he kindly under took, at my request, to prepare a complete theoretical investigation. I am happy in being per- mitted by Mr. Stuart to place before the Royal Society his mathematical discussion of the attraction of the coil, which 1 am confident will be found to be very complete and of great elegance. I append to it a comparison of the numerical results of the theory with the numerical results of experiment; and the agreement will be found to be so great as to justify entire confidence in the assumed law of galvanic action and the mathe- matical treatment of it, and a high estimate of the accuracy of the experimental observations. Investigation of the Attraction of a Galvanic Coil on a small Mag- netic Mass. By James Stuart, M.A., Fellow of Trinity College, Cambridge*. From investigations given by ak. we can deduce an ex- pression for the potential U at an external point Q of a closed circular galvanic current carried by a wire of indefinitely small section. Let a be the radius of the circle, let the distance of Q from C, the centre of the circle, be 7, and let the line CQ make an angle @ with the normal to the plane of the circle: then it can be shown that, when 7 is less than a, 7 Via eo Us2ak4 —1+ abi 9 gabat od peo ae Ve and when 7 is greater than a, * Abbreviated from the Appendix originally presented and read with the paper. 252 The Astronomer Royal’s Hzperiments on where & depends only on the intensity of the current, and where P,, Ps, P; are defined by the equation 1 s/1—22 cos 0+ 2? If, therefore, X represents the resolved part, perpendicular to the plane of the circle and towards it, of the force exerted by the current on a unit of magnetism placed at Q, and if Y represents the resolved part of that force parallel to the plane of the circle and directed from its centre outwards, then dU dU X=“ sin @— < cos 8, =1+P,¢+Pj27+ Po73+.... To calenlate these quantities, we know that P= cose, P,= 8 (cos? 0— 3 cos 8), P= 83 (cos? O—12 cos? 6+ 13 cos 6). We shall only consider the case of those points for which 7 is greater than a. Substituting these values in the expression which in such oe holds for U, we have 4 U= mk} 5 © 0s 0+ ae a (cos 6 — = cos 8) . 2S 2 128 76 sik From which, after some reduction, we obtain xX J ees eae aes (—1+48 cos? 8) + (c os? 6.— 7 00880 + 7.0086) - (9—90cos?A + 105 cost) 27k 16 = 75g (—75 +1575 cos? O—4725 cos 8+8465 cos® a) Y ? oe ae Ge | : Jane feted ymensimeens a8 , + yg (525 cos @—3150 cos? 6+ 8465 cos? 8) <> Karte Al 1 dale amaMell the Directive Power of Magnets, &c. 233 Kach of these expressions consists of a series of terms in ascend- . a . . : ing powers of ” which will be converging. We shall now seek to find X and Y fora galvanic current traversing a wire coiled into the form of a hollow cylinder, of which the internal radius is J, the external radius 6+, and the length is2f. We shall suppose the individual turns of the wire to lie so close as that each may be regarded as an exact circle. Let AB be the axis of the coil, so that A and B are the centres of its two faces; then AB=2f. Let O be the middle point of AB. Let P be the attracted point, P M its perpendi- cular distance p from AB. Let PAM=ea, PBM=8. Let C be the centre of any turn of the wire regarded as a circle of radius a, CP=r, POUM=0, OC=a;; then it is readily seen that for the whole cylindrical bobbin the forces X, Y are given by ; +f (°b+e XL { laieda: bh e —f b +f (°b+e bs = ( Mdz da, id L's -where L and M stand for the expressions on the right-hand side of (1) and (2) respectively, and where uw depends on the strength of the current. To perform the integrations for the length of the bobbin in 204 The Astronomer Royal’s Experiments on these expressions, we have the formule p=r.sin 0, Og S10 U0 > and Making these substitutions for dv and r, the integrals with re- spect to x become integrals with respect to 0, which can be easily evaluated by a continued application of the method of integra- tion by parts, the limits being from O=a to 0=f. If we then mtegrate the result thus obtained with respect to a, from the limit 6 to the limit 6+, we finally obtain —_— 3 3 : 7 a { — (cos 8— cos a) -+ (cos? B— cos® ar) : ~—5 3, aE ae {— 9 (cos 8 —ecosa)+ 83 (cos? 8—cos? a) " — 89(cos’8—cos°a)+ 15(cos’ B—cos’ a)} sy eu be ei {— 75 (cos@ —cos a) + 575(cos* 8—cos® a) 896p° 3 — 1590(cos® 8B —cos® a) + 2070(cos’ B— cos? «) — 1295 (cos? 8—cos? a) + 315 (cos! 8 —cos"a) } arp aime : Mite: FS) sind eta es om f+ (sin B—sin® a) t Ta b+ce—b?, 5 9 a A A goat 12(sin® 6—sin°a)+ 15 (sin? 6—smn “)5 7 4 b4¢ —2" § 4 120(sin? B—sin? 2) — 420(sin? @— sin? «) +3815 (sin!) B—sin'! a)! These expressions for X and Y will be converging for all points situated at a greater distance than b+c from any point of the axis AB, inasmuch as they are composed by adding together corresponding terms of series which are then all convergent. Among other points, these expressions hold for such as are situated on the axis external to the bobbin, and not nearer A or B than by the distance (6+). For such points, however, the the Directive Power of Magnets, &c. 235 expressions become illusory, assuming the form §; they may, however, be evaluated by the ES for the evaluation of vanishing fractions. Y is clearly zero. X may be more readily obtained directly from the expression for U; from that expres- sion we find that for a single circular current the attraction on such points is Seige t at ee K=2nk{ +4 3737 Seca Hence, in the case of a bobbin, if 2 be the distance of the attracted point from O, the middle point of the axis of the bobbin, we have 12S Bie? a? 8 at ie Wi a® drda (+ 73 354g a) “ie — 6° 2 2 ce Ty f2)? ete = Bick } ee iar pile T 40 (a 2 =p | F i) “Eas =a @+f fi a—f) re aan : which gives X for points situated on the axis fer which 2 is not less than (b+c+/). The expressions for forces which concern us now are those xX Y given by the general formule for — and —. And a moment’s glance at these will show that ines expla the apparent posi- tion of the pole at the very extremity of the coil; for in order to ascertain the values of the forces in a plane at right angles to the axis passing through the extremity of the coil, we must make a=90°, sma=1, cosa= 0; a if the other end of the coil be very distant, 8 may be taken = 0, sin 8=0,cosG=1. Substi- tuting these values, it will be seen at once that X, the longitu- dinal force, =O, ale Y, the transversal force, has a value einen indicates a force dir ected to the extremity of the coil. In order to make a complete comparison, I have, for all the eighteen stations treated m the former Tables, taken the values of a, 8, and p graphically. For 6 I have adopted 0:45, and for b+c0°7. These numbers correspond to the internal and ee | surfaces of the coil; but they appear to me best to represent (though doubtless with some inaccuracy) the quantities used in the theoretical investigation. Then I have (with the kind as- sistance of Edwin Dunkin, Esq., of the Royal Observatory) made 236 Prof. R. Clausius on a new Mechanical Theorem the complete calculation of the formule for every station. As the numbers first obtained were not immediately comparable, I have made them more nearly so by trebling the numbers given by theory and doubling those in the preceding Table. The re- sults are as follows :-— . | Trans- | Result of : ; ia Longi- Sana theceetoal i | heoretical | Experimental tudinal ote i B Soleo | result trebled. jresult doubled. nate. | Date Se "| or p. X. Y: | Dsaa sian (o X. x: eaeaeete —— ————| | 0:0 2°26 161 10, 18 40 — 160 0 |— 480 0}— 432 0 1:34 | 2:26 157 15,15 40 — 1684+ 30 |— 5044+ 90\— 4804 76 2:68 | 226 {151 0/13 25|— 208+ 82 — 624+ 246/— 6304 240 4-02 | 2-26 140 20,11 35 — 2974206 |— 891+ 618/— 900+ 650 5:36 | 2:26 121 55.10 15 — 3544503 |—1062 +1509|—1100 +1696 67 | 226 | 91 0 920 — 384855 |— 114 +2565|— 160 +2960 7-78 | 1:70 | 58 25, 6 10 + 5434771 |+1629 +2313) +2020 +3260 8-2 0:74 | 28 0 2 85 +1417,+688 |+4251 +2064) +4960 +2340) 0-0 3°73 151 0 29 oe 124 0 \— 372) 0)/— 368 0 1:34 | 3:73 (145 3024 42 — 128+ 32 |— 384+ 96)/— 378+ $2 2:68 | 3°73 1187 20 21 30 - 139+ 77 |— 417 + 231;— 400\+ 208 4:02 | 3:73 126 10,18 57 |— 150,4+-148 |— 4504 444)/— 434,4+ 424 5°36 | 3:73 |110 5,16 58;— 109 +248 |— 327,4+ 729|\— 246\+ 766 6:7 373 | 91 0 15 27 — 204295 |— 60-4 885)— 114/4 848 7283 | 3:44 | 738 0.138 24+ 8043808 |4+ 2404 924;4+ 2000/4 872 8-82 | 2:8 54 5,10 0 + 1794281 |4+ 5374 843/4+ 528)+ 820 9-49 | 1-82 | 34 35' 610 4+ 318 +223 |4+- 9544+ 669+ 9504+ 676 97 0-73 | 14 25 2 5 + BED al +1368 + 360/+1336)+ 372 In spite of some discordances in the large forces (which it was impossible to measure with accuracy), there is enough of agree- ment to show that confidence may be placed in the method of theoretically computing the attraction of the galvanic ceil. XXV. On a new Mechanical Theorem relative to Stationary Motions. By R. Crausivs*. ]‘ a memoir published in 18707, I have, for a material point which moves in a closed path, adduced and demonstrated an equation which stands in close connexion with the proposi- tion of least action and with Hamilton’s principle and yet is essentially distinct from them. In the same memoir I then en- * Translated from a separate impression, communicated by the Author, having been read before the Miederrheinische Gesellsehaft fur Natur- und Heilkunde on June 16, 1873. + “On the Reduction of the Second Proposition of the Mechanical Theory of Heat to general Mechanical Principles,” Phil. Mag. S. 4. vol. xlii. p. 161. relative to Stationary Motions. 237 deavoured to apply the equation to the science of heat. The subject, however, appears to me, even from a purely mechanical point of view, to be of so great importance that I have taken the trouble to pursue it further in this direction, and to give the equation as general a form as possible, by which also its appli- cation to special cases is of course facilitated and gains in cer- tainty. The result of this investigation I take leave to commu- nicate in the following. 1. It will serve our purpose first to briefly cite the equation in the same form as hitherto in order to connect with it our further considerations. Given a movable material point of mass m, which, under the influence of a force that has a force-function or, according to another nomenclature, ergal, moves in a closed path. Let the ergal be denoted by U, the velocity of the point by », and its period by z. Of the quantities which are variable during the motion the mean value shall be taken, which shall be signified by a horizontal stroke above the symbol representing the va- riable. Besides the originally given motion of the point, let us further consider one deviating infinitely little from it. The deviation may be occasioned by the point having begun its motion from another place, or having had at the commencement other components of velocity than with the original motion. Besides, the ergal may have undergone achange. The latter we will imagine expressed by this—that in the function U, in addition to the space-coor- dinates, one or more quantities c,, ¢,, &c. occur, which are con- stant during each motion, but may change at the transition from the one motion to the other. If now, for every quantity that comes into consideration, we regard the difference of the two values which it has in the ori- ginal and in the deviating motion as the variation of the quan- tity, and indicate it by 5, and for abbreviation collect the terms which relate to the quantities c,, co, &c. under the sign of sum- mation, the equation in question reads :— sU — ae Sc= 5 9 ov? +mv*slogi.. . . » (1) 2. In order to generalize this equation, it might be assumed that instead of one material point several are given, all moving in closed paths. If all their periods were equal, and changed in the same ratio on the one motion passing into the other, the extension of the equation to such a case would be of itself intel- ligible at once; but if the periods are different and change in different proportions, special considerations are needed for this extension. 238 Prof. R. Clausius on a new Mechanical Theorem The case is still more general where the points do not describe closed paths, but, though the coordinates of the points change in a periodical manner, the periods have various durations, and the durations may change in different proportions at the transi- tion from the one motion to the other. This case can be further enlarged thus—that periodical changes are not ascribed to the coordinates themselves, but it is merely assumed that the coordinates can be represented as functions of some quantities which undergo periodical changes. Finally the treatment can be made still more general, by not directly assuming concerning the quantities by which the coor- dinates are determined that they accomplish their changes pe- riodically, but fixing a less limiting mathematical condition, which is satisfied by periodical changes, but can also be satis- fied without the changes needing to be periodical. This is the method we shall select. 3. Before proceeding to this treatment of our subject, some mechanical considerations may be premised which will facilitate the understanding of it. Given a system of material points whose masses are m,, Mo, &e., which move under the influence of forces possessing an ergal. Ifthe positions of the points are determined by the rect- angular coordinates 2), Y, 2), Lo, Yoo 2, &e., the ergal U isa function of these coordinates. The vis viva T of the system, if we indicate the differential coefficient of a variable, taken ac- cording to the time, by an accent (thus for example putting dx, — =x,'), is expressed as follows :— THES (2? +y? +2". vga ok ee As is well known, there is a simple relation between T and U. Tn order to be able to write this, the sign to be chosen for the ergal U must be fixed more closely. Usually this sign is taken so that the differential of U represents the work done by the forces with an infinitely little displacement of the points, and hence that the proposition of. the equivalence of vis viva and work is expressed by the equation T=U-+ constant. In the form of the proposition, however, which (especially through the beautiful researches of Helmholtz) has more re- cently come into use, and in which we are accustomed to name it the theorem of the conservation of energy, it is more conve- nient to introduce the ergal U with the opposite sign, so that the negative differential of U represents the work, and hence we can put T+ U=constant. relative to Stationary Motions. 239 Then T and U are the two quantities which Rankine has named the actual and the potential energy, and whose constant sum is the total energy, or briefly the energy of the system. If we de- note the latter by E, the preceding equation reads :— PBS TA OT Teg HS) If now, for the determination of the positions of the movable points, mstead of the rectangular coordinates any other variables be introduced, which we will denote by q,, do,--+@n, of course the ergal U is to be regarded as a function of these variables. - As regards the other quantities occurring with the motion, and the equations holding for it, the forms which they assume when those general variables are employed are laid down by Lagrange in his Mécanique Analytique. In order to ascertain what form the expression for the wis viva takes, let us put for example, since the rectangular coordinates of the points are to be regarded as functions of those general variables, B=f(Q Yor+++ Qn): From this follows NC CL MCLE dG OL. A0d0a ae or, otherwise written, af df df, eee Ue ° e e 4, q, 1} dg, 1? dq, 4 ( ) Tn like manner can all the velocity-components of the movable : di tO a dee points be expressed. As the differential coefficients =--, —,...—> dq, qo’ dn are functions of the n quantities qg, the expressions of the velocity- components contain the n quantities g and the n quantities 4’, and are, in relation to the latter, homogeneous of the first degree. If we now imagine these expressions put in equation (2), we ob- tain for the vis viva T an expression which also contains the quantities q,, Jo,--- Qn and q',, q'o,.--@'n, and in relation to the latter is homogeneous of the second degree. From the last-mentioned circumstance it follows, further, that we can form the equation vg oF dT , ee ea ed Shh al she oT gi or, using the sign of summation, dT 8T => dq! q'. ° . 5 ° ° (5) 24.) Prof. R. Clausius on a new Mechanical Theorem As the differential coefficients of T in this equation will fre- quently recur in what follows, it will be advantageous to intro- duce for them a simplified symbol. For this we will chocse the letter p, and accordingly, understanding by v any of the integral numbers from 1] to n, put aT P,= dq’, (6) The preceding equation then becomes a= Spa. oc erphey i) opel te aati. (7) According to Lagrange, the differential equations of motion take for the general variables q the following form— d os) at dv EES Ral eto dt \dq,)~ dg, dq, or, pursuant to (6), dp, dV dU 4, As regards the equations given by Hamilton in his me- moirs of 1834 and 1835*, they are, if the initial values of the quantities 9),go,-+-+Qnand p,, Po.» + Pn be denoted by ky, hko,... kn and hh, hg, .. + hn, a8 follows :— t A} 2Tdt=Z(pdg—Adk) +t5E; . . . (1) 0 5 | (2 U)adt=3 (5-154) — Boy. « ait) These two equations are not essentially different the one from the other, because, presupposing the equation T+ U=H, the one immediately results from the other. Hence they can be designated as one equation in two different forms. In the first form of the equation the integral t i} eTdt 0 is to be regarded as a function of the quantities g,, qo,.-. Qn; ky, ka)-++ kn, and HK, and the equation can be analyzed into as many different equations as there are independent variations on the right-hand side. As soon as the function which that inte- gral represents is known, we can, from the equations resulting from the analysis, deduce by mere elimination of E all the first and second integrals of the differential equations of motion. * Philosophical Transactions, 1834 and 1835. relative to Stationary Motions. 241 The second form of the equation is still more convenient in the latter respect. In it the integral { \(E—U)de is to be looked upon as a function of the quantities 1, go) ++ + Jus ky, kay. ++ ky, and ¢; and when this function is known, we obtain through the analysis of the equation alone the first and second integrals of the differential equations of motion. 5. From the preceding it is evident that Hamilton’s principle is one of extraordinary importance for mechanics. Neverthe- less it 1s, for two reasons, not suitable for our purpose. In the first place, great as is its generality in other respects, in one direction it is not sufficiently general. In the equation there are two motions compared which differ infinitely little from each other ; and their difference may be reduced to this—that the initial coordinates and velocity-components of the movable points had somewhat different values with the one motion and with the other; but the ergal U is presupposed to be, with both motions, one and the same function of the space-coordinates. The dif- ference, however, between two motions can also be occasioned by the ergal having undergone a change which is independent of the alteration of the coordinates. In the science of heat this case is quite common, because with a body upon which certain external forces act, under the influence of which its molecules perform their motions, these forces may undergo a change which is expressed mathematically by a variation of the ergal, whereby of course a changed molecular motion is necessitated. Transi- tions of this sort from one motion to another cannot be treated by means of Hamilton’s equation. The second of the reasons above alluded to refers specially to stationary motions. If a stationary motion as such is to be more closely determined, the question is, not to give the posi- tions and velocities of all the individual points for single mo- ments of time, but much rather to fix the general character of the motion independent of time. An equation which is to serve for this purpose may certainly contain variable terms; but their variability must be confined to certain fluctuations of their values, which are repeated in a similar manner, so that the equation has to a later time essentially the same relation as to an earlier one. If, on the contrary, terms occur which are undergoing continu- ally greater variations, so that the equation has not the same relation to a later as it had to a former time, this circumstance makes it unsuitable for our purpose. We will now consider [lamilton’s equation from this point of view. In it occur the variations 64, dg,,...d6g%, the significa- Phil. Mag. 8. 4. Vol. 46, No, 805. Sept, 1873. S 2492 Prof. R. Clausius on a new Mechanical Theorem tion of which may be defined thus: 6g, is the difference between the value which g, has with the original motion at a certain in- stant and the corresponding value of q, with the deviating motion. But now it is doubtful which of the infinity of values successively taken by q, with the deviating motion is to be regarded as the corresponding value. Hamilton has certainly said nothing defi- nite on this point; but, by a closer consideration of his deve- lopments and equations, one can easily perceive how the varia- tions therein occurring are to be understood. If we commence with the values which the quantities q,, qo,..-@» with the original motion have at a certain time ¢, the corresponding values with the changed motion are those which the quantities have at a time ¢+ 6¢—in which the variation 6¢ is not determined, but the same for all quantities. That a common value is indeed to be attributed to the varia- tion d¢ throughout the system is at once evident from this, that in equation (I.a) d¢ appears as a quantity valid for the entire system. Another circumstance which leaves no doubt about this is the following. Hamilton presupposes, in the derivation of his equa- tions, the proposition of the conservation of energy, according to which the sum T+U is constant. But that proposition of course holds only when, in the formation of the quantities T and U, the variables which determine the positions and velocities of the points are brought into the calculation with the values they have at a common time, whether this time be ¢ or ¢+-d¢; but we must not combine values which refer to different times in order to form from them the quantities T and U. Accordingly, with equations thus produced, so long as the opposite is not expressly stated and shown to be admissible, it must be taken as evident that only simultaneously occurring values of all the variables are ever brought into the calculation. In order to see how variations which correspond to a common time-variation 6¢ behave, we will now select a simple case for consideration. We will, namely, presuppose that with the ori- ginal motion all the points describe closed paths, and with the deviating motion, again, all the points, starting from infinitely little-changed initial positions, describe infinitely near-lying closed paths, but that the periods of the different points are altered in different proportions. As the time-variation 6¢ can be taken at pleasure, we will first suppose 6¢=0; that is, we will regard as corresponding to one another such values of the variables as belong to one and the same time. If, then, a point has different periods with the two motions, the two positions which belong to one and the same time, reckoned from the commencement of the motion, are so relative to Stationary Motions. 243 much further distant from each other as the timeis greater. It hence follows that the reciprocally corresponding values of the variables dependent on the positions of the points become con- tinually more different as the time increases ; and therefore the variations of these variables do not undergo merely such fluctua- tions as repeat themselves in a similar manner, but much rather with increasing time ever greater variations of the variables must occur, If, instead of being supposed =O, the time-variation d¢ be accommodated to the changed period of one of the points, we can thereby cause the variations, at any rate, of those variables which depend only on the position of ¢hat point to alter only in a pe- riodical manner. For the rest of the variables, however, which depend on the positions of the other points, whose periods have changed in different proportions, there still exists the inconve- nience that with time ever greater variations occur, whereby the equation becomes as unsuited to our purpose as before. 6. I now turn to the explanation of the method employed by me for the treatment of stationary motions. To determine more closely the corresponding values of any quantity Z which varies in the course of the motion, and thereby also to give a more complete definition of the variation 6Z, which represents the difference of the corresponding values, we will select a quantity dependent on the time as the measuring quan- tity, and settle that those values of the variable Z which belong to equal values of the measuring quantity shall be regarded as corre- sponding values. If we first take the time itself for the measuring quantity, we obtain the already discussed species of variation, which we will now more closely characterize by putting the measuring quan- tity ¢ as an index to the 8 and consequently writing 6,2. But now, instead of the time ¢, another quantity ¢, which changes with the time, may be introduced as the measuring quantity, so that @ can be represented as a function of ¢, or in- versely ¢ as a function of ¢. With the original motion we will first put generally ; BPG) 2 tea toy aenkger were 6 AO) and with the deviating motion, in which the relation between the time and the quantity ¢@ can be somewhat different, we will put, the time being for distinction denoted by ¢*, PM=f\P)+efilg), + + + + + (9a) in which f and f, represent two yet undetermined functions, and ¢ shall be an infinitesimal constant factor. If now in these two equations the quantity @ has the same value, the times ¢ and ¢* are to be regarded as corresponding times. If, further, the S 2 2 44 Dr. T. C, Charles’s Analyses of Coal from above-considered variable has the value Z in the original motion at the time 7, and in the deviating motion the value Z* at the time @, Z and Z* are corresponding values of this quantity, and the difference Z* —Z is their variation. This kind of variation, in which @ is taken for the measuring quantity, shall be de- noted by 6,Z. Therefore the difference t—7?*, which according to the two preceding equations has the value ¢f,(@), has also to be denoted by dgf. We have previously represented the time by an undetermined function of ¢, which on the transition from the one motion to the other undergoes an infinitely little variation. In the nearer determination of this function we can be guided by the nature of the subject of investigation. In the subsequent investiga- tion a very simple form of the function is selected, which is closely connected with the conception of the phase introduced in my previous memoir. To elucidate the notion of the phase, let it be first assumed that the variations which the quantity Z undergoes in the course of the motion proceed periodically, and let the duration of a period be denoted by 7. For such a case I have formed the equation Sidhe ee and named the quantity thereby defined the phase of the varia- tion. With the deviating motion the duration of the periods may be denoted by 7+ 62, and then we may put (k= (4 Ot). hehe ee) If the phase ¢ has one and the same value in both these equations, ¢ and ¢* are corresponding times, and we have therefore S,t=tt¥—t= i. S16. Sioa al Just so for the quantity Z, those values are corresponding which belong to like phases; and consequently the variation dgZ has a very plain meaning. Variations of this sort do not with the time take ever greater values, but only change periodically, just as do the quantities themselves of which they are the variations. [To be continued. | XAXVI. Analyses of Coal from the Coal-Measures in co. Tyrone, and of a Lignite from Ballintoy, co. Antrim. By 'T. Cransroun Cuaries, M.D. &c., Chemical Assistant, Queen’s College, Belfast +. HE following results were obtained in the analysis of two specimens of coal from the Coal-measures in co. Tyrone, and of a lignite from Ballintoy, co. Antrim. A series of analyses + Communicated by the Author. the Coal-measures in co. Tyrone. 245 were made of different portions of these specimens; and asa considerable variability appeared to exist in their composition, so as to show the extremes of this variation, the results of three analyses of three different pieces of each have been given, these having been selected from a number of others closely resembling them. The analyses were made in the usual way, in a current of oxy- gen gas, the apparatus being swept at the end of the operation by a current of air. To avoid any loss from the potash-bulbs, the precaution was taken to attach two U tubes, one containing marble and caustic potash, and the other pumice moistened with sulphuric acid. The combustion-tube was more than half filled with copper oxide ; and in the remaining part was placed the pla- tinum boat and a long copper boat containing copper oxide, the platinum boat lying between the copper boat and the column of copper oxide. It was found most convenient to use a platinum boat at least 80 millims. long, as the combustion of the coal was thereby greatly facilitated. Not more than ‘15 to ‘3 grm. was employed for an analysis ; and this was takeu from a large quan- tity that had been powdered and well mixed. Before calculating the carbonic anhydride and water from the increase in weight of the potash-bulbs &c., certain corrections were applied. The amounts of these corrections had been previously ascertained by a number of blank experiments, in which known quantities of air and oxygen had been passed through the apparatus, and the weight of carbonic anhydride and water present determined. Though the air and oxygen were first purified by being sent through large U tubes containing caustic potash and sulphuric acid, there was always an increase in weight in the calcium- chloride-tube and the potash-bulbs ; it is therefore necessary to apply this correction in accurate experiments. (8) Coal from 5-foot |} (y) Cannel-coal (a) Lignite from Ballintoy, Main, Drumglass from Coalisland, co. Antrim. Colhery, co. Tyrone. co. Tyrone. (1) | 2); 8) | @ | @) @ |] ®@) @ | @& SS Eee —— —___— Carbon ...... 473 | 478 | 481 73°31 | 765 | 789 || 7338) 77-58) 79-07 Hydrogen ...| 631; 6:25| 596)| 7:02) 642; 630] 601) 593) 512 Oxygen and nitrogen...) 31:49| 30:85 | 30:64|| 13°77 | 12°93] 10°35;, 344) 2°77) 2-01 Sulphur ...... soe Meauivage lc ll dainnat 1-6 145). 1-5 ee ole eal Oil SEN, dae tt 149 | 15-1 | 15:3 43 | 2:7 | 2:95)) 14:87} 12:01 | 11°89 246 On the Nodal Lines of a Square Plate. (a) Wood-like in structure, of a dull brownish-black colour, cuts readily, and does not soil the fingers; particles do not cake when heated; sp. gravity 1°32 to 1°45; contains 17 to 18 per cent. of hygroscopic water. This lignite makes a very good fuel, but is not as rich in carbon as most of the lignites about Lough Neagh, which contain 51 to 58 per cent. (Sir R. Kane). Com- pared with other lignites its percentage of ash is high; but though it also contains a large quantity of hygroscopic water, yet in this respect it does not contrast so unfavourably with them. (8) Moderately brittle, of a brilhant black lustre, sp. gravity 1:29 to 1:305, hygroscopic water 7 to 8 per cent., burns rapidly, caking but little, and leaving a light porous coke; a slight ad- mixture of iron pyrites in thin scales; ash light, and of a dull reddish colour. From the large amount of carbon present, and the small amount of ash, this makes a very good burning coal. It is as rich in carbon as many of the English and most of the Scotch coals. (vy) Hard, compact, difficult to pulverize, of a dull black colour, powder brownish black, burns brightly, tumesces little, cakes but slightly, ash greyish white; sp. gravity 1:275 to 1:37, hygroscopic water 1°5 to 1°9 per cent., coke about 50 per cent. There is a considerable admixture of iron pyrites, which occurs in thin layers. This coal yields a large quantity of gas of high illu- minating quality ; and were it not for the large percentage of ash it contains, it would be equal to any of the English Cannel-coals. XXVIT. On the Nodal Lines of a Square Plate, By Lord Rayzzren, F.R.S. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, “FT REGRET to find that the investigation of one of the nodal lines of a square plate, published in your August Number, is to a great extent vitiated by the erroneous assumption that it is possible for a square plate to vibrate after the manner of a simple bar. The function representing such a motion satisfies the general differential equation, as well as the two necessary boundary conditions along the pair of edges for which the mo- tion is constant ; but on the other pair of edges one of the con- ditions is in general violated. This corresponds to the fact that if a plate is bent by couples acting along one pair of oppo- site edges, it will in general take a contrary curvature in the perpendicular direction. Several too confident assertions in the paper referred to must now be retracted; and the deviation of Dr. Strehlke’s measure- ments from my calculations are no greater than are fairly attri- butable to the imperfections of the latter. It appears that the On Objections to the received Principles of Hydrodynamics. 247 form of the nodal lines is not (as I had supposed) entirely in- dependent of the relation between the two elastic constants. I may, however, be permitted to remark that my calculation, though not strictly applicable to a glass or metal plate, belongs to an extreme case of the true solution ; for it would be correct if the nature of the material composing ‘the plate were such that the extension produced by a longitudinal force acting along a bar of it were unaccompanied-by lateral contraction. This condition of things, though probably not realized in nature, is approximated to in the case of substances such as cork (Thomson and Tait’s ‘ Natural Philosophy,’ § 685). I remain, Gentlemen, your obedient Servant, RAYLEIGH. XXVIII. Reply to some Remarks by Professor Challis*, “On Ob- jections recently made to the received principles of Hydrody- namics.’ By Rosert Moon, M.A., Honorary Fellow of Queen’s College, Cambridge +. hiss AM glad to find that my argument in proof of the equation = funct. (p, v), applicable to fiuid motion in one direction, has seauived the sanction of Professor Challis. When personal friends have concurred with opponents in regarding such a rela- tion between the pressure, velocity, and density as a wild sug- gestion, unworthy of a moment’s consideration, it will be readily understood that I am not insensible to the value of support. Professor Challis labours under a misapprehension, however, when he asserts that the “ general theorem includes the more particular case in which the pressure is a function of the density only,” and that, therefore, by my “own showing, it is legiti- mate to make the hypothesis that the pressure is always in exact proportion to the density.” For motion in one direction it is axiomatic that we must have in every fluid, in every case of motion, p=h (2), p=fo(t); v=f,(2t) ; whence it follows that, for every value of x and ¢ for which each of the foregoing equations represents a substantive relation be- tween the variables, we shall have p= funct. (p, v). It is not axiomatic, however, though it happens to be true, that in every fluid for particular cases of motion we may assume p=fiet), p=aflat); where a* is a constant whose value or values depend on the nature of the particular fluid dealt with. And it is neither axiomatic nor true, that in any particular * See Phil. Mag: for August. | + Communicated by the Auther. 248 Mr. BR. Moon en Objections recently made jluid whatsoever we shall have always, or generally, p=f(e), p=ef(at). . For proof of these latter propositions I must refer to the in- tegral (elsewhere derived*) of the equation of motion, Gy al eRe Oat cy ae CO) Ce aay viz. the trio of equations, p=—=44(v42), | a Atel bal ; . (2) o* Sareea PL BD a : . where uw=v-+ —, where « is an arbitrary constant, and ¢, Wy, Wo are arbitrary functionst. Suppose that when ¢=0, p and v are represented by the equations p=f,(z), v=f,(~) ; then we shall have, when ¢=0, from the first of (2), p= a + $l) + ey Paeriissie i) Hence, although p=a?f,(z) is an admissible assumption here, since by means of @ we can satisfy the equation Ofxle)=— Fx +64 L0)+ ray yet the number of different expressions for p which are equally admissible is simply infinite—since, if in (3) we put f,(z) for p, where f, denotes any function whatever, the equation so result- ing may equally be satisfied by properly assuming @ The above establishes that there is no fluid for which always, or ge- nerally, »=a’p. But, dismissing for the present this argument, if in general we have p= funcet. (p, v), 1 would ask upon what philosophical principle can we be called upon to accept, or even be invited to collect evidence in favour of, the law p=a’p, in support of which not the vestige of an a priori argument can be ad- duced, to the entire exclusion of a countless number of other laws which @ prior have precisely the same claim upon our attention ?° _ * See Phil. Mag. vol. xxxvi. p. 27. I regret that, in two subsequent papers in the Philosophical Magazine, p is erroneously written for D in the denominator of the fraction which occurs on the right-hand side of the second equation of the solution. ‘+ That equations (2) satisfy (1) may be verified by differentiating with respect to both # and? either of the last two of equations (2); then eliminating yf’, or ’., as the case may be, from the equations so ari- sing, and, finally, by eliminating ¢' from the last result by means of the derivative with respect to x of the first of equations (2). to the received Principles of Hydrodynamics. 249 With respect to the case I have proposed regarding the piston and the weight, of which Professor Challis has treated, he ap- pears to have failed in catching tke point of my objection. Ad- mitting for the moment that the piston would begin to descend with the accelerating force naa = with what accelerating force will the stratum of air begin to descend according to the ordinary theory ? At the beginning of the motion the pressure on the upper side of the stratum would be Mg, and that on the under side would equally be Mg. Hence, while at the beginning of the motion the piston, according to the received theory, would have a tendency to move represented by the accelerating force ae M+m’ the stratum in immediate contact with the piston at the same epoch would have no tendency to move whatever, a state of cir- cumstances which I maintain to involve a contradiction. If the introduction of the second weight does not produce in the stra- tum under consideration a tendency to move, what other circum- stance can occur which would produce in the stratum such a ten- dency? If it be answered that this will happen when the piston has descended through an indefinitely small space, I reply that the piston cannot descend through an indefinitely small space without the underlying stratum of air descending through a corresponding space, and that it is impossible that a stratum which has no tendency to move can descend through even an in- definitely small space. I am afraid that I cannot agree with Professor Challis as to the bearing upon Boyle’s law in the case of motion of the cases I have suggested where the density varies per saltum. Ifon one side of a given plane we have a density 2D, and on the opposite side a density D, then without waiting or attempting to decide what the motion would be under such circumstances, it appears to me that I cannot err in saying that, according to the received theory, the pressure of the first portion of the fluid on the second is double that of the second on the first, and that therefore to assert that Boyle’s law and the law of the equality of action and reaction hold in this case is simply to maintain a contradiction in terms. If the views I have endeavoured to unfold are correct, it will follow that the true function of experiment in determining the motion we have been considering is to determine the initial values of the pressure, density, and velocity. These being known, the values of the arbitrary functions ¢, r,, yr, can be ascertained, and the motion will be completely represented by the equations (2). P.S.—It may be remarked that, if it be intended that we shall 250 Notices respecting New Books. have p=a’o throughout the motion, it will not be enough that we have p=a?f,(v~) when ¢=0. We must have © x a ap=— + (0+ “). v p ° pP Eliminating v + * between this equation and the last two of (2) we shall obtain ¢wo equations between p, x, and ¢ only, which must needs be identical ; whence it can easily be shown that we must have | Numa a , ; Sinan and therefore b(u) =2au+C. 6 New Square, Lincoln’s Inn, August 7, 1873. XXIX. Notices respecting New Books. The Mare Seremtatis : ats Craterology and principal features. By W. BR. Brrt, /R.AS. London: Taylor and Francis. IX the year 1867 Mr. Glaisher, in his report of the Lunar Com- mittee of the British Association for the Advancement of Science, has this remark :—‘‘ Had the Mare Serenitatis undergone the close scrutiny in the course of this work which the Mare Crisium has in compiling the table in the report presented at Birmingham, this Committee could have pronounced decisively as to the state of Linné a little anterior to the announcement of change by Schmidt.” If the present unsettled state of the question of change, especially as regards Linné, be a reproach to Selenography, as it evidently must be when we find a popular writer announcing that an undoubted change in this remarkable crater had really taken place, and then some few years afterwards acknowledging that when he wrote in 1867 he “had not an adequate conception of the difficulties of the subject,” it becomes exceedingly important that difficulties which tend to retard the progress of our knowledge of the moon’s surface should be met in sucha way as to reduce controversy to its smallest extent. This Mr. Birt, in the monograph before us, has endeavoured to do by specifying no less than 333 distinct objects on or near the Mare Serenitatis, an extensive lunar plain of more than 400 miles diameter. The map, which has been thoroughly revised, contains every object which has been recorded since Hevel’s and Riccioli’s epoch to the present; and students who really wish to contribute to the settlement of the interesting question of change the monograph cannot fail to assist materially. The authority by whom any given object was first recorded is inserted in the table accompanying the map; and toeach object of special interest illustrative notes are appended. By the aid of the monograph in connexion with existing records, the history of any single object can be readily traced, and its existence or non-existence, with any changes it may have undergone, ascertained. _ [ 251 J XXX. Intelligence and Miscellaneous Articles. ON THE PASSAGE OF GASES THROUGH COLLOID MEMBRANES OF VEGETABLE ORIGIN. BY A. BARTHELEMY. es purpose of these experiments was to prove that those of Graham on the dialysis of gases through caoutchouc could be verified on natural vegetable colloid films, and principally on the cuticular surfaces of the leaf, and thus to justify the important part which I make the cuticle play in the absorption of carbonic acid by plants. Every body knows the Begoniacez with leaves spotted with white, which are cultivated in greenhouses, and the white spots of which are, as I have convinced myself, only elevations of the epiderm upon a layer of nitrogen. ‘The leaves of certain varieties, very thin on the living plant, are reduced, on fading during the winter in darkness, to the condition of a pellicle endued with elasticity and representing almost nothing but the cuticular layers. It was these colloid membranes which served me in repeating Graham’s experi- ment. I followed strictly the course of the illustrious physicist, save a few modifications of detail. One commences by ascertaining that the membrane is intact, presenting no rents, by the dialysis of air alone. Three experi- ments, made on the 16th, 17th, and 18th of March, gave the fol- lowing results at the end of six hours :— March 16. March 17. March 18. Volume of gas collected 5:2 cub. cent. 5°5 cub. cent. 7:0 cub. cent. Volume of oxygen ab- sorbed by pyrogallate + 1:9 Atala at: Gi PORIGS.... 2... - Proportion of oxygen .. 36 per cent. 41 percent. 31 per cent. Although the proportions of oxygen presenta rather wide devia- tion, due to the difficulty of repeating the experiments under the 29 2-2 39 same conditions of external pressure, temperature, and, especially, | of hygrometric condition, it may be concluded that oxygen passes more rapidly than nitrogen, and that air thus dialyzed contains on the average 36 per cent. of oxygen. ‘This number is a little below that found by Graham with caoutchouc. Having made this verification and obtained this important result, I proceeded to the comparison of the velocities of the three gases which most interest us. or this purpose, having set up a current of carbonic acid above the membrane, I noted the point to which the mercury had descended at the expiration of an hour; then, passing nitrogen or oxygen, | noted the time taken by the mercury to descend to the same level. In four experiments, with different membranes, I obtained the following results ;— Ist exp. 2nd exp. 3rd exp. 4th exp. Carbonic acid ....1 hour 1 hour 1 hour 1 hour Nitrogen 1.2.1). jase 13240" £5" 30" 14. ,, Oxygen hi Pee Bok G20" ee 5» 40" 252 Intelligence and Miscellaneous Articles. These experiments, made under conditions of pressure, tempera- ture, and hygrometric condition which cannot have been identical, are nevertheless sufficiently concordant with those of Graham, and permit me to conclude that the natural colloid surfaces of vege- tables have for carbonic acid an admissive power which is from 13 to 15 times as great as that which corresponds to nitrogen, and six or seven times as great as that which refers to oxygen. A few days afterwards I operated with perfectly dry carbonic acid, and only found, as the velocity relative to nitrogen, numbers varying between 9 and 11. It appears, therefore, that carbonic anhydride passes less quickly than hydrated carbonic acid. On replacing the vegetable membrane by caoutchoue, [ obtained a similar result. The difference produced by dried oxygen and nitrogen is less pronounced. I will remark, in conclusion, that these experiments prove the dialysis of carbonic acid through the cuticle of leaves, just as much as the experiments of Dutrochet on membranes and aqueous solu- tions prove endosmose by cellules, or the experiments on absorp- tion made by M. Dehérain with porous vessels, to which the Academy accorded one of its highest rewards. Ina word, cuticular respiration appears to me sufliciently proved by the presence of this membrane on all the organs, by the analogies of constitution, physical and chemical, with caoutchouc, by Graham’s experiments and the measurements of the passage of gases through colloid membranes, and, lastly, by the experiments of M. Boussingault, who attributes to the upper surface of leaves, destitute of stomata, a greater decomposing faculty than that of the lower surface riddled with these minute apertures——Comptes Rendus de V_ Académie des Sciences, Aug. 11, 1873. ON THE REFLECTION OF LIGHT INVESTIGATED BY M. POTIER. BY G. QUINCKE. The Comptes Rendus of the Paris Academy, Sept. 9th and 16th, 1872 (vol. Ixxv. pp. 617 & 674), contain two communications from M. Potier on the reflection and refraction of light at the boundary between two media. He has, with the sodium-flame, observed Newton’s coloured rings in a thin plate of glass the hinder surface of which was at the same time bounded by air or sulphide of carbon, or in thin lamelle between a glass lens and a metallic mirror. He moreover investi- gated the interference of two pencils of rays, one of which has undergone a metallic, and the other ordinary or total reflection at the base of a glass prism, in its interior. In some experiments the metallic mirror was replaced by a plane glass mirror beneath the surface of the lens, or by a liquid at the outer face of the prism. M. Potier is of opinion that the ether in the two media was divided by a transition-layer, and that the process of reflection or refraction may be conceived to take place within the transition- layer of two transparent media, in a plane parallel to their common boundary. This plane, he thinks, which formed the optical boundary of the two media for light polarized parallel to the plane y , Intelligence and Miscellaneous Articles. 2538 of incidence, was situated at different distances from the common boundary when, one of the two media being left constant, the | other was altered in such wise that the optical thickness of a thin lamella varied with the nature of the substances adjacent to it. With glass and air or sulphide of carbon, the difference between these distances was found by experiment to be =-); wave-length for light polarized parallel to the plane of incidence. The phase of the reflected light undergoes different variations with different incidence-angles, being O with grazing incidence and having a maximum value with normal incidence. The change of phase varies with the nature of the thin lamella between the lens and the plane mirror. The ray reflected from metal is retarded when the reflection is normal, the retardation amounting to 4 of a wave- length for silver and air, to 4 for silver and an essential oil. This retardation has a sensible influence when the thickness of a thin layer of metal upon a glass plate is determined from the different diameters of the Newton’s rings formed beneath a lens when laid upon a plate of metal and when laid upon a plate of glass. *« Moreover, with a retardation of the reflected ray, there was a corresponding change of phase in the transmitted ray; and in passing through a transparent lamella of silver, the phase must have been accelerated ;4, of a wave-length. This must be taken account of in the determination of the velocity of light in the interior of metals ; and this circumstance accounts for it if certain experimenters haye found the refraction-index of metals too small or negative. The phenomena in metals were more complicated, as there did not exist here, as in transparent substances, a plane, parallel to the boundary, in which the incident and the reflected ray, both polarized parallel to the plane of incidence, coincide, but only a plane in which the two had a definite difference of path. The situation of this plane varies with the nature of the substance over the metal, since the extinguishing-force of the metal, and, in a less degree, the nature of the substance above the metal, varied the constants of the elliptic polarization produced by metallic reflection—that is, the principal angle of meidence and the prin- cipal azimuth.” As, to my knowledge, no one except me* has investigated the refraction-indices of transparent layers of metal, I must refer to myself the expression “ certain experimenters,” and remark that to the above statements, save so far as they contain what was already | known, I cannot assent. My optical experimental investigations published in the Annalen contained, besides those methods which are described in the above- mentioned communications, some others, which have concordantly conducted to this result—*“ that, in order to be in accord with the known facts, we have to make the assumption that reflection and refraction take place in a transition-layer the thickness of which can be measured by experiment” ry. * Poge. Ann. vol. exx. p. 599: 1863. f Ibid. vol. exh. p. 398: 1871. 54 Intelligence and Miscellaneous Articles. In like manner the law given by our author, that reflection takes place in a plane parallel to the boundary surface of transparent substances, is not new. Assuming the change of phase on the passage through the boundary surface of transparent substances to be insensible, as all investigations hitherto appear to prove, that law was established more than twenty years since, by Stokes*, with the aid of the principle of reversion, without any special assumption of a dynamic theory of light under the presupposition that the effective forces depend merely on the situation of the particles in motion. In accordance with this law is the fact which I have established by experiment, “that with the same reflecting boundary surface of two transparent substances, for corresponding angles of incidence (which are mutually related as angles of imcidence and refraction), whether the reflection take place in the one or the other medium, the observed values of the difference of phase of the two ray-com- ponents polarized parallel and perpendicular to the plane of inci- dence are equal and contrary, and the amplitudes of the two components are in the same ratio. “ If the reflection is positive in the one medium, it is negative in the other, and vice versa” T. The distinction, originated by Jamin#, of transparent substances into those with positive and those with negative reflection (that is, with which the component polarized parallel to the angle of inci- dence is accelerated or retarded m comparison with the perpen- dicularly polarized component), cannot any longer be maintained, although it has recently been so in German manuals of physics. That the phase of the reflected light in the case of grazing incidence undergoes no change cannot be decided by the method made use of by our author. By interference of the direct and in the most decided manner grazingly reflected rays, I have proved§ that the change of phase is not, as M. Potier states, =0, but corresponds to half a wave-length, both for the light polarized parallel and that polarized perpendicular to the plane of incidence. For other incidence-angles than 90° the difference of the altera- tion of phase in two differently reflected rays, e.g. from glass and metal, can be only relatively determined; and I have determined | by experiment, both with the method made use of by our author and with some others, this difference for reflection in different substances, and have discussed in detail how far they deviate from the variety of change of phase required by the theory||._ Abstrac- tion made of the uncertainty (there, p. 226, fully discussed) of the magnitude of half a wave-length, the observations generally, but not always, give a maximum of difference of phase of two dissimi- larly reflected rays when J=0. The ray reflected from a metal was, relatively to that reflected from glass, accelerated when the * Camb. and Dubl. Math. Journal, vol. iv. p. 1: 1849. t+ Pogg. Ann. vol. exxviii. p. 369: 1866. ~ Ann. de Chim. vol. xxix. p. 303: 1850. § Pogg. Ann. vol. exli. p. 223: 1871. | Pogg. Ann. vol. exli. pp. 196-232, 384-388: 1871. Intelligence and Miscellaneous Articles. ZOO reflection was in air. There also the results of the earlier investi- gations by Airy* and Glant of Newton’s rings between lenses and plane mirrors of various materials are treated of, as well as the influence exerted upon experiments of this sort by condensed vapour or gas films on the reflecting surfaces. I would seek in such im- purities the reason of the difference between my measurements and those of other observers. Before the appearance of the communications in question, I had pointed outt “that the amplitude and phase of light in passing through thin layers of metal are changed simultaneously, the change depending on the thickness of the metal,” and also “ that the change of phase in refraction must vary also with the position of the plane of polarization.” At the same time, I showed how, independently of the sources of error of the formerly usual methods, a thin lamella of metal displaces interference-streaks as if the refraction-idex in the interior of the metal were <1§. On the same occasion it was explained how far it is justifiable to assume an acceleration of the phase when light passes through thin, transparent layers of metal, which M. Potier seeks to establish on theoretical grounds. When a lens is pressed upon a glass plate partially covered with a thin layer of metal, Newton’s colour-rings upon the metal appear displaced towards those upon the glass plate. The thickness of the metal cannot be calculated from this displacement, unless, as is correctly remarked in the communication mentioned, the changes of phase with reflection at the surfaces of the metal and the glass, or the difference between the two, be known. Hence I have never made use of this method for determining the thickness, but have pressed the lens upon the uncovered part of the glass plate until the lower surface of the lens touched the margin of the sharply bordered layer of metal. Contact was shown by the distortion of the colour-rings on the glass. The colour which was exhibited by the layer of air of the same thickness as the metal on the glass plate gave then the thickness of the latter]. Tt is at once seen that in this determination the knowledge of the change of phase with normal reflection is not requisite; and there- fore ignorance of it could not occasion any error in the rest of the conclusions deduced by me. . Finally, I have also shown how, in reflection from the same metal, the principal angle of incidence and principal azimuth, as well as the qualities generally of the reflected light, depend on the nature of the transparent medium in which the reflection takes place 9], and to what depth light of different colour and plane of polarization penetrates the metal ; so that, in relation to this also, M. Potier’s remarks cannot be said to be new.—Poggendorfl’s Annalen, vol. cxlviii. pp. 311-316. * Cambr. Trans. vol. iv.; Pogg. Ann. vol. xxvi. p. 123: 1832. + Absolute Phasenanderungen durch Refleaion: Berlin, 1870. t Pogg. Ann. vol. exli. p. 191: 1871. § Ibid. p. 186: 1871. \| Ibid. vol. exxix. p. 178: 1866. @ Ibid. vol. exsviii. p. 547 sq., exxix. pp. 182en217: 1866. Re ee 256 Intelligence and Miscellaneous Articles. EXPLOSIONS PRODUCED BY HIGH TONES. A great part of the known explosive substances contain more or less nitrogen. The simplest of these, and at the same time one of the least stable, is the combination of iodine with nitrogen. Iodide of nitrogen is very easily prepared by wetting finely powdered iodine on liquid ammonia. It is then filtered ; and the filter, while still moist, is taken out of the funnel and cut up into small pieces, which are dried separately. Although this substance while moist is quite harmless, yet as soon as it is dry it detonates with great violence on the slightest friction. But what is most remark- able is, this violent decomposition can be called forth by certain high tones. MM. Champion and Pellet have made the following interesting experiments upon it :—T'wo glass tubes of 15 millims. diameter, and 2:4 metres total length, are combined by means ofa strip of paper ; and upon each end is put a little piece of paper which contains 0:03 of a gramme of iodide of nitrogen. When one of these is caused to detonate, the other detonates likewise. The explosion of the second paper, however, is not effected by pressure of the air: this can be shown by introducing a small pendulum into the tube ; it is no more disturbed by the explosion than when the tube is blown strongly into with the mouth. If we fasten such papers to the strings of a double bass, or a violoncello, or a violin, we can demonstrate that the deep tones exert no action, while the high tones induce a detonation. The very high tones obtained by twitching the strings on the tail side of the bridge give the same result. The results were similar in experiments with Charese tomtoms : the deep-toned instruments effected no detonation; the high-toned ones constantly did so. Two parabolic concave mirrors of 0:5 of a metre diameter were set up at 2-5 metres distance one from the other. A small quantity of iodide of nitrogen was brought into the focus of one of them, and another small quantity was placed in the centre between the two mirrors. Some nitroglycerine was exploded in the focus of second miror: the iodide of nitrogen in the focus of the first mirror detonated ; that in the centre remained intact. Although other explosive substances placed in the focus of the second mirror pro- duced the same effect, yet this was not, as might perhaps be thought, a consequence of heat, because 0:03 gramme of nitro- glycerine, which does not develop more heat than 0-9 gramme of gunpowder, produced an explosion similar to that produced by from 8 to 10 grammes of powder. The mirror was then coated with lampblack, when the explosion of 10 grammes of powder did not induce any detonation of the iodide of nitrogen, while 0:03 gramme of nitroglycerine was still sufficient to do so.—Chi onique de V Industrie, No, 52, Jan. 29, 1873. fogs SO LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. —__<¢-—__+—_ [FOURTH SERIES.] OCTOBER 1873. XXXI. On a Relation between Heat and Static Electricity. By Freperick Gururte*, i ee experiments to be described concern a remarkable rela- tion between heat and static electricity, and may be briefly described as exhibiting (1) the difference in power which one and the same body at different temperatures possesses of discharging electricity of one kind, and (2) the difference in power which one and the same body at the same temperature has of dischar- ging the two kinds of electricity. A great many of my experiments involved the use of white- or red-hot metal balls. Those I used were the ordinary cast-iron balls about two inches in diameter, provided with eyes. An insulating handle was made by fastening a stout copper wire book by means of thinner wire to the end of an ebonite pen-holder about six inches long. When no insulation was required an ordi- nary iron hook was used. The iron balls were heated in a clear coke fire. Hach experiment was made never less than twelve, and mostly from twenty to thirty times, on different days. The two gold-leaf electroscopes which I used kept their charge with- out sensible loss for from five to ten minutes. § 1. Hzperiment.—A white-hot iron ball being hooked out of the fire by the insulating hook and brought into contact with the + conductor of an electrical machine, and then brought near to or touching the top of an electroscope, produces no divergence of * Communicated by the Author. (An abstract of this investigation appears im the ‘ Proceedings of the Royal Society,’ February 13, 1873: vol. xx1. p. 168.) Phil. Mag. 8. 4. Vol. 45. No. 806. Oct. 1873. T 258 Mr. I. Guthrie on a Relation between the leaves. It is in fact impossible to use a white-hot iron ball as a “proof plane” for + electricity. | § 2. Experiment.—A white-hot iron ball being hooked out of the fire, as in § 1, by the insulating hook, is made to touch the — conductor of the machine; it is then found to be incapable of influencing the electroscope by induction or by contact. The white-hot ball cannot serve as a proof plane for — electricity. § 3. Haperiment.—On the top of the electroscope is placed a wooden block covered with tinfoil. Above this are a few sheets of metal plate. Upon these is a tripod stand inverted, to which a metal chain is fastened. ‘The other end of the chain can be connected with the + or — conductor of an electric machine. A white-hot iron ball is placed on the tripod, and the chain is fastened to the + conductor. As long asthe machine is worked the leaves diverge; but on ceasing, they immediately drop together. § 4. Haperiment.—The arrangement being precisely the same as in § 8, the chain is fastened to the — conductor of the ma- chine. As before, the leaves only remain divergent while the machine is being worked. 8 5. Haperiment.—The chain in § 3 being removed, the white- hot ball is placed upon the tripod. It is found impossible to make the leaves diverge by a charge from a proof plane of 24- inch surface which has been charged by either the + or — con- ductor and then brought into contact with either the white-hot ball or any other part of the electroscope’s system. § 6. Hzperiment.—A white-hot iron ball on a metal hook (so as to be in earth-connexion) is held above the top of an electro- scope charged with + electricity. When at the distance of one or two inches, the leaves rapidly and completely collapse, and do not recover their divergence on the removal of the ball. § 7. Hzxperiment.—The electroscope is charged with — elec- tricity, the conditions being otherwise as in § 6. When the ball is at a distance of three or four inches the electroscope is rapidly, completely, and permanently discharged. § 8. Haperiment.—The electroscope being charged with + electricity, the white-hot iron ball is hooked out of the fire with: the insulating hook and brought above the electroscope. Perfect and permanent discharge takes place when the interval between the two is about one inch. | § 9. Haperiment.—The electroscope is charged with — elec- tricity, the experiment being otherwise as in § 8. The electro- scope loses its charge completely and permanently when the interval is two or three inches—that is, sensibly greater than with + electricity. | § 10. Hepertment.—An iron wire with a little cotton-wool fastened to one end is dipped into benzol, ether, alcohol, or bi- OEE Heat and Static Electricity. 259 sulphide of carbon; the liquid is ignited, and the flame is held above the electroscope charged with + electricity. Ata dis- tance of three or four inches immediate perfect and permanent discharge takes place. § 11. Hzperiment.—The same flames are found to discharge the — electricity of an electroscope at about the same distance. § 12. It will be noted that these flames included white lumi-_ nous smoky (benzol), white luminous (ether), feebly luminous (alcohol and bisulphide of carbon): They are all water-forming but the last. There is little, if any, difference noticeable in their power of discharge. pdoq — hdk t has a mean value that vanishes as the time increases, then the fol- lowing equation is valid :— 6(U—T) = =pq'd log i+ 3 in which the first sum on the right-hand side, like the sum pre- viously mentioned, contains n terms, which correspond to the n variables q,, Go»+++Gn3 while the second sum refers to the quanti- ties Cy, Co, &c. contained in U, which are constant during each mo- tion, but change their values on the transition from the one motion to the other. | Kiquation (II.) is my equation in the generalized form men- tioned at the commencement. While in Hamilton’s equation (I.) ? the integral } 2Tdi is to be regarded as a function of the vari- Se, ss eee 0 i ables 91, doy +++ Qn» Of their initial values £,, ka,...k,, and of the t energy HE, and in equation (I.a) the integral | (T—U)d¢t asa 1) function of q), Gay++* Ons Ay) hoy «++ kn, and ¢, in this equation the mean value U—'T appears as a function of the time-intervals i, tee, auo the quantities Ci) €, &e. Italso can be analyzed into as “many partial equations as there are independent varia- tions on the right-hand side, whereby, however, we of course obtain quite different equations from those resulting from the analysis of Hamilton’s equations. 8. In order to demonstrate the theorem, let us form for any one of the n variables the product pé,q, and differentiate this according to the time. ‘Thereby we obtain Sen CA U)) 0/8 4 (Pa) = rr nc ad a: =p8,( 7) +P ba d, =poq' + = O; Into this, for the abbreviated symbol p, we introduce from (6) relative to Stationary Motions. 269 fie dE the fuller expression dq!’ and further, agreeably to equation (8), put Then follows d ah cT dU ‘ a (V8) = qrdal + a, ba Ge B+ ++ (13) An equation of this form holds for each of the n variables; and if we imagine the sum formed from these n equations, we obtain d dU Up Pe = =35 buf +E 7 bg Was eee) Since we eney AN is a ee of the 2n quantities g,, Yo; .-g, and q',, g'4, +++ Qin, We can put oO.) = a 78a 454 dq a 4) an expression which contains the first two sums on. the right- hand side of our preceding equation. As regards the last sum in that equation, if in U the quantities 9g), q,---Gn were the only variables, it could be replaced by 6,U. But as in U, by hypothesis, other quantities c,, co, &c. occur, which, though in- dependent of the time, yet may change their values on passing from one motion to the other, therefore U 3,U=3 7, +25 5c. By the employment of hal two equations, (14) is transformed into Spy =3l—8U +35" be or, differently Bes Sua es pion (15) BE A alaagreas sae This equation, multiplied by df, then integrated from 0 to f, and finally divided by ¢, since / and & are the initial values of p and q, takes the following form :— t ae Bi if 3 (U—T)d= — EP ae ae Y seat, 0 In the last term of the right-hand side, by making use of the 270 Prof. R. Clausius on a new Mechanical Theorem mark for mean values, we can put 1¢¢dU aus “| Fe belt =F, be 0 Meanwhile, on tke left-hand side the integral-symbol may remain, and only the variation-symbol 6; be transposed, which is admissible with variations where ¢1s regarded as constant. Then the equation is Ge bq—hbk | dU 3| 5 (U— Ta] = Ee Oh sO oe tay. ¢ dc Here, instead of variations in which the time is regarded as constant, we will introduce on the right-hand side variations in which the phases belonging to the variables in question are con- sidered constant. The procedure to be employed in this alteration 1s easily found, as follows. Let any quantity dependent on the time be signified by D, we will put, with the original motion, Biss 5 and, with the different motion, Tk =F (0) +68 (04), in which ¢ and ¢* represent times corresponding to one another, F and F, signify any two functions, and e¢ is an infinitesimal constant factor. If now the variation 6,4 is to be taken, we have simply to put ¢*==¢ and then to fal the difference 75g whereby we obtain SLE y(t); while if the variation 6,Z is to be taken, for ¢* we must put that value of the time high corresponds to an unvaried value of dp, namely i*=t+ dot, and then again form the difference Z*—Z. We have thus 6gZ4=F (t+ dot) +eF\(¢+ bgt) — F(Z). This gives, neglecting terms of higher order with respect to Sgt and e, a SgZ—eF, (t) + 24 Sof, which, according to the preceding, we can also write thus, | 634=6,24 “bgt. ° if ° ° 3 ° (17) An equation of this form is to be constructed for each of the variables ¢,, Go) +++Qn, Wherein the phases ¢,, do,... dn are to be successively employed. We thus obtain for g,, with a little relative to Stationary Motions. 