j — ~~- — ^^"=~^ — = — ^ — » PB'j.mti , / 2sin2r \cos i 4 sin 7 ,,. a:,== ( -. — TT- ■• — rr- ) = . ^. . ^^ • ml ic ' Asm 2i -^ sm 2r /cos r sm m + sm Zr B2 sin 2i + sin 2r ' 2 sin 2r \cos i 4 sin r cos i 4 Prof. Powell on the Demonstration of FresnePs Formulas . 11. Here we may observe, in the numerator of Ay, 2 sin r cos t=: - sin 2t : and of Ap 28in2r^^' = i2 8in2t. cosr fi 12. It is also desirable to notice, that these expressions are the same as those given in Mr. Aiiy's Tract, § 129, under the slightly different form in which they directly result from the peculiar process there pursued, viz. writing sin (r — i) and — tan (r— a). Also the numerator of k' is positive for all values of (i— r), which is necessarily less than 90°, while the denominator becomes oo at (t + r) = 90°, which, according to Brewster's law, is the polarizing angle, and for greater values continues negative. 13. Prof. Maccullagh's formulas are, — for vibrations parallel to the plane of incidence, jj_ Bin (i-r) ,_ sin2t , .„,. '*-" sin (i + r)' '''~sin(f + r)' ^^ for vibrations perpendicular to the plane of incidence, ,f__ sin2i— sin2r __tan (e— r) ~" sin 2 j -f sin 2r ~ tan {i -f r)' 2sin2i _| tan(i— r) .^,. '"" 6in2i + sin2r tan(i+rj* These last are sometimes expressed under the forms Li __ s^^ (* "■ ^) ^^^ (* + ^) z. sin 2i "" cos (j—r) sin (t + r)' '~ cos {i—r) sin {i-\-r) ' 14. Comparing these formulas with FresnePs (distinguished by using roman letters), we may observe from (11), A'=-h', h,=h,fji, kf=k', k,=k,fi. Here also k, undergoes the same change of sign at the incidence of complete polarization. Densities and Vibrating Masses. 16. In deducing these formulas, it is in all cases necessary to express the ratio of the masses of sether simultaneously vibrating without and within the medium; and the differences in the respective formulas are mainly dependent on the very opposite suppositions made by the several philosophers as to the density of the sether in different media, — Fresnel supposing it more dense for Reflected and Refracted Light, 5 within the denser medium ; Cauchy, less dense ; and Maccullagh, equally dense in all media. The last-named writer has argued that refraction cannot be dependent on the density of the aether as such. He especially observes, that "in doubly-refracting crystals, the density, being independent of the direction, could not be conceived to vary with the refractive index'' (p. 39). And Prof. Stokes has observed, that in the vibrations of sether, '^ di- minution of velocity seems capable of being accounted for on several distinct hypotheses/^ 16. The expressions for the masses of sether vibrating in the same time without and within the denser medium, are obtained on these different suppositions as to the density of the sether, as follows : — If V be the velocity of the incident ray, v^ that of the refracted, and the index /x= — , then at di perpendicular incidence, the simul- taneously vibrating masses will be simply (m) _ ^ _ _ sin i (m^) "~i?y ""f^"" sinr* If the densities be S, 8^ then, according to the view of Fresnel, h^ > hf and 8^ sin^2 jjj^ and we must multiply in this ratio, which gives K) /** : If S=8p according to the view of MaccuUagh, ) (m) 17. In either case, for oblique incidences we must multiply by the rectangular breadth of the rays on the same base or section of the surface, which will be as cos i : cos r, or m _ (m) cos 2 ' . ' m^ ~~ (w^)cosr' Thus, according to Fresnel, 7w __ 1 cos i __ sin r cos i ntj" fjL cos r sin i cos r According to MaccuUagh, m __ cos i _ sin 2i ■ -^ my ~"^cosr"~sin3/ •> :*; i ,r„i 6 Prof. Powell on the Demonstration of FresnePs Formulas . ^8. It may here be observed, that if we admit equal densities, we must nevertheless suppose some retarding power in the sether within the denser medium. It is still conceivable that this may follow the same law as that of increased density, and that thus Fresnel's formula might still apply. Or again, this reduces itself to the condition, that for perpen- dicular incidence we should have W /^' which might be simply the original condition, without involving the division by /x*, as above, and might be dependent directly on some hypothesis assumed as to the constitution of the sether. 19. Expressing FresnePs values by roman letters, and com- paring with Maccullagh's, we have m _ m 1 m^ m^ fA^' 20. According to the view of Cauchy, the density is diminished in the denser medium. If we suppose it diminished, according to the same law, 8 a 1 m q cos i KT = /tt' and — =fi^ . Of Mf cosr 21. Mr. Power, taking a for the distances of the molecules without, and a^ within, the medium, obtains what is equivalent to m __ al^v cos i 8^v cos i a^Vy cos r SpVf cos r ' but having avoided any assumption of the law of refraction at the outset, he deduces (§§ 18, 28) the value which seems irreconcileable with the admitted principle /a=-, unless by supposing S=8., which would agree with Maccullagh's W 1 view. Or if we could have ^ = — ^, the expression would agree with FresnePs view ; or if ^ =/Lt^, with that of diminished den- sity. But as neither of these suppositions seem reconcileable with admitted principles, it will not be material to discuss them further. Equivalent Vibrations. 22. As to the general nature of the vibratory forces concerned, it wiU be on all hands admitted that the vibratory force of the for Reflected and Refracted Light , 7 external sether or incident ray is the sole exciting cause of that communicated, partly to the reflected, partly to the refracted ray ; so that the vibratory force of the incident waves must be distributed between the reflected and refracted. 23. An obvious geometrical relation is derived from the known directions of the incident, reflected, and refracted rays, which, with the parallel to one of them, form a triangle, whose angles being known, the sides are in the ratios of their smes : and the same relation subsists between the por- tions of the amplitudes at right angles to the rays, and supposed to lie in the same plane. 24. The triangle formed by the directions of the incident, reflected, and refracted rays, will have — The angle formed by the incident and reflected rays =2f incident and refracted rays =(2-- r) ... ... reflected and refracted rays = [i + r) . Then the sides, or parts of the rays or amplitudes intercepted will be A' _ sin [i—r) h^ ^ sin %i h~ ~" ~~ (HO sin(2 + r)' h sin(if-r)* 25. Again, these sides have mechanically the relation of the resultant and components of the vibratory motions in their re- spective directions. Hence this simple relation is adopted by Prof. Maccullagh to express the relative amplitudes or velocities : and this is the more remarkable, since (as he observes) they so nearly resemble the expressions adopted by Fresnel, on the op- posite hypothesis of vibrations perpendicular to the plane of in- cidence, with which this construction can have no relation. 26. For vibrations perpendicular to the plane of incidence, or when the vibrations of all the three rays are parallel to the sur- face of the medium, it is also inferred that the amplitudes must be mechanically equivalent, or, as more distinctly argued by Mr. Power, that ^^ a particle at the surface of separation will be at one and the same moment performing its phase to the inci- dent, to the reflected, and to the refracted rays, with transverse velocities proportional to the amplitudes of those rays respect- ively ;" and that ^^ since this particle cannot move in more than one way at once, it is clear that the two latter must be equiva- lent to the former, according to the law of the composition of velocities.^' 6 Prof. Powell on the Demonstration of FresnePs Formulas 27. But these are merely particular cases of the general theory of "equivalence of vibrations/' first, I believe, systematically proposed by Prof. Maccullagli as the basis of his higher investi- gation of the laws of reflexion and refraction at the surfaces of crystals. Yet some cases of it appear to have been assumed by Fresnel, though under a slight, but material, difference of view. The general principle common to both is, that in " two conti- guous media, the incident, reflected, and refracted vibrations are mechanically equivalent : " but a difference in conception of the distribution of the force among them gives rise to a corresponding difference in the form of the expressions ; on either view, how- ever, these expressions indicate conditions distinctively applying to vibrations respectively parallel and perpendicular to the plane of incidence. 28. Taking three co-ordinate planes, XY that of the surface, XZ that of incidence, and YZ perpendicular to incidence, any vibration h passing through the origin taken at the point of in- cidence, and inclined to XZ by an angle 0, and to XY by <^, may be resolved into y=:hsmO, a?=Acos^cos, z=hcos6sin(l>. Then for h of the incident ray we have <^=:i and 9 A' of the reflected ray we have = 2 and 6' • . • hfO{ the refracted ray we have 0 = r and O^. The law of equivalent vibrations, according to Prof. Mac- cuUagh, is expressed by these relations between the resolved parts respectively : — in z, h cos 6 sin i + U cos 6' sin i = h^ cos 6^ sin r ; in y, A sin ^ + h! sin &=^h^ sin 6^ ; in a: J h cos 6 cos i + h! cos 6^ cos i = h^ cos 6^ cos r. 29. Hence if the plane of vibration coincide with YZ perpen- dicular to incidence, ^=^' = ^^=90°, and the law becomes simply If it coincide with XZ, 0=0'=6f = 0, and it becomes h cos i H- h' cos i = hj cos r, A + A'=A,'5iU(/4). 'cos 7 ^ '' These two may be included in the formula (A,)=A,(sin^ + ^cos^). . . . (L) 5=90° gives (h,)=hi, and 6=0 gives (k,)=h,^^. for Reflected and Refracted Light. ^ Sucli is the principle of equivalent vibrations, according to Prof. Maccullagh; in other words, it is founded on the pro- position that " the incident and reflected vibrations are equivalent to the refracted,'' 30. It does not appear to what extent Fresnel had adopted any generalized view of this kind ; but in the deduction of his formula, he introduces an equation which is equivalent to , cos r , cos I ' for vibrations parallel to the plane of incidence ; and if we sup- pose this to be the expression for the law of equivalence, in that case we must also take for that oi perpendicular vibrations, h'-h'=h,. In other words, the law of equivalent vibration, according to FresnePs view, will differ from that of Maccullagh in that it affirms the proposition that " the refracted and reflected vibrations are equivalent to the incident.'' These values of h^, which we will call (L'), may be combined in the same expression as before (L). Equation o/vis viva. 31. That the amplitudes of the vibrations are the measures of the velocities of those vibrations whose time is constant, is obvious; and further, that the square of the amplitude or velocity, multi- plied by the vibrating mass, is the true measure of the intensity ; and consequently that the principle of vis viva, of which it is a simple application, is true, undoubtedly receives ample proof a posteriori, inasmuch as all the calculations founded on this principle agree to such extreme accuracy with the experimental results, whatever question may have existed as to its establish- ment a priori, 32. Mr. Power, assuming the general principle, but following an original analytical method, deduces directly expressions for the vis viva of the incident, reflected, and refracted ray respect- ively ; and applies them by introducing the same expressions for the amplitudes as those of Maccullagh, and on the same suppo- sition as to the directions of the planes of vibration, though not on the same hypothesis as to the constitution of the sether, with respect to which he is led to conclusions of a peculiar kind, and which have been considered by some as questionable, but the consideration of which is foreign to the present inquiry. 33. Assuming the ordinary formula for vibrations in ang plane, u-=:hmn-:—(vt''x); 10 Prof. Powell on the Demotistration of FresnePs Formulas if n be the number of vibrations in a unit of time^ v=n\; and for two media, —=fx, -- = -^ =n for homogeneous light. V. A. A,, 84. If we consider, first, a single line of vibrating molecules, we may investigate the vis viva of that line ; but from this pro- ceeding to the vibrating mass, we must multiply the previous ex- pression by the density (or equivalent retarding property), which we may express generally by 8 and S, for the external and in- ternal ffither; and by the rectangular breadths of the oblique rays on the same base or section of the surface, which will be respectively proportional to cos i and cos r : thus we shall have in general for the multipliers, B cos i and 8^ cos r ; the former for the incident and reflected, the latter for the refracted ray. 35. Mr. Power's investigation is restricted to a particular hypothesis as to the density, but may be more simply and gene- rally followed out thus : — For a length dx, in which the molecules have a common velocity, we may take for that velocity, imd for a single line of vibrating molecules, the vis viva I v*ar = — Tj — I C0B^—{vt—iC)ax, For a portion from a? to a7+X, the integral is easily found to reduce to ^ ; and thus for those limits, \^dx = — r — = 27r^nh^v = (p) ; and for the vibrating mass, as before explained (34), For the incident ray p=27r^nh^vB cos i . . . reflected ray p' = 27r^nh!^vB cos i . . • refracted ray j9^ = 2'7T%h^vPi cos r . But since the principle of vis viva gives p = j^' +/>y, we have the equation connecting the vires viva, fiB cos i{h'^'-h'^) = 8 1 cos rh^^, or generally m(A«-.A'2) = m^«; . (M) where, on substituting the values of m and m^ on the respective hypotheses, we can express the vires viva equally on the respect- ive views of Fresnel, Maccullagh, and others. r for Rejected and Refracted Light, 11 36. In some of these investigations, reference has been made to the mechanical doctrine of the impact of elastic bodies, to which the communication of vibratory motion in aether presents, so striking an analogy. The well-known equations expressing the law of impact are adopted directly as the basis of FresneFs proof in the case of vibrations perpendicular to the plane of in- cidence, giving rise to his formulas (H). The very same equation is deduced by MaccuUagh from his abstract dynamical principles, without reference to the above- mentioned analogy; but applied on the same hypothesis as to the vibrations, and on his assumption as to the density, it pro- duces his formulas (K). 37. This deduction, which is independent of any particular supposition as to densities or direction ofvibrations, is as follows: — Combining equations (L) and (M), we have h^^j^i _m^ _ {h-Vh!){h'-h!)_ h-Ji hf ""m ~ {h^lif ~A+A'' whence, ^^ = fi. . . . . . . . . . . (N) whence again, ■ (*+*'^=2-=*"»'^f-'=^; ' • • • (0) Deduction of Expressions for the Amplitudes. 38. (I.) On the hypothesis of equal densities, we have directly, on substituting in the equation (N) the values of the masses and dividing by k, supposed = 1, m=sin22, my=sin2r, ' y— si^^^—si^^^ I. __ 2 sin 2i ~" sin2i + sin2/*' '"" sin2i + sin2r* ' ' ^ ' These are MaccuUagh's formulas deduced in the same way, and here (as before) A;' changes sign at i-{-r = 9(f. 39. It is also evident that these values fulfil the equations of vis viva (M), viz. (yt2~F) = A:2-^^=sin22sin2r, . ^ ' ' yL6COS2 as well as that of equivalence of vibrations (L), A; + ^' = ^^=2sin2i; which last shows that they belong necessarily to vibrations jser- pendicular to the plane of incidence. 40. For vibrations joar«//ei to the plane of incidence : — since we iJi Prof. Powell on the Demonstration of PresnePs Formulas are here concerned only with the ratios of the amplitudes, we may suppose one of them the same as in the last case, and thence find the others, which will be different in order to fulfil the dif- ferent conditions. Thus assuming k,=hi, the condition of equi- valence (L) gives /A . jLh 1 cosr ^ . ^.cosr ... (n-\-h')=h. r=3sm3f ;=4smtco8r : ' cost cos I and from this, with that of vis viva (M), viz. cos r {h^ — h'^) = h^ r = 1 6 sin i cos i sin r cos r = (A + h') (h — h!) (A—//) =4 cos i sin r 2A = 4 sin i cos r + 4 cos i sin r 2h' = 4 sin t cos r — 4 cos i sin r ; and since always sin i > sin r and cos r > cos «, the last value is always positive. Hence dividing by h, considered = 1, hi^'Mz^ _^sin2f . . . (H) the same values as those derived from the geometrical construc- tion before mentioned (24). 41. '(II.) On the hypothesis of increased density (or of in- creased retardation supposed to be represented by the same law), we have for the masses 7w = sinrcos«, m^=sinicosr, in which, since sin r < sin i and cos i -^=4sin2isin2r==(it + ^')(^-^'). whence k-k'=2sm2i 2k = sm2r+ sin2i 2k' = sin 2r — sin 2i. Hence, as before, ,,__ sin 2r— sin 2i , __ 4 sin rcos i .^. ~" sin2r-f8in22' '"^ sin2r+sin2e* ' * ^ ' And since for i='m or (« + r) =90°, sin 2r=sin 2«, we have A;'=0; for incidences, i < ct, we have sin 2r < sin 2i, and therefore — A;'; and for i > ot sin 2r > sin 2z or + k', 44. Or again, without assuming the value of k^, we may proceed thus : from the equation of vis viva, ' sin z cosr ' * from the law of equivalence, ^ ' cosV Equating these, we have (F — ^'^) sin r cos^ r cos z = (Z: + ^^)^ sin z cos^ i cos r (F-P) sin 2r= (^ + yt')2 sin 2i F(sin 2r - sin 2i) = 2kk' sin 22 + ^^(sin 2% 4- sin 2r) j and observing that 2M' sin 2i=kU(^ (sin 2?— sin 2r) + (sin 2i + sin 2r) ) (A; + A;')^(sin 2r — sin 2f) = (A; + A:')^'(sin 2 i + sin 2r) A: (sin 2r — sin 2i) = ^'(sin 2r + sin 2z) cos z A: + A:' = 2 sin 2r, and thence k{=-2 sin 2r ; ' ' cosr or as before, dividing by k, J __ sin 2r — sin 2i t. _ 4 sin r cos i sin 2r + sin 2i' ' sin 2r -|- sin 2i 45. Now it is to be observed that these formulas differ from 14 Prof. Powell on the Demonstration of FresnePs Formulas those of Fresnel, as before given, in that the numerator of ^ is here negative for t < to- and positive for t > w. This difference is traceable to the process by which the deduc- tion of Fresnel's original form was effected ; it being made by means of two equations (see Airy's Tract, § 129), one of which is the same as the equation of vis viva, viz. sin r cos i{k^ — A/^) = sin t cos rk^^ ; the other is cos i{k — ^) = cos r k^, which involves a different assumption as to the principle of equi- valent vibrations, as before observed (30). 46. It will be desirable to follow the deduction of the for- mulas on this supposition. For vibrations perpendicular to the plane of incidence, from the vis viva, smrco.i ^ ^smicosr ' From this law of equivalence (30), {h-h')^=h,^. Hence {h^—h'^) sin r cos « = [h—h^Y sin i cos r, or {h + A') sin r cos i = (A — A') sin i cos r A(sin i cos r — sin r cos i) = A'(sin r cos i + sin i cos r), whence y__ sin (i— r) _ 2 sin r cos e 8in(2 4-r) ' sm(«+r) These differ from Fresnel's original formulas in the sign of A'. 47. For vibrations parallel to the plane of incidence, on the same supposition (30) we have 'cos I and thence, as in (44), {k'-k!^ sin2r=(^-;fc')^ sin 2« ; whence, in like manner, (A:— A:')A:(sin2i-sin2r)=:(^~^)^(sin2i-f sin 2r), and thence ^ sin 2i - sin 2r , , 4 sin r cos i sm 2t -f sm 2r' ' sm 2? h- sm 2r' for Reflected and Refracted Light, ' 15 which are the formulas of Fresnel as originally deduced, and in which (as before) we have + A:' for i < «r, and — A:' for i'^ 'ur. 48. Here, again, we might otherwise deduce the same for- mulas; as before (43) assuming A:y=2Ap we should have A:-/t'=/t^=2sin2r, cos I and (A;^— A:'^) =4 sin2r sin %i gives A; + A:' = 2 sin 22, whence ,, sin2z— sin2r , , 4 sin r cos 2 sm2«+sm2r ' sin22 + sm2r 49. In another point of view we may observe the relation sub- sisting between all the above formulas (generalizing a remark in Mr. Power's paper), as follows : — Trigonometrically, we have evidently, sin^(zH-r)— sin^ (i— r)= sin2isin2r, (P) [sin 22 + sin 2r] ^ — [sin 2i — sin 2r] ^ = 4 sin 22 sin 2r. (Q) 50. Also from /^, sin r = sin f, we have the identical equation 4/A sin r sin i cos^ i cos r = 4 sin^ i cos^ i cos r, or . fjb cos 2(sin 2r sin 22) = cos r(sin^ 22) ; whence, substituting in this equation the value from (P), it becomes /u.cos2[sin^ (2 + /*)— sin^ (i— r)] = cosr(sin2 22) ; or from (Q) we have fi cos i[(sin 22 + sin 2r)^— (sin 22— sin 2r)^] = cos r 4 sin^ 2a; which agree with the formulas of MaccuUagh, and the equation of vis viva on the hypothesis of equal densities. 51. Again, we have the identical equation 4 cos^2' sin 2 sin r cosr = 4/-t sin r cos^ i sin r cos r, or cos 2 (sin 22 sin 2r) =^6 cos r(4 cos^ i sin^ r) ; whence from (P) we have cos i [sin^(2 + r) — sin^(2 —r)] =ft cos y*(4 cos^ i sin^ r) ; or from (Q) we have cos 2 [(sin 22 + sin 2r)^-- (sin 22— sin 2r)^] =fjb cos r(16 cosSsinV) ; which agree with FresnePs formulas, and the equation of vis viva on the hypothesis of increased density. 52. But thus far nothing determines the plane of vibration. For this purpose we must apply the law of equivalent vibrations ; and in either case, since it is the squares of the amplitudes which enter the formulas, we may take + A', + h^, ± A:', + k^y according 16 Prof. Powell on the Demonstration of Fresnel's Formulas as they fulfil the conditioDs with the upper or lower sign : in this way we reproduce the foregoing results, which it is needless here to repeat. Experimental Evidence. 53. That the whole series of experimental results relative to polarization are accurately represented by the foregoing formulas, has been fully substantiated by the researches of Fresnel, Arago, Brewster, and others; but these changes aiFord no distinctive test between the several theories here adverted to. 54. It may be desirable more particularly here to notice the interpretation of the change of sign in these formulas. In general it is obvious, that in the elementary formula M=A sin -r— [vt^x); if we suppose x increased to ^+ -, we have At M' = Asin— fv/— a?— ^)=Asin —{vt—x) — ir \=—h%\n — {vt—x\ or that a difference of sign indicates a change of 180° in phase, and that this is equivalent to a change of jr in route. 55. This conclusion includes the solution of the difficulty as to the loss or gain of half a wave-length between reflexion at the first surface of a dense medium represented by sin («— r), where we have i > r ; and at the second, where we have i < r, which gives —sin (i— r), — a difficulty which so long embarrassed the early history of the theory, and which it is perhaps desirable to state thus clearly, though of so elementary a character, as it would sometimes appear to be still felt. There are, however, other cases when this change of sign is material. Intensities of Light, 56. The intensities of the reflected and refracted rays at dif- ferent incidences, as compared with that of the incident light, are measured by the vires vivce, that is, by the vibrating masses multiplied by the squares of the amplitudes or velocities. Thus, considering the intensity of the incident ray as unity, for (H) let : I=mA^ \^mfif, And for (K) let for Reflected and Refracted Light. 17 or dividing, m, ' m ' w —A. • tJ I — /I/ 1 , ' m ' whence, calculating the values of A', h^ and A/, k^ for the several incidences, we have the intensities directly. But from the equation of vis viva we have ^ m ' {^-n=^kr- rrif m Thus, knowing only the values h! and A:', we obtain at once those of the refracted intensities, instead of having to calculate h^ and kif which is a troublesome process ; thus we take simply 1^=1 -A'2^ J^=l-A;'2. And this, it will be observed, is independent of any hypothesis as to densities. 57. If we calculate I^ and Jy directly as above, the values of the amplitudes will differ according to the hypotheses of the density : but then we have to observe, as before, that (denoting FresnePs values by roman letters) we have (14) and (19) z. I. 7 1 my m, 1 and thus m ' m ' m ' m ' Thus, either way, the calculated intensities will be the same on either hypothesis. 58. To trace the intensities at different incidences : — (1 .) At the perpendicular incidence i = 0 and r = 0. Thus the formulas become A' =^, ^' = 7:' But the actual values may be found, since at perpendicular incidences we have (16), For equal densities, — ^ = - ; ^ m fjb' m For increased density, — = /jl. In either case the formula h' = '- will ffive - UTTW Phil. Mag. S. 4. Vol. 13. No. 76. July 1856. C 18 Prof. Powell on the Demonstration of FresnePs Formulas • This was Dr. Young's formula, deduced in an early stage of these inquiries. If we suppose /ia = 1*5, this will give I,= l_r=-96. Also ^^^,co8 (i-r)^^ cos (i + r) whence J = k!^ = h'^ ='04>, J^=-96. (2.) For the angle of complete polarization 2 + r=90°, sin (t — r) = cos 2r, sin (i + r) = 1, tan i = /^ = 1 -5 = tan 56*^ 1 9', I=A'2= cos«2r, J=l-A'«= sin22r, j^^a^tanM«-r)^ j=l«;t«=l. • CO ' (3.) In the limit of oblique incidence, t = 90°, sin (i — r) = cos r, sin (i + r) = cos r, I = A'2=1, J = l-r=0, tan(90-r) = tan(904-r), I^=jt'«=l, J^=l-A'2=0. (4.) For these and other incidences generally, the following table will show the approximate intensities. Intensities at different Incidences. ,* = l-5. Formulas H. Formulas K. i. r. I=A'2. I, = (l-A'2). J=k'^. J, = (l-fr'2). 0 ' 0 ' •040 •960 •040 •960 20 13 10 •047 •953 •034 •966 40 25 22 •077 •923 •014 •986 56 19 33 41 •J52 •848 •000 1000 60 35 16 •176 •824 •002 •998 80 41 2 •515 •485 •197 •803 90 - 41 49 1000 •000 1-000 •000 59. The necessary imperfections of photometry preclude any accurate verification of these numerical results ; but by throwing the two images of a round hole in an opake plate covering one end of a rhomboid of iceland spar on a surface of glass, at dif- ferent incidences, the eye can readily compare the intensities in some of the more marked cases, both of the reflected and the transmitted rays, of the two beams polarized in planes at right angles to each other; which show a general agreement with theory. for Reflected and Refracted Light. 19 60. The question whether the plane of vibration is parallel or perpendicular to the plane of polarization, has been lately dis- cussed at large by M. Haidinger, who, after an extended com- parative view of the experimental consequences involved in con- nexion with various optical phsenomena on either supposition, decides in favour of the superior simplicity and consistency of FresneVs view, that the plane of vibration is perpendicular to the plane of polarization. (See Phil. Mag. March 1856, vol. xi. p. 242, No. 71. The original is in Poggendorff's Annalen, Oct. 1855. See also Silliman^s Journal, Jan. 1856.) 61. A very refined and ingenious suggestion for a direct " experimentum crucis" was made by Mr. J. A. Dale to the British Association in 1846, but practical difiiculties appear to stand in the way of its application. (See ' Report,' 1846, Sec- tion A.) 62. But a more recent result of Prof. Stokes is perfectly con- clusive on the question of the direction of the plane of vibration. In his paper " On the Dynamical Theory of Diffraction ^' (Cam- bridge Transactions, vol. ix. part 1, 1849), he has estabhshed theoretically the conclusion, that the plane of vibration of a dif- fracted ray previously polarized, is in general different from that of the incident, except when perpendicular, and when parallel, to the plane of diffraction. For intermediate positions their directions are connected by a simple law, which may be expressed by saying, that if the arcs of inclination of the vibrations to the perpen- dicular to the plane of diffraction be measured on two semicircles intersecting in a common diameter coinciding with that perpen- dicular, and inclined to each other at the angle of diffraction, then the arc of inclination of the incident vibration, measured from the point of intersection, being taken as longitude, that of the diffracted vibration will be the corresponding right ascension. If the two semicircles, whose planes are respectivelyperpendicular to the directions of the incident and the difiracted rays, be inclined at an angle 6, equal to the angle of diffractive deviation, and if a^ and a^ be the inclinations of the diffracted and inci- dent vibrations measured from the inter- section (f, by Mr. Stokes's theory they are connected by the equation tan oLd= cos 6 tan ui, which leads to the construction here re- presented by the arc of a great circle pass- ing through the extremities of u^ and «£ perpendicular to the plane of a^. Whence it follows, that near the intersection {(f), C2 20 Mr. A. Cay ley on the Cones which pass through that is the perpendicular position, the changes in the inclination of the difiracted ray will be much less rapid, or the indications more crowded together, than near the parallel position (90^), or the plane of diffraction. But we can observe the changes only in the plane of polariza- tion. If, then, these changes are more slow near the perpen- dicular (0°), the planes of polarization are parallel to those of vibration; if near the parallel (90^), then they are perpendicular to those of vibration. A series of experiments of the most elaborate and accurate kind unequivocally show the latter to be the fact. 63. Thus experiment obliges us to adopt FresneVs hypothesis of vibrations perpendicular to the plane of polarization^ and by con- sequence (as here shown) either increased density or some other property eocpressed by the same law. In thus being compelled to relinquish the hypothesis of equal density, or at least the formulas expressing it, we do not, in fact, sacrifice anything in point of simplicity, the same amount of analysis being requisite to deduce the expressions on either sup- position ; and in giving up the beautiful geometry of Maccullagh, we do ample justice to his more substantial discoveries, — the general laws of equivalence of vibrations (whatever difference may arise on a subordinate point), and their connexion with the principle of conservation of vis viva, on which the whole theory reposes. There are, however, some other points hinted at in what precedes, which may demand further inquiry at a future opportunity. II. On the Cones which pass through a given Curve of the Third Order in Space. By A. Cayley, Esq.^ THE following investigation is connected with the theory of the cubic (a, b, c, d^jc, y)^, and in particular with a theorem that the determinant formed with the second differential coeffi- cients of the discriminant gives the square of the discriminant. Consider the coefficients a, 6, c, d as linear functions of co- ordinates, the equations flc-Z>«=0, bc'-ad=0, bd—c^=0 (equivalent, of course, to two equations) belong to a curve of the third order in space, the edge of regression of the developable surface obtained by putting the discriminant equal to zero, or which has for its equation -a«<^ + Gabcd- 4a<^ - 4b^d+ Sb^c^ = 0. And, moreover, the above forms are the general representations * Communicated by the Author. a given Curve of the Third Order in Space. 21 of any curve of the third order, and developable surface of the fourth order. The question arises, to find the equation of the cone of the third order having an arbitrary point for its vertex, and passing through the curve of the third order. This may be done by JoachimsthaFs method : let a, /3, 7, h be the values of a, by Cj d at the vertex of the cone, and in the equations of the curve, say in ac-62=0, bd-c^=0, for a, b, c, d write ua + vu, ub + v/5, uc + «;7, ud-\-vh', if from the equations so obtained u, v are eliminated, the resulting equation will be that of the cone of the third order. The substitutions in question give lJu^-{-'m!uv + Wv^=0, where L =2(flc-62), M =:«7 + ca-26^, N =2(a7~^2)^ y = 2{bd-c^), M' = 6S + (//3-.2cy, W = 2{^8-y^), The result of the elimination is 4(LN -^ M^) (L'N' - M'^) - (LN' + UN - 2MM02 = 0, and we have LN -M2 =4^{by-c^){a^-boc)-(coc-ay)% yW-W^ = 4^{c8-dy){by-cfi)-{bS-dy)^y LN' + L'N-2MM'=4(67-C)8)2 + 4(«y8-6a)(cS-)^+ {8a— 7c)r} + Q{ - acp-{-{rib - ^c)q -\- Ur) ■^B>{-{ud-^c)p-(^d-2yc)q 4- 28cr} =0, where a, b, c, d are current co-ordinates, and p, q, r are quadratic functions of a, b, c, d. The equation is (as it should be) satisfied by the equations (/?=0, ^' = 0, r = 0) of the given curve; it is also satisfied per se when P = 0, Q = 0, R = 0, 2. e. when the vertex is a point on the curve ; this indicates a change in form of the equation, and in fact the cone is in this case of the second order only. Suppose that the co-ordinates of the vertex are in this case given by 7^ = — = ^ = — {a an arbitrary quantity), it p 7 6 o" may be easily shown that the equation of the cone is or at full length, {bd-c^) + a(bc-ad) -\- a^ac-b'^) =0. In fact this equation is evidently that of a surface of the second order passing through the curve ; and there is no difficulty in showing that it is a cone. 2 Stone Buildings, MavM856. [ 23 ] * H ^M m. III. On a peculiar Power possessed by Porous Media {Sand and Charcoal) of removing Matter from Solution in Water, By Henry M. Witt^ F.C.S., Assistant Chemist to the Govern- ment School of Applied Science^. VARIOUS methods have been employed at different times for the purification of water for the supply of towns, but none has been found so practically convenient and efficacious as simple filtration through porous media, such as sand ; moreover, charcoal being known to possess a peculiar power of removing organic matters from solution, this substance has been sug- gested and occasionally employed either as a substitute for, or an auxiliary to, ordinary sand filtration. The following experiments were undertaken with the view of ascertaining by chemical analysis the more precise nature of the effects produced upon ordinary river-water, such as that of the Thames, by its passage through filters composed of these media respectively, and of comparing their powers ; but it is believed that the results obtained possess an interest extending con- siderably beyond the question to assist in the solution of which they were made. Before proceeding to the construction of experimental filters, I availed myself of the kindness of Mr. James Simpson, en- gineer to the Chelsea Waterworks Company, to investigate the results obtained by that Company's system of filtration as carried on up to the present time at Chelsea ; and I have much pleasure in embracing this opportunity of expressing my obligation to this gentleman, and specially also to his son, Mr. James Simp- son, jun., to whom I am greatly indebted for his very able cooperation throughout this inquiry. The system of purification adopted by the Chelsea Water- works Company at their works at Chelsea, consisted hitherto (for the supply has by this time commenced from Kingston) in pumping the water up out of the river into subsiding reservoirs, where it remained for six hours ; it was then allowed to run on to the filter beds. These are large beds of sand and gravel, each exposing a filtering surface of about 270 square feet, and the water passes through them at the rate of about 6^ gallons per square foot of filtering surface per hour, making a total quantity of 1687*5 gallons per hour through each filter. The filters are composed of the following strata in a descend- ing order : — * Communicated by the Author. 24 Mr. H. M". Witt on the Power possessed by Porous Media No. ft. 2 1 0 0 3 in. 6 0 6 8 3 Fine sand Coarser sand Shells. . . Fine gravel . 5. Coarse gravel These several layers of filtering mate _ fectly flat, but are disposed in waves, as seen in the sectional drawing; and below the convex curve of each undulation placed a porous earthenware pipe, which conducts water into the mains for distribution. ials are not placed per- the IS filtered Chelsea Waterworks, Thames Bank. Transverse Section of Filter. Downward Filtration. a. Water line. b. Top of fine sand. c. Collecting drain (perforated). Note. — Depth of water over the sand =4 ft. 6 in. The upper layer of sand is renewed about every six months, but the body of the filter has been in use for about twenty years. Samples of water were taken and submitted to examination — 1st. From the reservoir into which the water was at the time being pumped from the middle of the river. 2nd. From the cistern after subsidence and filtration. Experiments of this kind were made on three diff^erent occa- sions, viz. on the 12th of September and the 29th of December, 1855 ; and also on the 10th of May 1856 ; and the results are embodied in Tables I., II. and III., each containing four columns, — No. 1 showing the quantities of the several sub- stances originally present, represented in grains in the imperial gallon (70,000 grains) of water ; No. 2, the amounts present after filtration ; No. 3, the actual quantities separated in grains in the gallon of water ; and No. 4, the per-centage ratio which the amounts separated bear to the quantities originally present. of removing Matter from Solution in Water. 25 Results of Filtration through Sand at the Chelsea Waterworks, Table I.— September 12, 1855. 1. Originally present. 2. Present after filtration. 3. Amount separated. 4. Per-centage ratio of sepa- rated matter. Total solid residue (including suspended matter) 1 65-527 1-240 64-287 16-112 48175 12-240 20-170 41-290 0-674 40-616 24-237 0-566 23-671 nearly 7-559 1-100 1-820 36-98 45-63 36-82 all. 15-69 9-23 Organic matter Total mineral matter Total solu ble salts 40-616 11-140 18-357 Chlorine Chloride of sodium Table II.— December 29, 1855. 1. Originally present. 2. After filtration. 3. Amount separated. 4. Per-centage ratio of sepa- rated matter. Total solid residue (including susnended matter^ 1 31 -467 2-375 29-092 7-035 22057 8-675 1-667 2-747 2-962 24-153 1-889 22-264 1-403 20-861 8-402 1-546 2-547 2-372 7-314 0-486 6-828 5-632 M96 0-273 0-121 0-200 0-590 23-24 20-46 23-47 80-05 5'42 3-14 7-25 7-28 19-92 Total mineral matter... Suspended matter Total dissolved salts Lime Chlorine Chloride of sodium Sulphuric acid Table III.— May 10, 1856. 1. Originally present. 2. After filtration. 3. Amount separated. 4. Per-centage ratio of sepa- rated matter. Total solid residue (including suspended matter) 1 55-60 4-05 51-55 28-93 22-62 8-719 22-85 1-349 21-501 2-285 19-216 8-426 32-75 2-70 30049 26-645 3-404 0-293 58-90 66-66 58-29 92-10 1^ Total mineral matter Suspended matter Total dissolved salts By these analytical results (if entitled to confidence, and I may state that all due care and attention was given to ensure their accuracy) it is shown that this process of mere sand fil- tration is one of more importance, and of a more peculiar and interesting character, than has generally been supposed. It has been asserted as a principle that sand filtration can 26 Mr. H. M. Witt on the Power possessed by Porous Media only remove bodies niechanieally suspended in water, but I am not aware that this statement has been established by experi- ment; in fact, I am not acquainted with any published ana- lytical examination of the efifccts of sand filtration. These experiments supply the deficiency, and show moreover, that these porous media are not only capable of removing sus- pended matter (80 to 92 per cent.), but even of separating a certain appreciable quantity of the salts from solution in water ! viz. from 5 to 15 per cent, of the amount originally present, 9 to 19 per cent, of the common salt, 3 per cent, of the lime, and 5 of the sulphuric acid. It is curious also -that the proportion of matter removed in this way depends to a certain extent upon the degree of impurity of the water; the greater the quantity of matter originally present in the water, the larger the per-centage ratio of the salts removed, e. g. : — In Sept. In Dec. In May. Total impurity of water . . . 65-527 31*467 55-90 Per-centage of salts removed . 15*69 5*42 15*04 This point will, however, become more apparent by comparing these experiments with those made at Kingston, where the water is much purer, to which I shall have occasion hereafter more particularly to refer. This fact, of the power possessed by sand and other porous media, which rests for demonstration not only upon the three preceding experiments, but also upon others to be presently described, is one of great importance, not only in a hygienic and oeconomic point of view as relating to the great question of water supply, but also in its bearings upon agriculture and geology. It is possible that soils may remove matters from solution in water, not only by decompositions between the contained salts and the aluminous silicates of the soil (as demonstrated by Mc. Way), but also in virtue of this peculiar action. ! Again, water containing considerable quantities of saline matter in solution may, by merely percolating through great masses of porous strata during long periods, be gradually de- prived of its salts to such an extent as probably to render even sea-water fresh. This may in fact be one of the causes contributing towards the production of freshwater springs which ebb and flow with the tide in the vicinity of the sea : for instance, Darwin, in the ' Voyage of the Beagle' (vol. iii. p. 545), mentions that on Keeling Island, one of the coral reefs near the coast of Sumatra, there are freshwater wells which ebb and flow with the tide. Mr. Darwin, however, suggests another explanation of this of removing Matter from Solution in Water. 27 phsenomenon ; he says that " at first sight it would appear not a Uttle remarkable that the fresh water should regularly ebb and flow with the tide. We must believe that the compressed sand or porous coral rock acts like a sponge, and that the rain- water which falls on the ground being specifically lighter than salt, floats on its surface, and is subject to the same movements. There can be no actual attraction between salt and fresh water, and the spongy texture must tend to prevent all admixture from slight disturbances. On the other hand, where the foun- dation consists only of loose fragments, upon a well being dug salt or brackish water enters, of which fact we saw an instance on this small island.^^ Now I would not presume to deny the accuracy of this ex- planation, still it is possible that the phsenomenon may be a mixed one, and that the peculiar power which I have found to be possessed by porous media may contribute towards the re- sult by abstracting a portion (at least) of the salts from the sea- water during its passage through the porous rock. Moreover, there are certain difficulties in Mr. Darwin^s ex- planation. If the sand did not possess the power of removing salts from solution, to a certain extent at all events, the rain- water inside would tend, more or less rapidly, to become salt by the commixture with it of the sea-water from without, which would take place through the porous diaphragm so much the more readily on account of their difference of density, in virtue of the '^ osmotic force '^ so ably investigated by Professor Graham. Indeed, the last fact mentioned by Mr. Darwin, viz. that when the wall consists of loose fragments the wells are salt, tends to show that it is only the very finely divided sand, the porous me- dium offering a considerable extent of surface, which possesses the power of removing the salts, for if the non-commixture of the salt and fresh water arose only from their difference of density, the coarseness of the diaphragm would not materially affect it. As to the cause of this peculiar action, the only suggestion which I may venture to offer is, that it possibly arises from the weak chemical affinity in virtue of which salts are held in solu- tion in water, being overcome by a physical force, the attraction of cohesion, or more properly adhesion, exerted by the greatly extended surface of the porous body ; this is not a solitary in- stance of such weak chemical forces as solution being overcome by a physical attraction. Gmelin* instances several other ex- amples of the power of the physical force of '^ adhesion " to over- come weak chemical attractions, e. g. : " When vinegar is filtered through quartz sand, the first portion of liquid that runs through * Handbook of Chemistry, Cavendish Society's Translation, vol. i. p. 114. 28 Mr. H. M. Witt on the Power possessed by Porous Media is robbed of almost all its acid, and the vinegar does not pass through unchanged until the sand has become well charged with acid. Potato brandy diluted with water, and filtered through quartz sand, yields at first pure water, then a mixture of water and alcohol deprived of its fusel oil, and lastly, the original mixture unaltered : wood shavings also deprive vinegar of nearly all its acid ; charcoal acts still more powerfully*/' Now it is possible that these being organic compounds they may be oxidized, even into carbonic acid and water, under these circumstances; but whatever difference of opinion may arise respecting the caiLse, this cannot affect the simple experimental fact. It will naturally be asked, if sand possess this power, Are not the salts removed from the water accumulated in the sand, and would not this throw light upon the mode of formation of sand- stone conglomerate rocks ? To enable me to reply to this ques- tion, I have in my possession samples of sand, before use, and also after employment in the middle of the filter at Chelsea for no less than twenty years, and their analyses will form the sub- i'ect of a future communication ; pressure of other duties having litherto prevented me. from the completion of this important point in the inquiry. But, as before mentioned, the preceding are not the only ex- periments which I have made on this subject : the following were performed at Kingston, where the water is far purer, more par- ticularly for the purpose of ascertaining the effects of charcoal and comparing its powers with those of sand. A.t the time these experiments were in progress, the Company's filter-beds at Kingston, now just completed, were unfinished, and consequently, in order to ascertain the effects both of sand and charcoal on the comparatively pure water of Kingston, it became necessary to construct smaller experimental filters. The earlier experiments were upon the effects of charcoal, and several preliminary trials were made for the purpose of ascertain- ing the form of filter and rate of filtration which would nearest approximate to the operation as carried on on the large scale. In the first of these experiments, to which attention may be drawn, the water was pumped from the river into a cistern of slate, where a deposition of the greater portion of the suspended matter took place ; it was then conducted into the upper part of the right-hand compartment of a nearly cubical wooden cistern, this right-hand compartment being separated from the one on the left by a porous diaphragm, the walls of which were of wire- gauze, and the interior filled with fragments of oak charcoal, about the size of a hazel nut to a walnut : this charcoal dia- * Wagenmann, Poggendorff's Annalen, xxiv. 600. of removing Matter from Solution in Water, 29 phragm exposed a filtering surface of about 4'38 square feet ; the filtration was lateral and descending, the water entering at the upper part of the right-hand compartment, and passing out at the lower extremity of the left-hand division; the rate of filtration being half a gallon per minute. A sample of the water was analysed before passing into the filter, and after coming from it, after the continuance of the opera- tion for a certain number of hours. The results were as follows : — Table IV. Original water used. After 67 hours' action. After 91 hours' action. Com- parison. Amount sepa- rated. Per-cent- age ratio of quantity separated. Com- parison. Amount sepa- rated. Per-cent- age ratio ofquantity separated. Total residue Mineral salts Organic matter ... Chlorine 23-949 22-519 1-430 1054 1-737 23-668 0-475 0-281 0-*955 117 66-78 22076 21-618 0-458 0-9731 1-603 1-873 0-801 0-972 -081 0134 7-82 4-00 68-00 7-685 7-714 Chloride of sodium. After 115 hours' action. After 139 hours' action. • Total residue Mineral salts Organic matter ... Chlorine Chloride of sodium. 23-949 22-519 1-430 1-054 1-737 23-012 0-'620 0-885 1-457 0-937 0-81*0 0169 0-280 3-91 56-67 1603 16-10 23-411 22-44 0-971 0-973 1-603 0-538 0079 0-459 0081 0-134 2-242 3-66 32-10 9-73 9-8 This experiment exhibits more strikingly perhaps than any of the others, the very curious circumstance that in the employ- ment of charcoal the amount of impurity separated by it goes on increasing to a certain point, and then diminishes ; to which, however, I must again more particularly allude after describing the experiment comparing sand and charcoal simultaneously ; it demonstrates also very satisfactorily the power possessed by charcoal, like sand, of removing not only suspended matters, but also soluble salts, e. g. chloride of sodium : but to this point I shall again refer. Although very satisfactory as showing the power of charcoal under the circumstances of the experiment, yet it being pro- bable that by employing the charcoal in lumps, as was done, it had not a fair chance of exhibiting its peculiar properties, inas- much as only very imperfect contact was efiected between the impurities contained in the water and the particles of charcoal, it was resolved to try an experiment with charcoal in powder, or nearly so, in granules of the size of a pea. Moreover, even then we should have succeeded only in proving the absolute effect of 30 Mr. H. M. Witt on the Power possessed by Porous Media charcoal^ for we bad learnt that the resiilts thus obtained did not admit of comparison with those of filtration through sand at Chelsea, on account of the great difference in the original com- position of the water; therefore, in order to establish at the same time the absolute effect of charcoal as a filtering medium upon the purer water at Kingston, and also to compare it with that of sand, two experiments were made simultaneously with the same water, the one of filtration through charcoal alone, and the other through sand alone, both under precisely similar cir- cumstances. In both these experiments the filtration was not effected laterally as in the foregoing case, but downwards in the usual way through beds of the same size of the respective filter- ing media contained in wooden troughs, the water being ad- mitted at the top and passing off from below. The sand-filter had an area of 4 square feet, and consisted of the following materials : — ft. in. Fine sand 19 Shells 0 1^ Qravel 0 11 Coarse gravel 0 9 2 9 The rate of filtration being half a gallon per minute. Table V. — Results of Sand Filtration. Original water used. After 23 hours' action. After 120 hours' action: Com- parison. Amount sepa- rated. Per-cent- age ratio of quantity separated. Com- parison. Amount sepa- rated. Per-cent- age ratio of quantity separated. Total residue Mineral salts Organic matter ... Suspended matter. Chlorine 24-578 23-687 0-8906 3-509 0-862 1-420 23-87 22-858 1-012 2-663 0-708 0-829 0-*846 2-88 3-50 2i'm 23-69 23-04 0-648 0-671 1-105 0-888 0-647 02426 0-191 0315 3-613 2-73 2216 22-U Chloride of sodium. ^ Aftor 240 hovan' action. After 376 hours'^Action. Total residue Mineral salts Organic matter ... Suspended matter. Chlorine 24-578 23-687 0-8906 3509 0-862 1-420 22-534 21-517 0-917 1-88 0-674 1110 2044 2-170 • i-629 0-188 0-310 8-316 9161 46-423 21-8 21-8 22-507 21-698 0-809 1-584 2-071 1-989 1-925 8-426 8-397 54-85 Chloride of sodium. Apart from its special interest, as compared with the following experiment made simultaneously through charcoal, the following of removing mattei' from Solution in Water, 31 points are in themselves remarkable in the results obtained by this filtration through sand : — 1st. That the filter continued increasing in efficacy even till the conclusion of the experiment, i. e. for 376 hours, not having lost any of its power when the experiment was terminated. 2nd. That no weighable quantity of dissolved organic matter was removed by the sand in this experiment ; but it must be remembered that the quantity originally present was but small. 3rd. Its power of removing soluble salts was considerable ; as a maximum, 21 per cent, of the common salt being separated. Table VI. — Results of Charcoal Filtration. Original water used. After 72 hours' action. After 120 hours' action. Com- parison. Amount sepa- rated. Per-cent- age ratio of quantity separated. Com- parison. Amount sepa- rated. Per-cent- age ratio of quantity separated. Total residue Mineral matter ... Organic matter . . . Suspended matter. Chlorine 24-578 23-687 0-8906 3-509 0-862 1-420 22-13 21-375 0-755 2-448 2-312 01356 9-906 9-76 15-22 21-644 3-06 2-934 0-449 11-93 12-79 Chloride of sodium. After 240 hours' action. After 376 hours' action. Total residue Mineral matter . . . Organic matter ... Suspended matter. Chlorine 24-578 23-687 0-8906 3-509 0-862 1-420 20-821 2-79 3-757 0-7i'9 15-28 20-48 21-374 20-604 0-770 3-204 3-033 0-1206 1303 12-34 13-54 Chloride of sodium. On comparing this experiment with the preceding, the follow- ing points come out as showing the difference between the effects of sand and charcoal as filtering media. 1st. By the charcoal, speaking generally, a considerably larger quantity of the total residue contained in the water was removed than by the sand, their maximum results being respectively as follows : — 1 Amount origi- i nally present. Amount separated in grains in the gallon. , Amount separated in per -centage of the quantity present. 1 1 By sand. By charcoal. By sand. By charcoal. 1 24-578 grs. j in the gallon. 1 2-074 3-757 8-426 35-28 But, as might have been anticipated from the well-known 32 Mr. H. M. Witt on the Power possessed by Porous Media power of charcoal to remove organic principles from solution in water, its superiority over sand is more especially observable in this respect; no weighable quantity of organic matter being separated by the sand, whilst 15 per cent, of the quantity present was removed by the charcoal. Nevertheless the case is quite altered when more impure water is filtered through the same medium ; for instance, it will be remembered that sand does remove organic matter from water when the quantity present is somewhat greater. Thus, in Tables I., II. and III. it is shown that at Chelsea, where the quantity of organic matter present in the water rose to 2*375 grs. in the gallon, then the sand removed 20*46 per cent ; when the quantity present amounted to 405 grs., 66*66 per cent. ; and lastly, when to 9*909 grs., no less than 95*23 per cent, was removed ! Now this is a most striking and important result in a hygienic point of view. The evil consequences said to result from the water supply of London at present in use are mainly attributed to the organic matter present in the water ; but these analyses show that the more impure the water (within certain limits), the greater is the power of porous filtering media to remove these impurities, probably from the more perfect contact between the filtering medium and the impurities present. It is obvious that this would not go on ad infinitum ; it must not be supposed that I wish it to be inferred that the more organic matter there is present in a water, the more would necessarily be removed by sand filtration ; quite the contrary, it is highly probable that if the quantity had increased much beyond what was contained at the time of the performance of these experiments, a consider- able amount might have passed through unrestrained ; all I wish to be understood is, that within the limits of the quantities present when these experiments were made, sand was found incapable of removing any appreciable quantity of organic matter when the amount originally present in the water was exceedingly small; but that in the same ratio as the quantity present increased, the proportion separated rose. Now the power of charcoal, I believe, increases in a similar manner ; but no experiments could conveniently be made on the large scale at Chelsea to enable me to draw a strict comparison between the effects of sand and charcoal upon the more impure water there, similar to what had been made at Kingston with the comparatively pure water ; therefore to enable me to adduce ex- perimental evidence on this point, a comparative experiment was made on the small scale with an artificially prepared impure water. This water was prepared as follows : — To the sample of Thames of removing Matter from Solution in Water, 33 water collected at Kingston on the 8th of October, 1855, cow- dung and garden mould were added, in the proportion of 4 oz. of solid cow-dung (without straw) and 4 oz. of garden mould to 2 gallons of the water ; the whole was allowed to digest for a week, being frequently shaken during this period ; it was then allowed to settle for twelve hours, and the supernatant fetid fluid poured off and submitted to examination. It was found to contain in the gallon- Total residue . . . 71*772 grs. Organic matter . . 29-308 ... Mineral matter . . 42*468 ... And the results obtained by filtration respectively»through sand and charcoal are contained in the following Tables : — Table VII. — Action of Vegetable Charcoal on artificially impure Water. Original con- stituents. Present after filtration. Amount sepa- rated in grains in the gallon. Per-centage ratio of matter separated. Total residue Organic matter . . . Mineral salts 71772 29-308 42-464 33-86 3-50 30-36 37-912 25-808 12104 ...„ _._. 52-82 88-05 28-26 Table VIIL— Action of Sand. Original con* stituents. Present after filtration. Amount sepa- rated in grains in the gallon. Per-centage ratio of matter separated. Total residue Organic matter ... Mineral salts 71-772 29-308 42-464 70-23 27-85 42-38 1-542 1-458 0-084 2-14 4-97 0197 It must be borne in mind that these two experiments, being made only on the small scale in the laboratory, though strictly comparable with each other, do not admit of comparison with any of the others ; they serve only to demonstrate how far greater is the power possessed by charcoal of removing organic matters from solution than that of sand, though the differente in their action on soluble inorganic salts is less marked. Another point of distinction between the effects of charcoal and sand upon the Thames water at Kingston was this — that whereas the efficacy of the sand-filter continued increasing even up to the conclusion of the experiment, the amount of impurity separated by the charcoal arrived in all cases at a maximum after a certain number of hours, and then began to decrease, as will be more perspicuously shown by the following Table : — Phil. Mag, S. 4. Vol. 12. No. 76. July 1856. D 84 On some praperties of Porous Media* Tablb IX. ■Showing the period of maxiraum efficacy of the several filters. Amounts of total iwidue originally present in each case. Number of hours' action of the filter. Amount separated in grains in the gallon by Per-centage ratio of quantity separated by Sand. Charcoal, in granules. Charcoal, in lumps. Sand. Charcoal, in granules. Charcoal, in lumps. ?4-678 23-949 i 23-949 23-949 io . 24-578 , 23 949 V' 24-578 •;'' 24-578 hrs. 23 67 91 115 . 120 139 240 376 0-708 0-888 204*4 2071 2-868 2*934 3-757 0*281 1-873 nr§3> 6-538 2-88 3-'6i3 8-3 i 6 8-426 11-66 *U-93 15-28 117 7-82 3-M 2-242 1 3-204 13-03 Lastly, these experiments upon the comparatively pure water of Kingston show that charcoal, as well as sand, is capable of separating mineral salts from solution in water, as is evident by an inspection of the foregoing Tables. The following is a brief summary of the most important results of this investigation : — It has been shown, — 1st. That sand, charcoal, and probably other porous media, possess the very peculiar property of removing, not merely sus- pended impurities, but even dissolved salts from solution in water. 2nd. That charcoal enjoys pre-eminently the power of ab- stracting organic matter from solution : but that even sand like- wise is capable of effecting the same result, though to a far less extent. 3rd. That these powers, possessed by both these media, in- crease in intensity to a certain extent with the degree of in^- purity of the solution. ., 4th. That these properties of porous media have important bearings upon hygienic science, agricultural principles, and geo- logical phsenomena. The reader will not fail to have noticed, by the various ana- lyses given above, great variations in the composition of the river- water, between the two points at which experiments were made, viz. at Chelsea and Kingston, as well as at the different seasons of the year. To a number of analyses made during the year since May 1855, 1 hope to draw attention in a subsequent paper as elucidating these facts. r\^»viiv.'4*^wv .£ 35 ] IV. Compa7'ative View of the Cleavage of Crystals and Slate Rocks. By John Tyndall, Esq., F.R.S. ^c* WHEN the student of physical science has to investigate the character of any natural force, his first care must be to purify it from the mixture of other forces, and thus study its simple action. If, for example, he wishes to know how a mass of water would shape itself, supposing it to be at liberty to follow the bent of its own molecular forces, he must see that these forces have free aad undisturbed exercise. We might perhaps refer him to the dew-drop for a solution of the question ; but here we have to do, not only with the action of the molecules of the liquid upon each other, but also with the action of gravity upon the mass, which pulls the drop downwards and elongates it. If he would examine the problem in its purity, he must do as Plateau has done, withdraw the liquid mass from the action of gravity, and he would then find the shape of the mass to be perfectly spherical. Natural processes come to us in a mixed manner, and to the uninstructed mind are a mass of unintelligible confusion. Suppose half-a-dozen of the best musical performers to be placed in the same room, each playing his own instrument to perfection : though each individual instrument might be a wellspring of melody, still the mixture of all would produce mere noise. Thus it is with the processes of nature. In nature mechanical and molecular laws mingle and create apparent con- fusion. Their mixture constitutes what may be called the noise of natural laws, and it is the vocation of the man of science to resolve this noise into its components, and thus to detect the " music '' in which the foundations of nature are laid. The necessity of this detachment of one force from all other forces is nowhere more strikingly exhibited than in the phseno- mena of crystallization. I have here a solution of sulphate of soda. Prolonging the mental vision beyond the boundaries of sense, we see the atoms of that liquid, like squadrons under the eye of an experienced general, arranging themselves into batta- lions, gathering round a central standard, and forming themselves into solid masses, which after a time assume the visible shape of the crystal which I here hold in my hand. I may, like an ignorant meddler wishing to hasten matters, introduce confusion into this order. I do so by plunging this glass rod into the vessel ; the consequent action is not the pure expression of the crystalline forces ; the atoms rush together with the confusion of an unor- * A Discourse delivered at the Royal Institution on the evening of Friday the 6th of June, 1856, and printed in the * Proceedings ' of the Institution. D2 86 Prof. Tyndall on the Cleavage of ganized mob, and not with the steady accuracyof a discij)lined host. Here also in this mass of bismuth we have an example of this con- fused crystallization ; but in the crucible behind me a slower pro- cess is going on : here there is an architect at work " who makes no chips, no din/' and who is now building the particles into crystals, similar in shape and structure to those beautiful masses which we see upon the table. By permitting alum to crystal- lize in this slow way, we obtain these perfect octahedrons ; by allowing carbonate of lime to crystallize, nature produces these beautiful rhomboids; when silica crystallizes, we have formed these hexagonal prisms capped at the ends by pyramids; by allowing saltpetre to crystallize we have these prismatic masses, and when carbon crystallizes, we have the diamond. If we wish to obtain a perfect crystal, we must allow the molecular forces free play : if the crystallizing mass be permitted to rest upon a surface it will be flattened, and to prevent this a small crystal must be so suspended as to be surrounded on all sides by the liquid, or, if it rest upon the surface, it must be turned daily so as to present all its faces in succession to the working builder. In this way the scientific man nurses these children of his intel- lect, watches over them with a care worthy of imitation, keeps all influences away which might possibly invade the strict morality of crystalline laws, and finally sees them developed into forms of symmetry and beauty which richly reward the care bestowed upon them*. In building up crystals these little atomic bricks often ar- range themselves into layers which are perfectly parallel to each other, and which can be separated by mechanical means; this is called the cleavage of the crystal. I have here a crystal- lized mass which has thus far escaped the abrading and disin- tegrating forces which sooner or later determine the fate of sugar-candy. If I am skilful enough I shall discover that this crystal of sugar cleaves with peculiar facility in one direction. Here again I have a mass of rock-salt : I lay my knife upon it and with a blow cleave it in this direction ; but I find on further examining this substance that it cleaves in more directions than one. Laying my knife at right angles to its former position, the crystal cleaves again ; and finally placing the knife at right angles to the two former positions, the mass cleaves again. Thus rock-salt cleaves in three directions, and the resulting solid is this perfect cube, which may be broken up into any number of smaller cubes. Here is a mass of Iceland spar, which also cleaves in three directions, not at right angles, but oblique to each other, ♦ To Mr. Pattinson, of the Felling Chemical Works, Newcastle-upon- Tyne, I am indebted for some fine specimens of crystallized alum and carbonate of soda. Crystals and Slate Rocks. 37 the resulting solid being a rhomboid. In each of these cases the mass cleaves with equal facility in all three directions. For the sake of completeness I may say that many substances cleave with unequal facility in different directions, and the heavy spar I hold in my hand presents an example of this kind of cleavage. Turn we now to the consideration of some other phsenomena to which the term cleavage may be applied. This piece of beech- wood cleaves with facility parallel to the fibre, and if our ex- periments were fine enough we should discover that the cleavage is most perfect when the edge of the axe is laid across the rings which mark the growth of the tree. The fibres of the wood lie side by side, and a comparatively small force is sufficient to separate them. If you look at this mass of hay severed from a rick, you will see a sort of cleavage developed in it also ; the stalks lie in parallel planes, and only a small force is required to separate them laterally. But we cannot regard the cleavage of the tree as the same in character as the cleavage of the hayrick. In the one case it is the atoms arranging themselves according to organic laws which produce a cleavable structure, in the other case the easy separation in a certain direction is due to the me- chanical arrangement of the coarse sensible masses of the stalks of hay. In like manner I find that this piece of sandstone cleaves parallel to the planes of bedding. This rock was once a powder, more or less coarse, held in mechanical suspension by water. The powder was composed of two distinct parts, fine grains of sand and small plates of mica. Imagine a wide strand covered by a tide which holds such powder in suspension* : how will it sink ? The rounded grains of sand will reach the bottom first, the mica afterwards, and when the tide recedes we have the little plates shining like spangles upon the surface of the sand. Each successive tide brings its charge of mixed powder, deposits its duplex layer day after day, and finally masses of immense thick- ness are thus piled up, which by preserving the alternations of sand and mica tell the tale of their formation. I do not wish you to accept this without proof. Take the sand and mica, mix them together in water, and allow them to subside, they will arrange themselves in the manner I have indicated; and by repeating the process you can actually build up a sandstone mass which shall be the exact counterpart of that presented by nature, as I have done in this glass jar. Now this structure cleaves with readiness along the planes in which the particles of mica are strewn. Here is a mass of such a rock sent to me from * I merely use this as an illustration ; the deposition may have really been due to sediment carried down by rivers. But the action must have been periodic, and the powder duplex. 38 Prof. Tyndall on the Cleavage of Halifax : here are other masses from the quarries of Over Dar- wen in Lancashire*. With a hammer and chisel you see I can cleave them into flags ; indeed these flags are made use of for roofing purposes in the districts from which the specimens have come, and receive the name of " slatestone." But you will discern without a word from me, that this cleavage is not a crystalline cleavage any more than that of a hayrick is. It is not an arrangement produced by molecular forces; indeed it would be just as reasonable to suppose that on this jar of sand and mica the particles arranged themselves into layers by the forces of crystallization, instead of by the simple force of gra- vity, as to imagine that such a cleavage as this could be the product of crystallization. This, so far as I am aware of, has never been imagined, and it has been agreed among geologists not to call such splitting as this cleavage at all, but to restrict the term to a class of phae- nomena which I shall now proceed to consider. Those who have visited the slate quarries of Cumberland and North Wales will have witnessed the phsenomena to which I refer. We have long drawn our supply of roofing-slates from such quarries ; schoolboys ciphered on these slates, they were used for tombstones in churchyards, and for billiard-tables in the metropolis; but not until a comparatively late period did men begin to inquire how their wonderful structure was pro- duced. What is the agency which enables us to split Honister Crag, or the cliffs of Snowdon, into laminae from crown to base ? This question is at the present moment one of the greatest diffi- culties of geologists, and occupies their attention perhaps more than any other. You may wonder at this. Looking into the quarry of Penrhyn, you may be disposed to explain the ques- tion as I heard it explained two years ago. " These planes of cleavage/' said a friend who stood beside me on the quarry's edge, " are the planes of stratification which have been lifted by some convulsion into an almost vertical position." But this was a great mistake, and indeed here lies the grand difficulty of the problem. These planes of cleavage stand in most cases at a high angle to the bedding. Thanks to Sir Roderick Murchison, .who has kindly permitted me the use of specimens from the Museum of Practical Geology (and here I may be permitted to express my acknowledgements to the distinguished staff of that noble establishment, who, instead of considering me an in- truder, have welcomed me as a brother), I am able to place the proof of this before you. Here is a mass of slate in which the planes of bedding are distinctly marked; here are the * For the specimens from HaUfax I have to thank Mr. Richard Carter, and for those from Darwen I am indebted to Mr. J. Singleton. Crystals and Slate Rocks, 3§ planer of cleavage, and you see that one of them makes a large angle with the other. The cleavage of slates is therefore not a question of stratification, and the problem which we have now to consider is, " By what cause has this cleavage been pro- duced ?'' In an able and elaborate essay on this subject in 1835, Prof. Sedgwick proposed the theory that cleavage is produced by the action of crystalline or polar forces after the mass has been con- solidated. " We may affirm,'^ he says, " that no retreat of the parts, no contraction of dimensions in passing to a solid state can explain such phsenomena. They appear to me only resol- vable on the supposition that crystalline or polar forces acted upon the whole mass simultaneously in one direction and with adequate force.'^ And again, in another place : " Crystalline forces have rearranged whole mountain masses, producing a beautiful crystalline cleavage, passing alike through all the strata*/^ The utterance of such a man struck deep, as was natural, into the minds of geologists, and at the present day there are few who do not entertain this view either in whole or in partt- The magnificence of the theory, indeed, has, in some cases, caused speculation to run riot, and we have books pub- lished, aye and largely sold, on the action of polar forces and geologic magnetism, which rather astonish those who know something about the subject. According to the theory referred to, miles and miles of the districts of North Wales and Cumber- land, comprising huge mountain masses, are neither more nor less than the parts of a gigantic crystal. These masses of slate were originally fine mud ; this mud is composed of the broken and abraded particles of older rocks. It contains silica, alumina, iron, potash, soda, and mica mixed in sensible masses mechani- cally together. In the course of ages the mass became consoli- dated, and the theory before us assumes that afterwards a pro- cess of crystallization rearranged the particles and developed in the mass a single plane of crystalline cleavage. With reference to this hypothesis, I will only say that it is a bold stretch of ana- logies ; but still it has done good service : it has drawn atten- * Transactions of the Geological Society, ser. ii. vol. iii, p. 477. t In a letter from Sir Charles Lyell, dated from the Cape of Good Hope, February 20, 1836, Sir John Herschel writes as follows : — " If rocks have been so heated as to allow of a commencement of crystallization, that is to say, if they have been heated to a point at which the particles can begin to move amongst themselves, or at least on their own axes, some general law must then determine the position in which these particles will rest on cooling. Probably that position will have some relation to the direction in which the heat escapes. Now when all or a majority of particles of the same nature have a general tendency to one position, that must of course determine a cleavage plane." 40 Prof. Tyndall on the Cleavage of tion to the question ; right or wrong a theory thus thoughtfully uttered has its value ; it is a dynamic power which operates against intellectual stagnation; and even by provoking oppo- sition is eventually of service to the cause of truth. It would however have been remarkable if, among the ranks of geolo- gists themselves, men were not found to seek an explanation of the phsenomena in question, which involved a less hardy spring on the part of the speculative faculty than the view to which I have just referred. The first step in an inquiry of this kind is to put oneself into contact with nature, to seek facts. This has been done, and the labours of Sharpe (the late President of the Geological Society, who, to the loss of science and the sorrow of all who knew him, has so suddenly been taken away from us), Sorby and others have furnished us with a body of evidence which reveals to us certain important physical phsenomena, associated with the ap- pearance of slaty cleavage, if they have not produced it : the nature of this evidence we will now proceed to consider. Fossil shells are found in these slate-rocks. I have here several specimens of such shells, occupying various positions with regard to the cleavage planes. They are squeezed, distorted and crushed. In some cases a flattening of the convex shell occurs, in others the valves are pressed by a force which acted in the plane of their junction, but in all cases the distortion is such as leads to the inference that the rock which contains these shells has been subjected to enormous pressure in a direc- tion at right angles to the planes of cleavage ; the shells are all flattened and spread out upon these planes. I hold in my hand a fossil trilobite of normal proportions. Here is a series of fos- sils of the same creature which have suffered distortion. Some have lain across, some along, and some oblique to the cleavage of the slate in which they are found; in all cases the nature of the distortion is such as required for its production a com- pressing force acting at right angles to the planes of cleavage. As the creatures lay in the mud in the manner indicated, the jaws of a gigantic vice appear to have closed upon them and squeezed them into the shape you see. As further evidence of the exertion of pressure, let me introduce to your notice a case of contortion which has been adduced by Mr. Sorby. The bed- ding of the rock shown in this figure was once horizontal ; at A we have a deep layer of mud, and at mn a layer of compara- tively unyielding gritty material ; below that again, at B, we have another layer of the fine mud of which slates are formed. This mass cleaves along the shading lines of the diagram : but look at the shape of the intermediate bed : it is contorted into a serpentine form, and leads irresistibly to the conclu- Crystals and Slate Rocks. 41 sion that the mass has been pressed together at right angles to the planes of cleavage. This action can be experimentally imitated, and I have here a piece of clay in which this is done and the same result produced on a small scale. The amount of compression, indeed, might be roughly estimated by sup- posing this contorted bed mn to be stretched out, its length mea- sured and compared with the distance c d; we find in this way that the yielding of the mass has been considerable. Let me now direct your atten- tion to another proof of pres- sure; you see the varying colours which indicate the bedding on this mass of slate. The dark portion, as I have stated, is gritty, and composed of comparatively coarse particles, which, owing to their size, shape and gravity, sink first and constitute the bottom of each layer. Gradually, from bottom to top the coarseness di- minishes, and near the upper surface of each layer we have a mass of comparatively fine clean mud. Sometimes this fine mud forms distinct layers in a mass of slate-rock, and it is the mud thus consolidated from which are derived the German razor-stones, so much prized for the sharpening of surgical instruments. I have here an example of such a stone ; when a bed is thin, the clean white mud is permitted to rest, as in this case, upon a slab of the coarser slate in contact with it : when the bed is thick, it is cut into slices which are cemented to pieces of ordinary slate, and thus rendered stronger. The mud thus deposited sometimes in layers is, as might be expected, often rolled up into nodular masses, carried forward, and deposited by the rivers from which the slate-mud has subsided. Here, indeed, are such nodules enclosed in sandstone. Everybody who has ciphered upon a school-slate must remember the whitish-green spots which sometimes, dotted the surface of the slate; he will remember how his slate-pencil usually slid over such spots as if they were greasy ; now these spots are composed of the finer mud, and they could not, on accoimt of their fineness, bite the pencil like 42 Prof. Tyndall on the Cleavage of the surrounding gritty portions of the slate. Here is a beauti- ful example of the spots : you observe them on the cleavage sur- face in broad patches ; but if this mass has been compressed at right angles to the planes of cleavage, ought we to expect the same marks when we look at the edge of the slab ? The nodules will be flattened by such pressure, and we ought to see evidence of this flattening when we turn the slate edgeways. Here it is. The section of a nodule is a sharp ellipse with its major axis parallel- to the cleavage. There are other examples of the same nature on the table ; I have made excursions to the quarries of Wales and Cumberland, and to many of the slate-yards of Lon- don, but the same fact invariably appears, and thus we elevate a common experience of our boyhood into evidence of the highest significance as regards one of the most important problems of geology. In examining the magnetism of these slates, I was led to infer that these spots would contain a less amount of iron than the surrounding dark slate. The analysis was made for me by Mr. Hambly in the laboratory of Dr. Percy at the School of Mmes. The result which is stated in this Table, justifies the conclusion to which I have referred. Analysis of Slate. Purple Slate, two analyses. 1 . Per-centage of iron . . . 5*85 2. „ „ ... ^03 Mean . . 5-99 Greenish Slate. 1. Per-centage of iron . . . 3*24 2. „ „ ... 302 Mean . . 3-18 The quantity of iron in the dark slate immediately adjacent to. the greenish spot is, according to these analyses, nearly double of the quantity contained in the spot itself. This is about the proportion which the magnetic experiments suggested. Let me now remind you that the facts which I have brought before you are typical facts— each is the representative of a class. We have seen shells crushed ; the unhappy trilobites squeezed, beds contorted, nodules of greenish marl flattened; and all these sources of independent testimony point to one and the same conclusion, namely, that slate-rocks have been subjected to enor- mous pressure in a direction at right angles to the planes of cleavage*. * While to my mind the evidence in proof of pressure seems perfectly irresistible, T by no means assert that the manner in which I have stated it if inca])able of modification. All that I deem important is the fact that Crystals and Slate Rocks. 4& In reference to Mr. Sorby^s contorted bed, I have said that by supposing it to be stretched out and its length measured, it would give us an idea of the amount of yielding of the mass above and below the bed. Such a measurement, however, would not quite give the amount of yielding ; and here I would beg your attention to a point, the significance of which has, so far as I am aware of, hitherto escaped attention. I hold in my hand a specimen of slate with its bedding marked upon it ; the lower portions of each bed are composed of a comparatively coarse gritty material something like what you may suppose this con- torted bed to be composed of. Well, I find that the cleavage takes a bend in crossing these gritty portions, and that the tendency of these portions is to cleave more at right angles to the bedding. Look to this diagram : when the forces com- menced to act, this intermediate bed, which though compara- ratively unyielding is not entirely so, suffered longitudinal pres- sure ; as it bent, the pressure became gradually more lateral, and the direction of its cleavage is exactly such as you would infer from a force of this kind — it is neither quite across the bed, nor yet in the same direction as the cleavage of the slate above and below it, but intermediate between both. Supposing the cleavage to be at right angles to the pressure, this is the di- rection which it ought to take across these more unyielding strata. Thus we have established the concurrence of the phsenomena of cleavage and pressure — that they accompany each other ; but the question still remains. Is this pressure of itself sufficient to account for the cleavage ? A single geologist, as far as I am aware, answers boldly in the affirmative. This geologist is Sorby, who has attacked the question in the true spirit of a physical investigator. You remember the cleavage of the flags of Halifax and Over Darwen, which is caused by the interpo- sition of plates of mica between the layers. Mr. Sorby exa- mines the structure of slate-rock, and finds plates of mica to be a constituent. He asks himself, what will be the effect of pressure upon a mass containing such plates confusedly mixed up in it ? It will be, he argues, and he argues rightly, to place the plates with their flat surfaces more or less perpendicular to the direction in which the pressure is exerted. He takes scales of the oxide of iron, mixes them with a fine powder, and on squeezing the mass finds that the tendency of the scales is to set themselves at right angles to the line of pressure. Now the planes in which these plates arrange themselves will, he con- tends, be those along which the mass cleaves. pressure has been exerted ; and provided this remain firm, the fate of any minor portion of the evidence by which it is here estabUshed is of compa- rativelv httle moment. 44 Prof. Tyndall on the Cleavage of I could show you by tests of a totally different character from those applied by Mr. Sorby, how true his conclusion is, that the effect of pressure on elongated particles, or plates, will be such as he describes it. Nevertheless, while knowing this fact, and admiring the ability with which Mr. Sorby has treated this question, I cannot accept his explanation of slate-cleavage. I believe that even if these plates of mica were wholly absent the cleavage of slate-rocks would be much the same as it is at present. 1 will not dwell here upon minor facts, — I will not urge that the perfection of the cleavage bears no relation to the quantity of mica present ; but I will come at once to a case which to my mind completely upsets the notion that such plates are a neces- sary element in the production of cleavage. Here is a mass of pure white wax : there are no mica particles here ; there are no scales of iron, or anything analogous mixed up with the mass. Here is the self-same substance submitted to pressure. I would invite the attention of the eminent geolo- gists whom I see before me to the sti*ucture of this mass. No slate ever exhibited so clean a cleavage ; it splits into laminae of surpassing tenuity, and proves at a single stroke that pressure is sufficient to produce cleavage, and that this cleavage is inde- pendent of the intermixed plates of mica assumed in Mr. Sorby's theory. I have purposely mixed this wax with elongated par- ticles, and am unable to say at the present moment that the cleavage is sensibly affected by their presence, — if anything, I should say they rather impair its fineness and clearness than promote it. The finer the slate the more perfect will be the resemblance of its cleavage to that of the wax. Compare the surface of the wax with the surface of this slate from Borrodale in Cumberland. You have precisely the same features in both : you see flakes clinging to the surfaces of each, which have been partially torn away by the cleavage of the mass : I entertain the conviction that if any close observer compares these two effects, he will be led to the conclusion that they are the product of a common cause*. But you will ask me how, according to my view, does pressure produce.thisremarliiibl&r^ult. This may be stated in a very few words... ^,,.j» y(^ ,-^t*.rif ,')iii r? Nature is everywhere imperfect ! The eye is not perfectly achromatic, the colours of the rose and tulip are not pure colours, ♦ I have usually softened the wax by wanning it, kneaded it with the fingers, and pressed it between thick plates of glass previously wetted. At the ordinary summer temperature the wax is soft, and tears rather than cleaves ; on this account I cool my compressed specimens in a mixture of pounded ice and sialt, and wlicn thus cooled they spUt beautifully. Crystals and Slate Rocks. 45 and the freshest air of our hills has a bit of poison in it. In like manner there is no such thing in nature as a body of perfectly homogeneous structure. I break this clay which seems so inti- mately mixed, and find that the fracture presents to my eyes innumerable surfaces along which it has given way, and it has yielded along these surfaces because in them the cohesion of the mass is less than elsewhere. I break this marble, and even this wax, and observe the same result : look at the mud at the bottom of a dried pond; look to some of the ungravelled walks in Kensington Gardens on drying after rain, — they are cracked and split, and other circumstances being equal, they crack and split where the cohesion of the mass is least. Take then a mass of partially consolidated mud. Assuredly such a mass is divided and subdivided by surfaces along which the cohesion is compara- tively small. Penetrate the mass, and you will see it composed of numberless irregular nodules bounded by surfaces of weak cohesion. Figure to your mind^s eye such a mass subjected to pressure, — the mass yields and spreads out in the direction of least resistance*; the little nodules become converted into laminae, separated from each other by surfaces of weak cohesion, and the infallible result will be that such a mass will cleave at right angles to the line in which the pressure is exerted. Further, a mass of dried mud is full of cavities and fissures. If you break dried pipe-clay you see them in great numbers, and there are multitudes of them so small that you cannot see them. I have here a piece of glass in which a bubble was enclosed ; by the compression of the glass the bubble is flattened, and the sides of the bubble approach each other so closely as to exhibit the colours of thin plates. A similar flattening of the cavities must take place in squeezed mud, and this must materially facilitate the cleavage of the mass in the direction already indicated. Although the time at my disposal has not permitted me to develope this thought as far as I could wish, yet for the last twelve months the subject has presented itself to me almost daily under one aspect or another. I have never eaten a biscuit during this period in which an intellectual joy has not been superadded to the more sensual pleasure, for I have remarked in all such cases cleavage developed in the mass by the rolling- pin of the pastrycook or confectioner, I have only to break these cakes, and to look at the fracture, to see the laminated structure of the mass ; nay, I have the means of pushing the analogy further, I have here some slate which was subjected to * It is scarcely necessary to say that if the mass were squeezed equally in all directions no laminated structure could be produced ; it must have room to yield in a lateral direction. 46 Prof. Tyiidall on the Cleavage of a high temperature during the conflagration of Mr. Scott Rus- sell's premises. I invite you to compare this structure with that of a biscuit ; air or vapour within the mass has caused it to swell, and the mechanical structure it reveals is precisely that of a biscuit. I have gone a little into the mysteries of baking while conducting my inquiries on this subject, and have received much instruction from a lady friend in the manufacture of pufF- paste. Here is some such paste baked in this house under my own superintendence. The cleavage of our hills is accidental cleavage, but this is cleavage with intention. The volition of the pastrycook has entered into the formation of the mass, and it has been his aim to preserve a series of surfaces of structural weakness, along which the dough divides into layers. Puff-paste must not be handled too much, for then the continuity of the surfaces is broken; it ought to be rolled on a cold slab, to prevent the butter from melting, and diffusing itself through the mass, thus rendering it more homogeneous and less liable to split. This is the whole philosophy of puff-paste ; it is a grossly exaggerated case of slaty cleavage. As time passed on cases multiplied, illustrating the influence of pressure in producing lamination. Mr. Warren De la Rue in- forms me that he once wished to obtain white-lead in a fine granular state, and to accomplish this he first compressed the mass : the mould was conical, and permitted the mass to spread a little laterally under the pressure. The lamination was as perfect as that of slate, and quite defeated him in his effort to obtain a granular powder. Mr. Brodie, as you are aware, has recently discovered a new kind of graphite : here is the substance in powder, of exquisite fineness. This powder has the peculia- rity of clinging together in little confederacies ; it cannot be shaken asunder like lycopodium ; and w^hen the mass is squeezed, these groups of particles flatten, and a perfect cleavage is pro- duced. Mr. Brodie himself has been kind enough to furnish me with specimens for this evening's lecture. I will cleave them before you : you see they split up into plates which are perpen- dicular to the line in which the pressure was exerted. This testimony is all the more valuable, as the facts were obtained without any reference whatever to the question of cleavage. I have here a mass of that singular substance Boghead cannel*. This w^as once a mass of mud, more or less resembling this one, which I have obtained from a bog m Lancashire. I feel some hesitation in bringing this substance before you, for, as in other cases, so in regard to Boghead cannel, science — not science, let me not libel it, but the quibbling, litigious, money-loving portion of human nature speaking through the mask of science * For which I have to thank Mr. George Edraondson. Crystals and Slate Rocks. 4i7 — has so contrived to split hairs as to render the qualities of the substance somewhat mythical. I shall therefore content myself with showing you how it cleaves, and with expressing my conviction that pressure had a great share in the production of this cleavage. The principle which I have enunciated is so simple as to be almost trivial ; nevertheless, it embraces not only the cases I have mentioned, but, if time permitted, I think I could show you that it takes a much wider range. When iron is taken from the puddling furnace it is a more or less spongy mass : it is at a welding heat, and at this temperature is submitted to the pro- cess of rolling : bright smooth bars such as this are the result of this rolling. But I have said that the mass is more or less spongy or nodular, and, notwithstanding the high heat, these nodules do not perfectly incorporate with their neighbours : what then ? You would say that the process of rolling must draw the nodules into fibres — it does so ; and here is a mass acted upon by dilute sulphuric acid, which exhibits in a striking manner this fibrous structure. The experiment was made by my friend Dr. Percy, without any reference to the question of cleavage. Here are other cases of fibrous iron. This fibrous structure is the result of mechanical treatment. Break a mass of ordinary iron and you have a granular fracture ; beat the mass, you elon- gate these granules, and finally render the mass fibrous. Here are pieces of rails along which the wheels of locomotives have slided* ; the granules have yielded and become plates. They exfoliate or come off in leaves ; all these effects belong, I believe, to the great class of phsenomena of which slaty cleavage forms the most prominent example f. Thus, ladies and gentlemen, we have reached the termination of our task. 1 commenced by exhibiting to you some of the phsenomena of crystallization. I have placed before you the facts which are found to be associated with the cleavage of slate rocks. These facts, as finely expressed by Helmholtz, are so many tele- scopes to our spiritual vision, by which we can see backward through the night of antiquity, and discern the forces which have been in operation upon the earth's surface , ,a J n « " ^^^ *1^^ lio^ roared. Or the eagle soared." From evidence of the most independent and trustworthy * For these specimens and other valuable assistance I am indebted to Mr. Williams. t An eminent authority informs me that he believes these surfaces of weak cohesion to be due to the interposition of films of graphite, and not to any tendency of the iron itself to become fibrous : this of course does not in any way militate against the theory which I have ventured to pro- pose. All that the theory requires is surfaces of weak cohesion, however produced, and a change of shape of such surfaces consequent on pressure or rolling. 48 Prof. W. H. Miller on the Form of an Alloy of Bismuth. character, we come to the conclusion that these slaty masses have been subjected to enormous pressure, and by the sure method of experiment we have shown — and this is the only really new point which has been brought before you — how the pressure is sufficient to produce the cleavage. Expand- ing our field of view, we find the self-same law, whose foot- steps we trace amid the crags of Wales and Cumberland, stretching its ubiquitous fingers into the domain of the pastry- cook and ironfounder; nay, a wheel cannot roll over the half- dried mud of our streets without revealing to us more or less of the features of this law. I would say, in conclusion, that the spirit in which this problem has been attacked by geologists, indicates the dawning of a new day for their science. The great intellects who have laboured at geology, and who have raised it to its present pitch of grandeur, were compelled to deal with the subject in mass ; they had no time to look after details. But the desire for more exact knowledge is increasing ; facts are flowing in, which, while they leave untouched the intrinsic wonders of geology, are gradually supplanting by solid truths the uncertain speculations which beset the subject in its infancy. Geologists now aim to imitate, as far as possible, the conditions of nature, and to produce her results ; they are approaching more and more to the domain of physics, and I trust the day will soon come when we shall interlace our friendly arms across the common boundary of our sciences, and pursue our respective tasks in a spirit of mutual helpfulness, encourage- ment and goodwill. V. On the Form of an Alloy of Bismuth. By W, K. Miller, M.A.y F.R.S., F.G.S., Professor of Mineralogy in the Univer- sity of Cambridge ; with an Analysis of the Alloy , by Allan Dick, Esq.^ Metallurgical Laboratory y School of Mine^. THE specimen was obtained by Dr. Percy from Mr. Pers- house of Birmingham. The crystals belong to the prismatic system. The symbols of their simple forms are — c, 001 ; r. 111. ITie angles between normals to their faces are, — re 60 17 rr' 61 38 rr'' 89 4 Communicated by the Author. Prof. W. H. Miller on the Form of an Alloy of Bismuth, 49 The plane angles of the face c are 72° 17' and 107*^ 43'. Twins. Twin-face c. CO 59 26 ru 1 52 ur" 90 56 Cleavage, c, very perfect and easily obtained. Analysis. Specific gravity = 9*46. A well-crystallized portion of it was reduced to powder, ex- amined in the usual manner, and found to consist of sulphur, bismuth, copper, and nickel. Estimation of Sulphur. — 10*43 grs. were digested in warm nitric acid, till the sulphur which separated had melted into a globule. Weight of sulphur globule 0*19 gr. It was roasted, and the residue weighed 0*04 gr. This was dissolved in nitric acid and added to the original solution, from which the sulphuric acid was precipitated and weighed as sulphate of baryta. Weight of sulphate of baryta obtained 1'05 gr. Estimation of the Metals. — 10*43 grs. were dissolved as above, the solution diluted, and a current of sulphuretted hydrogen passed through it. The sulphurets were collected on a filter, and washed with acidulated water containing sulphuretted hy- drogen. The nickel was precipitated as oxide by caustic potash, reduced by hydrogen, and weighed as metal 0*59 gr. The sulphurets were dissolved in nitric acid, and the bismuth separated from the copper by means of carbonate of ammonia. The treatment with carbonate of ammonia was repeated in order to remove the last traces of copper from the precipitated bismuth, which was ignited and weighed 10*27 grs. The ammoniacal filtrate was evaporated to dryness and the ammoniacal salts expelled. The residue was dissolved in nitric acid, and the copper precipitated as oxide by caustic potash. Weight of oxide of copper 0*30 gr. Results tabulated. Bismuth .... 88-49 Nickel .... 5-65 Copper .... 2-29 Sulphur .... 2*82 99*25 Estimating the sulphur in combination with the copper and a portion of the bismuth, and considering these sulphides as foreign matter, the formula will be very nearly that of NiBi^, the atomic weight of bismuth being taken as 208. Phil. Mag, S. 4. Vol. 12. No. 76. July 1856. E f 60 ] VI . On the Density of the Earth, deduced from the Experiments of the Astronomer Royal, in Harton Coal-pit. By the Rev. Samuel Haughton, M.A.j Fellow of Trinity College, Dublin^. SOME time ago the following density of the earth was de- duced by me, by the aid of very simple considerations, from the pendulum observations of the Astronomer Royal in Harton Coal-pit, South Shields, as reported in the newspapers. The method of deducing the density is rough, and cannot be considered as having the same value as the more precise and detailed considerations on which Mr. Airy has based his own calculations ; yet as it is simple, and easily understood, it may prove of some interest to the readers of the Philosophical Maga- zine. It is based on the following facts : — 1st. From the fact that the seconds^ pendulum gains 2^ seconds per day at the bottom of the coal-pit, I infer that gra- vity at the surface is to gravity at the bottom of the pit as 19200 to 39201. 2nd. If a spheroidal shell be drawn through the bottom of the coal-pit similar to the spheroid forming the surface of the sea, the mass of the whole earth is equal to the mass of this spheroid, plus the matter exterior to it, including sea and land. The two foregoing propositions, being facts, will easily be ad- mitted ; I now add to them an hypothesis which very probably does not deviate far from the truth ; it is as follows : — That the attraction of the sea and land, external to the sphe- roid through the bottom of the coal-pit, does not differ sensibly from the attraction of a shell bounded externally by a similar surface, and having a mean density the same as the mean density of the sea and land external to the spheroid. If this be admitted, we can state the two facts already given as follows:— 19201 A . h\ ^ ^=T9200(l-^r)^' W A= (1+1^)8+?,% (2) In these equations — A is the mean density of the whole earth ; h is the mean density of the portion included by the sphe- roid passing through the bottom of the coal-pit ; p is the mean density of the land and water above the bot- tom of the coal-pit ; - is the ratio of the depth of the coal-pit to the radius of the earth. * Communicated by the Author. M, Berthelot on Formic Acid and Carbonic Oxide. 61 Assuming tlie depth of the pit to be 1260 feet, and the radius of the earth 4000 miles, we have — = f^rynn- Eliminating h from equations (1) and (2), and substituting this value of — , we find ^ = ^41^ (^^ To find the value of p, I make use of the following facts : — According to Humboldt, the mean height of the continents above the sea-level is 1000 feet ; and according to Rigaud, the relative areas of land and water are as 1 to 2*815. Hence, since the bottom of the coal-pit is 1200 feet below the sea-level, if we suppose all the land and water blended into one couche of a thickness of 1200 feet, and denote its mean density by p, we find, assuming the mean density of the land to be 2*75, 2200 X I X 2-75 + 1200 x w; x 1 = 1200(z^ + /)/); w denoting the area of water, and / the area of land ; and sub^ stituting for these their values, we obtain finally p = 2-059 (4) Substituting this mean density of the land and water at the surface for p in equation (3), we find A =5-480. ....... (5) This result agrees closely with the best experiments made with the torsion balance, and appears to be fairly deducible from th^ observed facts, considered in a general point of view. Trinity College, Dublin, June 18, 1856. VII. Chemical Notices from Foreign Journals, By E. Atkinson, Ph.D. [Continued from vol. xi. p. 461.] IN the April Number of the Annates de Chimie et de Physique, Berthelot has an important paper on the relation between Formic Acid and Carbonic Oxide. Carbonic oxide bears the same relation to formic acid that olefiant gas does to alcohol : — C^O^ + 2H0 = Q^WO\ Carbonic oxide. Formic acid. . C^H^ + 2H0 :^ C^H^O^; defiant gas. Alcohol, and formic acid, heated with strong sulphuric acid, gives carbonic oxide; just as alcohol, by the same treatment, gives olefiant gas. E2 52 M. Berthelot on the Decomposition of Hydrobromic Acid. On this relation Berthelot founds a new method for the forma- tion of formic acid, which consists in placing carbonic oxide under conditions favourable to the fixation of the elements of water. By enclosing carbonic oxide along with moist potash in a flask, and heating for several days, this condition is satisfied : the car- bonic oxide is perfectly absorbed by the potash, which is con- verted into formiate of potash, from which formic acid is obtained by appropriate methods. In the hope of uniting directly nascent carbonic oxide with the elements of water, Berthelot investigated the decomposition of oxalic acid at 100° C. under different circumstances; heated alone, it is, to a slight extent, decomposed into carbonic acid and carbonic oxide. This decomposition is much accelerated by the presence of acids, and is not due to a chemical but to a cata- lytic action. AVhen oxalic acid is heated to 100° C. with syrupy glycerine, a copious evolution of pure carbonic acid takes place. At the expiration of some time this evolution ceases, and the glycerine then contains half the carbon of the oxalic acid in the form of formic acid, which is not in combination with the glycerine, but merely dissolved like ammoniacal gas in water. Here the carbonic oxide and the water produced simulta- neously and in the nascent state from the decomposition of the oxalic acid unite to produce formic acid, the glycerine exercising merely a catalytic action. By repeatedly adding water to the glycerine and distilling, the whole of the formic acid contained in it passes over. This pro- cess is extremely productive, as nearly the theoretical quantity is obtained, and the glycerine may be used over and over again, for it is not acted on. By this means also pure carbonic oxide may be obtained ; for if in the preparation of formic acid, after the evolution of car- bonic acid has ceased, the glycerine be heated to 200°, the whole of the formic acid contained in it is decomposed into water and carbonic oxide, which passes off perfectly pure. When carbonic oxide is passed into a saturated solution of protochloride of copper in hydrochloric acid, a compound of the two bodies is obtained which crystallizes in pearly laminje, and Las the formula 4Cu2 CI, SCO 7H0. Berthelot found that hydrobromic acid, when left in contact with mercury for a very long time, is decomposed into bromide of mercury and hydrogen. The same change takes place, but much more rapidly, when these bodies are heated together to 100° C. This slow decomposition of hydrobromic acid by mer- cury is a new example of the influence of time on chemical action. M, Yremy on the Fluorides, >^^^ I 5S' Boussingault communicates some experiments on the use of arsenic in steeping grain for seed. This process has two objects, the one to protect the harvest from disease, the other to prevent the seed from being devoured by vermin. The substances generally- used are salt, glauber salt, lime, and sulphate of copper. But although these may hinder the development of cryptogamic sporules, they have little effect in preventing the seed from being eaten. The greatest part of the substance used remains in the husk, which the animal rejects. The most effectual means is the employment of arsenic ; this not only preserves the seed from decay, but if eaten by the vermin it destroys them, being so strongly poisonous. By using arsenic in a soluble form, such as the arsenite of soda, it may be added to the grain in perfectly definite proportions. Boussingault^s process is as follows: — A solution of arsenite of soda is prepared, which contains 57 grammes of arsenious acid in the litre. Of this arsenical solution 3^ litres are taken and added to 12| litres of w^ater. A hectolitre of corn is placed in a large tub, and these L6 litres of mixture are added, the corn being continually stirred. In about an hour the whole of the liquid is absorbed, and the grain is then dried. It is, of course, necessary to exercise extreme care in using the arsenical solution, and it is well to colour it strongly by the addition of sulphate of iron and prussiate of potash, so that its presence would be readily betrayed. This steeping is not an unprofitable affair, for it first effectually preserves the harvest, and secondly, by killing the vermin which might devour it, converts them into useful manure. An important paper by Fremy on the fluorides is published in the May Number of the same journal. The results he has arrived at are best seen from his own summary of them. 1. Hydrofluoric acid may be obtained anhydrous and pure, by calcining in an apparatus of platinum hydrofluate of fluoride of potassium previously well dried. In this state the acid is gaseous at ordinary temperatures ; it attacks glass and all sili- cious substances energetically, contrary to what has been asserted on the subject in the last few years. 2. All the experiments made, confirm the constitution of this acid as admitted by most chemists, viz. that it is a hydrogen acid. 3. The fluorides may be divided into three classes, each of which is characterized by the possession of important properties. The first class contains the anhydrous fluorides, and is analogous to the chlorides ; the second class, the hydrated fluorides, which comport themselves like the hydrochlorates ; in the third class are found the hydrofluates of the fluorides, which are true acid salts. 64 M. Wohler on an Ailotropic Modification of Silicon. 4. The anhydrous fluorides are remarkable for their stability ; the hydrated fluorides, on the contrary, are only slightly stable, and are decomposed even by being dried in racMO, hydrofluoric acid being disengaged, and a residue of oxyfluoride or oxide being left. 5. The auhydi'ous fluorides have a strong tendency to form double fluorides; this property is seen even with insoluble fluorides. These last compounds cannot be obtained by double decomposition, as they always retain, as a double salt, part of the soluble salt used in their preparation. 6. Hydrogen does not decompose all the fluorides, even at a high temperature ; it does not act on fluoride of calcium, but it reduces the fluorides of lead, of tin, &c. with the greatest ease. The reduction by hydrogen of metallic fluorides such as those of lead, tin, &c., which resist the reducing action of carbon, appears to demonstrate in a positive manner that these com- pounds contain no oxygen, and are really binary compounds. 7. All the fluorides, even those of potassium, sodium, and calcium, are rapidly decomposed by the vapour of water. 8. Oxygen and chlorine decompose fluoride of calcium at furnace heat, and liberate a gas which appears to be fluorine. 9. Vapour of sulphur does not act on fluoride of calcium, but this body is completely decomposed by the vapour of sulphide of carbon ; there is formed sulphide of calcium, and probably fluoride of carbon : the presence of silicious substances facihtates the reaction. 10. The analyses of the principal fluorides made, such as those of potassium, sodium, calcium, tin, lead, and silver, show that the equivalent of fluorine, as determined by Berzelius, is correct. 11. All the fusible fluorides are decomposed by the voltaic current, and disengage a gas which appears to be the radical of the fluorides. The author is still engaged on the subject, and promises still more extensive contributions. In the preparation of aluminium, Deville often accidentally ob« tained a dark gray crystalline substance, which was found to be silicon in a form analogous to that of graphite. Wohler com^ municates, in Liebig's Annalen for March, a method by which this ailotropic modification of silicon may be produced at pleasure. Aluminium is fused in a Hessian crucible with about twenty times its weight of perfectly dry silico-fluoride of potassium. On cooling, the slag in the crucible is found to contain a well-formed dark-coloured regulus, from which, by treatment with hydro- chloric acid, a crystalline mass is obtained, consisting of about 70 per cent, of the aluminium used. In this case the alumi- nium appears to determine the crystallization of the silicon, as melting cast iron determines that of graphite. M. Chiozza on the Artificial Production of Oil of Cinnamon. 55 The silicon in this condition forms large and small opake crystalline laminae possessing a metallic lustre, and very similar in appearance to natural and artificial graphite ; but it has more of a metallic lustre than these, and its colour inclines to a leaden It might be obtained in large crystals if the operation were conducted on a sufficiently extensive scale. Its exact crystalline form has not been determined ; but in some modifications of the experiment, large hexagonal plates have been obtained, the edges of which were curved like those of diamond. It is harder than glass, but not so hard as topaz. Its specific gravity is 2*49 ; less, therefore, than that of its oxygen compound, for the specific gravity of quartz and of rock-crystal is from 2*6 to 2* 8. It is not at all afiected by being heated in the alcohol and oxygen flame ; but when fused with carbonate of soda, it decom- poses the carbonic acid, carbon and carbonic oxide being produced, and the silicon itself being converted into silicic acid. It is slowly decomposed by caustic potash with evolution of hydrogen. Geuther investigated the products of distillation of the Tor- bane Hill mineral. They are composed principally of an oil containing paraffine in solution. The oil consists of a carbo- hydrogen homologous with olefiant gas. Gossmann and Atkinson communicate observations on lophine and some of its salts. For lophine they propose the formula Q42 JJ17 ]\j-2^ which differs very little from that adopted by Fownes, one of the original discoverers of this base. Breunlin proposes a new theory of the constitution of blue and green ultramarine. His view is, that ultramarine is a compound of a silicate of the formula of nepheline with a polysulphide of sodium. A translation of this paper was given in the preceding Number of this Journal. On the coast of Oldenburgh large quantities of a kind of prawn are caught, which are made into an artificial manure by being dried and powdered. Hanstein has analysed this sub- stance, and finds that it contains more nitrogen, but less phos- phates than Peruvian guano -, the deficiency in this latter consti- tuent might be made good by the addition of bone-meal. By the action of potash, cinnamic acid is decomposed into ben- zoic and acetic acids according to the following equation : — C9 H^ 02 + 2(KH0) = 02 H3 K02 + C7 H^ O^K + H2. Chiozza, who observed this decomposition, found that when a mixture of aldehyde and oil of bitter almonds is saturated with 5G MM. Limpricht and Ritter on Thioformic Acid, hydrochloric acid and gently heated, the hydride of cinnamyle or oil of cinnamon is produced. The author supposed that a change takes place here analogous to that observed when hydrochloric acid is passed into a solution of an organic acid in alcohol. Hy- drochloric acid acting on one of the aldehydes may produce the compound CIC^H^ or CIC^U^; and this acting on the other aldehyde, would produce hydrochloric acid and hydride of cin- namyle. Adopting the notation used by Chiozza, the change would be thus expressed : — CIH -f C7H6 0 = C1C7HS4-H2 0, Hydrochloric Benzoic Water, acid. aldehyde. CIC^H^ + C^H^O = cm -f C9H«0; Aldehyde. Hydrochloric Cinnamic acid. aldehyde. or CIH + C2H'*0=C1C^H3 + H20, Hydrochloric Aldehyde. ♦ Water, acid. ClCMi^ + cm^O = CIH + C9H80. Benzoic Hydrochloric Cinnamic aldehyde. acid. aldehyde. On passing sulphuretted hydrogen over dry formiate of lead, Wohler observed the formation of a body crystallizing in fine needles. This substance has been investigated by Limpricht and Ritter, who consider it to be a new sulphur acid, and they propose for it the name Thioformic acid. In its formation, a portion of the formic acid liberated by the sulphuretted hydrogen from the formiate of lead decomposes with the excess of sul- phuretted hydrogen into the new acid and into water : — C2 H^ OH 2HS = C2 H^ 02 S2 + 2H0. Foraiic acid. New acid. But the analyses made do not accord well with each other ; and from the reactions made on the small quantity produced, no useful conclusions can be drawn. The subject requires more complete investigation. In acting with nitric acid on oil of anise, it is generally assumed that hydruret of anisyle and oxalic acid are alone formed, thus : — C«o 1112 02 + 120 ^ c^^H^O^ + CMi2 08 + 2HO. Oil of anise. Hydruret of anisyle. Oxalic acid. But Limpricht and Ritter show that there is a well-marked intermediary stage in the reaction at which an acid containing 20 equivs. of carbon is obtained : — C^H'«O2 + 6HO + 4O = C20Hi8O»2. Oil of anise. New acid. Dr. Mohr on a Method of Estimating Chlorides. 57 The acid has been named Anisoinic acid. It crystallizes from an aqueous solution in small laminae, but on account of its great solubility it is difficult to obtain in good crystals. Analyses of its soda, silver, and baryta salts have been made. Limpricht proposes a nevv^ method for the formation of alde- hydes. He considers that in the formation of acetone, 2 equivs. of acetate of lime are necessary ; and he expresses the change as follows, using Gerhardt^s notation : — Acetate of Ume. Acetate of lime. Carbonate of Hme. Acetone. From one equivalent of the acetate, the radical acetyle, and from the other equivalent, methyle, unite to form acetone, the other elements forming carbonate of lime. By heating together acetate of lime and formiate of lime, an acetone is obtained which contains an equivalent of hydrogen in the place of methvle; in other words, an aldehyde, — Acetate of hme. Formiate of hme. Aldehyde. By distilling valerianate of lime with formiate, valeraldehyde is produced. This method has only theoretical interest, for the aldehydes are produced only in small quantities, and so mixed with empy- reumatic products that it is difficult to purify them. Mohr proposes a modification of the method of estimating chlorides by a standard solution of nitrate of silver, by which the point where the whole of the chlorine is converted into chlo- ride of silver is rendered more distinct. Mohr adds to the solution of the chloride to be estimated a little chrom'ate of potash solution, and then adds the nitrate of silver solution. As long as any chloride remains not precipitated, no chromate of silver is formed ; but when all the chloride is precipitated, the addition of even a drop in excess of the standard solution causes the formation of some chromate of silver, which is instantly seen by its characteristic red colour. In the April Number of the same Journal, Gorup Besanez gives the result of an investigation on the constituents of the contents of certain glands. Two years ago he announced the discovery, in the thymoid gland, of a weak basic body which he named thymine. This he has since investigated more closely, and finds that it is leucine. This body is an almost invariable constituent of the glandular juices, and is contained in largest quantity in the pancreas. He found in the pancreas a tolerably 6S M. Liebig on a new Method for Silvering Glass, large quantity of a new body, having the greatest similarity with leucine, both in appearance and chemical relation. It is homologous, and not identical with leucine. Its formula is C'o H»» NO*; that of leucine is C^^ hi3 ^q4 tj^^ Qt^er conclusions he has arrived at have merely a special physiolo- gical interest. Carius describes a compound of sesquioxide of manganese and sulphuric acid. It is obtained by headng binoxide of manga- nese with concentrated sulphuric acid. The excess of sulphuric acid is removed by washing with strong nitric acid, as the sub- stance is decomposed by water, and the nitric acid is afterwards expelled by a gentle heat. It has the formula Mn^ 0^, 3S0^. It forms a deep green powder, without a trace of crystallization ; attracts moisture with great avidity, and must be kept in closed tubes. By treatment with water it is converted into hydrated oxide of manganese, and is indeed the best source for this body. The Para nuts, the produce of a tree, the Bertholletia excelsa, which belongs to the family of the Lecythodece, contain upwards of 50 per cent, of a fatty oil. This oil, according to an inves- tigation of Caldwell, consists of stearine, palmitine, and oleine. According to Grimm and Ramdohr, the gas produced by the action of sulphuric acid on ferrocyanide of potassium is not pure carbonic oxide, but contains 11 per cent, of sulphurous acid. This appears to be reduced from the sulphuric acid by some of the carbon in the ferrocyanide. Liebig gives a new method for silvering glass in the cold, which answers its purpose extremely well. The silvering liquid consists of an ammoniacal solution of nitrate of silver, contain- ing caustic soda or potash. Before using, this is mixed with one-eighth or one-tenth of its quantity of a solution of sugar of milk, containing one part of sugar of milk to ten parts of water ; the glass plates to be silvered are then dipped into this mixture, and allowed to remain in about a quarter of an hour ; the silver- ing is then complete. The process is not costly ; a square metre of surface requires silver of the value of 5d, Liebig goes into the details necessary for ensuring success. Glass can only be permanently gilded with the aid of heat. The gilding liquid is composed of a solution of double chloride of gold and sodium, containing some caustic soda. At the time of using, alcohol and sether are added to it, and a gentle heat applied. As in the former case, certain precautions arc necessary, for which we must refer to the original paper. Royal Society, 69 Fleitmann communicates a process for estimating copper. The solution of copper, when freed from nitric acid and metals which might hinder the action, is precipitated by means of pure metallic zinc, and the precipitated copper well washed out. It is then dissolved in an acid solution of perchloride of iron : this takes place very rapidly, and gives twice the quantity of proto- chloride of iron, which may be estimated by permanganate of potash in the usual way. Wicke investigated the quantity of butter contained in goat's milk taken in the morning, at noon, and in the evening. The quantity of butter at those times is respectively as 4*6 : 4!'9 : 5*2. The average quantity of butter is 4*9 per cent. Cow's milk contains, according to Playfair, the same amount. Pebal continues his investigations on the constitution of citric acid. It is not possible with our limited space to give any adequate idea of his paper, as he enters very much into theore- tical considerations. VIII. Proceedings of Learned Societies, ROYAL SOCIETY. [Continued from vol. xi. p. 265.] Dec. 6, 1855. — Sir Benjamin Brodie, Bart., V.P., in the Chair. HE following communication was read : — " Results of the Examination of certain Vegetable Products from India."— Part I. By John Stenhouse, LL.D., F.R.S. Through the kindness of my esteemed friend Dr. Royle, I have been permitted to select such vegetable products from the extensive collection at the India House as seemed most likely to repay the trouble of investigation. My attention, during the last twelve months, has been chiefly directed to three of these vegetable sub- stances ; and the results of their examination I now take the liberty of submitting to the Royal Society, to be followed by those of the others as they may be completed. Datisca cannahina. The first of these substances which I examined consisted of a quantity of the roots of the Datisca cannabina, from Lahore, where this plant is employed to dye silk of a fast yellow colour. The roots, which had been cut into pieces about 6 or 8 inches long, were from a half to three-quarters of an inch in thickness. They had a deep yellow colour. A decoction of the leaves of the Datisca canna- bina was examined by Braconnot in 1816, who discovered in it a crystallizable principle, to which he gave the name of datiscine. T 60 Royal Society : — Braconnot, of course, did not subject this substance to analysis, but he described its appearance and properties in an exceedingly accu- rate manner*. The observations of Braconnot had fallen into such entire oblivion, however, that for many years past, we find in most of the larger systems of chemistry the term datiscine used as syno- nymous with inuline. 7'hus in Brande's ' Chemistry,* vol. ii. p. 1168, we find it stated that a vanety of names had been given to inuline, such as " dahline, datiscine," &c. The bruised roots were extracted in a Mohr's apparatus by long- continued digestion with wood-spirit. The liquor obtained, which had a dark brown colour, was concentrated by distilling off a por- tion of the wood-spirit. The brown syrupy liquid remaining in the retort, on being poured into open vessels and standing for some time, deposited a resinous matter containing merely traces of a cry- stalline substance. When this syrupy liquid, however, was treated with about half its bulk of hot water, the greater portion of the brown resin was rapidly deposited, and the mother-liquor having been poured off and left to spontaneous evaporation, deposited a considerable quantity of an imperfectly crystallizable substance resembling grape-sugar. These crystals are datiscine containing a considerable amount of resinous matter. The datiscine, however, is rendered perfectly pure by treatment with a solution of gelatine, to remove any trace of tannic acid, and repeated crystallizations out of weak spirits of wine. Properties of Datiscine. — Datiscine, when pure, is perfectly colourless. It is very soluble in alcohol, even in the cold, boiling alcohol dissolving any amount of it. By slow spontaneous evapora- tion, its alcoholic solutions yield small silky needles arranged in groups. Cold water does not dissolve much of it, but it is tolerably soluble in boiling water, the hot solutions on cooling depositing it in shining scales. Datiscine is not very soluble in ether ; but an ethereal solution, when evaporated, yielded larger crystals than were obtained by any other method. On adding water to an alcoholic solution of datis- cine, no precipitate is immediately obtained, unless the solution is greatly concentrated ; but on standing, very pure, pale yellow- coloured crystals of datiscine separate. When datiscine is heated to about 180° C, it melts, and if the heat be increased, it burns, evolving an odour of caramel, and leaves a voluminous charcoal. If datiscine be heated in a close vessel while a stream of dry air is slowly passed over it, a small quantity of a crystalline substance sublimes. Datiscine and its solutions have a very bitter taste ; and though it does not produce any change on test-paper, I think there is reason to regard it as a feebly acid body. It dissolves in solutions of the fixed alkalies and ammonia, also in lime- and baryta-water. The addition of an acid to these solutions causes the precipitation of the datiscine. The aqueous solution of datiscine is precipitated by neutral and basic acetates of lead, and chloride of tin. These precipitates have * Annales de Cliimie et de Physique, 1816, iii. 277. Dr. Stenhouse on certain Vegetable Products from India, 61 a bright yellow colour. Salts of copper produce greenish, and those of peroxide of iron brownish-green precipitates. In con- sequence of the lead salts forming such gelatinous precipitates, they could not be employed for determining the equivalent of datiscine. Action of dilute Sulphuric Acid on Datiscine. — When an aqueous solution of datiscine is boiled for a few minutes with very dilute sul' phuric acid, it deposits a crystalline substance. On examining the solution filtered from the crystals, very distinct evidences of the presence of sugar were obtained. These experiments show there* fore that datiscine, like salicine and similar bodies, belongs to the class of glucosides, and is a copulated compound of sugar and another substance which I shall call " datiscetine." Daiiscetine. — Datiscetine in its general appearance and pro- perties closely resembles datiscine, but on a closer examination these two substances are found to differ essentially both in com- position and properties. Datiscetine when pure assumes the form of fine needles which are nearly colourless. It is easily soluble in alcohol, a hot alcoholic solution, on cooling, depositing the greater portion in crystalline groups. It is almost insoluble in water, con- sequently datiscetine is precipitated from its alcoholic solutions by the addition of water. It dissolves in ether in almost any quantity, and is deposited on the evaporation of that liquid in needles. These properties of datiscetine enable us to obtain it in a tolerably pure state, even when very impure datiscine is employed in its pre- paration. Properties of Datiscetine. — Datiscetine has no taste. When heated it melts like datiscine, but the heat required is much higher than for that body. It recrystallizes on cooling. By operating very cautiously, a portion of the datiscetine may be su1)limed. The sub- limate, however, appears to be altered datiscetine. Datiscetine when burned does not emit the odour of caramel. Datiscetine, like datiscine, dissolves in alkaline solutions, and is reprecipitated by the addition of an acid. An alcoholic solution of acetate of lead added to an alcoholic solution of datiscetine produces a deep yellow precipitate, which can be easily washed both by alcohol and water. This precipitate therefore was subjected to analysis, and from the results obtained, the formula Cg^ Hg OiQ-}-2PbO was calculated, which agrees with the formula (C3Q Hj^ O^g) derived from the analysis of datiscetine. Analysis of Datiscine. — It is difficult to calculate a formula for datiscine, the numbers of which shall agree with those found by analysis. When, however, the decomposition of datiscine into datiscetine and sugar is taken into consideration, it seems probable that the formula for datiscine is Datiscetine + sugar = datiscine ^30 Hio O12 + C12 ^^12 ^12=^42 ^22 ^24' If the formula C42 H22 O24 be correct, the decomposition of datis- cine by dilute sulphuric acid would be analogous to that of salicine when treated in the same way. Dilute hydrochloric acid, like dilute sulphuric acid, decomposes 62 Royal Society: — datiscine, converting it into datiscetine and sugar. On boiling ail aqueous solution of pure datiscine for some hours, traces of sugar could be detected, thus showing that a small portion of the datiscine had been decomposed. It has been already shown that datiscine dissolves in cold so- lutions of potash without decomposition. When boiled, however, with a strong solution of potash for some time, decomposition takes place, and the precipitate, thrown down by the addition of an acid, has all the properties of datiscetine. In this respect, therefore, datiscine agrees with tannin and similar glucosides, which yield the same products when acted upon by acids and alkalies. Yeast and emulsine appeared to exert no action on solutions of datiscine. Action of Nitric Acid on Datiscine and Datiscetine. — Cold nitric acid of the ordinary strength acts violently upon datiscetine, brown vapours are disengaged, and a resinous substance is produced, which is ultimately dissolved, forming a dark red liquid, which, when evaporated, yields crystals of nitropicric acid. Datiscine treated in the same way yields nitropicric and oxalic acids. When datiscine is boiled with dilute nitric acid it dissolves, and the solution obtained, when cooled, deposits pale yellow crystals, which agree in every way with the properties ascribed to nitrosali- cylic acid. On allowing datiscine to stand in contact with dilute nitric acid in the cold it gradually dissolves, the solution, when left to eva? porate in vacuo, depositing a mixture of oxalic and nitropicric acids. Action of Potash on Datiscine and Datiscetine, — It was stated in a previous part of this paper that datiscine and datiscetine dissolve in cold solutions of the alkalies without decomposition, and that datis- cine, when boiled with potash, is decomposed with the formation of datiscetine. It only remained, therefore, to try the action of fused hydrate of potash. Datiscetine, when added in small successive portions to fused hydrate of potash, assumed a deep oiange colour, and then dissolved with the evolution of hydrogen gas. When the disengagement of hydrogen had ceased, the mass was dissolved in water and supersaturated with hydrochloric acid. A partly resinous substance separated, which, by sublimation, yielded perfectly colour- less, long crystals closely resembling benzoic acid. Their solution in water on the addition of perchloride of iron gave that deep violet tint which disappears on the addition of hydrochloric acid, and is so characteristic of salicylic acid. Action of Chromic Acid on Datiscetine. — On distilling datiscetine with bichromate of potash and sulphuric acid a liquid came over, containing no oily drops, but having the smell of salicylous acid, and which, when tested with a persalt of iron, formed a purple- coloured solution characteristic of that acid. It follows therefore, I think, from the experiments already de- tailed, that datiscine, like salicine, phloridzine, &c., is a glucoside, and that it approaches nearer to salicine than any other glucoside, with the exception of populine, yet known. Dr. Stenhouse on certain Vegetable Products from India. 63 I will conclude this account of datiscine by proposing the follow- ing practical application. As is well known, the colouring matter of madder, when boiled with dilute sulphuric acid, is changed into sugar and garancine, a new dye-stuff, which, for many purposes, is found superior to that originally present in the madder. Within the last twelve months Mr. Lieshing, by treating the colouring matters in weld and quercitron bark with dilute sulphuric acid, has resolved them into new colouring matters, which are but slightly soluble in water, and are found nearly three times more powerful as dye-stuiFs than the original colouring matters from which they had been produced. As datiscine, when boiled with dilute sulphuric acid, undergoes a perfectly similar transformation, being resolved into sugar and datiscetine, wliich has a much higher colouring power than the datiscine which has produced it, I have not the least doubt that silk dyers, who may hereafter employ solutions of Datisca cannabina, will find it highly advantageous to convert their datiscine into datiscetine by boiling it with dilute sulphuric acid. Oil of the Ptychotis Ajowan. The Ptychotis Ajowan is an umbelliferous plant well known in India for its aromatic and carminative properties. When its seeds are distilled with water they readily yield between five and six per cent, of an essential oil resembling in smell that of oil of thyme. When this oil is left in shallow vessels to spontaneous evaporation at low temperatures, it deposits a large quantity of beautiful crystals, which are identical with the stearopten brought from India by the late Dr. Stocks, and described by me in a short notice in the De- cember Number of the ' Pharmaceutical Journal' for 1854. The crude oil was rectified, and the portion which came over between 160° C. and 164° C. was collected separately and carefully rectified over sodium. Its boiling-point was found to be 172° C, and its composition isomeric with oil of turpentine, namely The stearopten obtained from the less volatile portion of the oil was purified, and formed large flat rhombohedral crystals, which have been carefully measured by Professor Miller of Cambridge. When subjected to analysis it gave the formula C^oHi^O^orC^oHigOiHO. In the notice of the stearopten of this oil which appeared in the 'Pharmaceutical Journal,' from the examination of the small quantity then at my disposal, a different formula was deduced, which I now withdraw, and substitute the preceding formula, Cgo Hi4 Og, in its stead. When the crystalline stearopten is digested for eight or nine days with the strongest nitric acid, it is gradually converted into a crystallizable acid, apparently containing no nitrogen. This acid is but slightly soluble even in boiling water, but is deposited in needles on the cooling of the solution. It is very soluble in alcohol 64 Royal Society : — and ether, from which it is deposited in crj'stals. Both its silver and its baryta salts are crystallizable, and appear very stable. It seems to me to be a new acid, and this I hope soon to be able to ascertain. When the stearopten is gently warmed with oil of vitriol it dissolves, and, on cooling, solidifies into a crystalline mass. This new compound, which is a copulated acid, dissolves readily in hot water, and, on cooling, is deposited in large scaly crystals, of a mother-of-pearl lustre. It forms both a crystallizable lead and baryta salt. When the stearopten is distilled with a mixture of peroxide of manganese and sulphuric acid, it yields a substance exceedingly analogous in almost every respect to the thymoil obtained by Lalle- mande by subjecting the stearopten of oil of thyme to similar treatment. As the details of Lallemande's experiments have not yet been published, it would be premature to pronounce with abso- lute confidence on the identity of the stearoptens from the Ptychotis and oil of thyme ; but if not identical, as I rather apprehend they are, they are certainly extremely similar bodies*. Gum of the Gardenia lucida, Roxb. (the Decamalee Gumof Scinde). The specimen of this gum on which I operated was evidently very old. It formed a hard, dry mass, of a dark brown colour, with numerous patches of a greenish-yellow matter disseminated through it. It had but a faint odour, unless freshly fractured or gently heated, when it smelt like the urine of the cat. A comparatively recent specimen of this gum, which I saw in the hands of the late Dr. Stocks, had merely the consistence of candied honey, and an exceedingly offensive odour. Dr. Stocks informed me that the fresh gum was employed as a dressing for wounds, as it kept off the flies. The resin was digested in strong spirit of wine, till a saturated solution was obtained. This, on cooling, im- mediately deposited some yellow amorphous flocks. These were separated by filtration, and the clear liquid slowly evaporated in vacuo. On standing a few days, it deposited a quantity of golden 3'ellow slender crystals, about half an inch in length. The crystals had considerable lustre, and were very brittle. To this crystalline substance I purpose giving the provisional name of gardenine. Gardenine is nearly insoluble both in cold and hot water. It dis- solves pretty readily in alcohol, but much less readily in ether; ether yielding bright yellow solutions, out of which it crystallizes on cooling. Alkalies, such as ammonia, do not appear to increase * Since this paper was communicated to the Royal Society, a notice of the Ptychotis oil, by Dr. Haines, of the Bombay College, was read before the last meeting of the Chemical Society. Dr. Haines has generally arrived at similar conclusions to my own. He regards, however, the carbohydrogen portion of the oil not as isomeric with oil of turpentine, but as Coo ^^u- His formula for the stearopten is the same as that given in this paper ; and he regards it as identical with Lallemande's thymole. Dr. Haines, however, appears not to have observed the crystalline acid pro- duced by the action of nitric acid on the stearopten. I Dr. Woods on the Heat of Chemical Comhination. 65 its solubility. It is more soluble in hot hydrochloric and sulphuric acids than in water, and is precipitated, apparently unchanged, on the addition of water. Its alcoholic solutions give no precipitate with aramonio-nitrate of silver, or with basic acetate of lead. When gardenine is digested with concentrated nitric acid, it is rapidly decomposed ; nitropicric acid, but apparently no oxalic acid, being produced. Unfortunately, from the very small quantity of resin at my dis- posal, I was unable to prepare a sufficient amount of the gardenine either to subject it to analysis or to examine it more particularly. Dr. Royle has, however, commissioned a large quantity of the resin from India, which I trust will ere long enable me to complete its examination. Gardenine appears to belong to the tolerably nume- rous class of indifferent crystallizable resins, of which it is certainly one of the most beautiful. January 10, 1856. — Admiral Beechey, V.P., in the Chair. The following communication was read : — *' On the Existence of Multiple Proportion in the quantities of heat, or equivalent alteration of internal space of bodies, caused by definite changes of state as produced by Chemical Combination or otherwise." By Thomas Woods, M.D. Gay-Lussac having shown that the combining proportions of gases and vapours are either equal in volume or some multiple of each other, and other chemists, particularly Playfair and Joule, having extended the same law to sohds and liquids, it is evident that specific volume of its combining equivalent is characteristic of matter. But as every substance is composed of matter and space, or of particles with some distance between them, as is shown by ex- pansion and contraction, whenever volume is altered there must be either an addition to or subtraction from the internal space of the body. This alteration of volume is evident in the case of bodies . expanding or contracting by gain or loss of heat ; but in chemical combination, where alteration of internal space must take place also (as shown by change of temperature, and because specific volume being characteristic of matter, this volume must change when the matter changes, by a substitution of a mixture of two kinds of matter for one), in chemical combination, I say, this alteration of internal space is not so plainly demonstrable. Still, in the change of tempe- rature, we have not only an evidence, but a measure of the change of state of combining bodies. For, the phenomena of heat being produced by a dual force acting equally in opposite directions, one body cooling or contracting as another becomes heated or expands, it may be taken for granted that whenever heat or expansion is found in one body, the opposite change is occurring in some other. Now, regarding this proposition as true, it is intended to be proved from the combinations of oxygen that the internal space of a substance is lost and gained in multiple proportion, in the definite changes of state of bodies, such as in the condensation of vapours into liquids, Phil Mag, S. 4. Vol. \%, No. 7Q, July 1856. F 66 Royal Society : — and liquids into solids, and the reverse ; and also in chemical combi- nations and decompositions ; and therefore that the space as well as the matter of which volume is composed can be only added to or taken away in what is called its combining equivalent. In order to find whether the heat of chemical combination, which is taken as equivalent to the alteration of internal space, is equally produced by the same substance uniting with others, or if not, if it is given out in multiple proportion, oxygen is made to combine with several other simple bodies, and the alteration of temperature noted. The method of oxidizing these substances, the details of each pro- cess being given in the paper, consisted in dissolving them in some suitable menstruum, — for instance, in sulphuric acid, liquor of potass, and nitric acid. When the two former are used, water is decom- posed to oxidize the dissolved body ; in the last case, the nitric acid is resolved into oxygen and binoxide of nitrogen, the former of which unites with the substance to be oxidized, the latter escaping. Other combinations and decompositions at the same time take place (as detailed in the paper), and being taken into account (decompositions absorbing as much heat as is produced by the combination of the constituents), the alteration of temperature by the oxidation alone is arrived at. In this manner eighteen diiferent metals were oxidized, but the heat of oxidation was obtained satisfactorily only with twelve. Other experimenters (Favre and Silbermann and Andrews) have, with a different object in view, found the heat of oxidation of fourteen other substances ; their conclusions are added as being from un- prejudiced sources, and the result of all the experiments is brought together in a table, in order to see whether the law of multiple pro- portion exists. The numbers found by the different experimenters are all calculated to the same standard. The unit of heat is the amount necessary to raise the temperature of 1000 grains of water 1° Fahr., and the quantity of the metal oxidized is an equivalent of each, oxygen = 1 . To find whether the law extends to change of state when no chemical combination takes place, the amount of heat given out by the condensation of an equivalent of steam, and by the solidification of an equivalent of water, is given. The following is the table giving the thermal equivalents of the several substances, the names of the experimenters, and the ratio of proportion. It is to be remarked, that the condensation of steam being in multiple proportion with the other thermal equivalents, the expansion of all other bodies into vapour must be included ; for I showed in the Philosophical Maga- zine for January 1852 (page 48), that all bodies expand into vapour in some multiple of their atomic volumes, and their atomic volumes being in ratio also, their expansion or gain of internal space in this definite change must be in multiple proportion. Dr. Woods on the Heat of Chemical Combination, 67 Table showing the quantity of heat produced in 1000 grs. of water by the oxidation of an equivalent of each substance, 0=1. Name of substance Units of oxidized. heat. Ratio. Name of Experimenter. Latent heat of ice . Latent heat of steam Iodine Chlorine Nitrogen Silver Selenium ... Mercury Palladium ... Molybdenum Carbon Arsenic Antimony ... Copper Cobalt Bismuth Nickel Lead Hydrogen ... Tin Phosphorus Cadmium . Iron Zinc ....... Manganese . Barium .... Aluminium. Sodium .... Potassium . •1603 1-287 •8 -1-6 1-6 1-6 27 2-4 2-42 3-38 33 4-8 4-8 4-9 4-8 4-82 6-5 6-2 7-8 80 81 8-18 7-95 9-6 10-4 12-8 1616 17-5 17-3 •1603 8 times -1603 5 times ^1603 I twice*-8"*J I 3 times -8 -j i- 4 times '8 < 10 times -8 12 times -8 13 times -8 16 times '8 20 times -8 j 22 times -8 Woods. Favre and Silbermann. Woods. Woods. Favre and Silbermann. Woods. Woods. Woods. Favre and Silbermann. Favre and Silbermann. Woods. Favre and Silbermann. Woods. Woods. Woods. Favre and Silbermann. Favre and Silbermann. Mean of Andrews and Favre and Silbermann. Favre and Silbermann. Woods. Mean of Andrews and Favre and Silbermann. Favre and Silbermann. Woods. Woods. Woods. Favre and Silbermann. Favre and Silbermann. Note. — I proved in a paper published in the Philosophical Maga- zine for October 1851, that " the decomposition of a compound body absorbs as much heat as the combination of the elements originally produced." I believe I was the first to prove this as a general propo- sition, and, by so doing, laid the foundation of almost all the thermo- chemical researches since carried on ; for, as far as I am aware, no process which took decomposition into account was used before my paper was published. In a paper read to the British Association at Belfast, and pub- lished in the Philosophical Magazine for November 1852, I proved that the intensity of chemical affinity might be measured by the quantity of heat produced by the combination. As regards the first of these papers, Mr. Joule published in the Philosophical Magazine for June 1852, a memoir proving exactly the same proposition, but giving me the merit of priority in a pre- liminary remark. It is, however, singular that Favre and Silber- mann bring forward in 1853 (Annates de Chimie et de Physique^ r2 tSB G^logical Society : — vol. XXX vii. p. 507) the very same experiments to prove the same fact, and give it as their own. As regards the second paper. In six months after its publication, Messrs. Favre and Silbermann {Annales de Chimie et de Physique, vol. xxxvii. p. 484) prove the same truth with the same experi- ments, using exactly the same metals, and give their memoir as producing an original idea. I notice these coincidences here as being remarkable, and because the propositions contained in the paper referred to are the ground- wrk of the present experiments, and also with a view to prevent an unconscious repetition on the part of Messrs. Favre and Silber^ mann. GEOLOGICAL SOCIETY. [Continued from vol. xi. p. 553.J May 28, 1856. — Colonel Portlock, Vice-President, in the Chair, The following communications were read : — 1. " On the Silurian Rocks of Wigtonshire." By J. C. Moore, Esq.. F.G.S. The objects of this communication were, — 1st, to point out a remarkable arrangement in the rocks which form the peninsula between the Mull of Galloway and Corswall Point ; and, 2ndly, to show the relative positions of the graptolitic schists of Wigtonshire and of the coarse conglomerate and limestones of Ayrshire. The author had already shown in a former communication that the rocks from the Corswall Lighthouse for a great distance to the south have, in the main, a southerly dip ; and that, after passing to the south of Port Patrick, the dip is found to be reversed, that is, to the north. By subsequent visits to this coast, Mr. Moore has been enabled to offer a detailed account of the numerous anticlinal and synclinal folds, exhibited more or less perfectly along this coast -section, a distance of more than 30 miles. These foldings of the beds have the anticlinals (the arches of which are occasionally preserved) thrown northward along the northern portion of the section ; their shorter or northern sides being vertical or nearly so, and their longer or southern sides being inclined at varying angles, often not more than 30°. The opposite conditions obtain in the southern portion of the section towards the Mull of Galloway. Sometimes the flexures are very numerous ; in one place as many as fifteen occur in five miles. On the east side of the Bay of Luce the coast-section, parallel to the above, affords confirmations of the same structure. The strata are undulated, with the axes of the folds toward the south, and the long sides of the folds gently dipping northward. The east coast of Loch Ryan may be regarded as a northern i)rolongation of this section, and, in conformity with the Corswall Point section, exhibits a section of rocks folded over towards the north. At Corswall Point, and in the corresponding section in Z/}ch Mr. C. Babbage on the Action of Ocean-currents. 69 Ryan, are coarse conglomerates of granite, porphyry, &c., and towards the middle of the section are schists with graptolites, which latter, from the general southern dip of the strata and the frequent absence of the axial arches, appear to overlie the former. The graptolite-schists, however, are the equivalent of the graptolitic and anthracitic schists of Dumfriesshire, Selkirkshire, and Peebleshire, and are really lower in stratigraphical position than the conglo- merates of Corswall Point and the conglomerates and limestone of the south of Ayrshire, of which the Wrae limestone, with its asso- ciated conglomerate, is the counterpart. The abnormal relative position of the conglomerates and graptolite-schists on the western coast of Wigtonshire is due, in the author's opinion, to an inversion of the rock-masses, similar to the great inverted flexures of strata seen in the Ardennes, the Eifel, the Appalachians, &c. This great folding up of the Silurian strata has thrown them into axial folds which have an E.N.E. strike, similar to that prevailing over the north of Ireland, the south of Scotland, and even in Norway, and must be due to some physical cause which has operated on a mag- nificent scale. In the author's opinion, the granites of Cairnsmuir, CrifFel, &c. have been protruded subsequently to the great move- ments above alluded to, and have somewhat deranged the E.N.E. strike. 2. "On the action of Ocean -currents in the formation of the Strata of the Earth." By C. Babbage, Esq., F.R.S. Communi- cated by W. H. Fitton, M.D., F.R.S., F.G.S. In the first part of this paper the author traced out the laws which regulate the distribution of very finely divided earthy matter, borne outwards from river-mouths and sea-clifFs into the ocean- currents, over extensive areas. The time that a particle of matter requires to fall through a given distance in a resisting medium depends — 1st. On the specific gravity of the particle itself. 