271 transposition of the terms, the equation 6:9, = 95,90 —7'85,t- By the insertion of these values equation (16) is changed into l GO ad — v dU. afi (U1) di] =3pq2e! Pod OE | 5 aU sy. (19 0 de Putting herein, from (12), ‘= 2,Dy y whence follows Onis $,01,, and ei! = ot, =6 lor?,, t t, we get t aft} (U—Tat| = Xpq'd logi— gs rice Be) tail (19) 0 In this equation, which holds for any time whatever, we will now take the mean values of all the terms. The last sum (which, indeed is independent of the time) is thereby unchanged. The mean value of the penultimate sum is, by hypothesis, for large times, to be put = 0. Im the rest of the terms we will only indicate the mean values. We thus obtain 3124 — that | = Spo lo 3 ae ‘| 5 (U— )dt| = pg iog 2+ & panes (20) a0 In this we have still to consider more closely the left-hand side. The expression t it (U—T) a is the mean value of U—T during the time from 0 to ¢, and therefore a function of ¢ which with the increase of ¢ comes ever nearer to the constant value U—'T, which represents the mean value for very large times. It does not, however, follow that the variation of this function, denoted by 6,, must also approxi- mate to a fixed boundary value. We have previously seen that, with a function whose changes consist only of fluctuations of constantly equal magnitude, the variation denoted by 6; may take ever greater values with increasing time. Corresponding to this, with a function of the kind new in question, which with increasing time makes ever smaller fluctuations, and thus ap- proaches towards a boundary value, it must be considered possible that the variation denoted by 6; makes fluctuations the magni- tude of which does not diminish as the time increases. It would are Prof. R. Clausius on a new Mechanical Theorem hence not be universally admissible to replace the variation 1c é 4 U-—T)d yy One| by the symbol ie ah 6(U—T), which represents the variation obtained when the mean value U—T is regarded as a quantity independent of the time and is variated., In our equation (20), however, the first of the two variations just mentioned does not itself occur, but only its mean value. This becomes constant for large times, as can indeed be seen from this, that an expression which becomes constant for large times stands on the right-hand side of the equation. Conse-. quently the previously mentioned distinction, based on the vari- ability of the variation, ceases ; and we can therefore employ the symbol &U—'T) for this constant-becoming mean value of the variation. ‘Thereby equation (20) is changed into §(U —T) = Spq' 5 log +3 Oe, or the equation (II.) which was to be demonstrated. 9. As an example of the application of the equation, we will take a simple special case for closer consideration. Given two material pomts which, according to any law, attract and, at certain distances, repel each other, and under the influ- ence of this force move about one another. As the centre of gravity of the system remains fixed, and the motion of both points takes place in one plane, we can deter- mine their position by two variables—their mutual distance r, and the angle @ which the line that joins them makes with a fixed straight line. If, namely, the masses of the two points be denoted by m and yp, their distances from their common centre of gravity are Yr and Mb iw + pe m+ fe If, further, by 6 be understood specially the angle which the part of the right line r from the centre of gravity “to the mass m makes with the positive z-direction of a rectangular-coordinate system taken in the plane of motion, the rectangular coordinates of the two points can be expressed as follows :— = cos 8, = —P _ psin 8, m + mb fo m ns ik Lo=— rcos9, y,=— rsin 0 MW -b be relative to Stationary Motions. 273 With the aid of these expressions the equation b ae) 2 can he transformed into the following :— nM 5 = (2? + yl?) + (al? + yl) wi me 2m+p Putting now r and @ in the place of the variables universally denoted above by g, and go, we obtain : 8 a J A= 7 — m+pe ’ Hy 29) an mp 26! | P2= 10 mip’ o From this results further, if R, R’, @, @!' denote the initial values of 7, 7’, 0, 0’, the equation 3 Peg — hdk _ _ my rdg,r— WSR +770'55,0 — R20'50 t Mm ++ t For the definition of the phases ¢, and ¢, we have, according 0 (12), the equations yO adios sama esis. sae aed) and the question now is, whether the time-intervals 2, and i, can be so determined that the mean value of the expression given in (23) shall vanish with increasing time. With even a super- ficial consideration of the motion in question, it is seen at once which time-intervals are to be selected as 2, and 2,, because the motion can be analyzed into two constituents—the alternate approach and recession of the two points, and the rotation of their connecting line—which can be considered singly, as varia- tions of the quantities rand @, The-variation of r is periodic; and if we take the duration of its period as z,, the portion of the fraction in (23) relating to 7, viz. (247902), 6. ww we (QD) , (23) dg ihe oe R/SR be Re Ie 3 the numerator of which changes only pericdically, evidently fulfils the condition that its mean value vanishes with increasing time. For the interval which refers to @ it will be convenient to take the time of a rotation of the connecting line, therefore the time in which the angle @ increases to 27. But as the successive rotations do not generally take place in equal times, we will un- Phil, Mag. 8.4. Vol. 46. No. 806, Oct. 1873. U OTA Prof. R. Clausius on a new Mechanical Theorem derstand by 7, the mean rotation-period of the connecting line. For the mean angular velocity 6’ we accordingly obtain the equation USO te | ee = ee S . ° e 6 s ® (25) lo Further, on account-of the proposition that the radii vectores of the points describe equal areas in equal times, we have the equation 729! = a, a * ° e e ‘8 e (26) where a isaconstant; and we can therefore put 1 = 1 =a5 and faa By employing these equations the identical equation 6! = Ol 4+ 6'—@6! ean be brought into the following form, and multiplying this equation by di, and integrating from 0 to t, we get which, on account of t=72,@, passes into bgp) ote e/ 0 r This expression for 9 may now be variated, ¢. being regarded as constant; we thereby obtain a 4) = NG Sa Se dt ee e © 2 5,0=30-+ 84] 0 Ce 2) 8) The expression is a fanction of ¢ which changes periodically; and its periods have the same duration as the quantity 7, namely 7. We must therefore endeavour to introduce for the variation of this expres- sion denoted by 6g, that variation which is denoted by 65, According to equation (17), for any function Z we can put © 65,425,244 2551, 8,0 =8,L42'80), relative to Stationary Motions. 275 from which it follows that 03,4 54,4 + Z!(8p,f—5,,). As we have, further, 5,,/=9, 8i, ==7 a 1 Og,f = h0i, =! oh the preceding equation changes into §,,2= =8,04(52— ya. pee aoe toe If we apply the kind of transformation hereby exemplified to the last. term of equation (28), we get ff GH Vs tik ae ey ‘ik a If now we consider the part of the fraction im (23) which refers to 0, we can give it a simplified form, since according to (26) r0'5¢,0—R?O'S0O a (6g,0—50) a bc ae a may be put; and when we introduce into this the preceding expression for 63,0, we obtain tel R20'50 wtslef(G De] se 2G Dm The first term on the right-hand side of these equations makes with increasing time ever smaller fluctuations and thus approxi- mates to zero; while the second term makes fluctuations of con- stantly equal magnitude. If, however, we take the mean value of the expression, the second term also vanishes, because the difference e = is changed into 5- s Therefore the part of the fraction relative to @, as well as the part relative to 7, fulfils the condition laid down in our theorem, that its mean value vanishes with increasing time. This having been established, we can apply to the present case the equation (I. ) given in the theorem, and obtain thereby the following— 6(U—T)= ory ie log 7, +7266 log i,) +3 ar be, » (32) (el ) U2 i) 76 Prof. J. D. Dana on some Results of which exhibits a peculiar relation between the time-intervals 7, and 7, and the mean values of the ergal and vis viva. If the mass w be taken as very great in comparison with m, so that the fraction pa may be supposed equal to m, the pre- ceding equation changes into that which holds for the motion of one material point about a fixed centre. This equation I derived separately in a memoir published a short time since*; and I then said that for two points moving about cach other the cor- responding equation could in like manner be derived. Here, however, the same equation has come out as a special case of a much more general one. To equation (II.) various other forms can be given, which are both theoretically interesting and convenient for use, wherein it can at the same time be brought into connexion with my theorem of the virial. These transformations and especially the applica- tion of the equation to the theory of heat I reserve for a subse- quent memoir. XXXIII. On some Results of the Earth’s Contraction from Cool- ing, including a discussion of the Origin of Mountains. By James D. Dana. [Continued from p. 219.] IV. Igneous Hyections, Volcanoes+. HE direct connexion of igneous ejections with the move- ments resulting from the earth’s contraction has been briefly illustrated in the course of the remarks on mountain- making{. It is apparent, without further discussion, that regions of great disturbances embrace the regions of great ig- neous ejections—that the oceanic slopes of the border moun tains, especially around the Pacific, the greater ocean, have been preeminently subject to such eruptions—and that in Tertiary times, when the earth’s crust was becoming too stiff to bend much before the lateral pressure, profound fractures instead of flexures were a common result of its action, igneous outflows were most extensive, and volcanoes were of increased size and numbers. The questions remaining are :— (1) Does the mobile rock owe its mobility in all cases, or any, to the movements of the rocks under lateral pressure—motion * Nachr. der K. Gesellsch. der Wiss. zu Gottingen, Dec. 25, 1872; Phil. Mag. July 1873. + For Part I. see p.41; Part II. p. 210; Part II. p. 217. { Supra, pp. 52, 137, 212, 214, the Harth’s Contraction from Cooling. 277 transformed into heat being its source, in conformity with the -views ably set forth by Mallet ? (2) Is the ejecting foree in eruptions a result of the same lateral pressure ? 1. Source of igneous fusion*.—The suggestion of Professor Hopkins with regard to the earth’s interior, which has been sus- tained on a preceding paget, offers for the source of igneous ejections the old one of viscous rock underneath the earth’s erust; but viscous rock at first as a layer, and later as remnants of the same layer, left after the long cooling. This author sug- gests that these isolated or detached portions may be the source of modern volcanic eruptions; and this view is favoured by Scrope, the eminent vulcanologist f{. The theory does not require that the isolated fire-lakes should exist now at the depth of the original viscous layer; for in the * T say nothing here on the nature or the degree of igneous fusion in plastic rock, as this is foreign to the subject under discussion. t Professor Hopkins’s argument from the amount of precession and nutation, in the Transactions of the Royal Society, 1839, 1840, and 1842, led him to the conclusion that “the thickness of the solid shell could not be less than about one fourth or one fifth of the radius of its external sur- face.” In his paper in the Report of the British Association for 1847 he repeats his conclusion, and then considers the possible steps in the process of refrigeration. Among the different conditions discussed, he supposes as one (the one he favours) the temperature of fusion to be increased much by the pressnre—at a rate much more rapid than ‘1° F. for an increase of pressure equivalent to about five atmospheres,” and adds that then “ we should probably have the condition under which solidification would com- mence at the centre. In this case, after incrustation had begun at the surface, the earth would consist of a solid central nucleus and a solid shell with fluid matter between them, as already explained, till the solidification should be complete.”” He then remarks, with regard to the present state of our globe, that “ under the condition here assumed, with the observed rate of increase of terrestrial temperature in descending, there could be no reasonable doubt of the earth’s entire solidity.”” He next treats more in detail of the process of solidification, and says, having in view the several conditions discussed, that ‘‘ the incrustation may have constituted the very first step in the solidification, or it may have taken place after the forma- tion of a solid nucleus surrounded by a superticial fluid envelope, according _ as the solidification began at the surface or centre; but in either case, as I have already intimated, the superficial crust when first formed must ne- cessarily have reposed on a fluid mass beneath.” He next explains his views as to the formation of the crust, and the final obliteration of the vis- cous layer; and states, with reference to volcanoes :—‘‘ By a continuation of this process it is obvious that the superficial crust of our globe must at length arrive at what I conceive, for reasons above assigned [in a paragraph on p. 33, speaking of the isolated sources of volcanoes], to be its present condition,—that of a solid mass containing numerous cavities filled with fluid incandescent matter, and either entirely insulated or perhaps com- municating in some eases by obstructed channels.” These cavities are made the sources of the material of volcanic eruptions. t Voleanoes, 2nd edit. 8vo, pp. 264, 268. 278 Prof. J. D. Dana on some Results of movements and flexures of the crust, and the opening of fissures for the escape of the mobile rock, great regions of it may have been pressed up and become isolated fire-lakes at a higher level. Or, as Professor Hopkins suggests, the subterranean sources of volcanic action may have been in shape lke inverted cones ex- tending far up into the crust, and may have finally been divided off into “smaller ones by a process similar to that by which the larger cavities were themselves formed from the general fluid mass, the position of each minor cavity being determined by the points in the roof of the larger one, where previous fractures had left the most perfect volcanic vents.” This last explanation holds if regions of volcanic vents date back to early geological time, so that modern volcanoes in an area are successors to In- definitely older ones, but is less applicable where the vents of a region are of Ceenozoic origin (as appears to be true of most of them) and a consequence of the later movements of lateral pressure. : The inference that igneous eruptions have generally been derived from a deep-seated source is sustained by the great lithological uniformity of ejections over widely distant ranges of surface. The eruptive rocks (or trap) of the Triassico-Jurassic areas of the Atlantic border from Nova Scotia to the Carolinas, already many times referred to*, all which belong to one epoch, are solely varieties of dolerite—rocks made up essentially of Labradorite and pyroxene, with more or less of magnetic iron- * These hills and dikes of “trap” (as they are ordinarily called) have great length and breadth in Nova Scotia. In the Connecticut valley they are very numerous, and in many lines—as laid down, especially for Con- necticut, by Percival in his ‘Geological Report.’ A copy of a part of his very accurate detailed map of the trap-region is reproduced im the writer’s ‘Manual of Geology,’ page 20. At the east and west bend in the dikes, south of the middle of the map, are the Hanging Hills of Meriden, 900 to 1000 feet high, situated about 20 miles north of New Haven (and 12 miles from the southern margin of the map); and the range which extends from these hills north contmmues to Mount Tom, near Northampton, in Massa- chusetts. The range to the east, south of this bend, continues southward to Lake Saltonstall, east of New Haven. Other lines cut through the me- tamorphie rocks: one of these lines of trap-ejections in the eastern meta- morphic region of Connecticut, as mapped by Percival, extends from Long- Island Sound, 6 miles east of New Haven, nearly to the southern boundary of Massachusetts, over 70 miles, with a nearly east-north-east trend, consisting of an interrupted series of dikes, intersecting metamorphie rocks of various kinds. A second independent Triassico-Jurassie trough exists in Connecticut, 15 to 20 miles west of the main one, over part of the towns of Southbury and Woodbury; and this also has its numerous trap dikes. The Palisades of New Jersey, bordering the Hudson River, are the northern part of a complex series that continues southward and westward through New Jersey and Pennsylvania into Virginia, following the course of the Triassico-Jurassic sandstone areas. There is also a series in the North-Carolina area, : the Rarth’s Contraction from Cooling. 279 ore in disseminated grains or crystals. Analyses have shown that the trap of this region in Connuecticut and New Jersey is essentially identical in constitution; and an examination and determination of the density of specimens of the same rock from North Carolina and Nova Scotia leaves no doubt that it is fanda- mentally alike throughout. The aspect of the ordinary speci- mens from these widely distant regions is closely the same ; and the density varies little from 3. The dolerite of Hast Rock, New Haven, Conn., gave Professor G. J. Brush for the specific gravity 3°09-3:085 ; from West Rock, ib., 3°045-3°07; from the vicinity of Raleigh, North Carolina (a specimen received by the writer from Professor Kerr, of Raleigh, and not distinguish- able by the eye from an Hast or West Rock specimen), 3°16. Professor Cook, of New Jersey, obtained for the dolerite of the Palisades (Geol. Rep. N. J. p. 215) 2°94. Professor H. How gives the writer, for a similar variety from Nova Scotia, 2°94. Complete analyses have not been made of many of these rocks. The following are analyses of the West-Rock (New Haven) do- lerite and that of the Palisades, New Jersey (seventy miles west of West Rock)—the former by W. G. Mixter, Assistant Chemist in the Sheffield Scientific School, and the latter by Professor G. Hi. Cook, of the New Jersey Geological Survey :— SiO”, 2A10°, FeO. MgO. CaO. yo Ign. 1. West Rock. 52°37. 12°31 13:13 6°03 10°74 2°62 0°94= 98:14 2. Palisades . 53'9 = =—17°5 BiOh e808 SO [23]. 100): There are variations in the dolerite of the regions above re- ferred to depending on the proportion of the felspar and also on the presence of water; but they occur in various parts of the several regions instead of characterizing any one of them. The dolerite of dikes in East Haven, Conn. (the town adjoining New Haven on the east), diminishes in lustre as the dike 1s more remote from the New-Haven line; and in the ridges near Sal- tonstall Lake, two miles distant, it is faintly glistening and of somewhat less hardness; and although generally solid through- out, it is in some parts vesicular (amygdaloidal). A precisely similar rock in all its characters occurs among the trap-hills (dolerite) of Meriden, called the Hanging Hills; and part of it is amygdaloidal. The same is found also in Nova Scotia. An examination of a specimen from the vicinity of Saltonstall Lake, by Professor O. D. Allen, shows the presence of 4°53 per cent. of matter driven off on ignition, after deducting the bygroscopic moisture (0°60). It indicates the presence of some hydrous mineral (chlorite apparently) in place of part of the augite or felspar; but the percentage of silica is 49°88, 50°10, according to two determinations by 8. T. Tyson, of the Sheffield Scientitic- 280 Prof. J. D. Dana on some Results of School Laboratory, and thus differs but little from that of the anhydrous dolerite of West Rock and the Palisades; the pro- portion is less instead of greater. There is hence a close simi- larity to the other dolerite, notwithstanding the presence of water. Since the dikes of this hydrated dolerite occur as parts of the same series as the others and in the same regions, and are of the same epoch and system of ejections, and moreover are exceptional instead of the prevailing kind, it is apparent that the hydrous character is owing to some exceptional condition attending or subsequent to the eruption. ‘The source of liquid rock was all one; and the material must therefore have been essentially one in kind; it could not have been locally hydrous. Portions of the erupted viscid material might have encountered water on the way to the surface and thus have become penetrated with it*; so that the viscid material at tue high temperature became altered in part—some of its augite to chlorite, and perhaps some of its felspar, with the lime of the augite, to zeolites, &e. Or else this kind of change may have taken place through infiltra- ting waters. The fact that the vesicular trap (now amyedaloidal) is that which is hydrated renders it rather probable that while zeolites and calcite may have been later made within the rock by superfical action or infiltrating waters, the chief change was contemporaneous with the eruption; for the vesicular character was undoubtedly then produced, and it was probably dependent on the same moisture that, penetrating the rock, caused the me- tamorphism or hydration through the mass. Bunsen, in his well-known paper on the igneous rocks of Iceland +, gives various * On this taking-in of moisture by liquid rock, Mallet, speaking of the Java in the conduit of a crater, makes the following remarks :—“ Within a few years it has been proved that capillary infiltration goes on in all porous rocks to enormous depths, and that the capillary passages in such media, though giving free vent to water (and the more as the water is warmer), are, when once filled with liquid, proof against the return through them of gases or vapours. So that the deeply seated walls of the ducts leading to the crater, if of such material, may be red-hot and yet continue to pass water from every pore (like the walls of a well in chalk), which is flushed off into steam that cannot return by the way the water came down, and must reach the surface again, if at all, by the duct and crater, overcoming in its way whatever obstructions they may be filled with. And this re- markable property of capillarity sufficiently shows how the lava (fused below or even at or above the level of infiltration) may become interpene- trated throughout its mass by steam-bubbles, as it usually, but not invari- ably, is found to be.”’ _ > Taylor’s Scientific Memoirs, New Series, Part I. p. 33. The secon- dary origin of the zeolites and chlorite found to penetrate some dolerite and other kinds of igneous rock, as well as fillmg the cavities within them, I sustained in an article in vol. xlix. of the first series of Silliman’s Journal (1845); and the various facts I have since observed have tended to confirm the Harth’s Contraction from Cooling. 281. facts illustrating this kind of metamorphism yielding chloritic and zeolitic minerals. There is hence nothing in the relations of the different kinds of dolerite in the Connecticut valley or any part of the Triassico- Jurassic regions of the Atlantic slope, either as to geographical position or chemical composition, that favours the idea of differ- ence of original subterranean source. Now such a similarity of product occurring at intervals over a region 1200 miles long, and im several parallel lines, shows some unity of origin. It evinces that the source must have been either the undercrust fire-sea, like the under-Appalachian as we have termed it, derived from the old viscous layer, or else plastic masses within the true crust, which crust, as it was made from the viscous layer by cooling, would have lke uniformity of mineral constitution. This example of igneous eruption is grand in scale, since the outflows are from tappings along a line more than a thousand miles long; and it may therefore serve well to test the general application of theories of igneous eruptions. It indicates that the original fire-sea was one of great extent. Professor. T. Sterry Hunt, in his paper “On the probable Seat of Voleanic Action’’*, and others of earlier date, while adopting the view of a nucleus made solid by pressure and of an exterior crust, with a viscid layer between, has proposed to sub- stitute for the viscous layer recognized as the source of volcanoes by Hopkins, one made by the “ aqueo-igneous fusion”? of part of the lower sedimentary beds of the supercrustt. The alleged causes of such fusion are :—(1) pressure due to the accumulation of superficial sedimentary beds; (2) increase of heat, by a rise of the isogeothermals—another effect of the same cause; and (3) the presence of moisture, a common feature of sediments—the moisture becoming, under the heating, superheated vapour, and so aiding by its great dissolving power in the result. Ina later article { he says, “I have taken pains [in former papers | to explain that the deeply buried layers of sediment, together with the superficial and water-impregnated portions of the solid nucleus, constitute a softened or plastic zone from which all me in the conclusion. In the paper referred to IJ attribute the change to infiltrating waters. The opmion has many advocates. * Silliman’s Journal, S. 2. vol. |. p. 21 (1870). + I use the term supercrust as it is explained on page 216—that is, for the part of the crust made by the action of exterior agencies over the outer surface of the true crust, the true crust being the part that was formed directly from cooling. t Geological Magazine, February 1868, 282 Prof, J. D. Dana on some Results of plutonic and volcanic rocks proceed, and which allows of the movements observed in the solid crust.” It will be perceived that the hypothetical viscous layer of Hunt lies between a rind made out of sedimentary formations and a solid nucleus which is at surface of sedimentary origin ; ~ and the viscous layer which Professor Hopkins regards as be- longing to a stage in the process of solidification is supposed to have been closed up, or some way put hors de combat. This substitution appears to be quite unnecessary, and the process incapable of producing the result claimed. As has been already explained*, the pressure from the gravitation of sedi- ments cannot produce the heat needed for the fusion, any more than it can cause the plications alleged to attend it. If, then, no fusion of sediments would have resulted from such a cause, there was no chance for the formation of the deep and extended plastic zone required to meet the demands of the grand system of oscillations the earth’s surface has experienced. In fact the conditions Professor Hunt’s hypothesis appeals to (that is, thick sedimentary accumulations, such as those of the Appalachian region) are far too local for the production of so vast.a plastie zone, even if fusion were a possible result of the accumula- tion. Again, the facts mentioncd on the preceding page give as positive a declaration against this origin of the material of ig- neous ejections through the fusion of sediments, The sedimen- tary strata along the Atlantic border, whether unaltered or metamorphic, deep-seated or superficial, vary every score of miles, and could not yield a uniform quality of fused material for the ejections. In the Connecticut valley the metamorphic rocks from New Haven, Conn., to Northern Massachusetts, a distance of a hundred miles, have an east-norih-east strike ob- liquely across the region of trap-ejections, and are on the west side chloritic mica-slate, diabase, chlorite slate, argillite, mica- schist, gneiss, and other micaceous rocks of various kinds; and the Archean (Azoic) rocks to the west in Dutchess Co., N. Y., and in Connecticut west of Winsted, are diverse varieties of gneiss and granitoid gneiss, containing orthoclase and albite or oligoclase with quartz, and sometimes hornblendic, but, as far as known, without Labradorite. Only wide diversity, not uni- formity, could come from such varied material. Dolerite is, moreover, the last rock to be looked for from any of it, except it be from the diabase. For it has a low percentage a silica (46 to 52 per cent.) and no free quartz, with 8 to 12 per cent. of oxide of iron, about as much of lime and also of magnesia * Supra, page 217. the Earth’s Contraction from Cooling. 283 with very little potash or soda; and in these constituents there is comparatively little variation. Hunt claims that the presence of moisture in many igneous rocks sustains the idea of derivation from the fusion of sediments —that is, from the fusion of rocks containing water. But it has been shown (on page 280) that the cases of hydrated dole- rite in the region referred to are local and exceptional, and that the ridges are so mixed up with those of the more common an- hydrous dolerite that all must have had one source. His argu- ment would be of some weight if there were no source for the moisture except in the region of fusion. The hydrated rock, moreover, is shown to have the low percentage of silica which belongs to the anhydrous dolerite. If subterranean fusion were somehow produced and a zone of mobile rock were thus made many scores of miles deep, with the material not simply plastic but of perfect liquidity, and the zone without obstructions in any part, so that there could be tidal movements or at least free-flowing currents throughout it, then, if the material entered into fusion were as diverse as the rocks of the Atlantic border, there might be such a mixing up and chemical digestion of limestone and every thing else, that the product would perhaps be doleritic—a rock low in silica (or basic). But these conditions are those of the earth’s liquid en- velope before and after refrigeration began, and of the viscous layer developed out of it, even probably to the basic character of the fused material ; and further, they are what Hunt’s method has no provision whatever for producing. The facts afforded by other parts of the globe and other pe- riods in its history add force to this argument. A doleritic or basaltic character is the prevailing one among the igneous erup- tions of all ages from Archean time to the present, and of all continents and oceans. Whitney and Pumpelly have described basic or doleritic rocks of Lower Silurian age from the Lake- Superior region, where they are the prevailing igneous rocks. Hunt has described and analyzed others, from Canadian locali- ties, of the Laurentian, the Lower Silurian era, and of later Paleozoic time. They are far the most abundant of the igneous products of the Tertiary and Quaternary over the Pacific slope. Similar facts might be cited from other continents*. More than three fourths of true igneous rocks are probably of this nature. Hence it is reasonable to pronounce such ejections * For comparison with the analyses on page 279, I add here others of the dolerite (trap) of (1.) the Giant’s Causeway, (I1.) Staffa, and (III.) Faroe, by Streng (Poge. Ann. 1853, vol. xe. pp. 110, 1L4—all of which are now supposed to be of Tertiary origin,—and another (1V.) of an Archean (Lau- 284 Prof. J. D. Dana on some Results of manifestoes of some kind of community of origin in the earth’s ejections, as well as announcements of the kind of material that constitutes to a large degree the deeper regions of the crust. There is, however, considerable diversity among true igneous. rocks. Besides the prevalent doleritic iron-bearing kinds, inclu- ding dolerite, peridotite, melaphyre, &c., to which the preceding observations relate, there are trachytic or felspathic rocks, whose constitution, especially in the case of the more siliceous varieties, comports with their origin from the fusion of granitic rocks or of sedimentary beds made of granitic material. They occur in the same regions in which doleritic dikes exist, as well as among volcanic products. Such a Cun pret ten does not, however, make it certain that the supercrust was their source ; for true granite and gneiss and even quartzites occur constituting old Archean terrains; and it may be that essentiaily the same kinds of rock are to some extent represented in regions of the infra-Archeean crust and even in the fire-seas. Basaltic and trachytic rocks often occur so combined in a single volcanic mountain, that we seem forced to find some other explanation of their origin than that of the fusion of unltke se- dimentary strata. As long since observed by Von Buch at rentian) dolerite from Grenville, Canada, by Hunt (Geol. Rep. Canada, 1863) :— : Cate G.=288. G.=296, UI IV. SiliGaeiel. datrsiciete ean Coals 47°80 49°40 50°35 Anlumativa’s bea sterile: ~ > AA ~~ “= ~ = ~ Ss 3 ~ 8 ~ SS) = ~ ~ R) = ~ S NM = = SS _— — — _— —~ —_— -_ oO — —_ _—_ > oO ~~ oe — | 318 Royal Society :— At the end of this time a cloudiness began to appear in the first bulb of F, and after half an hour in the second bulb: finally, a decided precipitate was obtained ; it was collected, washed, and on analysis proved to be carbonate of calcium. The experiment was repeated in a modified manner several times. It having been found that a faint turbidity in the lime-water was sometimes ob- tained before the addition of the beryl, it was traced to the pre- sence of minute quantities of organic matter in the chromate and sulphuric acid. To eliminate this source of error, the chromate and acid were mixed at the commencement of the operation, and the current of air was kept up until every trace of carbonic anhy- dride was removed; at this point the beryl was added, and the effect noted. The results, both with emeralds and the beryl A, how- ever, were always precisely the same. The apparatus was then recharged ; and when half an hour’s pas- sage of the air produced no milkiness in F, 5 milligrammes of char- coal were introduced into D; in two minutes the first bulb, and in four minutes all the bulbs were rendered milky. In another experiment, after the usual precautions, 5 mulli- grammes of graphite were acted on. In four minutes the first bulb, and in eight minutes all three bulbs were rendered milky. = The above experiments show, therefore, that the beryl A con- tains carbon, not in the state of a carbonate, but in a condition which is more slowly attacked than either free charcoal or graphite; and it is, I think, probably in the form of diamond, as has been shown to occur with the carbon contained in artificially crystallized boron*. The power of free chromic acid to attack the diamond with liberation of carbonic acid has been shown by the Messrs. Rodgers f. The presence of carbon in beryls does not appear to be inva- riable. After repeated experiments upon another large beryl from Haddam County, North America, I was unable to satisfy myself that it contained carbon. It is true that traces were found in the experiment ; but they were so minute that they might have been due to the difficulty of entirely excluding the presence of organic dust during the necessary manipulations t. The next point I wished to ascertain was the relation borne by the quantity of carbon in the beryl A to that in the emerald. For this purpose I employed a similar apparatus to that used by Dumas in his researches on the atomic weight of carbon previously alluded to. The minute error due to the apparatus was carefully determined by going through the whole process of heating the combustion-tube to redness for the same time as in the analysis, the current of oxygen passing through at the same speed, and finally * Wohler and Sainte-Claire Deville, Comptes Rendus, February 16, 1857. + R. E. Rodgers and W. B. Rodgers, Chem. Gaz. vol. vi. p. 356 (1848). t Since the above paragraphs were written, an interesting paper has been pub- lished by Prof. Silliman, “On the Probable Existence of Microscopic Diamonds with Zircons and Topaz in the Sands of Hydraulic Washings in California,” Chem. News, vol, xxvii. p. 212. Mr. Greville Williams on Emeralds and Beryls. 319 replacing the oxygen in the system of tubes by a current of pure dry air. No appreciable error was found to affect the carbon-de- termination ; but a correction had to be applied to the hydrogen. The necessity for minute precaution will be evident when it is con- sidered that 1 grm. of beryl A, or emerald, only yielded 3 milli- grammes of carbonic anhydride. Estimation of Carbon and Hydrogen in Peruvian Emerald and Beryl A. I. 0:9725 grm. beryl A gave 0:0030 carbonic anhydride and0‘0131 water. EY 10082 ._.,, ii » 0°0031 - re 0:0174 _,, Tit. 1°1690 ,, emerald ,, 00030 _,, - 0:0140 _,, or, per cent. :— Beryl A. Lewy’s ——A OF Emerald. Emerald I. II. (mean). Carbonic anhydride ............ 031 0°31 0:26 0-28 DMOMTTT TGA as ecdscscnstoscsopsoes 1:35 1-73 1-20 1-89 In working on such minute quantities, it is not easy to speak with certainty as to the proportion of hydrogen contained in eme- ralds and beryls which is not due to the water present; and the difficulty is increased by the fact, insisted upon by Boussingault*, that these stones.do not give off all their water below a red heat. If it be considered permissible, which I cannot admit, to calculate the hydrogen on the principle of deducting the water found on ignition in a crucible from that formed during the combustion in oxygen, and then calculating the percentage of hydrogen on the difference, as Lewy has done, the results would be as follows :— Beryl A. Lewy’s Se Emerald. Emerald I. iM, (mean). oy Ga (eee 0:08 0:08 0:07 0-08 Hydrogen ....ccsecsscosesesseeeee 0:06 011 0-04 appears to be some mistake in them. He found 0:24 per cent. of carbon in the morallons, and yet says that this number agrees with two of Lewy’s determinations, one of which (he says) gave 0-21, and another 0°25; whereas I find, on reference to Lewy’s - memoir, that that chemist obtained in the two experiments alluded to 0°21 and 0°25, not of carbon, but carbonic anhydride. As it was possible that some of the carbon found in these expe- riments mighthave been derived from the steel mortar used in the preliminary crushing of the emeralds and beryls, I pulverized some emeralds in a porcelain mortar, every precaution I could devise being taken to prevent any contact of organic matter. On burning * Loe, cit. 320 ) Royal Society :-— in oxygen, and passing the products of the combustion into lime- water, a copious precipitate of carbonate of calcium was obtained. On THE EFFECTS OF FUSION UPON EMERALDS AND BERYLS. On the Effects of Fusion upon Opaque Beryls—In order to study the effects of fusion upon beryls or emeralds, I found it necessary to use the oxyhydrogen blowpipe. Beryls and emeralds were amongst the numerous substances fused with this instrument by Clarke * as long ago as 1816. He states that the Siberian beryl fuses to a clear glass containing bubbles. The Peruvian emerald he found to melt very easily to a round, extremely beautiful bead free from bubbles ; it lost its green colour, and became like a white sapphire. My first experiments were made upon the beryl A; it weighed 62°54 grms., and its density was taken with great care previous to fusion. In the first experiment the whole crystal was suspended from the balance-pan, and weighed in water; in the second a few fragments were weighed in a Regnault’s flask with the usual pre- cautions. The values obtained were as follows :— Specifie Gravity of Beryl A before fusion. No. of experi-| ! | ear | Ww. | W'. | t. pt. | D. | ie 625400 | 39:0000 | 21-5 | -997986 | 2-65 II. 1-6838 10512 | 20:0 | -998259 | 2-66 In order satisfactorily to submit beryls to the action of the oxyhydrogen blowpipe, it was necessary to find a support capable of enduring the high temperature without burning away too ra- pidly, and also not containing sufficient inorganic constituents to complicate the results. After a few trials I selected square prisms of gas-retort carbon, taking care to ascertain by experiment that they were adapted to the purpose. Some specimens burn away very readily ; and others yield too much ash to permit of their being. employed successfully. The oxyhydrogen blowpipe employed was of the ordinary construction, and, with the exception of having several nozzles of various calibres to adapt it to different quantities of the substance to be experimented upon, needs no particular de- scription. These nozzles (which supply the oxygen) should be well formed, and free from internal irregularities. Instead of hydrogen, coal-gas was generally employed, as I have not found, for the pur- poses described in this paper, hydrogen to possess advantages suffi- cient to counterbalance the inconvenience of storing it in the large quantities required. _ The phenomena observed on submitting a fragment of beryl to the action of the flame are very beautiful ; but to obtain the best results, many precautions and some little practice are necessary. *« Schweigger’s Journ. vol. xviii. p. 237 (1816). Mr. Greville Willams on Emeralds and Beryls. 321 The coal-gas having been lighted and the oxygen turned on, the beryl at once begins to melt, and froths or, 1 rather, boils violently. By careful regulation of the supply of oxygen, the boiling entirely disappears ; but. the slightest excess of oxygen causes it to be renewed. ‘This property of oxygen, which is found to occur with other substances besides beryls and emeralds, I hope to study in greater detail. Having so adjusted the flame that the beryl fuses tranquilly, and is yet at the exact point of maximum heat (if the substance is not too large for the apparatus), it no longer lies as a shapeless mass on the carbon support, but gathers together, rises up, and forms a perfect bead—round, clear, and brilliant. To obtain the adjustment of position necessary for this result, it is indispen- sable to wear very dark glasses, so dark, indeed, that objects can scarcely be discerned through them in bright daylight. Without this precaution, the minute details of the globule cannot be observed, and it would be impossible to drive away the bubbles, which form instantly when the bead is moved in the slightest degree from the ‘proper position. The heat and glare would also soon seriously affect the sight; and, with every precaution, I have found, after the pre- paration of one or two hundred globules, that my sight appears (even after an interval of some months) to be slightly but deci- -dedly deteriorated. If all is working properly, the bead should be quite mobile ; and advantage of this must be taken to keep it in- cessantly rolling, and yet not remove it from the point where it gives out the most brilliant light. By this means the whole glo- bule is rendered transparent. If, on the other hand, it is allowed to remain without motion on the carbon (unless the globule be very minute), it will be found, when cold, to have a white opaque base, passing into the centre of the bead in a conical form, and entirely destroying its beauty. This exact adjustment of the position of “the bead at the pomt of maximum heat, combined with constant movement of the carbon support and perfect regulation of the proportions of oxygen and hydrogen, are indispensable to the pro- duction of the glasses, specimens of which accompany this paper. When thus fused, the globules obtained from the beryl A were elear and colourless, but generally contained a few minute air- globules and striz, which become obvious under the lens. Towards the end of this part of the investigation I succeeded in almost entirely avoiding these defects ; but I have been compelled for a time to abandon experiments in this direction in consequence of the strain thrown upon the eyes. : When chromic oxide is added to the beads, and they are again carefully fused, they acquire a fine green colour ; the tint, how- ever, is eee to that of the emerald. The green beads may, by an intense and prolonged heat, be rendered colourless. With cobalt oxide the beads afford beautiful blue glasses of any desired shade; and in all cases the results are the same as with the arti- ficial mixture of beryl ingredients to be described further on. The effect of fusion upon the beryl is to lessen the hardness and lower the specific gravity. The globules may be scratched by Phil. Mag. 8. 4. Vol. 46. No. 306. Oct. 1873. Z 322 : Royal Society :— quartz. The following numbers were obtained in a determination of the specific gravity :— Specific Gr avity of Beryl A. after ‘Ausien: ee etal crane | | ae | W. | \ joe | be | pt. D. — | ts | 29376 | 13710 | 272 | -996c08 en ee 9:3376 | 1-3699 | 27-0 | 096603 | 241 The beryls have, therefore, lost nine per cent. of their density i in passing from the crystalline to the vitreous state. i was desirous of carefully comparing this loss of density under- gone by bee with that of rock-crystal fused under the same cireumstances. According to an experiment quoted by Forbes*, the specific pa of quartz of undoubted aqueous origin, and also of quartz from granites, is 2°6, and that of rock-crystal, fused before the oxyhydrogen blowpipe to an amorphous glass, 2:2. According to the experiment of Le Royer and Dumas‘, the specific gravity of rock-crystal determined at 4° wn vacuo was 2°652. The yalue found by the Austrian Commission was 2°651223t. I have repeated with great care the determination of the eau eravity of rock- crystal, both before and after fusion, with the annexed results :— Specific Gr avity ¢ of AU a ystal before fusion. | No. of experi-| W, W'. a | ot. | D. ment. | — Seascale Se Oe a eee Ci re sf ee I. 19493 | 1-2154 ot | 998047 | 2:65 The above number is practically identical with those of Le Royer and Dumas and the Austrian Commission. Rock-crystal fuses very readily before the oxyhydrogen blowpipe, and, if care be taken, the beads obtained are beautifully clear and free from bubbles. Speafie Gravity of Rock-crystal after fusion. INo of experi : peri- iti W. W'. fe ot. D. ———— SS OO ee ee re Sal f ‘4116 | -2240 24 | -997367 | 2-19 | I. 4116 2961 25 | 997120 | 2-21 Tt. 4116 2998 24 | 997367 | 217 IV. 2876, |... 11882 |. 25..| 997120 | 218 Vv 1796 | 0877) 993655 | 219 Diener ee 2 Fe USGS ald dy sa heaeee ly deena eae 2:19 Rock-crystal loses, therefore, no less than seventeen per cent. of * Chem. Soc. Journ., new series, vol. vi. p. 225. iF Gmelin’s ‘Handbook of Chemistry,’ vol. ii. p. 354. + Ueber das Verhiltniss des Bergkrystall-Kilogrammes zum Kilogramme der 1S, Archive zu Paris (Wien, 1870). T am indebted to Prof, We H. Miller for this reference, Mr. Greville Williams on Emeralds and Beryls. 323 its specific gravity on passing from the crystalline to the amorphous state, or about a half per cent. less than is undergone by garnets, according to the observations of Magnus; whereas the ber yr A only lost nine per cent., or little more than halfas much. On the Effects of Fusion upon Emeralds.—On heating alone before the oxyhydrogen blowpipe, these emeralds bear a bright red heat without losing their colour; and at a heat which causes incipient fusion, the edges turn colourless and opaque, while the centre re- mains green. After fusion for a short time they yield an opalescent greenish glass, which, kept for a long time at the maximum tempe- rature of the blowpipe, becomes quite transparent and almost colour- less. The addition of chromic oxide causes the bead to become of a dull green colour, which is not improved by moderate heating. The fact that emeralds endure a temperature capable of fusing the edges without the centre losing colour, appears conclusive against the idea of the colouring-matter being organic. The beads produced by the fusion of emeralds resemble those formed in the same man- ner from beryls ; the phenomena during the fusion are also nearly alike; but it takes longer and a higher temperature to produce a colourless transparent bead with emeralds than with colourless beryls. The beads can be scratched by quartz; and the density is reduced to the same extent as with the beryl. te Specific Gravity of Emeralds (Canutillos) after fusion. | is No. of experi- ' arth: W. W'. t pt. | D. 1. 7439, 4334. 13 999430 | 2-40 The density of fused emeralds is therefore almost exactly the same as the globules obtained in a similar manner from the beryl A. Beryls, from the most various sources and of the greatest differ- ence in appearance, vary but little in specific gravity: thus a large erystal of beryl from Haddam County, North America, weighing 1089 grms., had its specific gravity determined by suspension; and the number obtained was 2°67. The beryl A from Ireland gave 2:66; and a beautiful transparent yellow crystal, the locality of which is doubtful, gaye 2°69, or exactly the same as the emeralds from Santa Ié. On the Effects of Fusion wpon an Artificial Mixture of Beryl In- gredients—Being desirous of trying the effects of fusion upon an artificial mixture of the same composition as that of a beryl, I made a series of careful analyses of the beryl A. The results of these analyses have led me to a laborious examination of the pro- cesses at present in use for the separation of alumina from glucina. The study of the original carbonate-of-ammonia process of Vau- quelin,.and the modifications of Rose, Joy, Hofmeister, and others, has taken twelye months of constant work; but even my earlier analyses enabled me to obtain a sufficiently close approxima- tion to the composition of the beryl A. he following were the Z2 824 Royal Society :— proportions used :— Sica ere aOR PSCC, CPOE: Am Nie EES stant 67'5 IAhaimimnat: eh s see BR ee 18°5 EAT) D ay: Mann ata NOmnNMa On SUMS SHEN RSE Uist Nh Amadis At a eG ae a 14:0 100-0 { did not introduce any iron or magnesia, as I regard them as ac- cidental impurities varying in amount. When a mixture of the above composition is exposed to the flame of the oxyhydrogen blowpipe, it fuses with almost exactly the same phenomena as with the natural beryl. It is, however, as might be anticipated from the absence of iron and chromium, much easier to get a colourless transparent bead with the mixture than with either emeralds or beryls. The greatest difficulty in this respect is, of course, found with emeralds. The specific gravity of the fused globules was determined, with the following result :— Specific Gravity of Artificial Amorphous Beryls. fet Ans Oe i No. of experi- 4 Beer W. | Wi t pt. D. | ie 5774 | 3394. | 13 -999430 | 2-42 or almost exactly the same as the density of native emeralds and beryls after fusion. When a small portion of chromic oxide is added to the artificial mixture and the whole is subjected to fusion, the resulting bead is of a rich yellowish green, and in many experiments approached to the emerald tint ; but, asa rule, the colour is more of a faded leaf- sreen ; and although I have never obtained a globule of the vivid tint of a fine emerald, the glasses, when well cut, are quite beau- tiful enough to serve as jewels. Prolonged heating gradually diminishes the colour, the bead gradually becoming of the palest bottle-green, and, finally, nearly colourless. This result is the same as with the emerald. The metallic oxide which yields the finest tints when fused with opaque beryls, or the artificial mixture, is that of cobalt. The manner in which this oxide withstands the intense heat of the oxyhydrogen flame is remarkable. All tints, from nearly black to that of the palest sapphire, can be obtained; and the resulting glasses, when cut, are extremely beautiful, and have almost the lustre of crystallized gems. The globules obtained by fusing the artificial mixture of beryl ingredients with didymium oxide show the characteristic absorption- spectrum of that metal in a very perfect manner, the lines being intensely black. ven when the bead is quite opalescent from insufficient heating, the black lines are beautifully distinct in the spectroscope. With a large quantity of didymium oxide the beads are of a lively pink, becoming more intense by artificial light, and, when cut, form very pretty gems. The presence of didymium in suflicient quantity raises the specific gravity. Mr. Greville Williams on Emeralds and Beryls. 325 Specific Gravity of Artificial Amorphous Beryls containing 1g Didymium, <1 nalts =f Bon eonte risk No. of experi- r = | bient W. Ww’. | z. | pt. | Di | | é 45 | | / I, |. 9467 5815 | 999655 | 2:59 | | the resulting number being almost as high as that of the emerald before fusion. Conclusions.—The evidence given in this paper, showing that co- lourless beryls may contain as much carbon as the richest-tinted emerald, taken in conjunction with the ignition experiments, and the results of the fusion of chromic oxide with colourless beryls and with an artificial mixture of the same composition, leaves me no room to doubt the correctness of Vauquelin’s conclusion, that the green colour of the emerald is due to the presence of chromic oxide. The fact that emeralds and beryls lose density when fused cannot properly be cited as proving that they have been made in nature at a low temperature ; for it is quite possible that they were crystallized out of a solution in a fused. mass, originally formed at a temperature high enough to keep the constituents of the emerald in a state of fusion, and that the crystals developed themselves du- ring a slow process of cooling or evaporation. The method employed by Ebelmen* for the artificial production of chrysoberyl, namely heating alumina, glucina, and carbonate of calcium with boracic acid in a porcelain furnace until a portion of the menstruum had eva- porated, yielded crystals of the true specific gravity, showing the density of minerals to be less dependent on the temperature at which they are produced than upon their crystalline or amorphous state. _ One crystalline gem (the ruby) has undoubtedly been produced in nature at a high temperature. I have frequently repeated Gaudin’sT experiment on the artificial formation of this stone, and can confirm most of his results. I did not, however, find the density to be quite the same as that of the native ruby or sapphire, which is, in different specimens, from 3°53 to 3°56. Artificial rubies of the finest colour made by me by Gaudin’s process had a specific gravity of 3°45, which is not three per cent. lower than that of the ruby. The reason for this close approximation will be found in the fact that fused alumina crystallizes on cooling. The erystalli- zation, however, is confused and imperfect, which causes the re- sulting product to be only partially transparent, and to have a slightly lower specific gravity than the natural gem. It is, conse- quently, scarcely correct to call the fused stones made by Gaudin's process “ artificial rubies.” I have convinced myself that rubies have been formed in nature at a temperature equal, or nearly equal, to that of the fusing-point of alumina, from the circumstance that the reaction between chromic * Ann. Chim. Phys. [3] vol. xxii. p, 223 (1848) ; vol. xxxiii. p. 40 (1851). t Ann, Pharm. vol. xxiti. p. 234, 826 Geological Society :— oxide and alumina, which results in the development of the red colour of the gem, is not effected at low or even moderately high temperatures, but requires a heat as high as that of the oxyhydrogen blowpipe. It is not necessary that the chromium should be pre- . sented to the alumina in the form of chromic acid. It appears, therefore, that the red colour of the ruby is not caused by the presence of chromic acid; it is, m fact, a reaction sui generis be- tween alumina and chromic oxide, which, as far as my experiments have gone, only takes place at very elevated temperatures. In my next communication I propose to give the results of a comparative study of two of the processes most generally em- ployed for the analysis of emeralds, beryls, and other minerals containing glucina and alumina—namely, the carbonate-of-ammonia process of Vauquelin, and the caustic-potash method devised by the same chemist, but modified by Gmelin, and generally associ- ated with his name. These studies are already far advanced. Specimens of various beryl glasses, cut and uncut, accompany this paper. GEOLOGICAL SOCIETY. [Continued from p. 174.] January 8, 1873.—Prof. Ramsay, F.R.S., Vice-President, in the Chair. The following communication was read :— ‘ Phe Secondary Rocks of Scotland.’’—First Paper. By John W. ‘Judd, Esq., F.G.S. Introduction. The Mesozoic periods are in Scotland represented only by a number of isolated patches of strata situated in the Highlands and Western Isles, which have been preserved from the destructive effects of denudation either through having been let down by great faults among the Paleozoic rocks, or through being sealed up under vast masses of Tertiary lavas. The Creracrovs rocks, exhibiting very ‘interesting characters and yielding a beautiful series of fossils, were discovered by the author of the paper during the past year on the mainland and in several of the islands of the west of Scotland. The Jurassic rocks, which were first described by Murchison, are now ‘shown to present a remarkable contrast with their equivalents in England, in being constituted, throughout their whole thickness, by alternations of marine and estuarine series of beds, in which respect they precisely resemble the equivalent strata of Sweden. The Trrasstc rocks have now been discevered in Sutherland, where their conformable relations to overlying beds containing a fine Liassic fauna, entirely confirm the conclusions concerning their age derived from Prof. Huxley’s studies of the remarkable reptiles yielded by them in Elgin. Part I. Strata of the Eastern Coast. These consist of a number of patches, situated around the shores Mr. J. W. Judd on the Secondary Rocks of Scotland. 327 of the Moray Firth, in the counties of Caithness, Sutherland, Ross, Cromarty, and Elgin. The preservation of these is shown to be entirely due to the operation of faults of enormous magnitude, which have let down the Mesozoic strata against the various Paleozoic rocks. Owing to an insufficient examination of the paleontological evidence, much misconception has hitherto prevailed concerning the geological age of most of these patches; but a careful study of their faunas enables us to reconstruct an almost unbroken history of the Triassic and Jurassic periods in the north of Scotland; while even concerning the Cretaceous much important evidence 1 is afforded by the boulders, which abound in the drifts. ‘The Keuper i is represented by the Reptiliferous Sandstone and the overlying calcareous rocks; the Rhetic by conglomerates in Suther- land, and probably elsewhere by estuarine beds, which are now, however, only preserved in great boulders. The Lower Lias is constit uted in its lower part by a thick series of estuarine beds, sandstones, shales and coals (hitherto referred to the Lower Oolites), and in its upper part by marine strata yielding a highly characteristic fauna. The Middle Lias is formed of clays seen ?v situ in Sutherland, and micaceous sandstones, only preserved in boulders; both furnish very fine series of fossils. The Upper Lias is probably represented by estuarine beds. The Lower Oolites are almost wholly made up of estuarine strata, containing coal-seams, which have been frequently worked in the past in mines which are now being reopened. The beds yield many freshwater fossils, which have attracted much attention, owing to the general resemblance they present to those of the Wealden. Of the Middle Oolites we have a wonderfully complete series in the east of Scotland. At the base isa calcareous sandstone crowded with Kelloway fossils; above this 300 feet of shales, yielding the well-known Ammonites and other fossils of the ‘‘ Ornatus-clays ” (Middle Oxfordian) ; still higher are beds of marine sandstone with a magnificent fauna, identical with that of our Lower Calcareous Grit. A thickness of 400 feet of estuarine sandstones &e., which covers the last, is surmounted by limestones, shales, and sandstones, with the fossils of the Coral Rag. The Upper Oolites, now for the first time recognized in Scotland, are of great thickness, and consist of alternations of estuarine and marine strata, yielding a splended fauna and flora. In their northern - extension these beds pass into the wonderful “ brecciated beds ”’ of the,Ord, which contain enormous transported blocks of Old Red Sandstone. The features presented by these strata are of the highest interest, and are very suggestive of the prevalence of peculiar phy- sical conditions in the area towards the close of the Jurassic period. The patches of Secondary strata on the coasts of Ross, usually called Lias, are shown to belong to the Lower, Middle, and Upper Oolites; and a mass on the coast of Elgin is demonstrated to be also of Oolitic age. In future papers the author proposes to describe the Secondary rocks of the west coast and islands of Scotland, and to discuss the 328 Geological Society. various theoretical questions suggested by a comparative study of the whole of the Scottish Mesozoic strata. | January 22, 1873.—His Grace the Duke of nie K.T., Paes President, in the Chair, ~ The following communication was read :— « On the Glaciation of Ireland.” By J. F. Campbell, Esq., F.G.S. The author stated that almost the whole of the surface of Ireland consists of glaciated rocks less or more weathered, or well preserved. The polished surfaces are covered in low grounds with drift. Boulder- clay, unstratified, is next to the rock; sands and gravels and peat _ bogs are above the clay. The solid rocks have been greatly worn away since the formation of the Antrim basalt; the drift since the Glacial period.. The hills and hollows in the rocks are the result of © wearing and “denudation ;” the débris is the “drift” partially rearranged. This was shown by examples in:—Ist, chalk and basalt in Antrim ; 2nd, mountain-limestone &c. in Sligo; 3, older rocks about Valentia and the south-west; 4, granites ai metamorphic rocks in Donegal and the north-east. The effect of the Atlantic on cliffs at Slieve Liag in Donegal, and elsewhere on the Irish coast, was noticed. It was shown from these large coast-sections that the upper surface now has no relation to the older contortion, fracture, and folding of these disturbed and faulted rocks, which he under newer and less- crumpled beds, up to the peat. The probable dimensions of the ice- engines which worked on the surface of Ireland was shown by com- parison of glaciers in Iceland, Norway, and elsewhere, with the Irish marks, which indicate ice of equal size. Beginning with the smallest and rising to larger systems, Irish marks indicate ice of equal dimensions, till horizontal grooves at 2000 feet above the sea indicate ice more than 2000 feet thick, moving over Ireland into the Atlantic in a south-westerly direction. It was shown that the ice at its max- imum probably extended from the Polar Basin to Cape Clear. In support of this view, boulders on Fairhead, and the denudation and glaciation of the central Highlands of Scotland, and of Scandinavia, Finland, and the United States, were shortly noticed. The question whether these extensive tracks were made by glaciers or by ice- bergs was discussed. The marks in Ireland and Scotland seem to the writer to indicate ice more than 2000 feet thick moving along the bottom of lochs, straits, and shallow seas, in water less than 1800 feet deep, with large local ice-systems upon high lands. It was — shown that glacier-ice aground in water is easier to push horizontally, and so to drive over impediments, in proportion to the weight lifted vertically by flotation. Rubbings from glaciated rocks placed beside shaded Ordnance maps of parts of Scotland and England, showed that similar forms had been somehow produced on sc ales of inches and miles upon the rock-surface of Scotland. The author’s conclusion is as follows :— Treland has been greatly denuded. Glacial and marine action Intelligence and Miscellaneous Articles. 29° are the most powerful known to me. Glaciers and the sea shaped Ireland, as I believe. Tivers and weathering have done little to obliterate the tool-marks of ice and the sea since the end of the last of a series of Glacial periods.” XLI. Intelligence and Miscellaneous Articles. ee ON SOLUTION OF NITRATE OF NICKEL AS AN ABSORPTION- PREPARATION. BY DR. H. EMSMANN. MONG the colour-spectra exhibited by coloured liquids, that of the beautiful apple-green solution of nickel in nitric acid ap- pears to me especially worthy of notice. Having filled a hollow prism with this solution, I found that the terminal colours (red and violet) in the spectrum were absorbed. ‘This was new to me; but in Mousson’s Physik auf Grundlage der Erfahrung this peculiarity of the solution of nitrate of nickel is cited as a thing known. Now, while with most coloured liquids the colour results as a mixture of all the spectral colours under the predominance of that of the substance in question, we have here the beautiful green as a mixture of the spectral colours with the exception of the red and the violet. This fluid is therefore particularly well adapted and convenient, not merely for showing in the course of instruction the phenomena of absorption of colours, but also for ascertaining the composition of the colours of substances. I keep, for the purpose of instruction, some of this solution ready in a glass phial, the sides of which are as nearly as possible parallel (I obtained such a one at a perfumer’s), and use it for de- monstrating the absorpticn. On pasteboard covered with black paper narrow strips of coloured paper are pasted, among which are different reds. One sort of red is not to be perceived through the liquid ; a second appears dark blue; a third, yellow. A violet stripe is likewise not to be perceived ; a white stripe appears green.. Titles of books, printed in red, looked at through the liquid appear dark ; and so do thered and violet parts on woollen embroidery. In most text-books of physics the phenomena of absorption have till now been for the most part only briefly touched upon. Wiill- ner’s Lehrbuch der Kx per ementalphysik forms an honourable excep- tion, since in it are given not only the different methods of inves- tigation, but also several examples of body-colours, with the account of the colours from the mixture of which they result. Coloured liquids generally seem to have been but little inv ‘estigated. Mousson cites didymium, chlorophyl, and blood. A comparison of the spectra of coloured liquids would be very desirable. Solution of sulphate of copper shows particularly violet, yellow, and blue in the spec- trum, in about the proportion 7:5: 2, and somered. In the spec- trum of sulphate of iron, green predominates. Ferrocyanide of potassium gives red, green, violet, and dark blue. The purpose of this note is chiefly to call the attention of my colleagues to the solution of nitrate of nickel, and to recommend 330 Intelligence and Miscellaneous Articles. its introduction into physical cabinets—Poggendorit’s Annalen, Erganzung, vol. vi. pp. 334, 335. | DETERMINATION OF THE FRICTION RESISTANCES IN ATWOOD’S : MACHINE. BY C. BENDER. The determination of the amount of friction in the wheel of the fall-machine is preceded by the determination of its moment of inertia. This can be done by applying a small overweight p to one of the two suspension-weights, determiming the acceleration y hereby produced, and the unknown moment of inertia from the formula bs gp Sea wherein P denotes the suspension-weight, equal on both sides, and g the acceleration of gravity. It 1s understood that for P and p in this formula their masses must be put. ) The above method cannot give exact results, since in it no ac- count is taken of the friction of the pin in the wheel; and it is especially useless where the machine worked with has no friction- rollers. Also the method according to which the moment of inertia of a composite body is calculated from that of its separate parts, referred to one and the same axis, cannot be employed here, because the constituent parts of such a wheel but rarely permit a convenient determination of the moment of inertia. Very convenient and accurate is the method which relies on the oscillations of a material pendulum. If / denotes the moment of inertia of a pendulum in reference to its axis of rotation, M its mass, and a the distance of the centre of gravity from the rotation- axis, the oscillation-period of such a pendulum is expressed by dL teh tomy | a ee ee seas 6-8 6 8 ees ewe (1.) Jn an experiment the wheel of the machine was placed on a horizontal smooth edge of wood (or A of steel), at the point a (see the annexed figure); —© and then the duration of an oscillation was de- termined very accurately. The experimental data were :— Weeieht of the wheel.) 5 254.008 ee ... 178°9 grammes, Diameter Or the wheel (string-groove) ae coe 12 centims. Distance of the rotation-axis a from the centre eis QiCLAVALY, 2 Ukivia sn we = Bun, the Maia se o,f LVS centims. VO. vA RALTOMS TO i ok cuic. co 2 cue bi mf tase, O20) S@cgmaae From formula I. there results k=8:°5836. According to a theorem of mechanics, the moment of inertia of a body, referred to any axis, is equal to its moment of inertia in reference to an axis through the centre of gravity parallel to the former, added to the preduct of the mass of the body into the square Intelligence and Miscellanecus Articles. 331 of the distance between the two axes. We will obtain according ’ to this theorem the moment of inertia x’ of the wheel in reference to the axis through its centre of gravity :— : 178°9 i’ =8°5836 aa fe 3°70: The weight of the heavy mass which at the circumference of a wheel opposes to a turning force the same resistance as the mass 3°7 at the unit of distance from the rotation-axis which passes oT OS = 10050 erms.; and this is the amount which must be brought into the reckoning in determining the acceleration in the Atwood machine. Jf in experimenting with the machine we take away the over- weight after the motion has continued a certain time, the entire system must, in consequence of its inertia, move further with a uniform velocity, which depends on the time or the height of the fall and on the acceleration which has been present. Such a uni- form motion, however, will be prevented by the friction of the axle of the wheel, introducing a uniformly retarding motion which, after a time, brings the system torest. It we regard the friction present as a constant force, under the influence of which a moving body attains the heceleration p, and assume that the motion is produced by an overweight of the mass m and has extended, at the removal of the overweight, to the distance /, in this case the velocity at- tained is 2 aN 2ul ~A/ 9 Fa mW Bal where M-+m denotes the entire mass set in motion, and g the acce- leration produced by gravity. If from the removal of the over- weight to the resting-point the system advances the distance o, the calculation of the velocity mentioned can be arrived at by assuming that any body whatever has, under the influence of the acceleration pt, travelled the distance oc. This gives the equation h— / 2uh= 20 , a 14d? ; through the centre of gravity is now found from 2gm M+m_ or gmh (M+ m)\(V o+ Vh)* For this » we can also form another expression; for if # denote the mass (or the weight cf the mass) which counterbalances the influence of the friction, we have as a secend equation p= Sanh eb Bi iu Ut It poe Po (i1T.) Before I proceeded to the determination of x, I satisfied myself whether the quantity o in equation LI. could be ascertained with oor Intelligence and Miscellaneous Articles. sufficient certainty, and especially whether the quantity p proves to be independent of h, equation II. For this end three experiments were carried out, in which m=2'2 grins. M+im=300 grms. g=981 centims. The results were :— For h=28 centims. 1. o=112, =112°3, and =112°8 centims. ; mean=112°3 centims. For h=25 centins. 2, ¢=86°5 or 86°8 or 87'°2; mean =87 centims. For h=23 centims. oy o— ole mean ol, According to formula II., from 1, p=0-°80 centim. ; ; from 2; p=0°88 centim.; from 3, p= -0°88 centim. In further experiments the amount of the friction itself was ascertained. According to the arrangement of the machine, 24 inches descent =65 centims. ; therefore 362-21 inches corresponded to the eee eens of gravity. The overweight m=1:514 was chosen - s0,. Ab ait as 150° and consequently ee = 2415 inches fall. 91-739 With h=9 inches, o=25 inches fall, and 2u= = a From equation IIT., « was now found =0°21 grm. We will call this weight the fr ietion-wei ight. In another experiment the friction of the pin of the wheel in its socket was increased by means of screws; and there resulted, under otherwise like circumstances, for h=9, o=16°5 inches fall, v=0°300. Both experiments were in periees accord with the calculation. The friction-weights I made of tinfoil, of the form of the usual fall-weights. In order to make use of the method of friction determineaie conveniently, it will be prudent to construct a Table, and to calcu- late the friction-weights with equal q. oe and h within. certain limits of o. For various reasons it is unnecessary to actually draw up such a Table here.—Poggendorff’s Annalen, vol. cxlix. pp. 122-126, A REMARKABLE INTERFERENCE-PHENOMENON OBSERVED BY M. SEKULIC. I was sitting one evening opposite to a looking-glass. Happening to cast a glance into it, I noticed on my head splendidly coloured interference-streaks. On more attentively considering the circum- stances which might occasion them, I remarked in the mirror three Intelligence and Miscellaneous Articles. 333 bright images—those of two petroleum-lamps and one stearine candle. As tobacco was being smoked in the room, I at first be- lieved that the smoke had produced a similar phenomenon as slightly moist air when it forms a halo round the moon or the sun, and that in consequence of this the appearance was seen. I could not, how- ever, perceive those halos round the flames, either in the looking- glass or in the air. Abandoning the attempt to fathom the cause, { occupied myself with the phenomenon itself, and perfectly recog- nized it as a phenomenon of interference, because the streaks widened as the angle of reflection increased. In the observation the flame- images and the image of the eye had the following position :— A is the image of the eye, L, that of the petroleum-flame before the looking-glass, L,, that of a second o, 4, y/ / petroleum-flame at a greater dis- M7 Yj tance, and L,,, the image of the é eandle burning on the table. The interference-streaks at L, and L,, are represented in their situation. As the phenomenon was observed in LE ; a public place, where there were ti, many other glasses and lights, I could not pursue the matter further ; but I resolved to repeat the experiment at home or in my study. To this end, I placed opposite to the looking-glass in my room, at about 6 metres distance, a petroleum-lamp; I then took a stearine candle in my hand, and so endeavoured to get the position which I had had in the first observation. After looking from several differ- ent points, and shifting the candle several times, I at length re- marked faint streaks round my chin; on further moving backwards and forwards, the streaks were very beautifully developed, but not so brilliant as on the first occasion. J now noted the ve position. L, was the light of the petroleum-lamp, L,, 4 that of the candle, and A the eye (of course seen in the glass). The streaks attained the greatest intensity when L,, was situated exactly under L,, and A was to note be seen a little sidewards between the two. The streaks ; widened out above L,—not nearly as about a slit, but yy, quite uniformly around the flame, so that it seemed to have no further influence on the streaks than to illumi- nate them. The flames were now left in their position, the glass taken down and carefully wiped and hung up again in the same place. The streaks were again visible. I had then carefully to in- vestigate whether dampness adhering to the glass, or particles of dust, called forth the phenomenon ; for I could not derive it from the laws of refraction and reflection in the clean mirror. I next dusted the mirror with lycopodium in such manner that around the light-images splendid halos appeared. The marked position was then taken, from which gorgeous interference-streaks were to be seen ; nay, they arose not merely around the lower, but also around A. e 3a tk Intelligence and Miscellaneous Ariicles. the upper flames; and since these must eross one another, the result was a coloured picture of crossing waves, than which none. more beautiful can be imagined. It was exactly, in form, like that which ensues when two stones are thrown upon the surface of still water; but it is distinguished by the magnificence of its colours. I publish this notice preliminarily, in order that this simple and very instructive experiment may be repeated; I intend, however, to sub- ject the phenomenon to scientific investigation, because the few expe- riments [ have at present made have led me to the conviction that, besides dust-particles, the hygroscopic moisture adhering to glass, though ever so little, is capable of producing it. I believe, further, that the degree of moisture may be inferred from the intensity of the streaks. Though, perhaps, of little value in relation to meteo- rology, it will incontestably give to many a physicist a good test for the degree of dryness of his glasses. The results of my further investigations I shall likewise commu- nicate to the Annalen.—Pogegendorfi’s Annalen, vol. exlix. pp. 126- 128. NOTE ON THE FILLING OF VESSELS WITH A VERY NARROW TUBE, ESPECIALLY THE CARTESIAN DIVER. BY K. L.. BAUER, OF KARLSRUHE, Frick (Physicalische Technik) and Weinhold (Vorschule der Haupe- rimentalphysik) recommend, in order to introduce a sufficient quan- tity of water into a Cartesian diver (best consisting of a hollow glass ball with a narrow tube), to partially expel the air by heating, and then to dip the open tube into water. For this procedure, however, or the use of the air-pump for the same purpose, another method, very simple, can be substituted as follows :— 1. Fill the cylinder intended for the diver-experiments with water; insert the empty swimmer in the usual position, in which the tube is directed downwards, and close the cylinder with a caout- chouc cap and binding-thread. ; 2. Exert a strong pressure on the elastic covering, and, continuing the pressure, incline the cylinder to the horizon so that the caoutchoue cap is perceptibly lower than the foot of the cylinder, and the diver, with the tube directed obliquely upwards, begins to ascend. At this moment, or when the swimmer has arrived at the top, remit the pressure, and air-bubbles will escape from the ball, which is now partly filled with water. If the cylinder had been completely in- verted, so that in its new vertical position the cap had been quite under the bottom of the cylinder, the diver would have ascended with great velocity, especially if the pressure had been interrupted immediately after the mversion. 3. If the cylinder be now restored to its original erect position (when the swimmer also returns to his initial place), and the above process be repeated, one very soon succeeds in filling into the diver so much liquid that, even after complete inversion of the cylinder, he will not ascend at all if strong pressure be continuously applied Intelligence and Miscellaneous Articles. 835 to the cap, and only very slowly if the pressure be relaxed. The Cartesian diver is now suitable for its ordinary use. 4, After reiterated repetition of the given procedure, the relaxa- tion of the pressure is useless; the diver is filled to such a degree that he remains below when the cylinder is turned upside down, the ball resting on the cap, and the tube pointing upwards. 5. Lf the cylinder be kept inverted, and the cap be pressed several times in quick succession, at each interruption of the pressure an air-bubble escapes, by which the diver becomes yet more completely filed. At last these means are no longer operative ; a minute air- bubble remains in the bali, but is of no import for its use as a diver, since the requisite degree of filling has been ewceeded. After the diver has been taken out of the cylinder, the water which has entered can be removed by a vigorous shaking, of course with the tube downwards.—Poggendorft’s Annalen, Hrganzung, yol. vi. pp. 332, 333. RESEARCHES ON THE SPECTRUM OF CHLOROPHYL. BY J. CHAUTARD. Conclusions—I. The spectrum of chlorophyl is characterized by certain bands, among which there is one, in the red, the special properties of which suffice to distinguish the solution. The quali- ties of this band are sensibility, certainty, and generality. a. Sensibility, by clear outlines, a fixed position, and a remark- able permanence through a solution so dilute as to contain less than >yo07- b. Certainty, by the division into two which it undergoes under the influence of the alkalies—a character which belongs neither to the lines of blood, nor to those of bile, nor to those of any other organic fluid. c. Generality ; that is to say, this line always appears wherever chlorophy! exists, pure or adulterated. II. Chlorophyl exists, in vegetables, in three different states, which can be perfectly recognized in the spectroscope—in leaves newly formed, in adult leaves, and in leaves dead or detached from the vegetable. a. In young leaves just expanding, the instability of the elements is very great, and is recognized by the appearance of temporary accidental bands under the action of chlorhydrie acid. b. In the second case the same acid gives rise, in the alcoholie solution, to quite another system of bands, which I call permanent accidental bands. c. Lastly, In alcoholic solutions of leaves from which the life has disappeared, or in those of fresh chlorophyl which have under- gone a certain amount of change, the permanent accidental bands appear immediately, without the intervention of chlorhydric acid. IIT. As the last consequence of the spectrum-analysis of chlo- rophyl, let us say that this substance, so easy to modify when con- sidered in the physiological point of view, is nevertheless much less 336 Intelligence and Miscellaneous Articles. alterable than it is generally believed to be. It resists the action of iodine, the acids, the alkalies, and the process of digestion, and retains, under the influence of these agents, if not its primitive composition and properties, at least some characters which permit its recognition in the midst of the most complex and varied mix- tures and after a considerable lapse of time. If the alcoholic tincture is destroyed pretty rapidly when exposed to the air, and especially in sunshine, the oily solutions oppose to the same agents a very remarkable resistance, of which we have set forth the consequences in certain questions of natural philosophy. —Comptes Rendus de ? Académie des Scrences, Sept. 8, 1873. ON THE DIRECT SYNTHESIS OF AMMONIA. EY W. F. DONKIN. The action of induced electricity on mixtures of certain gases has been lately shown by Sir Benjamin Brodie (Proc. Roy. Soe. April 3, 1873) to yield very interesting results. An obvious application of his method was to treat a mixture of dry hydrogen and nitrogen in a similar manner as those referred to above, with the view of effecting the synthesis of ammonia; and Sir B. Brodie kindly allowed me the use of his apparatus for the purpose of the experiment, which was conducted as follows :— A mixture of about three volumes of hydrogen with one of ni- trogen in a bell-jar over water, was passed through two tubes con- _ taining pumice moistened with alkaline pyrogallate and sulphurie acid respectively, then through a Siemens induction-tube, and into a bulb containing dilute hydrochloric acid. -The whole apparatus being first filled with pure hydrogen, about half a litre of the mixed gases was sent through the apparatus, the induction-coil not being in action; the bulb containing the acid was then re- moved and another substituted, containing an equal volume of the same acid. About half a litre of the mixed gases was now passed through the apparatus, submitting them to the action of the electricity. The contents of the two bulbs were next transferred to two test- tubes; and after adding excess of potash to each, Nessler’s test was applied. The first solution gave a faint yellow coloration, the second a rather thick reddish-brown precipitate. No attempt was made to estimate the quantity of ammonia formed, as it would vary with many of the conditions of the experiment. Since writing the account of the above experiment, which was made in Dr. Odling’s laboratory at Oxford on March 24, I have seen in the Compies Rendus for April 22, 1873, a note of an experiment by Messrs. Thénard of Paris, in which they observe the formation of traces of ammonia by the action of electricity on a mixture of hydrogen and nitrogen ; but no details of the mode of operating are given.—Irom the Proceedings of the Royal Society, .May 1, 1873. Erratum in Number 304.* In Dr. H. Morton’s paper, fig. 6 (page 94) should be fig. 9, and fig. 9 (page 97) should he fig. 6, and should be transposed as under. Fig. 6. g o Lo ll Ve faba. SS, tt £5 MUTT ai ii ‘Es Fig. 9. it oo PVOVSEUTAAQASAGARRARVEAANAUAAAERALAUESOQSRAATUUELOOBOOUIAGIAD | i To the Binder.—Please paste the above figures over those similarly num- bered on pages 94 and 97, which, as they now stand, are transposed. ; , ry +f ina heat : +4 x 5 } + i et ‘ THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES. ] NOVEMBER 1873. XLII. On the Action of a Blast of Sand in cutting hard Material. By Professor OspornE Reynoups, M.A.* R. TILGHMAN has discovered that sand will, when blown against any hard body, rapidly wear it away—that it acts in what may be called a systématic and not merely in a casual manner (that is to say, each grain produces its effect, and not merely one grain here and there just scratches the surface)— that the material of the sand is not necessarily harder than the material acted upon, but that the hardest bodies, such as steel files and diamond, may be cut by common sand or even by small leaden shot—that it is not necessary that the grains of sand should be of any particular size, the smaller grains producing apparently the same effect as the larger—and that the velocity with which the sand must be driven is after all nothing very considerable, that for glass a velocity of 50 feet per second is sufficient. : Now these facts, in addition to their value from a useful point of view, serve a scientific purpose, inasmuch as they call our attention to circumstances of impact which have hitherto passed unnoticed. When once our attention is called to them, we can see that these circumstances have been before us in a variety of shapes, and that they play a very important part in many mechanical phenomena, but never till now have they taken a shape sufficiently definite to compel attention. That one hard body will, when driven with sufficient velocity, * Communicated by the Author, having been read before Section A of the British Association, September 1873. Phil. Mag. 8. 4, Vol. 46. No. 307. Nov. 1873. 2A 338 Prof. O. Reynolds on the Action of a Blast of penetrate or fracture the body it strikes, or will itself be frac- tured, isa matter of such common experience, and may in some cases be so simply explained, that we have so far contented our- selves with the simple explanation, and have not endeavoured to distinguish between the different cases which occur. Up to the present time the laws of impact have been considered mainly with reference to the motion of the centres of gravity of the bodies, and very little attention has been paid to what actually occurs at the point of contact, Hence it is that the fact which it is my object in this paper to point out has been so far over- looked. This is, that at the instant of first contact the pressure between the bodies 1s independent of their size, and depends on the density of the body as well as on the hardness, so that a heavy soft body may cause as much pressure as a hard body. In the very striking process of the sand-blast we see at a glance evidence of two things which are contrary to our con- ception of what ought to.be; that is, (a) the effect is inde- pendent of the size of the particles, the small ones acting as soon as the large ones, and (0) the softer bodies penetrating the harder, as in the case of soft leaden shot penetrating the hard glass. In order to explain these we must consider what actually takes place at the point of contact. (a) The intensity of theyressure between bodies on first impact 1s independent of the size of the bodies. Although it is customary in mathematical works to consider the effect of impact on the masses of the bodies as instantaneous, we all know that itis not really so. Time is occupied in changing the motion of the centres of gravity of the bodies. The idea of a sudden change may, however, have arisen from confusion between what happens at the point of contact and at the centre of gravity. At the point of contact it is clear that the effect on the motion of the surfaces of the bodies must be instantaneous. After impact the surfaces of the two bodies move together; hence the motion of one or both of them must be instantaneously altered*. This effect, however, as will be presently proved, is in the first instance confined to the particles which come into contact. Even with hard bodies such as glass it takes time for the pressure to extend into the body. Hence on first contact it is only those particles in contact which are affected, and the rest of the body might be removed without altering the effect; that is to say, the first effect of the impact will be independent of the quantity of material behind the par- ticles which actually impinge. * This first occurred to the author while reading a paper “ On the Rup- ture of Iron Wire by a Blow,” by John Hopkinson, read before the Man- chester Literary and Philosophical Society, 1871-72. Sand in cutting hard Material. 339 ; (4) A soft body may cause pressure sufficient to crush a hard ody. The pressure necessary to force-in (to indent) the surfaces at the point of contact will depend on two things—(1) the inertia of the particles at the surface, (2) the support these particles receive immediately from behind. 1. The inertia will depend simply on the density; and if we regard all bodies as liquids, we may express this part of the pres- sure as similar to that of a jet against a surface. With liquid or very soft bodies this will be the only source of pressure. And in the case of hard bodies it seems probable that this part of the pressure will depend on the same laws as for liquid bodies; for there is close analogy between the flow of solids under pressure and that of liquids. 2. The support which the surface receives from behind will depend on the elasticity of the material and on the density. In the case of hard bodies such as glass, this will constitute almost the entire source of pressure. If the body were compressible in the same sense as gas, it would be the only source of pressure ; but in the case of elastic but incompressible bodies the inertia will affect the pressure, and it is assumed that it affects it in the same way as in the case of a liquid. When a soft body such as lead strikes a hard surface such as glass, if the velocity is sufficient, the inertia of the lead will cause enough pressure to crush or penetrate the glass, however small the projectile may be. It now remains to show more definitely how the pressure is connected with the velocity and nature of the bodies in impact. In doing this I shall assume, first, that the bodies are elastic, and, second, that they are incompressible fluids. By elastic bodies are meant bodies compressible in the same sense as gas is compressible; ordinary bodies are not compressible, and any calculations founded on their being so are necessarily erroneous. If, however, the bodies are first treated as elastic and then as fluid, and the results compounded, we shall probably arrive very close to the truth; at any rate we shall be able to judge whether they may be treated as one or the other without serious error: in this way we find that glass may be a as elastic, and lead as a liquid. Let A and B be two balls (for the sake of simplicity we will first suppose them equal and of the same material), and let A impinge on B with a velocity w. Then at the instant of impact, before the motion of the centres of the balls has been affected, the only result will be the inden- tation of the surfaces at C, the point of contact ; and it is clear that the surface of contact will be halfway between A and B, and 2A2 340 Prof. O. Reynolds on the Action of a Blast of therefore C will approach A with a velocity sand in the same way, that the relative velocity of B and C will be 5° Hence in this case the first effect of the impact will be to im- press a velocity on the surface of each ball relative to its centre equal to half the velocity of impact. Ifthe bodies had been of ~ different materials, the results would have been somewhat dif- ferent, although of the same character ; that is to say, these re- lative velocities would not be equal. In such case these velocities may be found in a manner which will be presently explained. Now, in order to impress this velocity on the surfaces, pres- sure must exist between the bodies. This pressure will depend on the velocities and on the natures of the bodies. To show this, let » = surface-velocity at C towards A, in feet per second. dX = the modulus of elasticity of A, d = the weight of 1 cubic foot, p = the intensity of pressure in pounds on the square foot. Then, for an elastic body, I shall show that ae ad Gy) Let O be the initial position of C, 6 and # the initial distance of any point P in OA from O, and #+€ its dis- tance at the time f¢. Then for the equilibrium of a per- pendicular lamina through P we have bi dE Soon map Gl RAP sale (1) dé De aa. eae (2) and from (1) and (2) we have TS LON AS APT. Go, Wee (3) e=f(\/ 21-2) the solution of which is And at C, where x=0, Sand in cutting hard Material. JB) Bat (/2), Gar/ BP (y/h4 and o =o; . substituting in (2), we have 8) ‘aie tie AY Sian Pde dee ana This, then, shows the relation between the pressure, velocity, and nature of the body. If uw is the velocity of impact and 2, d! ave the elasticity and density for the other body, we have _ VNad Nd /riIqi pa ey oi sade h Caen J rd +/ ra! from which v may be found when wu is known. We now come to the case of a liquid When a liquid is pro- jected against a surface, the pressure must be such as to overcome the momentum of the liquid; and in the case of continuous mo- tion, if the pressure were uniform over the surface in contact we should have ved pe ae tat eae And j in the case of impulsive motion it is clear that the pressure cannot be less than this. Hence if a stream of fluid B strikes a solid A, we have at the first instant # waa /M 7) from which we can find » when wu is known. 842 On the Action of a Blast of Sand in cutting hard Material. In the case of glass striking glass, we may take d= d'=150, A= 144 x 8,000,000 = 1,152,000,000, p=1,440,000 ; -, substituting in (4), we have 4 1440000 x 8 4/150 x 1152000000 =274 (feet per second). This would be the velocity just sufficient to crush the surface ; to produce an appreciable effect would require a somewhat higher velocity ; so that this value agrees very well with the result of experience, which is that a blast caused by a pressure of 4 inches of water is amply sufficient to cut glass. In the case of an ordinary solid body we have, by combining the two effects, LYON. p= Ad p+ ve vd Vg ow which gives the pressure in terms of the velocity impressed on the surface. It is important to notice that, so far as the strength of 2 the body itself is concerned, the last term = produces no effect, as this part of the pressure is balanced by the inertia of the sur- face itself, and that the first term ok Ad, will only hold so g long as it is less than the ultimate pressure which the material will stand. When it is greater than this, the ultimate pressure must be substituted for this term. In the case of lead we have ile; = 720,000 x 144; but this will only be true so long as the pressure is less than 4000 x 144, this being the maximum pressure the lead will stand; *. instead of va — v we substitute 576000 ; 712 ; . p=576000+ = (u—r)*. And if we take, as before, the pressure sufficient to crush the glass, On the Temperature and Physical Constitution of the Sun. 343 we have orp 854000 _ rasa, u—v=280, or a—250, since v=80 nearly. Hence with lead the velocity must be about eight times as great as with glass. XLII. On the Temperature and Physical Constitution of the Sun. (Second Memoir.) By F. ZOuuner. [Concluded from p. 304. ] § 7. i M. Faye has recently started the question why the masses of hydrogen perpetually hurled aloft, through eruptive pro- tuberances, from the interior of the sun have during the last thirty years not perceptibly augmented the chromosphere*, the above-given numerical values will suffice to answer this question, on the supposition of its premises, in accordance with the observa- tions. Apart, however, from this, even the hypotheses on which alone M. Faye’s question can have any meaning seem to me to be in direct contradiction to the view he has so often and so strenuously maintained, of the preponderantly gaseous constitu- tion of the body of the sun; for the augmentation of the atmo- spheric envelope of a heavenly body through eruptions of gas from its deeper-lying parts is inconceivable unless the space whence the gas issues is enclosed by an envelope impervious to the outer atmosphere. But if such an envelope does not exist, or if the then unknown processes of eruptive-protuberance deve- lopment take place outside the envelope and therefore in the lower strata of the atmosphere itself, the total quantity of this atmosphere can neither be increased nor diminished; for the volumes of gas thrown up are only portions of the atmosphere * Vide Comptes Rendus, vol. lxxv. p. 1669 (Dec. 16, 1872) :—“ TI have often asked myself whence came the hydrogenated flames of the chromo- sphere, which seem to be produced by continual violent eruptions. If the hydrogen issues unceasingly from the interior, how is it that it has not in- - ereased during the thirty years that protuberances, and even traces of the chromosphere, have been observed in eclipses, and during the three years that the chromosphere has been followed day by day? If it is not expelled beyond the sphere of the sun’s action, it must, notwithstanding its specific lightness and the total absence of all indications of descending currents, in some way reenter the body of the sun.” 344 M. F. Zollner on the Temperature and which have merely changed their places through disturbances of equilibrium—that is, have been removed from its lower to its higher regions. If, on the contrary, the sun is an incandescent liquid mass surrounded by a dense covering of vapours and gases which per- meate each other in accordance with Dalton’s law, then a por- tion of the gases (hydrogen for example) will be absorbed by the incandescent liquid surface, according to the proportion of the pressure at the base of the atmosphere*. Did, for instance, the atmosphere of our earth consist of carbonic acid of some atmo- spheres’ pressure, the superficial portions of the seas would con- sist of water impregnated with carbonic acid, out of which, on a local rise of temperature or diminution of pressure, a portion of the gas must escape in the form of air-bubbles at the place in question, in order to restore the disturbed equilibrium of the atmosphere. Could these currents of carbonic acid gas be made visible, they would probably, by the analogies in their form and frequency, remind us of the solar protuberances. How great, moreover, is the capability of a water-surface to form bubbles on the escape of gas previously absorbed, and on the bursting of the bubbles to give occasion to suddenly vanishing resistances, one may at any time convince one’s self by opening a bottle of soda- water. The height to which the fine drops of water are thrown, under the influence of the force thereupon developed, gives at the same time a means of measuring the initial velocities with which they leave the surface of the water. That even incandescent liquids, at their surface, possess in a high degree a capacity for forming bubbles under analogous but highly magnified conditions is made plain by direct observa- tions, namely Spallanzani’s at the mouth of a crater in Strom- boli :— ae glowing Java rose every two minutes to a height of about twenty feet, and then sank with velocity back again into the depth. Hach time, on reaching its greatest height, its sur- face puffed out, bubbles of several feet diameter swelled upwards and at length exploded with a loud report, bursting into a hun- dred fragments, which flew into the air with frightful violence and were precipitated rattling on the mountain as a shower of stones and scoria. . - Poulett Scrope, in the year 1819,. observed these phenomena take place in a precisely similar manner” +. Two years since, on the ground of these analogies and facts, * That incandescent liquids, even under a slight pressure, can dissolve aud absorb gases is shown by the observations of St.-Claire Deville on the solution of gases in melting glass (Comptes Rendus, vol. lvii. p. 965). ~ Naumann, Geognosie, 2nd ed. vol. i. p. 116 et segq. Physical Constitution of the Sun. 345 I formulated my view of the cause of the eruptive protuberances, and their connexion with the spots and facule, as follows* :— “ The eruptive protuberances are produced by differences between the pressure of a quantity of gas enclosed in or absorbed by the liquid, and the external pressure of the atmosphere increased by the cohesion and weight of the upper layers of the liquid. “ Accordingly eruptive protuberances will most readily arise in those places where the pressure to be overcome is the least, most rarely or not at all where this pressure is the greatest. Every ascending current in the atmosphere diminishes the pres- sure at the place, just as every descending current augments it. Now, as in the environs of the spots there are strong ascending currents and in like manner the facule are occasioned by currents of the same kind, these places must be peculiarly favourable for the development of eruptive protuberances” +. Respighi, in 1870, expressed these relations as general results of his observations, thus { :— “On the contour of the spots there ordinarily arise gaseous jets of extraordinary intensity and violence and of well-defined form.” ‘Usually the protuberances and eruptions are very frequent and much developed in the localities of the facule,” &c. Similar results were also arrived at by Father Secchi in the course of his numerous observations, which he sums up, in * Berichte d. K. Sachs. Ges. Feb. 11, 1871. + M. Tacchini thinks that only those protuberances should be regarded as eruptions, which have the form of a tree or a fan—that is, are narrower at their base than at their upper end. Without discussing more in detail the claims of such a view, it is clear that, for the explanation of those erup- tions, the physical couditions must necessarily be assumed to exist on the sun’s surface without which an eruption (the violent and sudden overcoming of a resistance by compressed gas) is not conceivable. Such a resistance can only be caused by asubstance which is in a more coherent state of ag- gregation than the gaseous; the existence of eruptive protuberances requires therefore necessarily the existence of a liquid mass, out of which the gases escape on the lessening of the pressure of the atmosphere resting upon them, like the bubbles from water containing carbonic acid. Hence, when M. Tacchini, from the circumstance that among the nu- merous protuberances only some 8 per cent. exhibit the eruptive character mentioned, believes himself justified in concluding that the general form of the protuberances is irreconcilable with the assumption of a solid or liquid constitution of the surface of the sun, it is clear from the remarks above made that the principle of majorities is logically inadmissible in the present case; for even if only one single protuberance out of the great number observed were recognized as an eruption, we should be compelled to attribute at least to the place in question of the sun’s surface those pro- perties by which alone the physical possibility of an eruption becomes con- ceivable. . t Atti della Reale Accademia det Lincei, Dec. 4, 1870. 346 M. F. Zollner on the Temperature and the abstract of a communication to the Paris Academy*, as fol- lows :— “1, The regions of the facule and spots are the richest in protuberances. “9. There are two sorts of protuberances :—one faint and light, spread like the light cirri in our atmosphere; the other denser, more compact, sharper, having a fibrous structure and peculiar optical characters.” That the more lively eruptions, which with greater velocity penetrate through the lower and more vaporous layers of the atmosphere, may drag portions of it upward above the lower limit of the chromosphere and exhibit its constituents spectro- scopically by bright lines, if the eruption be sufficiently vehe- ment, is a phenomenon to be expected. Corresponding to this, Father Secchi finds in the spectrum of the striking and intense protuberances above mentioned numerous lines of incandescent metals. He designates them on this account briefly as of me- tallic character, and (/. c.) sets forth their connexion with the spots in the following definite terms :— ‘1 then observed carefully all the eruptions having this cha- racter, which, for shortness, I will name metallic; and I found that every time one of these eruptions was observed at the eastern margin of the sun, a spot was visible on the following day. The connexion is so real that, during the last months, I have been able to predict the appearance of a spot by the mere inspection of the quality of the spectrum and the eruption. The five rota- tions of which I give the summary have themselves furnished twenty-four instances.” | Father Secchi (/.c.p. 2538) holds himself justified, on the ground of this connexion in space between the two phenomena, to draw a conclusion respecting the nature of their causal connexion :— “The conclusion from all we have just said is manifest. The spots are produced by the eruption, from the interior to the ex- terior, of masses of the metallic vapours I have indicated.” Why the converse of the conclusion here denominated “ mani- fest 7’ could not also satisfy the observations (“the eruptions are produced by the spots”’)—that is, why the spot cannot, as an occasioning cause precede the formation of the eruptive pro- tuberances, I have vainly sought in Father Secchi’s works for a reason at all solid; for the reason of the fact above noticed, that at the eastern edge of the sun the upper portions of the protu- berances first become visible, and on the following day, when the rotation of the sun has proceeded further, the till then concealed spot first comes into view, lies in relations so simple that it can- * Comptes Rendus, vol. Ixxvi. pp. 250-257 (Feb. 3, 1863). Physical Constitution of the Sun. 347 not be assumed that Father Secchi has here allowed himself to be misled to the inference of post hoc, ergo propter hoc. To enter upon a closer consideration of the cyclone theory of the sun- spots, recently set up by MM. Reye* and Fayet, I think I may at present decline, since, in the animated discussion of these views in the Paris Academy, Father Secchi and M. Tacchini have brought out the contradictions to simple facts of observa- tion into which the theory falls. I take leave to address to its advocates, without here discussing its physical bearings, the question put by Tacchini :—“ In “the face of observations so clear, so independent of hypotheses or preconceived ideas, is it possible to accept a theory which makes cyclones the sole cause of sun-spots?”?¢. I am moreover bound to thank Professor Reye for the correction (in p. 177 of his work) he has made of an error in my memoir ‘‘On the Law of Rotation of the Sun and the Great Planets” (p. 91), relative to the transformation of the sun-spots into streaks, after the analogy of the formation of streaks of cloud-like products observed on Jupiter and Saturn. From Carrington’s Table given by me in that memoir it is im- mediately seen that the difference between the velocities of diurnal rotation of two points of the sun’s surface, the helio- graphic latitudes of which differ 1°, amounts on the average not to 1°°6 (as incorrectly given by me), but to 1'°6. If at the conclusion of these considerations 1 once more reca- pitulate the view I have invariably, since the year 1865, advo- cated, of the nature of the sun-spots as scoria-like products of cooling resulting from radiation at the incandescent-liquid sur- face of the sun§, it is only for the purpose of showing how simply, if it be adopted, all those phenomena can be explained by which the opponents of this theory have hitherto seen them- selves necessitated to continual modifications of their views. As the briefest possible expression of the essential point of my theory, I select the representation given in 1869, in the Vierteahrschrift der Astronomischen Gesellschaft ||, and repro- duce it verbatim :— “The masses of scoria possess, as products of cooling, a con- siderably lower temperature than the glowing hquid mass, sur- rounding them on all sides, of the bright surface of the sun. The differences of temperature hereby determined must generate * *Die Wirbelstiirme, Tornado’s und Wettersaulen in der Erd-Atmo- sphare mit Beriicksichtigung der Sturme in der Sonnen-Atmosphire, dar- gestellt und wissenschaftlich erklart von Dr. Theodor Reye, ord. Professor a. d. Universitat Strassburg.’ Hannover, 1872. t Comptes Rendus, vol. |xxv. p. 1664. ~ Comptes Rendus, vol. lxxvi. p. 827. § Photometrische Untersuchungen (Leipzig, 1865), p. 246 sqq. || Jahrgang iv. Heft 3, pp. 165-179. 348 M. F. Zollner on the Temperature and in the atmosphere of elastic fluid above them currents analogous to the land- and sea-breezes on our earth as, according to expe- rience, established by difference of temperature between land and water on the coasts of the islands. Therefore, along the coast of a scoria island on the surface of the sun, winds must be evolved, which in general are directed perpendicular to the coast; but. these currents will, in the lower parts of the atmosphere, be di- rected outward from the interior of the island—in the upper, i. e. in the parts turned towards and visible to us, from without to the interior. There must thusarise at the borders of a mass of scoria whirlwinds, the axis of rotation of which follows hori- zontally its contour and is determined by it. “In the parts of the atmosphere above the scoria, on account of the less radiation, products of condensation must of necessity be formed, which, cloudlike in their nature, will have their con- sistence and shape determined in great measure by the atmo- spheric currents which are directed to the centre. If now the vapours have attained the elasticity corresponding to the lower temperature over the scoria (which will obviously be more and more nearly the case as the moving portions of the atmosphere ~ approach the centre of the island), the cause of cloudiness ceases, and we behold through the lightened and torn veil of cloud the underlying island of scoria as the nucleus of a spot. “The boundaries of this island are therefore, according to the theory, still concealed by the penumbre—which are the cloud- like products of cooling in the sun’s atmosphere above a scoria- mass, becoming visible to us. According to this, the portions of the atmosphere over the nucleus of a spot must be regarded as filled with vapours the elasticity of which corresponds to the lower temperature over the scoria island. Hereby, taking also into consideration the experiment described in the last Part*, the widening of the dark lines of the spectrum where they inter- * This is the experiment described by Kirchhoff in the year 1860 (Pogg. Ann. vol. cix. p. 297), by which it is shown that the insignificant quantity of incandescent sodium vapour in the mantle of an alcohol-flame can, by virtue of tts low temperature, widen and darken the sodium-lines in the solar spectrum when the solar rays are caused to pass through those flames. On this Kirchhoff remarks, ‘‘ There is at the first imstant some- thing surprising in the fact that the sodium in the little flame can percep- tibly reinforce the action exerted upon the rays of light by the sodium in the immense atmosphere of the sun. But the surprise vanishes when we consider that the brightness of the lines D in the solar spectrum is deter- mined by the temperature of the sun’s atmosphere, preeminently of its outer layers, and that the temperature of these is certainly very much higher than that of a gas-flame.” We see from this that the widenmg and darkening of some metal-lines in the spectrum of the sun-spots must not be regarded as an evidence of the greater quantity of absorbing vapours in those parts, but, primarily, only of the existence of a lower temperature of the absorbing gas-strata. Physical Constitution of tiie Sun. 349 sect a sun-spot is explained. Whether we look through the broken cloudy covering right to the scoria, or toa mass of cloud or mist resting zmmediately above it, which must consequently be cooler and ‘lower than the penumbra-cloud, may at first, as unimportant for the elucidation of the phenomena, be left unde- cided *. “From the nature of these whirlwinds it results, further, that towards the centre of a spot there is a descending current in the atmosphere—on the contrary, at the outer borders of the pen- umbra an ascending one. It hence follows that the inner border of the penumbra must lie deeper than the outer ; and therefore the entire structure of clouds which appears to us as a penumbra must descend conically, or in the shape of a funnel, in the direction of the centre of the nucleus. “The observed widening of the penumbra on the side next the margin of the sun is thus explained, in the known manner, as a phenomenon of the perspective. Just so the peculiar radial shading of the penumbra finds its explanation in the direction of the atmospheric currents. « Ave the above-mentioned whirlstorms powerful enough to carry up into higher regions the stratum to which is assigned the name of the chromosphere, these parts will appear to us as protuberances. Taking into account the direction of the whirl- ing motion, it follows that the ascending currents must be at the outer border of the penumbra; and this circumstance explains both the connexion of the protuberances with the sun-spots and also the processes of stronger light observed in the vicinity of the penumbra.” As a supplement to these explanations, I take leave at present to add only the following. According to the views here developed, the space occupied on the sun’s disk by the penumbra represents the region of circu- lation of those currents which are produced by the difference of temperature between the cooler mass of scoria and the surround- ing glowing-liquid surface, in the superincumbent atmosphere. The lower currents, directed centrifugally from the centre of the spot, must, as cooled masses, lower the temperature of the por- tions of the sun’s surface bathed by them. Taking into account the oppositely flowing upper current, in the penumbra we there- fore look through relatively hotter upon relatively cooler strata of gas; so that through the breaks in the upper condensation- * It is self-evident that we must not imagine our view of the mass of scoria of the nucleus of a spot to be so undisturbed and direct as that we have of the lunar surface. With the vapour-laden atmosphere of the sun and the still very high temperature of cooled scoria, it may be regarded as indubitable that our view does not fall direct upon the solid mass of the nucleus, but on the vapours condensed above it. 350 M. F. Zollner on the Temperature and clouds in the penumbra a somewhat darker background becomes visible than in the other parts of the solar surface. Hereby is explained the less brightness of the penumbra in general, as well - as the reversal of the relative brightness of the spectral les which has often been observed in it and at its boundaries. A more precise reason for this phenomenon is obtained from the above-cited experiment of Kirchhoff, and from the causes, fully discussed in the description of it, by which the relative bright- ness of the spectrum-lines is determmed. At the same time, by this view of the constitution and the physical causes of the penumbra, the relatively great variability of its boundaries be- comes explicable. § 8. Let me here be permitted a few remarks on determination of temperature of incandescent bodies in general. According to Kirchhoff’s theorem*, the ratio of the emissive power E to the absorptive power A is a function (the same for all substances) of the temperature ¢ and the wave-length X; so that, independently of the particular nature of the substance, we have the following relation :— 1D) A =Jyy. If the substance is not transparent, so that A=1 can be put, then is H=9, In relation to this yet unknown function, Kirchhoff (J. ¢. p. 292) remarks —“ It is a highly important problem to dis- cover this function. There are great difficulties in the way of its determination by experiment; nevertheless there appear grounds for the expectation that it will be thus ascertained, since it is in- dubitably of simple form, as all functions which do not depend on the properties of individual substances have hitherto been found to be. Only when this problem is solved will it be possible for the whole fruitfulness of the demonstrated theorem to appear.” In my inaugural dissertation +, which was published shortly before Kirchhoff’s memoir, and an abstract of which appeared in the same volume of Poggendorff’s Annalent, I have determined photometrically the light emitted by galvanically incandescent platinum wire, and at the same time measured, by observation of the resistance and the intensity of the current, the amount of * Poge. Ann. vol. cix. p. 291 sqq. - + Photometrische Untersuchungen, insbesondere uber die Lichtentwick- lung gliihender Platindrahte. Basel, 1859. { Vol. cix. pp. 244-275. Physical Constitution of the Sun. 351 heat developed in the wire with each value of the light-emission. The rays sent out by the wires were divided into two groups by the employment of a red and a green glass; and the variations of intensity of each were determined separately. The red glass absorbed all the rays from the violet end of the spectrum to the line D; while the green glass transmitted these rays, and ab- sorbed those from the red end to the same line. Accordingly, for the intensities employed, the two glasses were nearly comple- mentary, although in different degrees homogeneous. On account, however, of the great interest which, as remarked above, is now attached to the knowledge of the relation between the temperature and light-emission of an incandescent body, I thought it would be worth the trouble to examine whether a simple relation subsists between the amounts of light observed by me to be evolved by galvanically incandescent platinum wires and the quantities of heat developed in them. I take leave here to communicate first the data of observation taken from Table III. in the memoir mentioned (Pogg. Ann. vol. cix. p. 267), referring to the paper itself for a more precise account of the experiments. The fundamental units and their proportion in the quantities of light for red light (J,) and green light (J,) are unknown. In the arrangement of the observations the intensity of the gal- vanic current was always so regulated that with the different “wires the quantities of lignt emitted were the same; the heat developed differed according to the proportion of the different thicknesses of the wires. Wire No. I. had a thickness of 0°178 millim.; the other, No. IV., a thickness of 0°1035 millim. The quantities of heat developed were measured by the product of the resistance into the square of the current-intensity. Light. Heat. No. ; Jp Jy Wy Wiv (Red). | (Green). |(Wire I.).|(WireIV.). 1. 301 78 4-494 | 5-000 E 2. 670 174 5011 | 5-387 3. 1170 409 5418 | 5-948 4. 2500 831 5°984 | 6-345 5. 4132 |) 1611 6502 | 6-947 6. 5868 2450 6600 | 7:338 i 7500 3290 6°768 7-469 8. 8830 4333 6908 | 7-601 A glance at these values shows immediately that there is no proportionality between the light evolved and the heat developed 352 M. F. Zollner on the Temperature and in the wires, but the light-emission increases at a much quicker rate than the heat producing it. I therefore put J=a-e" and assumed, in a preliminary experiment, that for both groups of rays a=1; so that, on this hypothesis, l ogi = const. w The following Table contains the values of this quotient for each wire and for each of the two classes of rays. Red light. Green light. Noi Msp ae log Jp log Jp log Jy log Jy Wy Wiy Wy Wiv 1. 0°5717 0°5054 0-4210 03784 2. 05653 0°5249 0°4470 0°4158 3. 0:5669 0°5158 0:4815 04391 4. 0-5678 05356 04880 0°4603 5. 05562 0°5205 0°4933 0:4616 6. 0°5709 0°5135 0°5136 0-4619 7. 05725 0:5188 0°5197 0-4709 8. 05714 0°5192 0°5265 05784 From this we gather that, for the more homogeneous red rays, - the constancy of the required ratio indeed takes place with suffi- cient exactness. That the value of the constant a agrees closely with the arbitrarily chosen fundamental unit of light, is ob- viously a purely accidental circumstance. But, without approach- ing here to a more precise determination of the constant of the hypothetic function, the followmg brief remarks may be made respecting the less homogeneous green rays. Supposing that, for rays of the same wave-length, the ratio between the quantity of heat developed in a body and its emis- sive power is universally the one assumed, iy it is clear that, for a mass of rays which is not homogeneous, but, like that transmitted through the green glass, is continually taking up into itself new rays of less wave-length as the tempe- rature rises, c cannot be a constant quantity, but must much more increase with rismg values of w, in correspondence with a greater increase of the total quantity of light emitted. Now such a continual increase is in fact exhibited in the above values ped for green light. of the ratio Physical Constitution of the Sun. 353 If in the present observations we may neglect the slight vari- ations observed by Pouillet in the specific heat of platinum at high temperatures, the observed variations of the quantities of heat developed are proportional to the variations of temperature of the wires. The relation between the emissive power of a body and its temperature, for homogeneous rays, could then be represented by an analogous function, and thereby the determi- nation by experiment of Kirchhoff’s function in the way indi- eated, at least in its dependence on the temperature, be facilitated. For practical objects, however, of the determination of the temperature of opaque incandescent bodies in an optical way, even a theoretical knowledge of that function would not be ne- cessary, it would be sufficient to determine for several kinds of rays, in as different parts of the spectrum as possible, the con- stant in question, by which the light-emission as an exponential function is connected with the temperature of the incandescent body. Since this function must be the same for all opaque black bodies, independent of their other qualities, only the photome- tric comparison of the part in question of the spectrum with the analogous place in the spectrum of another opaque body of known temperature would be requisite, in order to deduce from the observed ratio of intensity, with the aid of that function, the unknown temperature of the second body. To give a clear idea of the course to be pursued, suppose the following arrangement of the apparatus. In front of the slit of a spectroscope two right-angled reflection-prisms are fixed with the reflecting faces directed to opposite sides, so that the rays from two sources of light, one on each side of the spectro- scope, are spread. out into two adjacent spectra. One of the sources is a galvanically meandescent plate of platinum, for which, in like manner as in the above-described experiments, the constant of the function of the hight-emission is empirically de- termined for a defined class of rays. Some direct calorimetric determinations of the temperature with different degrees of in- candescence could without difficulty be effected under the given conditions, for a first approximation, to form the basis of the method. If now the other half of the slit be illuminated by an opaque incandescent body of sufficient extent, so that the appa- rent surface fills up the eutire opening of the slit, the photome- trically determined ratio of intensities of the two spectra at the places.in question will, with the aid of the function ascertained for the platinum plate, immediately determine the temperature of the second body. For the photometric variation of the quan- tities of light the polarization principle would be suitable. For this purpose the rays from each of the two sources to be com- pared could, before they enter the reflection-prisms, be caused Phil. Mag. 8. 4, Vol. 46. No. 307. Nov. 1873, 28 354 M. F. Zollner on the Temperature and to pass through Nicol’s prisms the sections of which are per- pendicular to one another, so that the two spectra in the field of the spectroscope would consist of lights polarized perpendicu- larly one to the other. Ors] big a Fe OU Gon 2 AF (6) o From the rth equation we see that —p?[r] —p?6[r] + {7} + 8{7} is a small quantity of the second order; so that Approximately Simple Systems, 359 pe et dtr} a iS [el] + sai Hiya bihda ej r]+efr] ld where P,. denotes the value of p, before the change. The inter- pretation is that the altered period may be calculated from the potential and kinetic energies without allowance for the varia- tion of type which will in general accompany the change in the system, provided we are content to neglect the square of the change. This result, proved in a different manner, was given in a paper read before the Mathematical Society in June last*, and appears to be of considerable importance. It may be applied, for example, to the calculation of the beats of a slightly unsym- metrical circular plate, which are analogous to those often given by bells. An example or two will probably clear up any point that may be obscure (whether from defective exposition, or the extreme generality of the method) in the general theory. Consider the case of a string whose longitudinal density p is not quite constant. Since there is no change in the potential energy of a given configuration, 5{r } =0. On the other hand, if y=, sin — +f, sin ae ote be the form of the string at any time, E : 2 , T=3(p (4: sin + do sin = 4 He .) de=3 6% sin? = te +... +bida(p sin aU reli dv+.... Y i If p were constant the products would disappear, since ¢, &c. are the normal coordinates for a uniform string. As it is, the inte- gral coefficients, though not evanescent, are small quantities, Let p=p )+6p; then, in our previous notation, l So eearmhe tre { eee 3 i and therefore, by (4), 2('op-.. ,rmx Zips AS cana pi=P4 1 if Ai sin? dx ., bee Mendic eal clea) a formula from which the pitch of an approximately uniform string may be calculated. It should be noticed that no parti- cular selection of pg is necessary, since P? contains pp as a divisor. * «On some General Theorems relating to Vibrations,” by the Hon. J. W. Strutt. 360 On the Vibrations of Approximately Simple Systems. In order to find the variation of type, we have NS sh rma ST 1. Wo, dp, : or gag meee 7 sin dn 93 or, since p?: p?=7? : s?, a py ean sia : | 6,:9,= aye al a ee ee aie (6). The normal component vibration is accordingly given by y= (¥, cin 7 4g, sin = Hl ..) eos ( (pt—e), where p has the value given by (5), and ¢,:¢, the ratio just determined. As an application of this theory let us calculate the displace- ment of a node—for example, the node of the second component, which would be in the middle of the string, were it not for the i the ap- want of uniformity. In the neighbourhood of r= 5 proximate value of y iS y=, sin 5 Eee do Siu — + dg sin— = va{te att F pacos +... }, +. or T y=$,;—$3+ Os—-.- + 7 Oe 1 2 hat Aba veoh, where ] on =a— 5 Hence, when y=0, 3 i 6x= Dard, 1Pi—Pgths—eef ee ss (7) approximately, where "] QD 8 a4 ei) - sin = sin 57 da, The formula (7) gives the displacement of the node to the first order of approximation. The generality of the method will perhaps be better brought out by an application to a bar of nearly uniform density, where the normal functions are more complicated. If these be denoted by u,, Ua, &e., On the Specific Heat of Gases and Vapours. 361 y= cos pt }yu, + Potigt+ ...h, T= fp (die + hola + -+.)*da, ie 4) potdx, s[r] =) dp. wdx, pony — oP ude Pr - Pr=1 a \ porta 3 _ Pr J pueda on OT | eae J powtda ‘I do not stop to discuss the physical bearing of these results ; enough has probably been said to enable the reader to judge of the scope of the problem here considered, and of the simplicity of the mathematical machinery by which the’ solution may be obtained. September 23, 1873. XIV. On the Determination of the Specific Heat of Gases and Vapours at Constant Volumes. By R. C. Nicuots. [Continued from p. 290.] ; HE uncertainty of the ordinary method is ce indi- cated by the diverse results for the value of — — obtained by different observers, namely 1:348, 1-375*, 1 419. The last, however, that of Masson, does not greatly differ from the value calculated by the independent method from the velocity of sound, 1-41.22. The value of e—c, may be expressed by the general equation - a —=— Cc = — or ee where @ is the coefficient of expansion, p the weight of a cubic foot of the gas estimated in any given unit, at 32°, per unit of pressure on the square foot, and H the mechanical equivalent of heat. This expression will obtain equally if a, w, and H are taken for feerees Centigrade and metres. If the ratio = be represented by 7; 1 J a Cc (i — * = pH which expresses a definite relation between the constants c, 7, «, * Gay-Lussac. 362 On the Specific Heat of Gases and Vapours. w, and H; so that if any four of these are given, the fifth may be deduced independently of any other determination. According to Regnault’s observations, the density of air at 0° C. and a pressure of 760 millims. compared with mercury is 1 to 10517:3, by which estimation the value of w for a cubic foot will be 000088182. This gives e—c,='069166, whence c, ='16853 if c=-2377*. Assuming these values to be correct, So =] AOA, C The accuracy of the result e—c,=°069166 depends on that of the values of the coefficient of expansion, ‘003665 per degree Centigrade, the density of air as above, and the mechanical equi- valent of heat, 772 for one pound of water raised 1° Fahr. If in addition = be taken at 1°4122, c,='1678, and c='23696, 1 an independent determination of the specific heat of air for con- stant pressure, which is a little lower than that of Regnault. The value of —, as calculated from the velocity of sound, has 1 been given by Regnault at 1:3945; but this does not accord so well with his determination of the other constants as the value usually assigned, 1°4122. The specific gravity of hydrogen being about :0692, the value of c—c, for hydrogen is very nearly 1; and if E represent the atomic weight of any other gas (hydrogen being 1), c—C,= = (nearly), a coincidence which is remarkable, though apparently accidental. The observations of Regnault lead to the conclusion that the specific heat ¢ of all simple gases at temperatures and pressures sufficiently remote from their points of condensation, varies n- versely as their atomic weight; and since c—e, varies in the same manner, it follows that - must have the same value for all 1 these gases. This same conclusion was arrived at by Dulong from experiments on the velocity of sound. Although the expression for the value of c—c, is perfectly general, it must be observed that it varies directly with the co- efficient of expansion, «, which cannot be assumed to be the same for vapours or gases near their points of condensation as for per- * The same result will be obtained from the equations given in the pre- ceding part of this paper if the weight of 1 cubic foot of air be taken as 535°81 grs. at a pressure of 14°7346 lbs. and at 60°, instead of 535°68 grs. - at a pressure of 14°706 lbs. On some Results of the Earth’s Contraction from Cooling. 363 fectly elastic gases. Hence it is probable that c—c, is greater and c, less for aqueous vapour than would result from the general value of a. Athenzum Club, October 4, 1873. Erratum in No. 306. Page 289, last line of text, for p(V,— Vj) read p(V,—V). XLVI. On some Results of the Earth's Contraction from Cool- ing, including a discussion of the Origin of Mountains. By James D. Dana. [Continued from p. 289.] V. Formation of the Continental Plateaux and Oceanic De- pressions. sm my papers of 1846 and 1847 I attributed the formation of the great plateaux called continents, and of the oceanic depressions, to unequal contraction, observing that the oceanic crust, by being the later in consolidation, became more depressed through the continued contraction than the already firm or less- contracting continental crust. The steps in the process I pro- pose now to consider, as a means of further elucidating the subject. 1. Unequal contraction a fact. The fact of unequal contraction is manifest from the mequa- lity of level that exists over the sphere, dividing it into oceanic depressions and continental plateaux; and unequal contraction (the material of the crust being essentially the same over the two kinds of regions) implies an unequal rate of cooling. Moreover it is a necessary conclusion that the great areas first consolida- ting should have been first free from that chemical activity and those ebullition-like movements due to escaping vapours which are inseparable from the fluid condition of rocks under merely atmospheric pressure. 2. Location of the continental areas. The areas first to become quiet, and first to cool and consoli- date, would be the shallowest areas—that is,’ those beneath which the solid nucleus of the globe reached nearest to the sur- face ; for this approach to the surface would have been favoured by the chemical quiet, and the less depth would ensure more rapid cooling. The solid state of the interior mass, under the Hopkins’s theory, is due to the pressure of the outer portion, this pressure 364 Prof. J. D. Dana on some Results of being capable of producing an increase of density, and at some depth that density which belongs to the solid rock ; so that downward either from the plane at this depth, or from some level or levels below it, actual solidity would have existed. It may be that when exterior solidification (that is, the solidifica- tion of the crust) was about to begin, the outer limit of the in- terior solid mass under the solidifying areas was quite up to the spherical plane in which the rock of the interior had the density of solidity. It is at least certain that its limit was as near the surface as was possible under the temperature then existing. 3. Nature of the cooling crust, und of the liquid layer of which it was formed. ; The change of specific gravity or density which the rock- material underwent in passing from the liquid to the solid state is part of the data required: for conclusions on the subject im view ; and with reference to it we may first consider the nature of the rock-material. 7 The larger part of the igneous rocks of the globe are ejections, according to the evidence which has been presented, either from regions within the true crust of the earth (that is, the part situ- ated below the supercrust and which was a direct result of the cooling), or from the plastic layer or seas underneath. In either case they are testimony, and have long been so regarded, with respect to the outer liquid layer of the melted sphere. The next best testimony we have is that from the earlier of the sur- face formations—the Archzan (Azoic). Another source of con- clusions, appealed to effectually by Daubrée*, is the constitution of meteorites, and parallel facts in the earth’s igneous and meta- morphic rocks. Still another, used by Hunt, is reasoning from physical and chemical laws to the probable results under the supposed conditions of a cooling globe. We thus arrive at the following conclusions. (a) The more prominent minerals were the following :—(1) some iron-bearing species (bearmg also magnesia and lime) of the amphibole family, as augite, hornblende; (2) the iron-and-mag- nesia mineral chrysolite (or -olivine), to which Daubrée, on the evidence just referred to, gives great prominence; (3) species of felspar—either the lime felspar called anorthite, the lime-and- soda kind called Labradorite, the soda-and-lime kind oligoclase (and andesine), the soda felspar (containing usually some potash) albite, the potash felspar (contaiming usually some soda) ortho- * «Expériences synthétiques relatives aux Météorites. Rapproche- ments auxquels elles conduisent, tant pour la formation de ces corps pla- nétaires que pour celle du globe terrestre,”’ par M. Daubrée, Comptes Rendus, vol. \xii. (1866). the Earth’s Contraction from Cooling. 365 clase ; of which felspars the first two are lowest in silica, 45-55 per cent., the third intermediate in amount of silica, or 60 to 64 per cent., the last two the highest, 65 to 75 per cent.; (4) mag- netite (or magnetic iron-ore, Fe? 04, but often titaniferous) ; and (5) perhaps quartz or free silica, and mica. Serpentine and chlorite are omitted from the list on the ground that they are always metamorphic. The question with regard to quartz is discussed below. (b) The principal rocks in their relation to the subject before us fall naturally, as Elie de Beaumont first formally announced*, into two series, although there are intermediate kinds through which the two graduate into one another :—one, low in silica, or basic, containing less than 56 per cent. of silica; the other, high in silica, or acidic, containing 56 per cent. or more. The basic rocks include dolerite and the related igneous rocks, made up of augite and Labradorite, with sometimes anorthite or oligoclase, often chrysolite, and generally magnetite in dissemi- nated grains, and varying in specific gravity mostly between 2°8 and 3:2. The acidic comprise (1) most trachyte and related felspathic rocks, consisting of one or more of the felspars oligoclase, albite, or orthoclase, with usually a little hornblende and magnetite, and sometimes mica, and not unfrequently free quartz—sp. gr. =2°5-2°75; (2) syenite, consisting of orthoclase and horn- blende with quartz—sp. gr. =2°9-3°1; hyposyenite, consisting of orthoclase and hornblende without quartz—sp. gr. =2-9- 3°27; diorite, consisting chiefly of oligoclase or albite with hornblende—sp. gr. =2°80-3°1; granite, consisting of ortho- clase (sometimes along with albite or oligoclase), quartz, and mica—sp. gr. =2°6-2°75. (c) These igneous rocks are also conveniently arranged with reference to their origin into an iron-bearing and a compara- tively irun-free series. The former include the rocks containing as essential consti- _ * Bull. Soc. Géol. de Paris, (1I.) vol. iv. p. 1253 (1847). De la Beche has the idea in chapter xvili., on Igneous Rocks, of his ‘ Geological Re- searches’ (1834). Bunsen uses it in his memoir on the Volcanic Rocks of Iceland (Pogg. Ann. vol. Ixxxii. pp. 201 (1851); and also Durocher later, in his memoir on Comparative Petrology. + The name syenite belongs by right of priority to the quartz-bearing rock, as it was described from the locality Syene in Egypt, where that kind occurs ; and i therefore call the kind free from quartz hyposyenite. Syenite is a rock of the hornblendic series in all its geological relations, gradua- ting often into hyposyenite in Archean regions; and it is bad to make it, as some German lithologists do, a hornblendic variety of granite. It deserves to stand as a distinct species ; and it naturally leads off the horn- blendic or syenitic series of crystalline rocks, as granite does the non- hornblendic or granitic series. 