2nd. On its greater or less magnitude. 3rd. On its form. 4th. On the law of the resistance of the medium through which it falls. These several points were treated of by the author, who then proceeded to show under what conditions certain finely triturated substances, of given size and composition, suspended in a current of a given velocity, would be deposited in a sea of a given depth. He noticed also how the uniformity of a stratum might be interfered with by the varying conditions both of the sediment and of the sea-bottom. Altered relations between the specific gravity, the shape, and the size of the particles, when duly adjusted, render ocean-currents capable of either separating mixed substances, or of combining together different substances. Hence endless combina- tions arise from the variation of these conditions. Local elevations and depressions of the sea- bed, on which sedi- ment brought from a distance is deposited, were pointed out as probable causes of irregularities in stratified deposits, — giving origin. 70 Geological Society : — indeed, either to outliers or disconnected masses, which might be sometimes supposed to have been due to subsequent denudation. Sedimentary matter carried by ocean-currents to the profound depths of the ocean subside into these depths beyond the reach both of currents and of wave-action. The downward motion becomes continually diminished, and the particles ultimately come to ab- solute rest, or move through water of increasing density with ex- cessive slowness, so as to cover the ocean-bottom with an incoherent pulpy mass of fluid mud, of great thickness, and less dense for the most part in the upper than in the lower part, — or to form a similar mass of sediment suspended in mid- water. It was also pointed out that in the immense period of time during which this sediment is subsiding into the profound ocean-depths and massing itself into a mud-bed, various hydrographical changes might take place and cause new currents to bring different sediments over the same area, which newer deposits would descend into and be mingled with the older precipitates. The author proceeded to treat of the effects of an alteration of isothermal surfaces, caused by the interference of this more or less suspended mud- cloud with the conduction of heat from the earth's surface. Consolidation of the lower strata would be caused by the isothermal surfaces below the ocean rising upwards. Currents of heated water, similarly caused, might variously disturb the sediment and give it flexuous stratification. Heated water might be retained in portions of the sedimentary masses, and alter by its solvent power the constituent materials ; or the heated water might be converted into steam, or generate permanent gases, which might derange or alter the suspended material in various ways. If the sediment had not reached the bottom, but formed a freely suspended mud- cloud in mid-ocean, the effect of the interposed bed of fluid mud impeding the upward progress of heat from the lower region would necessarily be to increase the heat of the water below the mud, and thus place the sediment between the upward pressure of the heated water and the downward pressure of the overlying water. The ocean above would cease to derive its usual supply of heat from below, and become climatally altered. The now consolidated mud- bed would of its own weight either sink bodily down, and take different positions according to its consistency and the form of the ocean-bottom, or it would be contorted and broken through from the effect of the accumulated heat below. In tracing the results of this upward pressure and bursting, the author observed that on the enormously thick and partially consolidated stratified mass one or more weak points would admit of the formation of elevated domes, and that from the bursting of one of these domes, in a sea of much greater length than breadth, a vast wave would be propagated through the plastic matter, which would advance and be followed by others less perhaps in degree. As the original wave advanced, the diminishing depth of the ocean would cause the head of the wave to advance with greater speed than its base, impeded by friction on the ocean-floor, and give it its advancing form and a Mr. J. Plant on the Keuper Sandstone of Leicester. 71 steeper declivity in front than on its hind side; this might be carried so far that the foremost wave may even double itself over, and yet, owing to the plasticity of the mass, there might be no breach of continuity. To the transmission of such impulses through lemi-consolidated strata, the author refers for an explanation of the overlapping and inversion of strata seen in the Appalachian and other mountain-ranges. The paper concluded with remarks on the indications of the age, and causes influencing the structure of deposits, such as cleavage, &c., in connexion with the foregoing observations on sedimentary formations, and as illustrating, with them, some of the consequences of several physical causes which act through vast intervals of time upon the strata forming the crust of the earth. June 4, 1856. — Colonel Portlock, Vice-President, in the Chair. The following communications were read : — 1. "Notice of the Keuper Sandstone and its Fossils found at Leicester." By James Plant, Esq. Communicated by J. W. Salter, Esq., F.G.S. The author met with the following section of the Keuper and overlying beds in the immediate vicinity of Leicester, in a N.W. direction: — 1. alluvial deposits, containingremains of Deerand Oxen, with nuts, leaves, &c., 10 feet : 2. gravels and clays, with Elephants'- teeth, oolitic detritus, and boulders of syenitic and metamorphic rocks, 30 feet : 3. laminated clays and blue marls, 60 feet: 4. thin strata of Keuper shales, grey marl, and sandstone, with numerous irregular branched casts on the surfaces, usually called Fucoids, but referred by Mr. Plant to Gorgonice. 80 feet : 5. fine silicious white sandstone, in beds about 3 feet thick, occasionally intercalated with by a thin band of carbonaceous matter, 20 feet : 6. clays, thin sandstones, and grey marls, 35 feet: making a total of nearly 200 feet of Keuper beds. Besides the ramiform surface-markings above alluded to, the Keuper here exhibits ripple-marks, foot-tracks, and other superficial impres- sions, and yields some remains of plants, referred to Echinostachys and Voltzia, also numerous specimens of the little Posidonomya minuta, together with teeth and spines of Fish, fragments of bone, and coprolites. The author remarked that the Leicester Keuper most closely agrees with the same formation in Gloucestershire, as de- scribed by Murchison and Strickland, even in lithological characters. The Keuper beds are divisible into three chief members in each district, — the upper, thin sandy shales, with way-boards of green marl, — the middle, thick beds of soft white sandstone, — and the lower like the upper. 2. " Remarks on the Keuper of Warwickshire." By the Rev, P. B. Brodie, M.A., F.G.S. The old quarries on Shrewley Common, described by Murchison and Strickland, are now closed, but excavations near the Canal at Shrewley and Rowington have lately aflTorded sections and some fossils of the Keuper beds, as follows: — 1. Sandstone and marl, a 70 Geological Society : — few inclies; 2. Reddish marl, 4 inches; 3. Green marl, 4 inches; 4. Light-coloured, fine-grained sandstone divided by marls, 3 feet, with Posidonomya minuta. Fish-bones, and Ripple-mark; 5. Gritty sandstone, with teeth oiAcrodvs, and fish-bones and spines, 8 inches ; 6. Green marl, \ inch ; 7. Hard sandstone, with Posidonomya, 10 inches ; 8. Sandstone divided by green marls, 10 feet, with remains of Plants, Vollzia &\\d Calamites} 9. Red marl. Bones oi Labyrin- thodon were met with ; and Foot- tracks also occur, but their place in the series was not determined. Fucoidal markings are frequent throughout ; and ripple-mark is common in the sandstones. The Warwickshire Keuper very nearly agrees with that of Worcestershire, as described by the Rev. Mr. Symonds, but at Pendock the bed No. 5 is coarser, is still richer in osseous remains, and contains car- bonaceous matter. 3. " On a new genus of Cephalopoda, Diploceras (Orihoceras bisiphonatum of Sowerby). By J. W. Salter, Esq., F.G.S. In this communication the author pointed out the apparent rela- tions of this peculiar form, which has been figured in the ' Silu- rian System ' and in * Siluria.' It possessed ordinary septa, pierced by an excentric beaded siphuncle, and also had a deep lateral cavity passing down side by side with the siphuncle, and affecting at least seven, if not more of the uppermost septa. Mr. Salter remarked that the structural peculiarities of Ortho- ceras paradoxicum and of Gonioceras might elucidate the character of the shell in question ; but he thought that the study of Ascoceras and Cameroceras would be still more likely to throw light on the subject. Mr. Salter also described a new species oi Ascoceras (A. Barrandii), found not long since in the upper Ludlow rock, at Ludlow, and at Stansbatch in Herefordshire. 4. " On an Orthoceras from China." By S. P.Woodward, Esq., F.G.S. The specimen in question was one of several that were imported from China in 1854 by Mr. D. Hanbury. They are longitudinal sections in thin, polished slabs of limestone, and were obtained by Mr. Lockhart, of Shanghae, from some place 200 miles distant. They seem to have been used as screens, having been mounted in carved wooden frames with stands. Mr. Woodward described in detail the appearances presented by the fossil in question, which is probably of Devonian age, and offers some interesting facts as to the original relations of the siphuncle, the lining membrane of the shell, and other parts of the animal. The specimen exhibits appear- ances attributed to the gradual separation and ultimate colla])se of the lining membrane from the wails of the air-chambers towards the apex of the spire, during the life-time of the animal. He stated that the changes which this specimen has undergone appear to be these, — 1 . When buried in the sea-bed, the mud entered the sii)huncle and filled the interior of those chambers in which the siphuncle was incomplete. 2. Water, containing carbonate of lime in solution, penetrated the air-chambers and other closed spaces. Mr. Ibbetson on the Origin of veins of Gold in Quarts. 73 coating all the inner surfaces with tufa. 3. The shell was dissolved and removed before the consolidation of the surrounding mud, which thus obtained access to all those cavities whose calcareous lining was incomplete. 4. The cavities which the mud could not enter were filled, or nearly filled with crystalline carbonate of lime. Mr. Wood- ward concluded his paper with remarks on the structure and filling up of the siphuncle in Actinoceras and other allied forms of Cephalopoda. 5. " On Trap-dykes intersecting Syenite in the Malvern Hills, Worcestershire/* By the Rev. W. S. Symonds, F.G.S. The author described the dykes of greenstone and trap traversing syenite in a quarry between the Winds Point and the Obelisk. The syenite is altered by contact with the dykes, and the appear- ances closely resemble those observed by the author in the syenite on which the great bonfire was made on the Beacon Hill in January last. 6. "On the Movement of Land in the South Sea Islands." By James G. Sawkins, Esq., F.G.S. The author when visiting the Friendly Islands in 1 854 collected information relative to an earthquake which had lately occurred, accompanied by a sinking of the eastern and north-eastern portion of Tongataboo, and an uprise on the western coast, and the appear- ance of an island or shoal of black sand at a distance of thirty miles to the westward. Another earthquake occurred afterwards at Nina- poon, an island to the northward, which was not felt at Tongataboo. The author also referred to other indications of local movements of land in the Pacific Islands. 7. "On the possible origin of veins of Gold in Quartz and other rocks." By L. L. B. Ibbetson, Esq., F.R.S., F.G.S. Having mixed a solution of gold in nitromuriatic acid with five times its weight of water, and placed it in a Berlin evaporating dish on a thick sheet of copper over a gas-lamp, the author observed a crack in the basin, which was increasing. On transferring the solu- tion to another basin, he found that the crack presented a vein of gold ; the pure gold forming small nodular masses along the fissure, both inside and out, and resembling veins of gold in auri- ferous quartz-rocks. Under the circumstances of the low tempera- ture at which the solution was being evaporated, the diluted state of the solution still left unevaporated, and the diflference of the appearance of the nodular form of the gold- vein from the usual ap- pearance of the metallic gold obtained by evaporation from such a solution, the author thought it worth while to describe and exhibit the specimen to the meeting. [ 74 ] IX. Intelligence and Miscellaneous Articles. THE ABSORPTION OP HEAT BY DECOMPOSITION. To the Editors of the Philosophical Magazine and Journal. Gbntlemkn, Parsonstown, June 1866. TN an abstract of a paper sent by me to the Royal Society, pub- -■■ lished in the ' Proceedings' for January last, I claim the discovery of the law that " decomposition absorbs as much heat as the com- bination of the elements originally produced." In the ' Proceedings' of the Society for March following, Mr. Joule disputes my claim, and refers to papers of his published in the Philosophical Magazine, October 1841. He also says he sent a memoir to the French Aca- demy in 1846, which however was not published until 1852, in the Philosophical Magazine. As to the paper published in the Philosophical Magazine for October 1841, after carefully reading it, I cannot find anything in it which proves the law I have mentioned. Mr. Joule proves in it that the heat produced in a conductor by a galvanic cur- rent is in proportion to the resistance and the square of the inten- sity of the current, meaning by "intensity" the quantity passed through a certain resistance in a given time. When he caused the current to pass through an electrolyte, he found that this law did not hold good, that the same amount of heat was not pro- duced as when it passed through a solid body. He therefore con- cluded,— and he says he found by an experiment, which he does not describe — that part of the intensity of the current is used up in pro- ducing electrolysation, and therefore cannot be employed in evolving heat. Now, so far from any proof being here offered that " decom- position absorbs as much heat as combination produces," an exactly opposite doctrine is taught ; for the conclusion to be arrived at is, that if the intensity of the current was not lessened by electrolysa- tion, the same amount of heat would be produced in the electrolyte as in the solid conductor offering the same resistance, or in other words, that if the same quantity of galvanic current from the same source passed through an electrolyte and through a wire (an expe- riment easily made by accommodating the length of the wire to the resistance of the electrolyte), the same quantity of sensible heat would be generated. But this is quite opposed to the truth. In my experiments published in the Philosophical Magazine for October 1851, and in Mr. Joule's, published in the same Magazine for July 1852, it is shown that the current under these circumstances developes different amounts of heat, and that the difference is the quantity absorbed by decomposition. With respect to the memoir sent by Mr. Joule to the French Academy in 1846, although it proves the law referred to exactly in the same manner in which my paper does, it cannot interfere with my claim to the discovery, as it was not published for nine months after mine. In sdl cases I believe the first publication of a discovery decides the priority. The publication of his paper nine months Intelligence and Miscellaneous Articles, W| after mine can only affect me by offering additional evidence of the truth of my experiments. Since I published my paper in the Philosophical Magazine for Octo- ber 1851, thermo-chemical researches have been extensively carried on, and all based on the truth of the proposition I there proved, viz. ** that decomposition of a compound body absorbs as much heat as combination of the elements produced." Before that date no such experiments were thought of, that is, the amount of heat produced by the union of elements was in no instance calculated from any process taking decomposition into account. The reason why the combustion of a compound body, such as alcohol, does not produce as much heat as the elements would when separately ignited, was not even understood, — proofs that philosophers were not aware of the principle before my paper was published, and consequently had not perceived it in Mr. Joule's. I published a paper in the Philosophical Magazine for November 1852, proving that tlie intensity of the affinity of elements for oxy* gen might be measured by the quantity of heat their combination with that body produces. On referring to Mr. Joule's paper pub- lished in vol. XX. of the Philosophical Magazine for 1842, I find that he has there proved the same proposition. If I had known of this paper when I published mine, I would have quoted it in preference ; but at the same time I must say, that if the proposition hQ true and of importance, I have a right to claim its establishment ; for although Mr. Joule in 1842 brmgs it forward, in 1843 he rejects it. (See Phil. Mag. vol. xxiii. page 442.) It was therefore the more necessary subsequently to show it was correct. I have the honour to be. Your obedient Servant, Thomas Woods. . . - ON HEAT AS THE EQUIVALENT OF WORK. Hoppe has contributed a memoir upon this most interesting and important subject, which places the analytical theory in a remarkably clear, simple, and general point of view, so far at least as it relates to permanent gases. We shall give the author's investigation in extenso, making however a slight change in the symbols employed, so as to assimilate them to those usually employed by writers on the calculus in French or English. The temperature r of an enclosed permanent gas may be expressed as a function of the pressure p, and the volume v by the following formula, which is a combination of the laws of Gay-Lussac and Mariotte : — pt,= ^a+ar). (1) In this formula m represents the mass of the gas, a any definite pressure, that of one atmosphere for instance, h the density at the temperature 0° and pressure a. If we consider the temperature to 76 Intelligence and Miscellaneous Articles, be measured by the increments of volume of the gas itself, a will be absolutely constant, and Mariotte's law will be the only fact resting upon experience. Let ^ denote the quantity of heat which the mass m of the gaS must receive from without, in order to produce any changes whatever in p, V and r. Then considering p and v as independent variables, and r as a function of both, we can make d^ dr d^ ,dr =mc—', — z=:mc'—. dv dv dp dp The magnitudes c and c', defined in this manner, express the capa- cities for heat at a constant volume and at a constant pressure, and may for the present be regarded as constant. Substituting in these expressions the values of the partial differential coefficients of r as obtained from (1), namely, dr ^P . ^^ __ ^P dv"^ maa* dp ~ ma a we have dd __?cp ^ 6/^ __ ^c'v dv a a * dp a a* and hence for the total differential of .& dd= — (cpdv-\-c'vdp). a a, If now the gas pass from one state to another, so that^ and v change according to any definite law, p, v, and ^ become functions of each other, and we have ^^I-fc/^dv-{-c'/^dp\ (2) If tq denote the initial temperature, then from the equation (1) we have dr = (pdv + vdp) ; ma a and if we integrate between the same limits as those to which i& is referred, and multiply by mc', we have tnc'ir- Tq) -^c'( fp^^ + /»*). ... (3) which, subtracted from equation (2), gives ^-.W(r-ro)=^(c-c')j, (4) where q= fpdv expresses the work done in the change of state. The result is therefore as follows : — " The quantity of heat commu- nicated to a gas during any change of volume and pressure consists of two parts, one of which expresses the heat necessary to raise the temperature at a constant volume, while the other is a constant multiple of the work done." In particular we infer that this quan- Intelligence and Miscellaneous Articles. 77 tity of heat is in itself proportional to the work as soon as the initial temperature is regained, while the pressure and volume may have other values ; as pure loss of heat it appears, it is true, only after a complete restoration of the original condition. Let us now suppose that neither Mariotte's law nor the law of the invariability of the capacities is accurately true. If c and c' are sub- ject to any small changes in consequence of changes of pressure or temperature, we may consider them as functions of p and v, and write equations (2) and (3) as follows : — m / c'dr= — ( /c'pdvi- /c'vdp], whence by subtraction, a ^—m / c'dr= — / (c—'c')pdv. J act, J If now during the change there is only work consumed or work performed, if consequently J9c?u undergoes no change of sign, we may, by a known property of definite integrals, place the factors c and «i M0«'-'0vO»-iH t^oo O VO 0\V0 »^vO r^ irt r»- U-, t-^ W-, to u-ioo w-. t^v© ^oo t^ V*. t>. u^ irt ^ u-t w-ioo <4- OS rn o\ O « m r^oo O rt t^vo 0> 0\00 On •* O C>. c^OO rt O fl , OO 1 < » •«•«?« u^ «/^ \r\\r\ x£^ u-\ u^ to »o »/^ H g •u ro O to lO r>* O »o«0 O V» rt w^OO »/->« m O m ror^Osw-irt k-^m OOO O r^OO t« g ^*^«*-«l-^»'^^*»'^*'>»o«^»o*o »oso u-> »o »o lo lo lovo vovovo u-iw-tii-iTh] »o ^ _,., i Or^t>>Hiw-ii-iO\wtO'«l-t*^«OOq>HOOOOOvOr»H <«^oo t-- O VO M t^ 00 w-i 1 a r^rt tort m^c<-i'^ii»-5*-'«l-i05l-5i-Ti--+i4-Throrovr>corJ-Ti-Ti..^^.^ro^^ Os to a r^*H f4 ton ^0\ *00 HI T^ WiOO t< ■+ M O O >-' to tJ-vO cOtJ-O 0 OO t^w ^tOiotOtrtvOTl-Tl- u-^vO t^vO VO »OVO vO vO vO r- t^ t^vO vO vO vo t^ t^so vO »^ u-l ^ 1 a ' vg ' [.-^ O ^O t» •* •♦•I^OOO t^tor-rt ►HOO "d-VO N M O rJ-vO Tf- M-i o to Ov T^VO «J^ t) C»«coH»< iSvO'^^O 0\ 0\00 VO VO ^ oj- to tJ-oo O On r^vo t^OO t^vo OO w w o o j< 3 b b b b b bv 6 b b b\ bs bs on ov bv ov on on c\ b bv bv b> bv b> bv bN bv b b b '^ 1 ^ - rorotoc^e*»f|co*ntortt*t»NNt j OOOtltJ'-'OvOsNrlOOvON two "^ '4- '4- fOVO OS OsOO VO VO t^ r^vo t^ o « O Q bs b b b b bs bs b b b bs bv os cs os os o\ o\ os os ov ov os os os o\ os bs b b b bs t< 1 S 1 1 tt>^0»-iootnro 00 •ra-B fg H VO VO t^ t^vo N »^0O r^Tj-fOtJ mO O "-I OSNVO «opj -. Q m totOM T*-t-^vr> •uojsoa bs bs bs bs bs bs b\ bs os os bs bs bs bs cs bs bsoo os bs bs os bs os os bs bs bs bs bs bs <^ t^ I--VO "I ,#. tv f 1 O H OSVO VO rt «0 « t^v^ to to rj- O 8 VO tx HI tJ- -^J-sO O OsOsOst^tnO N OstJ-I^tJ-O « ^oo OO t^ C?\ r- N OO too© o ^OsO O O jo-o O 00 o , ^r^Os« t^w O « VOM r>.« r) ^jy^_ loi-. C7\vototot^rj-O00 O O O tooo to a 00 OS O « « OSVO H, HI O 00 t^vo w, tJ-vo VO u-> Os O OsVO to looo 00 00 t^ O « oO 7" a bs bs b b b bs bs b b b bs os b\ bs os bs bs bs bs b os os os os os os os o> o o bs OS e«Mtototortr«tototot«t<«t«ttofo« « li «>; »: H ^ 4 •^vd t^oe ox d M (1* «^ ^ •Aso t:.oe OS d h; H* «^ 4 >^vd t:.o<; bs d M S MMMMMMMMMMHHt«C4nHtye fcid^ ,Q'. into the two parts ^,;.j,jj owi ^*rit (r'+iiw QandQ'-Q, the first will be the quantity of heat transferred from K to K|, and the second the quantity generated from work. According to this view the double process appears as a process of the same kind as the two simple ones of which it consists, for the circumstance that the generated heat is not imparted to a third body, but to one of the two between which the transmission of heat takes place, makes no essential 92i M. R. Clausius on a modified Form of the second difference, because the temperature of the generated heat is arbitrary, and may therefore have the same value as the tem- perature of one of the two bodies, in which case a third body would be superfluous. Consequently, for the two quantities of heat Q and Q'— Q, an equation of the same form as (6) must hold, t. e. (Q'-Q)/[0+QF(^,/')=o. Eliminating the magnitude Q' by means of (7), and dividing by Q, this equation becomes Y(t,l<)=f(t')-f{l), (8) 80 that the temperatures t and ^' being arbitrary, the function of two temperatures which applies to the second kind of trans- formation is reduced, in a general manner, to the function of one temperature which applies to the fii'st kind. For brevity, we will introduce a simpler symbol for the last function, or rather for its reciprocal, inasmuch as the latter will afterwards be shown to be the more convenient of the two. Let us therefore make m=\> (9) so that T is now the unknown function of the temperature involved in the equivalence- values. Further, Tj, Tg, &c. shall represent particular values of this function, corresponding to the temperatures ^j, t^ &c. According to this, the second fundamental theorem in the mechanical theory of heat, which in this form might appro- priately be called the theorem of the equivalence of transform- ations, may be thus enunciated : If two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generation of the quantity of heat Q of the temperature t from work, has the equivalence-value and the passage of the quantity of heat Q from the temperature t^ to the temperature i^ has the value ^(%~t)' wherein T is a function of the temperature, independent of the nature of the process by which the transformation is effected. If, to the last expression, we give the form Q Q Fundamental Theorem in the Mechanical Theory of Heat, 98 it is evident that the passage of the quantity of heat Q, from the temperature t^ to the temperature /g? lias the same equivalence- value as a double transformation of the first kind, that is to say, the transformation of the quantity Q from heat, at the tempera- ture /j into work, and from work into heat at the temperature t^, A discussion of the question how far this external agreement is based upon the nature of the process itself would be out of place here ; but at all events, in the mathematical determination of the equivalence-value, every transmission of heat, no matter how effected, can be considered as such a combination of two opposite transformations of the first kind. By means of this rule, it will be easy to find a mathematical expression for the total value of all the transformations of both kinds, which are included in any circular process, however com- plicated. For instead of examining what part of a given quantity of heat received by a reservoir of heat, during the cir- cular process, has arisen from work, and whence the other part has come, every such quantity received may be brought into calculation as if it had been generated by work, and every quantity lost by a reservoir of heat, as if it had been converted into work. Let us assume that the several bodies Kj, Kg, K3, &c., serving as reservoirs of heat at the temperatures /j, t^, /g, &c., have received during the process the quantities of heat Q^, Qg, Q3, &c., whereby the loss of a quantity of heat will be counted as the gain of a negative quantity of heat ; then the total value N of all the transformations will be N=| + ^ + | + &c..=X§ (10) It is here assumed that the temperatures of the bodies Kj, Kg, Kg, &c. are constant, or at least so nearly constant, that their varia- tions may be neglected. When one of the bodies, however, either by the reception of the quantity of heat Q itself, or through some other cause, changes its temperature during the process so considerably, that the variation demands considera- tion, then for each element of heat dQ we must employ that temperature which the body possessed at the time it received it, whereby an integration will be necessary. For the sake of generality, let us assume that this is the case with all the bodies ; then the foregoing equation will assume the form N = •^Q :f^ (") wherein the integral extends over all the quantities of heat received by the several bodies. If the process is ?'eversible, then, however complicated it ma; be, we can prove, as in the simple process before considere i 94 M. R. Clausius on a modified Form of the second that the transformations which occur must exactly cancel each other, so that their algebraical sum is zero. For were this not the case, then we might conceive all the transformations divided into two parts, of which the first gives the algebraical sum zero, and the second consists entirely of transformations having the same sign. By means of a finite or infinite number of simple circular processes, the transformations of the first part must admit of being made in an opposite manner, so that the transformations of the second part would alone remain without any other change. Were these trans- formations negative, i.e. from heat into work, and the trans- mission of heat from a lower to a higher temperature, then of the two the first could be replaced by transformations of the latter kind, and ultimately transmissions of heat from a lower to a higher temperature would alone remain, which would be com- pensated by nothing, and therefore contrary to the above principle. Further, were those transformations positive, it would only be necessary to execute the operations in an inverse manner to render them negative, and thus obtain the foregoing impossible case again. Hence we conclude that the second part of the transformations can have no existence. Consequently the equation I '^=0 (II) is the analytical expression of the second fundamental theorem in the mechanical theory of heat. The application of this equation can be considerably extended by giving to the magnitude t involved in it a somewhat differ- ent signification. For this purpose, let us consider a circular process consisting of a series of changes of condition made by a Dody which ultimately returns to its original state, and for sim- plicity, let us assume that all parts of the body have the same temperature ; then in order that the process may be reversible, the changing body when imparting or receiving heat can only be placed in communication with such bodies as have the same temperature as itself, for only in this case can the heat pass in an opposite direction. Strictly speaking, this condition can never be fulfilled if a motion of heat at all occurs ; but we may assume it to be so nearly fulfilled, that the small differences of temperature still existing may be neglected in the calculation. In this case it is of course of no importance whether t, in the equation (II), represents the temperature of the reservoir of heat just employed, or the momentaiy temperature of the changing body, inasmuch as both are equal. The latter signi- ^cation being once adopted, however, it is easy to see that any Fundamental Theorem in the Mechanical Theory of Heat. 95 other temperatures may be attributed to the reservoirs of heat without producing thereby any change in the expression j -~ which shall be prejudicial to the validity of the foregoing equation. As with this signification of t the several reservoirs of heat need no longer enter into consideration, it is customary to refer the quantities of heat, not to them, but to the changing body itself, by stating what quantities of heat this body successively receives or imparts during its modifications. If hereby a quantity of heat received be again counted as positive, and a quantity im- parted as negative, all quantities of heat will of course be affected with a sign opposite to that which was given to them with reference to the reservoirs of heat, for every quantity of heat received by the changing body is imparted to it by some reser- voir of heat ; nevertheless, this circumstance can have no influ- ence upon the equation which expresses that the value of the whole integral is zero. From what has just been said, it follows, therefore, that when for every quantity of heat dQ, which the body receives or, if negative, imparts during its modi- fications the temperature of the body at the moment be taken into calculation, the equation (II) may be applied without further considering whence the heat comes or whither it goes, provided always that the process is reversible. To the equation (II) thus interpreted we can now give a more special form, as was formerly done to equation (I), in which form it shaU express a particular property of the body. . We shall thus obtain an equation essentially the same as the well-known one deduced by Clapeyron from the theorem of Carnot*. With respect to the nature of the modifications, we shall assume the same conditions as before led to the deduction of the equations (2) and (3) from (I), and which also suffice for the fulfilment of equation (II). Hence, the condition of the body being defined by its temperature t and volume r, we have .i ,>9ii -^mv dQ, = -TT dt -\- -r- dv,as&'fi yhod '^m^imdrj o/^ >. .M «B 8- ^ ^ lijoifijjiijxfloo iw hmo^lq jt Inasmuch as by (II) I -y^ must always equal zero, whenever t and V assume their initial values, the expression under the integral sign, which by the foregoing equation becomes \ dQ, ,, \ d(i^ ^^ i^^5« y^^' must be a complete differential, if t and v are independent vari- ables ; and the two terms of the expression must consequently /iiii JiuiJf ^' * Journ. de VEcole Polytechnique, tome xix. - Jvi wvOiJiia,. 96 M. R. Clausius on a modified Form of the second satisfy the following coudition, rf/1 dQ\_lfl dQ\ rf/\f * dv)^dv\T' dt)' From this we obtain dH 1 d /dQ\ dQ dt 1 d/dQ\ T'It\dv) dv •T^"T*7ArfJ or dQ dT rr. rd(dQ\ d(dQ\'] dv ' dt " IdtKdv ) dv\dt)A' ' • • (13) Substituting, from equation (3), the value of the within the [ ] , we obtain the desired equation, iQ rfT dp ■dH-w^-^-^di'- ' ' • which, on account of the relation dp dp dT dt^dT' dt' may be written thus : expression • . (13) dv-^-^di: . (13 «) If we compare this result with the before-mentioned equation established by Clapeyron, we shall at once see the relation which exists between the function T, here introduced, and that used by Clapeyron, denoted by C, and known as Carnet^s function, which I have also used in former memoirs. This relation may be ex- pressed thus : dT dt A , T = c (^^) We proceed now to the consideration of non-reversible circular processes. In the proof of the previous theorem, that in any compound reversible process the algebraical sum of all the transformations must be zero, it was first shown that the sum could not be negative, and afterwards that it could not be positive, for if so it would only be necessary to reverse the process in order to obtain a negative sum. The first part of this proof remains unchanged even when the process is not reversible ; the second part, how- ever, cannot be applied in such a case. Hence we obtain the following theorem, which applies generally to all circular pro- cesses, those that are reversible forming the limit : — The algebraical sum of all transformations occurring in a circular process can only be positive. Fundamental Theorem in the Mechanical Theory of Heat, 97 A transformation which thus remains at the conchision of a circular process without another opposite one, and which according to this theorem can only be positive, we shall, for brevity, call an uncompensated transformation. The different kinds of operations giving rise to uncompensated transformations are, as far as external appearances are concerned, rather numerous, even though they may not differ very essen- tially. One of the most frequently occurring examples is that of the transmission of heat by mere conduction, when two bodies of different temperatures are brought into immediate contact; other cases are the production of heat by friction, and by an electric current when overcoming the resistance due to imper- fect conductibility, together with all cases where a force, in doing mechanical work, has not to overcome an equal resistance, and therefore produces a perceptible external motion, with more or less velocity, the vis viva of which afterwards passes into heat. An instance of the last kind may be seen when a vessel filled with air is suddenly connected with an empty one ; a portion of air is then propelled with great velocity into the empty vessel and again comes to rest there. It is w^ell known that in this case just as much heat is present in the whole mass of air after expansion as before, even if differences have arisen in the several parts, and therefore there is no heat permanently converted into work. On the other hand, however, the air cannot again be compressed into its former volume without a simultaneous con- version of work into heat. The principle according to which the equivalence-values of the uncompensated transformations thus produced are to be determined, is evident from what has gone before, and I will not here enter further into the treatment of particular cases. In conclusion, we must direct our attention to the function T, which hitherto has been left quite undetermined ; we shall not be able to determine it entirely without hypothesis, but by means of a very probable hypothesis it will be possible so to do. I refer to an accessory assumption already made in my former memoir, to the effect that a permanent gas, when it expands at a constant temperature, absorbs only so much heat as is consumed by the external work thereby produced. This assumption has been verified by the later experiments of Regnault, and in all proba- bility is accurate for all gases to the same degree as Mariotte and Gay-Lussac's law, so that for an ideal gas, for which the latter law is perfectly accurate, the above assumption will also be perfectly accurate. The external work done by a gas during an expansion dv, provided it has to overcome a pressure equivalent to its total ex- pansive force j9, is equal to pdv, and the quantity of heat absorbed Phil Mag, S. 4. Vol. 12. No. 77, Aug, 1856. H 98 On a Fundamental Theorem in the Mechanical Theory of Heat, thereby is expressed by ^ dv. Hence we have the equation and by substituting this value of -, in the equation (13), the latter becomes d^ dp dt dt /T tf\ T=7 ^ ^ But, according to Mariotte and Gay-Lussac's law, a-\-t p= . const., ^ V where a is the inverse value of the coefficient of expansion of the permanent gas, and nearly =273, if the temperature be given in degrees C. above the freezing-point. Eliminating p from (15) by means of this equation, we have dT dt ., ^. Y=7+t' ^^^^ whence, by integration, T= (« + /). const. ..... (17) It is of no importance what value we give to this constant, be- cause by changing it we change all equivalence-values propor- tionally, so that the equivalences before existing will not be disturbed thereby. Let us take the simplest value, therefore, which is unity, and we obtain T=a + t (18) According to this, T is nothing more than the temperature counted from «°, or about —273° C. below the freezing-point, and, considering the point thus determined as the absolute zero of temperature, T is simply the absolute temperature. For this reason I introduced, at the commencement, the symbol T for the reciprocal value of the function /(/). By this means all changes which would otherwise have had to be introduced in the form of equations, after the determination of the function, are rendered unnecessary ; and now, according as we feel disposed to grant the sufficient probability of the foregoing assumption or not, we may consider T as the absolute temperature, or as a yet unde- termined function of the temperature. I am inclined to believe, however, that the first may be done with hesitation. \ ii A$^6i ,}^h, ,\^ .oVi ,^i .laV 4* .c^ .\^¥x .^r [ 99 ] XI. On the Influence of the Earth's Internal Structure on the Length of the Day. By Henry Hennessy, M.R.I.A.y Pro- fessor of Natural Philosophy in the Catholic University of Ireland^. THE period of a complete revolution of tlie earth around its axis of rotation, depends not only on the dimensions of the mass, but also on the distribution of the particles of which it is composed. The variations which in the course of ages may pos- sibly take place in the distribution of these particles will there- fore tend to produce some change in the length of the day. The question of the secular variation of the earth^s velocity of rota- tion has been already, to a certain extent, examined by Laplace f; but his investigation has regard solely to the contraction of the dimensions of the globe considered as a slowly cooling solid. If the interior of the earth is in a state of fluidity from heat, or in other words, if it consists of a solid exterior shell filled with a nucleus of matter in a state of fusion, from which state the por- tion now solid had gradually passed to its present condition, the inquiry assumes a different shape. Hitherto this, as well as every other question connected with the general structure and rotation of the earth, has been treated on the assumption that the portions composing the fluid underwent no change in their positions on entering into the solid state. This assumption formed not only the basis of the inquiries of Laplace, but even of more recent investigators, who professed to consider the purely physical conditions of problems relating to the Structure of our planet in a far more complete manner. The change of state of the matter composing the interior of the earth in passing from fluidity to solidity seems to have been thus entirely overlooked, although a little reflection might have suggested that such a change would possibly influence its structure to a very consider- able extent. In the first part of my " Researches in Terrestrial Physics %" the necessity of attending to this circumstance was distinctly pointed out, and the superfluous nature of the contrary assump- tion was formally declared. Experiments were quoted in the second part confirmatory of my views on this point, which I believe have never since been called in question. When we reflect on the remarkable results of the researches of Professor Bischof, M. Ch. Sainte-Claire Deville, and M. Delesse, upon the contraction of the principal materials of the solidified crust of the earth in passing successively from the fluid state through * Communicated by the Author. ^^^^ i^'^ ' :_^' -r |> u {'■ vi- f Mecanique Celeste, livre xi. - vs simply by virtue of the symbols , without the introduction of any extraneous construction or subsidiary consideration whatever. 11. Now Dr. Lloyd (in his 'Lectures on the Wave Theory,' part 2, p. 35), after stating the facts, gives the same deduction from theory, using MaccullagUs formulas ; but with due caution makes the inference only so far as to show the existence of a devia- tion to the same amount, without eocpressing in which direction. But according to these formulas, tan /3 is at first positive, and changes to negative at the polarizing incidence. Hence as to the direction of the deviation, if the formei' reasoning be correct, then in this case, on the same grounds, the symbols would indicate that the deviation at incidences less than that of polarization must be on the same side as the original plane, and after that incidence, on the ojyposite side ; which is the reverse of the former conclusion, and of the fact, 12. This, however, would appear to be only an additional reason to that already assigned for the rejection of Maccullagh's or for Reflected and Refracted Light. 109 theory. But it is easily seen that precisely the same remarks apply if, instead of Maccullagh^s formulas, we adopt either of the new forms of FresneFs, viz. — (B) which gives y^i), (C) which gives f ^=-j- j . The result of experiment would therefore seem equally decisive against the hypothesis (A), and against (B) and (C) applied to both N and k\ and would leave us to the sole adoption of FresneFs original formulas (D). But before coming to this conclusion, we must advert to another experimental case in which similar considerations are involved. Dr. Lloyd's Interference Eocperiment. 13. In an experiment long ago devised by Dr. Lloyd, a direct ray interferes with one reflected at a very oblique incidence from a plate of glass ; giving a set of stripes resembling generally one half of those formed in the experiment of Fresnel when two streams of direct light interfere (Mem. Roy. Irish Acad. vol. xvii. ]834). In this experiment, it is first to be remarked that the first dark band is intensely black, proving the equal intensity of the interfering rays ; in agreement with theory, which at the extreme incidence gives, on either hypothesis, reflected light of equal in- tensity with the incident (see former paper (§58)). 14. The stripes, however, present this peculiarity : on ordinary suppositions, since the rays at the extreme limit must be in accord- ance, there would first be half a blight band (reckoning from the edge) followed by a whole dark, then a whole bright band, and so on ; whereas, in fact, the first bright band is observed to be of the entire breadth of an interval, as if the system commenced from a point of discordance at the extreme limit, or as if the whole were shifted from the edge through a distance equal to half the interval of two bands. This was found to be equally the case whether the light was previously polarized in a plane parallel or perpendicular to the plane of incidence. In other words, the fact indicates a diffei'ence in phase of 180° between the incident and the reflected ray at the limit, and this equally in each case of the direction of polarization. 15. Now in FresneFs original formulas for vibrations perpen- dicular to the plane of incidence, a difference of sign, indicative of this difference o^ phase, occurs at all incidences in the formulas for h', and for vibrations parallel to the plane of incidence at 110 Prof. Powell on the Demonstration o/FresnePs Formulas all incidences greater than that of complete polarization in the formulas for V; that is, at very oblique incidences for rays polarized in one plane equally with those in the other ; in exact agreement with the observed fact. 16. This is the argument expressly adduced by Dr. Lloyd, derived directly^ without any subsidiary considerations, from the indications of the symbols ; and it has, I believe, been generally received as perfectly clear and conclusive. It should be remem- bered that Dr. Lloyd's paper was communicated and published in 1834, and refers to FresnePs formulas in the form in which he originally gave them, and before any modifications of the theory had been contemplated. Prof. Maccullagh's new views and for- mulas were first communicated to the Royal Irish Academy in 1837, and published in its Memoirs in 1838. Thus Dr. Lloyd's reasoning is of necessity wholly independent of any speculations on these newer principles, which, if applied to FresnePs theory, give the formulas with different signs, 17. Now so far as the mere symbols are concerned, we find in FresneFs formulas (B) this difference of sign, at great incidences, occurring only for A' ; and in the formulas (C) (as is the case also in Maccullagh's formulas) only for k! -, while in (B) for k', and in (C) for h', no such difference occurs. This result would therefore seem decisive in favour of FresneFs original formulas (D), to the exclusion not only of MaccuUagh's, but of Fresnel's, in the entire forms (B) and (C). 18. The reasoning both in this case and the former (9), (10), is indeed of a nature apparently so obvious, that I should not have thought it necessary to state it in detail, were it not that some considerations have been suggested which seem to set it aside, or at any rate to require a closer review of its meaning ; — and which may be stated as follows : — 19. For vibrations parallel to the plane of incidence, if we make a construction of the course of the rays, then, at an inci- dence very near the perpendicular, the vibrations k and k' respect- ively perpendicular to the incident and reflected rays will lie very nearly in one line ; and if we suppose them in the same direction, then in passing to an incidence extremely oblique, they will come into directions opposite to each other, owing merely to the posi- tion the rays have now assumed. Hence it is inferred, whatever relative directions of the vibra- tions we express by the signs + or — at 2 = 0 will be reversed when we pass to i=90°. And thus, for example, in the formula [Bk'), if at z=0° we suppose —A' and -hk to express opposite directions, then at t=90 the same signs would express accordant directions. But in fact at t = 90° we have -\-k! and -\-k, which on this principle therefore now express opposing directions. for Reflected and Refracted Light, 1] 1 20. In the case of FresnePs and Arago^s result (see above, (9)) of the change in the plane of polarization after reflexion, it should be remarked that the reasoning turns wholly upon the signs of the resulting equation for the tangents of the two related arcs ; and these are derived from the relative signs of the quantities which enter into the numerator and denominator simply as alge- braic quantities, and without any reference whatever to the inter- pretation of those signs as expressive of difference of phase, or any other physical conditions. The resulting relation is a purely tri- gonometrical one, and the direction in which the arcs are to be relatively measured would be just the same whatever might be the physical theory to which they were to apply. This case therefore can in no way be affected by any theory of the change of direction due to the position of the vibrations. Here, then, FresneFs original formulas exclusively apply. 21. The case then stands thus : — From the experiment of Prof. Stokes, Maccullagh^s formulas are set aside. From the experi- ments of Lloyd and Arago, so far as relates to vibrations perpen- dicular to the plane of incidence, Fresne?s formula (CA') is set aside, since it does not apply directly ; and for such vibrations the subsidiary theory as to the signs is inapplicable ; while Fres- nePs formula (Bh') fully agrees with experiment without any subsidiary explanation. This foi^mula then must necessarily he adopted exclusively. 22. It is only, then, in the case of vibrations parallel to the plane of incidence that the question remains between FresnePs formula (C^'), which applies directly to the experimental results, but rests on an hypothesis (No. III.) of equivalent vibrations open to question, — and his formula (B^'), which rests on Maccul- lagh's law of equivalent vibrations (No. II.), but does not apply to the experimental facts without a subsidiary interpretation as to the signs. 23. Now any subsidiary construction, if necessary for the right interpretation of a formula, only shows that that formula is sym- bolically incomplete, and does not include the expression of the whole case it is designed to represent. This, then, would be an additional reason for rejecting that formula and adopting the former in preference. 24. But this construction (19) is in itself not free from question and difficulty. For let us only consider the case at a point upon the surface : here we have an incident rectilinear vibration in a deter- minate direction ; but at its point of incidence it gives rise to a nascent circular wave, in which it is impossible to say that the vibration is more in one direction than another ; it has no recti- linear direction till we come to take the common tangent (as in the ordinary explanation of reflexion) to two successive waves ; 112 On a Construction for the Range of Projectiles. and there is nothing to determine the direction of vibration at the points coinciding with this tangent. We cannot therefore make any assumption as to its constancy at different incidences j there is nothing to show that it may not change from one inci- dence to another ; and we know that it does undergo such a change at the incidence of complete polarization. 25. On the other hand, the formula (C/;') applies directly to the phsenomcna without the aid of any subsidiary construction whatever, unless indeed the whole principle of the reasoning hitherto adopted be contested. But if we may still accept the reasoning of Fresnel and Arago, of Airy and Lloyd, as valid, then it follow^s that both FresnePs original formulas, and they alone, will apply directly to all the experimental results without any extraneous considerations. But one of them (A/) rests on an assumption as to the law of equivalent vibrations different from the other (A') ; and the question remains, whether that difference of assumption can be justiiicd, or whether any other view of the theoretical principles can be found to lead to the same results. I have thus stated in full detail the difficulties of this import- ant case ; and will only add, that I shall look with great inter- est to any attempts at removing them, which I hope this repre- sentation may be the means of eUciting from those mathematicians who have attended to the subject. XIV. Letter on Professor Galbraith's Construction for the Range of Projectiles. By J. J. Sylvester, Professor of Mathematics at the Royal Military Academy. To the Editors of the Philosophical Magazine and Journal. Gentlemen, PROFESSOR GALBRAITH'S geometrical construction for finding the elevations of a projectile corresponding to any given velocity and given range in a plane, horizontal or sloping, is truly elegant, and, if new, constitutes a real acquisition to the subject. It might be worth while for its accomplished author to see if some analogous construction can be found extending to the more general case where the field is a portion of a circle. I need hardly add that the isoscelism referred to is, except for some extreme suppositions (impossible to occur in practice), absolutely independent of the form of the field. As well-con stnicted names are, in fact, condensed lessons, lending an aid to the memory and imagination, of which modern mathematicians are only beginning to appreciate the importance, I suggest the following designations. On a Construction for the Range of Projectiles, 113 The point of projection and point of impact speak for them- selves ; the point vertically over the point of impact in the di- rection of projection may be called the point of aim. The line joining the point of aim and the point of impact is the drop or fall', the line joining the point of projection and the point of impact may be called the excursion ; and that joining the point of projection and the point of aim, the length of aim, A vertical section of the ground (plane or curved) through the axis of the gun may be called the field. We may then say, that, for the maximum range, the fall is always equal to the excursion, whatever the form of the field ; and that in general the locus of the point of aim, for a rectilinear field when the point of the projection and the velocity are given, is a circle to which, in the case of the angle of best elevation, the line of fall is of course a tangent. It would not be surprising if a good deal of elegant geometry (like ivy twining round an old wall) should hereafter associate itself with Mr. Galbraith's " circle of aim ; '^ a propos of projectiles, it is not unworthy of observation, that the velocities at any two points P and Q of the parabolic path are as the lines PT, QT which the tangents at P and Q mu- tually cut ofi" from one another, a remark which of course is easily seen to extend itself to the case of an elliptic orbit with the force in the centre. Ever, Gentlemen, Your faithful friend and reader, Woolwich Common, J, J. SYLVESTER. July 3, 1856. P.S. The value of Mr. Galbraith's method consists simply in the act of conception of the locus of the point of aim ; it was scarcely worth while (at this time of day) to append a synthetical proof of so simple a proposition, which may be got at immedi- ately by calling the length of aim p, its inclination to the ver- tical, 6y and that of the field to the vertical, i ; when by similar triangles (if H denote the quantity — , and tj the vertical distance of the point of projection from the field) we obtain the equation H "^ ^8m{i-e) p sin i ^ or '^ smz ^ ' * which obviously corresponds to the circle of Professor Galbraith. Phil. Mag. S. 4. Vol. 12. No. 77. Aug. 1856. I 114 Mr. H. M. Witt on the Variations in the 1 imagine this circle has been long known for the case of the point of projection being in the fields but it may have escaped notice for the more general case. The equality between the fall and the excursion for the angle of maximum range subsists, not merely for a rectihnear or curved section, but for the ground itself (whatever its form of surface) when the gun is supposed to admit of being laid to any angle, as well as at any elevation. XV. On the Variations in the Chemical Composition of the Thames Water ^ during the year between May 1855 and May 1856. By Henry M. Witt, F.C.S., Assistant Chemist to the Oovemment School of Science Applied to Mining and the Arts^, SO numerous are the chemical analyses of the water of the Thames which have been published during the last few years, and by chemists of such eminence have they been made, that it would appear altogether superfluous to make further ad- ditions to their number ; but one moat important fact has scarcely attracted sufficient attention, that any single analysis, however carefully and accurately executed, represents only the composition of that particular sample of water under examination, and not the general or average composition ; in fact the quantities of the several impurities of the water of the Thames diflfer, as might be expected, most essentially at the various points in its course, and at the several seasons of the year. To the variations in composition at different points of the river's course attention has been drawn long since, especially in the Report by Professors Graham, Miller, and Hofmann, to the Secretary of State for the Home Department, made in 1851 f, by whom it was recommended that the supply of London should in future be taken from some point above the tidal influence, further removed from the contamination of the London sewage. But great discrepancies have often occurred between the ana- lyses of the water at any particular point made by different ex- perimenters, due doubtless to the changes which take place at different seasons of the year; and it became evident that a cor- rect opinion of the composition of the water, at any special point of the river's course, could only be formed by making a large number of analyses extending over a considerable space of time, and from them deducing the mean composition. This desideratum was partially supplied by Dr. Robert Dundas Thomson, who, in the Quarterly Journal of the Chemical Society for July 1855 J, published the results of a series of analyses made * Communicated by the Author. t London : Taylor, Walton, and Maberly, X Vol. viii. p. 97. Chemical Composition of the Thames Water. 115 between the 1st of September 1854 and the beginning of the year 1855 ; but it is obvious that this inchides only a quarter of a year, and, moreover, only that particular quarter following the drought and heat of summer and autumn, the effect of the spring rains being altogether omitted. The analyses detailed below extended over the whole year^ viz. from May 1855 to May 1856 ; so that from them the maximum, minimum, and mean composition may be deduced for the whole year. Two series were undertaken, the one at Kingston, the present source of supply of the Chelsea and Lambeth Waterworks' Com- panies, the other at Chelsea, with the view of comparing the mean composition at these two points : the analyses of the former series were repeated about once a month (and, indeed, during a certain period when great fluctuations took place, once a week), and those of the latter four times in the year, viz. in June, October, and December 1855, and May 1856. At the commencement of the inquiry a complete analysis was made at each point, the results of which are given in detail ; but subsequently only the most important constituents were deter- mined, and the analyses are given as the direct results of ^expe- riments (without arranging the acids and bases together), to faci- litate present and future comparison. To commence with the composition of the water at Kingston : the following are the results of the original complete analysis. This sample was collected at the Chelsea Waterworks Com- pany's new works at Kingston (in common with all the other samples from this point, by my friend Mr. James Simpson, jun.), on the 26th of May, 1855. It had a temperature at the time of 62° F. (16°-6 C), that of the air being 63° F (17°*22 C). The following are the analytical results : — Table a.- — Direct results of Experiments calculated in 1000 grains of the Water. Experi- ment. Lime. Mag. nesia. Chlorine. Sulphuric Acid. Alkaline chlorides. Potas- slum. Sodium. Suspend- ed clay, sand, &c. 1 2 •10424 •1026 •00707 •00616 •0144 •03722 •03852 •0477 •03852 trace •0187 •0235 •0529 Mean... •10342 •0066 •0144 •03787 •03787 •0211 •0529 Inorganic residue. Organic matter. Total residue. Mean of three experiments.. •3260 •0233 •3493 12 m Mr. H. M. Witt on the Variations in the Table b, — Mean of the preceding calculated in grains in the gallon. Inorganic residue Organic matter Total residue 22-820 1-631 24-451 grs. Lime 7-240 Magnesia 0-462 Chlorine 1-008 Sulphuric acid 2-651 Alkaline chlorides .... 3-7669 Potassium trace Sodium 1-480 Suspended clay and sand . 3*603 Ammonia (as carbonate) . . '0034 Table c. — Saline Constituents in the gallon. Sulphate of lime Carbonate of lime . Carbonate of magnesia Chloride of sodium Chloride of potassium Carbonate of soda . Organic matter . . Suspended clay . . Carbonate of ammonia Total grs. 4-506 9-616 0-970 1-661 trace 1-950 1-631 3-603 0-0034 23-9404 Total residue obtained by experiment 24-45 1 The hardness by Dr. Clarke's soap-test was- Before boiling After boiling ir 6^ Loss by boiling . . 5° The foUowing Table shows the comparison of this analysis Chemical Composition of the Thames Water. 117 with the subsequent determinations of the more important con- stituents, with the dates when the samples were collected : — Table I. — Analysis of Thames Water at Kingston, 1855-56. (Direct experimental results.) Date of collection. May 26, 1855. Sept. 8, 1855. Oct. 8, 1855. Nov. 3, 1855. Dec. 29, 1855. Temperature of the water... Total residue (including sus- pended matter) Suspended matter (clay and sand) Organic matter (in solution) Total dissolved salts Chlorine Sulphuric acid Lime Magnesia 62° F. 24-45 3-603 60° F. 57* F. 42° F. Grains in the gallon. 631 217 008 651 240 462 Hardness before boiling Hardness after boiling . Loss by boiling , 18-37 23-949 22-750 3-107 1-025 i-ii*6 1-430 1-054 3-635 6-487 1-213 1-430 18-213 2-065 6-795 12-28 7 lf-0 42° F. 24-35 3-82 0-94 19-59 1-287 3-87 7-73 if-S 8-5 3-0 Jan. 15, 1856. Feb. 27, 1856. March 25, 1856. April 29, 1856. May 10, 1856. Temperature of the water. . Total residue (including sus pended matter) Suspended matter (clay and sand) Organic matter (in solution) Total dissolved salts Chlorine Sulphuric acid Lime Magnesia 46° F. 26-58 . 1-179 1-56 23-841 1-017 2-572 43° F. 44° F. 50° F. Grains in the gallon. Hardness before boiling Hardness after boiling . , Loss by boiling 13-2 22-22 28-148 20-736 3-729 1-34 0-97 1-430 22-989 1-90 IO-9T 0-588 18-898 2-108 8-533 135 lf-5 5-5 6-0 12-2 5r-25 F, 19-67 1179 0-627 17-864 0-702 1-732 7-493 12-3 N.B. The samples were collected in every case at 9 o'clock a.m. From which the following average composition may be de- duced ; — 118 Mr. H. M. Witt on the Variations in the Table II. — Average Composition of the Thames Water at Kingston for the year. Maximum. Minimum. Mean. In grains in the gallon. 28148 18-37 23-488 4-41 117 1 3-034 1-63 0-6fi 1050 22108 16-65 19-404 1-90 1-008 1 1-213 313 1-66 1-998 3-87 2065 2-633 10-91 6-487 * 7-884 13°-5 ir 12° 05 Suspended matter Dissolved salts Chlorine Or Chloride of sodium "1 (common salt) j Lime Hardness •• But (luring a part of the time the analyses were repeated more frequently ; in fact, during a period of about a month no less than seven analyses were made, which are exceedingly interest- ing, as showing to what extent the chemical composition may vary during that short space of time. Table III. — Analyses of the Thames Water at Kingston, be, tween January 21 and February 27, 1856. (Direct experimental results.) "'jjgg^^', Jan 25. Jan. 28. 1 Feb. 4. Feb. 12. Feb. 20. Feb. 27 Temperature of the water. 43°-5F.t 44' Total impurity Suspended matter Organic matter Dissolved salts Chlorine Or Cbloride of sodium "1 (common salt) J Hardness 22-183 321 1052 17-92 1-456 2-399 ir-52 23-521 3-419 J-112 18-990 1-749 2-882 lO°-8 39^-5 I 35° 47° In grains in the gallon. 24-96 4-41 ir-2 25-81 8122 0-917 21-772 0-845 V392 13*= 23-533 3-820 0-553 19-160 1-008 1-66 13''15 38°-5 24-578 3-509 0-8906 20-178 13°-3 43° 22-22 0-971 1-420 3337 13°-5 From which the following averages may be deduced : — Table IV. — Average Composition of the Thames Water at Kingston (from January 21 to February 27, 1856). Maximum. Minimum. Totalimpurity Suspended matter Organic matter Dissolved salts «..«M«f Chlorine Or Chloride of sodium.. Hardness Mean. In grains in the gallon of water. 25'81 4-41 1-112 20-288 1-749 2-882 13°-5 22-183 3-112 0-533 18-518 0-845 1-392 10°-8 23-99 3-761 1-665 19-403 2-594 2-137 12°-5 ' Chemical Composition of the Thames Water. U9 To proceed with the composition of the water of the river at Chelsea : the following are the results of the complete analysis made at the beginning of the investigation. The sample was collected by myself from the Chelsea Water- works Company's reservoir, at the time that it was being pumped in from the middle of the river on the 14th of June, 1855. The temperature of the water at the time was 62° F. (17°-5 C), that of the air being 58° F. (14°-44 C). Table a. — Direct results of Experiments calculated in 1000 grains of the water. Exp. Lime. Magfneeia. - Chlorine. Sulphuric acid. Alkaline chlorides. Potaa- sium. Sodium. Silica, alu- mina, and oxide of iron. 1 2 •10814 •016 •07068 •0733 •04546 •1687 •0269 •0461 •0634 Mean. •10814 •016 •07199 •04546 •1687 •0269 •0461 •0634 Exp. Total soluble matter. Total suspended matter. Inorganic. Organic. 1 Total. Inorganic. Organic. Total. 1 2 •4382 •0148 •453 •5679 •5103 •1267 •1267 •6946 •6470 Mew .,. •4382 '0148 •453 •5441 li^l •6708 Table b. — Mean of the preceding calculated in grains in the gallon of water. Suspended matter. Inorganic ..• Organic . Total . Soluble matter. Inorganic Organic Total . Lime Chlorine Sulphuric acid . Alkaline chlorides Potassium . . Sodium . . . Silica, alumina, and oxide of iron Phosphoric acid . . Ammonia (as carbonate 38-107 8-873 46-980 30-690 1-036 31-726 7-5737 1-1205 5-0356 3-1838 11-815 1-884 3-225 1-300 trace 0-033 120 Mr. H. M. "Witt on the Variations in the Table c. — Saline Constituents in the gallon. grs. Sulphate of lime 5-411 Carbonate of lime . . . . 9-744 Carbonate of magnesia . . . 2-352 Chloride of potassium . 3-599 Chloride of sodium . . , . 5-471 Carbonate of soda . . . 2-475 Organic matter .... . 1-036 Silica, alumina, and oxide of i ron 1-300 Phosphoric acid . . trace Ammonia (as carbonate) . 0033 Total soluble matter . . 31-421 Total residue obtained by experiment 31*726 grs. Total Impurity in the gallon. Soluble. Insoluble. Total. Inorganic . . 30-385 38-107 68-402 Organic . . . 1-036 8-873 9-909 Total . . . 31-421 46-980 78-401 Hardness — Before boiling . . 12°-62 After boiling . . 9°00 Loss by boiling . 3°-62 The water being so much more impure here than at Kingston, the variations in composition during the year are more consi- derable/as shown by the following comparison of four analyses, made in June, October, and December 1855, and in May 1856. Table V. — Analyses of the Thames Water at Chelsea during the year between May 1855 and May 1856. (Direct experimental results.) June 14, 1855. September 12, • 1855. December 29g 1855. May 10, 1856. Temperature of the water. 62°-5 F. 61° F, In grains in the gallon of water Total impurity , Suspended matter : — Organic Inorganic Dissolved matter : — Organic Inorganic Chlorine Sulphuric acid Lime Magnesia '. Hardness : — Before boiling After boiling Loss by boiling 78-40 65-527 41-652 8-873 38-107 8-206 16-031 3-600 7-360 1036 30-385 6-0356 3-1838 7-6737 0-67 40-62 1114 3-489 . 1-65 29092 1-667 2-962 8-676 1-1206 ll62 9-00 ilo 6-7 5-3 11-9 3-62 64146 11-247 28-930 1-349 22-620 1-956 3-073 8-719 1-189 13-5 9-3 4-2 Chemical Composition of the Thames Water. 121 From which the following average composition may be de- duced : — Table VI. — Average Composition of the Thames Water at Chelsea during the year. Suspended matter Organic Inorganic Dissolved matter :- Organic Inorganic Chlorine Sulphuric acid ... Lime Hardness Maximum. | Minimum. Mean. In grains in the gallpn. 11-247 38-107 1-60 40-62 1114 3-489 8-719 13°-5 3-60 7-36 0-67 22-62 1-667 2-962 7-573 ll°-9 7-423 22-73 116 36-62 6-403 3-225 8-196 12°-7 The following points cannot fail to be remarked in considering these numbers : — 1st. The very much greater variations in the composition of the water here than at Kingston. 2nd. The great decrease in impurity generally, but especially in the suspended matter which takes place during the winter, and increase in the summer, above the mean for the whole year. 3rd. The extraordinary fluctuations in the quantity of common salt present, the chlorine varying from 11*14 grs. in the gallon in September 1855 to 1*667 in December of the same year. 4th. That the amounts of sulphuric acid, and of lime and magnesia salts, remain, however, much more constant. But in order to present in the most striking form the supe- riority of the water at Kingston over that at Chelsea as a source for the supply of London, I have drawn up the following Table, exhibiting a — Table VII. — Comparison of the Mean Annual Composition of the Thames Water at Chelsea and at Kingston, Chelsea. Kingston. Excess at Chelsea above Kingston. Total impurity 67-933 130-153 J 1-16 36-62 6-403 3-225 8196 12°-7 23-488 3-034 1-05 19-404 1-213 2-633 7-884 12°-05 43-445 27119 0-110 17-216 5-190 0592 0-312 0°-65 Suspended matter : — Organic 7*423 Inorganic ... 22-73 Dissolved matter : — Organic Inorganic Chlorine Sulphuric acid .* Lime Hardness 122 Mr. H. M. Witt on the Variations in the Observe, — that the excess is chiefly in the suspended matter, and among the dissolved salts in the chloride of sodium ; but that the increase in the dissolved organic matter is but slight, nearly the whole of the excess of organic matter separating with the mud in an insoluble state. It must, however, be remembered, that in this Table the com- position of the water as its exists in the river is compared, not the composition when q/lfe/- filtration it is supplied to the public. But having previously investigated the effect of filtration upon the Thames water both at Chelsea and at Kingston*, I am enabled to draw a similar comparison of the composition of the water at these two points after filtration; which being likewise deduced from a large number of experiments, extending in fact over the whole year, may, I think, be relied upon as placing the question in an impartial light. On referring to my former paper in the Philosophical Maga- zine, it will be seen that during nine months the composition of the water at Chelsea after filtration was as follows : — Sept. 12, 1855. Dec. 29, 1855. May 10, 1856. Mean. Totftl residue 41-29 24-153 1-403 1-889 20-861 1-546 2-372 8-403 22-85 2-285 1-349 19-216 30-03 1-84 1-30 26-89 9-59 2-37 8-41 Suspended matter Soluble matter : — Organic 0-674 40-616 11-14 Chlorine ... "8-426 Lime ... Table VIII. — Comparison of the average Composition of the Thames Water at Chelsea and at Kingston after filtration, i. e, in the state in which it is supplied for public consumption. Excess of impu- Mean composi- Mean composi- rity in filtered tion at Chelsea tion at Kingston after sand filtra- water from after sand filtra- Chelsea over tion. tion f. that from Kingston. Total residue 30-03 23-91 6-12 Suspended matter 1-84 1-58 0-26 Soluble matter :— Organic 1-30 0-64 0-66 TnororaniR .. . ... 26-89 21-69 5-20 9-59 0-86 8-73 * See Phil. Mag. vol. xii. p. 23 (for July). t Deduced from Table V. page 8 of former paper. Chemical Composition of the Thames Water, 123 This last Table exhibits, I believe, a fair view of the question, and the numbers are in themselves so eloquent, that I leave them without any comment for the reader to make his own deductions from them. In conclusion, I must observe that my friend Mr. Simpson is of opinion, from his own practical experience in the matter, that the results detailed above can only be considered as representing the mean composition for the year during which the experiments were made j that, in fact, from the much greater increase in the volume of the upland water which comes down the river in some years, when the rainfall is sometimes almost double what it was during the past year ; and its diminution during others, when the rainfall does not exceed one-half what it then was, — there is every reason to believe that far greater fluctuations in com- position sometimes occur than have been demonstrated by this investigation. Appendix to paper '^ On a peculiar Power possessed by Porous Media of removing Matter from Solution in Water." Allow me to correct an error in figures which occurred at page 2 of my former paper, relative to the dimensions and volume of water passing through the filters at the Chelsea Waterworks. The total filtering surface there is about three-fourths of an acre, or 32,670 square feet, and the filtration taking place at the rate of one foot per hour, yields about 204,187 gallons of filtered water per hour. Since the publication of this paper, I have received the follow- ing letter from Mr. Robert Hunt, F.ll.S., Keeper of the Mining Records ; and the facts therein mentioned may serve to confirm my views respecting the peculiar power of porous media. " Museum of Practical Geology, Jermyn Street, July 12, 1856. " Dear Sir, — I have read your paper with pleasure and profit. Allow me to give you two examples, within my own knowledge, confirmatory of your views. "At Perran-poHh, some six or seven miles north of Truro, the heaps of w^aste [deads) from the old mines contain consider- able quantities of copper pyrites, which is, in the process of de- composition, converted into sulphate of copper. This salt is washed out by the rains, and the solution flows through the sands {blown sand) widely spread over that district. The sul- phate of copper is separated by the sand, and the sand contain- ing the copper is collected from time to time and sold to the copper smelters. Again, at Botallack Mine, the water which 124 Mr. J. Cockle on the Resolution of filters through the rocks from the Atlantic Ocean in the levels which are worked out under the bed of the sea, is found to have lost much of its original saltness. These facts are at your ser- vice. I trust you will continue the interesting inquiry which you have commenced. " I am, dear Sir, " Yours most truly, " H. M. Witt, Esqr " Robert Hunt/' XVI. On the Resolution of Algebraic Equations of the Fifth Degree, By James Cockle, M.A,y F.R.A.S., F.C.P.S., Bannster-at'LaWj of the Middle Temple^, 81. npHE last paper of ray series on the Method of Sym- -i- metric Products terminated at p. 138 of this Journal for Februaiy 1854 (S. 4. vol. vii.). The numbering of the para- graphs is resumed here. 82. The problem of (79) may be solved thus. Let Y^ vanish, and let the quintic in y be S^-5B2/3_5C2,2_5j)y_j;^0. . . . (m) Determine % and 11 from the quadratics Be2+(e-C)a=o, C(e2 + B3)-(D + B2)(B0-|-Il)=O, and Yj, Y3 and Y4 from the equations Y3Y,=B, Y,Y3^=0, Y3^=Xi, then the expression a Yg + «% + «% will give all the roots of (/w). 83. If, for the development of the right-hand side of the equa- tion of (66), we employ the notation of (25) and the '^ epimetric'' symbol of (69), and, further, if we make c(QrQ,») =c'(QrQ2") -5c''(Q,-Q/), where c' is a symmetric and c" an unsymmetric function, we have c"(Q,4) = -5-'6(^) = S,(^i2^A). c"(Qi3Q,) = 2Si(^,8^2^3)-S,(^,V^32), (/'(Qi^Q,^) =2S,(^i V«^3) + 81(^,^2^3), ^"(QiQa') = JiSi(«^i%V) + Si(^iV«^3)> * Communicated by the Author. Mr. Cockle adds, that his " expres- sion for Mj (see his ' Fragment/ &c., Phil. Mag. for December 1853,p.448, par. XX.) must be amended by the addition of the quantity — x("~y6) to it." Algebraic Equations of the Fifth Degree, 125 We also have (/(Qi^Q^) =a-X^) -5S(^i V%) and ^(Qi^Qs) = «^' W H- 5S (x^^x^x.^x^ - 5 S 1 (a^i^i^-ga^g) + :^ (^) . e (a;) . The last equation is a consequence of that of (73). There are, of course, two more equations resembling the latter three. I have elsewhere shown (see pp. 226 and 486 of vol. lii. of the Mechanics' Magazine) that when cr[x) is a symmetric product, all such functions as cr(a7'^), 5, Vj Vg Vg or otherwise varied, as may the other two pairs. These results will perhaps throw light upon the question of the solvibility of ■ the equation in s. If e(a7), e{x)j &c. can be determined, the general equation of the fiifth degree admits of finite algebraic solution. IQ Cambridge Terrace, Hyde Park, June 13, 1866. XVII. On a substance named Bleiniere in modern Treatises on Mineralogy, By II. J. Brooke, F.R.Si"^ THIS mineral, which is described as having been hitherto met with only at Nertschinsk in Siberia, has been recently found in Cornwall by Mr. Richard Tailing, of Lostwithiel. It is uncertain from what ores the Nertschinsk mineral has been produced, but the Cornish variety appears to have resulted from the decomposition of Jamesonite. The Siberian mineral appears to vary considerably in the pro- portion of its constituent elements. Hermann found the specimen which he analysed to be com- posed of — Protoxide of lead . . . 61-83 Antimonic acid . . . 31*71 Water G-46 Other specimens were found by PfafF and Hermann to contain variable proportions of arsenic acid ; and a reddish-brown spe- cimen from Siberia, recently examined by Mr. Allan Dick, at the Museum of Practical Geology in Jermyn Street, contains a large proportion of arsenic without any trace of antimony. Dif- ferent portions of the Cornish mineral have also been analyised by Mr. Dick, and are found to vary in their composition so much as to render it probable that no two specimens would furnish the same results. One portion consisted of — Oxide of lead .... (PbO) 4073 Oxide of antimony . . (SbO^) 47*36 Water 11-91 * Communicated by the Author. Mr. Sorby on the Theory of the Origin of Slaty Cleavage* 127 It seems to be a mixture of hydrated antimonite of lead^ with variable proportions of the oxides of lead and antimony. Since the examination of the Cornish ore by Mr. Dick, it has been analysed by Dr. Heddle with the following results, which agree with the supposition of its being a variable mixture of its component parts : — I. II. Oxide of lead . . 47-045 46-68 Antimonious acid . 42*216 42-44 Water . * . . 11*497 11-98 A brown variety consisted of — Oxide of lead 43-94 Antimonious acid and Antimony ochre Water ....;... 6-625 \. . . 46-70. XVIII. On the Theory of the Origin of Slaty Cleavage. By H. C. Sorby, F.G.S."^ I SHOULD not now have trespassed on the pages of the Philosophical Magazine, if it had not been that in Dr. TyndalFs paper on the comparative view of the cleavage of cry- stals and slate-rocks, published in its last Number, there is a most serious misapprehension of my opinions on that subject. In alluding to these, at page 44, he says, " I cannot accept his ex- planation of slate-cleavage. I believe that even if these plates of mica were wholly absent the cleavage of slate-rocks would be much the same as it is at present. I will not dwell upon minor facts, — I will not urge that the perfection of the cleavage bears no relation to the quantity of mica present ; but I will come at once to a case which to my mind completely upsets the notion that such plates are a necessary element in the production of cleavage.'^ Also somew^hat further on he speaks of " the plates of mica assumed in Mr. Sorby^s theory.''' Now this statement of my views respecting the origin of slaty cleavage is so entirely different from what is really the case, that I think it would not be proper for me to let it pass uncorrected. In proof of this I need only refer to my paper on the cleavage of the Devonian limestones of Devonshire, published in this Magazine (January 1856, 4th series, vol. xi. p. 20). 1 there describe that of a considerable number of specimens, including all the principal varieties I have seen in the district, and yet in no case do I attribute it to the presence of mica ; and do not even use that word in the whole paper, except in saying, at page 23, that 1 do . * Communicated by the Author. 128 Mr. Sorby on the Theory of the Origin of Slaty Cleavage. not see why those varieties of the limestone, which have been changed into dolomite, should not be called metamorphic, because they do not contain mica or such other minerals as occur in rocks to which that term is usually applied. I would also par- ticularly call attention to what I state in describing figs. 5 and 6, where I show that the difference in the structure of non-cleaved and cleaved, fine-grained organic clays, consisting, now, almost entirely of minute crystals of calcareous spar with no mica, or fragments of any other such material, can be explained on the theory of mechanical compression and change in dimensions. I think this will be sufficient to prove that Dr. Tyndall has unfortunately misunderstood my meaning, in concluding that I considered slaty cleavage to be invariably due to the change in the position of flakes of mica; and I much regret that this should have occurred, for it has led him to describe a number of most interesting experimental facts as if they disproved my theory, whilst, on the contrary, I hail them with the greatest pleasure as confirming it in the most remarkable manner. What I chiefly wish to impress on the attention of geologists and physicists is, that slaty cleavage is due to mechanical causes ; that cleaved rocks are compressed rocks; and that the com- pression in general has not only changed the arrangement of the unequiaxed particles of which they are composed, but in some cases has also altered their form. There are scarcely any rocks whose particles are not thus unequiaxed, and I must still main- tain that, other circumstances being the same, those have the best cleavage that are composed of particles whose length and thickness differ most. The example of wax described by Dr. Tyndall (Phil. Mag. July 1856, p. 44) is indeed most excellent. If a small quantity, so melted on a piece of glass as to be sufficiently thin, be examined when cold with a magnifying power of about 400 linear with polarized light, it is seen to be composed of prismatic crystals usually about jjy^-Q to ^^^nru^^ ^^ ^^ ^^^^ ^^^S ^^^ 3TjVit *^ TuiiTU*^ broad, being almost invariably very unequi- axed. These are arranged in imperfectly radiating groups, and interlace promiscuously in all directions ; and this is just such a structure as, according to my views, would, if it was compressed, give rise to a cleavage of so perfect a kind that I can readily believe that the presence of larger particles would only impair it. Similar remarks would also apply in the case of white-lead and graphite, as mentioned by Dr. Tyndall (ibid. p. 46) ; for carbonate of lead is seen with the microscope to consist of minute prismatic crystals, and graphite of thin scales. Though 1 do not consider mica a necessary element in the production of cleavage, yet still I think it is very much more Dr. Tyndall on Slaty Cleavage. 129 commonly instrumental in giving rise to it than is generally sup- posed. For instance, the slates of Penrhyn and Llanberis con- tain about half their bulk of mica, which cannot indeed be seen with the naked eye, because the flakes are on an average only yoVo *^ of an inch long and ^-^^^^th thick, and but few are much larger. "When, however, thin sections of these rocks are examined with a microscope these flakes are most distinctly seen, especially in the black slate of Llanberis village, which to the naked eye is just like a fine-grained black shale, scarcely at all micaceous in the usual application of that term. Chemical analysis also fully bears out this conclusion ; but I may perhaps as well state here that the characters of this mica appear to me to indicate that it was not deposited in its present condition, but agree very much better with the supposition of having been formed by a peculiar transformation of a deposit of clay, of a different kind to that which has occurred in mica-schist and rocks usually called metamorphic, as I shall describe in a paper I hope to be able to publish before long, on the chemical and physical struc- ture of the older rocks. This size of the grains in these slates is then very similar to that of the crystals of wax, or in other words, the grain is as fine as that of wax. Their particles also are of such an unequiaxed character as completely agrees with their remarkably perfect cleavage, and I could only attribute any other view of the subject to trusting to the natural appear- ance of the rock, without examining a thin section with suitable microscopical means. In conclusion I wish particularly to call attention to the fact, that in forming a theory of the origin of the cleavage of slate- rocks, we must not rest satisfied with one that merely accounts for the splitting — it must be such as will explain their actual ultimate constitution — the mountains must indeed be examined with the microscope ; for it shows that the cleavage is not mere joints or weak places, which do also occur most abundantly, but chiefly depends upon a structure extending to the mechanical arrangement of the ultimate grains of which they are composed. XIX. Observations on the preceding Paper. By John Tyndall, F.R.S. 5fc. THE history of the paper which has called forth the foregoing remarks is briefly as follows. In examining the influence of structure upon the magnetism of bodies, I had occasion to make numerous experiments on slate rocks, and in this way the desire arose on my part to make myself acquainted with the agencies by which the structure of such rocks was produced. Phil Mag, S. 4. Vol. 12. No 71, Aug, 1856. K 180 Dr. Tyndall on Slaty Cleavage, During an accidental meeting with Mr. Woodward, the geologist, in the pass of Llanberis, on Saturday the 30th of September, 1854, my longing for information on this head made itself mani- fest, and soon after my return to London I was gratified by the receipt of Mr. Daniel Sharpens papers on cleavage, sent to me by the lamented author ; and of a paper by Mr. Sorby, sent to me, I believe^ by Mr. Woodward. All these papers interested me in a high degree. Returning to my experiments in the autumn of 1865, and making use, as on former occasions, of pressure as a means of modifying the magnetic force, I was gra- dually led to a theory of slaty cleavage different, as I conceived, from that proposed by Mr. Sorby. I had previously seen at Glasgow a specimen of the cleavage produced by Mr. Sorby, by means, as he considered, of oxide of iron scales ; but that which I had succeeded in producing, without such scales^ being incom- pai-ably finer, I was naturally led to doubt the influence which he assigned to them. The foregoing remarks, however, represent me as labouring under a most serious misapprehension of Mr. Sorby^s opinions ; my statement of his views " is so entirely different from what is really the case, that it would not be proper to allow it to pass uncorrected.^^ Nobody can regret this misapprehension more than I do ; and all I intend to do at present is to show, by quo- tations from the paper to which I have referred, the basis of my interpretation of Mr. Sorby's views. Whether these quotations will justify my interpretation in the eyes of the i-eader I know not ; but I have at least the satisfaction of knowing that I by no means stand alone in the meaning which I have attached to Mr» Sorby's language. The paper which contains Mr. Sorby's theory of the cleavage of slate rocks is to be found in the Edinburgh New Philosophical Journal, vol. Iv. p. 137. At the commencement the writer states as follows : — P. 137. — **The examination of thin sections of slate rocks with high powers, and a comparison with those of similar mineral com- position not possessing cleavage, have led me to form a theory to account for their difference of structure materially different from any yet propounded, and which, in my opinion, not only does so most satisfactorily, but also explains perfectly every fact that I am ac- quainted with connected with the subject.** What this theory is the following extracts will explain : — P. 142. — *• Usually, besides wic«, there is found in good roofing- slate, like that at Penrhyn, a certain proportion of decomposed felspar, a few minute grains of quartz sand, and granules of phos- phate of iron. The red tint is produced by the presence of very numerous minute crystals of peroxide of iron, and the dark by those Dr. Tyndall on Slaty Cleavage, 131 of pyrites. From such slate there is every gradation to those con- taining little or no mica, but made up of more or less fine quartz sand and decomposed felspar in very variable proportions, hut these have only an imperfect cleavage. Other slates, as is well known, contain much chlorite and other minerals. On the present occasion I shall chiefly confine myself to the consideration of such slate as has a perfect cleavage. *' If a' thin section of a rock not having cleavage be examined, which has a similar mineral composition to those which, when having it, form good slates, it will be seen that the arrangement of the par- ticles is very different. For instance, the well-known Water-of-Ayr stone has no cleavage, but shows more or less of bedding. It con- sists of mica and a very few grains of quartz sand imbedded in a large proportion of decomposed felspar ; the peroxide of iron being col- lected to certain centres, and having the characters of peroxidized pyrites. The flakes of mica do not lie in the plane of bedding, but are incHned tolerably evenly at all angles, so that there is no definite line of structural weakness independent of that due to bedding ; which results chiefly from alternations of layers of somewhat difl^er- ent composition, and not from the arrangement of the ultimate par- ticles. This is, however, totally diff^erent in a rock of similar com- position having cleavage. If a section be examined, cut perpendi- cular to cleavage, in the line of its dip, it will be seen that though some of the minutest flakes of mica lie perpendicular to the cleavage or at high angles to it, by far the larger part are inclined at low, so that the majority lie within 20° on each side of it. In fact they are most numerous nearly in the plane of cleavage, and gradually but rapidly diminish in quantity in passing to higher angles ; so that there are twenty times as many nearly in the plane of cleavage as at 45° to it, and very few at 90°. Where a section is examined, cut perpendi- cular to cleavage in the line of the strike, it is seen that the arrange- ment is similar, but there is not near so rapid a diminution of the members in passing from the line of cleavage, so that there are comparatively several times as many more inclined at about. 45° to it than when the section is in the line of dip, and those at still higher angles are also much more numerous. In a section in the plane of cleavage, but few flakes are cut through so as to have a greatly un- equiaxed form ; but they are similarly arranged with respect to the line of dip, though not in so marked a manner. It is not merely the IdiXgQv flakes of mica that are thus arranged, but the whole of those unequiaxed particles which existed in the rock before the cleavage was developed. " When a cleavage crack in the thin sections is examined, it is clearly seen that the cleavage is due to the above-described arrange- ment of the particles, which it follows most perfectly ; not passing straight forwards, but turning about according to the manner in which the ultimate particles lie in every part. It therefore appears that the fissile character of slate is due to a line of structural weakness ^ brought about by the manner of arrangement of the ultimate unequiaxed particles. The natural cleavage cracks, of course, bear the same K2 182 Dr. Tyndall on Slaty Cleavage. relation to this arrangement as those so often seen in many crystal- line bodies do to that of their ultimate atoms. They appear, in general, to have been mainly due to meteoric agencies, their position having been determined by the structural weakness. In accounting, then, for so-called slaty cleavage, it is only requisite to show how such particles could have had their position so changed that their arrangement should be altered from that found in rocks not having cleavage to that in those having it, which explanation must of course be such as would agree with every other fact connected with the subject. " Now I trust I have already shown that there is abundance of evidence to prove that rocks having slaty cleavage have been greatly compressed in a line perpendicular to cleavage, and elongated to a certain extent in the line of its dip. Taking for the amount of these changes those I have already mentioned for the slate of Penrhyn and Llanberis, it is easy to calculate mathematically what would be the arrangement of the unequiaxed particles in such a rock as Water-of- Ayr stone if its dimensions were so changed. Supposing that A= the angle of inclination of the longer axes of any unequiaxed particle to the line along which the minimum elongation would occur, and that a= this angle after it had taken place, we should have, perpen- dicular to cleavage in the line of dip, tan «= ; in that of strike, 6 tana= ^" ^ ; and in the plane of cleavage, tana= -^^. From 3'75 1*6 these relations it necessarily follows, that the particles would then be arranged in precisely such a manner as is seen to be the case in such a rock having cleavage, the agreement being most perfect in every particular, both in kind and amount, as seen in sections cut in each direction. *' Though such calculations may be fully relied on, yet to satisfy myself that they were correct, I have tested them by actual experi- ment. Having mixed some scales of oxide of iron with soft pipe- clay in such a manner that they would be inclined evenly in all directions, like the flakes of mica in Water-of-Ayr stone, I changed its dimensions artificially to a similar extent to what has occurred in slate rocks. Having then dried and baked it, I rubbed it to a per- fect flat surface, in a direction perpendicular to pressure and in the line of elongation, which would correspond to that of dip of cleavage, and also, as it were, in its strike and in the plane of cleavage. The particles were then seen to have become arranged in precisely the same manner as theory indicates that they would, and as is the case in natural slate ; so much so, that so far as their arrangement is concerned, a drawing of one could not be distinguished from that of the other. Moreover, it then admitted of easy fracture into thin •flat pieces in the plane corresponding to the cleavage of slate, whereas it could not in that perpendicular to it." If the reader feel sufficient interest in the question, I would invite him to turn to my paper in the last Number of this Dr. TyndaW on Slaty Cieavaffe. 133 Journal, and decide for himself the extent to which I have erred in my statement of Mr. Sorby^s opinions. My experiments on this subject were all finished on the 27th of October, 1855, and at that time the paper from which the above citations are drawn was the only one which, as far as 1 am aware of, Mr. Sorby had ever published on the subject of cleavage. From November 1855 to June 1856 1 was far too busy with other matters to be able to devote any attention to the subject of cleavage, so that the lecture which has been the cause of this discussion was merely the utterance of views to which experiment had led me upwards of seven months before. My special object in the lecture was to account for the cleavage of ordinary roofing- slates, like those of Bangor and Borrodale — of such slates, in fact, as Mr. Sorby had in view when he pro- pounded his theory. In the above critique, however, Mr. Sorby refers exclusively to a paper on the cleavage of Devonian lime- stone, drawn up, 1 believe, at my suggestion, and published in the Philosophical Magazine for January 1856. ^'In no case," he observes, "do I attribute it [the cleavage] to the presence of mica ; and do not even use that word in the whole paper, except .... at page 23." Mr. Sorby surely cannot imagine that 1 attach any particular value to mica as such. It is shape, and not composition, that affects the question—" elon- gated particles," as 1 have somewhere expressed it in my lecture. And if mica occupies a prominent place there, it is because Mr. Sorby himself has given it that prominence, as the foregoing ex- tracts prove, while accounting for the cleavage of the particular kind of slate which formed the subject of my discourse. But even in this paper on the Devonian limestone, though mica is absent, it has its equivalent in elongated particles of sand and organic fragments, which perform the same functions in the limestone as the mica does in the Welsh and Cumbrian slate. So evident, indeed, does this equivalence appear to Mr. Sorby himself, that he makes use of the same experiment with the oxide of iron scales to illustrate both the action of the plates of mica in common slate, and of the "unequiaxed particles" in Devonian lime- stone. In proof of all this 1 refer the reader to the papers of Mr. Sorby ; and 1 would here once for all express the hope that he will accept none of my statements without this verification ; otherwise I may, although quite unwittingly, lead him into error. Figs. 5 and 6, to which Mr. Sorby calls particular attention, and which occur towards the conclusion of his observations on the cleavage of Devonian limestone, refer to a cleaved organic clay composed almost entirely of minute crystals of calcareous spar, which " appears as though the compression indicated by the joints of the encrinites and larger ci^stals, had afiected the 184 Dr. Tyndall on Slaty Cleavage. smallest, constituting the ultimate structure of the rock/' This case is so like that of iron, adduced in illustration of my views, that had it occurred to me, I should undoubtedly have referred to it in my lecture. To this class of facts Mr. Sorby ingeniously endeavours to attach my experiment with the wax. When a thin stratum of this substance, melted on a plate of glass and permitted to solidify, was examined by the microscope, he found , It to be composed of unequiaxed prismatic ci7stals. Without entering into the question as to the amount of cohesion between these crystals, I would say let them be chopped up into microscopic mincemeat, let the mass be rubbed away by emery, or pared into the finest shavings by glass ; let it be pounded, crushed, — in short let all mechanical means be applied to abolish this cry- stalline structure; let the wax be kneaded, as in my experi- ments, into dough, and submitted to pressure, — the same per- fect cleavage will be produced. To one and the same cause I have attributed the cleavage of such wax, and that of the slates of Wales and Cumberland. Mr, Sorby deduces from his expe- riments, that the volume of slate- rocks has been reduced one- half by the pressure which produced the cleavage. Without expressing any opinion as to the probability of this conclusion, let the structure of such a mass of fine slate mud, before com- pression, be considered. Its water has drained away from it, oozing through it where it encountered least resistance, and leaving what, to my mind, presents an innumerable assemblage of little ' mud masses clinging together at some parts and separated at others. The effect of pressure upon such, a mass must manifestly be to develope cleavage. The presence of unequiaxed particles may aid in producing this result, but the finer the mud, the more in fact it approaches to the wax in structure, the more perfect, to my mind, will the cleavage be. A day or two ago the presence of cream* cheese upon the table of a hotel suggested to me the idea of trying whether the squeezing of the mass had not developed in it a kind of cleavage. I was much pleased to find this to be the case. The experiment was performed by inserting the knife a quarter of an inch into the cheese and tearing the latter asunder. It is still simpler and better to pull the mass asunder with the fingers. The cheese yielded freely along the planes perpendicular to the direc- tion of pressure, but not across these planes. If this can be referred to the compression of crystals, it is something won for •science ; if not, it illustrates the action by which 1 suppose the structure of ordinary roofing-slate to have been produced. * The term * cream * ought, properly speaking, to have the negative sign prefixed ; the cheese was made with milk from which the cream had been withdmvm. Dr. Tyndall on Slaty Cleavage. 135 To Mr. Williams of Basingstoke I have been recently indebted for some very interesting specimens of iron plates, peeled off by the compressing and sliding action of railway trains. The specimens exhibit the laminated structure in a very striking degree. '' Prac- tically/^ says my intelligent correspondent, "it is a constant fault in rails : the men who are always handling and taking them up say that it is worst near the stations, where the break acts ; but sometimes they find one here and there upon the main road — not very often .'^ One of the specimens sent to me was of this latter class, and it had probably been submitted to the rolling of the trains for a period of eighteen years. In addition to the pressure, which of itself causes the granules of iron gradually to spread out, and thus tends to destroy their natural cohesion, when the wheel slides it has a tendency to displace the upper surface of the rail in the direction of motion. Suppose the rail to be divided into distinct strata, each of these being held to its neighbours by the cohesion of the iron. Whenever a train passes, a slight displacement occurs, and every such displacement tends to rupture the cohesion of the particles which hold each pair of strata together. The act is repeated, perhaps thousands of times, until finally the rail yields at the place where, owing to crystal- line or mechanical structure, the force which holds the strata together is weakest. When slate mud is compressed, its differ- ent layers cannot be expected to move laterally with exactly the same velocity ; they slide over each other, and this action, as in the case of the iron, must also tend to weaken the cohesion of the layers and to facilitate the cleavage of the mass. With regard to Mr. Sorby^s concluding paragraph, I confess that my sole object was to account for the " splitting '' of slate- rock. The facts observed by Phillips arid Sharpe, and added to in so important a degree by Mr. Sorby's researches, lead to a conclusion, first I believe announced by Sharpe, and assented to by all who have observed the facts, that the masses have been sub- jected to pressure in a direction at right angles to the planes of cleavage ; and the sole question to be decided was, whether this pressure was sufficient to produce the cleavage. Both Mr. Sorby and I say yes, — but on different grounds ; which of us is right (perhaps each of us has a little reason on his side) others must determine, and to them I now resign the consideration of the question. [ 136 ] XX. On certain Phanomena of Electrical Discharge. By Sir W. Snow Harris, FJIS. To the Editors of the Philosophical Magazine and Journal. Gentlemen, I HAVE duly considered Dr. Riess's notice of my memoir in your May Number, " On Electrical Discharge/' I regret exceedingly that it should have been treated by Cr. lliess in so dictatorial and intolerant a spirit. It will be my endeavour, however, in the few concluding observations I have to make, to avoid every thing calculated to provoke angry discussion, and confine myself strictly to facts and to the scientific merits of the question at issue between us, without any discourteous com- ment on the several personal animadversions and reflections on me, in which Dr. Riess has thought fit to indulge. Dr. lliess says that 1 had " long since set up a law upon the dependence of the electrical heat upon the charge of the bat- tery,'' and that he " ascertained this law to be incorrect, and set up another in its place." All this, however, as it here stands, is mere assertion, worth nothing as scientific evidence in reply to the facts and phcenomena set forth in my memoir. According to my view of the question, Dr. Riess has quite failed in his demonstration, which I conscientiously believe to rest entirely upon defective hypothetical assumptions, at variance with the known laws of ordinary electrical action. The essence of what I advanced and what I still maintain is this, that you cannot ex- tend your electrical battery by adding to the number of its jars, without at the same time increasing the resistance to the subse- quent discharge of the accumulation ; consequently a given quan- tity of electricity will experience more resistance when discharged from an increased number of jars, than when discharged from a smaller number ; so that you cannot take the resistance as con- stant. But, as I have shown, if you extend your battery-surface without division, as in accumulating the charge upon a very large jar instead of a very small jar, then in using the same charging rod you have the resistance nearly the same in each ; now in this case you find the effect on the wire of the thermo-electrometer invari- able. What then becomes of Dr. Riess's formula F=— , taking s to indicate the increased surface ? Why the surfaces may be as 1 : 2, and yet the effect of the discharge of a given quantity of electricity the same. According to Dr. Riess, the density of the accumulated electricity would be in such a case twice as great in the small jar ; so that if the effect were as he says, " pro- portional to the product of the quantity by its density," the same quantity discharged from a jar of half the surface should On certain P/uenomena of Electrical Discharge. 137 produce twice the effect ; whereas the effect is unchanged. Then again I am informed that my paper is full of errors, that without the necessary knowledge, I have deduced results unintelligible both to Dr. lliess and others, and he is " not aware that any one, either here or in England, had found these results more intel- ligible than he had done." All these things are very easily said ; but here is an extract from Far aday^s Researches, 12th series, 1363 : ^' Many philosophers have examined the circumstances of this limiting action in air, but as far as 1 know none have come near Mr. Harris as to the accuracy with, and the extent to, which he has carried on his investigations.^^ This, be it remembered, refers to the particular method of research so pointedly objected to by M. Riess, " if his memory is correct.-'^ That my researches may be ill understood by Dr. Ricss is possible, and yet that may not be altogether my fault ; it may equally arise from some source of misapprehension by him. We have an instance of this in his late notice of my memoir, in his remark relative to the resistance to discharge as depending on the transfer of the accu- mulation from the glass to its coating, and the accumulation of a given quantity of electricity upon an increased number of jars. These sources of resistance are evidently new to Dr. Riess, and so far as I can see, have never entered into his calculation ; now / have " ascertained by experiment " the fallacy of the significa- tion which Dr. Riess attaches to his symbol, as seen in my former communication. Again, Dr. Riess observes, " It is not true that I ascribed the unsuccessful experiments of Sir W. Harris to the faulty arrange- ment of his thermometer." I think it will be allowed, that before employing so strong an expression, somethmg like certainty upon the point in question should have been established. Well ! here is an extract from Dr. Riess^s paper {Annates de Chimie for 1838, tome Ixix. p. 116) : " Ilfaut attribuer a la construction imparfaite du thermometre, que les experiences de M. Harris sont restees in- fructueuses ; " and yet I am told that it is " not true" that M. Riess had referred what he calls my unsuccessful experiments to the imperfection of my instrument*. Nothing that Dr. Riess has advanced relative to Kinnersley^s thermometer, with the whole detail of which I have been long familiar, at all serves to convince me that my instrument in all its generality was not an entirely new instrument at the time it was first produced, at least so far as it is possible to produce a perfectly new instrument ; and I again repeat, that the main object of all the primitive air-electrometers, was the explosive violence of the electrical discharge in a confined space of air, Kinnersley's casual introduction of various substances m^oii # gee also De la Riye, Traits de VEUctridte, vol. ii. p. 154. 188 Sir W. Snow Harris on certain Phanomena into his cylinder, I consider as a mere coincidence, quite a secondary affair; the experiments came to nothing, and the "Immortal" Franklin gave these experiments with the '^wet thread," " blade of green grass," &c., fairly quoted by Dr. Riess, no encouragement whatever, as resulting from heat, and so the whole matter dropped ; and it has not, so far as I know, been ever revived until the present time. Now Dr. Riess labours to show that my instrument was a studied copy of these old instru- ments, Kinnersley's more especially, much in the same way as he improved upon Behrens^ electroscope, or copied my instru- ment ; whereas at the time I first invented my instrument)^ I can most rigidly affirm that I had not the shadow of Kinners- le/s air-electrometer in my mind. As I have stated, it origi- nated at a pressing moment, in a necessity for demonstrating experimentally to the Naval Department of the Government, and the Scientific Commission appointed to investigate and report on my method of securing the Royal Navy from liglit- ning, the relative superiority of copper for that purpose over iron, and some other metals ; at that time no very exact expe- riments had appeared, more especially with the ordinary elec- trical discharge. Now Dr. Wollaston, one of the most distin- guished philosophers in Europe of that day, did not consider the experiments I made with this instrument " unintelligible," as Dr. Riess says he has found them. On the contrary, in reply to an inquiiy whether he saw "any danger or liability to objection in the method proposed by Mr. Harris, of carrying off lightning from ships," &c., he observes, " Mr. Harris appears to me to be well acquainted with the subject, and fairly to esti- mate the operation of the element with which we have to con- tend," &c. I find it of course somewhat painful to be obliged to refer to such quotations ; but in justice to myself I think I am called on to expose, by an appeal to facts, how ill-supported are Dr. Riess's assertions of my want of knowledge, &c. of the question I have undertaken to discuss, and the " unintelligible " nature of my experiments, both to himself and " others." With respect to Dr. Riess's assertion, that I must be unac- quainted with the use of the thermometer, being still " unaware of the necessity of employing a calculation," &c., I think it may be seen by reference to what I stated, that I neither asserted nor denied the necessity of "calculation." I in no way meddled with the very loose ground on which Dr. Riess builds his con- clusion, and I took very especial care to explain my view of the operation of the instrument. In the present imperfect state of our knowledge of the causes of heat and electricity, and of our equally imperfect apprehension of the precise way in which my thermo-electrometer operates, I cannot but conclude that the of Electrical Discharge, 139 application of hypothetical formulse as a means of correcting its indications^ is a very unsafe and precarious course. Dr. Riess nowhere proves the application of the doctrines of specific heat to the operation of the instrument, nor does he in any way pretend to show how it operates, except upon an assumption. I by no means question Dr. Riess's analytical calculation, or the skill and ability it displays : I question its applicability to the nature of the experiment. Supposing it should turn out, as is by no means unlikely, that the expansive action is a sort of second- ary action, varying merely with the evanescent efi^ect on the wire, independent of the heating effect, but with which it may have some peculiar connexion, — what then becomes of Dr. Riess's elaborate conclusions ? Franklin, for example, evidently ima- gined that the expansive effects observed by Kinnersley were the result of vapour produced by the shock, or of a sort of smoke emitted by the wires, and so far did not assent to the heat doctrine upon which Dr. Riess now stakes his whole process of research. From some interesting experiments instituted since my memoir on this subject appeared, I am led to conclude that we have yet a vast deal to learn relative to the precise operation of this instrument, and that the view I took of it, as depending on the momentary mechanical expansion of a small column of air immediately surrounding the wire, is substantially correct. But until all this be well ascertained, I think it a much safer course to trust to an empirical experimental examination of the imme- diate indications of the instrument, and observe the general laws of its operation by comparison with well-known laws of electricity. Hence I pretend to say nothing about the " neces- sity " or otherwise, of some calculation for rendering " the data capable of comparison/^ Now as to my "unit measure," which Dr. Riess treats so slightingly: 1 believe the time is not far distant when he will be compelled in candour to change his opinion upon that question. I have lately submitted to the Royal Society a series of crucial experiments showing the perfect accuracy of this instrument as a measure of quantity, which I believe Dr. Riess will have great difficulty in disproving; nor do I stand alone in my interpretation of this question, however meanly Dr. Riess may profess to think of it ; and I am quite willing to stake the value of the differences existing between Dr. Riess and myself upon the soundness of our respective scientific views of this question alone. Faraday, in considering the question of my unit measure, thus expresses himself : " Suppose the unit-jar has about one- tenth the electrical capacity of the large jar, and that being 140 On certain Pfumomena of Electrical Discharge. charged up to its discharging point, it contains ten of positive electricity ; then these ten will pass on into the large jar as a discharge spark, and none will remain within the unit-jar. Now the conductor of the machine, the outside of the unit-jar, and the ball and wire of the large jar, will all appear positive to a carrier ball : but when the machine is turned, although a rise in positive condition will gradually take place on all the surfaces, still the mutual relation of n and w' (that is, the exploding balls) to each other, will be the same as before, and the mutual rela- tion of the inner and outer coating of the unit-jar will be to each other absolutely as before, for no external relation can alter their mutual relation, though it may affect the outer coatings, both of the large jar and the unit-jar. Whenever a spark does pass from n to n', the electricity passing must be equal; because the inductive relations of the coatings to each other through the glass, and the like relations of the balls n, ri to each other, remain absolutely the same. This is, as I think, a rigid conse- quence of the principles of inductive action." This quotation, independent of the great authority from which it is drawn, may perhaps help Dr. Riess to a better appreciation of the question, and serve in some degree to correct his notion, that my results, " so far as he is aware," are equally unintelligible in England as they are to himself " and others " in Germany. I am unwilling to extend my observations further on this present occasion, not having any predilection for a controversy which seems to border on so much painful matter of difference. I had, certainly, when I wrote the paper which appeared in your May Number, not the least intention of offering to Dr. Riess any personal affront. 1 was perhaps somewhat hasty in employ- ing the terms " systematic disparagement," which I used merely to represent a series of depreciating criticisms from time to time on my several experimental researches, laying in the path of Dr. Riess's subsequent inquiries, and which certainly appeared systematically connected with each other. I fully acquit Dr. Riess, however, of any premeditated injustice toward me, and I am not too proud to withdraw this expression in a way courteous and, I trust, satisfactory to Dr. Riess. My memoir, as a scientific document, I willingly leave to the dispassionate judgement of dis- interested persons, who will, I am sure, properly appreciate all I have advanced, and who will perhaps judge better than I can, whether Dr. Riess has really given any substantial reply to it or not. I remain. Gentlemen, Your obliged and faithful Servant, 6 Windsor Villas, Plymouth, W. Snow Harris. 8tb July, 18^6. [ 141 ] XXI. Proceedings of Learned Societies, ' B at\ Ti!! ROYAL SOCIETY. '*"' '' [Continued from p. 68.] Dec. 13, 1855.— Colonel Sabine, R.A., Treas. and V.P., in the Chair. rilHE following communication was read : — -*- " On the Structure and Development of the Cysticercus cel- luloses, as found in the Pig." By George Rainey, Esq. The Cysticercus cellulosce, in its mature state, consists of two parts : one a small oval cyst, composed of a very thin membrane, rendered uneven on its external surface by minute rounded projec- tions, and containing in its interior, granular matter, particles of oil, and a colourless fluid. This may be called its ventral portion. The other is folded inwards, occupying the centre of the cyst just described, but by pressure it may be made to protrude. This part is sometimes called the neck. Its length varies very much in dif- ferent Cysticerci, depending upon their age. It is hollow, having strong membranous parietes, wrinkled transversely, and composed both of circular and longitudinal fibres. The cavity has no visible communication with that of the ventral portion. It contains a multitude of small oval laminated calcareous bodies, which, when acted upon by acids, effervesce briskly, and become partially dis- solved, leaving only a small residue of animal matter. When the neck is protruded, the extremity farthest from the cyst is seen to present an enlargement, sometimes called the head, on the free surface of which there is a quadrangular area, occupied by four circular disks and a ring of hooklets. Each angle contains a disk, and the hooklets are placed in a circle around the centre of this space. The suctorial disks are traversed each by a passage taking rather a spiral course, and terminating in the cavity of the neck. The membrane composing a disk presents two orders of fibres, circular and radiating. The hooklets are generally twenty- six in number, thirteen long and as many short, arranged alter- nately a long and a short one. Each consists of a curved portion like a bird's claw, and a straight portion or handle; and at the junction of these two parts there are tubercles, two in the short hooklets, and only one in the long ones. The hooklets are crossed by two zones of circular fibres. They are also connected by radiating fibres, which occupy the spaces between each adjacent pair, like the interosseous muscles situated between the metacarpal bones and phalanges. The hooklets are disposed like radii, with their points turned outwards and the extremities of their handles inwards, which, not meeting, circumscribe a circular space whose centre corresponds to that of the quadrangular area before men- tioned. At this part there is no perforation answering to an oral orifice, but here the membrane is simply depressed so as to present a conical hollow. By pressure upon the neck, this membrane can be made to protrude in the form of a tongue-like process, to which the handles of all the hooklets are connected, so that when this 142 Royal Society : — part in the living animal is made to move, the handles of the hook- lets will be drawn in with it, and their points carried from the entozoon, and thus made to penetrate the part to which it attaches itself, lliese entozoa are chiefly found in the cellular intervals between the muscular fibres, contained in an adventitious cyst formed by the condensation of the surrounding tissues. No more than one entozoon is ever met with in one cyst. Development of the Cysticercus cellulosae. The earliest appearance of the incipient stage of the Cysticercus cellulosae is a fusiform collection of small cells and molecules in the substance of a primary muscular fasciculus, or immediately beneath its sarcolemma. These cells, in this condition of the entozoon, have only an imperfect or partial covering; however, they soon become completely enclosed in a well-defined membrane which is at first homogeneous, but which afterwards, sends out short, slender, projecting fibres, resembling short hairs or cilia. These hair-like fibres, though resembling in some respects cilia, differ from them in being much less sharply defined and less pointed ; however, for convenience sake, I shall speak of them as cilia. Their direction is remarkable. At either extremity of the fusiform animal they are reflected backwards at a very acute angle, like the barbs of a feather, their direction being of course opposite at the two ends. They become less and less inclined as they approach the middle of the body, where they stand out at right angles to the sur- face. The apparatus of cilia- like processes above described is evi- dently designed to give to the entozoon, whilst in this stage of its existence, the power of penetrating between the ultimate muscular fibrillae, and thus to enable it to force its way from the interior of a primary fasciculus into the spaces between the muscular fibres. This will be the effect of the friction of the fibriliae against the cilia, which will allow of motion in one direction only. And as its two ends must move in opposite directions, the cilia wiii also serve to aid the entozoon in its development longitudinally. That such is their ofl[ice will be apparent on examining a sufficient number of speci- mens ; in some of which the primary fasciculi will be seen to have been completely split up by these animals. But the correctness of this inference is more strikingly proved by the influence which the size and arrangement of the primary bundles of muscular fibres have upon the form and dimensions of the entozoa. Thus in the muscular parietes of the heart, where the primary fasciculi are smaller, and, from their frequent interlacing, shorter than in other parts, the cysticerci are, in this stage of their development, also very short and of a different form to those found in other muscles, composed of striped fibre, although in other respects perfectly similar ; and, when completely formed, those taken from the heart cannot be distinguished from those formed in other muscles. The cells which have been alluded to as forming the principal part of the Cysticercus thus far developed, and contained in the investment first described, are all of the same character, differing only in their form and size, according to Mr. Rainey on the Structure 0/ Me Cysticercus cellulosse. 143 their age and situation. Those situated about the centre, and form- ing the chief part of its bulk, are collected together into rounded masses, giving to many of the animalcules an obscurely annulose appearance. They are of an elliptical, or rather reniform figure. This form, however, is not essential to these cells, but merely re- sults from the circular shape of the masses into which they enter, the convexity of each cell being a part of the outline of its respective mass. These cells contain minute granules, or rather molecules, which are variously disposed in different cells, so as to present a variety of appearances, such as circular spaces, which might be mistaken for nuclei, but which seem rather to be pro- duced by a deficiency of the cell's contents at these parts, than by any distinct nucleus. The mode of formation of these cells must be examined in the growing parts of the animal, and for this purpose its extreme ends are best adapted. When one of these ends is about to have an addition made to its length, the investing membrane at this part becomes at first very thin, and then disappears. A clear space is next seen, having in some specimens the form of the part which is about to be added to the extremity of the entozoon ; in others it has no defined limit. This space contains, in some cases, nothing but extremely minute molecules, of different shapes; in others, these molecules are mixed with granules of various sizes, which have every appearance of having been pro- duced by the coalescence of the molecules ; and lastly, with these molecules and granules, there are in other examples very distinct globular cells, of a bright aspect, looking more like nuclei than perfect cells ; these soon become flattened oval, and ultimately take the elliptical form before described. All the time these changes are taking place in the molecules and cells, the membrane has been in progress of formation, so that when the molecules have disappeared, and their place has become occupied by perfect cells, the end of the animal is completed. The cilia are soon afterwards added. The lateral growth of these animals takes place in the same manner: the first indication is ^ separation of the cilia, which, it must be observed, are larger at the sides of an entozoon than at the extreme ends ; and then a thinning of the membrane supporting them ; and, lastly, the formation of globular cells, as before noticed. After the animals have become of a considerable size, and forced their way from the interior of the primary fasciculi into the cellular spaces between the larger muscular fibres, they still continue to grow, especially in breadth ; but they lose their cilia, and gradually acquire those parts which have been described as belonging to the neck. The first evidence of this addition is the appearance of inversion of the middle part of the cyst, forming a small hollow, the sides of which look as if thrown into folds containing granular matter, and the bottom presents a circular space in which are granular particles of various forms and sizes, but those in the centre are darker than the rest. It is from these particles that the suctorial disks, the hook- lets, and the first of the laminated bodies are about to be formed, but as yet none of these parts are recognizable. At a stage a little 144 Royal Society : — more advanced, this apparent inversion of the cyst has increased, the neck has become longer, and the appearance of disks, hook- lets, and laminated bodies is sufficiently distinct to be perfectly recognizable. The process of development is particularly apparent in the booklets, and perhaps there is no other instance of the growth of an animal tissue which presents such facilities for the examination of the manner in which it is effected. First, because the part of the entozoon on which these organs are formed, is sufficiently trans- parent to admit of examination by the highest magnifying powers without any previous dissection. Secondly, because the material of which they are composed is so characteristic, and so dissimilar to the surrounding parts, that it can be detected in the minutest possible quantities. And, thirdly, as only a few of these booklets are in progress of development at one time, and as these are in all stages of formation, every step in the progress of their growth can be traced from the merest molecule to a perfect booklet. This is important in reference to the general theory of development, as it furnishes an example of the formation of a complete set of organs, on a plan more simple, and at variance with the cell-theory of Schwann and others. Before one of these booklets takes on a recognizable form, it exists as a group of exceedingly refractive particles, all apparently of the same composition, and of a more or less globular form, but of veiy different sizes, some being so minute as scarcely to be visible by one- eighth of an inch lens, others being almost as large as the handle of a perfect booklet, while the rest are of all dimensions between these extremes. The next condition of a booklet is the apparent fusion or coalescence of some of these particles into the hocked part of the organ. Then the handle and tubercles are added, these having been previously formed by the fusion of the smaller particles, and these latter by the coalescence of the minutest and the minuter ones. Before the several parts are perfectly consolidated, their points of junction can be distinguished, and in other groups the fragments corre- sponding to those recently united can be recognized. Directly a booklet is found, it is of its full dimension ; and some of its parts are even larger and more clumsy-looking than in older booklets. The substance of the particles entering into these organs, after they are once formed, undergoes no change in its microscopical characters, but is the same after as before their union. It is im- possible to single out any one particle from the rest, which can be taken for the nucleus of a cell, or for what physiologists would call a nucleated cell; and thus there is nothing which indicates that these organs have been formed by transformation of previously ex- isting cells, but, on the contrary, there is every appearance that their formation is due to the simple coalescence of homogeneous molecules. Up to the present point, the facts which I have stated are so obvious, that their accuracy will, I think, not be questioned ; also the interpretation of them is not only that which appears to me the most natural, but is almost self-evident. There remain. Mr. Rainey on the Structure of the Cysticercus cellulosee. 145 however, some considerations of a more theoretical kind, though not of less importance. It will be asked, how the entozoon, in its earliest condition, such as I have described it, finds access to the interior of a primary fasciculus. Before attempting to answer this question, I must observe that my description commences from a condition of this entozoon so complete, that no one, on examining it in this state with the microscope, will deny its perfect similarity to those of the higher form. But there are other linlis in the chain which I must now consider, and which so far have been omitted only because I wished to keep that which is certain distinct from that which is probable. Before the cells and molecules already described accumulate in sufficient quantity to present the un- doubted character above mentioned, they are found aggregated in smaller groups, and even occurring individually in all the primary fasciculi of the diseased muscle ; their quantity, and the size and form of these groups, present the greatest possible irregularity in the different fasciculi. In some the molecular deposit looks like an early stage of fatty degeneration, but it has characters very different ; one is the shape of the molecules, which resemble in all respects those in the growing ends of an entozoon ; and another is, their situation, which seems to be between the primary fibrillse, tending to separate them longitudinally ; however that may be, it is an abnormal condition, and always co-existent with the higher forms of the Cysticercus ; and as the entozoon, as I have first described it, could not possibly have taken on that form all at once, these groups of molecules must therefore be looked upon as its antecedent stage, or as portions of Cysticerci in progress of development. But I also find in the specimens of muscle infested with these entozoa, many of the capillaries and smaller blood-vessels filled with organic molecules, which, so far as I am able to judge from the comparison of such extremely minute bodies, seem to resemble those molecules which are found in the primary fasciculi. The vessels filled with these molecules have their coats so thin as to be inappreciable, and some of the capillaries appear to be partially destroyed, and their molecular contents diffused among the sarcous elements. As this is an abnormal condition of the contents of these vessels, as well as of their coats, and, so far as my experience goes, is not found ex- cepting in conjunction with the earliest stages of the Cysticerci, I am inclined to believe that the molecules in question are the same as those in the primary fasciculi, and that it is by their coalescence in these fasciculi that the formation- cells of the Cysticerci are formed. Addendum, Dec. 6. — After an entozoon has left the interior of a primary fasciculus, and arrived at the space between the muscular fibres, it loses its ciliated investment, and increases in breadth. Its margin now seems to be formed entirely by the convexities of the globular masses of cells of which its body appears to be made up, causing it to present a crenate form similar to that of the ven- tral portion of the perfect animalcule, with this difference only, that these cells are compressed. The next change which is visible Phil, Mag, S. 4. Vol. 12. No. 77, Aug, 1856. L 146 Royal Society : — is the formation of folds, which become more perceptible as the animal increases in breadth, and which remain in the perfect entozoon so long as it is confined to a small space, but dis- appear when it gets to the space between the surface of a muscle and the fascia covering it. The unfolding in this last situation seems to be produced by the imbibition of fluid, and the consequent distension of the ventral part. These more advanced stages of the worm-form are best found in those specimens of diseased muscle in which the perfectly developed Cysticerci abound. Their number in proportion to that of the perfect animalcules varies considerably in different specimens. I have always succeeded in finding some of those of the worm- form along with the perfectly developed ones ; and in some cases there are as many of one kind as the other. After they have acquired a certain breadth — about one-twelfth, or the one-eighth of an inch, — the central part of the cyst appears to be drawn inwards, forming a hollow ; at the bottom of which, the granular material is deposited from which the suckers, booklets, and calcareous granules are formed, as above described. Jan. 10, 18.56. — Admiral Beechey, V.P., in the Chair. The following communication was read : — "On Insolinic Acid." By Augustus W. Hofmann, Ph.D., F.R.S. In attempting to purify cuminic acid by boiling with chromic acid, I observed that this acid experienced, on the part of this reagent, a progressive alteration. By twenty-four hours' ebullition, cuminic acid is completely converted into an acid insoluble in alcohol and ether, for which I propose the provisional name of insolinie acid; purified by the ordinary processes, this body furnished on analysis the following relations : — C9H4O,; but the analysis of the salts demonstrates that this formula must be doubled, insolinic acid being a bibasic acid. I have examined the following salts : — Insolinic acid Cjg Hg Og SUver salt Cjg (Hg Agg) Og Copper salt Cjg (Hg Cug) Og Barium salt C^g (Hg Bag) Og Calcium salt (at 1 00° C.) Cjg (Hg C&S Og (at 133° C.) C,g(HgCa,) Og Potassium salt (neutral) Cjg (Hg Kg) Og (acid) Cig(H7K) Og Potassium-sodium salt Cjg (Hg K Na) Og When considered by itself, insolinic acid has but slight claims on the attention of chemists ; but when viewed in connexion with other groups of bodies, it acquires increased interest. Some years since, Gerhardt pointed out that to the homologous series of monobasic fatty acids Cnj H^j O4, the lowest terms of which are formic and acetic acids, there runs parallel a homologous series of bibasic acids, C„2 Hnj-s Og, the simplest member of which is oxalic acid. Dr. Hofmann on Insolinic Acid. 147 These two series of acids are connected by the closest ties, and very conclusive experiments have demonstrated that the members of the former may be easily converted into those of the latter ; such is the case of the transformation of butyric into succinic acid, effected by M. Dessaignes under the influence of oxidizing agents. The following table exhibits these two series of acids arranged according to their carbon : — Formic acid Cg Hg O4 Acetic acid C4 H4 O4 Propionic acid C^. Hg O4 ;. Butyric acid Cg Hg O4 Valeric acid Cjq Hj^ O4 Caproic acid 0^2 Hjg O4 CEnanthylic acid C^^ ^u^a Caprylic acid C^g Hjg O4 Pelargonic acid Cjg Hjg O4 Rutic acid Cgo Hgo O4 Oxalic acid C4 Hg Og }, •■: C, H, O^ Succinic acid Cg Hg Og Pyrotartaric acid Cj^ Hg Og Adipic acid . ^ Cjg Hj^ Og Pimelic acid 0^4 Hjg Og • Suberic acid Cjg Hj4 Og • ^18 H16 Og Sebacic acid C20 H^g Og - * The existence and the mode of formation of insolinic acid prove that to the series of monobasic aromatic acids, Cn2^n2-%^^i the lowest known term of which is benzoic acid, there corresponds likewise a series of bibasic acids, 0^2 ^^2-8-2 08 = 0^2 H„2- 10 Og. Of this series few members are at present known, but the group of aromatic acids is itself very imperfect and limited. The two series comprise at present the following terms : — Benzoic acid 0^4 Hg O4 Toluylic acid Cjg Hg O4 •. •• :• OigHi^04 Cummic acid Cgo Hjo O4 ? C14H4O. j O16 Hg Og Terephthalic acid . , Phthalic acid , Insolinic acid C^g Hg Og '? O20 Hjo Og If we take the carbon as the standard of comparison, it is evident that the bibasic insolinic acid corresponds to the monobasic acid, which stands between toluylic and cuminic acid. In addition to this unknown acid, toluylic acid only is represented in the series of bibasic acids. There are, in fact, two bodies which may be regarded as representatives of toluylic acid, namely, phthalic and terephthalic acids. Benzoic and cuminic acid are not yet represented. 148 Royal Society. Jan. 17.—Prof. William Allen Miller, M.D., V.P., in the Chair. The following communication was read : — "Anatomical and Physiological Observations on the Organ of Vision, for the purpose of ascertaining the alterations caused by sec- tion of the Optic Nerve." By Augustus Waller, M.D., F.R.S. The author begins by referring to experimental researches already published by him on the effects produced on the nerves of living animals by section at diiferent points in their course ; and he briefly recapitulates the chief results of these experiments, as follows, viz. — 1 . Section of a spinal nerve on the distal side of its ganglion is fol- lowed by degeneration of the part of the nerve beyond the section, whilst the part still connected with the ganglion retains its integrity. 2. Section of the posterior root of a spinal nerve induces no change in the trunk or branches of the nerve beyond the ganglion, nor in the portion of the root which remains connected with the ganglion, whereas the part of the root attached to the spinal cord, but discon- nected with the ganglion, becomes disorganized. His conclusion from these experiments, which have been varied in different ways, is " that the spinal ganglion is the centre of the nutritive power of the nerve-fibres adherent to it." From other experiments, he concluded that the anterior spinal roots derive their nutritive influence from the spinal cord ; and he has little doubt *' that every nerve-fibre is in connexion with a nerve-cell, which exerts over it a peculiar influence which enables it to retain its structure," &c. He does not think it proved, however, that all ganglia exert an influence both in a cen- tral and peripheral direction like those of the posterior spinal roots, and indeed experiments have shown that certain ganglia, such as the superior cervical of the sympathetic, exert their sustaining power on the nerve-fibres connected with them, in one direction only. The investigation of the effects of section on the optic nerve, which forms the subject of the present communication, promised to yield interesting results on several grounds, and especially as calcu- lated to throw light on the relations of the fibres of the nerve to those of the opposite one in the optic chiasma or commissure, and on the question as to the manner in which they are connected with the brain. After some observations on the structure of the optic nerve, the author describes his experimental procedure. To see the nerve whilst operating, and thus be assured that the section was effected at the desired point, he began by dislocating the eyeball forwards from its socket, while the animal was under the influence of ether. This operation he found could be effected in the rabbit, by simply pressing the eyelids widely apart, and was unattended with any serious disturbance of the functions of the organ. In dogs the operation is more difficult, and occasions more injurious effects. When the eye is dislocated, its axis is inclined downwards and in- wards, and the optic nerve can be reached without difficulty ; so that it may readily be cut at any desirable distance behind its place of entrance into the eyeball, and may even by moderate traction be broken off immediately before the chiasma. Geological Society. 140 After stating various observations which he made on the dislocated eye, the author gives an account of the effects which resulted from section of the optic nerve. The condition of the retina after the operation, was studied during the life of the animal by means of the ophthalmoscope ; and, after death, its structure, as well as that of the optic nerve before and behind the place of section, the chiasma, the optic tracts, and connected part of the brain, was examined with the microscope. The elements of the retina, as well as those of Jacob's membrane, were found unaltered fotir months after the time of section. The distal part of the optic nerve (that left in connexion with the eye- ball), examined after the lapse of a month in one case, and of two months in another, was also discovered to be unaltered. On the other hand, the part of the nerve behind or on the central side of the section was invariably disorganized. The section was usually performed on the optic nerve of the right eye, and the disorganized fibres of its central segment could be traced back to the left optic tract, through the chiasma, where they obviously decussated with the sound fibres of the opposite nerve. The right optic tract had undergone no change ; the fibres of the left tract were disorganized as far back as the quadrigeminate bodies, except those running along the posterior or inner border of the tract *, which exception appears to the author to ilvour the opinion that fibres pass along the tracts and commissures from the quadrigeminate bodies of one side to those of the other side, without connecting themselves with the retina. On the other hand, the results of his experiments do not seem to him to countenance the notion of fibres running in the optic nerves from one retina to the other without connexion with the brain, nor the generally received doctrine that part of the fibres of the optic nerve are continuous with the optic tract of the same side ; on the contrary, the whole fibres of the nerve would seem to undergo decus- sation. The microscopic characters of the atrophied and disorganized nervous substance are described in the paper ; they were found to differ somewhat in the part of the nerve before and that behind the chiasma, owing no doubt to the different structure of these parts in the sound state. The changes produced in the geniculate and quadrigeminal bodies will be communicated in the succeeding part of the paper. ^ GEOLOGICAL SOCIETY. [Continued from p. 73.] June 18, 1856. — Special General Meeting. — Sir C. Lyell, Vice- President, in the Chair. It having been announced from the Chair that, in consequence of the lamented decease of Daniel Sharpe, Esq., the late President, the Meeting was called to elect a President and a Member of Council, the Meeting proceeded to ballot and unanimously elected Col. Port- lock, R.E., to the Office of President, and Hugh Fakoner, M.D., F.R.S., as a Member of Council. 150 Geological Society : — Ordinary Meeting, — Col. Portlock, President, in the Chair. The following communications were read : — 1. " Note on a Section of Mont Lacha near Mont Blanc." By Major S. Charters, F.G.S. In a letter to Dr. Fitton, the author enclosed a section of the anthraciferous schist of M. Lacha (containing Ammonites and Belemnites), that he had taken during a tour five years ago, and which shows the strata dipping northward at an angle of 75° ; whilst the lines of cleavage are perpendicular to the stratification. At first sight, says the author, the cleavage-planes might easily have been mis- teiken for stratification, but the strata are evident on careful obser- vation, and do not dip towards or under Mont Blanc, but their dip is normal, supposing Mont Blanc to be the centre of upheaval. 2. " Notice of the late Eruption of Manna Loa, Owhyhee." By W. Miller, Esq., H.M. Consul, Sandwich Islands. (Forwarded from the Foreign Office by order of Lord Clarendon.) In a letter dated January 9, 1856, Mr. Miller stated that the lava- stream originating in the eruption which broke out in August last, continued flowing to the date of his letter, at which time it appeared to have been arrested in the forest at a distance of about ten miles from Hilo. In a later communication, dated March 1, 1856, Mr. Miller describes the lava- stream as being sixty miles in length, and as having now reached within five or six miles of Hilo. There still intervenes about three miles' width of dense forest between it and the open ground towards Hilo, Byron's Bay. It has burnt its way through the forest at the rate of about one mile in two weeks. 3. "On the Geology of Varna and Neighbourhood, Bulgaria." By Capt. Spratt, R.N., F.G.S. Capt. Spratt first noticed a series of whitish calcareous sandstones and marls, nearly 1000 feet thick, overlaid by reddish sands and marls. The former are of marine origin and of Eocene tertiary date ; the latter are chiefly of freshwater origin. Near Varna the freshwater beds have been much denuded, and are not anywhere more than 200 feet thick. At Cape Aspro, fifteen miles south of Varna, both of the series — the grej' and the red deposits — are seen disturbed, and dipping to the south, but unconformably, one series (the lower) having an angle of 30°, whilst the upper dips at 20°. At Cape Emineh, south of Cape Aspro, and forming the termination of the Balkan, these beds are still more disturbed and dip to the north. Capt. Spratt then described the geological appearances along the coast southward. At the Gulf of Bourgas and in the vicinity are igneous rocks, and deposits formed from their waste. Granite occurs on the southern point of the bay. Returning to Varna, Capt. Spratt pointed out the localities of the fossils collected in the neighbourhood. The calcareous sandstones abound in casts of shells and in Oysters and Pectens immediately around Varna ; and contain Nummulites in profusion at the upper part of the Lake near AUahdyn. In this last-named neighbourhood the uppermost strata, left by the denuding agencies that have afi'ecte^ Captain Spratt on the Geology of Varna, 151 the district, are more durable than the underlying marls, &c., and have a thickness of about 20 or 30 feet. They consist of a stony mass of Nummulites, Operculince, and Orbit oides, With. Pectines, Tere- hratulce, and Ostrcdce. This harder portion of the superficial rock has become apparently weather-worn into vertical pillars, either isolated or still connected above by an horizontal layer of hard rock which has resisted the destructive action of the weather. Capt. Spratt observed that in some places in the vicinity the surface-rock was split by vertical cracks, so as to resemble an open pavement. These fissures, operated upon by atmospheric agencies, illustrate, in the author's opinion, the method in which the columnar fragments above alluded to, and other masses more or less spherical, remaining on the land, must have originated. The Nummulites contained in the dis- integrating rock have not been destroyed, but remain intact, lying about in heaps around the remaining nodules of limestone. Capt. Spratt referred to the possibility of this columnar state of the hard rock of the upper marine series having been brought about, during the period which intervened between the deposition of the marine series and that of the freshwater beds overlying the marine series in the neighbourhood, by means of water- action ; as it is possible that the columnar surface of the degraded eocene beds may have been covered up by the later deposits, and subsequently re- excavated. This opinion seems to be supported by the fact of columns occurring in a part of the Bay of Varna, at about 5 fathoms depth. But Capt. Spratt leans to the opinion that the columnar degradation is atmospheric, modern, and in actual progress. Capt. Spratt then described the geology of the coast north of Varna. The Eocene deposits (yellowish limestone and sandy marls) occur as far nearly as Mangalia. The reddish freshwater sands and marls then come in, overlying, and form generally the steppes of the Dobrudja. Land shells occur in some of the upper beds of this district. The author then dwelt on the points of correspondence between the rocks composing the termination of the Balkan with those of the Crimea, and of the steppes of the Dobrudja with the northern part of the Crimea. Capt. Spratt proceeded next to consider the age of the overlying red marls and sands ; and pointed out their resemblance to the fresh- water deposits on the northern shore of the Sea of Marmora, on the Macedonian coast, the northern end of Euboea, and the Locrian shore. In fact, almost all the Thracian peninsula is composed of freshwater deposits of brown and grey marls and sandstones, nearly horizontal and attaining about 500 feet of thickness, which appear to be contemporaneous with the upper pleiocene freshwater deposits on the western side of the Archipelago, in Eubcea and Macedonia, and in Rhodes, &c. on the south. The author concluded with a notice of a post-tertiary or recent marine deposit on the coast of the Dardanelles at a height of about 15 or 20 feet above the present sea-level. 4. " Notes on the Geology of Trinidad." By H. G. Bowen, Esq., F.G.S. The northern district of the Island of Trinidad, with the islands 152 Geological Society : — between it and the mainland, is composed of flagstones, slates, and schists, with quartz-veins and some dark- coloured intercalated lime- stone. These rocks are all apparently unfossiliferous ; the slates often abound with iron, and some of the quartz-veins are slightly auriferous. Stalactitic caves occur in the limestone of the Island of Gaspar Grande, and at Las Cuevas and Arouca. Alluvial beds of clay and gravel are extensive in this district, and are sometimes 60 feet thick. At Lateen Bay, in Chicachicare Island, a patch of aluminous clay-slate occurs, with seams of crystalline limestone. The soil of this northern district is fertile on the limestone, and barren on the slates. The slate-rocks appear to be the same as those of Venezuela, which overlie quartz-rock at Upata ; and rounded boulders of quartz-rock occur in the flagstones. In the south of the Island of Trinidad, red sandstone abounds, often ferruginous, and associated with clays which are often either bituminous or pyritous, and contain lignite and impressions of dico- tyledonous leaves. In the Erin district the clay-beds have been sometimes indurated and jasperized by heat. They affbrd also small chalybeate and sulphuretted hydrogen springs, and in the blue-clay formation are found hillocks throwing up mud and water, and ponds covered by a film of mineral tar. The mud-volcanoes throw up saline water and greyish mud, in a cold state, with iron-pyrites and water- worn pebbles of blue limestone like that of the northern part of the Island, and sometimes of sandstone. They do not appear to be connected with the sea ; and are most active at the close of the rainy season. At Moruga small hills of granular limestone occur, llie succession of deposits in this southern part of Trinidad appears to be — beginning from below — 1. Sandstone, variegated sands, lignitiferous clays (sometimes jasperized), and the Moruga lime- stone ; 2. Blue and brown clays, with bitumen; comprising the pitch-lakes, salt and alum springs, &c. ; 3. Modern marine sand foimation, from 50 to 100 feet thick ; and alluvial deposits, seldom more than 30 feet thick. The eastern coast of Trinidad appears to consist of the red sand- stones and bituminous clays as far north as Matura, beyond which the clay- slates set in. The western coast of the island, south of Port of Spain, which is built of the slate-rocks and limestone, exhibits only modern alluvial deposits, sometimes calcareous, frequently ferruginous, and resting towards the south on the red sandstone of the southern district. 