366 Prof. J. D. Dana on some Results of tuents one or more of the iron-bearing minerals (augite, horn- blende, and chrysolite, and often also magnetite), and are divided into two groups—the doleritic, containing pyroxene, and the sye- nitic, containing hornblende in place of pyroxene. The Jatter comprise those mostly (seldom wholly) free from these iron-bearing minerals, as the trachytic and granitic kinds. (d) The presence of quartz among the chief constituent mine- rals of the true crust is not certain. Of the above-mentioned rocks, the basic iron-bearing (or doleritic) kinds are far the most abundant among acknowledged igneous rocks; and this fact seems to indicate that quartz or free silica was not abundant in the original liquid rock of the globe. Its absence, which Mr. Hunt urges, is seemingly opposed by the fact that it is present in so many trachytes, as well as in syenite and granite and the related rocks. But Hunt is right in holding that im general granite and syenite (the quartz-bearing syenite) are undoubtedly metamorphic rocks where not vein-formations, as I kuow from the study of many examples of them in New England ; and the veins are results of infiltration, through heated moisture, from the rocks adjoining some part of the opened fissures they fill. These rocks, although common, present therefore no positive testimony on the side of the presence of quartz. Mr. Hunt urges, in support of his opinion, the experiment of Rose, in which fused quartz on cooling had the low density and other characters of the form of silica called opal, and not those of quartz. But the evidence is inconclusive, since a laboratory experiment cannot inform us what would be the condition of silica on cooling from fusion, provided the process of solidifica- tion took some millions of years. But Rose’s experiment does seem to settle the question as regards all quartz veins, since, if of igneous origin, their little width would have ensured compa- ratively rapid cooling ; and it thus sustains the evidence in favour of the view that such veins, like most mineral veins, were filled through the aid of heated moisture. Professor Hunt’s argu- ment from the probable condition of the material of the liquid sphere when about to solidify at surface—or the fact that the lime and magnesia now in our limestones and waters, and the soda in our waters, must have been mainly in the condition of silicates, and that therefore the free silica would thus be in combination—is of great weight; and, considering the vast amount of limestone in the earth’s formations, it favours the view derived from the prevailing doleritic character of igneous rocks, that silica was mostly, if not wholly, in combina- tion, and that the chief felspars present were the lime-and- soda species, Labradorite and oligoclase. Granite and syenite (common rocks of Archean terrains) are just the rocks that are the Earth's Contraction from Cooling. 367 likely to have been formed over the earth’s surface after the action on the crust of the foul atmospheric vapours that settled upon it as it began to solidify. If there were mainly doleritic material and other Labradorite mixtures in that crust, the result of the conflict would be a removal of part of the bases and the liberation of silica, maxing free quartz and quartz- bearing rocks. , Again, the general fact that the doleritic rocks, and even most trachytic, contain disseminated grains of uncombined oxide of iron in the form of magnetite (Fe? O*), adds to the strength of the argument against the general diffusion of quartz (that is, free or uncombined silica), if not proving its absence. (e) The presence of a large proportion of iron is a marked feature of most igneous rocks. This ferriferous quality is not characteristic solely of the doleritic and syenitic kinds; even the most purely felspathic trachytes usually contain some dissemi- nated magnetite and hornblende; and from this extreme there is a shading-off in trachytic rocks toward dolerites, syenites, or hyposyenites. It should be here understood that augite and hornblende are essentially identical in chemical constitution, though differing in crystallization. Hornblende has often a slight excess of silica, making the oxygen ratio of the bases and silica frequently 1:23, as in the felspar oligoclase, instead of 1:2, as in augite; and this may be a reason for its occurrence by preference in the trachytes, in which oligoclase and ortho- clase predominate, and that of augite in the dolerites, in which Labradorite is the predominant felspar. In Labradorite this ratio is 1: 14, and in Andesine 1:2. Mixtures of Labradorite and oligoclase, which constitute the base of some doleritic rocks (melaphyres, in which the silica constitutes over 55 per cent.), would have 1: 2 for this oxygen ratio when the proportion of Labradorite to oligoclase was 1 to 2. The basic iron-bearing feature of the first solidified crust is attested also by the nature of the lowest rocks of the super- crust—that is, by the Archzean formations overlying the true crust and directly or indirectly made from it. We find among the Archean terrains the felspar Labradorite far more abundant than in any later metamorphic rocks, the rock hypersthenite common (which is much like dolerite in elemental constitution), others (ossipyte and a chrysolitic hypersthenite) which are closely related to peridotite or chrysolitic dolerite, other rocks that are almost solely chrysolite, another (diabase) which has the com- position of a chloritic dolerite, other kinds (referred to byper- sthenite and diabase) which approach melaphyre. And besides, there are diorite, consisting of hornblende and albite or oligo- clase, and hyposyenite, consisting of hornblende and orthoclase. 368 Prof. J. D. Dana on some Results of These iron-bearing kinds of Archean metamorphic rocks much exceed in amount the granitic kinds that are free from _ iron. Moreover in these Archean formations, the granitic as well as the iron-bearing, there are immense beds of iron-ore, as seen in New York, Canada, Northern Michigan, Missouri, Sweden, and Norway, the thickness of single beds frequently exceeding a hundred feet ; and thus, although the surface over which Archean rocks are exposed is relatively small, its iron is in vast amount. In fact, unlike human history, the earth’s iron age was its earliest. Now, since these great iron-ore beds are of sedimentary or marsh accumulation (for they occur interstrati- fied with quartzite, chlorite, schist, syenitic schist, and other metamorphic rocks), the iron was gathered from the preexisting crust-rocks ; they therefore prove that iron was a very common ingredient in the original fused material of the surface of the liquid globe. (f) We hence have reason for the inference that the original fused material contained largely the ingredients of the iron- bearing rocks dolerite, peridotite, diorite, hyposyenite, besides trachyte and the related kinds, and, perhaps, in small proportions those of the quartziferous trachytes, if not of granite and syenite. It is not certain from present knowledge whether the slow cooling must not have made hornblende throughout the crast- mass in place of the akin species augite. Yet the considera- tions mentioned on the preceding page suggest that augite may have characterized the basic portions of the crust, and horn- blende the smaller acidic portions; and if so, the prevailing rock is strictly doleritic. (g) In view of the large proportion of iron, the mean specific gravity of the true crust can hardly be less than 2: 9, and probably it is as high as 3-0. (A) The method of distribution of the basic (doleritié) and the less abundant acidic (or trachytic) kinds in the earth’s outer viscid layer before solidification—whether in separate layers, the latter over the former, as Durocher urges, or whether in sepa- rate local streams or regions made by the boiling movements and the great oceanic-like currents in the liquid mass, through the principle of liquation on a large scale—need not be here considered. I merely add that observed facts seem to be best explained on the latter view, since the existence of the two layers is not proved by the study of the Archean terrains. If it existed at the beginning of solidification and the trachytic Jayer was thick enough not to have been obliterated by cooling before the era of the more recent trachytic ejections over the great Pacific slope, the constituents of the iron-bearing or dole- the Earth's Contraction from Cooling. 369 ritic rocks should exist but sparingly in the Archzan instead of being the prevailing kinds. 4. Change of Density and Volume in Solidification. All the rocks above mentioned have a higher density in the solid state than when in fusion. According to Delesse*, gra- nite decreases in density in passing from the stone to the glass conditiont 9 to 11 per cent.; syenite, syenitic granite 8 to 9 per cent.; diorite 6 to 8 per cent.; dolerite and melaphyre 5 to 7 per cent. ; basalt and trachyte 3 to 5 per cent. The difference in volume is thus large between a rock in the solid and glass states. As to the difference between the glass and liquid states, we have no precise observations, and only know that it is ex- ceedingly small f. From the above facts, sustaining the nearly total absence of quartz-bearing rocks from the crust, and therefore of granite or syenite, and the other considerations presented, we may take 8 per cent. as the probable average change of density for the earth’s crust between the stony and the liquid states ; which is equivalent to a change of volume from 100 to 92 per cent. in passing trom the liquid to the stone condition. 5. Process of Solidification and Continent-making. The crust over the areas of solidification, after attaining a thickness that would enable it to overcome by its gravity the cohesion in the liquid rock beneath, would sink in masses and then be remelted by the heat beneath, and this remelt- ing would cool somewhat the liquid layer. So this process of crusting and sinking with an overflow from either side, re- melting, and cooling, would go forward until the masses could sink without much remelting, to bring up at the level where the density of the liquid layer was that of the solid rock, if this liquid layer had not become so stiffly viscid by the cool- ing as to offer too great resistance to their reaching quite to this level. The sinking rock-masses may have had their density somewhat increased by the pressure to which they were subjected on descending; but whatever density they acquired, * Bull. Soc. Géol. de France, part 2, vol. iv. p. 13880 (1847). Delesse’s results agree nearly with those of St.-Claire Deville. Bischof in 1841 found the volume of basalt in the vitreous and crystalline states as 1 to 60-9298, the same in the fluid and crystalline states as 1 to 0°8960, and for granite the corresponding ratios 1 to 0°8420 and 1-07481. + It is to be here noted that the glass and stone conditions are distinct molecular states of the same substance—the former produced under rapid cooling, the latter under slow,—and that common glass will become stone if solidified under a prolonged cooling-process. ¢ Iam informed that at the Lenox Glass Furnace in Berkshire, Mass., no contraction is noticed in the cooling of the glass. Phil. Mag. 3.4. Vol. 46. No. 307. Nov. 1873. 2C 370 Prof. J. D. Dana on some Results of this density would determine the limit to which (setting aside resistance from viscidity) they would sink. It may be that portions went down until they came into contact with the nu- cleal solid mass. As the crust sank, the liquid material ad- joining would continue to flow over the solidifying area and add to the solidifymg material. Finally, a layer of crust-rock miles in thickness would have been made over the great continental areas. Throughout the other portions of the sphere, the surface, whether all liquid or in incipient solidification, would have the level of that of the continental areas. For the sake of the illustration, suppose ‘them to have been all liquid and the continental crust twelve miles thick, and the oceanic areas to go through the same pro- cess of solidification as had been completed over the continental areas; when, finally, the material of the oceanic regions had solidified down to the same plane with that of the continental (that is, to the twelve-mile limit), the oceanic crust thus formed would have become depressed in the consolidation (on the above ratio of 8 per cent. less volume for the liquid than for the solid) 5000 feet, or, if the layer consolidated was thirty-six miles thick, 15,000 feet—that is, supposing the continental part to undergo no contraction during the time. As such contraction would have been in progress from the continued cooling, the above 5000 feet is not the actual depth the basin would under the supposed circumstances have acquired ; and yet, since the change of volume in the cooling of solid rock is small, it is not very wide of the fact. _ The case here supposed is partly hypothetical, because the condition over the oceanic areas when the solidified crust of the continental areas was completed may have been that of incipient solidification, so that some of the contraction had already taken place. But, apart from this, it represents correctly, as it appears to me, the steps in the process, and illustrates how it is that great depressed areas would be an inevitable result, and why they should have comparatively abrupt sides or a basin- like character. The present mean depth of the oceanic areas below the mean level of the continental plateaux is probably about 16,000 feet. The thickness of the layer of liquid rock required to make a depression of 16,000 feet by its consolida- tion would be about 384 miles. But as contraction has gone on through time over both continental and oceanic areas, this is the mean excess of depression for the oceanic area. What part of this-excess existed when the oceanic depression was first made, there are no facts for satisfactorily deciding. If the coral-island ~ subsidence was due in any considerable part to radial contrac- tion beneath the Central-Pacific crust itself, it is probable that the excess has increased even in Ceenozoic time. the Earth’s Contraction from Cooling. 371 I find no explanation in the present state of science where- fore most of the dry land of the globe should have been located about the north pole, and of the water about the south. Physi- cists say that it indicates greater attraction, and therefore a greater density, in the solid material beneath the southern ocean. But why the mineral ingredients should have been so gathered about the south pole as to give the crust there greater density is the unanswered query. It may be that magnetite is much more abundantly diffused through the antarctic crust than the arctic. This is only one of many possibilities, and it is at present with- out a satisfactory fact to stand upon, beyond the general truth that iron was universally present. 6. Resulting Crystalline Texture of the Crust. The doleritic and trachytic rocks of the true crust, and what- ever else exists in its constitution, cannot be present with just the texture we find in the rocks of existing dykes and volcanic mountains. For, as above stated, the crust has cooled with in- conceivable slowness, far more extreme than that which has at- tended the formation of any of the coarsest granites and syenites, And since the coarseness of crystallizations is generally in pro- portion to slowness of cooling, the texture of the whole should have been after the character of the coarse Archzan syenite or hyposyenite and vein-granite, or else in much larger crystalliza- tions. One or another of the cleavable felspars is, in all proba- bility, everywhere present ; and since the cooling, and therefore the crystallization, has been in progress through many millions of years and still goes on, the probability is that the felspar erystallizations and cleavage-planes of the first-formed crust- layer were lengthened downward for very long distances, if not indefinitely. If so, the existence of a cleavage-structure in the crust as courses of easiest fracture, such as I have appealed to elsewhere in explaining the origin of the courses in the earth’s great feature-lines*, is not an unreasonable supposition: 7. The Continents always the Continental Areas. The above-stated effects of contraction lead to the necessary conclusion that the oceanic and continental areas were defined when the earth’s crust first began to form—if not also still earlier, during the progress of its nucleal solidification. It is hardly possible to conceive of any conditions of the contracting forces that should have allowed of the continents and oceans in after time changing places, or of oceans as deep nearly as existing oceans being madewhere are now the continental areas,—although it is a necessary incident to the system of things that the con- * Silliman’s American Journal (I1.), vol. iii. p. 381 (1847). 202 372 Prof. J. D. Dana on some Results of tinental plateaux should have varied greatly in their outlines and outer limits, and perhaps thousands of feet in the depth of some portions of the overlying seas, and also that the oceans should have varied in the extent of their lands. The many cha- racteristics of the continental borders—for example, the contrast between the landward and seaward slopes of the mountains and even of the plications constituting them, the positions of volea- noes and of regions of igneous eruptions and metamorphism, indeed all the features declare which side of each border-chain is the oceanic and which the continental, and protest against. speculations that would reverse the order. The early defining, even in Archean time, of the final features of North America, and the conformity to one system visibly marked out in every event through the whole history (in the positions of its outlines and the formations of its rocks, in the character of its oscilla- tions and the courses of the mountains from time to time raised), sustain the statement that the American continent is a regular growth. The same facts also make it evident that the oceanic areas between which the continent lies have been chief among the regions of the earth’s crust that have used the pent-up force in the contracting sphere to carry forward the continental de- velopments. If this was true of the North-American continent, the same in principle was law for all continents. Conclusion. I here close this reconsideration of the views brought out in my papers of 1847. Of the principles then presented, and briefly recapitulated in the opening pages of this memoir (No.3803, pp. 42-44, I have found reason to modify some points con- nected with Section 4 (on mountain-making) and part of Section 8 (or that on metamorphism) :—the former in consequence of some new considerations of my own and of two ideas, of funda- mental value, which I owe to LeConte*; the other in view of Mallet’s recent contribution to Vulcanology. I purposely avoided in my early papers any expression of opinion as to the nature of the earth’s interior (having had Hopkins’s argument of 1839-1842 in view); and hence there is nothing on this point in the statements then made that requires changet. The views on mountain-making now sustained suppose the * Introduced in Part I. (No. 303, p. 50) and Part II. (p. 217). + The later paper of Professor Hopkins, read before the British Associa- tion, did not appear in this country until after my articles of 1847 were in print ; and I have since then been deferring my adoption of the views now accepted from it until the idea of the earth’s interior solidity should have additional affirmation from the physical and mathematical side. This it has recently had through the writings of Sir William Thomson and others. the Earth’s Contraction from Cooling. 373 existence, through a large part of geological time, of a thin crust, and of liquid rock beneath that crust so as to make its oscilla- tion possible, and refers the chief oscillations, whether of eleva- tion or of subsidence, to lateral pressure from the contraction of that crust; and this accords with my former view, and with that earlier presented by the clear-sighted French geologist, Prévost. I hold also, as before, that the prevailing position of moun- tains on the dorders of the continents, with the like location of voleanoes and of the greater earthquakes, is due to the fact that the oceanic areas were much the largest, and were the areas of greatest subsidence under the continued general contraction of the globe. Beyond these points there are additions and modifications. In addition to admitting the nucleal solidity of the globe, and the present partial union of the crust to the nucleus, these in- clude the recognition of the following principles :— (1) That in mountain-making on the continental borders, the oceanic crust had the advantage, through its lower position, of leverage, or, more strictly speaking, of obliquely upward thrust, against the borders of the continents. (2) That among mountain elevations there are those which, like the Alleghanies, are the result of one process of making, or monogenetic, and those that are a final result of two or more processes at different epochs, or are polygenetic. (3) That there are two kinds of monogenetic ranges :—those that are geanticlinals, or anticlinoria, hike the region of the Cin- cinnati uplift; and those that were the result of a slowly pro- gressing geosynclinal, with consequently a very thick accumu- lation in the trough of sedimentary beds, ending in an epoch of displacements and solidification, and often of metamorphism of the sedimentary beds, as in the case of the Alleghanies and other synchnoria. (4) That great mountain-chains are combinations of syncli- noria and of anticlinorian elevations. (5) The principle advocated by LeConte (restricted as indi- cated), that plication, shoving along fractures, and crushing are the true sources of the elevation that takes place during the making of the second of the two kinds just mentioned of mono- genetic mountain-ranges or synclinoria. (6) That on the oceanic side of the progressing geosynclinal referred to there has been generally, as the first effect of the thrust against the continental border, a progressing geanticlinal which usually disappeared in the later history of the region— gravity, and the yielding and plication in the region of the geosynclinal, favouring this disappearance. 374 On some Results of the Earth’s Contraction from Cooling. (7) That the locus of the region of subsidence on a conti- nental border was in general along side of a region of thickly stiffened unyielding continental crust, and that pressure against the stable area beyond was one source of the catastrophe of mountain-making. (8) That each epoch of plication and mountain-making ended in annexing the region upturned, thickened and solidified, to the stiffer part of the continental crust, and that consequently the geosynclinal that was afterward in progress occupied a parallel region more or less outside of the former, either land- ward or seaward, and commonly the latter. (9) The principle adopted from LeConte, that the bottom of a geosynclinal becomes weakened as subsidence and surface sedi- mentary accumulations go forward, through the access of heat from below or the rise of the isogeotherms (the change of level in a given isothermal plane having been seven miles in the Appa- lachian region), and that this in an important degree has made possible the catastrophe from which synclinoria have resulted. (10) That while igneous eruptions and metamorphism have each attended the formation of synclinoria, still in cases where the plication was greatest the igneous eruptions have been least in amount or absent ; and that the most extensive igneous erup- tions have taken place on continental borders after the crust had become too much stiffened to bend freely before the lateral pressure. (11) That in the upturning and plication attending moun- tain-making the heat from the transformation of the motion was sufficient (in connexion with other heat from a rise of the iso- geotherms due to previous surface-accumulations) to cause metamorphism, and also the pasty fusion which obliterates all stratification and gives origin to granite, and which may fill cavities or fissures, and so make veins that have all the aspect of true igneous ejections; and, as a more extreme effect, it may produce, as Mallet says, the degree of fusion which belongs to plastic trachyte, and give rise to trachytic and other ejections through fissures or volcanic vents. But—- | (12) That the chief source of igneous rock is the plastic layer situated beneath the true crust, or the local fire-seas derived from that layer. The discussion has enlarged beyond its limits in my previous publications; and many additional facts and conclusions have been brought forward. The various conclusions go forth to be tested by the further developments of science. [Note.—The principle that the bottom of a geosynclinal be- comes weakened as subsidence and surface-accumulation go On the “ Black Drop” in the Transit of Venus. 375 forward, through the rise of the isogeotherms, and that “this in an ° important degree has made possible the catastrophe from which synclinoria have resulted,” is attributed (p. 374) to Professor LeConte. I should have credited to Professor T. Sterry Hunt the idea of the weakening of the bottom of a geosynclinal in the man- ner stated. To this idea Professor LeConte added the view that, through such a weakening, lateral pressure from the earth’s contraction (a force not appealed to in Professor Hunt’s hypo- thesis) was enabled to produce the catastrophe referred to; and this is the important principleadopted from his memoir.—J.D.D.] XLVII. On the “ Black Drop” in the Transit of Venus. By T. K. Assort, M.A., Fellow of Trinity College, Dublin*, ol west recent discussion in the British Association respecting the “ black drop” observed in the transit of Venus, in- duces me to send you an account of a simple experiment which furnishes a very striking illustration of that phenomenon, and may be considered as affording an experimental proof that the moment of formation of the “drop” is the moment of optical contact. A common penknife and a threepenny piece (the thinner the better), or any two even edges, provided one is curved, constitute a sufficient apparatus. Bring the two edges into contact and hold them between the eye and a tolerably bright light, such as the flame of a candle, or better a lamp- globe, or even a window. At the moment of actual contact the edges appear to be, not touching, but joined by a short liga- ment, precisely as in the case of the transit. It is necessary that the eye be so adjusted that the point of contact shall be the point of most distinct vision ; otherwise the ligament will appear longer but less distinct, and crossed by one or more short dark lines. Ifa coi with a milled edge be used, or a torn edge of paper &c., an appearance like Baily’s beads is presented. It is easy to arrange the objects in such a manner that they can be fixed at any required distance from each other short of actual contact ; and it will be found that the ligament is not formed until contact (actual or optical) occurs. Indeed it is only ne- cessary to bring the fore finger and thumb together and hold them up to the light im order to observe the phenomenon ; but it is less easy in this case to determine when optical contact oc- curs. Itis, however, easier to “ fix” the eye on the fingers than on the dark edges first mentioned. In each instance it is curious to observe the apparent adhesion of the hgament. An excellent example of the phenomenon may be produced by touching the edge or back of the knife with the point of a pin, holding the * Communicated by the Author. 376 Mr. C. Tomlinson on the Motions of Camphor latter so as to form a very acute angle with the blade. The ligament” will then be observed to fall from the point per- pendicularly to the apparent edge of the knife. If the point of the pin be now slipped down behind the knife, the acute angle will appear to be partly filled up ; and on moving the pin so as gradually to increase the angle (pivoting the pin round its point which is held below the edge), it will seem as if connected with the blade by a glutinous substance. XLVIII. On the Motions of Camphor and of certain Liquids on the Surface of Water. By Cuaries Tomuinson, F.R.S* 1. QO* a former occasion I contributed to this Magazine two papers on the Motions of Camphor and of certain Liquids on the Surface of Water'. These papers contain a large number of references to phenomena which during nearly two centuries have cropped up in the Transactions and Proceedings of various scientific societies at home and abroad, and in many of the foreign and domestic journals devoted to science. Having studied these varied phenomena during a number of years and published many papers thereon, it was with sincere pleasure that I recog- nized in the same field of research a fellow-labourer who, armed with a new theoretical instrument, succeeded in gathering in the abundant crop which had been so widely scattered during so long a period. By means of the principle of the surface-tension of liquids, Professor G. Van der Mensbrugghe, of the University of Ghent, has not only succeeded in binding together a magnificent sheaf of facts, but in doing so has contributed to the bundle a number of full and ripe ears of his own growing”. I must also take this opportunity of thanking him for the very kind terms in which he refers to my labours®. * Communicated by the Author. 1 Phil. Mag. for December 1869 and January 1870. 2 T must also associate with Prefessor Van der Mensbrugghe’s name that of Professor Carlo Marangoni, of the R. Liceo Dante of Florence. In 1865 he published a pamphlet, Sul’ espansione delle goccie d’un liquido galleg- gianti sulla superficie di altro-liquido, in which he adopts the principle of surface-tension in studying the conditions under which a drop of one liquid spreads upon the surface of another. 3 “M. Tomlinson avait étudié depuis plus de dix ans le phénoméne de V’extension des huiles et les mouvements de certains corps solides sur l’eau ; aussi je n’hésite pas 4 voir en lui le physicien qui a le mieux préparé la vraie théorie de ces phénomeénes, grace aux soins scrupuleux avec lesquels il a décrit les faits, en méme temps qu’au nombre et a la variété de ses ex- périences; je me plais a ajouter que la lecture de ses travaux a le plus contribués @ me suggérer les idées développées dans mon premier mémoire.” and of certain Liquids on the Surface of Water. 377 2. The object of his second memoir‘ is (I.) to furnish an additional number of facts by observers of repute bearing on the subject in hand (for which the author is in great measure in- debted to the Royal Society’s Catalogue of Scientific Papers), (II.) to meet certain objections that have been advanced against the theory, and (III.) to supply a few more experimental proofs. 3. In noticing the more remote facts, which are for the most part stated by Professor Van der Mensbrugghe in a very brief form, I must on several occasions enlarge considerably, since my own labours, begun so long ago as 1838, have in some cases anticipated more recent results. Many of my experiments have been already given in the two papers referred to above (see note !), so that in the present communication I shall endeavour as far as possible to avoid repetition. 4, And first as to the additional facts, omitting mere guesses, such as that of San Martino®, who, in 1793, attributed the mo- tions of camphor to electrical action, we come to Sir H. Davy®, who, in 1802, noticed that fragments of acetate of potash (then called acetite) move on the surface of water somewhat after the manner of camphor. The more irregular fragments rotate most quickly, whence it is concluded that the shifting of the centre of gravity had something to do with the phenomena, while the rectilinear movements were attributed to currents descending from the salient points of each fragment and so producing on it unequal pressures. 5. Carradori, in 1805, noticed’ that when a large drop of the milky juice of a euphorbiaceous plant is placed on the surface of water in a large vessel, a portion of the drop spreads, while another portion descends in threads which accumulate at the bottom. If, then, the vessel be inclined so as to spill some of the water and so renew the surface, on returning the vessel to its first position the agitation will cause some of the milky filaments to rise to the surface, where they spread like the first portion. 6. These and a multitude of other phenomena, as noticed in my first Experimental Essay®, were attributed by Carradori to a 4 «Sur la Tension superficielle des Liquides considérée au point de vue de certains mouvements observes 4 leur surface,” second mémoire, extrait du tome xxxvii. des Mémoires Couronnés &c., publiés par Acad. Roy. des Sci. de Belgique, 1873. 5 Nuovo Giorn. Enciclopedico d’Itaha, Marzo 1793. 6 Journal of the Royal Institution, vol. 1. p. 314. 7 « Dell’ attrazione di superficie, Mem. II.,”” Mem. di Matem. et di Fisica della Soc. Ital. delle Scienze, vol. xii. parte 2%. Many of Carradori’s results and some account of his contest with Prevost are given in the first of the two papers referred to in note °. 8 Experimental Essays, published in Weale’s Series, 1863. Essay I. On the Motions of Camphor on Water. 378 Mr. C. Tomlinson on the Motions of Camphor “superficial attraction” (attrazione di superficie), which Dutro- chet afterwards developed into the “epipolic force” (force épi- polique). 7. In 1819 Barlocei? covered fragments of camphor with gold leaf, and found that they did not move on the surface of water. The idea was that by preventing the formation of vapour, Ven- turi’s theory, which attributed the motions to the escape of vapour, would be supported. It is further stated that perfect cubes of camphor do not move on the surface of water, on account of their perfect symmetry. This, however, is a mistake which several observers have fallen into; and we suspect that the cutting and shaping and handling of the camphor so as to confer upon it a geometrical form made it dirty, and that this was really the cause of its want of motion, I have frequently placed beauti- fully formed oblate spheroids of camphor on the surface of water ; and these have continued to move about during some hours: but these figures were absolutely clean ; for they were formed by dis- solving camphor in strong sulphuric acid, and depositing a drop of the solution from the end of a clean glass rod upon the sur- face of clean water in a catharized glass 34 inches in diameter. The acid dialyzes off and leaves the camphor in a compact well- shaped button. Two or three drops may be deposited on the same surface; and the resulting buttons will sport about for a long time without interfering with each other’s motions. 8. In 1824 a writer in Thomson’s ‘Annals’! attributes the motions of camphor on water to the fact that the centre of gra- vity of each fragment and the centre of support are not in the same vertical. Another anonymous writer'! rejects this idea, on the ground that, if true, every irregular floating body ought to present the same phenomena as camphor. 9. I may here remark that during the many years in which the motions of camphor puzzled even the best observers, the idea was not seldom started that the shifting of the centre of gravity had something to do with the phenomenon. In 1863 Mr. Trachsel!? quotes an experiment by M. Gingembre (without reference), in which a cylinder of camphor, ballasted at one end with lead, was placed in water reaching halfway up the little pillar. After twelve hours’ contact the camphor was cut half through at the level of the water, but not equally all round. This experiment (which really originated with Venturi!) is quoted to show “the unequal power of solution in certain direc- tions of the crystalline mass,” and “this being one of the pro- ® Giorn. Accad. di Sct. Roma, vol. 1i. p. 226. 10 Second Series, vol. vii. p. 75. 11 Thid. 12 Chemical News, August 22, 1863. 18 Annales de Chimie, tome xxi. p. 262. and of certain Liquids on the Surface of Water. 379 perties of camphor pointed out by Mr. Lightfoot, and from which he derives his well-written explanation of the cause of these mo- tions when he says, ‘the water upon which it floats, being ca- pable of diffusing this vapour more readily in certain directions of the crystalline axis, thereby removes sufficient vapour-pressure at these points for the opposite side to drive about (by recoil) the nicely suspended particle.’ ” 10. In my reply to Mr. Trachsel'*, I state that nearly two years before I had pointed out the more rapid solution of cam- phor on a broken than on a natural surface, and also that the vapour theory was three quarters of a ceutury old. It was first started by Volta in 1787, adopted by Prevost in 1799 under the term jet gazeux, and is now being revived without any experi- mental basis being provided for it. 11. As to the disturbance of the centre of gravity being the cause of motion in a floating and partly soluble mass, we have only to secure a crystal of some soluble salt to a slice of cork by means of an india-rubber ring, so as to be a little hghter than water; and if this be set floating, the waste will be constantly disturbing the centre of gravity of the mass, so as to produce a rolling over and a slow progressive motion. But no explanation of this kind suffices to explain the gyrations of camphor, benzoic acid, citric acid, &c., which are so rapid under the most favour- able conditions (namely, chemically clean glass and water, and a bright, warm, dry day) as to extinguish the form of the frag- ments and make them appear like a grey cloud on the water. 12. In 1825 the brothers Weber! examined the subject of the camphor motions, and showed that a downy feather smeared with oil at the two ends will rotate on the surface of water. But other observers had already pointed out that an indifferent sub- stan¢e, such as sulphur, glass, earth, sugar, paper, &c. (as indi- cated by Carradori in 1808 '°), smeared with a fixed oil will rotate on the surface of water. But the first observation of this fact is older still. Franklin, in his celebrated letter to Brownrigg’’, on the action of oil in stillmg the waves, dated November 7, 1773, states that while visiting Smeaton near Leeds, he was about to show what he calls “the smoothing experiment” on a pond, when Mr. Jessop, one of Smeaton’s pupils, spoke of an odd appearance on that same pond. ‘‘ He was about to clean a little cup in which he kept oil, and he threw upon the water 44 Chemical News, September 12, 1863. 15 Wellenlehre. Leipzig, 1825. 6 Giornale di Fisica &c. vol.i. Pavia, 1808. 7 Memoirs of the Life and Writings of Benjamin Franklin, edited by his grandson, W. T. Franklin (Lond. 1819), vol. ii. p. 268. Also Phil. Trans. 1774. 380 Mr. C. Tomlinson on the Motions of Camphor some flies that had been drowned in the oil. These flies pre- sently began to move, and turned round on the water very ra- pidly as if they were vigorously alive.” ‘lhe experiment was repeated before Dr. Franklin, who says, “'To show that it was not any effect of life recovered by the flies, I imitated it by little bits of oiled chips and paper cut in the form of a comma of the size of a common fly, when the stream of repelling particles issuing from the point made the comma turn round the contrary way.” The Doctor adds that “ this is not a chamber experiment ; for it cannot well be repeated in a bowl or dish of water on a table.” The reason for this is want of chemical purity in the bowl or dish. The effect may be well shown im a clean glass 5 or 6 inches in diameter, by moulding small coracles of paper on the rounded end of a glass rod, pouring into one of these coracles a few drops of a volatile oil, and placing it on the surface of water. ‘The paper-comma experiment is sometimes referred to as originating with the brothers Weber; but in truth their labours added nothing to the subject, nor does it appear that they intended to do more than glance at it. They do not settle any thing, but, on the contrary, declare that the varied pheno- mena connected with the subject still remain unexplained!®, They are even inclined to fall back upon an electrical theory in order to explain the rapidity with whieh a drop of oil spreads on the surface of water. 13. In 1828 August’ described an experiment by Wirth, in which a metal ball is suspended at a short distance from the surface of water sprinkled over with powdered sealing-wax. On closing the hands over the metal ball the fragments of sealing- wax are set in motion, an effect attributed by Wirth to the mag- netism of the human body, but by August to currents of air due to differences in temperature. He supports this view by show- ing that the effect can be produced by the action of a heated cylinder”. 14. In 1836 Challis?' endeavoured to account for the spread- ing of a drop of oil on the surface of water by considering that the angle formed by the free surface of this drop and the com- 8 They say :—‘“‘ Die ganze Erscheinung ist noch gar nicht erklart.” Pogg. Ann. S. 2. vol. xiv. p. 429. *° This class of experiment originated with B. Prevost at the beginning of the present century (Ann. de Chim. vol. xxiv. p. 31). These experiments (of which the following is the leading one) are remarkable, and excited a good deal of attention at the time. If near the edge of a disk of tinfoil floating on the surface of water we present obliquely a rod of heated metal, or the focus of solar rays by means of a burning-glass, the disk moves away from the source of heat. This experiment, now so easily explained on the principle of surface-tension, led Prevost into some very elaborate specu- lations. 21 Phil. Mag. vol. viii. p. 288. and of certain Liquids on the Surface of Water. 381 mon surface of the two liquids must be very small, and that con- sequently a thin film of oil must spread over the whole surface of the water, while a second drop would assume the lenticular form. I give Professor Challis’s own words, since a similar theory was published by Du Bois-Reymond?? in 1858. He says:— “The angle of actual contact between two fluids is determined by the hydrostatical equilibrium resulting from the molecular attractions of the two substances, the fluids being treated as in- compressible. It thence appeared that this is an exceedingly small angle in cases in which the bodies in contact are not of very different specific gravities. Hence in the instance before us, the angle of contact (that is, the angle which the surface of contact of the oil and water makes with the upper free surface of the oil) is very small. But since the drop is convex both at its upper and under surfaces, this is apparently an angle of con- siderable magnitude. In fact the theoretical angle of contact, or that which the upper surface of the oil makes with an imagi- nary surface drawn parallel to its under surface, and just beyond the sphere of the molecular action of the water, would be found by calculation to be of sensible magnitude. Consequently, that the angle of actual contact may be exceedingly small, the por- tion of the upper surface of the oil that lies within the sphere of the molecular action of the water must undergo a flexure near the visible periphery of the drop. Now in fulfilling this condi- tion it seems probable that a very thin film of the oil spreads over the whole water surface (as there is no force to counteract), and gives rise at the same time to the visible spreading of the first drop. The film itself, being of less thickness than the radius of the sphere of the molecular action of the water, will not be perceptible to the senses. Such a circumstance having happened to the drop that first comes in contact with the water will prevent any that succeed from being similarly affected.” 15. It is remarkable that Professor Challis should have thought it theoretically probable that.a thin [invisible] film of the oil spreads over the whole surface of the water and assists the visible [and slower] spreading of the first drop, because in some oils (such as oil of cinnamon) this thin film is visible. On depositing a drop of this oil on the surface of clean water in a clean glass 34 inches in diameter, an exceedingly thin but visible film is instantly drawn over the whole surface of the water, while the denser film, which does not cover half the sur- face, spreads much more slowly. In the case of freshly distilled oil of coriander (the very remarkable cohesion-figures of which are given in one of my papers”), the first thin film is accompa- 2 Pogg. Ann. vol. civ. p. 193. 3 Phil. Mag. S. 4. vol. xxxiii. plate iv., June 1867. 382 Mr. C. Tomlinson on the Motions of Camphor nied by volleys of minute globules which extend to the edge of the water in radial lines. Other similar cases of essential oils might be cited ; and even in the case of solid fats the evidence of u thin invisible film covering the surface and arresting the camphor motions, seemed to be irresistible before the promulga- tion of the surface-tension theory. A stick of common mottled soap, or of tallow or lard, lowered into a large surface of water previously dusted over lightly with lyecopodium powder, instantly clears away a large circular space (extending nearly to the edge of the glass). This effect is much more satisfactorily explained on the surface-tension theory than on the existence of a thin invisible film. But in the case of oils, whether volatile or fixed, it must be considered that a much greater tensile force is ex- erted in spreading some oils than others. When a film formed by a drop of a volatile oil nearly covers the surface of the water, there is still a sufficient residual amount of surface-tension to cause fragments of camphor to perform their evolutions; they skate through the film, cutting it up in all directions. But in the case of a film formed by so large a quantity as a drop of any fixed oil, the camphor fragments are motionless, whether on the film itself or on the adjacent water-surface. This was formerly supposed to prove the existence of a fatty film which, though invisible, destroyed contact between the water and the camphor; but now, in accordance with the new theory, the fatty-oil film so far reduces the tension as to leave no residual force sufficient to give motion to the fragments. 16. But if, as I have shown, a freshly distilled volatile oil does not prevent the motion of the camphor fragments, some deductions must be made from the statements of the earlier ob- servers, which savour of the marvellous. Thus Volta, writing in 1787, says :—“ If the water be defiled with any foreign sub- stance, or its surface only slightly fouled with oily matter, if only the dust of the room or of one’s clothes be upon it, the looked-for motions of camphor and of benzoin will not take place, or will be so feeble as to be scarcely sensible**. So also Prevost”, writing in 1797, remarks that ‘if the surface of the water be touched with a pin previously dipped in oil, the motion of the camphor fragments instantly ceases, just as if they had been struck by lightning (comme foudroyées).” Venturi” also, in 1797, says, ‘‘ Touch the surface with oil, and an almost im- perceptible film instantly advances over the whole surface, repels the fragments, and strikes them motionless as if by magic.” 4 Volta’s Latin letter to Frank is contained in the Delectus Opusculo- rum Medicorum. Ticini, 1787. An English translation of this letter is given in my ‘ Experimental Essays.’ See note °. 25 Ann. de Chum. vol. xxi. p. 254. °° Thid. p. 262. and of certain Liquids on the Surface of Water. 383 17. Now in all these cases I venture to say that the experi- - ment was not performed under the most favourable conditions. It was known that the water must be free from grease; but I know of no reference on the part of these early inquirers to show that they took special means to make the vessel containing the water chemically clean, any more than the surface of the camphor or the knife with which it was cut or scraped. Hence, the initial tension of the water not being at a maximum, contact with a very slight portion of grease or oily matter would so far further lower it as to produce the sudden effects described. But if the experiment be repeated under the most favourable condi- tions, in which the surface-tension of the water is at its maxi- mum, the water may be touched with a fixed oil, and the iri- descent film resulting therefrom, though lowering the tension, will not do so to a sufficient amount to arrest the motions of the camphor fragments. For example, a shallow glass 4 inches in diameter was filled first with strong sulphuric acid and then rinsed out with tap-water and filled with the same. Fragments of camphor were extremely active on the surface, which was now touched with the point of a clean penknife that had been dipped into refined East-India rape-oil; a film of a splendid deep-blue colour was produced, which instantly opened into a sort of lace- pattern ; but the fragments of camphor continued to rotate, not so vigorously as at first, but still with vigour. If the film of oil be first formed on the surface and the camphor fragments thrown upon it, they will also rotate. Ifinstead of using the point of a knife to deposit the oil, a glass rod be employed and a drop be deposited, this, especially if the oil be heated, will flash out into a film, completely covering the surface of water in a vessel 6 inches in diameter. Under these conditions fragments of camphor do not rotate; but there is sufficient residual tensile force to give motion to creosote. A drop of this instantly re- pels the oil-film, cuts it up in all directions, and moves over the surface with great vigour, the only sign of diminished tension being that the cohesion-figure does not open out into the usual brittle are and so break up into a number of figures, but pre- serves one parent figure, from which volleys of small globules are discharged?’. 18. In the paper just referred to*® I give a number of cases in which a volatile-oil film arrests the motions of creosote, and then evaporating, the water (according to the new theory) so far recovers its tension that the creosote suddenly starts into life and increases In vigour as evaporation proceeds. ** Figures representing this action are given in the plate accompanying the paper referred to in note *. 2° See note **. 384 Mr. C. Tomlinson on the Motions of Camphor 19. Considering the mode in which surface-tension acts, it will naturally be supposed that the motions in question are not con- fined to camphor and a few other solids, nor to creosote and a few other liquids. In fact fragments of any body that act by suddenly lowering the surface-tension at the spot on which they fall are liable to these camphor motions. Many salts act in this way, the last that I have observed being sulphate of aniline. The following solids also rotate :—Borneol, naphthol, thymol, nitro- toluol: this was inactive on water at 56° F., but very active on water at 90°, a crystalline needle sweeping over the surface at right angles to the length of the crystal. Binitrotoluol on water at 96°. Hydrochlorate of toluidin: a crystalline fragment darted to and fro in short jerks, as if surprised at the novelty of its situation, and then, accepting the conditions, moved rapidly over the surface in circular sweeps and quickly disappeared. Acetamid behaved in a similar manner. Lactid and oxamethan also rotate rapidly. Sulphaldehyd rotates rapidly in wide sweeps and soon becomes motionless. The same phenomena are exhi- bited by benzoic anhydride. Amidobenzoic acid also rotates rapidly, and quickly disappears ; while the crystalline portion of nitrobenzoic ether sails round and round near the edge, and con- tinues to do so for a long time. Among liquids, a drop of toluidin on the surface of water, in a vessel 4: inches in diameter, affords an instructive illustration of surface-tension: the drop forms a figure for an instant some- thing like that of creosote; it then bursts as with an explosion, dotting the whole surface with smaller figures, each of which also explodes ; and the smaller particles resulting therefrom ra- pidly disappear amid lively agitations. A drop of phenyl-mus- tard oil quickly spreads into a large ragged film, which is torn into numerous fragments, covermg the surface; and then each fragment gathers itself up into a well shaped lens. A second drop rests as a lens. A drop of monochloracetic ether spreads rapidly over the surface and rebounds to the centre, breaks up into numerous ovoid masses, with colour, which rapidly dis- appear with a remarkable opening out. When the whole has disappeared, the motes on the surface rush wildly to and fro. Formiate of ethyl produces a very pretty rose-engine figure witha central boss. Oxalate of ethyl forms a wide film with iridescent edges, and then, in waving figures, quickly disappears. Iodide of allyl gives a colourless film over the whole surface, then ex- hibits a magnificent display of iridescence, breaks up and in- stantly disappears. The following liquids also present interest- ing phenomena :—Nitrobenzol, nitrobenzoic ether, nitrotoluol, and cymol. It would be easy to extend the list both of solids and liquids that afford instructive illustrations of surface-tension, and of certain Liquids on the Surface of Water. 385 whether on the surface of water or on that of other liquids. A drop of oil of lavender on the surface of liquid acetic acid forms a wonderfully active figure, which I have already noticed”, together with the figures of various liquids on the surfaces ot sulphurie acid, cocoa-nut oil, castor-oil, paraffin, spermaceti, white wax, olive-oil, lard, and sulphur, heated, where necessary, so as to render them sufficiently fluid®°. _ 20. In 1837 Dr. Pietro Savi?! had his attention directed to the following statements by De Candolle* with reference to the contractile motions of plants:—“Si l’on place sur l’eau des folioles, ou’ des fragmens de folioles, du. Schinus Molle, on voit Phuile volatile, contenue dans certaines cellules du tissu, s’echap- per, non par un flux continu, mais par des saccades intermit- tentes, qu’on ne peut, ce me semble, rapporter a d’autres causes qu’a quelque contraction des cellules qui renferment ce suc.” And again at page 287 of the same volume, with reference to the sudden and singular movements of the leafy fragments :— “ces mouvemens sont dus a des jets intermittens d’huile essen- tielle, qui sortent des cellules, trappent l’eau, et determinent dans le foliole un mouvement de recul semblable a celui de Péolipyle. On voit ici assez clairement un effet vital.” Dr. Savi shows, by a microscopical examination of the leaves im question, that no provision is made for the exertion of a con- tractile force, that fragments of the dried leaves move, that the motions are common to leaves of the Terebintacee, Euphor- biacee, Urticaceea, Asclepiadacee, and some others, and that the true explanation of these phenomena (which are physical, not physiological) is to be found in Carradori’s attraction of surface, as explained in his memoirs*®, - 21. In 1838 Morren** showed that a leaf of the Schinus Molle, or American pear, placed on water had a jerking motion, while the surface became covered with a film of a sweet-smelling oil. Another plant, the Passiflora fetida, is furnished with hairs, one of which, plunged into water, discharges a small drop of oil, which, rising to the surface, expands and contracts several times, and then apparently bursts with violence, the smaller portions going through similar changes. These are well-known effects of surface-tension common to several oils and other liquids, as is also an experiment by Zantedeschi®*, in which a »° Phil. Mag. for March 1862: 30 Phil. Mag. for November 1864. 31. Mem. Valdarnesi, 1837, vol. 11. p. 117. 82 Phys. Végét. vol. i. p. 38. 33 He refers to Mem. della Soc. Ital. vols. xi., xii., and xv. *4 Corresp. Mathém. et Phys. de M. Quetelet, 1838, vol. x. p. 339. °° Given by Luvini in his Saggio di un Corso di Fisica Elementare | Pint. Mag. 8. 4. Vol. 46. No. 807. Nov. 1873. 2D 386 Mr. €. Tomlinson on the Motions of Camphor few drops of valerianic acid poured into water rise to the surface, go through a variety of contor- tions and evolutions, and ex- cite the astonishment of the observer that dead matter should thus of itself become endowed with such active mo- tion. Some years ago I per- formed this experiment, and had a drawing made of one stage of the cortortions. If the annexed figure is sup- posed to be in rapid motion, constantly changing into simi- lar figures, and detaching pear-shaped lenses which immediately become eircular, a good idea will be formed of the behaviour of this liquid on the surface of water. A drop of isobutylic alcohol forms a similar figure, only more rapid in its action. 22. In 1838 I published a new method of producing New- ton’s rings®®, Referring to the facility with which oil spreads over the surface of water, it is stated that any oil, balsam, var- nish, or essence not soluble in water will answer the purpose, or, _ if the oil or balsam &c. be too viscid, it may be made sufficiently fluid by the action of heat. A single drop of oil &e. may form a circular film from 2 to 5 inches in diameter with or without colour, depending on the thickness. Supposing the film to be without colour, the finger dipped in ether (or a piece of porous wood, or a camel’s-hair pencil, or, as was afterwards adopted, a bit of sponge tied over the end of a glass rod) and held over the film, “‘ we instantly see a repulsion or recession of particles ; a black spot is formed; and round it the seven orders of rings appear in all their lustre and beauty. The rings remain just so long as the finger js wet with ether, which having evaporated, or the wet finger being removed, the rings contract in diameter and disappear altogether. These rings can be formed at any part of the surface of the film, and any number of times while the film endures.” Among the conditions enumerated are :—‘“‘ the glass and the water must be perfectly clean and free from grease; the surface of the water must be perfectly tranquil; a clean glass rod must be dipped into the oil, and a single drop only be placed (Torino, 1868), p. 236.. Professor Luvini has copied, at pp. 238, 239, the figures of creosote and coriander referred to in notes * and ”. 36 The Student’s Manual of Natural Philosophy, London, 1838. In the chapter entitled “The Soap-bubble,” at p. 545. and of certain Liquids on the Surface of Water. 387 upon the surface of the water; the ether must not touch the film, or it will destroy it, while if the ether be taken up by a body that has not a pointed or rounded termination the rings will not be formed, and there will only result a series of concentric figures, depending for form upon that of the end of the substance held over the film. Instead of ether we may employ solution of ammoniacal gas, pyroligneous ether, alcohol, or naphtha. Strong ammonia sometimes breaks up the film and scatters it over the surface of the water.” _ A turpentine film, which is at first colourless, soon begins to display colour as the film becomes thinner by evaporation—a remark that does not apply to a film formed by a drop of the fixed oils of olive, rape, castor, nut, &c. Films that exhibit some of the most splendid colours of thin plates may be formed from a drop of balsam of Peru or a turpentine varnish, such as copal varnish, carriage-varnish, gold size, black japan, &c. If the ether be held over one of these coloured films, “ we immediately get a series of rings as before, quite independent of the large rings which occupy the surface of the water... That part of the film subjected to the action of the ether no longer forms a portion of the original film, but is subject to the systematic arrangement which the ether produces. A film showing the colours of the 5th, 6th, and 7th orders only. is, at that particular part which is subjected to the action of the ethereal vapour, made sufficiently thin to exhibit the rings of the Ist, 2nd, 3rd, and 4th orders, or of the 2nd and 3rd, or of the 3rd and 4th,—all depending on the quantity of ether taken up, the rate of evaporation, and the proximity of the ether to the film—in other words, on the comparative thinness of the film. Should the drop of oil &c. form a lens instead of a film, the ether vapour will drive it with great energy over the surface of the water.” If the water be dusted over with a dry powder, the vapours of ether &c. will powerfully repel the particles. ‘‘ Turpentine and some of the volatile oils produce a similar effect upon powders ; and one volatile oil frequently repels a film formed by another.” The above details refer to the repulsion of films. ‘A strong and decided attraction may be exhibited by presenting to the film a drop of an acid of low boiling-point, such as nitric or pyroligneous acid. By such means an oil-film of the size of a crown-piece may be reduced to the size of a sixpence ; anda film exhibiting colour will have all colour destroyed by the proximity of the acid, whose influence is to thicken the film. Sulphuret of carbon and an aqueous solution of chlorine produce a similar result” (pp. 545-549). 2D2 388 Prof. Challis on Integrating Differenisat 23. In 1841 Sir David Brewster?’ reproduced some of my results, probably without suspecting that he had been antici- pated, although a full abstract of them was given in a then popular Journal of wide circulation®®. Brewster formed a film of oil of laurel on water placed in a black vessel, or on the sur- face of diluted or real ink. He justly describes the rings pro- duced as being splendid beyond description. He says :—“ These thin plates of oil of laurel exhibit some curious phenomena which I believe have not been noticed. If we wet with water, alcohol, or the oil of laurel itself, the extremity of a short piece of wire, such as a large pin, and hold the pin in the hand so that its head may be above and almost touching the film, the film will recede in little waves of circular shape which form a new system of coloured rings; and they become covered with the vapour from the fluid on the head of the pin in such small particles that they reflect no light, and the rings appear to be blackened. By withdrawing the pin the film is restored to its former state. The same effect is produced by heating the pin or the fluid upon it to promote evaporation” (p. 51, note). 24. We now come to the time when Dutrochet published his elaborate essays on what he termed the epipolic force; and as this forms a kind of middle term between the earlier and the more recent history of this wide subject, we may here conve- niently pause for a time. Highgate, N. 7th October, 1873. XLIX. On Integrating Differential Hquations by Factors and Dif- ferentiation, with Applications in the Calculus of Variations. By Professor Cuauuts, M.A., F.R.S., F.R.AS.* is | Bes method of integrating differential equations discussed in this communication depends on the following general theorem, which, as far as I am aware, has not been previously enunciated :— 3.02 ae The differential coefficients a, ae — &c. being represented by p,q, 7, &c., let F be a function of 2, y, p, g, r, &e. of any order and degree, and suppose that we have dF d?F W(x, y, p, 9g, &e. F, a ae ke.) =0, 7 Phil. Trans. Part I. p. 43. ** The Mechanics’ Magazine, Sept. 8, 1838, vol. xxix. p- 394. * Communicated by the Author. Equations by Factors and Differentiation. 389 the highest order of p, g, &c. not exceeding the highest order of the differential coefficientsin F. Suppose also that this equation is satisfied if F=0, which equation involves, as is known, the d?} consequences =~ =(); 75 equation y%r=0 which is reducible to an order lower than the order of '=0 is to be regarded as an integral of the latter equa- tion. Such integration of a given equation F =0 is in principle an extension of the method of integrating by factors, or of that by differentiation, or of a combination of both operations. Clairaut’s form, y=px+f(p), furnishes an instance of inte- grating by differentiation only. By differentiating we have qQ +f" p))=0, which equation is satisfied if g=0O, and, by consequence, if »=c and y=cx+c'. By substituting c for p in the given equation, it will be seen that c’=/(c), so that the proper form of the integral is y=cv+f(c). On eliminating c between this and the derived equation p=c, the original equation is re- produced. For exemplifying integration by a factor let us take the equation = 0, &c. Then any integral of the OE RO Dor Weg np?) Multiplying by the factor p we obtain EN ONES SAO V1+p? (14p%)? 4 V1+p? _ whence by integration y=c /1+p?, an equation of a lower order by one unit than that of the proposed equation, and con- sequently a first integral of the latter. A second integration gives y?2 ————_——_—- a+d=clog,* + a/ e+ =clog, (p+ /1+p%), the known equation of a catenary. If the proposed equation be 1+p?— qy=0, it would be made integrable by the factor P ;, and the same result as before 1 +p?)? would be obtained. In fact, differential equations differing in form are one and the same if the factors which make them inte- grable reduce them to the same form; but no general rule exists for finding the appropriate factor in each case. The foregoing instances come under the general theorem above enunciated, because, if we put F for Le Ses Es s, the equation V1 +p? (l+p?)? 390 Prof. Challis on Integrating Differential V(z,y, p, &e., F, &c.) =O becomes in the first case pF =6' in the other —? 2 3 =0, and each of these vanishes if F=(/ (1 + p?)2 For further illustration of the general theorem, I propose ‘i hp, h C=24)+ Tae. J=nAs 7 ee eee vl or, because Pi=pD, | hp h Lt), =L— ——————— = + —————— ! V1+p? ee V1+p? Hence it follows, since Y= V1 +p? that h eels h lige =? V1+ 2, and c= ia = ———__. V1+p? * 1p Consequently, by substitution in the equation of the catenary, ip h y a tte Vignes Tapaet Nae Be (p+ V1 Fp) This is the required differential equation. By substituting e(l+p?)—yVW14 p* for h, this equation takes the form t+ el=—py+ ep V/] tp? +clog.(p4/] +p), . (ae which equation of the first order contains the same constants | as the equation of the catenary. It is evident that the re-. sulting equation of the third order would be the same whether » c’ and h be eliminated by differentiation from the former equa- ‘ tion, or c' and ¢ from (a). Adopting the latter process, by dif- | ferentiating to get rid of c! we obtain 0=] +p? —yq—2cqr/] +p, or “c= V1 cE p* 1p SS sll ine q /1 +p? Differentiating again to eliminate c, the result is 2p YpY Oo= 2 3) (8) Li oY a ee which is the differential equation of a curve drawn parallel to a given catenary at an arbitrary distance from it. Equations by Factors ana Differentiation. 391 1 vi+p (I sy “required to find the factors M and N which will make ve N = identical with the right-hand side of the equation (8). let it | _gibstituting now, as before, F for (ce | | dF 3pq°y de oat ee ey e term in i which contains r is — a3 and this (I-pp))” ast be equal to the term — 2 /1+p? in (8), no other term 2)2 pone r. Consequently N= ae and a 1 Oe ee 2 MF+N__=MF— ay’ ite —gviltp as J 1 +p? 9 ie ad i r ey YPY = — -3/ 1+p?— —*+, , by hypothesis. | P “p YPY pos, MP=— pe + EV 14? - 3 : Vite? gy P 140%)! =(p +2 “ we \FraT eH M= fice 1 = Aye | Wiig tte) imnsequently the equation (@) is equivalent to | 2p : (l+p?)?dF (p+ TO+p))F+ Se 0; . id this equation is verified if F=0, because this supposition elves the consequence = =0. Hence by the general theorem ): complete solution of F=O not only gives a catenary, but j ‘braces all curves that may be drawn parallel to the catenary. nese curves, inclusive of the catenary, are plainly all involutes iia common evolute. Tt i is to be remarked that the integral of the equation (y), or | i ef 392 Prof, Challis on Integrating Differential its equivalent equation (8), may be considered to be an integral of F=0, although the order of the latter equation is inferior by one unit to that of (8). For since the equation sO is a ne- cessary consequence of F=O, the order of the latter equation may be taken to be the same as that of MF+N = =0. Also the d. equation (y) shows that the equation (8) is not satisfied if either F=0, or =0, but by both equations. For another example let a ayy vit Aap The integration of this equation by means of the factor p gives Be ay 3 y Warne ret Oe ete 8 iS b? being the arbitrary constant. This result does not admit of an exact second integration; but it can be proved that the curve it represents is describable by the focus of an hyperbola which is made to roll on a straight line. Following the same course as in the preceding problem, I shall now proceed to find the differ- ential equation of the first order of a-curve drawn parallel to a given curve of the kind just mentioned and distant from it by an arbitrary interval. Let 2,, y, be the coordinates of any point of the given curve, and #, y the coordinates of the point of the parallel curve cut by the normal at the point x, y,, or the normal produced. Then, h being the interval between the curves, we have p,=p and h h =y,— ———~, so that y, =y7y + ————.._ Hence, by substi- y Y\ Jl +p? Y\ y Jl +p? ? y tution in the equation (6), h y y h (y+ /1+p? ; re te Differentiating to eliminate 5’, and putting for shortness’ sake P for \/ 1+ p?, the result is ONC ONS ee (y+ p)(e Ps ) = 4($ pale par To eliminate / this equation is first to be solved as a quadratic with respect to A. It will be found that Equations by Factors and Differentiation. 