5. "On the fossils found in the Chalk-flints and Greensand of Aberdeenshire." By J. W. Salter, Esq., F.G.S., and W. Baily, Esq. A notice of the occurrence of chalk-flints and greensand in Aber- deenshire has been published by W. Ferguson, Esq., F.G.S. in the Proceed. Glasgow Phil. Soc. vol. iii. p. 33, and the Phil. Mag. 1850. p. 430, and some of the facts had been previously noticed ; but no lists of the fossils had been given. This communication showed the presence of characteristic Upper Greensand fossils in the low ground at Moreseat : Thetis minor, Area carinata, Pinna tetragona, and Galerites castanea. The Lima elegans of Nilsson is a new fossil for Britain, and is found with the ordinary Inocerami and Echinites Mr. Prestwich on the Middle Eocene Tertiaries. 153 of the Chalk in the rolled flints which form terraces round the hills in Aberdeenshire. The probable continuity, therefore, of these beds with those of the south of Sweden, where the same order of suc- cession prevails, is inferred ; the extension of the Upper Greensand so far north is a point of much interest. The Antrim beds are pro- bably Lower Greensand only : at least their age is doubtful. 6. ** On the Correlation of the Middle Eocene Tertiaries of England, France, and Belgium." By J. Prestwich, Esq., F.R.S., Treas. G.S. In a former paper the author had shown the correlation of the strata beneath the Bracklesham series in England, the Calcaire grossier and Lits Coquilliers in France, and the Upper Ypresiau system in Belgium, and which he had proposed to designate as the " London 7 ertiary Group," from the circumstance of these strata at- taining the largest and most distinct development in the English area. In the present paper Mr. Prestwich entered into an account of the structures of the deposits next above. In France this is the Calcaire grossier, which the French geologists have divided into four stages : — 1. a lower one of green sands, with few fossils ; 2. a middle one, of a calcareous freestone, abounding in marine organic remains (Grignon, Courtagnon, and other celebrated localities being in beds of this zone) ; 3. an upper division, of harder and more flaggy cal- careous rock, rich in Miliolites and Cerithium, mixed with a few fresh- water shells and the remains of plants and land animals ; and 4. a series of white and light green marls, apparently of freshwater origin. Each division attains at places a thickness of 30 to 40 feet, but the lower ones are thickest in the centre and west of the Paris basin ; whilst the upper ones, on the contrary, are thickest to the eastward. The total thickness of the deposit, therefore, rarely at any one place exceeds 100 feet, whilst the Upper Bracklesham series, with which it corresponds, is more than 500 feet thick. This diff'erence the author attributed to a more rapid subsidence of the English area than of the French at that geological period. This, he showed, was accom- panied by more marine conditions prevailing all through the English deposit, and by the continuance throughout of the same green sands which in France were confined to the lower division. That the whole series was, however, synchronous with the Calcaire grossier he considered proved by the circumstance, that, although the fresh- water beds which existed in France did not extend to this country, yet the organic remains of some of the beds of the Bracklesham series gave evidence of one upper division higher than the beds with the Venericardia planicosta and Cerithium giganteum of Bracklesham, for at the latter place the proportion of shells ranging up into the overlying Barton series was 30 to 100, whereas in some beds recently discovered by Mr. F. Edwards at Bramshaw, and apparently at the top of the Bracklesham series, the proportion is 46 to 100. The middle beds of the Bracklesham series show the closest affinity with the Middle Calcaire grossier, although there are only 140 species in common. The lowest division of this series is more fossiliferous in England than in France, showing a closer relation (43 to 100) 154 Geological Society, with the underlying beds than does the mass of the Calcaire grossier, in which the proportion is as 28 to 100. The total number of Molluscs in the Calcaire grossier of the Oise is 651, and in the Bracklesham series of Hampshire 368. Above this zone is the series of the Gr^s Moyen in France and Barton clays in England. Owing to the number of Calcaire gros- ser fossils which had been found at Barton, these beds had been considered synchronous with the Calcaire grossier, a view which the author himself had formerly adopted with reserve. Seeing, however, that the Bracklesham series probably represented all the divisions of the Calcaire grossier, and that the distinction between the Bracklesham and Barton series was of equal value to that between the Calcaire grossier and the Sables moyens, the author now correlated the Barton clays with the Sables moyens, as suggested by M. Graves, M. Dumont, Sir Charles Lyell, and M. Hebert. He, however, alluded to the difficulty of doing this upon the evidence of any small number of organic remains, or even of a few species con- sidered characteristic in one area ; and he showed that in the Barton clay itself, although there were many Gres moyen species (63), still there were a greater number of Calcaire grossier species (69). In the same way in the Laekenian system of Belgium, which overlaid the Bruxellian system (the equivalent of the Calcaire grossier), there are forty-five Calcaire grossier and Bracklesham sand species, and only forty-four Barton and Gres moyen species. But Mr. Prestwich showed that, taking the per-centage of species which range from the lower to the higher series, each area offered nearly an equal amount of distinction, as out of 100 species of the lower series there are in England 30, in France 35, and in Belgium 32, which range upwards. Mr. Prestwich mentioned that M. Graves had recognized several well-known Barton species, such as the Valuta depauperata, V. athleta, Oliva Branderi, Conus scabriusculuSy &c., in the Sables moyens of the Oise. The total known number of the Sables moyens species is 377, and of the Barton clays 252. These series the author proposed to term the " Paris Tertiary Group " (its lower part), as the several members of it were more complete in France than in England, and contained a richer and better- preserved fauna. This Paris group forms the great Nummulitic zone. Hitherto none of these Rhizopoda have been found in the London group. The author concluded with some general observations on the extent of the ancient seas and the position of the dry land, and took occasion to observe on the fact, that, although the several deposits in each country were so rich in organic remains, yet only a small proportion of them had hitherto been identified as com- mon to the several areas. Nevertheless the same genera prevailed, and the relative number of species of each genus was generally tolerably well maintained. He hoped, therefore, that Palaeontolo- gists would, in cases where there was now good reason to believe the strata to be synchronous, inquire into the extent of variation which the same species might undergo in areas where the sea had presented Intelligence and Miscellaneous Articles, 155 such diiFerent conditions of depth, mineral composition of sea-bottom, &c. A certain number of peculiar species must necessarily result from such different conditions, but the author considered it pro- bable that the same causfes would lead to the existence of such marked varieties as might, viewing each area separately and inde- pendently, cause some varieties to assume the permanence and importance of specific differences. Until the exact synchronism of any deposit is established, the Palaeontologist cannot always fully take these causes into consideration, and many admirable monographs on Tertiary fossils have necessarily been fouiinled, in a great measure, upon the differences actually app'arent, and persistent in the several areas. Mr. Prestwich stated that it was hi^ intention to continue this inquiry at a future period, and to examine into the correlation of the curious and interesting freshwater and fluviatile series overlying the Barton clay on the Hampshire coast and in the Isle of Wight. XXII. Intelligence and Miscellaneous Articles. ON THE HEAT ABSORBED IN CHEHICAL DECOMPOSITIONS. To the Editors of the Philosophical Maga-zitbe and Journal. Gentlemen, Manchester, July 4, 1856. IN your Number for this month, p. 74, Dr. Woods mis-states the results I arrived at fifteen years ago, and endeavours to support his own claims as an original discoverer by setting up one portion of my papers in contradiction to another. He says that when I caused the current to pass through an electrolyte, I did not find the same law to exist as when it passed through a metallic conductor. On the con- trary, he will find in my paper ^hil. Mag. Oct. 1841, pp. 270-274) the account of seven experiments, by which it was proved, that in an elec- trolytic cell the heat is evolved proportionally to the resistance to con- duction and the square of the current, — thesamelawwhichlhadshown to exist in the case of a metallic wire and in that of the cell of a bat- tery. Also at p. 275, he will see a general rule expressed as follows : — " When any voltaic arrangement, whether simple or compound, passes a current of electricity through any substance, whether an electrolyte or not, the total voltaic heat which is generated in any time is pro- portional to the number of atoms which are electrolyzed in each cell of the circuit, multi] liedby the virtual intensity of the battery." A foot-note to the word ' virtual ' explains its meaning by saying, that *' If a decomposing cell be in the circuit, the virtual intensity of the battery is reduced in proportion to its resistance to electrolyzation." I think that the meaning of the above proposition is sufficiently clear, but will nevertheless illustrate it by two examples. Suppose, first, we take a voltaic battery of 20 iron zinc pairs, and connect its ter- minals by a metallic wire. After a ceYtain interval of time, we find 100 atoms or chemical equivalents of zinc dissolved in each cell of 166 Intelligence and Miscellaneous Articles. the battery. Then the entire amount of heat evolved will be ex- pressed by 100X20= '2000. Suppose, secondly, we employ the same battery to decompose water ; the virtual intensity of the entire bat- tery circuit will then be 20— 3^=16f (seep. 272 of the above- named memoir) ; and when 100 atoms of zinc in each cell of the bat- tery have been dissolved, or what comes to the same thing, when 100 atoms of hydrogen have been liberated in the decomposing cell, the heat evolved by the entire circuit will be expressed by 100 X 16f = 1666. The difference between 2000 and 1666, or 334, represents of course the heat taken up in effecting the separation of 100 atoms of hydrogen from 100 atoms of oxygen, and liberating them in the gaseous state. In p. 276 it will be seen that I deduced the heat of combustion of hydrogen from the quantity of heat due to the intensity of battery required to electrolyze water. In other words, I found the heat of combustion of hydrogen by observing the heat lost in the voltaic cir- cuit when water was decomposed. My subsequent papers confirm and extend the facts arrived at in 1841, and indicate the effects of secondary actions in the battery, the laws which regulate the evolution of heat when positive metals, such as zinc, are employed as electrbdes evolving hydrogen, the mechanical value of chemical changes, &c. It is in giving a more defined expression to the law of the evolution of heat by combustion that Dr. Woods erroneously supposes I have contradicted myself. The passage he refers to (Phil. Mag. Dec. 1843, pp. 442, 443) sim- ply states " more explicitly, that it is not precisely the attraction of affinity, but rather the mechanical force expended by the atoms in falling towards one another, which determines the intensity of the current, and consequently the quantity of heat evolved." This mo- dification appeared to me necessary, inasmuch as, according to the mechanical theory of heat, the product of the attraction of particles into the distance they have to traverse in order to combine, rather than the attraction itself, is to be considered as the source of heat. If, therefore, my paper on the heat disengaged in chemical com- binations, sent to the French Academy in 1846, and published in the Philosophical Magazine, June 1852, were to go for nothing, my claim to priority would be completely established ; but I maintain, along with the most eminent scientific authorities, that a paper dates from the time that its receipt has been certified by a scientific body. My opinion is confirmed by the practice of the Royal Society and other learned bodies, who cause the date on which a paper comes to hand, as well as that on which it is read, to be duly certified. I may add, that Faraday has dated his * Experimental Researches ' from the time they were received by the Secretary of the Royal Society. My own paper was not only duly acknowledged in the Comptes Rendus for February 9, 1846, but was referred to a Commis- sion. It still remains in the possession of the Academy. I have the honour to remain. Gentlemen, Yours very respectfully, James P. Joule. Intelligence and Miscellaneous Articles. 157 CLEAVAGE OF COMPRESSED WHITE LEAD. 7 St. Mary's Road, Canonbury, My dear Tyndall, July 21, 1856. In an account of your lecture " On the Cleavage of Crystals and Slate Rocks" (Phil. Mag. vol. xii. p. 46), you have noticed my ex- perience in the consolidation of precipitated white lead, and have correctly stated the unfavourable results of my first attempts with conical moulds. It may be of interest to the readers of the Philo- sophical Magazine to learn that the difficulty was entirely overcome by substituting cylindrical moulds. By their employment the lateral spreading of the mass was prevented, and cakes of white lead were produced which broke with a conchoidal fracture, and which con- sequently could readily be ground to a granular powder. I am. Yours very truly, Warren De la Rue. ON THE BEHAVIOUR OF IODIDE OF SILVER TOWARDS AMMONIA, BY DR. A. VOGEL, JUN. The yellow precipitate furnished by iodide of potassium with ni- trate of silver, is not dissolved by ammonia, but acquires a paler colour therein. The author has found that this change of colour is owing to a combination of the iodide of silver with ammonia. — Buchner's Neues Repert. vol. v. p. 53. ELECTROLYTICAL INVESTIGATIONS. BY M. MAGNUS. It is well known that saline solutions do not follow the law of equivalent decomposition by the galvanic current, as established by Faraday, for Daniell found that they are decomposed in such a manner that, besides 1 equiv. of acid and base, 1 equiv. of hydrogen and oxygen are separated. Thus when a voltameter with dilute sulphuric acid is interposed in the circuit together with the saline solution, equal quantities of gas are evolved from both the saline solution and the voltameter ; but besides this, the salt is decomposed, and 1 equiv. of free acid is separated at the positive electrode, and 1 equiv. of free base at the negative. The decomposition in the saline solution is therefore twice as great as that in the voltameter. To explain this remarkable phsenomenon, or bring it into agree- ment with Faraday's law, Daniell found himself compelled to regard sulphate of soda, not as consisting of base and acid in accordance with the general view, but as composed of sodium with a compound of 1 atom of sulphur and 4 atoms of oxygen. He gave the name of oxysulphion to this compound, and was of opinion that all oxy salts have a similar composition ; so that sulphate of copper must be regarded as consisting of copper and oxysulphion, nitrate of potash. 158 Intelligence and Miscellaneous Articles. of potassium and oxynitrion, and so forth, an opinion which he has subsequently endeavoured to establish in a more comprehensive in- quiry published in conjunction with Professor Miller. Although this view agrees with that first put forward by Sir Humphry Davy regarding the composition of salts, and though much may be said in its favour upon purely chemical grounds, as has been done by Berzelius in the third volume of his Lehrbuch, yet many more reasons may be brought against it, as stated by Berzelius in the same place ; amongst which one of the principal is, that neither oxysulphion nor any of the analogous compounds has ytt been prepared. Almost all those who have occupied themselves with the decom- position of salts by the galvanic current since Daniell and Miller, have found themselves obliged to admit the correctness of Daniell's explanation. This is the case especially with Professor BuiF, in his memoir upon the Law of Electrolysis ; De la Rive in the recently published second part of his Traite d'electricite ; and E. Becquerel in his memoir Des lois qui prisident a '© decomposition electro- chimique des corps. Hittorff alone, in his investigation of the tra- velling of the ions, starts from a different explanation, which, how- ever, does not appear to get rid of the difficulties of the case. The author has, in the first plaee, repeated Daniell's experiments. He obtained the same general results ; but a full equiv. of acid and base was not always separated for 1 equiv. of oxygen, the former amounting only to between 60 and 80 per cent, of the equiv. of the oxygen. He then passed to the explanation of this apparently double decomposi- tion, and shows that for this purpose Daniell's supposition is unne- cessary. He is much more inclined to conclude from his experi- ments, that to separate a simple body from a compound the same force is always required, whether it is combined with only one simple body to form a binary, or with several bodies to form a saline com- pound. Starting from this point, it is not difficult to* prove that Faraday's law of equivalent decomposition is applicable not only to binary, but also to saline and all other inorgaitic compounds. Daniell, as appears from his reply tS the objections raised againsthim by Dr. Hare, found himself compelled to adopt his theory, especially because he could in no other way explain how the same current which bore the metal to the negative ele«rode should convey the oxygen and acid, and consequently two bodies in the opposite direction. But a transference, in the sense in which Daniell appears to have under- stood it, does not take place ; and it inay be shown, at least in cer- tain cases, that for I equiv. of m<^al or hydrogen which is set free at the negative electrode, 1 equiv^of acid and 1 equiv. of oxygen must be set free at the positive electrode. In order to mark these cases more decidedly, the author next occupied himself with the conditions under which the separation of a substance takes place from an electfolyte in which several sepa- rable substances ate present. He has found that the separation de- pends,— Meteorological Observations. 159 1 . On the density of the current ; 2. On the proportions in which the different substances exist in the fluid; 3. On the nature of the electrodes ; 4. On the greater or less facility with which one or the other sub- stance can be carried from stratum to stratum within the fluid, as well as on the obstacles which stand in the way of this transmission, either in the shape of porous walls or in any other form. — Bericht, der Akad. der Wiss. zu Berlin, 1856, p. 158. METEOROLOGICAL OBSERVATIONS FOR JUNE 1856. Chiswick. — June 1. Hazy: cloudy. 2,3. Very fine. 4. Very fine: cloudy: lightning at night. 5 — 7. Very fine. 8. Dull and cloudy. 9, 10, Very fine. 11. Cloudless. 12. Very fine: rain at night. 13. Rain. 14. Showery and boisterous. 15. Very fine : cloudy : clear and fine. 16. Very fine. 17. Showery. 18. Very fine : cloudy: rain. 19. Rain. 20. Showery. 21. Very fine : cloudy: rain. 22. Cloudy and fine. 23. Overcast. 24. Very fine : uniformly overcast. 25. Very fine. 26. Sultry. 27. Cloudless and hot. 28. Uniformly overcast: sultry : cold at night : range of temperature 45°. 29, 30. Clear and dry air. Mean temperature of the month 58''-65 Mean temperature of June 1855 57*98 Mean temperature of June for the last thirty years 60 '31 Average amount of rain in June 1*880 inch. Boston. — June 1. Cloudy: rain a.m. and p.m. 2 — 6. Fine. 7. Cloudy. 8 — 11. Fine. 12. Cloudy : rain p.m. 13, 14. Cloudy : rain a.m. and p.m. 15. Cloudy, 16. Fine. 17. Rain a.m. 18. Cloudy. 19. Cloudy: rain a.m. 20. Cloudy. 21. Fine : rain p.m. 22. Cloudy : rain a.m. and p.m. 23, 24. Cloudy. 25. Fine. 26. Cloudy : thermometer 86° p.m. 27. Fine : thunder p.m. 28. Cloudy. 29, Fine. 30. Rain a.m. and p.m. Sandwich Manse, Orkney. — June 1. Cloudy a.m. : drizzle p.m. 2. Drizzle a.m. : bright P.M. 3. Cloudy a.m. and p.m. 4. Cloudy a.m. : drops p.m. 5. Bright A.M. : cloudy p.m. 6. Cloudy a.m. and p.m. 7. Rain a.m. : bright p.m. 8. Clear A.M. and P.M. 9. Cloudy a.m. : drops, clear p.m. 10. Clear a.m. : showers p.m. 11. Rain a.m. and p.m. 12, 13. Bright a.m. : clear, fine p.m. 14. Cloudy a.m. : sleet-showers p.m. 15. Clear a.m. : cloudy p.m. 16. Showers a.m. : cloudy p.m. 17. Showers a.m. and p.m. 18. Bright a.m. : showers p.m. 19. Rain a.m. : bright P.M. 20. Cloudy a.m. : bright p.m. 21. Rain a.m. : bright p.m. 22. Bright A.M. and p.m. 23. Clear a.m. : cloudy p.m. 24. Fog a.m. : drizzle p.m. 25. Hazy a.m. : damp p.m. 26. Drops a.m. : rain, clear p.m. 27. Bright a.m. : damp p.m. 28. Damp a.m. : showers p.m. 29, 30. Clear a.m. : cloudy p.m. Mean temperature of June for previous twenty-nine years ... 52°'76 Mean temperature of this month 51 "47 Mean temperature of June 1855 52 -23 Average quantity of rain in June for previous sixteen years ... 2*24 inches. •uo)Ma •^aiiwniD •jiampmts •uo)8oa •lU'd I •3lDlA8Itl3 fe 6^ 6e >• «S f3 ^ 5: tt « « ^* Bt ^* I* 6f si te « &: ^ ^* g fe fe ^* 5^ a ^ ^ ft OS t*>o\«oo oxrtoo MOO O O O tot^*< rieo r>. t->.oo 0\t^ONrot<^t^Moooo ^ vnrt•»0•«*•T^»0TJ-w->^u-^w-^^J->l0•**0U^■^^Ti-T4-TJ■r^■<4-"->^0«0«/^•«t•• U1 O OO t^ T^t^^^vO0000 rt rtOO -^vo u^ O t^ ^J- on t^OO M lOOOO Ooovo OnO w-i «» vp vp p, O MOO 5^0p f^ ;^ J^^ vn t--v£) r0«0 *0 t--vp t-^ M t^OO OnOO OO 11 M OnOnOnOnO O 0>OnOnCnO\OnCnO\0\OnCnOnCnOnO\OnO OnOnOnOnOnO O •UI'B f8 •no^soa »i^ On t<^ ^ M vooo t<^ '^J-OO vO t^ fJ O O 00 t^VO to O\00 OO N ^ ^ tJ- tJ^OO OM O »OrOf<1f^00 mOO ON M O 00 ON t^ M On ON w-> ri- O OO •-• r^vo VO O "^ P> ^ O N lOOO On coOO CI On ■>4- w^vo rr) rooo On «0 VO t^ On p M It rj _M p p p 00 vn u-i On o 00 r-> •<*• iri ON ON O •-< m >h q O m On OS o» ON On b b b b b b b b on on on on b '^ o\ on on "o\ on b b b b b b b on « « f» e*^cotncnrococntOf« H c< f» com m m m m m rorocorororor^c* 00 M t^OO »<^ to M COOO rOVO O t^ONH COM u^tOM cooo »/^Ooo w t)-MVO r*- fo ON i-i o •* »^oo Or100vOrJr^t^O'*rlOc<- m r>.00 P M M rt n M M o p On t^ t^ M M On On^O On O On N m m _H m m rt m ON o^ b b b b b b b b b on *on 'on b b on on on on b on b b b b b b b b 2^ »2i 2"^ ^ »n\d t^oo CTv d M M •»}• >Ano t^OO On d M « o ro •4- «AvC> l*-00 ONO 1^ 1 THE LONDON, EDINBURGH and DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] SEPTEMBER 1856. XXIII. Further Researches on the Polarity of the Diamagnetic Force. By John Tyndall, F.R.S., Membre de la Societe Hollandaise des Sciences ; Foreign Member of the Physical Society of Berlin, and Professor of Natural Philosophy in the Royal Institution^. Introduction, A YEAR ago I placed before the Royal Society the results of an investigation " On the Nature of the Force by which Bodies are repelled from the Poles of a Magnet t*^^ The simul- taneous exhibition of attraction and repulsion in the case of magnetized iron is the fact on which the idea of the polarity of this substance is founded ; and it resulted from the investiga- tion referred to, that a corresponding duality of action was manifested by bismuth. In those experiments the bismuth was the moveable object upon which fixed magnets were caused to act, and from the deflection of the bismuth its polarity was inferred. But, inasmuch as the action is reciprocal, we ought also to obtain evidence of diamagnetic polarity by reversing the conditions of experiment; by making the magnet the mover able object, and inferring from its deflection the polarity of the mass which produces the deflection. This experiment would be complementary to those described in the communication referred to, and existing circumstances invested the experiment with a great degree of interest and importance. In fact an experiment similar to that here indicated was made by Professor W. Weber, previous to my investigation, and the * From the Philosophical Transactions for 1856, part i. ; having been received by the Royal Society November 27, 1855, and read December 20, 1855. t Philosophical Transactions, 1855; andPhil. Mag. for September 1855. Phil Mag. S. 4. Vol. 13. No. 78. Sept, 1856. M 162 Professor TyndalVs farthet' Researches result was such as to satisfy its author of the reverse polarity of diamagnctic bodies. I will not here enter into a minute descrip- tion of the instrument and mode of experiment by which this result was obtained ; for the instrument made use of in the pre- sent inquiry being simply a refinement of that made use of by M. Weber, its explanation will embrace the explanation of his apparatus. For the general comprehension of the criticisms to which M. Weber's resuHs have been subjected, it is necessary, however, to remark, that in his experiments, a bismuth bar, within a vertical spiral of copper wire, through which an electric current was transmitted, was caused to act upon a steel magnet freely suspended without the spiral. When the two ends of the bar of bismuth were permitted to act successively upon the sus pended magnet, a motion of the latter was observed, which in- dicated that the bismuth bar was polar, and that its polarity was the reverse of that of iron. Notwithstanding the acknowledged eminence of M. Weber as an experimenter, this result failed to produce general convic- tion. Mr. Faraday, in his paper " On the polar or other^ con- dition of diamagnetic bodies *,'' had shown that results quite similar to those obtained by M. Weber, in his first investigation with bismuth, were obtained in a greatly exalted degree, with gold, silver and copper; the eflfect being one of induction, and not one due to diamagnetic polarity. He by no means asserted that his results had the same origin as those obtained by M. Weber ; but as the latter philosopher had made no men- tion of the source of error which Mr. Faraday's experiments rendered manifest, it was natural to suppose that it had been overlooked, and the observed action attributed to a wrong cause. In an article published in his ' Massbestimmungen ' in 1852, M. Weber, however, with reference to this point, writes as follows : — ''J will remark that the article transferred from the Reports of the Society of Sciences of Saxony to PoggendorfF's Annalen was only a preliminary notice of my investigation, the special discussion of which was reserved for a subsequent communication. It will be sufficient to state here, that in the experiments referred to I sought to eliminate the inductive action by suitable combinations ; but it is certainly far better to set aside this action altogether, as has been done in the experi- ments described in the present memoir.'' One conviction grew and strengthened throughout these dis- cussions— this, namely, that in experiments on diamagnetic polarity great caution is required to separate the pure effects of diamagnetism from those of ordinary induction. With refer- * Experimental Researches, 2640, Philosophical Transactions, 1850 p. 171. on the Polarity of the Diamagnetic Force. 163 ence to even the most recent experiments of M. Weber — those to which he has referred at the conclusion of the above citation — it is strongly urged that there is no assurance that the sepa- ration referred to has been effected. In those experiments, as already stated, a cylinder of bismuth was suspended within a vertical helix of covered copper wire, and the action of the cylinder upon a magnet suspended opposite to the centre or neutral point of the helix was observed. To increase the action, the position of the cylinder was changed at each termination of the minute swing of the magnet, the amplitude of the oscillations being thus increased, and the effect rendered more sensible to the eye. Now, it is urged, there is every reason to believe that in these motions of a metallic mass within an excited helix' induced currents will be developed, which, acting upon the magnet, will produce the motions observed. The failure indeed to demonstrate the existence of diamagnetic polarity by other means has, in the case of some investigators, converted this belief into a certainty. Among the number whom M. Weber^s experiments have failed to convince, M. Matteucci occupies a prominent place. With reference to the question before us this philosopher writes as follows*:— "In reading the description of the experiments of M. Weber, we are struck on beholding the effects produced by moving the bismuth when there is no current in the spiral. Although the direction of oscillation in this latter case is opposed to that observed when the spiral is active, still the fact excites doubts as to the truth of the conclusions which have been drawn from these experiments f- To deduce rigorously the demonstra- tion of diamagnetic polarity, it would he necessary to substitute for the bismuth, masses formed of insulated fragments of the metal X, to vary the dimensions of the cylinder, and above all, to compare the effects thus obtained with those which would probably be obtained with cylinders of copper and silver in a state of purity. " We are obliged to make the same remarks on another series of experiments which this physicist has made to obtain anew, by the effects of induction, the proof of diamagnetic polarity. * Cours Special sur V Induction, p. 206. t It is not ray place to account for the effect here referred to. I may however remark, that there appears to be no difficulty in referring it to the ordinary action of a diamagnetic body upon a magnet. It is the result which Brugmann published upwards of half a century ago ; the peculiar form of this result in one of the series of experiments quoted by M. Weber must, I think, be regarded as purely accidental. — J. T. X Also in page 201 : — " II fallait done, pour prouver si I'influence d'un corps diamagnetique produit sur un aimant une variation de sens contraire h. celle developpee dans le fer doux, operer avec ce corps prive de conduc- tihilite." M2 164 Professor TyndalPs further Researches It is astonishing, that after having sought to neutralize the development of induced currents in the moving cylinders of' bismuth, by means of a very ingenious disposition of the spiral — it is astonishing, I repeat, that no attempt was made to prove by preliminary essays with metals possessing a higher conducti- bility than bismuth, that the same end could be obtamed. I cannot leave you ignorant that the doubts which I have ventured to advance against the experiments of M. Weber are supported by the negative result which I have obtained in endeavouiing to excite diamagnetic polarity in bismuth by the discharge of the . Leyden jar/' It will be seen in the following pages that the conditions laid down by M. Matteucci for the rigorous demonstration of diamag- netic polarity are more than fulfilled. The conclusions of M. Weber find a still more strenuous opponent in his countryman Professor v. Feilitzsch, who has repeated Weber's experiments, obtained his results, but who denies the validity of his inferences. M. v. Feilitzsch argues, that in the experiments referred to it is impossible to shut out ordinary induction, and for the rigorous proof of diamagnetic polarity proposes the following conditions*. "To render the experiment free from the action of induced currents two ways are open. The currents can be so guided that they shall mutually neutralize each other's action upon the magnet, or the induced currents can be completely got rid of by using, instead of a dia- magnetic conductor, a diamagnetic insulator.'^ To test the ques- tion, M. V. Feilitzsch resorted to the latter method : instead of cylinders of bismuth he made use of cylinders of wax, and also of a prism of heavy glass, but in neither case was he able to detect the slightest action upon the magnet. "However the motions of the prism might be varied, it was not possible either to cause the motionless magnet to oscillate, or to bring the magnet from a state of oscillation to one of rest." M. v. Fei- litzsch pushes his experiments further, and finds that when the bismuth is motionless within its spiral, the position of the mag- net is just the same as when the bismuth is entirely withdrawn ; hence his final conclusion, that the deflection of the magnet in Weber's experiments is due to induced currents, which are ex- cited in the bismuth by its mechanical motion up and down within the spiral. These divergent opinions upon a question of such vital bearing upon the general theoiy of magnetic phsenomena, naturally ex- cited in me the desire to make myself acquainted with the exact value of M. Weber's experiments. The most direct way of accomplishing this I consider to be, to operate with an instru- * Poggendorflf's Annalm, xcii. 377. on the Polarity of the Diamagnetic Force, 165 ment similar to that made use of by Weber himself; I therefore resolved to write to the constructor of his apparatus, but pre- vious to doing so the thought occurred to me of writing to M. Weber, to inquire whether his further reflections on the subject had suggested to him any desirable modification of his first instrument. In reply to my question, he undertook to devise for me an apparatus, surpassing in delicacy any hitherto made use of. The design of M. Weber was ably carried out by M. Leyser of Leipzig ; and with the instrument thus placed in my possession, I have been able, not only to verify the experi- ments of M. Weber, but to satisfy the severest conditions pro- posed by those who saw in the results of these experiments the efifects of ordinary induction. Description of Apparatus. A sketch of the instrument made use of in the present inves- tigation is given in fig. 2. BO, B'O' is the outline of a rectan- gular box, the front of which is removed so as to show the appa- ratus within. The back of the box is prolonged, and terminates in two semicircular projections, which haye apertures at H and H'. Stout bolts of brass, which have been made fast in solid masonry, pass through these apertures, and the instrument, being secured to the bolts by screws and washers, is supported in a vertical position, being free from all disturbance save such as affects the foundations of the Royal Institution. All the arrangements presented to the eye in fig. 2 are made fast to the back of the •box, but are unconnected with the front, so as to permit of the removal of the latter. WW are two boxwood wheels with grooved peripheries, which permit of motion being transferred from one wheel to the other by means of a string ss'. Attached to this string are two cylinders, mn, opy of the body to be exa- mined : in some cases the cylinders are perforated longitudinally, the string passes through the perforation, and the cylinders are supported by knots on the string. HE, H'E' are two helices of copper wire overspun with silk, and wound round two brass reels, the upper ends of which protrude from H to G, and from H' to G'. The internal diameter of each helix is 0*8 of an inch, and its external diameter about 1*3 inch; the length from H to E is 19 inches, and the centres of the helices are 4 inches apart; the diameters of the wheels WW being also 4 inches. The cross bar GG' is of brass, and through its centre passes the screw R, from which depends a number of silk fibres which support an astatic arrangement of two magnets, the front one of which, SN, is shown in the figure. An enlarged section of the instrument through the system of magnets is shown in fig, 4. The magnets 166 Professor TyndalPs further Researches are connected by a brass cross-piece, in which is the point of suspension P ; and the position of the helices is shown to be between the magnets. It will be seen that the astatic system is a horizontal one, and not vertical, as in the ordinary galvano- meter. The black circle in front of the magnet SN, fig. 2, is a mirror, which is shown in section at M, fig. 4 ; to balance the weight of this mirror, and adjust the magnets in a horizontal posi- Fig.l. Fig. 2. Fig. 3. I4|jM|^I il Fig. 4. w iS' 13^ tion, a brass washer, W, is caused to move along a screw, until a point is attained at which its weight has brought both the magnets into the same horizontal plane. There is also another adjustment, which permits of the magnets being brought closer together or separated more widely asunder. The motions of the compound on the Polarity of the Diamagnetic Force, 167 magnet are observed by means of a distant scale and telescope, according to the method applied to the magnetometer of Gauss. The rectangle da, did, fig. 2, is the outline of a copper damper, which, owing to the currents induced in it by the motion of the magnet, soon brings the latter to rest, and thus expedites ex- periment. It is well known that one end of a magnet attracts, while the other end repels the same pole of a magnetic needle ; and that between both there is a neutral point which neither attracts nor repels. The same is the case with the helices HE, H'E' ; so that when a current is sent through them, if the astatic magnet be exactly opposite the neutral point, it is unaffected by the helices. This is scarcely attainable in practice ; a slight residual action remains which draws the magnets against the helices ; but this is very easily neutralized by disposing an external portion of the circuit so as to act upon the magnets in a direction opposed to that of the residual action. Here then we have a pair of spirals which, when excited, do not act upon the magnets, and which therefore permit us to examine the pure action of any body capable of magnetic excitement placed within them. In the experiments to be described, it was always arranged that the current flowed in opposite directions through the two spirals ; so that if the bodies within them were polar, the two upper ends of these bodies should be poles of opposite names, and consequently the two lower ends opposed also. Supposing now our two cylinders to occupy the central position indicated in fig. 2 : even if the cylinders became polar through the action of the surrounding current, the magnets, being oppo- site to the neutral points of the cylinders, would experience no action from the latter. But suppose the wheel W' to be so turned that the two cylinders are brought into the position shown in fig. 1, the upper end o of ojo and the lower end n of mn will act simultaneously upon the suspended magnets. For the sake of illustration, let us suppose the ends o and n to be both north poles, and that the section, fig. 4, is taken when the bars are in the position shown in fig. 1. The right-hand pole 0 will attract S' and repel N, which attraction and repulsion sum themselves together to produce a deflection of the system of magnets. On the other hand, the left-hand pole n, being also north, will attract S and repel N', which two effects also sum themselves to produce a deflection in the same direction as the former two. Hence, not only is the action of terrestrial mag- netism annulled by this arrangement, but the moving force due to the reciprocal action of the magnets and the bodies within the helices is increased fourfold. By turning the wheel in the other direction, we bring the cylinders into the position shown in 168 Professor TyndalVs further Researches fig. 8, and thus may study the action of the ends m and p upon the magnets. By means of the screw R the magnets can be raised or lowered ; and at the end, t, of the screw is a small torsion circle which can be turned independently of the screw ; by means of the latter the suspending fibre can be twisted or untwisted with- out altering the level of the magnets. The front of the box is attached by means of brass hasps, and opposite to the mirror M a small plate of glass is introduced, through which the mirror is observed ; the magnets within the box being thus effectually protected from the disturbances of the external air. A small handle to turn the wheel W accompanied the instrument from its maker ; but in the experiments, I used, instead of it, a key attached to the end of a rod 10 feet long; with this rod in my right hand, and the telescope and scale before me, the experiments were completely under my own con- trol. Finally, the course of the cuiTcnt through the helices was as follows : — Proceeding from the platinum pole of the battery it entered the box along the wire w, fig. 2, which passed through the bottom of the latter ; thence through the helix to H', return- ing to E'; thence to the second helix, returning to E, from which it passed along the wire w' to the zinc pole of the battery. A commutator was introduced in the circuit, so that the direc- tion of the current thus indicated could be reversed at pleasure. Experiments. — Deportment of Diamagnetic Bodies. A pair of cylinders of chemically pure bismuth, 3 inches long and 0*7 of an inch in diameter, accompanied the instrument from Germany. These were first tested, commencing with a battery of one cell of Grove. Matters being as sketched in fig 2, when the current circulated in the helices and the magnet had come to rest, the cross wire of the telescope cut the number 482 on the scale. Turning the wheel W so as to bring the cylinders into the position fig. 1, the magnet moved promptly, and after some oscillations took up a new position of equilibrium; the cross wire of the telescope then cut the figure 468 on the scale. Reversing the motion so as to place the cylinders again central, the former position 482 was assumed ; and on turning further in the same direction, so as to place the cylinders as in fig. 3, the position of equilibrium of the magnet was at the number 493. Hence by bringing the two ends n and o to bear upon the astatic magnet, the motion was from greater to smaller numbers, the position of rest being then fourteen divisions less than when the bars were central. By bringing the ends m and p to bear upon the magnet, the motion was from smaller to greater numbers, on the Polarity of the Biamagnetic Force. 169 the position of rest being eleven divisions more than when the bars were central. As the positions here referred to will be the subject of frequent reference, for the sake of convenience I will call the position of the cylinders sketched in fig. 1, Position 1 ; that sketched in fig. 2, Position 2 ; and that sketched in fig. 3, Position 3. The re- sults which we have just described, tabulated with reference to these terms, would then stand thus : — I. Bismuth cylinders. Length 3 inches. Diameter 0*7. Position 1. 468 Position 2. 482 Position 3. 493 In changing therefore from position 1 to position 3, a deflection corresponding to twenty-five divisions of the scale was produced. Wishing to place myself beyond the possibility of illusion as regards the fact of deflection, I repeated the experiment with successive batteries of two, three and four cells. The following are the results : — II. 2 cells. 3 cells. 4 cells, Position 1. 450 439 425 Position 2. 462 450 437 Position 3. 473 462 448 In all the cases cited we observe the same result. From posi- tion 2 to position 1 the motion is from larger to smaller num- bers; while from position 2 to position 3 the motion is from smaller to larger numbers. It may at first sight appear strange that the amount of the deflection did not increase with the battery power ; the reason, in part, is that the magnet, when the current circulated, was held in a position free from the spirals, by forces emanating partly from the latter and partly from a portion of the external circuit. When the current increased, the magnetization of the bismuth in- creased also, but so did the force which held the magnets in their position of equiUbrium. To remove them from this position, a greater amount of force was necessary than when only the resi- dual action of a feeble current held them there. This fact, cou- pled with the circumstance that less heat was developed, and less disturbance caused by air currents, when a feeble battery was used, induced me for some time to experiment with a battery of two cells. Subsequent experience however enabled me to change this for five cells with advantage. Notwithstanding the improbability of the argument, still it may be urged that these experiments do not prove beyond a 170 Professor TyndsWs further Researches doubt that the bismutli cylinders produce the motion of the mag- nets in virtue of their excitement by the voltaic current ; for it is not certain that these cylinders would not produce the same motion wholly independent of the current. Something of this kind has occurred to M. Leyser * in his experiments, and why not here ? In answer to this, I reply, that if the case be as here suggested, the motion of the magnet will not be changed when the cun'ent surrounding the bismuth cylinders flows in the opposite direction. Here is the experiment. III. Position 1. 761 Position 2. 742 Position 3. 701 We observe here that in passing from position 2 to position 1 the motion is from smaller to larger numbers ; while in passing from position 2 to position 3 the motion is from larger to smaller numbers. This is the opposite result to that obtained when the current flowed in the opposite direction ; and it proves that the polarity of the bismuth cylinders depends upon the direction of the current, changing as the latter changes. It was pleasant to observe the prompt and steady march of the magnet as the cylin- ders were shifted in the helices. When the magnets, operated on by the bars of bismuth, were moving in any direction, by bringing the two opposite ends of the bismuth bars into action, the motion could be promptly checked; the magnets could be brought to rest, or their movement converted into one in the opposite direction. I may add to the above a series of results obtained some days subsequently in the presence of Professors Faraday, De la Rive and Marcet. IV. Bismuth cylinders. Position 1. 670 Position 2. 650 Position 3. 630 The difference between positions 1 and 3 amounts here to forty divisions of the scale; subsequent experience enabled me to make it still greater. It was found by experiment, that when the motion was from lower to higher numbers it denoted that the poles NN', fig. 4, were repelled from the spirals, and the poles SS' attracted towards them. When, on the contrary, the motion was from larger to smaller numbers, it indicated that the poles NN' were attracted and the poles SS' repelled. In the position fig. 1, therefore, of Tables III. and IV. the poles NN' were repelled by the ends no of the' bismuth cyhnders, and the poles SS' attracted ; while in * Scientific Memoirs, New Series, vol. i. page 184. on the Polarity of the Diamagnetic Force. 171 the position fig. 3, the poles NN' were attracted by the ends MP, and the poles SS' repelled ; the ends n and o, therefore, acted as two north poles, while the ends m and p acted as two south poles. Now the direction of the current in the experiments re- corded in the two tables referred to was that shown by the arrows in fig. 4. Standing in front of the instrument, the direction in the adjacent face of the spiral H'E' was from right to left, while it was from left to right in HE. From this we may infer that the polarity of the bismuth cylinders was the reverse of that which would be excited in cylinders of iron under the same cir- cumstances. The assertion however shall be transferred from the domain of deduction to that of fact before we conclude. Let us now urge against these experiments all that ever has been urged by the opponents of diamagnetic polarity. The bis- muth cylinders are metallic conductors, and in moving them through the spirals induced currents more or less powerful may be excited in these conductors. The motion observed may not, after all, be due to diamagnetic polarity, but to the currents thus excited. I reply, that in all cases the number set down marks the permanent position of rest of the magnets. Were the action due to induced currents, these currents, being momentary, could only impart a shock to the magnets, which, on the disappearance of the currents, would return to their original position. But the deflection is permanent, and is therefore due to an enduring cause. In his paper on " Supposed Diamagnetic Polarity,^^ Mr. Earaday rightly observes, — " If the polarity exists, it must be in the par- ticles, and for the time permanent, and therefore distinguishable from the momentary polarity of the mass due to induced tempo- rary currents, and it must also be distinguishable from ordinary magnetic polarity by its contrary direction.^^ These are the precise characteristics of the force made manifest by the experi- ments now under consideration. Further, the strength of induced currents depends on the con- ducting power of the mass in which they are formed. Express- ing the conducting power of bismuth by the number 1'8, that of copper would be expressed by 73' 6*, the conductivity of the latter being therefore forty times that of the former. Hence the demand made by the opponents of diamagnetic polarity, to have the experiments repeated with cylinders of copper ; for if the eff'ect be due to induced currents, they will show themselves in copper in a greatly increased degree. The following is the result of a series of experiments made with two copper cylinders, of the same dimensions as the bismuth ones already described. * Philosophical Magazine, Series 4, vol. vii. p. 37. 172 Professor TyndalFs further Researches V. Cylinders of Copper. Position 1. 754 Position 2. 754 Position 3. 755 Now if the effects obtained with bismuth were due to induced currents, we should have the same effects forty times multiplied in the case of copper, in place of which we have scarcely any sensible effect at all. Bismuth is the only substance which has hitherto produced an action in experiments of this nature; another illustration, however, is furnished by the metal antimony, which possesses a greater conductive power, but a less diamagnetic power than bismuth. The following results were obtained with this sub- stance : — VI. Cylinders of Antimony. Length 3 inches. Diameter 0*7. Current direct* . Current reversed f. Position 1. 693 244 Position 2. 688 252 Position 3. 683 261 On comparing these numbers with those already obtained with bismuth, we observe that for like positions the actions of both metals are alike in direction. We further observe that the results are determined, not by the relative conductive powers of the two metals, but by their relative diamagnetic powers. If the former were the determining cause, we should have greater deflections than with the bismuth, which is not the case ; if the latter, we should have less deflections, which is the case. The third and severest condition proposed by those who object to the experiments of M. Weber is to substitute insulators for conductors. T call this condition severe for the following rea- sons : — according to the experiments of Faraday J, when bismuth and sulphur are submitted to the same magnetic force, the re- pulsion of the former being expressed by the number 1968, that of the latter will be expressed by 118. Hence an action which, with the means hitherto used, was difficult of detection in the case of bismuth, must wholly escape observation in the case of sulphur, the intensity of whose excitement is nearly twenty times less. The same remarks apply, in a great measure, to all other insulators. But the admirable apparatus made use of in this investigation has enabled me to satisfy this condition also. To Mr. Faraday • As in III. and IV. t As in I. and II. % PhU. Mag. March 1853, p. 222. on the Polarity of the Diamagnetic Force, 173 I am indebted for the loan of two prisms of the self-same heavy glass with which he made the discovery of diamagnetism. The bismuth cylinders were withdrawn from the helices and the prisms of glass put in their places. It was now necessary to have a perfectly steady magnet, the expected result being so small as to be readily masked by, or confounded with, a motion arising from some extraneous disturbance. The feeble warmth developed in the helices by a current from two cells I found able to create air currents of sufficient power to defeat all attempts to obtain the pure action of the prisms. To break up these currents I stuffed all unfilled spaces of the box with old newspapers, and found the expedient to answer perfectly. With a fresh battery, which delivered a constant stream throughout the duration of an expe- riment, the magnet was admirably steady*, and under these favourable conditions the following results were obtained : — VII. Prisms of Heavy Glass. Length 3 inches. Width 0'6. Depth 0*5. Current direct. Current direct. Current direct. Position 1. 664 Position 2. 662 Position 3. 660 Thus in passing from position 1 to 3, or vice versa, a permanent deflection corresponding to four divisions of the scale was pro- duced. By raising or lowering the respective prisms at the proper moments the amplitude of the oscillations could be con- siderably augmented, and when at a maximum, could be speedily extinguished by reversing the motions of the prisms. In six different series of experiments made with this substance the same invariable result was obtained. It will be observed that the deflections are in all cases in the same direction as those pro- duced by bismuth under the same circumstances. The following results were afterwards obtained with the same prisms in the presence of M. De la Rive; the current was "direct.'^ VIII. Position 1. 652 Position 2. 650 Position 3. 648 On the negative result arrived at with this substance, it will be remembered that M. v. Feilitzsch bases one of his arguments against the conclusions of M. Weber. Calcareous spar was next submitted to experiment. Two cy- linders of the transparent crystal were prepared and examined in the manner already described. The results are as follows : — * It was necessary however to select a portion of the day when Albe- marle Street was free from cabs and carriages, as the shaking of the entire building, by the rolling of these vehicles, rendered the magnets unsteady. 174 Professor TyndalVs further Researclies IX. Cylinders of Calcareous Spar. Length 3 inches. Diameter 0*7. Current direct. Current direct. Current direct. Position 1. 699-5 Position 2. 698*5 Position 3. 697*5 Here, asin the other cases, the deflection was permanent, and could be augmented by the suitable raising or lowering of the respect- ive cylinders. The action is small, but perfectly certain. The magnet was steady and moved promptly and invariably in the directions indicated by the numbers. It will be observed that the deflections are the same in kind as those produced by bis- muth. The intrusion of other employments compelled me to post- pone the continuation of these experiments for several weeks. On taking up the subject again, my first care was to assure myself that the instrument retained its sensibility. Since the experiments last recorded it had been transported over several hundred miles of railway, and hence the possibility of a disturb- ance of its power. The following experiments, while they cor- roborate the former ones, show that the instrument retained its power and delicacy unimpaired : — X. Bismuth cylinders. Current direct. Current reversed. Position I. 612 264 Position 2. 572 230 Position 3. 526 200 The deflections, it will be observed, are the same in kind as before ; but by improved manipulation the effect is augmented. In passing from position 1 to 3 we have here a deflection amounting in one case to 64, and in the other to 86 divisions of the scale. To Mr. Noble I am indebted for two cylinders of pure sta- tuary marble; the examination of these gave the following results : — XI. Cylinders of Statuary Marble. Length 4 inches. Diameter 0*7. Current direct. Current reversed. Position 1. 601 215 Position 2. 598 218 Position 3. 596 220 Here, in passing from position 1 to 3, we have a permanent on the Polarity of the Biamagnetic Force. 175 deflection corresponding to five divisions of the scale. As in all other cases, the impulsion of the magnet might be augmented by changing the position of the cylinders at the limit of each swing. The deflections are the same in kind as those produced by bismuth, which ought to be the case, as marble is diamag- netic. An upright iron stove influenced by the earth's magnetism becomes a magnet with its bottom a north and its top a south pole. Doubtless, though in an immensely feebler degree, every erect marble statue is a true diamagnet, with its head a north pole and its feet a south pole. The same is certainly true of man as he stands upon the earth's surface, for all the tissues of the human body are diamagnetic. A pair of cylinders of phosphorus enclosed in thin glass tubes were next examined. XII. Cylinders of Phosphorus. Length 3*5 inches. Diameter 0*63. Current direct. Current reversed. Series I. Series II. Position 1. 620 670 224 Position 2. 618 668 226 Position 3. 616 666 228 The change of the bars from position 1 to 3 is in this case accompanied by permanent deflection corresponding to four divisions of the scale. The deflection indicates the polarity of diamagnetic bodies. The magnet wa§ remarkably steady during these experiments, and the consequent clearness and sharpness of the result pleasant to observe. Xlll. Cylinders of Sulphur. Length 6 inches. Diameter 0*7. Current direct. Current reversed. Position ] . 658-5 222 Position 2. 657 223*5 Position 3. 655*5 225-5 XIV. Cylinders of Nitre. Length 3*5 inches. Diameter 0*7. Current direct. Current reversed. Position 1. 648*5 263 Position 3. 647 265 176 Professor 'TyndalVB fiirt her Researches Finally, as regards solid diamagnetics, a series of experiments was made with wax ; this also being one of the substances whose negative deportment is urged by M. v. Feilitzsch against M. Weber. XV. Cylinders of Wax. Length 4 inches. Diameter 0*7. Current direct. CuiTent reversed. Position 1. 624-5 240 Position 3. 623 241 The action is very small, but it is nevertheless perfectly certain. The argument founded on the negative deportment of this sub- stance must therefore give way. When we consider the feeble- ness of the action with so delicate a means of examination, the failure of M. v. Feilitzsch to obtain the effect, with an instru- ment constructed by himself, will not excite surprise. Thus in the case of seven insulating bodies the existence of diamagnetic polarity has been proved ; the list might be aug- mented without difficulty ; but sufficient, I trust, has been done to remove the scruples of those who saw in M. Weber's results an action produced by induced currents. A portion of the subject hitherto untouched, but one of great interest, has reference to the polar condition of liquid bodies while under magnetic influence. The first liquid examined was distilled water ; it was enclosed in thin glass tubes, corked at the ends, and by means of a loop passing round the cork the tubes were attached to the string passing round the wheels WW'. Previous to use, the corks were carefully cleansed, so that any impurity contracted in cutting, or by contact with fer- ruginous matters, was completely removed. The following are the results obtained with this liquid : — XVI. Cylinders of Distilled Water. Length 4 inches. Diameter 0*65. Current direct. Current reversed. Position 1. 605 246 Position 2. 603 248 Position 3. 601 250 The experiment was many times repeated, but always with the same result ; indeed the polarity of the liquid mass is as safely established as that of iron. Pure water is diamagnetic, and the deflections produced by it are the same as those of all the other diamagnetic bodies submitted to examination. I on the Polarity of the Diamagnetic Force, 177 From the position which it occupies in Mr. Faraday's list*, I had also some hopes of proving the polarity of sulphide of car- bon. The following results were obtained : — XVIL Cylinders of Bisulphide of Carbon. Length 4 inches. Diameter 0*65. Current direct. Current reversed. Position 1. 631 210 Position 2. 629 213 Position 3. 626 216 As in the case of distilled water, we observe a deflection in one directien when the current is " direct '^ and in the other when it is " reversed/' the action in the first case, in passing from posi- tion 1 to 3, amounting to five, and in the latter case to six divi- sions of the scale. The polarity exhibited is that of diamagnetic bodies. Deportment of Magnetic Bodies. Thus far we have confined our examination to diamagnetic substances ; turn we now to the deportment of magnetic bodies when submitted to the same conditions of experiment. Here we must select the substances suitable for examination, for all are not so. Cylinders of iron, for example, of the same size as our diamagnetic cylinders, would, through the intensity of their action, quite derange the apparatus ; so that we are obliged to have recourse to bodies of smaller size or of feebler magnetic capacity. Besides, the remarks of writers on this subject render it of importance to examine whether bodies through which the magnetic constituents are very sparingly distributed present a veritable polarity the same as that exhibited by iron itself. Slate rock usually contains from eight to ten per cent, of oxide of iron, and a fragment of the substance presented to the single pole of an electro-magnet is attracted by the pole. A cylinder of slate from the Penrhyn quarries near Bangor was first examined. It was not found necessary to increase the effect by using two cylinders, and the single one used was suspended in the right-hand helLx H'E'. The deportment of the substance was as follows : — XVIII. Cylinder of Penrhyn Slate. Length 4 inches. Diameter 0*7. Current direct. Current reversed. Position 1. 620 280 Position 2. 647 240 Position 3. 667 198 * Phil. Mag. March 1853, p. 222. Phil Mag, S. 4. Vol. 12. No. 78. Sept, 1856. N 178 Professor TyndalPs further Researches Comparing these deflections with those obtained with diamag- netic bodies, we see that they are in the opposite direction. With the direct current a change from position 1 to 3 is fol- lowed, in the case of diamagnetic bodies, by a motion from higher to lower numbers ; while in the present instance the motion is from lower numbers to higher. In the former case the north poles of the astatic magnet are attracted, in the latter they are repelled. We also see that a direct current acting on diamagnetic bodies produces the same deflection as a reverse cur- rent on magnetic ones. Thus, as we promised at a former page, the opposite polarities of diamagnetic and magnetic bodies are transferred from the region of deduction to that of fact. XIX. Cylinder of Caermarthen Slate. Length 4 inches. Diameter 0'7. Current direct. Current reversed. Position 1. 664 300 Position 2. 690 235 Position 3. 720 185 The deflections in this case are also indicative of magnetic po- larity. These two cylinders were so taken from the rock that the axis of each lay in the plane of cleavage. The following experiments, made with a cylinder of the same size, show the capability of a rock of this structure to be magnetized across the planes of cleavage. XX. Cylinder of Slate : axis of cylinder perpendicular to cleavage. Current direct. Current reversed. Position 1. 655 240 Position 2. 678 205 Position 3. 695 192 Chloride of iron was next examined : the substance, in powder, was enclosed in a single glass tube, which was attached to the string passing round the wheels WW' of the instrument. XXI. Cylinder of Chloride of Iron. Length 3*8 inches. Diameter 0*5. Current direct. Current reversed. Position 1. 185 990 Position 2. — 230 Position 3. 990 185 on the Polarity of the Diamagnetic Foh:e, 179 The deflection here indicates ordinary magnetic polarity. The action was very powerful. When swiftly moving in any direc- tion, a change in the position of the cylinder instantly checked the magnet in its course, brought it to rest, or drove it forcibly in the opposite direction. The numbers 185 and 990 mark indeed the utmost limit between which it was possible for the magnet to move ; here it rested against the helices. Two glass tubes were filled with red oxide of iron and exa- mined. The action of the poles of these cylinders upon the magnets was so strong, as to efface, by the velocity imparted to the magnets, all distinct impression of the numbers on the scale. By changing the position of the tubes within the helices, the magnets could be driven violently through the field of view, or could be held rigidly against the respective helices. As in all other cases, the centre of the cylinders were neutral points, and the two ends of each were poles of opposite qualities. The po- larity was of course the same as that of iron. A small quantity of iron filings was kneaded thoroughly in wax, and a cylinder formed from the mass. Its deportment was also very violent, and its polarity was of course just as clear and pronounced as that of a solid cylinder of iron could possibly be. Sulphate of iron was next examined : the crystallized sub- stance was enclosed in two glass tubes and tested in the usual manner. XXII. Cylinders of Sulphate of Iron. Length 4*5 inches. Diameter 0*7. Current direct. Current reversed. Position 1. 510 510 Position 2. 600 370 Position 3. 700 220 The red ferroprussiate of potassa is a magnetic salt ; with this substance the following results were obtained : — XXIII. Cylinders of red Ferroprussiate of Potassa. Length 4*5 inches. Diameter 0*65. Current direct. Current reversed Position!. 610 250 Position 2. 630 220 Position 3. 655 197 In this case also the crystallized salt was enclosed in glass tubes. N2 180 Professor TyndalPs further Researches Two glass tubes were next filled with carbonate of iron in the state of powder : the following are the results : — XXIV. Cylinders of Carbonate of Iron. Length 4 inches. Diameter 0*5. Current direct. Current direct. Current direct. Position 1. 185 Position 2. 620 Position 3. 740 In all these cases the deflections show that the bodies are polar after the manner of iron. As the complement of the experiments made with diamagnetic liquids, we now pass on to the examination of the polarity of mag- netic liquids. A concentrated solution of sulphate of iron was enclosed in two glass tubes and submitted to examination. XXV. Sulphate of Iron solution in tubes. Length 4 inches. Diameter 0*65. Current direct. Current direct. Current direct. . Position 1. 548 Position 2. 600 Position 3. 648 A solution of muriate of nickel, examined in the same manner, gave the following results ; — XXVI. Muriate of Nickel solution in tubes. Length 3*6 inches. Diameter 0*65. Current direct. Current reversed. Position 1. 605 224 Position 2. 632 200 Position 3. 650 185 A solution of muriate of cobalt yielded as follows : — XXVII. Muriate of Cobalt solution in tubes. Length 3*6 inches. Diameter 0*65. Current direct. Current reversed. Position 1. 630 262 Position 2. 645 235 Position 3. 660 202 In all these cases we have ample evidence of a polar action the reverse of that exhibited by diamagnetic hquids. These, I be- lieve, are the first experiments on which the action of either liquid magnets or liquid diamagnets upon a suspended steel magnet has been exhibited. on the Polarity of the Diamagnetic Force. 181 Thus far then the following substances have been submitted to examination : — Diamagnetic bodies. Magnetic bodies. Bismuth. Penrhyn slate. Antimony. Caermarthen slate. Heavy glass. Slate perpendicular to cleavage. Calcareous spar. Chloride of iron. Statuary marble. Sulphate of iron. Phosphorus. Carbonate of iron. Sulphur. Ferrocyanide of potassium. Nitre. Oxide of iron. Wax. Iron filings. Liquids. Liquids. Distilled water. Sulphate of iron. Bisulphide of carbon. Muriate of nickel. Muriate of cobalt. Every substance in each of these lists has been proved to be polar under magnetic influence, the polarity of the diamagnetic bodies being invariably opposed to that of the magnetic ones. In his investigation on the supposed polarity of diamagnetic bodies, Mr. Faraday made use of a core of sixpenny pieces, and obtained with it the results he sought. Wishing to add the testimony of silver as a good conductor to that of copper, two cylinders were formed of sixpenny pieces, covered with paper, and submitted to experiment. The following are the results obtained : — XXVIII. Silver cylinders (sixpenny pieces). Current direct. Current direct. Current direct. Position 1. 724 Position 3. 774 Position 3. 804 The action here was prompt and energetic, strongly contrasted with the neutrality of copper ; but the deflection was permanent, and could not therefore be the result of induced currents. Fur- ther, it was a deflection which shows magnetic polarity, whereas pure silver is feebly diamagnetic. The cylinders were removed and examined between the poles of an electro-magnet; they proved to be magnetic. On observing this deportment of the silver, I tried the copper cylinders once more. The results with a direct current were, — XXIX. Position 1. 766 Position 2. 767 Position 3. 768 Here almost the same neutrality as before is evidenced. Deeming that the magnetism of the cores of silver was due to 182 Professor TyndaiVs further Researches magnetic impurity attaching itself to the paper which covered them^ a number of fourpennv pieces were procured, washed in ammonia and water, and enclosed in thin glass tubes. The fol- lowing were the results :— XXX. Silver cylinders (fourpenny pieces). Current direct. Current direct. Current direct. Position 1. 490 Position 2. 565 Position 3. 660 Here also we have a very considerable action indicative of mag- netic polarity. On examining the cylinders between the poles of an electro-magnet, they were found decidedly magnetic. This, therefore, appears to be the common character of our silver coins. The tubes which contained the pieces were sensibly neutral. Knowing the difficulty of demonstrating the existence of dia- magnetic polarity in ordinary insulators, M. Matteucci suggested that insulated fragments of bismuth ought to be employed, the insulation being effected by a coat of lac or resin. I constructed a pair of cylinders in accordance with the suggestion of M. Mat- teucci, Tne following are the results they yielded with a direct current :— XXXI. Position 1. 730 Position 2. 750 Position 3. 768 Here we have a very marked action, but the polarity indicated is magnetic polarity. On subsequent examination, the cylinders proved to be magnetic. This was due to impurities attaching themselves to the resin. But the resin may be done away with and the powdered metal still rendered an insulator. This thought was suggested to me by an experiment of Mr. Faraday, which I will here describe. Referring to certain effects obtained in his investigations on sup- posed diamagnetic polarity, he writes thus : — '' If the effect were produced by induced currents in the mass, division of the mass would stop these currents and so alter the effect j whereas, if produced by a true diamagnetic polaritf/, division of the mass would not affect the polarity seriously or in its essential nature. Some copper filings were therefore digested for a few days in dilute sulphuric acid to remove any adhering iron, then well- washed and dried, and afterwards warmed and stirred in the air, until it was seen by the orange colour that a very thin film of oxide had formed upon them ; they were finally introduced into a glass tube and employed as a core. It produced no effect whatever, but was as inactive as bismuth." (Exper. Resear.2658.) . Now when bismuth is powdered and exposed to the action of on the Polarity of the Diamagnetic Force* 183 the air, it very soon becomes tarnished, even without heating. A quantity of such powder was prepared, and its conducting power for electricity tested. The clean ends of two copper wires proceeding from a battery of Grove were immersed in the powder ; but though the wires were brought as near as possible to each other, short of contact, not the slightest action was observed upon a galvanometer placed in the circuit. When the wires touched, the needle of the galvanometer flew violently aside, thus proving that the current was there, but that the powder was unable to conduct it. Two glass tubes were filled with the pow- der and submitted to experiment. The following results were obtained : — XXXII. Cylinders of Bismuth Powder. Length 3 inches. Diameter 0*7. Current direct. Current reversed. Position 1. 640 230 Position 2. 625 245 Position 3. 596 260 These deflections are the same in kind as those obtained with the cylinders of massive bismuth. This experiment responds perfectly to the conditions proposed by Mr. Faraday. We have here no cessation of action. The division of the mass does not affect the result seriously or in its essential nature, and hence the deportment exhibits the characteristics of " a true diamag- netic polarity." In summing up the results of his inquiry on this subject, Mr. Faraday writes thus : — " Finally, I am obliged to say that I can find no experimental evidence to support the hypothetical view of diamagnetic polarity, either in my own experiments, or in the repetition of those of Weber, Reich and others It appears to me also, that, as magnetic polarity conferred by iron or nickel in small quantity, and in unfavourable states, is far more easily indicated by its effects upon an astatic needle, or by pointing between the poles of a strong horseshoe magnet, than by any such arrangement as mine or Weber's or Reich's, so dia- magnetic polarity would be much more easily distinguished in the same way." I was struck, on reading this passage, to find how accurately the surmise has been fulfilled by the instrument with which the foregoing experiments were made. In illustration of the powers of this instrument, as compared with that made use of by Mr. Faraday, I may be permitted to quote the follow- ing result from his paper on supposed diamagnetic polarity so often referred to : — " A thin glass tube, 5^ inches by three- quarters of an inch, was filled with a saturated solution of proto- 184 Mr. C. Marett on the causes of the Intervals sulphate of iron, and employed as an experimental core ; the velocity given to the machine at this and all average times was such as to cause five or six approaches and withdrawals of the core in one second; yet the solution produced no sensible indication on the galvanometer/' Referring to Table XXV., it will be seen that the instrument made use of in the present inquiry has given with a solution of protosulphate of iron a de- flection amounting to no less than one hundred divisions of the scale. Mr. Faraday proceeds : — " A tube filled with small cry- stals of protosulphate of iron caused the needle to move about 2° Red oxide of iron produced the least possible effect.'' In the experiments recorded in the foregoing pages, the crystal- lized sulphate of iron gave a deflection of nearly two hundred divisions of the scale, while the red oxide gave a deflection as wide as the helices would permit, which corresponds to about eight hundred divisions of the scale. The correctness of Mr. Faraday's statement regarding the inferiority of the means first devised to investigate this subject, is thus strikingly illustrated. It might be added, that red ferroprussiate of potash and other substances, which have given us powerful effects, produced no sensible impression in experiments made with the other instru- ment. Thus have we seen the objections raised against diamagnetic polarity fall away one by one, and a body of evidence accumu- lated in its favour, which places it among the most firmly established truths of science. This I cannot help thinking is mainly to be attributed to the bold and sincere questioning of the principle when it seemed questionable. The cause of science is more truly served, even by the denial of what may be a truth, than by the indolent acceptance of it on insufficient grounds. Such denials drive us to a deeper communion with Nature, and, as in the present instance, compel us through severe and labo- rious inquiry to strive after certainty, instead of resting satisfied, as we are prone to do, with mere probable conjecture. Royal Institution, November 1855. XXIV. An attempt to investigate the causes of the Intervals between High-water and Slack-water, and between the turn of Tide near the Shore and in the Offing. By C. Marett, M,A., Trinity College f Cambridge"^. IT is well known to all accurate observers on the subject, that in tidal channels and in tidal rivers, the turn of tide, or slack-water, never exactly coincides with high- water, and that the tide near the shore always stops and turns before the tide in mid- * Communicated by the Author. between High-water and Slack-water, V ' 185 channel ; but as far as I am aware, no attempt was made to give a satisfactory explanation of these phsenomena until the publication, by the present Astronomer Royal, of the article on Tides and Waves in the Encyclopedia Metropolitana. In that article, very ingenious explanations of many of the phsenomena in question are given from the analytical results of most unpromising hypotheses, — hypotheses admitted to be so much at variance with the real state of things, that the coincidence of the results is very extra- ordinary and unexpected. Though undoubtedly these results would take place on the hypotheses alluded to, I now venture to offer another explanation of the same, or of some of the same phsenomena, founded upon considerations which I have been unable to reconcile with the above-mentioned hypotheses. They may, however, hereafter be reconciled, and it will be very sin- gular if they cannot, and if it should turn out that two inde- pendent causes produce the same result ; for it can hardly be doubted that the actions explained in this paper do really take place, and nrdst produce some effect on the tidal motions. Explanation of Tide and Half -tide. Let us suppose A to be an estuary or the open sea, in which the tide rises and falls alter- nately and uniformly 13 feet in six hours, this assump- tion being made for the sake of simplicity. Let R be a reservoir or inland sea in communication with A by the channel C, and of inde- finite size, i, e. so large that the quantity of water flow- ing through C in six hours does not perceptibly affect the general level in R; it is then obvious that in time the water in R will attain the mean level of the water in A, i. e. 6 feet above low- water mark in A. Let us now suppose it low water in A at 0^; the stream will then be ebbing out of R through C with the velocity due to the fall of 6 feet : as the tide in A rises the water in C will rise, but will continue to ebb from R through C till the water in A attains its mean height of 6 feet, which will be at 3^. The stream will then turn and begin to flow through C into R, rising at the same time till 6^, when it will be high water in A; the water in A will then begin to fall, but will continue to flow into R till 9^, when the water in A attains its mean level; the stream will then turn in C and ebb, the water falling at the same time till 12^, 186 Mr. C. Marett on the causes of the Intervals when the series will recommence. We have therefore in C — Tide flowing from 3 till 9 ... ebbing from 9 till 3 ... rising from 0 till 6 ... falling from 6 till 12 which is the system usually called tide and half-tide, and is ex- plained (Encijc. Metr. 'Tides and Waves/ §§ 184, 507) upon independent considerations founded on the motions of water in waves. Explanation of High-water occurring before the turn of tide. Let us now suppose that R is of limited area, which seems to be the ordinary case of a river or channel, and that the water flowing through C in six hours will affect the level of the water in R 6 feet ; for the sake of simplicity let us suppose the rising and falling of the water in R to be uniform, viz. one foot per hour. Then at low water in A, the height of the water in R will be 4 ft. 6 in., as I shall proceed to show ; for, assuming it to be so and the time to be 0*^, the water in A will then begin to rise, and the water in R will fall, ebbing through C, till 1^ 30"», at which time the levels will be the same in both, having fallen 1 ft. 6 in. in R and risen 3 ft. in A. The stream in C will then turn and flow into R, the water in R rising at the same time till 6^, at which time the height of the water in R will be 7 ft. 6 in., in A 12 ft. The water in A and C will then begin to fall, but still flow through C till 7^ 30"^, when the water in A and R will be at the same level, viz. 9 feet : the stream in C will then turn and ebb, and will continue to ebb and also to fall till 12 hours, when it will be low- water in A and 4 ft. 6 in. in R. The series will then recommence, and the original hypothesis, that at low water in A the height would be 4ft. 6 in. in R, is therefore correct, as it is the only permanent system. We shall have therefore in C,— Tide flowing from 1^^ 30°^ to 7^ 30"^, ... ebbing ... 7^^ 30"^ to 11^30^, ... rising ... 0^ 0^ to 6^ 0^, ... falling ... 6^ 0^ to 12^ 0°^, high-water and low- water each occurring one hour and a half before slack- water. Similarly, if R were smaller, it might be shown that high-water would be nearer slack-water, and ultimately, when R becomes nothing, or at the end of the chan- nel C, high- water would coincide with slack-water. — Tides and Waves, §335. Now if we take any section of a river, we may regard that section as C, and the portion of the river above it as R, and we have an explanation of the phsenomenon observed in rivers^ i between High-water and Slack-water, 1^7^; modified of course by the quantity of fresh water in ordinary rivers. That this is the true theory of the interval between high-water and slack-water, may also be inferred in a simpler manner from the following considerations. Let an observer station himself at any point in a tidal river, say at Putney Bridge, just before high-water : the tide will then be flowing up strongly in the middle of the river, slowly along the shore (see below) ; at high- water it will cease flowing along the shore and rise no higher, and in a short time will begin to fall, but will still run up in the middle. Now we know that high-water at Richmond and other places will not take place for more than an hour after high-water at Putney, and that the level of the water at Richmond is at this time lower than at Putney. But where is the water to come from which makes high- water at Richmond ? obviously it must come from below through Putney Bridge : and it is the water flowing up to make high-water at Richmond which causes the middle of the river to continue flowing at Putney after high- water ; and when a sufiicient quantity of water has flowed to make the level at Richmond as high or a little higher than at Putney, the tide will turn at Putney. Explanation of the turn of tide near the shore before it turns in the offing. Let us now suppose an obstacle OB in the channel C, then whilst the tide is flowing, the water in OBM will not run with the same velocity as that in the main channel, but will merely have the velocity necessary to bring sufficient water into OBM, so that the water in OBM may continue to rise with the rise of tide. Now when the tide has ceased to rise, the water in OBM will cease to run at all, though, as before shown, the water in C will continue to flow : and when the tide begins to fall, the water in OBM will ebb (with the velocity necessary to take the water out of OBM, at such a rate as that the water in OBM may fall with the fall of tide), though the water in C will still continue to flow. It is obvious that OBM is a representation of the ordinary slack-water along the margin of rivers, occasioned either by actual projections or by the friction of the shore and shoals, or by the set of tide. I add a few observations taken by me at Putney on a very calm afternoon, 9th of Nov. 1851, when there were many leaves, &c. floating on the stream. There was nothing particularly remarkable in the tide, but I am not aware that a similar set of observations are to be found in print, and the study of a tide of this sort may be instructive. 188 Dr. Atkinson's Chemical Notices from Foreign Journals : — 3h Qm p^i^^ Tide ceased along shore, flowing in the middle. S^ 15"^ „ Ebbing close to the shore and falling. 3^ 30"°^ „ Tide turned in the middle, having fallen about 15 inches. The margin of ebbing tide gra- dually grew wider on both sides of the river till it covered the whole river. The water at each point was not at rest more than 3"™. 3h 4Qm ^^ Tide ebbing along shore ; faster about 20 yards off; not so fast in the middle. 4^ 5"* „ Tide in full ebb, fastest in the middle : back- waters along shore; having sunk about 3 feet 6 inches. XXV. Chemical Notices from Foreign Journals, By E. Atkinson, Ph,D, [Continued from p. 59.] CANNIZAKO found that hydruret of benzoyle, Ci^ H« 0^, was converted by the action of an alcoholic solution of potash into benzoic acid, C^'* H^' O'*, and the alcohol corresponding to it, Qi4jj8Q2^ According to Cannizaro and Bertagnini*, the hy- druret of anisyle undergoes, under the same circumstances, a like change, being converted into anisic acid, C^^ H^ 0®, and into an alcohol corresponding thereto, C^^H^^O'*, anisic alcohol. Anisic alcohol distils without decomposition at 250°, and melts at 23°. It crystallizes in hard, white, brilliant needles. By oxidizing agents, and also when left in the air in contact with platinum black, it is converted first into hydruret of anisyle, and then into anisic acid. Anisic alcohol, when warm, dissolves several salts, as benzoate and acetate of potash ; and organic substances, as salicine, hippuric acid ; on cooling, these crystallize out. With potassium it forms a compound, hydrogen being liberated; treated with hydrochloric acid gas, a body is obtained which appears to be the chlorine compound of the radical contained in the anisic alcohol. The same chemists endeavoured to produce from hydruret of salicyle (salicylous acid), C^'^H^'O'*, the corresponding alcohol, but without success. Casselmannt makes some interesting contributions to our knowledge of the oxy chlorides. It was his object, in investi- gating these bodies, to endeavour to replace the oxygen con- tained in them by chlorine ; and as the chloride of phosphorus, * II Nuovo Cimento, vol. i. p. 99. t Liebig's Annalen, May 1856, p. 213, I M. Casselmann on the Oxychlorides. 189 PCP, corresponding to the oxychloride, PO^ CF, is known, the latter substance was chiefly used in the research. He expected that by acting on oxychloride of phosphorus with substances which,, under certain circumstances, readily exchange chlorine for oxygen, the pentachloride of phosphorus would have been obtained. In this direction the comportment of the chlo- rides of aluminium, magnesium, and zinc, and of the bichloride of tin, was investigated, but without the expected results. On the other hand, interesting compounds of oxychloride of phos- phorus with these chlorides were obtained, which Casselmann describes at length. The compound of oxychloride of phosphorus with bichloride of tin, 2Sn CP + PO^ Cl^, he had previously described. It forms large colourless crystals, and when pure, distils unchanged. On account of the readiness with which this compound, and indeed all the compounds of this nature, attract moisture, they are ex- tremely difficult to get quite pure ; their preparation is effected in an apparatus by which the access of moisture is prevented. Berzelius viewed oxychloride of phosphorus as a compound of phosphoric acid and pentachloride of phosphorus, 5P02CF=2PO^ + 3PCP. Such a compound would give with bichloride of tin, phosphate of tin, and the compound of pentachloride of phosphorus with bi- chloride of tin (PCP + 2SnCP), previously described by Cassel- mann. But as the compound of oxychloride of phosphorus with bichloride of tin may be volatilized, no phosphate of tin can be contained in it, and Berzelius's view is hence not correct. Oxychloride of phosphorus exhibits a strong tendency to com- bine with bichloride of tin. When brought into contact with the compound of bichloride of tin and bichloride of sulphur, SnCF + 2SCP, the compound of oxychloride of phosphorus with bichloride of tin is obtained, bichloride of sulphur being set free. When chloride of aluminium is mixed with oxychloride of phosphorus in a sealed tube, a white mass is obtained, which on heating, dissolves in the excess of oxychloride of phosphorus ; and on cooling, the compound of oxychloride of phosphorus with chloride of aluminium is deposited in clear colourless needles. Its formula is AP CF + PO^ CF. With chloride of magnesium a compound is obtained which has the formula 2MgCl + PO^ CF. With chloride of tin a compound crystallizing in rhombic plates is obtained. With metallic oxides the oxychlorideof phosphorus decomposes, so that a metallic phosphate and a metallic chloride are formed. It cannot therefore be considered as phosphoric acid in which 190 M. Mayer on Phosphate of Lithia, oxygen is replaced by chlorine ; for if so, it ought to combine directly witli the metallic oxide. Oxychloride of phosphorus in its compounds with metallic chlorides has the greatest similarity with pentachloride of phosphorus, and ought rather to be con- sidered as this body, in which chlorine is replaced by oxygen. Mixed with oxychloride of chromium, an action takes place which may be thus expressed : — 5PO«Cl« + 12CrO«Cl = 18Cl + 5P05 + 3Cr«0«+3Cr«CP. Casselmann also made experiments to ascertain the existence of the oxygen radical, assumed by Gerhardt to exist in oxy- chloride of phosphorus. He was led to the conclusion, that, as is the case with the compounds of phosphorus with chlorine, phosphorus is the only electro-positive element. Casselmann is making similar experiments with the chloride of benzoyle, C^* H^ 0*, CI, and the chloride of acetyle, C^ H^ 0^ CI. Berzelius described a double salt of phosphate of lithia and phosphate of soda obtained by mixing a lithion salt with phosphate of soda. This was used for the detection and esti- mation of lithia until Rammelsberg showed that the composi- tion of the salt varied materially. He viewed it as SNaOl PQ5 3LiO J^^ ' and considered the two bases as isomorphous and capable of replacing each other. Mayer* made numerous atten^ts to prepare this salt, but invariably obtained a salt, which, after being well washed out, was tribasic phosphate of lithia. Phosphate of lithia forms a heavy white crystalline powder, similar in appearance to phosphate of soda and magnesia. It is soluble in 2539 parts of pure water, and in 3920 parts of ammoniacal water. Mayer founded on the insolubility of this salt a process for the separation of lithia from the other alkalies, which, if it does not satisfy all the requirements of a good analytical method, seems better than the methods usually employed. Kopp has an article f on the boiling-points of corresponding chlorine and bromine compounds, and on the formulse of silicium and titanium compounds, which bear especial reference to a recent paper by Hofmann on the formulse of titanium compounds. In comparing the boiling-points of various corresponding bromine and chlorine compounds, Kopp was led eight years ago to the conclusion, that the former, when they contain Br^, in the ♦ Liebig's Annalen, May, p. 193. t Ibid. p. 266. Kopp on the Boiling-points of Bromine andChlorineCompounds. 191 place of Cl„ boil also by .a? x 32 degrees higher than the latter. From this, he reasoned, a criterion was obtained as to how many equivalents of chlorine or bromine were contained in correspond- ing bromine and chlorine compounds. As bromide and chloride of silicon differ by 3 x 32 degrees in their boiling-points, Kopp inferred that their formulae were respectively Si Br^ and Si CF. The observations on boiling-points made at that time in cor- responding chlorine and bromine compounds justified the assump- tion of that relation, but Kopp thinks now that that remark in its original generality is no longer true. In the last few years many new compounds have been discovered whose boiling-points do not agree with this rule, and the boiling-points of many bodies known at that time have since been determined in a more accurate manner. Kopp gives a list of such boiling-points, from which it appears, that, although in many cases of corresponding compounds containing bromine or chlorine the difference of boil- ing-points is a constant one, yet this is not universally the case, and it cannot be said that the difference of boiling-points is always the same for the same difference of formulae. Hofmann has lately announced that the boiling-point of bromide of tita- nium differs from that of chloride of titanium by 95°, =3 x 31°'7, and reasons from this that the formula of bromide of titanium is Ti Br3, and of the chloride, Ti CF. Kopp says, that although the difference in the boiling-points of chloride and bromide of silicon affords a support to the idea that their formulae are Si CP and Si Br^, yet it by no means proves it. From a purely chemical point of view we cannot decide which of the formulae. Si CP, Si CP, Si CI, for chloride of silicon is correct. Relations are found to exist between the chemical composition and certain physical properties, some of which may be urged for the formula Si CP, and some for the formula Si CP or Si^CP. In the case of titanium, the analogy of several of its com- pounds with tin, the atomic weight of which must be considered as fixed, and especially the isomorphism of rutile, TiO^, and of native tinstone, SnO'^, as well as of Brookite, and of the crystal- lized oxide of tin obtained by M. Daubree, appear to establish its equivalent, and the formula of many of its compounds. That the bromides and chlorides of titanium and silicon exhibit the differences in boiling-points is undoubtedly interesting ; but it does not appear allowable to change the formulae Ti CP, Ti Br^, &c., which are estabhshed on sure foundations, to Ti CP, Ti Br^, only on account of a difference in the boiling-points of two com- pounds which has no connexion with any general rule. Relations between the physical qualities and chemical composition may be consulted for the determination of atomic weights and of for- 192 M. Limpricht on some Compounds of Salicylic Acid, mulse^ where chemistry does not herself possess the means of fixing these weights and these formulae in a relatively certain manner. But formulse which only express a relation concerning a single physical quality cannot be accepted as chemical formulse, especially if they disagree with indubitable chemical analogies. Reynoso proposed a method for the determination of phos- phoric acid, which consisted in combining the phosphate with a known quantity of metastannic acid. By subtracting from the weight of the compound of phosphoric acid and metastannic acid formed, the metastannic acid used, the quantity of the phosphate is obtained. Although an excellent method, it has many diifi- culties which hinder its application. To remove these, and to make the method applicable to all cases, Reissig* proposes a modification of it, which consists in separating the phosphoric acid from the metastannic acid, and determining it directly as phosphate of magnesia and ammonia. Schlossberger^t has detected crystals of oxalate of lime in the Malpighian vessels of the spider. Piria has lately shown that salicylic acid is bibasic. From this point of view Limpricht J has submitted several compounds of this acid to an investigation. Salicylamide, regarded as H >N, must be considered, on the bibasic view, as sali- H J cylamic acid, ^ „ ^ >0^, and Limpricht has prepared several of its salts. By the action of heat, salicylamic acid loses 2 equivs. of water, and is converted into salicylimide, Ci4H7N04-2HO = Ci4HSN02. The sethyle- salicylamic acid was also obtained by the action of ammonia on methylsethyle salicylic aether. Limpricht is still en- gaged in the investigation. Kolbe § describes a new method for the formation of benzoic aldehyde. Since the researches of Chiozza and Gerhardt, the existence of compound radicals containing oxygen has been placed out of doubt, and the benzoyle theory of Liebig and Wohler is again generally received. According to this, benzoic acid, chlo- ride, hydruret, and cyanide of benzoyle are compounds of the radical benzoyle, C'^ H^ 0^, or (C^^ H'^) C^ 0^. If, now, the hydrogen in hydruret of benzoyle, C^'* H^ 0*, H, * Liebig's Annalen, June, p. 339, t Ibid. vol. xcviii. p. 354. X Ibid. May, p. 256. § Ibid. June, p. 344. M. Kraut on Toluric Acid. 193 really occupies the same place as the chlorine in chloride of ben- zoyle, C^'^H^O^ CI, this latter, or some other haloid compound of benzoyle, ought, by an appropriate action of hydrogen in the nascent state, to be converted into hydruret of benzoyle, C^4H5 0^C1 + 2H = Ci^H^O^H + HCl. Chloride of benzoyle. Hydruret of benzoyle. The ready decomposability of chloride of benzoyle renders it un- fitted for this reaction, but the change takes place with cyanide of benzoyle ; for when it is treated with hydrochloric acid, and granulated zinc added, decompositiou of the cyanide takes place, the odour of hydrocyanic acid is evolved, and the mass contains a large quantity of hydruret of benzoyle, which is separable by distillation. The same change occurs when cyanide of benzoyle is treated with mercury and hydrochloric acid. Kraut* found that toluylic acid, when taken into the system, gives rise to the formation of a new acid. The toluylic acid was taken in doses of several grammes at a time without any percept- ible efi'ect on the organism ; the urine had afterwards a distinctly acid reaction. The new acid, which Kraut names toluric acid, is obtained from the urine by the methods used for extracting hip- puric acid from that source. Toluric acid crystallizes in the rhombic system in hard lus- trous crystals. It is easily soluble in alcohol and in boiling water, from which it crystallizes on cooling. It decomposes the earthy carbonates, forming with the bases crystalline salts. The formula of the acid is C^o Hi^ NO^ and of its salts C^o W N0«. Treated with hydrochloric acid, it undergoes a change entirely analogous to hippuric acid under the same circumstances, being converted into toluylic acid and alcohol. Toluylic acid undergoes, hence, in passing through the organ- ism, a similar change to benzoic acid ; with loss of water it assi- milates the elements of glycocoU : thus — C14 H6 04 + C^ IP NO'^-2HO = Ci8 H^ NO^. Benzoic acid. GlycocoU. Hippuric acid. Ci^H^ 0^ + 04 HSNO4-.2HO = C20HiiNO^". Toluylic acid. GlycocoU. Toluric acid. Kraut confirms the statement of Hofmann, that cuminic acid passes through the body unchanged. Professor Schmidt f of Dorpat has investigated the boracic acid fumaroles of Monte Cerboli in Tuscany. In order to check * Liebig's Annalen, June, p. 360. f Ibid. p. 273. Phil. Mag. S. 4. Vol. 12. No. 78. Sept. 1856. O 194 Prof. Schmidt on the Boracic Acid Fumaroles. the assertion of Payen, that the fumarole vapours, before their passage through the waters of the lagoons, contain no boracic acid, the following experiment was made. A large glass funnel was fastened over one of the jets of vapour issuing from the ground, and connected by means of a leaden pipe and several long wide glass tubes with empty glass balloons, which served as condensers. The gas evolved was a mixture of much carbonic acid with a small quantity of sulphuretted hydrogen. Small quantities only of nitrogen, and no oxygen were found. The liquid condensed in the receiver reddened litmus paper, but ren- dered turmeric paper brown ; and a quantity of it evaporated to dryness and treated with sulphuric acid, imparted to the alcohol flame the characteristic green colour of boracic acid, proving that boracic acid exists preformed in the fumarole vapours. The condensed liquid contained, besides, carbonic acid and ammonia in considerable quantity. Distinctly estimable amounts of silica, baryta, iron, alumina, lime and magnesia, were also found. From a series of experiments, Schmidt supposes that the fumarole hquid contains about O'l per cent, of boracic acid, and thinks that it is in the form of borate of baryta. Hessel* found that by the addition of a certain quantity of cal- cined gypsum to muddy wines, they were clarified and rendered somewhat stronger, retaining their original taste and flavour. Gypsum has the same effect on muddy beer, with the exception that it is rendered more bitter. Two important methods for the artificial production of urea are given by Natansonf. He shows that carbamide and urea are identical. When carbonic aether is heated with excess of am- monia in a closed tube to 100° C, urethane alone is formed ; but if the temperature of the tube be raised to 180°, the boiling- point of urethane, it is converted by the excess of ammonia into urea. In the empty parts of the tube a sublimate of undecom- posed urethane is deposited : the aqueous solution contains urea. If this solution be evaporated to dryness and kept some time at 100° C, the urethane volatilizes and urea remains behind. In ] 838 Regnault obtained, by the action of phosgene gas on ammonia, a white saline mass, which comported itself as a mix- ture of carbamide and sal-ammoniac. In this mass urea must probably have been contained ; but if the gases had not been well dried, its quantity would have been small in comparison to the other substances, and it might easily have escaped detection. Natanson prepared the phosgene gas by passing carbonic oxide * Liebig's Annalen, June, p. 334. t Ibid. p. 287* M. Natanson on Acetylamine. 195 through perchloride of antimony. It was conducted along with ammonia^ both gases being quite dry, into a capacious vessel. The mass obtained was treated with absolute alcohol, the alco- holic solution evaporated to dryness, and the residue dissolved in a small quantity of cold water. On the addition of nitric acid, the characteristic nitrate of urea is obtained. The presence of urea was confirmed by other reagents. Natanson* found that by the action of chloride of elayle on ammonia, a base, the oxide of acetylammonium, was produced. The investigation of this he has resumed, and communicates now his results. He finds that oxide of acetylammonium splits up at a higher temperature into acetylamine and water, — g ^NO, H0= H ^N+2H0. hJ hj An alcoholic solution of pure hydrated oxide of acetylammo- nium is heated in a retort until all the alcohol has distilled ofi"; if the temperature be then raised, drops of water containing acetylamine dissolved pass over. This water results from the decomposition ; and after it has almost ceased to come over, the temperature is raised to 220° C, at which point yellowish oily drops come over, which consist almost entirely of pure acetyl- amine. Above that point other products of decomposition are formed, and the acetylamine passes over in very small quantity. On rectification, the acetylamine was found to boil at 218° C. Pure acetylamine is an almost colourless, oily liquid, of peculiar adherent odour. Its specific gravity is 0*975. At ordinary tem- peratures it smells like aldehyde-ammonia ; the vapours of boil- ing acetylamine smell like pure aniline. Acetylamine is miscible with alcohol and water, but not with aether. On dry litmus it has no action, but on the addition of water the paper becomes blue. It has a caustic taste. Sodium has no action on it. Acids form with it salts which have all the characters of the salts of acetyl- ammonium. On the addition of potash to a solution of the sulphate, the characteristic odour of acetylamine is not perceived. Acetylamine is eliminated therefore in the form of the inodorous oxide of acetylammonium. In the air, acetylamine attracts moisture and carbonic acid; in contact with hydrochloric acid gas, white vapours are formed. With solutions of the metals, many characteristic reactions are observed. When acetylamine is heated with iodide of sethyle, an iodide of the sethylated base is obtained. By treatment with potash * Liebig's Annalen, June, p. 291. 02 196 M. Natanson on Acetylamine. this yields a brown oil, which is a base, and forms compounds with acids. It is probably sethylacetylamine, C* H^ >N. H J By the action of chloride of elayle on aniline in closed tubes at 200° C, and subsequent solution of the contents of the tubes in water, a mixture is obtained of the hydrochlorates of aniline and of acetylaniline, which are separable by ammonia, aniline being precipitated. Acetylaniline, when purified, is a light brown, tasteless, and inodorous powder, which is soluble in alcohol and rethcr, but insoluble in water. It does not crystallize, and it forms with acids salts which are also uncrystallizable. It gives wit;h bichloride of platinum a double salt. Acetylaniline is cott- er Hn stituted according to the formula C^^H^ >N, and its formation Hj - may be thus expressed : — C4H4C12 + 2Ci2H7N=Ci2H7NHCl + Ci«H9N, HCl. Chloride of Aniline. Hydrochlorate Hydrochlorate of elayle. of aniline. acetylaniline. Compounds corresponding to the amides are also formed by ace- tylamine. If butyric sether be mixed with an alcoholic solution of acetylamine, the whole solidifies to a mass of fine crystalline needles. These are the acetylamide of butyric acid : — (C«H7 02+^^^^\n). The comparison of the properties of acetylamine and of oxide of acetylammonium is an instructive contribution to the ammo- nium theory. Here the separation into the corresponding am- monia and water takes place at 150° C, while ordinary oxide of ammonium probably sufi'ers this change below 0°. Acetylamine has all the characteristic properties of the ammonias, and, like them, has no action on perfectly dry litmus paper. On the ad- dition of water and acids, it forms salts corresponding to the ammonia salts, losing its characteristic properties; but by the addition of strong bases is set free as the strongly alkaline oxide of acetylammonium. Natanson considers these relations as sup- porting an opinion already expressed by him, that the ammonias are the neutral products of decomposition of the oxides of am- monium, the real bases. The same chemist describes a modification of Gay-Lussac's method of determining the specific gravity of vapours, in which vei-y small quantities only of substance are required. [ 197 ] XXVI. Remarks on Slaty Cleavage, and the Contortions of Rocks. By Sir John F. W. Herschel, Bart., F.R,S. ^c. Dear Sir, CoUingwood, July 27, 1856. LET me thank you for several instances of obliging attention in forwarding me copies of your scientific papers on diamag- netism, and quite recently of your lecture on the Slaty Cleavage^ which appears to me a singularly happy explanation of that odd phsenomenon. I may mention an illustration of the same nature with some others you have introduced, which occurs in the manufacture of the coin of the realm. One part of the process consists in '^ ringing ^^ each piece of gold or silver coin (after receiving the impression) . Every piece which will not ring on dashing it against a stone is rejected and re-melted ; and such are numerous. Now the cause of this can be no other than minute air-blebs in the bars out of which the laminae of metal are rolled by a flatting-mill, each bleb being flattened out into an infinite- simally thin film of air parallel to the faces of the coin, and so producing a solution of continuity, and of course destroying the harmonic vibration. There are one or two points suggested by your views of the slaty cleavage which harmonize so entirely with certain ideas I have long held about geological stratification in general, that I cannot forbear mentioning them. I refer to the contortions of strata which are usually accounted for (as Poulett Scrope has done) by the protrusive violence of igneous rocks crushing together and doubling up the strata. To me it has always seemed that this feature might be more tranquilly produced thus : — Suppose A A the ocean surface, and B B B its bed, forming a basin having irregularities C C in it. Let sediment be deposited over the whole, uniformly, till the inequalities are filled in and the bottom is reduced to a, generally speaking, basin-like depres- sion. Then up to a certain point the friction of the bed will retain the deposited mud on its slope, and in this way strata nearly of uniform thickness (and parallel) will be formed. 198 Sir J. F. W. Herschel on Slaty Cleavage. But as the thickness of the whole increases, the weight will overcome the friction, and the still soft strata will yield inwards from all sides towards the central portion of the bed, increasing the thickness of the strata there, and at the same time crumpling up the strata into contortions, &c. The whole affair may go on with any degree of slowness*. Now as this process goes on, the middle thickness will increase^ and that by a general lateral compression and vertical dilatation of the whole central mass. And here we have the condition which your theory requires for the slaty cleavage, wfiich (be it observed) does not absolutely require violent force (for mere force cannot produce any rearrangement of molecules), but only inter^ molecular movement in a given fixed direction. Thus we see the blebs in slow-moving lava currents drawn out in length ; and thus we see liquids, in which excessively fine spicular crystals are floating, assume a silky appearance when stirred or agitated (I have a most beautiful case of the kind under my eye at this moment) by the tendency of the particles to arrange themselves when in motion all in one direction, according to the laws, not of pressure but of friction, a distinction which is quite necessary to be borne in mind. Infinitesimal films of mica disseminated through amorphous mud would afford a precise parallel to this case. Your account of the fibrous structure in tough iron is quite beautiful, and perfectly accounts for the exceeding toughness and tenacity of bar iron formed by welding together smaller bars, &c. In fact, such a bar is a rope of iron wire held together as the fibres of a hempen rope are, by lateral friction, and each portion being per se of trivial length compared with the whole. I am sure you will excuse me for writing to you in this desul- tory manner, which perhaps I am not entitled to do; but the fact is, that since reading, a great many years ago, Wells's little tract on dew, I have not met with anything which seems to bring so many loose- lying phsenomena under a general and very simple principle. I remain, dear Sir, Yours truly, J, Tyndall, Esq., F.R.S. ^c. J. F. W. Herschel. ♦ In forcing down tlie strata, while still in some degree yielding, down ike general slope of the ocean bed, they must often be driven over its larger inequaUties in a way very likely to contort and corrugate them ; and this, too, equally whether the softness be that remaining in them previous to their consolidation, or be produced anew by invasion of heat from below producing semifusion and weakening their support. [ 199 ] XXVII. Preliminary Notice on the Electric Conducting Power of the Alkaline Metals. By A. Matthiessen, Ph.D."^ OF the physical properties of the metals of the alkalies and alkaline earths very little is at present known ; and having some of them at my disposal, I thought it would be interesting to study some of their most important properties. I have com- menced, under the direction of Professor Kirchhoff, in the Hei- delberg Physical Laboratory, with the electric conducting power of the alkaline metals, and have found that of potassium at ordi- nary temperature, compared with that of silver at 0° = 100, to be— - 201 Of sodium . . . 36*6 Of lithium . . . 18-7 The manner in which the wires were pressed and the method of observation I shall describe as soon as I have determined their conducting power at different temperatures, as well as that of the metals of the alkaline earths. An interesting fact is the rapid diminishing of the conducting power at the point of fusion. With potassium it diminishes gradually between the temperatures 50° to 57° C. ; whereas with sodium, suddenly at about 96°, as the following data show : — That of sodium is at — 75° C. . . 24-44 85° C. . . 23-41 95° C. . . 22-42 97° C. . . 16-23 110° C. . . 15-36 120° C. . . 14-17 Compared with silver at 0°=100. This difference in the behaviour of these metals may be ex- plained by the observation lately made by Regnault, in his paper " On the Specific Heat of Simple Bodies " {Ann. de Chim. et de Phys. vol. xlvi. p. 257), wherein he states that potassium does not pass directly from the liquid to the solid state, like sodium, but becomes first semi-fluid and then gradually solid, which fact is plainly shown by comparing the conducting power of the two metals at their fusing -points. The conducting power of potassium is at — 40° C. . 17-21 49° C. . 16-44 53° C. . 14-81 58° C. . 12-91 56° C. . 12-21 57° C. . 11-54 70° C. . , 11 80° C. . 10-65 * Communicated by the Author. [ 200 ] XXVIII. On Ruhian and its Products of Decomposition*, By Edwaed Schunck, FM.S. Part III. Combined Action of Alkalies and Oxygen on Ruhian. IN the preceding part of this paper t I have given an account of the action of alkalies on rubian and of the products of decomposition thereby formed. I have shown that these pro- ducts are, with one exception^ identical with those which the action of strong acids gives rise to, the rubianine produced by acids being merely replaced by rubiadine when alkalies are em- ployed. Now though I found this to be in all cases the final result of the action of alkalies, there still remained a possibility of the existence of bodies intermediate between rubian and the final products of decomposition. Such bodies do in reality exist, but their formation is dependent, at least in part, on the simul- taneous action of oxygen. If to a solution of pure rubian baryta water be added in excess, if a current of carbonic acid gas be passed through the solution, until the whole or a great part of the baryta has been converted into bicarbonate of baryta, and the filtered solution be left ex- posed in a shallow vessel to the atmosphere, its surface becomes covered in a short time with a thin film of a beautiful scarlet colour, which, when viewed under a lens, is seen to consist of small interlaced crystals. If this film be broken so as to cause it to sink to the bottom, a new one is formed on the surface of the liquid. This process continues for some time, but at last ceases. On gently evaporating the solution, an additional quan- tity of this red substance separates in thick flocks. After being collected on a filter and washed with cold water, it appears of a fine scarlet colour. On drying it becomes brown, but if then reduced to powder the colour changes to a cinnabar-red. If it be suspended while still moist in water, and a current of car- bonic acid gas be passed through the liquid, it dissolves again entirely, forming a yellow solution ; but if this solution be eva- porated, its colour changes to red, and it again deposits red flocks, after which it becomes almost colourless. The red flocks contain two organic substances in combination with baryta. On adding to them dilute sulphuric acid the former dissolve, giving a yellow solution. The excess of sulphuric acid having been removed by means of carbonate of lead, the solution is filtered, and the insoluble matter left on the filter is treated several times * From the Philosophical Transactions, Part II. for 1855, having been received by the Royal Society June 13, 1855, and read June 21, 1855. t See Phil. Mag. vol. v. pp. 410, 495. Dr. Schunck on Ruhian and its Products of Decomposition. 301 with boiling water, after which it generally retains only a slight pink tinge. The filtered solution deposits on evaporation a quantity of yellow crystalline needles. After evaporating to dryness there is left a yellow mass, the surface and edges of which have a dark yellowish-brown tinge. On adding to this mass a small quantity of cold water, part of it dissolves with a deep yellow or reddish-yellow colour, while a yellow powder" remains undissolved. The latter consists of a peculiar acid, to which I shall give the name of Ruhianic Acid. After being col- lected on a filter and washed with cold water, it is purified by solution in boiling water, to which a little animal charcoal may be added. On filtering the solution boiling hot and allowing to cool, it crystallizes in beautiful lemon-yellow needles, which, if the solution was at all concentrated, entirely fill the liquid. The substance dissolved by the cold water is left on evaporation in the shape of a reddish-yellow or brownish-yellow substance, re- sembling rubian itself in appearance and all its properties. As analysis showed it to be formed from rubian by the elimination of several equivalents of water, I shall call it Ruhidehydran. The liquid filtered from the red flocks, consisting of the baryta compounds of the two substances just named, has still a dark brownish-yellow colour, and contains a third organic substance in solution. In order to ascertain whether the whole quantity of the two former substances has been separated, and whether the solution still contains any unchanged rubian, it is well to add caustic baryta to the liquid, to supersaturate the latter with carbonic acid and to evaporate again. If no more red flocks separate on evaporation, but only a deposit of carbonate of baryta be formed, then the process is completed. On now adding to the filtered solution basic acetate of lead a red precipitate falls, while the liquid becomes colourless. The former, being sepa- rated by filtration and washed with water, is to be decomposed with sulphuric acid in the cold, and the excess of acid having been removed with carbonate of lead, sulphuretted hydrogen is passed through the filtered liquid, and the latter, after being filtered again from the sulphuret of lead, is evaporated to dry- ness, when it leaves a dark brownish-yellow substance, resem- bling rubian in appearance, but difi'ering in being somewhat deliquescent. To this substance I will give the name of Rubi- hydran. The liquid filtered from the lead compound of this substance sometimes contains sugar, but this is entirely a se- condary product of decomposition, formed at the cost of one or more of the primary products, and indicates the formation at the same time either of rubiadine or alizarine. The same products of decomposition may be obtained by adding to the solution of rubian a solution of bicarbonate of 202 Dr. Schunck on Rubian and its Products of Decomposition, baryta made from chloride of barium and bicarbonate of soda, and evaporating in contact with the air until red flocks begin to appear, or by adding caustic baryta to the solution, allowing the mixture to stand exposed to the air for some time and filtering, when the insoluble baryta compound left on the filter will yield rubianic acid and rubidehydran, and the liquid rubihydran. The same process of decomposition takes place, if caustic soda, ammonia, or lime water be added to a wateiy solution of rubian, and the mixtures be allowed to stand exposed to the air for some time. On now adding chloride of barium to any one of them a dark red precipitate falls, which being collected on a filter, washed with water and then treated in the same manner as the red flocks obtained by means of bicarbonate of baryta, afibrds in each case rubianic acid and rubidehydran, while the liquid contains rubihydran. If a small quantity of any acid be added to a watery solution of rubian, and if the acid be then neutralized with carbonate of baryta, the small quantity of bicarbonate of baryta formed is sufficient to induce a decom- position of the rubian, for the filtered solution on exposure to the air very soon begins to deposit red flocks, which consist of rubianic acid and rubidehydran in combination with baryta. It is for this reason that I have recommended the employment of carbonate of lead instead of carbonate of baryta for the purpose of neutralizing the sulphuric acid used in purifying rubian*. Even oxide of lead is a sufficiently strong base to cause rubian to undergo this process of decomposition, when oxygen is pre- sent at the same time. If rubian be precipitated from its watery solution by means of basic acetate of lead, and the lead compound be left exposed to the air for a short time, it will be found no longer to contain unchanged rubiuu. If the com- pound be decomposed with sulphuric acid in the cold, and the excess of acid be neutralized with carbonate of lead, the filtered solution deposits during evaporation crystals of rubianic acid, and leaves at last a brown deliquescent mass, which unless it be strongly dried is with difficulty removed from the vessel con- taining itf. In short, whenever rubian is brought into contact at the same time with oxygen and an alkaline or other strong base, it undergoes decomposition. Hence it follows, that in preparing the so-called xanthine according to the methods pro- * See Phil. Mag. for March 1862, p. 222. t In purifying i-ubian by precipitation with basic acetate of lead, as de- scribed in the first part of this paper, care must be taken to wash the pre- cipitate with alcohol and not with water. If the former be employed, de- composition is almost entirely prevented, whereas in using water the rubian in the precipitate imdergoes complete decomposition during the short time necessary for edulcoration. Dr. Schunck on Rubian and its Products of Decomposition. 303 posed by Kuhlmann, Berzelius, Eunge and Higgin, as well as the ruberythric acid of Rochleder, the use either of alkaline earths or basic acetate of lead being prescribed by all these chemists^ products of the decomposition of rubian must in every case be formed. For the purpose of preparing the three bodies which result from this process of decomposition, it is not necessary to employ pure rubian. If madder be extracted with boiling water, and sugar of lead be added to the extract, a purple precipitate is produced, and ammonia being added to the filtered liquid, the whole of the rubian is precipitated together with some chloroge- nine in combination with oxide of lead. The precipitate is de- composed with sulphuric acid in the cold, and the excess of the acid is removed by means of carbonate of lead. To the filtered solu- tion a quantity of baryta water is to be added, and the baryta is then converted into bicarbonate of baryta by a stream of car- bonic acid gas. The solution is left exposed to the air for some time and then slowly evaporated. The red flocks which are deposited are collected on a filter as they form, and after being treated in the same way as the flocks from pure rubian, yield rubianic acid and rubidehydran. The liquid filtered from these flocks contains chlorogenine as well as rubihydran, and the separation of the latter becomes therefore rather more diffi- cult. This may however be effected by precipitating it with basic acetate of lead, filtering, washing the precipitate with water, then redissolving it in warm acetic acid, and again precipitating by means of a little ammonia. The last precipitate contains hardly any chlorogenine, and after being put on a filter and washed, is decomposed with sulphuric acid in the cold. The excess of acid is removed by carbonate of lead, the liquid is fil- tered, sulphuretted hydrogen is passed through it, it is again filtered from the sulphuret of lead, and on being evaporated leaves the rubihydran free from chlorogenine. Should it still contain a little of the latter substance, in which case its watery solution turns green on being boiled with muriatic or sulphuric acid, the precipitation with basic acetate of lead must be re- peated. It frequently happens, that besides the usual products of decomposition, a quantity of rubiadine is also formed. In this case the red flocks deposited on evaporating the barytic solution yield, on being decomposed with sulphuric acid, besides the substances soluble in water, a yellow powder, which is inso- luble both in cold and boiling water, and which consists of im- pure rubiadine ; but this, like the sugar, which is also sometimes formed during the process, is without doubt a secondary product of decomposition. Indeed the formation of the one is most pro- bably dependent on that of the other. 204 Dr. Schunck on Rubian and its Products of Decomposition, The process of decomposition just described is always accom- panied by an absorption of oxygen. In order to ascertain the quantity of the latter which an alkaline solution of rubian was capable of absorbing, I took 4*2280 grms. of rubian, which after deducting the inorganic matter with which it was contaminated, was equivalent to 4*1049 grms. of the pure substance, dissolved it in hot water, poured the solution into a graduated tube, added to it a solution of about 6 grms. hydrate of baryta, filled the rest of the tube with mercury, and then inverted it over mercury. Oxygen gas was then introduced, and the liquid was from time to time agitated with the gas, in order to bring every portion, and especially the red flocculent precipitate produced by the baryta, and which sank to the bottom of the solution, into fre- quent contact with it. After 143 days I found that 147 cubic centimetres of gas had been absorbed. The contents of the tube were then removed and filtered. There remained on the filter a red baryta compound, which, on being treated as usual, yielded rubianic acid and rubidehydran, as well as a small quan- tity of alizarine. To the red liquid sulphuric acid was added ; the excess of acid was removed with carbonate of lead, and sul- phuretted hydrogen having been passed through the filtered liquid, the latter, after being filtered again from the sulphuret of lead, was submitted to distillation. The distillate was acid, and after being neutralized with carbonate of soda and evapo- rated, left a saline residue having all the characters of acetate of soda. Acetic acid is therefore another product formed in this process, but whether this acid is an essential product of decom- position or not, still remains doubtful. The residue of the distillation contained rubihydran, which was separated by pre- cipitation with basic acetate of lead, as before described, and a little sugar, which was obtained from the liquid filtered from the lead precipitate. The sugar and the alizarine were probably secondary products of decomposition formed from the rubianic acid by the action of the alkali. Rubianic Acid. — This substance really merits the name of an acid, for though its acid properties are not well marked, the fact of its giving crystallized compounds with the alkalies is a suffi- cient indication of the class in which it should be placed. It crystallizes from its watery solution in silky needles of a pure lemon-yellow colour, which when dry form a light, bulky inter- woven mass. Sometimes it is slowly deposited from its watery solution in grains and masses of an indistinctly crystalline form, which have an orange tinge. This diifference in appearance is due to some impurity, which may be removed by redissolving the acid in boiling water and adding a little animal charcoal, when the acid crystallizes rapidly from the filtered solution in Dr. Schunck on Rubian and its Products of Decomposition. 205 needles, as just mentioned. The watery solution has a light yellow colour, reddens litmus paper slightly, and has a distinctly bitter taste, though not so intensely bitter as that of a solution of rubian. It is soluble in alcohol, but not in aether. AVhen heated on platinum foil it melts and then burns with a smoky flame, leaving a slight carbonaceous residue. When heated in a tube it melts to a brownish-red liquid, which on being allowed to cool becomes solid and crystalline, but on being heated again more strongly gives fumes, which condense on the colder parts of the tube to a liquid, which soon solidifies, forming a mass of shining needles. When slowly heated between two watch-glasses, there is formed on the upper glass a sublimate of shining orange- coloured crystals, having the appearance and all the properties of alizarine, while a considerable carbonaceous residue is left on the lower glass. Concentrated sulphuric acid dissolves rubianic acid easily even in the cold, forming a dark red solution, which on being boiled becomes of a dark reddish-brown colour, without evolving much sulphurous acid. If sulphuric acid be added to a watery solution of rubianic acid, and the solution be boiled, dark yellow or orange-coloured flocks begin to be deposited, which increase as the boiling continues. On allowing to cool they often separate in such quantities as to render the liquid quite thick. These flocks are quite uncrystalline, though some- times small yellow crystalline grains are found among them, which consist of undecomposed acid, and disappear on con- tinuing the action for some time longer. These flocks consist of alizarine almost in a state of purity. On dissolving them in alcohol and evaporating spontaneously, a quantity of beautifully crystallized alizarine is obtained. The liquid filtered from the flocks contains sugar, which is obtained with its usual appear- ance and properties on neutralizing the acid with carbonate of lead, filtering, passing sulphuretted hydrogen through the liquid, filtering again, and evaporating. Muriatic acid acts in precisely the same manner on rubianic acid as sulphuric acid. Nitric acid dissolves rubianic acid even in the cold, forming a yellow solution, which on being boiled disengages nitrous fumes and becomes colourless. The solution on evaporation leaves a brown syrup, which contains oxalic acid. Rubianic acid is not decom- posed on being treated with boiling solutions of phosphoric, acetic, oxalic or tartaric acids ; it merely dissolves in them, and crystallizes out again unchanged on the solutions cooling. If chlorine gas be passed through a watery solution of rubianic acid, the yellow colour of the solution slowly disappears. If there are any crystals of undissolved acid floating in the liquid, these disappear very slowly, and the gas must be passed through for a long time in order to efiect their decomposition. The 206 Dr. Schunck on Rubian and its Products of Decomposition* solution now appears colourless, but slightly milky. No yellow flocks are formed, as in the case of rubian, but the solution, on standing for some time, usually deposits a quantity of brown- ish-yellow crystals. If a solution of chloride of lime be added to a watery solution of rubianic acid, the latter turns blood-red, but in a few moments the colour disappears, and the solution becomes quite colourless. Rubianic acid dissolves in caustic potash and soda in the cold with a lively cherry-red colour. If caustic potash be added to a strong watery solution of the acid, nothing separates on stand- ing ; but if carbonate of potash be employed instead of caustic potash, there is deposited almost immediately a quantity of dark-coloured crystalline needles. These needles are the potash salt. When collected on a filter, slightly washed with water and dried, they form a beautiful puce-coloured silky mass. When dried either in the water-bath or in vacuo, the colour changes to a bright red, but after a few minutes' exposure to the atmo- sphere the original colour is restored. Rubianic acid is so weak an acid, that water alone is sufficient to separate it from its combination with potash. When the potash salt is treated with boiling water it dissolves with a red colour, but the solution on cooling and standing deposits yellow crystals of the acid itself. Mere treatment with cold water produces to some extent the same effect; for if the salt be placed on a filter and washed with cold water, numerous small yellow specks, caused by the sepa- ration of the acid, become visible. When caustic or carbonate of soda are added to a boiling watery solution of the acid, the solution deposits on coohng a quantity of small bright red sphe- rical grains, which generally form a mass so bulky as to render the liquid thick and gelatinous. When this mass, which con- sists of the soda salt, is placed on a filter, an almost colourless liquid runs through, leaving the salt on the filter in a soft spongy state, from its retaining mechanically a large quantity of water. The round grains of which it consists, though they have a some- what crystalline appearance, are not in reality crystalline. In consequence of its sparing solubility in water, which is less than that of the potash salt, it may be washed with cold water with- out dissolving. When dry it is dark red, and gives a red powder. It dissolves again in boiling water with a red colour, and the solution on cooling forms a thick jelly, which however is con- verted, on standing, into a mass of yellow crystalline grains con- sisting of acid. If a solution of rubianic acid in caustic potash or soda be supersaturated with any stronger acid, the solution becomes yellow without depositing anything, but after some time the acid separates in yellow crystals. But if the alkaline solution, containing a considerable excess of alkali, be boiled, its Dr. Schunck on Rubian and its Products of Decomposition. 207 colour changes gradually from red to purple, and after prolonged boiling to violet, similar to that of a solution of alizarine in caustic alkali, the colour being generally so intense as to deprive the solution of its transparency. Acids now produce an imme- diate precipitate of dark yellow flocks, while the liquid becomes almost colourless. If the action of caustic alkali has not been continued long enough to produce a complete decomposition of the acid, then after some time crystals of the latter appear in the midst of the flocculent precipitate. The flocks consist of alizarine, but less pure than when the decomposition is effected by means of sulphuric or muriatic acid. On decomposing a considerable quantity of the acid by means of caustic soda, and treating the precipitated flocks in the same manner as those formed by the decomposition of rubian with acids or alkalies, I obtained, besides alizarine, a trace of verantine and a small quantity of a substance resembling rubianine or rubiadine*. The liquid filtered from the flocks contains sugar. Rubianic acid dissolves in caustic ammonia with the same colour as in caustic potash or soda, but with much greater difficulty than in the latter. The solution does not change its colour, however long it may be boiled, and on adding an excess of a stronger acid, the rubianic acid crystallizes out unchanged. On'evapo- rating the ammoniacal solution to dryness it loses part of its ammonia, leaving some yellow crystals of acid surrounded by a red uncrystalline coating like gum. The latter dissolves in cold water, but on evaporation the solution again gives yellow crystals. If to a boiling watery solution of the acid carbonate of ammonia be added, the solution becomes red, and deposits on cooling crystals of the ammonia salt, which have the same colour and appearance as the potash salt. These crystals may be dried without losing their ammonia, but, like the other alkaline salts, are decomposed on redissolving them in boiling water, the solu- tion depositing on cooling crystals of the acid. Baryta water gives in a watery solution of rubianic acid a beautiful crimson flocculent precipitate, while the liquid becomes colourless. If carbonic acid be passed through the liquid the precipitate gradually dissolves, forming a clear yellow solu- tion ; but if this solution be left exposed to the air, its surface becomes covered with a red film, and on evaporation it deposits a quantity of red flocks, until at length the whole of the acid * This substance is light yellow and crystalline. When heated it is volatilized, giving a sublimate of yellow shining needles and scales. It is insoluble in boiling water, but dissolves in boiling nitric acid, and crystal- lizes out of the solution again on cooling in yellow needles. It is preci- pitated from its alcoholic solution by acetate of copper, but not by acetate of lead. 208 Dr. Schunck on Rubian and its Products of Decomposition, seems to be again precipitated in combination with baryta. Lime-water produces in a watery solution of the acid a light red precipitate, while the liquid becomes colourless. If carbonic acid be now passed through the liquid the precipitate dissolves, forming a yellow solution, which on exposure to the air becomes red, but gives no red film, and on evaporation deposits no flocks, but leaves at last a red mass, which dissolves again in boiling water. Acetate of alumina and peracetate of iron produce no change in a watery solution of the acid. Nevertheless the latter is entirely removed from its solution by hydrate of alumina, to which it communicates a light red colour, and also by hydrated peroxide of iron, though not so easily as by alumina. Rubianic acid dissolves easily in a boiling solution of perchloride of iron, forming a dark greenish-brown liquid, which contains proto- chloride of iron. The solution deposits nothing on standing, and on evaporation only a small quantity of black powder sepa- rates, which is probably a compound of alizarine and oxide of iron. Acetate of copper gives in watery and alcoholic solutions of the acid a brownish-red precipitate, which is soluble in boil- ing acetic acid. Neutral acetate of lead turns the watery solu- tion of the acid red, but produces no precipitate ; basic acetate of lead, however, gives a copious red flocculent precipitate, just as in a solution of rubian. An alcoholic solution of the acid gives with an alcoholic solution of acetate of lead a light red pre- cipitate, which after filtration of the alcoholic liquid dissolves in pure water. On adding nitrate of silver to an aqueous solution of the acid and boiling no change takes place, but on the addi- tion of a few drops of ammonia a dark reddish-brown precipitate slowly subsides as a fine powder, which is soluble in an excess of ammonia, forming a red solution, which does not change, and shows no signs of any reduction taking place when it is boiled. On adding chloride of gold to a watery solution of the acid no change takes place even on boiling, but on the addition of a little caustic alkali metalUc gold is deposited, partly as a brown powder, partly in shining scales. If rubianic acid be mixed with water to which a quantity of erythrozym has been added, the yellow crystals of the acid gradually disappear, and are converted into alizarine. The liquid is found to contain sugar. It is impossible to dye with rubianic acid. Mordants acquire in boiling solutions of the acid no more colour than in solutions of rubian or rubianine. On submitting the acid to analysis the following results were obtained : — I. 0*4605 grm., formed by the action of bicarbonate of baryta on rubian, dried in the water-bath and burnt with chromate of lead, gave 0*9445 carbonic acid and 0*2250 water. Dr. Schunck on Ruhian and its Products of Decomposition, 209 II. 0-4030 grra. of another preparation, obtained by the action of bicarbonate of baryta, gave 0*8240 carbonic acid and 0-2020 water. III. 0-2750 grm., formed by the action of caustic soda on rubian, gave 0*5605 carbonic acid and 0*1390 water. IV. 0*4750 grm., obtained by means of ammonia, gave 0*9670 carbonic acid and 0*2295 water. V. 0*2920 grm., obtained by means of caustic lime, gave 0*6000 carbonic acid and 0*1490 water. These analyses give in 100 parts — I. II. III. IV. V. Carbon . . 55*93 55*76 55*58 55-52 56*04 Hydrogen . 5*42 5*56 5*61 5*36 5*66 Oxygen . . 38*65 38*68 38*81 39*12 38*30 corresponding to the formula C^^ H'^ 0% as the following cal- culation shows : — Eqs. Calculated. Carbon ... 52 312 56*01 Hydrogen . . 29 29 5*20 Oxygen ... 27 ^16 38-79 557 100*00 Rubianate of potash was prepared by dissolving the acid in as small a quantity of water as possible, adding an excess of carbo- nate of potash, allowing the salt to crystallize, collecting it on a filter, washing it with just sufficient water to remove the excess of alkali, and drying. On analysing it I obtained the following results : — I. 0*3580 grm., dried in the water-bath and burnt with chro- mate of lead, gave 0*6830 carbonic acid and 0*1590 water. 0*5590 grm. gave 0*0780 sulphate of potash. II. 0*4850 grm. of another preparation, dried in vacuo y gave 0*9250 carbonic acid and 0*2070 water. 0 8140 grm. gave 0*1150 sulphate of potash. These numbers lead to the following composition : — Carbon . Hydrogen Oxygen . Potash . 595*2 10000 100*00 100*00 The soda salt, prepared in the same way as the potash salt, was also analysed, but the analysis led to no satisfactory results. A compound with baryta was obtained by dissolving the acid in water and adding ammonia and chloride of barium. The precipitate, which was bulky and of a fine crimson colour, was Phil Mag. S. 4. Vol. 12. No. 78. Sept, 1856. P Eqs. Calculated. I. 11. 52 312 52*42 5203 52*01 28 28 4*70 4*93 4*74 26 208 34*97 35*50 35*62 1 47*2 7*91 7*54 7*63 210 Dr. Schunck on Rubian and its Products of Decomposition. placed on a filter and washed with water. During the washing its bulk diminished and the colour changed to red, probably in consequence of its losing part of its baryta. Analysis showed it to be a basic compound, in which the acid is to the base as 2 : 3. The neutral baryta salt was obtained by adding chloride of barium to a watery solution of rubianate of potash, when a red precipitate fell, which was collected on a filter, washed with water, and dried in vacuo. I. 0-6020 grm. of the latter compound, burnt with chromate of lead, gave 1*0800 carbonic acid and 0*2580 water. 0-5180 grm. gave 0-0925 sulphate of baryta. II. 0*4440 grm. gave 0*7870 carbonic acid and 0*1900 water. 0*4890 grm. gave 0*0870 sulphate of baryta. These numbers lead to the formula C^^ gas Q^^+BaO + HO, as the following comparison of the experimental results with the theoretical composition shows : — Eqs. Calculated. I. II. Carbon . . 52 312 49*24 48-92 48*34 Hydrogen . 29 29 4*57 4-76 4-75 Oxygen . . 27 216 34*11 3460 3524 Baryta . . 1 766 12*08 11*72 11*67 633*6 100*00 100-00 10000 A lead compound was prepared by adding to an alcoholic so- lution of the acid acetic acid and acetate of lead and then a little ammonia, taking care to leave an excess of rubianic acid in solu- tion. The red precipitate was collected on a filter, washed with alcohol and then dried, at first in vacuo, and then for several hours in the water-bath. Its analysis gave the following results: — 0-5490 grm. gave 0*6760 carbonic acid and 0*1580 water. 0-6600 grm. gave 0-3760 sulphate of lead. These numbers correspond in 100 parts to- Carbon 33*58 Hydrogen 3*19 Oxygen 21*32 Oxide of lead 41*91 The most probable formula for this compound is 2C^^ H^^ 0*^ 4- 7PbO, though the numbers found by experiment agree better with the formula 2C^^E^ 0^-{-7^hO, as will be seen from the following calculation : — Eqs. Calculated. Eqs. Calculated. Carbon . . 104 624 33*22 104 624 33*55 Hydrogen . 56 56 2*98 54 54 2*90 Oxygen. . 52 416 22*17 50 400 21*51 Oxide of lead 7 781*9 41*63 7 781*9 42*04 1877*9 100*00 1859*9 100*00 Dr. Schunck on Rubian and its Products of Decomposition. 211 Another specimen of the lead salt, prepared by precipitating an alcoholic solution of the acid with an alcoholic solution of basic acetate of lead, was found to have a composition agreeing tolerably well with the formula C^^ h^s Q^s + 9PbO. When this precipitate was redissolved in a mixture of alcohol and acetic acid, and a fresh precipitate was produced by means of a little ammonia, the latter was found to contain acid and oxide of lead in the proportion of 1 equiv. of the former to 6 equivs. of the latter. It appears, therefore, that these lead precipitates are by no means uniform in composition. The silver salt was obtained by dissolving the acid in boiling water, adding a small quantity of ammonia and then nitrate of silver, when it fell in the form of a dark chocolate-coloured floc- culent precipitate, which, when viewed under a lens, was some- times seen to consist Of small crystalline needles. The preci- pitate was collected on a filter and slightly washed with water. As it was found to dissolve in water with a reddish-brown colour, as soon as the excess of nitrate of silver was removed, the edul- coration was completed with alcohol, in which the salt is insoluble. After being dried in vacuo — 0*6300 grm. gave 0*1370 grm. chloride of silver, equivalent to 0-11076 or 17*58 per cent, of oxide of silver. The formula C52H28 0^+AgO requires 17*47 per cent. The alizarine and sugar obtained by the decomposition of rubianic acid with acids and alkalies, I found to have the usual composition, as the following analyses will show : — I. 0*2190 grm. alizarine, obtained by the action of sulphuric acid on rubianic acid, dried at 100° C, yielded 0*5550 carbonic acid and 0*0850 water. II. 0*3320 grm. alizarine, formed by the decomposition of rubianic acid with caustic soda, dried at 100° C, gave 0*8480 carbonic acid and 0*1195 water. These numbers give in 100 parts — I. II. Carbon . . . 69*11 69*66 Hydrogen . . 4*31 400 Oxygen . . . . 26*58 26*34 The sugar derived from the decomposition of rubianic acid with sulphuric acid was prepared for analysis by heating it, after the solution had been evaporated to a syrup, for some time at 100°C. until it became sufficiently brittle to be pulverized, when 0*3600 grm. yielded 0*5840 carbonic acid and 0*2060 water, corresponding with the following composition : — P2 212 Dr. Schunck on Rubian and Us Products of Decomposition, Eqs. Calculated. Found. Carbon . . . 12 72 44-44 44-24 Hydrogen. . . 10 10 617 6-35 Oxygen . . . 10 80 49-39 49-41 162 10000 100-00 This specimen of sugar had therefore the same composition as that obtained by the action of erythrozym on rubian*. The analysis of the acid, its compounds and products of de- composition just detailed, lead to the conclusion that its compo- sition must be expressed by the formula C** H^ 0% and that it belongs to the class of the so-called glucosides, the copula con- tained in it being alizarine. Its decomposition, by means of strong acids and alkalies, into alizarine and sugar, is symbolized by the following equation : — C62H«027 + 5HO = 2C^4H504-f2C^2H»20^2. In order to remove all doubt concerning the true formula of this substance, I determined the quantities of alizarine which were obtained by decomposition of weighed quantities of the acid with sulphuric acid and with caustic soda. 1-7210 grm. rubianic acid, dried at 100° C, gave, when de- composed with sulphuric acid, 0'7310grm. dry alizarine =42*47 per cent. 1-2020 grm. rubianic acid yielded, when decomposed with pure caustic soda, on precipitation with sulphuric acid, 0*5430 grm. alizarine=45-17 percent. Assuming the formula C^^ H^^ 0^ to be correct, 100 parts of acid should, according to theory, afford 43*44 of dry alizarine. If Strecker^s formula for alizarine, C^® H^ 0^, were the correct one, then the only possible formula for rubianic acid, though the calculated composition would then not agree very well with that found in my experiments, would be C^^ W^ 0^, in which case the quantity of alizarine derived from 100 parts of acid would be 62' 70. It will be seen, therefore, that the view which I have adopted of the constitution of the acid derives considerable support from these determinations. A comparison of the composition of rubian and rubianic acid shows that the latter can only be derived from the former by means of oxidation. In order however to remove all doubt on this point, I made the following experiment. A solution of rubian was divided into two equal parts. One half was boiled to expel all the air it might contain, then mixed with a certain quantity of caustic soda, and immediately put into a bottle, which the liquid just sufficed to fill, and which was then closed * Phil. Mag. for June 1853, p. 424. Dr. Schunck on Ruhian and its Products of Decomposition. 213 air-tight. The other half was mixed with the same quantity of caustic soda and left exposed to the air. After twenty-one days both liquids were examined in the same manner. The soda was supersaturated with acetic acid, the liquid was again rendered alkaline with ammonia, and then chloride of barium was added, which gave in each case a red precipitate. This precipitate was treated as usual with sulphuric acid and carbonate of lead, and the filtered liquid was evaporated to dryness. From that part of the solution which had been enclosed in the bottle I obtained in this manner a quantity of a substance resembling rubian, which was probably rubidehydran, but not a trace of rubianic acid; whereas, by adding baryta water to the liquid filtered from the precipitate with chloride of barium, leaving the mix- ture to stand exposed to the air for some time, filtering and treating the substance left on the filter with sulphuric acid as usual, I obtained a small quantity of the acid. On the other hand, the precipitate with chloride of barium from the second half of the solution, which had been left in an open vessel, yielded at once 0'60 grm. of rubianic acid as well as a quantity of rubidehydran, but the liquid filtered from this precipitate, on being mixed with baryta water and treated as before, gave no more acid. Hence it follows that the presence of oxygen is as essential as that of alkalies to the formation of this acid. As regards the manner in which the formation of rubianic acid takes place, we may suppose it to be effected in two ways. Assuming 1 equivalent of rubian to absorb 10 equivalents of oxygen, it may then yield 1 equivalent of rubianic acid, 4 equi- valents of carbonic acid, and 5 of water, as the following equa- tion will show : — C66 H34 030 _,_ 100 = C^2 H29 0^7 + 400^ + 5H0. But since acetic acid is found among the products of decom- position, it is possible that this acid takes the place of carbonic acid, and the equation will then appear as follows : — cm H34 030 + 20 = C^2 H29 Q^^ + C^ H^ 0^ + 2H0. It is a very remarkable circumstance, that a body like rubianic acid, which belongs to a class of a highly complex nature, and having in general a high atomic weight, should owe its forma- tion to a process of oxidation. It is probably the first known instance in which the formation of a body of this class by means of oxidation has actually been observed. Some years since Rochleder described a body obtained from madder to which he gave the name of ruherythric acid*. This body, like rubianic acid, is decomposed by strong acids into ali- zarine and sugar, and the other properties mentioned by Roch- * Berichte der Wiener Academic, April 1851. 214 Dr. Schunck on Rubian and its Products of Decomposition. leder are similar to those of rubianic acid. It is therefore very probable that the two acids are identical. But the description given by Rochleder of his acid is not sufficiently minute to enable me to come to a decision as to their identity, and the composition ascribed to it by him (C 54'48, H 5*16, 0 40*36 per cent.) differs so much from that of rubianic acid as almost to lead one to beheve that they are not the same. Until therefore the properties and composition of ruberythric acid have been more accurately studied, it will be impossible to arrive at any positive conclusion on this point, and for the present the two acids must be considered as distinct*. Rochleder has ventured to express his conviction that rubian is nothing but impure ruberythric acidf. The experiments which I have here described must lead to the conclusion that such an opinion cannot for an instant be entertained. If rubianic acid and ruberythric acid are identical, then Rochleder has only committed the common error of mistaking a product for an educt. Rubidehydran, — As obtained by the method above described, this body is not perfectly pure. It may be purified by redis- solving it in water, evaporating the solution to a syrup, and then adding a quantity of alcohol, which precipitates a reddish-yellow glutinous substance mixed with sulphates of lime, magnesia, and soda. The alcoholic liquid having been allowed to clear, is de- canted and evaporated to dryness, when it leaves a dark yellow or reddish-yellow, brittle, transparent residue like gum or var- nish, which cannot be distinguished from rubian in appearance. It still gives, when burnt, a quantity of ash, consisting of sul- phates of lime and magnesia, but I did not attempt to purify it any further, for fear of inducing a change in its composition. Rubidehydran resembles rubian exactly in most of its properties. It is not in the least deliquescent. If it shows any tendency to deliquesce on exposure to the air, this must be attributed to its containing some impurity. It has a strongly bitter taste. The watery solution is yellow, and when boiled, with the addition of sulphuric or muriatic acid, deposits yellow flocks, and after cool- ing appears almost colourless. Like rubian, it is also decom- posed on boiling the watery solution with the addition of caustic potash or soda, the solution becoming purple and depositing yellow flocks on supersaturating the alkali with acid. It is not precipitated from its aqueous solution by any earthy or metallic ♦ The easiest way of arriving at a conclusion would be by determining the amount of alizarine which ruberythric acid by its decomposition is capable of yielding. If Rochleder's formula C^^ H^o O^ be accepted, it should give 67*04 per cent, of alizarine. Variations of several per cent, in the amount of aUzarine obtained would still allow a positive decision to be arrived at. t Ann. der Chem, und Pharm. vol. Ixxxii. p. 215. Dr. Schunck on Rubian and its Products of Decomposition, 215 salt, with the exception of basic acetate of lead, which produces a red precipitate, while the liquid becomes colourless. The alcohol solution, however, gives, with an alcoholic solution of neutral acetate of lead, a red precipitate, similar to the last, which is soluble in water. When exposed in a dry state to the action of heat, and to that of chlorine in its watery solution, rubidehydran behaves exactly like rubian. It may, however, be distinguished from rubian by its not yielding a trace of rubianic acid, when its watery solution is mixed with caustic soda or baryta and left exposed to the atmosphere for some time. Its products of decomposition with acids differ also from those of rubian. If a solution of the substance in water be boiled with the addition of sulphuric acid, yellow flocks are deposited, which consist principally of alizarine, with some rubiadiue and a little verantine and rubiretine, but not a trace of rubiauine, while the filtered liquid contains sugar. Rubidehydran yields therefore the same products with acids as rubian does with alkalies, which makes it very probable that rubian, when acted on by alkalies, is first changed, in part at least, into rubidehydran. In calculating the composition of this substance from the analysis, I took it for granted that the lime and magnesia found in the ash are contained originally in it as sulphates, and there- fore always treated the ash obtained in the first instance with sulphuric acid, in order to replace that portion of the sulphuric acid which might have been reduced during the process of igni- tion, and then made the corrections accordingly. I. 0'4360 grm. rubidehydran, formed by the action of bicar- bonate of baryta on rubian, dried at 100° C. and burnt with chromate of lead, gave 0*8005 carbonic acid and 0'2130 water. 0-2790 grm., on being incinerated, left 0-0150 grm. ash, which after being treated with sulphuric acid and heated again, weighed 0*0325 grm. =11*64 per cent. II. 0*4950 grm., formed by the action of lime-water on rubian, gave 0*9750 carbonic acid and 0*2320 water. 0*6220 grm. left 0*0200 grm. ash, which after treatment with sulphuric acid, weighed 0*0340 grm. =5*46 per cent. III. 0'4795 grm., obtained by means of caustic baryta, gave 0*9540 carbonic acid and 0*2320 water. 1*0785 grm. left 0*0245 grm. ash, which after treatment with sulphuric acid, weighed 0*0455 grm. =4*21 per cent. IV. 0*4990 grm., obtained by means of ammonia, gave 0*9780 carbonic acid and 0*2320 water. 0*7385 grm. left 0*0155 grm. ash, which after treatment with sulphuric acid, weighed 0*0395 grm. = 5*34 per cent. 216 Dr. Schunck on Rubian and its Products of Decomposition. After making the due corrections for the ash in the way just described, these numbers correspond in 100 parts to — I. II. III. IV. Carbon . . . 5666 5681 56*06 5646 Hydrogen . . 6-13 550 5*54 5-45 Oxygen . . . 3721 37*69 38*40 3809 leading to the formula C^' H^* 0*^ as the following calculation shows : — Eqg. Calculated. Carbon ... 56 336 56*75 Hydrogen . . 32 32 5*40 Oxygen ... 28 224 37*85 592 100*00 The lead compound was prepared by dissolving the substance in a small quantity of water, adding an alcoholic solution of acetate of lead, separating the red precipitate which was formed, by filtration, adding a little ammonia to the filtered liquid, taking care to leave an excess of rubidehydran in solution, fil- tering the precipitate and washing it with alcohol. 0*5705 grm. of this precipitate, dried in the water-bath, gave 0*6110 carbonic acid and 0*1465 water. 0*3180 grm., treated with sulphuric acid and heated, left 0*2200 grm. residue, which on being treated with hot water, yielded to the latter 0*0140 grm. sulphate of magnesia, leaving 0*2060 sulphate of lead. These numbers lead to the following composition : — Eqs. Calculated. Found. Carbon . . 56 336 29*20 29*20 Hydrogen 32 32 2*78 2*85 Oxygen . . 28 224 19*48 » Oxide of lead 5 558*5 48*54 47-66 1150*5 100*00 The deficiency in the oxide of lead in this analysis arose without doubt from the oxide being in part replaced by mag- nesia. It appears therefore that rubidehydran diff'ers from rubian merely by containing the elements of two equivalents of water less, and the origin of the different products of decomposition to which it gives rise may therefore be explained in the same manner as in the case of rubian. Of its products of decomposition with acids 1 only obtained alizarine in quantities and of the degree of purity requisite for analysis. It had the usual composition of that substance, as the following analysis will show : — Dr. Schunck on Rubian and its Products of Decomposition, 217 0'2500 grm. of the crystallized substance lost, on being heated in the water-bath, 0'0460 water =18'40 per cent. 0-2800 grm. of the dry substance gave 0*7110 carbonic acid and O'lOSO water, corresponding in 100 parts to — Carbon . . . 6925 Hydrogen . . 4'08 Oxygen . . . 26*67 Ruhihydran. — This substance, like rubidehydran, bears a great resemblance to rubian, the body from which it is derived. It is obtained on evaporation of its solutions as an uncrystalline, transparent mass like gum, having a dark brownish-yellow colour and a bitter taste. When quite dry it is brittle and may be easily pulverized, but on exposure to the atmosphere at the ordinary temperature it rapidly attracts moisture and becomes soft, a pro- perty by which it may be distinguished from rubian and rubide- hydran. On being heated in a tube it gives less crystalline sublimate than rubian does. Its watery solution, on being boiled with the addition of sulphuric or muriatic acid, becomes muddy, and slowly deposits a quantity of yellow flocks mixed with some brown resinous drops. The liquid must be boiled for a consider- able time in order to effect the entire decomposition of the ru- hihydran contained in it and make it appear colourless. The flocks on being collected on a filter are found to consist chiefly of rubiretine, verantine, and rubiadine, with only a very small quantity of alizarine, while the filtered liquid contains sugar. The products of decomposition with acids are therefore the same as those of rubidehydran, the only difference being in the rela- tive proportions of the products formed. It is not decomposed, when treated with boiling phosphoric, oxalic, tartaric or acetic acids. If a watery solution of ruhihydran be boiled with caustic potash or soda, the colour of the solution, which was red on the first addition of alkali, changes to reddish- or yellowish-brown, but only a few purple flocks are deposited. This circumstance also serves to distinguish this substance from rubian and rubi- dehydran, the watery solutions of which, when mixed with caustic alkali and boiled, deposit an abundance of the purple compound of alizarine and alkali. Nevertheless the ruhihydran is completely decomposed by the caustic alkali, for on adding an excess of acid to the liquid a quantity of yellow or light brown flocks are pre- cipitated like those produced by the action of acids, while the liquid becomes almost colourless. When chlorine gas is passed through the watery solution, it produces exactly the same effects as in watery solutions of rubian or rubidehydran. It is the behaviour to chlorine, which more than any other reaction proves that these substances have a similar composition, and forms perhaps the most 218 Dr. Schunck on Rubian and its Products of Decomposition, characteristic mark of distinction between them and rubianic acid. Rubihydran is not precipitated from its aqueous solution by any reagent except basic acetate of lead, which produces a light brownish-red precipitate, which is paler and less bright than the precipitates produced by the same reagent in solutions of rubian or rubidehydran. The liquid filtered from this pre- cipitate has still a light yellow colour, and ammonia produces in it a fresh precipitate of a pale pink colour, after which it appears colourless. Rubihydran is soluble in alcohol, but not very easily. From the manner in which it is prepared it may be inferred, that it is incapable of yielding rubianic acid by the influence of the same agents which lead to the formation of the latter from rubian. In order to obtain this substance in a per- fectly dry state, it is necessary to heat it in the water-bath con- tinuously for a day or two. In two analyses I obtained numbers corresponding respectively with the formulae C^' H'*^ 0"*^ and (^56 JJ42 Qs» \ Qjjjy succeeded once in obtaining it of the same composition, or as free from water as when in combination with oxide of lead. On this occasion it gave the following results : — 0'3940 grm. gave 0*7440 carbonic acid and 0"2130 water, numbers which lead to the following composition : — Eqs. Calculated. Found. Carbon . . . 56 336 51-29 51-50 Hydrogen . . 39 39 5-95 6-00 Oxygen . . . 35 280 42-76 42-50 655 100-00 10000 On being burnt this specimen left no ash. The lead compound was prepared by dissolving the substance in alcohol and then adding acetate of lead and ammonia, taking care to leave an excess of rubihydran in solution, filtering, wash- ing the precipitate with alcohol and drying, at first in vacuo, and then for several hours in the water-bath. I. 0'8740 grm. of this compound gave 0*6720 carbonic acid and 0-1970 water. 0-7270 grm. gave 0-5850 sulphate of lead. II. 0-8860 grm. gave 0-6820 carbonic acid and 0-1930 water. 0-8465 grm. gave 0-6805 sulphate of lead. In 100 parts:— I. II. Carbon 20-96 20-99 Hydrogen .... 2-50 2*42 Oxygen 1734 17-44 Oxide of lead . . . 59-20 5915 100-00 100-00 The amount of oxide of lead here stands in no simple relation Dr. Schunck on Rubian and its Products of Decomposition. 219 to that of the other constituents. If the oxide of lead be de- ducted, then the rubihydran combined with it will have the following composition in 100 parts : — I. II. Carbon 51-37 51-38 Hydrogen .... 6-12 5-92 Oxygen 4251 4270 100-00 100-00 It will be seen that this is exactly the composition of the substance itself according to the analysis given above, and it follows that the composition of rubihydran, both in a perfectly dry state and when in combination with oxide of lead, is ex- pressed by the formula C^ H^^ 0^^. It differs therefore from rubian by containing the elements of 5 equivalents more of water. That it should yield the same products of decomposition as rubian and rubidehydran is therefore not at all extraordinary. The rubiadine which is formed by the decomposition of rubi- hydran with acids may be obtained in a state of greater purity and with much greater facility from this, than from any other source. It is separated from the other products of decomposi- tion in the manner I have described when treating of the action of alkalies on rubian. It is purified by dissolving it in boiling alcohol and adding to the boiling solution hydr^ted oxide of lead, when it crystallizes from the filtered solution in beautiful golden-yellow, glittering scales, some of which assume the form of regular four-sided tables, possessing all the properties of ru- biadine*, but evidently freer from impurities than when obtained by the action of alkalies on rubian. I. 0'3060 grm. of this substance, dried at 100° C, gave 07795 carbonic acid and 0-1380 water. II. 0*2580 grm. of the same, recrystallized from boiling alco- hol, gave 0-6600 carbonic acid and 0*1190 water. From these numbers it may be inferred that its composition is as follows : — Calculated. I. II. Carbon . . 32 192 69-31 69-47 69-76 Hydrogen . 13 13 4-69 5-01 512 Oxygen . . 9 72 26-00 25-52 25-12 277 100-00 100-00 100-00 * In examining these crystals I discovered a property of rubiadine which I had not previously observed. If the ammoniacal solution, which is red, be mixed with chloride of barium, it deposits a quantity of dark brownish- red needle-shaped crystals, which are evidently the baryta compound of rubiadine, while the liquid loses almost all its colour. The rubiadine de- rived directly from rubian also yields these crystals. 220 Prof. Stevelly on the Doctrine of Parallel Lines The formula C^* H^^ 0^, to which these analyses lead, differs from the one formerly given, C^* H** 0®, by 1 equivalent of water. I prefer the former, since the substance employed in the last analyses was evidently purer than that used in any previous one. It will be seen also, that the formula just given is con- firmed by an examination of the products of decomposition of rubian with chlorine. [To be continued.] XXIX. The Doctrine of Parallel Lines considered in a new Method. By John Stevelly, LL.D.y Professor of Natural Philosophy in Queen's University , Ireland. To the Editors of the Philosophical Magazine and Journal. Gentlemen, Belfast, July 3, 1856. HAVING been lately engaged teaching my youngest son the elements of Euclid, 1 was again induced to waste some hours on a subject on which in my schoolboy and college days I, in common I suppose with every schoolboy and collegian since the days of Euclid, had over and over again wearied myself in vain. On this occasion, however, the matter presented itself to my mind in a form which, to me at least, was quite new, and which seems to afford a solid foundation for the doctrine of parallel lines, and to place the subject in a form not perhaps un- suited to elementary instruction. If you agree with me, and think it worth a place in your valuable Magazine, it is at your service. I am. Gentlemen, with much respect. Your obedient Servant, John Stevelly. .JZ. Definition, Let two straight lines in ^ the same plane [wxditiA yz) be ~ said to be parallel when both stand at right angles to the same straight line (A, B). }/ IB 2: Cor, I. Hence two parallel lines, if produced indefinitely on either side, can never meet. (Otherwise a triangle would be formed with an external angle equal to an internal remote angle, as both are right. This would contradict the 16th of Euclid's first book.) Cor, II. Hence equally distant points from A and B, taken along wx and yz on each side of AB, are equally distant from considered in a new Method. 221 D w m ^ V E / A C €0 Z B each other. (This can be shown as a simple consequence of the 4th of Euchd's first book ; but is manifest more simply by supposing wK^y to be folded over upon AB ; for, on account of the right angles, wA, kx and ^/B, ^z would coincide throughout their entire length.) Proposition. Lemma I. Let wx and yz be two parallel lines, AB the line to which both are perpen- dicular. Take D and E, equally distant from A and B, on the same side of AB. Bisect AB in C. Erect Cm perpendicular to AB. Then shall Cu meet DE as in m, a point which bisects DE ; and Cm shall stand perpendicularly to DE. For Cm is parallel to both wx and yz, and therefore, if produced, can never meet either {Cor. I. Def.). Therefore if produced, it must cross DJS between D and E. Suppose at m, now join Am and Bm. Then in the triangles ACm and BC?w we have the sides AC and Cm respectively equal to BC and Cm, and the angles contained by these sides (both right) equal, therefore (4th, first book of Euclid) Am = Bm, and the angles CmA=CmB, and CAm = CBm; and since the angle DAC=EBC (both right), hence mAD = mBE. Then in the triangles mAD and mBE we have the sides DA and Am respectively equal to EB and Bm, and the angles contained by those sides also equal ; therefore (4th, Euclid's first book) Dm=Em ; and the angle DmA=EmA. Therefore we have DmC = DmA + AmC = EmB + BmC = EmC, and therefore mC perpendicular to DE, and bisects it. Q.E.D. Corollary, Hence also angle EDA = DEB. Proposition. Lemma II. Let AD and BE (fig. 1 or fig. 2) be any parallel and equally long lines both perpendicular to AB. Join D and E. Then shall the joining line stand perpendicularly both to AD and to BE. Take four points, a, d, V, and Z>, the two first near to and equally distant on each side from A ; the two latter, the same distances on each side of B. Erect the four lines ad, dd\ 6V, and he, each perpendicular to AB, and each equal in length to AD or BE. Join d with ^ by the straight line dd\ and e' with e by the straight line e^e. These joining lines are each respect- ively at right angles to AD and BE (produced if necessary), and are bisected by them {Lemma I.). At D, draw the straight line 222 Prof. Stevelly on t/ie Doctrine of Parallel Lines wDx at right angles to AD, and at E the line tu^Ex' perpendi- Fig. 1. d Mr d' e' m' . 1 _ ■ tv D 3C w' 0 E a' a 1 L <3 t/ 1/ "A 0 Fig. 2. ^^ D ^ r^ u^ a;' E ^ / . [ d m d' e C n€ e a J L (i ^ I < I \ I cular to BE. Then if d and c?' can be conceived not to be in the line wx, they must stand either equally above it, as in fig. 1, or equally below it, as in fig. 2 (as may be shown in a round- about manner by a mere application of the 4th of Euclid^s first book, or), as may be (more) readily seen to be evident by con- ceiving wl^Kad to be folded over on the line AD ; when wl^ must coincide with a:'D, ak. with a' A, and ad with cid^ ; therefore d with d' and the point where ad meets wx, with the point where a'd! meets it. The same is true of the perpendicular line lu'Ex', and the points e' and e. And since one line Cu stands perpen- dicular to AB at C, which at the same time bisects ab, AB, and a'b', we may conceive the left-hand side of either figure to be so folded over Cu as to coincide in all similar lines and correspond- ing points with the right-hand side of that figure ; and therefore fig. 1 or fig. 2 must represent the circumstances, if the lines wx, wx', dd\ and e^ can be supposed not to be coincident through- out : also on that supposition, wx, if produced indefinitely, could never meet dnJe-y nor could dmd' ever meet idEx', Hence, if we now join D with m' by a straight line, no part of that join- ing line can in fig. 1 fall below Da?, nor in fig. 2 above it (other- wise two straight lines would enclose a space). Nor can any part of the same Dm' fall in fig. 1 above eW, nor in fig. 2 below considered in a new Method. .223 it (for a similar reason) ; and therefore Dm' must always lie between wx and dd\ and between vJx^ and ee^, if they do not all coincide, let the points a, a , b', and b be taken closer to A and B, or further from them. But smcealwdLys ad = AD = a' d' = b'ef==SE=be, we may make m' approach unlimitedly close to Eby takingi'B =Bd unlimitedly small ; and similarly m will approach unlimitedly to D, and e'e to rn'of, and d'd to wx ; and therefore in the limit they all coincide ; and Dm', which in the limit coincides with DE, is perpendicular to AD ; and therefore DE (which never changes its position) is always perpendicular to AD ; and similarly (or by corollary to Lemma I.) to BE. Q.E.D. Cor. I. Hence any line which is perpendicular to one of two parallel lines AD, must, if pro- duced, meet the other, and be perpendicular to it also. For if a line be perpendicular at any point D to AD, take BE=AD and join DE; this joining line, being perpendicular to both, must coincide with the perpendicular to AD atD. Cor. 11. Hence all common perpendiculars to two parallel lines meet them at equal di- stances from A and B. Cor. III. Hence all common perpendiculars to two parallel lines must be equal to one another throughout, and each must be equal to AB. For since DE (any joining line) and AB are both perpendicular to AD, they also are parallel ; and since BE is perpendicular to both, AB=DE. Prop. 27 of Euclid's First Book, If a line (xy) falling on two other lines {wx and yz) make the alternate angles equal {wxy — zyx)y these lines shall be parallel. For bisect xy in C, and let fall CA perpendicular on wXj and CB perpendicular on yz. Then in the triangles xAG and ?/BC, ^C = yC, and the angle Qxh. = CyB (hypothesis) and angle a?AC = 2/BC (right); therefore (26th of Euclid's first book) the angle a?CA=?/CB. But a?CA + ACy = two right angles (13th of Euclid's first book) = BCy-f i/CA. Therefore AC and CB are one continued line, and perpendicular to both wx and yz, which are therefore parallel. Q.E.D. 224 Prof. Stevelly on the Doctrine of Parallel Lines. Proposition 28 of Euclid's First Book Follows at once, as in Euclid, from Prop. 27. Prop, 29 of Euclid's First Book. Any line (ccy) which falls upon two parallel lines {wx and yz) makes (1) the alternate angles equal (as wxy=zyx)', (2) any external angle equal to the internal, remote on the same side ; and (3) the two internal, on the same side, together equal to two right angles. (1.) From x let fall xz perpendicular to yz ; and from y, yw perpen- dicular to wx. These lines are also respectively equal to each other, and perpen- dicular, the first to wXy the latter to yz (Cor. I. and III. Lemma II.). Hence in the two triangles, three sides of one equal respectively three sides of the other. Hence (8th of Euclid's first book) the angle wxy=zyx. The alternate angles are equal. From which the other two parts follow obviously as in Euclid. The other propositions follow as in Euclid, without any aid from the 12th axiom, which then becomes an easy deduction from the above, thus (as in the notes to Elrington's Euclid). Euclid's 12ih Axiom. If angles xwA -H wAz are together less than two right angles, the lines shall, if produced, at length meet on that side. — - — . ~~ i V a of a" 1' / ■ — 1 \h y / i a"^"^ ^_™-^^^j^ w I X Draw k^ so as to make xwA'\-wA^-=- two right angles, kz^ is parallel to wx (as proved above). Let fall AB perpendicular to WXy and take Al = 12 = 23 = &c. Let fall 1«, 2a', 3«", &c. perpendiculars on A-?', and draw 16, 2c, &c. perpendicular to these. It then is obvious from Cor. III. Lemma II., and from 26th of first book of Euclid, that 2a' is twice as long as 1 a, 3a" three times as long, and so on. Hence as we assume equal distances along kzy the perpendiculars must at length become longer than BA, and therefore these points and also the line kz must at length pass to the other side of wx. Q.E.D. [ 225 ] . XXX. On Scheutz's Calculating Machine. , By G. B. Airy, Esq.,, Astronomer Royal. To the Editors of the Philosophical Magazine and Journal. Royal Observatory, Greenwichj Gentlemen^ August 25, 1856. I RE MARK that in your Supplementary Number for July you have transcribed the Report of the Royal Society's Com- mittee on M. Scheutz's Calculating Machine. I had the pleasure of examining that machine shortly after its arrival in this country, and I cannot refrain from expressing my general admiration of the beauty of its arrangements, and my assurance that such a machine is not likely to get out of order, and that it can be con- structed at comparatively small expense. I am also impressed with the ability and accuracy of the Committee's Report. But I wish to guard myself from giving an opinion on the utility of the machine ; remarking only that, as I believe, the demand for such machines has arisen on the side, not of computers, but of mechanists. Permit me, however, to point out to you a course of computa- tions, of a most mechanical and monotonous kind, which is going on frequently in every place of extensive and systematic calcu- lations, and to which I think the attention of the constructors of mechanical computing machines might advantageously be directed. An immense number of computations consist of parts follow- ing each other in the following order : — 1st. Independent calculations are made (for instance, from the lunar tables) for equal intervals (for instance, for every twelve hours) . 2nd. The differences of the computed numbers are taken, probably to the fourth order, as a check on th« accuracy of the computed places. 3rd. Differences of the first and second order are formed, ap- plicable to the interpolation of places for every hour. 4th. These differences are appKed to form the places for every hour. The most tedious of these operations is the second (I assume that the first can never be dispensed with) . This second operation appears to be well adapted to mechanical action. Speaking (for the present) without mature consideralfton, I should conceive, that, by reversing the order of the figures oU some of the wheels, and with some other instrumental changes, and by feeding the proper wheels continually with new computed numbers instead of new differences, the additive operations of M. Scheutz's engine might be made subtractive ; and the new Phil Mag. S. 4. Vol. 12. No. 78. 8ept, 1856. Q 226 . Royal Society : — final result in every case might be a fourth difference instead of a number formed by fourth differences. At any rate, I conceive that the object is within the reach of mechanical contrivance. If this could be done, I really believe that a very iinportant benefit would be conferred on computers. Of the other operations, the fourth would be effected by a very simple difference-engine ; possibly also the third might be con- veniently done by mechanism, though it is sufficiently simple in numerical calculation. I am. Gentlemen, Your obedient Servant, G. B. Airy. XXXI. Proceedings of Learned Societies, ROYAL SOCIETY. [Continued from p. 149.] Jan. 17, 1856.— Prof. William Allen Miller, M.D., V.P., in the Chair. r| "^HE following communication was read : — X " On some of the Metamorphoses of Naphthalamine." By A. W. Hofmann, Ph.D., F.R.S. &c. The great facility with which some of the nitro-hydrocarbons can be reduced by means of iron and acetic acid — the modification of Zinin's process, lately proposed by M. Bechamp — enables us to obtain the corresponding bases in larger quantity, and to examine their derivatives more minutely. One of the bases, for the preparation of which this process is par- ticularly applicable, is naphthalidine, or as it is more appropriately called, naphthalamine. Mr. "William H. Perkin is engaged in exa- mining the deportment of this substance with chloride of cyanogen, and the following is a summary of the results he has at present obtained. Fused naphthalamine, when submitted to the action of chloride of cyanogen, absorbs this gas with great avidity, and is gradually con- verted into a dark resinous mass. This is the hydrochlorate of a new base, which has received the name of menaphthalamine, in con- sequence of the analogy of its origin with that of melaniline, derived by a similar process from aniline, Menaphthalamine is separated from the hydrochlorate by potassa, washed and repeatedly recrystallized from alcohol. It contains and is formed according to the equation 2C,o Hp N + Cj, NCI = C,, H,7 N3 HCl. Naphthala- Chloride of Hydrochlorate of mine. cyanogen, menaphthalamine, Mr. Perkin has verified this formula of menaphthalamine by the Dr. Hofmann on the Metamorphoses of Naphthalamine* 227 analysis of the hydrochlorate and of the platinum salt, which respectively contain C42H17N3, HCland C42H17N3, HCl, PtClg. Among the various metamorphoses which menaphthalamine im- dergoes under the influence of agents, the deportment of this sub- stance with cyanogen has especially engaged the attention of Mr* Perkin. Menaphthalamine, like melaniline, absorbs two equivalents of cyanogen, and is converted into a slightly crystalline buif-coloured substance, which retains feebly basic properties. The analysis of this body, which, from its composition, may be termed dicymenaphthalamine, has led to the formula C46H,7N3 = C4,H,,N3 + Cy,. Dicymenaphthalamine is insoluble in water, moderately soluble in alcohol and ether. It dissolves readily in acids. The latter solution, when precipitated by potassa, immediately after it has been made, yields unchanged dicymenaphthalamine ; but if the solution be allowed to stand for a few moments, a yellow substance is precipi- tated, which is no longer a salt of dicymenaphthalamine. The composition of this yellow body, which, in accordance with the terminology adopted in the aniline series, may be called menaph- thoximide, is represented by the following formula — and its formation is illustrated by the equation — C46 Hi7 N. + 4H0 + 2HC1 = C4, B.,, N3 O4 + 2NH4 CI. Dicymenaph- Menaphthox- thalamine. imide. In fact, the mother-liquor of this substance contains a large amount of ammonia. Menaphthoximide may be viewed as binoxalate of menaphthala- mine minus 4 equivalents of water — C^^itN^HC^O^, HC^O^- 4H0 = C46Hi,N3 04; Binoxalate of menaphthalamine. Menaphthoximide. and this view is corroborated by the deportment of the substance with potassa, which reproduces menaphthalamine and oxalic acid. From the preceding experiments, it is obvious that the deport- ment of naphthalamine with chloride of cyanogen is perfectly analo- gous to that of aniline. The subsequent metamorphoses of the newly-formed compound also exhibit the same analogy. Aniline series. Naphthalamine series. Aniline ^12^7 ^ Naphthalamine .... C^a ^9 ^ Menaphthalamine . . C42 Hj; Ng Dicymenaphthalamine C^g Hj; Ng Menaphthoximide . . C^q Hjy Ng O4 Results of much interest are to be expected from the examination of the products formed by the action of heat on menaphthoximide, Q2 Melaniline .. C26HJ3N3 Dicymelaniline Cg^ H^g N^ Melanoximide C30H13N3O4 228 Royal Society :— It is probable that this reaction would produce the naphtlialamine term, corresponding to anilocyanic and cyanic acid. Cyanic acid. . .'. Cj H NOj Anilocyanic acid Cj4 Hg NO3 Naphthocyanic acid jDja Hg NO^ Menaphthoximide, when heated, yields, in fact, a vapour of a most penetrating organic odour ; but Mr. Perkin has not yet obtained sufficient material for a more minute examination of the body to which it belongs. January 31. — The Lord Wrottesley, President, in the Chair. The following communication was read : — " Account of Pendulum Experiments undertaken in the Harton Colliery for the purpose of determining the Mean Density of the Earth." By G. B. Airy, Esq., Astronomer Royal. In the first section of this paper, the author explains the reasons, founded on calculation, which appeared to make it probable that the comparison of gravity at the top and the bottom of a mine would give means of determining the earth's mean density with accuracy, perhaps superior to that obtained in the Schehallien or the Cavendish experiment ; and which induced him first in the summer of 1826 (in concert with Dr. Whewell), and again in 1828 (with Dr. Whewell, Mr. Sheepshanks and others), to try the experiment in the Dolcoatli mine near Camborne in Cornwall. These attempts were both frustrated by accidents having no connexion witli the essential parts of the experiment. After a lapse of many years, he found that several circumstances (of which one was the general familiarity with the manipulation of the galvanic telegraph and the facility of applying it to the comparison of widely separated clocks) were very favourable to a repetition of the experiment ; and having selected the Ilarton Colliery in the neighbourhood of South Shields as a fit place, in which two stations could be found in exactly the same vertical but at 1256 feet difference of height, and being assured of every assist- ance from the owners of the mine, he proceeded with the experi- ments in the months of September and October 1854. The principal instruments employed were two detached pen- dulums on iron stands, the property of the Royal Society, which were most carefully repaired by Mr. Simms ; graduated arcs, baro- meters, thermometers, &c.; two clocks, one the property of the Royal Society, which were fitted for this purpose with inclined gilded reflectors upon the pendulum bobs, intended to be illuminated by the light of lamps passing through holes in the side of the clock- cases ; galvanometer-needles attached to the clock-cases, with circuit- breakers ; a galvanic battery at the upper station ; a journeyman- clock at the upper station, fitted with an apparatus by which it completed the galvanic circuit at every 1 5^ of its own time ; and two galvanic wires passing down the mine-shaft and forming a closed circuit through the battery, the journeyman-clock, and the two galvanometers. . The working party consisted of Mr. Dunkin (superintendent) and Mr. G. B. Airy on the Mean Density of the Earth. 229 Mr. Ellis from the Royal Observatory, Mr. Pogson from the Obser- vatory of Oxford, Mr. Creswick fr(^ the Observatory of Cambridge, Mr. G. Rumker from the Observatory of Durham, and Mr. Sim- monds from Mr. Carrington's Red Hill Observatory. The plan of operations was this. Simultaneous observations of the two pendulums (one in the upper and the other in the lower station) were kept up incessantly during the whole working time (day and night) of one week ; then the pendulums v/ere interchanged and were observed in the same manner through another week ; after this the pendulums were twice interchanged, but the two last series of observations were so much shortened that both were included in one week. Each pendulum had six swings of nearly four hours each, on every day of observation ; and between the end of one swing and the beginning of the next, numerous galvanic signals were passed for the comparison of the clocks. The second section gives the details (as far as space permits) of the comparisons of clocks by the galvanic signals. On examining the proportion of rates, it was found that there was distinctly a per- sonal equation in the observation of the galvanic signals. Approxi- mate values for the different observers were obtained, and the pro- portion of rates was corrected (where necessary) for these equations. The third section describes the general system of observing the pendulums and reducing the observations. For ascertaining the time of a coincidence of the vibration of the detached pendulum with that of the clock pendulum, the mean of the times of the first disappearance and the last re-appearance was employed. Several coincidences were observed at the beginning of a swing and the mean was taken : and several were observed, and the mean taken, at the end of the swing. From these means, a mean interval of coin- cidences was obtained ; from which the ratio of the actual rate of the detached pendulum to that of the clock pendulum was found. This requires several corrections. The correction depending on the arc of vibration, with no data except the first and last arcs of vibration, and no assumption of a mathematical law for the intermediate arcs, is made to depend on the results of experimental observations on the numerical decrease of the arc by a peculiar process. The corrections depending on the temperature and the atmospheric pressure are based mainly on Sabine's experiments. The fourth section contains an abstract of the Pendulum Obser- vations at the Upper Station, with the corrected logarithm of the rate of the detached pendulum on the clock pendulum for every swing ; and the fifth section contains a similar abstract for the Lower Station. The sixth section gives the computation of the logarithm of the rate of the lower detached pendulum upon the upper detached pen- dulum (for which the preceding sections have furnished the ele- ments). Then is given in detail the investigation, by the Theory of Probabilities, of the formula for the best combination of the results of the different swings. The advantage of the method of incessant 230 Royal Society :— observations with numerous comparisons of the clocks is pointed out. The formula is applied to the four series of observations ; and the results of the first and third series agree very closely, and those of the second and fourth series agree very closely, showing that the pendulums had undergone no sensible change. By comparing the mean of the first and third series with the mean of the second and fourth, the proportion of pendulum rates at the upper and loWer stations is obtained independently of the pendulums employed. The conclusion is that gravity below is greater than gravity above by tftififlth part, with an uncertainty of -jyTfth part of the excess ; or that the acceleration of a seconds' pendulum below is 2" '24 per day, with an uncertainty of less than O^'Ol. Reasons however are given for believing that the uncertainty is greater than this quan- tity. The seventh section contains a description of the operation for measuring the depth of the mine. It 'then treats of the process to be employed for computing the proportion of gravity at the upper and lower stations (without reference to the experiments), on an assumed proportion of the density of the mine-rocks to the earth's mean density. It is shown that, supposing the upper surface of the ground about Harton to have the true spheroidal form, it is unne- cessary to give any attention to the irregularities of the surface on distant parts of the earth. It is also shown that there is no reason to doubt the correctness of the law of decrease of the attraction of the earth's nucleus as dependin^on the elevation of the station, un- less there be some serious irregularity in the arrangement or density of the matter immediately below Harton. Assuming this to be in- sensible, the theory of correction for the inequalities of ground in the neighbourhood of Harton is then considered. The elevation of the upper station is about 74 feet above high water ; and as it ap- pears from this that the depth of inequality can in no case amount to one-tenth of the depth of the lower station, it is easily found that the excess or defect of attraction will bo computed with sufficient accuracy by supposing the excess or defect of matter to exist abso- lutely at the surface ; in which case the effect on the upper station is nothing, and that on the lower station is easily computed. For depressions like that of the sea bounded (at least for the purposes of computation) by a straight Une near the mine, but unlimited in the other direction, a simple formula is found. For the apphcation of these theorems it was necessary to have a map giving the elevations of the ground at various points. By instruction of the Mayor and Corporation of South Shields, the Corporation Surveyor, Christopher Thompson, Esq., prepared such a map. In the use of it, it was found convenient to adopt as unit of linear measure the depth of the mine. A hne at the distance of •ten depths very nearly touches the cliffs of Tynemouth, of French- man's Point, and of some points further to the south-east. The land generally is divided into squares whose sides are one depth each, and these are grouped as appears convenient for representing ap- proximately the form of the ground by compartments each of a uni- Colonel Sabine on the larger Magnetic Disturbances, 231 form elevation through its extent. The principal requirements are, besides taking account of the depression of the sea beyond the ten- depth line, to estimate the effect of the curvature of the coast to- wards the mouth of the Wear, to compute the eifect of the hollow of Jarrow Slake, and generally to make proper allowance for the absence of matter in the valley of the Tyne. There are also some small elevations to be considered. The general result is, that the attraction of the regular shell of matter is to be diminished by about al^th part. Putting D for the mean density of the earth, d for that of the shell, the fraction ^I^I&J^^ is computed to be 1-00012032 (gravity above - ^ — 0-00017984 X ^. The pendulum experiments give 1-00005185. The comparison of these gives — = 2-6266. The eighth section contains a detailed account of the strata passed through in sinking the Harton shaft, and the specific gravities of many of the beds as determined by Professor W. II. Miller. The result for the mean specific gravity is 2*50. Substituting this in the equation given by the pendulum experiments, the mean specific gra- vity of the earth is found to be ^'^idQ, Adverting to the excess of this number above those given by the Schehallien and the Torsion- rod experiments, the author remarks that it is very difficult to assign the causes or the measures of error in either of the experiments, but expresses his belief that the result of the present experiment may compete on at least equal terms with the others. Feb. 14.— Dr. W. A. Miller, V.P., in the Chair. The following communication was read : — ** On Periodical Laws discoverable in the Mean Effects of the larger Magnetic Disturbances." — No. III. By Colonel Edward Sabine, R.A., D.C.L., Treas. and V.P.R.S. In two previous papers bearing the same title as the present (Phil. Trans. 1851, Art. V., and 1852, Art. VIII.*), the author showed, from the hourly observations of the magnetic Declination at Toronto and Hobarton, that the magnetic disturbances of large amount, and apparently irregular occurrence, commonly called mag- netic storms, are found, when studied in their mean effects, to be governed by periodical laws of systematic order and regularity, and to exhibit periods whose duration is, respectively, 1, a solar day ; 2, a solar year ; and 3, a period of about ten of our solar years, corresponding both in duration and in the epochs of maximum and minimum variation, to the approximately decennial period discovered by Schwabe in the phsenomena of the solar spots. In the present paper the author communicates the results of a similar investigation into the laws of the disturbances of the two other magnetic elements at Toronto, namely, the Inclination and the Total Force, derived from the hourly observations of the horizontal and vertical Forces during the five years from July 1843 to June 1848 ; affording, as he states, * See also Phil. Mag. S. 4. vol. i. p. 498, and vol. iv. p. 232. 232 Royal Society, a full confirmation of the existence of periodical laws regulating the disturbances of the Inclination and Total Force corresponding to those which he had previously deduced from the disturbances of the other magnetic Element, viz. the Declination. Feb. 21.— The Lord Wrottesley, President, in the Chair. The following communication was read : — "On the Bromide of Titanium." By F. B. Duppa, Esq. A comparison of the boiling-points of corresponding chlorine and bromine compounds, led Prof. Kopp to the interesting discovery, that on the average their boiling-points rise 32° C. for every equivalent of bromine which is substituted for an equivalent of chlorine. ^ Boiling-point. Difference. Chloride of ethyle, C^ H^ CI . . . . 1 1° C. 1 ,.^ Bromide of ethyle, C4 H., Br . . . . 4 1° C. / •^"• Dichlorinated ethylene, C4 H4 CL 67° C. Xan — o^'^'i Dibrominated ethylene, C4 H^ Br^ 1 33°-6 C. / ^^"''^ ^ '^"^• Terchloride of phosphorus, P Cl.^ . 78° C. \ q7_ o w 09 1 Terbromide of phosphorus, P Br.^ . 1 75° C. / ^ ^ - '^ >< -^^^ 3 • If this difference be constant for all chlorine and bromine com- pounds, it becomes obvious that very important inferences in respect to the atomic constitution of these substances may be derived from the determination of their boiling-points. This result has, in fact, been happily applied by Prof. Kopp, as a criterion to determine the equivalent of silicium, a matter of such uncertainty as to have led to the admission of not less than three formulse for silica — SiO SiOg SiOg. From the difference between the boiling-points of chloride (59° C.) and that of bromide (153° C.) — a difference which amounts to 94=3 X 31i — Kopp derives the formulae SiCla and SiBrg, as representing the atomic constitution of the chloride and the bromide of silicium, and he accordingly fixes the equivalent of silicium at 21 '3. In order, however, to prove the general validity of Kopp's obser- vations, it was necessary to re-examine the boiling-points of cor- responding chlorine and bromine compounds which exhibited dis- crepancies, and to extend the inquiry to as great a number of new compounds as possible. The bromine-compound of titanium was unknown. Mr. Duppa has produced this substance by passing a current of bromine over an intimate mixture of pure titanic acid and carbon. The reaction takes place at a bright red heat, and furnishes a brown hquid, which solidifies in the receiver to a crystalline mass. Distilled with an excess of mercury, which removes any free bromine that may be present, the bromide of titanium presents itself as an amber-yellow compound, exhibiting a magnificent crystalline structure ; it attracts moisture with the greatest avidity, and is converted into titanic and hydrobromic acids. Bromide of titanium has a specific gravity of Intelligence and Miscellaneous Articles. 233 2*6. The fusing-point was found, 39°. The boUing-point was exammed by Mr. Duppa with a considerable quantity of substance, the purity of which had been ascertained by analysis. It was observed to be 230° C. The boiling-point of the chloride of tita- nium, as observed by Dumas, and confirmed by Mr. Duppa, is 135°. The difference, 230— 135 = 95 = 3 x 31^, is exactly the same as that observed between the boiling-points of chloride and bromide of silicium. This observation furnishes an additional support to the analogy of silicium and titanium, while it points unequivocally to the formulae TiCl.3 and TiBrg, as representing the atomic constitution of these two compounds. Titanic acid, hitherto universally represented as a binoxide TiOg, would then assume the formula Ti03 in perfect analogy with that of silicic acid. The equivalent of titanium would then be changed from 24*29, the number at present adopted, to 36*39. The protoxide of tita- nium would in this case become a sesquioxide, and the compound hitherto viewed as sesquioxide would have to be considered as an in- termediate oxide — as a combination of the sesquioxide with the ter- oxide, in fact, as a bititanate of sesquioxide of titanium. Formulce of the Titanium Compounds, Old Notation. New Notation. Ti= 24-29 Ti=36-39. TiO First oxide Ti,03 Ti^Oy Second oxide Ti4 09=Ti3 03, 2Ti03 TiO, Acid Ti03 TiCl3 TiClg Chloride TiBr^ Bromide TiBr3. It is scarcely necessary to observe, that an alteration of the equiva- lent of titanium on the ground of the difference of the two boiling- points, would be hazardous, if not supported by additional experi- mental evidence, and that further researches on the series of titanium are required in order to establish whether the proposed alteration actually affords a simpler expression for the combining relations of this remarkable element*. XXXII. Intelligence and Miscellaneous Articles. ABSORPTION OF HEAT BY DECOMPOSITION. To the Editors of the Philosophical Magazine and Journal. Gentlemen, Parsonstown, August 1856. TN reference to Mr. Joule's continued wish to be thought the ori- -*- glnator of the discovery that chemical decomposition absorbs heat, allow me to say that I am sorry to prolong a discussion which involves chiefly personal interests. I would not again urge my claim * Some observations on this paper bv Dr. Kopp will be found at p. 190.— Eds. '^ • *' ' $34 Intelligence and Miscellaneous Articles, to the discovery which I am sure the scientific world will allow me when the matter is properly weighed, were it not for the statement Mr. Joule makes at the commencement of his reply in your Maga- zine for the present month. He says I mis-state the results he arrived at, and that I endeavour to support my claim to an original discovery by setting one part of his papers against another. To neither of these accusations can I silently submit. As to the first, my statement is, that Mr. Joule passed a galvanic current through a wire and found a certain quantity of heat generated, and that he then passed it through an electrolyte and did not find the same amount of heat produced for an equal resistance. There is no mis-statement in this ; and Mr. Joule in his reply shows it so clearly, that I have only to quote his own words to prove it. He says (p. 155 of the Number of this Magazine for this month), " Suppose, first, we take a voltaic battery of 20 iron zinc pairs, and connect its ter- minations by a metallic wire. After a certain interval of time, we find 100 atoms or chemical equivalents of zinc dissolved in each cell of the battery. Then the entire amount of heat evolved will be ex- pressed by 100 X20= 2000. Suppose, secondly, we employ the same battery to decompose water ; the virtual intensity of the entire bat- tery circuit will then be 20 — 3i=16f (see p. 272 of the above- mentioned memoir) ; and when 100 atoms of zinc in each cell of the battery have been dissolved, or what comes to the same thing, when 100 atoms of hydrogen have been liberated in the decomposing cell, the heat evolved by the entire circuit will be expressed by 100 X 16|= 1666. The difference between 2000 and 1666, or 334, represents of course the heat taken up in eflfecting the separation of the 100 atoms of hydrogen from 100 atoms of oxygen, and libera- ting them in a gaseous state." Now here, when the metallic wire is used, there are 2000 units of heat produced ; but when the electro- lyte is used there are only 1666. The same amount of heat is not evolved in the first and second case ; such is the result I stated he arrived at, and such he says is a mis-statement. I do not under- stand why he makes the assertion. There is a diflference, 334, between the result of the two experiments ; and the cause of this diflference, or rather the first determination of the cause, is just the question at issue between Mr. Joule and me. He says, "it repre- sents of course the heat taken up by the separation of the oxygen and hydrogen." Of course it does; but when did Mr. 3 om\q first tell the world of this simple fact ? Nine months after I published it in October 1851 in this Magazine. In 1841 Mr. Joule published a paper in the Philosophical Magazine proving, that the heat deve- loped by a galvanic current is proportional to its intensity. When the current passed through an electrolyte, Mr. Joule thought part of the intensity was used up in causing electrolysis, and that the remainder only was etFective in producing heat ; that for this reason (to use his own example already quoted), instead of 2000 units there ■were only 1666 units of heat produced ; ascribing the difference 334, not to the separation of the oxygen and hydrogen, as he does now, but to the diminished intensity of the battery. In this supposition, however, he was quite in error. There is no loss of intensity or Intelligence and Miscellaneous Articles, 235 quantity of galvanic current except what is caused by the bad con- ducting power of the electrolyte, and the same amount of heat is evolved in a solid and liquid conductor by the same electromotive power if it acts against the same resistance ; but part of the heat so pro- duced is absorbed by the decomposition or separation of the elements. It is not that the galvanic current is diminished by effecting elec- trolysis, otherwise than it is when it passes through a badly conducting solid, for the whole current is effective, and the whole amount of heat due to it is produced ; but simply that part of that heat is rendered latent by the decomposition. If a compound body is decomposed without using the battery at all, and that heat is absorbed, or does not make its appearance, that loss of heat cannot be ascribed to diminished intensity of galvanic current. If, for instance, potassium be thrown on water, the oxygen unites with the potassium and the hydrogen escapes, the water being decomposed. Now does the combination of the potassium and oxygen produce as much heat in this case as if the elements were presented to each other in a free state } Decidedly it does ; but the decomposition of the water absorbs part of it and renders it latent : and this quantity so rendered latent is the same as the combination of the oxygen and hydrogen would themselves produce. This is the principle of my discovery. Mr. Joule, in the paper he refers to, published in this Magazine in 1841, does not at any time even hint at an absorption of heat by decomposition, or by anything else. He merely says that decomposition prevents part of the current being effective in producing heat ; so far from saying heat is absorbed, he says it is not evolved at all. His paper would never lead to the sup- position that decomposition produced by superior chemical affinity would cause absorption of heat. That is my discovery, and there- fore I claim to have laid the foundation of all the thermo- chemical researches which take decomposition into account. None were carried on before the publication of my paper in 1 85 1 . Mr. Joule says, that, independently of his paper in 1841, he should have priority because he sent a paper to the French Academy in 1846. I do not know exactly the etiquette followed in such cases ; all I know is,'that I worked very hard for a long time to find whether certain theoretical conclusions were experimentally correct ; and finding that they were so, I condensed the labour of months into a short paper and published it, believing it might be of use. This paper having been then made the foundation of other researches, Mr. Joule interferes and says he knew all about it long before I did. I have no doubt oi what he states ; but that knowledge not having been published, did me no good, and perhaps it might still be a dead letter if I had not brought it out by having worked myself. I there- fore think if there is any credit to be attached to the discovery, that I deserve not only my own but his. But as to this paper sent to the French Academy, has it been published exactly as it is in their hands } Perhaps the absorption of heat might not be shown in it at all. I say this, because Mr. Joule brings forward his paper of 1841 to prove that he was aware of this truth : and really if I were wish- ing to show proof of his not having at that time known anything 236 Intelligence and Miscellaneous Articles. about it I would point to that paper. In the first place, he does not speak of it ; and in the second place, when about to calculate the amount of heat produced in the cell of a voltaic pair composed of zinc and silver, he says (p. 266 of the paper he refers to in vol. xix. Phil. Mag. 1841), "Before I proceed to give an account of some experiments on heat evolved in cells of voltaic pairs, it is important to observe that every kind of action not essentially electrolytic must be eliminated," &c. He then, in calculating the heat produced, makes allowance for the combination of the oxide of zinc and sul- phuric acid, but does not at all mention the absorption of heat pro- duced by decomposition of the water, which is of greater amount, in the opposite direction. The several data to be taken into account in calculating the amount of heat produced by the solution of zinc in sulphuric acid are, — the oxidation of the zinc, the combination of the oxide of zinc and acid, and the absorption of heat by decomposition. This last Mr. Joule does not allude to at all ; and when it is considered that he sets out with the determination to eliminate all actions which might in- terfere with the proper amount of heat being arrived at, it must be concluded that at that time he did not know that heat was absorbed by decomposition. Now as to Mr. Joule's second charge, that I set up one part of his papers against another, I can only say I merely quote his own words to show that opinions he once held he afterwards altered, and that I endeavoured to show his first opinions were correct. If any contradiction appears, he should rather blame himself than me. He says I erroneously suppose he contradicts himself. The matter stands thus : — Mr. Joule proved experimentally (vol. xx. Phil. Mag. 1842) that the amount of heat produced by oxidation might be taken as a measure of the intensity of the attraction of affinity between the combining bodies ; but in a subsequent paper (Phil. Mag. vol. xxiii. p. 442) he says that " it is not precisely the attraction of affinity, &c. which determines the intensity of the current and consequently the amount of heat evolved." This is the contradiction he says I erro- neously imagine. Without being aware that these papers had been published, I had myself proved experimentally the first proposition ; and when Mr. Joule claimed it, I at once, on referring to his first publication, admitted his claim ; but added, that if the proposition were true I should still consider I established it, as that although he first held, he afterwards rejected it. In endeavouring to establish a claim to a disputed discovery, it is impossible not to make reference to previous papers written by the disputing parties. I have done so without having the least wish to take any undue advantage of anything which has been written, or which has not, but which ought to have been written if the truth had been recognized. I trust that nothing I have said can make it appear that I have not the highest respect for such a philosopher as Mr. Joule, of whose high talents and achievements in science his , country ought to feel proud; or that I am not deeply grateful for Intelligence and Miscellaneous A7iicles. 237 the many discoveries, and great and important truths, he has so laboriously proved and so freely given to the world. I have the honour to be. Gentlemen, ■• Yours very respectfully, Thomas Woods, M.D. OBSERVATIONS AND EXPERIMENTS UPON THE EMPLOYMENT OF IODIDE OV POTASSIUM AS A REAGENT FOR OZONE. BY S. CLOEZ. The experiments of Marignac, Fremy, and Becquerel have done most to clear up the question of the nature of ozone ; they prove completely the possibility of imparting to chemically pure oxygen all the properties of this mysterious substance. Iodide of potassium being one of those substances upon which ozone is capable of acting, paper soaked in a solution of starch con- taining 0*002 of its weight of this iodide has been proposed, under the name of the ozonometric reagent, not only to indicate the presence of ozone, but also to measure the quantity contained in the air. If the coloration of this paper could only be produced by ozonized oxygen, its employment would leave nothing to be desired. But this is not the case ; acid vapours act upon iodide of potassium in the same manner as active oxygen ; the essential oils exhaled by plants have the same action, and prove that moist air, under the influence of the direct light of the sun, colours the reagent, although we can- not suppose the air to be ozonized. The experiments upon nitrification which the author is carrying on simultaneously at the Museum of Natural History and the Poly- technic School, have led him to investigate what part the ozonized oxygen said to exist in the air may play in the formation of nitric acid. After a great number of trials he has not yet succeeded in establishing with certainty the part taken by ozone in the phseno- menon of nitrification, effected in the absence of azotized or ammo- niacal substances, but his experiments have convinced him that the numerous attempts to prove the presence of ozone in the air and measure, its quantity by means of iodized paper, are not of the least value. It is an admitted fact that the coloration of the paper takes place every day in the country, and in places where there are many trees and an active vegetation, whilst many observations prove that in the most populous parts of towns the paper is very rarely and very slightly coloured. The author has found that in the Garden of Plants the iodized paper is constantly coloured by exposure, especially in the neighbourhood of resiniferous trees, and frequently in a very short time, but that at the Polytechnic School, in the vicinity of which there are few trees, but a dense population living in unhealthy houses, the paper exposed daily to the air under the same conditions as that at the Museum has not been coloured once in six months. M. Cahours has observed a similar contrast between his garden at Neuilly and the Hotel des Monnaies in Paris. Resiniferous trees, aromatic plants, and all the parts of vegetables which contain volatile oils, act much more strongly than inodorous 238 Intelligence and Miscellaneous Articles, plants upon iodized paper in their vicinity. By passing moist air through a tubulated bell-glass covering the plants to be experi- mented on, and exposing the iodized paper to the air at its exit from the bell, it will be seen that whenever the plant is capable of pro- ducing odorous volatile substances, coloration takes place ; in the opposite case the paper remains white. From some experiments recently published, it would appear that the oxygen disengaged by the green parts of plants under the influ- ence of light is in the same state as the gas produced by the electro- lytic decomposition of water, or the nascent oxygen prepared in the cold by the action of sulphuric acid upon binoxide of barium. The author has found that this oxygen has no effect upon iodized paper. He placed some aquatic plants in a bottle filled with rain-water containing about half its volume of carbonic acid, exposed the appa- ratus to the sun, and collected the gas under a test tube filled with water ; the gas produced no coloration of iodized paper by contact for six hours. As it might be objected that the gas had lost its oxi- dizing power during the short space of time occupied in collecting it, he adapted to the neck of the bottle containing the plants, a glass tube of 3 decimetres in length, covering its lower half with black paper, and introducing a strip of test paper both into this and into the por- tion left exposed to the light. The apparatus was exposed for two days to the sun ; 2*25 litres of moist gas were evolved, the whole of which passed over the iodized paper, of which the strip protected, from the light was unchanged, whilst the other was strongly coloured. This is the constant effect of the action of light upon iodized paper in the presence of moist oxygen. It cannot be admitted that, as advanced by Schonbein, and lately repeated by Scoutetten, light ozonizes the air, for although the active modification of oxygen is not permanent, it may be kept for several hours ; and if light possessed the property attributed to it, moist air exposed to the sun, and removed for a short time from the action of the solar rays, ought to act upon iodized paper in the manner of ozone ; but this is never the case. However long the air may be exposed to the sun, it is never ozonized. — Comptes Rendus, July 7, 1856, p. 38. ON THE PRESENCE OF MERCURY IN THE NATIVE ARGENTIFEROUS COPPER OF LAKE SUPERIOR. BY M. HAUTEFEUILLE. The author received 200 kilogrammes of this mineral to ascertain its value. Its gangue consisted principally of calcareous spar, which was got rid of by dilute muriatic acid ; its weight was 50*476 kilogrms. The copper was covered with larger and smaller tufts of metallic silver, which were removed by the graver. Fragments of copper were selected which did not appear to have had any silver on the surface, and cut into the centre; the author found in them 0*002 of silver ; the whole gave 0008 of silver when melted. The total weight of copper was 138-560 kilogrms. The silver removed by the graver was assayed by the humid way and estimated at 0*993, but the assay presented the following phae- nomenas— 1, the liquid was scarcely limpid ; 2, the chloride of silver Meteorological Observations. 239 did not acquire colour when exposed to a bright light, hence the author concluded that mercury was present. To settle this point, the author boiled the chloride of silver with a plate of gold, a little tin, and muriatic acid ; the gold plate was amalgamated. He then treated 150 grms. of the silver separated by the graver by M. Le vol's process, seeking for the mercury in the liquid deprived of silver and containing the double acetate of ammonia and mercury. By means of protochloride of tin he obtained of metallic mercury 0-0035 = 0'038 kilogrms., the silver being 10'906 kilogrms. Thus this copper contains, — Kilogrms. Per 1000. Copper 138-560 0*69280 Silver 10-906 0*05453 Mercury 0-038 0*00019 Gangue 50*496 0*25248 200*000 — Comptes Rendus, July 21, 1856, p. 166. METEOROLOGICAL OBSERVATIONS FOR JULY 1856. Chiswick. — July 1. Cloudless, with very dry air. 2. Dry haze : very fine. 3. Clear and very fine. 4. Fine : overcast : slight rain. 5. Fine: overcast : very fine. 6. Very fine : lightning, with rain at night. 7. Densely clouded : rain. 8. Very heavy rain, cold and boisterous. 9. Fine. 10. Very fine. 11. Cloudy: sUght drizzle : fine. 12. Overcast. 13. Very fine : overcast : cloudy. 14. Very fine: overcast. 15. Cloudy and fine : lightning, with rain at night. 16. Rain: heavy clouds and showers : very fine. 17. Very fine. 18. Overcast : drizzly : very fine.' 19. Fine: overcast. 20. Slight drizzle: overcast: rain. 21. Very fine. 22. Sultry. 23. Slight fog : very hot : cloudy : Ughtning. 24. Shower : very hot. 25,26. Exceedingly fine. 27. Overcast: rain. 28. Cloudy: very fine : hazy. 29. Shght fog : very fine. 30. Uniform haze : very fine. 31. Slight fog : very sultry : clear and fine. Mean temperature of the month 61'*-20 Mean temperature of July 1855 62-99 Mean temperature of July for th e last thirty years 63*11 Average amount of rain in July 2558 inches. Boston.— inly 1 — 4. Fine. 5. Cloudy. 6. Cloudy : rain p.m. 7. Cloudy : rain A.M. and P.M. 8. Fine: rain a.m. and p.m. 9. Fine : rain p.m. 10. Fine. 11. Cloudy. 12. Cloudy : rain a.m. and p.m. 13. Cloudy. 14. Fine. 15. Cloudy. 16. Cloudy: rain a.m. and p.m. 17. Fine. 18. Rain a.m. and p.m. 19. Fine. 20. Cloudy. 21, 22. Fine. 23, 24. Cloudy. 25. Fine : rain p.m. 26. Cloudy. 27. Cloudy : rain a.m. 28—31. Fine. Sandwich Manse, Orkney, — July 1. Bright a.m. : clear p.m. 2. Clear a.m. and p.m. 3. Clear a.m. : showers p.m. 4. Drizzle a.m. and p.m. 5. Cloudy a.m. : drizzle, showers p.m. 6. Showers a.m. : drizzle, showers p.m. 7. Rain a.m. : bright P.M. 8. Drizzle, showers a.m. and p.m. 9. Drizzle, showers a.m.: cloudy P.M. 10. Cloudy a.m. and p.m. 11. Cloudy a.m. : rain p.m. 12. Bright A.M. : bright, fine, thunder p.m. 13. Bright a.m. : cloudy, fine p.m. 14. Clear, fine A.M.: cloudy, rain p.m. 15. Cloudy a.m. and p.m. 16. Drizzle a.m.: rain p.m. 17. Clear a.m. and p.m. 18. Rain a.m. : showers p.m. 19, 20. Drizzle a.m. : damp p.m. 21. Bright, fine a.m. and p.m. 22. Clear, fine a.m. : cloudy, fine P.M. 23. Rain a.m. : cloudy, fine p.m. 24, 25. Bright a.m. : bright, fine p.m. 26. Clear a.m. : showers p.m. 27. Bright a.m. : showers p.m. 28. Showers a.m. : cloudy, fine p.m. 29. Clear, fine a.m. : rain p.m. 30. Bright a.m. : hazy p.m. 31. Cloudy, fine a.m. : rain p.m. Mean temperature of July for previous twenty-nine years ... 55°-22 Mean temperature of this month 54*77 Mean temperature of July 1855 59*19 Average quantity of rain in July for previous sixteen years ... 2*45 inches. •ao)Mg I \A OQ 2 B S £•§ i| ^ i « 2 •JiapiujqO •^iMpires *i9Ui|ao •UO^SOQ •tu'd I ri o S •ra-B f8 •uojsog I O O O O (4 o p n o I r 18 i i : O 5j- ^ en t^ w O O t^ « s^|i8sgi|||iisi|gii|^f.-i l( fl I ^ ^' » !i !"' ii^i'^ii^^^^iii^iiii'^ii 1^ f^ tJ- tJ-oo It rh Ti- w tn t*^ t^ looo O O O t^ t^ r^^ oo lO in *o lo vovo to >0 to w^ VT) u->vo ^'^vo vo vO lo vn vr> lo "O r-- p p b b b b> b\ C?\ 'o 'o\ On on b> O OS On on b^ on b> 'o\ 'o, "on on 'o> on On 'o\ 'o\ O On b b tncocotHHNMHC<«rOHtOrO IV |N»vO »< r-x OS u-ioo t^ri rt rj-M COM ^lomw Ost-Ncl ON-<4-iororJ-t^t--r-sw www O>0O lo Th •p t^oo f^^ P O O O 0nOn0\0nOnO\0n0nO>On0n0\OnOsCs0n0n0n0n0\O\0n0s0n0\0n0s0 torotor»NNHcfO 'ao)8oa QS S3 On to CO O v© l^vo lo 5j- «^ t^ 00 f» O rt «<^«o»i ^o\r>-rt co tooo O ' . . - - - r* r r* p f^ ?^ y^ r^ r* p^?® r^^ p^^ r^ p p O O O O 0\OnO\OnOnO\0>OnOnOnO\0\0 O OxONCNOiON'oNONb COCOCOCOC>00 On O w c5 to tJ- lovd MHHtHMMf-lOHt^OHHt^ o ^ .00 On O •-• c« c< to CO THE LONDON, EDINBURGH a.nd DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] OCTOBER 1856. XXXIII. On the Application of the Mechanical Theory of Heat to the Steam-engine. By R. Clausius*. 1. AS our present modified views respecting the nature and -l\. deportment of heat, which constitute the mechanical theory of heat, had their origin in the well-known fact that heat may b^ employed for producing mechanical work, we may natu- rally anticipate that the theory so originated will in its turn helj) to place this application of heat in a clearer light. At all events the more general views thus obtained must enable us to pro- nounce safely upon the efficiency of the several machines for thus applying heat, as to whether they already perfectly fulfil their purpose, or whether and to what extent they are capable of being perfected. Besides these reasons, which apply to all thermo-dynamic machines,^ there are others, applicable more particularly* to the most important of them — the steam-engine, which appear to render a new investigation of the latter, conducted according to the principles of the mechanical theory of heat, desirable. It is precisely with respect to vapour at a maximum density that this new theory has led us to laws which differ essentially from those formerly accepted as true, or at least introduced into former calculations. 2. I may here be allowed to refer to a fact proved by Rankine and myself, that when a quantity of vapour at its maximum den- sity, enclosed by a surface impenetrable to heat, expands and thereby displaces a moveable part of the enclosing surface, e. g, a piston, with its full force of expansion, a part of the vapour * From Poggendorff's Annalen, vol. xcvii. p. 441. Phil. Mag. S. 4. Vol. 12. No. 79. Oct. 1856. R 242 Prof. Clausius on the Ajyplication of the Mechanical must undergo condensation; whereas in most works on the steam-engine, amongst others in the excellent work of Do Pambour*, Watt's theorem, that under these eircumstances the vapour remains precisely at its maximum density, is assumed as a fundamental one. Further, in the absence of more accurate knowledge, it was formerly assumed, in determining the volumes of the unit of weight of saturated vapour at different temperatures, that vapour even at its maximum density still obeys Mariotte's and Gay- Lussac's laws. In opposition to this, I have already shown in my first memoir f on this subject, that the volumes in question can be calculated from the principles of the mechanical theory of heat under the assumption, that a permanent gas when it ex- pands at a constant temperature only absorbs so much heat as is. consumed in the external work thereby performed, and that these calculations lead to values which, at least at high temperatures, differ considerably from Mariotte's and Gay-Lussac's laws. Even the physicists who had occupied themselves more espe- cially with the mechanical theory of heat, did not at that time coincide with this view of the deportment of vapour. William Thomson in particular opposed it. In a memoir J presented to the Royal Society of Edinburgh, and published a year later, in March 1851, he only regarded this result as a ])roof of ^he im- probability of the above assumption which I had employed. Since then, however, he and J. P. Joule have together under- taken to test experimentally the accuracy of this assumption §. By a series of well-contrived experiments, executed on a large scale, they have in fact shown, that, with respect to the perma- nent gases, atmospheric air and hydrogen, the assumption is so nearly true, that in most calculations the deviations from exacti- tude may be disregarded. With carbonic acid, the non- perma- nent gas they investigated, the deviations were greater. This is in perfect accordance with the remark I made on first making the assumption, which was that the latter would probably be found to be accurate in the same measure as Mariotte's and Gay- Lussac's laws were ap])licable to the gas. In consequence of these experiments, Thomson now calculates the volumes of satu- rated vapours in the same manner as myself. There is reason to believe, therefore, that the accuracy of this method of calcu- lation will be gradually more and more recognized by other physicists. • * ITi^orie des Machines h. Vapeur, par le Comte F. M. G. de Pambour. Paris, 1844. t Poggendorff's Annalen, vol. Ixxi^. p. 368; Phil. Mag. July 1851. X Transactious of the Royal Society of Edinburgh, vol. xx. part 2, p. 261 . § Phil. Trans, vol. cxliii. part 3, p. 357 J and vol. cxHv. part 2, p. 321. Theory of Heat to the Steam-engine, 243 3. These two examples will suffice to show, that the principles upon which our former theory of steam-engines was founded have suffered such essential modifications through the mechanical theory of heat, as to render a new investigation of the subject necessary. In the present memoir I have attempted to develope the prin- ciples of the calculation of the work of the steam-engine in accordance with the mechanical theory of heat. I have, how- ever, limited myself to the steam-engines now in use, without at present entering into a consideration of the more recent and cer- tainly very interesting attempts to employ vapour in a super- heated state. In recording the results of my investigation, I shall only assume my last memoir, " On a modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat*,^' as known. This will of course necessitate the deduction, in a somewhat different manner, of results which are no longer new, but have already been found by myself or others; I believe, however, that this repetition, by leading to greater unity and facility of comprehension, will not be found superfluous. At the proper places I shall, to the best of my ability, cite the works wherein these results first appeared. 4. The expression " a machine is driven by heat^^ is not of course strictly accurate. By it we must understand, that, in consequence of the changes produced by heat upon some kind of matter in the machine, the parts of the latter are set in motion. We shall refer to this matter as that which manifests the action of heat. If a continuously-acting machine is in uniform action, all accompanying changes occur periodically, so that the condition which at a given time prevails in the machine and all its parts returns at equal intervals. Hence the matter which manifests the action of the applied heat must at such regularly-recurring periods be present in the machine in equal quantity, and in the same state. This condition can be fulfilled in two different ways. First. One and the same quantity of matter may always remain in the machine, when the modifications which this matter suffers during the action of the machine will be such, that at the end of each period it will regain its original condition and recommence the same cycle of changes. Secondly, The machine may always expel the matter which served to produce the effect during a period, and in its place receive from an external source just as much matter of the same kind. 5. The last method is the one usually employed in most * Poggendorff's Annalen, vol. xciii. p. 481 ; and Phil. Mag. August 1856. R2 244 Prof. Clausius on the Application of the Mechanical machines. This is the case, for instance, in machines with heated air as at ])resent constructed ; for after every stroke, the air which moved the piston in the driving cylinder is expelled into the atmosphere, and in its place an equal quantity of air from the same source is received into the feeding cylinder. Similarly in steam-engines without condensers, steam is driven from the cylinder into the atmosphere, and in its place fresh water is pumped from a reservoir into the boiler. Further, a similar method is at least partially adopted even in steam-engines provided with a condenser as usually constructed. In them the water condensed from the steam is only partially pumped back into the boiler, for being mixed with the cooling water, a part of the latter also reaches the boiler. The remaining part of the condensed water, together with the remaining part of the cooling water, has to be got rid of. The first method has lately been employed in steam-engines propelled by two vapours, e. g. those of water and aether. In these machines the steam is condensed solely by contact with metallic tubes filled with liquid sether, and the water thus pro- duced is then completely pumped back into the boiler. In the same manner the vapour of the sether in the metal tubes, which are merely surrounded by cold water, is condensed and subse- quently pumped back into the first space intended for the vapo- rization of the aether. In order to maintain a uniform action, therefore, only so much fresh water and aether is necessary as will replace the leakage consequent upon imperfect construction. 6. In a machine of this kind, where the same matter is con- tinually re-employed, the several changes which this matter suf- fers during a period must, as above stated, form a closed cycle, or, according to the nomenclature in my former memoir, a cir- cular process. On the contrary, machines in which a periodical reception and expulsion of matter occurs are not necessarily subject to this condition, though they may also fulfil it by expelling the matter in the same condition in which it was received. This is the case in steam-engines with condensers, where the water is ultimately expelled from the condenser in the hquid state, and at the same temperature as it had when removed from the condenser to the boiler*. In other machines, the condition, when expelled, is different from what it was when received. For example, heated-air machines, even when provided with regenerators, expel the ait * The cooling water, which enters the condenser at a low and leaves it at a high temperature, is not here taken into consideration, inasmuch as it does not form a part of the matter manifesting the eflFect of the applied heat, but merely constitutes a negative source of heat. Theory of Heat to the Steam-engine, 21-5 at a higher temperature than it formerly had ; and steam-engines without condensers receive water in the hquid, and expel it in the gaseous form. Strictly, therefore, the complete circular pro- cess is not fulfilled in these cases ; nevertheless we may always conceive a second machine appended to the given one which shall receive the matter from the first, reduce it in some manner to its original condition, and then expel it. Both machines may then be regarded as constituting one and the same machine, which will fulfil the above condition. In many cases this addi- tion may be made without introducing greater complexity into the investigation. For example, a steam-engine with a condenser at a temperature of 100° C. may be substituted for a machine without a condenser, provided we assume the latter to be fed with water at 100"" C. Hence, if we assume that machines which do not fulfil the above condition are theoretically completed in the above manner, we may apply the theorems concerning the circular process to all thermo- dynamic machines, and thereby arrive at conclusions which are quite independent of the nature of the processes executed by the several machines. 7. In my former memoir I have represented the two funda- mental theorems which hold good in every circular process by the following equations : — . , ^ ,, . ,,. . msiimUnm i'» f^ = - N, ... . . ^>^^y -''t ^ wherein the letters have the same signification as tefore, viz.— ■ V^ A is the equivalent of heat for the unit of work. W represents the external work performed during the circular process. Q signifies the heat imparted to the changeable body during a circular process, and r»fT?Ls flip i Oilt fo mo'iOfj/lj ofit bna ,?ra ^o baf Substituting the above-found value of Q^ in this equation, it becomes = r(«^-^or^-To.N). . . (2) AX5^ If, a4 a 'fip?^eial (^s6, the whole circtdar process is reversible, then -■91' i4; N = 0, '^^ the above equation becomes " '■■"*'i(«.-.rT)- • ■ ■ o ■This expression differs from the preceding one only in the absence V' q' of the term — -^ N. Now as N can only be positive, this term 'must necessarily be negative; and thus we see, that, under the above conditions with respect to the communication of heat, the greatest possible amount of work is obtained when the whole process is reversible ; and that every circumstance which renders one of the operations in the circular process not reversible, dimi- Theory of Heat to the Steam-engine. 249 nishes the amount of work, — a conclusion which results easily from a direct consideration of the subject. The equation (2) leads to the value of the amount of work in a manner opposite to that usually followed. The amounts of work done in the several operations are not separately deter- mined and then added togetlier, but, instead of this, the maxi- mum of work is first found, and the losses occasioned by the several imperfections of the process are subsequently deducted from it. If, with respect to the communication of heat, we introduce a still more limited condition, and assume that the whole quantity of heat Q^ is also imparted to the body at a constant tempera- ture Ti, then the integration which embraces this quantity of heat may also be executed, and gives Qj whereby the equation (3) for the maximum of work assumes the form O T _T w=J-li^. (4) In this special form the equation has already been deduced by William Thomson and Rankine from a combination of Carnot's theorem, as modified by me, and the theorem of the equivalence of heat and work*. 10. Before we proceed, from these considerations which apply to all thermo-dynamic engines, to treat of the steam-engine, we must first premise something concerning the deportment of vapours at a maximum density. In a memoir of mine,, published as early as 1850, ''On the Moving Force of Heat," &c., I have already established the equations which show the application of the two fundamental theorems of the mechanical theory of heat to vapours at a maxi- mum density, and I have there employed these equations in de- ducing several consequences. But as in my last memoir, " On a modified Form of the Second Fundamental Theorem of the Mechanical Theory of Heat," I proposed a somewhat difierent mode of treating the whole subject, it appears preferable to me to assume the last memoir only as known. I shall therefore deduce those equations once more, in a diff*erent manner, by means of the results established in my last memoir. It was there assumed^ in order to apply the general equations which were first established to a somewhat more special case, that the only foreign force, acting upon the changing material, which required consideration in determining the external work, * Phil. Mag. July 1851. 250 Prof. Clausius on the Application of the Mechanical was an external pressure equally intense at all points of the sur- face, and directed everywhere at right angles to the same ; and further, that this pressure always changed so slowly, and con- sequently at each moment differed so little from the opposite expansive force of the body, that in calculation the two might be considered equal. Let then p be the pressure, v the volume, and T the absolute temperature of the body. We introduce the last instead of /, the temperature counted from the freezing- point, because thereby the formulae assume a simpler form. The equations already established in this case are, dT\dv) dvUTj-^'dT • • • ^^^^^ These equations shall next be applied to the still more special case of vapours at their maximum density. 11. Let M be the mass of the matter whose vapour is to be considered, and which is placed in a perfectly closed expansible vessel. Let the part m be in a vaporous, and the rest, M— m, in a liquid state. This mixed mass shall be the changing body to which the foregoing equations are to be referred. The condition of the mass, as far as the same here enters into consideration, is perfectly determined as soon as its temperature T and its volume v, i. e. the volume of the vessel, are given. For, according to hypothesis, the vapour is always in contact with the liquid, and therefore remains at its maximum density ; so that its condition, as well as that of the liquid, depends only upon the temperature T. It only remains to be seen, therefore, whether the magnitude of each of the parts in different conditions is perfectly determined, from the condition that both parts together exactly fill the space enclosed by the vessel. Let s represent the volume of the unit of weight of vapour at its maxi- mum density where the temperature is T, and a that of the unit of weight of liquid, then v=wi.*4-(M— m)(r The magnitude s never occurs hereafter except in the combina- tion s—a, so that we will introduce another letter for this differ- ence, and make u=s-—a; (5) ^n consequence of which the foregoing equation becomes 01 liii* i;=7ww-f-M<7, (6) Theory of Heat to the Steam-engine. 251 and we have ^— u • • • '^^^ :wni^%^f.U ,•! ,«JW By this equation m is expressed as a function of T and v, because u and cr are functions of T. 12. In order to be able to apply equations (III) and (IV) to our case, we must next determine the magnitudes -p and -j^. If the volume of the vessel increases by dv, then the quantity of heat which must be imparted to the mass in order to maintain a constant temperature will be generally expressed by -j-dv. dv But this quantity of heat is expended solely in the vaporization which takes place during the expansion ; so that if r represents the heat required to vaporize the unit of mass, the above quan- tity of heat may also be represented by and we have But according to (7), hence dm , r—f-dVy dv dQ _ dm dv ^ dv' dm dv ^ = ^ (8) dv u ^ ' Let u,s next assume, that whilst the volume of the vessel remains constant, the temperature of the mass increases by c?T j then the general expression for the requisite quantity of heat will be dT"^^' This quantity of heat consists of three parts : — (1) The liquid part M—m of the whole mass suffers an incre- ment of temperature dT, for which, c being the specific heat of the liquid, the quantity of heat {M-m)cdT is necessary. . s (2) The vaporous part m will also undergo an increment of temperature dT, but it will be thereby compressed so as still to 252 Prof. Clausius on the Application of the Mechanical remain at its maximum density for the increased temperature T + rfT. For an increment of temperature dT, we will represent by h . dT the quantity of heat which must be imparted to the unit of mass of vapour during its contraction, in order that at every density it may have precisely that temperature for which this density is a maximum. The value and even the sign of the magnitude // is at present unknown. The quantity of heat ne- cessary in our case will therefore be mhdT. (3) During the elevation of temperature, a small quantity of liquid, represented generally by — dT becomes vaporized, for which the quantity of heat is necessary. Herein, according to equation (7), dm _^ v — Ma- du M da dT" 5?~'^~'^*Zr _ m du M. da- u'dT'^U'df' so that by substitution the last expression becomes ,n.iiT .^*«. J^duMda\^^ ^.!>if».M. ><:<.. r.w, ^u dT u dT/ Equating the sum of these three quantities of heat and the former expression -7™ dT, we obtain the equation 13. As indicated by equation (III), the above expression for -^ must be differentiated according to T, and,t^e.qxpreasipii f(^ -~ according to v. > The magnitude M is constant, the magni- a X tudes M, Hll]n^goyy of Heat to the Steam-engine. 259 siderable ; and as it is for the most part distributed throughout the vapour in small drops^ so that it can readily participate in any changes of temperature which the vapour may suffer during expansion, we shall incur no great inaccuracy if, in calculation, we consider the temperature at any moment as the same through- out the whole of the mass in the cylinder. Further, in order to avoid complicating our formulas too much, we will for the present determine the total amount of work done by the vapour pressure, without taking into consideration how much of this work is useful, and how much is again con- sumed by the machine itself in overcoming friction, and in work- ing any pumps, which, besides the one in the figure, may be necessary to the efficiency of the machine. This part of the work may be afterwards determined and deducted, as will sub- sequently be shown. With respect to the friction of the piston in the cylinder, how- ever, we may remark, the work consumed in overcoming it can scarcely be considered as lost. For heat is generated by this friction, and consequently the interior of the cylinder kept warmer than it would otherwise be, and thus the force of the vapour increased. Lastly, inasmuch as it is advisable first to study the actions of the most perfect machines before examining the influence of the several imperfections which practically are always unavoidable, we will add to these preliminary considerations two more sup- positions, which shall afterwards be again relinquished. First, the canal from the boiler to the cylinder, and that from the cylinder to the condenser, or to the atmosphere, shall be so wide, or the speed of the machine shall be so slow, that the pressure in the part of the cylinder in connexion with the boiler shall be equal to that in the boiler itself, and similarly the pressure on the other side of the piston shall be equal to the pressure in the condenser or to the atmospheric pressure; and secondly, no vicious space shall be present. 20. Under these circumstances, the quantities of work done during a circular process can be written down, without further calculation, by help of the results above attained ; and for their sum they give a simple expression. Let M be the whole mass which passes from the boiler into the cylinder during the ascent of the piston, and of it let m, be the vaporous, and M— m^ the liquid part. The space occupied by this mass is , ^i^ where u^ is the value of u corresponding to T^. The piston is raised therefore until this space is left free under it ; and as this takes place jOi^der. the,^tioii of the pressure jOj, corresponding to 260 Prof. Clausius on the Application of the Mechanical Tp the work performed during this first operation is W,=miWijt?i + Moy, (18) The expansion which now follows is continued until the tem- perature of the mass enclosed in the cylinder sinks from T^ to a second given value Tg. The work thus done, which shall be W^, is given immediately by equation (IX), if Tg be taken therein as the final temperature, and for the other magnitudes involved in the equation the corresponding values be substituted, thus Wg=m2Wa;?2— 7WiWijt?i+ -^\rnir^ — m^^ + ^ci^^—T^'], (19) By the descent of the piston, which now commences, the mass, which at the close of the expansion occupied the volume TWgWg H- Mo-, is driven from the cylinder into the condenser, and has to over- come the constant pressure Pq, The negative work hereby done by this pressure is W3=-7W2M2;^0-M(7po (20) Whilst the piston of the small pump now ascends, so as to leave the free space Mi in the boiler must be overcome, and therefore it does the negative w^ork W5=:-M(7J0, (22) By adding these five magnitudes together we obtain the fol- lowing expression for the work done by the vapour pressure, or, as we may say, by heat, during a circular process : W'=l[m,r,-m^, + Mc(T,-T,)]+mA(j»,-;,„). . (X) n ,.> With respect to the magnitude m^ which must be eliminated firom this equation, it will be observed that, if for Wg we substi- tute the value .T.( as given in (VI), it only occurs in the combination m.^r^, and for this product we have from equation (VII) the expression T T OT3ra=m,ri^ -McTg log^ y^msii^mWheory of Heat to the Steam-engine. 261 By employing this expression, therefore, we obtain an equation the right-hand side of which contains only known quantities ; for the masses mj and M, and the temperatures Tj, T^, and Tq, are assumed to be. immediately given, and the magnitudes r, p, and -^ are supposed to be known functions of the temperature. cc J. 21. If in the equation (X) we set T2=Ti, we find the amount of work, for the case that the machine works without expansion, to be W' = miMi(;?i— jt?o) (23) If, on the contrary, we suppose the expansion to be continued until the vapour sinks from the temperature of the boiler to that of the condenser, — which case cannot of course be strictly realized, but rather forms a limit which it is desirable to approach as much as possible, — we have only to set T2=Tq, when we obtain W'=l[m,»-,-moro+Mc(T,-T<,)]. . . (34) Eliminating mQVQ by means of the equation before given, in which we must also set T2=To, we have W'= l[m,r,?!^« + Mc(T.-To+T„log^)]*. (XI) 22. If to the foregoing equation we give the form W' = m,.,.^^° + M.(T,-T„).l(l+ ^^jog|e), (25) then the two products Mc(Tj — Tq) and myVi which appear therein together represent the quantity of heat furnished by the source of heat during a circular process. For the first is the quantity of heat which is necessary to raise the temperature of the liquid mass M, coming from the condenser, from Tq to Tj ; and the * The above equations, representing the amount of work under the two simphfying conditions introduced at the close of § 19, were developed by me some time ago, and publicly communicated in my lectures at the Berlin University as early as the summer of 1854. Afterwards, on the appearance, in 1855, of the Philosophical Transactions for the year 1854, 1 found therein a memoir of Rankine's, "On the Geometrical Representation of the Expan- sive Action of Heat, and the Theory of Thermo-dynamic Engines," and was surprised to find that at about the same time Rankine, quite indepen- dently, and in a different manner, arrived at equations which almost en- tirely agreed with mine, not only in their essential contents, but even in their forms ; with this exception only, that Rankine did not consider, that, when entering the cylinder, a quantity of liquid is mixed with the vapour. By the earlier publication of this memoir I lost, of course, all claim to priority with respect to this part of my investigations; nevertheless the agreement was so far satisfactory as to furnish me with a guarantee for the accuracy of the method I had employed. 262 Prof. Clausius on the Application of the Mechanical latter is the quantity consumed in vaporizing the part m, at the temperature Tj. As m^ is but little smaller than M, the last quantity of heat is far greater than the first. In order more conveniently to compare the two factors with which these two quantities of heat are multiplied in equation (25), we will alter the form of the one which multiplies Mc(Ti— Tq). If, for brevity, we make then and so that we have ,p^ , (26) To _1-^ T,-To Z Z^ <2^ = —3 + 3:3 + 3:4+ ^''•••- Hence the equation (25) or (XI) becomes W'=m,...^ + Mc(T.-T„).|(^ +0+6+ ^'=--)(2'^ It is easy to see that the value of the infinite series, which distinguishes the factor of the quantity of heat Mc(Tj — Tq) from that of the quantity of heat mj^Tj, varies from \ to 1, as 2" increases from 0 to 1. 23. In the case last considered, where the vapour by expan- sion cools down to the temperature of the condenser, we can easily obtain the expression for the work done in another man- ner, without considering the several operations which constitute the circular process. For in this case every part of the circular process is reversible. We can imagine that the vaporization takes place in the con- denser at the temperature T^, and that the mass M, of which m^ is vaporous and M — Wq liquid, enters the cylinder and raises the piston ; further, that by the descent of the piston the vapour is first compressed until its temperature is raised to T„ and then that it is forced into the boiler ; and lastly, that by means of the small pump the mass M is again conveyed in the liquid form fcom the boiler to the condenser, and allowed to cool there to nNn$sts>iv^^o^y of Heat to the Steam-engine. 263 the original temperature Tq. The matter here' passes through the same conditions as before, but in an opposite order. All communications and abstractions of heat take place in opposite order, but in the same quantity and at the same temperature of the mass; all quantities of work have opposite signs, but the same numerical value. Hence it follows, that in this case no uncompensated trans- formation is involved in the circular process, and we must con- sequently set N = 0 in equation (2), by which we obtain the fol- lowing equation, — already given in (3), with the exception that W is here put in the place of W,- -=k«.-4:t)- In our present case, Q, denotes the quantity of heat imparted to the mass M in the boiler, that is, Qi=mirj+Mc(Ti-To). In determining the integral j -7=p, the two quantities of heat Mc(Ti — Tq) and m^r^ contained in Qi must be separately con- sidered. In order to execute the integration extending over the first quantity, we have but to give to the element of heat dQ, the form Mc^T, and this part of the integral is at once expressed by McJ^ _=Mclog^. During the communication of the latter quantity of heat, the temperature is constant and equal to Tj, and consequently the part of the integral referring to this quantity is simply By substituting these values, the foregoing expression for W becomes W'= i-[m,., + Mc(T, -To) -To(^+ Mc log|l)] and this is the same expression as that contained in equation (XI), which was before obtained by the successive determination of the several quantities of work done during the circular process. 24. From this it follows, that if the temperatures at which the matter manifesting the action of heat receives heat from the source of heat, or imparts heat to some external object, are considered as previously given, then the steam-engine, under the conditions made in deducing the equation (XI), is 2, perfect machine; that 264 Prof. Claudius on the Application of the Mechanical is to say, for a certain amount of imparted heat it famishes as much work as, according to the mechanical theory of heat, is possible at those temperatures. It is othei'wise, however, when those temperatures, instead of being given, are also considered as a variable element, to be taken into consideration in judging the machine. One uncompensated transformation not included in N, which, with respect to the applicability of heat, causes a great loss, arises from the fact that the liquid, during the processes of heating and evaporation, has far lower temperatures than the fire, and consequently the heat which is imparted to it must pass from a higher to a lower temperature. The amount of work which can be produced by the steam-engine from the quantity of heat w,ri + Mc(Ti — To)=Qi, is, as may be seen from equation (27), somewhat smaller than Qj t^-Tq A * T, ' If, on the contrary, we could impart the same quantity of beat Qi to a changeable body at the temperature of the fire, which may be T', whilst the temperature during the abstraction of heat remained Tq, as before, then by equation (4) the greatest possible amount of work to be gained in such a case would be ■M AT'- In order to compare the values of these expressions in a few examples, let the temperature /q of the condenser be fixed at 50° C, and for the boiler let us assume the temperatures 110°, 150°, and 180° C, of which the two first correspond approxi- mately to the low- and the ordinary high-pressure machines respectively, and the last may be considered as the limit of the temperatures hitherto employed in steam-engines. In these cases the fraction dependent upon the temperatures has the fol- lowing values : — />. 110^ 150° 180' T,-To 0157 0-236 0-287 whereas the corresponding value for the temperature of the fire /', assuming the latter to be only 1000° C, is 0-746. - 25. We may here easily discern, what has already been ex- pressed by S. Carnot and several other authors, that in order to render machines driven by heat more efficient, attention must be particularly directed towards the enlargement of the interval of temperature between Tj and Tq. \»o$i\j>N Theory of Heat to the Steam-engine. 265 For instance, machines driven by heated air will only attain a decided advantage over steam-engines when a method is found of allowing them to work at a far higher temperature than steam- engines, in consequence of the danger of explosions, can bear. The same advantage, however, could be attained with over-heated vapour ; for as soon as the vapour is separated from the liquid, it is just as safe to heat it further as to heat a permanent gas. Machines employing vapour in this condition may possess many of the advantages of the steam-engine besides those of air- machines, so that a practical improvement may sooner be ex- pected from these than from air-machines. In the machines above mentioned, where, besides water, a second more vaporizable substance was employed, the interval Tj — Tq is increased by lowering Tq. It has already been sug- gested, that this interval might be increased in a similar manner on the upper side, by the addition of a third liquid less vapor- izable than water. In such a case the fire would be immediately applied to the evaporation of the least vaporizable of the three substances, the condensation of this to the evaporation of the second, and the condensation of the second to the evaporation of the third. Theoretically, there is no doubt that such a combi- nation would be advantageous; the practical difficulties^ how- ever, which would have to be overcome in realizing such a scheme cannot of course be predicted. 26. Besides the above-mentioned defect, arising out of the very nature of our ordinary steam-engines, these machines suffer from many other imperfections, which may be ascribed more immediately to defective construction. One of these has already been considered in the foregoing development, and allowed for in equation (X), that is to say, the expansion cannot be continued nearly far enough to allow the vapour in the cylinder to reach the temperature of the condenser. If, for example, we assume the temperature of the boiler to be 150°, and that of the condenser to be 50°, then the Table in § 16 shows, that, for the above purpose, the expansion must be prolonged to twenty-six times the original volume ; whereas in practice, owing to many inconveniences attendinggreat expansions, three or four, and at most ten times the original volume is attained. Two other imperfections, however, are expressly excluded in the foregoing : these are, first, that the pressure of the vapour in one part of the cylinder is smaller than in the holler, and in the other part greater than in the condenser', and secondly, the pre- sence of vicious space. We must consequently extend our former considerations sO as to include these imperfections. =:^/"? b >i'r?.,i) /s itjl.rjijih.j [To be continued.] '*' fr -/r^J ., wfRr.rjHrw XXXIV. On the Demonstration o/Fresnel's Formulas for Reflected and Refracted Light. — No. III. By the Rev. Baden Powell, M,A,y F.R.S. ^c, Saviiian Professor of Geometry in the Uni- versity of Oxford*. 1. TN two former papers (Phil. Mag. July and August 1856), Jl especially in the last paper, I have shown that, on received principles, the original formulas of Fresnel are apparently neces- sary for the application of theory to certain experimental results, to the exclusion of some newer modifications, though deduced on more systematic theoretical groundji. In opposition to this, however, another view has been sug- gested (as there mentioned), which, if true, would set aside all the reasoning hitherto adopted on the subject, but which to me seems open to great doubt in itself. It is, however, clear that FresnePs original formulas cannot both be deduced on any common principle hitherto proposed, it being, as far as yet appears, necessary to assume a separate hypothesis for each of the two cases, and these not apparently reconcileable with each other. 2.^ If the considerations I have adduced in my second paper (§§ 24, 25) be regarded as well founded, it becomes highly im- portant to find some mode of deducing both FresnePs original formulas on a common principle. But whether the arguments I have advanced be thought valid or not, it must still be allowed, on all hands, to be a matter of some interest if possible to suggest a proof free from the objec- tions mentioned. Since writing those papers, it has appeared to me that this may be effected, provided the following considerations be ad- mitted relative to the law of equivalent vibrations, which (as before hinted) appears to be the doubtful element in the former investigations. 3. In the case (a) of vibrations perpendicular to the plane of incidence, and where the incident, reflected and refracted, vibra- tions are all parallel to each other and to the surface, there is no difficulty. Here there is no geometrical construction from which to find the relation of the amplitudes. In this case the proof of equivalence depends directly on mechanical considerations alone, agreeably to the reasoning referred to before (first paper, § 26). Here hy h', and h^ being the mechanical values of the amplitudes, we have simply for the law of equivalence, h,=:h-^h'. 4. In the case (13) of vibrations parallel to the plane of inci- * Communicated by the Author. On FresnePs Formulas for Reflected and Refracted Light. 267 dence, we have the obvious geometrical construction of the tri- angle formed by the known directions of the rays, and conse- quently of the amplitudes at right angles to them, and in the same plane (first paper, § 23) . In this triangle, the angles being (e— r), (2-fr), and {7r—2i), the ratios of the sides will be (as before) I _ sm 2i h! sin {i — r) h h ^m{i-\-rY A sin(i + r)* 5. On MaccullagVs theory oi equal densities, it will be remem- bered that this construction represents the mechanical equiva- lence, and the sides thus give the values of the amplitudes. The close agreement of these values with those for the ampli- tudes in case (a) deduced on the hypothesis of increased density, — to which no such construction can apply, — has been already remarked (first paper, §§ 25, 41). But these values cannot be those of the amplitudes in case (/3) on the hypothesis of increased density, since experimental results essentially require a different relation in this case from that in case (a). 6. From the triangle, however, we have this obvious and simple relation of equivalence, h^ = h cos {i—r) + A' cos [i + r) ; or expressing these components parallel to h^ by [h) [h!), we have But in this construction, it must be borne in mind that if we assume the side h^ as the value of the refracted amplitude, it is represented geometrically on the same scale with the other sides by which we measure the components ; and for its actual value it is necessary to take into account its diminution in the more retarding medium in the ratio of the refractive index ; or if {h^) 268 Prof. Powell on the Demonstration of PresnePs Formulas be this physical value, we must take (A,)=A,i=((A) + (A'))l Thus both cases of equivalence may be included in one expression {0 being the inclination of the plane of vibration to that of in- cidence), ^^^^ _^ ^^^,^^ ^^^ 0 + cos ^ i ) = (h,), where ^=90° gives case (a), and ^=0° gives case {j3). 7. If this be admitted as the true expression of the law of equivalence, we can deduce both FresneVs original formulas from this law of equivalence combined with that of vis viva, viz. {h^'-h"')m=hi^m,. (a) For vibrations perpendicular to the plane of incidence, the law of equivalence, {h + h') = h,, combined with the law of vis viva, gives (h--h')^:=^=h + h. But on the hypothesis of increased density or retardation, as before (first paper, § 17), m __ sin r cos i ^■"sinecosr ^^^^ ^^\f^S> ^;' (h — h') sin r cos i = ( A + A') sin i cos r, , avodfj or A (sin r cos i — sin i cos r) = A' (sin r cos i -\- sin i cos r) ^fii mo'fl ^I:*^ _ -(sin(i-r)) ^ ^ 2 sin r cos a )HT A sin(2 + r) ' h sin(2 + r)' iJsufK^ 8. (/3) For vibrations parallel to the plane of incidence, the law of equivalence (writing kh!k^ instead of [h) {h') {h^), ai li 6B omac oxiJ my i ^^^-'^ t.'-^^ ^^ J-^ -f-^ (£ni»3 (B) OKBO ni iud , (^ + k') - = A:^, .^qua b^d aw (»)^ 68f>) ^ .eaiiisnab coiftbiittd wiyi tfesilawftf t?i« vimy giveavisedo ad oeIb x^m il 9jdi ni i(lfio. oJ boj^o'l^'i a a! oiu| an to yi<(^f>aB adJ iIs^IIjjodbM bnB 3r>dw ^93ii*ini^i5r^ffiS^^fc^<(i'f^% 98bo •dhf^.^iq j>ili ill ^iiuf^ii^/ rM(iD'iij«j(|« Jofi^i Y:qohjaii iBoiiifiibam sdt "^^ ■ . . ! p. I ^ J } 993 3W floilBsiigyvni ;«_ , ^ smrcose ^ sm^ ^ sin2j ^ ^ ^^^^^^^^^ anoitBidi'/ m, sm e cos r sin^r ^ smgndo^ni ^Bnibto nf ssb') (yfc-AO sin 2i= (AdrJ') sin.2r. I ?.oWk«'vvvI for Reflected and Refracted Light. -o^i Joi 269 A' __ sin 22— sin 2r _tan {i—r) rjljsv kof^iV^fiq aui* j<» k "" sin 2i + sin 2r ~~ tan {i -f r) 1 u -^ A;^ = (X: + A:') -2sin22— =4sinrcos2 aoiaaa-iqxa 9fio jr /^ /^ ^oe/iO iflod 8Uiil -fli io '^/ _ 4 sin r cos 2 __ /^ tan {i—r) Vcosi' "^nhd % k ~ sin %i + sin 2r ~ \ tan (i + r) / cos r >^«9t)io 9. These amplitudes are portions of the sides of the triangle taken in the ratio of the components ; and if in that ratiq W^F*^ given we substitute the value of -j-f we find -t M \ ' ^ (#)v j^vgiij (i—r) cos {i + r) _ sin 22- sin 2r ''^' (A) sin (i + r) cos (z- r) sin 2z -f- sin 2r' which coincides with the value just deduced on the principle of the vis viva. Thus for both cases we have FresneFs original formulas. 10. It is also worthy of remark, that as the investigation of case (a) is obviously equivalent to the direct application of the formula for impact, viz. ^^^^ ■t,4,.«3d}oqTd siW ao iM „= ^:ra, j>,=-?5-; - •" '■ --• ■■"■'■- m + m^ ' m + ml so on the principle here adopted for case (/3), it is easily seen that the same is true, if here, instead of m m^ we take (as above (8)) u^ ,ix h ^^, -:. .^ , . msmz . ft. 1 / X m, smr . ^ (m) = -^ = sm 2i and (m,) = —k — — = sm 2r. ' smr ' " smz The result is the same as would be obtained directly from the equations W + W ' W + K) ' ' 11. It is also remarkable that this result is the same as if in case (a) we had supposed increased density, but in case (/3) equal densities. It may also be observed, that in the investigations of Fresnel and Maccullagh the analogy of impact is referred to only in the case of vibrations perpendicular to the plane of incidence, where the mechanical analogy is not apparent ; whereas in the present investigation we see that that analogy applies also to the case of vibrations parallel to the plane of incidence, which is the actual case in ordinary mechanical impact. . "sS>t ms {^i — f) Erratum in first Paper. § 37, line 2, dele " or direction of vibrations." [ 270 ] XXXV. On Rubian and its Products of Decomposition. By Edward Schunck, F.R.S. [Concluded from p. 220.] ACTION of Chlorine on Rubian, — If a current of chlorine gas be passed through a watery solution of rubian, the latter begins immediately to deposit flocks of a lemon-yellow or orange co- lour. These flocks continue to be formed as long as the solu- tion retains any portion of its yellow colour. When the action is completed the liquid appears colourless. The flocks, the quantity of which is considerable compared with that of the rubian employed, consist almost entirely of one substance, which I shall call Chlororubian, though this name is not perfectly ap- propiate, since it is not formed from rubian simply by the sub- stitution of hydrogen by chlorine. If these flocks, after being collected on a filter and washed until all the acid and chlorine are removed, be treated with a little cold alcohol, the latter dissolves a small quantity of a substance, which after the eva- poration of the alcohol is left as a yellow or yellowish-brown resinous residue. This substance melts at the temperature of boiling water ; it contains chlorine, and dissolves in caustic alkalies with a dirty purple colour. The chlororubian may be purified by simply dissolving it in boiling alcohol. It crystal- lizes on the solution cooling in small orange-coloured needles, which increase very much in quantity after standing for several hours. The acid liquid, filtered from the yellow flocks formed by the action of chlorine, contains sugar, which may be obtained by neutralizing the acid with carbonate of lead, filtering, evapo- rating the liquid to a small volume, decolorizing with animal charcoal, filtering, evaporating to dryness, and treating the residue with alcohol. The alcohol after filtration and evapo- ration leaves a yellow syrup having all the properties of sugar, as usually obtained by the decomposition of rubian. Chlo- rorubian may be prepared as well from impure as from pure rubian. It is only necessary to extract madder with boiling water, add sugar of lead to the extract, add ammonia to the liquid filtered from the precipitate, decompose the red precipi- tate produced by ammonia with sulphuric acid, and pass chlorine gas through the filtered liquid. The first portions of chlorine generally produce a dirty yellow flocculent precipitate, which, being separated by filtration, is found to consist of the resinous easily fusible substance just mentioned. On passing chlorine through the filtered liquid, pure yellow flocks of chlororubian are precipitated, which are purified as before by crystallization from boiling alcohol. V ' " Chlororubian has the following properties. After crystalliza- tion from alcohol and drying, it forms a mass of a light orange Dr. Schunck on Rubian and its Products of Decomposition. 271 colour, consisting of small crystalline needles. It has no per- ceptible taste at first, but on chewing it for some time it pro- duces a slightly bitter taste. When heated on platinum it melts and burns with a smoky flame slightly tinged with green, and leaves a considerable quantity of charcoal. On being heated in a tube it melts to a brown liquid, and gives fumes which condense on the colder parts of the tube to a white crystalline sublimate, consisting of star-shaped masses, while much carbonaceous resi- due is left. On being treated with boiling water chlororubian dissolves in considerable quantity, forming a yellow solution, which on cooling deposits a great part of the substance, not in crystals, but in amorphous masses consisting of spherical grains. The boiling alcoholic solution, if very concentrated, also deposits part of the substance on cooling in amorphous, spherical, trans- lucent grains, which have the appearance of drops of oil, but by redissolving these in fresh alcohol, crystals of the usual appear- ance are obtained. The alcoholic solution does not redden litmus paper in the least. The watery solution gives no precipitate with nitrate of silver, but if chlororubian be treated with boiling nitric acid, it is decomposed with an evolution of nitrous acid, forming a colourless solution, in which nitrate of silver produces a pre- cipitate of chloride of silver. The action of sulphuric and muri- atic acids, caustic alkalies and chlorine on chlororubian, I shall treat of presently. Chlororubian dissolves in boiling solutions of the carbonates of potash, soda and ammonia, forming blood- red solutions, which deposit nothing on cooling. Baryta water imparts to the watery solution a deep red colour, and on boiling dark red flocks are deposited, while the liquid becomes almost colourless. Lime water turns the watery solution red without producing any precipitate, but the ammoniacal solution gives with chloride of calcium a light red flocculent precipitate, while the supernatant liquid becomes colourless. The watery solution gives no precipitate with the acetates of alumina and peroxide of iron. On being treated with a boiling solution of perchloride of iron, chlororubian dissolves with a brownish-yellow colour, which after some time becomes dark brown, while a black powder is deposited. The alcoholic solution of chlororubian does not change on being mixed with an alcoholic solution of acetate of lead, but the watery solution gives with basic acetate of lead a light red precipitate, the liquid retaining a reddish colour. The alcoholic solution gives no precipitate with acetate of copper. An alkaline solution of chlororubian reduces chloride of gold to the metallic state, even in the cold. Chlororubian produces no eff'ect on mordants, on trying to dye with it in the usual manner. On submitting chlororubian to analysis the following results were obtained : — . , . ^72 Dr. Schuuck on Jhthkm%nd its Products of Decomposition. Ivh 0*4100 griu., dried in the water bath and burnt with chro- inate of lead, gave 0*7690 carbonic acid and 01 860 water. 0*4760 grm., burnt with lime, gave 0*1260 chloride of silver. II. 0*4780 grm. of the same, recrystallized from boiling alco- hol, gave 0*8950 carbonic acid and 0*2100 water. III. 0*5170 grm. of another preparation gave 1*0270 car- bonic acid and 0*2400 water. 0*7720 grm., burnt with lime, gave 0*2015 chloride of silver. IV. 0*4425 grm. of the same preparation as the last gave 0*8320 carbonic acid and 0*1960 water. 0*5450 grm., on decomposition with fuming nitric acid to which a little nitrate of silver was added, gave 0*1380 chloride of silver. V. 0*4975 grm. of a new preparation gave 0*9330 carbonic acid and 0*2240 water. \\ , 0*8580 grm., burnt with lime, gave 0*2180 chloride of silver. VI. 0-5320 grm. gave 1*0000 carbonic acid and 0*2380 water. 0*9370 grm., burnt with lime, gave 0*2450 chloride of silvefi These numbers correspond in 100 parts to — jb I. II. III. IV. V. :VI.50'ik Carbon . . 51*15 51*06 51*20 51-27 51*14 51*26: Hydrogen . . 5-04 4*88 4*87 4*92 5*00 4*97 Chlorine . . 6*54 „ 6*45 6*26 6*28 6*46 Oxygen . . 37*27 „ 37*48 37*55 37*58 37*31 There are several formulae which give a composition in 100 parts agreeing tolerably well with these numbers, but only one which at the same time explains the manner in which chlororu- bian is formed. This formula is C** H*^ ClO^^, which gives the- following composition : — ^■* Eqg. 'ii : Carbon ... 44 264 50*92 id bam Jibc- Hydrogen . . 27 ri:;275uu>m.Y&r^ ba& ^luoloo aok'M-- .Chlorine, .t . .1 85*4 6*8fl'^ r: ....^i^ xmj Oxygen . ba^ ,t^ 192 37*06 oi 618*4 100-00 *»i Assuming this formula to be correct, then rubian, when acted'^ on by chlorine, loses 1 equivalent of hydrogen, which is replaced by chlorine, at the same time taking up 6 equivalents of water and sphtting up into chlororubian and sugar, as will be se^^* from the following equation : — ' C^H*»0«>+6HO-f2Cl=C44H^C1024 + Ci^IP2 0'2 + ClH. Action of Acids on Chlororubian. — If chlororubian be treated with boiling dilute sulphuric or muriatic acid, it first dissolves to a yellow liquid, but on continuing to boil, the solution sudr * denly becc|me8 milky and dejbbsit? a ferge .q^uantity of yellow ' Br. Schunck vn Rubian and its Products of Decomposition, 273 crystalline flocks. The filtered liquid is almost colourless, and contains sugar. The flocks consist entirely of a body, to which, as it has the composition of rubiadine in which 1 equivalent of hydrogen is substituted by chlorine, I shall give the name of Chlororubiadine. It is purified by collecting the flocks on a filter, washing them with water, and dissolving them in boiling alcohol, which on cooling and standing, deposits yellow shining crystals, which are larger than those of chlororubian. Chlororubiadine has the following properties. When cry- stallized from alcohol and dried, it has the appearance of a yellow mass, consisting of small shining crystalline needles and scales. When heated on platinum it melts to a brown liquid, and then burns with a yellow flame bordered with green, leaving much carbonaceous residue. When heated in a tube it melts and gives penetrating fumes, smelling of muriatic acid, and forming on the colder parts of the tube a sublimate which is at first oily but soon becomes crystalline. It is insoluble in boiling water. Dilute nitric acid does not affect it, even on boiling. Nitric acid of sp. gr. 1*52, however, dissolves it, even in the cold, forming a dark orange-coloured solution. If nitrate of silver be added to this solution, no precipitate is produced ; but if the solution be boiled, an evolution of nitrous acid takes place, the solution becomes turbid, and gives a copious deposit of chloride of silver. Concentrated sulphuric acid dissolves it in the cold, forming an orange -coloured solution, from which it is precipi- tated again by water in bright yellow flocks. If the solution in the acid be boiled its colour changes to a deep purple, without much sulphurous acid being evolved, a small quantity of a white crystalline sublimate making its appearance afterj some time on the sides of the vessel near the surface of the liquid. Chlororu- biadine is easily dissolved by caustic soda with a purplish-red colour, and by ammonia and the carbonates of potash, soda and ammonia, with a blood-red colour. The ammoniacal solution loses its ammonia on evaporation, and leaves the substance behind as a bright yellow residue. On adding chloride of ba- rium to the ammoniacal solution, the baryta compound crystal- lizes out on standing in long needles, arranged in large fan- shaped or star-shaped masses of a beautiful red colour, while the liquid becomes almost colourless. The baryta compound, when treated with boiling water, only dissolves in part, some chlororubiadine being left undissolved. If a current of carbonic acid be passed through the filtered solution, the whole of the chlororubiadine is precipitated in yellow flocks, the liquid be- coming colourless. The ammoniacal solution gives with chloride of calcium, after some time, a dark red uncrystalline deposit, and also loses its colour. A boiling solution of perchloride of Phil. Mag. S. 4. Vol. 12. No. 79. Oct. 1856. T 274 Dr. Schunck on Rubian and its Products of Decomposition. iron does not dissolve chlororubiadine, nor does the colour of the solution change during boiling. The alcoholic solution of chlororubiadine reddens litmus paper. The solution gives no precipitate with acetate of lead, not even on the addition of ammonia, but with acetate of copper it gives after some time a copious light brown precipitate. Acetate of alumina and per- acetate of iron produce no change in the alcoholic solution. An alkaline solution of chlororubiadine reduces chloride of gold to the metallic state. The composition of chlororubiadine was determined by the following analyses : — I. 0*5650 grm., dried at 100° C. and burnt with chromate of lead, gave 1*2630 carbonic acid and 0*2130 water. 0*4850 grm., burnt with lime, gave 0*2200 chloride of silver. II. 0*4620 grm. of a second preparation gave 1*0260 carbo- nic acid and 0*1760 water. tG-j!. j itirw i- )MJJ^;L• III. 0*5475 grm., made from the last by dissolving it in ammonia, adding chloride of barium, filtering the liquid from the dark flocks which were precipitated, allowing the baryta compound to crystallize, decomposing it with muriatic acid, and crystallizing what was left by the acid from boiling alcohol^ gave 1*2280 carbonic acid and 0*2100 water. -^ 0*6260 grm. gave 0*2775 chloride of silver. IV. 0*4980 grm. of another preparation, obtained like the last from the bai*yta compound, gave 1*1130 carbonic acid and 0*1905 water. 0*7680 grm. gave 0*3455 chloride of silver. Hence the following composition may be deduced : — Eqs. Calculated. I. II. III. IV. ^ Carbon . 32 192 61-65 6096 60-66 61-17 60*95 Hydrogen. 12 12 385 418 4-23 426 4-25 Chlorine. 1 35-4 1136 1121 ,1^{^^M^'^. H'lO Oxygen . 9 _72_ 23-14 23-65 ^r ^^^23*^ ' 23-70 311*4 10000 10000 10000 100-00 The baryta compound I found to have no very simple compo- sition. It was prepared, as above described, by dissolving cry- stallized chlororubiadine in ammonia, adding chloride of barium, filtering from a few flocks that were precipitated, and allowing to crystallize in an air-tight flask, filtering, washing with water, and drying in vacuo, 0*8370 grm. of the crystals lost, on being heated for some hours in the water-bath, 0*0690 water =8*24 per cent. 0*5770 grm. of the substance thus dried gave, when burnt with chromate of lead, 1*0965 carbonic acid and 0*1790 water. 0*5660 grm. gave 0*1350 sulphate of baryta. These numbers lead to the formula 4C^^ W^ ClO^-f-SBaO, as Eqs. Calculated, Found. .,,„ ,P^,,, ,„768„,i 5205 51-82 ^. j.i.trK ^ o'ti -imfW^} '■}>■' 3-25 3-44 . . 4 141-6 9-59 9> . . 36 288 1954 )f ii)i'i©irta SoiJij^'i 229-8 15-57 15-65 Dr. Schunck on Ruhian and its Products of Decomposition. 275 the following comparison between the theoretical composition and the experimental results will show : — Carbon Hydrogei)^ Chlorine Oxygen Baryta 1475^ 100-00 The sugar which is formed from chlororubian together with chlororubiadine may be obtained in a crystallized state, which is not the case with the different specimens of sugar derived from the other processes of decomposition to which I have subjected rubian. If sulphuric acid be employed for the decomposition of chlororubian, and the acid after filtration of the flocks of chloro- rubiadine be neutralized with carbonate of lead, the filtered liquid yields on evaporation a sweet syrup. If this syrup be treated with alcohol, a part of it dissolves with a yellow colour. If the alcoholic solution, after separation from the insoluble part, be mixed with several times its volume of aether, it becomes milky and deposits again a yellow syrup, which after standing some time becomes filled with small yellowish crystals, so as almost to form a solid mass. This mass is pressed between blotting-paper, in order to remove the mother-liquor, and the crystals are dissolved in boiling alcohol, to which a little animal charcoal is added. The filtered solution on evaporation gives a syrup, which is soon converted into a mass of white crystals. These crystals have the properties and composition of crystal- lized grape-sugar. 0-5015 grm. of the crystals, dried in vacuo ^ gave 0-6830 car- bonic acid and 0-3380 water. ^j«Itiese ^l^|^l[^ers lead to the following composition : — f)»ho' ryi'FvfH Eqs. Calculated. Found. Carbon . . 12 72 36-36 37-14 Hydrogen . 14 14 7-07 7-48 * Oxygen . . 14 112 56-57 55-38 1^ 198 10000 10000 t It will now admit, I think, of little doubt, that the uncrystal- lizable sugar obtained from rubian in other processes of decom- position is merely modified grape-sugar. The formation of chlororubiadine and sugar from chlororubian is a very simple process. The latter loses three equivalents of water and splits up into chlororubiadine and sugar, as will be evident from the following equation : — C'^H27C1024^C^2Hi2C109 4.Ci2Hi2 0»2-f3HO^ax{i' ' T2 ' 276 Dr. Schunck on Ruhian and its Products of Decomposition^. I have adopted the name of chlororubiadine, under the assump- tion that the true formula for rubiadine is C^H^^O^. Never- theless I have not succeeded in converting the latter into chloro- rubiadine by means of chlorine, nor in substituting the chlorine in chlororubiadine by hydrogen and thus forming rubiadine. If chlororubiadine be suspended in water to which an amalgam of potassium (1 part of potassium to 100 mercilry) is added, it dissolves with a dirty red colour without much hydrogen being evolved. The liquid gives a greenish-yellow flocculent precipi- tate on the addition of nitric acid. This precipitate contains no chlorine, but it docs not contain any rubiadine, since it gives, after being dried and heated between two watch-glasses, none of the crystalline sublimate characteristic of rubiadine. The liquid filtered from this precipitate gives an abundant precipi- tate with nitrate of silver. Hydrosulphate of ammonia dissolves chlororubiadine, forming a red solution, which on standing becomes of a fine purple, and after some hours brownish-red. If nitric acid be added to the solution as soon as it has acquired a purple colour, an orange- coloured flocculent precipitate falls. This precipitate is free both from sulphur and chlorine, the chlorine of the chlororu- biadine being found in the filtered liquid, but it contains no rubiadine. It is only partly soluble in boiling alcohol, but dis- solves easily in boiling nitric ,acid, the solution depositing on standing some long dark yellow sword-shaped crystals. If crystallized rubiadine, obtained by the decomposition of rubihydran with acid, be dissolved in caustic alkali and repreci- pitated with acid, and if the precipitated flocks after filtering and washing be suspended in water, and a current of chlorine gas be passed through the liquid, the flocks become somewhat paler in colour. If they be now collected on a filter and washed with water and then treated with cold alcohol, the greater part dis- solves, leaving undissolved a small quantity of a white powder, which has all the properties of a body which I shall describe presently, and which is formed by the action of chlorine on chlororubian. If the alcoholic solution be evaporated to dryness and a little cold alcohol be again added to the residue, the alco- hol again dissolves a great part, leaving undissolved a yellowish- green granular powder, which resembles but is not identical with chlororubiadine. The alcoholic solution leaves on evapo- ration a brown, transparent, resinous substance. This substance contains a large quantity of chlorine. It dissolves in caustic soda with a brown colour, and is reprecipitated by acids in yellow flocks, which melt in the boiling liquid to brown oily drops. I found it to contain the following quantities of carbon and hydrogen : — Dr. Schunck on Ruhian and its Products of Decomposition, %77 0*3090 grm., dried at 100° C. and burnt with chromate of lead, gave 0-6090 carbonic acid and 0*1060 water, corresponding in 100 parts to — Carbon .... 53-75 Hydrogen. . . . 3*81 The formula C^^ H^^ CP Q^^=zQ^^ W^ CP O^-f HO requires in 100 parts— • -:,edJi77T -b: M-,..-.^-, .:= -.- Carbon -^rrT^fyrif ,.; ;» ^.^^*9Q,,;^ .^^i , ,..<■r^o■■ on' mmimi> fiin Hydrogen . Jn^^tytrfiut iS'^Itihbe offrf ,p^pp|.h> fi Oxygen, a,.«;|.^r i,.;t,. 22*50 ,r..f; «.r,> I may mention by the way, that the brown resinous substance which, as 1 stated above, is formed in small quantities along with chlororubian by the action of chlorine on rubian, is very similar both in properties and composition to this substance. It was prepared simply by passing chlorine through a solution of rubian, collecting the yellow flocks which were formed in the first instance separately, washing them with water, and treating with cold alcohol. The filtered solution was evaporated to dry- ness, when it left a resinous substance resembling rubiretine. 0*4] 30 grm. of this substance, dried in the water-bath, gave 0*8200 carbonic acid and 0*1500 water. 0*3010 grm., burnt with lime, gave 0*2160 chloride of silver. These numbers correspond in 100 parts to — -i r^i-i'jo -^mhiit'i-i -iD&iqVi bfi,6 iit TT 1, ' u f b^MosaiB t)(? J>i^i^ dtrw nsib^rfk^^^ ■j^^.n -jp.f ...:rv.r.: ^xygen,.^ .p^ .^.^ ..^._. ^^Kyi)r^^^^^^^^ F,o..c... ^J .' By the action of chlorine on chlororubiadine, a body very similar to these but dififering in composition is formed. If finely pounded chlororubiadine be suspended in water and a stream of chlorine gas be passed through the liquid for some time, tiie powder becomes lighter in colour, but not white. If it now be collected on a filter, washed with water, and treated with boiling alcohol, it dissolves in the latter, forming a yellow solu- tion, which deposits nothing on cooling, but on evaporation leaves a transparent dark yellow amorphous substance like resin, which remains soft for a long time, and only becomes bard and brittle after being heated in the water-bath for some time. This substance, when heated on platinum, burns with a yellow flame, leaving much charcoal. When heated in a tube, it melts and gives acid fumes and a yellow oily sublimate, in which on cooling some white crystals make their appearance. The alco- holic solution gives no precipitate with nitrate of silver, but 278 Dr. Schunck on Rubian and its Products of Decomposition. the substance on being treated with boiling nitric acid is dis- solved and decomposed, and nitrate of silver now gives an abun- dant precipitate. It is soluble in concentrated sulphuric acid with a brown colour, but on boiling the solution no sulphurous acid is evolved. Caustic soda dissolves it easily with a brown colour. On being analysed it yielded the following results : — ■ 0*3910 grm., dried in the water-bath, gave 0*6675 carbonic acid and 0*1 100 water. 0'4055 grm. gave 0*4990 chloride of silver. In 100 parts it contained therelbrer-i^ Carbon . :^'- 1'^ 46-55 Hydrogen. . . . 312 Chlorine . , . . . 30-42 Oxygen . . . . . 19-91 Since the carbon here is to the chlorine as 32 C : 3J CI, this substance must either have been a mixture, or it must have lost chlorine during the process of drying. Action of Caustic Alkalies on Chlororubian. — The action of alkalies on chlororubian differs essentially from that of acids. The chlorine in chlororubian is so loosely combined that the aflSuity of the alkaline metal is sufficient to remove it, and hence all the organic products of decomposition formed by the alkali are free from chlorine. If chlororubian be treated with a solution of caustic soda it dis- solves easily, forming a red solution. If this solution be heated for some time, it deposits a quantity of dark reddish-brown flocks. When these flocks cease to be formed, the liquid, which is still red, is filtered, the flocks are washed with water until the excess of soda is removed, and they are then treated with boiling muriatic acid, by which their colour is changed to yellowish-brown. After being collected on a filter and washed with water, they are then treated with boiling alcohol, in which they are but little soluble, placed on a filter, washed with alcohol and dried. After drying, there is obtained a yellowish-brown powder which has the fol- lowing properties. It is almost insoluble both in alcohol and in caustic alkalies, though the latter impart to it a dark reddish- brown colour. It is not dissolved by hydrosulphate of ammonia. It contains no chlorine. When heated in a tube it gives a yel- low crystalline sublimate, which dissolves easily in caustic alkalies. Its composition was determined by the following analyses : — I. 0-3980 grm., dried at 100° C. and burnt with chromate of lead, gave 10330 carbonic acid and 0*1390 water. J.. II. 0*3910 grm. gave 10150 carbonic acid and 0*1370 water. III. 0-4000 grm. of a new preparation gave^l*0350 carbonic acid and 0*1435 water. e32Hioo8. C'2H"0«. 72-18 69-81 376 4-00 24-07 2619 Dr. Schuuck on Rubian and its Products of Decomposition, 279 In 100 parts it contained therefore-r-^^,,^ «^ ^^^ * , I. ...ft.-..,.., .....J, ra. ?..-..;,:■ tHOii Carbon . . . 70*78 70*79 70-56 >.- Hydrogen . . 3-88 3-89 ,3-^8 , Oxygen . . . 25-34 25-32 ; ^ ^,. J^4S Z,^ It is doubtful whether this body contains 44 or 32 equivalents of carbon. The formulae 0^4 H^^ 0^^ C^^ H^^ 0« and C^^ hh 0^ require in 100 parts respectively the following amounts of the three constituents : — C44 H" 012. Carbon . ^,^.^, 70-58 Hydrogen Q\f S'74i Oxygen . . . 25-68 If the first formula be adopted, then this substance is formed from chlororubian by the latter losing its chlorine, which com- bines with sodium and is replaced by oxygen, while 13 equiva- lents of water are eliminated, in accordance with the following equation :— sy^^o-toV oUik ' C44 H27 ci024+!iJaO=C44 H^4 oi2 + NaCl+ 13H0. If one of the two latter formulae be adopted, then chlororubian first splits up into chlororubiadine and sugar, and the former then loses its chlorine which is replaced by oxygen, while either five or four equivalents of water separate, as will be seen from the following equations : — C44 H27 C1024 _^ NaO = C32 H»o 08 + C^^ H^^ 0^^ + ^aCl + 5H0, C44 H27 C1024 + NaO = C^^ Rii 0^ + 0^2 H12 012 + NaCl + 4H0. The first formula agrees best with the results of analysis. Nevertheless, it seems improbable that chlororubian, when sub- jected to the action of so potent an agent as caustic soda, should not, in the first instance at least, be decomposed in the same manner as with strong acids. On the other hand, if this were the case, chlororubiadine should, by the action of caustic alkalies, be converted into the same body as chlororubian, which is not the case. If chlororubiadine be treated with caustic soda in the same way as chlororubian, it first dissolves with a purple colour, but the solution on boiling slowly deposits reddish-brown flocks and loses the greatest part of its purple colour. The flocks on being treated with boiling muriatic acid, acquire an orange colour, and after being collected on a filter and washed, are found to be almost insoluble in boihng alcohol ; but notwith- standing their resemblance to the body formed from chlororubian, they differ from the latter in containing a large quantity of chlo- rine, only a small quantity of the latter having been abstracted bythealkah. ^ -<., r ^ ^ , 280 Dr. Schunck on Rubian and its Products of Decomposition, 0-3610 grm. of this substance, diied at 100° C, gave 0-8620 carbonic acid and 0-1060 water. 0-2920 grm. gave 0-1110 chloride of silver. In 100 parts it contained therefore-TniU!, -^ . MuuHvr^ . Carbon . . .-i-ii^t^^^ ii;urtKn3hjibii Hydrogen. . Mvoqi9fW, ^'^^V aonrJedue Chlorine . . . .' 9*^9 oJ °« no\- Oxygen .... 22*23 Should the body formed from chlororubian by caustic alkalies be found to contain 44 equivalents of carbon, the most appro- priate name for it would be Oaryruhiani The liquid filtered from this body is still red. On adding to it sulphuric acid, a yellowish-brown flocculent precipitate falls. This precipitate consists of several bodies. If after being filtered and washed it be treated with boiling alcohol, a part dissolves, leaving undissolved a dark brown substance, which after drying becomes black. This substance is doubtless a product of the de- composition of sugar, as it has the same properties and very nearly the same composition as the body, insoluble in alcohol, which I obtained by the decomposition of rubian with caustic soda*. 0-1760 grm. of this substance gave 0-4360 carbonic acid and 0-0650 water, corresponding in 100 parts to — ]^ Carbon .... 67*56 Hydrogen. . . . 4-10 Oxygen .... 28*34 On adding acetate of lead to the liquid filtered from this pre- cipitate, a brown precipitate falls, which after being filtered off, washed with alcohol and decomposed with boiling muriatic acid, yields brown flocks. These, on being dried and treated with cold alcohol, yield to the latter a body resembling and probably identical with rubiretine, while a brown powder is left undissolved, having the properties and composition of verantine. 0*1755 grm. of the latter, after being purified by redissolviug in a boiling mixture of alcohol and ammonia, then adding an excess of acetic acid, collecting the pulverulent deposit formed on cool- ing, and washing with alcohol, gave 0-4170 carbonic acid and 0-0680 water. . fe ,100 parts it contained therefore — Carbon .... 64*80 Hydrogen .... 4*30 > -' Oxygen .... 30'90 ^ Tfaif liquid filtered from the lead precipitate is yellow. It giy^^ with water a yellow precipitate, which, after being filtered r Dr. Scbunck on Rubian dhd its Products of Decomposition, 28l' off and washed witli water, dissolves again in boiling alcohol, with the exception of a little brown flocculent matter. The al- coholic solution, on evaporation, leaves a yellow uncrystalline substance resembling impure rubiadine, which contains no chlo- rine, gives when heated a sublimate like that from rubiadine, and forms with baryta a compound which crystallizes in dark reddish- brown needles. I obtained so small a quantity of this substance that I was unable to arrive at any positive conclusion as to whether it is identical with rubiadine or not. The residue left on evaporation of the alcoholic solution was analysed without any attempt being made to purify it, when it was found to l^^ve. a composition nearly approaching that of rubiadine. i ^f fT 0*2980 grm. gave 0*7525 carbonic acid and 0*1450 water, corresponding in 100 parts to^ — Carbon §£«iiojy iJTiv/ 68*86 -^ ^^ hodanYf bmi >4.x.v .. ...;.. . Hydrogen';-?^ iiWQid. 5-40 viogaibflir 'gimn-J : ^o!> uii \q louL Oxygen . d nmi- 25*74 ^i-^M earaoD^d , The formation of this body, as well as that of verantine and rubiretine, from chlororubian, I am unable to explain in a sati^-- factory manner. ^ If the excess of sulphuric acid, with which the four last bodies have been precipitated, be neutralized with carbonate of lead, the filtered liquid leaves on evaporation a saline mass, which, on being pulverized and treated with warm alcohol, communicates to the latter a reddish-brown colour. The alcoholic liquid, after being filtered from the insoluble matter consisting of sulphate of soda, leaves on evaporation crystals of chloride of sodium sur- rounded by a brown syrup of sugar. Action of Chlorine on Chlororubian. — If finely pounded chloro- rubian be mixed with water, and if, after the mixture has been placed in a large bottle or other suitable vessel, a current of chlorine gas be passed through it, no change is perceptible for some time ; but if the bottle be closed, after the space above the liquid has been filled with chlorine, the latter is gradually ab- sorbed, the colour of the chlororubian becomes paler, and after several days it appears perfectly white. The process is not accelerated by the action of sunlight, but frequent agitation of the liquid and powder with the gas assists it. The white pow- der into which the chlororubian is changed consists of a body to which I will give the name of Per chlororubian. After collecting it on a filter and washing out the chlorine and acid with water, it is to be dissolved in boiling alcohol, from which it crystallizes on the solution cooling in colourless, transparent, flat, four-sided tables, exhibiting a beautiful iridescence. If it should not be quite colourless, it must be redissolved in boiling alcohol, to which a 282 Dr. Schunck on Rubian and its Products of Decomposition. little animal charcoal may be added. On filtering boiling hot and allowing to cool, the solution then yields perfectly colour- less crystals. It may also be obtained directly from rubian, by continuing to pass chlorine through a watery solution of the latter, uutil the yellow precipitate produced at first has become white, but by this means it is not obtained as pure as from cry- stallized chlororubian. Perchlororubian has the following properties. When heated on platinum it melts to a brown liquid, and then burns with a smoky yellow flame edged with green, leaving little carbonaceous residue. If slowly and carefully heated it may be entirely vola- tilized, yielding a sublimate of bright micaceous scales. But if it be suddenly heated, if, for instance, it be thrown into a red- hot tube, it is decomposed with a kind of explosion, giving off an acid smell, and forming a large quantity of soot with little or no crystalline sublimate. It is insoluble in water, but soluble in alcohol and aether. The alcoholic solution does not redden litmus paper. Concentrated sulphuric acid dissolves it on heat- ing, the solution, on being heated to the boiling-point, becoming slightly brown, but giving off very little sulphurous acid. The colder parts of the tube become covered with a crystalline sub- limate, consisting probably of the substance itself. Nitric acid of sp. gr. 1*37 has no effect on it, even on boiling. Nitric acid of sp. gr. 1'52 dissolves it on boiling without decomposing it, for on adding water, the substance is precipitated unchanged in the shape of a crystalline deposit, and nitrate of silver produces in the liquid no precipitate of chloride of silver. Perchlororubian is quite insoluble in strong caustic soda lye, even on boiling, as well as in ammonia. - It dissolves easily, however, in hydrosul- phate of ammonia on boiling, and on now adding nitric acid and boiling, nitrate of silver produces an abundant precipitate. The alcoholic solution gives no precipitate with an alcoholic solution of acetate of lead. Its analysis led to the following results : — I. 0*4945 grm., dried at 100° C. and burnt ^with chromate of lead, gave 0*6730 carbonic acid and 0*0610 water. 0*4350 grm., burnt with lime, gave 0-7770 chloride of silver. II. 0*3930 grm. of another preparation gave 0*5330 carbonic acid and 00585 water. 0*2730 grm. gave 0*4930 chloride of silver. These numbers lead to the following composition :- Eqs. Calculated. I. II. Carbon . . . M 264 37*09 3711 36-98 Hydrogen . . 9 9 1-26 1*37 1-65 Chlorine. . . 9 318*6 44*77 4416 44*64 Oxygen . . . 15 120 16*88 17*36 16*73 711-6 10000 10000 10000 ,.«osV\^Mr. J. P. Hennessy on the Theory of Parallels. 283 It appears, therefore, that in passing into perchlororubian, chlororubian loses 9 equivalents of water and 9 of hydrogen, 8 of the latter being substituted by chlorine, since ». C44H27ci024 + l7Cl = C'*4H9CFOi^ + 9HO + 9ClH. It is a singular circumstance, that the 9 equivalents of chlorine in this compound are much more firmly combined with the other constituents than the 1 equivalent contained in chlororubian, which the mere action of alkali is sufficient to separate. From the experiments just described it may be inferred, that chlororubian is a conjugate compound containing sugar. It resembles Piria^s chlorosalicine, which, by the action of acids, yields chlorosaligenine and sugar, just as chlororubian gives chlororubiadine and sugar. Though chlororubian is not, strictly speaking, a product of substitution of rubian, still it retains some of the properties of the latter ; for instance, that of giving, with alkalies, products of decomposition differing from those formed by acids. In all the processes of decomposition previously described, rubian is decomposed in no less than three different modes, just as if it were a compound or mixture of three dif- ferent bodies, whereas, when acted on by chlorine, it yields only one series of products. It behaves in the latter case as if it were simply a conjugate compound containing sugar. It splits up into sugar and a chlorinated body, and the latter, by the action of acids, again splits up into sugar and a second chlo- rinated compound. This series of products corresponds exactly with one of the three series in the other processes of decompo- sition, the bodies belonging to the two other series not making their appearance even in the form of products of substitution. XXXVI. A Note on Professor Stevelly^s Paper on the Theory of Parallels. By J. P. Hennessy*. LEGENDRE solves the so-called difficulty of parallel lines by introducing, as it appears to me, the very same principle as that which is employed by Mr. Stevelly. In his Elements de Geo- metrie, douzieme edition, p. 20, he shows that every property of parallel lines can be easily estabhshed if the proposition, that the three angles of every triangle are equal to two right angles, be first proved. This proposition, the thirty-second of Euclid, he accord- ingly makes his first theorem, and he demonstrates it in two dif- ferent ways. He first gives an elaborate proof of it in the text, and he afterwards deduces it in his notes from the principle of homo- geneity. His first and most important demonstration is rigorous * Communicated by the Author. 281 MpyJ^'P. Hennessy on the Theory of Parallels: and complete. No mathematician can for a moment entertain a doubt as to its correctness. It is, however, open to one fatal objec- tion, an objection which applies with equal force to Mr. Stevelly's demonstration, — that it introduces amongst the propositions of Euclid a method of proof which is totally foreign to the pure and simple reasoning of plane geometry. This is, the doctrine of limits. That Mr. Stevelly employs this method is placed beyond all doubt when he speaks of " making m! approach un- liniitedly close to E by taking b^B = Bb unlimitedly small," &c. But there seems to me to be another objection to Mr. Stevelly's demonstration. The introduction of the method of limits, even if allowable, was quite unnecessary. It is only necessary where we adhere to Euclid^s definition of parallel lines. Mr. Stevelly very properly, I think, put aside that definition and substituted one of his own. In the third volume of the present series of the Philosophical Magazine, it will be seen that the question is treated, as far as a change of definition is concerned, in a similar manner. Instead of Euclid's* definition, I made use of the fol- lowing : — " Parallel lines are such, that if they meet a third right line, the two interior angles on the same side will be equal to two right angles." From this, as I stated at the time, all the properties of parallel lines can be deduced. The researches in question were but slightly connected with this subject, and I did not think it ne- cessary to give many reasons for choosing such a definition. I was contented with showing that it obviated in certain cases the necessity of employing reductio ad absurdum. It has, however, always appeared to me that the difficulty which seems to surround the theory of parallel lines is owing, not so much to any inherent peculiarity in the theory itself, as to the manner in which it has been discussed by geometers. There appears to have been an unwillingness to do for parallel lines what has been done for every other geometncal conception. Before investigating the various theorems connected with the square or with the circle, Euclid took a distinct property of each, in logical phraseology a differentia^ and on that he built his defi- nition. But he did not adopt the same course with respect to parallel lines. In reality he gave no definition whatsoever of them. Attention has been called to the fact that his so-called definition is negative f; and it is hardly necessary to say, that a negative proposition cannot possibly be considered a definition. * An interesting driticism on Euclid's definition, which supports the view I ventured to take as to its inadequacy, has lately been published. See "Wedgwood's * Geometry/ p. 5. t Philosophical Magazine, February 1863. Mr. J. P. Hennessy on the Theory of Parallels. 285 ^'' Now when we regard a pair of parallel lines, just as we regard a "Square or a circle, as a simple geometrical figure, and when we seek for its definition, we find that there are a large number of properties (propria) from which to choose. A different property has been chosen by Wolfius, D'Alembert, Varignon, R. Simson, and a host of others who have written on the sub- ject. The definition given by Wolfius, but which a distinguished writer* suggests was borrowed by him from Clavius, seems to me, according to analogy, to be the most philosophical. None of these geometers attempted to solve the difficulty by going back to the fundamental principles of definition, or by carefully analysing those other definitions which have been found to suc- ceed. It is, however, a remarkable fact, that if we now adopt this course we in one case get a definition exactly the same as that borrowed from the Geometria Practica. "> *5i*i iif ^j/io Euclid defines a circle to be, — iwjrrf*! yb " A plain figure bounded by one continued line, called its cir- cumference; and having a certain point within it, from which all right lines drawn to its circumference are equal." ^^O! It thus has, like a system of parallel lines, two essential ele- ments. In the one there is a continued line and a point, in the other there are two right lines. The definition of the circle depends on a property possessed by every possible right line drawn from the point to the continued line. That property is, mutual equa- lity. Now we know that the right lines from the point to the continued line are all perpendicular to it. So that Euclid's de- finition depends essentially upon the equality of all perpendi- culars drawn from one element of the circle to the other. This leads us very naturally to Wolfius's definition : — " Parallel right lines are such, that perpendiculars from every point in one upon the other are equal." From this, as well as from the one I formerly gave, all the properties of parallel lines may be deduced ; the only difference is, that this definition makes the demonstrations rather complex. If, in the same way, an analysis is made of Euclid's definition of a square, it will be seen to bear a very close analogy to the definition of parallels in which an equality of angles to a con- stant quantity is made the difibrentia. Having defined a rhombus to be " an equilateral quadrilateral figure," he defines a square as '^ a rhombus each of whose angles is equal to a right angle." No serious objection has ever been made to this definition ; and yet when we treat parallel lines in a similar way, we are charged with assuming something that ought to have been proved. I do not think such a charge can be upheld for a single moment. To say, when two parallel lines are intersected by a third * Dr. Larduer. -riuv; -, ^« ... 