393. F being substituted for y— 5 - a Hence, putting for brevity 3 R for a+ 55 — = and Q for ri we shall have Hence, a to get rid of A, a =o (FQ +R)? + Che Fe + 2R Ze, da da Consequently, by squaring to remove the radical, (FE+05) +4(FE 07 )RE—4FQ5 2 =0. (6) This is the differential equation it was required to find; and since, as is readily seen, it is satisfied if both F=O and a = (0) we may infer, just as in the preceding problem, that the complete integral of the equation 2a eden ale Wet 2) Ali +p? (1+. p?)? embraces all curves parallel to a certain curve described by the focus of an hyperbola rolling on astraight line. It is plain that the curve itself must be included among those embraced by the integral. The same result may be obtained by conducting the argument in a somewhat different manner, as follows. If instead te substi- tuting F, R, and Q for the respective functions y— > 4 4 pt 37 a+ x = and aA, we had operated with the functions them- selves, in place of the equation (¢) we should have obtained he PEG No Leip Pane, abe 3 2__p2 4a? ( (Pp— Bib) g2— ") =P*p(P?-+ gy)*(Bpg?—P*). . (a) Let us now suppose that F= =o Ep ~+-4. Then from this 0O=y— Pica be equality and its first derived equation it will be found that cola) baal ay ay -) PedE QPipP Pip) 2Rp. apg? ay dx ay? Reet aye lly) BPs. By substituting these values of g and 7 in the equation (7), and 394 Prof. Challis on Integrating Differential putting S for p(1— 34), that equation after due simplifications 2 becomes PdF 2PpF 2aS /PF P i Ly a Tt ye ye tar Sale “) (PpF + 2a8) aydz = ay y? is es ee dE 2P%pF ae This is the equation in the present instance which corresponds to the equation ~~ =0 in the general theorem. Now it is readily seen that this equation is not verified either by F=O or by = =0; but if both F=0 and = =0, it is reducible to ~ g 28P oe by cee? on py a y which equation is satisfied if S=O, and also if ik Pe ENA Py) B= 3G = y 7 )=2- Da The supposition that S=0O gives p=0 and y= = which results (since p=O is satisfied if y=0) accord with those derivable from the equation (6) when 6?=0. The other value of S is identical with its assumed value; which proves that the equation (7) is satisfied by F=0 and - other form of the equation (e), this result is confirmatory of the inference already drawn from the latter. The forms of the function F assumed im the last two instances occur in the processes for solving two well-known problems in the Calculus of Variations. In Chapter IV., art. 57, of Mr. Todhunter’s ‘ Researches in the Calculus of Variations’ (an Essay which obtained the Adams Prize in 1871), one of these problems is thus enunciated :—“ Required the plane curve joining two given points which by revolving round a given axis in its plane will generate a surface of minimum area.” After referring to dis. cussions of this problem by several previous writers, and stating that the result given by the ordinary rules of the Calculus of Variations is a catenary of which the axis of x is the directrix, Mr. Todhunter proceeds to examine this solution. He first admits, as established by previous researches, that ‘ sometimes two catenaries can be drawn, sometimes only one, and sometimes none,” and then finds, by carrying the investigation further, that ‘¢when two catenaries can be drawn the upper corresponds to a =0. As the equation (7) is only an- Equations by Factors and Differentiation. 39 minimum and the lower does not, and that when only one ca- tenary can be drawn it does not correspond to a minimum.” According to these results it would seem that the problem does not always admit of a continuous solution. ‘To prove that this conclusion cannot be true, it suffices to remark that it is possible to draw through the given points any number of continuous curves which by revolution about the axis would generate sur- faces of different magnitudes—and that, as the decrement of magnitude from one surface to the next inferior cannot go on unlimitedly, a limiting minimum surface must eventually be reached, the magnitude of which the Calculus of Variations ought to be capable of determining. Consequently there must be some fault or defect in the usual process of solution. It is true, as Mr. Todhunter has pointed out, that a discontinuous solution may be deduced from the equation y=c/1-+p?; for if c=0, and p be not infinite, y=0, and, c being zero, if p be infinite y has arbitrary values. Hence the conditions of the problem might be satisfied by the two ordinates to the given points and the portion of the axis of x between them. But this discontinuous solution affects in no manner the validity of the foregoing argument for a continuous solution. The difficulty thus encountered will, I believe, be found to be completely removed by the new process of integration I have proposed, which rests on the principle that if a differential equa- tion containing F and a vanishes when F=O and “=0, an integral of that equation of an order lower than that of F is an integral of F=0. In the present instance the function F is SMI OS Vi+p® (1+p%)*’ and it has been shown that the equation (8), which belongs to any involute of the evolute of the catenary obtained by inte- d¥ SS Consequently, by the rule just stated, such involute is an integral of F=O, and may be employed for solving the proposed problem. On account of the additional arbitrary constant contained in this integral, it is always possible to make the involute pass through the two given points. The other problem is thus stated in Chapter V., art. 73, of the work already cited:—‘‘To determine a solid of revolution the surface of which is given, so that it may cut the axis of revo- lution at given points and have a maximum value.” The solu- tion I am about to propose would be applicable if the generating grating F=0, is satisfied if F=O0 and 396 Prof. Challis on Integrating Differential line of the surface terminated at two given points not on the axis; but for the sake of simplicity I shall take the problem as above enunciated. The history of the various attempts that have been made to solve this problem is very instructive relatively to the principles of the Calculus of Variations, especially as regards the distine- tion between continuous and discontinuous solutions. With respect to the principle of discontinuity, it may first be remarked that the integral of the equation designated as M=O in Mr. Todhunter’s work (the same that I have usually called A=0O) may either give one line, or two or more lines. But m such cases there will be, according to Algebraic Geometry, a factor corresponding to each line, and the answer to the question may be given by parts of lines terminating at points where two lines cross each at finite angles of inclination. This is the case in the solution I gave of the Problem of the Brachistochronous course of a Ship, which is considered by Mr. Todhunter (Chap. I., art. 12) to be the first instance of a solution exhibiting this kind of discontinuity. The problem before us presents another in- stance of the same kind, inasmuch as we know beforehand that the spherical form is that for which the volume for a given sur- face is a naximum, and that consequently one solution of the problem should be given by a straight line coincident with the axis of revolution and a semicircle terminating at both ends in that line. It is found in fact that this solution is deducible from the equation (6) when 6? is supposed to vanish, in which case y=0, which is the equation of the straight line, and __“ __. which is the differential equation of the cirele. Ware p Moreover the differential equation pM=O, which requires the factor p for effecting the integration, 1s satisfied by y=O, the equation of the straight line, which causes p to vanish, and by x? + y?=4a?, the equation of the circle, which causes M to vanish. This discontinuous solution was given by the Astronomer Royal in the Number of the Philosophical Magazine for July 1861. Again, as has been already stated, the integral of the equation (o) gives the curve which is described by the focus of an hyper- bola rolling on a straight line. But, contrary to what might have been expected, this curve by no means gives the solution of the problem. It is wholly inapplicable if the positions of the extremities of the curve, whether on or off the axis, be given; but if the abscissze only of the extreme ordinates be given and the surface generated by the revolution of these ordinates and the curve joiming their extremities be also given, the solution shows that the form of this curve is that traced by the focus of a rolling hyperbola, that the extreme ordinates are equal, and Equations by Factors and Differentiation. 397 that the connecting curve joins on to the ordinates continuously. The discovery of this discontinuous solution, which differs in kind from that discussed above, is due to Mr. Todhunter. We have not, however, as yet arrived ata solution which gives a single continuous curve joining the given points—although, from considerations exactly like those adduced in the case of the preceding problem, it is certain that such a solution exists. The difficulty, as in that case, is overcome by employing the proposed new method of integration, which in the present in- stance consists in first deducing from the equation (6) the dif- ferential equation of the first order of any curve parallel to the curve traced by the focus of the rolling hyperbola, and then showing that the equation (7) resulting from the elimination of the constants from that differential equation is verified if F=0 dF : ; a ayq and —=0, the function F being y —- ———=+——*>*—.. The of J/1 +p? a (1+p%)* parallel curve, as | have already argued, is under these cirewm- stances an integral of F=0; and since its equation contains one more arbitrary quantity than the equation of the curve itself, it is capable of satisfying the given conditions of the problem. I have ascertained, for instance, that if the given surface be of small amount for a considerable distance between the given points on the axis, the form of the curve is like the arc of a bow ; but if the amount of surface be large for a small interval between the points, the curve approaches the circular form. Under the supposed circumstances such forms might be ante- cedently expected to be given by the results of the analytical calculation. The foregoing solutions of the two problems do not essentially differ from those I proposed in an article contained in the Phi- losophical Magazine for July 1871. But the latter solutions were effected by actually finding the equations of the evolutes corresponding to the two series of involutes ; whereas the present research has shown that this process was not necessary, and that the new integration is virtually an extension of the recognized methods of integrating by factors and by differentiation. The principle of the application of this new method in these two in- stances may be briefly stated as follows. A differential equation F=0 of the second order may have an integral containing three arbitrary constants, but only on the condition that the differen- tial equation of the third order obtained by eliminating these constants from the integral is verified by the two equations F=0 and = =0, and not by either singly. The reason is, that as the equation ~~ = (0 1s a necessary consequence of =O, the 398 Dr. E. J. Mills on Statical and latter equation, in case the above condition can be fulfilled, is really of the third order. I have now reached the conclusion of my researches in the Calculus of Variations, having succeeded at length in removing from its analysis the reproach of failing to solve a class of pro- blems which unquestionably should thereby be capable of solu- tion. For instance, it is obvious that there must be a conti- nuous surface of revolution which for a given amount of surface and a given length of the axis encloses a maximum volume. But so far was this problem from being solved, that, on account of its peculiar difficulties, those who from their reputation as analysts might be expected to furnish a solution, have only endeavoured to show that it is insolvable. Probably, there- fore, it will be held to be excusable that in my first attempts to solve it I adopted views and processes of reasoning which I had afterwards to abandon as untenable. I persevered, how- ever, in my efforts to arrive at the solution, not being able to admit the possibility of the failure of analysis; and the re- sults now communicated I consider to be a justification of this course. Cambridge, October 8, 1873. L. On Statical and Dynamical Ideas in Chemistry.—Part IV. (conclusion). On the Idea of Motion. By Eomunp J. Mitts, D.Se.* ConrENTS. A criterion of scientific progress is needed. This criterion is an idea common to all the sciences—namely, the idea of pure motion. It was first announced by Herakleitos of Ephesus; we afterwards trace it through the Platonic Sokrates, the Sophists, Aristotle, the Epicureans, and the Skep- tics. It reappears in Hobbes and Hegel. Ferrier and Spencer compared with reference to this idea. All conscious knowledge is but knowledge of motion. The science of the naturalist, mathematics, and geology are illus- trations of the directive force of the idea. In chemistry—-which has not, like those sciences, assumed a “ new” phase—a theory of absolute limits prevails; but its great epochs are intelligible only by the light of this eri- terion: its imaginary pursuits; study of the chemical process neglected. The extinction of ethics. Questions. Summary. Practical tendency of the discussion. Ilorapov pon ameikafwy Ta ovTa. ]° a chemist, in the course of his researches, were to suspend . for a moment his more immediate investigation and ask himself Is this Progress? he would have a difficult question to answer. I do not think it advisable that this question should often be asked, or that every chemist should ask it. But it does arise in the most legitimate manner; and, as it has a tran- * Communicated by the Author. Dynamical Ideas in Chemistry. 399 scendant importance in the economy of intellectual effort, an answer is imperatively required. Moreover, as in every science the same demand springs up, how vast must be the interests concerned, how great the value of a right response ! The question stated presupposes that a deficiency or a require- ment does actually exist—in other words, that the science from which the question comes in some respect differs from the general scientific level. Now in Part I. of these papers*, I pomted out what is the universal criterion of progress—namely, “the most general idea existing at a given time as a factor in every branch of science.” My position may be illustrated by an experimental usage. Suppose a phenomenon has to be observed by reading off a number; this is done, not once, but many times, and the average result is calculated. The average is certainly more va- luable than either of the observations taken singly ; and, if these are regardetl as combining towards an end, it is contained to a greater or less extent mm each of them. The idea of pure motion is asserted to be the mean or general idea sought. I now pro- pose to explain more fully in what sense this assertion is made, and to discuss more at large than was possible in Parts IJ. and III. the nature of the criterion itself. The general nature of the criterion establishes its universal applicability. But I address myself more especially to chemists ; and their science is at the present time, and at this instant to the judicial reader, in the very crisis when the adoption of a real criterion is of the supremest consequence. Sad in the poverty of symbolic resources, miserably unreasoned and deficient in power, it urgently requires an entire reform of its prevailing theory. The student more especially, and the teacher (who is in each instruction a necessary artificer of prejudices), have need to pause, and find or verify that “word,” which, like the xpu- TuKos AOyos of St. Pault, is to divide and penetrate all the problems of knowledge. The history of the idea of pure motion is comparatively brief and simple. Herakleitos of Ephesus (460 B.c.), who first an- nounced it, had clearly seen its vast importance and universal applicability ; and, though termed by his successors The Dark (Zxorevvos), he was undoubtedly understood by many of them. The Sokrates of Platot seems on the whole, to accept Hera- kleitos’s doctrine§ and frequently alludes to it; where he treats Phil. Mag. 8. 4. vol. xxxvii. p. 461. Hebrews, chap. iv. verses 12, 13, In the Theetetus. § Ferrier (Lectures on Greek Philosophy, vol. i. pp. 145, 146) writes of Herakleitos, “‘ here, if anywhere, is the embryo of the solution of the enigma of the universe. 1 am convinced that the unity of contraries is the law of * 1. ! ++ 400 Dr. E. J. Mills on Statical and it humorously, the sport is rather at the expense of his auditors’ intelligence than concerning his subject. Herakleitos pointed out the illusory nature of the seeming permanence or stationary condi- tion of things: “every thing moves, and nothing remains,” he said. The flowof a river is an apt illustration of the fleeting nature of the world; in which, indeed, the only reality is the act of transition, or the “ becoming ;” not inception and results, but process. Inthe instant of “ becoming ” he conceives the contrary determinations of being and not-being united,—a notion which Professor Ferrier has beautifully illustrated by the well-known geometrical expla- nation of two opposite forces combining in a continuous curvi- linear path. The sophists, especially Protagoras, applied this doctrine, though not with the highest success, to justice and morals, chiefly in the interest of the freedom of the individual will. In the Aristotelian philosophy, the conditions of nature are summed up as motion, space (the possibility of motion), and time (the measure of motion) ; but, in Aristotle, the idea becomes less pure, is circumscribed with limits in the detail, and loses in elasticity and vigour. The same is true of the Epicureans; but it formed the latent basis of their philosophy, as likewise of the Skepticism of every age. In much more modern times, the idea of motion was most distinctly grasped by Hobbes, as may be seen by referring to his ‘Humane Nature,’ 2nd edition (1650), from which work I have taken the following statements. “That the Subject wherein all things—that all life, all nature, all thought, all reason centres in the oneness or conciliation of Bemg and not-Being. A firm grasp of this doc- trine, a clear insight into its truth, and a vigorous enforcement of it and its consequences, would lead to the construction of a truer philosophy than that which is at present so much in vogue. That philosophy is founded entirely on the denial of the unity of contrary determinations in the same subject. It takes two opposite conceptions, and holding them apart it shows that reason is baffled in its attempts adequately to conceive either of them. It is in this way that Sir W. Hamilton and Mr. Mansel achieved what they conceive to be a great triumph in proclaiming, or, as they think, in proving the impotency of human reason. But what if the conceptions thus set in opposition to each other are not conceptions at all, but are mere moments or elements of conception?”? Compare with this the followin passage from Herbert Spencer (First Principles, 2nd edit. p. 277). ‘The law we seek, therefore, must be the law of the continuous redistribution of matter and motion. Absolute rest and permanence do not exist... .. And the question to be answered is—What dynamic principle, true of the meta- morphosis as a whole and in its details, expresses these ever-changing relations? ..... a Philosophy rightly so-called can come into existence only by solving the problem.’’ And again, p. 285, “ While the general his- tory of every aggregate is definable as a change from a diffused impercep- tible state to a concentrated perceptible state and again to a diffused imper- ceptible state, every detail of the history is definable as a part of either the one change or the other. This, then, must be that universal law. .... Dynamical Ideas in Chemistry. 401 Colour and Image are inherent, is not the Odject or thing seen. That there is nothing without us (really) which we call an Image or Colour. That the said Image or Colour is but an apparition unto us of the motion, agitation or alteration which the Object worketh in the Brain, or spirits, or some internal substance of the head. That as in Vision, so also in conceptions that arise from the other Senses, the subject of their inherence is not the Object, but the Sentient.” (p. 9.) Hobbes also says that the reflex stroke from the brain to the impressing object constitutes our sense of colour, form, sound, etc. What is really outside is “motions, by which these seem- ings are caused.” (p. 18.) “ Conceptions and apparitions are nothing really, but motion in some internal substance of the head.” (p. 69.) “ All evidence is conception .... and all conception is imagi- nation, and proceedeth from Sense.” (p. 185.) Hobbes does not seem to have anywhere definitely stated the final conclusion deducible from the above propositions. But they involve a sorites; the beginning of which is the mental act, the end of which is motion: motion is therefore exclusively our being. ‘The argument may be exhibited as follows. I only know of events by sensations, which can only be represented as motion ; the organs or parts of my body whereby I know these are themselves events, both to me and other intelligences. All knowledge of events is therefore knowledge of motion. In “events” are included the emotions, will, and intellect of other persons; consequently my own. A moving body is merely di- rected or relative motion. This theory must apply at least to all conscious knowledge*. The last philosopher who can be said to have advocated the idea of pure motion was Hegel. In his dialectical method, which always advances “from notion to notion through nega- tion ”—in his doctrine of being, as always (pendulum-like) va- nishing into nothing and back again—ain these and other prin- cipal features of Hegel’s system, we observe, as its author acknowledged, the restoration of the Herakleitic principle. It would be a mistake, however, to suppose that Hegel, in endea- vouring to trace out with much minuteness the universal preva- lence of his dialectic, agrees at all poimts with his Grecian pre- decessor; but, on the whole, his fundamental idea is most con- vincingly the same. The philosophic aspect of the idea of pure motion, as portrayed in the preceding paragraphs, indicates the prevalence of that ideal influence from very early historic times until now; and * Further expositions of Hobbes’s view will be found in his work ‘The Leviathan’ (1651), pp. 3, 352, 369, 374, 375. Phil. Mag. 8. 4. Vol. 46. No. 307. Nov. 1878. 2K 402 Dr. E. J. Mills on Statical and shows, moreover, how natural it is and must be to man’s mind to acquire. Great thoughts, however, do not remain for ever without fruit, even when held unconsciously by ignorant people. Secret and imperceptible, they grow. Hence it becomes impor- tant to ascertain whether there are any decided practical evi- dences of the idea of pure motion in modern science. The science of the naturalist had always proved dark and dif- ficult whenever an attempt was made to transcend facts and verge upon principles. Its valuable functions were those of a warehouseman and clerk—to collect and register; its specula- tions hovered over the facts rather than rested upon them. The light but pungent satire of Reybaud must be admitted to have had its point. ‘‘ Celui-ci, me disait-il, appartient corps et ame aux entomozoaires; il a eu la chance de découvriy une quin- ziéme articulation dans un insecte, et des antennes que personne n’avait soupconnées avant lui.... I] passera a la posterité avec son hymenoptére, sans compter une espéce de scolopendre qui lui ade grandes obligations. Supprimez cet homme de la communauté humaine, et voila des scolopendres qui n’occupent pas, dans échelle des étres, le rang qui leur appartient. Lui seul a pu en faire huit genres, douze sous-genres, sans compter les variétés.” Wide as was the naturalist’s scope, his chief duty was the discovery, description, and arrangement of species— species believed, for the most part, to have been distinctly created, and to be each one of them an instance of a break in nature. But the subtle principle of motion, altogether opposed to :sta- tionary points, or discontinuity, can now be seen to have been ever asserting itself, asserting itself in more or less fanciful theories of archetypes, of the emanations of beings from few sources, of a fundamental identity of origm for animals and plants*. At length, with seeming but not veritable suddenness, the beautiful and harmonious hypothesis of Darwin and Wallace arose, and ere long was found to comprehend within its grasp the varied forms of the world’s life. For many years to come it will be the finest task of the naturalist to work at the verrfica- tion of that hypothesis, though we have even now the present value of such verification. Darwim’s theory is familiar to every one; the principle of it may be gathered from the following statements of its originator t :—“ A French author, m opposition to the whole tenor of this volume, assumes that, according to my view, species undergo great and abrupt changes, and then * It remaims for the philosophic chemist and physicist to bridge over the artificial barrier between “ living and non-living matter,”’ and to prove that life is the common property of all sensuous objects. + On the Oxigin of Species by means of Natural Selection (1866), pp. 146, 232, 246. | Dynamical Ideas in Chemistry. 403 he triumphantly asks how this is possible, seeing that such mo- dified forms would be crossed by the many which have remained unchanged.” “ Why should not nature take a sudden leap from structure to structure? On the theory of natural selection we can clearly understand why she should not; for natural selection acts only by taking advantage of slight successive variations; she can never take a sudden leap, but must advance by short and sure though slow steps.” “On the theory of natural selection we-can clearly understand the full meaning of that old canon in natural history, ‘natura non facit saltum. This canon, if we look only to the present imhabitants of the world, is not strictly correct; but if we in- clude all those of past times, whether known or ‘not yet known, it must by my theory be strictly true.” Here, then, we have, stated in the clearest language, explicit evidence that the great principle acquired by the naturalist, and now governing the entire extent of his observations, is continuity, a derivative form of the idea of motion. I turn tothe science of algebra. It, too, has gone through a ‘new”’ phase, and now exists under conditions which are most aneiom though these conditions have been developed in the most gradual and. orderly manner from the” time of Newton, as by him fromhis predecessors. It, too, is morphological; through it every branch of modern mathematics has again become young. The interoperation of algebraic forms corresponds ‘to those con- flicting conditions of nature by which species are produced and maintamed: But what sun was it that gave such light to the mathematician? The same that shone on that other continent of the naturalist. “Time was when all the parts of the subject were dissevered*, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected bya thousand fresh ties ; and we may confidently look forward to a time when they ate form but one body with one soul. Geometry formerly was the chief borrower from arithmetic and algebra; but it has since repaid its obligations with abundant usury ; and if I were asked to name, in one word, the pole-star round which the mathema- tical firmament revolves, the central idea which pervades as a hidden spirit the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, itis this!” * Sylvester, British Associatien’s Report (1869), Transactions of Sec- tions, p. 7. ou 4.04: Dr. BE. J. Mills on Statical and In the antagonism between continuity in mathematics and alleged absolute limits in chemistry, we see the reason why so few chemists are mathematicians, and so few mathematicians chemists. Geology has, in recent years, shaken itself free from the fet- ters of the cataclysmal school, and finds in existing forces, con- tinuously exerted, an adequate explanation of her special phe- nomena. Chemistry still looks with half-averted face upon all dynamical doctrines. But her great centres of historic conflict are intelli- gible only by their aid. Acid, Alkali, Base, and Salt are not capable of definition as particular things* ; the principle of con- tinuity alone renders them clear. Chemical Substance is homo- geneous, not discontinuous substance ; Chemical Functions are modes of motiont. The Atomic Theory, triumphant still, 1s more suspected than before; but it is indeed a better servant to pure dynamics; for it places before the mind, daily and most distinctly, the fatal consequences of the assumption that quan- tity consists of parts{. Grave and mature chemists now inves- tigate the position of a particular atom in an aromatic compound, and find it at the side, in the middle, or near some other portion of an open or closed chain. In the mean time we hear nothing of the chemical process. Such are our dreams; we think them so regular, orderly, and reasonable. And so they are, until the morning ; then we shall be the first to laugh at ourselves. For my own part, the perusal of modern chemical literature fills me with an abiding sense of sorrow and shame. In the practical side of philosophy the idea of motion, in va- rious derived forms, is alsofound ascendant. It is for the most part to philosophers that the intellectual bias of modern nations is due; and the characteristics of contemporary society, having been so derived, are in the main dynamical. The sentiments, the affections, the passions of mankind have been flooded with liberty and power. It has been found advisable, and even ne- cessary, to remove many of the older educational restraints, and to qualify at least the social distinctions we preserve. The science of ethics has expired, with all necessity for formal sanc- tions. The notions of right and wrong can now be derived his- torically, and are no longer mysterious. While Idealism has, on the one hand, restored to its supreme and lawitul rank the individual Self, it should be the business of the schools to make men know that; in the mean time, the wide demand for liberty of the will is not only audible but imperative. But it is evident that, as soon as the ethical sanction is defined as liberty or free- * Phil. Mag. S. 4. vol. xxxvii. p. 461. T Ibid. 8. 4. vol. xl. p. 259. { Ibid. 8. 4. vol. xlu. p. 112. Dynamical Ideas in Chemistry. 405 dom, no sanction any longer exists ; act and motive are identical. This strange phenomenon of the destruction of a science has been witnessed by the present generation ; it is as rare in human history as the extinction of a star. With regard to other departments of practical philosophy, I need merely state the names of politics, religion, and sociology, and leave it to the candid reader to consider whether their nearer history has been more characterized by freedom or definition. To his judgment I also relinquish the questions whether liberty, toleration, the scientific spirit, and the growth of all our noblest interests, are not more likely to be fostered by cultivating the sreat standard I have discussed than by the dogma of an absolute limit. Where can we find “contentment, but in proceeding ”*? or peace, but in action? or hope, but in the drift of nature ? Thus, then, having reflected upon the principles of our daily actions and the more recondite sources of our scientific life, we see rising from them all, like a spirit out of darkness, the perfect majesty of motion. Thisis the centre, this is the vast and ever- receding circumference of fulfilled desire. All beauty, all life, all thoughtful power, are contained in it and are it. Like a river it has glided on, silent, devious, unperturbed. From a Grecian source toward the untravelled sea the stately ships of science take freight and spread their sails upon its bosom; the gilded craft of music, of poetry, and of rhetoric disport there ; and the tiny barks of incipient civilization have but that single channel. It has drained, refreshed, and fertilized every conti- nent of thought and feelmg. At a distance from its margin are chiefly found the hideous desert and the dry rocks of old dog- matic conflict ; but nearer to the shore come soft oases; and its banks are fertile vales, content, and sweet and tranquil. All remote inspirations, all scattered fragments of knowledge, are ~ but dew or clouds exhaled at first from its surface, or wafted from its waves. Ah, Shade of Herakleitos! leave his urn, and weep no more; for the teachings of that mighty mind are not only understood, but have been verified, and we can now coordinate them from new forms. Henceforth it remains but to apply his great idea, now seen to be the widest generalization from experience—to turn round, and, journeying backward into detail, take that as both map and compass on the road. Henceforth, for us who have chosen the criterion, all that is good and desirable is mo- tion, all that is evil and to be dreaded is a limit. Let no one strive to reconcile them. * Hobbes. 12 Pemberton Terrace, St. John’s Park, N. [ 406 ] LI. Notices respecting New. Books. An Elementary: Treatise on the Differential Calculus, contavnng the Theory of Plane Curves, with numerous Hxamples. By BEntaMIn Wittiamson, 4.0, Fellow and Tutor, Trinity College, Dublin. Second Edition, Revised and Enlarged, London: Longmans, Green, and Co. 1873. (Pp. 367.) “E noticed the first edition. of this book, shortly after its pub- , lication, about a year and a half ago (April 1872). There is therefore no need to say much on the present occasion. The revi- sion to which the work has been subjected consists partly m a change of arrangement of some of the articles (¢..g..the chapter on La- erange’s Theorem, which was Chap. 20in the first edition,is Chap. 7in the second), partly in the addition of articles here and there through- out the volume (e. g. the articles on Linear Transformation, Nos. 292-294 added to the chapter on Change of the Independent Va- riable), partly in the insertion of additional Examples. The total number of changes is considerable, and the result of the whole is to increase the volume by 24 pages ; still the changes do not make what can be regarded as a substantial alteration in the work. It only remains, therefore, to congratulate the author on the rapid sale of the first edition, and to express a, hope that his very useful book will continue to find many readers. LII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 326. ] May 1, 1873.—William Spottiswoode, M.A., Treasurer and Vice-President, in the Chair.. rue following communication was read :— ‘On the Effect of Pressure on the Character of the Spectra: of Gases.” By C. H. Stearn and G. H. Lee. The variations in the spectra of gases which accompany changes of density have been studied by Pliicker and Hittorf, Frankland and Lockyer, Willner and others. Jt appears. to us that one cause to which these changes may be due has been overlooked, and that many of the observed variations are entirely independent of the density of the gas. Ifa Leyden jar be placed in the circuit, and the current from an induction-coil be passed through a Pliicker’s tube containing nitrogen with the traces of hydrogen generally present, the followmg well-known pheno- mena are observed. When the gas is near atmospheric pressure, the lme-spectrum of nitrogen is briliant, and the I* lme of hydrogen is broad and nebulous. As the pressure is reduced, the lines of nitrogen gra- dually fade out, and the band-spectrum appears, while at the same Royal Society. 407 time the F line of hydrogen becomes narrow and well defined. If fresh gas be admitted, the lme-spectrum reappears, accompanied by a widening of the I line. _ That these changes are not dependent on the density of the gas, appears from the followimg experiment :— A sealed tube containing nitrogen, with traces of hydrogen at a pressure of about 2 millims., was placed before the spectroscope. A second tube was connected with the air-pump, and the current passed through both tubes, a Leyden jar being placed in the cireuit. ‘When the pressure in the second tube was high, the line-spec- trum of nitrogen appeared brilliantly in the sealed tube, and the F line was broad and nebulous; as the exhaustion proceeded these lines faded out, and the F line became narrow, in precisely the same manner as if the sealed tube had been in process of exhaustion. The explanation appears to be that the production of the line- spectrum of nitrogen, and the expansion of the F lme of hydrogen, depend entirely on the intensity of the charge communicated to the Leyden jar. When the pressure of the gas between the elec- trodes is high, the discharge does not take place until the jar is fully charged; butas the exhaustion proceeds a less and less charge is communicated to the jar, and the discharge at last is virtually not more than that of the simple current. The same effect may be produced by interposing a break in the circuit, the length of which may be increased as the pressure in the tube is reduced. Pliicker and Hittorf appear to have used a break, as in their paper in the Philosophical Transactions, Nov. 1864, they speak of the expansion of lines obtained by increasing the charge of the jar by an interposed stratum of air. They do not, however, appear to have noticed that the reduction of pressure im the tube was only equivalent to a diminution of the charge of the jar,.and that to this cause many of the changes of spectra which accompany the reduced pressure ought to be ascribed. We are continuing our experiments on the effect of temperature: on the spectrum, but prefer to reserve this portion of the subject for the present. May 8.—Francis Sibson, M.D., Vice-President, in the Chair. The following communication was read :— “Researches in Spectrum-Analysis in connexion with the Spec- trum of the Sun.”—No. I. By J. Norman Lockyer, F.R.S. The observations in this paper are a continuation of those referred to im the previous communication bearing the same title. They deal (1) with the spectra of chemical compounds, and (2) with the spectra of mechanical mixtures. L. Chemical Compounds, _ Several series of salts were observed ; these series may be divided into two :—-Ist, those in which the atomic weights varied in each 4.08 Royal Seciety :— series ; 2nd, those in which the associated elements varied in each series. The following salts were mapped :— Pb KE, -Pb:CL, Pb Br,, Pb Ls; : Sr F,, Sr Cl, Sr Bree Ba F, Ba. Cl, Ba Br, Bal; Mg E,, Me Cl ive ie: Me L; Na i NaCl, Na Br, Na I. The conditions of the experiments are described. The same alu- minium cups, described in the first paper, were used ; and the poles were arranged in such a manner that they could at will be sur- rounded with any gas or vapour. Hydrogen was used in some of these experiments ; it was purified in the usual manner by drying and freemg from traces of sulphuretted hydrogen; it was then passed over clean-cut pieces of sodium, and admitted to the poles. An induction-spark from 5 one-pint Grove cells was used, the circuit being without the Leyden jar. The lead compounds behaved (in air) as follows :— The fluoride gave the eleven longest lines of the metal ; but four were very faint. The chloride gave nine lines; one of these was very short. The bromide gave six lines; but one was a mere dot on the pole. The iodide gave four lines distinctly and two as dots, one of which was scarcely visible. It is pointed out that the decrease in length and number of lines follows the increase in the atomic weight of the non-metallic element, the lines dying out in the order of their length. Barium was next experimented on, the same series of salts bemg used. A marked departure from the results obtained in the case of the lead compounds was observed, especially in the case of the fluoride, its spectrum being much the simplest ; in fact it consisted of only 4 limes. Strontium behaved like barium; and so did mag- nesium fluoride. This anomalous behaviour was found to be most probably due to the exceedingly refractory nature of these fluorides, all of them being quite infusible, and non-volatile in any spark that was used. Sodic fluoride, sodic chloride, sodic bromide, and sodic iodide exhibited a behaviour exactly the reverse of that of lead; 7. e. the iodide showed most of the metallic spectrum. The difference between flame-spectra and those produced by a weak electric discharge are then discussed. Beads of the chlorides &c. were heated in a Bunsen gas-flame. Bal, gave a “ structure” spectrum (since proved to be due to the oxide) and the line at wave-length 5534°5, by very far the longest metallic line of ba- rium. The bromide behaved like the iodide; and so did the chlo- ride, except that its spectrum was more brilliant. Baric fluoride gave scarcely a trace of a spectrum, the oxide structure being scarcely visible, and 5534°5 very fait mdeed. The strontium salts follow those of barium—4607°5, the longest strontium line, appearing in conjunction with an oxide spectrum. The strontic fluoride, however, refused to give any spectrum whatever. These Mr. J. N. Lockyer on Spectrum-Analysis. 409 results are compared with those obtained with the weak spark ; and it is shown that the difference is one of degree: ¢. g. baric bromide gives 25 lines in the spark; these are the longest lines. In the flame it gives but one line; but this is the longest of all the barium lines, and indeed very far exceeds all the others in length. When the flame-spectra are compared with those pro- duced by the low-tension spark, the spectra of the metals in the combination are in the former case invariably more simple than in the latter, so that only the very longest line or lines are left. Some experiments made by Mr. Rh. J. Friswell to determine the cause of the similarity of the spectra of the various salts of the same metal observed in air are then given, the conclusion being that the spectrum observed is really that of the oxide. Kirchhoff and Bunsen’s, Mitscherlich’s, and Clifton and Roscoe’s prior conclusions on the points investigated are stated at length ; and it is shown that the observations recorded, taken in conjunc- tion with the determination of the long and short lines of metallic vapours, are in favour of the views advanced by Mitscherlich, Clif- ton, and Roscoe. Jor while the spectra of the iodides, bromides, &c. of any element in air are the same, as stated by Kirchhoff and Bunsen, the fact that this is not the spectrum of the metal is established by the other fact, that only the very longest lines of the metal are present, increased dissociation bringing in the other metallic lines wn the order of their length. The spectra have been mapped with the salts in hydrogen: here the spectra are different, as stated by Mitscherlich ; and the metallic lines are represented according to the volatility of the com- pound, only the very longest lines being visible in the case of the least- volatile one. The following are the conclusions arrived at :— 1. A compound body has as definite a spectrum as a simple one; - but while the spectrum of the latter consists of lmes, the number and thickness of some of which increase with molecular approach, the spectrum of a compound consists in the main of channelled spaces and bands, which increase in hke manner. In short, the molecules of a simple body and of a compound one are affected in the same manner by their approach or recess, so far as their spectra are concerned ; in other words, both spectra have their long and short lines or bands. In each case the greatest simplicity of the spectrum depends upon the greatest separation of molecules, and the greatest complexity (a continuous spectrum) upon their nearest approach 2. The heat required to act upon a compound, so as to render its spectrum visible, dissociates the compound according to its volatility: the number of true metallic lmes which thus appear is . a measure of the dissociation; and doubtless as the metal lines increase in number the compound bands thin out. Mitscherlich’s observations, that the metalloids show the same structural spectra as the compound bodies, is then referred to, and 410 Intelligence and Miscellaneous Articles. the question is asked whether the molecules of a metalloid do not in structure lie between those of elements on the one hand and of compounds. on the other. These considerations are applied to-solar and stellar spectra. The general appearance of the solar spectrum shows that in all probability there are no compounds in the sun. Secchi’s maps of a large number of stellar spectra are referred to as now indicating beyond all doubt the existence of compound. vapours in the atmosphere of some stars; and it is suggested that the phenomena of variable stars may be due to a delicate state of equilibrium in the temperature of a star, which now produces the great absorption of the compound and now that of the ele- mental molecules. Il. Mechanical Mixtures. The second part of the paper deals with the mechanical mix- tures. Maps of the spectra of alloys of the following percentages are given: :— Sn and Cd_ percentages of Cd 10-0, 5:0, 1-0, 0°15. Pb and Zn s x Zn, 10:0,, 5:0, 0, Orde Pb and Mg i s Me 10-0, 1:0, 0-1, 0-01. It is poimted out that the lies disappear from the spectrum as the percentage becomes less, the shortest lines disappearing first —and that although we have here the foreshadowing of a quan- titative spectrum-analysis, the method is so rough as to be imap- plicable. - It is then stated that further researches on a method which pro- mises much greater accuracy are In progress. The bearing of these results on our knowledge of the reversing ‘layer of the sun’s atmosphere is then discussed. LUI. Intelligence and Miscellaneous Articles. ON THE CONDENSATION OF GASES AND LIQUIDS BY WOOD-CHAR- COAL. THERMIC PHENOMENA PRODUCED ON THE CONTACT OF LIQUIDS. AND CHARCOAL. LIQUEFACTION OF THE CON- DENSED GASES. BY M. MELSENS. BSORPTION of chlorine by wood-charcoal may go on until it represents a weight of chlorine equal to that of the charcoal ; consequently the condensing force of the latter may serve to realize the liquefaction of the non-permanent gases. Charcoal put into a tube similar to Faraday’s A-shaped tube is saturated with chlorme. The two extremities of this siphon tube being then sealed at the lamp, if the long branch of the tube be heated in a water-bath of boiling water, and the short branch be dipped into a freezing-mixture, a considerable quantity of chlorine leaves the charcoal and resumes the gaseous state; and under the Intelligence and Miscellaneous Articles. 411 influence of the pressure developed, this gas liquefies in: the cooled short branch.. I have in this way obtained several cubic centimetres of pure liquid chlorine. On taking the tube out of the bath, the liquid chlorine commences spontaneous ebullition, and again condenses on the charcoal, while the short branch becomes covered with a frost. This succession of phenomena can be reproduced, so.to say, inde- finitely ; and the experiments, easy to perform at. public lectures, permit the audience to observe the various phases. Although I can only consider my experiments a trial, I have ex- tended them to the liquefaction of several gases absorbed by the charcoal when cold and disengaged by a temperature not rising above 100° C.:—chlorine, ammonia, sulphurous, hydrosulphurie, and hydrobromic acids, chloride of ethyle, and cyanogen. The liquefaction of each of these gases: can be demonstrated in lectures when explaining the history of those bodies. Reflecting on the feeble thermic effects ascertained by Pouillet when pulverulent mineral matters are soaked with water, oil, alco- hol, or acetic ether, and on the somewhat greater effects exhibited when the same liquids are absorbed by organized substances, I asked myself if we could not succeed in ascertaining pronounced thermic effects by placing in contact with cellules of charcoal liquids which do not act upon it—-water, alcohol, ordinary ether, sulphide of carbon, and bromine. The experiments exceeded: my expectation. For example, with 1 part of charcoal and from 7 to 9 parts of liquid bromine, the rise of temperature exceeds 30° C., operating on only from 5 to 10 grammes of charcoal. With charcoal well freed: from gas, heated and. cooled in. vacuo, the heating due to the imbibition of bromine would doubtless be much more considerable. The volatile liquids condensed in the pores of the charcoal (bro- mine, cyanhydric acid, sulphide of carbon, ordinary ether, and alcohol) are: not expelled, or only partially, by a temperature of 100° C. at the ordinary pressure. J made the experiment with a Faraday tube, operating as described for the liquefaction of the gases. A: tube filled with charcoal saturated with alcohol does not permit any to distilat 100°. [The tubes were exhibited to the Academy; and with them the principal experiments (the liquefaction of chlorine, cyanogen, &.) have been repeated in the laboratory of the Ecole Centrale. The condensation of liquid bromine by charcoal, effected upon a few grammes, gave rise to a brisk rise of temperature, the mix- ture passing in a few minutes from 20° to 45°. |— Comptes Rendus de V Académie des Sciences, October 6, 1873. NOTE ON THE POSSIBLE EXISTENCE OF A LUNAR ATMOSPHERE. BY E. NEISON, ESQ. _ Owing to the many difficulties with regard to the. constitution of 412 Intelligence and Miscellaneous Articles. the lunar surface involved in an assumption as to the absolute non-existence of a lunar atmosphere, it would appear of far greater probability that some such atmosphere, however limited, exists. Not only, as Dr. De La Rue has remarked, is it difficult to conceive any chemical formation of matter without an atmosphere, but it is also difficult to even find matter exhibiting the features and proper- ties of that constituting the lunar surface, which under the known conditions would not either yield an atmosphere, or require for formation the presence of substances that would. The absolute absence of any atmosphere has never yet been de- monstrated, but only the fact that it does not exceed certain limits, generally supposed much more restricted than is actually the case. In consequence it is usually granted that some atmosphere might exist ; it is also assumed that it must be of most extreme tenuity ; and the subject is dismissed as a matter of indifference, without inquiring whither the admission might carry us, so far as relates to this atmosphere’s power of fulfillmg the same purposes as our own terrestrial one. But it would be of interest to ascertain how far this possible lunar atmosphere might not effect for the lunar surface those changes &c. that our own does for the terrestrial surface, and whether in fact it might not amply suffice for maintenance of at least some form of vegetable life. For the present, however, this must be deferred. The only point restricting the extent of a lunar atmosphere of the nature supposed appears to be its refractive power, more especially as shown by the occultation of stars by the moon. Irre- spective of the circumstance that these do not invariably answer conclusively in the negative, it does not appear to be generally recognized that we may have an atmosphere whose maximum power of refraction would not be equal to one second of arc, and yet be of very considerable amount. For, of however great tenuity in com- parison with our dense terrestrial atmosphere, it would be in reality present in large quantity—to be estimated in fact, with regard to each square mile of surface, by very many thousands of tons. There can be but little doubt but such an atmosphere would exert a very considerable influence on the lunar surface, render possible the existence of many substances that appear to constitute a great portion of that surface, and explain many selenographical observations of great interest that at present appear to point to some such solution, and thus support the hypothesis of the exist- ence of a definite lunar atmosphere.—Monthly Notices of the Royal Astronomical Society, June 1873. A CONTRIBUTION TO THE HISTORY OF THE HORIZONTAL PEN- DULUM. BY PROF. SAFARIK. As it is for the most part only some time after date that I get a sight of scientific journals that do not treat of my special depart- ment (chemistry), I first became acquainted recently, through the Intelligence and Miscellaneous Articles. 413 Philosophical Magazine, with M. Zéllner’s great memoir “On the Origin of the Earth’s Magnetism, and the Magnetic Relations of the Heavenly Bodies.” In § 24 of this (like every thing that comes from M. Zollner) ingenious and thoughtful treatise, there is a de- tailed account of a new instrument, which in November 1869 had been brought by M. Zéllner to the notice of the Saxon Royal Society of Sciences, in a memoir “‘ Ona new Method for measuring Attract- ing and Repelling Forces”—which had remained unknown to me. He proposes to name the new instrument “horizontal pendulum,” mentioning also that, in 1863, M. Perrot had proposed for the same purposes, and described in the Comptes Rendus of the Paris Aca- demy, an instrument resting on the same principles. Jt is of high interest, and will certainly interest M. Zéllner to learn, that, more than a generation since, in Germany his instru- ment was not only described and figured, but also applied to expe- riments, although no particulars of the results are given. Singularly, the matter goes back to a man whose name has no good sound in connexion with the exact sciences, and from whom it certainly would be least expected—Gruithuisen of Munich. I feel so much the more obligation to render him this late justice, as seven years since, in a longer memoir published in the Bohmische Museum- zeitschrift, vol. xxxix., “‘On the present State of Lunar Investiga- tions,” I took the fanciful philosopher of Munich somewhat sharply to task—in fact, designated him as selenoprotophantast. I feel now myself, in somewhat riper years, that this asperity towards one far advanced in age, and so much my senior, who, with all his ex- travagancies, always proceeded in good faith, was perhaps not in place; and I hereby gladly retract, not the substance of my words, but the too great acrimony of their form. The very first Part of Gruithuisen’s Analekten fiir Erd- und Him- melskunde (Munich, 1828, 80 pages 8vo) opens witha truly original andremarkable paper of 45 pages, by the editor, ‘‘ On the Proposal to dig a hole through the earth; whether the condition of the air at great depths can be ascertained in any other way, by the excava- tion of a tunnel transversely through a mountain-range or an arm of the sea, by the catachthonic observatory, its mathematical and optical instruments, and also by the elkysmometer.” (The words in italics are so in the original.) At a time when (of course mostly through the fault of Gruit- huisen himself and those like him) all so-called physical investiga- tion of the heavens had fallen into such discredit that, in conse- quence of a natural reaction, professional astronomers rigorously insisted on acknowledging as the substance of Astronomy merely places and times, therefore merely motions and their variations— that (to mention only one instance) even the discovery of the dark ring of Saturn by Galle at Berlin (in the presence of Midler!) and Vico at Rome, in 1838, could be suppressed or at least remain un- noticed (incredible but true)—at such a time Gruithuisen’s memoir could not but seem preposterous; at the present time, when celes- tial physics are developing so promisingly, much therein contained 414, Intelligence and Miscellaneous Articles. will be read only with surprise. I can here intimate only that Gruit- huisen proposes, partly, to sink perpendicular shafts of several thousand feet depth, and partly to drive horizontal galleries in the direction of a chord (under the Alps! toa length of 15 miles) through the ground, and, together with practical locomotive purposes, to apply them to physical-astronomical vestigations. JL. ¢.p. 21, we read, “ But it is moreover incalculable what the astronomer in such a tunnel, provided with a shaft as dry as possible, for observations deserving attention, could accomplish. Common people would set up a terrible roar of laughter, if told that, under the mountains, at such depths an excellent observatory could be built, m which to make observations of a peculiar sort, which would furnish us with data in the highest degree desirable and to be expected, and a quan- tity of useful data at present unknown, which must supply to both practical and theoretical astronomy new aids for still greater geo- metrical accuracy and a great number of new results. To this sub- terranean observatory I will give the name of catachthome observa- tory or catachthonum.” Now I believe that at the time when the above was printed others besides merely common people would have set up a terrible roar of laughter, if they had seen Gruithuisen’s dissertation. The chief instruments of the catachthonium were, according to Gruithuisen, of two kinds :—first, large, accurately turned rings at the mouths of the shafts, m order on them as on ring micrometers, from a distance of from 100 to 2000 feet, to observe the transits of the stars by day also (in consequence of the presumed visibility of the stars from deep pits), and (p. 22) “to obtain immediately clear geocentric observations perfectly free from refraction.” On this it says, at p. 28, ‘‘ What even these few instruments could accomplish and settle in relation to the proper motions of many fiaed stars, the sol- stice, precession, nutation, aberration, the course of the moon, and the like, way be expected to be so much the more, as the position of the most simple insiruments must be the most invariable possible, because here the variations of the temperature are almost =0; so that the necessary clocks do not require even a compensation-pendulum ; and, besides, there is absolutely nothing present which could be sub- ject to so much as a slight variation of temperature; wherefore ihe place of such an observatory cannot be supplied by any observa- tory above ground, however efficient.” Here we have Lamont and Carrington’s subterranean observatories anticipated a generation previously. The second principal instrument of the catachthonium was to consist of fine plummets suspended on wires from 150 to 1500 feet in length, in order thereon (according to p. 32) to make “observable the motion of the earth in rts orbit,” “and perhaps even the difference in the annual velocity of this motion.” Namely, at pp. 30 and 31 it is shown that, durmg each rotation of the earth, the rotational ve- locity of a point in the equator is once added to the orbital velocity, and once subtracted from it, and thereby are preduced variations in the horizontal component of the earth’s gravitation, which depend Intelligence and Miscellaneous Articles. 415 on the double difference of the two velocities. With a plumbline of only 10 feet length, Gruithuisen made some observations which (1. ¢. p..33) had been related in his work entitled “ Lieblingsobjecte auf dem Felde der Naturforschung” (Munich, 1817), pp. 69 é seq., 26, 77, 128. I have not been able to procure a sight of this work. In the Analekten, l. c. pp. 33, 34, it says of these observations :— “In my very fizst experiments it proved that this instrument (which I named elkysmometer) exhibits effects which depend not on accidental causes, but on the actions of the gravity and motion of the earth and the wmereasing nearness of other large heavenly bodies, which latter would announce themselves through the plummets so posi- tively and distinctly, even if we had no ebb and flood. The eastern deviation of the elkysmometer-thread was most striking from 8 to 9 o'clock in the morning..... It was also unmistakable that the moon exerted an attraction on the elkysmometer, especially in the morning, when she was just between the sunand the earth.” Also the elkysmometer indicated to him “earthquakes, even from other parts of the world” (/. c. p.. 34); and on p. 37 the superiority of long piumblines to short ones is demonstrated in detail; deed a table is given at the end for the reduction of very small sines to arcs for the sake of observations on very long elkysmometers. With the rough arrangements described, there is no doubt that Gruithuisen’s results depended on ‘accidental external disturbances, and perhaps in part on illusion, as a short calculation is sufficient to show that, here, plummets would scarcely ever lead to any result. Only the name proposed by him (éAxvepa = traction, é\kw= I draw), though it is not correctly formed and should have been “ helko- meter,” deserves to be adopted. But the most remarkable thing comes last. In his Neuen Ana- lekten fiir Erd- und Himmelskunde, Band i. Heft 1, published at Munich in 1832 (finished, according to p.72, “am 27 Juli 1832”), pp- 39 & 40, there is a memoir entitled, “ Ritter Bessel’s Experi- ments on the Force with which the Earth attracts bodies of various natures, and of the Hditor’s Elkysmometer and Hengeller’s Swing Balance.” After a report, occupying only 19 lines, on Bessel’s pendulum- experiments with gold, silver, lead, iron, zinc, brass, marble, clay, quartz, water, meteoric iron, and meteoric stone, all of which gave, to less than ~;479, the same length for the simple seconds-pendu- lum, it says verbatim * :— “‘ By these experiments one of my most anxious wishes is ful- filled. Already twenty years since (in 1812), I suspended on wires of several fathoms length bodies of various natures, in order to try whether the opposite. positions of the moon towards them would effect any deviation from the vertical line. But as the place was not faultless for such experiments, I held that the results of the experiments were not worth publishing. A pendulum of such a length I called an elkysmometer when a scale to be read with a * The figure is a faithful fac-simile of the original. 416 Intelligence and Miscellaneous Articles. telescope was attached to the wire beneath. I thought to have per- ceived thereon the daily alternation of forward and backward mo- tion of the earth’s surface in relation to the earth’s motion in its orbit, and so also with all certainty very distant earthquakes, &c. I wish that some one may find an opportunity to make these obser- vations in a pit, with due accuracy. Reichenbach has proposed for it a very large level [compare A. Wagner’s observations of earth- quakes in South Europe on the level of the large transit-instrument at Pulkowa]; and I believe that the swing balance made by one of my pupils (of the name of Engeller), adapted on a large scale might, as a preliminary arrangement do excellent service :— ‘“‘ Tt consists of a horizontal lever a6 of brass, on which is fixed at one end a brass ball ¢ as a weight; d is a fine wire, by which the lever is suspended ; instead of the counterpoise, the other arm of the lever is fastened to the floor by the wiree; and the instrument becomes the more delicate the nearer the wire d comes to the wire e. The ball ¢ can oscillate only horizontally, and is visibly (according to Hengeller’s experiments) attracted by a cannon-ball. It would be very meritorious to institute observations on this instrument.—G.” This is therefore Zollner’s horizontal pendulum complete, scale- reading by telescope and all, though perhaps not with reading-off by mirror; and after the above statements there is certainly no doubt that M. Zollner’s bold idea, of demonstrating the variations of the gravity of the earth and of cosmic attractions by terrestrial observations at one and the same place, had already in 1817, there- fore full 52 years previously, been expressed and proved experi- mentally by Gruithuisen in Munich—and further that the horizontal pendulum, proposed for this purpose by Zollner, had been con- structed and put to the test of experiment, at the latest, in 1832, thus at least 37 years before Zollner, by a Munich student, a pupil of Gruithuisen, of the name of Hengeller, although unfortunately nothing further about the observations is communicated than that they proved the usefulness of the instrument for the end proposed. Thus, then, this important thought, like so many similar, did not come to light at once and complete, but emerged in a less perfect form a long time previously in isolated original minds, and, because the time was not ripe for it, passed away unnoticed. Hengeller must have been a genius; and since he studied between 1828 and 1832 at Munich, where Gruithuisen was Professor, it might per- haps still be possible to learn something more about his personality. —Siizung der math.-naturw. Classe der k. béhmischen Gesellsch. d. Wissenschaften, November 15, 1872. d b THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. ———__~<»—__—— [FOURTH SERIES.] DECEMBER 1873. LIV. On Diffraction-Spectrum Photography. By Henry Dra- PER, M.D., Professor of Analytical Chemistry and Physio- logy in the University of New York*. [Ilustrated by a Photograph (PLats IV.) printed by the Alberttype process. | HERE are, as is well known, two methods by which spectra may be obtained :—lIst, by the action of a prism ; 2nd, by a system of closely ruled lines. In the latter case it is convenient to speak of the contrivance employed as a grating, and of the spectrum as an interference- or diffraction-spectrum. A casual inspection shows that there is a great difference between the spectra produced by these two methods ; and close investigation proves that the diffraction-spectrum is by far the more suitable for accurate scientific work. For this reason it has seemed de- sirable to make a trustworthy map of those parts of the diffrac- tion-spectrum which can be photographed on collodion, and to attach to it a scale for reading the wave-lengths of the rays. The Plate (Pl. IV.) accompanying this memoir is from collodion photographs made by myself, transferred to a thick plate of glass, the latter process being known asthe Alberttype. For the entire success of this transfer | am indebted to my friend Mr. E. Bier- stadt, the owner of the patent in America. The glass is then used in a printing-press in the same manner as a lithographic stone. The picture is absolutely unretouched. It represents, therefore, the work of the sun itself, and is not a drawing either made or corrected by hand. It consists of two portions—first, the upper, which gives all * Communicated by the Author, to whom we are also much indebted for the impressions of the beautiful photograph. Phil. Mag. 8. 4. Vol. 46. No. 308. Dec. 1873. 2F 418 Dr. H. Draper on Diffraction-Spectrum Photography. the lines of the spectrum from near G to O, or from wave-length 4350 ten-millionths of a millimetre to 3440. Above that is placed a scale which is a copy of Angstrém’s, from just below G to H,, with the same-sized divisions carried out from H, to O. The second, or lower, is a magnified portion of the same negative, having H, and H, about its middle, and extending from wave- length 4205 to 3736. It follows, therefore, that’ the limes in the solar spectrum are correctly represented in their relative positions. The only errors are those which may have arisen from mal-adjustment of the scale. The precautions that were taken to avoid such errors will be described. With a certain correction, to be mentioned hereafter, it may also be stated that the relative shadings and intensities are preserved. The value of such a map depends on the fact that it not only represents parts of the spectrum which are with difficulty per- ceived by the eye ,(though they may be seen by the methods of Stokes and Sekulic), but also that even in the visible parts there is obtained a far more correct delineation in those portions which can be photographed. In the finest maps drawn by hand,,such as those in the celebrated “Spectre Normal du Soleil” of Ang- strom, the relative intensity and shading of the lines can be but partially represented by the artist, and a most laborious and painstaking series of observations and calculations on the part of the physicist is necessary to secure approximately correct posi- tions of the multitudes, of Fraunhofer lines. Between wave- lengths 3925 and 4205 Angstrém shows 118 lines, while my original negative has at least 293. For such reasons many attempts have been made to procure good photographs of the diffraction-spectrum. The earliest were by my father, J.W. Draper; his results were printed in 1843-44 in a work entitled “On the Forces which produce the Orga- nization of Plants.” ‘This memoir was accompanied by plates drawn from his daguerreotypes ; and the wave-lengths, which he first suggested as the proper indices for designating the Fraun- hofer lines, were used as a scale. Since that time the most important experiments in this direc- tion have been by Mascart and Cornu. These eminent physi- cists, however, have resorted to the plan of taking portions of the spectrum on a small scale, and subsequently making enlarged drawings therefrom. This course introduces the defects of hand work, and the artistic difficulties of copying intensity and shading, as well as the omission of fine lines. In the photographs of the spectrum which I have taken, J have tried to get as large a portion as I could at once, and on as large a scale as possible. JI have usually obtained images Dr. H. Draper on Diffraction-Spectrum Photography. 