286 M. T. Plateau on the recent Theories of the Constitution of right line, that a figure is formed in which the angles at each side are equal to two right angles, is certainly not assuming, either in form or in fact, more than Euclid assumed when defining a square. It has been said that such a definition is imperfect, because we cannot by its aid give a demonstration of the twelfth axiom. This, I think, is another point in which the theory of parallels has been treated unfairly. In the first instance, there is an unwillingness to assume proper premises ; on the other hand, when a full and fair definition is chosen, it is said to be inadequate, because it cannot touch certain propositions which are naturally beyond its reach. The twelfth axiom has, in fact, as much connexion with parallel lines, as the theory of the para- bola has with that of the circle ; yet no one would assert that the definition of a circle was defective because by it we cannot prove, for instance, that " no two right lines in a parabola bisect each other.*' Mr. Stevelly appears to think that his demonstration is suited for elementary instruction. I regret that I must also differ with him on this point. As it is merely a matter of opinion, and can- not admit of any proof one way or the other, I do so with extreme diffidence. Perhaps, however, I may venture to remind him, that a distinguished physicist and mathematician like himself is, from the nature of his position, often incapable of forming a very accurate notion as to whether a certain train of reasoning is ele- mentary or otherwise. What may appear very simple to him, may not be so to one whose mental training is of a different character. Jermyn Street, Sept. 3, 1856. XXXVII. On the recent Theories of the Constitution of Jets of Liquid issuing from Circular Orifices. By M. T, Plateau*. WHEN, in 1849, at the end of the Second Series of my " Experimental and Theoretical Researches on the Figures of Equilibrium,*' &c.t, I published a complete theory of the constitution of jets issuing from circular orifices, and protected from eveiy external influence, I thought that the same would have been immediately adopted, seeing that it was deduced with absolute rigour from the results of accurate experiments, and consequently that it explained all the details and all the laws of the phsenomenon. I was wrong : at the commencement of the ♦ From the Bulletin de V Academic de Belgique, No. 6. vol. xxiii; com- municated by the Author. t M^. de VAcad. de Belgique, vol. xxiii. Scientific Memoirs, vol. v. p. 684. \o $mUi^ Jets of Liquid issui7ig from Circular Orifices. 287 past year two different theories were proposed; one by Dejean*, the other by Magnus f. Nevertheless, as I did not find any reference to my theory, and consequently any opposition to it, either in the short analysis which Dejean has given of his still unpublished research, or in Magnus's memoir, 1 resolved to wait and leave its success to time. Another theory, however, has just appeared. In the report presented to the Academy last January {, upon my Third Series §, where I explain the action of vibrations on jets, Maus returns to the constitution of jets not subjected to this action. He declares his inability to adopt my theory, and indicates his reasons for the same; afterwards he developes his own views. As I cannot, under these circumstances, remain longer silent, I propose to compare, as briefly as possible, the three theories above mentioned with my own. It is well known that Savart, in his able research on jets of liquid II, after having by ingenious experiments discovered all the peculiarities in the constitution of jets issuing from circular ori- fices, gives an essay on the theory of these phsenomena in the form of a conjecture simply. He attempts to show that the efflux itself imparts a vibratory motion to the liquid in the vessel, and to that which passes through the orifice ; that these vibra- tions or pulsations at the orifice, being perpendicular to the plane of the latter, alternately press out and draw in the liquid as it issues, and thus occasion the annular protuberances or expan- sions whose existence he established, the movement of transla- tion, and the development of, and final conversion into, isolated masses. Dejean admits the existence of pulsations, but explains their production differently. In his analysis he does not say to what cause he attributes the separation of the masses which compose the discontinuous part of the jet. Magnus, in his very interesting memoir, treats principally of the phsenomena which manifest themselves when two jets meet under certain angles, and of the singular forms of jets issuing from differently shaped orifices. He enters but little into the question of the constitution of jets issuing from circular orifices. He does not assume the existence of pulsations, and in the case of a jet falling vertically and withdrawn from every external influence, he attributes the separation of the mass to the tension resulting from the acceleration in the velocity of the falling * Comptes Rendus, vol. xl. p. 46/. t PoggendorflF's Annalen, vol. xcv. p. 1 ; and Phil. Mag. for Feb. 1856. X Bull, de I'Acad. de Belgique, vol. xxiii. part 1. p. 4. § We hope to be able to find room for a translation of this Third Series in a future Number of the Magazine. — Eds. II Annales de Chimie et de Physique, vol. liii. 1833, p. 33/, 288 M. T. Plateau on the recent Theories of the Constitution of liquid; which tension, at a sufficient distance from the orilicc, becomes strong enough to overcome the cohesion between two adjoining sections of the jet. Lastly, Maus adopts, with Dejean, the hypothesis of pulsations, the production of which he, on his part, explains by considera- tions of his own ; but convinced that pulsations alone could not determine the formation of the isolated masses, he assigns the discontinuity of the jet to the same cause as Magnus. The above theories are based, therefore, upon two hypotheses, — that of pulsations at the orifice, and that of rupture caused by the acceleration in the descent of the liquid. I will now endea- vour to show that both these hypotheses are inadmissible. Before doing so, however, 1 hope to be allowed to express my deep veneration for the memory of Savart. In my researches oa jets I have continually had recourse to the beautiful researches of that illustrious physicist ; and although I here combat the, hypothesis of pulsations, I still can recognize in the same a trait of genius. In fact, although pulsations do not exist in a jet protected from every external influence, the case is difi'erent when vibrations are transmitted to the liquid from an external source. The pulsations then become a reality, they exercise upon the jet the pressures and tractions attributed to them by Savart, and it^ is by considering these pressures and tractions that I have beeri^ enabled to explain, in my recently published Third Series, all th^^ phsenomena which depend upon the influence of vibratory motions-^ Proceeding to our examination of the two hypotheses in ques^'^ tion, let us commence with that of the rupture of the jet. The idea of an effect of this kind produced by acceleration of velocity is anterior to the research of Magnus. Hagcn, who made many experiments on jets issuing from circular orifices, speaks of th;^^ same in a memoir presented to the Academy of Berlin in 1 849, " On the Discs formed by the meeting of two Jets of Liquid, and on the resolution of isolated Jets into Drops*,'' but he mentions the idea only in order to refute it. After some a priori con- siderations relative to the probable existence of another cause, he thus expresses himself: — "This probability becomes a certainty when we reflect that* one and the same jet, whether it issues vertically upwards 6^. downwards, resolves itself into drops at almost the same distance! from the orifice. In the first case the velocity of the liquid may- be almost destroyed by gravity, whilst in the second it may be' doubled; and still the phsenomenon is not essentially different '^ in the two. The fact is still more striking in horizontal jets, ' where the effect of gravity almost vanishes. In these the velo- * city varies only with the increase of inclination; with strong' vyl) >j' »i<^*# Poggendorff's Annalen, vol. Ixxviii. p. 451. "K ^'"^'Ms of Liquid issuing from Circular Orifices. 289 charges and small orifices, this inclination, and consequently the variations in velocity and diameter, are insignificant in the part of the jet we are considering, so that we should conclude that the jet ought to be perfectly uniform ; nevertheless it resolves itself into drops at a determinate point/' To these facts we may add another deduced from Savart's experiments. When a jet issues obliquely upwards, within cer- tain limits of inclination, the discontinuous part becomes scat- tered in a vertical plane and forms a kind of sheaf. Now a glance at the figure which represents such a jet in the plates accompanying Savart's memoir, will show that the sheaf has its origin very near the summit of the curvature of the jet, and con- sequently at a point where the velocity, retarded from the orifice, has not yet become sensibly accelerated. Thus, in the first place, in jets issuing horizontally under a sufficient charge through orifices of small diameter, the discon- tinuity first occurs at a point where the velocity is scarcely in- creased, and consequently where the tension between two conti- guous sections cannot have become considerable ; in the second place, in jets issuing obliquely upwards under a sufficient charge and through a suitable orifice, the discontinuity commences at a point where the increase of velocity is still less ; and lastly, in jets issuing vertically upwards, the discontinuity occurs notwith- standing the retardation of velocity ; a retardation which, instead of separating two contiguous sections, evidently tends to press them closer towards one another. Although these reasons ought to be regarded as conclusive, Magnus might nevertheless reply that neither Savart nor Hagen state that the jets in question were protected from the small efiects of vibrations proceeding from external noises, and from the shock of the discontinuous part against the liquid into which they fell. Now, according to Magnus, vibrations propagated in a jet are a powerful cause of rupture, because by means of them one section of liquid is drawn backwards, whilst the one imme- diately preceding it is, on the contrary, pushed forwards. But if so, then in ascending jets the rupture ought to take place at the contracted section itself, that is to say, very near the orifice, for there the jet has the least thickness, and the velocity of trans- lation has. not yet suffered sensible diminution. In fact, at a greater distance from the orifice, the increasing thickness of the jet and the gradual diminution of velocity — from which latter results, as I have remarked, a tendency of the sections to approach each other — would render the rupturing action of vibrations more and more difficult. = '\o ^aiitym^i a/It dM'^ *(Su<> ^ivm^f \^r» I have, however, repeated the. expe,riment of the sheaf ; first by allowing full liberty to the small effects of external vibrations, Phil. Mag, S, 4. Vol. 12. No. 79. Oct. 1856. U 290 M. T. Plateau on the recent Theories of the Constitution of and afterwards by employing the precautions indicated by Savart for deadening these effects. In the first case, the result was sen- sibly conformable to the engraved figure of which I spoke, which figure no doubt corresponds to conditions of change and orifice analogous to those in my experiment ; and in the second case, the result, as will be seen, was not essentially different. The jet issued from an orifice 3 millims. in diameter at an angle of about 35° with the horizon ; the amplitude of the jet, that is to say, the horizontal distance from the orifice to the most exterior part of the sheaf, varied, according to the diminution of the charge, from 1'45 metre to 1-27 metre; and the height of the summit of the jet above the level of the orifice varied from 0*34 metre to 0*32 metre. In the second observation, a carpet folded several times until its thickness amounted to 8 centims., was interposed between the vessel from which the jet issued and the massive table upon which it rested, and under the feet of which cushions were placed. The vessel into which the sheaf fell was placed upon a truss of hay, and the sheaf glided down a thick plank suitably inclined. Besides this, the orifice at the bottom was furnished with a contrivance, similar to that described by Magnus, for preventing any rotations in the liquid ; the limpid portion of the jet was also regular, or nearly so. Notwithstanding all these precautions, the effect of the small vibrations proceeding from exterior noises was not completely annulled ; for the continuous and limpid portion of the jet suffered intermittent shortenings, and even speaking in the neighbourhood of the jet was sufficient to render these shortenings more visible. It will be admitted, however, that the vibrations which still remained must have been very feeble ; nevertheless the sheaf manifested itself quite as well as under the free influence of these vibrations, and its origin never receded beyond the summit more than 12 centims. |^ Again, if in a jet flowing downwards and withdrawn from every external influence, the tension caused by the acceleration of velocity were the cause of disunion, the length of the conti- nuous part ought to be independent of the diameter of the orifice. For under the same charge, the total tension between two con- tiguous strata of molecules, and the total cohesion which unites the same, will evidently each be proportional to the number of molecules which compose these strata. If, therefore, for any orifice, and at a given distance from the same, the tension were equal to the cohesion, so that the adhesion between two strata was overcome, the same ought to take place at the same distance in a jet issuing under the same charge from a larger or smaller orifice ; for at this distance the increase of velocity would be the same as in the first jet, and the total actions of tension and co- hesion would have both increased or diminished in the same pro- " ' "' " jm\f Liquid ^mr^fibm Circular Orifices. 291 portion. On the contrary, however, experiment shows that the length of the continuous portion is nearly proportional to the diameter of the orifice. Lastly, it is easy to see, a priori, that the tension due to acce- leration of velocity does not in reality produce any tendency to disunion. In fact, if this tension separated the liquid molecules, the density of the continuous part would diminish from above downwards j now a little reflection on the relative mobility of molecules of liquid will soon convince us that this diminution of density is impossible ; for as soon as two molecules tend to se- parate, another is displaced and steps between them, whence it follows that the only effect of tension will be to lengthen the jet by making it thinner; and as the acceleration is uniform throughout the whole extent of the jet, it is evident that its sole tendency will be to diminish the diameter of the jet from the orifice downwards in a perfectly regular and continuous manner, without occasioning a tendency to rupture at any point. Thus theory and experiment unite in proving the complete inadmissibility of the hypothesis of rupture. Let us next con- sider that of pulsations. We may at once remark, that the latter appears in itself diffi- cult to justify, seeing that Dejean is not satisfied with Savart^s explanation, and that Maus attempts another. In fact, in the efflux of a jet completely protected against external influences, where everything appears to be in favour of continuity, the only natural manner of conceiving alternate diminutions and augmen- tations in the velocity of efflux to arise, would be to suppose, with Savart, that the friction of the liquid against the edges of the orifice sets the latter in vibration, and that these vibrations are transmitted to the liquid. But Savart assured himself that when the borders of the orifice are touched with a solid and resisting body — which ought to arrest, or at least deaden the vibrations, — no change whatever in the nature of the jet is perceptible. The vibrations of the sides of the orifice therefore cannot occasion the pulsations of the liquid ; but to whatever cause these pulsations may be attributed, they must, if they exist at all, consist of a vibratory motion of the liquid, which motion would necessarily be communicated to the sides of the orifice j so that by hinder- ing, as Savart did, the vibrations of these sides, the pulsations of the liquid ought to be impeded also, and the state of the jet to be modified ; how is it, then, that the jet suffers no appre- ciable modification ? ^'^;;:^^,^ . J';^,^^'^^,^^'!^^ '/ Further, Savart, w&n eiEiiimm'g'tlife atinirfar expansions 6i the continuous part of the jet, according to the method he de- scribes, was not able to prove their existence except at a little distance from the orifice ; and Hagen, who discovered a method V2 292 M. T. Plateau on the recent Theories of the Constitution of of his own for this kind of observations, affirms the same thing in his memoir above cited. Hence if these protuberances, which are carried by the translatory motion of the hquid, proceed from the orifice itself, they there project very little. But, according to Savart's experiments, they are more perceptible the further they are observed from the orifice, until near the extremity of the continuous part they become greatly developed, and finally at the extremity they detach themselves successively as isolated masses. Savart does not expressly mention the contractions which alternate with these expansions, but it is evident that the latter cannot become developed and acquire greater volume ex- cept at the expense of the intermediate portions, so that these parts must necessarily become hollower and thinner the more the protuberances project. Now let us suppose for a moment that the expansions and contractions are due to the pulsations at the orifice, and that, as Savart thought, this vibratory motion communicates itself to all the continuous part of the jet. Ac- cording to this hypothesis, each portion of the liquid pressed outwards, when leaving the orifice, by a compressing pulsation, would during its transport soon become changed into a contrac- tion by the opposite vibration which it would execute, then again into an expansion, afterwards into a contraction, and so on; whilst each portion originally contracted by a receding pulsation would at the same time suffer inverse variations. But, accord- ing to the above, these successive changes of each portion of liquid, or the vibrations they perform during their movement of translation, increase in amplitude from the orifice to the extre- mity of the continuous part, and that in an enormous proportion; for near the orifice the expansions and contractions are so minute, that by the most delicate method of observation their commence- ment cannot be ascertained. Now it is impossible to account for this increase in the amplitude of the vibrations in the jet, which increase, in fact, would constitute an efi^ect without a cause. '^5 From this examination, we conclude that the hypothesis of *piilsations at the orifice, engendered by the efflux itself, and causing a vibratory motion in the jet, ought to be rejected, as well as that of rupture produced by the acceleration in the velo- city of translation of the liquid. ''' ': ' ' ' ifii/i./.h' In order to omit nothing, I ought to mention that Magnus denies the existence of these expansions in a jet protected from every external influence. But his only motive for doing so is the aspect of the limpid portion of the jet, which appears per- fectly white. " It has the appearance,'^ says he, " of a solid of revolution formed of the whitest glass, for the least motion can- not be perceived in it." Now Savart, when speaking of the lim- pid portion of jets freely exposed to the small vibratory motions Jets of Liquid issuing from Circular Orifices. 293 proceeding from external noises and the fall of the liquid into the vessel which receives it, expresses himself thus : — '' No traces of protuberances can be detected in this portion of the jet/^ and in the resume at the end of the memoir, he says, " This first part of the jet is calm and transparent, and resembles a rod of crystal." Nevertheless it is in this same portion of the jet that he has proved, by means of his ingenious contrivance, the presence of expansions the more developed the greater the distance from the orifice at Tvhich they are observed. The non-existence of expan- sions, therefore, cannot be concluded from the quiescent and white appearance of the limpid portion of a jet : this appearance is merely an illusion caused by the small prominency of the ex- pansions in this portion of the jet, and the rapidity of their trans- latory motion. Had Magnus employed Savart^s method, or that of Matteucci*, or one of those of Billet- Selisf^ he would certainly have detected the existence of expansions, even when the jet was protected from external vibratory action ; for seeing that rupture is impossible, the separation of the mass must necessarily be ascribed to the formation of contractions which become more developed as they approach the extremity of the continuous part, and which necessitate expansions whose development passes through the same phases of augmentation. By the side of the inherent difiiculties of the hypotheses just discussed, let us place the principles of my theory. All physicists are now acquainted with my method of neutral- izing the action of gravity upon a large mass of liquid, and at the same time leaving it free to obey molecular actions. By means of this, and afterwards of another method, I have been able to obtain liquid cylinders and to study their properties. I have thus corroborated the. following, facts (see^myv Second Series, §§ 37 to 68) J : — 'is^do lo-BorLterff 3te':>flob Tgoitr 1. A liquid cyUnder constitlites'a figure of stable equilibrium as long as the ratio between its length and its diameter does not exceed a certain limit between 3 and 3*6. I will here add, that an a priori method, of which I have hitherto only published the result, gave for exact value of the limit the quantity tt, that is to say, the i:atio bet^eei^t^e.circumferencie^nd; the. diameter of a circle.iii it.'»dirt^fyooi; orft vd baoubn-ci -yim^in \j tu/1) ' 2. Beyond this limit the cylinder constitutes a figure of un- stable equilibrium, so that it cannot be obtained in a permanent state except by means of certain hindrances. 3. A liquid cylinder whose length is very great in comparison to its diameter, converts itself, by the spontaneous rupture of " '."*" ^ * Comptes Rendus, 1846, vol. xxii. p. 260. -anp no^f Annates de Chimie et de Physique, 1851, vol. xxxi. p. 326. /. -mil orCvl J Taylor's Scientific Memoirs, vol. v. p. 62|, .!> j/iviioij j,^ Jon erioiiom 8it>r "to nomoq hm 094 M. T. Plateau on the recent Theories of the Constitution of equilibrium, into a series of isolated spheres, equal in diameter, equidistant, and having their centres on the line which forms the axis of the cylinder; in the intervals between these are spherules of different diameters, having their centres on the ■ame line. 4. This transformation commences with the origination of regulai'ly placed contractions alternating with expansions ; after- guards both one and the other become more developed ; the con- tracted parts becoming thinner, the expanded ones thicker. When the centres of the contracted parts become sufficiently thin, they do not* rupture suddenly, but the liquid, receding on both sides of each of the centres towards the expanded parts, still leaves the latter for an instant connected two and two by a thread sensibly cylindrical. Lastly, these threads transform themselves in the same manner as tne cyHnders ; and by the rupture of threads still more attenuated, resulting from their own contractions, they leave the isolated masses which form the above spherules, whilst the larger masses proceeding from the expanded parts of the original cylinder, and which are at equal distances asunder, assume spherical figures. 6. This spontaneous alteration and this transformation, whose final result is the formation of isolated spheres with spherules arranged in the intervals, are not peculiar to cylinders: they accompany every other liquid figure of which one dimension is considerable compared to the other two. Lastly, I recognized many other properties which will be found described in my Second Series, but which need not be here repeated. For the sake of those who have not repeated my experiments, I will here mention, in support of the above facts, a phsenomenon observed by all physicists. When, along a thin wire held hori- zontally, an electric discharge capable of fusing, but not of melt- ing it, is passed, the wire becomes first heated to a white heat, and at the same time bent in consequence of its elongation ; afterwards it is observed to resolve itself into a great number of separate globules, which fall, and whose form when cool is found to be rounded. Now this wire, at the moment of fusion by the passage of electricity, constitutes a liquid figure which satisfies the condition above expressed in 5. I may add that Beer, in a memoir published in 1855*, after having applied mathematical analysis to the facts described in my first series, incidentally treats of the question of the stability of liquid cylinders. Starting solely from data relative to the molecular constitution of liquids, he arrives, by a priori reason- ing and by calculation alone, at the result which 1 have myself * Poggendorff*8 Annalen, vol. xcvi. pp. 1 and 210. Jets of Liquid issuing from Circular Orifices, 295 obtained, though by an entirely different method ; that is to say, he finds for the exact value of the limit of this stability the quantity tt. This calculation, therefore, which fully corroborates mine, sanctions one of the principal results of my observations ; it shows the absolute necessity of it, and gives the precise mea- sure of the phsenomenon. Now a jet of liquid issuing in any direction whatever, fulfils the condition expressed in 5; that is to say, it constitutes a liquid figure whose length is considerable when compared with its transversal dimensions. It should then of necessity alter its form, in order to transform itself gradually and in a continuous manner into a series of isolated spheres with interposed spherules; and the phsenomenon ought to manifest itself by the formation of contractions and expansions which develope themselves more and more without changing their nature, until the generation and rupture of the threads take place as above described. But the liquid of the jet having a motion of translation, which carries with it the expansions and contractions, it is during this journey that each of them completes all its progressive modifications ; so that each protuberance leaving the orifice in its rudimentary state, does not attain to that of an isolated mass until at a greater or less distance from the orifice. Further, a fresh quantity of hquid being always supplied, the transformation must be inces- santly repeated. Hence the continuous and discontinuous parts of the jet ; hence also the origination of expansions and contrac- tions scarcely perceptible near the orifice, but becoming more and more developed as they move onwards with the liquid, until the expansions arriving one after another at the extremity of the continuous part, successively detach themselves and pursue their course as isolated masses, which assume, or tend to assume, a spherical form; hence, too, the spherules interposed between these masses ; and lastly, the laws discovered by Savart, con- necting the length of the continuous part, as well as the tone produced by the shock of the jet, with the charge and the dia- meter of the orifice. To render this last deduction evident, however, it would be necessary to have recourse to facts, which, fearing to extend this note too much, I have not here stated. It will be seen that the fundamental part of my theory con- sists, not of hypotheses, but of facts and their inevitable con- sequences ; which consequences are so strict, that, had not the admirable research of Savart revealed to us the true constitution of jets of liquid issuing from circular orifices, we might have pre-^ dieted the same with all its details and laws from my experiments. My theory does more : it shows that the laws indicated by Savart are only the limits, which are more and more approached the stronger the charges and the smaller the orifices, a deduction 296 (M Jfh of Liq\dd isming from Circular Orifices. which the tabulated observations of the ilhistrious French philo- sopher fnlly contirWr ''i' '>»*^ ^^^ ^^'>' «' l»n»pfl o/lr ,Hoi,tom y;fot.;i • I have still to establish 'thfeC«il*edon<%etwkn«i^4h(eory'aiifd the T^hanomcna resulting from the influence of tones ; as already stated, this was done in my Third Series. When vibrations are in reality communicated to the vessel and the liquid it contains, the principle of pulsations at the orifice ceases to be a vague and improbable hypothesis, and becomes almost a certainty. Now I "have demonstrated that when the tone which acts upon the jet is exactjy in unison mth the one which the shock of the discon- tinuous part against a stretched membrane would produce, the expansions and contractions causied by th(, vibrations executed at the orifice coincide perfectly with the expa:isions and contractions due to the molecular forces, so that there is absolute concuiTcnce between the two actions. From this simple principle I have afterwards deduced the explanation of all the phjenomena ob- served by Savart. If, in this collection of theoretical researches, I have had V recourse to hypotheses, they are purely accessory, and serve only « to explain certain facts too complicated to admit of our appre- 1 dating th6 action of the several elements concerned in their pro- - duction. .^ Let us pass, lastly, to the arguments upon which Maus bases ■a' his opposition^ - They are stated in the Idbwing passage of the ^gxeport :— i^^'^'to ^-ooiif'to '!>> s'lC'drltrTi fsih '\o ^ fivn t H-mH// jMUfMi:' 8'* ''I find it difficult to admit, with Plateau, that in a s^phsenomenon principally produced by gravity, this force ought to be completely eliminated in order to attribute the configura- -ration of the moving mass exclusively to molecular forces, which 8'' are far inferior to gravity. '« ^/ .ofo/i/r« «fi ffoitj'^jgri ^'jinii 3ii " My hesitation increased when if6?andv'that^ iii 6rder'to jtis- n'tify the elimination of gravity, Plateau considered this force as only acting upon the jet when leaving the orifice, without con- sidering its action upon the liquid contained in the vessel ; which action, by its manner of attracting the liquid molecules towards the orifice, exercises upon the form of the jet an influence which cannot be doubted when we consider the phsenomena known as the contraction and inversion of a jet. • ^f'The beautiful experiments with jets of liquid, repeated every year by Prof. Richelmi at the hydraulic establishment of LaParella near Tui-in, havmg shown me a kind of opposition between ori- i; flees of different shapes and the profiles which they produce in o; the jet at a short distance from them, have not prepared me for Qii disregarding the interior action on the form of the jet.^fj^ ; It is impossible to find real objections here. Without doubt gravity causes the liquid to leave the vessel and thus produce M. Heintz on some Experiments with Chloroform, 397 the jet ; but once having left the orifice and acquired its trans- latory motion, the liquid is left to the free action of its molecular forces, whether the same be more or less energetic than gravity j just as the hands of a walch continue to be moved by internal mechanism, whilst it itself is transported from one place to an- other. Maus, indeed, himself admits this when, in another place, speaking of the acceleration of velocity as a cause of rup- ture, he says, '^ and when this action has been prolonged suffi- ciently to divide the liquid mass, molecular forces intervene in' order to give to the isolated masses the spherical form which the drops possess." . The contraction of the jet plays an important part in the theory of Maus ; but in mine, the simple consequence of this phseno- menon of contraction is, that I have not to consider the action of molecular forces except from the transverse section of the jet where this contraction ends, for it is only beyond this point that the jet assumes its elongated form. With respect to the inversions which manifest themselves in jets issuing from non-circular orifices, I may remark that they have nothing in common with the expansions and contractions which precede the separation into isolated masses ; for the latter are carried with the translation of the liquid, whereas the inver- sions occupy fixed positions in the limpid portion of the jet. . aPurther, Maus will find, on referring to that part of Magnuses memoir which treats of the influence of orifices of difi'erent shapes, that it is precisely by causing the intervention of molecular forces that the author has completely succeeded in explaining these inversions. I cannot conclude without acknowledging the merit of Mag- nuses research as a whole. As already remarked, the passages to which I have objected form but a small part of the whole; the rest appears to me very remarkable^^ weli^iaiHaitiiearetic as in an experimental point of view, rod// iaf 3if1 nofrn '^rfftnf? doidv/- o*iSSSy W*^ Chemical Notices from Foreign Journals, srnwrM^^-'.Mi^'i'M.o'K.^ -^2^ E. Atkinson, P^.Z>. .;. , [Continued from p. 196.] bni>HwV'>^\'^V;^ ^ " HEINTZ* communicates the particulars 'of some experiments with chloroform. They mostly affbrded negative results, but possess nevertheless a considerable degree of interest. In the expectation of producing formyle, C^H, he enclosed sodium along with chloroform in a sealed tube and exposed it to a high temperature. But no action was observed, although the ' • u ■': -■ MI ,* Poggendorff' s Annalen, June. 298 M. Heintz on some Experiments with Chloroform, temperature was kept for some time at 200° C. When potassium is heated in chloroform vapour a violent explosion takes place. By acting on formiate of lead with chloroform, he hoped to get anhydrous formic acid, thus : — ^ 8(PbOC«HOa) + C«HC18 = 3PbCl + 4(C^H08). Formiate of lead. Chloroform. Anhydrous formic acid. But formiate of lead is not acted upon by chloroform at any temperature at which it would not be decomposed if heated alone. For he found, on heating formiate of lead to about 200° C. under exclusion of air, that it is decomposed into me- tallic lead, carbonic acid, and hydrogen. Heintz thought that by acting on chloroform with ammonia, if any action took place which was not accompanied by decompo- sition of the formyle, it might be according to two equations ; — ' C^ H CP-f4NH3=3(NH4 CI) + 0^ H N, Chloroform. C2HCF + 6NH3=3NH4C1 + 3(NH2)C2H, By the first of these actions a nitride of formyle might be ob- tained, and by the second a formyltriamine. At ordinary temperatures the two substances do not act on each other. When chloroform is passed with excess of ammonia through a heated tube, no action takes place till the temperature approaches a red heat, when chloride and cyanide of ammonium w:q formed :— C« H CP-f 5NH^=3(NH4C1) + NH4C2N ; nim^ Chloroform. Chloride of Cyanide of ammonium. ammonium. and if the temperature be raised high enough, paracyanogen is produced from the decomposition of the cyanide. The action is different in the presence of water. In that case it may be expressed by the formula — C3HCP+4HO-fNH3=NH4 0, C2H03 4-3(NH4C1). Formiate of ammonia. If the aqueous solution of ammonia with chloroform be heated to 180° C, formiate of ammonia and chloride of ammonium are formed. If the alcoholic solution of ammonia be heated with chloroform to 190°, some formiate of ammonia is formed, together with cyanide of ammonium. Sometimes neither the one nor the other of these bodies is produced; when this is the case, para- cyanogen is formed in some quantity. Along with these bodies a little sethylamine is formed ; but this arises from the action of ammonia on the alcohol, and is quite independent of the chloroform. Action of Chloride of Sulphur on Formiate of Baryta. 299 The same chemist investigated* the action of chloride of sul- phur on formiate of baryta and acetate and benzoate of soda. By the first of these actions he hoped to get anhydrous formic acid. But such is not the product of the action; there are formed monohydrated formic acid and carbonic oxide : thus — 4(BaO,C2H03)+3ClS=2S,BaOS0^3BaCl,4CO,2(C'^H03HO). Formiate of Monohydrated baryta. formic acid. The reaction gives a method for the preparation of monohydrated formic acid, which consists in mixing four equivalents of an an- hydrous formiate with four equivalents of water, and then adding three equivalents of chloride of sulphur. By distilling the mix- ture at a temperature of 100° C. to 120° C, pure monohydrated formic acid is obtained. An acid formiate of soda or potash cannot be formed, and hence themethodusedbyMelsens for producing monohydrated acetic acid from binacetate of potash is inapplicable in the case of formic acid. Heintz found that chloride of sulphur acts on anhydrous organic salts in such a manner, that a chloride and sulphate of the metal are produced and sulphur separated ; and the sulphur separated crystallizes from boiling alcohol partly in the form of rhombic octahedra, and partly in that of long acicular crystals. The same is the case with sulphur separated by acids from solution of sulphide of sodium or potassium. Anhydrous acetate of soda gives with chloride pf sulphur anhydrous acetic acid according to the equation— ^ „' |>^)iff^<;i oif^ 4(NaO, C4 H^ 0^) +3C1 S = Na CI, NaO SO^ 2S, 4(0^ H^ O^). Acetate of soda. Anhydrous acetic acid. But there are formed at the same time various collateral products, especially sulphur compounds, and in certain cases a liquid heavier and less volatile than water, and not miscible with it. In the endeavour to produce anhydrous acetic acid by heating acetate of mercury, there were produced acetone, and a substance containing more oxygen than it, but which was not formic acid. When chloride of sulphur acts on anhydrous benzoate of soda, chloride of benzoyle is first formed, which reacting on an excess of benzoate of soda, produces anhydrous benzoic acid and chlo- ride of sodium : — 2(Ci4H50^NaO) + 3ClS = 2S + NaOSO^+NaCl + 2(C'4H^^j), Benzoate of soda. /.,.v ,*,.,.. vi,i,,. r^^ ^ • -, /. r t ' ' r ft Chloride oi . ■mu ■ ih'yn^ojqei ^^(ho6 benzoyle. ; C14 H^ ^j + (NaO, C'4 H5 0^) = 2(0^^ ^5 qs) _,_ Na CL rni'^ „, , . , „ Benzoate of soda. Anhydrous ''■. , Chloride of benzoic acid, benzoyle. 5 * Poggendorff*s Annalen, July. 300 M. H, Rose on Boracic jEther, This method of preparing anhydrous benzoic acid has the advan- tage over the original method of Gcrhardt, that the material chloride of sulpliur is cheaper and more easily pi^^fiTi^ ^fe^ .ft© pentachloride and oxychloridc of phosphorus. , ,,|., .fif^f ^ ,}:[ * h'»Heinrich Rose* obtained boracic ajther by distilling together a mixture of sulphovinate of potash with excess of fused boracic acid. At a temperature of 100° to 120° C, a colourless mobile liquid, of a strong setherial odour, passes over, having all the properties ascribed to boracic tether by its discoverer. If, in the preparation of this body, anhydrous materials be not em- ployed, water passes over with the distillate and gradually de- composes the aether, boracic acid being liberated, -^nouimi^ m The analysis of the sether was made in the following 'maii'rlfeH—r A weighed quantity, 0-967 grm., of the sether was left in a closed vessel in contact with water for many days. It was then eva- porated to dryness with a weighed quantity, 2*180 grms., of car- bonate of soda; the mass gently ignited and weighed. It weighed 2*260 grms. The carbonic acid contained in this was determined ; it amounted to 0*736 grm., and hence the boracic acid was 0*246 grm., or 25*44 per cent., the theoretical number being 24 per cent. Ebelmen, the discoverer, found 22*3 per cent., but the method of analysis employed by him involved a loss. >'-<^'- })' Rose attempted by the same method to produce from silicate of soda, and carbonates and phosphates of the alkalies, the cor- responding silicic, carbonic, and phosphoric aethers, but in vain. Equally unsuccessful were similar attempts to form from bichro- mate and from molybdate of potash their respective aethers. No aluminic aether was obtained by distilling pure aluminate of soda (prepared by heating together atomic weights of alumina and carbonate of soda) with sulphovinate of potash. Nor by the action of chloride. of, aluminium .on.alcohoIwa^ a more farourabl/e result arrived at. ^ . r raiirrT/r . \r\ xr j *^ ^ Wilkens f has an article on artificial ultramarine, in which he Adverts to the views put forth by Stolzel % on the constitution of this body. Wilkens considers that in artificial ultramarine a certain constant compound is contained, but mixed with other foreign bodies. Resting on a number of careful analyses, as well as on its reactions and properties, he considers blue ultra- marine to have the formula — '^, 2(AP03 SiO^) + AP03 3Si03 + NaO S202 + 3NaS. ^no-ria The formula which Wilkens derives from his analyses is different * Poggendorff*8 Annalen, Jva^ii . »njiT. .>^f.M .firf^ * ; ;t Liebig*8 Annalen, July. ' ' -f Phfl. Ma^."J\irie. M. Wilkens on Artificial Ultramarine. But from that proposed by Breunlin*, wlio considers it to be a com- pound of a mineral of the formula of nepheline with pentasul- phide of sodium. But both chemists agree in the fact, that when decomposed by acids, one equivalent of sulphur is liberated as sulphuretted hydrogen, and four equivs. as free sulphur. Wilkens thinks that hyposulphite of soda, with sulphide of sodium, is the colour- ing principle of a silicate of alumina. The sulphur in ultra* marine cannot be replaced by any other body, nor can the sodium. Experiments carefully made with this view, with potash, lime, and magnesia, afforded no ultramarine. Iron exerts no influence in producing the blue colour. Green ultramarine, which always precedes the formation of blue, is considered by Wilkens to be a sulphide of sodium com- pound, but he had arrived at no certain results as to its consti- tution, since, from the various methods of its formation, it occurs of very different form and composition. saw ?ddi ill beamUuy) hiofi oniodTR') ^ ''^ Od^'^ bt)i - r Dr* ' Grimm t dfescribes -a i^(^ platinum salt;= OH' ' adding caustic ammonia to a hydrochloric acid solution of protochloride of platinum, which had not been neutralized with carbonate of ammonia, a beautiful garnet-red crystalline compound was thrown down. On continuing the addition of ammonia, Mag- nus's salt gradually formed in green flakes ; but the same red crystals were constantly formed, and only disappeared on lon^- continued boiling with excess of ammonia. They were onccs ob- tained in distinct quadratic octahedra of a ruby colour. 'ip^'i The salt is difficultly soluble in cold, but more easily in hot water. It is insoluble in alcohol, but completely soluble in am- monia and carbonate of ammonia. The analyses lead to the supposition that it is a compound of protochloride of platammohium with chloride of ammonium, TT3 l^N, Cl + NH'*Clj but as some of its reactions are not in -J ... i +.^u"df='^' accordance with this view, the author reserves a dedision on the point for further investigation. , = '^'^ToitJ investigated and describes several benzoyle compounds, derivatives of benzoic acid. In the preparation of nitrobenzoic acid a slight modification of the usual method was adopted. Melted benzoic acid was added in small portions to a mixture of strong sulphuric and nitric acids and gently warmed for half an hour. By this method no binitrobenzoie acid is formed ; and on * Phil. Mag. June, Supplementi>««K p'^tiobfc^s^^o*! ' t Jj\Qh\g'% Annalen, July, p. 95.1 .m'^^^J: IWai'>f 100, 802 M. Voit on the Derivatives of Benxoic Acid, the addition of water to the acid mixture, nitrobenEoic acid alone is precipitated. The acid is also obtained by adding chloride of benzoyle to the acid mixture. The nitrobenzoic acid was converted into benzamic acid, for which Voit proposes the name amidobenzoic acid, as expressing its constitution better. This was effected in the usual manner by treatment with sulphide of ammonium. After filtering off from the separated sulphur and adding hydrochloric acid, a com- pound of amidobenzoic acid with that acid is obtained. Of amidobenzoic acid, the silver salt alone had been hitherto known. Gerland studied some compounds which it forms with acids, in which it plays the part of a base. Voit describes in this paper the baryta, lime, soda, magnesia, and strontia salts, all of which are crystallizable, and perfectly well defined. The lime and baryta salts were prepared by neutralising the hydro- chloric acid compound of amidobenzoic acid with their car- bonates. From the baryta salt the others were prepared. Binitrobenzoic acid is obtained by boiling benzoic acid with a mixture of sulphuric and nitric acids until the evolution of nitrous fumes ceases. On allowing the mixture to cool, the acid is deposited in brilliant crystals. It is more difficultly soluble in water than nitrobenzoic acid. By treating this acid with sulphuric acid and alcohol, oily drops are formed, which on standing become solid. These drops are binitrobenzoate of sethyle. It is soluble in warm alcohol, from which it crystallizes on cooling in long silky needles. By treat- ing this aether with an alcoholic solution of ammonia, the binitro- benzamide is obtained, crystallizing in silvery scales. By acting on an ammoniacal solution of binitrobenzoic acid with sulphur- etted hydrogen, it is converted into binamidolensoic acid, sul- phur being eliminated. On the addition of hydrochloric acid to the solution filtered off from the Sulphur, green crystals of a compound of hydrochloric acid and binamidobenzoic acid are gradually formed. Binamidobenzoic acid is obtained in the free state by digesting its compound with sulphuric acid with carbonate of baryta. It crystallizes in small greenish-pointed crystals, which arc soluble in water, alcohol, and £ether, tasteless, and without action on vegetable colours. .,,,^ ,;, .^i Binamidobenzoic acid is remarkable from tne property of (M)inbining with acids, which it possesses in a high degree. It exhibits a similar comportment to that observed in the case of aniline, — that substitution products retain in general the chief character of the compound from which they are derived, but that the replacing substance does not entirely lose its chemical cha- racter in the substitution product, but impresses it more upon the compound as the number of equivalents replaced by it in- Action of Chloride of Bensoyle on Aldehyde-ammonia. 303 creases. Benzoic acid is known as a strong acid; with the entrance of one equivalent of amide, which induces basicity, basic properties show themselves, for amidobenzoic acid forms com- pounds not only with bases, but with acids ; with the entrance of a second equivalent of amide, the properties of an acid are entirely lost, for binamidobenzoic acid forms compounds with acids alone. The formula of the hydrochloric acid compound of binamido- benzoic acid is C^^ ^4 (NH^)^ 0^, 2HC1. It crystallizes in white needles ; it is precipitated by strong hydrochloric acid from its aqueous solution in flocks, which change into these needles. When its aqueous solution is mixed with bichloride of platinum, a body is obtained which appeared to be <' adt s ^ C14H4(NH2)2 0^2(HC1, PtCP). The sulphuric acid compound of binamidobenzoic acid is obtained by dissolving the hydrochloric acid compound in dilute sulphuric acid. Its formula is C^^ H^ (NH^)^ 0^ 280^ HO. It crystallizes in colourless plates. With nitric, acetic, and oxalic acid, binamidobenzoic acid forms well-defined compounds, all of which crystallize. Limpricht* found that the action of acetate of iron on nitro- benzoic acid was the same as that of sulphide of ammonium, benzamic acid being produced. In the hope of obtaining a compound corresponding to the alcohol radicals, Limpricht f tried the action of chloride of ben- Q14JJ6Q2^ zoyle on aldehyde-ammonia. Butinsteadof thebody ^4 tjs qs fi which would be formed according to the following equation, — CI J "*" NH-* / - C^4H502/ + ^^^ ^^' Chloride of benzoyle. Aldehyde-ammonia. New body, fo'i '^{i^jjbiKr:, a substance was obtained having the composition C^^H^'^N^O^, of the production of which Limpricht gives no explanation. It crystallizes from alcohol in fine concentrically grouped needles. It is not soluble in water. Treated with potash, it gives ammonia, resin of aldehyde, and benzoic acid. With peroxide of lead and sulphuric acid, benzamide and aldehyde are formed. These bodies are also the product of the action on it of nitrous acid. Its alcoholic solution reduces neither silver nor mercury. Limpricht observes that the formula contains the elements of benzamide^ iiiaH(iaii;> sJa ;*«o1 v;i^i-.u>' A,- -•> >= ■..■ -■■■■■ ■. .-:.;'i.;4-''. jiiS * Liebig's Annalm, July, p. 118. t Ibid. p. 119. , 3j|> 304 Dr. Vohl on Phaseomannite, and cinnamide, . ., ^ Cinnamide. Benzamide. and also that the analyses of liipparaffine (a product of deconi'^ position of liippuric acid) agree very closely with those of this body. ,1' Dr. "Vohl* describes a triple salt of sulphate of,magnesia> manganese, and zinc. It is obtained by leaving to spontaneous evaporation, at a temperature of 9^ C, a mixture in equivalent proportions of the sulphates of magnesia, zinc, and manganeses It crystallizes in large plates, and columns of a clear rose colour< of the form of sulphate of magnesia, and has the following com^^ position :— y* MgO, SO3 + MnO,SOHZnO,SO3 + 2IH0. ! If sulphate of potash or ammonia be added, the corresponding triple salt, with 18 equivs. of water, is obtained, 3 equivs. of water being replaced by an alkaline sulphate. ]. The isame" dhtithifet obtainedf frbm the unripe fruit of the Pkaseolus vulgaris, a new saccharine matter. The fresh unripe fruit is heated some time in steam, or dipped in boiling water and then pressed in a mill. The juice is mixed with yeas^h and submitted to fermentation, then neutrahzed with chalk, the mass evaporated and exhausted with alcohol. On gentle evaporation, a body crystallizing in needles was obtained. The comportment of this substance with sulphate of copper and' free alkali, as well as its unfermentiscibility, place it near man- nite; on the other hand, its corapoi'tment in dry air and its composition, are very different from those of that body. The formula of the body dried at 100° C. is C^i H^^ O^^, that of man- nite is C^^ H^^O^^.*^ Vohl proposes for it the name Phaseoman- nite, and promises a more complete account ]ivhen he is able to prepare more substance. GossmannJ recommends the use of manganate of potash as a decolorizer of organic bodies, and states that he has employed it in purifying uric, hippuric, and cyanuric acids, vvitk great success. " ' ' * * Liebig's Annakn, July, p. 124. f Ibid. p. 125. J Ibid. Sept* p. 373. ,il^# XXXIX. Proceedings of Learned Societies, ROYAL SOCIETY. [Continued from p. 233.] ^j r February 7, 1856. — Colonel Sabine, R.A., V.P. and Treasurer, ,^ the Chair. | '"r^HE following communications were read : — -*■ **0n the Vitality of the Ova of the Salmonidse of different Ages ; in a Letter addressed to Charles Darwin, Esq., M.A., V.P.R.S. &c." By John Davy, M.D., F.R.S. Lond. and Edinb. &c. My dear Sir, — In a letter which I had the honour to address to you last year " On the Ova of the Salmon in relation to the distri- bution of Species," I have expressed the hope that some of the results of observations therein described may aid in solving the question as to the period, the age, at which the impregnated ova of fish are most retentive of life, and consequently are in the state best fitted for transport without loss of life. Joining with you in considering the subject in need of and deser- ving further inquiry, I have taken the earliest opportunity that has offered of resuming it. The experiments which I have made, and which I shall now describe, have been more limited than I could have wished, having been confined to the ova of the Charr, as I was not able to obtain the ova of the Salmon or any of its congeners in a fit state for the trials required. The ova of the Charr which have been the subject of my experi- ments, were from living fish brought to me from the river Brathay, a tributary of "Windermere, on the 9th of November. They were ob- tained by the pressure of the hand on the abdomen of the females under water, and immediately after their expulsion a portion of liquid milt, procured in the same way from a male, was mixed with them for the purpose of impregnation. The ova thus treated, 654 in number, procured from two fish, were transferred, after little more than an hour, to a shallow glazed earthenware pan, of a circular form, about a foot in diameter, with- out gravel, the water in which, afterwards, was changed daily once, and once only. The vessel was kept in a room of a temperature fluctuating from about 55° Fahr. when highest, to about 40° when lowest. The water used was well-water of considerable purity, and before used it was allowed to acquire the temperature of the room. •Two modes occurred to me as likely to afford the means of testing the vital power of the ova, or their power of endurance without loss of vitality ; viz. one by subjecting them for a limited time to a tem- perature raised above the ordinary temperature ; the other, by having them conveyed to a considerable distance. For the trials first proposed, the ova were put into a thin glass vessel half-full of water, which was placed in a water-bath and heated to the temperature desired. The first experiment was made on ova taken from the general stock one day after their expulsion. Six, for two hours, were exposed to a temperature varying from 79° to 80° of Fahr. The result was, Phil, Mag, S. 4. Vol. 12. No. 79. Oct, 1856. X 30(i Rvj/al Society :— that they became opaque in the course of twenty-four hours, all but one, and that, some days after, underwent the same change, denotmg loss of vitality. The second experiment was made on the 10th of November. Six ova were similarly exposed for two hours to a temperature rising gradually from 70° to 78° ; the result was similar : on the following day they were all found opaque. The third experiment was made on the 11th of November. The same number of eggs were exposed for an hour to a temperature falling from 70° to 69°. Two shortly became opaque ; four retained their transparency during a month, though in reality dead, which was denoted by their bearing no marks of development when seen under the microscope, those ova which retained their vitaUty being at that time well advanced. The fourth experiment was made on the 1st of December ; the ova, the same number, were exposed to a temperature rising from 75° to 78° for an hour and twenty-two minutes. Three became opaque, other three retained their transparency and vitality, and in due time were hatched, the first on the 31st of December, the last on the 7th of January. The fifth experiment was made on the 13th of December. Six ova were exposed for an hour and twenty-five minutes to a temperature falling from 82°, which it was at the beginning, to 78°, which it was at the end. Two became opaque ; in these no marks of progress could be seen of development, thus indicating that they were dead at the time of trial. Four remained transparent ; in these, under the microscope, embryo-fish were seen with an active circulation of the blood-corpuscles. One of them was hatched on the 31st of Decem- ber ; one, the last, on the 6th of January. The sixth experiment was made on the 20th of December, on six ova, containing living embryos. They were exposed for an hour and twenty-eight minutes to a temperature of about 98°, and this during the whole time. When taken out, they had not lost their trans- parency, but in each the heart's action was arrested, and death was the result : they all sooner or later became opaque, from the common cause, the imbibition of water. The seventh experiment was made on the 21st of December, on six ova, in which the circulation was distinct in the foetal fish. After an exposure for an hour and five minutes to a temperature of 70° rising to 82°, in five, on cooling, the circulation was found active ; in one, stopped, which was dead ; two were hatched on the 5th of January ; three, the remainder, on the 7th of the same month. The eighth experiment was made on the 23rd of December, on six ova, each containing a living foetus. They were exposed to a tem- perature falling from 84° to 82° during an hour and twenty minutes. Examined after the water had cooled, in one, the circulation was seeu pretty distinct ; m two, very feeble ; in three, the blood-corpuscles appeared to be stagnant. Examined on the following day, the cir- culation was seen active in all. One was hatched on the 5th of January, the other five in the two following days. Dr. Davy ow the Vitality of the Ova of the Salmonidse. 307" -^ The ninth experiment was made on the 24th of December. Six ova were exposed for two hours and four minutes to a temperature faUing from 72° to 70°. Examined a quarter of an hour after, and before the water was cold, the circulation was found vigorous in all. One was hatched on the 2nd of January, the remainder between the. 5th; and 8th. ikot-Br^ The tenth experiment, and the last of its kind that I have to describe, was tnade on the 2nd of January. Six ova, in each of which the circulation was distinct, were exposed for four hours to a tem-* perature varying from 70° to 72° — ^the greater part of the time 72°. Examined immediately on being taken out, the circulation was seen uninterrupted in three, arrested in the other three. In three-quarters of an hour, when the water had cooled nearly to the temperature of the room, 55°, the circulation was found to be renewed in the latter. In the interval, one of the former was hatched, and a vigorous fish produced ; on the following morning four more had come forth, and in the one remaining egg the foetal circulation was vigorous ; it was hatched on the 4th of January. I beg now to pass to the other series of experiments referred to, those in which trial of the vitality of the ova was made by sending them to a distance. The method was briefly the following. The ova were lightly packed in wet wool contained in a tin-plate box per-^ forated in its bottom to admit air, and covered with a wooden cover that had been soaked in water, with the intent of preserving moisture. The box was wrapped in tow, loosely covered with oiled paper, and the whole, in an envelope of common writing-paper, was well secured by a binding of thread. Thus prepared, the ova were sent by post to Penzance, in Cornwall, a distance exceeding 500 miles, with tha request that they should be sent back by return of post unopened. . The first experiment was made on the 9th of November. The number of ova sent was thirty, taken from the common stock without selec- tion. They were received on their return on the 14th of the same month. On taking them out, all were found transparent ; but, with the exception of one, all became opaque on being put into watei^ and that one, after a few days, also underwent the same change. : i' The second experiment was made on the 14th of November. Twenty ova then sent were returned on the 18th. AH became opaque on being put into water. jr/x« The third experiment was made on the 1st of December. Twenty ova then sent were returned on the 5 th. Put into water, eleven became opaque within a minute; most of these were slightly shrivelled. After three hours, two more became opaque. After forty- eight hours, four only remained transparent ; in these, under the microscope, the circulation was found active in two ; in the other two it could not be detected. One was hatched on the 31st of December, the other died before hatching. The fourth experiment was made on the IStli of December. Twenty-two ova then sent came back on the 17th. During the interval there was a severe frost ; the thermometer here in the open air was constantly below the freezing-point, and it would appear to X2 308 ' ... Royal Society :-^ '. \ have been much the same throughout Eugland. When examined, eleven of the ova immediately became opaque on immersion in water. In the other eleven there was no loss of transparency, and in these, imder the microscope, the circulation was found active. Those which had become opaque were placed in a pretty strong solution of common salt, by which their transparency was restored, the saline solution dissolving the coagulum. Now examined, no traces of development could be detected under the microscope in any one of them, — showing that they had been dead before they were sent away. On the following day, the 18th of December, the eleven transpa- rent ova were repacked, and again sent the same distance. They came back on the 22nd ; they retained then their transparency ; placed in water, a feeble circulation was to be seen in two under the microscope ; in nine the blood-corpuscles had ceased to flow ; these became opaque. Of the two in which the circulation was perceptible, one was hatched on the 28th of December ; the young fish in thei other died, it would appear, in the act of breaking the membrane, itS' head, on the 29th, having been found protruding, but the heart'a^ action stopped. The fifth experiment was made on the 26th of December. Ten ova, in which the circulation was active, and the foetus in each well advanced, were sent off on the day mentioned, and returned on the 31st. The weather, during the whole time, was mild, the frost having ceased. When opened, the ova were all found hatched, and the young fish dead, as might have been expected. When put into water, not one of them showed any signs of remaining vitahty; they were all examined under the microscope. i<<>,i'':j> .i.jiil n ni The sixth and last experiment was made On tiiiejmdlneedmcBiratl)^^^iifuBe,dw:«ltii upon. .V... ':,y\i\\ uri -iO(jr;)^i[= r ni ■r>n:,tiV'iYiJO^ ]v.^iiaiT^ 1 am, my dear Sir, yours very truly, Mb "io ilLesketh How, Ambleside, - . JofiN DAtlYsdt no January 10, 1856. -ginuir^mo^ mum 9fio Biii iii :hii')h ■' "Note on a new Class of Aloohil^." ^ ' By M^-^Aii^.^'ilMottrBbaadlf A. W. Hofmann, Ph.D., F.R.S. &c. -ooioiii/ a>r^ On submitting to dry distillation glycerine, either alOne of toge* ther with bisulphate of potassium or anhydrous phosphoric acid, M. Redtenbacher obtained a remarkable product, to which he gave the name of acroleine. Presenting all the characters of an aldehyde, and approximating more particularly to vinic aldehyde by the general aspect of its reactions, this substance changes under the influence of oxidizing bodies, especially of oxide of silver, an acid being formed, named by this philosopher acrylic acid, an acid which stands in the same relation to acroleine as acetic acid does to aldehyde. ;;j The researches of MM. Will and Wertheim on the essential dils of mustard and of garlic, tended to indicate a relation between these 810 *^ ' ^^''^ Royal Sodety: — substances on the one hand and acroleine and acrylic acid on the other, a result which was established by the more recent investiga- tions of MM. Berthelot and De Luca. On studying the action of iodide of phosphorus on glycerine, these chemists obtained an iodine- compound named by them iodide of propylene, which is an analogue of the chloride and bromide of propylene, previously produced by MM. Cahours, Reynolds, and Hofmann, when submitting to the action of chlorine and bromine the gases which are formed when either amyUc alcohol or valeric acid and its homologues are exposed to the influence of heat. MM. Berthelot and De Luca have further shown that the result of the mutual decomposition of iodide of propylene and sulpho- cyanide of potassium is an oil identical with that obtained on distil- ling the seeds of black mustard with water in an alembic. By this remarkable experiment it is most clearly demonstrated that the vola- tile oil of mustard belongs to the propylene series, a relation which had been previously pointed out by Capt. Reynolds, but which he has omitted to establish by experiment. If, then, we admit the exist- ence of a hydrocarbon, Cg H5, analogous to ethyle, C4 H5, we get CaHjCl Chloride of propylene. C4H5CI Chloride of ethyle. Cj Hg Br Bromide of propylene. C4 Hg Br Bromide of ethyle. Cg Hg I Iodide of propylene. C4 Hj I Iodide of ethyle. i- Cj Hg S Essential oil of garlic. C4 Hg S Sulphide of ethyle. Vv Cj Hg C2 NSj Essential oil of mustard. C4 Hg Cg NS3 Sulphocyanide of ethyle. C5H4O3 Acroleine. C4H4O2 Aldehyde. ^ C, H4 O4 Acrylic acid. C4 H4 O4 Acetic acid. All that now remained was to discover the keystone of this edifice, in other words, to establish the existence of an alcohol to which the preceding compounds might be referred, and by the aid of which a still more numerous series of ethers, both simple and compound, ^ jind analogous in every respect to the derivatives of ordinary alcohol, might be obtained. After many protracted and unsuccessful attempts, we have succeeded in producing the alcohol and ether of this series, for which we propose retaining the name of the acryle series. ' In order to arrive at this result, we have submitted several silver- *^^salts to the action of iodide of acryle. There are but few acids whose salts lend themselves conveniently to this reaction. Among the - Tarious salts which we have examined with this view, the oxalate of silver has furnished the most satisfactory results. This salt is most violently attacked by iodide of acryle ; the reaction is complete after two or three hours' digestion. The oxalate of acryle formed in this process, when separated from the iodide of silver, washed with water, dried over chloride of calcium, and redistilled, presents itself as a colourless transparent liquid, heavier than water, possessing a peculiar aromatic odour. It boils at 207^, and by analysis has been proved to contain ^ , fJHO— C/TIH'iO iij When treated with ammonia, oxalate of acryle furnishes oxamide and the alcohol, which was the object of our researches. This , alcohol — acrylic alcohol — is a colourless transparent liquid of a j< peculiar, somewhat pungent odour, resembling that of mustard, and MM. Cahours and Hofmann on a new Class of Alcohols, 311 which in fact is more or less characteristic of nearly all the members of the acryle series. ♦. The analysis of acrylic alcohol has led to the formula ' Cg Hg 62=4 vols, of vapour. This compound is isomeric with acetone and with propyle-alde- hyde, from which substances, however, it differs essentially by th« aggregate of its properties. Acrylic alcohol burns with a much more luminous flame than ordinary alcohol. It mixes in all proportions with water. Treated with potassium, it disengages hydrogen and is converted into a trans- parent gelatinous mass, which is the acryle-term corresponding to potassium- alcohol. This potassium compound is violently attacked by iodide of acryle ; a precipitate of iodide of potassium is thrown down, and a liquid is formed lighter than water, and insoluble in this fluid. This new substance corresponds to ordinary ether ; its formation is illustrated by the following equation : — C^ (H5 K)02+C(. H5 I=KI+ Ci, Hi„ O2. The same product is formed by the action of iodide of acryle upon oxide of silver or of mercury. On treating the new potassium-alcohol with iodide of ethyle, or the ethyle-potassium-alcohol with iodide of acryle, an aromatic liquid is produced, which is obviously the mixed ether of the ethyle and acryle series. If acrylic alcohol be distilled with chloride, bromide or iodide of phosphorus, the chloride, bromide and iodide of the acryle series are reproduced with the greatest facility. Acrylic alcohol dissolves in concentrated sulphuric acid, without separation of carbon ; the liquid, mixed with water and neutralized with carbonate of barium, furnishes a crystalline salt, which contains Cg H, BaS, 08=BaS04, (Cg H^) SO4. This is the sidphovinate of the series. On treating the 'mixture of acrylic alcohol with concentrated sulphuric acid, a most violent reaction takes place ; the alcohol is entirely carbonized with evolution of sulphurous acid. Anhydrous phosphoric acid affects the alcohol with less energy. The mass darkens with evolution of a transparent colourless gas, burning with a luminous flame. The analysis of this gas remains to be made. Acrylic alcohol is rapidly attacked by oxidizing agents. A mix- ture of sulphuric acid and bichromate of potassium acts with tre- mendous violence ; the products of the reaction being acroleine and acrylic acid, or its products of decomposition. The same transform- ation is effected by spongy platinum. When treated with potassa and bisulphide of carbon, the new alco- hol solidifies at once into a mass of splendid yellow needles, which correspond to xanthate of potassium. By the aid of the alcohol itself, its sulphovinic acid, or its iodide, all the terms of the acryle series may be produced with the greatest , 312 Hoyal Society r — facHity.*J We xf\\\ ' spedfy ^^^^ following compounds, the study of which we haTeroore or less completed. I '^ m ^-^irjtu Invif),' u hi/m/ Acryle-oxamethmiCi or o!cam«te of^aet^yle, is readily formed by adding alcoholic ammonia in small quantities to oxalate of acryle, until a permanent precipitate is produced. The filtered solution de- posits on evaporation the oxaniate in magnificent crystals. Carbonate of acryle is an aromatic oily liquid, lighter than water. It is formed like the other carbonic ethers, by the action of sodiunL upon the oxalate. An alcoholic solution of this substance, when treated with baryta, furnished carbonate of barium and aery he alcohol. Benzoate of acryle is readily produced by the action of chloride of benzoyle upon acrylic alcohol. It is a liquid heavier than water, which boils at 220°, and possesses an aromatic odour, similar to that of benzoic ether. The analysis of this substance leads to the formulaain!.!,.... e^Hi„0,=C„[H,(C,H,)]0,r^-a ■ The same body is easily produced by the mutual reaction of iodide of acryle and benzoate of silver. . ;? o / m\ Acetate of acryle, obtained by the action of iodide of acryle Upon' acetate of silver, is a liquid lighter than water, of an odour resem- bling that of common acetic ether. According to our analysis, it contains C,„H,0,=C,H,(C,H,) O,. ! Cyanate of silver is most violently attacked by iodide of acryle, even in the cold. The heat generated during this reaction is so powerful that the whole of the new product distils over. The sub- stance thus obtained has an incredibly penetrating odour, and causes lacrymation in the highest degree. The analysis of this colourless transparent liquid, which boils at 82°, led to the formula ,11 .'J) ^) C„H,NO,=C,(C„H,)NO,. ;. .'p. 1 This is the cyanate of acryle. Gently warmed with a solution of am- monia, this liquid readily dissolves, and the solution deposits upon evaporation magnificent crystals, which are nothing but acrylic urea, C,H,N,0,=:C,H3(C,H,)N,02, corresponding to thiosinnamine, the long-known sulphur-urea term of thisserie^, ■ , CeH8N2S2 = C2(H^C„H,)N,S,. .]ii-t^\^i'^ Aniline produces with cyanate of acryle an aualogoujl»8ub6tiihce,' which crystallizes remarkably well. ; ; i I ' > When treated with water, cyanate of acryle is gradually converted into a solid crystalline substance. The compound obtained in this manner has the composition and all the properties of sinapoline or diacry lie urea. Its formula is and its formation is illustrated by the following equation : — 2C8H5NO2+ 2H0 = Ci4 H13N2 O2 + 2CO2. V ,, J V ., ' Y '' Cyanate of acryle. Sinapoline. r - ^ Cyanate of acryle is decomposed by a concentrated solution of potassa ; a solid substance is rapidly formed, which floats upon the surface of the solution, and which is nothing but the same sinapoline. MM. Cahours and Hofmann on a new Class of Alcohols. 313 whilst a strongly alkaline liquid passes into the receiver, which is a mixture of several bases, in which we have traced, already.. , yd h-jmiot Tid:>B9t bi .<\(1) Methylamiue. ho ,^iwvn\V>wvyv.o-^\\roK ^•)i7vjn '^o 9tfiii?z<) nj > (2) Propylaraine,.BriTOfmfri3 oiloifoale iinrh};.*. •'>]» (mLV,iU)> ij'natiit . ' (3) Acrylamine.MjrqD'nq hi-HinuiYM] n iitrin The latter substance boils between 180° and- 1 90°vf" All' curate tempts to produce a well-crystallized platinum-salt of this base have hitherto failed. The experiments detailed in the preceding sketch' incontestably demonstrate the existence of, a mew series i of alcpfheH ; the i third tj^m of which is acrylic alcohol.: lyrMfluna /llhivn >i AviS- u'V, v,.\-py^,',si^\\ Like ordinary alcohol, this new alcohol furnishes a series of deriva- tives, which may be formulated in a similar manner. The following tables exhibit the terms of the acryle series hitherto prepared in juxtapositioa with the corresponding members of the ethyl series :- • i/imnccf Sib yd hsojjboTdvligKs s^r , i.u' (!ib& adT Acryle Terms. \ 'lovli V ^^^^^^ ^®Wf 'i a Hg O^ AlcohoL^^.. ,^j^..^.j.^.J 1p,H, O, . ^^^^^^^ C, H, O or 1 ^^y^^^ mU.'t3Jd?^Ui.i4^4^5 ^ % lo ^2flio^^2 J .W ' .ix,j)^ oijoi.b^io)^, lo J6d.i -jmid Cfl H. CI Chloride (^. H. 1^1 -'^. Cl Ul Br BroriA:\).M^)^j:>Jti^K Br '''"'""'' Cg H5 I Iodide :;la.7liisdIofir.i-..-C4H,; I to siBneyO Cg (K, Cq BrJ^fl.^ Xanthate of potassium Cg (K, C4H5) S4 Og iub G2 (Cg H5) NS2 Sulphocyanide Cg (C4 H^) NSg ;; , r,'»«I Cg (Cg H5) NO2 Oxycyanide or cyanate Cg (C4 H^) NO^mqannit r nr r TT ^AT c! / Sulphuretted acryle- 1 ^ j j ^2VJ^.^^6"5MN2»2 \ urea— Thiosinnamine j \ Avtv.w..^^, od* ri ^rdT C2(H3,CgH5)N202 Acryle-urea,Ethyle-urea C2 (H3, C4H5) NgO ,p^„ r TH rr TT MN n / l>iacryle-urea, Diethyle- 1 p. .„ re H n N O^'"^ C2[H2(C6H5)2]N202 -[ ginapoUne-urea / ^2 1^2 yya^M ^^2^? C.rCgHOO.or 1^ ,. rC2(C4H5)04or clHgCCgHA Oxamate . .Hj.eP.F-:.^,C4(H; C4HJ0, ^^^^^^ C (C^H,)(^ or T Carbonate. .•l?V!--f^ ([^^H.) O^ cmirrrA C4 H3 (Cg H.) O4 Acetate .... ■ila«a:A«>. ,io^/€:4 (H3, C4 H5) O4 ' ' Ci4 H, (Cg H,) O4 Benzoate . . C . . .'.^^.v- €^4 H^ (C4 H,) O^ ,. .1.0 Cg H5 SO4 HSO4 Sulphovinic acid .... C4 H5 SO4 HSOij (Cg H,) H2 N { ^;tf,r:: . . . ^^^^'- } (C4 H,) H2 N ^ XT ^ f , Aldehyde^ t ^loijBunol rH hnn C6H4O2 J Acrylic, Ethylic, [C4H^0^-^,. L Acroleine J _';,!_l.^Jj" r TT n / Acid. Vc' ri^"fi'{^ ^^m!Mor hr>(ini\/ Acrylic; acetic >,«-.-i ^f^-Sli 'io otBrmyO n W^'qri 8tBoft did Hydrocarbon* ^ i s'lj^rgli'i bHo8 r . bW/jJoj^ ^ <^ ?iinia OflifiH 1 Propylene ?, Acetene / ,f miff f loa ^jd J I0 ooi^TtrB 814 Royal Society : — Acrylic alcohol, the history of which we have endeavoured to sketch in the preceding pages, and in the study of which we are now engaged, is the third term of a series of alcohols, which is parallel to the ordinary alcohols of the formula Cn2Hn2 + 2 02, and the prototype of which is ethylic alcohol. The acid corre- sponding to this alcohol is acrylic acid, as has been stated. Che- mists are already acquainted with several homologues of acrylic acid, which stand to the series of fatty acids in the same relation which exists between our new alcohol and common alcohol. Cyanide of acryle, which is readily procured by the action of iodide of acryle upon cyanide of silver, but which as yet we have not been able to obtain in a state of perfect purity, when submitted to the action of potassa, will obviously furnish an acid, homologous to acrylic acid equally as cyanide of propyle is transformed into butylic acid. We terminate this note with a synoptical table of the two homo- logous groups. Group of Alcohols. Group of Acids. C, Ha O2 C, H4 O2 Methylic C3 O4 (Carbonic ?) C3 Ha O4 Formic C4 H4 O3 C^ Hfi O2 Ethylic C4 Hj O4 C4 H4 O^ Acetic Ce H« Oj Acrylic C9 Hr O^ Propylic Cg H4 O4 Acrylic Cg Hg O4 Propionic Cg Hh O2 Cr HjoOa Butylic €„ Hg O4 €« H^ O4 Butylic CioHjoOa C,oH,2 02 Amylic C,o Hf, O4 Angelic CjoH,o04 Valeric C12H12O2 C12H14O2 Caproic Ci2H,o04 C,2H,2 0i Caproic C,4 H,4 O2 C,4 H16 O2 Ci4 H,2 O4 0,4 H,4 O4 CEnanthylic CigH.gOa CigHigOa Caprylic C,6Hi4 04 C,a H,6 04 Caprylic CagHsgO, CagHagO, C36H34O4 Oleic Cj, Hgg O4 Stearic This table exhibits a considerable number of gaps, which the pro- gress of science will not be long in filling up. Even now we have established by experiment that bromide of amylene suffers many changes, which are perfectly analogous to those which we have wit- nessed in the acryle series, and even the derivatives of olefiant gas appear to exhibit in many respects an analogous deportment. Feb. 21, 1856.— The Lord Wrottesley, President, in the Chair. The following communication was read : — ** Account of the Observations and Computations made for the purpose of ascertaining the amount of the deflection of the Plumb- Line at Arthur's Seat, and the Mean Specific Gravity of the Earth." Communicated by Lieutenant-Colonel James, R.E., F.R.S. &c. Col. James begins by observing, that as the Royal Society has, from the very commencement of the Ordnance Survey of the United Kingdom, taken a deep interest in its progress, he has great pleasure in announcing to the Society that all the computations connected with the Primary Triangulation, the measurement of the Arcs of > Meridians and the determination of the figure and dimensions of the earth are now completed, and that the account of all the operations and calculations which have been undertaken and executed is now in ' ttie press, and will shortly be in the hands of the public. ^ In the progress of these operations it has been found, on deter- mining the most probable spheroid from all the astronomical and 'geodetic amplitudes in Great Britain, that the plumb-line is consider- Lieut.-Col. James on the mean specific gravity of the Earth. 315 ably deflected at several of the principal Trigonometrical Stations, and at almost every station the cause of the deflection is apparent in the configuration of the surrounding country. The deflection of the plumb-line at Arthur's Seat is 5"-l, and at the Royal Observatory at Edinburgh it amounts to 5"' 63 to the South. The unequal distribution of matter in the vicinity of these Stations — the great trough of the Firth of Forth being on the North and the range of the Pentland Hills on the South — presents an obvious cause for the deflection ; but as the contoured plans of the county of Edinburgh have been published and the best attainable data acquired for estimating the amount of local attraction at the above-mentioned stations, it appeared desirable specially to investi- gate the matter, both on account of its scientific interest and with a view to confirm the results arrived at from the previous investigation 6f all the observed latitudes. Col. James accordingly decided on having observations taken with Airy's Zenith Sector on the summit of Arthur's Seat, and at two other points near the meridian line on the North and South of that mountain, at about one-third of its alti- tude above the surrounding country. The observations were made by Serjeant-Major Steel of the Royal Sappers and Miners, during the months of September and October last, and 220 double observations of stars were taken at each Station. The reductions and computations connected with these observations, as well as the computations of the local attraction at the Calton Hill, were entrusted to Captain Clarke, R.E., by whom the account now communicated of the mathematical investigation of the observed data has been drawn up. Col. James has himself examined the geological structure of Arthur's Seat and of the whole of the county of Edinburgh, and has caused determinations to be made of the specific gravity of all the different rocks, with the view of estimating the mean specific gravity of the whole mass ; but he observes, that although the geological structure of Arthur's Seat is well exposed, and its mean specific gravity, 2*75, has been employed for deducing that of the earth, viz. 5*1, still it is not a mountain he should have selected for this special object. Accordingly he was pleased by discovering — ron re- ferring, since these observations were made, to the correspondence of the Survey, — that the late Dr. Macculloch had been employed from 1814 to 1819 in examining the whole of Scotland for the purpose of selecting a mountain which, from its homogeneous structure, size, and form, would be best suited for the purpose referred to, and that he had pointed out the Stack Mountain in Sutherlandshire as admirably answering the required conditions. The transfer of the whole force of the Survey from the North of England and Scotland to Ireland, prevented the late General Colby from undertaking this investigation ; but as the Survey of Scotland is now in full progress, Col. James purposes early in the spring to have the Stack Mountain and the surrounding country surveyed and contoured, and to have observations taken for determining the attraction of its mass, and he trusts by the close of the present year to lay the results before the Royal Society. 316 Cambridge Philosophical Society : — After these preliminary explanations, a detailed account is given of the mathematical investigation, and the paper, which was illus*; trated with plans and geological sections, and a model of Arthur's Seat, concludes with the following statement of the principal re* suits r— * 1 . " The effect of the attraction of the Pentland Hills is observed ? in nearly equal amouA(Liat eiiohto£\tii»v^de #tatjOBS)Oni Arthui*s Seat. '!-)/if,v yilDhJQOiy 'lo v:)i:riT«ifp ods (6 hi^iu-.ji'jm hi noil 2. ''The calculated attractioDtf-fil^itfaftiiiiatt 0|£iAM^Tfflqfie^ the three stations are, — n\]omo-\\^'j[o Aoihi aib V) iiiili:>oo ^\— iUy.ivn o^oilv/' .liuDii- ' ' •; iil .noU South Statipi^,oi:r-vj{o ^^\?^t5d 1 "ti .stVorth StatiQn.bnj3 ,A= 2"-25 Nort^-nuD 9r{9'^.?^3^«*^ dloHv/ V'-98 Soutb*r>ii3 oAi and, since the observed dlfl^ctipn at Aitttir's Seat is 5"* 27, the apparent effect of the Pentlands is 4"' 93 at the summit of the hill. 3. "Of this deflection of 4"*93, the computed attraction due to the configuration of the ground within a radius of fifteen miles accounts for about 2"* 6; and, inasmuch as we know that the igneous rocks of Arthur's Seat and the Pentland Hills have an origin at a great depth below the surface of the earth, the difference between the observed and computed attraction is probably owing in part to the high specific gravity of the mass of rock beneath them. ,; 4. "The deflection at the Royal Observatory, Calton Hill, bein^ 5"- 63 South, exceeds that at Arthur's Seat by 0"-/0. Of this de;, flection, 0"*60 is due to the configuration of the ground comprised- within a circle of a mile and a quarter round the Observatory. 5. "The latitude of Arthur's Seat or points in the neighbourhood varies to the amount of 0"*02 between high and low water. 6. "The mean density of the earth, determined from the observa-r tions at the three stations on Arthur's Seat, is 5*14, with a probable, error of +'07 due to the probable errors of the astronomical ampli- tudes." "■ 91ft -^iaaDJni hv loiiijupti •:>iiT ^ bnu ,ain9iijjoCAMBRiDGE philosophical sociETY^nol ai iBlimia ^tContmued from vol. xi. p. 405.] ^^^^ ^^^^^^^,^^ ,,.j .^^^ Feb. 11, 1856. — A paper was read by Mr. Maxwell of Trinity College, on Faraday's Lines of Force, in continuation of aiormet^^ paper (Phil. Mag. vol. xi. p. 404). r i< j jxtjHoi-j rii '-'a .>loq oitsngiira This paper was chiefly occupied with "flie exteosioii' of tfcie tti€fthifd> of lines of force to the phaenomena of electro- magnetism, by means^ of a mathematical method founded on Faraday'eidea'of an "electro*.^' tonic state." auin^im fci' Jiiioiio ' In order to obtain a clear view of the phaenomena to be isxplained,^ we must begin with some general definitions of quantity and inten-- sity as applicable to electric currents and to magnetic induction. It was shown in the first part of this paper, that electrical and mag-- netic phaenomena present a mathematical analogy to the case of a fluid whose steady motion is afl^ected by certain moving forces and resistances. [The purely imaginary nature of this fluid ha& been Mr. Maxwell on Faraday^s Lines of Force. 317 already insisted on.] Now the amount of fluid passing through any area in unit of time measures the quantity of action over this area ; and the moving forces which act on any element in order to over- come the resistance, represent the total intensity of action within the element. In electric currents, the quantity of the current in any given direc- tion is measured by the quantity of electricity which crosses a unit area perpendicularly to this direction ; and the intensity, by the resolved- part of the whole electromotive forces acting in that direc- tion. In a closed circuit, whose length =/, coefficient of resistance =k, and section =C^, if F be the whole electromotive force round the circuit, and I the whole quantity of the current. Oil) aS'^N"! 81 ttB98 j" J[_/y5._p j_C^F jnogdo &iii ooiiia Jhw Jlid odj ^0 dlmr ■: C^ ' ik ' '^ >: 1:0 ioo^^i i noun {q& "^ftSiWi^sW^hmwith respect to electric curreilfi'.T^fe^llenip- plied to cases in which the conducting power of the medium is dif- ferent in different directions. The general equations were given aud S^eral cases solved. ' y^' ^ ^ , '/' .' ^^in magnetic phsenomena, the distinction of quantify and' infceiisiiy' is less obvious, though equally necessary. It is found, that what Faraday calls the quantity of inductive magnetic action over any surface, depends only on the number of lines of magnetic force which pass through it, and that the total electromotive effect on a conduct- ing wire will always be the same, provided it moves across the same system of lines, in :, whatever manner it does so. But though the quantity of magnetic action over a given area depends only on the number of lines which cross it, the intensity depends on the force required to keep up the magnetism at that part of the medium ; and this will be measured by the product of the quantity of magnetiza- tion, multiplied by the coefficient of resistance to magnetic induction in that direction. The equations which connect magnetic quantity and intensity are similar in form to those which were given for electric currents, and from them the laws of diamagnetic and magnecrystallic induction may be deduced and reduced to calculation. We have next to consider the mutual action of magnets and elec- tric currents. It follows from the laws of Ampfere, that when a magnetic pole is in presence of a closed electric circuit, their mutual action will be the same as if a magnetized shell of given intensity had been in the place of the circuit and been bounded by it. From this it may be proved, that (1) the potential of a magnetized body on an electric circuit is measured by the number of lines of magnetic forc^ due to the magnet which pass through the circuit. (2) That the total amount of work done on a unit magnetic pole during its passage round a closed curve embracing the circuit depends only on the quantity of the current, and not on the form of the path of the pole, or the nature or form of the conducting wire. The first of these laws enables us to find the forces acting on an electric circuit in the magnetic field. Give the circiiit any displace- 318 Cambridge Philosophical Society :-- ment, either of translation, rotation, or disfigurement, then the dif- ference of potential before and after displacement will represent the force urging the conductor in the direction of displacement. The force acting on any element of a conductor will be perpendicular to the plane of the current and the lines of magnetic force, and vnW be measured by the product of the quantities of electric and magnetic action into the sine of the angle between the direction of the electric and magnetic lines of force. The second law enables us to determine the quantity and direction of the electric currents in any given magnetic field ; for, in order to discover the quantity of electricity flowing through any closed curve, we have only to estimate the work done on a magnetic pole in passing round it. This leads to the following relations between a, jSj y^, the components of magnetic intensity, and a^ b^ c^, the resolved parts of the electric current at any point, 0 = ^1-.^, b =^^—\ c=^-^. ^ dz dy* ^ dx dz* ^ dy dx ' In this way the electric currents, if any exist, may be found when we know the magnetic state of the field. When a.^dx~\-(i^dy-\-yx^^ is a perfect differential, there will be no electric currents. Since it is the intensity of the magnetic action which is immedi- ately connected with the quantity of electric currents, it follows that the presence of paramagnetic bodies, like iron, will, by diminishing the total resistance to magnetic induction while the total intensity is constant, increase its quantity. Hence the increase of external effect due to the introduction of a core of soft iron into an electric helix. From the researches of Faraday into the induction of electric cur- rents by changes in the magnetic field, it appears that a conductor, in cutting the lines of magnetic force, experiences an electromotive force, tending to produce a current perpendicular to the lines of motion and of magnetic force, and depending on the number of lines cut by the conductor in its motion. It follows that the total electromotive force in a closed circuit is measured by the rate of change of the number of lines of magnetic force which pass through it ; and it is indifferent whether this change arises from a motion of this circuit, or from any change in the mag- netic field itself, due to changes of intensity or position of magnets or electric currents. This law, though it is sufficiently simple and general to render intelligible all the phaenomena of induction in closed circuits, con- tains the somewhat artificial conception of the number of lines pass- ing through the circuit, exerting a physical influence on it. It would be better if we could avoid, in the enunciation of the law, making the electromotive force in a conductor depend upon lines of force external to the conductor. Now the expressions which we obtained for the connexion between magnetism and electric currents supply us with the means of making the law of induced currents depend on the state of the conductor itself. Mr. Maxwell on Faraday's Xmes of Force, 319, We haye seen that from certain expressions for magnetic intensity we could deduce those for the quantity of currents, so that the cur- rents which pass through a given closed curve may be measured by the total magnetic intensity round that curve. Here we have an integration round the curve zV^e/^ instead of one over the enclosed sur^ face. In the same way, if we assume the mathematical existence of a state, bearing the same relation to magnetic quantity that mag- netic intensity bears to electric quantity, we shall have an expression for the quantity of magnetic induction passing through a closed cir- cuit in terms of quantities depending on the circuit itself, and not on the enclosed space. Let us therefore assume three functions oixy z, O'of^oyo, such that «i 61 Ci being the resolved parts of magnetic quantity, dz dy ' dx dz ' dy dx' then it will appear that if we assume -~, — V^, -~- as the expres- dt dt dt sions for the electromotive forces at any point in the conductor, the total electromotive force in any circuit will be the same as that ex- pressed by Faraday's law. Now as we know nothing of these in- ductive effects except in closed circuits, these expressions, which are true for closed currents, cannot be inconsistent with known phaeno- mena, and may possibly be the symbolic representative of a real law of nature. Such a law was suspected by Faraday from the first, although, for want of direct experimental evidence, he abandoned his first conjecture of the existence of a new state or condition of matter. As, however, we have now shown that this state, as described by him (Exp. Res. (60.)), has at least a mathematical significance, we shall use it in mathematical investigations, and we shall call the three functions ao, /3o, 70. the electrotonic functions (see Faraday's Exp. Res. 60. 231. 242. 1114. 1661. 1729. 3172. 3269.). That these functions are otherwise important may be shown from the fact, that we can express the potential of any closed current by the integral J(«.««J+*A|+<'.yo|)*. and generally that of any system of currents in a conducting mass by the integral m (aoffg + /3o&2 + 70^2) ^ ^y dz- The method of employing these functions is exemplified in the case of a hollow conducting sphere revolving in a uniform magnetic field (see Faraday's Exp. Res. (160.)), and in that of a closed wire in the neighbourhood of another in which a variable current is kept up, and several general theorems relating to these functions are. proved. M'^PH'ik 820 Cambridge Philosophical Society. March 10. — A paper was read by L. Barrett, Esq., on the Distri- bution of the MoUusca on ,^. Qqs^ti g^^Jto)«fiy. , X W«.Axmal» of Nat. Hist. May 1856.) ^^^ v^,^^^yi ,m V '"^V^V^ ^^ ^"^ April 28. — Also, a paper was read " On the Question what is the Solution of a Differential Equation." By Professor De Morgan. This paper is a short supplement to § 3 of a paper on some points of the integral calculus (Camb. Trans, vol. ix. part 2). It discusses the principles on which such an equation as y'*=a-, giving is generally affirmed to be completely solved when br&e. It-dwells on the distinction between a relation and an equation, which may express the alternative of one or more relations ; it points out several cases in which conclusions applicable to the simple relation only are affirmed of any equation ; and, with reference to the question asked in the title, discusses the manner in which the answer depends on the cross-question, what degree of discontinuity is allowed to be iniK. plied in the word 5o/m?ww ? v^ May 12. — A paper was read by Mn WaiAurVon oA Self-repeating Series, in continuation of a former pap6r. The author showed in his former paper on self-repeating seriea<- printed in vol. ix. part 4. of the ' Transactions ' of the Society, that in the fraction which generates a series of either of the following ^^' . V . [" < ^^j^^^^i, iBoidqoaoiiilS 9riJ rrj dou- on bib I "hifi^mM Hii^t^mc>llV3fipi(i &i imiiuo omfivli??, ^tva \j«ft Yd b^ouboiq si doidvy^ ined * adJ isdi ,?.i3W wj?I xlA .^nrri) aiii doiJv/ ?.all««+'^ + 2^'»+^^-^'S^*»+^r4- &c/:-:^i°^ iBnohioqoiq ei P„.,, ui^rxv^ ' . T "* t'^* "^ bsavloijoofo the numerator of such fraction is a recurrent function 6f/. He also then determined the coefficients of the several powers of t in such numerator to be given linear functions .of the; differences (as the case may be) of 0^", or of 0^'*+^ ^- -^^ '^•t'r ii In his present paper, from the n pairs of equal coefficients which the recurrent numerator contains, the author obtains n linear equations between the 2n differences concerned ; and selecting any n of these differences, he concludes that each of them can be expressed in terms of the other n differences not so selected ; and consequently that no formula, expressed in terms of the differences of 0^ or 0^"^^ need contain more than n of those differenccil i^'Wb) - I'J^ He gives the equations requisite for'obtluiiing A**'^''(0'^') in terras of (A*^ A""\ . . . A^ 4')02'*; and ^«+i+/'(o2»+i), in terras of (Afffi i>Jl^^^a^^3i^A?J<;a?)0''*"*''* ; and he applies these and other of his equations to the elimination of particular differences of zero fr^lf^q sundry formulas. ,., A|£|^^,Mr. Bashforth exhibited models illustrating the Moon's moabn. 'r -hieid '^di^' /^^^^%^^i-' t r, :■ •qjs ^i 9tiiitiH '' t^uioq ifii0tioqmi oAi ain^mriaqxo'shf iiiOTt«9DUl/ STY Intelligence and Miscellaneous Articles. 323 ened in English, in return another is softened. But, then, does Sir William think that the proper tone is hit in his memoir, in which such expressions as " clumsy way," " commonplace and unsound objection," and "somewhat learned endeavour," are made use of against me? If so, I need no excuse for having adopted a tone which he thinks improper. In reference to his memoir in the Philosophical Transactions for 1 834, I have charged Sir W. Harris with want of the necessary knowledge. Such a charge must be put up with by every one who draws from experiments untenable results, which it would have been impossible for him to have done had he been acquainted with the works of Franklin, ^pinus. Coulomb, and Poisson. I am compelled to assume, that, nineteen years ago, I demonstrated that law of electrical heat which is attacked by Sir William, and that it has not yet been refuted. This law is not one of the points of my electrical labours regarding which doubts have been raised ; on the contrary, it has been accepted by all physicists who treat of electricity in detail, and has proved to be in complete agreement with all the experimental and theoretical investigations which have since been made. If Sir W. Snow Harris be in a position to show the untenability of this law, he will do good service to science. I am not quite clear as to what the author aims at with the resist- ance in the battery. If Sir William supposes the resistance between glass and coating to be constant when the battery is enlarged, he produces no change in my formulae, in which the sum of all con- stant resistances is indicated ; if he regards this resistance as variable, he throws over his own law of electrical heat. In the following remark. Sir William is partly right. In my letter it runs, it is " nicht richtig " (which corresponds with the English " not correct") that I ascribed the unsatisfactory experiments of Sir W. Harris to the " faulty arrangement " of his thermometer. I had before me my original German memoir of 1837 (which I also referred to), in which the censure pronounced cannot be applied to the thermometer, but it had entirely escaped me that in 1838, I had worked up this memoir in French, when I ascribed those experiments to the imperfect (imparfaite) construction of the thermometer. It is therefore clear that I attempted to account to myself for the failure of Harris' experiments in different ways at different times, — by the inexact mode of measuring the electricity, the faulty mode of dis- charging the battery, and the want of sensibility in the thermometer. Latterly the first two causes appeared so sufficient to me, that I forgot the third. ' Sir William characterizes the heat- experiments of Kinnersley with the thermometer as " casual," " a mere coincidence," " quite a se- condary affair," and asserts that the experiments came to no result, which must raise the astonishment of any one who has ever even glanced at Kinnersley's letter. Kinnersley invented his thermometer solely with the view of refuting an opinion of Franklin's regarding the electrical heat, and introduces it with the words, " it fully determines that controverted point, whether there be heat in the electric fire." He deduces from his experiments the important point, " Hence it ap- Y2 dd4 Intelligence and Miscellaneous Articles. peai^; that the ekctric fire, though it has not sensible heat when in ft stateof rest, will, by its violent motion and the resistance it meets with, produce heat in other bodies when passing through them, provided they be small enough. A large quantity will pass through a large wire without producing any sensible heat ; when the same quantity passing through a very small one, being then confined to a narrower passage, the particles crowding closer together and meeting with greater resistance will make it red-hot and even melt it." The cir- cumstance that Franklin regarded the experiments without the ther- mometer as more demonstrative than those made with it, cannot justify us in attributing to Kinnersley the object* of measuring " the explosive violence of the discharge." Whether Sir William, when describing his thermometer, was or was not acquainted with Kinnersley's thermometer is of no conse- quence now, but it is otherwise when he describes his as a peculiar instrument, after he has become acquainted with Kinnersley's. Equally inexcusable is his claiming for himself (Phil. Mag., vol. xi. p. 358) a method of measuring electricity, although he must be aware that it was described by Haldane. Of the "perfect accuracy" of his unit- jar Sir William is so entirely convinced, that he prophesies that I shall soon be compelled to recognize it, and binds himself down to an offer which I will not be so ungenerous as to accept. I believe that I can prove, from the quotation at the close of his letter, that Sir William has no correct conception of the mode of action of his unit-jar ; and X repeat, that, according to the theory of the Leyden jar prevailing at the present day, the measurement with the unit-jar is inexact. Experiments, therefore, which are to show the accuracy of the unit-jar, must de- monstrate the incorrectness of the theory of the Leyden jar, or they remain valueless ; for no physicist will employ a method which is theoretically inaccurate, when he has a theoretically accurate method at his command. In conclusion. Sir William Harris gives an assurance, which I read with some astonishment, that he had not the intention of personally affronting me. I must confess that I have not found " a personal affront " in his memoir, but a not quite proper mode of carrying on a scientific discussion. I have the honour to be. Gentlemen, Your obedient Servant, Berlin, Atigast 22, 1856. P. Riess. OBSERVATIONS ON OZONE, RELATING TO A RECENT PAPER OF M. CLOEZf. BY M. BINEAU. ^ %^as long been known to every chemist, that, under very various influences, iodide of potassium accompanied by starch gives rise to |t blue coloration, and no one can have supposed that the so-called ozonometric paper of M. Schcinbein was only impressionable by ozonized oxygen. But M. Schonbein and most observers who, like * With his thermometer. >inj>iBi^ .M Jilt See Phil. Mag. for September, p. 237. Intelligence and Miscellaneous Articles. 335 myself, have employed his paper in experiments on the atmo- sphere, have adopted as the most probable opinion that which attributes to ozone the bluish colour produced in the natural atmo- sphere. The probability of this opinion does not appear to me to be invalidated by the results of M. Cloez. Thus, — 1. At a distance from laboratories or workshops whence hyponitric acid is evolved, the existence of rutilant vapours in the atmosphere appears to me very improbable. Again, I do not believe that the nitric acid produced by storms remains long without being neutralized, either by ammonia, or by the lime of the calcareous particles which float in the air in most countries ; and especially I do not think that this acid exists beyond the drops of rain, the in- fluence of which ]\I. Schonbein has recommended to be carefully avoided. Moreover, the hypothesis of the coloration of iodized starch by the nitric acid existing in the air has already been dis- cussed by M. Schonbein, in consequence of observations made by M. Heller at Vienna. The latter having observed the nitrification of potash in the air, attributed this effect, and also the spontaneous coloration of iodized starch-paper, to atmospheric nitric acid. But M. Schonbein ascertained that this acid, diffused in the air in suffi- cient quantity to redden litmus paper rapidly, acted but slowly upon paper with iodized starch ; from which he concluded, that if the natural air contains minute quantities of this acid insensible tp lit- mus, they can have no action upon iodized paper. t^Blonp 2. M. Cloez has observed the production of a blue colour in paper exposed to the emanations of aromatic plants; but is it not the same with regard to phosphorus ? Do we not see the oxidation of this body accompanied by an appearance of ozone, when the too active excess of the phosphorized vapours does not destroy the effect first produced ? and do we there attribute the coloration of the paper to other bodies than ozone } 3. If light be capable of giving moist air the property of acting upon ozonometric paper only in a closed space, this fact, whatever interest it may possess, has no bearing upon the usual meteorolo- gical observations relating to ozone. I may add, that the exposure of the paper to the sun has one incontestable inconvenience, that of increasing the fugacity of the colorations produced, by the too rapid volatilization of the iodine. Therefore I have always recommended the observers who have lent me their assistance to avoid, as a general rule, the influence of the direct solar rays. — Comptes^Rendm, July 21, 1856, p. 162. NOTE ON THE ENDOSMOSE OF GASES. BY J. JAMlN. Dobereiner once filled a cracked bell-glass, standing in water in a pneumatic trough, with hydrogen gas. Although the sides of the crack were very closely pressed together, the hydrogen filtered slowly through this fissure and became diffused in the atmosphere. What was remarkable in this experiment is, that during the issue of the hydrogen a partial vacuum was produced in the bell-glass, and that the water rose several inches above the exterior level. This inter- esting observation was not then carried any further, but M. Magnus 826 Intelligence and Miscellaneotis Articles. afterwards took it up, using designedly-cracked glasses, and demon- strated that if, on the one hand, the hydrogen escapes outwards, the air, on the other, travels in an opposite direction and penetrates into the glass. By placing over the apparatus an uncracked bell-glass, so as to circumscribe the exterior atmosphere, Magnus also ascertained that the pressure increased in the air whilst it diminished in the hydrogen. There were therefore here two gases in contact tlirough a capillary passage, both of which traversed this communication in opposite directions so as to unite ; and the hydrogen filtering more rapidly than the air, a difference of pressure was soon proved. This was, for gases, the phsenomenon of endosmose which Dutrochet had de- tected in liquids. Since this period other facts of the same kind have been added to those just referred to. Marianini having placed a soap-bubble in- flated with air in carbonic acid gas, saw it increase in size at first, and then burst. Other experimenters have produced the endosmose of gases through porous vessels or thin partitions, and the general fact has been placed beyond all dispute, although no convenient pro- cess for exhibiting it has been discovered, and nothing has led to a suspicion of the remarkable energy with which it is produced. I have to lay before the Academy a certain means of proving this en- dosmose and studying it in all its details. I take a porous vessel of unglazed porcelain intended for the Bun- sen's batteries, wash it with alcohol, and after leaving it to dry for several days, lay on its surface a coat of collodion dissolved in aether, or gutta-percha in sulphuret of carbon. This coat must be very thin, and envelope the entire surface of the vessel with a very con- tinuous and equal varnish. I close it with a cemented obturator, which gives passage to two tubes, of which one bears a stopcock, whilst the other is open at both ends, and about 3 metres in length. I fix the whole vertically on a support, when the apparatus exhibits the porous vessel at its upper part, and the two tubes descend verti- cally from it; the longer of these dips into a trough filled with water, and the other, which bears the stopcock, serves for the intro- duction of the gases to be studied. I now pass in a current of hydrogen, which circulates in the porous vessel, returns by the long tube, and escapes through the water surrounding its base. This current of gas must be very abundant, and be maintained for several minutes ; the stopcock is then closed. At this moment the pressure diminishes in the porous vessel, the level of the water rises with remarkable rapidity, and in twenty seconds it attains a maximum height which varies from 2 to 2*50 metres. The liquid soon sinks gradually, and in a few minutes the internal pressure has again become equal to that of the atmosi)here. In its intensity, and almost in its rapidity, this experiment is equal to that with cracked glasses ; it sliows that two unequal gaseous currents are established, and that the difference of pressure which is their consequence may exceed a fifth, and attain nearly a fourth of an atmosphere; and as, at the moment when the maximum is ob- served, the gases are already mixed, the effect perceived is inferior to that which would be produced if these gases had remained pure. A Meteorological Observatiom^f^'^\^\ 327 It will be easily understood that the inverse experiments might be made with equal success. The porous vase might be surrounded with hydrogen and filled with air, when the interior pressure would increase instead of diminish. Almost all the gases which I have studied furnish the same mani- festations with less energy, and it appeared to me that the pressure always diminished with the gas which filters best, and increased with that which is the worst to filter. These experiments, like all those on the endosmose of liquids, must be explained, as it appears to me, by the theory proposed by M. Magnus, which makes endosmose depend, in the first place, on an unequal power of filtration of the two liquids in presence ; and secondly, on a special force which sets them in motion, — a force which may be an affinity, an electrical action, or even a simple molecular action. — Comptes Rendus, July 28, 1856, p. 234. METEOROLOGICAL OBSERVATIONS FOR AUG. 1856. Chiswick. — August 1, 2. Slight haze : very hot. 3. Hot and sultry. 4. Over- cast : very hot. 5. Cloudless and hot. 6. Cloudy : slight haze : very fine. 7. Clear : hot and sultry. 8. Cloudy : overcast : very fine : rain. 9. Slight rain. 10. Cloudy and fine. 11. Very fine : cloudy : rain. 12. Cloudy : very fine. 13. Very hot : heavy rain at night. 14. Cloudy and fine : rain. 15. Cloudy and fine. 16. Very fine : thunder, lightning and rain at night. 17. Slight rain at half-past eight A.M. : excessively heavy rain commenced, nearly an inch fell in one hour : cloudy at night. 18. Cloudy. 19. Overcast : rain. 20. Foggy : overcast : heavy rain at night. 21. Densely clouded : boisterous, with heavy clouds and showers. 22. Partially overcast : cloudy : very fine. 23. Fine. 24. Cloudy and fine. 25. Slight showers. 26. Very fine. 27. Uniformly overcast : very fine. 28. Cloudy and fine : rain. 29. Very fine. 30. Slight fog: very fine. 31. Very fine : rain at night. Mean temperature of the month 63°-40 Mean temperature of Aug. 1855 00-00 i%, Mean temperature of Aug. for the last thirty years 61 '97 Average amount of rain in Aug 2-413 inches. Boston. — Aug. 1 — 3. Fine. 4. Cloudy. 5, 6. Fine. 7. Fine : thunder, light- ning and rain a.m. and p.m. 8. Fine. 9. Cloudy : rain a.m. and p.m. 10. Cloudy. 11, 12. Fine. 13. Cloudy. 14. Cloudy : rain a.m. 15, 16. Fine. 17. Rain A.M. and P.M. 18. Cloudy : rain a.m. and p.m. 19. Cloudy. 20. Cloudy: rain A.M. and P.M. 21. Rain a.m. and p.m. 22. Cloudy : rain a.m. 23. Cloudy. 24. Rain. 25. Cloudy. 26. Cloudy: rain p.m. ;\,J^j.,j91oudy: rain a.m. 28. Cloudy : rain A.M. and P.M. 29 — 31. Cloudy. V'^,.. , ,|, Sandwich Manse, Orkney. — Aug. 1. Drizzle a.m. : fog p.m. 2. Clear, fine a.m. : clear p.m. 3. Bright a.m. : cloudy p.m. 4. Bright a.m. : clear, fine, aurora p.m. 5, 6. Bright a.m. : clear, fine p.m. 7. Bright a.m. : cloudy, fine p.m. 8. Cloudy a.m. and p.m. 9. Cloudy a.m. : cloudy, fine p.m. 10. Bright a.m. : cloudy p.m. 11. Drops A.M. : drizzle P.M. 12. Bright a.m. : thunder-showers p.m. 13. Clear a.m. : bright p.m. 14. Bright a.m. : vapour, fine p.m. 15. Damp a.m. : drizzle p.m. 16. Damp a.m. : clear p.m. 17 — 22. Cloudy a.m. and p.m. 23. Cloudy a.m.: cloudy, drops P.M. 24. Bright a.m.: cloudy p.m. 25. Rain a.m. : showers p.m. 26. Showers a.m. : drizzle, showers p.m. 27. Cloudy a.m. and p.m. 28. Rain a.m. : drops p.m. 29. Showers a.m. : drops p.m. 30. Clear a.m. : cloudy p.m. 31. Rain a.m. : clear, aurora p.m. fis^ Mean temperature of Aug. for previous twenty -nine years ... 55°-03 r. Mean temperature of this month 53-22 ^' Mean temperature of Aug. 1855 56-10 ^^^ Average quantity of rain in Aug. for previous sixteen years ... 3-01 inches. 1 ''^:!^ ?■ — : r?.3 :?p f . to M o\>A : r) eo . p p j*.p : r r • OO H .5. •ua ^iiiiii'Hiiiiiiiiiii'i-i'iiiii^i .«,d, "«si"S«igisii-i»gss^s-^aii»'»"i£«i i f1 ^1 a a OS lo 0 1- ■+ lovo p «o w •uojsog PJ M O W-, rs, ,J. t^vo t«^e« 0\0 Ov+Vi-ir^^VO rt>oVl-MVO «Cd wVi-Ox • t*-so t>^ O ^ O vnvo »» u-,vo 0\ 0\V0 ^i-rl u^n roQ -"i-O b if 1 00 «« 0\ t^ •*0O OO O «OtH^O lOtO u-,0O 0 «^ 1-- t^OO 00 VO 0\V0 VO t-- M VO •* r^ 00 CTvOO 00 00 t^OO 00 t^OO 00 00 OO t^ t^ t^ t>.vo vovovovovovovo r^t^t^t^t>.t^ vb B i 1 i O w M f< js p p^oo pv c»p t^ t-^ y\ t^ p\ _c?\oo 00 b b b b b b b\ b\ bv bv on bv bv b\ b> cs on bs b cot bv bv bv bv 'ov o» bv bv Mt)Mt)c4Ht4t< 1* i 3 fo CO t^ M VO t~. O «^vO tJ- O t-^ « t~ b b b b b b b bv bv on b\ bv b^ b ^ o t-^ ■* t> « tJ- ^ t-^oo Ov M VO Ov t^vo Ov Ov O 00 00 t~^00 ov t^ tOVO r^ vrivo Ov^O V Ov bv OS bv bv bv bv b\ *ov bv bv bv bv t4t1r)Ht4r)NHc)HHt)t4 «o 1 <0 00 OvOO V bv bv bv b •ao)soa OOmtJ-OvOtI-O <^vO rl fo H t- VO »o »ovo t»vo ^rlrtrJHro'^H ■. O to t^ t^OO t^ tOVO OOOOVOHt^OVOO to rj- M c O « OO M vc ^ bv bv bv bv bv M M M M t) b\ bv ON bv b^ b\ b\ bv bv b\ bv bv bs b\ bv ctn bv bv bv bvoo bv bv bv bv c «Nc4MMMNNNrlc4c)M(4c)rS N »-• ONTj-t^Tj'Vo t^oo "I 00 •^ O O O « •-• O 00

jD tJ- ^^ tJ- ^ ,<>* y^ P P OO Ov t-^ t^OO OvOO s bv bv ON bv bv bv bv bv b b bv bv bv bv bv bv bv t to Q Ov to O •*0C Th w->\0 00 w 1^ O « O ^ tovo w-iOst^Tj-totoi-i voOOO H ►- O O '^ t» « O t^OO OO 00 0\ OVOO CTv Ov VO TJ-vO w-> ■ ov ■+VO ■* M M N t» t1- .^ u-, to V OVOO (X) _M M Ov V bv bv bv b b bv r) « M to to N 1^ ii M c« to ^ v>vd t^oo ov d M f< ro 4- «^vo r^oo Ov d « fJ to 4" vovd I'^-oo dv d m ««MM«MM„„MHe ECENT experiments have added largely to the class of facts AV that relate to the composition of colours, but nothing, as far as I am aware, has been done towards explaining the facts by any theory of light. The undulatory theory, if it be true, must admit of this application. In a communication to the British Association, published in the Report of 1834 (p. 544), I gave explanations in accordance with that theory of some facts relating to the composition of the colours of the spectrum, so far as to establish a presumption that an analogy exists between the composition of colours and the composition of small vibrations. T* > x ^ ^his subject I propose now to recur. There is a peculiarity about the class of facts to be explained which must first be noticed. Colour is a sensation, not a mate- rial existence. It is, however, certain that corresponding to every sensation of colour there must be definite physical circumstances. But experiment has proved that when the external circumstances are the same, the sensations are not always the same in diff"erent individuals. The difiierence consists for the most part in the absence in some of sensations perceived by the majority, as in J cases of colour-blindness. Admitting, for the moment, the truth i p; of the undulatory hypothesis of light, the undulations of the J; sether may be conceived to excite in the nerves of the eye vibra- |^ tions which in general correspond to the exciting undulations, 3 but, owing to peculiarity of organization, may in some cases r:f 1 g, deviate from this normal character ; for it cannot be imagined * Communicated by the Author. Phil Mag. S, 4. Vol. 12. No. 80. Nov, 1856. Z 880 Prof. Challis's Theory of the Composition of Colours that if the parts of the eye were acted upon by the setherial un- dulations in exactly the same manner in two individuals, the sensations would be diflferent. Now the undulatory theory of light ought to be capable of giving a reason for every positive sensation perceived by a great number of persons, but is not required to account for the absence of the sensation, or for a different sensation, in a few persons ; because it may be pre- sumed that these exceptional cases are due to causes unconnected with the laws of setherial undulations. In the undulatory theory of light, the formula which expresses the physical circumstances corresponding to the sensation of a pure colour is the following, — vrsmsmrr- {oe—at + c)f in which v is the velocity of a vibrating element of the aether at the distance a; measured parallel to the direction of the motion from a fixed origin, and at the time / reckoned from a given epoch, m is its maximum velocity, a is the velocity of propagation of the undulations, — is the time of one vibration backwards and a forwards, and c is a constant which is given when the velocity of vibration is given at a given position and a given instant. The theory assumes that the colour-sensation produced by a simple series of undulations depends only on \. Hence it may be theoretically inferred that the colours of a pure prismatic spectrum are uncom pounded. For experiment has proved that both the colour and the angle of refraction for a given angle of incidence depend, the substance being given, only on the value of X ; whence it necessarily follows from the above supposition that a ray of definite refrangibility is uncom- pounded. This is so strict a deduction from the undulatory theory, that if it should be contradicted by facts, that theory fails in limine. Two kinds of facts have been thought to contradict it ; one de- rived from the composition of colours, the other from phsenomena of absorption. The objections drawn from the former will be met in the course of this communication by showing that the phsenomena of the composition of colours can be explained on the supposition that the colours of the spectrum are pure. At present I will say a few words on the phsenomena of ab- sorption. We owe to Sir David Brewster the remarkable discovery, that a ray of a pure spectrum, on entering certain absorbing media which do not allow of its free transmission, may give rise to rays of various colours ; and to Professor Stokes the additional dis- on the Hypothesis of Undulations. 331 covery, that this effect is produced even by rays more refrangible than those of the visible spectrum. This property, without dimi- nishing the intensity of the colours which are freely transmitted, causes a peculiar dispersion to take place at the surface of the medium, and from points contiguous to the surface, the quality and quantity of which may be modified by the thickness of the absorbing substance. Do these facts, it may be asked, prove that a ray of definite refrangibility is composed of rays of differ- ent colours ? A good theory of light ought to give an answer to this question. Not being able to form the slightest conception how a theory of light which makes the vibrations of individual atoms of the sether the exponents of visible properties of light can be brought to bear on this point, I venture to state that the question may be answered if the undulatory theory be based on hydro dynamical principles. In the pages of this Journal I proved long since, by general hydrodynamical equations, that the function which, as stated above, expresses the properties of an uncompouuded ray, is not arbitrary, nor due to the mode of disturbance, but arises out of relations of a compressible fluid to time and space, which are shown by the analysis to be indepen- dent of particular disturbances. Consequently any disturbance proper for producing light will in general give rise to rays of all refrangibilities. When a ray of the spectrum enters an absorb- ing medium whose atomic arrangement does not allow of its transmission, the ray-undulations must be broken up, and the sether suffers disturbance by the action of the atoms at rest on the undulations, as really as when atoms by their motion disturb the sether at rest. According to this view, the generation of new light in an absorbing medium does not prove that the intromitted ray was compounded, since there is no resolution of the original ray, but a new disturbance. Now I think that I am right in saying that Sir David Brewster, in his examination of spectra produced by absorbing media, received this new (epipolic) light in conjunction with light freely transmitted ; and that, owing to this circumstance, the colour of the latter appeared modified. At least this inference seems to be justified by the experiments of M. Helmholtz, who proved that the modifying light is decom- posable by the prism, and got rid of the effect of it by insulating as much as possible the freely transmitted light (see Phil. Mag. S. 4. vol. iv. Dec. 1852). But M. Helmholtz does not appear to be aware that the experiments he made to account for what Sir David Brewster saw, were proper for getting rid of dispersed light peculiar to absorbing media, which originates in the ab' sorted rays and varies according to the degree of absorption, and that the insulation of the rays transmitted by the media was Successful in removing the dispersed light, just because these Z2 332 Prof. Challis's Theory of the Composition of Colours rays do not give rise to such dispersion. By taking into account that absorption generates in greater or less degree epipolic dis- persion, all the phsenomena witnessed by the two experimenters may, 1 think, be explained consistently with the principle that a ray of definite refrangibility is uncompounded. I proceed now with the theory of the composition of colours. The analytical formula which expresses that a ray is com- pounded of two or more simple rays is the following : — t;=»isin — (a?— «/4-c)+m'sin^(ar — ff^ + c')+ &c. Assuming now that composition of colours corresponds to com- position of setherial undulations, the following explanations are given by the undulatory hypothesis of the leading facts which ob- servation has established respecting the composition of colours: — (1) The general fact of the composition and resolution of colours is explained by the principle of the coexistence of small vibrations on which the above formula depends. (2) The result of compounding any number of undulations for which \ is the same, is a series of undulations expressed by o__ the formula V=M sin— - (a?— «^4-C), in which V is the alge- braic sum of the separate velocities, and M is a function of m, m'y &c., and of the phases c, cf, &c. of the component undula- tions. Accordingly it is found by experiment that the compo- sition of rays of a given colour produces a compound ray of the same colour. The coefiicient M, which involves c, c*, &c., must, however, be distinguished from the coefficient m of a simple series of undulations. (3) If the values of v at a given time be represented by the ordinates of a curve of which the abscissae are the values of so^ this curve will in general cut the axis of ^ in a great number of points with irregular intervals between them. When this is the case, the result of the composition of the different rays is white light, and the degree of whiteness is greater the greater the irre- gularity. There is here a strict analogy to sound-sensations* As sounds are not all musical, so light is not all coloured. It may be admitted, that as colour in a simple ray is due to regu- larity of wave-intervals, so in every instance of the production of colour, the sensation is due to some species of regularity of recurrence in the waves. It may also be remarked, that the irregularity to which whiteness is due exists whatever epoch be selected, and consequently that whiteness is independent of the phases of the component undulations. This is known to be the case from experience. . (4) The effect of compounding two simple colours is expressed on the Hypothesis of Undulations, 333 in this theory by the formula *q»ih rf^rf« ot e^rf 3vr«. v=msinrr- (w^at + c) +m'sin— y {cc—at-rc'). Let m'=m + ^, i-=|(l + y,andi=l(i-^). Then, the time being given, the expression may be put under the form v = 2msm{-j- +Cilcosf-y- H-Cg I +/ism( — p +C3 j. A At present we will leave out of consideration the term contain- ing /JL. The other term taken by itself shows that the axis of x will be cut by the curve at a series of points separated by the common interval L, which is an harmonic mean between \ and X', and at another series of points separated by the common interval /. As the ratio of the greatest and least values of \ for light is nearly that of 3 to 2, / will be at least equal to 5L. Hence the second series of recurrences will always be slower than the first ; and in case \' be not much larger than \, they will be much slower. The following considerations will show that in this case this second trigonometrical factor will have little or no sensible effect on the quality of the compound light. It is known from experiment, that if a stream of light be interrupted at short intervals by breaks, the sensation of light is still continuous. Suppose, therefore, the parts of the curve contiguous to those points of its intersection with the axis of ic which depend on the second factor, to be suppressed ; the remaining portions will have the quality of regularity of recurrence which is necessary to pro- duce colour, and the colour will plainly correspond to the wave- length L, which is intermediate to X and X'. The suppressed portions, not satisfying the condition of regularity of intervals, may cause a sensation of whiteness, and thus have the effect of diluting the colour. These theoretical deductions agree exactly with a law first given by Newton as a result of experiment, viz. that " if any two colours be mixed, which in the series of those generated by the prism are not too far distant from one another, they, by their mutual allay, compound that colour which in the said series appeareth in the midway between them.^^ This law is confirmed by the experiments of M. Helmholtz. (Phil. Mag. S. 4. vol. iv. p. 532.) According to the theory, the condition that m = m! must be approximately fulfilled. The effect of the term containing //, will be to introduce irregularity of intervals, and therefore whiteness ; 884 Prof. Challis's Theory of the Composition of Colours and if /L6 be considerable, the whiteness may overcome the sensa- tion of colour. Also it is evident, that, to produce the interme- diate colour, the quantities of the two colours must be mixed in certain proportions. The eflfect of an excess of one of the colours will be to alter the tint ; but as the change of tint must be con- tinuous, the only change that can occur is an approach of the compound colour to that of the rays which are in excess. Speak- ing theoretically, the intermediate colour is most perfectly pro- duced when the number of rays of each kind is the same, and when m=m' for each pair of rays. (5) The following passage occurs in Sir John HerschePs Treatise on Light (art. 516): — "Blue and yellow combined produce green. The green thus arising is vivid and rich ; and, when proper proportions of the elementary colours are used, no way to be distinguished from the prismatic green. Nothing can be more striking, and even surprising, than the effect of mixing together a blue and yellow powder, or of covering a paper with blue and yellow lines drawn close together and alternating with each other. The elementary tints totally disappear, and cannot even be recalled by the imagination. One of the most marked facts in favour of the existence of three primary colours, and of the possibility of an analysis of white light distinct from that of the prism, is to see the prismatic green thus completely imitated by a mixture of adjacent rays totally distinct from it both in refrangibility and colour." According to this statement, a mix- ture of blue and yellow powders has the same effect as a mixture of blue and yellow light ; for in the second mode of making the experiment, it is clear that the eye receives a mixture of blue and yellow rays. I have made this experiment in another manner, by placing one upon the other two pieces of blue and yellow rib- bon, and holding them up to the light. The resulting green is very decided, and is plainly due to a mixture of lights. M. Helmholtz has established by his experiments, that the mixing of coloured substances produces effects different from those of mixing prismatic colours, and in particular that prismatic blue and yellow do not produce green, or only a greenish-white. The existence of green, in however small a degree, is a phsenomenon which the theory ought to account for, and which in fact it does account for in the manner explained in art. (4). Why the green is so much less conspicuous than the white will be shortly con- sidered. At present it is important to remark, that the experi- ment above adduced proves that blue and yellow light may pro- duce a vivid green. Consequently it must be concluded that a difference of some kind distinct from tint exists between the blue and yellow of that experiment, and prismatic blue and yellow. Now the theory I am proposing involves a mathematical condition on the Hypothesis of Undulations. 335 which points to such a difference. It is possible that, in the prismatic colours, the condition m—m! may be less exactly ful- filled than in the colours of substances. A probable reason may be given for such a circumstance. Sunlight is generated within the sun's atmosphere at a great depth below the exterior bound- ary, and the ray- undulations have consequently to traverse a medium which may absorb them in different degrees according to the value of X. The absorption might stifle particular rays, and change the value of m for others ; and if one colour, as yellow, were transmitted more readily than the rest, the value of m for this colour would be larger than for the others, supposing that originally m was the same for all. Thus the excess of brightness in the yellow part of the spectrum may be owing, not only to a greater number of yellow rays, but also to greater intrinsic brightness of each yellow ray. Now the coloured light of substances, though derived from sunlight, is yet new light, because it is produced at their surfaces, or within a small depth below their surfaces, by disturbances of the solar undulations similar to those already described with reference to absorption, which is, in fact, a phsenomenon of the like kind, differing only in degree. This terrestrial light, not having passed through a large extent of atmosphere, may satisfy the condition m=m', and in this respect differ from solar light, for which the value of //< in a mixture of blue and yellow rays may be consider- able. Such a difference would account for the more complete production of green by the blue and yellow of terrestrial sub- stances, than by the blue and yellow of solar light. Our theory shows that there would be no reason to conclude, from even a perfect imitation to the sense of green by a mixture of yellow and blue, that the green of the spectrum is a compound colour. (6) " Red with green gives a yellow, which, less saturated, is paler than the simple yellow." "Green gives with indigo a bright blue, which, however, is much duller and whiter than that of the spectrum ; with violet also it gives a bright blue." (Helm- holtz, Phil. Mag. pp. 525 and 526.) These facts, which relate to the colours of the spectrum, are in accordance with the theory. The dullness and whiteness of the resulting colour is owing, not only to the difference of wave-lengths of the components, but also to difference in the intrinsic brightness of the individual rays. For it may be remarked, that in the combination of colours, the wave-lengths of which differ considerably, the result is more de- cidedly coloured in the above instances than in that of the mix- ture of yellow and blue, although in this combination the differ- ence of wave-lengths is not so great as in the others. The excess of whiteness of the blue and yellow compound may there- 336 Prof. Challis's Theoiy of the Composition of Colours fore be ascribed to a large value of fi, that is, to a large diflference of intriusic brightness in the two kinds of rays. / ju .,li ui /it (7) The following is, according to this theory, the explanation of the conjplementiu'y colours of the solar spectrum. We have seen that when the ratio of X to \' for two colours does not differ much from a ratio of equality, the result of combining the colours is an intermediate colour with a mixture of whiteness. In pro- portion as that ratio deviates more from a ratio of equality, the whiteness will increase, because those points of intersection of the (2'n'x \ —J- +^2 ) in art. (4) will be brought nearer to each other and produce a greater amount of irregularity. Consequently there must be some ratio of \ to X' for which the whiteness so predominates as to destroy all colour. "When this ratio is reached, the colours become complementary. Since we are dealing v^th sensations, it is not too much to assume that sensations produced by undula- tions of the aether have some analogy to sensations produced by undulations of the air. Respecting musical sounds, we know that if \ and X' for two such sounds differ very little from each other, the result of the combination is to the sense musical. On increasing the difference, beats begin to be heard, which corre- spond to incipient whiteness. On still further increasing the difference, we reach complete discord, or unmusical noise, answer- ing to perfect whiteness. M. Helmholtz has given (Poggendorff^s Annalen, vol. xciv.) the following interesting results respecting the ratio of the wave-lengths of complementary colours :- >inRf}n''0'^ '3iM iu 'yr> 'nit to >•>! •■•,'An jiiT >lJr;'Ki.'/-3iW lO il'ii { Colour. Wave-length. tJomplementary colour. Wave-length. *]^atioo^wave-' lengths. Red. 2425 fireen-blue. 1818 1-334 Orange. 2244 Blue. 1809 1-240 Gold-vellow. 2162 Blue. 1793 1206 Gold-yellow. 2120 Blue. 1781 1190 Yellow. 2095 Indigo-blue. 1716 1-221 Yellow. 2085 Indigo-blue. 1706 1-222 Green-yellow. 2082 Violet. 1600 1-301 These experimental results show that the ratio of the wave- lengths of the complementary colours of the spectrum varies from about the ratio of 4 to 3 for red and green-blue, to about the ratio of 6 to 5 for gold-yellow and blue. The production of whiteness with a less difference of wave-lengths in one combination than in another would, according to this theory, be due to a greater difference of intrinsic brightness of the component rays. We have already given a probable reason for concluding that this difference may be greatest when yellow, the predominant colour x'm»i>Wvl \y> vn the Hypothesis ofUndulationsiJl'Ati' 337 of sunlight, is one of the components. The explanation given by the theory of there being no prismatic colour complementary to green is, that there is no colour the ratio of whose wave-length to that of green can be expressed by sufficiently low numbers. (8) Again, it may be remarked, that, in sound-sensations, the combination of waves whose leng-ths are in the ratio of 4 to 3 produces harmony; whilst, according to this theory of colour- sensations, the same ratio of wave-lengths of yellow and blue results in whiteness, which is analogous to unmusical noise. There is, however, a remarkable fact bearing on this point which must be taken into consideration. On proceeding to still greater differences of wave-lengths, when. we come to a combination of red and violet colours, the ratio of whose wave-lengths is nearly that of the low numbers 3 and 2, the result is purple, a decided colour, in which the eye seems to be able to distinguish the com- ponents, as the ear distinguishes the components of a harmony. The analogy to sound here returns, with the difference that light- harmony does not appear to have so wide a range as sound-har- mony. Possibly rose colour may be a harmonious result from a mixture of wave-lengths of red and blue in the ratio of 4 to 3. (9) The method of combining colours by a painted revolving disc, and that of receiving in the same direction colours trans- mitted through, and reflected from, plate-glass (Helmholtz, Phil. Mag. p. 530), are, theoretically speaking, methods of varying the relative intensities of the two kinds of rays, and the value of the difference /jl for each pair. In the case of the revolving disc, in which different kinds of impulses act in succession, the degrada- tion of the vibrations of the particles of the eye in the compara- tively large interval between one kind of impulse and the next succeeding one, is equivalent to a difference in the values of m and m' for two kinds of impulse which take effect simultaneously. The amount of difference, or the value of fju, depends on the velo- city of the motion of the disc. It is probable, however, that suc- cessive impulses can in no case be exactly equivalent to simul- taneous impulses, because in the former the individual rays admit of being combined so that the intervals between the impulses will be different for each pair. It is also to be observed, that in the other experiment, when the intensities of the two parcels of light are so adjusted that neither colour is predominant, the values of m and m' for the individual rays will generally be un- equal, because the intrinsic intensity of a reflected ray is, ceteris paribus, less than that of a transmitted ray. Hence a tendency to whiteness in the compound may be expected. Several other inferences drawn by M. Helmholtz from his expe- riments are in accordance with this theory. For instance, that the extreme colours of the spectrum, red and violet, cannot be com- 338 Prof. Clausius on the Application of the Mechanical pletely imitated by any combination ; that the theory of three primitive colours must be abandoned, the colours produced by the combinations of any three being not so pure and vivid as those of the spectrum; and that white can be obtained in an, infinite number of ways without the eye being able to distinguish one white from another. In fact, the number and variety of the explanations of this class of phaenomena given by the undulatory theory may be adduced as a confirmation of its truth. No other theory of hght has made the least approach to such explanations. Cambridge Observatory, October 10, 1856. XLII. On the Application of the Mechanical Theory of Heat to the Steam-engine. By R. Clausius. [Continued from p. 266.] 27. ^T^HE influence exercised by the difference of pressure in -I- the boiler and cylinder upon the work performed has hitherto been most completely treated of by Pambour in his work on the Thiorie des Machines a Vapeur, Before entering upon the subject myself, therefore, I may be allowed to state the most essential parts of his treatment, altering only the notation, and neglecting the magnitudes which have reference to friction. By this means it will be easier, on the one hand, to judge how far this treatment is no longer in accordance with our more recent knowledge of heat, and, on the other, to add to it the new method of treatment which, in my opinion, must be substituted for the former one. 28. The two laws which, as was before mentioned, were for- merly very generally applied to steam, form the basis of Pam- bour's theory. The first of these is Wattes law, according to which the sum of the latent and sensible heat is constant. Prom this law it was concluded, that when a quantity of steam at its maximum density is enclosed within a surface impenetrable to heat, and the volume of the enclosing space is either increased or diminished, the steam will neither become over-heated nor partially condensed, but will remain precisely at its maximum density ; and it was further assumed that this would take place quite independently of the manner in which the change of volume occurred, whether thereby the steam had, or had not, to overcome a pressure corresponding to its own expansive force. Pambour supposed that the steam in the cylinder of a steam-engine de- ported itself thus ; and at the same time he did not assume that the particles of water, which in this case are mixed with the steam, could exert any appreciable influence. Further, in order to establish a more accurate relation between Theory of Heat to the Steam-engine, 339 the volume and the temperature, or the volume and the pressure of steam at a maximum density, Pambour applied, secondly, Mariotte's and Gay-Lussac^s laws to the same. If, with Gay- Lussac, we assume the volume of a kilogramme of steam at 100° C, and at its maximum density, to be 1696 cubic metres, and reflect that the corresponding pressure of one atmosphere amounts to 10,333 kilogrammes on every square metre, then from the above law we obtain the equation M * ' " , ^_ 10333 273 + ^ ,^Q, , = 1.696.-^.^-^3-^, .... (28) where, with reference to the same units, v and jo represent the volume and the pressure corresponding to any other tempera- ture t. Herein it is only necessary to substitute in place of ^ the values given in the tension series in order to have, according to the above assumption, the proper volume for each temperature. 29. In order, however, to be able conveniently to calculate the value of the integral Jpdt which plays an important part in the formula for the work done by a steam-engine, it was necessary to find the simplest possible formula between v and p alone. If, by means of the ordinary empirical formulae for jt?, the tem- perature t were eliminated from the above equation, the results would prove to be too complicated; hence Pambour preferred forming a special empirical formula for this purpose, to which, according to the process of Navier, he gave the following general form : — b+p ^ ' wherein B and b are constants. He then sought to determine these constants, so that the volumes calculated from this formula might agree as nearly as possible with those calculated from the foregoing one. As this could not be done with sufficient accu- racy, however, for all the pressures which occur in steam-engines, he established two different formulae for machines with and with- out condenser. The first of these was 20000 .^^ . ^=i200T^' (^^^) which agrees best with the above formula (28) between f and 3^ atmospheres ; but is also applicable for a somewhat wider interval, from about ^ to 5 atmospheres. ■ >. . ; 340 Prof. Clausius on the Application of the Mechanical The second^ for machiues without oondenseFs^ is- - m . "^aoao^'^ • • • • (^^*^ which is most correct between 2 and 6 atmospheres, though the range of its applicability extends from about I5 to ]0 atmo- spheres. • i!'»;ii // k'-,ai 8HiJ .^ txli h 30. The magnitudes dependerit ti^on the dimensions of the steam-engine, which enter into the determination of the work, shall be here^ somewhat differently from Pambour's method, represented in the following manner. Let vf be the whole space left free to the vapour during a stroke in the piston, the vicious space being also included. Let the vicious space form a frac- tional part € of the whole space, so that this space itself will be represented by et/, and that described by the surface of the pis- ton by (1— e)r'. Further, let the part of the whole space left free to the vapour up to the moment of disconnecting the cylinder and boiler (also inclusive of vicious space) be represented by ei/. Consequently the space described by the surface of the piston during the entrance of the vapour will be expressed by {e—e)vf, and that described by the same during expansion will be (1 —e)v^. In order to determine, in the next place, the amount of work done dunng the entrance of the vapour, the pressure acting in the cylinder during this time must be known. This is at any rate smaller than the pressure in the boiler, otherwise no influx of vapour could occur ; but the magnitude of the difference can- not in general be stated ; for it depends not only upon the con- struction of the engine, but also upon the engine-driver, how far he has opened the valve in the tube leading from the boiler, and with what velocity he drives the machine. These things being changed, the above difference may vary between wide limits. Further, the pressure in the cylinder need not be con- stant during the whole time of influx, because the velocity of the piston may vary, as well as the magnitude of the influx orifice left free by the valve or the slide. With respect to the last circumstance, Pambour assumes that the mean pressure to be brought into calculation in determining the work may, with sufficient accuracy, be set equal to that which exists in the cylinder at the end of the influx, and at the moment of disconnexion from the boiler. Although I do not think it advisable to introduce such an assumption — which is only adopted for numerical calculation in the absence of more certain data — at once into the general formulae, yet here, whilst explaining his theory, I must adopt his method." —y.^' Pambour determines the pressure existing in the cylinder at the moment of disconnexion by means of the relation, established Theory of Heat to the Steam-engine, 341 by him, between volume and pressure ; assuming at the same time that the quantity of steam which passes from the boiler into the cylinder in a unit of time, and therefore the quantity which passes during a stroke of the piston, is known from special observations. As before, we will represent by M the whole mass which enters the cylinder during a stroke, and by m the vaporous part of the same. As this mass, of which Pambour only con- siders the vaporous part, fills the space ev^ at the moment of dis- connexion, w^e have, according to (29), the equation m.B - ^ ^■■- "^^ bTK^ where jt?2 represents the pressure at the same moment. From this equation we deduce vsiiq adtlo 'X>'6kFr« ^)d^ v >, _- ^ •-" _^, in 'p 7(f ?yv ^ /^q\ f\-- - ' - ' ' ^^ ev' . . J . • . . V 7 " Multiplying this magnitude by (e— e)i;', the space described by the surface of the piston up to the same moment, we obtain the following expression for the first part of the work : — ■hi iuiroif' ^ The la;w according to which the pressure changes during the expansion which now follows, is also given by equation (29). If at any moment v represents the variable volume, andj»? the cor- responding pressure, then «ij,oa aiiti iioqi; ^1^0 ioii aiiU'^^ m.B ^irjt^jg ttd inT^n^-'^ ai ton His expression must be substituted in the integral ['^ ^^^^ ^^ , ■ ^biw nadv/ii)d yifiv VJiXH aoipjftlf^ avodii sdt ,bo2flfiilD ^nxod and the integration effected between the limits v = ev^ SLiid.v:=v^; whence, as second part of the work, we obtain ■W2=mB.logi --v'(l--e>&.^4fi'^?^nYt^(^> 'lii order 'to' detefmihe the negative work doiie by the reacting pressure during the descent of the piston, this reaction must itself be known. Without at present inquiring into the relation which exists between the reaction and the pressure in the con- denser, we will represent the mean reaction by /?o, so that the work done by it will be expressed by There yet remains the work necessary to convey the quantity M of liquid back again into the boiler. Pambour has not sepa- 842 Prof. Clausius on the Application of the Mechanical rately considered this work, but has included it in the friction of the machine. As I have included it in my formulse, however, in order to have the cycle of operations complete, 1 will also here add it for the sake of easier comparison. As shown by equations (21) and (22), estabhshed in a former example, this work will on the whole be expressed by W,= -M(2) To condense the part m^ at the temperature TJ^' 3'>i7fi*/Jii9 !-:•;> '^in .mi iiiiii e5iJO-iuqii£^6! .; ic y-s ^t'^^^l ^^^ J:i4ff»«0qqu** Sff .(f^X TP cool the part f* from T^ to To,'oa *in bnc liroqs/ ^idi V ..; > . a — /ic(T2--To). ' - ' ^^-^^'^ :?2mvlqn« ^m ^'<4) To evaporate the part fir. at the temperature Tii''"^^^^ ?f^-4] Hence me total quantity of heat, .rf aw ^jA :i\ji\d 311 , Q=m,^.-mjr-, + Mc(T,-T,)-|^/2^Jv,-2';;tc(t-tyi • (36)^,, The quantities of work may be found as follows : — -f ^ (1) In order to find the space described by the surface of the piston during the entrance of the vapour, we know that at the end of that time the whole mass M + /-t occupies the space ^ fS\ "t'>^ Ji nh By adding these four magnitu^^^, 7\^^ql^,^f^ij\ fei;.tli^ ^.Me jYPrls; W. the foUowing expression :-r-^^x^ ^^^ ^4^ x.,ifu/i«i niiUr ul ,1 S W=m2«2(yi.-;?2)-Ma-(;?i-yi)->oWo(;'i'-;'o)- • (37) PhiL Mag. S. 4. Vol. 12. No. 80. Nov, 1856. 2 A 846 Prof. Clausius on the Application of the Mechanical If in the equation (1), which was Q=A.W, we substitute the values of Q and W thus found, and then bring the terms involving m^ to one side of the equation, we have m^[r^ + Au^(p'i-'Pi)'] =miri + Mc(Ti-T2) +/Xoro-/Ac(T5-To) + Aii,ono(p'i-Po)'^AMa{p,^p',) (XIII) By means of this equation the magnitude m^ is expressed in terms of other magnitudes, all of which are supposed to be given. 35. If the mean pressure ^j were considerably greater than the final pressure p^, it might happen that the value of m^ would be less than nti + fiQ, which would denote that a part of the vapour originally present had become condensed. This would be the case, for instance, if we were to suppose that, during the time the vapour was entering the cylinder, the pressure there was nearly equal to that in the boiler, and that by the expansion of this vapour already in the cylinder, the pressure ultimately sunk to the smaller value jo^. On the contrary, if jo'j were but a little greater, or indeed smaller than j[?2> ^^^^ ^^^ ^2 ^^ should find a value greater than mj + /Zq. The latter ought to be considered as the rule in steam-engines, and amongst others it holds for the special case oipf^-=p^ assumed by Pambour. We have thus arrived at results which differ essentially from Pambour's views. Whilst he assumes that the two different kinds of expansion which successively take place in the steam- engine are governed by one and the same law, according to which the original quantity of vapour is neither increased nor diminished, but always remains exactly at its maximum density, we have found two different equations which point to different deportments. By the equation (XIII), fresh vapour must be produced by the first expansion during the entrance of the steam ; and according to the equation (VII), a part of the then existing vapour must become condensed when the further expansion takes place, after disconnecting the cylinder and boiler, during which time the work done by the vapour corresponds to its full expansive force. As these two opposite actions, consisting of an increase and a diminution of vapour, which must also exercise opposite influ- ences on the work performed by the machine, partially cancel one another, the ultimate result may, under certain circumstances, be approximately the same as that to which Pambour's simpler assumption leads. We must not, however, on this account ne- glect to consider this difference when once established, especially if we wish to ascertain in what manner a change in the construc- tion or driving of the steam-engine will affect the magnitude of its work. W^w^ Theory of Heat to the Steam^enffine*^ *"'^^ 347 86. According to what was said in § 8, we can easily deter- mine the uncompensated transformation which occurs in the ex- pansion by referring the integral contained in the equation N=-J$ to the several quantities of heat expressed in § 34. The quantities of heat m^r^, —m^r^, and /jlqTq are imparted at the constant temperatures Tj, Tg, and Tq, so that these parts of the integral are, respectively, ^1^1 ^2^9 and '^0^*0 Ty' T^' ^"""^ To' The parts of the integral arising from the quantities of heat Mc(Ti — Tg) and /u-c(Tg— Tq), are found, by the method adopted in § 23, to be T T Mclog^ and - fic log rfr- ig ■'•0 ^ By putting the sum of these magnitudes in place of the above integral, we obtain for the uncompensated transformation the value N=-^' + ^_Mclog^-^ + ^logJ. . (38) ■■■1 -*-2 ^2 ■•^O ■*^0 37. We can now return to the complete circular process which occurs in an acting steam-engine, and consider the several parts of the same in the same manner as before. The mass M, of which the part m^ is vaporous and the rest liquid, issues from the boiler, where the pressure is supposed to be jOp into the cylinder. As before, the mean pressure acting in the cylinder during this time shall hep'^, and the final pressure jo^. The vapour now expands until its pressure sinks from p^ to a given value p,^j and consequently its temperature from Tg to Tg. After this the cylinder is put in communication with the con- denser, where the pressure is jOq, and the piston returns through the whole of the space it has just described. When the motion is somewhat quick, the reaction which it now experiences will be somewhat greater thanjOQ ; to distinguish it from the latter value, we will represent the mean reaction by ^0- Similarly, the pressure of the vapour which remains in the vicious space after the piston^s motion is completed will not ne- cessarily be equal either to p^ or to jo'q, and must consequently be represented by another symbol jo%. It may be greater or less than p'q, according as the communication with the condenser is cut off somewhat before, or somewhat after the conclusion of the piston's motion ; for in the first case the vapour would be a little 3A2 348 Prof. Clausius on the Application of the Mechanical further compressed, whereas in the latter case it would have time to expand a little more by partially passing into the condenser. Lastly, the mass M is conveyed back from the condenser into the boiler, when, as before, the pressure Pq acts favourably, and the pressure jji has to be overcome. 38. The expressions for the amounts of work done in these processes will be quite similar to those in the simpler case before considered, except that a few simple changes in the indices of the letters will have to be made, and the magnitudes which refer to the vicious space will have to be added. In this manner we obtain the following equations. For the time during which vapour passes into the cylinder, we have, according to § 34, W, = Kw2 + Mcr-/iXoyu • • • (39) where m"o is simply substituted for Wq. By putting M + /i- in place of M, we have, from equation (IX), for the expansion from the pressure p^ to the pressure p^, ■W« = m^;73-»l2W2;?2-t-T Kr2-.W^g+ (M+/a)c(T2-T3)]. (4^) /^ 0.3 yd For the return of the piston, during which time its surface tra- verses the whole space occupied by the mass M + />«, at the pres- sure jOg, diminished by the vicious space /jLQu!'Q + fjLa, we have W3=-(m3W3 + Mo— /^ott"o)/o. . . . (41) Lastly, for th^ conveyance of the ma^s M back into the boiler, we have );jyolt|^9 t)di mo;i't bjawUU* od bi0oo Consequently the whole work is W= ^K^2-^3^8+ (M-f7/i)c(T2-T3)] +m2«2(y,-;>2) 1 ^ [. (43) The masses mg and wzg which are here involved, are given by the equations (XIII) and (VII), if in the former we put p''^ in the place o( Pq, and change the magnitudes Tq, t-q, and Uq in a similar manner, and in the latter we substitute M + z^forM. Nevertheless, although it is possible to eliminate 7n^ and m^ by means of these equations, I will here merely replace w^ by its value ; it being more convenient in calculation to consider the equation which thus results in connexion with the two before obtained. The following, therefore, is the most general form of the system of equations which serve to determine the work of ,t)ie^^te«^m-engine ; — ^^ (XIV) \^*i>wi!V»\ Theory of Heat to the Bteam^engim) •N't*"! 349 + ?/i3W3(;?3-/o) +/^oA(Fo-y o)-M(r(/o-i?o) ' ^;^:)£-*y.c(T2 -n) + A/.o^"o(y 1 -A) + AM(7( ;?, --p\) ^ = ^ + (M +/i)c log ^2.^.1. ;^^: ii *.£{ Ar ^39. Before endeavouring to render these equations more con- venient for application, it may not be without interest to show how, for an imperfect steam-engine, the same expressions may- be arrived at by a method before alluded to, and opposite to the one just applied. In order to avoid prolixity in this digression, however, we will only consider two of the imperfections provided for in the above equations, viz. the presence of vicious space, and the existence of a smaller pressure in the cylinder than in the boiler during the time that the vapour is passing into the former. On the other hand, we shall assume the expansion to be com- plete, therefore Tg=To, and the magnitudes T^, T'^, and T"q to be equal. In this determination we shall have to employ the equation (2), to which we will give the following form : — The first term on the right-hand side of this equation denotes the work which could be obtained from the employed quantity of heat Qi, which in our case is represented by m^r-^ + Mc(Ti — TJ, did not two imperfections exist. This term has been already calculated in § 23, and found to be i[m.r, + M '' Substitut^§^%^j|)^o^^^^fg^OKiflH,,^g^fgregoin^ equation. we have ^._ ,, -iirno'-b ^^^ MriiK^oq. ^r ?j rfer/aii ■ W'= i[m,.,~^%r,-hMc(T,-To)-(M + /.)cTolog|^ +^,r,]. That this equation actually coincides with the equations (XIV), may be easily seen by using the third in order to eliminate % from the first, and then setting T3=To=T^o=T'o. In the same manner we might make allowance for the loss of 850 Prof. Clausius on the Application of the Mechanical work occasioned by incomplete expansion. To do so it would only be necessary to calculate the uncompensated transformation produced in the passage of the vapour from the cylinder to the condenser, and to include the same in N. By this calculation, which need not here be executed, we obtain precisely the expres- sion for the work which is given in (XIV). 40. In order next to be able to apply the equations (XIV) to a numerical calculation, it will be necessary first to determine the magnitudes pf^y p'q, and jo"q more precisely. "With respect to the manner in which the pressure in the cylinder varies during the entrance of the steam, no general law can be instituted, because the entrance canal is opened and closed in such a variety of ways in different machines. Hence no defi- nite universal value can be found for the relation between the mean pressure />',, and the final pressure p^, as long as the latter is strictly interpreted. Nevertheless this will be possible if the signification of ^^^ be slightly changed. The cylinder and boiler cannot of course be instantaneously disconnected ; more or less time is always required to move the necessary valves or slides, and during this interval the vapour in the cylinder expands a little, because, the orifice being diminished, the steam which enters is less than that which corresponds to the velocity of the piston. In general, therefore, we may assume that at the end of this time the pressure is already somewhat smaller than the mean pressure y,. But if, in calculation, instead of restricting ourselves to the end of the time necessary for closing the entrance canal, we allow ourselves a little freedom in fixing the time of disconnexion, we shall be able to obtain other values for p^. We can imagine the point of time so chosen, that if, previously to the same, the whole mass M had entered, the pressure at that moment would have been precisely equal to the mean pressure calculated up to the same time. By thus substituting the more definite momentary disconnexion in place of the actual gradual one, we incur but an insignificant error, as far as the amount of work is concerned. We may therefore adopt this modification of Pambour's assump- tion, and set p'l =Pq, reserving, however, for special consideration in each particular case the proper determination, according to the existing circumstances, of the moment of disconnexion. 41. With respect to the reaction p'q at the return of the piston, •'it is evident that, under otherwise equal circumstances, tne dif- ference^Q— j9q will be smaller the smaller Pq is. In machines ,with a condenser, therefore, it will be smaller than in machinegj without a condenser, where p^ is equal to one atmosphere. In locomotives, the most important machines without condensers, there is usually a particular circumstance tending to magnify \^m. Theory of Heat to the Steam-enffine* 351 this difference. The steam, instead of being allowed to pass off into the atmosphere through a tube as short and wide as possible, is conducted into the chimney and there made to issue through a somewhat contracted blowpipe in order to create an artificial draft. In this case an exact determination of the difference is essen- tial to the accuracy of the result. In doing so, regard must be had to the fact, that in one and the same machine the difference is not constant, but dependent upon the velocity with which it works ; and the law which governs this dependency must be ascertained. - Into these considerations, and into the investiga- tions which have already been made upon the subject, I will not here enter, however, because they do not concern the mechanical theory of heat. In machines where the vapour from the cylinder is not thus employed, and particularly in machines with a condenser, jo'q dif- fers so little from Pq, and therefore can change so little with the working velocity, that it is sufficient for most investigations to assume a mean value for jo'q. Seeing, further, that the magnitude p^ occurs only in one term of the equations (XIV), which term involves the factor <7, it can have but a very small influence on the amount of work j so that without hesitation we may put, in place of jOq, the most probable value oip'^. As already mentioned, the pressure /?% in the vicious space may vary very much, according as the cylinder is cut off from the condenser before or after the end of the piston^ s motion. But here, again, in equation (XIV), this pressure, and the magni- tudes dependent thereon, occur only in terms which involve the small factors fi and //-q ; so that we may dispense with an accu- rate determination of this pressure, and rest satisfied with an approximate evaluation. In cases where no particular circum- stances are present to cause p"q to differ essentially fromjo'^, their difference, like the difference between p'^ andjOg, may be neglected, and the most probable value of the mean reaction in the cylinder may be assumed as the common value of all the magnitudes. This value may be represented simply by jOq. By introducing these simplifications, the equations (XIV) become W= ];Kn-m37-3+Mc(Ti-T3)+/.o^o-/^in>ni\f .(it Of the four pressures, only two, /), and/?Q, can be assumed as known. The first is given immediately by the manometer on the boiler, and the second may at least be approximately deduced from the indications of the manometer attached to the condenser. The two others, p^ and p^, are not given ; but in their place we know the dimensions of the cylinder, and at what position of the piston the cylinder is cut off from the boiler. From these we may deduce the volumes occupied by the steam at the moment of disconnexion and at the end of the expansion, and these two volumes will then serve as data in place of the pressures p^ and j^g. We must now bring the equations into such a form that the (lYr calculation may be made by means of these data. 43. Let v'j as in the explanation of Pambour's theory, again be the whole space, including vicious space, set free during one stroke in the cylinder ; ei/ the space set free up to the time of disconnexion from the boiler ; and ev' the vicious space. Then, according to what was before said, we have the following equa- tions : — , f i 'kiiiQai auujo oiij ill ^^ 'i^-^ta 4'(M + /A) HScrndffrB*^ -^o rrofinrfRfny^ odi al ^r? ^ JaJ M ...,.,, 44. In order to refer these equations, which now express the work done in a stroke or by the quantity m^ of vapour, to the unit of weight of vapour, we have to proceed in the same manner as when the equations (35) were changed into (XII) ; that is to say, we divide each of the three equations by m^j and set M v' W Hereby the equations become '(XVI) b9l§9ff. W: r, + lc{T,^T,) -(V-/nii yjij m /jovi-o yn wiModi "to ^^i}iur (XVII) 854 Mr. A. Cayley on the Theory of Logarithms, equation, afterwards the temperature Tg from the third, and lastly, we employ all these to determine the work from the first equation. In doing so, however, we encounter a peculiar difficulty. In order to calculate T, and Tg from the two last equations, they ought in reality to be solved according to these temperatures. But they contain these temperatures not only explicitly, hut implicitly, p and g being functions of the same. If, in order to eliminate these magnitudes, we were to replace p by one of the ordinary empirical formulae which express the pressure of a vapour as a function of its temperature, and g by the differential coeffi- cient of the same, the equations would become too complicated for further treatment. We might, it is true, like Pambour did, help ourselves by instituting new empirical formulae more con- venient for our purpose, which, if not true for all temperatures, would be correct enough between certain limits. Instead of here entering into such experiments, however, I will draw attention to another method, by which, although the calculation is some- what tedious, the several parts of the same are capable of easy execution. [To be continued.] XLIII. Second Note on the Theory of Logarithms. By A, Cayley, Esq,^ THE theory of logarithms, as developed in my first note (Phil. Mag. April 1856), may be exhibited in a clearer light by considering, instead of log a + log 3 — log ai = E7n, the equation log— =log6 — log« + E7ri, a form which more readily enables the accounting a priori for the discontinuity in the value of E. Writing then for b, a the complex values oJ + y*, x + yi, we have log-^^=log (^4-/i)-log (ar-hy«) +E7ri; x-ryi where, according to the assumed definition of a logarithm, log {pB + yi) = log \^x^ + y^ + i ( tan" ^ - + evr J, in whicn Idg V'a?*-!-^* is the real logarithm of \/a?^-f-y*, and tan~* — is an arc between the limits — tt* + tt^ The coefficient X 3 2 e is equal to zero when x is positive ; but when x is negative, then esE-hl or —1, according as y is positive or negative, ^0«Si'Vii^>ii.|;iyiliOommunicated by the Author. Mr. A. Cayley on the Theory of Logarithms. 355 i. e, we have (iioTi g'f Q'ii:k{liVj OV/ „ '•• And of course the other logarithms in the equation have an ana- logous signification. Hence, attending to the equation - - .. ' tan'V^^ta»-^<*^tan-^^^^^4-e^'^^^^ where^ when l+«^ is positive, e"' is equal to zero; but when 1 + ay8 is negative, e'" is equal to + 1 or — 1, according as /3— a is positive or negative, or what is the same thing («, ^ being of opposite signs when 1 + a/S is negative), we find where e, e', e'', e'" are defined by the conditions — 0!=+, 6 = 0, _^^ , . ^ ■ _ ,A V.' X ar ;^'' Tn| v-rrv: '- -;•'-': ■a?TO00i5 3d:? «'"^''' ..yl_j„_,.^^ y-y'- v ^'"^ X X X X X 9i Suppose, to fix the ideas, that ^, y are each of them positive, we have 6=0; and considering the several cases,— Here a?a?' + 2/2/'^ +, 1+ — ^ = + ; and consequently not X X only €^=0, but also 6"=0, €'"=0, and thence E=0^,^ ^^ ^^^m^ Here €'=0. Moreover, xx' being positive, dex^-hyy^ and 14-^ 5^^ will have the same si^o. If they are both positive, then e^'ssO, Mff«VA. Cayley on the Theory of hogaaiithti/ii, e'^'imOj but if they are both negative, then // n\ ^Wm^n^-^ 9rn* {8ince.«r«' = 4- ) and V";=>± 1 j^ .|> r->|i,>i 11* fSmWfnMfms^J^ either case we have Er=0. "''^^'^ '^ »> -'ohr.rfoo MA arrd f^cftlf •)i.jHiere/«!'««:+l = y, «. 6.nf(9/l.,s\^AUo a?a/ being negative, yy '<» irijl-Rifir^ xat/^-yj/ and 1 + — ^ will have oppositiB signs. Suppose first xa^+yt/ i^ positive, then €"=0. And 1+ — ^ being negative, wehave€'''=+l=|^-|-~^, u e. €'"=-1. Bwiii xx^ -Vyi/ is negative, then €''= ± 1 = o?^'— ^y ^ ~ (^, — — J (since xoi^ \x X y is negative) = — -„ i, e. €"= + 1. And 1 + ^ ^ being posir tive, we have €"'=0. Hence in each case Ea=0. , / , , -coiiJ^n.'A .AtiiiisJbiiij Here 6^== ± 1 ^ j/^ «. ^. 6'= — 1. Also xx' and y^ being each negative, 0:^;^+^^ wUl be negative, and therefore ^r .; i .,J^ J. e. if 2, > 2-,thene"=-l; but if ^ < Sthen6"=+1. And ;.3/' ? a? 1 H- - ^ being positive, ^" = 0. Hence if ^ > ^, then X ad E=l-1=0; butif ^<-^, then E=14- 1=2. Consider {x,y) {a^, y') ,,^f^^^.-^i as the rectangular coordi- nates of two points A, A'. In the case which has been ^j^;;^;^;;^ ;^^"^' ^^. considered, the point A has been taken in the positive o.>dtlo>^L!. .., quadrant; and the prece- ^^ uf *>iIm of i 3 ding discussion shows that . .^,,i^y4 ^/^ ,j „,, we have always E = 0, ex- ^y^ ^^ j^.^^^^ ^ ^i ^, ^^^^ cept in the case where the y^{y) finite line AA' meets the ,# ^, ,„b .»«il9d I M'm^ii a,i negative portion ot the ^ < « " axis of X, in which case we have E= +2. The same thing is Mr. A. Cayley on the Theory of Logarithms. 357 true generally in whichever quadrant A is situated, i. e. we haVe always E = 0, except in the cases in which the finite line AA' meets the negative portion of the axis of x. But when this happens, then if the line AA', considered as drawn from A to A', passes from above to below the axis of x, we have E = + 2 ; but if the line AA', considered as drawn from A to A', passes from below to above the axis of x, then E= — 2. So that treating the points A, A' as the geometrical representations of the com- plex numbers x+yi, x' -^y'ij we have in an exceedingly simple form the precise determination of the discontinuous number E(=0 or +2) in the formula ' ' % ^ "^ ' ; ^^ ,DYm-gt,ix log^^ =log(^'+yi)-log(^+2^?y+E7re. ^^-^'^^^ V^ Consider in general the definite integral;'^' ^ ± — ^'^ ^^S" '^? ^^^ bonis' --: f +'=r^ noifj ^97rJi?go0 ^ rrc QjyuaH where ^i'', ,^'are compilex num- bers of the forma? + yi,s;' + y'i', and take A, A' as the geome- trical representations of these limits, and the variable point P as the geometrical repre- sentation of the complex vari- „ able u. The value of the definite integral will depend to a certain extent on the series of values which we sup- pose u successively to assume ^ in passing from z to z', or what is the same thing, on;r9ii? the path of the variable point P from A to A'. For (excluding altogether the case in which the path passes through a point for which u becomes infinite) it is well known that the value of the definite integral is the same for any two paths which do not include between them a point for which (pu becomes infinite; but when this condition is not satisfied, then the value of the definite integral is not in general the same for the two paths*. In order therefore to give a pre- cise signification to the notations, we must fix the path of the point P, and it is natural to assume that the path is a right line ;0=:.i-«i=a * The theorem is, I believe, due to M. Cauchy. See the memoir of M. Puiseux, Recherches sur les Fonctions Algebriques^LiowYiWei y9lt xv^ p. 365-480, where the subject is elaborately discussedv^ci^^ Of ,m. lO mii 858 Mr. A. Cayley on the Theory of Logarithms, (of course there are an infinity of paths which give the same value to the definite integral, or as we may call them, paths equivalent to the right line ; but the consideration of these would be a need- less complication of the definition, and it is better to attend to the single path — the right line). The definition is at once converted into an analytical one; we have only to assume t«=^H-r(x:'— r), and to suppose that the new variable r passes from r=0 (which gives u:=z) through real values tor = l (which gives u-s^s^), i. tf. we have as the equivalent analytical definition of the definite integral between the complex limits e, ^ the equation j udu=(sf'^x)\ u must not become infinite for any value of u along the path in question, i, e, \z '{'r{s^ —zy] must not become infinite for any real value of r between the limits r=0, r= 1. Suppose next, the path being defined as above, or in any other manner, that iu is a function of u such that (j>lu—(f>u. Then if ^u is continuous along the entire path, we have i but if iu is discontinuous at any points of the path, e. g. at the point M=Wp and at no other point, then t' (f>u du = f^ — (f>i{u^ + a') + <^>^{u^ — a) — tf)^, where Uj—af, Ui-^a! are values indefinitely near to «,, the path being from z through u^—a to Uj-i-a! and thence to z'. Or if we represent the break 0/Wy + a')— <^^(wy-f «) by the symbol V, then we have Suppose now f=tan-*-^ + c7r, where, as before, tan""* — denotes an arc between the limits , H — , and , a 07=—, €=±l=y', and to fix the ideas, consider ^ as the xr-coordinate of a surface^ Mr. A. Cayley on the Theory of Logarithms. 859 the other two coordinates being x and y. If x be negative and y be indefinitely small and positive, then 6= +1, and we have f=7r ; but if {oo being still negative) y be indefinitely small and negative, then 6=— 1, and therefore f= — tt, i. e. there is a break or abrupt increment 27r of the coordinate f in passing across the negative part of the axis of as from a negative to a positive value of y, or as we have before called it, from below to above ; this is the only discontinuity in the surface, the form of the surface being, in fact, what is intended to be represented in the annexed figure. .te;[.(^^%+ lfii|t-"^8i: iioda 'F"^ iif tamer Suppose now sr=o(^ -{-yHj z=x + yij and consider the definite integral fjcf :>if> ..M 0' f ft'^it ^^h; ■,0 '«4-,u \t,3l3rfw the path beinsr, as before, a riffht line. We have by the equiva- lent analytical definition, i,^^• • ^ , ^^^ ^^ ^^^j where the new variable r is real. And in like manner consider- ing the integral « t f rf* it fM^ i n '^»*% i/7.i?»^ f d^"^^ yfi ^9f3Xfw the path being in this case also a right line, we have ^ z' C^du fs' \ C' dr :5 s. ^tjtahis^ a lo ^aum^i^^-^. 360 Mr. A. Cayley on the Theory of Logarithms, where the new variable r is real. The two integrals in r are identically the same^ and consequently we have in every case 1 . . y Now log' tt= — ; and in passing from m = 1 to ti= — , there is no u z discontinuity in the value of log w = log >/^M^ + i(^tan-' |- + €7rj, , ^ji jno- , if for the moment u-=.'p'\-qi ; hence the value of the integral on the left-hand side is simply log - . The value of the integral on the right-hand side is in like manner, log s' — log z in the case in which the finite right line from u-=.z to u^z^ does not meet the negative part of the axis of x ; but when this happens, then there is a discontinuity in the value of the logarithm, and the integral on the right-hand side will be log,?'— log;?— 27ri, or log^' — log2' + 27r2, according as the right line considered as drawn from z to ^ passes from below to above or from above to below the negative part of the axis of x. We have therefore in every case (E being defined as above) log-sr' — logs' + ETr? forthe value of the integral on the right-hand side, and the relation between the two integrals gives, as it ought to do, the equation log — = log 2^^ — log sr -f- E7ri, z or in the form in which it was before written, ^°^^+^* =log(a^+ya)-log(a?-f-yO + E7n. The preceding discussion shows that the discontinuity in the value of E(— 0 or +2) arises from or is most intimately con- nected with the geometrical discontinuity which necessarily exists in the surface x=tan~^~, whenever we define the sym- X bol tan~' in such manner as to give a unique value to the coor- dinate z. Stone Buildings, Sept. 19, 1856. ,y,,. », j,i «ffi^yi-)tr?r owt <)/iT -)*«^»'f »» '< dUfihisy w^n Sift 9? mI/t XiilV. On the Action of Nitric Acid on Alcohol at common Tem- peratures. By Dr. H. Debus*. NITROUS aether is decomposed, according to Berzelius, by contact with water, lime-water, or a solution of sulphate of iron, into saccharic or malic acid, nitric oxide, and other sub- stances. Although the observation on which this assertion is founded was made fifty years ago, no contradiction of it seems to have become public, as it is still repeated in some of the latest handbooks on organic chemistry. The formation of saccharic acid from the radical sethyle appeared to me interesting enough to deserve a more minute examination, in order to determine the conditions on which it depends. I repeated carefully the expe- riments of Berzelius with pure hyponitrite of oxide of sethyle, water, and lime-water. In employing the latter, large quantities of nitrite of lime and traces of formiate of lime were produced. Pure water caused a great evolution of nitric oxide. After the decomposition was completed, the water contained nitric acid and very small quantities of an organic acid, which gave the reactions of formic acid. Similar results were obtained with sul- phate of iron and nitrous aether. In no case was malic or sac- charic, or any other organic acid except formic or oxalic acid, produced. These facts are fully explained if it is assumed that nitrous aether is decomposed into alcohol and nitrous acid ; the latter would form, according to circumstances, either nitrite of lime, or be converted into nitric oxide and nitric acid. A portion of the alcohol is oxidized to formic and oxalic acids. The acid mother-liquor from which, according to Black's method, the hyponitrite of oxide of sethyle separates, is said to contain large quantities of saccharic acid. The examination of this liquid did not confirm this assertion, but led to other not less interesting results. In order to obtain this liquid the following method was em- ployed : — A narrow and tall bottle, of about 700 cubic centims. capacity, was charged with 320 grms. alcohol of 0'863 sp. gr. at 60° F., and put in a place where it could remain undisturbed during the period the experiment was going on. By means of a tube which had been drawn out to a narrow point at one end, 100 grms. of water were permitted to collect slowly under the alcohol, and 200 grms. of red fuming nitric acid under the water, in such a way that alcohol, water, and acid formed three distinct layers. The mouth of the bottle was then provided with a perforated cork, holding a bent glass tube, the other end of which dipped into a * Communicated bv the Author. Phil Mag, S. 4. Vol. 12. No. 80. Nov. 1856. 2 B 862 Dr. Debus on the Action of Nitric Acid small quantity of water. The temperature of the room was kept constant at 20*^ C. The nitric acid from one side and the alcohol from the other mix slowly with the water and meet each other. The alcohol is partly converted into nitrous aether, which escapes, and partly oxidized. An evolution of gas is observed, weak at the beginning, but strong at the end of the process. After the lapse of six or eight days, the three layers of water, alcohol, and nitric acid have completely mixed, the generation of gas ceases, and the operation is finished. The liquid contains in this state, acetic, formic, oxalic, nitric, glycolic, and a new acid; also different kinds of aethers and aldehydes. The mixture is evaporated on the water-bath, in quantities not exceeding 20 or 30 grms., till it assumes the consistency of strong syrup. If more than 30 grms. are evaporated at one time, then the substances to be prepared from it do not crystal- lize. Alcohol, nitrous aether, nitric, acetic, and formic acids, the aldehyde of acetic acid, and other volatile substances escape. Glycolic, oxalic, and the new acid, with a peculiar kind of alde- hyde, remain in the evaporating basin. The contents of the latter are dissolved in a little water and neutrahzed with carbonate of lime. As soon as the effervescence has ceased, the liquid is mixed with an equal volume of strong alcohol. Nearly all the lime-salts are thrown down, whilst the aldehyde remains in solu- tion. The precipitate is collected on a filter of linen, pressed, and then treated with a suitable quantity of boihng water. After filtering off from undissolved carbonate and oxalate of lime, the filtrate yields, on cooling and standing, a crystallization of a new compound of lime, which I propose to call glyoxylate of lime. On evaporating the mother-liquor, another quantity of the same substance may be obtained. If the liquid is further concentrated, a double salt of glycolate and glyoxylate of lime is separated. From the mother-hquor of the latter no more crystals can be prepared by evaporation. But if some slaked lime is added till it becomes alkaline, and it is boiled for a short time, filtered, and the excess of the lime removed by carbonic acid gas, it yields to the last drop crystals of glycolate of lime. The liquid from which these lime-salts had been precipitated by alcohol leaves, after evaporation on the water-bath, a thick brown syrup, which is shaken with absolute alcohol. Except a small quantity of glycolate of lime, nearly the whole dissolves. The solution is filtered, and the alcohol distilled off at 100° C. A thick liquid remains in the retort, which belongs to the same class of compounds as the aldehyde of acetic acid ; it unites with ammonia, oxide of lead, and bisulphite of soda. Of this sub- stance I shall treat in another paper. on Alcohol at common Temperatures, 363 Glyoxylate of Lime, C^ H^ Ca 0^*. The crude salt is purified by repeated crystallization from boil- ing water. It forms small, hard prisms, which can be heated to 160° or 170° C. without undergoing any alteration in weight. They become yellow at 180° C, lose water and carbonic acid, whilst oxalate and glycolate of lime and a resinous substance remain. Exposed to a higher temperature on a piece of platinum foil, the smell of burning sugar is emitted, and carbonate of lime formed. One part dissolves in 177 parts of water at 8° C. The solution may be boiled without producing any decomposition of the glyoxylate of lime ; it is precipitated by alcohol, and shows the following behaviour with reagents : nitrate of silver or baryta and chloride of copper do not produce a precipitate ; acetate of lead throws down a white crystalline salt, which easily dissolves in acetic acid; lime-water acts in a similar manner. The pre- cipitate is soluble in acetic acid immediately after its formation, but not after it has stood some time, or been exposed to a higher temperature. Oxalic acid separates the lime completely as oxa- late of lime, and liberates the glyoxylic acid. A small quantity of solid glyoxylate of lime, heated with a solution of nitrate of silver and ammonia in a test-tube, produces a bright coating of silver on the glass. Analysis gave the following results : — I. 0-2165 grm., dried in vacuo, furnished 0*172 grm. CO^ and 0*055 grm. water. 0*1945 grm. dissolved in water and precipitated by oxalate of ammonia gave, after treatment according to the usual method, 0*090 carbonate of lime. II. 0*5175 grm. furnished 0*409 grm. CO^ and 0*1265 HO. 0*405 grm. gave 0*183 grm. carbonate of lime. III. 0*330 grm. gave 0*151 grm. carbonate. of lime. A small quantity of the substance burnt with soda-lime did not yield any ammonia. The residue did not contain a nitrogen compound. Another quantity of the same material was heated with potassium ; no cyanide of potassium was produced. There- fore the glyoxylate of lime does not contain nitrogen. In 100 parts, — I. II. III. Carbon . . 21*70 21*55 -Hydrogen . 2-80 2*71 ... . Calcium . . 18*50 18*07 18*3 Oxygen * C=12, H=l, Ca=20, 0=16. 2B2 864 Dr. Debus on the Action of Nitric Acid The formula C« H« Ca 0* requires— Carbon . . . 2 24 21-64 Hydrogen , . 3 3 2-70 Calcium . , . . 1 20 1801 Oxygen . . . . 4 64 57-65 111 10000 To a cold solution of glyoxylate of lime, lime-water was added till it became alkaline. After standing half an hour the white precipitate was filtered off, well washed, and treated with water and carbonic acid. The excess of the latter was removed by boiling. The precipitate now consisted of carbonate and oxalate of lime ; the filtrate from it yielded, after evaporation, crystals of glyoxylate of lime. 0-185 grm., dried in vacuo, gave 0*085 carbonate of lime, or — 18-3 per cent, of calcium. The formula C« H^ Ca 0* requires— 18*01 per cent, of calcium. The filtrate from the precipitate by lime-water was also freed from its excess of lime by CO* and then evaporated ; crystals of glycolate of lime were obtained. 0-162 grm., dried in vacuo, lost at 100° C. 0'035 water. The same quantity, dissolved and precipitated by oxalate of ammonia, gave 0-066 Ca* 0 CO^. Or in 100 parts,— Water ..... 216 Calcium .... 16-2 The formula 2(0* H^ CaO^) + SH* O requires— Water 221 Calcium .... 16-3 A solution of glyoxylate of lime, made alkaline with lime-water and boiled for a short time, was decomposed into glycolate of lime and oxalate of lime. The same result was obtained when the cold mixture was allowed to stand a few days. Consequently, when lime-water is added to a cold solution of glyoxylate of lime, the latter combines with more lime and forms an almost inso- luble substance. Slowly at common, but very fast at a high temperature, this compound resolves itself into glycolate and oxalate of lime and water, — 2C«H3CaO* + CaHO = C«Ca2 0* + C«HSCa03-{-2(HHO). Sometimes I obtained the glyoxylate of lime crystallized, not in prisms, but in long needles. As the appearance of both was very different, I thought it necessary to examine them more minutely. on Alcohol at common Temperatures, 366 100 parts of water at 8° C. dissolved 0'56 of the prisms and 0*50 of the needles. Both solutions gave the same reactions with general reagents. 0*558 grm. of the prisms, boiled with a clear solution of caustic lime for a short time, then acidu- lated with acetic acid, and the oxalate of lime filtered off and converted by the usual method into carbonate of lime, yielded 0254 of the latter substance. This corresponds to 0"325 of oxalate of lime. 0-391 grm. of the needles, treated in a similar manner, gave 0-176 Ca^ 0 CO^ or 0-225 oxalate of lime. Therefore from 100 parts — {prisms 58-2 oxalate of lime needles 57*5 If the decomposition takes place according to the equation-— 2(C2 W Ca 0-*) + Ca HO = C^ Ca^ 0^ + (C^ H^ Ca 0^) + 2W0, y ,_• ^ -^- ' Oxalate of hme. Glycolate of lime. then 57*6 per cent, of oxalate of lime should have been found. These experiments show that both kinds of crystals belong to the same substance, and, moreover, they confirm the formula C2 H3 Ca 04 for glyoxylate of hme. The preparation of a double salt of glyoxylate and glycolate of lime was described in the beginning of this paper. It forms a white crystalline powder, more easily soluble in hot than in cold water. The warm saturated solution solidifies on cooling, form- ing a mass like gelatine, which after a few days' standing becomes crystalline. Nitrate of silver, chloride of copper, acetate of lead, and lime- water, give the same reactions with this substance as with glyoxy- late of lime. By repeatedly dissolving the compound in hot water and recrystallizing it, it appears to be decomposed into C^H^CaO^andC^H^CaO^ Analysis gave the following results : — 0-246 grm., dried at 120° C, gave O'llO grm. Ca^O CO^. 0-148 grm., dried at 120° C, yielded 0-048 grm. water and 0-119 grm. CO^. In 100 parts,— Carbon . . . 21 '92 Hydrogen . . 3-60 Calcium . . . 18-00 The formula 2{C^ W Ca 0^) + C^ H^ Ca 0^ + H HO requires-- Carbon ... 21*49 Hydrogen . . 3*28 Calcium . . . 17-91 Oxygen 866 Dr. Debus on the Action of Nitric Acid 0-642 grm., dried in vacuo, lost at 120° C. 0-0495 grm. water, corresponding to 7-71 per cent. If the above formula is multiplied by two, and three atoms of water of crystallization added, 7*45 per cent, should be obtained according to calculation. It is apparent that the composition of this substance, dried at 120° C, is nearly the same as that of glyoxylate of lime, — 3(C* H8 Ca 0^) H-2H = C« W Ca^ Oi«=2(C2 H^ Ca O^) '^ ' +C2H8Ca03-}-H«0. Glyoxylate of lime. In order to check the analysis, the double salt was boiled with lime-water. It was decomposed, and its glyoxylate of lime con- verted into oxalate and glycolate of lime. Ill parts of glyoxy- late of lime should yield 64 parts of oxalate or 50 parts of car- bonate of lime. If, therefore, the formula 2(2(C2 H3 Ca 04) + C« H^ Ca 0^ + H^ O) + SH^ 0 represents the composition of this compound, it should yield, after boiling with caustic lime, and conversion of the oxalate of lime into carbonate, 27'6 per cent, of the latter. 0-362 grm., dried in vacuo, gave 0*094 grm. Ca^ 0 CO^, or 26-2 per cent. If the unstable character and the great difficulty of preparing this double salt in a pure state be taken into consideration, then both numbers seem to agree as well as could be expected. Glyoxylic Add, C^ H^ 0^. In order to obtain this acid, its lime-salt is dissolved in water and oxalic acid added as long as a precipitate of oxalate of lime is formed. After filtering, the clear liquid is evaporated in vacuo. The glyoxylic acid remains as a thick transparent syrup. It absorbs in this state moisture very rapidly from the air, and dis- solves easily in water. The solution neutralizes potash and soda, and decomposes the carbonic acid compounds of all bases very rapidly. Oxide of silver is partly dissolved and partly reduced to metallic silver. The solution of glyoxylic acid, exposed in a retort to a temperature of 100° C, loses first water, and then the acid itself distils slowly over. It could not be obtained in a solid state. Heated in a test-tube by the flame of a common spirit-lamp, it boils, emits white fumes, and evaporates almost entirely without turning black. Glyoxylate of Potash, C^ H^ Ka 0*. To glyoxylic acid is added a solution of carbonate of potash till about three quarters of the acid are neutralized. The liquid is then evaporated in vacuo until it yields with alcohol a copious on Alcohol at common Temperatures, 367 precipitate. As soon as this takes place, the whole of the solu- tion is transferred to a glass cylinder and mixed with double its volume of strong alcohol. The compound required separated as an oily liquid, which soon solidified to a white crystalline mass. Glyoxylate of potash is white, absorbs moisture from the air, and dissolves with great facility in water; it crystallizes only with difficulty in small prismatic crystals. Glyoxylate of Ammoniaj C^ H^ Am 0^ Is obtained by precipitating glyoxylate of lime with its equi- valent quantity of oxalate of ammonia, and evaporating the filtrate from the oxalate of lime in vacuo, A hard crust is formed con- sisting of small white crystals. By recrystallization it can be easily purified. The glyoxylate of ammonia dissolves slowly, but in large quantities, in water. The solution, especially when strong, is decomposed by boiling, and carbonic acid and a brown resinous substance formed. Alcohol dissolves very little of this salt, but does not precipitate its watery solution. The solid compound, heated on a piece of platinum foil, leaves a large quantity of coal, which burns only with difficulty. Glyoxylate of silver could not be prepared in a pure state. A concentrated solution of it evaporated in vacuo, by absence of light, yields white crystals contaminated with metallic silver; the solution is neutral, and deposits a coating of silver on the glass when exposed to the light. It appears that the glyoxylic acid contains two atoms of hy- drogen which can be replaced by metals. The lime- salt unites with more lime and forms a compound nearly insoluble in water, which is decomposed by carbonic acid into carbonate of lime and glyoxylate of lime. A similar compound, containing baryta instead of lime, can be prepared. Both decompose very soon after their formation, and therefore could not be analysed. By adding acetate of lead to glyoxylate of lime, a white crystalline precipitate is thrown down. This precipitate dissolves easily in acetic acid and nitric acid ; if heated in a test-tube with some liquid nitrate of silver and a few drops of ammonia, a bright coating of silver is formed on the glass. 0*2706 grm., dried at 100° C. and burnt with chromate of lead, gave 0-076 CO^ and 0-0265 water. 0'165 grm. of the same substance yielded 0-117 metallic lead. In 100 parts, — Carbon ..... 7*6 Hydrogen .... 1*08 Lead 70-90 ^ ..,,... , Oxygen 368 Dr. Debus on the Action of Nitric Add The formula C* H* Pb' 0"* would require — bioB oflvxoyb Carbon ... 2 24 8-d ' ' Hydrogen . . 2 » 2 0-67 Lead .... 2 207*6 697 Oxygen ... 4 64 " 297-6 It contains therefore a little more lead than the calqulation requires, a circumstance which occurs frequently with lead com- pounds, on account of their inclination to form basic salts. Some experiments to substitute less than one atom of hydrogen in one atom of glyoxylic acid did not lead to any positive result. A certain quantity of the acid was divided into two equal parts ; the one exactly saturated with carbonate of potash, and then the other mixed with it. After evaporating the liquid in vacuo a thick syrup remained, which could not be made to crystallize. On adding alcohol, glyoxylic acid was extracted, and an oily mass separated which soon became solid, and proved to be the salt C'H^KO*. 0*284 grm., dried in vacuo y gave 01 62 chloride of potassium, corresponding to 30 per cent, of potassium. The formula C^H^KO'* requires 30*2 per cent. A similar result was ob- tained with the lime-salt. The action of nitric acid on alcohol and the formation of gly- oxylic acid is explained in the following manner : — If from one atom of alcohol two atoms of hydrogen are deducted and two atoms of oxygen added, w^e obtain the formula of glycolic acid, — C^H60 + 30;p,,C^H403 + H^O-io^iBloo -': Alcohol. Glycolic acid. Water. '^'^ ^"^^^ When'water, alcohol, and nitric acid act upon each other at about 16° C, and as soon as these three substances have mixed, the liquid is treated as described, only glycolate of lime is obtained. "When the same experiment was repeated at about 20° C, and especially when the mixture was allowed to stand for a few weeks after the action had apparently ceased, much glyoxylate of lime and less glycolate of lime was found. Therefore it seems as if the glyoxylic acid was formed at the expense., of the glycolic acid,—- . ,,,,^^ J (,'^.n-urv , By allowing more time, or a higher tern perature^ the oxidatioa does not stop short at the production of C'^ H"* 0^, but the latter takes up one atom of oxygen more, and becomes converted into on Alcohol at common Temperatures. 369 glyoxylic acid. In all cases small quantities of oxalio acid were also produced :— C^H^O^ + 0 = CMI^O^ -f- H^O Glyoxylic acid, i:) Oxalic acid. Water. The great facility with which glyoxylic acid, under the in- fluence of the strong bases_, resolves itself into gly colic and oxalic acids and water, would lead to the view that it was composed of these three substances, and* that its salts were merely double salts of oxalic and glycolic acids. The formula of the lime-salt would be accordinglyi-ii^''^ J ^^-^^ 'jjsf^ii^oiis o^ y.h- ■ ] C2 H Ca 6v || Geometry without Axioms, p. 84-98. AA\ \»-A\^A<^VMv>/ro7?i the Definitions of Euclid, 373 until the produced parts are equal to AB and AC. Draw DB, DE, and EC. The angles BAC and BAD are equal to two right angles (XIII.)*, and are therefore equal to each other ; the angles DAE and CAE are also equal to two right angles; therefore the four angles at A are right angles. In the triangles BAC and BAD, two sides of the one (BA and AC) are equal to two sides of the other (BA and AD), and the included angles are equal ; hence BC is equal to BD, and the angles ABC and ACB are equal to ABD and ADB. In the same way the sides DE and EC can be shown to be equal to each other and to DB and BC ; and the angles in each triangle to be respectively equal. Hence (from the definition of a square) these four angles are right angles ; and ABC and ACB are half right angles. Therefore the right-angled isosceles triangle ABC contains two right angles. Lemma I. If one of the angles (ABC) at the hypothenuse of a I ^^ right-angled, triangle be equal to half a right angle j the tri- ,^ angle is isosceles. Y\ If AB and AC are not equal, let AC be inade equal to AB ; and draw BD. As BAD is an isosceles right-angled triangle, the angle ABD is equal to half a right angle. But ABC is equal to half a right angle ; therefore a part is equal to the whole, which is absurd; therefore AC must be equal to AB. Lemma II. If in two triangles (ABC and DEE), two sides of the one (AB and BC) be respectively equal to two sides of the other (DE an^EF), and an angle (BAC), greater than a right angle, in the one be equal to an angle (EDF) in the other, the two triangles are equal in every respect. Let the triangles be applied to each other so that the bases \ 1^ .bDY*jh|«Kr> s'lari BC and EF coincide. Then DE will lie on AB. If not, let DEF take the position BDC. Join A and D. As AB and BD are equal, the angles DAB and ADB are * The references are made to Mr. Potts' large edition of Euclid. 874 On a Solution of the Theory of Parallels, equal. Therefore BDA is greater than a right angle. Therefore in the triangle ADC there is one angle greater than two right angles, which is impossible (XVII.). Nor can the triangle ED C lie above or below AB and AC (as the dotted lines in the figure), for the angles at A and D are equal (XXI.) ; therefore ED must fall on AB, and therefore the triangles are, in every respect, equal. Proposition II. The three interior angles of every right-angled triangle are together equal to two right angles. Let ABC be a right-angled tri- p angle ; produce AB till AD is equal to AC, and take, in AC, AE equal to AB. Draw DC and BE. At the point B draw BE perpendicular to AD. As the triangle DAC is an isosceles right-angled triangle, the angles at D and C are equal to half right angles (Prop. I.) . The triangle BDF is isosceles, because one angle, DBF, is a right angle, and another, BDF, is half a right angle (Lemma I.). The angle CFB is greater than a right angle, and, being the supplement of half a right angle, is equal to CEB, for the angle AEB is equal to half a right angle (Prop. I.) . BE is equal to BD ; BD is equal to EC ; therefore BF and EC are equal. In the triangles BFC and CEB, two sides, and an angle greater than a right angle, are respectively equal ; therefore the triangles are equal in every respect (Lemma II.) ; therefore the angles EBC and ECB are equal to the angles FCB and FBC. Now the angles FBE and FCE are each half right angles ; therefore the angles EBC and ECB are together equal to half a right angle. To these add ABE, which is half a right angle, and BAE, which is a right angle ; then the three interior angles of the right-angled triangle ABC are together equal to two right angles. Proposition III. The three interior angles of every triangle are together equal to two right angles. Let fall upon the greater side AC the perpendicular BD. In each of the right-angled tri- angles thus formed there are two right angles (Prop. II.). Taking away the two right angles at D, there remains the three angles of the triangle ABC, together equal to two right angles. Prof. Stevelly on the Doctrine of Parallel Lines. 375 ri(It was in the attempt to establish this theorem that M. Le- gendre deviated from the method of EucUd by employing the doctrine of limits. Setting out frAn this theorem, the demon- strations of the various properties of parallels are simple and obvious. To give these final propositions would be only to repeat what M. Legendre has done ; for to that distinguished geometer must belong the merit of having shown that the whole question depended upon a proof of the 32nd proposition. His proof of that proposition is inadmissible ; but his subsequent demonstra- tions are in accordance with the principles of plane geometry. Although the proof just given of this theorem will probably be acknowledged to be consistent both with the definitions and with the method of Euclid, nevertheless I cannot regard it as the most satisfactory solution of the difficulty. It may be in- teresting as the first successful attempt of the class to which it belongs. But the real solution I still believe to consist in treat- ing the conception of parallel lines, as we treat any other geo- metrical conception, with a clear and unequivocal definition. 119 Jermyn Street, October 8. 1856. XL VI, On the Doctrine of Parallel Lines, By Professor Stevelly. To the Editors of the Philosophical Magazine and Journal. Gentlemen, Holywood, Oct. 13, 1856. FOR the personally kind terms in which Mr. Hennessy has stated his objections to the method of treating the doctrine of parallel lines which I lately communicated to you, I beg to ex- press my acknowledgements. I also feel much gratified that he does not profess to have detected any defect in the chain of rea- soning on which the proofs are founded. I trust, however, Mr. Hennessy will not consider me deficient in courtesy when I add, that regard for scientific truth compels me to say, that there is scarcely an assertion which he has made in that paper, or in the one to which he refers in (the fifth not) the third volume of the present series of this Journal, in which I can concur. Since a detailed examination of the defective logic and incor- rect statements contained in those papers would far exceed any reasonable limits, and since an examination of even two or three of the most obvious would wear too much the appearance of con- troversy, and seem to invest the entire subject with a very undue share of importance, I shall simply select one as an example, because of its close connexion with the subject of my communi- 376 Prof. Stevelly on the Doctrine of Parallel Lines. cation, and because it affords a fair specimen of the defective logic and incorrect reasoning which pervade the whole. To sustain his position, tlftit the method of limits resorted to by me, if allowable, was unnecessary, Mr. Ilennessy asserts that he has shown in the third (fifth ?) volume of the present series^' of this Journal, that the entire doctrine of parallel lines may be derived from the following definition : — " Parallel lines are such, that if they meet a third line, the two interior angles on the same side will be (together) equal to two right angles." Now it is quite certain that this definition, as such, does not give a solid foundation for the doctrine of parallel lines, neither does it warrant the deductions derived from it in the paper referred to. Let us examine it even partially. I meet two lines, wx and , i i, yz, so related to "a third" \^ ",i '^jpy line, loy, that the two interior — angles on the same side are together equal to two right angles. Well, the definition fairly warrants me in calling these lines " parallel.'* This is the essential difi'erence which distinguishes them from other pairs of lines, and from which all their properties must be proved to flow. Now the 29th propo- sition of Euclid's Elements calls on me to prove that " any " line, as ivy, which cuts those, also makes the two interior angles on the same side together equal to two right angles. This is a relation of these two lines to all others which cut them which requires to be proved, and which neither the above definition nor any other definition can warrant us to assume as a truth without proof. It is a '^ property " which must be shown to be an essential concomitant of that which has already fixed the rela- tion of those two lines to one another, and to all others which cut them, and which we have by the definition merely agreed shall entitle us to denominate them " parallel lines " in any individual case in which we find it to obtain. And yet this simple assump- tion is all that Mr. Hennessy gives in the paper referred to as proof of the 29th and 27th of Euclid's first book of Elements. When I was a boy at school, I thought for a day or two that I had proved the entire doctrine of parallel lines by defining them to be such, that if *' any line " was drawn across them they would make the alternate angles equal. But I am happy to add that I detected my false logic before I had committed myself by its publication. I am. Gentlemen, Your obedient Servant, «yn;» John Stevelly. XL VII. • On a powerful Form of the Induction Coil, with some new Statical and Thermal Effects of the Induced. Cttrrent. By Jonathan N. Hearder, Phjmmth^. > ^^^ oiju^u^^ i ON reading in the Philosopliical Magazine for January 1855, an account of the very interesting experiments performed by Prof. Grove with a powerful induction coil constructed by M. RuhmkorfF of Paris, I immediately made inquiries respecting the instrument, bat learnt that its construction was such, every part being thoroughly imbedded in melted shell-lac, that nothing was known of its internal arrangement. Having often promised myself to make an instrument of the same kind, I proceeded at once to act upon known principles in the construction of an induc- tion coil, in which the secondary wire should be, as far as prac- ticable, perfectly insulated, taking care at the same time to com- bine with it the facility of removing and relaying it to correct errors or repair injuries. My first attempt was eminently successful, since I produced effects far exceeding those of M. Ruhmkorff's, with about one- third of the quantity of secondary wire reported to be contained in his machine. In March of the present year, I delivered a paper on the subject to the members of the Plymouth Institution and Devon and Cornwall Natural History Society, and then first exhibited the machine in public. Subsequently in the same month it was also exhibited before the members of the Plymouth Mechanics' Institute by an eminent electrician of London, who, when lecturing on the subject of the induction coil, availed him- self of the opportunity of comparing it with one of M. Ruhm- , korff's machines, and who at once gave his decision in favour of my arrangement. I should have published a description of it at the time, but having furnished him with minute particulars of the construction of my apparatus, together with my views respect- > ing the scientific principles involved in its action, for the purpose of insertion in a new work on electricity which he had then almost ready for publication, I promised not to do so until his work was out. It has not, however, yet appeared; and I have, now learnt that the same gentleman has recently delivered a lee- , ture on the induction coil at one of the scientific institutions of the metropolis, in which he brought forward a machine professing to be an improvement on M. Ruhmkorff's apparatus ; and as it is almost identical in construction and arrangement with mine, I have felt some little surprise at his not having made the slightest allusion to the fact of my having constructed one prior to the, one which he had brought forward, particularly since at his own especial request I had refrained from publishing any particulars of my own arrangement. In the course of an extended series * Communicated by the Author. Phil. Mag. S. 4. Vol. 12. No, 80. Nov. 1856. 2 C 378 Mr. J. N. Hearder on a powerful Form of investigations with my instrument I had occasion to relay the secondary wire, and in doing so I only put on five-sixths of the original quantity, but I have had the satisfaction to find the sta- tical power of the machine nearly doubled. I exhibited this new arrangement at the Royal Cornwall Polytechnic Institution on the 17th of September last, and was honoured by the Society's first silver medal. The main object of the present paper is to detail some of the results of my investigations with it on the character of the induced current, as I have discovered some facts which, as far as I know, are quite new, and which seem to deve- lope a new law of electrical action. 2. Hitherto, I believe, the only thermal effects observed in metallic conductors by the action of the induced current of the induction coil, have been the incandescence of the end of the negative terminal, w^hich, when made of very fine wire, melts and burns, and the partial combustion of portions of metallic filings when the spark passes between them as they lie strewed upon a non-conducting surface, as is evidenced by the colour of the spark varying with the nature of the metal used. Whilst the spark in its passage through inflammable bad conductors, such as paper, cotton, gunpowder, and even through inflammable non-conduc- tors, such as aether, alcohol, turpentine, &c., readily kindles them, yet the same cun-ent made to pass through an extremely fine wire in a closed circuit docs not sensibly heat it. In this particular the spark of the induction coil resembles that of a dis- charge from a Leyden jar when made to pass through an imper- fectly conducting circuit, such as a wet string, or tube of water ; for it is to be observed, that although a charge from a Leyden jar or battery, when passed at once through a fine wire, may be sufficient to melt and dissipate it, yet it will not sensibly heat the same wire when water is in any way made part of the circuit, though the same spark will in the latter case inflame gunpowder, whilst through the perfectly conducting circuit it disperses it without ignition. There can be very little doubt that the dis- charge requires a certain amount of time to pass through the imperfect conductor, and that the metal is thus able freely to transmit the electricity with its reduced velocity, and is conse-- quently not heated by it. Effects analogous to these are pro- duced by the induction coil ; for although the soft static spark between the terminals will inflame gunpowder, yet the discharge from a Leyden jar, when its coatings are in connexion respects ively with each terminal, merely disperses it, as when charged with frictional electricity. 3, I had often felt that if any definite thermal results could be obtained from the action of the Leyden jar in connexion with the induction apparatus, a channel would be opened up through which an accurate comparison might be made between the cha- .«nr{^ l^* oj the Induction Coil. '^ .>*i^ 379 racter of frictional and voltaic electricity, and I believe that I have now succeeded in indicating a path through which this important object may be obtained. In order to examine the thermal eiFects of the Ley den jar, I had recourse to a modifica- tion of Sir W. Snow Harrises thermo-electrometer, which I intro- duced about twenty-six years since, in order to adapt the mstru- ment for voltaic as well as frictional electricity, and for which, in 1844, I received the first bronze medal of the Devonport and Stonehouse Polytechnic Exhibition. 4. My apparatus differs from that of Sir W. Snow Harris only in the construction and arrangement of the air-vessel which contains the wire. In Sir W. Snow Harrises instrument (Phil. Mag. No. 73. May 1856, p. 343, fig. 5), the wire passes hori- zontally and diametrically through a glass globe, having external brass caps on the ends of the wire for the purpose of making connexions. The air-chamber which I employ is a cylinder about 3- inches diameter, with two necks like a small electrical cylinder placed vertically. The necks are capped with brass ; the lower one screws upon the reservoir of the bent indicating tube, ^nd the upper one is furnished with a stuffing-box, through which passes vertically a sliding wire surmounted with a binding screw, and formed at the lower and inner extremity into a for- ceps. The test wire hangs vertically in the axis of the cylinder, the upper end being attached to the sliding forceps, whilst from the lower end hangs a short detached forceps, the tail of which can be lowered into a brass cup containing mercury. This cup is in connexion with the brass screw of the reservoir upon which the cylinder is screwed, and to which is also attached a second binding screw for completing the circuit. There is also an ad- justing valve in the cap of the reservoir. The advantages of this arrangement are, that it affords the greatest facility for changing the wire, the stuffing-box being made to unscrew from the cap of the cylinder, whereby the wire with its lower forceps can be lifted out of the mercury and other wire substituted, or the length of the same wire varied in a few moments. The instrument also affords facilities for examining the effects of the voltaic arc, &c. The principle, however, is the same as that originally contrived by Sir W. Snow Harris, who has the merit of having first applied it as a measure of electrical forces ; and with the exception of the air-chamber and its appliances just described, is in all other respects similar in construction to his. 5. I was anxious to know whether the discharge from the Ley den jar, when charged by the induced current, possessed the same character as that obtained from the charge of an electrical machine ; for I could scarcely bring myself to believe, that, in the rapid succession of discharges which I could procure from my coil, amounting sometimes to more than 200 per second 2 C 2 o8u Mr. J. N ,new^aer%i ia powerful Form through an interval of 0*5 of an inch, the jar was really as fully charged as when charged in the ordinary way. I therefore in- stituted a set of experiments which have developed some curious and interesting results, and which, as far as I know at present, are quite new. 6. I introduced between the secondary terminals of the coil a thermo electrometer in connexion with a Lane's discharger, but although I varied the length of the sparks from 0 to 1 inch, no heating effect was produced upon the wire in the instrument. ^ 7. 1 connected the coatings of an insulated Leyden jar, con- taining about 3| square feet of surface, respectively with the two terminals of the coil, and completed the circuit of the jar by a thermo-electrometer in connexion with a graduated Lane's dis- charger. On causing a rapid series of discharges to pass, the fluid instantly rose in the stem and remained fixed pretty perma- nently at nearly 100 degrees, or about one hundred times higher than it would have risen with a single discharge from the same jar with the ordinary electrical machine. The platina wire hang- ing in the cylinder of the electrometer was thrown into the most energetic vibration during the passage of the sparks, so as to become crippled in several places. 8. The thermo-electrometer was removed, and a piece of very jfine iron wire, about 4 inches long, placed between insulated for- ceps, was substituted for it in the circuit. On passing the dis- charges, the wire became blue, vibrated rapidly, and crippled in several places; and whilst occasionally suspending and repro- ducing the action of the coil^ the wire suddenly melted at one of the crippled places,; .;'';,* j "^ ,^ _ ' 9. Another piece of the same wire/ about 3 inches in length, was next introduced, and on passing the discharges it instantly T)ecame red-hot through nearly its whole length and fused into globules. The experiment was repeated with shorter pieces with nearly the same results, the wire sometimes fusing throughout .its whole length, and sometimes bfeakiijg ^ into fragments par- tially burnt. , ( " v I , ^^f'.'^.T ^? '^, . ' ' 10. The foregoing rematt able changie^iii tti^iheVm^l character of the current when intercepted and, as it were, measured out by the jar, induced the following experiment : — The thermo-electro- meter was introduced into the circuit of the jar as before, and two other thermo-electrometers were introduced into the portions of ,the circuit leading from the terminals of the coil to the coatings of the jar. By this arrangement, the current which charged the Jar had to pass through these electrometers in its course. On I setting the machine in action, the electrometer which completed '^the circuit of the jar indicated the same thermal effect upon the included wire, whilst the other two electrometers were not in the slightest degree affected, clearly showing a marked difference w^^'^ \ of the Induction Coil.. , , ,. in the velocity of the current under the two different con- ditions. 11 . In the foregoing experiments, the discharging electrometer was fitted with platina points, between which discharges can be obtained of a greater length than between balls ; but in order to place the experiment under conditions which would admit of better comparison with the effects of the ordinary electrical machine, I substituted balls for points in the discharger. On placing them at such a distance from each other as to allow the discharges to pass, the fluid instantly rose to a definite height in the tube, nearly 100 degrees ; and whilst thus permanent, the balls of the discharger were gradually approximated to each other, with no diminution of effect, until they were in absolute contact, when, the circuit being closed and the jar no longer capable of receiving a charge, the fluid instantly fell nearly to zero, the residual amount of expansion being due to the heat absorbed by the glass surface, &c. during the continuation of the experiment. On the slightest separation of the balls from each other the fluid rose to 100 degrees, and remained tolerably permanent until they were separated beyond the striking interval, when the fluid again fell as soon as the discharges ceased. ^^ 12. The balls were next placed rather within the greatest striking distance ; and instead of allowing the spring to vibrate and produce the ordinary rapid succession of discharges, 1 held it in my hand and broke contact at successive single slow inter- vals, in order to ascertain the value of a single discharge; this I found to be only 1 degree on the scale of the instrument. On making an interruption of the circuit, the action of the fluid was precisely of the same character as if the jar had been charged by the electrical machine, that is to say, the fluid rose with a sudden impulse and instantly subsided. On repeating the intetruptions at rather quicker intervals, so as to make each successive inter- ruption before the effect of the preceding one had quite subsided, the fluid was made to rise 1 degree in succession for each dis- charge, so that 1, 2, 3, and so on to 12 discharges, just raised the fluid correspondingly to 1, 2, 3, to 12 degrees. There was some little difficulty in manipulating in this way, as the discharge did not always take place at each interruption in the circuit, owing to variations in the character of the metallic contact at the interruptor, arising from the oxidation of the platina surfaces; but as far as they went they were sufficient to show that the extra- ordinary result first noticed was due to a rapid succession of units of effect gradually accumulating in the transmitting wire. 13. Having thus established a means of comparing the effects of the coil with those of the ordinary electrical machine, and having ascertained the value of a unit of discharge under the influence of the induction coil, it rext became necessary to com- Mr. J.N. Heardcr on a powet'ful Form B^^iare this with a similar unit when charged by the electrical 3iiiachine; and this I found, with tlie striking distance which I had employed, as nearly the same as so small an indication on the scale as 1 degree would enable me to judge. On increasing or diminishing the striking distance of the balls when using the electrical machine, the fluid indicated the action of the well- -established law, that the effect is in proportion to the square of -4he striking distance, the charged surface being constant. No f%uch law as this was however observable with the induced cur- rent ; for, on the contrary, it was ascertained by subsequent ex- periments that the effect on the wire was diminished when the striking distance was prolonged beyond a certain limit, a fact at -variance with hitherto-recognized laws of electrical action. ,5 As the foregoing experiments wei*e performed with a large ■ jar, which required that the induction coil should be very in- ' tensely excited, thereby rendering its action less permanent, 1 subsequently employed smaller jars, and found the same class of results to accompany their action, but with others which the conditions of the first experiments had not enabled me to discover. 14. Having satisfied myself that the nature of the charge in the jar was the same with the induction coil as with the machine, • I next proceeded to examine the effect of varying the extent of .surface; and as my object was more to compare results with ,'each other, under the action of the induced current, than to establish any connexion between these phsenomena and those of "the common electrical machine, I resumed the use of points in ^the discharger, which, from the greater length of spark obtain- "•ible by them, enabled me to vary the striking distance over a greater extent, and thereby more closely to examine the differ- i-*iences of effect.' ^»if'f '^^'^^ oie/j s.Ur'xMnjqx*) lo • i 15. A' jar containing 3 s(|Tiare feet of surface was employed, Yand the thermo-electrometer gave an indication of about 90 de- grees, falling 3 or 4 degrees as the points were withdrawn to the greatest striking distance nearly 0*3 of an inch, but rising again as the distance lessened, until they were brought so near that the negative point became heated, at which time the fluid fell 20 or 80 degrees, the diminution of temperature in the electrometer being greater as the negative point became hotter. As soon as the negative terminal became heated, the noise of the sparks was much less, and they assumed a more diffused and flame-like '• eharacter. On withdrawing the points again from each other, the temperature in the electrometer increased as the heat of the negative terminal diminished ; and when the points had been so far withdrawn that the negative terminal ceased to be heated, • the sparks suddenly resumed their noisy character, and the fluid -^^^ suddenly rose to about 90 degrees. 16. A jar of 1 square foot, but of rather thinner glass, pro- ^«**^^ Iv of the Induction Coil, ,(' ?M 383 duced a maximum temperature of 35 degrees, but the sparks between the terminals were much longer, averaging about 0-4 of an inch. The temperature fell a few degrees on pushing the striking distance to its greatest extent, but was pretty constant at all distances between the extreme length and the shorter in- terval, about 0*1, at which the negative point became ignited. 17. A jar of half a square foot, of rather stouter glass, about the same thickness as the large jar, gave a maximum temperature of 15 degrees, and the maximum length of spark was 0*5 of an inch ; but the negative terminal now became heated, when the striking distance was reduced to 0*2 of an inch ; but between these extremes the temperature indicated by the electrometer was not influenced by any variation in the length of the sparks. 18. On comparing the results of these jars with each other, they appear to have produced effects bearing a direct relation to the extent of their coated surfaces; for although the jar of 1 square foot gave an effect rather more than was due to its relative surface, yet being thinner it was capable of holding rather a stronger charge ; and without the least desire to coax results, the simple relation of effects to causes appearshere strikingly manifest. 19. In a subsequent series of experiments an extra unit of measure, containing a quarter of a square foot, was added; and here the effects were in relation to each other as 1, 2, 4+12, corresponding to the relative extent of the surfaces of the jars, the thin jar of 1 square foot (4 + ) still remaining the exception. When however two jars of 3 square feet were connected as a bat- tery, so as to double the surface of the last element, the resulting temperature was only 115 degrees, and the spark between the terminals much shorter. 20. In each set of experiments care was taken to conduct the whole as speedily as was consistent with accuracy, so as to obtain the whole of the results before the action of the voltaic battery began to subside ; and it was curious to remark, that as it gra- dually lost power, so the largest jar gradually lost the relation- ship which it originally bore to the others. :■■ 21. The results here detailed appear to indicate, that, with a given surface, the heating effect of the electrical discharges does not vary with the length of the spark within given limits, other things remaining the same. J 22. That the heating effect of different surfaces appears to be in the direct simple ratio of their respective areas, up to the point at which the quantity of electricity transmitted by each wave of the induced current is capable of developing the maxi- mum effect of the coated surface in relation to its own tension. h 23. On varying these experiments by exciting the coil more or less powerfully, the same relation between surface and heating effect was observed whatever was the value of the unit indicated 384 On a powerful Fm^d^ the Induction Coil. ^^ by the electrometer, exceptin** that as the power of the instru- ment was giTater or leas, so the extreiTie indications of the largest ^sui'fuce con-espondingly increased or diminished. ^^' 24. Jt is well known that the soft static sp^rk between the "ttfrniinah of the coil inflames gunpowder, whilst the explosive ^^dischargcs when the jar is connected only disperse it without inflainmati'jn. Hence it would appear that there is a difference 'in the velocity with which the wave or current is transmitted; 'lor although the quantity must be very considerable, yet its i'Vclocity appeal's to a certain extent retarded in its passage through ^the induced wire, and that the effect of the jar appears to be ^0 measure out cei'tain quantities, which are transmitted with greater energy and velocity through that poition of the circuit forming the connexion beUveen its own inner and outer coatings, than through those portions by which these coatings are supplied, and hence the difference in the thermal effects of these different vpprtions of the circuit upon metallic wires and gunpowder. •^Y' 25. In order to test the correctness of the foregoing opinion, ^t! small jar of half a square foot was connected in the ordinary tttanner with the coil (par. 7), and a thermo-electrometer placed In the circuit of the jar. A portion of gunpowder was placed V between the points of the discharger. On passing the discharges, ^'the gunpowder was dispersed, but the electrometer indicated the •iisual rise of temperature. On now inserting a wet string as a portion of the circuit of the jar, the discharges lost their noisy character and inflamed the gunpowder, but the thermo-electro- meter remained perfectly unaffected. >^ • 26. Whatever be the character of this secondary wave, or of '''the sources from whence it is derived, it is clear that an amount W^ electrical disturbance is produced far exceeding what we have *iio 'fuJaiJ-ifiib 1 XLVIII. Note on Prof. Q\di\x.^\\Ji^^^ Application of the Mechanical ti'iioTheory of Heat to the Steam-engine. By J. P. Joule, Esq.^ ^'^ni S the motives which induced Professor Thomson and myself -^jL to undertake experiments on the thermal effects of fluids in motion appear to me to be somewhat misunderstood by Professor R. Clausius in his paper published in the October Number of this Magazine, I may be allowed to refer to Prof. Thomson's paper "On the Dynamical Theory of Heat" (quoted by Clausius), of which Part IV. is devoted to the discussion of a method of discovering experimentally the relation between the ■ mechanical work spent and the heat produced by the compression of a gaseous fluid. In it, referring to the hypothesis first assumed by Mayer, that the work spent in compressing a gas is exactly equivalent to the heat evolved, he notices my paper " On the ' Changes of Temperature produced by the Rarefaction and Con- densation of Air,'' in which the hypothesis is verified as far as the limits of experimental accuracy permitted. Prof. Thomson then ' proceeds, § 72-77 f, to point out a method whereby an excess- • ively delicate test of Mayer's hypothesis may be obtained for any Vi-rmif Communicated by the Author. f Phil. Mag. vol. iv. p. 429. 386 Dr. Heddle on the " Davidsonite " of Thomson. tcDiperature, — the method, in fact, which we have employed in onr experiments referred to by the celebrated German physicist. At the commencement of the memoir* containing the first results of these experiments, we remark that Mayer^s hypothesis, which has been adopted by lloltzmann, Clausius, and other phi- losophers, had been verified approximately for air at ordinary temperatures by my experiments, and by Prof. Thomson's theo- retical investigation, founded on a conclusion of Carnot's which requires no modification in the dynamical theory of heat. I may add, that in Prof. Thomson's account of Carnot's theory, com- municated to the Royal Society of Edinburgh, April 1849, the formula is demonstrated which gives Carnot's function in terms of the temperature, and the ratio of the work spent to the heat evolved in compressing air kept at the same temperature. The results we have arrived at in our joint investigation have tended certainly to develope our views, and to give a more definite know- ledge of the constitution of elastic fluids, but they do not con- tradict our original statements, pubhshed before the appearance of Prof. Clausius's papers. Oakiield, Moss Side, ■■! Oct. 20, 1856. J 'i '<< n II 'li .w. XLIX. Note on the " Davidsonite " of Thomson. By Dr. Heddle f. SOME time ago I obtained from the Rev. Dr. Fleming a por- tion of a crystal of " Davidsonite," which he requested me to analyse. The Doctor informed me that he had obtained from it fflucina, and believed it to be merely beryl, and not a distinct species, a conclusion at which I had myself arrived from a simple mineralogical examination of the substance. The crystal on ana- lysis afforded 12*52 per cent, of glucina. I do not give the full analysis, as the specimen was contaminated with plates of mica and grains of quartz, which 1 was unable entirely to exclude ; from this cause the proportion of glucina must be somewhat greater than that stated. Setting aside the above mechanical impurities, the analysis in all respects agreed with that of beryl. Thomson considered the substance to be oblique, as his crystal had an oblique termination ; this was the result of one of the terminal planes truncating so deeply as to carry off all the others. All the crystals are rough and coarse. The localities at Aberdeen are Tory, opposite the mouth of the harbour, and the Rubieslaw quarry ; at both it occurs in coarse- grained granitic veins, which traverse the ordinary compact gra- nite of the district. At Rubieslaw the crystals of felspar in these veins are twins of very large dimensions. * Phil. Mag. vol. iv. p. 481. t Communicated by the Author. luhnojqm^ ^p^ciedmgs ol Learned Societies. im ifnh a/fi :^aififBlnoo royal society. ^/.^'■\Air>n^ii\ .-^'1 . ,f}f ti [Continued from p. 316.] Jan. 31, 1856. — The Lord Wrottesley, President, in the Chair. THE following communication was read : — *' A Description of a new Sphygmoscope, an Instrument for indicating the Movements of the Heart and Blood-vessels ; with an Account of Observations obtained by the aid of that Instrument." By S. Scott Alison, M.D. The sphygmoscope (fig. 1) consists of a small chamber containing spirits of wine or other liquid, provided with a thin india-rubber wall, where it is to be applied to the chest. At the opposite extre- mity the chamber communicates with a glass tube, which rises to some height above the level of the chamber. Liquid is supplied to the instrument until it stands in the tube a little above the level of the chamber. The pressure of the column of liquid in the tube acts upon the elastic or yielding wall of india-rubber and causes it to pro- trude. This protruding part or chest-piece is very readily affected by external impulse ; it yields to the slightest touclv and being pushed inwards, causes a displacement of the liquid in the non-elastic chamber, and forces a portion of liquid up the tube. The protruding wall of india-rubber is driven inwards when it is brought in contact with that portion of the chest which is struck by the apex of the heart, and a rise in the tube takes place. When the heart retires, the india-rubber wall, affected by the pressure of the column of -i.-.M .tali .?'. 3m , 'dil djid <■ fmnt tismaiiio bed od toHf j'pjb a ion bim .1^' HfTiJH? B mori havriTs^ 'p no Istg'/T*) odT ' 'jdlavig ioft oh 1 /: • 0 io ^iatfifq cBfw f- LDfyjx \ dhijh/o ot ■^■yni ijmo'ig jmiwornos od Jsui ^^^i)i'Ii.lqmi [sohijiibam t/n: ' * ; ,jupifdc Fig. 1, ,glijiljO ; lO^iiiodT idu riB hmi. f icfrin:ir-)t •tM-dT HA iociijiii afiroq(funj!»;t! 388 ^ , X , ^ , , Moyal Society : — > | f / t (\ forced in by the apex of the heart ia denoted by a corresponding rise in the tube, and the amount of protrusion of the india-rubber wall which takes ])lace when the heart retires is denoted by a corre- sponding fall in the tube. The tube is supplied with a graduated scale to denote the rise and fall with exactitude. The glass tube is provided at the top with some contrivance, such as a brass screw and collar, to prevent the egress of the liquid when the instrument is not in use, or a bulb with an orifice may be supplied. When employed, the glass tube is left open to permit of the passage, pf the air to and fro. ,, ,,,j,ij The sphygmoscope is mounted upon a stand. The chamber and tube are fitted to a horizontal arm, which is made to move up and down so as to carry the instrument to the desired height. The b^ is so made as to secure the requisite immobility. i (iino The glass tube is a foot or more long, and the round bore is about the one-eighth part of an inch. If the bore be much larger, the movement will be inconsiderable ; if much less, capillary attraction will interfere and prevent free motion. When the instrument is to be employed, mounted upon its stand, it is placed upon a firm table with the chamber projecting beyond it. The person whose heart is to be examined is seated upon a firm chair, with his chest erect and free from motion. The protruding india-rubber wall of the chamber or chest-piece is delicately made to touch the fifth intercostal space so as to receive the blow of the apex of the heart. The liquid in the tube is now observed to be in mo- tion. With persons in ordinary health, the hquid rises and falls about an inch. This rise and fall, after taking place three or four times, is followed by a much longer rise and fall to the extent of three or four inches, due to the advancement and retirement of the wall of the chest during the acts of respiration. The shorter rise and fall are again repeated and are again followed by the longer rise and fall caused by the motions of the chest. During the longer rise and fall due to respiration, the beat and retreat of the heart are still to be recognized by brief interruptions in the rise and fall of the liquid. When difficulty is experienced in obtaining the shock of the heart sufficiently strong to give an appreciable rise and fall, the examinee should make a moderate expiration, and then hold his breath and incline the chest somewhat forward. When the action of the heart is feebly felt at the preecordial region, it may be necessary to apply the instrument to the naked chest; but this is not necessary in the great majority of cases, and it will generally suffice to make the shirt and waistcoat fit tight to the skin. In many trials the sphygmoscope has succeeded in indicating the movements of the heart through the tightly buttoned coat. Thin persons are very favourable for exami- nation ; on the other hand, the corpulent less readily affect the in- strument. The movements of the heart, though best indicated at the fifth intercostal space, are to be denoted at other parts of the chest, and in some examples of disease and of large and powerful heart, even in the epigastric region. The moving arm proves convenient in apply- Dr. Alison on a new Spkygmoscope, 389 lug the instrument to these parts. In many persons with no very excited heart, it is sensibly acted on at the scapular and infra-dorsal regions. ■■ -'''-.,: - ::;, y\y>,A -mI: .ij;:/' ^ By means '6f this instrumeiit^'th6*'bbseri^gf can ascertain the fre- quency of the beats of the heart, but as this can be effected in most cases with accuracy at the radial artery, no particular advantage is gained from it in respect to this point. The duration of the impulse of the heart upon the chest is well measured by this instrument : the time occupied by the rise, is the time occupied by the impulse. A slow rise after a rapid rise shows a slow beat after a rapid one, and vice versa, a slow fall after an ordinary fall, shows a slow retirement after an ordinary one. An intermittent pulse is marked by an imperfect rise, followed by an ordinary fall, and then by a long rise. The rise is sometimes slower than the fall, which is occasionally found to be abrupt. This is observed when the heart, by reason of its great size, and of the some- what bent back posture of the thorax, suddenly falls away from the walls of the chest. The movements of the auricles under ordinary circumstances are not indicated by the sphygmoscope, though when it is placed over them, the liquid in the tube is moved upwards and downwards ; but as these movements are synchronous with the movements upwards and downwards of another instrument placed at the apex, it may be inferred that the ventricle is the cause of them all. In some examples of greatly excited heart, as in phthisis, the instrument has revealed movements which seemed to proceed from the auricles ; but further observations are required to settle this point, as well as the question whether the movements of the aorta, in a state of excitement, communicate any influence to the instrument. The instrument, placed upon the heart, indicates strokes of that organ which are so feeble as to have no corresponding pulse at the wrist. No pause whatever in the movement of the liquid has been at any time observed when the sphygmoscope has been carefully placed so as to receive the full beat, and fall back with freedom. This would go to show that the heart, however slow, is in constant mo- tion, and, contrary to the belief of many physiologists, enjoys no pause. There is certainly no pause in the descent of the liquid, which takes place when the heart retires from the thoracic walls, in the middle of which movement it has been said a very short pause is to be observed in living animals having the heart exposed. The force with which the heart beats at the fifth intercostal space may be ascertained by closing the upper extremity of the glass tube, and observing the extent to which the enclosed air is compressed. When the heart is excited, the liquid in the sphygmoscope rises and falls more than usual ; but the rise and fall of the excited enlarged heart is much the same as the rise and fall of the excited normal organ. For the most part the enlarged heart gives movements to the instrument when placed upon the ribs and sternum, whilst the 390 *, Roi^al Society .^-^ no?f(A M normally sized heart affects more exclusively when it is placed upon the fifth intercostal space. The sphyguioscope indicates with exactitude both the absolute and* the comparative influence upon the heart, of food, cordials, stimu- lants, and tonic medicines. It does the same in respect to depress- ing causes, such as hunger, cold, and sedatives. With the aid of this instrument the fact is demonstrated, that the action of the heart may be great when the pulse is small, — that the heart may strike the instrument with force when the pulse scarcely affects the liquid of the hand-sphygmoscope. It affords a remarkable proof that the pulse is one thing and the heart's action another, and teaches that the pulse is only an approximate sign of the state of the heart. It is found also, that while cold at the surface and extremities may depress the pulse, the heart may remain little enfeebled, or even become excited, and that warmth and friction applied to the extremities may cause an excited pulse without there being any accompanying increased force of the heart. The influence of respiration upon the action of the heart is mani- fested, in some degree, by the instrument placed over the region of the heart. If the breath be stopped after an ordinary expiration, the movement of the liquid is seen to be increased. It a very long and forcible inspiration be made and the breath then suspended, the movement is somewhat reduced ; but when the respiration pig. 2. is again allowed to take its normal course, the movement is ^ seen to be increased for a short time. The sphygmoscope rises during the first sound of the heart 1; and falls at the second. The sphygmoscope reduced (fig. 2), deprived of its stand, having a level elastic wall instead of protruding one, and having a glass tube with an almost capillary bore, forms a remarkably delicate indicator of the pulse*. It is so deli- cate in its impressions that it is appreciably affected by the regurgitant wave in the jugular veins, and by the wave in arteries greatly smaller than the radial. From its nicety in manifesting the beat of the blood-wave, it is very valuable, and is called the hand-sphygmoscope. By means of this hand instrument applied to the arteries, a comparison is readily ma le between the tim^ of the beat of the heart and the rise of the arteries under the influence of the blood-wave. This instrument is much more delicate than the finger in such an inquiry. The impressions made upon the fingers of two hands fail to be conveyed with suf- „ , ficient nicety to the mind to tell with certainty the relative sphvgrao. time of the beat of the heart and arteries. Excei)t in cases of scope. * Since this instrument was contrived, the author lias learned that a sphygmo- meter of much the same construction was invented some tw«ity years ago by Mons. le Docteor Ilerrison, and that a memoir ui>on it was presented to the In- stitute of France. The liquid employed was mercury — too heavy to indicate feeble impulses, and the moveable wall was of gold-beater's skin, which is inelastic. It may be added, that M. Magendie reported against the practical application of the invention. t.tn.r lOlft Dr. Alison on a new Sphygmoscope, S91 extreme slowness, the sensations obtained from the two hands im- pressed at nearly the same time, do not admit of a distinct difference in respect to time being made out. It has been to this very defect that the erroneous idea, that the beat of the heart and the beat' of the pulse are synchronous, or nearly so, has owed its origin and continuance. The hand-sphygmoscope, placed upon the radial artery, shows a rise of the liquid while there is a fall in the sphygmoscope placed over the heart. As the liquid in the one instrument starts from below, the liquid in the other starts from above, and as the liquid \ in the one reaches the top of its ascent, the liquid in the otheri reaches the bottom of its descent, to renew their opposing course. The movements in the two instruments at the same instant are always ; opposed, and the whole time occupied in the movement of one in- strument in one direction appears to be occupied by the movement of the other in the opposite direction. The movements alternate with as much apparent exactitude as the arms of a well-adjusted balance. When the lapse of time between the beat of the heart and the pulse at the wrist was first observ^ed, suspicion of disease of the aorta was entertained, but the subsequent examination of many persons proved that this alternation was natural. In some twenty persons subjected to examination, the complete alternation has been made out without the shadow of a doubt. These persons were of all ages above childhood, and had the pulse of different degrees of rapidity ^ from 60 to 100. Hand-sphygmoscopes placed upon the carotid, the brachial, the radial, the femoral, and the dorsal artery of the foot, rise at the same instant, and fall at the same point of time. These facts prove the existence of two great laws not previously ■ enunciated, — 1st, that the heart's beat alternates with the pulse at i the wrist ; 2ndly, that the pulse of arteries beyond the chest takes place in all parts at the same instant, and without any appreciable interval. The pulse, it appears, occurs during the retirement of the hearfe^ from the thoracic walls, and the collapse or fall of the arteries takes ? place during the impulse of the heart. During the rise in the hand- sphygmoscope placed over the arteries, the second sound of the heart has been distinctly heard, and during the fall, the first, softer < and more prolonged sound has been easily distinguished. '■ The horse has been subjected to examination, to learn the relative' * time of the beat of the heart and arteries, but the respiratory move-' • ments and the motions of the animal have hitherto restricted the^ application of the instruments. However, it has been most distinctly ascertained, by the hand placed upon the heart and upon the plantar artery, that between the beat of these parts there is a decided inter- val. The slowness of the action of the heart in the horse renders this experiment less open to error than in man. In these experi- ments upon the horse, Mr. Ajfayor;, the eminent veterinarian, gave his ' valuable aid. iVii^i;t^i^.L;vsj- • -^Vj^j^dvj, _ ] The sphygmoscope forms a good pneumoscope. It delicatelyn. 392 Royal Society : — measures the rise and fall of the chest in respiration. It Hkewise declares the relative duration of inspiration and expiration, and may thus prove useful in the detection of incipient phthisis, and other pulmonary diseases. When the liquid has attained its highest eleva- tion at the end of inspiration, it immediately begins to fall ; but when it has reached the lowest point at the end of expiration, it remains there some instants. The ascent is slower than the descent. After the fall of an ordinary expiration, a forced expiration gives a second fall. The sphygmoscope may be employed without a stand and is then more portable (fig. 3), but from the want of a fixed basis, and from the motion of the ribs on which it must rest, its manifesta- tions are less extensive and satisfactory. It may be maintained in situ with an elastic band placed around the thorax. When em- ployed without a stand, as it must rest upon the Fig. 3. ribs, the elastic wall of the chamber should be plain, and not protruding. The hand-sphygmoscope is an exceedingly delicate instrument, but requires great care and nicety in its construction. It may be made by taking about an inch and a half of a gutta percha tube, half an inch in diameter, slightly widening one extremity of it to make a chamber large enough to hold a small horse-bean, and fastening with thread a piece of thin india-rubber, or of Bourgeaud's india-rubber bandage, securely over it for the elastic and moveable wall. The liquid is now supplied, and the glass tube, with a very fine flat bore, say ^V^^ ^^ ^^ inch, and provided with a ring of india-rubber, obtained by cutting oiF a small portion of a fine india-rubber tube, for a "washer," is now inserted and the instrument is ready for use. The hand-sphygmoscope discovers the blood-wave in regurgitation of the jugular veins ; it responds to the radial of the newly- born infant ; it rises and falls with the movements of the brain of the infant, though some months old, as that organ rises and falls under the influ- ence of its arteries. There is no doubt that, ap- plied to the fontanelles before delivery, it will Portable Sphyemo- inform the obstetrician whether the foetus be dead scope. or alive, and, in cases of diflicult labour, supply important evidence for his guidance. The hand-sphygmoscope apphed to the radial artery, and to the fontanelles of a dying infant three months old, has indicated to the author the influence of respiration upon the circulation. During inspiration, the column of liquid in the tube was found to fall as if sucked down, and during expiration to spring again. In practical surgery, the hand-sphygmoscope may possibly be employed with advantage, for it will rise with the wave or fluctuation of liquid tumours. It may be placed where the fingers cannot reach. Prof. Thomson on the Electro-dynamic Properties of Metals, 393 The rise in the instrument is greater in liquid than in aeriform tumours on account of the compressibility of air, and the fall is more rapid and decided when the contents of the tumour are liquid. For the most part, the hand-sphygmoscope is best applied simply with the aid of the fingers. It is delicately held between the tips of the thumb, fore- and middle-fingers, the nails resting on the examinee. The elastic wall is on no account to be pressed down with a dead weight upon the vessel. It is to be nicely lowered to the level of the artery when collapsed. When the artery rises, it will strike the elastic wall, and as the chamber is fixed by the fingers, the entire blow is communicated to the liquid and it rises in the tube. During the retirement or collapse of the artery, the elastic wall resumes its level condition and draw* the liquid down the tube. This motion of the liquid allows the instrument to be employed though the open end of the tube be dependent. When it is desired to avoid the varying pressure experienced when the instrument is held between the fingers, some such apparatus as was invented by Dr. E. S. Blundell, or an elastic band suitably applied around the wrist, will be useful. The sphygmoscope is for several purposes renderedmore convenient of application by interposing, between the chamber and the glass tube, a piece of india-rubber tube of suitable bore and length. In this way the comparison of the beat of the heart and the pulse of an artery is much facilitated, for the glass tubes of the two instruments employed may be brought parallel and close to each other, so that the opposite motions of the liquids in the two tubes are, by near contrast, rendered easier of observation. In employing this adapta- tion, care must of course be taken that the india-rubber tube is of the same calibre and length in both instruments. It is hoped that the sphygmoscope will aid in the acquisition of additional knowledge of the movements and condition of the heart, the situation of which within a case of bone, wisely provided to secure it from injury, has this disadvantage for the physiologist and phy- sician, that the action and condition of the organ are with difiiculty made out. By means of the sphygmoscope, that small amount ot movement which is manifested at the exterior of the chest may be rendered more appreciable to our senses, and more available for phy- siological and curative purposes ; and perhaps information may be obtained by this instrument which has hitherto been procurable only by the practice of vivisection. Park Street, Grosvenor Square, London, Jan. 12, 1856. Feb. 28.-- The Lord Wrottesley, President, in the Chair. The following communication was read : — The Bakerian Lecture. — " On the Electro-dynamic Properties of Metals." By Professor William Thomson, F.R.S. The Lecturer gave an exposition of the substance of a paper pre- sented by him to the Society under the above title. The paper consists of five parts, namely: — 1. On the Electric Convection of Heat ; 2. On Thermo-electric Inversions ; 3. On the Effects of Mechanical Strain and of Magnetization on the Thermo-electric Qualities of Metals ; 4. On Methods for comparing PhiU Mag. S. 4. Vol, 12. No. 80. Nov, 1856. 2 D 894 Royal Society : — and testing Galvanic Kesistances, illustrated by Preliminary Experi- ments on the Effects of Tension and Magnetization on the Electric Conductivity of Metals ; 5. On the Effects of Magnetization on the Electric Conductivity of Iron. 1. In the first part a fnll account of the experiments, of which the results were communicated to the Royal Society in April 1 854 *, is pre- ceded by a short statement of the reasoning, founded on incontrovertible prmciples regarding the source of energy drawn upon by a thermo- electric current, which led the author to commence the experimental investigation with the certainty that the property looked for really existed whether he could find it or not. In confirmation of the extra- ordinary conclusion then announced,— that an electric current in an un- equally heated conductor, if its nominal direction be from hot to cold through the metal, causes a cooling effect in iron, and a heating effect in copper, — the author describes new experiments which he has recently made, and which are as decisive in leading to the same conclusion as those by which he had first established it. He also describes ex- periments by which he had recently given an independent demon- stration that brass has the same property as copper, and platinum the same quality as iron, with reference to electric convection of heat ; results anticipated f, one as certain, and the other as highly probable, from the previous results regarding electric convection in copper and iron, and from the known thermo-electric relations between these metals and the others. 2. The phsenomenon of thermo-electric inversion between metals, discovered by Cumming, forms the subject of the second part. A mode of experimenting is described, by which inversions may be readily detected when they exist between any two metals, and, when thermometers are available, the temperature of neutrality determined with precision. Various results of its application are mentioned, of which some are shown in the following Table : — -14*' Cent. -12°-2 -l°-5 8°-2 36° 38° 44° 44° 47° P3 Brass Pi Cadmium Pi Silver Pi Zinc Pa Lead Pa Brass Pa Tin Lead Brass Silver Zinc 53" 64° 71° 72° 99° 121° 130° 162°-5 237° 280° P2 Double wire of PaUadium, 11-31 gn., and Cop- per, 19-41 gr«. Pi Copper Silver Gold Gold Zinc Pi Brass Pi Lead Pi Tin Iron Cadmium Iron Silver Iron Copper The number at the head of each column expresses the temperature Centigrade by mercurial thermometers, at which the two metals written below it are thermo- electrically neutral to one another ; and the lower metal in each column is that which passes the other from bismuth towards antimony as the temperature rises. Pj, Pj, P3 denote three particular specimens of platinum wire, used by the author as standards. * See Phil. Mag. July, 1854. t See Phil. Mag. July 1854 ; also " Dynamical Theory of Heat," Part VI. § 135 ; Phil Mag. vol. xi. p. 292. Prof. Thomson on the Electro-dynamic Properties of Metals. 395 It was also found that Aluminium must be neutral to either Pg, or Brass, or Pg, at some temperature between —14° C. and 38° C. ; that Brass becomes neutral to Copper at some high temperature, pro- bably between 800° and 1400° ; Copper to Silver, a little below the melting-point of silver ; Nickel to Palladium, at some high tempera- ture, perhaps about a low red heat ; and Pg to impure mercury (that had been used for amalgamating zinc plates), at a temperature be- tween — 10° and 0°. Probably Pg becomes neutral to pure mercury at some temperature below — 10° C. 3. In the third part, eifects of mechanical strain, and of magnet- ization on the thermo-electric qualities of metals, are investigated. The author had previously communicated to the Royal Society* results he had obtained regarding the thermo-electric qualities of copper and of iron wires under longitudinal stress, namely, that the former exhibits a deviation towards bismuth, and the latter towards antimony, from the same metal in an unstrained state. The only kind of stress applicable to a solid which has no direc- tional attributes, is uniform pressure or traction in all directions. Hence it appeared probable to the author that a simple longitudinal stress would induce different thermo-electric qualities in different directions, in any homogeneous non-crystalline metal subjected to it. But he had found (see Phil. Mag. July, 1854) that the thermo- electric effect of longitudinal traction on a wire, either of iron or of copper, is sensible to tests he could readily command, and more so in the case of the former than in that of the latter. He therefore made experiments to test the difference of thermo-electric quality in different directions in a mass of iron under stress, and fully established the conclusion that the thermo-electric quality across lines of traction differs from the thermo-electric quality along lines of traction, as bars of bismuth differ from bars of antimony. The experiments he has already made nearly establish the conclusion that unstrained iron has intermediate thermo-electric quality between those of the two critical directions in iron under distorting stress. The experiments of Magnus show that wires hardened by wire- drawing have different thermo-electric qualities lengthwise from wires of the same substance softened by annealing. The author has veri- fied, that in copper, iron, and tin, simple traction, leaving permanent elongation, leaves also a thermo-electric effect, the same as Magnus had found by wire- drawing, which is a composite application of lon- gitudinal traction and lateral compression ; and that in a variety of metals, namely, iron, copper, brass, tin, platinum, permanent lateral compression (by hammering) leaves still the same thermo-electric effect, as Magnus had found by wire-drawing. In cadmium, not examined by Magnus, and lead, which had not a given result, the experiments now adduced show a thermo-electric effect of hammering, the same as in all the other metals except iron. Zinc wire was also tested, and found to exhibit the same effect as copper, though Magnus had found a reverse quality as due to wire-drawing. The discrepance in this case is probably due to the peculiar effect of * April 1854. See PhU. Mag. July, 1854. 2D2 396 Royal Society, annealing on zinc wire, making it brittle and crystalline, which might give a different condition, as the "annealed" in Magnus's experi- ment, and the "unhammered" in the experiment now adduced. Setting aside this case, the author concludes that generally the effect of permanent lateral compression is the same as that of permanent longitudinal extension, or of hardening by wire-drawing, upon the thermo-electric quality of a wire placed longitudinally in an electric circuit; that in iron it is a deviation from the constrained metal towards bismuth, and that in all the other metals mentioned it is a deviation towards antimony ; and that in copper and iron it is the reverse of the effect experienced by the same metal while under the stress that caused the strain. Since no kind of strain, except uni- form condensation or dilatation in all directions, is free from the directional attribute, it appeared probable to the author that the thermo-electric effects remaining in a metal left with a longitudinal strain, retained after the stress that caused it is removed, must be different in different directions. He therefore experimented on iron hardened by longitudinal compression, and found that it deviates from soft iron towards antimony, or in the contrary way to iron hardened by longitudinal traction. From this, and from the results quoted above, it follows that in iron hardened by compression in one direction, the thermo-electric qualities in this direction differ from those in lines perpendicular to it, as antimony differs from bismuth ; that the reverse statement applies to iron hardened by traction in one direction ; and that these differing thermo-electric qualities have in' each case the thermo-electric quality of soft iron intermediate between them. These various results show that the character of the effect in each case is decided by distorting stress or by distortioriy and leave entirely open, and only to be answered by further experiments, the questions : what is the thermo-electric effect of pressure or traction, applied uniformly in all directions to a metal? and what is the thermo- electric effect of a permanent condensation or dilatation remaining in the metal, when freed from the force by which that condensation or dilatation was produced ? Experiments are also described, by which the author found that in soft iron under magnetic force, and in that retaining magnetism, when removed from the magnetizing force, directions along the lines of magnetization deviate thermo-electrically towards antimony ; and that directions perpendicularly across the lines of magnetization in soft iron, deviate towards bismuth, from the unmagnetized metal. He illustrates this conclusion by an experiment on a riband of iron, magnetized nearly at an angle of 45° to its length, and heated along one edge while the other is kept cool. When the two ends, kept at the same temperature, are put in communication with the elec- trodes of a galvanometer, a powerful current is indicated, in such a direction, that if pursued along a rectangular zigzag from edge to edge through the band, the course is always /row across to along the lines of magnetization through the hot edge, and from along to acros9 the lines (^magnetization through the cold edge. Cambridge Philosophical Society, 397 4. In this part of the communication, attempts made by the author to find the effects of various influences on electric conductivities of metals are described. One of these, with a very unsatisfactory method for testing resistances, led to the conclusion that longitudinal magnetization diminishes the conducting quality of iron wire. The general plan for testing resistances, which he subsequently adopted as the best he could find, and which has proved very satisfactory, is next explained ; and as an illustration, a single experiment on the relative effect of an equal longitudinal extension on the resistances of iron and copper wires is described. The conclusion established by this experiment is, that both by extension with the tractive force still in operation, and by permanent extension retained after a cessa- tion of stress, the conductivity of the substance is more diminished in iron than in copper ; or else that it is more increased in copper than in iron, or increased in copper while diminished in iron, if it is not in each metal diminished, as the author is led by a partial in- vestigation of the absolute effect in each metal to believe. 5. The result previously arrived at regarding the effect of longi- tudinal magnetization on the conductivity of iron is confirmed ; and an experiment that would have been found impracticable by the less satisfactory method, proves the same conclusion for magnetized steel wire, with the magnetizing influence away. Two very different experiments show further, that the electric conductivity of magnetized iron is greater across than along the lines of magnetization. A last experiment, showing that iron gains in conducting power by mag- netization across the lines of the electric current, leads to the con- clusion that there is a direction inclined obliquely to the lines of magnetization, along which the conductivity of magnetized iron would remain unchanged on a cessation of the magnetizing force. CAMBRIDGE PHILOSOPHICAL SOCIETY. [Continued from p. 320.] Feb. 25. — A paper was read, " On a direct method of estimating Velocities, Accelerations, and all similar magnitudes with respect to Axes moveable in any manner in Space, with applications." By Mr. Hayward, of St. John's College. The frequent recurrence, in many different investigations of kine- matics and dynamics, of exactly corresponding equations, suggests the inquiry whether they do not result from some common principle, from which they may be deduced once for all. An investigation based on this idea forms the first part of this paper, and the result is the method mentioned in the title. This calculus shows how the variations of any magnitude, capable of representation by a straight line of definite length in a definite direction, and subject to the parallelogrammic law of combination, may be simply and directly determined relatively to any axes what- ever. If such a magnitude (m) be estimated in a given direction, its intensity in that direction will be represented by the projection on 398 Cambridge Philosophical Society : — it of the line which represents u. If this given direction be not fixed, but move according to a given law, the projection of u upon it will change by the alteration of its inclination to the direction of u ; and the rate of that change is easily calculated, whence an expres- sion for the acceleration of the resolved part of u along a given axis as due to the motion of that awis. If u itself be variable, its variations may be conceived to be due to an acceleration / in a definite direc- tion, which in the time dt produces a quantity /rff in the direction of / to be combined with u by the parallelogrammic law ; hence result expressions for the changes in intensity and direction of u. If, u being variable, the variations in its intensity estimated along a given moveable direction be sought, it will consist of two parts : one, that due to the resolved part of/ in the given direction ; the other, that due to the motion of the axis, which is the same as if/ had not existed, or u had been constant: hence expressions for the total acceleration of the resolved part of u along the given moveable axis. If u be resolved along three rectangular axes, these expressions take the forms of familiar kinematical and dynamical equations. These results furnish immediately expressions for the relative velocities of a point with respect to moving axes when its absolute velocities in their directions are given, and vice versd. They also furnish very ready means of estimating accelerations in variable di- rections ; as, for instance, the radial and transversal accelerations of a point moving in a plane or in space, or the tangential and normal accelerations in the same case. These are some kinematical appli- cations of the calculus. The dynamical applications form the second part of the paper. Here^the general problem of the motion of a system, so far as it is due to external forces, is divided into two steps; one ixom. force to momentum, the other from momentum to velocity. If the momenta of the particles of a system be reduced like a system of forces, they produce a single linear momentum and a single angular momentum, just as a system of forces produces a single force and a single couple. The linear momentum is (in our received language) the momentum of the mass of the system collected at its centre of gravity ; the an- gular momentum is a magnitude the constancy of whose intensity in a given axis is equivalent to the assertion of the principle of the conservation of areas for that axis, and the constancy of whose direc- tions determines the " invariable plane " as a plane perpendicular to it. The momentum, whether linear or angular, is a magnitude to which the previous calculus applies, and the resultant force and resultant couple are respectively the accelerators of the two kinds of momentum : hence the equations obtained in the first part, inter- preted with respect to these magnitudes, furnish equations in any required form for the determination of the momenta at any instant. The step from force to momentum is independent of the nature of the system, that from momentum to velocity requires the system to be particularized. In the paper the case of an invariable system only is considered, and in particular its motion of rotation about its centre of gravity. The axis of rotation or angular velocity is related in Mr. Ha3rward on a Method of estimating Velocities, ^c. 399 direction to that of angular momentum, as the radius of the central ellipsoid with which it coincides to the normal at its extremity. Hence an angular momentum constant in intensity and direction, in general gives rise to an angular velocity variable in both respects, and vice versd. The question then becomes, to determine the acce- leration of angular velocity due to the motion of the system. This is obtained by determining the acceleration of angular momentum for a line fixed in the body, which is then shown to be a maximum for the normal to the plane containing the axes of angular momentum and velocity ; then the acceleration along this line is the total acce- leration of angular momentum due to the motion, and the accelera- tion of angular velocity determined from it (just as the angular velo- city is determined from the momentum) is that due to the motion of the system. Also the acceleration of angular velocity due to the forces is related to the resultant couple and its axis, just as the an- gular velocity to the angular momentum. Thus the accelerations of angular velocity due both to the motion and to the forces being determined, the intensity and direction of the angular velocity at any time is to be found by combining these effects by integration. The problem is worked out in the case of the axis of the resultant couple being coincident with that of angular momentum, so that this remains fixed. The paper concludes with a simple solution of the problems of Foucault's gyroscope as applied to show the effects of the earth's rotation, the simplicity arising from the method of this paper enabling us at once to refer the motion to those axes (neither fixed in the body nor in space) whose motion it is desired to determine. April 28. — A paper was read on the Theory of Heat, by Mr. A. A. Harrison of Trinity College. The object of this paper was to show that there is considerable reason for supposing that radiant heat is identical with light, and that they both consist of vibrations of the ultimate particles of matter. There is a strong presumption of this from the facts, that every body heated to a certain temperature, dependent only on the nature of the surface, emits light as well as heat ; and that " whenever light manifests itself, heat appears along with it" (Kelland) : the difference between radiant heat and ordinary heat is, that radiant heat is due to vibrations in planes normal to its direction of propagation, and that ordinary heat consists of vibrations in all three dimensions. The author endeavoured to show, in the first place, that the mo- tions of the particles of matter, which must be caused by friction, or in the union of two gases in combustion, is suflEicient of itself to account for the following phsenomena of heat : — I. That a body once heated continues of the same temperature, with the exception of heat lost by radiation, conduction, &c. This follows immediately from the principle, that in any system of par- ticles held together by mutual attractions and repulsions, the vis viva is independent of the time, and depends merely on the position of the particles. n. That bodies expand by heat. Before proceeding to this, the author argued that in gases the 400 Cambridge Philosophical Society : — repulsive force varies inversely as the cube, and not, as usually stated, the simple power of the distance ; that it is not true, without some limitation, that the force varies as the inverse first power, was urged from the fact that such a force would decrease more slowly than one varying as the inverse square, and consequently would be the force observed in astronomical phaenomena ; and even the oxygen of the ocean would repel that of the air instead of attracting it. That the force varies as the inverse cube was deduced from the law of elas- ticity, that the density varies as the pressure ; for if a particle repels other particles with a force varying as the inverse cube, it repels a fixed plane of them with a force varying as the inverse first power. That this is the case may be seen, by considering that though the particle repels particles similarly situated with a force varying as the inverse cube, yet the number of such particles varies directly as the square of the distance, and therefore the whole effect upon the plane varies inversely as the first power. And if this is true for a plane, it is also true for the solid side of the containing vessel ; for any solid may be considered as made up of a succession of planes. The law being the inverse cube, it follows that in any position the sum of the forces exerted by any particle on two particles, one on each side of it, is least when that particle is half-way between them, and increases the further the particle is removed from the middle point. This is seen directly, for the value of - ^ , -l - — t^ — is least when .r=0, and increases until a:=a. And therefore, in order to produce the same force, it would be necessary that the mean distance should be increased ; and hence if the particles of any aeri- form body be in motion, the force exerted by them would be greater than when at rest ; that is, if the pressure to be supported be con- stant, the average distance of the particles must increase, and the body must expand. III. That every aeriform body not in contact with a liquid expands in the same proportion. This was accounted for by the circumstance, that the increase of pressure depends only upon the ratio of the dis- turbance to the original distance, and not at all upon the absolute distance. IV. That air and elastic fluids give out heat on compression. By compression the absolute distance of the particles from one another is diminished ; but the absolute motion remaining the same, the rela- tive motion is increased. V. That the same amount of heat is generated in two gases sub- jected to the same pressure ; for the absolute distance of the particle in both being diminished in the same proportion, and the absolute motion remaining unaltered, the relative motion is increased in the same proportion in both. VI. The specific heats are inversely as the atomic weights. Here it was necessary to show that mass is not necessarily proportional to the quantity of matter, as usually stated ; or rather, that a body may have a different mass when considered with regard to the molecular force from what it has with respect to the force of gravity. With Mr. A. A. Harrison on the Theory of Heat, 401 regard to elasticity of gases, the weight of any single particle is so small as not to affect the result. The question remains, whether we know anything of th^ masses of different particles relatively to this repulsive force. To determine their masses we have these data. In several different gases equivalent volumes under the same pressure occupy the same space, that is (assuming the Daltonian theory, that equivalent volumes contain the same number of particles), that each particle of the two different gases exerts an equal pressure on the adjacent particles : and hence with reference to this law, the mass of a single particle in each of these two different gases is the same, and therefore the " vis viva " of equivalent weight or volumes subject to the same motion is the same for both ; that is, the quantity of heat of an equivalent of each is the same, and therefore the specific heat of a given weight is inversely as its equivalent number or atomic weight. With reference to the phaenomena of radiation, it may be shown from theoretical considerations that the inverse cube is the law required. Tlie inverse first is impossible, for then there could be no vibrations. For the same reason the inverse second is impossible (Camb. Phil. Trans, vol. vii. p. 98). The inverse fourth is also im- possible, for then there could be no vibrations, and the velocity would be infinite (vol. vi. p. 325). It has also been shown that neither the second nor the fourth would satisfy the conditions of the equations (vol. vii. p. 419). Hence, from the theory of radiation, it is supposed that the luminiferous sether consists of solid particles, attracting one another with a force varying as the inverse square (vol. vii. p. 110), and repelling with a force varying as the inverse cube. Now from the Daltonian theory, and the law of elastic fluids, it has been shown that the ultimate particles of our atmosphere com- pose such an aether. But if our atmosphere is the luminiferous aether, we must next inquire whether it does pervade space. Omitting variations of temperature, and merely considering the atmosphere as subject to the two forces of elasticity and gravity, we have for the equation of a column of air on a unit of surface, dp=-—<— pdz, or — P-z=z-i. — , where A;=i-, ^ z'' ^ pdz z""- p Integrating this, we find that^ and p, though they become extremely small, never vanish ; and therefore, if these laws are absolutely true, our atmosphere does pervade space. It may be well to obviate the objection, that black substances radiate heat best, and white substances light. This arises from employing the same word radiation to denote two different things : by radiated heat is meant heat given out from a heated body ; by radiated light is meant the secondary radiation from the surface of a body exposed to light. If Sir J. Leslie's experimental calculation of the heat lost from the sun be correct, there is no need of any theories to account for its generation. 402 Cambridge Philosophical Society, From the foregoing arguments and facts, it was urged that mo- tions and forces, which certainly exist in cases of combustion, would produce phsenomena exactly similar to thofe of heat, and therefore that part of the pha?nomena usually attributed to heat are due to this motion ; and if part of them, probably the whole. And further, that if the phsenomena of radiation of heat are explained by this motion of the particles of matter, light is simply radiated heat of considerable intensity ; and that imponderable substances, whether under the names of aether, caloric, or phlogiston, are equally ima- ginary. Also, a paper was reaS by Mr. Maxwell on the Elementary Theory of Optical Instruments. The object of this communication was to show how the magnitude and position of the image of any object seen through an optical in- strument could be ascertained without knowing the construction of the instrument, by means of data derived from two experiments on the instrument. Optical questions are generally treated of with respect to the pencils of rays which pass through the instrument. A pencil is a collection of rays which have passed through one point, and may again do so, by some optical contrivance. Now if we sup- pose all the points of a plane luminous, each will give out a pencil of rays, and that collection of pencils which passes through the in- strument may be treated as a beam of light. In a pencil only one ray passes through any point of space, unless that point be the focus. In a beam, an infinite number of rays, corresponding each to some point in the luminous plane, passes through any point ; and we may, if we choose, treat this collection of rays as a pencil proceeding from that point. Hence the same beam of light may be decomposed into pencils in an infinite variety of ways ; and yet since we regard it as the same collection of rays, we may study its properties as a beam independently of the particular way in which we conceive it analysed into pencils. Now in any instrument the incident and emergent beams are com- posed of the same light, and therefore every ray in the incident beam has a corresponding ray in the emergent beam. We do not know their path within the instrument, but before incidence and after emergence they are straight lines, and therefore any two points serve to determine the direction of each. Let us suppose the instrument such that it forms an accurate image of a plane object in a given position. Then every ray which passes through a given point of the object before incidence passes through the corresponding point of the image after emergence, and this determines one point of the emergent ray. If at any other distance from the instrument a plane object has an accurate image, then there will be two other corresponding points given in the inci- dent and emergent rays. Hence if we know the points in which an incident ray meets the planes of the two objects, we may find the incident ray by joining the points of the two images corresponding to them. It was then shown, that if the image of a plane object be distinct. Intelligence and Miscellaneous Articles, 403 flat, and similar to the object for two different distances of the object, the image of any other plane object perpendicular to the axis will be distinct, flat, and similar to the object. When the object is at an infinite distance, the plane of its image is the principal focal plane, and the point where it cuts the axis is the principal focus . The line joining any point in the object to the corresponding point of the image cuts the axis at a fixed point called the focal centre. The distance of the principal focus from the focal centre is called i\\Q principal focal length, or simply the /oca/ length. There are two principal foci, &c. formed by incident parallel rays passing in opposite directions through the instrument. If we sup- pose light always to pass in the same direction through the instru- ment, then the focus of incident rays when the emergent rays are parallel is the first principal focus^ and the focus of emergent rays when the incident rays are parallel is the second principal focus. Corresponding to these we have first and second focal centres and focal lengths. Now let Qi be the focus of incident rays, P^ the foot of the per- pendicular from Qj on the axis, Q^ the focus of emergent rays, Pg'the foot of the corresponding perpendicular, FiFc^ the first and second principal foci, AjAg the first and second focal centres, then PiFi^PiQi^F,?, AiFi P2Q2 f^a; lines being positive when measured in the direction of the light. Therefore the position and magnitude of the image of any object is found by a simple proportion. In one important class of instruments there are no principal foci or focal centres. A telescope in which parallel rays emerge parallel is an instance. In such instruments, if m be the angular magnifying power, the linear dimensions of the image are — of the object, and m the distance of the image of the object from the image of the object- glass is — of the distance of the object from the object-glass. Rules were then laid down for the composition of instruments, and sug- gestions for the adaptation of this method to second approximations, and the method itself was considered with reference to the labours of Cotes, Smith, Euler, Lagrange, and Gauss on the same subject. LI. Intelligence and Miscellaneous Articles, NOTE ON THE EMPLOYMENT OF INDUCTION APPARATUS. MER- CURIAL INTERRUPTOR. BY L^ON FOUCAULT. TN most kinds of induction apparatus, the inductive current id •*■ rendered intermittent by the action of an interruptor which peri- odically produces contact between the extremities of the circuit. 404 Intelligence and Miscellaneous Articles, Amongst all the metals which have hitherto been tried for the arma- ture of these points of contact, platinum has succeeded best ; its high fusing-point and its slight tendency to oxidation indicating it as pre- ferable to the ordinary metals for presenting long resistance to the corrosive action of the spark which passes at each interruption. Nevertheless when the apparatus is in action for a certain time, pla- tinum itoelf is at last attacked ; the surfaces of contact become de- formed, presenting hollows, or enlargements at each other's expense, the texture of the metal alters, and at length the interruptor ceases to perform its functions. This tiresome result arrives sooner in pro- portion to the strength of the current, and when this acquires an intensity above a certain limit, the pieces of the interruptor are sol- dered together at the first contact, and become quite useless. In attempting to increase progressively the phsenomena of induc- tion, I met with a difficulty which appeared to be rather serious in this imperfection of solid contact, and like many others no doubt, I thought of having recourse to mercury. In my first essays I perceived that it would be impossible to distri- bute an intense current continuously with naked mercury ; by this means the interruption is never sufficiently sudden, the inductive ac- tion remains weak, the surface of the metal becomes oxidized in a few moments, and it emits abundant vapours which in course of time do not fail to exert their deleterious action. I was thus led to cover the mercury with a stratum of distilled water, or better still, with a stra- tum of alcohol, which at once remedies the inconveniences attending the employment of mercury alone. Thus the interruption of the current is produced under alcohol with a dry sound which indicates a sudden stop ; it gives rise to a strong spark of induction, the alco- hol soon becomes turbid, but it does not cease condensing the vapours given off from the point of rupture, at the same time that it protects the surface of the mercury from oxidation. The apparatus thus con- tinues to act with regularity as long as the battery is capable of maintaining the inducing current. Regarded in a mechanical point of view, the employment of a liquid conductor such as mercury introduces a happy modification into the constitution of the interruptor. The oscillating piece known as the hammer being no longer limited in its movements by the firm obstacle which it met with in its anvil, may be replaced by an elastic plate, which vibrates by its own spring under the influence of an electro-magnet. This plate, being curved at its extemity and ter- minated by a platinum point, closes the circuit of the inductive cur- rent sixty times in a second, by penetrating more or less into the mercury. The contact thus established, notwithstanding its short duration, is nevertheless perfect ; in itself it only presents a resist- ance which may be neglected in comparison with those spread through the circuit, and as the elastic piece vibrates in perfect liberty, the contacts succeed each other at regular intervals of time, as may be seen from the uniformity of the sound given by an apparatus in action. The series of sparks at the extremity of the induced wire participates in the same character, and in the crepitating sound which Intelligence and Miscellaneous Articles, 405 they give off, the ear recognizes a distinct tone conformable with that of the vibrating plate. At the same time that it regulates the sparks, this new inter- ruptor, when applied to the ordinary machines in use, is capable of in- creasing their power to a certain extent. It generally acts so as to •render the effects proportionate to the intensities of the current dis- tributed, whence it follows that it is particularly in the employment of strong currents that it presents a marked advantage over the in- terruptors with solid points of contact. It is even imprudent with a single machine of ordinary dimen- sions, to attempt to force the intensity of the inducing current beyond a certain limit, for this will infallibly cause the induced coil to burst internally. But by combining several machines, the sum of the tensions being divided between the various elements of this kind of battery, we may direct upon the whole the action of a number of couples proportional to that of the machines, which in- creases in the same proportion the distance passed over by the spark between the two extremities of the induced series. This system of combination applies without difficulty to the excellent machines con- structed by M. Ruhmkorff, provided they are only combined in pairs. The hammers are suppressed and replaced by permanent conduct- ors, the two inducing wires are united one after the other, and the interruptor, accom])anied by the condenser of the extra- current, is introduced into the circuit. By this precaution each machine must retain its discharge wires at a normal distance ; both also retain their commutators, which serve respectively to direct the two parts of the current in such directions that tensions of opposite signs may accumulate at the internal extremities of the induced wires ; and lastly, these being put in communication, the external ends which remain free, become the two poles of the system, and furnish sparks at a distance of 30 to 35 millimetres. When it is desired to place more than two machines under the conduct of the mercurial interruptor, it becomes necessary to isolate the additional machines with particular care. In fact, in comparison with the very strong tensions which are manifested in the induced wire in the neighbourhood of the extremities, the inducing wire which penetrates the axis of the coils must be regarded as an inert conductor, and if this conductor approaches the induced coils at points more or less distant from those in which the tensions are null, it presents a complete course for the discharge. It is therefore important to effect an absolute isolation between the inducing wire and the interior of the induced coil in the additional machines, and this isolation is effected by slipping a glass tube into the annular space which separates the two concentric coils. As soon as this condition was fulfilled by the care of M. Ruhmkorff, four combined machines gave the effects of tension, which might have been ex- pected, and the sparks darted across an interval of 7 or 8 centi- metres.— Comptes Rendus, July 7, 1856, p. 44. 406 Intelligence and Miscellaneous Articles. NOTE ON COLONEL SABINE's PERIODIC AND NON-PERIODIC TEM- PERATURE VARIATIONS AT TORONTO (PHIL. TRANS. 1853). BY S. M. DRACH, ESQ., F.R.A.S. To the Editors of the Philosophical Magazine and Journal, Gentlembn, In page 152, the Annual formula is convertible to f,=44°-23-21°-81 sin (a+81° 27'=a')--l°-06 cos (2a-hl61° 32' = 2a'-l°22')~'80cos(3a + 257°42'=3a' + 13°21') + •22 cos (4a + 307° 27'=4o'-18° 2I')--88sin(5a+50°-41 =:5a' + 3°-26)-h-325cos6a=44°23'-21°-81sina'-l-06cos2a' — • 80 cos 3a' +• 22 cos 4a' - • 88 sin 5a' nearly, at 30° a month, 81° 27'= 2 months and 21 days; which, counted backwards from January 15, brings us to the third week in October, the epoch of mean annual temperature. Would therefore the meteorological year from October year n to September year n -)- 1 inclusive produce more approximative results ? Oct. 13, 1856. S. M. Drach. ON A ZEOLITIC MINERAL (ALLIED TO STILBITE) FROM THE ISLE OF SKYE, SCOTLAND. BY J. W. MALLET, PH.D. The specimen to which the following description refers has been in my possession for several years, and has attached to it a lable bearing the name *' Hypostilbite;" but analysis shows it to be a mineral quite distinct from Beudant's hypostilbite of the Faroe Islands, and differing also from both stilbite proper and epistilbite. It occurs as a mass of minute crystals, resembling white loaf- sugar, breaking easily, and crushing under the fingers into a coarsish crystalline powder. The separate grains, viewed under the micro- scope, appear as single prismatic crystals, or little groups of three or four, nearly transparent, colourless, and with a pearly lustre, especially on two opposite faces, — closely resembling stilbite in fact in general appearance. The crystalline form could not be satisfactorily made out, but seemed to be monoclinic. Hardness a little greater than that of calcite. Specific gravity =2*252. Strong muriatic acid poured over the pulverized mineral at night had the next morning formed a distinct jelly. On analysis the following results were obtained : — Atoms. Silica 53-95 1-191—3 Alumina 20-13 -392—1 Lime 12-86 -459-1-17 Magnesia trace Potash (with a little soda). . -87 Water 1242 1-380—3-52 100-23 Meteorological Observations. 407 Neglecting the small quantity of alkali, these numbers lead us nearly to the formula 2(CaO, Si03) + 2(A12 O^, 2Si03) + 7H0, which differs completely from that of stilbite, CaO, Si03 + Al20^ 3Si03 + 6HO, or that of epistilbite, CaO, Si05 + Al2O3, SSiO^ + SHO. The per-centage of water is also far too small for hypostilbite. The mineral appears to be a distinct one, and does not seem to have resulted from the gradual decomposition or change of any other; but it is perhaps scarcely desirable to add to the already numerous names of stilbite-like minerals by adopting a new one for this sub- stance until additional analyses of these nearly related species shall permit of their more accurate classification. — Silliman's American Journal for September 1856, p. 179. METEOROLOGICAL OBSERVATIONS FOR SEPT. 1856. Chiswick. — September 1. Very fine : thunder and lightning at night, but without rain. 2. Shower : very fine: clear. 3, 4. Heavy dew in the mornings : very fine. 5. Slight fog : cloudy and fine. 6. Slight fog : rain at night. 7. Very fine. 8. Foggy : very fine. 9. Dense fog : very fine : cloudy. 10. Slight haze : very fine. 11. Overcast. 12. Cloudy: very fine : rain. 13. Cloudy. 14. Clear and fine. 15. Fine : overcast. 16. Clear: fine. 17. Overcast: rain. 18. Rain : very fine. 19. Clear, quite cloudless : very fine. 20. Very clear : cloudy and cold : slight frost at night. 21. Fine : rain. 22. -Clear: showery: fine. 23. Clear : cloudy : bright sun at intervals. 24. Clear : heavy showers. 25. Clear : dense clouds : fine. 26. Fine : rain at night. 27. Heavy rain. 28. Rain : heavy showers. 29. Cloudy and fine. 30. Very fine : cloudy : fine at night. Mean temperature of the month 54°'41 Mean temperature of Sept. 1855 56*11 Mean temperature of Sept. for the last thirty years 56*95 Average amount of rain in Sept 2*455 inches. iJos^ow.— Sept. 1 — 4. Fine. 5. Cloudy. 6. Fine. 7. Fine : rain a.m. 8, 9. Fine. 10. Cloudy. 11, Cloudy: rain a.m. 12. Cloudy. 13. Cloudy: rain a.m. and P.M. 14. Fine. 15. Cloudy. 16. Fine. 17. Cloudy: rain p.m. 18,19. Fine. 20. Cloudy. 21,22. Fine: rain p.m. 23. Cloudy. 24— 26. Fine. 27—29. Cloudy : rain a.m. and p.m. 30. Cloudy. Sandwich Manse, Orkney. — Sept. 1. Clear a.m. : clear, aurora p.m. 2. Bright A.M. : clear p.m. 3. Clear a.m. : cloudy p.m. 4, 5. Clear a.m. and p.m. 6. Bright a.m. : cloudy p.m. 7. Drizzle a.m. : damp p.m. 8. Damp a.m. : fog p.m. 9. Fog A.M. and p.m. 10. Fog a.m. : showers p.m. 11, 12. Bright a.m. : showers P.M. 13. Showers, bright a.m. : cloudy p.m. 14. Drizzle, bright a.m. : showers P.M. 15. Showers A.M. and P.M. 16. Showers a.m. : rain, lightning p.m. 17. Showers a.m. : clear p.m. 18. Sleet showers a.m. : showers p.m. 19. Cloudy A.M.: showers P.M. 20. Showers a.m. : cloudy p.m. 21. Bright a.m. : showers P.M. 22. Rain a.m. : showers p.m. 23. Bright a.m. : showers p.m. 24. Rain a.m. : showers p.m. 25. Showers a.m. and p.m. 26. Clear a.m. : clear, aurora p.m. 27. Hoar-frost a.m. : showers, aurora p.m. 28. Damp a.m.: cloudy p.m. 29. Showers a.m. and p.m. 30. Showers a.m. : clear p.m. Mean temperature of Sept. for previous twenty-nine years ... 52°'28 Mean temperature of this month 50 *83 Mean temperature of Sept. 1855 52*74 Average quantity of rain in Sept. for previous sixteen years ... 2*82 inches. •ao)M>a •ipimtiqD •^tAputis 'Xauvo •ao)80g •oi'd I ^ 8SS iii^ii^^i^U^i^lUU''^tH'li I i i 1 2 « ^ I « i « H i « E I i ^ «* i ^ i M ^ ^ ^ ^ ^ ^' ^' c ^ ^ V « ^' fe S V S S* ^ ^ ^' fe ^' ^ ^ d k ^' B^ ^ ^' ^' oS « Be E rl a. IS §1 a s On •ni'B ^8 ■UO)BOS u^ tr> li-i ti-> v/^ ■I !i >ao)8oa -I O O ►■ t<^oo rj-oo VO y^ t^vo Mt-~0' T»- u->oo t^ j^ f^ 5* r*" ."* i*^ r^ y^ r*^ ^p ."* f^ r*"*? y^ p *? 5^ r^ r ^ y^^ P On '(^v On On b\ On On C7\ *0 On 0\ On On On On On On On On On on Onoo OO 00 Onoo 6o OO Os t^ O t^ «^ CO t>,00 w OO On OnVO O COVO C) 00 VO OO w O ONVO On CO OnOO VO OO NO t^ H r>. On N p OO yo t>^oo rvoo p p Onj-" « p t^oo oo onvo « m p OnOnO O OnOnOnOnOnOnO O OnO O O OnOnOnOnOnOn'onOn'onOnOOOO On On r)Hmrot4r)cir)(4HrocoMrororoDr4r4MNMMc)t4r4NMnc< C< tONO to On t^ w »0 t4 T*- tovo ThclvO rol^>«t-0 H On •«}-vo OHOw^tOHO»^MO t^OO H ON On ^ t-^ w-> Onoo tJ-vo ONt^ONrJ-Tt-t^HOO en u^vo VO .^^M toco— locoo t*-0O OO >-> « _« Ov t-^OO 00 00 Ov •-> M p N "I HI 0\00 On O O ^^ C» H y^^ « O ■<»• f^ OvO O O OnOnOnOnOnOvO O O O O O OnOnOnO O OnOnO>OnOnOvOnOnOn c»cococofc» ^ ir»vd t^OO OS d M c< CO «4- ^ONO ^ THE LONDON, EDINBURGH a.nd DUBLIN PHILOSOPHICAL MAGAZINE AND ' JOURNAL OF SCIENCE. » [FOURTH SERIES.] DECEMBER 1856. LII. On Slaty Cleavage, and the Distortion of Fossils, By the Rev. Samuel Haughton, Professor of Geology in the Uni- versity of Dublin^. THE first person, so far as I know, who distinctly put for- ward a purely mechanical theory of slaty cleavage, was the late Mr. Sharpe, in two papers read before the Geological Society of London, December 2, 1846, and November 1, 1848. These papers are published in the third and fifth volumes of the Quar- terly Journal of that Society, and form a most valuable basis of well-observed facts on which to establish a mechanical theory of slaty cleavage. At the close of the second of these papers, Mr. Sharpe sums up his observations as follows : — "Thus all our observations and deductions ultimately con- verge to the conclusion, that the cleavage must be attributed to pressure caused by the elevation of great masses of rock under conditions of which we are ignorant. And if to this conclusion it should be objected that no similar results can be produced by experiment, I reply that we have never tried the experiment with a power at all to be compared with that employed ; and that this may be one of many cases where our attempts to imitate the operations of nature fail, owing to the feebleness of our means, and the shortness of the perigd during which we can employ them.'' The objection thus alluded to by Mr. Sharpe has been com- pletely removed by the illustrative experiments of Professor Tyndall, who deserves the thanks of geologists for the light he has thrown upon this obscure question. In common, I believe, * Communicated by the Author. Phil Mag, S. 4. Vol. 12. No. 81 . Dec. 1856. 2 E 410 The Rev. S. Haughton on Slaty Cleavage, with many geologists I adopted Mr. Sharpe's views, and have from time to time collected data for forming a more precise me- chanical theory than that put forward in general terms by Mr. Sharpe. I was, in short, convinced that if the theoiy were true, it would bear accurate numerical investigation, and admit of being stated with great precision. With a view to this numerical testing of the theory, I have accumulated a great number of observations and measurements of distorted fossils, which I think are suflScient to enable me to state precisely the laws of slaty cleavage and distortion of fossils. I shall now proceed to state the results I have arrived at, and to illustrate them by detailed examples ; and I shall afterwards point out the extent to which Mr. Sharpens results agree with my own, and how far they anticipate them. The first fact observed by me was the following : — I. If the trace or intersection of the plane of cleavage and plane of bedding be drawn, the greatest distortion or elongation of the fossils lying in the plane of bedding is parallel to this intersection. In explanation of this law, it should be stated that each species of fossil has a certain normal undistorted form which may be ascer- tained, and that the measurements of the different parts bear, within certain narrow limits, a constant ratio to each other; so that when we examine a distorted fossil, we can calculate the amount of relative extension or compression it has undergone in any direction. Suppose, for example, that we draw any two lines at right angles to each other, and that the ratio of M to N is the ratio of the measurements of a known fossil shell taken parallel to those two directions, and that the ratio of m to n is the ratio of the measurements of the distorted fossil taken in the same directions ; then, if we denote by p the distortion parallel to M, we shall have m N ... P-n^'U W If the fossil had been originally of a circular shape, it would become an ellipse by distortion, and p would be the ratio of two rectangular diameters, which in one case become the axes of the ellipse ; and it is plain, from the properties of an ellipse, that the maximum value of the fraction denoted by p will correspond with the axes of the ellipse. I have calculated the value of p repeatedly, from measure- ments made on fossils from different districts of the south of Ireland, North Wales, Cornwall, and Devonshire, and have always found that the major axis of the ellipse of distortion is parallel to the intersection of the planes of cleavage and bedding. Having thus obtained a tangible starting-point for my theory, I began to and the Distortion of Fossils, 411 examine what effect the angle between the planes of cleavage and bedding produced on the amount of distortion. The following law expresses the result of my measurements : — II. The distortion of fossils produced by cleavage — estimated in a given direction^ such as parallel to the intersection of the planes of cleavage and bedding — varies with the angle between these planes, being greatest when the angle is greatest, and least when the angle is least. The distortion depending upon the angle between the planes of cleavage and bedding may be calculated numerically from the following expression : — A= VPsin2 the angle between these planes, and P, Q numbers ; P being always greater than Q. The mode of determining the numbers P and Q will be presently explained. In addition to the two laws of distortion already mentioned, there is a third law, which is so easily observed that it has forced itself on the notice of every person who has paid even a slight attention to this interesting subject. It maybe stated as follows : — III. The compression in a cleaved rock is greatest in a direction perpendicular to the planes of cleavage. Having ascertained satisfactorily the truth of the laws of dis- tortion just given, I proceeded to form a general theory by the aid of the following considerations. It has been beautifully proved by Cauchy, that if a perfectly homogeneous, uncrystalline mass be subjected to pressures, twists, strains, &c. of any kind, it will settle into a condition of equili- brium, subject to the following law : — Imagine a small sphere in the mass before distortion ; this sphere will become an ellipsoid after distortion ; and if the distortions in the principal planes be known, we can calculate the forces which produced the distortion in the mass. This hypothetical problem in mechanics, solved by Cauchy, is illustrated by the phsenomena of cleaved rocks ; and since, by the measurement of the distortion of the fossils, we can ascertain the amount of distortion in each plane of bedding, we can readily obtain data for calculating the axes of the ellipsoid of distortion, and so obtain an idea of the direction and magnitude of the force which has cleaved the rocks and distorted the fossils. The mode of determining the axes of the ellipsoid is as follows : — Since, by the first law, the intersection of the planes of cleavage and bed- ding is an axis of the ellipse of distortion in all planes of bedding, it must be an axis of the ellipsoid. Also it is certain, from the third law, that the compression is a maximum perpendicular to 2E2 412 The Rev. S. Haughton on Slaty Cleavage, the planes of cleavage ; from this fact we may infer that a line perpendicular to the plane of cleavage is also an axis of the ellip- soid, and that the third axis will lie in the dip of the cleavage plane and perpendicular to the other two axes. If we assume the axes of the ellipsoid to be a, b, c, the axis of a being the intersection of cleavage and bedding, the axis of z perpendicular to the cleavage plane, and the axis of y in the dip of the cleavage plane ; if , ' denote the angles made with the plane of cleavage by two planes of bedding, both passing through the axis of x ; and if -, -7 be the distortions in these planes esti- p p' mated parallel to the intersection of cleavage and bedding, then it is easy to see that we have the following equations from the nature of an ellipsoid : — sin^ 1 ^ ^ b^ ~~ p^ sin*<^' cos*<^' 1 11 ' .' Solving these equations for -r and -, we find — 'srf ^o 81 o c (3) (sin (f> sin ' \ /sin <^ sin <^'\ * 1/ sin (') sin (' = 10°, ry =1*088 Athyris concentrica dofifw ,- biw -i. =1-102 Spirifer clathratus '^*''*'^ Mean . . 1-095 Introducing the values of ^, (j>'j /o, p' here given into equations (4) and (5), we obtain — > ^^ 1^0X1 llexia i. joq^h a 1=1-026 0 — = 2-426 c -^ ^WrsA.,.^~\,^. (A) From these results I infer that the slate of Ardoginna has been relatively compressed perpendicular to its cleavage nearly two and a half times, and that this result has been brought 414 The Rev. S. Haughton on Slaty Cleavage, about by a force acting very nearly in the line perpendicular to cleavage, because there is scarcely any difference in the amount of distortion in different directions in the plane of cleavage itself, as is shown by the close agreement of the axes a and b. The ellipsoid of distortion in this case is nearly an oblate ellipsoid of revolution, whose equatorial diameter is nearly two and a half times its polar diameter. The slate of Ardoginna is merely a compressed and hardened mud ; it is a bluish shale, with occasional black partings. Example 2. — Carboniferous Slate of South Petherwin, Cornwall. The next example of cleavage which I shall select is the car- boniferous slate of South Petherwin, near Launceston in North Cornwall. The slate of this district and its fossil remains have a striking resemblance to the carboniferous slate beds of many parts of the south of Ireland, which I believe to lie on the same geological horizon. The fossils I have used to determine the amount of cleavage are Spirifer disjunctus and Athyris conceU" trica. The former of these fossils is closely allied to Spirifer clathratus, of which it is probably only a variety. In calculating the distortion, I have assumed for the normal proportions of this fossil — Length =189 Breadth of hinge-line =474 Length of rib making 60° with hinge =308 For Athyris concentrica I have used the normal proportions already given. The data obtained as the mean of many mea- surements are as follow : — <^==17°, i«l'480 <^'=12°, i^= 1-263. From these data we obtain, by means of equations (4) and (5),— a i=0'990 !