419 from below G (wave-length 4307) to above O (wave-length 3440), of about 12 inches (‘305 metre long). I have succeeded, how- ever, in photographing from near 5 (wave-length 5167) to T (wave-length 3032), by resorting to a ruled speculum plane and a concave speculum mirror; but the photographic and optical difficulties in securing an enlarged spectrum of that length are great*, Of course in such a research as this an essential is a finely and evenly ruled plane of glass or other material. Those which I have used were made by a machine devised and constructed by Mr. L. M. Rutherford, whose beautiful lunar and prismatic spectrum-photographs are so well known to the scientitic world. The plate generally employed is of glass ruled with 6481 lines to the inch; the ruled part is 1,8, inch (‘027 metre) long and {oo (016 metre) wide. It is unquestionably much more nearly perfect than similar gratings made by Nobert and others; for the character of the photographs and the uniformity of the orders on either side of the normal, together with its, behaviour under a searching examination, show that it leaves little to be desired. As it is on glass and gives a bright transmitted spec- trum, I have constructed the remainder of the optical apparatus of glass achromatized according to the plan used by J. W. Draper in 1843, except that I have not silvered the ruling, and there- fore have used the refracted and not the reflected beam. The slit is ;8, of an inch (02 metre) long and ;4¢ of an inch (-00023 metre) wide ; the jaws are of steel ; and there is not only a micro- meter-screw for separating them, but also one for setting them at an angle. Occasionally I have taken photographs with the jaws | of an inch (‘00028 metre) apart at the top, and =1_ (00019 metre) at the bottom, so as to obtain different intensity in the two edges of the spectrum. Most of the photographs have been of the spectrum of the third order, which has certain conspicuous advantages. In the first place it is dilated to such an extent as to give a long image and yet one not too faint to be copied by a reasonable exposure of the sensitive plate; and in the second place the spectrum of the second order overlaps it in such a way that D falls nearly upon H, and 6 upon O. These coincidences are serviceable in determining the true wave-lengths of all the rays. The only point of special interest in connexion with the pho- * Since writing the above I have succeeded in photographing the lines of the visible spectrum from 6 downward; and the picture comprises not only the regions including HE, D, C, B, a, and A, but also the ultra-red rays. The great groups «, 8, y below A, discovered by my father in 1843, are distinctly reproduced. 22 420 Dr. H. Draper on Diffraction-Spectrum Photography. tographic part of the operation is the device for avoiding the un- equal action on the sensitive plate of different rays of the spec- trum. It has been commonly supposed until the recent memoirs of J. W. Draper, that there are in the spectrum three different types of force in three different but overlapping regions. Heat was supposed to be principally found at the less refrangible end, light in the middle, and actinism at the more refrangible. But he showed that this error has partly arisen from using pris- matic spectra, which condense the red end and dilate the violet, and do not present the rays in the true order of their wave- lengths, and partly from the nature of our ordinary photographic substances. He proved that actinism, or the power of cheinical decomposition, does not particularly belong to the violet end of the spectrum, but is found throughout its whole length. . But bromide and iodide of silver as used in collodion photography are more easily decomposed by vibrations of certain lengths and periods than by others ; and hence the excess of action seen at the violet end is a function of certain silver compounds, and not of the spectrum. Other substances, as carbonic acid, show maxima elsewhere, as in the yellow region. The solar beam is therefore not compounded of three forces, light, heat, and acti- nism, but it is a series of ethereal vibrations which give rise to one or other of these manifestations of force, depending on the. surface upon which it falls. In order to provide against this excees of action in certain parts of the spectrum, I introduced a system of diaphragms placed in the vicinity of the sensitive plate and removed at suit- able times during the exposure. The region from wave-length 4000 to 4350 only requires about one tenth of the time de- manded by that from 3440 to 3510. In the negative which produced the accompanying Plate the line O had 15 minutes, and G 21 minutes; and the former is underexposed. These exposures seem at first sight unusually long for a wet collodion surface; but it must be remembered that the slit used was only ;i9 of an inch wide, and that the diffraction-grating gives an almost complete circle of spectra round itself, amongst which this thin band of light is divided. A beam =o of an inch (00023 metre) wide is spread out in this case into a streak about 78 feet (23°77 metres) long. After the production of spectra that were in focus from end to end, it was next necessary to attach a scale to them by which the wave-lengths might be read. At first I tried by reducing Angstrom’s maps to the proper dimensions to accomplish this object; but tue undertaking proved to be difficult, and was un- successful, because, though the original drawing on the stone was undoubtedly correct, the paper proof of it, which I had, had Dr. H. Draper on Diffraction-Spectrum Photography. 421 stretched unequally in printing ; and on applying a photographic reduction to my spectra, coincidence could not be obtained. As, however, the subject of providing a scale for these diffraction - spectra is of prime importance in giving value and precision to the wave-lengths presented in this memoir, [ propose to describe fully the method eventually employed in fitting a scale to the photograph. The wave-lengths of the ultra-violet rays have never, so far as I know, been either determined or published except by J. W. Draper in 1844, Mascart in 1866, and Cornu in 1872. J. W. Draper’s memoir has a steel engraving of some of the principal lines, from which the wave-lengths may be approximately read. The large plate which accompanies Mascart’s long and valu- able memoir is of the prismatic spectrum; but he furnishes in addition the following Table of wave-lengths:— 3819-0 3728°8 3580°2 3440: 1 3360°2 3285°6 81775 The numbers do not entirely coincide in all cases with my photograph, as I will show further on. The detailed results of M. Cornu have not appeared in any publication that has reached me. I have used as a basis the numbers given by Angstrom for the rays D,, 5,, and G; and if there should be any small error in his determinations, my scale will require a proportionate cor- rection, which can easily be effected. At first it seemed better to take G and H as fixed points; but the line H is so broad, and has so many component lines, that its position is uncertain, moO ToOAazSse and, moreover, being almost at the limit of visibility in Ang- stroma’ s apparatus, it was more open to errors of measurement. These reasons led me to take advantage of the fact that the second spectrum overlaps the third, the ray D of the second being near H of the third, and 8 of the second near O of the third. It is obvious that we have thus the means of ascertaining the wave- lengths of three parts—one at each end, and one in the middle of my photograph. As the rays D and } cannot impress them- selves on collodion by any length of exposure that it is conve- venient to give, and as in my method of working the ultra-violet rays could not be seen simultaneously with them, it was neces- sary to resort to the following device. I placed in front of the sensitive plate and close to it two fine steel points, one of which 422 Dr. H. Draper on Diffraction-Spectrum Photography. was carefully adjusted to the position of D, of the second order, and the other to J, of the second order. When, therefore, after a suitable exposure to the ultra-violet spectrum of the third order the collodion picture was developed, there were two sharply defined images of the steel points superposed on the spectrum. The point which had been coincident with D, of the second order was then found to have cast its shadow on H, of the third order; and the point at 5, of the second order had impressed itself near O of the third cenkes. By a simple calculation it was thus rendered evident that a given ray in the compound line H, was of the wave-length 3930°1 ten-millionths of a millimetre, al that another line near O had the wave-length 3444°6. By looking at the photograph the reader will see that 3930 falls upon a fine division in Ho, which is beautifully shown in both the spectrum with the scale and the enlarged proof below. Of course the ray G of the third order, the wave-length of which is known, had impressed itself photographically on the collodion. Having thus ascertained the wave-lengths of three fixed points in the photograph, the next step was to apply a scale reading to a single ten-millionth of a millimetre, and, if possible, fractions thereof. After many abortive attempts to use that part of Angstrém’ s map which lies between G and H, and to attach thereto an additional length of scale sufficient to extend to the end of the ultra-violet region, I was compelled to resort to a linear dividing-engine, and rule a scale which was about twice the length of the photographic reduction shown in the accom- panying Plate. Ofcourse this necessitated drawing in by hand the same systems of lines and lettering as are shown on Ang- strom’s chart ; and this I did as carefully and faithfully as I could. It only remained to reduce this divided scale to the proper size to fit the spectrum-photograph ; after many trials it was accomplished. It is proper in this place to make a criticism on my scale and to point out a small error, which may be due, however, to an incorrect determination of the wave-lengths that I have used as fixed points. Taking the distance from G (wave-length 4307) in the photograph to the fixed line 3980 in H, and dividing it into 377 parts, and then prolonging these divisions towards O, it was found that the third fixed point was not attained, but that there was,an error of about two divisions. But if the po- sition of D, in Angstr6m’s determinations be incorrect to the extent of one ten-millionth of a millimetre, or if this small error should be partly attributed to D, and partly to G, my scale will be correct. Future measures of the wave-lengths of these rays and of 4, can alone settle this delicate point; for the deter- Dr. H. Draper on Diffraction-Spectrum Photography. 423 minations of Mascart and Angstrém and Thalen differ nearly to the extent mentioned above. The same remark is true of Ang- str6m compared with Ditscheiner, while the difference between Angstrom and Van der Willigen is more than three times the amount necessary to remove my discrepancy. In any case the photograph is correct, as it is the work of the sun, and is only open to errors arising from imperfect flatness in the field of a fine lens, and that field only subtending an angle of about 4°. The angular aperture of the lens viewed from the sensitive plate is 20’. I trust, therefore, that the photograph may be of perma- nent value to physicists; for any one can affix another scale if this be erroneous. An examination of the photographed spectrum shows many points of interest, some of which are best seen in the spectrum with the scale above, and some in the portion enlarged below. The latter is magnified about twice, and comprises the region from wave-length 3736 to 4205. Ihave also made photographs on the same scale as Angstrém’s map, but have not as yet printed them. The capital letters which are attached to the region above H are according to the nomenclature of Mascart, although the wave-lengths assigned by him to those letters do not coin- cide exactly im all cases with the lines in my photograph; for instance, the line L, which he regards as single, is in reality triple, and does not correspond to 3819 but to 3821; M is cor- rectly designated by 3728, but it is double; N is really at 3583 and not at 3580. It has been suggested that. it would be proper to return to the old nomenclature of Becquerel and J. W. Dra- per, who simultaneously discovered these lines in 1842-43; but the designation of position by wave-length in reality renders the letters unnecessary. The spectrum above H, when compared with the region from G to H, is marked by the presence of bolder groups of lines; and most conspicuous are those between 3820-3860, 3705-3760, 3620-3650, 3568-3590, 3490-3530. The first of these groups is strikingly shown in the enlarged photograph. I am not as yet able to offer an opinion as to the chemical elements produ- cing these groups; for almost all the photographs of the ultra- violet spectra of metalline vapours that I have thus far made were produced by a quartz train, and have not yet been reduced to wave-lengths; indeed that is a separate field of inquiry, and could not be comprised in a memoir of this length. I have also tried to utilize the photographic spectra of the late Professor W. A. Miller, published in the Transactions of the Royal Society for 1862; but, for some reason (probably insufficient intensity of the condensed induction-spark), his pictures do not bring out the peculiarities of the various metals in the striking manner 424 Dr. H. Draper on Diffraction- Spectrum Photography. that is both necessary and attainable. The diffraction-spectra of metalline vapours that I have made are not yet ready for use. The probability is that each of these groups will be found to be due to several elements, asis plainly seen in the group H. This compound line, which is commonly spoken of as being caused by calcium, iron, and aluminium, is in reality much more complex ; for there can readily be counted in it more than fifty lines in the original negative; and a careful inspection of the accompanying paper picture shows a large proportion of them. This observation leads us to a more general statement. The exact composition of even a part of the spectrum of a metal will not be known until we have obtained photographs of it on a large scale. The coincidences which were so thoroughly examined by Mr. Huggins (Trans. Roy. Soc. Dec. 1863) will only disappear when we can, in addition to the position of a line, have a clear idea of its size, strength, and degree of sharpness or nebulosity. The eye is not able to sce all the fine lines ; or even if it does, the observer cannot map them with precision, nor in their relative strength and breadth. For example, in Angstrém’s justly cele- brated chart, of which the G—-H portion is copied in this Plate ; and in the construction of which the greatest pains were taken by him, many regions are defective to a certain extent. The region from 4101 to 4118 is without lines ; yet the photograph shows in the enlarged copy seventeen that can easily be counted, and the original negative shows more yet. The reader, of course, understands that a paper print of a collodion picture is never as good as the original, the coarseness of grain in the paper, want of contact in transferring, &c. effect such a result. Moreover the Alberttype process depends on a certain fine granulation which is given to the bichromated gelatine ; and this forbids the use of a magnifier upon these paper proofs. It is only just, however, to Mr. Bierstadt to state that, without his personal su- pervision, such sharp and fine-grained proofs could not have been obtained, and that no other printing-press process that I know of could have accomplished this work at all. As an illus- tration of the difficulty of depicting, the relative intensity of lines, we may examine 3998, which in Angstr6m’s chart is shown of equal intensity with 4004, while in reality it is much fainter, and instead of being single is triple, as is well shown in the en- larged spectrum. sf When, however, we compare Angstr6m’s chart with the pho- tograph, it requires, as the above remarks show, a critical exami- nation to detect defects, and we have a striking confirmation of the surprising accuracy of the Swedish philosopher. So also in comparing Mascart’s excellent map of the prismatic spectruin with the photograph, the difficulty of depicting all the Dr. H. Draper on Diffraction-Spectrum Photography. 425 fine lines is seen. In the group L he shows 12 lines, while even in the Alberttype copy of my photograph 25 can be counted, and in the original negative many more. From H to Lhe shows 70 lines; in my Plate 138 can be observed besides many unre- solved bands. In the earlier part of this memoir it was stated that the rela- tive intensities of the lines in the spectrum were correctly repre- sented if a certain allowance was made. If an unshielded col- lodion plate were presented to the image of the spectrum, there would be produced a stain very dense from G to H, fainter above H, and still fainter below G. But this stain would not represent the actinic force of the sun, it would merely be an index of the decomposability of a mixture of iodide and bromide of silver. I have for this reason adopted the idea of J. W. Draper, that force is equally distributed through the spectrum, and have tried to produce a photograph of equal intensity throughout. This has been accomplished, as I have before stated, by suitable dia- phragms. But whether this view be correct or not, lines which are not far distant from one another are presented virtually with- out any interference by diaphragms, and must therefore be cor- rect both as to shading and intensity. Besides the points above mentioned, there are many theore- tical considerations suggested by the photograph which it does not seem expedient to enter upon fully at present. Among such is the possibility of arriving at an estimate of the sun’s tempe- rature by interpreting the apparent bands, such as those near G and H, by the aid of Lockyer’s researches on the temperature of dissociation of compounds. No one has yet ascertained whether there are or are not unresolvable bands in the solar spectrum. If they do exist, the compounds to which they be- long, and the necessary temperature for dissociation, remain to be determined. : It would seem also to be possible to find out whether, as as- serted by Zollner, there is a liquid envelope round the sun, by a search for more diffused bands in its photographed spectrum. In the hope that this photograph may prove to be of value to scientific men for further investigations upon the sun and the elements, I have caused a number of extra copies to be printed, and shall be glad to present them to any one who can make use of them. University, Washington Square, New York. — [ 426 ] LV. On Hamilton’s Dynamic Principle in Thermodynamics. By C. Sziry*. | a a memoir published not long since+, I have maintained that the equation which expresses the second proposition of the mechanical theory of Heat is in complete agreement with the dynamical equation which is named after Hamilton, and that, accordingly, in reply to the question “ 'To which equation in dynamics can the second proposition of thermodynamics be reduced ?” we must point directly to Hamilton’s equation. I was moved to the publication of my considerations on this subject chiefly by the circumstance that neither Boltzmann nor Clausius, in their memoirs{, has once mentioned Hamilton’s principle; and they are the only writers who up to that time had occupied themselves with the above question. Both seem to consider that, in order to bring in accordance, it was neces- sary to deduce an equation yet unknown in dynamics; both remark that the equations deduced by them exhibit a certain affinity with the principle of least action; but neither of these two philosophers has taken any notice of Hamilton’s principle and its close relations to the equations in question. Hereupon M. Clausius published a memoir § which refers ex- clusively to mine above mentioned; and at the very commence- ment he therein readily acknowledges that the connexion scught becomes much more striking when one compares the proposition im question, not (as he and Boltzmann had done) with the prin- ciple of least action, but with Hamilton’s. At the same time Clausius suggests the cause which prevented him from turning his attention to Hamilton’s principle when treating upon the above-mentioned connexion. Namely, in many text-books of dynamics (for instance, Jacobi’s Vorlesungen tiber Dynamik) Ha- milton’s equation is cited in a form which differs essentially from the original, in consequence of the peculiar variation. Now, if Jacobi’s form only be kept in view instead of the primitive form, * Translated from a separate impression, communicated by the Author, from Pogeendorff’s Annalen, vol. exlix. pp. 74-86. tT ‘‘Hamilton’s Principle and the Second Proposition of the Mechanical Theory of Heat,” Phil. Mag. S. 4. vol. xlui. p. 339. Pogg. Ann. vol. exlv. 295. ; : + Boltzmann, “Ueber die mechanische Bedeutung des zweiten Haupt- satzes der Warmetheorie,”” Sitzungsberichie der Wiener Akademie, vol. liii. p- 210. R. Clausius, “Ueber die Zuriickfihrung des zweiten Haupt- satzes der mechanischen Warmetheorie auf allgemeine mechanische Prin- cipien,” Pogg. Ann. vol. exlu. p. 433; Phil. Mag.S8. 4. vol. xlii. p. 161. § Pogg. Ann. vol. exlvi. p. 585. ‘On the Connexion of the Second Proposition of the Mechanical Theory of Heat with Hamilton’s Principle,” Phil. Mag. S. 4. vol. xliv. p. 365. On Hamilton’s Dynamic Principle in Thermodynamics. 427 it is indeed true that it is not very conceivable how any con- nexion capable of being clearly indicated can exist between that re and the second proposition of the mechanical theory of eat. Clausius then quotes the original form of Hamilton’s equation used by me, and proves that Boltzmann’s equation (23a), rightly interpreted, perfectly corresponds with Hamilton’s, is indeed identical with it. But what he concedes in relation to Boltz- mann’s equation, that he decidedly questions in reference to his own; nay, he declares without hesitation the correspondence impossible. ‘Thus the same question is again raised which has been discussed in the Annalen, between Clausius and Boltz- mann*, on the occasion of the claiming of priority by the latter, namely :—Does there actually exist a difference, and, if this is the case, what is the difference, between the equation of Clausius and that of Boltzmann? I believe that I am now entitled—nay, after the reply of Clausius, am bound to enter into the discussion of the question, at least in regard to Hamilton’s equation. I will first discuss the equation which Clausius claims as his own. For the more convenient elucidation of the matter, we will first of all, as Clausius does, confine ourselves to the considera- tion of the periodic motion of a single point. Glven, therefore, a material point which with the original motion describes a closed path, or moves between two given points. The only forces act- ing on the movable point shall be such as possess a force-func- tion (or, as Clausius is accustomed to express it, an ergal)—that is, forces of which the components can be represented by the partial differential quotients, taken negatively, of a function of the coordinates of the pomt. Let us now suppose that this mo- tion undergoes an infinitesimal alteration. With the changed motion let the point likewise describe a closed path, or move between two points, which latter may be either identical with those previously given, or, if not so, fulfil the condition that the quantity OB x3) AY dz has the same value at the terminal point of the motion as at the initial point. Then let z denote the period of the motion, T the vis viva, U the force-function ; and let us agree to indicate the mean value of the variables by putting a horizontal stroke over * Pogg. Ann. vol. cxlii. p. 211: ‘Zur Prioritaét der Auffindung der Beziehung zwischen dem zweiten Hauptsatze der mechanischen Warme- theorie und dem Principe der klemsten Wirkung; von L. Boltzmann.” Ibid. vol. exliv. p. 265: “‘ Bemerkungen zu der Prioritatsreclamation des Hrn. Boltzmann; von. R. Clausius.” 428 M. C. Szily on Hamilton’s Dynamic them (for example, a= zfeadt): then the equation to which Clausius in his answer appeals, and which he marked (18) in his first memoir on this subject*, is the following :-— dU dU dU a eit , aE - 6% + agi + qe eS OT +21 6 logit. ocean Now this is the equation to which Clausius refers as his own, and which, he quite correctly remarks, has a more general appli- cability than Hamilton’s. It is also indeed impossible to find complete accordance between this and Hamilton’s equation. I must, however, observe that I have not reckoned ¢hzs equation as Clausius’s and designated it as such; neither can I now so de- signate it; for this equation was known five years since, as it was given and demonstrated in the first volume of Sir William Thomson’s work, so widely diffused and frequently cited amongst physicists, the ‘Treatise on Natural Philosophy,’ Oxford, 1867 (translated into German by G. Wertheim: Brunswick, 1871). If, namely, the equation (9) in the section ‘‘ Dynamical Laws and Principles” + be written with Clausius’s notation, it exhibits the following form :— m= jw, 4U dU dU (2iT) =i 3T + Gp et ie dy+ |. seen Now it is clear that this equation is identical with equation (1) above cited. Moreover, for a second and not less important reason I could not, when speaking of the equation of Clausius, mean the above- mentioned equation of Thomson: namely, Thomson’s equation is of such generality that, without a special hypothesis, it cannot be brought into consonance with the second proposition of the mechanical theory of heat. For if we could apply this equation in its entire generality to that motion which we call heat, then (as we shall see further on) the second proposition of the mecha- nical theory of heat would not be true. We can, however, most simply bring Thomson’s equation into harmony with the second proposition of thermodynamics, if we make a term vanish from the dynamic equation, putting it =O. And because it was * Pogg. Ann. vol. exlii. p. 442; Phil. Mag. S. 4. vol. xl. p. 167. This is equation (2) of his memoir ‘‘ Ueber die Anwendung einer von mir auf- gestellten mechanischen Gleichung”’ &c., Nachr. der kgl. Ges. d. Wiss. xu Géttingen, 1871, p. 248; Math. Ann. von Clebsch u. Neumann, vol. iv. p. 232; Phil. Mag. S. 4. vol. xl. p. 321. + In order fully to set forth the importance of this equation, Thomson adds :—“ This, it may be observed, 1s a perfectly general kinematical ex- pression, unrestricted by any terminal or kinetie conditions.” Principle in Thermodynamics. 429 Clausius who showed which term must be omitted from that equation, and under what assumption this can be attained, I think that the complete truth of the historical development is attained when we, as I have done, designate as Clausius’s the special equation* resulting from the assumption above alluded to, viz. OU = 6) ele lost. ys. ieee co a(S) Now, what is the difference between this and Hamilton’s equation ? Before entering further into the clearing-up of this question, let us inquire generally what kind of conditions must be fulfilled in order to bring Thomson’s equation into agreement with the second proposition of the mechanical theory of heat. For the sake of a more convenient survey, I will write Thomson’s equa- tion in a somewhat different form. If E denote the total energy, therefore the sum of ‘I’ and U, wecan, after a slight transforma- tion, write equation (2) as follows :— sE= ) isu ae e+ Gy pa FB) or, if we restore i definite integral in A last term, from which the mean value denoted by the horizontal stroke has arisen, we obtain w= OD) 2 eu -(S eee 7° pe Nee If, finally, we divide the entire si dati by T, it pegs ree log (iT) + al, [su — (= ba + ‘i dy + a =e | dt. It is plain that this equation, which is He identical with Thomson’s, can ouly be brought into the form of the second proposition when it is ‘possible to put the last term equal to the total variation of any invariable function of the coordinates— that is, when \ [su —( oe 80+ Gute au 7 8) | dt=iTsF. . | 6 Supposing : ae ma into the last equation, and the symbols of the differentials substituted for those of the variations, then ak id Fr =d2 log (iT) +aF. * This is Clausius’s equation (21) in Pogg. Ann. vol. exlii. p. 442; Phil. Mag. S. 4. vol. xlii. p. 170. 430 M. C., Szily on Hamilton’s Dynamic If we integrate this equation throughout an entire cyclical process, taking at the same time into consideration that iT as well as F (according to the assumption) has at the beginning and at the end of the process the same value, then is ak ger! Thomson’s equation is therefore only then in complete accord- ance with the second proposition of the theory of heat, when the equation of condition (equation 6) is satisfied. Let us now see in what manner this. condition is fulfilled, on the one hand, in Hamilton’s, and, on the other, in Clausius’s equation. Hamilton founded his equation on the assumption* that the form of the force-function does not change with the change of the motion, that hence 6U depends solely on the variation of the space-coordinates—that is, that See tee a eae a az) =0. ee dy In consequence of this, oF=0, and equation (5) takes the following form :— sna el) sre 2 This (8) is Hamilton’s equation. Now, in what consists the assumption made by Clausius? He admits that even the form of the force-function may change; he only lays down this condition}, that the variation which results from the change of form of the feroeiunauions taken at its mean value, is equal to 0, and therefore = aU dU aU oU— ae 62 + — Bi oy + qe 2 =% that is, f [su (ant bY — U 82) ]a=0. . 0) 0 Therefore according to sad eee. also éF=0. Consequently equation (1) takes the form of equation (3), viz. SU=oT +278 logi. * Phil. Trans. 1834, p. 249, sub (1 ). t Pogg. Ann. vol. sali pp. 442-446, sub (18)-(22); Phil. Mag. S. 4. vol, xlii. pp. 167-170. Principle in Thermodynamics. 431 This is Clausius’s equation. Now I affirmed that this equation, and not Thomson’s, is iden- tical with Hamilton’s. This assertion -of mine I still maintain in its full extent; and I believe that after the preceding state- ments Professor Clausius will urge no objection to it. Still, although Clausius’s mathematical contemplations on this subject have not led to an altogether new equation, but have for their result merely Thomson’s and Hamilton’s equations some- what transformed, it would be a great mistake to suppose that those highly important disquisitions had remained unfruitful. As Boltzmann on his part, so I also most willingly acknowledge that the portion which chiefly refers to the change of form of the force- function was absolutely necessary—nay, that only with their aid could Hamilton’s equation have been, with any result, introduced into the mechanical theory of heat. Hamilton has proved his equation only for the case in which the form of the force-func- tion undergoes no change when the motion is changed; but from the researches of Clausius it follows that the same equation (Hamilton’s) can be made use of also when the form of the force- function changes, provided that the mean value of the resulting variation be =O. Such an extension of the validity of Hamil- ton’s equation was at all events requisite, because in the thermo- dynamic theory changes of state of bodies come into consideration which are not dependent merely on space-alterations, but also on the changed form of the force-function. Let us now examine how far Hamilton’s equation must be modified to make it applicable to the case in which we have to do not merely with a single point, but with the change of mo- tion of an entire system of points. And indeed let us just take a system the individual points of which do not travel their paths with equal vires vive or in equal times. Professor Clausius remarks, quite correctly, that in this case Hamilton’s equation is not immediately applicable, and consequently special investi- gations were necessary. When, however, we consider the matter a little more closely, we find that in the form (8) of Hamilton’s equation no other modification is required than that which, relative to the energy, naturally results from the notion of a heterogeneous system of points; that is, we have only to prefix the sign of summation to the right- and left-hand terms, and to extend this summation to all the points of the system. Thus, whilst Hamilton’s equation expresses the variation of the energy for one point as follows, sh= ee) we obtain the variation of the energy relative to an entire system 432 M. C. Szily on Hamilton’s Dynamic of points ina perfectly analogous form by the equation papa sce"), (10) But this modification is truly so slight, and follows so natu- rally from the notion of the system, that we may regard equa- tion (10) as the necessary consequence of Hamilton’s equation. As, however, this equation does not occur in Hamilton, and he limited the employment of the summation-symbol to the case of the points all accomplishing their paths in the same time, it will perhaps not be unadvisable to effect a special demonstration, after Hamilton’s method, of equation (10). It is moreover to be remarked that this equation is first found in Boltzmann, and that the demonstration here given deviates essentially from his only at the commencement, and afterwards only with respect to the arrangement. Let m be the mass of any point whatever of a system, 2, y, z its rectangular coordinates, v the velocity, T the vs viva, U the force-function, E the energy, and z the period of a revolution. T and U have different values at different places in the path; but their sum (that is, EZ) will remain constant so long as the point describes the same path. Hence this quantity is indepen- dent of the time. Let the motion of the point undergo a change: instead of its former closed path and periodic motion, let it fol- low a new closed path infinitesimally different from the previous one. In this new path the mass of the point alone remains as before; all the rest of the quantities are in general changed. Let the variations springing from the change of path be denoted by 6. It follows, from the conception of the energy, that sE=6T+ 6U. If we multiply this equation by the time-element and integrate it from O to z, and at the same time take into account that both E and oF are independent of the time, then e - { (8T +8U) de 0 Let us form analogous expressions for the other points of the system, and sum them: Sane ‘(8T +8U)dt, wineh can also be written ee _— SsE=> jae Ae Sis “ae +H SU = (Se Be + Uy, a) |e dy Principle in Thermodynamics. 433 Supposing now that the last term on the right-hand side (that is, the sum of the mean values of the variations resulting from the change of form of the force-function) is =O, there remains 3oE=3;{ (or any Oo J = By + aa wo dx dz Substituting dT = mv bv and dU dU ORS dg 8+ G8 + *) me =m(<2 Beas We FE We sphiie ae ey m és, where ds signifies the variation in the length of the path, we obtain We dv BE=3;{ a vd» — F ds Br { obs dt =0,85,—m488p— ( » HOS 0 ct) where the indices 0 and 1 in the integrated portions denote the ‘initial and final values of the quantities. But as the path is closed and the motion periodic, Now ) at, 5s,= ds, and v, =. ssp! “fm (v80-+» ae Taking into consideration that vdt = ds, by a slight simplification we get xen=3) ) ‘m3 (0°dt). 0 Accordingly If we bring the constant mass under the variation-symbol and reverse the succession of the integration and variation, we have SeE=3- 5f ‘era 0 . or, designating the mean value by a horizontal stroke, sspax PA) Now this is the equation which we wished to demonstrate. Phul. Mag. 8. 4. Vol. 46. No. 308. Dec. 1873. 2G 434 ~ Lord Rayleigh on the Fundamental I will remark finally that, when the paths of the points are not closed, the transition from closed paths to those not closed can be effected in precisely the same manner, whether we write the Hamilton-Boltzmann equation in its primitive form or in the logarithmic form as modified by Clausius. In truth the form of the equation does not occasion, nor does it prevent, in this case the difficulties mentioned by Professor Clausius at the end of his memoir. For an easier view of the question, let us compare the dates of the development of that dynamic equation to which the second proposition of thermodynamics is reducible. Hamilton set up the equation in the year 1834, but presupposed in the demon- stration that the system of points is homogeneous, and the form of the force-function invariable. In 1868 Boltzmann applies this equation to a heterogeneous system, and, for the first time, brings it into the well-known form of the second proposition of the mechanical theory of heat. In 1871 Clausius proves that the same equation is also valid when the form of the force-function changes, but the mean value of the resulting variation =O. Consequently, within these thirty-eight years, only the validity, the applicability, of the equation has been extended, without the equation itself undergomg any essential alteration, even in form. I repeat the concluding words of wy previous memoir :—“ What in thermodynamics we call the second proposition, is in dynamics no other than Hamilton’s principle, the identical princip!e which has already found manifold applications in several branches of mathematical physics.” LVI. On the Fundamental Modes of a Vibrating System. By Lord Rayiuien, M.A., F.R.S.* (Piers motion of a conservative system about a configuration of stable equilibrium may be analyzed into a series of nor- mal component vibrations, each of which is entirely independent of the others. When one of the components exists alone, the mo- tion is simple harmonic, the period of the vibration and the phase at any given moment of time being the same for all parts of the system. In such a case the system is said to vibrate in a fun- damental mode. In order to represent the most general kind of motion, the whole series of normal components must be ima- gined to exist together, the amplitude and phase of each being arbitrary. The number of the normal components, which also expresses the degree of freedom enjoyed by the system, may be either finite r infinite, though, strictly speaking, every natural system be- * Communicated by the Author. Modes of a Vibrating System. 435 longs to the latter class. It is only by the introduction of limi- tations, such as attributmg to various parts absolute rigidity, that the position of the whole is reduced to dependence on a finite number of coordinates. But even after every permissible simplification has been made, there remains a large and import- ant class of systems whose configuration cannot be defined with- out the specification of an infinite number of coordinates, or, which comes to the same, of a function of one or more indepen- dent variables. Under this head must be included all strings, bars, membranes, plates, &c. which are treated as capable of: continuous deformation. To each fundamental mode corresponds what may be called a normal function. To determine these in the case of any parti- cular system is a problem which may tax, and will usually over- tax, all the power of analytical expression which the mathemati- cian possesses ; but whether expressed in terms of simple func- tions or not, the normal functions must be thoroughly discussed, not to say tabulated, before the solution of the problem can be considered complete. The normal functions appear analytically as the solution of a differential equation containing a constant at this stage unde- termined ; and the first step is the formation of this charac- teristic equation. The usual method proceeds by the considera- tion of the forces actually acting on an element in virtue of its connexion with the rest of the system. For example, the ele- ment of a flexible string is acted on by the tensions at its two extremities ; and the equation of motion expresses the fact that the actual acceleration of the element is proportional to the re- sultant of the tensions when resolved in the transverse direction. The characteristic equation is obtained on the introduction of the assumption that the whole motion is simple harmonic. The second method, which was (I believe) first employed by Green, depends on the use of what we now call the potential energy ; and my present object is to point out its advantages. For this purpose | will take, as neither too easy nor too difficult, the problem of the transverse vibrations of a thin uniform rod whose natural condition is straight. The potential energy V is for each element of length propor- tional to the square of the curvature ; and thus, if y denote the transverse displacement of the element whose distance from one end of the rod is x, we have Ld [C2 2 ye (2) Be a a ea where the integration must extend over the length of the rod, from 0 to /, 2G2 436 Lord Rayleigh on the Fundamental If p be the longitudinal density, we have by the Principle of Virtual Velocities as the variational equation of motion, 8V + py5y=0; vik aoe oe er where oy refers to a hypothetical variation of y, which is subject only to the condition of not violating the connexion of the system. In the formation of (2) we have, as is usual, neglected the reaction of the elements of the bar against the acceleration of rotation. In order to deduce the ordinary form of the differential equa- tion and the terminal conditions, we require to transform the expression 6V. By the usual method we find Q Sie BT ay oO de _pJ Uy doy —B4 oY (a and therefore, asin the Calculus of es d4 af Boa + pi =0. 1S SS ae eee eal The integrated terms give us the conditions to be satisfied at the extremities, namely d*y sdy_,. @ a x Apt de aoe ad 5 OY = 05 ee There are three cases to be considered. Ata clamped end oy and Ve vanish, and the equations (4) are satisfied without any further supposition. Ata free end dy and 5 ty are arbi- dx trary, and hence a? a — _— 0, on =O ee th i Se ee (5) are the conditions to be satisfied in such a case. The third ease occurs when the end is constrained to be a node, but the direc- tion of the rod is left free. Since 6 2 is arbitrary, the condi- tions are y=0, Ten. ne The general equation (3) and the terminal conditions are the same as would be found without the use of the potential energy by the ordinary method. Modes of a Vibrating System. 437 In order to determine the normal functions, we assume that y=u_cos pt, where u is a function of z. We thus obtain dtu | Boa SiS UR Ri eRe ie aaa by from which w is found as the sum of four distinct functions of x (which it is not necessary to write down), each multiplied by a coefficient, which is up to this point arbitrary. The four equa- tions expressing the terminal conditions determine the ratios of the four coefficients, and cannot be harmonized without ascribing special value to p. The condition expressing the compatibility of the four equations limits p to certain definite values which appear as the roots of a transcendental equation. Correspond- ing to each admissible value of p there is thus a normal function in which every thing is definite except a constant multiplier. Since the most general motion may be compounded of the normal component vibrations, it foliows that the most general value of y nay be expressed in the series YPM POU t see vie vo tee + (OD where u,, Uv, &c. are the normal functions, and ¢,, do, &c. arbi- trary coefficients. The determination of ¢, &c. is effected by meaus of the characteristic property of the normal functions, that the product of any two of them vanishes when integrated over the length of the rod. From this it follows that 1 i (rn ae=s,f TELE A ae Sai oar eye) 0 0 The fact that the normal functions are conjugate (which is the name given to functions possessing the property above stated) may be proved from the form of the functions, or better from the differential equation and terminal conditions which define them. The last course is that which has been followed by the distinguished mathematicians who have treated of the present and similar questions. If uw and v be two normal functions corresponding to pand p’, we have from (7), Pi 7h, 2 / yy) nig ( d*y | d*u B eg | )f mide ={ ag v dx? dx dy d 3 2 2 gp) ED et dD ie een Oe de * da de® dw dw” as may be found by integrating by parts. The integrated terms are to be taken between the limits, and vanish in each case, 438 On the Fundamental Modes of a Vibrating System. whether the end be clamped, free, or supported. Hence i ( p!? — p?) ( uvda =0, kee ‘ e/ 0 from which we infer that any two normal functions correspond- ing to different periods are conjugate. This process may perhaps seem as simple as could be expected ; but a little consideration will show that in the derivation of (11) we have in fact retraced the steps by which the ordinary differ- ential equation was itself proved, and that the true foundation of (11) zs the variational equation from which we originally started. In the equation referred to, namely oV + \ py Syda ==) dV is a symmetrical function of y and dy, as may be seen either from its form in the present problem, or by the general theorem proved below. Suppose that y refers to the motion correspond- ing to a normal function u, so that 7 +p?y=0, while dy is pro- portional to another normal function v; then t | 6V =p? ( puvde. e 0d Again, if we suppose, as we are equally entitled to do, that y varies as » and oy as u, l oV =" puvda and thus, as before, ' ( pi? -1"){ puvda =0. If p and p’ are different, l v= ( uvdneQOin eu (ie oi le eee 0 The symmetrical character of 6V is a simple consequence of the fact that V is a homogeneous quadratic function of the co- ordinates. If we-suppose that V=F{11} Wit +. + {12} vivet.--, and let yr, become x, + Ay, &c., we find AV={I1} yA, +... + {12} hy Ay +yoAd,)+...— +43{11} (AW)? +.,..4+ {12} AW Awe +..., or, passing to the limit, : SV = {11 poy t -.. + {12} (ydapo+ Poot) +..+5 which is a symmeirical function of Wy, &c. and dy, &e. Prof. Ch. V. Zenger on a new Spectroscope. 439 The reader will now perceive that the proof of the conjugate property will be scarcely altered if, instead of the bar, we substi- tute a membrane or plate, whose thickness or material need not be uniform. Denoting the transverse displacement of any point by w, we have as the variational equation, SV + || pwdw dx dy =0; from which precisely, as before, we deduce ( p'* —p?) \\ uw da dy=0. It is, I hope, now clear that great advantage results from the direct employment of the variational equation. The reason of the advantage appears to lie in the fact that every thing required to be known is here embraced in one equation, while the ordinary * differential equation necds to be supplemented by the boundary conditions, which are indeed of the same mechanical importance as itself, The same method may be applied to the general system. Lagrange’s equation of motion for a vibrating system may be written 2 (@)ay4... 48v=0 dt dnp, where T is the kinetic energy. Ifthe actual motion denoted by vr, &c. be a normal component vibration, each coordinate varies as cos pt, and the general equation may be written eereeter ew Or. V2 Ssh COROT IS) where T, is the same function of W,, y,, &c. that T is of yy, &e. By the same reasoning as before we infer that if Ww, &c. refer to one normal component and dy, &c. to another having a different period, ros Wit hoe Sa eae mm On it LVII. On a new Spectroscope. By Professor Ch. V. Zuncrer*, 1” the spectroscopes usually employed the maximum of dis- persion is attained by the combination of several prisms ; but this entails a very great loss of light by absorption and reflec- tion at the numerous surfaces of the prisms. It is obvious that feeble intensity of light, or, even when the light is strong, feeble physiological action of the red and violet rays of the spectrum much interferes with exactness and distinctness of vision, espe- cially in the spectral analysis of starlight. * Ordinary is here used in opposition to variational, not to partial. + Communicated by the Author. 44.0 Prof. Ch. V. Zenger on a new Spectroscope. Any contrivance by which this loss could be avoided and yet the same amount of dispersion be secured would be very advan- tageous for spectrum-observations on feeble, and even on strong light. "For this purpose I employ only a single prism of the least- absorbent material and the greatest dispersion attainable. It seemed to me that a prism of pure transparent ice-spar would best fulfil this condition, as its index of refraction is :— ry= 1°6531, ny = 16838, An=0°0802 ; so that its dispersion is greater than that of crown glass, and but little less than that of flint glass, while it absorbs very little of the extreme red and violet rays. To explain the action of the new spectroscope, let ABC (fig. 1) be the section of a rectangular prism of spar; the solar Fig. 1. V ray Sma falling at right angles on the surface AB, the angle of in- cidence w is equal to the angle of the prism. After refraction the red ray falls in the direction m)m on the surface of a cylin- drical mirror and is reflected from it in the direction mR; and the violet ray will be reflected, at a greater angle, in the direc- tion m, V. The diagram shows at once that the effect of the cylindrical surface am m, 1s to produce an increase of the angle of disper- slon mimym,=¢ to RAV=. It is easy to account for the in- crease, if the angle of the refracting prism, the distance between the prism and the mirror, and the radius of curvature of the Prof. Ch. V. Zenger on a new Spectroscope. 44] mirror be given. In the first place, the angle of dispersion produced by the prism itself will be p=r,—T5) equal to the difference of the angle of refraction for the red and the violet rays: , sin 7, =, . SIN @ ; sin 7,=7,. SiN w. If the angle of the prism is not too large, the sines may be re- placed by the angles: T= 1N7,@ ; 7, =N,® ; TT, = (n,— 22), o=(n =n, )o=@.An. .° 6. (Y) The angle of incidence (2) at a given distance between the aurror and of the prism (fig. 2) is 1=r—otp, op being the angle of aperture of the mirror. PigkZ. In the tringle mm 0, mo :mo= sini: sin (r—w); or approximately mo:mo=i:r—w; r—w=(n—l1)o. 442 Prof. Ch. V. Zenger on a new Spectroscope. M0 =am, + ao=a+p, if a be the distance of the prism from the mirror, and p its radius of curvature; we then obtain :— a = ae or i=(~ +1) @-lo. . @) For the extreme red and violet rays we get ;— eG nee yo in=(E +1)(m—1)o, in-o=(’ +1)(m—n)o, n=E +1)—-I)a, in—b=(E +1) Ano. Bes The triangle 4/m, contains the angle w of the red and violet rays after the reflection from the mirror ; and it measures the in- crease of dispersion produced by the reflection from the cylin- drical surface. If, therefore, yy is known, the ratio between the angles # and yr gives the real increase of dispersion produced in that way. The angle Adm,, as an exterior angle of the triangle lg, 1s him,=$+ 21; and 27 being the exterior angle of the triangle him,, we obtain :-— W+ b+ 2t=21,, + h=2(i,—1), i= VEE (4) Combining (8) and (4), we get :— + _ fa wy =(E +1).0. Ay, od=@. An, ¥+o=2(- +1)e. An, v= (4 +1)0.dn; + ie bake Bian 2 ¥=(= +1), Lo ala To receive the spectrum on the surface of the mirror the angle p must be sufficiently great; it is given by the equation p=l—(7—o) 3 Oe (7) p=i—(n—l)a, Prof. Ch. V. Zenger on a new Spectroscope. 4.43 or a =(-— +1 )(n—l)o—(n—l)o; p=(5 +1)(-—lo—(m—1) a = —-(n—l)o. Hay tae If f be the focal length of the mirror, we have p Zidaeed! “=f and = - oh a and we finally obtain :—the angle of dispersion : GN NTs avian! ahha a) ce altace (I.) the angle of reflection : BREA i=(s +1)(m—l)o;. . . . (IL) the difference of the angles of reflection for the extreme red and violet rays Ai=(¥. +1)o. An, sD UE the increase of dispersion being 7 Y= (af+1). Wee REE aie al 0. The angle of aperture required for the reflecting surface of the mirror becomes S=p(m—lo- 2s WV) The equations (I.) to (V.) give all the dimensions for the construction of the spectroscope itself. Suppose the prism to be of crown glass, flint glass, sulphide of carbon, or ice-spar, we obtain :— / Crown glass. CS,. Flint glass. —_ Ice-spar. His. Lb447 1°7025 EGAUt 1°6833 pore 3 MD 240 1°6182 1:6277 1°6531 Ane. 0°0204 00843 0:04:34: 0:0302 If the increase of the angle of dispersion be ¢, or p=o¢=21, the focal length of the mirror f=2 centims., p=4 centims., then the distance isa= 40 centims.; . =20 ; and the other values may be calculated as follows :— Crown glass. CS... Flint glass. Ice-spar. ~ . 0:0204a 0:0843 w 0:0434.0 0:0802. vy. . 042840 1:7703@ 0:91140 0°6342 Ai. . 0°2244@ 0:9273o 0:4774@ 0:3322 Sin.) oco4om 7°025@ 6°7ll@ 6:-531lw ~Q- Adc Prof. Ch. V. Zenger on a new Spectroscope. It is obvious that ice-spar has the advantage of not absorbing large portions of the extreme red and violet rays, not refracting so much as flint glass or bisulphide of carbon, while yet its dis- persion is nearly as much as that of flint glass; it requires therefore not so large an aperture of the mirror as flint glass or bisulphide of carbon. Supposing the angle of the prism to be 10°, we obtain :— = 0°302, y= 6:342, Ai= 3'322, S =65°31. For 26° :— > = 0:604, yr = 12-684, Ai= 6644, S =130°62. For more than 30° the reflecting mirror cannot give the whole spectrum at once, unless it has an aperture of 195°°93; and then it would: reflect the rays on both sides of the prism, instead of only one as shown in the diagram. In the case of the angle » being 10°, the refracting angle of the prism should be nearly 211°, or three prisms must be used of 60°-70° to get the same dispersive power in a common spec- troscope. If the angle be 20°, six prisms of 60°-70° nearly should be used to get the same effect, and so on. If the angle of incidence be not equal to zero, the dispersion increases to, very approximately, n? sin? 2 o=(1 + 9 Joan, and the preceding equations become :— p=(1t “OP *).0. An, ma n2 sin? 7 w= (% +1) (14 ; ).0.An, Br lie a n® sin? 7 Ae (x +1) 475" *)o.dn . (UL) There is a practical difficulty in getting exactly cylindrical sur- faces; but it is possible to use spherical surfaces instead, if only a narrow zone of the middle part of a convex or concave silvered glass mirror be used. All the formule quoted above may be applied to it, and the dispersion augmented without fear of mar- ring the exactness and definition of vision. Prof. Ch. V. Zenger on a new Spectroscope. 445 The new spectroscope, therefore, consists of a brass tube with a slit at one end and closed at the other end (fig. 3). The slit Fig. 3. must be narrow and short, and the prism very near to it, turning by a pinion (p) in its case. The mirror, inclined a certain angle p to the axis of the tube, reflects from the other, closed end the spectrum into a brass tube lateral to the former, containing a small telescopic apparatus to receive sharp images of the spec- trum reflected by the convex spherical mirror, and to magnify them to ten times the diameter. The mirror is adjusted in such a way as to bring only a narrow zone of its middle part into operation, the rest of the surface beg protected by a cover with a narrow slit in the direction of the rays emerging from the prism, and parallel to the reflecting zone of the mirror. To increase the effect of the mirror, it can be brought nearer to the closed end of the tube, and the side tube moved in the same direction with it. Yet it seems more advisable to fix both at such a distance as will give the greatest separation of the spec- tral lines attainable without a great loss of light and a diminution of the exactness of the image, London, October 17, 1873. [ 446° ] LVILI. Reply to Professor Challis’s further Remarks* “ On the Received Principles of Hydrodynamics.” By Roxsert Moon, M.A., Honorary Fellow of Queen’s College, Cambridge. tC his recent paper Professor Challis reiterates, in a slightly different form, his argument derived from the equation p=funct. (p, v), without taking any notice of my refutation of it. Putting u,v, w for the resolved parts of the velocity, and x, y, & for the coordinates of a particle at the time ¢, he assumes that the motion in three dimensions of any fluid may be repre- sented by the five following equations; viz. “ p=f(2,y,2,t), p=fl%, 42,0), u=fslt.y2,t), | (a) v=f,(v,y,2,t), w=fs(x, y, 2, tt. Eliminating a, y, 2, ¢ from equations («), Professor Challis obtains the equation F(p, p, u,v, w)=0, which he assumes to be capable of being “satisfied by an arbitrary relation between the quantities —that is, by one which is independent of the particular problem.” “The arbitrary condition,” says Professor Challis, “has the effect of defining the fluid; and evidently the number of differ- ent kinds of fluids is unlimited.” I must here point out the very extraordinary character of the admission made by Professor Challis when he asserts that the number of fluids is unlimited, each fluid being defined by the relation between p, p, u,v, w prevailing in it—his sole object, so far as I understand it, being to prove that one only of this unlimited number of fluids, and that a fluid in which the highly * See Phil. Mag. for Oetober last. + Communicated by the Author. t From this view I must express my dissent, believing that the equa- tions (#) are insufficient to determine the motion. in the case in question. Not wishing upon the present occasion, however, to enter upon a fresh field of controversy, I shall content myself with observing that this assump- tion of Professor Challis contradicts his subsequent assumption that the resultant of the elimination of 2, y, z, ¢ from equations («) will be a per- fectly arbitrary function of p,p,u,v, w. For in the case of equilibrium the five equations (#) reduce to the pair p=i{hilasy, S t) bro» p=4{fi(2,y, es t)rn93 e « a! ee (8) the elimination between which of z gives p= funct. (p,#, y)3 which is irreconcilable with Boyle’s law in the case of equilibrium, unless we suppose that x and y both disappear along with z in the elimination. But this would require the functions on the right-hand sides of equations (8) to be of a special form; from which it follows that the functions f,, f, must be of a special form, and therefore the result of elimination from them of x, y, ¢ cannot be perfectly arbitrary. On the Received Principles of Hydrodynamics. 447 special relation p=a*p obtains has the slightest claim on our attention. Waiving this consideration, however, I join issue with Pro- fessor Challis on the point of our being able to assign to the relation I'(p, p, u,v, )=0 a definite form which is independent of the particular problem. By assigning a definite form to the arbitrary function F(p, p,u, v, w)=0, it is not true, as assumed by Professor Challis, that we simply define the fluid. We doa great deal more. We define the fluid, and at the same time impose conditions on the motion existing in it. In proof of this I must again direct attention to the analytical arguinent of my Jast paper, which Professor Challis does not appear to have examined. Confining ourselves to motion in one direction—suppose that we have a cylindrical tube filled with any particular fluid (say air of the mean density of the atmosphere) ; and suppose that at a given time ¢ we have a disturbance extending over a limited portion of the column. Let the velocity and density throughout the disturbance at the time ¢ follow any law whatsoever consist- ent with continuity; then I have shown in the paper in ques- tion that the pressure prevailing throughout the disturbance at the same time may follow any law whatever consistent with con- tinuity* ; from which it is evident that Professor Challis’s argu- ment, in proof “ that it is allowable to make for fluid in motion the hypothesis that the pressure varies as the density always and at all points,” must be fallacious. I observe that Professor Challis mistakes the points on which I mainly rely for my “ objections to the received principles of hy- drodynamics.”’ My main argument is this :—Taking, in the case of motion in one direction, p=h (2), p=folat), v=fs(xi). I hence derive the equation p= tunct. (p, v); whence it follows that the equation of motion New hap v= 2 as | dt? + D de will be satisfied by the three relations * It must be borne in mind that the condition of continuity requires that at the limits of the disturbance the velocity shall be zero, the density =D, the atmospheric mean density, and the pressure =a’D. 448 Mr. R. Moon’s Reply to Prof. Challis’s further Remarks a a aioe sb (v as a : p ? (2 ! jal ot = v4 ~ (@) -# B vhs -D 1 dw ft chs (AA p etnies oes Baya A result more rigorously deduced or more analytically complete is not to be found in the whole range of mathematical physies ; and my main objection to the received theory of hydrodynamics is that its upholders must arbitrarily set aside the above rela- tions, being such as have been described, substituting in their room the equation p=a’p with such emasculated results as have been or may be* derived from it—an equation, be it remembered, which is unsupported by a single fact, which is opposed to every sound principle, and as to which all that can be said in its favour is that, in the infancy of the theory, the founders of the theory seized upon it in desperation, amidst the overwhelming difficulties by which they were beset, as the only law of pressure prevailing under any circumstances that up to that time had ever been so much as suggested. But although I do not rest my main objection to the received principles of hydrodynamics upon the two points to which Pro- fessor Challis refers, [regard the views I have put forth in rela- tion to those cases as of importance as showing in a popular manner, conclusively and at a glance as it were, the wholly un- tenable character of the existing theory of fluid pressure. As to the first of these cases, Professor Challis writes :—‘ Mr. Moon founds an argument on the immediate juxtaposition of two densities one of which is double of the other; in other dp 1 (aNd terms, he admits that — dy MAY have an infinite value.” I do not know on what ground Professor Challis attributes to me this admission; for, although on entirely different princi- ples+, [ am as satisfied as he can be as to the impossibility of * Tt is well known that the only solution of the equation of motion under these circumstances which has ever been demonstrated is that de- rived by Poisson, containing a single arbitrary function, and involving a relation between the velocity and density which it is quite impossible can always or even generally subsist. Ina recent Number of the Philosophical Magazine I have shown, as I believe irrefragably, that this solution of Poisson’s is the most general which, consistently with the relation p=a’p, the equation of motion admits of. + Professor Challis regards equality of pressure in all directions as a law upon which “‘ the whole of analytical hydrodynamics depends.” It is true that the founders of the theory of fluid motion im three dimensions, in their on the Received Principles of Hydrodynamics. 449 variation of pressure taking place per saltum. Of course if we admit the equation p=a’p, variation per saltum of density and variation per saltum of pressure necessarily go together; but in a discussion as to the truth of that equation it is evident that its validity cannot be assumed. But though believing variation of pressure per saltum to be impossible, I see no more difficulty in supposing a variation of density per saltum to occur in a fluid than in supposing two fluids of different densities to be in contact, or that two solids of different densities may be pressed together. Till, therefore, Professor Challis has shown variation of density per saltum to be impossible in a fluid, I shall-consider myself entitled to insist on all the consequences which, according to the received theory, would flow from its occurrence. As to the second case, where a weight is suddenly placed upon a piston supported by a vertical column of air, Professor Challis admits that the dilemma I have suggested “is fairly in- ferred and demands explanation.” If it be true that the di- lemma is. fairly inferred, I think that most persons will regard it as incapable of explanation, and as necessarily involving a modification of the existing theory. Professor Challis’s explanation consists in supposing that as soon as the weight is added, there will be a tendency to an excess of pressure on the upper side [of the stratum immediately under- neath the piston] due to the disturbance of pressure in the solid piston.” If the words in italics mean any thing, they mean that there will be an increased pressure of the piston on the air, at the same time that, according to the received theory of pressure in elastic fluids, no increase can have taken place in the pressure of the air upon the piston; which is manifestly a contradiction of the law of the equality of action and reaction. Whatever dis- turbance of pressure may exist in the other parts of the solid piston, none such can occur at its base consistently with the rela- ‘tion p=a’p, until the lapse of an interval of time after the depo- ‘sition of the additional weight upon the piston. At the same time I think that a true and complete theory of early struggles in connexion with the subject, did have recourse to the assumption of the truth of this law; but, so far is it from being an adequate foundation for a general theory of fluid motion, its retention is simple strangulation to the theory, and accounts for the limited and unpromising progeny which trace their origin to it. The true foundation of the theory of fluid motion is the principle of continuity (continuity of motion, that is, -as well as continuity of mass), from which it results, as can readily be shown, that any element of the fluid mass will comport itself exactly in the same manner as an element of a rigid body would do. under the same cir- cumstances, and may therefore be dealt with accordingly. Phil. Meg. S. 4. Vol. 46. No. 308. Dec. 1873. 24H 450 Mr. A. W. Bickerton on a new Relation the motion which would take place under the circumstances sup- posed might be evolved by having recourse to considerations similar to those which Professor Challis has suggested—viz. by considering first what would happen if the column of air were a perfectly rigid bar, next by considering the effect of a slight deviation from perfect rigidity, and finally by inferring from that analogy what would take place in the actual case. I hope hereafter to have an opportunity of developing what has been thus briefly sketched. Avranches, October 11, 1873. LIX. On a new Relation between Heat and Static Electricity. By A. W. Bickerton, F.C.S., Associate of the Royal School of Mines, Lecturer on Experimental Science, Winchester College, and the Hartley Institution, Southampton*. QO* reading the able paper on the above subject by Dr. Guthrie in the October Number of the Philosophical Magazine, it occurred to me that the relationship might be most satisfactorily and easily explained by the assumption that currents of air passing over an electrified body carry off their electricity. The necessity for the assumption of a coercive force existing between these two physical forces (as suggested in the ‘Proceedings of the Royal Society ’) is thus removed. The following experiments seem to me to prove in a most de- cisive manner the correctness of my hypothesis. Cold air, or cold gas of any kind, even at considerable pres- sure, when discharged against a charged Peltier’s electrometer is incapable of taking away its electricity ; but I found that with a stream of hot air the electroscope was rapidly discharged. In one of the Professor’s experiments a heated platinum wire is placed above an electrified body, the body being instantly discharged. I thought it possible that the induced electricity on the heated wire might charge the air in its vicinity with elec- tricity ; this charged air passing by attraction down to the elec- trified body would neutralize it. To ascertain if such a current of air existed, I placed the platinum spiral in the upper part vt a gas-jar, a thermometer being passed through the cork so that its bulb was a short distance below the spiral. A brass knob connected with an electric machine was passed up into the jar so as to be close to the thermometer, about 2 mches below - the spiral. The knob was also in connexion with a small qua- drant electroscope. The machine was worked; and when the * Communicated by the Author. between Heat and Static Electricity. — 451 spiral was heated, a marked diminution in the indications of the electroscope was observed. After the apparatus had again attamed the normal temperature, the current was sent continu- ously, the rise of the thermometer being noted every minute*, and the brass ball being electified and left unelectrified in alter- nate minutes. The thermometer indicated on the average a rise of one degree when the ball was not electrified and five degrees when it was electrified—thus proving the existence of a downward current of hot air when the ball was electrified. Each time the machine was worked the sudden rush of air from the white-hot spiral caused its temperature to be appreci- ably lowered. On filling the vessel with smoke, the upward convection-currents of heated air showed themselves plainly. On working the machine, the sudden downward rush of smoke from the spiral to the ball was very striking. The smoke dis- appeared with surprising rapidity when the ball was electrified ; it was doubtless burnt in passing over the heated spiral. Re- peated experiments proved that the smoke was consumed very much more rapidly when the ball was electrified than when not electrified. If heated air be the cause of the discharge, the heated wire will possess no power of discharge through rock-salt. This is actually the case ; the ignited wire may be placed ever so close to a charged Peltier’s electrometer without discharge, if a plate of rock-salt be interposed between them; but remove the salt, and discharge is instantaneous. : An induction-coil giving a spark 54, inch will give a spark 4 ich if the electrodes are at a high temperature. A 1-inch spark becomes 13 inch under the same conditions. As it might be said that the lengthening of the spark of the coil was due to rarefaction of the air, the following experi- ment was made. Platinum wires were fused into the ends of a short piece of combustion-tube. The spark from the small coil passed through a distance of 5%, of an inch when the glass, except the fused ends, was strongly heated; the air of course was here almost at the same density. As it is possible to ex- plain the apparent conductivity of glass observed by Dr. Guthrie on the above supposition of air-currents, I sent the spark from the small coil through the heated end of a closed glass tube. I also found that the current from four Grove’s cells would pass through 14 inch of heated glass and deflect a galvanometer. This power of conductivity is attained at a red heat, and in- creases enormously with slight increase of temperature. Thus, * A clock striking minutes with the hand making a complete revolution in the same time was used in all time experiments. 