> (B) ^=8-889 J This result is very similar to that already found for the car- boniferous slate of the Co. Waterford, and proves that the ellipsoid of distortion is nearly an oblate eUipsoid, whose polar and the Distortion of Fossils* 415 axis is little more than one-fourth of its equatorial axis. The nearly equal amount of compression or extension along the axes a and b, or in the strike and dip of the cleavage planes, is a fact that continually reappears in different districts, and produces a remarkable result in the appearance of the fossils ; viz. that in the plane of cleavage the fossils appear to have undergone little relative distortion, although in some cases, as at Tintagel, they have undergone a considerable extension, preserving their rela- tive normal proportions. Example 3. — Carboniferous Slates of Tintagel, Cornwall, These slates are somewhat lower down in the geological se- quence than those of Petherwin, from which they differ remark- ably in appearance, being glossy, and of a greenish-yellow colour. Much of this difference may, however, arise from the fact of their being much more cleaved, and retaining traces of having been exposed to much greater pressure. The fossils used for the calculation of the amount of distortion were the specimens of Spirifer disjunctus, described by Mr. Sharpe, and now deposited in the Geological Museum in Jermyn Street. I have used in my calculation the normal measurements already given. The following are the results obtained from many measure- ments:— ^=0, — = 1*494 Spirifer disjunctus J (ft' = 12°, —=2*514 Spirifer disjunctus. From these data I readily obtain, by equations (4) and (5), — a i-= 1-494 o -=9-839 c We here obtain evidence of an enormous amount of compres- sion perpendicular to the planes of cleavage, being, in fact, rela- tively ten times greater than the compression in the cleavage plane. I should be induced to infer from this result, that the mud or sub- stance from which the rock was formed must have been in a very peculiar condition at the time of compression, perhaps like one of those bulky hydrated precipitates of alumina or peroxide of iron so familiar to the chemist, or like the mud cloud depositing (C) 416 The Rev. S. Haughton on Slaty CleavagCj itself in a very deep sea, so ingeniously imagined lately by Mr. Babbage. Whatever may have been the primary conditions under which this compression took place, it is certainly interest- ing to have an exact numerical measure of its amount. Example 4,-^Lingida Beds of the Loiver Silurian epoch, Abereiddy Bay, Pembrokeshire, These beds consist of a soft, black, carbonaceous shale, and present the appearance of having been considerably compressed. There is no distortion of fossils in the cleavage plane itself, a fact that falls in with what I have before noted of the shales of Water- ford and South Petherwin. The fossils on which I have made my calculations are Lingula Phillipsii (Salter)* and Calymene duplicata. The normal shapes of these fossils are here given : — Lingula Phillipsii . Length =184 Breadth = 173 Calymene duplicata . Length of body . . . =121 Length of tail . . . . = 64 Maximum breadth of body =143 Breadth ofbody two-thirds 1 __-|Q-f down from the thorax. / ~ Breadth of tail ... =108 The following data were obtained by the measurement of the distorted specimens of these fossils :■ — '=13°, -, = 1-950 Lingula Phillipsii 1*893 Lingula Phillipsii 1 1*846 Lingula Phillipsii 1*725 Calymene duplicata 1*732 Calymene duplicata Mean . . 1*829 From these data w^e obtain, as before, — 1 = 1 a I- -=6*881 c (D) * I would here express, once for all, the great obligations I have been under to Mr. J. W. Salter of the Geological Survey, Jermyn Street. His and the Distortion of Fossils, 417 This amount of compression is greater" than I found for any- other slates, excepting the remarkable slates of Tintagel and Garth. Example 5. — Green Grits of Llyn Padarn, Llanberis, Lower Silurians lying below the Trap Beds of Snowdon. In this case I was enabled to obtain measurements of distorted fossils in three distinct planes, and thus secure a kind of expe- rimentum cruets for the mechanical theory of cleavage. The fossil I made use of is Orthis expansa, of which the following are the normal measurements : — Orthis expansa . Breadth of hinge . . . . = 238 > ■; Breadth of shell .... =289 Length of shell =274 Breadth of vascular impression =143 Length of vascular impression = 144 By these measurements and those of the distorted fossils, I obtained the following : — ^ =33°, i= 1-433 9 i^'=43, ~ = l-552 ^iii lo .M;:.£;I^*u>^ <^" = 90°, -i^ = 1-961. r The third of these measurements gives a direct value of — , viz. 1*961, with which the value calculated from the first two data should agree. The agreement is very good, as appears from the following : — a J = l-195 ^ (E) i = 1-881 c It is remarkable that the compression in this case, perpendi- cular to the cleavage planes, is very small compared with the compressions determined in the slates already discussed. This doubtless arises from the fact, that sandstones resist the cleavage action or pressure better than slate or mud. This singular fact, of a less compression existing in sandstones than in slates, and accurate knowledge of the forms of the palaeozoic fossils was of the greatest service to me, and he allowed me free access to all the specimens in the Museum, and assisted my investigation greatly by his judgement. 418 The Rev. S. Haughton on Slaty Cleavage y a proportionably less-developed cleavage, is a solid argument in support of the mechanical theory of cleavage. In addition to the examples already given, I have measured several others in which I could only obtain a single position of the plane of bedding in relation to the cleavage plane ; this is not sufficient to determine the three axes of the ellipsoid of dis- tortion ; but if we assume, as is probable, that this ellipsoid is one of revolution, we can readily obtain an approximate value of the compression due to cleavage as follows : — Assuming b equal to unity in one of the equations (3), we find, after some simple reductions, — c sin^ • • • • ^ ^ The following examples of the application of equation (6) are taken from my note-book : — Example 6. — Silurian Black Slates of Moel Benddu, Dinas Mowddy, South of Bala, North Wales. The fossil whose distortion was measured in this case was the Asaphus Powisiij and its normal shape was assumed as follows : — Asaphus Powisii . Length of head =338 Length of body =386 ' Length of tail =448 ^ Breadth of body =838 From these measurements, compared with the distorted spe- cimens from Moel Benddu, I found — 1 Asaphus Powisii. <^=65°, -r=:3-020 whole fossil 3-230 tan 2-562 body 3-265 head 2-584 body 8-033 tail Mewi . . 2*949 From these data, I find by equation (6), — a i;= 8-697 (F) and the Distortion of Fossils, 419 Example 7. — Silurian Black Slate of Garth, opposite Port- madoc, North Wales. The fossil used in this example was a tail of the Ogygia scu' tator, whose normal dimensions were found to be as follows : — Ogygia scutator . Breadth of tail =355 Length of tail =203 From these measurements, compared with the distorted fos- sils, we find — <^ = 11°, -=2-335; P from which we obtain, by the aid of equation (6), the following results : — a (G) This result corresponds to a greater amount of compression than I found in any other case, not even excepting Tintagel, where the cleavage is uncommonly well developed. Example '8. — Carboniferous Slates of Carrigaline, Co. Cork* The carboniferous slates of this district are of the same geo- logical age as the slates of Ardoginna, Co» Waterford, and of the same mineral character^ being dark and carbonaceous at inter- vals^ with patches of smooth brown shale between the dark mud bands. The fossil used to determine the amount of compression is the Orthis crenistria, whose breadth equals its length in the normal condition. The measurements of the distorted fossil are as follow : — Orthis crenistria . Length =±193 Breadth =409 From the specimeUj on which these measurementa were taken, I obtained the following data : — <^=80°, i =2-119; r from which, by means of equation (6), I find — 420 The Rev. S. Haughton on Slaty Cleavage, 1 = 1 a I-' - =2-144 c (H) This result indicates an amount of compression quite com- parable with that observed in the Ardoginna and Ardmore slates of the same age, and may be considered as characteristic of the carboniferous slates of the entire south of Ireland. It now remains to state how far the results I have obtained correspond with those .arrived at by Mr. Sharpe. At the 87th page of the Quarterly Journal of the Geological Society of London, Mr. Sharpe sums up the results of his obser- vations as follows : — 1st. In cleaved rocks there is a compression of the mass in a direction everywhere perpendicular to the planes of cleavage. 2nd. An expansion of the mass in the direction of the dip of the cleavage. 3rd. No proof has been found that the rocks have suffered any change in the direction of the strike of the cleavage planes. Mr. Sharpe also mentions incidentally in the course of his paper the following fact, of the importance of which he does not seem to have been aware : — 4th. When the plane of bedding is considered, the shells all appear contracted in a direction perpendicular to the strike of the cleavage plane across the bed. On comparing these results with the laws of cleavage distor- tion given in the preceding part of this paper, it will be observed that the first and fourth fall in with Laws III. and I. The second and third statements do not accord with my observations, and I am inclined to think that they are hasty generahzations, as it would be extremely difficult to ascertain the absolute com- pression or expansion undergone by the rock in any direction. It is evident that the whole subject of cleavage and its mecha- nical origin is very imperfectly understood, and a desire to throw even a little light upon so interesting a subject must be my excuse for offering so imperfect a statement of the numerical results which may be deduced from the measurement of the proportions of the -distorted fossils which are found abundantly in many highly cleaved rocks. It may be worth while to sum up the preceding results in the form of a table, so as to admit of their easy comparison with each other. Prof. Stokes on a Theory of the Composition of Colours. 431 Table showing the Relative Compression of Cleaved Rocks. II II :2 2 1% g . Intersection of cleavage ' and bedding Dip of cleavage Perpendicular to clea-' vage 1-000 1026 2-426 1-000 0-990 1-000 1-494 3-889: 9-839 1000 1000 6-881 1-000 1-195 1-881 1000 1-000 3-697 1000 1-000 11-105 1-000 1-000 2-144 The preceding Table is, I believe, the first attempt to estimate numerically the amount of compression necessary to produce cleavage in rocks ; and it is to be hoped that the attention of geological observers may in future be more directed to the obser- vation of the relative position of the planes of cleavage and bed-* ding, and of the distortion of the fossils : such observations, to be of any value, should be made in the field, by persons com- petent to judge of the shape of the fossil forms, and carefully instructed as to the precise points necessary to be observed. An opportunity of obtaining the information requisite for a perfect mechanical theory of cleavage is afforded by the means of observation possessed by the Staff of the Geological Survey of Great Britain and Ireland. If the operations of such a survey were conducted with the science and skill necessary for carrying out such an important work, nothing would be wanting to com- plete the data requisite for the solution of many interesting pro- blems in physical geology. But it is much to be feared, that so long as geologists remain in the half-educated condition with which they are at present contented, that such an amount of intelligent observation is not to be looked for; and that those who wish for satisfactory foundations of facts on which to build their theories, must even be content to take their hammers in their hands, and having strapped on their knapsacks, to seek in the field of nature the facts for themselves. Trinity College, Dublin, October 20, 1856. LIII. Remarks on Professor Challis's paper , entitled " A Theory of the Composition of Colours/' &^c. By Professor G. G. Stokes*. MY object in the present communication is not to discuss Professor Challis's theory, but to rectify some statements as to the experimental facts of the case, as well as one relating * Communicated by the Author, 422 Prof. Stokes's Remarks on Prof. Challis's paper, to the extent of some researches of my own. I have, however, on some points expressed opinions, respecting the justice of which it is only one who is famihar with certain classes of optical expe- riments who can feel the confidence that I entertain. From the paragraph commencing at the foot of page 330, it is plain that Professor Challis has made some confusion between three perfectly distinct things : Sir David Brewster's controverted analysis of the solar spectrum by means of absorbing media* ; his discovery of the phsenomenon of internal dispersion f; and my own discovery, that a beam of rays of prismatic purity (whether belonging to the visible or invisible portion of the spectrum is indifferent) may, by their action on certain media, produce light which may be decomposed by the prism into portions extending over a wide range of refrangibility, and having colours answering to their refrangibilitiesj. As to the first, it was asserted by Sir David Brewster that light of prismatic purity may have its colour changed by passing through absorbing media. This has nothing to do with "internal" or "epipolic'' dispersion, or "fluorescence.'' Glass coloured blue by cobalt, for instance, has none of these properties, although it is one of the media which exhibit most strikingly the phae- nomena adduced by Sir David Brewster, Were such a change of colour made out, it would be a point of the utmost importance to consider in reference to any physical theory of light. But while none deny that the appearances are as stated by Sir David Brewster, the inference to be drawn from those appearances remains open to discussion. Airy §, Helmholtz ||, and Bernard^, by operating in a different manner, have come to the conclusion that the colour is not changed ; and Helmholtz has attributed the apparent change partly to the mixture of a very small quan- tity of stray light, partly to the effects of contrast. Having been much in the habit of analysing the light transmitted by coloured solutions, and having repeatedly seen the phsenomena on which Sir David Brewster relies, I may be permitted to ex- press my belief that the change of colour is only apparent, being an illusion depending upon contrast, and that this is one of the cases in which the direct evidence of the senses must be con- trolled. Were the change of colour real. Prof. Challis's state- ment (p. 330), that " experiment has proved that both the colour and the angle of refraction for a given angle of incidence depend, * Edinburgh Transactions, vol. xii. p. 123. t Edinb. Trans, vol. xvi. p. 1 1 1 ; and Phil. Mag. vol. xxxii. (1848) p. 401 . X Philosophical Transactions for 1862, p. 463. § Phil. Mag. vol. xxx. p. 73. II Poggendorff's Annalen, vol. Ixxxvi. p. 601. 5r Report of the Meeting of the British Association at Liverpool in 1864, 2nd part, p. 6. entitled *^A Theory of the Composition of Colours" 423 the substance being given, only on the value of X/^ would cease to be true. As to the second, the principal phsenomenon consists in this : that when a beam of sunlight, condensed by a lens, is admitted into certain perfectly clear {i. e. not muddy) media, the path of the rays is marked by light, of different colours in different cases, which emanates in all directions. As the real nature of this remarkable phsenomenon was not at the time understood, and the phsenomenon itself was confounded with the effects of mere suspended particles, it is needless to discuss its possible bearing on any theory of the sensation of colour under this head. As to the third, the new light emanating from the media which possess the property in question is just like any other light of the same prismatic composition. In its physical pro- perties it retains no traces of its parentage, and its colour depends simply upon its new refrangibility, having nothing to do with that of the producing rays, nor to the circumstance of their belonging to the visible or the invisible part of the spectrum. Hence, in speculating on the sensation of colour, this phseno- menon may be set aside as not bearing upon the question. I may remark, however, that with regard to the sensation of colour, an analogy has often struck me between the retina and a fluorescent substance, or rather a mixture of three or more fluorescent sub- stances : but this is only an analogy. It is not true, as Professor Challis seems to suppose (p. 332), that absorption is always, or even generally, accompanied by epipolic dispersion. Among the great variety of coloured me- tallic solutions, I have hitherto found that property only in solu- tions of salts of sesquioxide of uranium. I make this remark merely by the way, to prevent misconception : I perfectly agree with Professor Challis in believing that a ray of definite refran- gibility is uncompounded ; in fact, it was my firm belief in that doctrine which led me to make out the phsenomenon of the change of refrangibihty of light. The superposition of two coloured glasses or ribbons by no means gives the effect of the mixture of the two colours. Various methods of mixing colours are enumerated by Mr. Maxwell at the end of his paper, entitled " Experiments on Colour,^' &c., in the twenty-first volume of the Edinburgh Transactions, p. 275. The production of white by a mixture of blue and yellow is by no means confined to prismatic blue and yellow, but takes place just as well with the colours of coloured bodies. In making ex- periments with the spectrum, in order to neutralize, when pos- sible, a prismatic colour of given intensity by another prismatic colour, so as to produce white, two points must be attended to : the place of the second colour in the spectrum must be properly 424 Prof. Stokes's Remarks on Prof. Challis's paper, chosen, and the intensity of the light properly regulated. Hence any speculations as to the cause of the variations of intensity in the solar spectrum can have no bearing on the subject before us, seeing that the relation between the intensities of the mixed colours necessary for the production of whiteness is a matter of experimental adjustment. The reason why the superposition of two coloured bodies does not give the mixture of the colours is known, and is very simple. The composition of the light transmitted through a coloured glass may very conveniently be represented by a curve, in the manner of Sir John Herschel, in which the abscissa x denotes refrangibility, measured, suppose, by the distance from the ex- treme red in some standard spectrum, and the ordinate y denotes the intensity ; so that ydx is the quantity of light between the refrangibilities x and x + dx, the intensity in the incident light being taken equal to unity, for simplicity's sake, whatever be the value of x, as we only care to compare intensities for the same value of X, Let y, y' be the ordinates in the curves belonging to two glasses, y^ the ordinate belonging to the tint obtained by superposing the glasses, y^ the ordinate belonging to the mixed tint, as procured, for instance, by a double-image prism, in which case each of the superposed differently coloured images has half the brightness of the original. Then y^ = yy', but y^=^{y-^ y'), and it is easy to see how different may be the curves whose ordi- nates are y^, y^ respectively. Thus, let the scale of abscissae be such that the spectrum extends from x=0 to x-^ir, and let j/ = ^(l — cosa?)^, y==^(l4-cosa?)'^. In this case ?/^=y\rsin'*i2?, which vanishes at the extremities, and is a maximum in the mid- dle ; whereas y^=\[\ -f cos^ x), which is a maximum at the two extremities, and a minimum in the middle. In the former case, the tint would be a sort of green, a pretty full colour; in the latter, a sort of dilute purple. The colours of two ribbons may very con- veniently be mixed in equal proportion by placing them side by side, and viewing them through a double-image achromatic prism; and it will be seen how different the mixed colour is from that seen on superposing the ribbons and holding them up to the light. I cannot agree with Professor Challis, that ^' the coloured light of substances, though derived from sunlight, is in fact new light," except so far as relates to that portion which arises from fluor- escence. But fluorescence is often absent altogether; and even when it exists, the colour thence arising must in most cases be but a small fraction of the whole colour observed when the sub- stance is freely exposed to white light, not viewed under absorb- ing media. I think that any one who has been in the constant habit of analysing by the prism the light transmitted through entitled "A Theory of the Composition of Colours," 425 clear coloured fluids or solids, and the light transmitted through or reflected from dyed or other coloured substances, must be forced to admit, that, setting aside a comparatively small number of cases in which the colour observed is referribJe to other causes, the colours of natural bodies are due to absorption. The excep- tions are colours due to fluorescence, as in the case of solutions of quinine, or to regular chromatic reflexion, as in the case of gold, copper, platino-cyanide of magnesium, murexide, &c., not to mention such colours as those of the rainbow, &c., which result from the general properties of bodies with regard to their action on light, not from any speciality of the substance by which the colours happen to be produced. The mode in which I con- ceive absorption to operate in occasioning the colours observed in dyed ribbons, flowers, coloured powders, &c., I have more fully explained elsewhere*. Now absorption is best studied in clear solids or solutions,. where it is not complicated by irregular re- flexions or refractions. But when such media are studied by the aid of a pure spectrum, there cannot be a moment's hesitation that the colour of the transmitted light is due to the abstraction from the incident white light of some of the component rays, as ex- plained by Newton. The colour results, not from the light acted on by the medium, but precisely from the portion left unafi*ected. Hence its origin is celestial (supposing the sun to be the source of the light employed), not terrestrial. But if the colours of natural bodies arise from absorption, the origin of those colours must be deemed celestial too. To make the origin of the green colour of a leaf terrestrial, but that of the green colour of the light transmitted through an alcoholic solution of the colouring matter celestial, notwithstanding that the two greens agree in their very remarkable prismatic composition, would be needlessly and most capriciously to multiply the causes of natural phseno- mena. The light which gives us the sensation of greenness when we look at a leaf is, I conceive, no more terrestrial in its origin than the sun's light reflected from a mirror is terrestrial, as not retaining the direction which it had in travelling to us from the sun. It is only in the phsenomenon of fluorescence, and the closely allied phsenomenon of phosphorescence, that the light emitted can be considered as new light having a terrestrial origin. * Philosophical Transactions for 1852, p, 527. Phih Mag. S. 4 Vol. 13. No. 81. Dec. 1856. 2 F [ 426 ] LIV. On the Application of the Mechanical Theory of Heat to the Steam-engine, By R. Clausius. [Concluded from p. 354.] 46. TIETHEN the tension series for the vapour of any liquid ▼ ▼ is known with sufficient accuracy, the values of the magnitudes ff and T^ for the several temperatures can be calcu- lated from it, and arranged in tables in the same manner as is usually done with the values of jo. In the case of steam, hitherto almost solely used for machines, and for the interval of temperature extending from 40° to 200° C, between which the application takes place, I have, with the help of Regnault's tension series, made such a calculation. Strictly, I ought to have differentiated according to / the for- mulae which Regnault used in calculating the several values ofp below and above 100° C, and then to have calculated ff by means of the new formulse thus obtained. But as it appeared to me that those formulse did not fulfil their pui'pose perfectly enough to justify so large an amount of labour, and as the calculation and institution of another suitable formula would have been still more tedious, I contented myself with using the numbers already calculated for the pressure in order approximately to determine the differential coefficient of the pressure. For example, p^^ and jt?j48 being the pressures for the temperatures 146° and 148°, I have assumed that the magnitude 2 represents with sufficient accuracy the value of the differential coefficient for the mean temperature 147°. In doing this, I have for temperatures above 100° used the numbers given by Regnault himself*. With respect to the values below 100°, Moritzf has lately drawn attention to the fact that the formula employed by Regnault between 0° and 100° was, especially in the vicinity of 100°, somewhat incorrect in conse- quence of his having used logarithms of seven places in calcula- ting the constants. In consequence of this, Moritz has calcu- lated those constants with logarithms of ten places, basing his calculations on the same observed values ; and he has published the values of ^ — as far as they differ from Regnault's, which only occurs above 40°, — thus deduced from the corrected formulse. I have used these values. As soon as g is calculated for the several temperatures, the * M^. de VAcad. des Sciences, vol. xiii. p. Q2b. t Bulletin de la Classe Fhysico-matMrnatique de VAcad. de St. P^terS' bourff, vol. xiii. p. 41. Prof. Clausius on the Mechanical Theory of Heat, 427 calculation of T.y also is attended with no further difficulty, because T is determined from the simple equation T=273 4-^. I have collected the values of ^ and T .^ and given them in a Table at the end of this memoir. For the sake of completeness, I have also added the corresponding values of p ; those above 100° being calculated by Regnault, those below by Moritz. To each of these three series of numbers are attached the differences between every two successive" numbers ; so that from the Table the values of the three magnitudes can be found for every tem- perature ; and conversely, for any given value of one of the three magnitudes the corresponding temperature can be seen. After what was before said of the calculation of g, it need scarcely be mentioned that the numbers of this table are not to be considered as exact, they being only communicated in the absence of better ones. As, however, the calculations with refer- ence to steam-engines are always based upon rather uncertain data, the numbers can without hesitation be used for this pur- pose, there being no fear that the uncertainty of the result will be much increased thereby. As to the method of application, however, another remark is still necessary. In the equations (XVII), it is assumed that the pressure p and its differential coefficient g are expressed in kilo- grammes to a square metre ; whereas in the table the same unit of pressure, a millimetre of mercury, is retained as that referred to in Regnault's tension series. In order, notwithstanding this, to be able to apply the table, it is only necessary to divide every term in those equations, which does not contain either p or q as factor, by the number 13*596. This number, which is nothing more than the specific gravity of mercury at 0° C, compared with water at its maximum density, will for the sake of brevity be represented by k. This change of the formulae, however, scarcely increases the calculation, inasmuch as it is equivalent to substituting every- where, in place of the constant factor y , — which, according to Joule, has the value 423*55 already mentioned, — the other con- Btant, J__i:?3^_31.1505. (4,e) Ak-JSWQ-^^^^^^' .... I4b} W when, instead of the work W, the magnitude -y- will be found K in the first instance, and will subsequently merely have to be multiplied hy k. 47. Let us now return to the equations (XVII), and consider first the second of them. 2F2 428 Prof. Clausius on the Application of the Mechanical This equation may be written in the following form : — T,^«=C+a(/,-/8)-*(;>i-M . . . (47) wherein the magnitudes C, a, and b are independent of t^, and have the following values : — C 1 [>•■ i,vf'-o-^(T.-To) \1] b = AkieY-la) (47fl) Of the three terms on the right-hand side of (47), the first far exceeds the others ; hence it will be possible, by successive ap- proximation, to determine the product T^ff^, and thence also the temperature t^- In order to obtain the first approximate value of the product, which we will call Ty, let us on the right side of (47) set t^ in the place of t^, and correspondingly jOj in place of jOg* then Ty=C (48) The temperature /', corresponding to this value of the product, can be sought in the table. In order to find a second approxi- mate value of the product, the value of i' just found, and the corresponding value of the pressure p', are introduced into (47) in the places of t^ and p^j whereby, having regard to the former equation, we have Ty=Ty + «(^i4-0-^(Pi-y). .-. . (48«) As before, the temperature /", corresponding to this value of the product, is given by the table. If this does not with sufficient exactitude represent the required temperature t^, the same method must be repeated. The newly-found values t" and p" must be substituted in (47) in place of /g and p^y whereby with the assist- ance of the two last equations, we have T'yf^TV + a{t'-t")-b(p'^p% . . (48^) and in the table we can find the new temperature i'". We might proceed in this manner for any length of time, though we shall find that the third approximation is already within jl^dth, and the fourth within xoVzj^^th of a degree of the true value of the temperature /g. 48. The treatment of the third of the equations (XVII) is precisely similar. If we divide by Y—la, and for facility of cal- Theory of Heat to the Steam-engine. 429 culation introduce Briggs's logarithms (Log) in place of natural logarithms (log) by dividing by M the modulus of this system, the equation will take the form (,3=C + «LogJ, (49) wherein C and a are independent of Tg, and have the following values : — M.AA(V-/c7) J Again, in equation (49) the first term on the right is greatest, so that we can apply the method of successive approximation. In the first place, Tg is put in the place of Tg, and we obtain the first approximate value of yg, viz. /=C, (50) from which we can find the corresponding temperature t^ in the tables, and thence the absolute temperature T'. This is now substituted for Tg in (49), and gives y'=y+«Log|f, ...... (5o«) whence T" is found. Similarly we obtain . y"=/+«Logy„ . . ... . (504) and so forth. 49. Before proceeding to the numerical application of the equations (XVII), the magnitudes c and r alone remain to be determined. The magnitude c, which is the specific heat of the liquid, has hitherto been treated as constant in our development. Of course this is not quite correct, for the specific heat increases a little with increasing temperature. If, however, we select as a common value the one which is correct for about the middle of the inter- val over which the temperatures involved in the investigation extend, the deviations cannot be important ones. In machines driven by steam, this mean temperature may be taken at 100° C; this being, in ordinary high-pressure engines, about equally distant from the temperature of the boiler and that of the con- denser. In the case of water, therefore, we will employ the 430 Prof. Clausius on the Application of the Mechanical number which, according to Regnault, expresses its specific heat at 100°, and thus set c= 1-0130 (51) In the determination of r we shall start from the equation X= 606-5 + 0-305. ^ given by Regnault as expressing the whole quantity of heat necessary to raise the unit of weight of water from 0° to the temperature t, and afterwards to evaporate it at that temperature. According to this definition, however. cdt-\-r, Jo so that -£■ -J"' Jo i r =606-5 +0-305. ^- 1 cdt. Jo In order to obtain precisely Eegnault's value of r, we ought to substitute for c in the above integral, the function of the tem- perature which Regnault determined. For our present purpose, however, I think it will suffice to give to c the constant above selected, by means of which it cdt=l'01S.t, 10 and the two terms in the above equation involving t combine to form the single one ^0-708 . t. At the same time we must alter the constant term of the equa- tion a little, and determine it so that the formula will correctly express that observed value of r which in all probability is most accurate. As a mean of thirty-eight observations, Regnault found the value of \ at 100° to be 636-67. Deducting the quantity of heat necessary to raise the unit of weight of water from 0° to 100°, which, according to Regnault, amounts to 100*5 units of heat, and contenting ourselves with one decimal, there remains rioo=536-2*. Employing this value, we obtain the following formula : — r«*607-0-708.^ (52) The following comparison of a few values calculated herefrom, with the corresponding ones given by Regnault in his tables f, * In his tables Regnault gives, instead of tliis, the number 536*5 ; tbe reason is, however, that instead of the above value 63667 for X at 100°, he used the round number 637 in his calculations. t Mitn, de I'Aoadt, des Sciences, vol. xxi. p. 748. Theory of Heat to the Steam-engine. 431 will show that this simplified formula agrees sufficiently well with the more accurate method of calculation above alluded to : — t. 0°. 50°. 100°. 150°. 200°. r according to equation (52) r according to Regnault . . . 607-0 606-5 571-6 571-6 536-2 536-5 500-8 500-7 465-4 464-3 50. In order to be able to distinguish between the eiFects of the two different kinds of expansions to which the two last of the equations (XVII) refer, it will perhaps be best to consider in the first place a steam-engine in which only one of them takes place. We will commence, therefore, with one of the machines which are said to work without expansion. In this case e, which expresses the relation of the volumes before and after expansion, equals 1, and at the same time Tg=T2; so that the equations (XVII) assume a simpler form. The last of these equations becomes identical, and therefore vanishes. Further, many terms of the first will admit of elimi- nation, because they now become like the corresponding terms of the second, from which they before differed only by containing Tg instead of T^. Introducing the above-mentioned quantity k at the same time, we now obtain W k' (V. V(I - €) [Pc.-Pq) - lcT{p^ -Po) AkUn +p< -Po) (XVIII) The first of these two equations is exactly the same as the one which we also obtain by Pambour^s theory, if in (XII) we make 6=1, and introduce V instead of B. The difference therefore consists merely in the second equation, which takes the place of the simple relation between volume and weight assumed by Pambour. 51. To the quantity e, which occurs in these equations and represents the vicious space as a fractional part of the whole space set free to the vapour, we will give the value 0'05. The quantity of liquid which the vapour carries with it on entering the cylinder varies in different machines. Pambour states that it amounts on the average to 0*25 in locomotives, but in stationary engines to much less, probably only to 0'05 of the whole mass entering the cylinder. In our example we will make use of the latter number, according to which the ratio of the whole mass entering the cylinder is to the vaporous part of the same as 432 Prof. Clausius on the Application of the Mechanical 1 : 0*95, Further, let the pressure in the boiler be five atmo- spheres, to which the temperature 152°*22 belongs, and let us suppose that the machine has no condenser, or, in other words, let it have a condenser with the pressure of one atmosphere. The mean reaction in the cylinder is accordingly greater than one atmosphere. As before mentioned, the difference in loco- motives may be considerable, but in stationary engines it is smaller. With respect to stationary engines, Pambour has altogether neglected this difference ; and as our only object at present is to compare the new formulse with those of Pambour, we will also disregard the difference, and let jt?o=l atmosphere. In this example, therefore, the following values will have to be made use of in equations (XVIII) : — 6=005 '=W9E-''^'^ . (53) ;?i=3800 Po=760 To these must be added the values ^ = 13-596 0-= 0-001, which are the same for all cases; and then in the first of the equations (XVIII), besides the required value of W, the magni- tudes V and P2 alone will remain undetermined. 52. We must now examine the least possible value of V. This value corresponds to the case where the pressure in the cylinder is the same as that in the boiler, so that we have merely to put;?i in the place oip^ in the last of equations (XVIII) in order to obtain In order at once to give an example of the influence of the vicious space, I have calculated two values of this expression, corresponding respectively to the cases where no vicious space exists (e=:0), and where, according to supposition, 6=0-05. These values, expressed as fractions of a cubic metre to one kilo- gramme of vapour from the boiler, are 0-3637 and 0-3690. The latter value is greater than the former, because, first, the ksTi«^» Theory of Heat to the Steam-engine. 433 vapour entering the vicious space with greater velocity, the vis viva of its motion is converted into heat, which in its turn causes the evaporation of the accompanying Hquid; and secondly, because the vapour before present in the vicious space contri- butes to the increase of the ultimate quantity of vapour. Substituting both the above values of V in the first of equa- tions (XVIII), and in the one case again making € = 0, whilst in the other 6=0-05, we have as the corresponding quantities of work expressed in kilogramme-metres, the numbers .'^•<>^^'<^- 14990 and 14450. According to Pambour^s theory, it makes no difference whether a part of the volume is vicious space or not j in both cases this volume is determined from the equation (29Z>) by giving to p the particular value jOj. By so doing we obtain 0-3883. This value is greater than the one (0*3637) before found for the same quantity of vapour, because hitherto the volume of vapour at its maximum density was esteemed greater than, according to the mechanical theory of heat, it can be, and this former estimate also finds expression in equation (296). If, by means of this volume, we determine the work under the two suppositions 6=0 and 6=0*05, we have 16000 and 15200. As might have been concluded immediately from the greater volume, these quantities of work are both greater than those before found, but not in the same ratio ; for, according to our equations, the loss of work occasioned by vicious space is less than it would be according to Pambour^s theory. 53. In a machine of the kind here considered, which Pambour actually examined, the velocity which the machine actually pos- sessed, compared with the minimum velocity calculated, according to his theory, for the same intensity of evaporation and the same pressure in the boiler, gave the ratio 1*275 : 1 in one experiment, and in another, where the charge was less, 1'70 : 1. These velo- cities would in our case correspond to the volumes 0*495 and 0*660. As an example of the determination of work, we will now choose a velocity between these two, and set simply, V = 0*6. (.>xr ; ^v. In order next to find the temperature t^ corresponding to this value of V, we employ the equation (47) under the following special form : — T2^2=^6577 + 56*42 . (^1-^2) -0*0483 . [p^-p^, (55) 434 Prof. Clausius on the Application of the Mechanical Effecting, by means of this equation, the successive determina- tions of /, described in § 47, we obtain the following series of approximate values : — ^ a =133-01 /^'rz: 134-43 /^''= 134-32 /""= 134-33 Further approximate values would only differ from each other in higher decimal places ; so that, contenting ourselves with two decimal places, the last number may be considered as the true value of /g. The corresponding pressure is jD2= 2308-30. Applying these values of V and p^, as well as those given in § 51, to the first of the equations (XVIII), we obtain W= 11960. Tambour's equation (XII) gives for the same volume 0-6, the work W= 12520. 54. In order to show more clearly the dependence of the work upon the volume, and at the same time the difference which exists between Pambour's and my own theory in this respect, I have made a calculation, similar to the last, for a series of other volumes increasing uniformly. The results are comprised in the following Table. The first horizontal row of numbers, separated from the rest by a line, contains the values found for a machine without vicious space. In other respects the arrangement of the Table will be easily understood. V. t^. W. According to Pambour. V. W. 0-3637 15§-22 14990 0-3883 16000 0-3690 0-4 0-5 0-6 0-7 0-8 0-9 1 152-22 14912 140-83 134-33 12903 124-55 120-72 117-36 14450 14100 13020 11960 10910 9880 8860 7840 0-3883 0-4 0-5 0-6 0-7 0-8 0-9 1 15200 15050 13780 12520 11250 9980 8710 7440 We see that the quantities of work calculated according to Pambour's theory diminish more quickly with increasing volume Theory of Heat to the Steam-engine, 485 than those calculated from our equations ; for at first the former are considerably greater than the latter^ afterwards they approach a little nearer, and finally they are absolutely less. The reason is, that, according to Pambour's theory, the same mass, as at first, always remains vaporous during expansion ; whilst, according to our theory, a part of the liquid accompanying the vaporous mass afterwards evaporates, and the more so the greater the expansion. 55. In a similar manner we will now consider a machine which works with expansion, and we will further select one with a condenser. With reference to the magnitude of the expansion, we will suppose that the cylinder is cut ofi* from the boiler when the piston has completed one-third of its journey. Then foi* the determination of e we have the equation e-€=^(l-€); whence, retaining the former value, 0*05, of e, e= ^ =0-3666 As before, let the pressure in the boiler be five atmospheres. By good arrangement the pressure in the condenser may be kept below one-tenth of an atmosphere. As it is not always so small, however, and as the reacting pressure in the cylinder always exceeds it a little, we will assume the mean reaction to be one- fifth of an atmosphere (or 152 miUims.), to which the tempera- ture ^o=60°'46 corresponds. Retaining the former assumed value of /, therefore, the quantities requiring application in this example are e =0-36667 6 =0-05 / =1-053 \ (56) j0i = 3800 In order to calculate the work, we now only require the value of V to be given. To guide our choice, we must first know the least possible value of V, which we can find, as before, from the second of the equations (XVII) by putting p^ in the place of jOg, and changing the other quantities dependent on jo accord- ingly. In this manner we find for the present case the value 1-010. Starting from this, we will assume, as a first example, that the actual velocity of the machine^s motion has to this minimum a 436 Prof. Clausius on the Application of the Mechanical ratio of 3 : 2 nearly ; so that setting V=l-5, we will determine the work for this velocity. 56. The temperatures /, and /g must now be determined by setting this value of V in the two last of equations (XVII). For the machine without a condenser, the determination of t^ has been sufficiently explained ; and as the present case differs from that one only by a different value for e, which was there equal to 1, it will be sufficient to state here that the final result is /2=137''-43. The equation (49), which serves to determine ^g, now takesj, the form iJa.T.. ^3=26-604 + 51-515 Log|^, .... '(57) a^id £coia it we -obtain the following approximate values : — t' = 99-24 H' =101-93 f" =101-74 t"" =101-76. We may consider the last of these values, from which the follow- ing ones would only differ in higher places of decimals, as the proper value of t^ ; and we may use it, together with the known values of t^ and Iq, in the first of the equations (XVII). By so doing we find W=31080. When, assuming the same value of V, we calculate the work according to Pamboui'^s equation (XII), — whereby, however, the values of B and b are not taken from equation (29b), as in the machine without condenser, but from equation (29a) intended for machines with condensers, — we find W= 32640. 57. In a manner similar to the foregoing I have also calcu- lated the work for the volumes 1*2, 1*8, and 2*1. Besides this, in order to illustrate by an example the influence which the several imperfections have upon the work, I have added the fol- lowing cases : — (1) The case of a machine having no vicious space, and where at the same time the pressure in the cylinder during the entrance of the vapour is equal to that in the boiler, and the expansion is carried so far that the pressure diminishes from its original value Pi to Pq, If we fjirther suppose that Pq is exactly the pressure °\t>.%V^vv Theory of Heat to the Steam-engine. 437 in the condenser, this case will be the one to which equation (XI) refers, and which for a given quantity of heat — the temperatures at which the heat is received and imparted being also considered as given — furnishes the greatest possible quantity of work. (2) The case of a machine, again, having no vicious space, and when the pressure in the cylinder is again equal to that in the boiler, but where the expansion is not, as before, complete, but only continued until the ratio e : 1 is obtained. This is the case to which equation (X) refers; only in order to determine the amount of expansion, the change caused by the same in the temperature of the vapour was before supposed to be known, whilst here the expansion is determined according to the volume, and the change of temperature must be afterwards calculated therefrom. (3) The case of a machine with vicious space and incomplete expansion, and where, of the former favourable conditions, the only one which remains is that during the entrance of the vapour the pressure in the cylinder is the same as in the boiler, so that the volume has its smallest possible value. To these cases may be added the one already mentioned, where the last favourable condition is relinquished, and the volume has a greater than its minimum value. For the sake of comparison, all these cases, with the exception of the first, are also calculated according to Pambour's theory. The reason of the exception is, that the equations (29«) and {29b) do not here suffice ; for even the one which is intended for small pressures cannot be applied below one-half, or at most one- third of an atmosphere, whereas here the pressure ought to de- crease to one-fifth of an atmosphere. The following are the numbers given by our equations in the first of the above cases : — Volume before expansion. Volume after expansion. W. 0-3637 6-345 50460 For all the rest of the above cases the results are given in the following Table, where the numbers referring to a machine with- out vicious space, are again separated from the rest by a hori- zontal line. The volumes after expansion are alone given, because the corresponding ones before expansion, being in all cases smaUer in tie, prppprtioix 9;f ^ ; i^ijiay be easily found ; — {iiifrrTril/'foLrrifr^Offt mo'm^^sin tit '.mit o ■ >ij/3g9iq vd-s YJj^^za sr ^c^^ jedi ^^^c-'y ui/r ^tv*- If ■ ..^n^ 4S8 Prof. Clausius on the Application of the Mechanical V. ^«. 'i W. According to Pambour. V. W. 0-992 152-22 11371 34300 1032 36650 1-010 12 15 1-8 21 152 22 145-63 137-43 13102 125-79 113-68 108-38 101-76 96-55 92-30 32430 31870 31080 30280 29490 1032 1-2 1-5 1-8 2-1 34090 33570 32640 31710 30780 58, The quantities of work in this Table, as well as those in the former Table for machines without condensers, refer to a kilogramme of vapour coming from the boiler. It is easy, however, to refer the work to a unit of heat furnished by the source of heat ; for eveiy kilogramme of vapour requires as much heat as is necessary, first to raise the mass / (somewhat more than one kilogramme) from the temperature it had when entering the boiler up to the general temperature of the same, and then at that temperature to convert a kilogramme of it into vapour. This quantity of heat can be calculated from former 59. In conclusion, I will add a few remarks on friction, re- stricting myself, however, to a justification of my having hitherto disregarded friction in the developed equations, by showing that instead of introducing the same at once into the first general expressions for the work, as Pambour has done, it may also, ac- cording to the same principles, and according to the manner of other authors, be afterwards brought into calculation. The forces which the machine has to overcome during its action may be thus distinguished : — (1) The resistance exter- nally opposed to it, and in overcoming which it performs the required useful work. Pambour calls this resistance the charge of the machine, (2) The resistances which have their source in the machine itself, so that the work expended in overcoming them is not externally of use. All these resistances are included in the term friction ; although, besides friction in its more limited sense, they comprise other forces, particularly the resistances caused by pumps belonging to the machine, exclusive of the one which feeds the boiler, and which has already been considered. Pambour brings both these kinds of resistances into calcula- tion as forces opposing the motion of the piston ; and in order conveniently to combine them with the pressures of the vapour on both sides of the piston, he also adopts a notation similar to the one ordinarily used for vapour pressures ; that is to say, the Theory of Heat to the Steam-engine, - 439 symbol denotes, not the whole force, but that part of it which corresponds to a unit of surface of the piston. In this sense let the letter R represent the charge. A further distinction must still be made in the case of friction, for it has not a constant yalue in each machine, but increases with the charge. Accordingly Pambour divides it into two parts : that which is already present when the machine moves without charge, and that which the charge itself occasions. With respect to the last, he assumes that it is proportional to the charge. Accordingly, the friction referred to the unit of sur- face is expressed by f+S.-R, where / and S are magnitudes which, although dependent upon the construction and dimensions of the machine, are, according to Pambour, to be considered as constant in any given machine. We can now refer the work of the machine to these resisting forces instead of, as before, to the driving force of steam ; for the negative work done by the former must be equal to the positive work done by the latter, otherwise an acceleration or retardation of motion would ensue, which would be contradictory to the hypothesis of uniform motion hitherto made. During the time that a unit of weight of vapour enters the cylinder, the surface of the piston describes the space (1 — e)V, hence for the work W we obtain the expression W=(1-6)V[(1+8).R+/]. On the other hand, the useful part of this work, which for di- stinction from the whole work shall be symbolized by (W), is expressed thus, (W) = (l-e)V.R. Eliminating R from this equation by means of the former, we have the equation (W)^^-^/-)^-/ .... (58) by means of which, V being known, the useful work (W) can be deduced from the whole work W as soon as the quantities /and 8 are given. I will not here enter into Pambour^s method of finding the latter quantities, as this determination still rests upon a too in- secure basis, and as friction is altogether foreign to the subject of this memoir. 440 Prof. Ckusius on the Application of the Mechanical Table containing the values, for steam, of p, its differen- millimetres of mercury. tial coefficient ■f-=-g, and the product T.^r expressed in at in Cen- tigrade degree*. 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 76 76 77 78 79 80 81 82 83 84 85 86 87 «8 P- 54-906 57-909 61054 64-345 67-789 71-390 75-156 79091 83-203 87-497 91-980 96-659 101541 106-633 111-942 117-475 123-241 129-247 135-501 142011 148-786 155-834 163164 170-785 178-707 186-938 195-488 204-368 213586 223-154 233-082 243-380 254060 265132 276-608 288-500 300-820 313-579 326-789 340-464 354-616 369-258 384-404 400-068 416-262 433-002 450-301 468-175 486-638 A. 3-003 3145 3-291 3-444 3-601 3-766 3-935 4]12 4-294 4-483 4-679 4-882 5-092 5-309 5-533 5-766 6-006 6-254 6-510 6-775 7-048 7-330 7-621 7-922 8-231 8550 8-880 9-218 9-568 9928 10-298 10-680 11072 11-476 11-892 12-320 12759 13-210 13-675 14-152 14-642 15-146 15-664 16194 16-740 17-299 17-874 18-463 2935 3074 3-218 3-367 3-522 3-683 3-850 4-023 4-203 4-388 4-581 4-780 4-987 5-200 5-421 5-649 5-886 6-130 6-382 6-642 6911 7-189 7-475 7-771 8076 8-390 8-715 9049 9-393 9-748 10113 10-489 10-876 11-274 11-684 12106 12-539 12-984 13 442 13-913 14-397 14-894 15-405 15-929 16-467 17-019 17-586 18-168 18-765 A. 0-139 0144 0149 0155 0-161 0-167 0 173 0180 0185 0 193 0-199 0-207 0-213 0-221 0228 0-237 0-244 0-252 0-260 0-269 0-278 0-286 0-296 0-305 0-314 0-325 0-334 0344 0-355 0-365 0-376 0-387 0-398 0-410 0-422 0-433 0445 0-458 0-471 0-484 0-497 0 511 0524 0-538 0-552 0-577 0-582 0-597 919 965 1014 1064 1116 1171 1228 1287 1349 1413 1480 1549 1621 1695 1773 1853 1936 2023 2112 2205 2301 2401 2504 2611 2722 2836 2954 3077 3203 3334 3469 3608 3752 3901 4054 4213 4376 4544 4718 4897 5082 5272 5469 5671 5879 6093 6313 6540 6774 A. 46 49 50 52 55 57 59 62 64 67 69 72 74 78 80 83 87 89 93 96 100 103 107 111 114 118 123 126 131 135 139 144 149 153 159 163 168 174 179 185 190 197 202 208 214 220 227 234 itv^itt^y, Theory of Heat to the Steam-engine, Table {continued). 441 in Centi- grade degrees. 89 90 91 92 93 94 95 96 ^7 98 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 486-638 505-705 525-392 545-715 566-690 588-333 610-661 633-692 657-443 681-931 707-174 733191 76000 787-59 816-01 845-28 875-41 906-41 938-31 971-14 1004-91 1039-65 1075-37 1112-09 1149-83 1188-61 1228-47 1269-41 1311-47 1354-66 1399-02 1444-55 1491-28 1539-25 1588-47 1638-96 1690-76 1743-88 1798-35 1854-20 1911-47 197015 2030-28 2091-90 2155-03 2219-69 2285-92 2353-73 2423-16 2494-23 2567-00 2641-44 19-067 19-687 20-323 20-975 21-643 22-328 23-031 23-751 24-488 25-213 26017 26-809 27-59 28-42 29-27 30-13 31-00 31-90 32-83 33-77 34-74 35-72 36-72 37-74 38-78 39-86 40-94 42-06 43-19 44-36 45-53 46-73 47-97 49-22 50-49 51-80 5312 54-47 55-85 58-68 60-13 61-62 63-13 64-66 66-23 67-81 69-43 71-07 72-77 74-44 18-765 19-377 20-005 20-649 21-309 21-985 22-679 23-391 24-119 24-865 25-630 26-413 27-200 28-005 28-845 29-700 30-565 31-450 32-365 33-300 34-255 35-230 36-220 37-230 38-260 39-320 40-400 41-500 42-625 43-775 44-945 46-130 47-350 48-595 49-855 51145 52-460 53-795 55-160 56-560 57-975 59-405 60-875 62-375 63-895 65-445 67020 68-620 70-250 71-920 73-605 75-315 A. 0-612 0 628 0-644 0-660 0676 0-694 0-712 0-728 0-747 0-765 0-783 0-787 0805 0-810 0 855 0-865 0-885 0-915 0-935 0-955 0-975 0-990 1010 1-030 1-060 1-080 1-100 1-125 1-150 1-170 1185 1-220 1-245 1-260 1-290 1-315 1-335 1-365 1-400 1-415 1-430 1-470 1-500 1-5-20 1-550 1-575 1-600 1-630 1-670 1-685 1-710 T.^'. 6774 7014 7262 7516 7778 8047 8323 8608 8900 9200 9509 9826 10146 10474 10817 11167 11523 11888 12266 12654 13051 13458 13872 14296 14730 15178 15635 16102 16581 17072 17574 18083 18609 19146 19693 20253 20827 21410 22009 22624 23248 23881 24533 25199 25877 26571 27277 27997 28732 29487 30252 31030 240 248 254 262 269 276 285 292 300 309 317 320 328 343 350 356 367 378 388 397 407 414 424 434 448 457 467 479 491 502 509 526 537 547 560 574 583 599 615 624 633 652 Qm 678 694 706 720 735 755 765 778 FML Mag, ^.4, Vol. IS. No. 81. Dec. 1856. 2 G Prof. Clausius on the Mechanical Theory of Heat. Table {continued). in Cfcnti- grode degrees. 140 141 M'2 143 144 145 146 147 148 149 150 151 152 153 154 155 J56 157 168 159 160 161 163 163 164 165 166 167 168 169 170 171 172 173 174 176 176 177 178 179 180 181 189 183 184 185 186 187 188 189 190 2641-44 2717-63 2795-57 2876-30 2956-86 3040-26 3125-65 321274 3301-87 3392-98 348609 3581-23 3678-43 3777-74 387918 3982-77 4088-56 4196-59 4306-88 4419-46 4634-36 4651-62 4771-28 4893-36 5017-91 5144-97 5274-64 5406-69 5641-43 5678-82 5818-90 5961-66 6107-19 6255-48 6406-60 6660-65 6717-43 6877-22 7039-97 7205-72 737462 7546-39 7721-37 7899-52 8080-84 8265-40 8453 23 8644-85 8838-82 9036-68 9237-96 9442-70 A. 76-19 77-94 79-73 81-56 83-40 85 29 8719 89-13 91-11 93-11 9514 97 20 99-31 101-44 103-69 105-79 108-03 110-29 112-57 11401 117-26 119 66 122-08 124-65 127-06 129-57 132-15 134-74 137-39 14008 142-76 145-53 148-29 15112 153-95 156-88 159-79 162-75 165-76 168-80 171-87 174-98 178-15 181-32 184-66 187-83 19112 194-47 197-86 201-27 204-75 ff- 76-316 77-065 78-836 80-646 82-480 84-345 86-240 88160 90-120 92110 94-126 96-170 98-255 100 375 102-615 104-690 106910 109160 111-430 113-740 116-085 118-460 120-870 123-315 125-805 128-315 130860 133-445 136065 138735 141-420 144-145 146-910 149-705 152 535 156-415 158335 161-270 164-250 167-275 170 335 173-426 176-565 179 736 182940 186-195 189-425 192-796 196-166 199-566 203-010 206-490 1-750 1-770 1-810 1-835 1865 1-895 1-920 1-960 1-990 2-015 2-045 2-085 2-120 2-140 2-175 2-220 2-250 2270 2-310 2-346 2376 2-410 2-445 2-490 2-610 2-545 2585 2-620 2-670 2-685 2-725 2-766 2-795 2830 2-880 2-920 2-935 2-980 3025 3-060 3090 3140 3-170 3-206 3-256 3-280 3-320 3-370 3-400 3446 3-480 T.ff. 31030 31828 32638 33468 34312 35172 36048 36939 37850 38778 39721 40680 41660 42659 43671 44703 45757 46830 47915 49022 50149 5J293 52468 53642 54851 56073 57317 68582 69868 61182 62508 63856 66228 66618 68030 69470 70934 72410 73912 76441 76991 78561 80160 81779 83421 86091 86779 88493 90236 91999 93791 95605 A. 798 810 830 844 860 876 891 911 928 943 959 980 999 1012 1032 1054 1073 1085 1107 1127 1144 1165 1184 1209 1222 1244 1265 1286 1314 1326 1348 1372 1390 1412 1440 1464 1476 1502 1529 1550 1570 1599 1619 1642 1670 1688 1714 1743 1763 1792 1814 On a new Arrangement of the Induction Coil, Table {continued). 443 t in Centi- grade degrees. P- A. 9- A. T.^r. A. 190 191 192 193 194 195 196 197 198 199 200 9442-70 9650-93 9862-71 10078-04 10297-01 10519-63 10745-95 10976-00 11209-82 11447-46 11688-96 208-23 211-78 215-33 218-97 222-62 226-32 230-05 233-82 237-64 241-50 206-490 210005 213-555 217-150 220-795 224-470 228185 231-935 235-730 239570 243-455 3515 3-650 3-595 3-645 3-675 3715 3750 3-795 3-840 3-885 95605 97442 99303 101192 103111 105052 107018 109009 111029 113077 115154 1837 1861 1889 1919 1941 1966 1991 2020 2048 2077 LV. On a new Arrangement of the Induction Coil. By Jonathan N. Hearder, Plymouth^. 1. TN my communication to the last Number of tlie Philoso- A phical Magazine, I confined myself to the announcement of a few of the novel results which I had obtained from investiga- tions with my induction coil. I might have given many more, but purposely refrained from doing so until I had had an opportunity of repeating my experiments with a still more powerful machine, as certain indications had led me to believe that many of the results which have hitherto been announced as peculiar to the action of the induction coil, have been disguised by the mode of construc- tion of the instruments of M. RuhmkorfF; such, for example, as the ignition of the negative terminal only, and the comparative inertness of the terminal proceeding from the inner portion of the coil. These and other effects appeared to me to indicate that M. Ruhmkorff^s secondary coil could not be perfectly insu- lated from the primary one, and that the true statical condition of the two terminals could not consequently be accurately ascer- tained and compared. 2. It happened in the first arrangement of my machine, that I was led to construct all its elements separate and independent of each other, for the purpose of ascertaining how modifications of any of them influenced the action of the rest. The secondary coil in this case was perfectly insulated, and I was frequently struck with unexpected results, especially in the improved arrange- ment of my first machine alluded to in my last paper, since both terminals would sometimes become heated, and the inner terminal was possessed of such high statical intensity that it could not be handled with impunity. In a still more powerful machine * Communicated by the Author. 2 62 444 Mr. J. N. Hearder on a new Arrangement of which I have recently constructed, and which I am about to describe, these phsenomena are more strikingly evident ; and but for the arrangement which I have adopted, I believe that they would not have been developed. 3. The machine consists of a gutta-percha bobbin of about 12 inches in length, the cylindrical centre of which is large enough to receive the primary coil with its core. Upon this bobbin is wound the secondary coil, consisting of fine copper wire covered with silk, and carefully varnished with shell-lac, which is allowed to dry previously to winding on. The consecutive layers of the wire are separated from each other by a stratum of oiled silk or sheet gutta-percha. I am thus enabled to wind off and relay the wire to repair accident ; and I have more than once found the advantage of the arrangement; for, on forcing my first machine to a very extreme point of tension, the internal insula- tion broke down, and on winding off the wire I discovered the cause of the accident, and was able to apply the appropriate remedy. The contact breaker which I employ is similar to that of my medical coil machine, consisting of a very stiff brass spring, armed at one end with a piece of iron, to be attracted by the end of the iron core, and breaking contact by means of a platina stud fixed about the centre of its length, and pressing against a contact screw also armed with platina. The condenser is, as in Kuhmkorff^s machine, enclosed in the base of the instrument. The secondary coil is rather less than three miles in length. My exciting battery is a modification of Grovels nitric acid battery, the zinc being excited with muriate of ammonia instead of dilute sulphuric acid, by which the amalgamation of the zinc is dis- pensed with, and the battery is in every respect equally powerful. With twelve cells the following effects are produced with the coil. 4. The spark at the interruptor is loud, brilliant, and flame- like, frequently throwing out a flat sheet of flame of a peculiarly distinctive character, as large as a shilling, or even larger. By a connecting screw the condenser can be detached, when the ordi- nary secondary spark appears at the break very different from that which occurs when the condenser is used. 5. Each secondary terminal gives sparks to an uninsulated conductor, which are longer when the opposite terminal is com- municating with the ground, sometimes more than an inch in length ; and on connecting the terminals with a graduated Lane's discharger furnished with platina points, torrents of sparks in bundles pass between them at a distance of 2*5 inches. At 2*75 sparks still pass, but not in such quantities ; and on modifying the vibrations of the spring with the finger, so as to vary slightly the pressure, occasional sparks will pass nearly 3 inches in length. 6. On approximating the points to within 0*4 or 0*5 of an \(^\^^^^^^ the Induction Coil, - ■"'^''^ 445 inch, both become white-hot, the negative being rather hotter than the positive ; and on substituting fine iron wires for the platina points, both enter into combustion. Fine platina wires become white-hot at the ends, melt, and run back into globules. 7. Through the flame of alcohol a flood of sparks will pass between 8 and 9 inches in length, producing a curious zigzag circuit, and accompanied with very loud crepitations. >-■ 8. In an exhausted receiver, 3 feet in length and 4 inches in dia- meter, a splendid ribbon of light is produced of the most exqui- site colours, the centre line being bright, and surrounded by an intense crimson light, shading off into violet and purple. I have only yet tried a receiver of these dimensions, but should consider from appearances that the light would pervade a much longer vacuum. 9. I have only tried Gassiot^s cascade in a flower vase 10 inches high, but there can be no doubt that a flower vase of 2 or 3 feet in height would be equally well illuminated, as 1 was obliged to use only 3 or 4 cells, otherwise the action of the machine was too strong. The contrast in the appearance of the light on reversing the current is most beautifully exhibited. On making the inside of the vase positive, the electricity appears to flow in an immense sheet out over the edge to a considerable distance, and fall upon the plate of the pump ; but on reversing the cur- rent, a totally diffbrent appearance is produced : the sheet appears now to envelope the vase more closely, and to flow up and turn in over the rim,' the direction of the current in each case being too decided to be mistaken. 10. I have not yet heard of any effects from a single machine which have at all approximated to these results ; and as I believe that the arrangement is not only more powerful, but possesses important advantages over that adopted by M. Ruhmkorff, I have not hesitated to bring it before the scientific world. I find it, however, absolutely necessary to identify myself with the process of manufacture, as even the most careful workmen are apt to overlook what may appear- to them trifles, but which are, however, in fact the main causes of success or failure. I am also satisfied that the foregoing effects, although of an unusual cha- racter, are but trifles compared with what may be obtained from a judicious extension and modification of the principles ; and I even doubt whether I have yet attained the maximum effect from the secondary wire of the machine which I have now described, as the secondary current, although increased by extra battery power, depends more upon the magnetic intensity of the iron core than upon any modified conditions of the battery current and primary coil, except so far as they shall combine to exalt the magnetic condition of the included core. [ 446 ] liVI. Memorandum rejecting a new System of Roots of Unity, By Sir William Rowan Hamilton, LL.D., M.R,I,A., F.R.A.S., 8fc., Andrews^ Professor of Astronomy in the Uni- versity oj Dublin, and Royal Astronomer of Ireland^, I HAVE lately been led to the conception of a new system, or rather /flmt'/y of systems, of non-commutative roots of unity, which are entirely distinct from the ijk of the quaternions, though having some general analogy thereto ; and which admit, even more easily than the quaternion symbols do, of geometrical inter^ pretation. In the system which seems at present to be the most interesting one, among those included in this new family, I assume three symbols, i, k, \, such that ^8=1, /^=1, xs=l, \=i/c; } .... (A) where ifc must be distinguished from kl, since otherwise we should have \^'= 1, \= 1. As a very simple specimen of the symbolical conclusions deduced from these fundamental assumptions, I may mention that if we make we shall have alsof so that /I is a new fifth root of unity, connected 'with the former fifth root X by relations of perfect reciprocity. A long train of such symbolical deductions is found to follow : and every one of the results may be interpreted, as having reference to the passage irom face to face (or from corner to corner) of the icosahedron (or of the dodecahedron) : on which account, I am at present disposed to give the name of the " Icosian Calculus/^ to this new system of symbols, and of rules for their operation. Some ad- ditional remarks on this subject may soon be offered to the Phi, losophical Magazine, under the title, already sanctioned by the Editors, of '' Extensions of the Quaternions." Observatory of Trinity College, Dublin, October ^9, 1866. * Communicated by the Author, t Jn faci;, by (A), lr=t.tic.JC»=:t(K»t)V=(4K«)», 8l«q [ 447 ] Line of the j P. J. Mar To Richard Taylor, Esq. LVII. On the Anticlinal Line of the London and Hampshire Basins. ByY.i. Martin, Esq. My pear Sir, AS you have with much kindness hitherto afforded me space in the Philosophical Magazine for the publication, in ewtenso, of everything I have had leisure to bring before the public on the much- vexed question of the Weald Denudation, I beg the favour of a continuance of your good offices in the same direction. By some the subject may be considered rather stale ; but so long as there exists a doubt on the public mind of whether we are to refer the phaenomena of the great denudations around us to the slow sempiternal erosion of weather and water, as we see them now in operation, or to call in the assistance of seasons of paroxysmal violence and activity under other conditions, any contribution which tends to throw light on such a subject can- not be viewed with indifference. I am, dear Sir, Your obliged friend and Servant, P. J, Maiitin* In my description of some of the parallel lines of elevation which constitute the great anticlinal, and by their contortion broke up the superficial strata and prepared them for removal, at p. 50. vol. ii. 4th series, Phil. Mag., will be found the follow- ing foot-note : — " Of the manner in which these parallel linea may pass uninterruptedly and sometimes silently through a country, we have a good example in the case of Portsdown Hill in Hampshire, High Down near Worthing in Sussex, and the cliffs of Seaford in the same county, all elevations of the same cha-, racter, lying in the same course east and west, with a dip opposed to the prevailing one of the intervening country. An elevatory force acting with greater intensity at these points can alone ex- plain the coincidence.^^ I had previously described these emi- nences in my publication in 1828 as chalk outliers-by-protrusion. Within the last two years a better acquaintance with the country has shown me that the line in question does not pass through it so clandestinely, but that the chalk is brought to the surface, obscured here and there by " drift ^^ in all the linp of coun- try south of the South Downs from Seaford by High Down, through the Manwode, south of Chichester, and by Ports- down into Hampshire, as far as Fareham and Titchfield, where it is lost under the Hampshire tertiaries. In all this course of at least sixty miles, tertiary formations are to be found 448 Mr, P. J. Martin on the Anticlinal Line of north and south of it. As I have elsewhere said, it is variable in its character. At the points indicated, as above, by the remarkable eminences of Portsdown and High Down, the dip into the northern synclinal is gentle and easy ; but it is in otliers more abrupt and inchning to the character of what Mr. Hopkins calls flexure*, like the one-sided saddle at Farnham and the Hogsback in Surrey, or even to direct upcast or fault ; for in its passage from Portsdown eastward by Emsworth, I find that on the south side of the hamlet of Prinstcd, wells reach the chalk through ten or twelve feet of gravel; whilst on the north side of the same, within the short distance of 200 yards, wells are sunk 60 or 70 feet in London clay, and then water is only procured by perco- lation from above. I have not at present evidence to prove that this line of elevation has so much the character of a '^ fault '' or sharp flexure elsewhere, but there is good reason to believe that this is very much the case in all the line of country through which it can be traced between Portsdown and High Down. How- ever this may be, it is certain that all the flat country south of the Downs, ranging from Bedhampton at the foot of Portsdown to Brighton, including Hayling and Thorney Islands, the estuary of Chichester Harbour, and the peninsula of Selsey, is intersected by this chalk ridge with a trough of tertiaries on each side. The importance of this arrangement cannot be too highly appreciated, as bringing so great an accession to that category of parallel linings or foldings of which the great anticlinal is composed, and carrying the phsenomena of denudation along with it so far out of the range of the Weald Valley. This great tract of country has been so completely rasee, it is so flat and so copiously be- strewed with drift, and so little raised above the level of the sea, as to have impressed some early observers with the notion of a sea-bed comparatively modern, of which the chalk downs were the clifi'-bound coast. It is unnecessary to say that this idea is here entirely repudiated. The enormous quantity of angular flint, the entire removal of the chalk to which that flint belonged, the thick beds of fertile loams and brick-earths manufactured on the spot and mixed up with these angular flints, the absence of rounded gravel except such as has been obviously derived from the eocene immediately contiguous to the chalk, — all bespeak a tumultuary activity by far transcending the erosion and attrition of an ordinary sea-board. The drift of this flat and remarkable district admits of a natural division into two kinds — the diluvial, and the boulder or glacial. The former is the loamy drift with angular flints, as before said, so copiously spread over the northern division. The southern, comprising the peninsula of Selsey, and all the coast of Brackles- * Transactions of the Geological Society, vol. vii.p. 17. ^ mithe London and Hampshire Basins. 449 ham Bay to Chichester Harbour, is occupied by the boulder- drift. The line of demarcation of these two kinds of drift runs nearly parallel with,, and close upon the protruded chalk-anticlinal above described*. I have not been able to find evidence of the existence of the boulder-drift west of Chichester Harbour, in Thorney or Hayling, and it dies out as we come north from Sel- sey, though there is ample proof of its ancient extension over a much larger surface ; blocks of granite and of other crystalline rocks are found at Siddlesham, Hounston Common, and in Bird- ham. The occurrence of these granitic boulders on the Sussex coast w^as first noticed by Mr. Dixon in his summary of the Geo- logy of the Bracklesham district f; he does not seem, however, to have been aware of their importance, or to have understood the true geological relations of the deposit in which they were found. Mr. Godwin Austen has also recognized the existence of this deposit, and has described and speculated on it in a paper read before the Geological Society, of which an abstract is given in the ' Quarterly Journal,' vol. xii. p. 4. It is composed of loam or brick-earth, extensive beds of rounded gravel and angular flint, the former much predominating, with here and there large erratic blocks, the whole exhibiting the heterogeneous and tumultuary character of the boulder-drifts of the eastern counties. Of the position and the true geological relations of this important de- posit more will be said by-and-bye ; for the present it will be well to return to a further consideration of the angular flint, or — Diluvial Drift. — Much valuable detail of the nature and dis- tribution of this drift has been given by Sir R. I. Murchison in his paper ^' On the Flint Drift of the South Downs " (Quarterly Journal of the Geological Society, Feb. 1, 1852). The soil of the greater part of the flat country under review is entirely com- posed of it, and it lies especially deep between the base of the Downs and the chalk-anticlinal above described. An attentive study of the country, with a due consideration of the nature of the stratified beds below, and of the convulsive changes they have undergone, must bring the conviction that the loams, brick- earths, beds of impacted angular gravel, and all the other super- ficial phsenomena of this deposit, are the result of diluvial cur- rents operating through geological periods more or less prolonged, and recurring at longer or shorter intervals. Good illustrative sections of these gravels are to be seen on each side of the road from Slindon Common, where Sir R. Mur- chison says they appear in great force, to Chichester. At Ball Hut they are loosely mixed up with the sands of the lowest * This line of demarcation is not sharp and well defined, but there is a manifest and marked difference north and south of it. t Dixon's * Geology of Sussex/ p. 14. ;.^i:. ,i '. 460 Mr. P. J. Martin on the Anticlinal Line of tertiary, a pit of which was some few years since open by the road side near the nursery garden. Further west, at Crocker Hill and Boxgrove, the angular tiints are largely mixed up with eocene shingle, and so it continues on to Goodwood. At West Hamp- net they are closely impacted with clays derived from the stratum above mentioned. Further on, between the workhouse and the city, close by the Lavant, and near the public-house at the turn- ing to Goodwood, a pit was open three or four years ago, from whence flints were turned out with so much chalk-rubble about them and so white as to look like chalk-stones. I have not seen anything like it except at Brighton, and under the Downs at Boxhill in Surrey. Further west in the Portfield the gravels are again smaller and more washed. At Rumboldswick, again, they become larger, and the same in the direction of Donnington and Appledram, and are here again mixed and impacted with the subjacent clays. South from these points the surface of the Manwode country is chiefly tertiary clay and sand, till the boulder-drift falls in from the coast. If any stress be laid on the diff'erence of colour in these gra- vels as indicative of their age or of their sera of formation, let it be admitted. The flints by the side of the Lavant are not so much pounded as those at the West Hampnet brick-yard, where they are for the most part broken into small fragments and impacted with clay-loam ; and they are white, because they have not been washed out of the chalk rubble that surrounds them. Even their superposition, if it be clearly made out, argues nothing more than that they have been outspread after the washing, smashing, and impaction of the brown (brown because mixed up with ferruginous) clay, near or on which they lie. Unwashed flints are spread out in like manner at Brighton, in the valley of the Mole near Boxhill, and on the outskirts of the foot of the North Downs from Dorking to Keigate ;— and are here and there to be found in chalk-rubble drift on the plateau of the upper greensand in West Sussex. This white gravel, if it may be so called, was brought into notice in my former publication on ter- tiary drift (see Phil. Mag. for October 1851) ; and its super- position, be that granted, argues nothing more than another diluvial sweep, — else, why is it, and how came it there ? West of Chichester, towards Emsworth and the foot of Ports- down Hill, the same features are observed, more brick^earth and clay-impacted gravels, the stratified London or Plastic clays appearing here and there on the surface. From this part of the country, along the Forest of Bere, and skirting the Downs, this band of angular flint-gravel, sometimes loosely and sometimes closely bound together, and mixing with eocene shingle, crosses over the chalk-dome of the Alton Hills, and uniting here and thqre the London and Hampshire Basins, 451 with the debris of the tertiaries still persistent on the chalky to the back of the North Downs, where the same zone is resumed with the same appearances, and extends from Guildford to Can- terbury. There is an important break in the series between Basingstoke and Guildford, owing to the peculiar upcast of the chalk between Crondall and the last-mentioned place. With this exception, the same general character is to be observed in ^11 this spread of supracretaceous gravel. 1 have dwelt more on these phsenomena, because they are, and especially in the Chi- chester country, so strikingly opposed to every notion of gentle attrition and gradual abrasion. Neither at Chichester, nor in any part of the great plain in which it stands, are there any terraces or signs of modern sea-beds properly so called. And with regard to the sudden rise of the chalk downs out of this level and deceptive surface, it is to be attributed to two causes. The first, the natural propainence of a stoney stratum in a strongly denuded country. The second, the vicinity of some subordinate anticlinals, or other causes of intu- mescence running from Bowhill* by West Dean, Singleton, and East Dean, some signs of which are to be seen in a chalk quarry at the top of Duncton Hillf. East of this country, and on towards the Adur, the hills are tilted, as I have elsewhere ex- plained, by the long anticlinal of Greenhurst which rules the escarpment of the Downs from Duncton to Wolfstanbury. It is this sudden rise of the chalk out of the plain which Sir C. Lyell has figured in his ' Manual ' as illustrative of a line of sea-cliffs (p. 276, 5th edit.), — a position 1 conceive to be quite untenable, The chalk was hard, the tertiaries soft and destructible ; a strong denuding force brought the former forward with more than usual prominence, the tilting of a proximate line of elevation assisting in the work. With all but religious faith in the doctrines of the author of what may be called the philosophy of modern geology, I grieve to find that our theories of the Weald can be made tq approximate in so few points. Almost all the illustrations Sir C. Lyell has brought to bear on his own views, I consider, like this, to be fallacious, and founded on an erroneous principle. The best approach to a true theory of the denudation has been made by my friend Dr. Fitton, in his little book on Hastings. But he has done his work too timidly. * See Ordnance Map. t Another curious illustration of this line of disturbance and excavation exists in a miniature mole which runs along the valley. The infant Lavant ia here a mere winter-bourne, and its channel fills only after long-continue4 rains. I am credibly informed that it makes its appearance at Singleton, and runs strong there, and disappears in an adjoining meadow, breaking out again about a mile off at West Dean, for a fortnight before it ^Us its channel full the whole way. 452 Mr. Hennessy on the Importance of an Adequate Definition Mr. Hopkins walls himself up, as I have elsewhere said, in an imaginary line of demarcation, and fails of candying his specu- lations out to their legitimate conclusion. lie breaks up the Weald, but docs not dispose of the materials. Does he leave them to be disposed of by the gentle means of erosion, by sea- boards or under-currents, or by atmospheric wear ? The erosion by sea-boards it cannot be, for there are no beaches ; there are lacerated escarpments, but there are no cliffs; there are chasms and ravines, but these do not bear the marks of having been " fiords '' or estuaries ; and there are bare rocks, but these have no stratified beds with their attendant fossils at their feet, nor are accompanied by any of the other ordinary signs of sea-beds. [To be continued.] LVIII. On the Importance of an Adequate Definition in developing the Theory of Parallel Lines, By J. P. Hennessy* PROFESSOR STEVELLY'S criticism, in the last Number of the Philosophical Magazine, on a paper of mine which was published nearly four years ago, raises two distinct questions. It raises, in the first place, a question as to the logical value of the reasoning in my paper. On this I do not think it necessary to offer any observations. To do so, would be to approach too close to what every man of science must wish to avoid, — a personal discussion. I am quite certain that a discussion of such a nature could have no claims whatever to occupy the valuable space of the Philosophical Magazine. I trust, therefore, that Mr. Stevelly will not feel I am treating him with any discourtesy if I allow all the assertions as to ''defective logic and incorrect reasoning" to pass by unan- swered f. But the position taken by Mr. Stevelly raises another and more important question. It brings forward the very point on which, in my opinion, the Theory of Parallels will be found to depend. This is, the question as to the sort of definition we are at liberty to employ. * Communicated by the Author. t With regard to the opinion I may happen to entertain as to the details of his demonstration, Mr. Stevelly observes, — " I am much gratified that Mr. Hennessy does not profess to have detected any defect in the chain of reasoning on which the nroofs are founded." For fear of misapprehen- sion, I may remark that 1 did not oflfer any opinion on that subject, for a very simple reason. "When I had pointed out that the whole principle of Mr. Stevelly's method was taken — inadvertently I am sure — from a French geometer, it did not appear necessary to go any further. The minor details of a " New Method," which was thus deprived of all claim to originality, could hardly be expected to command much attention. • vv. .tsoft *^ developing the Theory of Parallel Lines, 453 Mr. Stevelly's position is by no means a novel one. In looking over the voluminous history of the subject, one is struck by the large number of persons who object to anything like a full and adequate definition. The objection is generally made on the ground that the definition "assumes^^ something; or that it contains a " property ;" or that it " involves a petitio prin- cipii.'^ It is hardly necessary to say, that such objections imply a misapprehension of the first principles of formal logic. In framing a definition, something must be assumed; and that something must be a property. When the property is incor- porated in the definition, it becomes its differentia. In speak- ing, as logicians, of the properties of any conception that we may have thus defined, the difi*erentia is no longer included. The properties are all susceptible of being deduced from the definition; but, to expect that its own differentia should be deduced from it in a similar manner, is, undoubtedly, a grave mistake. Such a mistake will arise from a confusion between the difi'erentia and the propria; and it appears to have, not unfrequently, impeded the proper settlement of this question. For example, Mr. Stevelly says, referring to the definition in which a case of the 29th proposition is made the differentia (that the two interior angles on the same side will be together equal to two right angles), — " The 29th proposition of Euclid^s Elements calls on me to prove that ' any^ line, which cuts those [two parallel lines], also makes the two interior angles on the same side together equal to two right angles. This is a relation of these two lines to all others which cut them which requires to be proved, and which neither the above definition nor any other definition can warrant us to assume as a truth without proof. It is a 'property^* which must be shown to be an essential concomitant of that which has already fixed the rela- tion of those two lines to one another, and to all others which cut them, and which we have by the definition merely agreed shall entitle us to denominate them 'parallel lines ^ in any individual case in which we find it to obtain.^' Here, in consequence of a confusion of the differentia and propria, the remarkable oversight is committed of expecting a proof of the very thing that has been assumed, and on which any demon- stration must rest. It would be quite impossible to give a demonstration of the differentia and propria of any complete geometrical conception. The proprium chosen for a differentia becomes an ultimate premiss in the sorites. As far as suscepti- bility of proof is concerned, it is altogether outside the domain of demonstration. * Had Mr. Stevelly called it by its right name, the " differentia," he would at once have seen his mistake. , . , 454 Mr. Hennessy on the Importance of an Adequate Definition In attempting to decide on the diflFerentia of parallel lines, or of any other geometrical conception, it is of importance that we should cai'efully ascertain how far we are privileged to go ; that is, we should ascertain how much a mathematical definition is permitted, and expected, to include. It is obvious that the nature of the definition will depend in a great measure on whether we believe, on the one hand, that " it entitles us merely to denominate certain lines parallel in any individual case;^' of whether, on the other hand, there is something besides the mere meaning of a term, as a nominal definition, involved in it. The views of Dr. Whewell on this subject are well known. He* has always upheld the real character of mathematical definition* Even Mr. Mill recognizes t something more than an arbitrary name* There is, however, no necessity to go further than the writings of Dr. Whately to find the strongest confirmation of the views I have ventured to put forward. " The term definition,^' he says, " is used with some laxity ; and much confusion has thence resulted. Such definitions as the mathematical, must imply every attribute that belongs to the thing defined.^' Again, he says, — " In mathematics there is no distinction between nominal and real definition ; the meaning of the term and the nature of the thing being one and the same : so that no correct definition what^ soever of any mathematical term can be devised,which shall not imply everything which belongs to that term.'' The next point to determine is, whether we are at liberty to take any adequate proprium we choose for the difierentia. That we are entitled to do so there cannot be the slightest doubt* On the plainest logical principles, it would be absurd to suppose that any property, possessing sufficient comprehension and clearness, could be, by any arbitrary arraigement whatever, distinguished from the others, and set aside as incapable of being employed in definition. And, on the other hand, we are fully at liberty, in case any advantage appears to be gained by such a course, to strip a definition of its discretive form, and to place it amongst the propositions {. It would be indeed very difficult to point out any striking pro- prium of parallels which has not at some time or another been made a differentia, by the second class of geometers, alluded to * Philosophy of the Inductive Sciences, vol. i. p. 92; vol. ii. pp. 598,599. t In speaking of the definition of a circle (System of Logic, vol. i. p. 336). X The tery course here alluded to has been tftken by many Continental geometers. In this country, amongst others, the author of the article " Geometry" in the Encyclopadia Metropolitana has adopted it. After giving a definition, practically the same as Wolfius's, he observes, — " We have preferred the definition above given, and have made the property ot parallel hnes never meeting a proposition instead of a definition. "-*-Pttre Sciences, vol. i. p. 3l3. in developing the Theory of Parallel Lines, 45S' on a formeroccasion*. M. Varignon,M.EtienneBezoutand many others^ have suggested that case of the 29th proposition of EucUd, which states that the exterior angle is equal to'the interior and op- posite. From this, down to Mr. Stevelly's, we have had definitions of all sorts. The list commences with such as fulfil Dr. Whate^ ly^s idea of what a mathematical definition should be, and ter- minates with such as are inadequate and useless. There is one test that every logician would employ in examining the practical value of ordinary definitions, which should be applied to these. It depends on the relative ease with which we find the properties flow from the definitions. The number of writers who have gone out of their way to get a definition which involves in the deductions from it, to use Dr. Lardner^s phrase, ^^ a labyrinth of complicated and indirect demonstration," is remarkable. Eor the purpose of assisting in the choice of a definition of parallels, I made an analysis of the definitions of a circle and a square. The advantages derived from an examination of Euclid^s definitions are not confined to the development of the analogies then found to exist. Let us, for instance, take four of the most important : — I. Riffht line : — That which lies evenly between its extremities* II. Right angles : — When a right line standing on another right line makes the two adjacent angles equal. III. Circle : — A continued line, having a point within it, from which point all right lines to the continued line are equal. IV. Parallel lines :— Such as cannot meet when produced. Of the first it is sufiicient to say that it is not framed in the accurate language of geometry. In fact a geometer, as such, can attach no meaning to the phrase lying " evenly." The de->; finition has therefore never been used. The second and third are clear, adequate, and perfectly logical. The fourth is certainly clear enough, but it appears to be inadequate, and, as a defini- tion, to be illogical. To remedy the defect of the first and fourth, Euclid has given two axioms. The necessity for employ- ing some positive property in treating parallel lines is thus cleslrly stated in Dr. WhewelFs ' Essay on Mathematical Reasoning : '•—* " We must have some positive property, besides this negative one, in order to complete our reasonings respecting such lines. We have, in fact, our choice of several such self-evident proper- ties, any of which we may employ for our purpose, as geometers well know ; but with Our naked definition, as they also know^ we cannot proceed to the end." Instead^ however, of choosing' some positive property of parallel lines, Euchd, unfortunately^ attempted to meet the difficulty (a difficulty arising in the fii'st * Phil. Mag. vol. xii. p. 372. : 456 ^^^^- On the Theory of Parallel Lines. instance solely from inadequate definition) by an indirect course. All straight lines drawn in the same plane are lines which will (1) either meet (2) or not meet ; and, instead of stating some positive property of the second class, Euclid gives a property of the first class. His definition, for such we may call it, of lines that will meet, may have involved, as its differentia, other pro- perties instead of that which he has chosen. There can how- ever be little doubt that for the immediate purpose in view — a definition of lines that will meet — no property could be better chosen than the one which appears as the differentia of the so- called 12th axiom. * '^"*'" '^ '''^'^ Juiuur// unh ; -".Mtii k> lu With these remarks we tliay|yrotiefed'to'66nsid^t'th6inith6diate difficulty with which geometers have to deal. It appears to be this : Euclid's 35th definition is acknowledged to be defective, the 12th axiom has also been condemned, and the question arises, with what single definition can we replace both of these ? Upon the answer to this question must depend our method of treating the theory of parallels. Enough has been stated in this, and in former communications, to indicate the course 1 would take the liberty of suggesting. It is, that a full and adequate definition should be laid down ; such a definition, for instance, as that given by Vaiignon, in which a case of the 29th proposition is proposed as the differentia. In substituting a definition for the 12th axiom, the example of Euclid may, however, to a certain extent, be followed with advantage. I venture to think that we should deviate from the course adopted by him, to the extent of stating a positive property of parallel lines instead of stating a property of lines that are not parallel; but, in other respects, the defini- tions may be, as nearly as possible, similar. If so, the defini- tions, compared together, would stand thus : — Lines which wee/,— make, with an intersecting line, two interior angles together less than two right angles. For which we are to substitute. Parallel lines, — make, with an intersecting line, two interior angles together equal to two right angles. This definition of parallels has no practical advantage over Varignon's ; but, as it is probably the one which Euclid himself would have chosen had he to remove the 12th axiom, we ought perhaps to retain it, on the ground that any alteration of his ' Elements ' should be as slight as possible. This definition is not arbitrary ; it is not merely an assumed form of words. It is necessarily involved in a fundamental con- dition under which the mind contemplates the first truths of geometry, a condition prior to experience, and independent of it, — the idea of space. It may therefore, perhaps, be said that it implies an axiom as well as a definition. Such an objection, I On the Oxidation of the Constituents of Ammonia. 4i^7 apprehend, would be only verbal, for it amounts to saying that it contains a real as well as a nominal definition. It is an objec- tion which may be raised in regard to any adequate mathemati- cal definition whatever. " We might/^ says Dr. Whewell, " begin by defining a right angle to be the angle made by a line which stands evenly between the two portions of another line ; and we might add an axiom, that all right angles are equal. Instead of this, we define a right angle to be that which a line makes with another when the two angles on the two sides of it are equal. But in all these cases we express our conceptions of a necessary relation of lines ; and whether this be done in the form of defi- nitions or axioms, is a matter of no importance.^^ That Euclid^s 12th axiom is the same in kind as his definition of a circle, right angles, &c., has been universally acknowledged. In the celebrated controversy on the grounds of mathematical reasoning, D'Alembert calls it a definition, and, except in the mere question of nomenclature, which cannot afi'ect the point I have attempted to establish, his opponents agree with him. It appears to be of some importance that we should bear this fact in mind when discussing the theory of parallels. The Cloisters, Inner Temple, fy ,^ij; November 8, 1856. LIX. On the Oxidation of the Constituents of Ammonia hy Porous Media, with some Remarks on Nitrification, By Prof. Schon- BEiN of Basle^. My dear Faraday, .... O INCE I last wrote to you I have actively continued my ^^ researches on the phsenomena of contact, and obtained some results which are curious enough. You know perhaps, that, according to my former experiments, ozonized oxygen at the common temperature oxidizes both the elements of ammonia, forming with that compound nitrate of ammonia ; whilst, as you are well aware, common oxygen under the same circumstances does not at all afi'ect either gaseous or aqueous ammonia. The same oxygen, however, on being piit in contact with certain mat- ters, acquires the power of engendering, with ammonia, nitrous acid, i. e. nitrite of ammonia. Platinum and copper are such matters. Moisten the former metal (in the state called platinum black) with a strong solution of ammonia, leave these substances exposed for a short time to the action either of common oxygen or atmospheric air, then treat the metallic powder with some di- stilled water, and you will easily detect in the liquid the pre- * Communicated by Professor Faraday, Phil. Mag. S. 4» Vol. 1^. No. 81. Dec. 1856. 2 H 4SSS On the Oxidation of the Constituents of Ammonia. sence of nitrite of ammonia. The simplest way of doing so is to add to the water some dilute sulphuric acid, and paste of starch containing a little pure iodide of potassium (free even from the slightest trace of iodate) ; nitrite being present, the mixture will become dark blue. Assisted a little by heat, even compact platinum is capable of causing common oxygen to produce a nitrite with ammonia. Put some drops of a strong solution of ammonia into a bottle containing air, introduce into the vessel the heated coil of a thick platinum wire, hold over this coil a strip of filtering-paper to which sticks starch paste containing some iodide of potassium, and on being acidulated with dilute sulphuric acid, you will per- ceive the paste instantaneously turn dark blue. Whilst the hot platinum coil remains within the bottle, whitish vapours make their appearance, which, on being taken up by distilled water, give to that fluid all the properties of a nitrite solution. On acidulation with dilute sulphuric acid, it deeply and instantane- ously blues the starch paste containing the iodide, and a strong reaction will be obtained, though the heated coil may have remained in the bottle but for a few seconds. The platinum coil does not require to be heated to redness to produce this effect, but those of iron wire, &c. must have that temperature to enable oxygen to produce a nitrite with ammonia. I mentioned above copper as another substance which was capable of causing ordinaiy oxygen to oxidize both the elements of ammonia at the common temperature, and I may add that its action even surpassed that of platinum. To convince yourself of the truth of my statement, put about 50 grms. of minutely divided copper (such as is obtained by reducing oxide of copper by hydrogen) into a bottle containing oxygen or air, moisten the metallic powder with a solution of ammonia, close or cover the bottle, and you will soon see the vessel fill with whitish fumes, which are nitrite of ammonia ; for if you introduce into the bottle a strip of paper covered with acidulated starch paste contain- ing some iodide of potassium, it will rapidly be coloured blue. Or if strips of filtering- paper impregnated with distilled water be suspended in it but for a shopt time, they will contain perceptible quantities of nitrite of ammonia, as you may easily satisfy your- self by applying the above-mentioned test. Even a moistened glass plate or watch-glass used to cover the vessel will receive within a very few minutes so much of the nitrite formed as to enable you to ascertain its presence by the most striking reactions. To complete my statement, I must not omit to mention that copper powder, soon after having been moistened with liquid am- monia, exhibits a rise of temperature, no doubt resulting from the fonnatioil of the nitrite of ammonia. Mr. H. Wedgwood on a System of Geometry, 459 The blue liquid obtained on shaking copper powder with aqueous ammonia and oxygen or atmospheric air, also contains, besides oxide of copper, nitrite of ammonia ; for if you add some soda to it and boil it to drive off the ammonia and throw down the black oxide of copper, a solution is obtained which, after being evapo- rated to dryness, leaves behind a yellowish salt which consists principally of nitrite of soda. This substance, on being mixed with powdered charcoal and heated, deflagrates, yields with sul- phuric acid strong fumes of nitrous acid, rapidly discharges the colour of indigo solution strongly acidulated by oil of vitriol, and colours brownish a solution of protosulphate of iron containing free sulphuric acid, &c. Common, pure, or atmospheric oxygen, on being put in contact with copper powder and aqueous am- monia, is so rapidly absorbed that I succeeded in depriving com- pletely a whole cubic foot of atmospheric air of its oxygen within a few minutes. Copper and ammonia may therefore be used as eudiometric agents, and for the preparation of nitrogen from com- mon air. The facts above stated appear to me to bear closely upon the important question of nitrification, proving, beyond any doubt, that, under the influence of the contact of some ponderable mat- ters, inactive oxygen is capable, even at the common temperature, of oxidizing both the constituents of ammonia. Before long I hope to be able to give you some more details on nitrification, a chemical phsenomenon which at this present moment deeply engages my attention Yq^j^s most faithfully, Basle, Nov. 10, 1856. C. F. ScHONBElN. LX. Some Remarks on a System of Geometry derived from an Analysis of our ideas of Direction and Position, By H» Wedgwood, Esq.^ THE cardinal definitions on which I find that the whole fabric of demonstration may be made to rest are substan- tially these : — A straight line is a line continuing throughout in the same direction. Parallel straight lines are lines lying in the same direction from given points in the course of each respectively, though not forming part of the same straight line. A plane is a surface passing through every point which can be reached from a given point by motion transverse to a certain constant direction, that is, through every point which can be reached from a given point without motion in a certain constant direction. It will be seen that the whole of these definitions depend upon * Communicated by the Author. 2H2 460 Mr, H. Wedgwood on a System of Geometry the conception of sameness of direction at different points of a system ; the species defined in the two first being traced out by a point actually moving in the same direction under certain con- ditions, and in the third by a point moving under the sole con- dition of a negation of motion in a certain constant direction. When a point is made to describe a line of any shape, it must begin to move in some one direction ; and as long as the stroke is continued in the same unaltered direction, the result will be a straight line under the proposed definition. So if a straight line AB be given, and it be required to draw a straight line parallel to it through a point C, the definition instructs us to draw the line CD in the same direction from C with that marked by the straight line AB at A. If the problem be to draw a plane through A under the guidance of the definition, a direction AN must be given in which the generating point is to be wholly void of motion on setting out from A ; and if B be any subse- quent point in the plane, the generating point in passing through B must be wholly void of motion in a direction identical with that marked by the line AN at A. As the motion of a point along a straight line is constantly directed to the point at the extremity of the line, little difficulty is commonly felt with respect to the first definition, but an am- biguity is suspected when the term is applied to parallel lines. It is asserted that the only meaning of the sameness of direction of two straight lines passing through the points A and B, and having no points in common, is the equality of the angles made with the straight line joining AB ; and it is asserted, that there is a covert assumption that if the straight lines make equal angles with AB, they will make equal angles with a straight line intersecting the parallels at any other points. To others, perhaps, the objection does not present itself in so definite a form ; but they feel uncertain whether the expression of ' sameness of direction ' be not used in a somewhat different sense in respect of parallel lines than when applied to successive portions of the same straight line, and in the former case they are inclined to doubt whether the standard of identity of direc- tion be not derived from the notion of parallelism rather than vice versd. In answer to these objections, I propose to indicate the sense in which identity of direction is uniformly to be understood in these definitions, and the reasoning founded upon them, by reference to a moveable scale which admits of application to directions measured from different points in a system, and en- ables us to fonn an estimate of their identity or divergence. One main cause of the difficulty which has been felt in deter- mining the elementary composition of the simplest species of derived from an Analysis of our ideas of Direction and Position. 461 geometrical figure is, I believe, the fact that the knowledge of position and figure is acquired by the exercise of distinct facul- ties— sight and touch ; and thus, while we are seeking the ulti- mate analysis of the conceptions in question, our attention is distracted by the two classes of phsenomena. Now it is well known that the born-blind are as capable of geometrical reason- ing as those in full possession of their faculties. It is plain, then, that all that is necessary for the groundwork of demon- stration must be given independent of sight ; and it will tend to simplify the inquiry into the real foundations of the science, if we place ourselves in the mental condition of the blind, and consider all knowledge of position for which the student must have credit in the course of demonstration, to have been acquired by actual motion through the several points of the system to which the reasoning relates. The positions ascertained by such a course of experience will of course have reference, in the first instance, to the station of the observer at the commencement of the experiment ; and in order to provide him with a definite point of departure, we shall suppose him to make some one point in his own body coincide with a certain point A in the external system. The structure of his bodily frame will then supply him with three standard direc- tions transverse to each other, up and down, right and left, fore and aft, diverging from the point A in the external system, and by reference to these he will distinguish any intermediate direction. Now let the observer begin to move in any direction, in the direction due forwards for example, and by such a motion let him arrive at a second point B. He will carry with him the consciousness of the same standard directions, up and down, right and left, fore and aft, which will now be recognized as di- verging from the point B instead of A. But as these directions have reference only to the structure of the observer's own body, it is necessary, in order to preserve any correspondence between the analogous directions in the external system at B and at A (between right and left at B, and right and left at A, for instance), that the observer should avoid all rotation of his own body in the external system during the passage from A to B. To that efifect we shall introduce the condition, that while he is moving from one point to another in the external system, no change shall be made in the direction of the point towards which he is moving, as measured on the scale of his bodily structure ; that is to say, that if B be directly in front of the observer when he begins to move from A, his motion shall be such as to keep that point directly in front as long as he is moving towards it. With this condition as to the mode in which the observer is supposed to make himself acquainted with the system submitted to his 462 Mr. H. Wedgwood on a System of Geometry, investigation, the directions diverging from any point in the system must be understood as defined by reference to the stand- ard directions of the observer's own body ; and a direction in the external system at B will be the same with a given direction at A when it occupies the same position in respect of up and down, right and left, fore and aft. A straight line in the external system extending directly in front of the observer, or directly to his right when he is stationed at B, will be recognized as lying in the same direction with a straight line directly in front or directly to the right when stationed at A ; and so of straight lines extending from A and B respectively, and lying in simUar intermediate positions between fore and aft and right and left. Now let us examine the import of these conditions applied to the case of straight lines AC, BD passing in parallel directions through the points A and B respectively. The meaning of pa- rallelism under the definition will be, that the line BD occupies the same position among the standard directions in the body of an observer moving from A to B without rotation in the system, with that which was filled by the line AC when the observer was at A. On thus comparing the directions of AC and BD by the standard of his own bodily structure, the observer must pass from A to B by some definite path, to which alone the relation of parallelism would seem to refer. But what if he had gone by any other track ? Would he then have found the line BD in the same position among the lines of his own bodily standard ? Here we have the condition that the observer is brought to the same point B by a straight line AB, and by a track of some other nature ; and as points are known in geometry by position alone, it must be supposed that the position attained by the straight line AB is recognized as identical with that attained by the other track. Let AB be supposed, for example, to extend directly to the right of the observer in his original position at A, whence it follows that A will lie at the distance BA directly to his left when he arrives at B. Then if X be the point to which he is brought by the other track, it is plain that he cannot iden- tify the points B and X without being sensible, when situated at X, that A is placed directly to his left at a distance equal to BA. Thus it appears that an observer moving, under the neces- sary conditions, from the same original position in a system at A, will be similarly placed in the system at any second point B, whether he attain that point by a straight line or by a track of any other description ; and any fixed straight line in the system passing through B will in either case occupy the same position among the directions of his bodily scale. Thus the straight lines AC and BD may be considered as lying in the same direc- tions at A and B respectively, independent of any reference to Prof. Clausius on the Mechanical Theory of Heat. 463 the particular path by which the observer may pass from one of those points to the other. But if the directions of the lines at A and B can be conceived as absolutely identical, the lines will also be in the same direction with each other at any other points C and D, inasmuch as each straight line is everywhere in the same direction. LXI. Reply to a Note of Mr. Joule, contained in the November Number of the Philosophical Magazine. By Prof. Clausius*. IN the November Number of this Journal a note appears from Mr. Joule, which refers to a passage in my memoir " On the Application of the Mechanical Theory of Heat to the Steam- engine,^^ where the experiments conducted by Mr. Joule and Mr. Thomson are mentioned. The note concludes with the fol- lowing words : — "The results we have arrived at in our joint in- vestigation have tended certainly to develope our views, and to give a more definite knowledge of the constitution of elastic fluids, but they do not contradict our original statements, published before the appearance of Prof. Clausius^s papers.^' I can only explain this note, and particularly the conclusion of it, so far as Mr. Joule himself is concerned, by referring it to a misunder- standing of my meaning. But as I believe that I myself, by an inaccuracy of expression, have given rise to this misunderstanding, I feel it to be my duty to say a few words here in explanation. I believe that the note has been chiefly called forth by the fol- lowing words in my memoir, which precede the reference to the experiments mentioned : — " Even the physicists which had occu- pied themselves more especially with the mechanical theory of heat did not at that time (1850) coincide with this view of the deportment of vapour.^* As Mr. Joule, so far as I know, has nowhere published his views on the deportment of vapour, these words could not of course refer to him ; but I ought perhaps, in order to avoid such a misunderstanding, have expressly limited the statement to such physicists as had applied the mechanical theory of heat to vapours at their maximum density. With respect, further, to the deportment of gases, which, in the portion of my memoir already referred to, is brought into connexion with the deportment of vapours, I never entertained the least doubt that Mr. Joule, in his beautiful investigations " On the Changes of Temperature produced by the Rarefaction and Condensation of Air,^^ had started from a perfectly correct point of view, and that the results of the new experiments above mentioned do not contradict his former statements, but, on the contrary, have served to confirm them in all essential particulars. Zurich, Nov. 16, 1856. * Communicated by the Author. [ 464 ] LXII. Notices respecting New Books, Mat&iaux de Construction de V Exposition Universelle de 1855. Par A. Delesse. Paris, 1856. Pages 420. 'T^HIS is a valuable report on the building materials of all kinds, ■■- whether natural or artificial, which were displayed at the Paris Exhibition. M. Delesse was peculiarly qualified to undertake the task of drawing up this report, from his intimate acquaintance both with geology and chemistry, and from his former researches on the chemical composition of rocks. The report contains the results of a large number of chemical analyses, as well as of experiments on the strength and other physical properties of the materials exhibited. We may refer particularly to the chapters on marbles and cements, as containing a large amount of novel and interesting information. From the latter we extract the following observations on the cements of Canada. Thorold Cement. — ^This cement, from Thorold near St. Catherine in Upper Canada, is prepared by calcining an argillaceous limestone of the Upper Silurian formation. The limestone is grayish-black, and emits an argillaceous odour when breathed on ; but the cement itself has a yellow colour. The specimen examined did not effer- vesce with acids, and contained only 3*37 per cent, of water. It set in fifteen minutes with a disengagement of heat. A specimen immersed in water ten minutes after being moistened, set under the water, and presented finally the same cohesion as another specimen which was not immersed till two hours after it had set. The resist- ance to traction of this cement was about 0'85 kil. It was found to consist of — Lime 53-55 Magnesia 2*20 Silica 29-88 Alumina and peroxide of iron .... 12' 70 Sulphate of lime 1*58 Quebec Cement. — At Quebec in Lower Canada, a limestone belong- ing to the Inferior Silurian is quarried for the purpose of making cement. The rock which yields it was discovered by Captain Bad- deley of the Royal Engineers. It is an argillaceous, compact lime- stone, destitute of fossils, and strongly coloured by carbonaceous matter. The cement itself was yellow, and effervesced feebly with acids ; it lost, when heated, 11*6 per cent, water and carbonic acid. It set at the end of twenty-six minutes. The resulting mass was not so hard as that from the Thorold cement. Its resistance to traction was about 0*49 kil. Its composition was as follows : — Lime 52*49 Magnesia traces Silica 27-401 3Q.^g Alumina and oxide of iron 12-66 j Sulphate of lime , 7*95 j 42-58 Notices respecting New Books, 465 Although the composition of this cement is not very different from that of the Thorold cement, it is nevertheless of inferior quality. Chasy Cement. — The Geological Commission of Canada has pre- sented a magnesian limestone belonging to the Inferior Silurian, which might serve to prepare a cement. This limestone, which ex- tends over more than fifty miles, is argillaceous, compact, and homo- geneous. Its colour is gray. Although containing magnesia, it produces rather a lively effervescence with acids. Its composition is — « "to riJh . r Carbonate of lime 45-30 BVii ao Carbonate of magnesia 12*77 Argillaceous residue 19'77 ,«Jii9£,: Alumina and oxide of iron 12*52 ./TOi?' Water and loss 9*64 Oneida Cement. — This is prepared from an earthy dolomite, which is of a deep gray colour, effervesces slowly with hydrochloric acid, and loses by calcination 37*5 per cent, water and carbonic acid. It occurs in the Upper Silurian formation. Its composition is, — Carbonate of lime 39*91 Carbonate of magnesia 34*15 Silica and argillaceous residue .. 15*851qo.io > Alumina and oxide of iron .... 6*25 j : Water 3*84 , Magnesian Mortar. — The Geological Commission of Canada pre- sented a specimen of a very remarkable rock formed of carbonate of magnesia. It resembled a granular marble so closely that it might have been mistaken for one, although it contains only insignificant traces of carbonate of lime. It is besides ferriferous, and in certain places is coloured green by oxide of chromium. It contains also quartz, disseminated in white hyaline grains. The following ana- lysis agrees with a previous examination by Mr. Hunt : — ;^ Carbonate of magnesia 58*29 Carbonate of iron 9*06 Carbonate of lime traces Quartz 30*12 Water and loss 2*55 This carbonate of magnesia might be advantageously worked for the preparation of the magnesian mortar, not alterable by the action of sea- water, which has been recently proposed by M. J. B, Vicat. [ 466 ] LXIII. Proceedings of Learned Societies, ROYAL SOCIETY. [Continued from p. 397-] February 21, 1856. — The Lord Wrottesley, President, in the Chair. THE following communication was read : — " On the Thermal Efifects of Fluids in Motion." By Professor WilUam Thomson, F.R.S., and J. P. Joule, Esq., F.R.S. A very great depression of temperature has been remarked by some observers when steam of high pressure issues from a small orifice into the open air. After the experiments we have made on the rush of air in similar circumstances, it could not be doubted that a great elevation of temperature of the issuing steam might be observed as well as the great depression usually supposed to be the only result. The method to obtain the entire thermal effect is obviously that which we have already employed in our experiments on permanently elastic fluids, viz. to transmit the steam through a porous material and to ascertain its temperature as it enters into and issues from the resisting medium. We have made a preliminary experiment of this kind which may be sufficiently interesting to place on record before proceeding to obtain more exact numerical results. A short pipe an inch and a half diameter was screwed into an elbow pipe inserted into the top of a high pressure steam-boiler. A cotton plug placed in the short pipe had a fine wire of platina passed through it, the ends of which were connected with iron wires passing away to a sensitive galvanometer. The deflection due to a given difference of temperature of the same metaUic junctions having been previously ascertained, we were able to estimate the difference of temperature of the steam at the opposite ends of the plug. The result of several experiments showed that for each lb. of pressure by which the steam on the pressure side exceeded that of the atmo- phere on the exit side there was a cooling effect of 0*2 Cent. The steam, therefore, issued at a temperature above 100° Cent., and, consequently, dry \ showing the correctness of the view which we brought forward some years ago * as to the non-scalding property of steam issuing from a high pressure boiler. February 28. — The Lord Wrottesley, President, in the Chair. The following communication was read : — The following Letter was read, from Professor Hansteen of Chris- tiania. For. Mem. R.S. : — To the Royal Society of London. As a Corresponding Member of the Royal Society, I have the honour herewith to transmit a Research " On the Secular Changes of the Magnetical System of the Earth, and more specially on the Secular Variation of the Magnetical Inclination in the Northern * See letter from Mr. Thomson to Mr. Joule, published in the Philosophical Magazine, Nov. 1850. Royal Society, 46t Temperate Zone," separately printed from the * Memoirs of the Roy. Soc. of Sciences of Copenhagen,' By calculating newer and more ancient observations of the magnetical declination, I have ascertained the movement of the four magnetical polar regions, which T had already found in my work ' Untersuchungen liber den Magnetism us der Erde' (Christiania, 1819, with Atlas) ; whereof the two northern ones have a motion from west to east, the two southern ones in the contrary direction ; and have attempted thereby in general to declare the cause of the known variations, as well of the system of declina- tion as of that of inclination and of intensity. As I am indebted for the greatest part of the materials to English observations, I have found it my duty to render my thanks to English science, and to express my hopes of future exertions towards the solution of this, in my thought, most interesting problem of the general physics of the globe. Most respectfully. Observatory in Christiania, CHRISTOPHER Hansteen. December 31, 1855. March 6. — Colonel Sabine, R.A., V.P. and Treasurer, in the Chair. The following communications were read : — " Supplement to the * Account of Pendulum Experiments under- taken in the Harton Colliery;' being an Account of Experiments undertaken to determine the correction for the Temperature of the Pendulum." By G. B. Airy, Esq,, Astronomer Royal. Adverting to the circumstance that, in the Harton Experiment, there was a mean difference of 7° between the temperature above and below, and that a careful determination of the coefficient for tem- perature-correction was therefore necessary, the author describes the process by which the correction was now investigated by experiment on the same pendulums which were used in the Harton Experiment. Two rooms were selected at the Royal Observatory, Greenwich, having firm stone floors, and admitting of being heated, one by a stove in the room, the other by a hot-air-apparatus below. One pendulum was mounted upon its iron stand, with clock and other apparatus, in one room, and the other in the other room. Care was taken that the pendulums and their thermometers should be effec- tually protected from radiation. The two clocks were compared by carrying a chronometer from one to the other, and remarking the time of coincidence of beats ; a method which admits of very great accu- racy, when (as in this instance) the distance through which the chronometer is to be carried is small. In the Fifth Series (counting the series in sequence to those of the Harton Experiment), Pendulum 1821 was kept in heat, and Pendulum 8 cool, and continuous obser- vations were kept up during forty hours. In the Sixth Series, Pen- dulum 8 only was kept in heat, and observations were again kept up during forty hours. The Seventh and Eighth Series were similar, respectively, to the Fifth and Sixth. The temperatures are referred to two of the thermometers used in the Harton Experiment, and to two other thermometers supplying the place of two of the Harton 468 Royal Society : — " '""" thermometers which cannot be found. The observations were con- ducted entirely by Messrs. Dunkin and Ellis, Assistants of the Royal Observatory. On discussing the results of the observations, there appears to be reason for supposing that a change has taken place in one of the pendulums after the Seventh Series. This appears from the circum- stance that, though the Fifth and Seventh Series agree well, the Sixth and Eighth are discordant ; and also from this circumstance, that the abstract relation between the two pendulums given by the Fifth, Sixth, and Seventh Series, agrees closely with that found at Harton ; but if the Eighth Series is included, there is a considerable dis- cordance. If the Eighth Series is rejected, it appears that Colonel Sabine's coefficient ought to be increased by about -j^^th part ; and on intro- ducing this correction into the computations of the Harton Experi- ment, the result for the earth's mean density is 6-809. If the Eighth Series is retained, the correction is reduced to less than one- fourth of that just mentioned, and the earth's mean density is 6-623. The author subjoins an investigation with which he has been favoured by Professor Stokes on the effect of the rotation and ellip- ticity of the earth in modifying the numerical results of the Harton Experiment. It appears that the numbers found in the paper ought to be multiphed by , __equatoreal centrifugal force gravity e=ellipticity Z= latitude of place. On converting this formula into numbers, for Harton, the factor is found to be 1*00012, which produces no sensible change in the result. At the equator the factor would have been 1*00679. " On the Mathematical Theory of the Stability of Earthwork and Masonry." In a Letter to Prof. Stokes, Sec. R.S. By W. J. Mac- quorn Rankine, Esq., C.E., F.R.S. In the preparation of my course of lectures, I ha\|f found it neces- sary to re-investigate much of the above-named branch of mechanics, and I have now a paper in preparation on the subject, which I pro- pose to offer to the Royal Society when it is ready. In the mean- while, it appears to me that the two fundamental principles on which my researches are based are of such a nature, that they may very properly be communicated to the Royal Society at once. They are as follows : — I. Principle of the Stability of Earth. At each point in a mass of earth the directions of greatest and least compressive stress are at right angles to each other -, and the Mr. Rankine on the Stability of Earthwork and Masonry, 469 condition of stability is, that at each point the ratio of the difference of those stresses to their sum shall not exceed the sine of the angle of natural slope of the earth, 6(1 07 TI. Principle of the Transformation of Structures. ''"Lei a structure of a given uniform transverse section be stable under a system of forces represented by given lines in the plane of section : — Then will any other structure whose transverse section is SL projection by parallel lines of that of the first structure upon any other plane, be stable under the system of forces represented by the projections, upon the new plane, of the lines representing the first system of forces. ..,,^. Example of the application of this principle. Let fig. 1 be an equilibrated arch with its abutments of the form (for example) proposed by M. Yvon-Villarceaux, suited for a hori- zontal extrados EF. OK, OA, and AB being given, all the dimensions of the arch and abutments are functions of those three quantities. It is required to design an arch, fig. 2, for an extrados ef at any given inclination, of any given span cd (measured parallel to the ex- trados), and in which ok=OKy oa=OA, and a6=AB, are the same as in the primitive arch fig. 1 . /aainBiLo'iff; Solution. On any vertical plane passing through BK, and not coinciding with the plane of fig. 1, draw cod of the given length and incHnation, intersecting COD in O. Join Ce, Dd, and project the 470 Royal Society : — whole of fig. 1 on the new plane by lines parallel to Cc, Dc?. The projection so obtained will be the figure of the arch and abutments required. Moreover, if the lines K, R, fig. 1, represent in length, direction, and position, the resultants of the pressures of the abut- ments on their foundations in the original arch, then will r, r, fig. 2, the projections of R, R, represent the corresponding resultants in the new arch ; and in like manner, the thrust at a is the projection of the thrust at A. Glasgow, 18th February, 1856. W. J. MacquoRN RankiNE. Note. The horizontal foundation courses in fig. 2 do not form part of the projection of fig. 1, but are supposed to be added after the completion of the projection. March 13. — Sir Benjamin C. Brodie, Bart., V.P., in the Chair. The following communication was read : — " On the presence of fibrils of soft tissue in the Dentinal Tubes." By John Tomes, Esq., F.R.S. Referring to the structural characters of dentine, and to the pre- vailing behef that the dentinal tubes in the normal condition contain fluid, the author goes on to show that the recognized histological characters fail to account for the high degree of sensibility exhibited by the dentine when diseased, or when suddenly exposed by the removal of the enamel. It is found, moreover, that the dentine is not uniformly sensitive throughout, but possesses a much higher degree of sensibihty at the peripheral distribution of the dentinal tubes than deeper in the sub- stance of the tooth ; and it is urged that these facts cannot be accounted for by the presence of a fluid in the dentinal tubes, nor by supposing that the hard unyielding dentine is intrinsically en- dowed with sensation. This view of the matter is borne out by the fact, that all sensibility is at once lost if the pulp of the tooth be destroyed. Finding that the dentine owed its sensibihty to the presence of the dentinal pulp, and knowing that the tubes have open extremities in contact with the pulp, the author was induced to examine care- fully the contents of the tubes. The investigation resulted in disco- vering that the dentinal tubes, instead of containing fluid only, give passage to fibrils of soft tissue, which pass from the pulp into the tubes where these open upon the surface of the pulp-cavity, and from thence may be traced into the branches. The fibrils may be demon- strated by fracturing a perfectly fresh tooth, and then with a sharp knife taking very thin sections from the dentine near the edge of the pulp-cavity. The dentine will, when cut, break up into small fragments, and from the edges of these the fibrils may be seen extending. Sometimes a small portion of the pulp will be found adherent, in which case the fibrils may be seen to extend from that tissue into the dentine. The fibrils may be shown in a more striking manner by decalcifying a section, and then, when it is placed upon a slide^ tearing the specimen across the direction of the tubes. By Mr. Tomes on Fibrils of soft tissue in the Dentinal Tubes. 471 this manipulation, the fibrils will be dragged out from one fragment, and will be seen projecting from the edge of the other. The fibrils, when isolated and examined with a high power, with- out the presence of a reagent, show some indications of tubularity, but not with sufficient distinctness to enable the author to determine whether they are tubes or solid bodies. Their appearance is very like that of the ultimate fibrils of spinal nerves, and they possess a character in common with these, in the presence of minute globules of dense transparent matter exuded from the broken ends, and some- times from the surface of the fibril. It is not easy to determine in what manner the fibrils commence in the pulp. In some prepa- rations they appear to be connected with cells situated a short distance within the pulp, in others they may be traced to a greater depth, where they are lost in the tissue of the pulp, and may possibly be connected with the nerves, which in this part are very abundant. But in the absence of exact knowledge as to the manner in which the dentinal fibrils are related to the elements of the pulp, the author considers that there is sufficient evidence to warrant the conclusion that they are organs of sensation, the distribution of which through the substance of the dentine endows that tissue with its sensibility. This conclusion is borne out by the occurrence of the following conditions. If a fragment of enamel be broken from the surface of the dentine, the exposed portion of the latter tissue is highly sen- sitive to the contact of foreign bodies ; but if the force producing the injury be sufficient to rupture the nerves and vessels where they enter the root of the tooth, the dentine loses its capability of feeling pain. Again, if the dentine be exposed by the gradual wearing away of the enamel by mastication, the surface evinces no sensibility, a circumstance accounted for by the fact that the dentinal tubes have become consolidated, either at the surface exposed, or at some point between the surface and the pulp-cavity. Diseased teeth furnish further evidence in favour of the foregoing views. If a carious tooth, in which the disease has advanced but slowly, and the carious por- tion is dark in colour and tolerably firm in consistence, be examined, it will be found that the dentinal fibrils have become calcified, and in a favourable section they may be seen projecting from the edge of the specimen, or lying broken in short lengths in the tubes. On removing the diseased part of the tooth in such a case, no pain is experienced until the instrument reaches the healthy dentine. Sup- posing, however, the disease to have been rapid in its progress, the carious tissue will be light in colour, and, as compared with the pre- ceding example, soft in consistence. The removal of the affected part in this case is frequently attended with considerable pain. Exami- nation will then show that the dentinal fibrils have not been conso- lidated, but may be found here and there extending into the softened tissue without having suffered any appreciable alteration of appear- ance. Daily experience shows that a tooth may remain useful for a long time after the pulp, and consequently the dentinal fibrils, have been destroyed. If, however, a tooth which has been so circumstanced be 472 Royal Society : — examined, it will be found that one of two actions has been set up. Either additional cementum will have been developed upon the surface of the fang, or its bulk will have become diminished by absorption. Similar conditions supervene when the crown of a tooth has been lost by caries. In old persons we find the teeth are lost without apparent disease in the dental tissues. The teeth become loose and fall out, the roots being in such cases translucent like horn. This condition is the result of consolidation of the dentinal fibrils, and is followed by absorption of the cementum and dentine. Cases may be found in which the whole of the fang has been absorbed, but reduction ,ta two-thirds or half of the normal bulk is very common. ...ill The concurrence of the foregoing changes m the sensibiHty of the tooth, with the destruction or consolidation of the dentinal fibrils, will, the author considers, justify the conclusion, that the dentinal fibrils, in a state of integrity, are necessary to the normal condition of dentine. q April 10. — Col. Sabine, R.A., V.P. and Treasurer, in the Chair^^ The following communications were read : — "Account of 'Experiments on the Vagus and Spinal Accessory Nerves." By Augustus Waller, M.D., F.R.S. The important functions of the organs more or less completely dependent for their innervation on the vagus nerve, have afforded the reason of so many attempts by previous physiologists to determine the exact influence exerted by the fibres arising from different sources which are intimately blended together in the trunk of the mixed vagus. Since Sir Charles Bell's discovery of the different func- tions of the anterior and posterior roots of the spinal pairs, it has become still more important to determine how far the same law holds good with regard to the vagus nerve, and whether at its origin, it is a purely sensory nerve, receiving its motor fibres from the internal branch of the spinal accessory and perhaps from other sources. Ac- cording to Bischoff and Longet, the vagus at its origin and as far as the upper ganglion, is purely sensory, and becomes possessed of motor power from its junction with the internal branch of the accessory, and from other branches derived from motor nerves (Longet). The obser- vations of Bernard have led him on the contrary to adopt the opinion, that the vagus at its origin is a mixed nerve ; because after destroying the spinal accessory, no effect on the functions of the heart, stomach, or lungs was observed, and the only organs visibly dependent on the spinal accessory were the larynx and pharynx. After bearing testi- mony to the correctness of the observations made by Bernard with regard to the effects immediately following destruction of the spinal accessory, the author considered it desirable to apply to the determina- tion of this question his new means of investigation, in addition to those previously employed. His first observations on the vagus, published in the * Comptes Rendus ' of the Academic des Sciences, 1852, had already led him to entertain the idea, that the vagus proper was a purely sensory nerve. They first consisted in cutting this nerve Dr. Waller on the Vagus and Spinal Accessory Nerves, 473 between its upper and lower ganglia, the section comprising the internal branch of the spinal accessory. After the animal had been kept alive for a sufficient period to cause disorganization of the nerve fibres, the central and distal portions were examined microsco- pically. In the central portion, the fibres of the internal branch of the spinal accessory included in the section were all in a sound state ; some of the fascicles of origin of the vagus were also sound ; the remaining fascicles of origin of the vagus consisted of dis- organized fibres. The analogy existing between the results as to the last-mentioned fibres, and those which follow section of the sen- sory roots of the spinal nerves, led the author to the conclusion, that the disorganized fibres of the fascicles of the vagus were like- wise sensory, and had their trophic centre in its lower ganglion, while the sound fibres probably had their trophic centre in the upper ganglion. On these grounds, and some others affording concurrent testimony, he concluded that the vagus in itself was probably a purely sensory nerve. In the distal end, the part below the second ganglion consisted likewise of a mixture of sound and altered fibres. When tested by galvanism on the living animal, it was found that the nerve had lost all power of exciting movement in the various organs which it supplies, and that such branches of known motor power as the recurrent and the crico-thyroid were disorganized in their structure. It was evident therefore that the lower ganglion did not arrest the disorganization of the motor fibres contained in the vagus, because, as has been proved by the author in other cases, when the disorganization of the motor fibres of nerves distributed to muscles is arrested, — as by the superior cervical ganglion of the sympathetic nerve, or by the effect of hybernation in the frog, — the motor power of these nerves is retained. In the present observations, the accessory nerve was divided at its origin by Bernard's process of evulsion of its roots, and after the lapse of about a fortnight the vagus was tested by galvanism, and examined by the microscope, in order to ascertain the functions which it had lost, and the fibres which were disorganized, the sound vagus on the opposite side being taken as a standard of com- parison. On the sound side, galvanism of the vagus caused each time strong dilatation of the glottis by the retraction of the corresponding arytenoid cartilage. On the operated side, galvanism produced a slight movement of the glottis on the same side by drawing inwards of the arytenoid. On the heart, the action of galvanism of the sound vagus was manifest by the stoppage of the pulsation of the carotid arteries and the diminution of their calibre. On the operated side, no in- fluence on the pulsation of the vessels was observed by galvanizing the vagus. When the heart was exposed by removing a portion of the thorax, and keeping up artificial respiration, galvanism on the sound vagus produced complete stoppage of the heart's action, while on the opposite side, irritation of the vagus exerted no influence on the heart. Phil. Mag. S. 4. Vol. 1%. No. 81. Dec. 1856. 2 I 474 Royal Society : — The stomach being exposed was found distended with food. Gal- yanism of the sound vagus caused evident contractions of this organ, which were strongest at the neck or constriction which it usually presents (in the rabbit), — from whence they radiated in both direc- tions, becoming more and more faint. On stimulating the other vagus, from which the accessory had been virtually eliminated, no perceptible influence was observed. Microscopic examination showed that the cervical part of the yagus of the side operated on contained numerous disorganized fibres, almost all collected together in a single fasciculus, which in- cluded only a few normal fibres. In the recurrent branch were dis- organized fibres, corresponding very closely to those found in the vagus, above it. Below the recurrent, the vagus and its cardiac, pul- monary and gastric branches consisted almost entirely of normal fibres, most of which, as is well known, are nucleated fibres. From the foregoing observations, the author draws the conclusion, that from the spinal accessory are derived the greater part of the motor fibres contained in the vagus, which govern the movement of the larynx, the heart, and the stomach. He likewise infers from the microscopic examination of the vagus below the recurrent, that the motor fibres distributed to the heart and stomach belong almost exclusively to the nucleated or * Remak ' fibres. The author purposes communicating in a future paper his researches on the other organs supplied by the vagus. The above experiments were principally carried out in the labora- tory of M. Flourens at the Jardin des Plants, who facilitated in every way the researches, and where the author had the able assistance of Drs. Philipeaux and Vulpian. "Extract of a Letter to George Rennie, Esq., F.R.S., from P. A. Secchi, Director of the Astronomical Observatory of the Collegio Romano, containing explanatory remarks on a drawing of the Lunar Spot * Copernicus,' presented by him to the Royal Society." Dated Rome, March 13, 1856. " As to the drawing of the spot of the moon, it is a first attempt to obtain an accurate representation of the interesting spot * Coper- nicus.' In such large dimensions, photography directly taken with the telescope has been impossible ; I therefore made first an accurate triangulation of the spot with the micrometer, and the principal points were thus laid down on the chart, after which opera- tion the rest was filled in by the eye alone. The power used has been always either 1000 or 760. As it was impossible to carry through such a work in a single night, on the first night of good opportunity a general outline was taken, and on the other evenings particular drawings were made, and all these parts, taken in different grades of hght and shadow, were afterwards harmonized together and compared with the moon when the point of light was seen to be the same as on the first night. So this work occupied more than six months, that is, all the favourable positions (two at each lunation) which could be obtained. I do not pretend it to be yet accurate Mr. J. Phillips on a Drawing of ' Copernicus' 475 enough to be transferred from photography* to any kind of en- graving, but I am watching every good occasion to make it complete. But before bestowing more time and labour, I should be glad to know the impression such a work may make among the scientific men of England. I must observe that the most distant outliers of the crater have not been included," &c. " Notes on the Drawing of * Copernicus,' presented to the Royal Society by P. A. Secchi." By John Phillips, Esq., F.R.S. Of the few attempts which have been made of late years to pre- pare drawings f, on a large scale, of selected lunar mountains, this contribution from the Roman Observatory appears to be one of the most successful. It is on a scale of magnitude (about 10 geogra- phical miles to one inch) such as only the larger modern telescopes can command, and characterized by such firmness of definition as to do honour alike to the maker of the instrument and to the artist engaged in the delineation. It may assist those who have not attempted, with their own hands, any drawings of this kind, and desire to form a right judgement of the value of this work of P. Secchi, if I send for comparison a drawing of Gassendi, executed from my object-glass of Q\ inches (Cook), with a focal length of 1 1 feet. The drawing is on a scale of 20 geographical miles to an inch, and Gassendi thus appears of half the linear dimension of Copernicus, being really almost of the same diameter. > Placing together the two drawings, and remembering the appear- ance of Copernicus, as I have seen it through telescopes, some re- flections arise which it may be permitted me to express, in the hope that we are now fairly entered on the long career of discoveries in the moon, to which the attention of astronomers has been of late systematically drawn by the Earl of Rosse and a Committee of the British Association. In proportion as the power of the telescope rises, the seemingly simple *ring mountains' of the moon exhibit as much diversity of outline and structure as the larger terrestrial volcanoes when accu- rately mapped. Thus while Gassendi, — 40° from the central meri- dian of the moon, and 17° south | of the equator, — has the obliquely elliptical contour due to a circle in that position, Copernicus, 20° from the central meridian, and 10° north of the equator, has its most conspicuous peripheral crest formed of seven principal nearly straight elements, approaching to equality in length, and meeting in points which are situated almost exactly in a circle of 24 geographical miles radius. Here is a very important partial difference, coupled with a very important general agreement. While Gassendi, with peaks 9000 feet high, projects like a huge narrow wall into the Mare Humorum, and hangs over the interior plain in precipices as steep and many times as high as those over the * The figure presented to the Society is a photographic copy of the origin^ drawing. — (Ed.) t As distinct from m&te plans. The drawings must however be based on exact plans. - X The Poles being named after the type of Madler's noble work, * Der Mond.' 213 476 Royal Society : — Atrio del Cavallo, Copernicus, seated in the midst of broad land, on a base of 1 20 geographical miles, rises in many broken stages, brist- ling with a thousand silver-bright crests, — a perfect network of rough and complicated ground, crossed by lights and shades, which have a history of their own, — and toward the inside falls off by many irre- gular terraces, down to an interior plain, as if the whole area had yielded, and the surface had been formed by enormous land-slips. Four sharp notches are traced across the narrow ridge of Gassendi, cutting it deeply, like the hollows left by decomposing lava dykes 500 feet broad ; one deeper and broader opening unites the inner plain with the outer Mare Humorum, and one far wider opening leads to an accessory crater, over whose awful depth the cliffs, 10,000 to 12,000 ft. high, spread black shadows round some central rocks. In these particulars Copernicus offers a very different aspect. Its high crest, of 10,000 feet, is only cut through by one straight narrow meridional groove, though broken by numerous fissures in other parts, and is in all parts so irregular, partially undulated, and varied with small crateriform points, and enclosed areas, resembling craters, as to offer little analogy to any truncated cone of eruption. The highest summit, on the left-hand (west) side — a huge rock — ^is conspicuous by its broad, deep and extended shade. What suggests a vast lava current, is equally remarkable on the northern slope. Regarding now the central plains of these mountains, we remark in each several low ridges of rather sinuous forms, and several small mounds (half a mile or more across), of which three central digi- tated masses, not 'pierced by craters, are the most elevated, and catch the earliest lights of morning which glance over the rocky borders of the basin. Had the drawings been executed at the instant of sunrise on the central meridian line of the basin, these points would have stood up on 'the soft edge of the light and shade, as bright as the Swiss mountains at sunrise or sunset, but not like them reddened by the optical property of the atmosphere. Gassendi has at least two (I have somewhere a memorandum of more) small craters within the central plain. None such appear in this drawing of Copernicus. In many other lunar mountains the centre is occupied by a crater-formed hill, as Vesuvius stands within Somma ; in others the hill remains a smooth rounded mass, but its crater is lost ; and a further stage of decay seems to be seen in Gassendi and Copernicus, where the central mass is broken into fragments and scidptured by ramified hollows. May we ascribe these effects to the former action of a lunar atmosphere, now absorbed in the oxi- dated crust of the moon ? If so, the lunar mountains have a history of water, as well as records of fire, and we must look on the sinuous ridges of the Mare Humorum with eyes accustomed to the gravel mounds of Norway and Ireland ; study the degraded craters after the models of the Eifel ; and map the *rillen*' with reference to Talleys of erosion as well as of eruption. In questions of this kind we shall find such drawings as this of the Roman astronomer of priceless value. Studied, scrutinized, ♦ I have some curious results regarding these beautiful objects. Mr. W, Gravatt on Rotatory Motion. 