2H 2 452 Onda new Relation between Heat and Statice Electricity. if a small sphere of glass have two platinum electrodes fused into the two sides and it be gradually heated, the galvanometer does not move for some time; but after the first movement 1s observed, the needle quickly passes up to 90°. If we assume that hot air possesses the power of carryimg off + electricity more readily than —, the whole of Dr. Guthrie’s apparently contradictory experiments of the different effects of + and — electricity may be easily explained. Thus a heated body cannot be charged with + electricity, because the heated air carries it off. A body near a heated conductor cannot be charged with —, because it induces + electricity in the heated body ; this electrifies the heated air, and the electricity is then carried to the electrified — body and neutralizes it. Faraday proved that air at ordinary temperatures carried off — electricity most easily. Hence the experiments of Faraday, Dr. Guthrie, and myself, taken in conjunction, prove the two following principles :— Ist. That at low temperatures — electricity is taken away by air most easily; at certain temperatures both electricities are carried off with equal facility, and at high temperatures + electricity most easily. 2nd. That high-tension electricity can be conveyed away at low temperatures; and as the tension gets lower and lower, it requires the air to be of higher and higher temperatures to carry it off. To illustrate the second principle, I placed a needle on the knob of a fully charged Peltier’s electrometer and left the point within ;3, of an inch of an earth-connected brass ball; after two hours the electroscope had only lost half a degree; and on passing a current of hot air, or putting a heated point near it, the electricity was instantly discharged. The lengthening of the electric arc after the current is once established may be due to these principles, especially from the well-known fact that the part of the + carbon where -induc- tion is strongest wears away most rapidly; while the slight wear of the other carbon is as much down the sides as at the point, and hence it remains pointed. It is further confirmed by the fact that if the electric current pass between two electrodes of different oxidivable metals, the space about the light becomes filled with particles of the oxide of the + pole. | 453 ] LX. A Discourse on Molecules. By J. CLurx Maxwe xt, M.A., F.R.S., Professor of Experimental Physics in the University of Cambridge*. Fs atom is a body which cannot be cut in two. A molecule is the smallest possible portion of a particular substance. No one has ever seen or handled a single molecule. Molecular science, therefore, is one of those branches of study which deal with things invisible and imperceptible by our senses, and which cannot be subjected to direct experiment. : The mind of man has perplexed itself with many hard ques- tions. Is space infinite, and if so, in what sense? Is the ma- terial world infinite in extent, and are all places within that extent equally full of matter? Do atoms exist, or is matter in- finitely divisible ? - The discussion of questions of this kind has been going on ever since men began to reason; and to each of us, as soon as we obtain the use of our faculties, the same old questions arise as fresh as ever. They form as essential a part of the science of the nineteenth century of our era as of that of the fifth century before it. We do not know much about the science organization of Thrace twenty-two centuries ago, or of the machinery then employed for diffusing an interest in physical research. ‘There were men, however, in those days who devoted their lives to the pursuit of knowledge with an ardour worthy of the most distinguished members of the British Association; and the lectures in which Democritus explained the atomic theory to his fellow-citizens of Abdera realized, not in golden opinions only, but in golden talents, a sum hardly equalled even in America. To another very eminent philosopher, Anaxagoras, best known to the world as the teacher of Socrates, we are indebted for the most important service to the atomic theory which, after its statement by Democritus, remained to be done. Anaxagoras, in fact, stated a theory which so exactly coutradicts the atomic theory of Democritus, that the truth or falsehood of the one theory implies the falsehood or truth of the other. The question of the existence or non-existence of atoms cannot be presented to us this evening with greater clearness than in the alternative theories of these two philosophers. Take any portion of matter, say a drop of water, and observe its properties. Like every other portion of matter we have ever seen, it is divisible. Divide it in two, each portion appears to retain all the properties of the original drop, and among others * Read before the British Association at Bradford, September 22, 18/2, 454. Prof. J. C. Maxwell on Molecules. that of being divisible. The parts are similar to the whole in every respect except in absolute size. Now go on repeating the process of division till the separate portions of water are so small that we can no longer perceive or handle them. Still we have no doubt that the subdivision might be carried further if our senses were more acute and our instru- ments more delicate. Thus far all are agreed; but now the question arises, Can this subdivision be repeated for ever ? According to Democritus and the atomic school, we must auswer in the negative. After a certain number of subdivisions the drop would be divided into a number of parts each of which is incapable of further subdivision. We should thus in imagi- nation arrive at the atom, which, as its name literally signifies, cannot be cut intwo. Thisis the atomic doctrine of Democritus, Epicurus, and Lucretius, and, I may add, of your lecturer. According to Anaxagoras, on the other hand, the parts into which the drop is divided are in all respects similar to the whole drop, the mere size of a body counting for nothing as regards the nature of its substance. Hence, if the whole drop is divi- sible, so are its parts down to the minutest subdivisions, and that without end. The essence of the doctrine of Anaxagoras is that parts of a body are in all respects similar to the whole. It was therefore called the doctrine of Homoiomereia. Anaxagoras did not, of course, assert this of the parts of organized bodies such as men and animals; but he maintained that those inorganic substances which appear to us homogeneous are really so, and that the uni- versal experience of mankind testifies that every material body without exception is divisible. The doctrine of atoms and that of homogeneity are thus in direct contradiction. But we must now goon to molecules. Molecule is a modern word. It does not occur in Johnson’s Dictionary.. The ideas it embodies are those belonging to modern chemistry. A drop of water (to return to our former example) may be divided into a certain number, and no more, of portions similar to each other. Each of these the modern chemist calls a mole- cule of water. But it is by no means an atom, for it contains two different substances, oxygen and hydrogen; and by a cer- tain process the molecule may be actually divided into two parts, one consisting of oxygen and the other of hydrogen. According to the received doctrine, in each molecule of water there are two molecules of hydrogen and one of oxygen. Whether these are or are not ultimate atoms I shall not attempt to decide. We now see what a molecule is, as distinguished from an atom. A molecule of a substance is a small body such that if, on the Prof. J. C. Maxwell on Molecules. 455 one hand, a number of similar molecules were assembled together, they would form a mass of that substance; while, on the other hand, if any portion of this molecule were removed, it would no longer be able, along with an assemblage of other molecules similarly treated, to make up a mass of the original substance. Every substance, simple or compound, has its own molecule. If this molecule be divided, its parts are molecules of a different substance or substances from that of which the whole is a mole- cule. An atom, if there is such a thing, must be a molecule of an elementary substance. Since, therefore, every molecule is not an atom, but every atom isa molecule, I shall use the word mo- lecule as the more general term. I have no intention of taking up your time by expounding the doctrines of modern chemistry with respect to the molecules of different substances. It is not the special but the universal interest of molecular science which encourages me to address you. It is not because we happen to be chemists or physicists or specialists of any kind that we are attracted towards this centre of all material existence, but because we all belong to a race endowed with faculties which urge us on to search deep and ever deeper into the nature of things. We find that now, as in the days of the earliest physical spe- culations, all physical researches appear to converge towards the same point, and every inquirer, as he looks forward into the dim region towards which the path of discovery is leading him, sees, each according to his sight, the vision of the same quest. One may see the atom as a material point, invested and sur- rounded by potential forces. Another sees no garment of force, but only the bare and utter hardness of mere impenetrability. But though many a speculator, as he has seen the vision recede before him into the innermost sanctuary of the incon- ceivably little, has had to confess that the quest was not for him ; and though philosophers in every age have been exhorting each other to direct their minds to some more useful and attainable aim, each generation, from the earliest dawn of science to the present time, has contributed a due proportion of its ablest in- tellects to the quest of the ultimate atom. Our business this evening is to describe some researches in molecular science, and in particular to place before you any de-. finite information which has been obtained respecting the mole- cules themselves. The old atomic theory, as described by Lu- cretius and revived in modern times, asserts that the molecules of all bodies are in motion, even when the body itself appears to be at rest. These motions of molecules are, in the case of solid bodies, confined within so narrow a range that even with our best microscopes we cannot detect that they alter their places at 456 Prof. J. ©. Maxwell on Molecules. - all. In liquids and gases, however, the molecules are not con- fined within any definite limits, but work their way through the whole mass, even when that mass is not disturbed by any visible motion. This process of diffusion, as it is called, which goes on in gases and liquids and even in some solids, can be subjected to expe- riment, and forms one of the most convincing proofs of the mo- tion of molecules. Now the recent progress of molecular science began with the study of the mechanical effect of the impact of these moving molecules when they strike against any solid body. Of course — these flying molecules must beat against whatever is placed among them; and the constant succession of these strokes 1s, ac- cording to our theory, the sole cause of what is called tie pres- sure of air and other gases. This appears to have been first suspected by Daniel Bernoulli ; but he had not the means which we now have of verifying the theory. ‘The same theory was afterwards brought forward in- dependently by Lesage, of Geneva, who, however, devoted most of his labour to the explanation of gravitation by the impact of atoms. Then Herapath, in his ‘ Mathematical Physics,’ pub-. lished in 1847, made a much more extensive applicaticn of the theory to gases; and Dr. Joule, whose absence from our Meet- ing we must all regret, calculated the actual velocity of the mo- lecules of hydrogen. The further development of the theory is generally supposed to have begun with a paper by Kronig, which does not, however, so far as I can see, contain any improvement on what had gone before. It seems, however, to have drawn the attention of Pro- fessor Clausius to the subject ; and to him we owe a very large part of what has been since accomplished. | - We all know that air or any other gas placed in a vessel presses against the sides of the vessel, and against the surface of any body placed within it. On the kinetic theory this pres- sure 1s entirely due to the molecules striking against these sur- faces, and thereby communicating to them a series of impulses which follow each other in such rapid succession that they pro- duce an effect which cannot be distinguished from that of a con- tinuous pressure. If the velocity of the molecules is given and the number varied, then since each molecule on an average strikes the sides. of the vessel the same number of times, and with an impulse of the same magnitude, each will contribute an equal share to the whole pressure. The pressure in a vessel of given size is there- fore proportional to the number of molecules in it—that is, to the quantity of gas in it. Prof. J. C. Maxwell on Molecules. 457 This is the complete dynamical explanation of the fact disco- vered by Robert Boyle—that the pressure of air is proportional to its density. It shows also that, of different portions of gas forced into a vessel, each produces its own part of the pressure independently of the rest, and this whether these portions be of the same gas or not. Let us next suppose that the velocity of the molecules is in- creased. Each molecule will now strike the sides of the vessel a greater number of times in a second; but, besides this, the impulse of each blow will be increased in the same proportion, so that the part of the pressure due to each molecule will vary as the square of the velocity. Now the increase of velocity cor- responds, on our theory, to a rise of temperature; and in this way we can explain the effect of warming the gas, and also the law discovered by Charles, that the proportional expansion of all gases between given temperatures is the same. The dynamical theory also tells us what will happen if mole- cules of different masses are allowed to knock about together. The greater masses will go slower than the smaller ones, so that on an average every molecule, great or small, will have the same energy of motion. The proof of this dynamical theorem, in whieh I claim the priority, has recently been greatly developed and improved by Dr. Ludwig Boltzmann. The most important consequence which flows from it is that a cubic centimetre of every gas at standard temperature and pressure contains the same number of molecules. This is the dynamical explanation of Gay-Lussac’s law of the equivalent volumes of gases. But we must now de- scend to particulars, and calculate the actual velocity of a mole- cule of hydrogen. uy A cubic centimetre of hydrogen, at the temperature of melting — ice and at a pressure of one atmosphere, weighs 0-00008954 gramme. We have to find at what rate this small mass must move (whether altogether or in separate molecules makes no dif- ference) so as to produce the observed pressure on the sides of the cubic centimetre. This is the calculation which was first made by Dr. Joule ; and the result is 1859 metres per second. This is what we are accustomed to call a great velocity. It is greater than any velocity obtained in artillery practice. The velocity of other gases is less, as you will see by the Table; but in all cases it is very great as compared with that of bullets. We have now to conceive the molecules of the air in this hall flying about in all directions at a rate of about seventy miles in a minute. If all these molecules were flying in the same direction they would constitute a wind blowing at the rate of seventy miles 458 Prof. J. C. Maxwell on Molecules. a minute; and the only wind which approaches this velocity is that which proceeds from the mouth of a cannon. How, then, are you and I able to stand here? Only because the molecules happen to be flying in different directions, so that those which strike against our backs enable us to support the storm which is beating against our faces. Indeed, if this molecular bombard- ment were to cease even for an instant, our veins would swell, our breath would leave us, and we should literally expire. But it is not only against us or against the walls of the hall that the molecules are striking. Consider the immense number of them, and the fact that they are flying in every possible di- rection, and you will see that they cannot avoid striking each other. Every time that two molecules come into collision the paths of both are changed and they go off in new directions. Thus each molecule is continually getting its course altered ; so that, in spite of its great velocity, it may be a long time before it reaches any great distance from the point at which it set out. I have here a bottle containmg ammonia. Ammonia is a gas which you can recognize by its smell. Its molecules have a velocity of six hundred metres per second; so that if their course had not been interrupted by striking against the molecules of air in the hall, every one in the most distant gallery would have smelt ammonia before I was able to pronounce the name of the gas. But instead of this, each molecule of ammonia is so jostled about by the molecules of air that it is sometimes going one way and sometimes another, and, like a hare which is always doubling, though it goes a great pace, it makes very little pro- gress. Nevertheless the smell of ammonia is now beginning to be perceptible at some distance from the bottle. The gas does diffuse itself through the air, though the process is a slow one; and if we could close up every opening of this hall so as to make it air-tight, and leave every thing to itself for some weeks, the: ammonia would become uniformly mixed through every part of the air in the hall. - This property of gases, that they diffuse through each other, was first remarked by Priestley. Dalton showed that it takes place quite independently of any chemical action between the interdiffusing gases. Graham, whose researches were especially directed towards those phenomena which seem to throw light on molecular motions, made a careful study of diffusion, and obtained the first results from which the rate of diffusion could be calculated. Still more recently the rates of diffusion of gases into each other have been measured with great precision by Professor: Loschmidt, of Vienna. He placed the two gases in two similar vertical tubes, the Prof. J. ©. Maxwell on Molecules. 459 lighter gas being placed above the heavier, so as to avoid the formation of currents. He then opened a sliding valve so as to make the two tubes into one; and after leaving the gases to themselves for an hour or so, he shut the valve, and determined how much of each gas had diffused into the other. As most gases are invisible, I shall exhibit gaseous diffusion to you by means of two gases (ammonia and hydrochloric acid) which when they meet form a solid product. The ammonia, being the lighter gas, is placed above the hydrochloric acid with a stratum of air between; but you will soon see that the gases can diffuse through this stratum of air and produce a cloud of white smoke when they meet. During the whole of this process no currents or any other visible motion can be de- tected. Every part of the vessel appears as calm as a jar of un- disturbed air. But, according to our theory, the same kind of motion is going on in calm air as in the interdiffusing gases, the only dif- ference being that we can trace the molecules from one place to another more easily when they are of a different nature from those through which they are diffusing. If we wish to form a mental representation of what is going on among the molecules in calm air, we cannot do better than observe a swarm of bees, when every individual bee is flying furiously, first in one direction and then in another, while the swarm, asa whole, either remains at rest or sails slowly through the air. In certain seasons swarms of bees are apt to fly off to a great distance, and the owners, in order to identify their property when they find them on other people’s ground, sometimes throw handfuls of flour at the swarm. Now let us suppose that the flour thrown at the flying swarm has whitened those bees only which happened to be in the lower half of the swarm, leaving those in the upper half free from flour. If the bees still go on flying hither and thither in an irregular manner, the floury bees will be found in continually increasing proportions in the upper part of the swarm till they have become equally diffused through every part of it. But the reason of this diffusion is not because the bees were marked with flour, but because they are flying about. The only effect of the marking i is to enable us to iden- tify certain bees. We have no means of done a select number of molecules of air, so as to trace them after they have become diffused among others, but we may communicate to them some property by which we may obtain evidence of their diffusion. For instance, if a horizontal stratum of air is moving horizon- tally, molecules diffusing out of this stratum into those above 460 Prof. J. C. Maxwell on Molecules. and below will carry their horizontal motion with them, and so tend to communicate motion to the neighbouring strata, while molecules diffusing out of the neighbouring strata into the mo- ving one will tend to bring it to rest. The action between the strata is somewhat like that of two rough surfaces, one of which slides over the other, rubbing on it. Friction is the name given to this action between solid bodies; in the case of fluids it is called internal friction, or viscosity. It is, in fact, only another kind of diffusion—a lateral diffu- sion of momentum ; and its amount can be calculated from data derived from observations of the first kind of diffusion, that of matter. The comparative values of the viscosity of different gases were determined by Graham in his researches on the traus- piration of gases through long narrow tubes; and their absolute values have been deduced from experiments on the oscillation of disks by Oscar Meyer and myself. Another way of tracmg the diffusion of molecules through calm air is to heat the upper stratum of the air in a vessel, and to observe the rate at which this heat is communicated to the lower strata. This, in fact, is a third kind of diffusion—that of energy ; and the rate at which it must take place was calculated from data derived from experiments on viscosity before any direct experiments on the conduction of heat had been made. Professor Stefan, of Vienna, has recently, by a very delicate method, succeeded in determining the conductivity of air; and he finds it, as he tells us, in striking agreement with the value predicted by the theory. » All these three kinds of diffusion (the diffusion of matter, of momentum, and of energy) are carried on by the motion of the molecules. The greater the velocity of the molecules and the further they travel before their paths are altered by collision with other molecules, the more rapid will be the diffusion. Now we know already the velocity of the molecules ; and therefore, by experiments on diffusion, we can determine how far, on an average, a molecule travels without striking another. Professor Clausius, of Bonn, who first gave us precise ideas about the motion of agitation of molecules, calls this distance the mean path of a molecule. I have calculated, from Professor Lo- schmidt’s diffusion-experiments, the mean path of the mole- cules of four well-known gases. The average distance travelled by a molecule between one collision and another is given in the Table. It is a very small distance, quite imperceptible to us even with our best microscopes. Roughly speaking, it 1s about. the tenth part of the length of a wave of light, which you know is a very small quantity. Of course the time spent on so short a path by such swift molecules must be very small. I have eal- Prof. J. C. Maxwell on Molecules. 461 culated the number of collisions which each must undergo in a second. They are given in the Table, and are reckoned by thousands of millions. No wonder that the travelling power of the swiftest molecule is but small when its course is completely changed thousands of millions of times in a second. The three kinds of diffusion also take place in liquids; but _the relation between the rates at which they take place is not so simple as in the case of gases. The dynamical theory of liquids is not so well understood as that of gases; but the principal dif- ference between a gas and a liquid seems to be that in a gas each molecule spends the greater part of its time in describing its free path, and is for a very small portion of its time engaged in encounters with other molecules ; whereas in a liquid the molecule has hardly any free path, and is always in a state of close encounter with other molecules. Hence in a liquid the diffusion of motion from one molecule to another takes place much more rapidly than the diffusion of the molecules themselves, for the same reason that it is more expeditious in a dense crowd to pass on a letter from hand to hand than to give it to a special messenger to work his way through the crowd. I have here a jar, the lower part of which contains a solution of copper sulphate, while the upper part con- tains pure water. It has been standing here since Friday, and you see how little progress the blue liquid has made in diffu- sing itself through the water above. ‘The rate of diffusion of a solution of sugar has been carefully observed by Voit. Com- paring his results with those of Loschmidt on gases, we find that about as much diffusion takes place in a second in gases | as requires a day in liquids. The rate of diffusion of momentum is also slower in liquids than in gases, but by no means in the same proportion. The same amount of motion takes about ten times as long to subside in water as in air, as you will see by what takes place when I stir these two jars, one containing water and the other air. There is still less difference between the rates at which a rise of temperature is propagated through a liquid and through a gas. In solids the molecules are still in motion, but their motions are confined within very narrow limits. Hence the diffusion of matter does not take place in solid bodies, though that of motion and heat takes place very freely. Nevertheless certain liquids can diffuse through colloid solids, such as jelly and gum ; and hydrogen can make its way through iron and palladium. We have no time to do more than mention that most won- derful molecular motion which is called electrolysis. Here is an electric current passing through acidulated water, and causing oxygen to appear at one electrode and hydrogen at the other. 462 Prof. J. C. Maxwell on Molecules. In the space between the water is perfectly calm; and yet two opposite currents of oxygen and of hydrogen must be pass- ing through it. The physical theory of this process has been studied by Clausius, who. has given reasons for asserting that im ordinary water the molecules are not only moving, but every now and then striking each other with such violence that the oxygen and hydrogen of the molecules part company and dance about through the crowd, seeking partners which have become disso- ciated in the same way. In ordinary water these exchanges produce, on the whole, no observable effect ; but no sooner does the electromotive force begin to act than it exerts its guiding in- fluence on the unattached molecules, and bends the course of each toward its proper electrode till the moment when, meeting with an unappropriated molecule of the opposite kind, it enters again into a moreor less permanent union with it till it is again dissociated by another shock. Electrolysis, therefore, is a kind of diffusion assisted by electromotive force. Another branch of molecular science is that which relates to the exchange of molecules between a liquid and a gas. It includes the theory of evaporation and condensation, in which the gas in question is the vapour of the liquid, and also the theory of the absorption of a gas by a liquid of a different sub- stance. The researches of Dr. Andrews on the relations be- tween the liquid and the gaseous state have shown us that though the statements in our elementary text-books may be so neatly expressed as to appear almost self-evident, their true interpretation may involve some principle so profound that, till the right man has laid hold of it, no one ever suspects that any thing is left to be discovered. These, then, are some of the fields from which the data of molecular science are gathered. We may divide the ultimate results into three ranks, according to the completeness of our knowledge of them. To the first rank belong the relative masses of the molecules of different gases, and their velocities in metres per second. These data are obtained from experiments on the pressure and density of gases, and are known to a high degree of precision. In the second rank we must place the relative size of the mo- lecules of different gases, the length of their mean paths, and the number of collisions in a second. These quantities are de- duced from experiments on the three kinds of diffusion. Their received values must be regarded as rough approximations till the methods of experimenting are greatly improved. There is another set of quantities, which we must place in the third rank, because our knowledge of them is neither precise, as in the first rank, nor approximate, as in the second, but is only Prof. J. C. Maxwell on Molecules. 463 as yet of the nature of a probable conjecture. These are :—the ab- solute mass of a molecule, its absolute diameter, and the number of molecules in a cubic centimetre. We know the relative masses of different molecules with great accuracy ; and we know their relative diameters approximately. From these we can de- duce the relative densities of the molecules themselves. So far we are on firm ground. The great resistance of liquids to compression makes it pro- bable that their molecules must be at about the same distance from each other as that at which two molecules of the same sub- stance in the gaseous form act on each other during an encounter. This conjecture has been put to the test by Lorenz Meyer, who has compared the densities of different liquids with the calcu- lated relative densities of the molecules of their vapours, and has found a remarkable correspondence between them. Now Loschmidt has deduced from the dynamical theory the fol- lowing remarkable proportion :—As the volume of a gas is to the combined volume of all the molecules contained in it, so is the mean path of a molecule to one eighth of the diameter of a molecule. Assuming that the volume of the substance, when reduced to the liquid form, is not much greater than the combined volume of the molecules, we obtain from this proportion the diameter of a molecule. In this way Loschmidt, in 1865, made the first estimate of the diameter of a molecule. Independently of him and of each other, Mr. Stoney in 1868, and Sir W. Thomson in 1870, published results of a similar kind, those of Thomson being deduced not only in this way, but from considerations derived from the thickness of soap-bubbles and from the electric properties of metals. According to the Table, which I have calculated from Loschmidt’s data, the size of the molecules of hydrogen is such that about two millions of them in a row would occupy a milli- metre, and a million million million millions of them would weigh between four and five grammes. In a cubic centimetre of any gas at standard pressure and temperature there are about nineteen million million million molecules. All these numbers of the third rank are, I need not tell you, to be regarded as at present conjectural. In order to warrant us in putting any confidence in numbers obtained in this way, we should have to compare together a greater number of independent data than we have as yet obtained, and to show that they lead to consistent results. Thus far we have been considering molecular science as an Inquiry into natural phenomena. But though the professed aim of all scientific work is to unravel the secrets of nature, it has another effect, not less valuable, on the mind of the worker. 464: Prof. J. C. Maxwell on Molecules. It leaves him in possession of methods which nothing but scien- tific work could have led him to invent ; and it places him in a position from which many regions of nature, besides that which he has been studying, appear under a new aspect. The study of molecules has developed a method of its own, and it has also opened up new views of nature. When Lucretius wishes us to form a mental representation of the motion of atoms, he tells us to look at a sunbeam shining through a darkened room (the same instrument of research by which Dr. Tyndall makes visible to us the dust we breathe), and to observe the motes which chase each other in all directions through it. This motion of the visible motes, he tells us, 1s but a result of the far more complicated motion of the invi- sible atoms which knock the motes about. In his dream of nature, as Tennyson tells us, he “ Saw the flaring atom-streams And torrents of her myriad universe, Ruining along the illimitable inane, Fly on to clash together again, and make Another and another frame of things For ever.” And it is no wonder that he should have attempted to burst the bonds of Fate by making his atoms deviate from their courses at quite uncertain times and places, thus attributing to them a kind of irrational free will, which on his material- istic theory 1s the only explanation of that power of voluntary action of which we ourselves are conscious. ? As long as we have to deal with only two molecules, and have all the data given us, we can calculate the result of their encounter; but when we have to deal with millions of mole- cules, each of which has millions of encounters in a second, the complexity of the problem seems to shut out all hope of a legi- timate solution. The modern atomists have therefore adopted a method which is, I believe, new in the department of mathematical physics, though it has long been in use in the section of statistics. When the working members of Section F get hold of a report of the census or any other document containing the numerical data of economic and social science, they begin by distributing the whole population into groups, according to age, income-tax, education, religious belief, or criminal convictions. The number of dividuals is far too great to allow of their tracing the his- tory of each separately ; so that, in order to reduce their labour within human limits, they concentrate their attention on a small number of artificial groups. The varying number of individuals in each group, and not the varying state of each individual, is the primary datum from which they work. Prof. J. C. Maxwell on Molecules. 465 This of course is not the only method of studying human nature. We may observe the conduct of individual men and compare it with that conduct which their previous character and their present circumstances, according to the best existing theory, would lead us to expect. Those who practise this method endeavour to improve their knowledge of the elements of human nature in much the same way as an astronomer cor- rects the elements of a planet by comparing its actual position with that deduced from the received elements. The study of human nature by parents and schoolmasters, by historians and statesmen is therefore to be distinguished from that carried on by registrars and tabulators, and by those statesmen who put their faith in figures. The one may be called the historical, and the other the statistical method. The equations of dynamics completely express the laws of the historical method as applied to matter; but the application of these equations implies a perfect knowledge. of all the data. But the smallest portion of matter which we can subject to ex- periment consists of millions of molecules, not one of which ever becomes individually sensible to us. We cannot, therefore, ascer- tain the actual motion of any one of these molecules; so that we are obliged to abandon the strict historical method and to adopt the statistical method of dealing with large groups of molecules. The data of the statistical method as applied to molecular science are the sums of large numbers of molecular quantities. In studying the relations between quantities of this kind we meet with a new kind of regularity, the regularity of averages, which we can depend upon quite sufficiently for all practical purposes, but which can make no claim to that character of ab- solute precision which belongs to the laws of abstract dynamics. Thus molecular science teaches us that our experiments can never give us any thing more than statistical information, and that no law deduced from them can pretend to absolute preci- sion. But when we pass from the contemplation of our experi- ments to that of the molecules themselves, we leave the world of chance and change, and enter a region ‘where every thing is cs and immutable. _ The molecules are conformed to a constant type with a preci- a which is not to be found in the sensible properties of the bodies which they constitute. In the first place, the mass of each individual molecule and all its other properties are abso- lutely unalterable. In the second place, the properties of all molecules of the same kind are absolutely identical. Let us consider the properties of two kinds = molecules, those of oxygen and those of hydrogen. Phil. Mag. 8. 4. Vol. 46. No. 308. Dec. 1873. 21 466 Prof. J. C. Maxwell on Molecules. We can procure specimens of oxygen from very different sources—from the air, from water, from rocks of every geo- logical epoch. The history of these specimens has been very different ; and if during thousands of years difference of cir- cumstances could produce difference of properties, these speci- mens of oxygen would show it. In hke manner we may procure hydrogen from water, from coal, or, as Graham did, from meteoric iron. Take two litres of any specimen of hydrogen, it will combine with exactly one litre of any specimen of oxygen, and will form exactly two litres of the vapour of water. Now, if during the whole previous history of either specimen, whether imprisoned in the rocks, flowing in the sea, or careering through unknown regions with the meteorites, any modification of the molecules had taken place, these relations would no longer be preserved. But we have another and an entirely different method of comparing the properties of molecules. ‘The molecule, though indestructible, is not a hard rigid body, but is capable of internal movements ; and when these are excited, it emits rays, the wave- length of which is a measure of the time of vibration of the mo- lecule. By means of the spectroscope the wave-lengths of different kinds of light may be compared to within one ten-thousandth part. In this way it has been ascertained not only that mole- cules taken from every specimen of hydrogen in our laboratories have the same set of periods of vibration, but that light having the same set of periods of vibration is emitted from the sun and from the fixed stars. We are thus assured that molecules of the same nature as those of our hydrogen exist in those distant regions, or at least did exist when the light by which we see them was emitted, . From a comparison of the dimensions of the buildings of the Egyptians with those of the Greeks, it appears that they have a common measure. Hence, even if no ancient author had re- corded the fact that the two nations employed the same cubit as a standard of length, we might prove it from the buildings them- selves. We should also be justified in asserting that at some time or other a material standard of length must have been carried from one country to the other, or that both countries had ob- tained their standards from a common source. But in the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another; and yet this light, which is to us the sole evidence of the existence of these Prof. J. C. Maxwell on Molecules. 4.67 distant worlds, tells us also that each of them is built up of mo- lecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arc- turus, executes its vibrations in presisely the same time. Each molecule, therefore, throughout the universe bears 1m- pressed on it the stamp of a metric system as distinctly as does the metre of the Archives at Paris or the double royal cubit of the Temple of Karnac. No theory of evolution can be formed to account for the simi- larity of molecules ; for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction. None of the processes of nature, since the time when nature began, have produced the slightest difference in the properties of any molecule. We are therefore unable to ascribe either the existence of the molecules or the identity of their properties to the operation of any of the causes which we call natural. On the other hand, the exact equality of each molecule to all others of the same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article, and pre- cludes the idea of its being eternal and self-existent. Thus we have been led, along a strictly scientific path, very near to the point at which science must stop. Not that science is debarred from studying the internal mechanism of a molecule which she cannot take to pieces, any more than from investiga- ting an organism which she cannot put together. But in tracing back the history of matter, science is arrested when she assures herself, on the one hand, that the molecule has been made, and on the other, that it has not been made by any of the processes we call natural. | Science is incompetent to reason upon the creation of matter itself out of nothing. We have reached the utmost limit of our thinking faculties when we have admitted that because matter cannot be eternal and self-existent it must have been created. It is only when we contemplate, not matter in itself, but the form in which it actually exists, that our mind finds something on which it can lay hold. That matter, as such, should have certain fundamental pro- perties—that it should exist in space and be capable of motion, that its motion should be persistent, and so on, are truths which may, for any thing we know, be of the kind which metaphysi- cians call necessary. We may use our knowledge of such truths for purposes of deduction ; but we have no data for speculating as to their origin. But that there should be exactly so much matter and no more 212 468 Prof. J. C. Maxwell on Molecules. in every molecule of hydrogen is a fact of a very different order. We have here a particular distribution of matter—a collocation —to usé the expression of Dr. Chambers, of things which we have no difficulty in imagining to have been arranged otherwise. The form and fiencene of the orbits of the planets, for in- stance, are not determined by any law of nature, but depend upon a particular collocation of matter. The same is the case with respect to the size of the earth, from which the standard of what is called the metrical system has been derived. But these astronomical and terrestrial magnitudes are far inferior in scien- tific importance to that most fundamental of all standards which forms the base of the molecular system. Natural causes, as we know, are at work which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages ca- tastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built—the foundation stones of the material uni- verse—remain unbroken and unworn. They continue this day as they were created—perfect in number and measure and weight; and from the ineffaceable characters impressed on them we may learn that those aspirations after accuracy in measurement, truth in statement, and justice in action, which we reckon among our noblest attributes as men, are ours because they are essential constituents of the image of Him who in the beginning created, not only the heaven and the earth, but the materials of which heaven and earth consist. - Tasie of Molesuli Data. ie al Car- | Car- xygen.| bonic | bonic igges. oxide. | acid. ‘Mass of molecule (hydrogen = 1) ] 16 14 22 op Velocity, mean (square metres | )g59 465 | 497 396 : per second), at 0° C. ......... if Rank {| Mean path, tenth-metres...... 965 560 482 379 II. | Collisions in asecond(millions)| 17750 | 7646 | 9489 | 9720 Rank f{ Diameter, tenth-metres......... 58 7°6 8-3 9:3 Ill. Mass, twenty-fifth grammes... 46 | 736 644 | 1012 ! ok Mr. O. Heaviside on the Differential Galvanometer. 469 TaBLe of Diffusion. (Centimetre)? ~—___———__*“_ measure. Second Caleulated.| Observed. A ae 07086 | 0:7214 \ USO U5 eae 0°6519 06422 | SS 0 a 0°5575 =| 05558 ! Diffusion of matter observed mee i... 0-1807 | 01802 ¢ by Loschmidt. 7 re 01427 | 0-149 | 7 Lia ae 01386 01406) | 2 eo es Serer | 1:2990 =| :4-49 Miateve sae ietek fasta. be. 00-1884 | 0-213 Diffusion of momentum oS a 0°1748 =| 0-212 (Graham and Meyer). SR ee 0:1087 | 0-1 17 | an SiaieDuataicletnialy sisipi.sls'cicicis\), | |, .wjs,e'e'e 6,0 ee Jai Diffusion of temperature 2 LE et ee a el eee 1:077 ie tev ed hy Steliti Se eee Maes 0-183 eae Cane-sugar in water... ......... 0-00000865 || y ‘t (or ina day ......... fae dae 2 0:3144) oe | Salt in water ......... he setae 0-000001]16 | Fick. | LXI. On the Differential Galvanometer. By Outver Heavisrpz, Newcastle-on-Tyne*. HE great similarity between the systems of resistance-mea- suring by means of the differential galvanometer and Wheatstone’s vridge, the latter having been probably suggested by the former, must have struck Sey) one who has had any thing to do with them. In each case do we make one resistance a fourth proportional to three others, and, knowing the three, deduce the fourth. As in the bridge for every resistance to be measured there is a certain arrangement of the three other sides which gives the most sensitive balance, so with the differential galvanometer there must be a best arrangement for any parti- cular case, which it is the object of this paper to point out. The expression for the strength of the current through the galvanometer in Wheatstone’s bridge is ad —be ‘a+b+e+d : (1) (a+6)(c+d) 4 eer c)(6+ d) t ear os < teed oy (where v is the electromotive force of the battery, H the current * Communicated by the Author. ee 470 Mr. O. Heaviside on the Differential Galvanometer. through e, and the resist- ances as in the diagram) when at a balance and therefore ad—bc a vanish- ing quantity. To deduce from this the expression for the force acting on the needle in the differential galvanometer, let a and 6 be the two coils. Then, in the first place, by Kirchhoff’s rule, Aa—Bb=Ee, where A, B, E are the currents in a, 6, and e respectively; and next, that as e is absent in the differential-galvanometer arrange- ment, we must make e infinite. Therefore, multiplying (1) by e and making e= o, we obtain j ad—be “atb+c4+d (2) (angina > eee at+b+ctd for the differential galvanometer. This can, of course, be ob- tained independently of any consideration of Wheatstone’s bridge, but makes it evident that the best arrangement of the differential galvanometer with a given battery may be derived from the Wheatstone’s-bridge formule by making e infinite in them. These formule are as follows (Phil. Mag. February 1878). When ¢, d, e, and f are fixed, ony [2 aETER , dite dacene Aa— Bb= (3) we fh in EEE cd-+df+fe eae ctd+e°”’ and if c be not arbitrarily fixed, a=/ ef, *) b=a/ ao 48, | pee 8s ae aren eal #525 which is the most sensitive arrangement possible with a given Mr. O. Heaviside on the Differential Galvanometer. 471 galvanometer and battery. Finally, if the best resistances for the galvanometer and battery are also to be employed, we must make every branch of the bridge of the same resistance, viz. that of d, the resistance to be measured. Making e=o in (3) and (4), they become a=/'5 (od+ df + fo, (cd+df+fe), . (5) pe AJ" (cd +f +fo © (cd + df + fe) and w= 00, b=/ddif,s - 2 + + te ee ©) c= a; which may also be obtained by differentiation from (2). These formule, (5) and (6), would not be of any particular use if we had no means of varying at will the resistance of the coils aand 6. This cannot be accomplished directly without consi- derable complication; but by means of shunts the same end may be reached. Thus, using (5), if the coils of our galvanometer have resistances greater than those best suited for the particular resist- ance to be measured, by means of shunts we may reduce their resistances to the required extent. And here a remarkable pecu- larity presents itself. In general when a galvanometer is shunted, its resistance and sensibility are reduced and i in the same propor- tion. Not so with the differential galvanometer ; for its sensi- tiveness will be increased or reduced by shunts according as the normal resistances of its coils are greater or less than their best values in the particular case under consideration. The accuracy of (5) may be easily verified experimentally. Proceeding to examine (6), we meet practical impossibilities, and can only carry it out by making the resistance of the coil a as great as possible by not shunting it. But as the values of 6 and ¢ in (6) correspond to a= o, it will be necessary to find their values when a=a. Therefore, regarding both a and d as constant, and 0 and ¢ variable, subject to the condition ad—bc=0, we shall find by differentiating (3) that c =a/ai.0t8 Te o=a/ aa 2th —s vives the most sensitive arrangement for measuring a resistance d with a battery whose resistance 1s f. (7) 472 Prof. W. F. Barrett on certain remarkable Molecular It is an evident conclusion that differential galvanometers in- tended for measuring resistances comprised within wide limits, both high and low, should have coils of long fine wire, having necessarily a high resistance ; for a galvanometer with coils of short and thick wire is only suitable for measuring small resist- ances; whereas if it have coils of fine wire it is suitable for both high and low resistances—for the latter by shunting. LXII. On certain remarkable Molecular Changes occurring m Iron Wire at alow red Heat. By W. F. Barrett, F.CS., Professor of Experimental Physics in the Royal College of Science, Dublin*. N the ‘ Proceedings of the Royal Society’ for January 28, 1869, Mr. Gore published the important fact, that when an iron wire is heated to bright incandescence and then allowed to cool, a momentary elongation, or, as Mr. Gore believed, di- minution of cohesion, of the wire occurs just after it has besun to contract by coolmg. The main pomts in Mr. Gore’s paper are as follows :—A thin iron wire fixed at one end to a binding- screw 1s attached at the other to an index which multiplies any motion of the wire; the wire is strained horizontally by a feeble spring; and matters are so arranged that the wire can be heated by an electric current or by a row of gas-jets. When heated, the wire expands and the spring pulls the index over. A sketch of the instrument is given in the Philosophical Magazine for Jaly 1869. Mr. Gore states that no anomalous action is observed on heating the wire to bright incandescence ; but when the heating is discontinued and cooling begins, the index moves back until a moderate red heat is attained, when suddenly the pointer gives a jerk or kick, mdicating a momentary elongation of the wire during the progress of its contraction. This effect is perfectly certain, and always occurs at this particular temperature. Mr. Gore states that ivon wire of a certain thinness and a certain tension of the spring is necessary, and that the phenomenon is apparently confined to cooling tron, no such change being evi- dent during the heating or cooling of wires drawn from the wide range of other metals he has examined. Further, Mr. Gore has investigated the production of induced currents during the cooling of magnetized iron bars, one portion of which had been heated to redness; and the result showed that the iron bar “‘snddenly increased in magnetic capacity during cooling at a particular temperature of moderate red heat.” Having occasion to show Mr. Gore’s discovery in the course of a lecture delivered some eighteen months ago to the Dublin 5: Communicated by the Author. Changes occurring in Iron Wire at a low red Heat. 478 Royal Society, Mr. Gore kindly furnished me with his own ap- paratus. By attaching to the movable cross piece a light mirror, from which a brilliant ray of light was reflected to a scale on a distant wall, the effect sought was not only vastly magnified, but one or two new facts also revealed themselves. (i) During the heating of the wire a slight and momentary re- trogression of the beam was noticed at the temperature corre- sponding to the powerful jerk that occurred on cooling: some smaller tremblings of the beam were noticed at higher and lower temperatures; but these seemed due to irregular heating and cooling. (11) It was evident that the anomalous deportment of the iron occurred approximately at the critical temperature when iron undergoes its principal magnetic change. Mr. Gore having stated in a letter to me, written in May 1872, that he had no intention at present of making any more experiments in the direction of his discovery, and adding the subject was quite open to me, I felt at liberty to pursue the inquiry thus suggested. It was not, however, till this autumn that I could find the necessary leisure; and the follow- ing results were then obtained. My best thanks are here due to Professor Guthrie for his hearty welcome to use his laboratory at South Kensington, where the experiments have been conducted. I Employing twenty Grove cells, I have had no difficulty in obtaining this anomalous behaviour with moderately thick iron wires. These have the advantage of allowing the effect to be studied more leisurely, the phenomenon sought for occurring several seconds after the interruption of the current. The tem- perature at which the momentary jerk occurs seems to be lower in thick wires than in thin ones, the critical point being a mode- rately bright or cherry-red heat in thin iron wire, say No. 23, and a very dull red heat in thick wire, say No. 20; the latter wire is, in fact, in the stage just preceding obscurity when the effect occurs. The internal temperature of the thicker wires is no doubt masked by the cooling of their surface, whereas in thin wires the cooling throughout is extremely rapid, and moreover the transitions of temperature cannot be so well noted. IT. With No. 21 hard iron wire I have had no difficulty in ob- taining the jerk during heating. In this case the movement is in the reverse direction of that which occurs during cooling ; that is to say, it indicates a momentary retraction, occurring, as closely as can be judged, at the same temperature at which the elongation takes place in cooling. | — 474 Prof. W. F. Barrett on certain remarkable Molecular With a steel wire 25 centims. long and No. 22 B wire gauge the following observations were made—a battery of ten Grove cells being used, capable of raising this length of wire to a bright white heat. The imdex stood at 0 on the scale before contact was made, the wire being cold. After contact, as the wire became heated, the index regularly passed to 24; here it promptly retreated to 22, then steadily passed onwards to 34, the wire now glowing white-hot. Breaking contact, the index returned regularly to 20, then rose suddenly to 27, after which it continued its backward course till it finally rested at 2, the wire now being cold again. The action of the spring stretches the wire when hot, hence the index does not return to zero. Allowing for this stretching, the figures would be proportionally lower where the jerk occurs on cooling, viz. 18 to 25. Here are two more out of many experiments with the same wire:— ; 1. Wire cold ; contact made; index rose from 0 to 25, jerked back to 23, then rose to 83; wire bright red. Wire bright red; contact broken; mdex fell from 33 to 19, jerked forward to 25, then fell to 4; wire cold. 2. Wire cold; contact made ; index rose from 0 to 25, jerked back to 284, then rose to 32; wire bright red. Wire bright red; contact broken; index fell from 32 to 20, jerked forward to 243, then fell to 4; wire cold. The following diagram (fig. 1) illustrates the motion of the index on heating and cooling the wire. Fig. I. ‘Origa Tred eo" Releasing the tension of the spring, the forward motion on Changes occurring in Iron Wire at a low red Heat. 475 cooling is, as might be expected, much lessened, whilst the jerk back is scarcely affected. Increasing the tension of the spring, the forward jerk is correspondingly increased and the back- ward jerk diminishes, and can be made to disappear. Il. Is this anomalous action, then, due to a momentary change in the cohesion of the wire? If so, at a certain point during the progress of heating, the molecules of iron have a sudden ac- cession in elasticity, and at an approximately corresponding point during cooling, they incur a sudden Joss in elasticity. — If, however, this molecular change be entirely due to alteration in cohesion, then the removal of the spring ought to cause the anomalous behaviour to disappear. But it does not. Without the spring, an iron wire can be seen by the naked eye to undergo a momentary contraction during heating, and a momentary and more palpable elongation during cooling*. Fixing one end of the wire and bending the other extremity at right angles so that it may dip into a trough of mercury, and thus preserve contact with the battery, both actions can be seen; the sudden outward thrust on cooling is very conspicuous. Heating the wire by gas-flames, the same result is given. : All kinds of iron do not exhibit this behaviour ; and some show itin a more or less marked degree. I have not been able to detect any change, in heating or cooling, in certain specimens of good soft iron wire; but in hard iron wire, and notably in steel wire, it is very apparent. The wire, moreover, requires to be raised to a very high temperature before the jerk is seen on cooling. I have not observed the momentary elongation on cooling when the wire has only been heated to a point just beyond that at which it would otherwise occur. The behaviour of iron wires of different degrees of purity and of widely different thicknesses are points I hope to examine in a subsequent inquiry. I may here also mention that the precise magnetic condition of the iron at the moment at which the jerk occurs, together with its electric resistance and its thermo-electric position+, are ques- tions upon which I have already made some experiments, but not enough to justify the publication of any results at present. * A striking lecture experiment may be made by simply stretching some harpsichord-wire between two supports, and heating the wire to whiteness by acurrent. On allowing the wire to cool, it gradually straightens itself till just as it reaches the point of obscurity, when it suddenly drops for an mstant. It is extraordinary that this action has not been frequently observed. t Professor Tait’s remarkable investigation on this point is alluded to subsequently. TTR ARR eee 476 Prof. W. F. Barrett on certain remarkable Molecular Ly. On September 12th I was examining the condition of the wire in a darkened room, when a new and unexpected change revealed itself. During the cooling of the wire it was found that just as it reached a very dull red heat, a sudden accession of temperature occurred, so that it glowed once more with a bright red heat. Uluminating the index and scale of the appa- ratus, which was watched by an assistant, it was at once found that the reheating of the wire occurred simultaneously with the mo- mentary elongation. Necessarily no change of this kind can be ob- served on heating; but the reglowing of the wire on cooling is most uniform and conspicuous*. The wire must first be heated to whiteness ; and then, being allowed to cool, just as it reaches a point of barely visible redness a sudden cherry-red glow takes - place, passing as a wave of heat from one end of the wire to the other, or from both ends to the centre. The measured progress of this wave of temperature along the wire is extremely beautiful to observe. On first sending the current through the wire, the heating begins at one extremity and runs along to the other; on breaking contact, this reheating sweeps along the wire im the contrary direction. This peculiar movement, therefore, may be caused by the unequal thickness of the wire; though I do not think this is the explanation, as the reheating would then move in the same direction as the heating (namely, from the thinner to the thicker parts of the wire), and this is not the case. I hope shortly to investigate this further. | When the wire is heated by a row of gas-flames, the same re- sults take place, although the heating by the battery is a far neater and more satisfactory way. It is a real accession of temperature, a sudden increase in thermal as well as luminous radiation. This is evident from the following experiment. A wide glass tube (fig. 2) was fitted with corks at each end, so that the iron wire could be enclosed air-tight within the tube. At one end the cork was perforated to allow the insertion of a narrow glass tube bent at right angles, the lower end of which dipped into coloured water. On heating the wire to whiteness by the current, some of the en- closed air was expelled, and on breaking contact the liquid rushed up the tube, but midway suddenly stopped in its course, and was depressed some two inches. At this moment the assistant, who was watching the wire, gave notice the wire drooped and glowed again. ‘There is no difficulty in repeating this experi- * Nevertheless during heating I thought [ detected a momentary pause in the progyess of the reddening of the wire, just after incandescence had been reached. Changes occurring in Iron Wire at a low red Heat. = 477 ment, nor in exhibiting its action to a large class. Wherever the momentary expansion of the wire is feeble or absent, there t likewise this recalescence, as it might perhaps be termed, 1s also feeble or absent. I am anxious to procure wires of nickel and cobalt; for, from the reasons set forth in another paper, the action might certainly be expected to occur in those metals as well as in iron, probably with nickel at a lower and with cobalt at a higher temperature than in the case of iron. Ve Besides the molecular changes here detailed, there are indica- tions of the existence of other disturbances during the heating and cooling of an iron wire, notably the emission of a peculiar dry crackling sound, like the crepitation that occurs on magnetizing and demagnetizing iron; and this, too, occurs at the critical temperature. But so many matters of interest have arisen du- ring this investigation, that the present paper can only be regarded as the results of a preliminary inquiry. VI. The molecular disturbances to which iron is thus seen to be subject, at a particular temperature, are no doubt associated with an even wider range of phenomena than are here indicated. Professor Tait’s experiments, which were read by me after most of the foregoing facts had been obtained, show that iron exhibits a most remarkable and anomalous thermo-electric deportment at ared heat. In his Rede Lecture* that eminent physicist points out that “ the cause of this is that while, as Sir W. Thomson dis- covered, the specific heat of electricity in iron is negative at ordinary temperatures, it becomes positive at some temperature | * Nature, June 12, 1873. 478 Prof. W. F. Barrett on the Relationship near low red heat, and remains positive till near the melting-point of iron, where it appears possible from some of my experiments that it may again change sign.” And further on Professor Tait suggests the idea “that iron becomes, as it were, a different metal on being raised above a certain temperature. This may possibly have some connexion with the ferricum and ferrosum of the chemist, with the change of magnetic properties of iron, and of its electric resistance at high temperatures.” Professor Tait adds the interesting fact that he has found an anomalous thermo- electric behaviour in nickel similar to that in iron, and, as one might venture to anticipate, at a much lower temperature. Thus two separate lines of mquiry have converged on the same point—namely, that a profound molecular disturbance takes place in iron at a low red heat. In connexion with future theories of magnetism, this fact is likely to be of considerable © importance, inasmuch as it seems probable that this disturb- ance is confined to the magnetic metals, and that it occurs at or about the temperature when they leave or reenter this condition. LXIII. On the Relationship of the Magnetie Metals. By W. F. Barrett, F.C.S.* Bpe remarkable similarity in the chemical and physical pro- perties of the magnetic metals has no doubt often attracted attention ; but lam not aware that any definite collation of these properties has ever been made. This I propose briefly to do in the following paper. The extraordinary homology these metals are thus seen to exhibit furnishes instructive evidence concerning the molecular state of a magnet. By magnetic metals 1 mean those metals which possess magnetic properties under ordinary circumstances—namely, iron, nickel, and cobalt. First we will compare their physical characteristics. The specific gravity of the thirty-eight known metals ranges from lithium 0°59, to platinum 21°5, a difference of nearly 21; whereas the specific gravity of iron is 7°8, nickel 8°3, and cobalt 8°5, an extreme difference of only 0:7. The specific heat of these three metals is also nearly identical ; and their atomic heat is the same. Their conductivity for sound is almost absolutely the same; and so far as their heat and electric conductivity have been determined they are also alike. Their dilatation by heat is the same, and so also is the amount they lengthen by mechanical stram. They belong, I believe, to the same system of erys- tallization, namely the monometric, though too little is known * Communicated by the Author, having been read before the British Association at Bradford, September 1873. ; of the Magnetic Metals. 479 on this point. The enormous cohesive power of iron, nickel, and cobalt in the solid state signalizes these substances as the most tenacious of metals. To overcome this cohesion a very high and somewhat similar temperature is required, and their melting-point is only exceeded by the platinum group of me- tals. Their refractory character renders them not volatile even at the temperature of the hottest furnace. When, however, they are volatilized by means of the electric spark, their in- candescent vapours yield a spectrum which has a close and curious resemblance. This teaches us that the molecules of these bodies, freed from the thrall of cohesion, vibrate in periods which are closely akin. A comparison of the chemical properties of the same metals furnishes a similar result. The ratio of the combining weight of the metallic elements ranges from hthium 7, to bismuth as 210, or a difference of 203. When we compare the magnetic metals, we find the combining weight of iron is 56:0, nickel 58°5, and cobalt 58:5, or a difference of only 2°5. Chemists class these three metals in the same group from the similarity of their chemical behaviour, and also the identity of their combi- ning energy or atomicity. In strong nitric acid iron becomes endowed with a so-called passive condition, not acted upon, as it is in the dilute acid. Likewise I find nickel is capable of assuming a passive state in strong nitric acid. Cobalt, itis true, was violently acted upon ee similar Br caractaners) but that, I believe, was due to the fact that the cobalt contained iron largely, and so an electrolytic action was probably set up. I have been unable to obtain pure cobalt—a very difficult matter, I believe. A series of very similar chemical compounds are formed by these metals, mostly characterized by the brilliancy of their co- lour. The protosalts of iron are generally bluish green, of nickel emerald green, and of cobalt of a rose-colour. It is moreover a well-known fact that this rose-colour of certain co- balt salts passes into a bright green when they are warmed. Now, when the metal cobalt is moderately heated it increases in magnetic power, thus differing from its congeners, iron and nickel, which are in their maximum magnetic condition at the ordinary temperature, and at ordinary temperatures present the ereen-coloured salts*. What has been said concerning the likeness of iron, nickel, and cobalt, in many respects holds true of manganese and chro- mium, also feebly magnetic metals. Placed in the same group _ * The therapeutic effect of the salts of these metals one would expect to be somewhat similar; and in confirmation of this I hear that nickel has lately often been used advantageously to replace the medicinal properties of iron. 480 On the Relationship of the Magnetic Metals. with the former metals chemically, they are physically charac- terized by their extraordinary tenacity and difficult fusibility. Manganese has lately been used to replace nickel in the alloy of German silver, and with excellent results I am informed. It is also worthy of note that the compounds of these five metals are conspicuous by the brilliancy of their colours, all their salts ex- erting a selective absorption on light, and their oxides dissolved in borax yielding well-known and characteristic tints—a com- paratively rare feature outside this group. Further, it is well known that the ores of cobalt and nickel are almost invariably found associated in the earth and with difficulty separated. It is also noteworthy that both nickel and cobalt are usually present in meteoric iron—the average composition of meteorites being 90 per cent. of iron, 8 per cent. of nickel, and 0:5 per cent. of cobalt, curiously enough often with a trace of the other feebly magnetic metals, manganese and chromium. This uniform coincidence in the properties of iron, nickel, and cobalt, suggests the practical inference that nickel and cobalt might be obtained in a malleable and ductile condition when sub-' mitted to a process similar to that by which wrought iron is pro- duced. At present it is impossible to procure nickel or cobalt wire, though there seems no reason why they could not be made if a demand arose. Nickel wire would probably prove very useful from its high tenacity and comparative freedom from oxidation. The following Table sums up some of the most striking points of contact in the physical properties of the three magnetie metals par excellence. Table showing the Physical Relationship of the Magnetic Metals. | Den- . |Specific Dilatation | Conductivity t Sub- | sity. aw heat. |Atomic eT aa. Ee stance.| Water = 8 3 Water| heat. | by by | for heat. | for sound *:| aoa 2 | =1, ae =n heat*. |strain*.| Silver= 1, Arlt) ot | Skee pe eros ake Ca rk iron | 7:8 | 56:0 |0°1188) 6:38 | 0926 | :0387 168 15:3. | Very high. Nickel.| 83 | 58:5 |0-1091| 6:33 | -0899| -03894 ‘131 14:9 “ Cobalt.| 8:5 | 58:5 |0°1070) 6:26 | -0981j| 0436 172 14:2 s From this Table it is evident that the molecular constitution of the magnetic metals is essentially alike, largely differing from bodies which are not magnetic. And this being so, further evi- dence is afforded that the evolution of ordinary magnetic pheno- mena is in some way associated with the peculiar and similar structure of the molecules of iron, nickel, and cobalt. * For the figures in this column I am indebted to a paper by M. A. Masson, in the Annales de Chimie et de Physique for 1858. In the heat column the decimal would, of course, have to be moved four places to the left to express the coefficient for 1° C. The dilatation by strain was of one metre of the body under a weight equal to itself. [ 481 ] LXIV. Intelligence and Miscellaneous Articles. ON VARIOUS CASES OF INTERMISSION OF THE VOLTAIC CURRENT. BY A. CAZIN. we pursuing the researches which I have undertaken on the heat *. of electromagnets, I have had occasion to observe several cases of intermission of the voltaic current, which, I believe, have not Yet been brought into notice. Experiment 1.—A voltaic circuit is formed of 20 average Bunsen elements and a coil of 960 turns containing an iron tube 8 centims. in diameter and about 1 millim. thick. It can be closed or opened at will by means of a platinum point and a layer of mercury, which communicate respectively with each of the rheophores. When the platinum is not in contact with the mercury, and they are put into communication with the armatures of a condenser with a glass plate (armed surface 3 square metres), a continued rustling is heard in the iron nucleus. The same effect is produced when, the condenser being omitted, a layer of alcohol is interposed between the mercury and the platinum poimt. The noise ceases when the alcohol is removed so that the platinum and mercury are sepa- rated by a layer of air, and also when the point is dipped into the mercury. These facts indicate that the current passes through the glass in the first case, and through the alcohol in the second, and that zts passage 1s intermittent. The nucleus of iron undergoes a rapid succession of alternate magnetizations and demagnetizations ; and each demagnetization occasions a faint sound in the nucleus. The rapid succession of these noises constitutes the rustling which is heard. When the iron nucleus resounds, a galvanometer indicates only a continuous current. In fact it cannot indicate any thing else when the intermissions are very close to one another. I think that the cause of the intermission is the condensing action of the glass and the alcohol; when the two faces of the insulating body, which are in contact with the rheophores, have acquired a certain electrie potential, a discharge takes place through the insu- lating layer; the magnetism of the nucleus increases during the charging of the condenser, aud diminishes during its discharge ; the noise is produced during the diminution of the magnetism ; after each discharge a certain time elapses before the condenser is recharged ; and the same phenomenon is reproduced indefinitely. It is readily ascertained that the nucleus resounds during the di- minution of its magnetism: we have only to immerse the platinum point in the mercury, and then withdraw it; at the moment when the spark issues at the point of interruption, a relatively intense sound is heard in the nucleus. It is solely the rupture of the cir- Phil. Mag. 8, 4. Vol. 46. No. 308, Dec. 1873. 2K 482 Intelligence and Miscellaneous Articles. cuit that gives rise to this sound; the closing produces no effect, at least in my apparatus. M. de la Rive, in 18438, discovered that a current interrupted by means of a rheotome produces a sound in the iron of an electromag- net; but I think that the phenomenon I have just described has not been previously signalized. Listening for a sound in thenucleus of an electromagnet may be regarded as a new process of investigation; we have seen that it reveals the intermission of the current in circumstances in which the known methods are insufficient.. I will mention an mstance which shows that this method accords with the others when they can be employed simultaneously. Experiment 2.— When the spark from the rupture of the prece- ding circuit is observed with the aid of the revolving disk, after the manner made known by me to the Academy on the 7th of April last, the spark appears compound. When it bursts in alcohol, and the platinum point and the mercury are connected with the arma- tures of the condenser, the revolving disk shows that the spark 1s composed of four or five successive bright strokes; the mtervals between the strokes diminish from the first onwards. (L have already described the division of this spark by another process, Bulletin de la Société Philomathique, 13th May,*1865; and the journal U’ Institut, 31st May, 1865.) The sound produced by the rupture-spark presents a a similar mode of division; it is the same with that which is heard in the ‘condenser, and with that which takes place in the nucleus: these three sounds are composed exactly in the same manner. The production of a sound in the condenser proves that there is a partial discharge through the imsulating substance, although at no part does this appear to be pierced. The sound of the condenser is augmented by i increasing its sur- face, up to a certain limit which cannot be exceeded. At the same time the spark between the mercury and the platinum point is seen to dimmish. These modifications indicate a change in the distri- bution of the electricity—which could be mathematically analyzed by regarding the alcohol of the interruptor as the insulating plate of a second condenser united to the first by the armatures of the same sign. I think there is no essential difference between the intermission of the current which accompanies the breaking of the circuit in the circumstances I have just described, and that presented we my fir st experiment. Experiment 3.—The platinum point of the mercury Sema is screwed into a fixed nut, so that it can be raised or lowered. The mercury and the point communicate respectively with the armatures of a condenser of 1 square metre surface. The rest of the circuit is arranged as before. The point being dipped into the mercury, is gradually raised until Intelligence and Miscellaneous Articles. 483 the spark springs through the alcohol. The point then remaining fixed, a succession of sparks is set up and persists for a long time. These sparks are lively and sonorous, and can readily be counted. | The level of the mercury visibly oscillates beneath the pont. A possible cause of the oscillation is :—the spark being formed by the vapour of the mercury, the elastic force of this vapour depresses the level of the liquid; this returns to its former level, passes it in virtue of its acquired velocity, and rejoins the platinum point. Fall- ing again, the mercury produces a fresh interruption, and the same phenomenon is repeated. This purely mechanical cause cannot be the only one; for the circumstances favourable to this new mode of automatic interruption are those which accompany the decomposition of the rupture-spark into a small number of successive bright strokes. This correlation is recognized by changing the extent of the condenser, which alters the number of the divisions of the spark. Thus, on continually diminishing the surface of the condenser, the sparks are seen to follow ene another more and more rapidly; and finally, when the condenser is omitted, there is only a crepitating voltaic arc. It is probable that the oscillation-period of the mercury comprises a de- finite number of intermissions in the discharge of the condenser, and that these two causes are in mutual dependence. I believe that the discharge through air, under the form of a voltaic are, and the discharge through glass, of which experi- ment 1 supplies an example, are comparable; and that the well- known crepitations of the voltaic are are due to the same cause as the phenomena of which I have just spoken. All these facts may be brought into connexion by a single proposition: the insertion of a suitable resistance in the voltaic curcmt determines the intermission of the current. 'The laws of the intermission will have to be studied with the interposition of a condenser, because the periods are long enough to be observed with facility. The laws found in this man- ner will afterwards be generalized, and must conduct us to the known laws of the currents which are regarded as continuous. We cannot omit to derive from the whole of these considerations the important conclusion that the current is a succession of modifica- tions accomplished periodically in the curewt.—Comptes Rendus de V Acad. des Sciences, vol. lxxviui. pp. 1095-1098. EXPERIMENTS ON EVAPORATION. BY M. STEFAN. Atmometric experiments have hitherto led to no results expres- sible in the form of laws. The conditions under which they were made were not simple enough; yet they were sufficiently varied. The science of evaporation, especially of the diffusion of vapours, remained an unoccupied field. 2K2 SUhe eet, ee i 484 Intelligence and Miscellaneous Articles. In the experiments whose results are here given, the more vola- tile liquids, and in the first place ether, were employed. In order to avoid the great lowering of the temperature at the surface, nar- row tubes were chosen for evaporating-vessels, instead of the wide vessels hitherto usual. 1. The velocity of the evaporation of a liquid from a tube is inversely poportional to the distance of the level of the liqud from the open end of the tube. This law holds with rigorous exactness when the dis- tance of the level a little exceeds 10 millims. 2. The velocity of the evaporation is independent of the diameter of the tube. This result was obtained from experiments with tubes the diameter of which varied from 0°3 to 8 millims. 3. The velocity of the evaporation increases with the temperature, so far as with this the vapour-pressure of the liquid rises. If p be the maximum of elasticity of the vapour corresponding to the tem- perature of the observation, P the atmospheric pressure under which the liquid evaporates, the velocity of the evaporation is propor- tional to the logarithm of a fraction of which P is the numerator, and P—>p the denominator, If the pressure of the vapour becomes equal to that of the air, this logarithm becomes infinitely great, and sig- nifies that under this condition the liquid boils. . Experiments were also made on evaporation in closed tubes. | If the open end of a tube, the other end of which is closed, be dipped in ether, bubbles form and issue continually from the tube, and, at first, the tumes in which successiwely equal numbers of bubbles form are proportional to the odd numbers. If the immersed tube contains hydrogen instead of air, the same number of bubbles form in one fourth of the time. Hvaporation proceeds iv hydrogen four times as rapidly as in air. The same result was also furnished by an experiment in apparatus in which a liquid can be brought to evaporation in an open tube in various gases. It consists of a T-shaped glass tube; into its ver- tical arm enters the tube containing the liquid to be evaporated ; through the horizontal cross-piece a continual current of the gas is conducted. : If a tube provided with a cock be dipped with the cock open in ether, the level of the liquid within the tube will sink below that outside ; and, at first, the depths to which the mterror level sinks below the exterior in definite times are as the square-roots of those tumes.— Sitzung der math.-naturw. Classe der Kaiserl. Akad. d. Wissensch. en Wien, Oct. 23, 1873. 485 INDEX to VOL. XLVI. ABBOTT (T. K.) on the “black drop ” in the transit of Venus, 375. Airy (G. B.) on the directive power of large steel magnets and of gal- vanic coils in their action on exter- nal small magnets, 221. oe on the direct synthesis of, 336. Atmosphere, on the possible existence of a lunar, 411. Atwood’s machine, on the determi- nation of the friction-resistances in, 330. Barrett (Prof. W. F.) on molecular changes occurring in iron wire at a low red heat, 472; on the relation- ship of the magnetic metals, 478. Barthélemy (A.) on the passage of gases through “colloid membranes of vegetable origin, 251. Bauer (K. L.) on the filling of vessels with a very narrow tube, especially the Cartesian diver, 334. Bees, on the form of the cells of, 103. Bender (C.) on the determination of the friction-resistances in Atwood’s machine, 330. Bickerton (A. W.) on a new relation between heat and static electricity, 450. Birt (W. R.) on the moon’s libration, 305. Books, new:—Proctor's Light Science for Leisure Hours, 77; Selections from the Portfolio of the Editor of the Lunar Map, 79; Astronomical and Meteorological Observations made in 1870 at the United States Naval Observatory, 171; Birt’s Mare Serenitatis, 250; Proctor’s The Moon, her Motions, &c., 312; Williamson’s Elementary Treatise on the Differential Calculus, 406. Camphor, on the motions of, on the surface of water, 376. Cartesian diver, on the, 334. Cazin (A.) on various cases of inter- mission of the voltaic current, 481. Central motions, on the relations be- tween the characteristic quantities occurring in, l. Challis (Prof.) on the principles of hydrodynamics, 159, 309, 446; on integrating differential equations by factors and differentiation, 388. Champion (M.) on explosions pro- duced by high tones, 256. Charles (Dr. T. C.) on the compesi- tion of certain coals from co. Tyrone, and of a lignite from Bal- lintoy, 244. Chautard (J.) on the spectrum of chlorophyl, 335. Chemistry, on statical and dynamical ideas in, 398. Chlorophyl, on the spectrum of, 335. Circles, on a new method for examin- ing the divisions of graduated, 174. Circuits, on induced currents and de- rived, 84. Clausius (Prof. R.) on the relations between the characteristic quanti- ties occurring in central motions, 1; on a new mechanical theory rela- tive to stationary motions, 236, 266. Coal, analyses of, from the coal-mea- sures of co. Tyrone, 244. Colloid membranes of vegetable ori- gin, on the passage of gases through, 251. Culley (R. S.) on Jamin’s compound magnets, 176. Currents, on induced, 84. Dana (Prof. J. D.) on some results of the earth’s contraction from cooling, and on the origin of mountains, 41, 131, 210, 276, 363. Diffraction-grating, on the use of a, in a solar spectrosvope, 87. 486 Diffraction-spectrum photography, on, 417. Donkin (W. F.) on the direct syn- thesis of ammonia, 336. Draper (Prof. H.) on diffraction- spectrum photography, 417. Earth, on some results of the con- traction of the, 41, 131, 210, 276, 363. Edlund (E.) on the nature of galvanic resistance and on a theoretic de- duction of Ohm’s law, 201. Electrical figures on conductors, on, 86 Electricity, on the law for the propa- gation of, 73; on a relation be- yas heat and static, 257, 450. Emerald, on the colourimg-matter of the, 314. Emsmann (Dr. H.) on solution of nitrate of nickel as an absorption- preparation, 329. Energy, on the measure of work in the theory of, 219. Equations, differential, on integrating, 388. Evaporation, experiments on, 483. Eyepiece-micrometer, on a conveni- ent, for the spectroscope, 176. Feddersen (W.) on thermodiffusion of gases, 50. Fluorescent relations of certain hy- drecarbons found in petroleum dis- ‘ tillates, on the, 89. Galvanic coil, on the attraction of a, on a small magnetic mass, 231. resistance, on the nature of,201. Galvanometer, on the differential, 469. Gaseous pressure, note on, 87. Gases, on thermodiffusion of, 55; on the passage of, through colloid membranes of vegetable origin, 251; on the determination of the specific heat of, at constant vo- - lumes, 289, 361; on the effect of ' pressure on the character of the spectra of, 406; on the condensa- tion of, by wood-charcoal, 410. Geological Society, proceedings of the, 173, 326. Glaisher (J. W. L.) on the form of the cells of bees, 103. Gruithuisen’s horizontal pendulum, on the, 412. Guthrie (F.) on a relation between heat and static electricity, 257. INDEX. Hamilton’s dynamic principle in ther- modynamics, on, 426. Heat, on the determination of de- grees of, in absolute measure, 62; on the formula for the, developed by a galvanic current, 201; ona relation between, and static elec- tricity, 257, 450. Heaviside (O.) on the differential gal- vanometer, 4169. “Highton (H.) on duplex telegraphy, 88 Hydrocarbons, on the fluorescent re- lations of certain, 89. Hydrodynamics, on the principles of, 159, 247, 309, 446. Interference-phenomenon, on a re- markable, 332. Tron, on the maximum of magnetism of, 140; on the effects of magneti- zation in changing the dimensions of bars of, 177 ; on certain remark- able molecular changes occurring in, at a low red heat, 472. Jago (Dr. J.) on visible direction, 80. Lee (G. H.) on the effect of pressure on the character of the spectra of gases, 406. Light, on the reflection of, 252. Lignite, analysis of a, from Ballintoy, 244. Liquids, on the condensation of, by wood-charcoal, 4]0. Lockyer (J. N.) on spectrum-ana- lysis, 407. Lorenz (L.) on the determination of degrees of heat in absolute mea- sure, 62. Lunar atmosphere, on the possible existence of a, 411. Magnetic metals, on the relationship of the, 478. permeability, on, 140. Magnetization, on the effects of, in changing the dimensions of iron and steel bars, 177. Magnets, on Jamin’s compound, 176; on the directive power of large steel, 221. Maxwell (Prof. J. C.) on molecules, 453. Mayer (Prof. A. M.) on the effects of magnetization in changing the di- mensions of iron and steel bars, 177. Mechanical theorem, on a new, rela- tive to stationary motions, 236, 266. INDE X. Melsens (M.) on the condensation of gases and liquids by wood-charcoal, 410. Metals, on the relationship of the magnetic, 478. Metamorphism, observations on, 217. Mills (Dr. E. J.) on statical and dy- namical ideas in chemistry, 398. Molecular changes,- on certain re- markable, occurring in iron wire at a low red heat, 472. . Molecules, on, 453. Moon, on the libration of the, 305. Moon (R.) on gaseous pressure, 87 ; on the transmission of sound through air, 122; on the measure of work in the theory of energy, 219; onthe principles of hydrody- namics, 247, 446. Morton (Prof. H.) on the fluorescent relations of certain solid hydrocar- ee found in petroleum distillates, Motion, on the idea of, 398. Mountains, on the origin of, 41, 131, 210, 276, 363. Neison (E.) on the possible existence of a Junar atmosphere, 411. Nichols (R. C.) on the determination of the specific heat of gases and vapours at constant volumes, 289, 361. Nickel, on the maximum of magne- tism of, 140; on solution of nitrate of, as an absorption-preparation, 329. Nodal lines of a square plate, on the, 166, 246. Oceanic depressions, on the formation of, 363. Ohm’s law, on a theoretic deduction of, 201. Pellet (M.) on explosions produced by high tones, 256. Pendulum, on the history of the hori- zontal, 412. Petroleum, on the fluorescent rela- tions of certain hydrocarbons con- tained in, 89. Philips (J. A.) on the composition and origin of the waters of a salt spring in Huel Seton Mine, 26. Photography, on diffraction-spec- trum, 417. Potier (M.) on the reflection and re- fraction of light, 252. 487 Quincke (G.) on a new method for examining the divisions of gradu- ated circles, 174; on the reflection of light, 252. Rayleigh (Lord) on the nodal lines of a square plate, 166, 246; on the vibrations of approximately simple systems, 357; on the fundamental modes of a vibrating system, 434. Reynolds (Prof. O.) on the action of a blast of sand in cutting hard ma- terial, 337. Rood (Prof. O. N.) on a convenient eyepiece-micrometer for the spec- troscope, 176. Rowland (H. A.) on magnetic perme- ability, and the maximum of mag- netism ofiron,steel, and nickel, 140. Royal Society, proceedings of the, 80, 314, 406. Vv v Safarik (Prof.) on the history of the horizontal pendulum, 412. Sand, on the action of a blast of, in cutting hard material, 337. Schneebeli (H.) on electrical figures on conductors, 86. Sekulic’ (M.) on a remarkable inter- ference-phenomenon, 332. Sound, on the transmission, in one direction, of, through air, 122, Specific-gravity bottle, on a, for li- quids spontaneously inflammable in contact with air, 308. Spectra of gases, on the effect of pres- sure on the character of the, 406. Spectroscope, on the use of a diffrac- tion-grating as a substitute for the train of prisms in a solar, 87; on a convenient eyepiece-micrometer for the, 176; ona new, 439. Spectrum-analysis, researches in, 407, Stationary motions, on a new me- chanical theory relative to, 236, 266. Stearn (C. H.) on the effect of pres- sure on the character of the spectra of gases, 406. Steel, on the maximum of magnetism of, 140; on the effects of magneti- zation in changing the dimensions of bars of, 177. Stefan (Prof.) on evaporation, 483. Stuart (J.) on the attraction of a gal- vanic coil on a small magnetic mass, 231. Sun, on the temperature and physical 488 constitution of the, 290, 343; on the spectrum of the, 407. Szily (C.) on Uamilton’s dynamic principle in thermodynamics, 426. Telegraphy, on duplex, 88. Thallene, on the spectrum of fluores- cent light from solid, 93. Thermodiffusion of gases, on, 55. Thermodynamics, on Hamilton’s dy- namic principle in, 426. Tomlinson (C.) on the motions of camphor and of certain liquids on _ the surface of, 376. Tones, on explosions produced by high, 256. Trowbridge (J.) on mduced currents and derived circuits, 84. Tribe (A.) on a specific-gravity bottle for liquids spontaneously inflam- mable in contact with air, 308. Unitates, on negative and fractional, 36. Vapours, on the determination of the specific heat of, at constant vo- lumes, 289, 361. Venus, on the “black drop” in the transit of, 375. INDE X. Vibrating system, on the fundamenta modes of a, 434. Vibrations of approximately simple systems, on the, 357 Vision, on monocularand binocular, 80. Volcanoes and igneous ejections, on, 276: Voltaic current, on various cases of intermission of the, 481. Walenn ( W. H.) on negative and frac- . tional unitates, 36. Water, on the motions of camphor and of certain liquids on the sur- face of, 376. Waters, on the composition and origin of the, of a salt spring in Huel Seton Mine, 26. Williams (G.) on emeralds and beryls, 314. ; Young (Prof. C. A.) on the use of a diffraction-grating in a solar spec- troscope, 87. Zenger (Prof. C. v.) on a new spec- troscope, 439. Zollner (Prof. F.) on the temperature and physical constitution of the sun, 290, 343. END OF THE FORTY-SIXTH VOLUME. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. ALERB U FLAMMAM, TAN 99 1074 ) ; JULY 1873. No. 303. |, a, Published the First Day of every Month.—Price 2s. 6d. | ; THE LONDON, EDINBURGH, ayn DUBLIN | PHILOSOPHICAL MAGAZINE, | Set adel EX LOA. Sian Ds A. AND | JOURNAL OF SCIENCE, Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘Journal, and Thomson’s ‘Annals of Philosophy.’ 1 CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Knr. LL.D. F.RB.S. &c. AND WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S. eee eee eee FOURTH SERIES. N° 303.—JULY 1873. || | WITH A PLATE, Mlustrative of Mr. J. A. Putixres’s Paper on the Composition and Origin of the Waters of a Salt Spring in Huel Seton Mine. OSM LNs cones Pea Ta rar aA oe LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London, Sold by Longmans, Green, Reader and Dyer; Kent and Co. ; Simpkin, Marshall and Co.; and Whittaker and Co. ;—and by A. and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam, New York :—and Asher and Co., Berlin. es ae ._BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE, 22 Albemarle Street, London, W. The NEXT ANNUAL GENERAL MEETING will be held at BRADFORD, commencing on Wednesday, September 17, 1873. - President Elect. J. PRESCOTT JOULE, D.C.L., LL.D., F.R.S. 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Information about Local Arrangements may be obtained by application to the ~ Local Secretaries, Bradford. GEORGE GRIFFITH, M.A., Assistant General Secretary, Harrow. SELECTIONS FROM THE PORTFOLIOS OF THE EDITOR OF THE LUNAR MAP AND CATALOGUE. The first issue of these Selections. just ready, contains papers by the Rev. T. W. Wess, Mr. Netson, Mr. Pratt, and the Editor, with illustrated Notices of recent Observations and Comparisons with older observations. Copies of this issue may be obtained by forwarding Post-office orders (payable to W. R. Birt) to the Editor, addressed Cynthia Villa, Walthamstow, Essex. The amount of sub- scription for this issue is five shillings. The second issue is expected to be ready in October. Nearly ready. REPORT OF THE FORTY-SECOND MEETING OF THE BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE. Held at BRIGHTON, 1872. JoHn Murray, Albemarle Street. THE LONDON, EDINBURGH, AND DUBLIN Philosophical Magazine and Journal of Science. A Journal devoted to Physics, Astronomy, Mechanics, Chemistry, Mineralogy, and the Allied Sciences. Monthly, price 2s. 6d. Complete sets (in Numbers) may be obtained at the following prices ;— A few sets of the First Series, from 1798 to 1826 (wanting a few plates), in 68 volumes. Price £12. . The Second Series, from 1827 to 1832, in ]1 volumes. Price £2 4s. | The Third Series, in 37 volumes, from 1832 to 1850. Soh ees Tay or and Francis, Red Lion Court, Fleet Street, E.C. [ADVERTISEMENTS continued on 3rd page of Cover. _ Six Elementary Lectures on Rocks and | Metallic Minerals, ADAPTED TO A JUVENILE AUDIENCE, } by Professor TENNANT, at his residence, 149 Strand, London, W.C. On July 14, 15, 16, 1?¢7, 18, 19, at ll a.m. and 3 p.m. Terms :—Half a Guinea for the Course ; Five Shillings for Children of Fellows of the fol- lowing Societies— Geological, Zoological, Chemical, Royal Microscopical, Royal Geographical, Royal Horticultural, Geologists’ Association, and Society of Arts. . Pror. TENNANT will probably repeat the Lectures on MINERALOGY given during ‘the Christmas Holidays, and the Lectures on GHOLOGY given during the Easter ‘Holidays. _ Mr. TENNANT is commissioned to offer for Sale a first-class Collection of MINERALS ‘at Godstone, Surrey, containing 3800 Specimens. Also a Collection of MINERALS and ROCKS, containing 800 Specimens, near Barnstaple. Mr. TENNANT expects shortly to have ready for sale a choice and extensive collection of RECENT SHELLS, MINERALS, ROCKS, and FOSSILS, in a large and well-made ‘Cabinet of 108 Drawers, with Glass Bookcase on the top. The Cabinet was the property a the late Mrs. Mawe, and contains her private collection of Recent Shells and Minerals. “Amongst the latter are some Crystals of Gold, figured in Mawe’s Travels in Brazil, and “supposed to be unique. The Bookcase contains many of the recent works on Geology by Buckland, Lyell, Mantell, Murchison, Phillips, and others, and 25 Vols. of the publica- — of the Palzontographical Society, &c. . hee a b; Mr. TENNANT, having recently received many choice Specimens, has been able to = several Collections previously advertised for sale. They can be had at all prices, Be arying from Five Thousand Pounds to Two Guineas, and are suitable for the Nobleman’s gallery, the Amateur’s study, and for the working Student. % e Flementary Geological Collections at 2,5, 10, 20, 50, to 100 guineas each, and every requisite to assist those commencing the study of this interesting branch of Science, a knowledge of which affords so much pleasure to the traveller in all parts of the world. i A collection for Five Guineas, to illustrate the recent works on Geology, by Ansted, ‘Buckland, Lyell, Mantell, Murchison, Page, Phillips, and others, contains 200 specimens, eo a plain Mahogany Cabinet, with five trays, containing the following specimens, viz. :— - Mryerats which are either the components of Rocks, or occasionally imbedded in “them—Quartz, Agate, Chalcedony, Jasper, Garnet, Zeolite, Hornblende, Augite, Asbestos, | Felspar, Mica, Talc, Tourmaline, Spinel, Zircon, Corundum, Lapis Lazuli, Calcite, Fluor, [Belenite, Baryta, Strontia, Salt, Sulphur, Plumbago, Bitumen, &c. _ Native Metats, or Meratiirerous MINERALS; these are found in masses or beds, in yeins, and occasionally in the beds of rivers. Specimens of the following Metallic Ores are put in the Cabinet :—Iron, Manganese, Lead, Tin, Zine, Copper, Antimony, Silver, Gold, Platina, Mercury, Titanium, &c. e Rocks : Granite, Gneiss, Mica-slate, Clay-slate, Porphyry, Serpentine, Sandstones, Lime- “stones, Basalt, Lavas, &c. F Pauzozorc Fossits from the Cambrian, Silurian, Devonian, Carboniferous, and Permian Rocks. _ Szconpary Fossits from the Rheetic, Lias, Oolite, Wealden, and Cretaceous Groups. - Tertrary Fossits from the Plastic Clay, London Clay, Crag, &c. _ In the more expensive collections some of the specimens are rare, and all more select. ‘ JAMES TENNANT, Mineralogist (by appointment) to Her Majesty, 149 Strand, London, W.C. [July 1873. CONTENTS oF N° 803.— fourth Series. I. On the Relations between the characteristic Quantities occurring in Central Motions. By R. Cuaustus............ 0.00... 2 ee page 1 II. On the Composition and Origin of the Waters of a Salt Spring in Huel Seton Mine, with a Chemical and Microscopical Examina- tion of certain Rocks in its vicinity. By J. Arruur PHILzIes, M.Inst.C.E., F.G.S., F.C.8., &e. CWith a Plate.) ..°.... ee 26 III. On Negative and Fractional Unitates. By W. H. Wateyn.. 36 IV. On some Results of the Earth’s Contraction from Cooling, in- cluding a discussion of the Origin of Mountains. By James D. Dana. 41 V. On Thermodiffusion of Gases. By W. Fepprrsen, of Leipzig. 55 VI. Determination of Degrees of Heat in Absolute Measure. By L. Lorgnz, of Copenhagen ™ . 00004 0 9S te a ts 62 VII. Notices respecting New Books :—Light Science for Leisure Hours. Second Series. By Ricnarp A. Proctor, B.A.—Selections from the Portfolios of the Editor of the Lunar Map and Catalogue. 77-79 VILL. Proceedings of Learned Societies :— Royat Society :—Dr. J. Jaco on Visible Direction: being an Elementary Contribution to the Study of Monocular and Bin- ocular:-Vision 2. 0. eee. oe a RO 80 IX. Intelligence and Miscellaneous Articles :— On Induced Currents and Derived Circuits, by John Trow- bridge: =. 2¥oe SASS A ee eS ee On Electrical Figures on Conductors, by H. Schneebeli ...... 86 Note on Gaseous Pressure, by Robert Moon, M.A., Honorary Fellow of Queen’s College, Cambridge... ............-.000e 87 Note on the use of a Diffraction-“ erating” as a substitute for che Train of Prisms in a Solar Spectroscope, by Prof. C. A. Vout — nS seats an oe ne ae see 0S 87 On Duplex Telegraphy, by H. Highton .............., she hs ee *,." Itis requested that all Communications for this Work may be addressed, post-paid, to the Care of Messrs. Taylor and Francis, Printing Office, Red Lion Court, Fleet Street, London. 1 ol. 46. AUGUST 1873. No. 304. Published the First Day of every Month.—Price 2s. 6d. TOL, Oe ee eG ee) ee ee ae | THE LONDON, EDINBURGH, ann DUBLIN 1 | PHILOSOPHICAL MAGAZINE, | e f | AND : : JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘Journal,’ and Thomson’s * Annals of Philosophy.’ 3 4 | j CONDUCTED BY ] SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. | SIR WILLIAM THOMSON, Kn. LL.D. F.R.S. &e. : AND | { WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S. | ee FOURTH SERIES. | Ne 304.—AUGUST 1873. WITH TWO PLATES, Ulustrative of Mr. H. A. Rowzann’s Paper on Magnetic Permeability, and the Maximum of Magnetism of Iron, Steel, and Nickel. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and | Co. ; and Whittaker and Co. ;—and by A. and ©. Black, and Thomas Clark, Edin- a burgh ; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam, 4 New York :—and Asher and Co., Berlin. PROFESSOR TYNDALL’S AMERICAN LECTURES. Now ready, with Lithographic Frontispiece and 59 Diagrams, in crown 8vo, cloth, price 7s. 6d. LECTURES ON LIGHT, Delivered in the United States of America in the years 1872 and 1873; with an Appendix. By JOHN TYNDALL, LL.D., D.C.L., F.R.S., Professor of Natural Philosophy in the Royal Institution of Great Britain. —* —e London: Longmans, GREEN, and Co., Paternoster Row. MR. PROCTOR’S NEW WORK ON THE MOON. ; In One Volume, crown 8yo, cloth, with 22 Lithographic Plates, Charts, and Dia- { grams, 1 Wood Engraving, and 3 Lunar Photographs by Rutherfurd, of New York, price 15s. THE MOON; HER MOTIONS, ASPECT, SCENERY, AND PHYSICAL CONDITION. By RICHARD A. PROCTOR, B.A. Cantab., Hon. Sec. R.A.S., Author of ‘ Other Worlds than Ours,’ ‘ Saturn and its System,’ ‘The Orbs Around Us,’ &e. London: LonGMANS, GREEN, and Co., Paternoster Row. cee nee —— Now ready, with Engravings, 8vo, 12s. AN INTRODUCTION TO PHYSICAL MEASUREMENTS, | with - APPENDICES ON ABSOLUTE ELECTRICAL MEASUREMENT, etc. | By Dr. F. KOHLRAUSCH. Translated from the Second German Edition by T. H. WALLER, B.A., B.Sc., and H. R. PROCTER, F.C.S. SE a A i i as J. and A. CourcHILL, New Burlington Street. Now ready, price 24s. | REPORT OF THE FORTY-SECOND MEETING OF THE BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE. Held at BRIGHTON, 1872. JoHN Murray, Albemarle Street.’ suumassusiaaynttinmmmmnsmnmnastrneniommerece cig biel ais [ADVERTISEMENTS continued on 3rd page of Cover. | The Turners’ Company of London. THE FREEDOM OF THE COMPANY, together with their SILVER MEDAL AND THE FREEDOM OF THE CITY, Are offered to any one Workman or Apprentice for the best Workmanship in Hand- turning in IVORY, and the like Rewards for the best Workmanship in STONE (Por- hyry, Granite, Jasper, Agate, Serpentine, Marble, Spar, Stalagmite, Alabaster, Jet, Coal, eestone, &c., are examples of what may be used), jeremy to be delivered, by permission of the Lord Mayor, at the Mansion House, in the City, between September 29th and October 3rd, 1873, and to remain the property of the Artist. Inquiries as to the conditions of the Competition to be made of the Clerk of the Company, WILLIAM MOORE SHIRREFF, Esq., 59 Mark Lane, E.C,, or Professor ee 149 Strand, London, W.C., by either of whom printed particulars will be orw: . Mr. TENN ANT is commissioned to offer for Sale a first-class Collection of MINERALS at Godstone, Surrey, containing 3800 Specimens. Also a Collection of MINERALS and ROCKS, containing 800 Specimens, near Barnstaple. Mr. TENNANT expects shortly to have ready for sale a choice and extensive collection of RECENT SHELLS, MINERALS, ROCKS, and FOSSILS, in a large and well-made Cabinet of 108 Drawers, with Glass Bookcase on the top. The Cabinet, was the property of the late Mrs. Mawe, and contains her private collection of Recent Shells and Minerals, Amongst the latter are some Crystals of Gold, figured in Mawe’s Travels in Brazil, and supposed to be unique. The Bookcase contains many of the recent works on Geology by Buckland, Lyell, Mantell, Murchison; Phillips, and others, and 25 Vols. of the publica- tions of the Palzontographical Society, &e. Mr. TENNANT, having recently received many choice Specimens, has been able to enrich several Collections previously advertised for sale. They can be had at all prices, varying from Fiye Thousand Pounds to Two Guineas, and are suitable for the Nobleman’s gallery, the Amateur’s study, and for the working Student. Flementary Geological Collections at 2, 5, 10, 20, 50, to 100 guineas each, and every requisite to assist those. commencing the study of this interesting branch of Science, a knowledge of which affords so much pleasure to the traveller in all parts of the world. A collection for Five Guineas, to illustrate the recent works on Geology, by Ansted, Buckland, Lyeil, Mantell, Murchison, Page, Phillips, and others, contains 200 specimens, in a plain Mahogany Cabinet, with five trays, containing the following specimens, viz. :— Mixerits which are either the components of Rocks, or occasionally imbedded in them—Quartz, Agate, Chalcedony, Jasper, Garnet, Zeolite, Hornblende, Augite, Asbestos, Felspar, Mica, Talc, Tourmaline, Spinel, Zircon, Corundum, Lapis Lazuli, Calcite, Fluor, Selenite, Baryta, Strontia, Salt, Sulphur, /lumbago, Bitumen, &c. Native MerAts, or Meraviirerous MineERALs ; these are found in masses or beds, in veins, and occasionally in the beds of rivers. Specimens of the following Metallic Ores are put in the Cabinet :—Iron, Manganese, Lead, Tin, Zinc, Copper, Antimony, Silver, Gold, Platina, Mercury, Titanium, &c. Rocks : Granite, Gneiss, Mica-slate, Clay-slate, Porphyry, Serpentine, Sandstones, Lime- stones, Basalt, Lavas, &c. ‘ rr iia Fossiis from the Cambrian, Silurian, Devonian, Carboniferous, and Permian ocks, Seconpary Fossixs from the Rhetic, Lias, Oolite, Wealden, and Cretaceous Groups. Tertiary Fossirs from the Plastic Clay, London Clay, Crag, &c. In the more expensive collections some of the specimens are rare, and all more select: JAMES TENNANT, Mineralogist (by appointment) to Her Majesty, 149 Strand, London, W.C. [August 1873. ‘CONTENTS or N° 804.—Fourth Series. X. Fluorescent Relations of certain solid Hydrocarbons found in Petroleum Distillates. By Hznry Morton, Ph.D., President of the Stevens Institute of Technology. \.vhi0. 3. ce we ee tes page 89 XI. On the Form of the Cells of Bees. By J. W. L. Gratsur, B.A., Fellow of Trinity College, Cambridge. .'....... ..5....2% 103 XII. On the Integration of the Accurate Equation representing the Transmission in one direction of Sound through Air, deduced on the Ordinary Theory. By Rozpertr Moony, M.A., Honorary Fel- low of Queen’s College, Cambridge ...... 02.0... 00. eee ee eee 122 XIII. On some Results of the Harth’s Contraction from Cooling, including a discussion of the Origin of Mountains. By Jamus D. DANA eae Pie oe ae Re a ee 131 XIV. On Magnet Permeability, and the Maximum of Magnetism of Iron, Steel, and Nickel. By Henry A. Rowzanp, Instructor in Physics in the Rensselaer Polytechnic Institute, Troy, N.Y. (With DwoPlates. ii 8 Maat cas ae er, 140 XV. On Objections recently made to the received principles of Hydrodynamics. By Professor Cuanris, M.A., LL.D., F.RS., BUR OAgS 2 oo ee a Se gis a cittade CERES © ERS a cee nae, te 159 XVI. On the Nodal Lines of a Square Plate. By Lord Rayzeten, BRS: (Hone J; W. STRUTT) 2. ee 166 XVI. Notices respecting New Books :—Astronomical and Me- teorological Observations made during the year 1870, at the United- - States Naval Observatory sci sews okie cba ci aoe bree nee ees ie Lil. XVIII. Proceedings of Learned Societies :— | Grotogican Socrery :—Mr. C. J. A. Muyer on the Punfield Section; Mr. W. J. Sorzas on the Coprolites of the Upper Greensand Formation, and on Flints.............. .. 1738-174 XIX. Intelligence and Miscellaneous Articles :— On a new Method for examining the divisions of Graduated | Cigles by Gy Qimneke. 3 oa ee ee 174 | On a convenient Eyepiece-micrometer Oe the Spectroscope, by Protessar O7NRood so. ee ee aS Us On Jamin’s Compound Magnets, by R. 8. Culley, Esq. ...... 176 *,* It as requested that all Communications for this Work may be addressed, post-paid, to the Care of Messrs. Taylor and Francis, Printing Office, Red Lion Court, Fleet Street, London. ie SEPTEMBER 1873. No. 305. Published the First Day of every Month.—Price 2s. 6d. v | ) THE i LONDON, EDINBURGH, anp DUBLIN : PHILOSOPHICAL MAGAZINE, | AND : : : F JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘ Journal, and Thomson’s ‘Annals of Philosophy,’ a / Pa i Fr NG ge oe M, EID, CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Knv. LL.D. F.RB.S. &c. AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S. F.CS. : FOURTH SERIES. | N° 305._SEPTEMBER, 1873. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, | Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co. ; and Whittaker and Co. ;—and by A. and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin:—Putnam, i New York :—and Asher and Co., Berlin. oe ea ROYAL SCHOOL OF MINES. DEPARTMENT OF SCIENCE AND ART. During the Twenty-third Session, 1873-74, which will commence on the Ist of October, the following COURSES of LECTURES and PRACTICAL DEMONSTRATIONS will be given :— . Chemistry. By E. Frankland, Ph.D., F.R.S. . Metallurgy. By John Percy, M.D., F.R.S. . Natural History. By T. H. Huxley, LL.D., F.R.S. yonersley ; \ By Warington W. Smyth, M.A., F.R.S., Chairman. Geology. By A. C. Ramsay, LL.D., F.R.S. . Applied Mechanics. By T. M. Goodeve, M.A. . Physics. By Frederick Guthrie, Ph.D., F.R.S. . Mechanical Drawing. By the Rev. J. H. Edgar, M.A. The Fee for Students desirous of becoming Associates is £30 in one sum, on entrance, or two annual payments of £20, exclusive of the Laboratories. Pupils are received in the Chemical Laboratory, under the direction of Dr. Frankland, and in the Metallurgical Laboratory, under the direction of Dr. Perey. These Laboratories will be reopened on October Ist. Tickets to separate Courses of Lectures are issued at £3 and £4 each. Officers in the Queen’s Service, Her Majesty’s Consuls, Acting Mining Agents and Managers, may obtain Tickets at reduced prices. Science Teachers are also admitted to the Lectures at reduced fees. His Royal Highness the Prince of Wales grants two Scholarships; and several others have also been established by Government. For a Prospectus and information apply to the Registrar, Royal School of Mines, Jermyn Street, London, 8.W. TRENHAM REEKS, Registrar. CONIA ROO — Note.—By order of the Lords of the Committee of Council on Education, the instruction in Chemistry, Physics, Applied Mechanics, and Natural History will be given in the New Buildings, in the Exhibition Road, South Kensington. NEW EDITION OF MITCHELL’S ASSAYING. Just published, in 8vo, with 199 Woodcuts, price 31s, 6d. A MANUAL OF PRACTICAL ASSAYING. By JOHN MITCHELL, F.C.S. Fourth edition, in which are incorporated all the recent valuable improvements in Assaying made in this country and abroad; including Volumetric and Colori- metric Assays, and the Blowpipe Assays. | Edited and for the most part rewritten by WILLIAM CROOKES, F.R.S. &e. ‘The work, as it now stands, may safely be taken as a guide by buyers of ores, and by all persons engaged in the industry of chemical manufacture.””—Mining Journal. , London: Longmans, GREEN, and Co., Paternoster Row. PROFESSOR TYNDALL’S AMERICAN LECTURES. Now ready, with Lithographic Frontispiece and 59 Diagrams, in crown 8vo, cloth, price 7s. 6d. LECTURES ON LIGHT, Delivered in the United States of America in the years 1872 and 1873; with an | Appendix. By JOHN TYNDALL, LL.D., D.C.L., F.R.S., Professor of Natural Philosophy in the Royal Institution of Great Britain, London: LonemMaAns, GREEN, and Co., Paternoster Row. [ADVERTISEMENTS continued on 3rd page of Cover. ree ° eer Se _ ~—-... _—_—-- - ar ey ie Tt The Worshipful Company of Turners, Londcu, OFFER THE FREEDOM OF THE COMPANY, together with their SILVER MEDAL AND THE FREEDOM OF THE CITY, to any one Workman or Apprentice for the best Workmanship in Hand Turning in TVORY, and the like Rewards for the best Workmanship in STONE (Porphyry, Granite, Jasper, Agate, Serpentine, Marble, Spar, Stalagmite, Alabaster, Jet, Coal, Freestone, &c., are examples of what may be used). Specimens to be delivered, by permission of the Lord Mayor, at the Mansion House, in the City, between September 29th and October 5rd, 1873, and to remain the property of the Artist. Inquiries as to the conditions of the Competition to be made of the Clerk of the Company, WILLIAM MOORE SHIRREFF, Esq., 59 Mark Lane, E.C., or Professor “ean tae 149 Strand, London, W.C., by either of whom printed particulars will be orwarded. Professor TENNANT’S LECTURES on MINERALOGY, applied to GEOLOGY and the ARTS, at King’s College, will be resumed on Wednesday morning, October &th, at nine o’clock, and the eyening Lectures on Thursday the 9th. ‘Lhe public are admitted on paying the College Fees. PRIVATE INSTRUCTION in GEOLOGY and MINERALOGY can be had at 149 Strand. Mr. TENNANT expects shortly to have ready for sale a choice and extensive collection of RECENT SHELLS, MINERALS, ROCKS, and FOSSILS, in a large and well-made Cabinet of 108 Drawers, with Glass Bookcase on the top. The Cabinet was the property - of the late Mrs. Mawe, and contains her pzivace collection of Recent Shel!s and Minerals. Amongst the Jatter are some Crystals of Gold, figured in Mawe’s Travels in Brazil, and supposed to be unique. The Bookcase contains many of the recent works on Geology by Buckland, Lyell, Mantell, Murchison, Phillips, and others, and 25 Vols. of the publica- tions of the Palzontographical Society, Kc. Mr. TENNANT, having recently received many choice Specimens, has been able to enrich several Collections previously advertised for sale. They can be had at all prices, varying from Five Thousand Pounds to Two Guineas, and are suitable for the Nobleman’s gallery, the Amateur’s study, and for the working Student. Flementary Geological Collections at 2,5, 10, 20, 50, to 100 guineas each, and every requisite to assist those commencing the study of this interesting branch of Science, a knowledge of which affords so much pleasure to the traveller in all parts of the world. A collection for Five Guineas, to illustrate the recent works on Geology, by Ansted, Buckland, Lyeli, Mantell, Murchison, Page, Phillips, and others, contains 200 specimens, in a plain Mahogany Cabinet, with five trays, containing the following specimens, viz. :— Mixerats which are either the components of Rocks, or occasionally imbedded in them—Quartz, Agate, Chalcedony, Jasper, Garnet, Zeolite, Hornblende, Augite, Asbestos, Felspar, Mica, Talc, Tourmaline, Spinel, Zircon, Corundum, Lapis Lazuli, Calcite, Fluor, Selenite, Baryta, Strontia, Salt, Sulphur, Plumbago, Bitumen, &c. Native Meraus, or Meractirerous MineRALS; these are found in masses or beds, in veins, and occasionally in the beds of rivers. Specimens of the following Metallic Ores are put in the Cabinet :—Iron, Manganese, Lead, Tin, Zinc, Copper, Antimony, Silver, Gold, Platina, Mercury, Titanium, &c. Rocks : Granite, Gneiss, Mica-slate, Clay-slate, Porphyry, Serpentine, Sandstones, Lime- stones, Basalt, Lavas, &c. ‘Paxrzozoic Fossiis from the Cambrian, Silurian, Devonian, Carboniferous, and Permian - Rocks. Seconpary Fossixs from the Rhetic, Lias, Oolite, Wealden, and Cretaceous Groups. Tertiary Fossits from the Plastic Clay, London Clay, Crag, &c. In the more expensive collections some of the specimens are rare, and all more select. JAMES TENNANT, Mineralogist (by appointment) to Her Majesty, 149 Strand,London,W.c. — [October 1873. CONTENTS or N ° 306.—Fourth Series. XXXI. On a Relation between Heat and Static Electricity. By PREDERICK GUTHRIE 3.255, OU aN, wee de eens wee one page 257 XXXII. On a new Mechanical Theorem relative to Stationary Motions. «By WR. Cuaustus) sc)... S..5eeG Ne ee 266 XXXII. On some Results of the Earth’s Contraction from Cool- ing, including a discussion of the Origin of Mountains. By Jamus D. Dana.—Part IV. Igneous Ejections, Voleanoes.............. 276 XXXIV. On the Determination of the Specific Heat of Gases and Vapours at Constant Volumes. By R. C. Nicwors, Esq. ........ 289 XXXV. On the Temperature and Physical Constitution of the Sun. (Second Memoir.) By EF. Zoi 2... 290 XXXVI. On the Moon’s Libration. By W. R. Brat, F.R.AS., OMS oie iin ate heels Ce oP Oo ee 305 XXXVII. Specific-gravity Bottle for Liquids spontaneously In- flammable in contact with Air. By Atrrep Tripn, Esq. ........ 308 XXXVIITI. On the received principles of Hydrodynamics, in re- ply to Mr. Moon. By Professor Cuatris, M.A., LL.D., F.BS., PUA Se ca his eee co eb heen oh ee, ee 309 XXXIX. Notices respecting New Books :—The Moon, her Mo- © tions, Aspect, Scenery, and Physical Condition. By Ricwarp A. PROCTOR. bias eon. Soca pit be eas a0 did Vote 2G 6 aCe 312 XL. Proceedings of Learned Societies:— _ Royat Socrety :—Mr. Grevirte Wittiams on Emeralds and Beryls.—Part I. On the Colouring-matter of the Emerald.. 314 Grotoeicat Socrery :—Mr. J. W. Jupp on the Secondary Rocks of Scotland; M. J. F. Camesent on the Glaciation of Ire- Jamis 6 cl kOe Re ee ei ee 326-329 XLI. Intelligence and Miscellaneous Articles :— On Solution of Nitrate of Nickel as an Absorption-Preparation, by Dr. He Emesmanm: 0 n6206 6025 Gs a. oto ee cee 329 Determination of the Friction Resistances in Atwood’s Machine, by CO, Benders. is. eee einai. So or 330 A remarkable Interference-phenomenon observed by M. Sekulic. 332 On the Filling of Vessels with a very Narrow Tube, especially the Cartesian Diver, by K. L. Bauer, of Karlsruhe ...... 334 Researches on the Spectrum of Chlorophyl, by J. Chautard.... 335 On the Direct Synthesis of Ammonia, by W. F. Donkin...... 336 *,.* It is requested that all Communications for this Work may be addressed, . post-paid, to the Care of Messrs. Taylor and Francis, Printing Office, Red Lion Court, Fleet Street, London. Vol. 46. OCTOBER 1873. No. 306. 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 ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. SIR WILLIAM THOMSON, Knz. LL.D. F.R.S. &c. & 6 AND . WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.CS. FOURTH SERIES. N° 306.—OCTOBER 1873. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co.; and Whittaker and Co. ;—and by A. and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam, New York :—and Asher and Co., Berlin. At the end of September will be published by the undersigned, ASTRONOMISCHE UNDULATIONSTHEORIE, oder die Lehre von der ABERRATION DES LICHTES, yon Dr. E. KETTELER, Professor an der Universitat Bonn. With 44 Wood Engravings printed in the text. 18 sheets. Price 2 Thalers. September 1, 1873. Bonn: P. NEUSSER. NEW EDITION OF MITCHELL’S ASSAYING. Just published, in 8vo, with 199 Woodcuts, price 31s. 6d. A MANUAL OF PRACTICAL ASSAYING. By JOHN MITCHELL, F.C.S. Fourth edition, in which are incorporated all the recent valuable improvements in Assaying made im this country and abroad ; pelues Volumetric and Colori- metric Assays, and the Blowpipe Assays. Edited and for the most part rewritten by. WILLIAM CROOKES, F.R.S. &e. “The work, as it now stands, may safely be taken as a guide by buyers of ores, and by all persons engaged in the industry of chemical manufacture.” —Mining Journal. London: Longmans, GREEN, and Co., Paternoster Row. Just published, in 4to, on fine paper, with Six Plates, price 3s. 6d., Part XII. of RELIQUIZ AQUITANICE ; Being Contributions to the Archeology and Paleontology of Périgord and the adjoining Provinces of Southern France. By EDOUARD LARTET and HENRY CHRISTY. Edited by @.. RUPERT JONES, F.R.S., F.GjS., &e., Professor of Geology, Royal Military and Staff ‘Colleges, Sandhurst. This Work will be illustrated with numerous well-executed Lithographie Plates of the Weapons, Tools, and Ornamental Work, in. Stone, Bone, and Horn, of the Prehistoric Cave-dwellers of Périgord; also of the Osseous Remains of the Con- temporaneous Animals. To be completed in about 15 Parts (price 3s. 6d. each). WixiiaMs and Norears, 14 Henrietta Street, Covent Garden, London, and 20 South Frederick Street, Edinburgh; J. B. BAILLiERE & FILs, Paris. Now ready, with: Engravings, avo, 12s.. AN INTRODUCTION TO eg wee: MEASUREMENTS, Wait APPENDICES ON ABSOLUTE ELECTRICAL MEASUREMENT, ere. By Dr. F. KOHLRAUSCH, Professor at the Grand Ducal Polytechnic School at Darmstadt. Translated from the Second German Edition by T. H. WALLER, B.A., B.Sc., and H. R. PROCTER, F.C.S. J.and A. CouRCHILL, New Burlington Street. Now. Sead. with 48 Wood Engrayings, foolscap ha: Bs, NOTES ON NATURAL PHILOSOPHY. By G. F. RODWELL,.F.R.A.S., Solem Master in .Marlboroqugh College, late Lecturer on Natural Philosophy in Guy’s Hospital. “There cannot be a doubt that this little book will be of use to seience teachers -and.science-students.’ —Naiure. J. & A. CourcHiuu, New Burlington Street. [ADVERTISEMENTS continued on 3rd page of Cover. Vol. 46. NOVEMBER 1873. No. 307. Published the First Day of every Month.—Price 2s. 6d. THE i LONDON, EDINBURGH, anp DUBLIN | PHILOSOPHICAL MAGAZINE, AND + we STI JOURNAL OF SCIENCE. Being a Continuation of Tilloch’s ‘ Philosophical Magazine,’ Nicholson’s ‘ Journal,’ and Thomson’s ‘ Annals of Philosophy.’ 3 ee, = la F ” aes CONDUCTED BY ‘SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. | SIR WILLIAM THOMSON, Knr. LL.D. F.R.S. &e. AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.AS. F.CS, FOURTH SERIES. N° 307.—NOVEMBER 1873. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co.; and Whittaker and Co. ;—and by A. and ©. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam, New York :—and Asher and Co., Berlin. vers | Just published, price 2s. 6d., post free 3s., THE UNIVERSITY COLLEGE CALENDAR. The CALENDAR for 1873-74, containing the Bye-laws, Regulations, Memo- rials, List of Students, Exhibitioners, &c., together with much useful information respecting the College and School. TAYLOR and Francis, Red Lion Court, Fleet Street, E.C. Just published, price ls., post free 1s. 5d. ROYAL COLLEGE OF SURGEONS OF ENGLAND. The CALENDAR for 1873, containing the Charters, Bye-laws, Regula- tions, Lists of Fellows, Members, and Licentiates in Midwifery and Dental Sur- gery, together with much useful information respecting the College. TAYLOR and Francis, Red Lion Court, Fleet Street, E.C. New Edition, price 3s. 6d. SPECIMENS OF ENGLISH POETRY. Printed for the use of CHARTERHOUSE SCHOOL. TAYLOR and Francis, Red Lion Court, Fleet Street, E.C. Vol. IIL., with Four Plates, price 18s. FARADAY’S EXPERIMENTAL RESEARCHES IN ELECTRICITY. “The three volumes of ‘ Experimental Researches in Electricity ? now published contain a series of remarkable investigations, which certainly offer the most stri- king evidence of the value of inductive philosophy that has ever been published in the English language.” —Atheneum. TAYLOR and Francis, Red Lion Court, Fleet Street, E.C. In 1 vol. 8vo, with Three Plates, price 15s. cloth. EXPERIMENTAL RESEARCHES IN CHEMISTRY AND PHYSICS. By MICHAEL FARADAY, D.C.L., F.R.S., Fullerian Professor of Chemistry in the Royal Institution of Great Britain. “In conclusion, we can only repeat the assertion with which we commenced this article. This is a book which ought to be in the library of every scientific man.”’— Literary Gazette. TaYLor and Francis, Red Lion Court, Fleet Street, E.C. THE LONDON, EDINBURGH, AND DUBLIN Philosophical Magazine and Journal of Science. A Journal devoted to Physics, Astronomy, Mechanics, Chemistry, Mineralogy, and the Allied Sciences.. Monthly, price 2s. 6d. Complete sets (in Numbers) may be obtained at the following prices :— A few sets of the First Series, from 1798 to 1826 (wanting a few plates), in 68 volumes. Price £12. The Second Series, from 1827 to 1832, in 11 volumes. Price £2 4s. The Third Series, in 37 volumes, from 1832 to 1850. 3 eG: TAYLOR and Francis, Red Lion Court, Fleet Street, E.C. [ADVERTISEMENTS continued on 3rd page of Cover. Prorzsson TENNANT’S LECTURES on MINERALS and ROCKS, at King’s Col- ege, are given on Wednesday and Friday mornings, from nine to ten o’clock, and on Thursday evenings from eight to nine. The Lectures commenced in October, and will be continued to Easter 1874, The public are admitted on paying the College Fees, Strand. A Course of Six Elementary Lectures, adapted to a Juvenile Audience, will be given during the Christmas holidays by Professor TENNANT at his residence, 149 Strand, WC. Terms :—Half a Guinea for the Course; Five Shillings for Children of Fellows of the following Societies—Geological, Zoological, Chemical, Royal Microscopical, Royal Geo- graphical, Royal Horticultural, Geologists’ Association, and Society of Arts, Mr. TENNANT expects shortly to have ready for sale a choice and extensive collection of RECENT SHELLS, MINERALS, ROCKS, and FOSSILS, in a large and well-made Cabinet of 108 Drawers, with Glass Bookcase on the top. The Cabinet was the property of the late Mrs. Mawe, and contains her private collection of Recent Shells and Minerals. Amongst the latter are some Crystals of Gold, figured in Mawe’s Travels in Brazil, and supposed to be unique. The Bookcase contains many of the recent works on Geology by Buckland, Lyell, Mantell, Murchison, Phillips, and others, and 25 Vols. of the publica- tions of the Palzontographical Society, &e. Elementary Geological Collections at 2, 5, 10, 20, 50, to 100 guineas each, and every requisite to assist those commencing the study of this interesting branch of Science, a knowledge of which affords so much pleasure to the traveller in all parts of the world. 100 Small Specimens, in Cabinet with Three Trays .......... to) 2.0 OG Specimens, larger, in Cabinet with Five Trays .......... 5 ig tenes 0 300 Specimens, larger, in Cabinet with Hight Drawers ......., 1010 0 Specimens, larger, in Cabinet with Twelve Drawers ...... al PD take guineas each, with every requisite to assist those commencing the study of these interesting _ branches of Science, a knowledge of which affords so much pleasure to the Traveller in all In the more expensive collections some of the Specimens are rare and all more select. A collection for Five Guineas, to illustrate the recent works on Geology, by Ansted, Buckland, Lyeil, Mantell, Murchison, Page, Phillips, and Others, contains 200 specimens, in a plain Mahogany Cabinet, with five trays, containing the following specimens, viz. :— MINERALS which are either the components of Rocks, or occasionally imbedded in _ them—Quartz, Agate, Chalcedony, Jasper, Garnet, Zeolite, Hornblende, Augite, Asbestos, _ Felspar, Mica, Tale, Tourmaline, Spinel, Zircon, Corundum, Lapis Lazuli, Calcite, Fluor, | Selenite, Baryta, Strontia, Salt, Sulphur, Plumhago, Bitumen, &c. Native MeETaAts, or METALLIFEROUS MINERALS; these are found in masses or beds, in veins. and occasionally in the beds of rivers, Specimens of the following Metallic Ores are _ hn the Cabinet :—Iron, Manganese, Lead, Tin, Zine, Copper, Antimony, Silver, Gold, Jina, Mercury, Titanium, &e. : ‘Rocks : Granite, Gneiss, Mica-slate, Clay-slate, Porphyry, Serpentine, Sandstones, Lime. stones, Basalt, Lavas, &c. . Pa.zxozoic Fossits from the Cambrian, Silurian, Devonian, Carboniferous, and Permian Rocks. SEconDaRy Fossizs from the Rheetic, Lias, Oolite, Wealden, and Cretaceous Groups. Tertiary Fossits from the Plastic Clay, London Clay, Crag, &c. In the more expensive collections some of the Specimens are rare, and all more select. _ JAMES TENN ANT, Mineralogist (by appointment) to Her Majesty, 149 Strand, London, W.C, [November 1873. CONTENTS or N° 307.—Fourth Series. XLII. On the Action of a Blast of Sand in cutting hard Material. By Professor Osporne Ruynoups, M.A. ........0....0005. page 337 XLII. On the Temperature and Physical Constitution of the Sun. (Second Memoir.) By F. Zonnnme ©. a oe 343 XLIV. On the Vibrations of Approximately Simple iii By Lord Rayinies, PBS. i ke a 357 XLV. On the Determination of the Specific Heat of Gases and Vapours at Constant Volumes. By R. C. Nicnomts............. Forsch XLVI. On some Results of the Earth’s Contraction from Cooling, including a discussion of the Origin of Mountaims. By Jamus D. Dana.—Part V. Formation of the Continental Plateaux and Oceanie Depressions «02.6 peed fs Se SOE A 363 XLVII. On the “ Black Drop” in the Transit of Venus. By T. K. Asport, M.A., Fellow of Trinity College, Dublm ............ 375 XLVIII. On the Motions of Camphor and of certain Liquids on . the Surface of Water. By Cuarnes Tomurson, F.R.S......... . 876 XLIX. On Integrating Differential Equations by Factors and Dif- ‘ ferentiation, with Applications in the Calculus of Variations. By m Professor Cuarzis, M.A., F-R.S., FURAS. ........00..0:5 eee 388 4 ~ .L. On Statical and Dynamical Ideas in Chemistry—Part IV. ~— | (conclusion). On the Idea of Motion. By Epmunp J. Mutts, D.Se. 398 | | LI. ‘Notices respecting New Books :—An Elementary Treatise on 4 4 the Differential Calculus, contaiing the Theory of Plane Curves, with numerous Examples. By Benzamin Wittramson, A.M., Fellow and Tutor, Trinity Gellege, Dublin {22.5.0 406.) LIL. Proceedings of Learned Societies :— . Royat Socrery :—Messrs. C. H. Stmarn and G. H. LEE on the Effect of Pressure on the Character of the Spectra of Gas | Mr. J. N. LocxyEr’s Researches in Spectrum-Analysis i connexion with the Spectrum of the Sun.—No. IT. .... 406-410. LUT. Intelligence and Miscellaneous Articles :— On the Condensation of Gases and Liquids by “Gibod-charenad : Thermic Phenomena produced on the Contact of Liquids and q Charcoal. Liquefaction of the Condensed Gases, by Ms Mel- ™ BERS G ORNS sls views ss cs be rele brett Oh Ns ao a oe 410 On the possible Existence of a Lunar Atmosphere, EA E. Neisors Hpac We aes Se teh ik 2 se 411 A Contribution to the History of the Horizontal Pendulum, by Professor Safarik ........ 00.0 cceeeeceees ld oe 412 ol ET Nin RS rt at Eee ens hae eee *,* It is requested that all Catan stineaans for this Work may be addressed || post-paid, to the Care of Messrs. Taylor and Francis, Printing Office, Red} : Lion Court, Fleet Street, London. Vol. 46. DECEMBER. 1873. No. 308. 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 ‘ Philosophical Magazine,’ Nicholson’s ‘ Journal, and Thomson’s ‘ Annals of Philosophy.’ CONDUCTED BY SIR ROBERT KANE, LL.D. F.R.S. M.R.ILA. F.C.S. SIR WILLIAM THOMSON, Kwnr. LL.D. F.R.S. &c. aa AND WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S. F.CS. _~—. —_ FOURTH SERIES. N° 308.—DECEMBER 1873. WITH A PLATE, Illustrative of Dr. H, Drapzr’s Paper on Diffraction-Spectrum Photography. LONDON: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London. Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and Co.; and Whittaker and Co. ;—and by A. and C. Black, and Thomas Clark, Edin- burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam, New, York :—and Asher and Co., Berlin. Syllabus of Six Elementary Lectures on Mineralogy, ADAPTED TO A JUVENILE AUDIENCE, WITH A VIEW TO FACILITATE THE Stupy or GEOLOGY anp or MINERAL SUBSTANCES UsED IN THE ARTS, which will be given by J. THNNANT, E.G.S., Professor of Geological Mineralogy at King’s College, London, Mineralogist to Her Majesty, &c., at his residence, 149 Strand, London, W.C. On December 29, 31, 1873, and January 2, 5, 7, 9, 1874. Terms :—Half a Guinea for the Course; Five Shillings for Children of Fellows of the following Societies :—Geological, Zoological, Chemical, Royal Microscopical, Royal Geo- graphical, Royal Horticultural, Geologists’ Association, and Society of Arts. The Course will commence with a description of the Physical and Chemical characters of Minerals in general. PuysicaL Cuaractsers.—Crystallization, Cleavage, Fracture, Frangibility, Hardness, Lustre, Colour, Flexibility, Double Refraction, Touch, Taste, Odour, Streak, Powder, Ad- hesion to the Tongue, Magnetic and Hlectric Properties, Phosphorescence, Specific Gravity. CuEmicaL CHARACTERS.—Use of the Blowpipe, Action of Acids, &c. ; The principal simple Minerals will be next separately considered, and the readiest mode of distinguishing them described. The following is the order adopted :— A. Harthy Minerals.—Rock-crystal, Amethyst, Cairngorm, Avanturine, Cat’s-eye, Opal, Chalcedony, Flint, Onyx, Agate, Carnelian, Heliotrope, Jasper, Hornstone, Chert, Garnet, Idocrase, Axinite, Epidote, Augite, Hornblende, Asbestos, Tremolite, Actinolite, Felspar, Zeolites, Mica, Talc, Chlorite, Calcite, Fluor, Selenite, Baryta, Strontia, Salt, Cryolite, &. B. Combustible Minerals.—Sulphur, Bitumen, Coal, Jet, Amber, &c. C. Minerals used in Jewelry.—Diamond, coloured varieties of Corundum—Sapphire, Ruby, Topaz—called oriental stones; Spinel, Turquoise, Topaz, Emerald, Beryl, Hyacinth, Tourmaline, Lapis-lazuli, &c. D. The Metalliferous Minerals will be fully described in the Practical Course. The Course of Instruction will include a minute description of all the substances enter- ing into the composition of Rocks, and of those minerals which are also used in the Arts, illustrated by an extensive collection of characteristic specimens and diagrams of the principal crystalline forms, &c. To be followed in the Easter Holidays by Six Elementary Lectures on Geology, April 6, 7, 8, 9, 10,11, at 3 p.m. DzscrireTivE Grotogy.—Classification of Rocks into Aqueous, Volcanic, Plutonic, and — Metamorphic. Mineral Composition of Strata.—Arenaceous, Argillaceous, Calcareous.—Chronological Classification of Sedimentary Rocks, with descriptions of the principal Fossils belonging to each great deposit. Tertiary, or Cainozorc Srrtes.—Cave-Deposits, Crag, Isle of Wight, and Bagshot series, London Clay, Woolwich Beds. SEconDARY, oR Mesozoic Suries.—Cretaceous, Wealden, Oolitic (Upper, Middle, and ‘ Lower), Triassic Groups. Primary, oR Paumozorc Srrizs.—Permian, Carboniferous, Devonian, Silurian, and Cam- brian Groups. The mode of collecting, cleaning, and arranging Fossils, Minerals, and Rock-specimens will be described. In the Summer Holidays by Six Elementary Lectures on Practical Geology. The lessons delivered on the subject of Geology are intended to have especial reference to the important practical applications of that science to Engineering, Mining, Architec- ture, and Agriculture. The Granites, Syenites, Porphyries, Greenstones, Clays, &e. will be described, and the Minerals peculiar to each noticed. The application of Geology to pursuits connected with mining operations for Coal, Iron, Copper, Tin, Silver, Gold, Mercury, Antimony, Zinc, Cobalt, &e. will be specially considered. The student is directed how to proceed in examining a new country, to collect and record his observations, and mark his specimens, in order to render them useful to more experienced geologists at home. In order more fully to exemplify the applications of the Science, Mr. Tennant accompa- nies his Classes to various Museums in London, including the Museum of Practical Geology and the British Museum; also on excursions into the country, in which the actual field- work of the Geologist is explained and illustrated. *,* Mr. Tennant’s lectures at King’s College will be resumed on Wednesday morning, January 21st, and the evening lectures on Thursday the 22nd. [December 1873. CONTENTS oF N° 808.—Fourth Series. LIV. On Diffraction-Spectrum Photography. By Hmnry Dra- per, M.D., Professor of Analytical Chemistry and Physiology in the University of New York. (Illustrated by a Photograph printed by | the Alberttype process.).. 5.0005 [Fn o.oo page 417 LY. On Hamilton’s Dynamic Principle in Thermodynamics. By OC SAY Get Oe ee oy a ole seks ahetls «ok Vink 426 LVI. On the Fundamental Modes of a Vibrating System. By Lord RAyiupien, MiA.) FR Se oo ea a ee 434 LVII. On a new Spectroscope. By Professor Cu. V. Zenczr .. 439 LVIII. Reply to Professor Challis’s further Remarks “On the Received Principles of Hydrodynamics.” By Rosprert Moon, M.A., Honorary Fellow of Queen’s College, Cambridge .............. 446 LIX. On a new Relation between Heat and Static Electricity. By A. W. Bicxzrron, F.C.S., Associate of the Royal School of Mines, Lecturer on Experimental Science, Winchester College, and the Hartley Institution, Southampton. ......2....%.. 05. Sa 450 LX. A Discourse on Molecules. By J. Crunk MaxweEtt, M.A., | F.R.S., Professor of Experimental Physics in the University of Cambridge 2.0 bo eae eee ee 458 LXI. On the Differential Galvanometer. By Oxiver Huavisipz, Newcastle-on-Tyne . oo. ee ee ee le oe 469 LXII. On certain remarkable Molecular Changes occurring in Iron Wire at a low red Heat. By W. IF. Barrer, F.C.S., Professor of Experimental Physics in the Royal College of Science, Dublin .. 472 LXIIT. On the Relationship of the Magnetic Metals. By W. F. Bampnet, ECB. i i ea a eens ee eee 47% LXIV. Intelligence and Miscellaneous Articles :— On various cases of Intermission of the Voltaic Current, by A. Cad oh ee ene oa ees os oe er 48; Experiments on Evaporation, by M. Stefan ................ 48; Pde bei oe a ee ee oe oe 48 | With Title-page, Contents, &c. : | «,* It is requested that all Communications for this Work may be addresse) post-paid, to the Care of Messrs. Taylor and Francis, Printing Office, Re Lion Court, Fleet Street, London. af 4] 5 & S8S SMITHSONIAN INSTITUTION LIBRARIES NMC 3 9088 90012 4116