477 enriched with new discoveries, it may be the model for all time to come in this line of research. It may be followed by two other drawings of the same mountain, — one at the moment when the sun is on the meridian of the central hillocks, to show the light streaks, which hide themselves when the sun is low, and another in the clear afternoon of the lunar day (as much after midday, as this drawing was taken before noon), when every little crack and cavity becomes again distinct, but greatly altered in aspect, and the whole landscape changes under the eye of the observer ; the plains grow- ing grayer and softer, and revealing many minute low undulations ; the hills looking more and more rugged, and burning with narrower, brighter and more angular tracts of silvery light. "A Third Memoir on Quantics." By Arthur Cayley, Esq., F.R.S. The object of the author in the present memoir is chiefly to col- lect together and put upon record various results useful in the theo- ries of the particular quantics to which they relate. The tables at the commencement relate to binary quantics, and are a direct sequel to the tables in the author's second memoir upon Quantics, Phil. Trans, vol. cxlvi. (1S56). The definitions and explanations in the next part of the present memoir are given here for the sake of conve- nience, the further development of the subjects to which they relate being reserved for another occasion. The remainder of the memoir consists of tables and explanations relating to ternary quadrics and cubics. .,, "Elementary Considerations on the subject of Rotatory Motion.'* By W. Gravatt, Esq., F.R.S. The author explains the subject of rotatory motion in a series of propositions by the use of prime and ultimate ratios. He com- mences with a simple problem, determining the law of the forces by which a particle of matter is deflected into any given course, and pursues the inquiry by a consideration of the effect of these forces as referred to a sphere, going on to the investigation of the character of the motion of any body enclosed within an imaginary sphere, such sphere itself being supposed to revolve upon two axes inclined at any angle to each other. Hence the author determines the position of some point of the circumscribing sphere momentarily at rest, or in other words, of the resultant axis, from which he insists that all centrifugal forces must really be calculated. His first application of the law thus enunciated is to the motion of the peg-top ; and upon the principles he has already laid down, he shows that there is in the first instance rotation round a momentary horizontal axis, calling up rotation round a momentary vertical axis ; and that the ratio of the velocities of these two rotations, together with the length of the peg, determines the angular inclination of the top, contrary to the received explanation as given by Euler and other mathematicians. The law is further applied to the effect produced upon a falling body by the axial rotation of the earth, in the discussion of which. La Place, in the opinion of the author, has committed two important 478 Royal Society : — errors ; one in denying any deviation towards the equator, the other in his calculation of the amount of the deviation towards the east. This is followed by an investigation of the motion or direction of flight of a cannon-ball or shell fired in a northerly or southerly direction, from which it appears that a large shell will be subject to a de^^ation from the true line of projection, in consequence of the earth's rotation, amounting to no less than 22 feet. The author then refers to the well-known experiment of M. Fou- cault for proving sensibly the rotation of the earth, and shows from calculation that the errors which would be sufficient to vitiate the results in this experiment are so extremely minute and so difficult of avoidance by any perfection of manipulation which can be employed, that its performance cannot perhaps be safely adduced as proving such rotation. The. author illustrated his views by the exhibition to the meeting of a model apparatus, in which the vertical and horizontal motions may be variously combined, but which could not be intelligibly de- scribed without a series of complicated drawings unfitted for the compass of a mere abstract. April 17. — The Lord Wrottesley, President, in the Chair. The following communication was read : — " On the Condition of the Oxygen absorbed into the Blood during Respiration.*' By George Harley, M.D. The author commences by explaining, that his researches were instituted with the view of ascertaining whether the doctrine main- tained by Magnus in regard to the gases interchanged in the lungs during respiration were correct — namely, that the gases in question enter into no chemical combination with the constituents of the blood, either in passing to or from the tissues and organs of the body, but form merely a physical mixture with the circulating liquid. The principal object of the inquiry was to determine the following points : — ^ 1 . Has blood the property of chemically combining with the re- spired oxygen ? 2. "Which of the constituents of the blood enter into combination with oxygen ? 3. Do these constituents, by combining with oxygen, simply become oxidized, or do they also yield carbonic acid gas ? 4. What are the agents which control these changes ? After describing the method of investigation, and the apparatus employed, the author proceeds to relate a few of the analyses which he considered as the most conclusive. Instead of confirming the riew of Magnus, that gases enter into no chemical combination with blood, his results led him to conclusions of an opposite character, which serve to confirm the more generally received doctrine. In one set of experiments a certain quantity of fresh oX'blood was first shaken with renewed portions of air until it had become thoroughly saturated with oxygen, then introduced into a graduated glass vessel with 100 per cent, of ordinary air, corked carefully up, Dr. Harley on the Oxygen absorbed into the Blood. 479 and kept during twenty-four hours in a room of moderate tem- perature. In order to favour the mutual action of the air and blood, the vessel was frequently agitated. At the expiration of twenty-four hours the gas was analysed by Bunsen's method. In an example cited the follovnng was found to be its composition : — Oxygen 10*42 1 , ^ . .. .^ Carbonicacid .... ^.o^]tot^^o^jgm:=.\b'A7 Nitrogen 84*53 100-00 On comparing this with the composition of the common air (oxygen 20*96 ; carbonic acid 00*002 ; nitrogen 79*038) which had been introduced into the vessel, it is seen that 10*54 per cent, of oxygen has disappeared, while 5*05 per cent, of carbonic acid now exists, where only a trace of its presence could before be detected. Similar results were obtained with defibrinated blood. In a case where defibrinated arterial blood from a calf, after complete satura- tion with oxygen, was kept in contact with an equal volume of air during twenty-four hours, and treated exactly as in the previous ex- ample, the gas on analysis yielded in 1 00 parts, — £Ee-a<:id:::.":96}*''''^°wn=ir29 Nitrogen $2*71 100*00 showing in this case also that the air which had been imprisoned during twenty-four hours along with blood, no longer possessed its original composition, but that some of its constituents had been materially increased, while others had diminished in a manner no less marked. It would appear from these examples that the blood had probably become oxidized in two ways ; first, by giving off a quantity of car- bon, and secondly by directly combining with oxygen. As to the portion of oxygen which has disappeared, and which is not accounted for by the carbonic acid evolved, it may have combined partly with another portion of carbon, to form a limited amount of carbonic acid, which by the law of absorption is retained in the blood ; and partly with hydrogen or some other oxidable constituent of the blood, without yielding a gaseous product. These two experiments it will be observed point to exactly the same conclusions, and together with a number of others, where the mode of procedure was similar, and which were attended with similar results, have satisfied the author as to the fallacy of Magnus's doc- trine, " that the oxygen received during respiration into the blood is kept there merely by the law of mechanical absorption, and enters into no chemical combination with that liquid." Had this assertion been well-founded, such a change as has been seen to occur, in the 490 Royal Society : — composition of the air enclosed along with blood, saturated as the blood already was with oxygen, could not have happened. After having ascertained that air underwent certain changes in composition during its contact with blood, it next became an object to discover by which of the constituents of the blood these changes were induced' With this view the author successively subjected the organic compounds of the blood separately to the action of air, by a similar process to that adopted in the case of the blood itself. A certain quantity of fresh fibrine, moistened with water, was satu- rated with oxygen, placed in a receiver along with eight volumes of air, and kept during twenty-four hours at a temperature of from 20° to 25° Cent. At the expiration of this time the gas on analysis was found to have the following composition : — CaSc'acid : : : : n-i;} ^^^^^ oxygen=17'98 Nitrogen 82-02 100-00 thus showing that fibrine takes up a certain quantity of oxygen, and gives off a stated amount of carbon combined with oxygen in form of carbonic acid gas. The next experiments were made upon albumen, but as that sub- stance could not be obtained in a pure, and at the same time un- coagulated state from blood, the albumen of the hen's egg was employed, which possesses very similar characters. It was found that when a certain quantity of the white of the hen's egg was well saturated with oxygen, and afterwards kept in contact with an equal volume of air during a certain number of hours at a temperature of 36° Cent., the gas on analysis gave in 100 parts, — Oxygen 17*05 Carbonic acid 209 Nitrogen 80-86 10000 proving, in common with the experiments on the blood and on fibrine, that albumen also possesses the property of absorbing oxygen and disengaging carbonic acid. Some comparative experiments were also made upon serum and upon blood-coagulum, in which it was found that the air confined along with the serum yielded on analysis — Oxygen 16*74 Carbonic acid 2-30 Nitrogen 80-96 100-00 \ Dr. Harley on the Oxygen absorbed into the Blood, 481 while that confined with the coagulum contained — , ' Oxyeen S'^7 m po^narf-, Carbonic acid 7-29 tOHHoi. Nitrogen .....,,;.'.' ....... 84-14 70 tfR TO jTorVi/; It thus appears that the oxygen exerted a much more powerful action on the coagulum, which contained the fibrine and blood-cor- puscles, than on the serum, which contained only albumen. The ex- periment thus corroborated the results previously obtained with pure fibrine and pure alhumen. The pure fibrine was seen to produce a much greater change in the composition of the atmospheric air than the pure albumen from the hen's egg. The difference in the case of the coagulum and the serum was so much marked, that the author felt anxious to find out whence it proceeded ; and under the impression that the hsematine in the corpuscles might have mainly contributed to the result (as other organic colouring matters possess the property of absorbing oxygen and giving off carbonic acid gas), he took a small quantity of pure blood-hsematine prepared by Verdeil's process, and put it into a vessel along with 1000 volumes of ordinary air. After the air had been kept in contact with the hsematine for some months, the gas was analysed and found to contain — Oxygen 16*01 Carbonic acid 3*80 Nitrogen 80*19 JDw^fi-. 100*00 t,^ The pure colouring principle of the blood, therefore, by exposure to ordinary air, gives off carbonic acid gas, and becomes oxidized in two ways ; first by a loss of carbon, and secondly by direct combination with oxygen. The author considers that this last result furnishes additional evidence of the correctness of an opinion he hazarded two years ago*, imputing to the colouring matters of the vegetable and animal economy a more important office in the function of respiration than they before had been considered to possess, and regarding their principal function in organized beings as the absorbing of oxygen and exhaling of carbonic acid — a view altogether irrespective of Liebig's well-known hypothesis, which assigns the above office to the iron of the blood-hsematine. The author concludes by expressing the hope that his experi- ments will be considered as at least serving to establish one import- ant fact respecting which further evidence was wanted, namely, that the entire volume of the respired oxygen is not transmitted in an uncombined state (as Magnus believes) to the various organs and tissues of the body, but that a portion of it enters into chemical com- bination with some of the organic constituents of the blood. * Verhand. Physik-Medizin. Gesellsch. zu Wurzburg, Bd. v. 1854 ; and Erd- mann's Joum. f. prakt. Chemie, Bd. Ixiv. H. 5. 1855. 482 Geological Society. OEOLOGICAL SOCIETY. [Continued from p. 166.] November 5, 1856. — Colonel Portlock, President, in the Chair. The following communication was read : — " On the Stereognathus Ooliticus, from the Stonesfield-slate.'* By Prof. Owen, F.R.S., F.G.S. The subject of this paper was a small mammal, represented by a fragment of a lower jaw retaining three molar teeth, which was ob- tained by the Rev. J. Dennis from the Stonesfield-slate of Oxford- shire, and named Stereognathus Ooliticus by Mr. E. Charlesworth. This specimen, described in detail by Prof. Owen at the British As- sociation Meeting in September last, indicated, in the author's opi- nion, an animal allied to some extinct genera of even-toed pachy- derms, viz. the Hyracotherium, Microtherium, and Hyopotamus of the Tertiary deposits ; and he concluded therefore that the Stereognathus was most probably a diminutive non-ruminant Artiodactyle of omni- vorous habits. With regard to the zoological reasons for referring this peculiar and ancient fossil to the type of animal form above alluded to, the Professor entered at some length into the analysis of the mental pro- cesses by which the palaeontologist aims at the restoration of an unknown mammal from such a fragment as the fossil under notice. Its mammalian character is decided by the two-fanged implantation of the teeth, and its pachydermatous affinities are evidenced by the peculiar sex-cuspid and cingulated molars. These zoological rela- tions are determined from the knowledge that such structural pecu- liarities obtain in certain known pachydermata. Morphology, there- fore, or the study of form, rather than physiology, or the known relation of organs to function, is the guide in this determination ; but the Professor expressed his opinion that this example could not be cited as showing that there is no physiological, comprehensible, or rational law (in contradistinction to the morphological or empiri- cal) which can be a guide in the determination of fossil remains. He did not think that all such determinations rest upon the apj)lica- tion of observed coincidences of structure, for which coincidences no reason can be rendered ; for, although in many instances of this law of correlation, as demonstrated by comparative anatomy, the sufficient or physiological cause of them is not known ; yet, in other instances, the application of the principle has been suc- cessfully illustrated. The truth or fact (said Prof. Owen) of a phy- siological knowledge of a correlated structure, and of the applica- tion of that knowledge to palaeontology, is not affected or de- stroyed by instances adduced from that much more extensive series of correlated structures of which the physiological condition is not yet known. \ [ 483 ] LXIV. Intelligence and Miscellaneous Articles. NOTE ON THE OPTICAL PROPERTIES OF TRANSPARENT BODIES SUBMITTED TO THE ACTION OF MAGNETISM. BY M. VERDET. MANY physicists have indicated the relations between the rotation of the plane of polarization produced under the influence of magnetism and various physical properties of transparent bodies. M. De la Rive, in the first volume of his TrctzVe de V Electricity, in refer- ring to the experiments of M. Bertin, calls attention to the fact that the rotation is generally stronger in proportion as the index of re- fraction is greater. Two substances cited in the Table which M. Bertin has inserted in his memoir *, form exceptions to this rule ; these are alcohol and aether, which are more refractive than water, and which, nevertheless, under the influence of magnetism, rotate the plane of polarization of light at an angle considerably less. In commencing my investigation I have had more particularly in view to determine the extent of application of De la Rive's rule, which various reasons, unnecessary to be reproduced here, led me to regard as well founded. I have consequently measured the index of refraction of a considerable number of substances, and I have then compared the action which they exert upon polarized light, when placed l)etween the poles of an electro-magnet. So as only to em- ploy well-defined bodies and such as can be easily obtained of equal thickness, I have operated exclusively upon liquids, and particularly upon saline solutions. My experiments on the whole have not been favourable to the rule which I was endeavouring to verify, and I think that I may conclude from them that there exists no relation between the index of refraction, and that which, for the sake of brevity, 1 may be allowed to call the magnetic rotatory power. The following Table contains the results of a certain number of experi- ments in which the rule proposed by De la Rive is shown to be very evidently in the wrong. Average Complete rotation t Nature of the substance. index of produced by a thick- refraction, ness of 44 mm. Distilled water 1-334 4° 00 Solution of muriate of ammonia (dilute) .... 1*359 4 45 „ „ protochloride of tin (dilute) 1*364 5 27 „ „ muriate of ammonia (concentrated) 1*370 6 29 „ „ carbonate of potash 1*371 4 21 „ „ chloride of calcium 1*372 4 55 „ „ protochloride of tin (dilute) 1*378 6 10 „ „ chloride of zinc 1*394 5 57 „ „ protochloiide of tin (concentrated) . 1*424 8 16 „ „ nitrate of ammonia 1*448 3 44 Liquid chloride of carbon (C^ CI*) 1*466 5 12 M. Bertin has ascertained that certain substances, namely, nitrate of ammonia and protosulphate of iron, when dissolved in water, * Annales de Chim. et de Phys. 3rd series, vol. xxiii. t I give the name of complete rotation to the difi'erence of the two azi- muths of the tint of passage corresponding to two opposite directions of the current. 484 Intelligence and Miscellaneous Articles. dimmish the magnetic rotatory power of the solution. M. E. Bec- querel has made an analogous observation upon the protochloride of iron, and he believed that it might be said in a general why, that the rotation of the plane of polarization due to the influence of mag- netism varies in an opposite ratio to the magnetic power of the bodies. The experiments referred to by M. E. Becquerel do not allow us to consider this law as absolute. Thus we see by them, that the rotation of water being represented by 10, those of the two unequally concentrated solutions of protochloride of iron are repre- sented by 9 and by 3, and that of a solution of sulphate of nickel by 13*55; in other words, of these magnetic solutions there are two which produce a weaker rotation than water, whilst the third pro- duces a stronger one. Nevertheless, the extreme weakness of the rotation of a concentrated solution of protochloride of iron, approach- ing the observation of M. Bertin on the protosulphate of iron, seems to indicate that there is a peculiar mode of action in the ferruginous compounds deserving of careful study. I have dissolved in water a certain number of proto- and per-salts of iron (chlorides, sulphates, nitrates), and found that in all cases the rotatory power of the solution was less than that of water. But what is more, if, taking into account the density and composition of the solution, we calculate the rotation that would be produced by the quantity of water alone which it contains in a given thickness, we find a number constantly superior to the rotation observed. Things take place therefore as though the dissolved iron salt pos- sessed a rotatory power in the opposite direction to that of water. I proposed to ascertain whether this hypothesis was the true explanation of the phaenomena, and I think I have succeeded in pro- ving it. After numerous fruitless attempts to procure a solid or readily fusible ferruginous body, sufficiently transparent with a thickness of 1 to 2 centimetres, and not exerting of itself any action upon polarized light, I succeeded completely by dissolving the salts of iron in vehicles, such as alcohol and aether, capable of taking up a considerable quantity of the salt, and endowed with so weak a mag- netic rotatory power, as to show the direction of the rotatory power of the dissolved compound. Thus by mixing 8 grammes of anhy- drous perchloride of iron with 32 grammes of rectified sether, I obtained a liquid of a strong red-brown colour, but perfectly limpid, which under the influence of magnetism deviated the plane of polar- ization to the left under circumstances in which water and other transparent substances deviate it to the right, and vice versd. With 32 grammes of sether and only 4 grammes of the perchloride, I obtained a liquid which, under the influence of the electro-magnet which I had at my disposal, scarcely exerted any action upon polar- ized light. Alcoholic solutions gave me exactly similar results. Moreover, it is easy to ascertain that the ajtherial or alcoholic solu- tions of alkaline or metallic salts behave in general like aqueous solutions. It is therefore to the iron salt dissolved in sether or alcohol that we must attribute the remarkable phaenomenon which I have just made known, and from this we must conclude that the Intelligence and Miscellaneous Articles, 485 salts of iron submitted to the action of magnetism exert an action opposite to that of the generality of transparent substances upon polarized light. I shall propose to call the magnetic rotatory power of water, heavy glass, sulphuret of carbon, and most transparent bodies direct, and that of the salts of iron inverse. It was natural to inquire whether any other magnetic salts, besides those of iron, would not present analogous phsenomena. I am not in a position to give a certain opinion except upon the salts of nickel and manganese ; of these I have examined a certain number, such as the sulphate, nitrate, and chloride of nickel, and the sulphate and chloride of manganese ; and I have ascertained that in solution they possess a direct rotatory power, which is added to that of the water. They present no difference therefore from the ordinary metallic salts. I can say nothing certain as to the salts of chrome and cobalt : these compounds have such a great colouring power that their solutions must be very dilute if we wish to have them sufficiently transparent; the influence of the dissolved salts is then very weak in comparison with that of the solvent, and I have been unable to ascertain posi- tively its direction, the apparatus at my command not being suffi- ciently powerful. I need not point out the new difficulty which the opposition of the optical properties of the salts of iron and nickel presents to the establishment of any theory of the phsenomena. At any rate it is impossible to say simply that the rotation of the plane of polarization is weak in proportion as the magnetic capacity is strong, since we find magnetic bodies presenting rotatory powers in opposite directions. Lastly, I have examined the solution of nitrate of ammonia, which, according to Bertin, possesses a magnetic rotatory power less than that of water. The fact is perfectly correct, but it must be inter- preted quite otherwise than in the case of the salts of iron. Nitrate of ammonia is so soluble in water that we may easily prepare solu- tions containing 60 to 66 per cent, of the salt. The magnetic rotation of the plane of polarization produced by these solutions is weaker than that of pure water, but it is much greater than that which would be produced by the quantity of water alone which enters into the solution. The experiment, therefore, merely proves that the nitrate of ammonia gives the solution a rotatory power less than that of water, but still in the same direction. — Comptes Rendus, Sept. 8, 1856, p. 529. ON THE POSSIBILITY OF THE SIMULTANEOUS EXISTENCE OF OP- POSITE ELECTRICAL CURRENTS IN THE SAME CONDUCTING WIRE. BY PROFESSOR G. BELLI. The author's object in this paper is to show that the galvanometer, by means of which many physicists have endeavoured to solve the above question, is not adapted to furnish its solution. This has already been pointed out by M. Soret, in a particular case, upon the foundation of some considerations exactly analogous to those now put forward in a much more general manner by M. Belli. The latter shows that, — 486 Intelligence and Miscellaneous Articles, In any system of conducting wires isolated from the ground, or communicating therewith by one or several points, and submitted to the simultaneous action of several batteries acting with any force and in any direction, the galvanometric effects which must be pre- sented by any one of these wires are precisely the same, whether we regard the currents produced by the differences as independent or not, that is to say, either according to one or the other of the two following theories : — 1 . That each battery determines its particular system of currents, and that each wire is traversed simultaneously by all the unaltered partial currents, on condition that the currents of each battery taken separately are subjected to the laws of Ohm, and submitted not only to the resistance of the battery which produces it, but also to that of all the other batteries. 2. That in each wire we have a single current furnished by the composition of the forces with which the different batteries set elec- tricity in motion. M. Belli has taken up a certain number of particular cases, and shown that the facts constantly agree with the two theories (at least if we admit the conditions enunciated above), and that consequently we must seek for some other method of determining which of the two hypotheses is the true one. — // Nuovo Cimento, vol. ii. p. 401. MEASUREMENT OF THE SPEED OF A RAILWAY TRAIN BY MEANS OF ELECTRO-MAGNETTSM. BY W. C. M'^REA. The wheels of a car rotate a certain number of times in going over a given space of road ; for example, suppose a car- wheel to be eight feet in circumference, it will rotate 660 times in going the distance of a mile. Now, if the car were so constructed that the body would always remain at an equal distance from the axle, which is prevented by the motion given it by the springs, it would not be difficult to bring the wheel at each revolution to so bear upon a lever, as to ro- tate a wheel inside the car, w^hich might have a.& many cogs as the car-wheel rotates times in going a mile. Or, by a series of clock- work wheels, the indicating wheel might contain a fractional number of cogs in proportion to the number of times which the car- wheel would rotate in a given distance. The difficulty occasioned by the unsteady motion of the car, owing to the springs, may be overcome by the use of a magnet, battery, and galvanic circuit ; the latter to be so arranged as to be broken at each revolution of the car-wheel or axle. So by this means the operation of the magnetic contrivance would be to move the speed- indicator the distance of one cog. A contrivance of this kind may be so constructed as not to require winding, in order to have it in readiness for use. The indicator may be so constructed as to have an index placed over it, in such a position that the hand on the indicator should move it a sufficient distance to show at each successive rotation the num- ber of miles already travelled. The kind of battery most suitable for such a contrivance would be that of the '* sand battery/' which, if properly constructed, may b6 Meteorological Observations. 487 made to act with as much certainty as any other, and at far less ex- pense. This battery should be constructed with sand of such quality as is used by the manufacturers of glass, that is, free from dirt of any kind. The battery cup may be that of the ordinary kind, as used in Grove's battery ; or if larger glass or porcelain jars can be obtained, they would doubtless be better, affording an opportunity for the use of larger plates of zinc and copper ; these should be placed about an inch apart, and the sand packed tightly around them. The zinc should be amalgamated, and the copper rubbed with a piece of emery- paper before placing in the cup ; the sand should then be well moist- ened with sulphuric acid, diluted in the usual proportion for battery purposes. Intensity may of course be increased by increase of acid. A battery of this kind would stand for some weeks, only requiring the addition of a little acid each day, according as the strength of that first put in became exhausted. A series of cups of this kind could be carried on a train without the difficulties which would arise from that of almost any other battery. — Journal of the Frank' lin Institute, October 1856, p. 217. METEOROLOGICAL OBSERVATIONS FOR OCT. 1856. Chiswick. — October 1. Exceedingly fine. 2. Cloudy. 3. Cloudy and fine : rain. 4. Rain : cloudy : rain. 5. Rain : cloudy : fine : lightning at night. 6. Foggy : rain : cloudy. 7. Hazy and drizzly : rain at night. 8. Heavy rain : densely over- cast. 9. Overcast. 10. Hazy : fine. 11. Heavy rain : uniform haze : slight rain at night. 12. Foggy : uniform haze. 13. Dense fog : very fine : cloudy. 14. Foggy : overcast : fine. 15. Rain. 16. Overcast : showery. 17. Fine : overcast : hazy. 18. Very fine. 19. Dense fog : very fine. 20. Foggy : very fine. 21. Foggy : exceedingly fine. 22. Very dense fog : exceedingly fine. 23. Foggy : very fine. 24. Fine. 25. Foggy : heavy clouds : fine. 26. Hoar-frost : hazy : very fine. 27. Frosty : haze: fine. 28, 29. Very dense fog. 30. Hazy clouds : overcast : fine. 31. Uniform haze : rain: cloudy. Mean temperature of the month 51°'28 Mean temperature of Oct. 1855 50 '28 Mean temperature of Oct. for the last thirty years 50 -00 Average amount of rain in Oct 2-802 inclies. Boston.—Oct. 1, 2. Fine. 3. Fine : rain p.m. 4. Rain a.m. and p.m. 5. Cloudy. 6. Fine. 7,8. Rain a.m. and p.m. 9 — 12. Cloudy: rain a.m. and p.m. 13. Cloudy. 14. Fine. 15. Fine: rain a.m. and p.m. 16. Cloudy: rain p.m. 17. Fine. 18. Cloudy. 19. Fine. 20, 21. Cloudy. 22, 23. Foggy. 24. Fine. 25—28. Cloudy. 29. Foggy. 30,31. Cloudy: rain a.m. Sandwich Manse, Orkney. — Oct. 1. Bright, fine a.m.: cloudy, fine p.m. 2» Bright, fine a.m. : drops p.m. 3. Hazy a.m. : drops p.m. 4. Hazy a.m. : drops, show^ers p.m. 5. Showers a.m. : clear, aurora p.m. 6. Clear, fine, hoar-frost a.m. : clear, aurora p.m. 7. Clear, fine, hoar-frost a.m. : cloudy p.m. 8. Bright a.m. : cloudy p.m. 9. Cloudy, fine a.m. : clear p.m. 10. Cloudy, fine a.m. and p.m. 11. Bright, hazy a.m. : cloudy p.m. 12. Clear, fine a.m. and p.m. 13. Bright, fine a.m. : cloudy p.m. 14. Damp a.m. : clear p.m. 15, Damp a.m. : cloudy p.m. 16. Showers a.m. : drizzle p.m. 17. Cloudy a.m. : rain, clear p.m. 18. Bright a.m. : drizzle p.m. 19. Bright, fine a.m. : drizzle p.m. 20. Bright, fine a.m. : clear, aurora P.M. 21. Fog a.m. : cloudy p.m. 22. Cloudy, fine a.m. : showers p.m. 23. Clear, fine a.m. : clear, aurora p.m. 24. Clear, frost, fine a.m. : clear, aurora P.M. 25. Damp A.M. : rain P.M. 26. Drizzle a.m. : damp p.m. 27. Drizzle a.m. and P.M. 28. Damp a.m. : cloudy p.m. 29. Hazy, fine a.m. : clear p.m. 30. Cloudy, fine a.m. : cloudy p.m. 31. Cloudy, fine a.m. : clear, fine p.m. Mean temperature of Oct. for previous twenty-nine years ... 47°"57 Mean temperature of this month 48 -84 Mean temperature of Oct. 1855 45*72 Average quantity of rain in Oct, for previous sixteen years ... 5*09 inches. •^siApcrag 'iduvo •ao)toa •^UktniO 8S^ ^S"gs|ii"|^-gsisE:'^iii^||ii^ •](3iMptras s « « ^ •U0)80a I i « « ^ S S fl B « s ^ « « ^ 1 1 ^ « «! .^1 S || fcSaS-ixIs^'l^oJ^i^ C Hf OS «^ r< «^>0 H On •-• «^vO to Os O 0\vO wt u^ xt) ti t< oo r!*- cl _« « m on r-- « bNOsbNONONboobbbbbbNONOsbbbbbbbbbbbboNOxb r* p r* r^ T*" r^ r* r f^ ® t^ on "on on on 'o\ On b b b "o b b b b on On b\ on b b b b b b b b b b b b On on ■ao)Bog O r) Lo M o r4 cooo 0*Of»i-^0NTj-0r<^Tj- t*-oo u^O»oO»oOOO'* -+0 i*r^r^r r^i^y^.'*.^ *^*p m r^ ^-i o voo© oo ©o r^ t^ onoo o o o o onoo t^v© OnOnO\OsOnO\OnOnOnONOnOnO\ONOnOnOnOnOnOn"onO>OnO O O b On On On On MMt4r)MNt4r)r)Nc vo OO to 0\ t^ t^ f^^ 00 f^oo s^rr^P^^r^F^T^^F^r "^ ^ to ■^ •^ to ro N 11 M o On 0\ Os On On On On On b O ON O O 0\ On On O O O b O O O O O O O O O O O t\ t* ti fi n n H r» totoH foeon « ct co«otototototoco«ococoroeotoro OO O «p w-> ^ ^vO o w OnOnO tOlTN^t^OO OVO M QOO t-N-ONOVO to M Cl O too© tJ- N VO M On tOVO On tJ- u->vO ih mooOO Osb "-"OO t^N ^N tou-iw 00 00 00 r^ao ONO\0t»'-'0"^M onvo t< totos m tj toTj-^^i-Tj-tototi m ro 4 »o\o t^oo d\ d « fJ «^ •4- »ovd t^oo ON c5 w « to 4- '^vo I^OO On d M rttJ«««Hr«t«r»toto s THE LONDON, EDINBURGH and DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE.. SUPPLEMENT to VOL. XIL FOURTH SERIES. LXV. Memoir on the Specific Heat of some Simple Bodies, and on the Isomeric Modifications of Selenium. By M. V. Reg- NAULT*. DULONG- and Petit were the first to announce the remark- able physical law, that " the specific heats of simple bodies are reciprocally proportional to their atomic weights." The experiments on which they had established this law were not numerous, and many of them have been found to be contradictory, in consequence of the considerable changes which more exact analyses, and a more complete knowledge of chemical compounds, have produced in the adopted atomic weights of some simple bodies. Nevertheless the numerous experiments which I made fifteen years ago, on all the simple bodies which I could procure in sufficient quantity, proved that the law of Dulong and Petit ought to be admitted ; not, indeed, in the rigorous acceptation which those celebrated physicists had claimed for it, but as an approximative law, which may be usefully appealed to in many scientific considerations. In fact, according to the precise enun- ciation of this law, the product of the specific heat of a simple body by its atomic weight ought to be a constant number; whereas in my experiments on solid bodies, this product varied from 36 to 41. This variation arises from the fact, that the calorific capacity of bodies, as determined in our experiments, comprehends not only the specific atomic heat, that is to say, the quantity of heat necessary to elevate the temperature of the atom one degree, but also the heat which disappears in causing the expansion of the body, or in the molecular changes which pro- duce its successive softening, or determine the variations of its crystalline groups. These secondary effects absorb quantities of caloric which are by no means reciprocal to the atomic weights of the bodies, and each of which varies according to the limits of the temperature within which it is observed, * From the Annates de Chimie et de Physique for March 1856. Phil. Mag. S, 4. No. 82. Suppl Vol, 12. 2 K 490 M. Regnault on the Specific Heat of Simple Bodies y To be convinced of this, it is sufficient to compare between themselves the specific heats of some simple bodies taken at diflfer- ent points of the thermometric scale; it is immediately seen that their relations change sensibly with the temperature ; and as the atomic weights remain the same, it is evident that the product of the specific heat by the atomic weight may vary with the temperature unequally in each case. In short, the specific heat of the same body is often very dif- ferent, according as it is estimated in the solid, liquid, or gaseous state. Thus, while for all the solid simple bodies which I studied in my previous memoirs the product of the specific heat by the atomic weight varied between 36 and 41, the same product is only 24 for those simple gases, such as oxygen, hydrogen, and nitrogen, which deviate little from Mariotte's law, and it is 29*5 for chlorine and gaseous bromine, which show a considerable deviation. Further, the gases which follow Mariotte's law pretty closely, maintain their calorific capacity sensibly constant at dif- ferent points of the thermometric scale ; while this calorific capa- city increases rapidly with the temperature in those gases which deviate considerably from this law, as is the case with carbonic acid. This last observation would of itself be sufficient to prove that the law of Dulong and Petit cannot be admitted as an exact physical law. However this may be, no one doubts now that the law of Dulong and Petit, when only applied to simple bodies in the same physical condition, can be of great help in chemistry as a guide in selecting atomic weights for simple bodies, when che- mical considerations permit several equally probable to be adopted. It was from reasoning on this law that I proposed to change the atomic weights of the alkaline metals, and of that of silver, and to take values half those which chemists have usually adopted. It cannot be long before this change, which is in accordance with isomorphism, is adopted. Convinced of the utility of obtaining, as speedily as possible, the specific heats of simple bodies which have not yet been deter- mined, I have never neglected to make experiments when I was able to procure any of these bodies in a sufficient quantity and in a sufficiently pure condition. The Universal Exhibition which took place this year at Paris affi)rded me a favourable opportunity, by putting at my disposal simple bodies, often very pure, and on which I had not hitherto made experiments. These new experiments were made with the apparatus and by the process described in my first memoir*. The only modifica- tion of the former method consisted in the estimation of the correction which must be made in the elevation of temperature ♦ Annates de Chimie et de Physique, 2nd series, vol. Ixxviii. p. 20. and on the Isomeric Modifications of Selenium. 491 undergone by the calorimeter, on account of perturbations pro- duced by external causes. This modification exercises, however, little influence on the results. The method of proceeding was as follows : — 1. The variation of temperature A^, which the calorimeter underwent from disturbing causes alone, was observed during three minutes, the water being continually agitated by means of a small stirrer which formed part of the apparatus. 2. The calorimeter was placed rapidly under the oven, in which the little basket containing the substance experimented upon had been raised to a temperature accurately determined, and about 100 degrees. The basket was then quickly lowered into the water of the calorimeter, and this was then returned to its original position in front of the telescope which served for reading the thermometer. It took half a minute to place the calorimeter beneath the oven, and to make the necessary ar- rangements for lowering the basket ; during this time the calo- rimeter underwent a variation of temperature similar to that which had occurred in the same time during the first period. The lowering of the basket only required a few seconds ; and as this basket was immediately agitated, the water assumed in less than a minute its maximum temperature when the substance was a good conductor of heat. At the end of the fourth minute the calorimeter was brought to its first position, and its tempe- rature might be read off^. 3. From minute to minute the temperatures of the calorimeter and of the surrounding medium were observed till the seventh minute. 4. Lastly, an observation was made of the variation of tempe- rature which the calorimeter underwent from disturbing causes alone during the three succeeding minutes, that is, from the seventh to. the tenth. Representing by — • A, the value in water of the calorimeter with its appendages, that is, the immersed part of the thermometer and the little agitator j M, the weight of the substance submitted to experiment ; p, the value in water of the basket ; T, the temperature indicated by the thermometer of the oven, corrected for that portion of the column which is outside ; ^', the temperature of the calorimeter at the end of the seventh minute ; A^, the elevation of temperature observed between the end of the third minute and that of the seventh ; A^', the elevation which it would have undergone if it had not been influenced by disturbing causes ; 2K2 492 M. Regnault on the Specific Heat of Simple Bodies, c, the unknown specific heat of the substance ; we have (MC+jo)(T-^) = AA(9'. Let us suppose that during the first period of three minutes the temperature of the calorimeter is inferior to that of the sur- rounding air; it will undergo an increase of heat a. If, on the contrary, this temperature is, during the last period of three minutes, higher than that of the surrounding air, the calorimeter would be cooled by a quantity a'. It was admitted that for from 3 minutes to 3^ minutes the calorimeter continued to undergo the same variation of temperature as in the three preceding minutes, and that it would undergo an elevation of temperature ^. At 3^ minutes the basket was immersed in the calorimeter ; it was supposed that from 3^ to 4 minutes the temperature of the calorimeter was not influenced by disturbing causes, because during this period the calorimeter traversed almost completely its variation of temperature. From 4 minutes to 7 minutes the temperature did not change sensibly, and it might be admitted that the perturbation produced by external causes was equal to that exhibited during the three succeeding minutes, that is from 7 to 10 minutes. According to that we should have o This mode of proceeding is only suited for bodies which are good conductors of heat ; for others, a tolerably long time is necessary before the thermometer of the calorimeter attains its stationary temperature. It is hence necessary to calculate the change of temperature which external causes prodjice during each minute. If t and i' represent these surrounding tempera- tures during the initial and terminal periods of three minutes, we might put ^=A(e'-i') + K, A and K being the constants which would be determined by the experiments themselves. The variation of temperature produced in each minute for a temperature t of the calorimeter, and an external temperature t, would be A(^-/) + K. and on the Isomeric Modifications of Selenium, 493 Osmium, I owe to the kindness of M. Fremy the osmium which has served for my experiments ; the metal was in the form of spongy masses loosely aggregated, and of a bluish metallic lustre. The following are the results of three experiments : — I. II. III. M . . . 60&r.63 55&r-60 55g''-37 P . . 2gr.258 2gr-258 2&r.258 T . . . 97°-50 97°-49 98°-08 & . . . 8^-50 6°'58 9^-00 M' . . . 0^-76485 0°-75212 0°-72311 A . . 483g'--02 483^^-02 483gr-02 c . . . 0-0310 0-0308 00301 Mean . . . 0-03063. The equivalent of osmium, according to Berzelius, is 1244*2, which would give to osmic acid the formula OsO^. The pro- duct of the equivalent by the specific heat we have found to be 38*109 j it is therefore comprised within the two limits 36 and 41 which we have met with in other simple bodies. Hence the value found for the specific heat of osmium verifies the formula which chemists usually assign to the compounds of this metal. Rhodium. The rhodium on which I experimented formed part of the beautiful display of MM. Desmoutis, Chapuis and Co., manu- facturers of platinum ; it formed a simple forged cylinder, resem- bling in appearance metallic platinum. In the experiment of determining its specific heat, the cylinder was attached simply by a very fine steel wire, the calorific capacity of which might be neglected. M . . . 98gr-07 98gr-07 98^^-07 p »• • . ... .*• T : . . 97°-52 97°-45 97°-40 ff . . . 23^-34 19°-20 23°*25 A^' . . . 0°-9318 0°-9749 0°-9681 A . , . 422g'^'54 422gr.54 422g'--54 c , . . 0-05357 0*05368 0-05499 Mean . . . 0-05408. According to Berzelius, the equivalent of rhodium is 652*1 ; the product of the equivalent by the specific heat is thence 35-26; this number is a little less than those which have been found for other simple bodies ; but the difference is vei*y small, and 494 M. Regnault on the Specific Heat of Simple Bodies, might arise from the presence of a small quantity of foreign metal, probably of iridium. Iridium, I have already given, in my first memoir on the specific heats of simple bodies, some experiments on a specimen of iridium which had been lent to me by M. de Meyendorfi^. I had found for the specific heat 0*03683, which, multiplied by the equivalent generally adopted, 1233-2, gave 45*43. This number being far too high, I supposed that the metal was impure. The new specimen on which I experimented came from the Ex- hibition of MM. Desmoutis, Chapuis and Co. ; it formed half of a disc strongly aggregated by percussion, and weighed 509&^*21. In the experiment the metal was attached by a fine steel wire. M . . 509&r*21 509gr-21 5098^-21 5098^-21 P ' ... •t* ••• ••• T . . 97°-87 97°-15 97°*81 97°*47 6' . . 22°-34 2r-64 24°*15 24^-59 Aff . . 3°*3808 3°*1787 3°*2494 3°*1620 A . . 422&r-54 422&r-54 422g'*54 4228^*54 c . 0*03703 003570 0*03649 003597 Mean . . . 00363. This value differs very little from that which I found for the iridium of M. de Meyendorff. The product of the specific heat by the atomic weight is 44*76, which is not comprised within the limits of variation which we have observed in other simple bodies. This anomaly may be explained in two ways : either the metal is impure, or its atomic weight is inexact. If the metal is not pure, which appears probable from the low density which I found, it could only be mixed with palladium, rhodium, or ruthenium ; for platinum and osmium would not change its specific heat, since they have the same atomic weight. It is scarcely probable that it is palladium, in consequence of the chemical properties of the latter metal, and of the nature of the mineral used in the preparation of iridium. It could only be rhodium or ruthenium, whose atomic weights are only half that of platinum ; or some metal still unknown which would be simi- larly circumstanced. It is desirable that those chemists who are at present engaged on the study of those metals which accompany platinum, would be good enough to direct their attention to this point. Aluminium. The aluminium which I employed in ray experiments was pre- pared by M. Deville; it had been cast in the form of four ingots. and on the Isomeric Modifications of Selenium. 495 I. II. III. IV. V. VI. M ... 147^"-80 147'^ '■•80 I47^'-80 147«'"-80 147^'-80 147«'-80 p 2-'-335 28"^ 335 2S'--335 28'-335 2e'-335 2e'"-335 T 97'-54 97^-33 97°-2l 96°-82 97°-59 Q7°7Q 0' 25°-81 28°-07 24°02 26°- 18 23°-92 22°-68 A0' ... 5° 5197 5°-3866 5°-6361 5°-4628 5°-6974 5^-7821 A 422C'-54 422s'--54 4223'--54 422e'-54 4228^-54 4228 '^•54 c 020471 0-20801) 0-20436 0-20581 0-20581 0-20490 Mean 020556. The product of this specific heat by the equivalent 170*98, which is usually given to aluminium, is 35*15. This number is a little less than the analogous products obtained for other simple bodies; but this seems to indicate that the metal on which I operated was far from being pure. In fact, according to an ana- lysis which M. Salvetat was good enough to make at my request, the metal contained, — Silicium 2*87 Iron 2-40 Copper 6*38 Lead traces Aluminium (by difi'erence) , 88*35 100*00 We can calculate very closely the specific heat of pure alumi- nium from that which we have found for the impure metal, and from the specific heats of the metals which are mixed with it. It is merely necessary to make a supposition on the specific heat of silicium which has never yet been determined. Let us as- sume that it is 0*1425, because the product of this specific heat by the equivalent 266*7 of silicium is 38. But this presupposes that the formula of silicic acid is SiO^, which is far from being demonstrated. Whatever it may be, the error which would result from the falsity of this assumption would be of little importance for the object which at present occupies us. We should find thus for the specific heat of pure aluminium 0*2181 ; and the product of this number by the equivalent of aluminium is 37*29, which is entirely within the prescribed limits. Hence the value which we have found for the specific heat of pure aluminium confirms the formula Al^O^ which chemists have been led to adopt for alumina, from the isomorphism of this substance with the sesquioxide of iron. Since then I have succeeded in procuring purer aluminium which had been prepared by M. Rousseau; it only contained traces of silicon, and 2 per cent, of metallic iron. Two deter- 496 M. Regnault on the Specific Heat of Simple Bodies, minations which I made of the specific heat have given the fol- lowing results : — M . . . . 134«r-81 1248nr-595 p .... 2P-030 28rr030 T . . . . 97°-44 97°-31 ^ . . . . 15°-51 13°-71 a rM A^' . . . . 5°-9445 5°-6308 A . . . • 422^^54 422^^-54 c .... 0-21236 0-21212 Mean . . . 0-21224. ^^the 2 per cent, of metallic iron which the metal contains be taken into account, the specific heat of pure aluminium will be found to be 0*2143, and the product of this specific heat by the equivalent is 36 64. Cobalt. The display of Messrs. Johnson and Matthey of London con- tained some beautiful samples of cobalt and nickel ; I have taken advantage of them to make some new determinations of their specific heat. Unfortunately both the metals contained carbon, particularly the nickel. M Y' T 6' A c . 218gr-29 218gr-29 . 97°-84 97°-83 . 25°-90 2r-80 4°-3861 4^-6110 . 422^^-54 422s^-54 . 0-10686 0-10706 Mean 0-10696. The product of this specific heat by the atomic weight 369 gives 39*47. This specific heat is probably a little too great ; it is however identical with that which I found for cobalt in my former experiments. Nickel. In my previous experiments, I found for nickel prepared by the calcination of the oxalate in a closed vessel the specific heat 0*1086. My new experiments have given a slightly difi'erent value; but the nickel of Mr. Johnson was very carburetted, as was easy to observe on dissolving it in hydrochloric acid. M . 229gr-78 229^*78 T . 97°*92 97°*93 6' 21°-41 20°*46 A^ 5°*0295 5°-0854 A , 452gr.54 422&r.54 c 0-1110 0-1109 Mean . . . 011095 , and on the Isomeric Modifications of Selenium, 497 The product of this specific heat by the atomic weight 369*7, usually given to nickel, is 41-00. It is probable that the specific heat of pure nickel is considerably less, and that it does not exceed 0-103. Sodium, My former researches on the calorific capacity of the binary compounds, and of the salts formed by the alkaline metals, showed that it was necessary to divide by 2 the atomic weights which have hitherto been adopted by chemists*. Direct re- searches on metallic potassium have led me since then to the same conclusion f. It was of importance to verify this result with metallic sodium, which is now procured so easily in a great state of purity, and the manipulation of which does not present so many difficulties as does that of potassium. M. Liebig sent me, about six years ago, a certain quantity of sodium which he had had expressly prepared for this purpose in his laboratory at Giessen ; but my various occupations have until now prevented me from making the experiment. I made determinations on the sodium of M. Liebig which had been perfectly well kept in her- metically sealed tubes, and on sodium recently prepared by M. Rousseau. On breaking the tubes which contained the sodium of M. Liebig, I was able to confirm the fact that the metal presented two very distinct physical conditions. In the one, the sodium was per- fectly malleable, could be bent in every direction without break- ing, and presented no trace of crystallization. In the other, on the contrary, the metal was extremely brittle, and exhibited in its fracture pentagonal dodecahedra of the most perfect regularity. These dodecahedra could be even detached from the mass with the greatest ease, and presented then most perfect crystals, whose diameter sometimes exceeded 3 millimetres. This difference was owing probably to the presence of a small quantity of potassium. I cast the melted sodium under naphtha in a brass mould, fig. 1. This mould is composed of a cylinder, abcdj slightly conical, on which is screwed a bot- tom, cdf pierced by a central hole, /. In this hole is fitted a cylinder, also slightly conical. The melted substance is run into the circular space; when it has solidified on cooling, the bottom, cd^ is unscrewed, the substance is taken out as well as the cylinder e/, and the sodium is obtained in the form of a cylinder bored in the direction of its axis. The cylinder of sodium was wiped dry immediately on cooling; the external surface * Annates de Chimie et de Physique, 3rd series, vol. i. p. 192 et seq. t Ibid. vol. xxvi. p. 266. 498 M. Regnault on the Specific Heat of Simple Bodies, which had been in contact with the air was cut off and the cylinder immediately covered with tinfoil, the weight of which had been previously determined. It could then be weighed at leisure, and the experiment for determining its calorific capacity be arranged. I have thought it necessary to determine it, at temperatures below 0 degree, in order to avoid the anomalies proceeding from the successive softening which sodium suffers at more elevated temperatures. In order to subject the substance to a uniform temperature, and susceptible of an accurate determination, I used the appa- ratus represented at fig. 2, which may serve also for higher Fig. 2. temperatures. Tlhis apparatus is composed of an oblong trough, C D E F, resting on a support M N. An inclined tube of brass traverses this trough, and its two open extremities pro- ject at the exterior. It is in the middle of this tube that the substance is kept which has to be raised to a fixed temperature. In the present case, the cylinder of sodium, K, was fixed by silk threads w^hich traversed the two orifices of the tube AB, and were maintained by the two caps which closed them. A ther- mometer, T, the bulb of which is inserted in the central hole of the sodium cylinder, is fixed by means of a stopper on the cap A. The trough is filled with a mixture of pounded ice and crystal- lized chloride of calcium, which is constantly agitated. The temperature gradually descends, but some time is necessary before the minimum is reached, which then rests stationary for ten or fifteen minutes. It is at this time that the calorimetric experiment is made. In the calorimeter, V, a determinate quantity of naphtha was placed, which had been previously distilled over metallic and on the Isomeric Modifications of Selenium. 499 sodium. But it was necessary to determine the value in water of the calorimeter thus arranged. With this view, I made on the calorimeter the determination of the calorific capacity of lead between the surrounding temperature and that of boiling water. As the specific heat of lead is known within these limits of tem- perature, it was easy to deduce from the experiment the calorific value in water of the calorimeter filled with naphtha. The fol- lowing are the results of the experiment : — Weight of lead . . . 636^^-45 636^-45 Specific heat of lead . . 0^^-03140 0^^-03140 T 96° 77 97°-076 6' 14°-165 ' 15°-085 A^' 10°-1691 10°-1691 Log A 2-2071712 2-2104166 Mean of log A = 2-2087939. I wished to verify this value by an experiment made on the same mass of lead cooled in the refrigerating mixture : I obtained hence— p 636g'--45 T -28°-030 6' -f 6°-31 A(9' 4°-2795 LogA . . . . 2-1994784 I have assumed that the specific heat of lead between —28 degrees and the surrounding temperatures was 0-0310. I found, in fact, — Between +15° and 98° 0-03140 (1) -78° ... +30° 0-03065 (2) and the mean 0-310 may be admitted as applying to the tempe- ratures comprised between —28 and -1-7 degrees. The value of log A given by this experiment is a little less than that furnished by the two preceding. I have adopted the mean of the three values, that is 2-2056887. Here are the results which I obtained with sodium : — Sodium of M. Liebig. Sodium of M. Rousseau. t ^ > , ^ ^ I. II. III. IV. Weight of sodium 58^^-918 58^^-918 56«'--580 56«>--580 Weight of tinfoil 2g'-152 2»'-'152 2^^-700 2«''700 T -34^-573 -30°-126 -29°-276 -21°-628 6' 4°-7121 5°-0756 7°-242 7°-041 A^' .... 4°-2787 3°-9356 3°-7913 3°-0315 c 0-29480 0-30267 0-29205 029742 Specific heat of tin . . 0-0562. The experiments Nos. II. and IV. were made with cylinders 500 M. llegnault on the Specific Heat of Simple Bodies, of sodium which had been used for the experiments Nos. I. and II. To this end, immediately on taking the sodium out of the naphtha, the tinfoil was unfolded and rapidly wiped dry with tissue-paper, as also was the metal itself, and the cylinder imme- diately replaced in the tube surrounded by the cooling mixture. The experiments Nos. III. and IV. are less precise than Nos. I. and II. ; first, because the metal had undergone a more profound alteration in contact with the air, and then because the tempera- ture of the cooling mixture having begun to ascend, the thermo- meter at the moment of the experiment only marked a relative minimum, which did not continue, and which ap})lied less exactly to the whole mass of the metal than the absolute and stationary minimum at which the determinations Nos. I. and III. had been made. It is hence better to take only the mean between Nos. I. and III., which would give for the specific heat of metallic sodium 0-2934. The product of this specific heat by the atomic weight 287*2, which chemists assign to this metal, is 84*2 ; but the product by 143-6, the half of this atomic weight, is 42*1. This latter product alone is comprised within the limits which we have recog- nized for other simple bodies. It is therefore evident that the atomic weight of sodium is 143-6, and that the formula of soda ought to be written Na^O, and not NaO. It is assumed that the fusing-point of sodium is about 90**. I wished to determine it with accuracy. I poured melted sodium into a large glass tube, dipped in the melted metal a mercurial thermometer, and observed the course of its cooling. In many experiments the thermometer became stationary at a temperature which, corrected for that portion of the column which was not plunged in the metal, corresponded precisely to 97°-63. The stationary temperature observed during the cooling is therefore 97°'63, and it is the only element of this kind susceptible of an accurate determination. Potassium. I have not thought it necessary to make new determinations of the specific heat of potassium ; the experiments already on record {Ann. de Chim. et de Phys. 3 id series, vol. xxvi. p. 266) are sufiicient for the conclusions which may be drawn as to the atomic weight of this metal. As potassium undergoes a gradual softening with the temperature, its specific heat experiences a material increase, and its value may be found perceptibly too great. But I have made some experiments for determining exactly its fusing-point, which treatises of chemistry generally place at about 55 degrees. Potassium prepared by M. Rousseau was melted in a large glass tube under naphtha. After the solidification of the metal. ^* arid on the Isomeric Modifications of Selenium. 501 the whole of the naphtha was removed, and the metal having been again brought to the liquid state, the thermometer was plunged into it, and the heat raised to above 100 degrees. The progress of the cooling of the thermometer was observed, the tube being kept in the surrounding air. In a former experiment the thermometer showed no rest at any point ; it descended gra- dually from 100 to 20 degrees. But in constructing a delinea- tion of the curve of cooling, it was easy to observe that the curve completely changed its form about 55 degrees; its ordinates underwent from this point a much less rapid diminution. I recommenced the experiment, and agitated the thermometer slightly with a view of overcoming the molecular inertia, and of ascertaining the diminution of fluidity. The thermometer de- scended regularly as far as the division 325 of its scale, then it rose suddenly to 327*2, at which point it was steady for some seconds ; it then resumed its downward march, although more slowly than before. The fluidity of the metal diminished gradually ; it had a buttery consistence towards 300 divisions ; but it was only at 280 divisions that it was no longer possible to move the thermometer. The 327*2 divisions of the thermometer^ corrected for that portion of the column not immersed, correspond to 55°*43. It might be concluded from thence, that the temperature at which the tendency to crystallization commences to increase in liquid potassium is 55"*43, but that it acts with far too little energy to resist the cooling, and bring about a stationary temperature, as is the ease with sodium, and generally with bodies which solidify suddenly. The foU owing are the series of temperatures which I have observed : by taking the time as absciss, and the temperature as ordinate, the curve maybe graphically represented, and we can observe the influence which the heat disengaged gra- dually by the solidification has had on the progress of the cooling. O' . . "" TlA '. . 2J. . 3 . . 3i. . H . . 5 . . 5J . . 6 . . 75-42 71*25 67*48 63-98 60*61 57*70 55-24 55-43 55-10 54*37 53*74 52-99 52-25 51-46 4-17 3-77 3-50 3-37 2*91 2*46 0*33 0*73 0*63 0*75 0*74 0*79 7 ' 2 8 81 10 10^ 11 11^ 12 121 13 ^f^^ 50-60 . . 49*60 "i^i^ 48-62 rp-4 47.53 ^^s^-) ,9V 46.45 offtp 45-25 milio 44-00 '^ :^^X 42*80 n& ,)^i^ 4[.52 V^-i ^40-28 ^'2 -:- 39*00 .a. .., 37.72 . . 36-50 . ; 35*32 0*86 1*00 0-98 0*99 1*08 1*20 1*25 1*20 1-28 1*24 1*28 1*28 1-22 118 502 M. Regnault on the Specific Heat of Simple Bodies, It will be seen from this Table that the rapidity diminished regularly up to the third minute, as it ought to do according to the law of Newton, for the quantity of heat lost is proportional to the excess of the temperature of the body above the surround- ing medium. From the third minute, the heat disengaged by solidification commenced to disturb the law of cooling ; a remark- able point is observed on the curve, which is disturbed in its former course up to the thirteenth minute at which the observa- tion is discontinued. Hence when the potassium had attained the temperature of 35 degrees in its cooling after liquefaction, it had even then not entirely disengaged its latent heat of fusion*. Lithium. It would be most interesting to know the specific heat of lithium, for it could be decided thence whether lithium was to be ranged among the alkaline metals with sodium and potassium, or among the metals of the alkaline earths with barium and cal- cium ; in other words, whether the formula of lithia ought to be written Li^O or LiO. Bunsen has lately given a very convenient method of preparing lithium by electrolysis. I tried this pro- cess, and it succeeded admirably ; but it would have been difficult to prepare with the chloride of lithium which I was able to pro- cure, a quantity of metal necessary for an exact determination of its calorific capacity. I preferred to operate at first on chloride of lithium, with the intention of using afterwards the metal itself if I could succeed in procuring it in sufficient quantity. The chloride of lithium was prepared from carbonate of lithia, from the Exposition of M. Batka of Prague. The carbonate was first washed with cold water, then dissolved in hydrochloric acid, the solution evaporated to dryness, and then treated when cold with strong alcohol. The substance dissolved almost entirely. The filtered liquid was again evaporated, and the chloride of lithium melted in a silver crucible. The liquid matter was poured into a small brass mould, from which it was extracted on cooling in the form of a cylinder pierced in the direction of its axis. As chloride of lithium is at least as deliquescent as chlo- ride of calcium, I folded it immediately in tinfoil and suspended it in the oven for specific heats. The calorimetric experiment * I determined, by the same method, the stationary temperatures which occur during the crystallization of sulphur and of iodine after their fusion. In these two bodies the thermometer rests suddenly, and remains stationary for several minutes. I found — For the temperature of the crystallization of sulphur... 1 13°"60 For the temperature of the crystalFization of iodine ... IIS^^'SS These two temperatures are obviously identical. and on the Isomeric Modifications of Selenium, 503 was made by placing it in naphtha in the calorimeter. The results are as follow : — Chloride of lithium . 62^^-030 82gr-100 Tin 2gr-155 2gr-365 T 96°-69 97°-01 & 12°-88 13°'79 Al9' 8^-9338 ll°-6339 I did not endeavour to determine directly the specific heat of chloride of lithium from the quantity of heat acquired by the calo- rimeter charged with naphtha. 1 preferred to compare it directly with that of chloride of sodium placed under exactly the same conditions. I cast therefore melted chloride of sodium in the same mould, folded it in tinfoil, and determined its calorific ca- pacity with the calorimeter charged with the same quantity of naphtha. The following is the table of results : — Chloride of sodium . 79«^-410 69^-330 \ Tin lg'--895 l^'-'SSS T 98°-09 97°-31 & 13°-28 15°-85 A(9' 8°-7369 7°-3532 The specific heat of chloride of sodium was found to be 0*21401 in my former experiments [Ann. de Chim. et de Phys. 3rd series, vol. i. p. 154). By introducing this value into the two determi- nations, the elements of which I have just given, we can calcu- late the value in water of the calorimeter charged with naphtha ; we find thus, — ii:i/ >^/. According to experiment No. I. . . 166*03 -'f'^i'-'j II. . . 166*44 =■'•*'''• Mean .... 166*24 !!!^.|;/-i^ The two experiments on chloride of lithium, calculated with this element, give for the specific heat of this body, — According to experiment No. 1. . . 0*28096 *' 11. . . 0*28331 i;" Mean .... 0*28213 "^ The product of this specific heat by the atomic weight 524*90, usually attributed to chloride of lithium, is 148*09. Now we have found for this product, with the chlorides R^ Cl^, — Chloride of potassium .... 161*19 , . Chloride of sodium 156*97 The number obtained for chloride of lithium is obviously less ; but the difference is in that sense in which it might be presup- posed; for we may remark in general, \\i?ii for bodies of the same 504 M. Regnault on the Specific Heat of Simple Bodies, chemical composition, the product of the specific heat by the atomic weight is the lower the less the atomic weight is. Besides, for the chlorides of the formula R CI*, this product is — For chloride of calcium . . . 114'72 For chloride of barium . . . 116-44 I think it may be thence concluded, that the formula of chloride of lithium is R*C1*; and that lithium ought to be ranged among the alkaline metals, and not among the alkaline earths. Nevertheless, as the product of the specific heat by the atomic weight is decidedly less for chloride of lithium than for the chlorides of potassium and sodium, it would be advantageous to confirm this conclusion by a determination of the specific heat of the isolated metal ; this I shall not fail to do if I succeed iu procuring a sufficient quantity of it. Tellurium. I made formerly some determinations of the specific heat of tellurium, by uniting the various specimens which were to be found in the collections, and in the possession of the dealers in chemical products in Paris. I found thus the number 0*05155, which, multiplied by 806*5, the equivalent of the body, gives the number 41*57. This product is a little more than that generally found for simple bodies, the purity of which is not open to suspicion. The Austrian display presented beautiful specimens of tellu- rium, which had been prepared at the Mint of Vienna by M. Alexander Lowe. I did not allow the opportunity to escape of making new experiments on a product which I had reason to be- lieve was purer than that with which my previous experiments had been made. A notice published by M. Lowe indicates the mode of preparation which he had followed. Here is a brief abstracc of it :— The mineral is the auriplumbiferous tellurium of Offenbanya in Transylvania, which contains on an average in 100 parts, — 3 parts oi gold, 5 of tellurium, 30 of lead in the state of sul- phuret, and a quartzose gangue. This mineral, reduced to the state of coarse powder, was treated with weak hydrochloric acid to dissolve the carbonates, then attacked in a leaden vessel by concentrated sulphuric acid, which converted the galena into in- soluble sulphate of lead, and dissolved the tellurium as sulphate of oxide of tellurium. The liquid, clarified by having been allowed to stand, was transferred into another leaden vessel containing water, to which hydrochloric acid had been added to prevent the separation of oxide of tellurium. The tellurium may be separated from this solution by means of metallic zinc ; but it is then very impure, because it is depo- , , and on the Isomeric Modifications of Selenium. 505 sited along with all the metals precipitable by zinc, and mixed besides with those which the zinc itself contains. It is better to effect this precipitation by sulphurous acid gas ; the pulveru- lent tellurium is then melted in a crucible to a regulas. In order to obtain chemically pure tellurium, it is necessary to distil the tellurium precipitated by sulphurous acid in a stream of hydrogen. It is then melted in a crucible. Tellurium forms thus a regulus of a metallic lustre, which is the whiter the purer it is, and presents on its surface crystalline ramifications in the sbape of fern leaves, like those exhibited by antimony. Its specific gravity, according to M. Lowe, is 6*18. I made expeiiments, first on tellurium simply precipitated by sulphurous acid, and then on that distilled in a current of hy- drogen. Tellurium not distilled. M . . . ler^'-'S^ 167«''-34 167^-34 1678'--34 .T.^.s,.;, . 97°-57 98°-21 98°- 17 98°-06 & . . 20^00 21°-48 22°-27 20°-66 A^' . l°-5988 l°-5680 l°-5505 l°-5752 A ^... . 422^-54 422«^-54 422^-54 422^-54 a , , . 0-05205 0-05160 0*05158 0-05136 Mean 0-05160 (which is identical with that which I found in my former experiments). The product of the specific heat by the atomic weight 806*5 is 41-65. ^ .^ Distilled Tellurium, ^''* ' M . . . . 148^^-15 148^'--] 5 T .... 98°-28 98^-33 ^ . . . . 17°-88 18°-92 A^ I' :^^, . i°-3384 1°-3191 A T "^''^ . 422^^-54 422^'--54 .... 0-04748 0-04727 .'« "' Mean .... 0-04737. ' The product of this specific heat by the atomic weight is 38*20. The latter result ought to be received ; we see that it is com- prised within the limits of variation observed in very jpure simple Selemum, I formerly determined the specific heat of selenium by uniting the specimens which were then to be found in the various col- lections in Paris. The substance was in the form of small pen- cils, or of medallions of Berzelius. I found for this specific heat the number 0*08371, which, multiplied by the atomic weight 491, gives the product 41-097. The exhibition of M. Batka of Prague contained a large quan- Phil Mag. S. 4. No. 82. Suppl. Vol. 12. 2 L 506 M. Regnault on the Specific Heat of Simple Bodies, tity of selenium. I seized on this opportunity to make some new experiments, which have led me to observe many curious properties of this body. This selenium is not quite pure, it con- tains about 2 per cent, of tellurium ; but this quantity is far too small to modify the physical properties of the body, M. Salvetat obtained from an analysis the following results : — Tellurium 2*25 Sulphur traces Selenium (from the difference) . 97*75 10000 Berzelius thus describes the physical properties of selenium (second edition of the French translation, vol. ii. p. 189) : — " When selenium cools after having been distilled, it assumes a mirror-like surface, of a deep colour, verging towards a reddish- brown, and having a metallic lustre rather like polished haema- tite. The fracture is conchoidal, vitreous, having a leaden-gray colour and a metallic lustre. When allowed to cool slowly after having been melted, its surface becomes unequally granular, of a leaden-gray, and ceases to reflect. It has a fine-grained frac- ture, is rough, and the mass is extremely like a fragment of metallic cobalt. Fusion, followed by a sudden cooling, destroys this appearance, and gives to selenium the characters which I described at first When selenium is reduced to powder, it becomes of a deep red, but has a strong tendency to collect together at various points : the friction of the pestle imparts to it a polish, and turns it gray, as is the case when bismuth and antimony are powdered. In thin plates selenium is transparent, and has a deep ruby-red colour. It is softened by heat, becomes semifluid at 100 degrees, and fuses completely a few degrees above. In cooling, it remains for some time soft, and may then, like sealing-wax, be drawn into slender and very flexible threads, which, when flattened slightly, care being taken to keep them soft, show better than any other form the transparency of sele- nium. In reflected light these threads are gray, and have a metallic lustre ; viewed by daylight they are transparent, and of a ruby-red I found its specific weight to vary between 4*30 and 4-32. A slow cooling and a grained fracture have no influence on its density." According to M. Sacc {Ann. de Chim. et de Phys. 3rd series, vol. xxi. p. 120), selenium softens at 200, and melts completely at 250 degrees. When cooled, it commences to become viscous at 150 degrees ; at 200 degrees it ceases to adhere to the bulb of the thermometer ; at 155 degrees it sticks to the sides of the vessel, and solidifies completely at 1 50 degrees ; from whence we may conclude that its melting-point is 200 degrees, and that .'v and on the Isomeric Modifications of Selenium, 507 at which it solidifies 150 degrees. Nevertheless as this last can- not be fixed with precision, because selenium remains along time pasty, we must believe that the point of solidification of selenium is at 200 degrees, like its melting-point, and that it is repre- sented by the moment at which melted selenium ceases to adhere to the bulb of the thermometer which is plunged in it. The characters which these two chemists assign to selenium are not very precise. Experiments which I have made on a mass of selenium weighing 250 grms. have allowed me to fix them better*. Selenium exists, in fact, in two isomeric modifications; the vitreous modification and the metallic modification. In these two states selenium presents very distinct physical properties ; and the passage from the one to the other is attended by very curious phsenomena, the production of which is not difficult. When selenium melts to a state of perfect liquidity, and is cast in a small trench-shaped mould formed of thin sheet brass, or in a glass tube, it solidifies in the form of a black mass with a bril- liant surface, the fracture of which is exactly like that of black glass or of obsidian, and which has by no means a metallic aspect. This vitreous mass presents, when transparent, the colour of ruby-red in very fine splinters. Its dust remains gray under the pestle, and the red colour is not developeS. even by rubbing the pestle on a sheet of paper. I have always obtained selenium in this vitreous state, when, after having been melted, I have even allowed it to cool slowly. ■ But if selenium be so heated that its temperature rises very slowly, at the moment at which the thermometer indicates 96 to 97 degrees, the temperature rises suddenly with great rapidity, and in a few minutes it exceeds 200 to 230 degrees. If the sub- stance is then examined, it is seen that its physical condition has been completely changed. Its surface presents a bluish-gray colour, and it has a fresh metallic lustre. Its fracture, instead of being vitreous, is in very fine metallic grains, quite resembling that of gray cast iron. Under the hammer the mass flattens perceptibly before breaking, and the fracture has then very de- cided metallic lustre. The file likewise produces surfaces having * At the time of publishing this memoir, I was acquainted with no other researches than those I have named. Since then I have become acquainted with a memoir, read by M. Mitscherhch at the Academy of Sciences in Berlin in June 1855 ; that is at the time at which I was engaged on these experiments. A translation of this memoir is printed in the Annates de Chimie et de Physique for March 1856. It will be seen there, that M. Rit- torf had observed before me, that selenium disengages heat at the moment of its molecular transformation ; but the quantity of heat which he has given is far less than that which I have found in my experiments. Not- withstanding this, I have thought better to preserve the original text, which gives my experiments in the order in which they were made. 2 L2 608 M. Regnault on the Specific Heat of Simple Bodies, a metallic polish. In short, selenium exhibits, in this modifica- tion, the metallic character as decidedly as tellurium. Vitreous selenium may be maintained many hours at a tempera- ture of 90 degrees without undergoing the isomeric modification. Metallic selenium is a better conductor of heat than vitreous selenium. This fact is easy of demonstration when the specific heat is determined ; with vitreous selenium, the time required before the thermometer of the calorimeter attains its maximum temperature is two or three times as long as with metallic selenium. Some selenium, melted at a temperature of 300 degrees, was thrown into very cold water ; it solidified in large intertwined threads, having a very hard and vitreous fracture. The substance exhibited the same aspect as when allowed to cool in the air after fusion. Vitreous selenium does not lose its characteristic properties by being pulverized. I placed selenium, recently powdered, in a glass tube, in the axis of which was a mercurial thermometer, and arranged the tube in the oven for specific heats kept at a temperature of 100 degrees. When the thermometer had reached 97 degrees, it mounted suddenly and with great rapidity until it reached 160 degrees. The substance had changed its aspect : it had agglomerated, and had assumed the metallic appearance. Selenium, precipitated in the state of red powder from its solutions, belongs to the vitreous modification. To assure my- self of this, I dissolved 50 grms. of selenium in nitric acid ; then after having evaporated it to dryness and redissolved it in water, I precipitated the selenium by a current of sulphurous acid. The precipitate, quickly washed with water, was dried in vacuo. The pulverulent selenium was heaped up in a glass tube round the bulb of the thermometer, and the tube placed in the oven heated to 100 degrees. At about 94 degrees the thermometer assumed a very rapid upward march till it reached 150 degrees. The sub- stance was aggregated together in several metallic gray masses, and had separated from the thermometer. In consequence of the latter circumstance, the thermometer had not reached a higher point. The following are the experiments which I made on the spe- cific heat of metallic selenium : — M . . 1128^-20 112^-20 200^-90 2008'-90 T . . 98°-13 98°-33 96°-08 97°-69 ff . . 2I°-25 23°-88 20°14 18°-49 A^ . l°-9454 l°-8952 3°-4289 3°-2543 A . . 422^-54 422»^-54 422»^-54 422?r-54 c . , 007517 0-07563 0-7675 0-7709 Mean .... 0-07616. The atomic weight of selenium is 49 J . The product of the and on the Isomei'ic Modifications of Selenium. 509 mean specific heat by the atomic weight is 37*39. This product is comprised within the limits which we have found for other simple bodies. To determine the specific heat of vitreous selenium, I could not use the ordinary apparatus, because the substance undergoes its isomeric transformation at 93 degrees. I used the apparatus represented by fig. 2, the trough being filled with hot water. The water of this trough was kept stationary by means of a gas lamp j it was constantly agitated by means of the palette agi- tator m up q. Selenium recently melted was cast in the small brass vessel, fig. 1 j this vessel was placed in the middle of the tube AB, where it was maintained by the help of two silk threads attached to the upper and lower base of the vessel, in order to move it readily in lowering the thermometer. Weight of selenium . ISSs'-S 185k^-6 Weight of brass vessel . 81^-2 S\^'2 T 87°-285 77°'338 & 19°-49 17°-93 M 4°-4333 3°-7614 A 422°-54 422°-54 c 0*1036 0-1026 Mean .... 0*1031. The specific heat which we have thus found for vitreous sele- nium is much greater than that which we have obtained for metallic selenium, which only amounts to 0*07616. But this may arise from the fact that vitreous selenium is much more easily softened by heat than metallic selenium, and that at the temperature of 80 or 90 degrees it already contains a consider- able part of its latent heat of fusion. In order to decide if selenium possesses different specific heats in its two isomeric states, it was necessary to determine them at very low temperatures, at which neither of the two varieties of sele- nium undergoes a perceptible softening during the period of the temperature to which they are subjected. The selenium was previously melted in the ordinary mould ; it was then in the form of a large cylinder, having in the direction of its axis an aperture in which was placed the bulb of the mercurial thermometer em- ployed to indicate the temperature. The cylinder attached to its two silk threads was kept in the middle of the tube A B, fig. 2 ; and the vessel C D E F was filled with a cooling mixture formed of ice and crystallized chloride of calcium, which was continually agitated. The cooling of the thermometer was followed till it reached its minimum, at which it usually remained ten minutes. At this moment the calorimetric experiment was made. The following are the results obtained with vitreous selenium and with metallic selenium : — 610 M. Regnault on the Specific Heat of Simple Bodies, 1 Vitreous selenium. Metallic selenium. p . 209^-615 209^-615 209^-57 209^-57 T . . -27°-408 -20°-516 -20°-270 -15°-852 e' . 8°-441 6^-99 7°-019 6°-774 A^ r-3254 l°-0202 0°-9911 0°-8496 A . . 422^'--54 422»"54 422^^-54 422^'--54 c 007461 0-7476 0-07323 0-07570 Means . . 007468. 007446. Hence at low temperatures the two isomeric modifications of selenium have exactly the same calorific capacity. This result is similar to that which I obtained with the two isomeric modi- fications of phosphorus, ordinary phosphorus, and red phos- phorus. In two such different conditions, phosphorus showed calorific capacities which were evidently equal (Ann. de Chim. et de Phys. 3rd series, vol. xxxviii. p. 129). Vitreous arsenious acid and opake arsenious acid also exhibit no difference in their specific heats. It is nevertheless remark- able that the enormous disengagement of heat which is mani- fested at the moment at which vitreous selenium is transformed into metallic selenium, should not produce any change in the calorific capacity of this body. Selenium presents no fixed point of fusion or of solidification ; when heated, it softens gradually, and only becomes completely liquid at a temperature above 250 degrees. Every one knows that in its viscous state it may be drawn out in very fine threads. I melted a great mass of selenium in a large glass tube, and kept in the middle of the liquid a mercurial thermometer, and followed from minute to minute the cooling of the thermometer. From 260 to 40 degrees the decrease of the thermometer was perfectly regular; at no point was there remarked one of those intervals of delay, more or less prolonged, which are always observed at the moment of a change of condition in bodies which pass from the liquid to the solid state. I give here the series of temperatures observed from minute to minute : — ti . . 201-2 i;. , . 185-7 2 . . 172-35 8 . . 162-5 4 . . 153-2 5 . . 144-7 6 . . 137-45 7 . . 130-9 8 . . 124-5 15°-5 9 . . 118-7 13-35 10 . . 113-3 9-85 11 . . 108-0 9-3 12 . . 103-4 8-5 13 . . 98-5 7-25 14 . . 94-25 6-55 15 . . 90-25 6-4 16 . . 86-4 17 . . 83-0 o 5-8 5-4 5-3 4-6 4-9 4-25 4-0 3-85 3-4 *^^^'hnd on the Isomeric Modifications of Selenium. 511 In a second experiment, in order to render the cooling slower, I arranged the tube containing the melted selenium in the oven heated to 100 degrees. We have thus — / 0 1 2 3 4 .6 . 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 241-6 2298 219-3 510-2 201-7 194-4 187-6 181-6 175-95 1709 166-4 162-4 158-8 155-6 152-9 150-4 148-1 146-3 144-7 143-25 142-0 140-75 139-65 138-75 137-85 137-0 136-25 135-5 134-7 o 11-8 2^9 . . . 133-9 10-5 30 . . . 133-2 9-1 35 . . . 129-2 8-5 40 . . . 125-35 7-3 45 . . . 121-9 6-8 50 T- i^''. 119-1 6-0 55 . . . 116-8 5-65 60 . . . 115-0 5-05 65 ' .'^« r'^\ 113-40 4-5 70 . . . 112-80 4-0 75 . . . 112-60 3-6 80 . . . 112-55 3-2 85 . . . 113-0 2-7 90 . . 114-05 2-5 95 . . 115-9 2-3 100 . . 117-9 1-8 105 . . . 120-75 ■ 1-6 110 . . . 121-3 ■ 1-45 115 . . . 118-9 ' 1-25 120 . . . 116-0 ]-25 125 . . . 113-35 1-10 130 . . . 1 J 1-25 0-90 135 . . . 109-65 0-90 140 . . . 108-45 0-85 145 . . . 107-55 0-75 150 . . . 106-8 0-75 155 . . . 106-3 0-80 160 . . . 105-7 165 . . . 105-1 0-80 0-70 0-80 0-77 0-69 0-60 0-46 0-36 0-32 0-12 0-04 0-00 + 0-09 + 0-21 + 0-37 + 0-40 + 0-57 + 0-11 -0-48 0-58 0-53 0-42 0-32 0-24 018 0-15 0-10 0-12 0-12 It will be remarked that the cooling proceeded almost regu- larly until the 55th minute, when the thermometer indicated 116°-8; the rapidity of the cooling diminished then in an ano- malous manner till the 75th. From the 75th to the 80th the thermometer remained almost stationary ; it then entered on an upward march until the 110th minute, where it showed 121°-3, a temperature almost 9 degrees higher than that which was indi- cated at the 80th. It then assumed anew an evidently regular descending march. Thus the only anomaly remarked during the cooling took place at about 120 degrees; and the inverse march which the thermo- meter takes, proves that the solidification then makes rapid pro- 512 M. Regnault on the Specific Heat of Simple Bodies, gress, or that a molecular movement is effected which disengages a considerable quantity of heat. But this is not the movement which transforms vitreous selenium into metallic selenium ; for the mass of selenium taken out of the oven after the 165th minute still preserved its vitreous aspect in the fracture, even when quite cool. Experiments on the Heat disengaged by Selenium at the moment of its isomeric transformation, I wished to determine as exactly as possible the quantity of heat which selenium disengages in undergoing its isomeric trans- formation in the oven heated to 100 degrees. To this end, I melted the selenium in the mould represented in fig. 1, only replacing the cylinder ab by a very fine brass tube open at both ends. The mould thus filled with selenium was suspended, when cool, in the oven heated to 100 degrees, the bulb of the thermometer of the oven being adjusted in the central tubulure. In order to pre- vent the thermometer from being too much cooled by the current of air which must necessarily be established through this tubulure at the moment at which selenium disengages heat, a lute of bread paste was spread on the inferior orifice. The following is the succession of temperatures observed : — 4-63 9-3 23-9 530 1 0 . . . 72-83 10 . . . 79-45 20 . . . 84-35 30 . . 88-15 35 . . 89-8 40 . . 91-3 45 . . 92-85 50 . . 94-6 55 . . 96-5 56 . . 96-95 57 . . 97-5 58 . . . 980 59 . . . 98-65 60 . . . 99-3 61 . . . 10005 62 . . . 100-8 63 . . . 101-7 64 . . . 102-9 65 . . . 104-1 66 . . . 105-7 67 . . . 107-8 68 . . . 110-67 0-66 69' . . 115-3 0-49 70 . . 124-6 0-38 71 . . 148-5^ 0-33 71i . . 161-4 0-30 7l| . . 177-2 0-30 71f . . . 193-0 0-35 72 . . 201-5^ 0-38 72^ . . . 210-1 0-45 72-^ . . . 212-5 0-55 72| . . . 213-3 0-50 73 . . . 214-0^ 0-65 73^ . . . 214-2^ 0-65 7H . . 214-2 0-75 73| . . . 214-1 0-75 74 . . . 213-9 0-90 75 . . . 212-0 1-20 76 . . . 2080 1-20 77 . . . . 200-8 1-60 78 . . . 192-6 2-10 79 . . . 185-2 2-87 80 . . 179-1 81 . . . 173-4 13-5 o -O-l -1-9 -4-0 7-2 8-2 7-4 6-1 5-7 8^ . . . 168-6 83 . . . 164-5 84 . . . 160-5 85 . . 157-0 86 . . 153-25 87 . . . 150-6 88 . . . 147-7 89 . . 145-1 90 . . . 142-6 91 . . . 140-1 92 . . . 137-9 1-8 93 . . . 135-8 4-1 94 . , . 133-8 4-0 95 . . 131-9 3-5 96 . , . 130-2 3-75 97 . . 128-25 2-65 98 . . 127-0 2-9 99 . . . 125-6 2-6 100 . . . 124-2 2-5 105 . . . 118-35 2-5 110 . . . 113-95 2-2 115 . . . 110-6 120 . . . 108-0 and on the Isomeric Modifications of Selenium, 513 o 2-1 2-0 1-9 1-7 1-95 1-25 1-4 1-4 1-17 0-88 0-67 0-52 It is seen from this table that up to 93 degrees the ther- mometer rose constantly with a decreasing rapidity, as ought to be the case, for it was thus approximating to the surrounding temperature, which was 100 degrees; but from 94 degrees the ascending march of the thermometer was accelerated, at first feebly, but afterwards with rapidity. At the 61st minute the thermometer exceeded the surrounding medium. From the 71st to the 72nd minute it increased 53 degrees ; its ascending march was then somewhat slower, and it was at the 73rd minute that it reached its maximum of 214 degrees. From thence the thermometer assumed a descending march, which was at first accelerated up to the 78th minute, because the substance still emitted heat which partially compensated for the eflect of the cooling causes : at last the rapidity of the cooling abated, the excess of temperature becoming less and less. It is besides evident that this superelevation of temperature of more than 114 degrees, is far less than that which would have taken place if the disengagement of heat, in consequence of the molecular transformation, instead of being successive, had been instan- taneous, and if the substance had not been obliged to divide its heat with foreign bodies, and to lose it by radiation. Thus in the experiment before us, the weight of selenium is 200 grammes. Assuming that its specific heat is 0*0769, as we have found it between 15 and 90 degrees, this selenium corre- sponds, in its calorific capacity, to 15^'-42 of water. The brass vessel which contains it weighs 81e''-15, and corresponds to 7^-70 of water. We may assume that this case is at the same tempe- rature as the selenium which it contains. In this case if x represents the temperature to which selenium would have been raised had it been alone, we should have 15-42 .a?= (15-42 + 7-70) . 114, whence ^=170°-9. Thus the temperature would have been raised 171 degrees if the 514 M. Regnault on the Specific Heat of Simple Bodies, selenium had been alone ; and we still neglect the heat which our complex system has lost by radiation in the oven from the 61st minute, at which it began to exceed the temperature of the oven, to the 73rd minute, at which it reached its maximum tem- perature. It cannot be admitted that at the moment at which the ther- mometer indicates its maximum temperature, the molecular transformation is complete, and that the calorific source ceases to act ; for from the 73rd to the 78th minute the rapidity of the cooling increased, which proves that a disengagement of heat constantly decreasing was opposed to the normal cooling of the system. If we assume that the heating cause had ceased at the 78th minute, and that from this time the cooling took place proportionally to the excess of the temperature of the system above the surrounding medium, we could then calculate approx- imatively the temperature which the system has lost by radiation from the 61st minute to the 73rd. The loss of temperature during each minute from the 72nd to the 78th would have been at least 8°*2 if the body had not disengaged any heat. But the variation of temperature was — 72 to 73 + 13-5 73 to 74 - 01 74 to 75 - 1-9 75 to 76 - 40 76 to 77 - 7-2 77 to 78 - 8-2 Comparing these coolings with that of 8°'2, which would have been the normal cooling, we see that there ought to have been disengaged — From 72' to 73' a quantity of heat which would have raised the thermometer, if it had not been compensated for by ^ the cooling 8*2 From 73' to 74' a quantity which would have raised the thermometer to From 74' to 75' „ From 75' to 76' From 76^ to 77' From 77' to 78' „ „ Number of degrees by which the temperature would have been increased up to the 78th minute, if there had been no cooling by radiation 27*8 We may now assume, supposing that the loss of heat by radiation was, during the ascending period of the thermometer, equal to that observed during the descending period, for equal 81 6-3 4-2 10 0-0 and on the Isomeric Modifications of Selenium. 515 excesses of temperature of the system above the surrounding medium:— Mean temperature. Cooling. .., ; , ) '"'^ From 71 to 72 V r^ . 175-5 5*7 70 to 71 . . . 136-6 2-1 69 to 70 . . . 120-0 1-0 , ■^''■- ■' 68 to 69 . . . 113-0 0-7 KOr. ;. ^- g7 to 68 . . . 109-2 0-5 66 to 67 .. . 106-8 0-34- 65 to 66 . . . 105-0 0-25 64 to 65 . . . 103-5 0-17 63 to 64 . . . 102-3 0-12 62 to 63 . . . 101-3 0-07 61 to 62 . . . 100-5 0-02. M*) 10;97 Thus the system would have lost by radiation, during the ascending period of the thermometer, 10°-97. By these two causes, the total elevation of the thermometer was too little by 27°-8 + 10°-97, or by 38°-77. Hence, if the losses by radiation had not existed, the ther- mometer would have been raised to 214 + 38-77, that is to 253 degrees ; and if the selenium had not been enclosed in an en- velope of brass, which divided with it the heat emitted, the elevation of temperature experienced above 100 degrees would have been oo, given by the formula 15-42.2?=23-12 . 153, whence ^=229°. According to this calculation, which is only approximative, the temperature of dry selenium would have been raised from 98 to 329 degrees in consequence of the molecular transformation, if all the heat disengaged had been effective. I sought to determine, in another manner, the quantity of heat which selenium disengages during its molecular transform- ation, and made the following experiment : — The small vessel of brass containing the selenium recently melted was placed in the oven for specific heats, exactly as in the preceding experiment. When the thermometer of the oven began to rise above 100 degrees, in consequence of the molecular transformation, the calorimeter for specific heats was arranged, and at the moment at which the thermometer of the oven exhi- bited the maximum, the small vessel was rapidly lowered into * As the cooling was not observed in the second period under 1 08 de- grees, the last partial coolings were calculated by means of the formula A^= A^l ; 6 representing the excess of the temperature above 100 degrees. The constant was calculated according to the observation (69 to 70), that is, 1*00 was assumed to be equal to A 20, whence A=^V' ' ' 516 M. Regnault on the Specific Heat of Simple Bodies, the calorimeter. In this manner the total quantity of heat could be determined which the system possessed at the moment at which the thermometer of the oven indicated its maximum. The following are the data of the calorimetrie experiment : — Weight of selenium 200^*45 Weight of brass vessel Sl^^'lS Value in Maximum reached by the therrao- water 7^'"*62. meter of the oven 200°-5 Final temperature of the calorimeter 24°*65 Elevation of temperature after cor- rection 9°115 A 422P--54 The quantity of heat acquired by the calorimeter, and which is equal to that which the system gave up in setting itself in equi- librium with it, that is, in decreasing to 24°* 65, is 422-54 . 9°-115 = 3851-5 units of heat. This quantity of heat is composed of two parts : — 1. Of that which would have been imparted to it by the oven, if the selenium had not spontaneously disengaged heat. 2. Of the quantity of heat which the molecular transform- ation of the selenium liberated. It is the latter quantity of heat which it is important to know ; we shall obtain it by subtracting from the total quantity of heat given by the experiment, that which vitreous selenium gives up when it cools from 98 degrees (the maximum to which bodies usually reach in our oven) to 24'65. But we have found that the specific heat of vitreous selenium is 0'1036 between 19°'5 and 87°'3 ; if we assume that it is the same between 24°*65 and 98°*0, the augmentation which tlie specific heat may undergo from 87 to 98 degrees being attributable to the molecular trans- formation, selenium in falling from 98 to 24-65 would abandon a quantity of heat represented by 200-45 X 0-1036 X 73-35 = 1523-2 The envelope of brass in cooling the same \ __ 558*9 number of degrees 7*62 x 73*35 . ./ ~2082-l We obtain therefore for the number of units of heat disengaged by the molecular transformation, 3851-5 — 2082-1 = 1769-4, which have been produced by 200^^-45 of selenium. This number would heat 200^-45 of selenium, supposing it to be the metallic modification by ^^ .p^,^,^^^, or by 116-00, which differs little from the 114-2 which we have observed directly on the thermometer of the oven at the moment at which it indi- cated the maximum. But like the last, it must undergo im- and on the Isomeric Modifications of Selenium. 517 portant corrections; for during all the time which the ther- mometer has taken to rise from 93 degrees to its maximum, the system has lost by radiation a considerable portion of the heat which would become free in consequence of the molecular trans- formation. To be able to calculate this loss of heat, I transcribe the table of observations of temperatures made before the time at which the selenium was lowered into the calorimeter. Variation in minutes. 1 0 . . . 72-83 5 . . . 7600 10 . . . 78-6 15 . , . 81-0 m . . . 82-9 25 . , . 84-65 30 . , . 86-3 35 . , . 87-7 40 . , . 88-95 45 . . 90-1 50 . . 91-2 55 . . 92-4 56 . . 92-55 57 . , . 92-8 58 . . . 93-0 59 . . 93-2 60 . . 93-45 61 . . 93-8 62 . . 94-1 63 . . 94-4 64 . . . 94-6 65 . . . 94-8 m . . . 95-15 67 . . . 95-45 68 . . . 95-75 0-63 0-52 0-48 0-35 0-35 0-33 0-28 0-25 0-23 0-22 0-24 0-15 0-25 0-20 0-20 0-25 0-35 0-30 0-30 0-20 0-20 0-35 0-30 0-30 Variation in minutes. 69 . . . 961 0-35 70 . . . 96-45 71 . . . 96-7 72 . , , 97-2 73 ^^-rr . 97-7 74 . . . 98-05 75 . . . 98-5 76 . . . 99-1 77 . . . 99-7 78 . . . 100-3 79 . . . 101-0 80 . . . 101-95 81 . . . 103-1 82 . . . 104-15 83 . . . 105-7 84 . . . 107-8 85 . . . 110-9 86 . . . 116-5 87 . . . 127-6 88 . . . 147-6 89 . . . 187-0 90 . . . 200-4 As the thermometer now rose only slowly, the system was lowered ; it was placed in the calorimeter at the 92nd minute. VTe see here again that the rapidity of the heating goes on diminishing up to the 58th minute, when the thermometer shows 93 degrees; from the 58th to the 65th minute, this rapidity remains perceptibly constant, assuming then an ascending march. We may therefore suppose then that the molecular transform- ation commences at 93 degrees, and that selenium, during its passage from 93 to 98 degrees, is only heated by the radiation of the enclosure. If it be admitted that the molecular transform- ation has not commenced from 76 to 93 degrees, we might, as- suming Newton's law, calculate from the numbers of this period the heat which the enclosure has communicated to the system, 0-35 0-25 0-50 0-50 0-55 0-45 0-60 0-60 0-60 0-70 0-95 1-15 105 1-55 2-10 3-10 5-60 11-10 20-00 39-40 13-4 518 M. Regnault on the Specific Heat of Simple Bodies. We may put AO=^A0, 6 representing the excess of tempe- rature of the enclosure, and A^ the increase of temperature which the system obtains in 1 minute. To calculate the con- stant A, we might put, according to the observation from 5 to 10 minutes, — 0-48 = A(98 - 77-3) = A(2007), whence A=g^=0-0233. We may calculate from this formula the elevation of tempera- ture which the enclosure has given in each minute. 4 iiin •m^jm From the 78th minute, when the system exceeds 100 degrees, fto the 92nd minute, when it is plunged into the water of the calorimeter, it loses necessarily a certain quantity of heat, in consequence of its excess of temperature above the enclosure, which does not exceed 100 degrees. We proceed to estimate this loss of temperature from the observations of cooling, which followed the molecular transformation in the experiment of page 513. We shall thus obtain ^ temperature. Cooling. \m From 78 to 79 . . 100-65 0-02 79 to 80 . . 101-47 0-07 80 to 81 . . 102-50 0-12 81 to 82 . . 103-6 .0-17 82 to 83 . . 104-9 0-25 83 to 84 . . 106-8 0-34 84 to 85 . . 109-4 0-50 85 to 86 . . 113-7 0-70 86 to 87 . . 122-0 1-10 87 to 88 . . 137-6 2-20 88 to 89 . . 167-3 4-20 89 to 90 . . 193-7 8-00 90 to 91 . . . 200-0 8-40 91 to 92 . . 200-0 8-40 TAl .n: 34-47 Thus the system ought to have lost by radiation about 34°-5 of temperature; and the final temperature would have risen as much if this loss had not taken place. But we observe that 34°-47 of temperature lost by the system corresponds to a num- l^r of units of heat represented by (200-45 X 0-1036 + 7-62)34-47 = 978-6, > * which, added to 3851-5, which the calorimeter has given directly, furnishes a total of 4830-1. If we subtract the 2082-1 units of heat, which we may suppose On an Improved Construction of Ruhmkorff's Induction Coil, 519 to have been communicated to the system by the enclosure, we obtain 2748 units of heat, which would raise 200«f'"*45 of metallic selenium from 0 degree to the temperature •;. or(J iloirivr O74Q -- * rtf!tn '^^^^ -180°-15. .n 200-45-0-0761 This elevation of temperature is less than that which we have found by the first mode of calculation ; but I shall show that it is necessarily too little, for in the preceding calculation we have assumed by inference, that at the moment at which the thermo- meter marked the maximum in the oven, and at which it was plunged into the calorimeter, the molecular transformation was complete. But we know from the first experiment, that even then the substance still continued to disengage heat, and we allowed for that in our first calculation. In recapitulating, I think we may conclude from these expe- riments that vitreous selenium disengages during its transform- ation into metallic selenium a quantity of heat, which would elevate the latter by more than 200 degrees. I formerly found [Ann. de Ch. et de Phys. 3rd series, vol. i. p. 205) an analogous disengagement of heat during the trans- formation of soft sulphur into ordinary sulphur, but the quan- tity of heat liberated was much less, for it only raised the tem- perature of the substance 12 to 14 degrees. It is true that the sulphur is then brought almost to its fusing-point, so that part of the heat disengaged may be disguised by partial fusion. LXVI. On an Improved Construction of Ruhmkorfi'^s Induction Coil. By C. A. Bentley, Esq. To the Editors of the Philosophical Magazine and Journal. , 128 Sloane Street, Chelsea, Gentlemen, Dee. 3, 1856. AS many of your readers may be interested in the production of induction coils, I take the liberty of sending a short, but, I trust, concise description of one I have constructed ; and as it is the result of two years' experience, it will no doubt prove valuable to those interested in electro-magnetic induction. The instrument referred to gives an induction spark 2 inches long in air of ordinary density when excited by four or five cells of Grove's battery; and the quantity of static electricity is so great, that it will charge a quart Leyden jar two hundred times per second, the discharge taking place through an interval of 1:| inch. The thermal phsenomena are also very striking ; for when the secondary wires are separated about three-quarters of an inch, 520 On an Improved Construction of Ruhmkorff^s Induction Coil, an arc of flame passes the interval, and fuses electrodes present- ing twenty times the sectional area of the wire from which the current is produced : the flame can at the same time be acted upon by a permanent magnet in the same manner as the voltaip arc. This heating power appears to depend, not upon the quan- tity of electricity passing, but upon the resistance it can over- come ; consequently the thermal eflfects disappear in vacuo, to be reproduced upon the gradual admission of air or other resisting media. My induction apparatus differs from Ruhmkorff^s in three important parts of its structure: flrst, in the method of insu- lation; secondly, in the contact breaker; and thirdly, in the formation of the condenser. Ruhmkorff, as your readers are aware, insulated his secondary wire with shell-lac; but as this substance, though an excellent insulator, is liable to crack, I have adopted gutta-percha tissue for the insulation of my wire; and I apply it in the form of ribbon an inch wide, which I obtain by cutting slices from a firm roll of that substance; four or five layers are necessary between each layer of wire, as the current from a single layer is sufficiently intense to strike through one- tenih of an inch of air. The contact breaker is a most important part of the apparatus, for without the one I have contrived I do not obtain nearly so. great a quantity of static electricity. It consists of a strong steel spring, fastened firmly at one end, and having the platinum contact piece in the centre, behind which is a piece of iron to be^ attracted by the iron core; at the other end of the spring is a screw, by which I can force the two contact pieces together with a force of one ounce^to ten pounds; the steel spring therefore^ vibrates from its centre, and it is only when the whole of the battery current has traversed the primary wire that the iron core has sufficient power to draw the two contact pieces asunder. It may be interesting to state, that the condenser has not the slight- est effect on the guaaliiy of electric force developed in the second- ary wire, but increases the intensity to an enormous extent; and as it is better to have it as large as possible, I have formed mine of 120 sheets of tinfoil, 6x12, placed between double that num- ber of varnished sheets of paper, the alternate sheets of foil being brought out and soldered to appropriate binding-screws. The length of secondary wire in the coil described is 2 miles, and its gauge No. 35. The primary helix is formed of 30 yards of No. 14 wire, and is wound on an iron wire core 9 inches long and If inch diameter, in which is placed as an axis an iron rod to support the coil, which I place in a box constructed for that purpose. Such, then, is the very slight description I have to offer of an Prof. Challis on the Transmutation of Rays of Light, 531 instrument which produces a spark five times the length of those produced by any of Ruhmkorff^s arrangements ; but as he was certainly the originator of these instruments, and therefore de- serves nearly all the credit, I hope that mine and those pro- duced by others will still be called RuhmkorflP^s coils. Yours obediently, C. A. Bentley. LXVII. On the Transmutation of Rays of Light ; with a Reply to the ^' Remarks " of Professor Stokes in the December Number. By Professor Challis*. BEFORE replying to the Remarks which Professor Stokes has made on certain parts of my communication in the November Nuriiber, entitled " A Theory of the Composition of Colours/^ I am desirous of entering upon some theoretical consi- derations by which the views there advanced, and the arguments by which 1 support them, will be better understood. I commence with saying, that, consistently with all I have hitherto written on the undulatory theory of light, I shall suppose the sether to be a continuous medium so constituted that variations of its pressure are proportional to variations of its density, and shall admit for the explanation of phsenomena of light only such properties of the me- dium as may be deduced from this constitution by calculating on hydrodynamical principles. Also for the present purpose it will suffice merely to enunciate those deductions which bear upon the phsenomena of light with which this communication is imme- diately concerned, and to mention that proofs of them, which I am prepared to maintain, have been given in articles contributed at various times to this Journal. When a medium, constituted as above supposed, suffers a con- tinuous vibratory disturbance by the motions of the atoms of any extraneous substance, or when a state of continuous vibratory motion of the sether suffers disturbance by the passive action of atoms at rest, the consequences, as deduced by the analysis, are the following : — (1) The state of the disturbed sether at each instant, both as to velocity and condensation, results from the composition of an indefinite number of separate motions, such that each has an axis of symmetry parallel and transverse to which vibrations take place according to a law expressed by the function msm— - (x—at-i-c). * Communicated by the Author. Phil. Mag, S. 4. No. 82. Suppl Vol. 12. 2 M 522 Prof. Challis on the Transmutation of Rays of Light, (2) The compound character of the motion, and the form of the above function, are independent of the nature of the dis- turbance. (3) The number of the separate motions, the directions of their axes, and the values of the arbitrary constants w, \, and c, must be such as to satisfy the circumstances of the disturbance, and will be different for different kinds of disturbance. .: ^\C\^2\\ (4) When the sether in motion suffers disturbance by encoun- tering atoms actually or relatively at rest, and the original motion is a simple series of vibrations of the kind above described, or is compounded of several such motions with parallel axes and dif- ferent values of w, \ and c, the result of the disturbance may in either case consist of an indefinite number of separate motions having their axes in various directions, and having values of m, \ and c altogether different from the values of these quantities in the original motion. This general result includes the parti- cular cases in which the axes of the new vibrations are parallel to the common direction of those of the original motions, or de- ^viate from it by small angular inclinations. (5) The limits of the values of X in the disturbed state of the medium depend on the circumstances of the disturbance; and when the disturbance is of the kind mentioned in (4), are not necessarily the same as the limits of the values of \ in the ori- ginal motions. (6) The motion in each of the components of the disturbed motion is symmetrical about an axis, whatever be the motions of the disturbmg atoms, or the original motions relatively disturbed by the atoms. These properties of a continuous elastic fluid, being assumed to correspond to phsenomena of light, give the following theo- retical results : — By (1) and (2) every portion of light consists of rays, and the general character of the rays is independent of the circumstances under which the light is generated. ^! By (3) the whole quantity of the light, the directions of its propagation, and the intensities, refrangibilities, and phases of the component rays, are dependent on the particular circum- stances of the disturbance. When the circumstances of the disturbance are as supposed in (4) (which is the case appropriate to the present inquiry), light may produce new light, which may differ from the original light in intensity, colour, composition, and direction of propaga- tion. This effect I have called a " Transmutation of Rays ;" and I beg it may be understood, that in making use of these terms I mean only to express a result deduced from the mathematical Prof. Challis on the Transmutation of Rays of Light. 523 As the directions of propagation of the transmuted rays depend only on the circumstances of the disturbance, the new rays might, consistently with this theory, be propagated only in directions coinciding nearly with the direction of propagation of the original rays. By (5) it might happen, consistently with the theory, that light is not produced under the circumstances supposed in (4), the values of \ for the transmuted rays not falling within the limits proper for visibility ; or, that rays for which the values of X do not fall within the limits of visibility give rise to visible rays. By (6), the transverse motion being always alike in all direc- tions from an axis, the transmuted light can in no case be polar- ized light. I proceed now to the consideration of the '' Remarks.'^ And in the first place, I am quite ready to admit that Professor Stokes is entitled, by his experimental acquaintance with the class of phsenomena under consideration, to set me right in regard to matters of fact, and the terms which appropriately describe them. His remarks have led me to see that I have improperly used the word " epipolic " to signify true internal dispersion in general, of which the phsenomenon that the word strictly applies to is only a particular phase. This misapplication of the term, although the sense in which I use it is explained on its first in- troduction, has not without reason caused some misapprehen- sion of my views. I am not, however, prepared to admit that I have " confused three distinct things,'^ not being able to perceive good reasons for the distinctions that Professor Stokes makes. In the very complete discussion of the various phsenomena which is contained in his paper on Change of Refrangibility (Phil. Trans. 1852, part 2. p. 463), I could not make out a distinction between the second and third kinds of phsenomena, both being apparently referred to true internal dispersion and change of refrangibility ; and with respect to the first, 1 had reasons, partly theoretical, for referring them to the same head. Change of refrangibility appeared to me the single appropriate idea which embraces all the phsenomena, so far as they are not attributable to known causes. I am aware that several experimenters have referred the first kind to known causes and to " subjective illu- sion.^' But Sir David Brewster does not admit this explanation, and I did not consider myself at liberty to disregard the opinion on this point of so able and experienced an experimenter. It must also be remembered, that the experimenters referred to had no suspicion of a change of refrangibility, this idea having been first admitted by Professor Stokes after his discovery that invi- sible rays might give rise to visible. The absence of any such conception is particularly apparent in the experiments of M. 2 M 2 6i24^^ Prof. Challis on the TVansmutation of Bays of Light, Helmholtz (published in Poggendorff's Annalen in 1852), which are proper for decomposing hglit that might have such an origin, but not proper for discovering that origin. In further explana- tion of these views, it should be stated that I am led by the theory explained at the beginning of this communication to admit that the new light due to change of refrangibility is not necessarily dispersed in all directions, but may in certain sub- stances deviate but little from the direction of the original light. This, however, is a point which experiment must decide. Jo The remark that the phsenomenon of change of refrangibility *^ may be set aside in speculating on the sensation of colour," is altogether irrelevant, the question being not about sensation of colour, but as to whether or not a ray of prismatic purity is com- pounded. From the fact of change of refrangibility by absorbing media, it might fairly be argued that light admits of a resolution different from that effected by the prism. It was therefore an important preliminary to my theory of the composition of colours to establish that this is not the case. Professor Stokes has said that "were a change of colour made out, it would be a point of the utmost importance to consider in reference to any physical theory of light." This importance equally attaches itself to a change of refrangibility, and on this account I endeavoured to explain the fact by reference to the mathematical theory which is stated more at length at the beginning of the present communi- cation. Professor Stokes has shown that he felt the necessity of some theory by speculating largely on the subject in arts. 226 to 236 of his paper, but has not attempted to give a mathematical theory. The other remarks relate chiefly to composition of colours. Professor Stokes does not admit that a composition of blue and yellow lights can produce green. Referring to an experiment I made with a blue ribbon and a yellow ribbon put in contact and held to the light, which appeared to give a green colour, he says, '^the superposition of two coloured glasses or ribbons by no means gives the effect of the mixture of the two colours;" and then adduces an argument which does not apply to the ribbons, because light from one is received through the interstices of the other. He makes no allusion to an experiment by Sir John Herschel on which I chiefly relied, in which blue and yellow lines are drawn on paper close together and alternating with each other. Unquestionably in this instance the eye receives a mix- ture of blue and yellow lights. I have repeated the experiment and find the result to be green. The green is remarkably con- trasted with blue, if the blue lines be extended beyond the yellow. I did not question the fact that " the production of white by a mixture of blue and yellow is by no means confined to Prof. Challis on the Transmutation of Rays of Light. 525 prismatic blue and yellow, but takes place just as well with the colours of bodies/^ seeing that at the end of the paragraph marked (9) I endeavour, with whatever success, to account for it theo- retically. As little did I question that '^ in making experiments with the spectrum, in order to neutralize, when possible, a prismatic colour of given intensity by another prismatic colour, so as to produce white, two points must be attended to : the place of the second colour in the spectrum must be properly chosen, and the inten- sity of the light properly regulated ; •'■' for I thought I had ex- plained theoretically in the paragraph marked (4), why one of these points must be attended to, and in the paragraph marked (7) why the other must be attended to. There is also another fact which my theory embraces, viz. that when two given colours are mixed, the gradations of colour obtained by varying the pro- portions depend on the source of the light. Thus with sunlight the gradations of a mixture of yellow and blue pass from yellow through diluted yellow, white, and diluted blue, to blue ; whereas in a mixture of yellow and blue from certain sources, the grada- tions pass through green. It is necessary that I should now explain in what sense I used the terms *' terrestrial light.^^ The most general composition of a parcel of light may be expressed analytically as follows : — i.ii. 27r 27r "^"^^ 'Um >Y = 7n sin—- (x — at + c) -\- m' sin -^ {a^ — at -\- c') + &c,y5tB;t*T '*o^j; ^ ^ ^ong^ t&e number of terms being unlimited, and the values of m^ ni^, &c., and of A,, X', &c., either all different, or some equal. The effect of ordinary reflexion and refraction is to alter all the coeffi- cients m, m', &c. in a given ratio, and sometimes the phases of the rays, the separate rays retaining their individuality, and the character of the light being in no respect altered. The effect of absorption proper is to alter by quantities depending on the absorbing substance the coefficients m, m', &c., reducing some of them to zero while the rays retain their individuality, and to change the phases of the rays, but not to change the vahies of X, X', &c. The effect of true internal dispersion is to alter X, X', &c., and completely to change the character of the light. The last effect may sometimes and in some degree accompany the second. Light modified in the second of these ways I have called terrestrial light, because the modification takes place by the action of the constituent atoms of some terrestrial substance on sunlight. The term may, however, be extended to other light which is not direct sunlight, or sunlight of the first kind. This statement will explain in what sense I considered the coloured light of substances (which I ascribe to absorption) to be " new '..■: ■.■^■\i.\iioo ^fi&^m on '^a p4 w 526 Prof. Magnus on the Allotropic Condiiom of Sulphur, light.'' It is on the change of the values of m, m', &c. that the difference between the composition of prismatic colours and the composition of the colours of substances depends. I willingly admit, on Professor Stokes's authority, that " ab- sorption is not always, nor even generally, accompanied by epi- polic dispersion." Speaking of " certain absorbing media," I said that " absorption generates in greater or less degree epipolic dispersion," meaning, as already explained, internal dispersion. I quite concur in referring the natural colours of bodies to absorption. This doctrine I taught long since in optical lectures, and never doubted of its truth. From the foregoing consideration of Prof. Stokes's Remarks, it appears that there is no material difference in our views except on two points : the real character of the phsenomenon presented by certain absorbing substances which has been ascribed to subject- ive illusion, and the question of fact whether blue and yellow lights in any instance produce a green compound. Cambridge Observatory, December 12, 1856. LXVIII. On the Allotropic Conditions of Sulphur, By G. Magnus *. MITSCHERLICH has recently shown f that sulphur com- bined with a fat or an oil, dissolves in sulphur and imparts to it an extremely strong colour, so much so that one part of tallow heated with 3000 parts of sulphur furnishes an intensely red mass. I have repeated these experiments, and have con- vinced myself that not only the fats, but also a great number of other substances produce a similar action. Besides the fats, the following substances are particularly distinguished for the strong colour they produce: — stearic acidj paraffine, wax, spermaceti^ fossil wax (ozocerite) ; colophony, mastic, gutta percha, and caoutchouc produce a somewhat less strong colour ; and amber, sugar, starch, and cotton colour still weaker, but even then intensely. The latter only exercise a colouring action when brought into the sulphur heated to 300° C. and well mixed with it. Some of these substances may have still contained small quantities of fat ; of many of them this can scarcely be main- tained, but it may be thought that they have acquired a colouring action from having been touched with greasy fingers. In order to meet any objection of this kind, I placed some crystals of white sugar-candy in distilled water, and when the * Translated from PogcendoHTs Annalen, vol. xcix. p. 145. t Journal fur Praktische Chemie, vol. Ixvii. p. 369. Prof, Magnus on the Allotropic Conditions of Sulphur, 527 external layer was dissolved, dried them in porous paper, and without touching them with the fingers, introduced them into the hot sulphur which had been purified by two distillations. Even this coloured the sulphur. The colour which is imparted to sulphur by sugar, starch, cotton, &c., is indeed more brown than red, but its solution in bisulphide of carbon shows always the pure red colour. From this it is clear, that other than fatty substances colour sulphur, and the red colour of sulphur cannot serve as an evidence of the presence of a fat. It appears that very various substances so decompose at a higher temperature, that a certain constituent of them unites with the sulphur and forms with it the strongly colouring body. I have, however, not yet been able to ejQPect its separation from the excess of sulphur. The colouring property of this compound is so great, that not only sulphur which has been touched by the hands is coloured red by the fat which is thereby imparted to it, when heated to 300° C, but also sulphur which has been several times heated to 300° C, and each time poured out, assumes a reddish colour even when it has not been touched by the hands. This probably arises from small particles of dust which during the cooling settle upon it from the air, and enter into the colouring compound at each new melting. By these experiments I have been led to several facts con- cerning the allotropic conditions of sulphur. In the establish- ment of these I had the assistance of M. R. Weber, and to such an extent, that the research may be considered as executed by us in common. If common yellow sulphur be heated to 350° C, or to that temperature at which, after it has been viscid, it becomes fluid again, and if it be then allowed to cool slowly, it is, as is well known, completely or almost completely soluble in bisulphide of carbon. In order that it may be so, it is good to shake it repeatedly during the cooling, for otherwise that portion on the side of the vessel would cool too rapidly and thereby become insoluble in bisulphide of carbon. For if sulphur, which has been heated to 300° C, be allowed to cool too rapidly, it is no longer completely soluble in bisul- phide of carbon, but leaves, according as the cooling has been more or less rapid, a greater or lesser part undissolved. If the cooling be effected in such a manner that the sulphur be poured in a thin stream into cold water, the well-known white sulphur is obtained. This leaves undissolved, as will be seen from the following Table, from something over thirty to something over forty per cent, of its weight *. * M. Ch. Saint-Claire Deville states in his treatise Des modifications du 528 Prof. Magnus on the AUotropic Conditions of Sidphur, But the soluble part of soft sulphur contains still two different modifications of sulphur. For if a part of the bisulphide of carbon be distilled off from the solution, and the liquid be then allowed to cool, octahedral sulphur crystallizes out. If this be removed from the liquid and a fresh quantity of bisulphide of carbon be distilled off, so that on cooling some more octahedral sulphur is obtained, there remains, after repeating this operation, a tough mass which can be drawn out in threads. This still contains sulphur. If left to itself the bisulphide of carbon evaporates, and the sulphur separates as a crummy mass. This sulphur was manifestly still more soluble in bisulphide of car- bon than octahedral sulphur, for it separated after the latter. Notwithstanding this, after it has been once separated from the bisulphide of carbon, it does not again dissolve in it. If the crummy mass, as is sometimes the case, still contains small crystals of sulphur, these are dissolved, but the crummy sulphur,, is insoluble even in boiling bisulphide of carbon. If the soft sulphur, from which the crummy mass has been prepared, has been only once heated to 300° C, and if all con- tact with the fingers has been avoided, the crummy mass has a pure yellow colour. If, on the contrary, the soft sulphur has been several times melted and poured out, it appears more or less red-coloured. On this account I have hitherto designated it as red sulphur. Since it is soluble in bisulphide of carbon, but once separated from this solution does not again dissolve in it, it is distinguished as well from the soluble as from the inso- luble sulphur, and must be regarded as a particular allotropic modification. It comports itself in this respect just like silica, which I have also already* noticed with regard to red sulphur. With the exception of the colour, which, as was mentioned, may vary, it exhibits all the properties which have been ascribed to it. If it is melted and slowly cooled, it changes into common soluble sulphur. The remarkable comportment of the quickly cooled soft sul- phur appears to depend on the presence of this modification ; for if soft sulphur be allowed to lay so long that it has become hard and brittle, for which, as is known, several days arc neces- sary, it contains much less of this modification than in the fresh, soft condition, as is seen on comparison of the columns 3 and 7 of the following Tables, in which the experiments have been collected. soufre sous Vinfluence de la chaleur et des dissolvants {Ann. de Chim, 3 ser. xlvii. 99), that he found 35 per cent, in it. * Phil. Mag. ser. 4. vol. viii. p. 182. Prof. Magnus on the Allotropic Conditions of Sulphur. 529 Soft Sulphur lextracted with Bisulphide ,jpf,Cai^bpn, immpdJAt^lv ad^uini Juo.t)xi!b. o^cooli^G- .-ibsdiitoo Joo3o) b3f/oik fiodiiii) «idT -ISO lo Qili mo GHimmes. i -^ 71 sbiiiqliSS'- rter 'Gaye Insoluble sixlphur. 33-82 per cent. 38-49 ... 42-00 ... 3604 ... 46-07 ... Crummy sulphur. 5-32 per cent, 2-48 ... i^'^ 507 3-57 3-91 2-79 Uidqlua anicJiio'i / *IJjdqIj78 k.di iv7)ol4 The same Sulphtif pei*fectly hardfeii^d 1^8-tiin "^^ 1 11 ill u I-; Grammes* ^.,. After days. Insoluble sulphur. Gave \- Crummy sulphur. 7\ , ;liL> 4 ■ ■ 7 " 4 36-36 per cent. 3700 ... 3607 ... 39-70 ... 0-84 per cent. 1-57 '4x)^^i 0-64 0-77 0-69 !!'byi .'^! Whether in the change of the soft sulphur into the hard the crummy sulphur contained in it is changed into insoluble or soluble sulphur, I must for the present leave undecided. It might indeed be believed that this could be settled by comparing the quantity of insoluble sulphur contained in the soft, with the quantity of the same present after it has become hard. But, as is seen from the present experiments, such determinations cannot be executed with sufficient accuracy; partly because the inso- luble sulphur from its porous condition easily retains some bisul- phide of carbon ; but chiefly because we cannot be certain, in spite of all precaution, that the hardened sulphur under inves- tigation reaches the water at exactly the same temperature, and is cooled under exactly the same circumstances, — is thus in the same state as the soft sulphur corresponding to it. The quantity of crummy sulphur cannot indeed be determined with perfect certainty, but still with sufficient nearness to show that it is present in the soft sulphur in considerably greater quantity than in the hard. On this account I think I may assume, that the flexibility and elasticity of soft sulphur arise from the presence of this modification. This supposition is rendered more probable by the fact, that even very small quantities of other admixtures change the com- 530 Prof. Magnus on the Allotropic Conditions of Sulphur. portment of sulphur in a similar manner; for if sulphur be coloured intensely red or black by one of the above substances, for which only 0'0003 of its weight of parafiine is necessary, and if it be then suddenly cooled, either by pouring it in cold water or on a glass plate, it remains for a long time so soft and greasy that the individual parts of it can be joined together and united into one piece. It may then be drawn out in long thin threads, and retain this adhesive state for several hours, often even for a day, — a comportment which I have also already described in the black sulphur. But not only the manner of solidifying is altered by this small admixture, but also in the liquid condition does this sulphur exhibit a different comportment to the ordinary sulphur; for it is viscid indeed at a higher temperature, but much less so than common sulphur. Since the soft and greasy condition of the black sulphur arises from the admixture of so small a quantity of a foreign substance, it is also probable that the flexibility and elasticity of the yellow so-called soft sulphur results from the small quantity of crummy sulphur which it contains. Such changes in the properties, by the presence of small quantities of foreign substances, are indeed not frequent ; yet is an example not wanting, and we only need to be reminded, in this respect, of the change of iron into steel. The various allotropic conditions of sulphur are hence the following : — 1. Prismatic sulphur. 2. Octahedral sulphur. Both soluble in bisulphide of carbon. 3. Insoluble sulphur. 4. Crummy sulphur, which in the fresh state is soluble in bisulphide of carbon, but once separated from it does not again dissolve in it. This has been hitherto described by me as soluble and inso- luble red sulphur. For if soft sulphur contains even the smallest quantity of colouring substance, it remains constantly with the crummy sulphur, because, like this, it is more soluble in bisul- phide of carbon than common sulphur, and hence remains behind with it in the mother liquor, and also, on the complete removal of the bisulphide of carbon, adheres to it in the sohd form. 5. The black sulphur, which, since it results from an admix- ture of foreign substances, cannot indeed be considered as an aUotropic condition, but as an especial modification of sulphur, because it is distinguished from the various conditions of sul- phur not only by the colour, but also by the above-mentioned properties. .'uj\\^\u> [ 531 ] ' m zisng^ JU>^. Obi '^ LXIX. Chemical Notices from Foreign Journals, ,.^■^^^■^■.[ By E. Atkinson, Ph.D. J;, [Continued from p. 304.] r BERTHELOT* has lately made a very important step in the synthesis of organic compounds. Some time ago he showed that by bringing olefiant gas in contact with the elements of water, alcohol was formed. He has now shown that olefiant gas may be produced by the union of its elements, and has thus completely eflfected the synthesis of alcohol by means of the simple bodies which constitute it. When a mixture of bisulphide of carbon and sulphuretted or phosphuretted hydrogen is passed over metallic copper heated to dull redness, there are formed hydrogen, marsh gas, a small quantity of naphthaline, and a considerable quantity of olefiant gas. The marsh gas was separated by means of appropriate solvents, and the olefiant gas absorbed by means of bromine. From the bromine compound the olefiant gas was liberated by a method which Berthelot gives, and its identity established by converting it first into sulphovinate of baryta, and then into the benzoic sether. In the above reaction the copper takes sul- phur from the bisulphide of carbon and the sulphuretted hy- drogen, and the carbon and hydrogen thus set free unite to form olefiant gas. The naphthaline, hydrogen, and marsh gas may be considered as products of the decomposition of olefiant gas. It must be noticed that the sulphide of carbon is obtained by the direct union of carbon and sulphur. In the dry distillation of formiate of baryta, marsh gas, CH^, olefiant gas, C^ H'*, and propylene, C^ H^, are obtained. Now Berthelot has shown f that the formiates are produced by the direct union of carbonic oxide and the elements of water ; and that not only olefiant gas, but also its homologues, may be directly converted into the corresponding alcohols. Here we have another method of the synthesis of alcohol from its elements, for carbonic oxide is formed by the direct union of carbon and oxygen. Propylene is also formed when carbonic oxide, CO, and marsh gas, CH^, are heated together to dull redness in a closed tube. In the dry distillation of acetate' of soda, olefiant gas, C'^ H"*, propylene, C^ H^ butylene, C^ H^ and a little amylene, C^« Hi«, are obtained. It will be observed that the acetates are prepared from alcohol, which in turn is prepared from olefiant gas. From these various carburetted hydrogens, as was before said, their corresponding alcohols may be obtained. Hence we have the means of building up from one alcohol other and higher alcohols. i,^ ^iwO,. , .y ^ Comptes Rendus, July 28, 1856. t Phil. Mag. July, 1856. 532 M. Wurtz on a new Series of Alcohols, The various carburetted hydrogens obtained in these experi- ments were combined with bromine. From their respective bro- mine compounds they may be liberated in a pure state by being heated in a sealed tube in contact with metallic copper, water, and iodide of potassium. If the copper be left out, the hydruret of the carburetted hycb'ogcn is obtained ; thus from bromide of olefiant gas, C* H'*Br*, the gas C"* H^ ; from bromide of propylene, C«H«Br«, the gas C^ H^ are obtained. From these facts of the relation of carburetted hydrogen to alcohol on the one hand, and of the relation of alcohol to other organic bodies on the other, the complete synthesis of a vast number of organic bodies may be considered as possible. " ^ Wurtz* describes a new series of alcohols. The compound aethers, it is known, are formed by the union of one atom of an acid with one atom of alcohol. Berthelot has found, on the other hand, that glycerine unites with three atoms of an acid to form the neutral fatty bodies. There is the same relation between alcohol and glycerine as there is between a monobasic acid and a tribasic acid. If spirit of wine is a monoatomic alcohol, gly- cerine may be considered as a triatomic alcohol. From these views Wurtz considered that there must be a series of inter- mediary combinations, whose molecule would be diatomic, and would correspond to the bibasic acids. By combining with two equivalents of acid, they would form compounds intermediate between the aethers and the neutral fatty bodies. Wurtz has suc- ceeded in forming by way of synthesis such an alcohol, which he names glycol. It is the type of a series, for the method by which it is formed is susceptible of a general application. By acting on acetate of silver with iodide of sethylene, C* H"* P, a body is obtained the formation of which is expressed by the following equation : — C4Hn2 + 2(AgOC4H3 03) = 2AgI + C^2Hioo8. Iodide of Acetate of silver. New body. Kthylene. This new body is the acetate of the new alcohol glycol. When pure, it is a perfectly colourless, neutral liquid, boiling at 185° C, and distilling unchanged. It is heavier than water, in a large quantity of which it is soluble. r.jj j^q The alcohol itself, glycol, is obtained by acting on acetate of glycol with hydrate of potassa. It is in the pure state a colour- less, slightly viscid liquid, having a distinctly saccharine taste. It boils at about 195° C. Its vapour is inflammable ; it is soluble in all proportions in water and alcohol. From the mode of its formation it is evident that the new * Comptes RenduSf July 25 and Sept. 1. M. Wurtz on a new Series of Alcohols. 533 alcohol contains the group sethylene or olefiant gas, C* H'*. It IS derived from the type, two equivalents of water tt2 J^O"*, by the substitution of sethylene for two equivs. of hydrogen ; and the acetate of glycol contains two equivs. of the radical acetyle re- placing the other two equivalents of hydrogen,— ' ■ '•- 4gp-^ ^2, equivs. water. Glycol. Acetate of glycol, ^^^^i^ The relations in which alcohol, glycol, and glycerine stand to each other are seen from this table : — ^ Type g|0' . .Type g,|0^ .^^ Type ^3 J0«. .,3,^ "Monoatomic alcohol. Diatomic glycol. Triatomic glycerin^f *'^'"'^ Alcohol. ,,^^^^J'^! Glycol. .Ethylic glycerine. '^^^''^^f^ -^thylic glycerine is not as yet known, but Wurtz has obtaltiibdf a body which is very probably the acetate of sethylic glycerine : ordinary glycerine would be represented by the formula tts > 0^. Wurtz has also obtained a benzoate of glycol by acting on benzoate of silver with iodide of sethylene. By the action of bromide of propylene, C^ H^ Br^, on acetate of silver, the acetate of propylic glycol is formed, — QG 116 Br2 ^ 2 AgO 04 H3 0^ = 2Ag Br + ^^4 h3 02)2/ ^^ > and by the action of bromide of amylene, C^^ H^^Br^, on acetate of silver, the acetate of amylic glycol. Indeed to each alcohol of the series C" jj»+2 qs there seems to correspond a glycol. Acetal, C^2 Jji4 q4^ which was discovered by Dobereiner among the oxidation products of alcohol, is considered by Wurtz to be a glycol in which two equivalents of hydrogen are replaced by sethyle, C^ H^ r 0^ ; if this be the case, one or both of the sethylic groups must be capable of being replaced by methyle. Experi- ment has proved that this is the case. By oxidizing a mixture of wood-spirit and alcohol two compounds were obtained, boiling respectively at 85° and 55°, and having the formulae — 534 M. Lallemand on Thymole, If we represent acetic aether, binacetate of glycol, and triace- tate of glycerine, by the following formulae, — (C^ H3 0«), C4 H^ 0, or A^ C^ H^ 0, acetate of aethyle, (C* H8 0^)2, C* H* 0«, or Ai* C^ H* 0», binacetate of glycol, (C* H3 03)8, Q6 H5 Qs^ or Ae3 C« H^ O^trinacetate of glycerine, we see the application to organic chemistry of the law in mineral chemistry, that the number of equivalents of acid which saturates a base is in relation with the number of equivalents of oxygen which it contains. In the oil of thyme a solid crystallizable matter is contained, to which the name thymole has been given; its formula is (^20 jji4Q2^ and it is hence homologous with hydrated oxide of .phenyle, C'^H^'O^. Its discoverer, Lallemand, has been work- ing out its analogy with this substance, and has arrived at some interesting results*. By the action upon it of nitric acid he has obtained a compound, trinitrothymic acid, ^'^^ o(^c\4,\ ^^ homo- logons with trinitrophenic or picric acid, C5^^q/T\jrv4\02, and which offers in its physical properties the greatest similarity with this latter acid. By acting upon thymole with chlorine, various sub- stitution products are obtained, one of which, pentachlorinated thymole y C^^ pif 0^, forms hard colourless crystals of the same form as the thymole itself. These fuse without alteration at 98° C, and are decomposed at a temperature of 200° C. into carbon, hydi'ochloric acid, a new carburetted hydrogen, and a sohd substance, which, when purified, crystallizes from alcohol in silky JJ4 needles. It has the formula C^* ^14 0*, and may be regarded as a derivative of the body C^'* H^ 0^, isomeric with benzoic alcohol, and the homologue of hydrated oxide of phenyle and of thymole. It might be called quadrichlorinated benzinole. The new carburetted hydrogen is a homologue of marsh gas. It bums with a beautiful white flame, and combines with chlo- rine in equal volumes. Its density at zero is 1*15, and it is not liquefied at 20° below zero. Its formula is C'*!!^; marsh gas, at a condensation of 4 volumes, being C* H"*. Lallemand n2ime% it hiformene. mIt ,/_- The decomposition by whicM jit is obtained may be thus ex- pressed:— -^ *' '' * Comptes Rendus, August 18, 1866, p. 3/5. M. Berthelot on the Compounds of Mannite with Acids » 535 ^' ' 2(C2o ^p 02) = C14 H^ 02 + 6H CI + C'* H8 -f 2Cp + C^^j^j Pentachlorinated Quadrichlori- BiformeuCk j^py^.^^^v thymole. nated benzinole. From biformene a large number of new bodies may be obtained, and from it, as from propylene, a new series of alcohols may be derived. n;-j By the action of chlorine a heavy setherial liquid is obtained, boiling at 102° C, and having the formula C^ H^ CP ; this, acted upon by potash, gives rise to the formation of a light volatile liquid, of an setherial alliaceous odour. Its formula is C'* H^Cl, or that of monochlorinated biformene. Bromine and iodine act on biformene in the same manner as chlorine. When the iodine compound of biformene, C'* H^ P, is placed in contact with oxide of silver, a considerable action ensues; a liquid is obtained having an odour like that of wood- spirit, and which gave on analysis numbers corresponding to the formula C^ H^ 0^, which would be dimethylic alcohol. By acting on mo- nobrominated biformene, C* H^ Br, with oxalate of silver, bromide of silver and the oxalate of the new alcohol are obtained. This gives, on treatment with ammonia, oxamide and the new alcohol. When potash is enclosed with monobrominated biformene in a sealed tube, and exposed to a temperature of 100° C, the sether of the new alcohol is formed. It is a dense gas, burning with a white flame, and is only slightly soluble in alcohol. Sulphuric acid absorbs about 200 times its volume of bifor- mene, which is not separated on the addition of water. On the addition of carbonate of baryta, a salt is obtained analogous to sulphovinate of baryta, of the formula 2S0^, C"^ HgO, BaO. By appropriate treatment it will give the alcohol C^ H^^ 0^. Berthelot* publishes a continuation of his researches on the neutral compounds of saccharine matters with the acids. He has produced with mannite and the acids, a series of compounds analogous to those formed by glycerine and the acids. These compounds are produced in general by the direct action of the two substances, in closed tubes, and at a temperature of 200° to 250° C. It is by the same method as that by which, according to Berthelot^s experiments, the artificial neutral fatty matters and the compound aethers are formed. These new compounds are separated and purified like the glyceric compounds, by taking advantage of their neutrality, their resistance to alkalies, and their insolubility in sether. They are so similar in appearance to the glyceric series, that they might readily be confounded. They have the same general aspect, a like fusibility, and analogous * Annates de Chimie et de Physique^ August 1856. ^ M4I. Berthelot and De Luca on Glyterihe. 86lubility in the same solvents. But the mannitic compounds possess a greater fixity, a less fluidity, and a stro^nger tend- ency to assume the solid form, although these tendencies are not so marked as to excite attention. The compounds are decora- posed, under the prolonged influence of the alkalies, with the formation of mannitane, or anhydrous mannite, C® H^ 0^, which' difi^ers from mannite by one equivalent of water, and is trans- formed into mannite by prolonged contact with water. Manni- tane is also formed by heating mannite to 200° C. ^ With acetic acid mannite forms only one compound, a bittef liquid substance ; the compound of mannite mth butyric acid is in- teresting, inasmuch as both its constituents are entirely derived from the fermentation of sugar, and yet it has all the characters of a neutral fatty matter. With palmitic, and with stearic acid, mannite forms compounds which are crystalline and resemble palmitine and stearine; when melted, they appear like wax. W^ith oleic acid, a neutral, almost colourless substance is obtained, of the consistence of modeller's wax. Benzoic acid unites with mannite in two proportions. The first, which consists of one equivalent of acid and one of mannite, is a viscid, almost solid substance ; in the other, one equivalent of mannite unites with three of benzoic acid. Both these resemble resins, and are very ■ stable and difiicult of decomposition. «« Mannite forms with tartaric acid an acid compound which is^ tribasic. It bears the same relation to the benzoic acid com- pound of mannite which sulphovinic and tartrovinic acids do to benzoic aether. The mannitartaric acid forms with lime a neutral salt containing four equivalents of water, and with magnesia a basic salt containing thirty equivalents of water. Mannite, heated with oxalic acid to 100°, experiences the same decomposition as does glycerine under the same circum- stances* ; carbonic acid free from carbonic oxide is liberated, and. , at the same time formic acid is produced, which remains com-7 bined with the mannite. With hydrochloric acid, mannite forms a neutral crystalline compound. By enclosing mannite in a sealed tube along with potash and bromide of sethyle, a compound of mannite and alco- hol is formed, analogous to the mixed alcohols of Williamson. The compounds of mannite with sulphuric acid and with nitric acid are already known. They are also strictly analogous to the compounds formed by glycerine with those acids. Berthelot and De Lucaf have investigated the action of the chloride and bromide of phosphorus on glycerine. The action of * Phil. Mag. July, 1866. t Comptes Rendus, July 14. ¥lH On the Conversion of Albumen into Urea. 537 chloride of phosphorus is the same as that of hydrochloric acid ; bodies are formed which have already been described by Berthelot. By the action of bromide of phosphorus a large number of brom- hydrines are produced ; a class of bodies consisting of glycerine which has assimilated hydrobromic acid, and lost the elements of water in various proportions. Of these, the principal are mom^ bromhydrine, epibromhydriney and dibromhydrine. Dibromhydrine, C^ H^ Br^ 0^=0^' H^ 0^ + 2H Br-4H0, is a neutral liquid of an eetherial odour similar to that of chlorhy- drine. It boils at 219°, and is twice as heavy as water. When ammonia is pased into its alcohohc solution, bromide of potassium is formed, and the bromide of a new base, qlycerani'* mine = N ^g jje q4 r Br. The base, separated from the bromide by treatment with caustic potassa, is liquid, very soluble in water and in sether. It is not volatile with the vapour of water, and cannot be distilled without decomposition. It forms with bi- chloride of platinum a crystalline double salt. This is the first example of a base containing a saccharine matter. Heated with metallic tin to 140 degrees, dibromhydrine is decomposed with the formation of bromide of tin, and of a pe- culiar organic compound containing tin ; insoluble in water, but soluble in sether, but which could not be obtained in a crystal- line form. Treated with perbromide of phosphorus, dibromhydrine affords compounds in which more equivalents of hydrogen are replaced by bromine. M. Bechamp* has furnished a most important contribution to physiological chemistry, in effecting a direct proof that the urea in the animal oeconomy is derived from albumen or other ana- logous bodies. He has shown that albumen may be transformed directly into urea by a slow oxidation produced by permanganate of potassa at a temperature of 80°. M. Dumas, who announced this discovery to the Academy^ stated that he had frequently tried to effect the same change. He endeavoured to imitate the process which takes place in the blood by slowly oxidizing the albumen in the presence of an alkali. He had employed bichromate of potash, oxides of mer- cury and silver, and peroxide of lead with alkalies, but without success. , s^*?>ai mm w^ym^, '^ mms.^*- «5AJAi*'v^?uJv.-^ M. Dumas communicated on the same occasion the results of some experiments of M.Picard,on the presence of urea in the blood and its diffusion through the organism. Long ago Prevost and Dumas had concluded that urea was eliminated by the kidneys, * Comptes Rendus, September 8. Phil, Mag, S. 4. No. 82. Suppl Vol. 12. 2 N 538 On the occurrence of Organic Adds in Mineral Waters, but not produced by tbeni. M. Picard has completed the proof of this theory. By the addition to blood of nitrate of mercuiy he was able to separate every trace of urea from it, and was thus able to compare the proportion of urea in arte- rial with that in venous blood. The arterial blood of a dog con- tained 00365 per cent, of urea, while venous blood contained only 0'0186 per cent. In the human subject, he found that blood which passes through the kidneys would furnish 28 grms. of urea. Now the quantity of urea contained in the daily secre- tion of urine amounts to 27 or 28 grms. The arterial blood which arrives at the kidneys contains more urea than that which passes from it, and the quantity of urea lost in traversing the kidneys corresponds to the quantity found in the urine. Hence the kidneys do not produce urea, but merely eliminate it. In the mineral water of Bruckenau in Bavaria, Scheerer* has found formic, acetic, propionic, and butyric acids. The method of detection was as follows : — Very large quantities of the water were evaporated to a small bulk, and the precipitate which formed was filtered off. The filtrate was distilled with excess of sul- phuric acid, and the acid distillate neutralized with baryta. The poixed baryta-salts were extracted with warm alcohol, which left formiate of baryta undissolved; the presence of this salt was established by the usual confirmatory tests. To the alcoholic solution of the other baryta-salts sulphate of silver was added, by which the silver-salts were obtained. From the properties of the silver-salts separated out by suc- cessive crystallization, and from determinations of the silver contained in them, evidence of the presence of acetic, propionic, and butyric acids was obtained. Scheerer considers that these , acids are formed by the gradual decomposition of certain con- stituents of plants dissolved by the rain-water. He considers that this change is promoted by the alkaline carbonates, which are present in largest quantities in those waters which contain the greatest proportion of these acids, and also by the presence of the oxides of iron and manganese. The occuri'ence of organic acids in mineral waters is more frequent than is generally thought : Lehmann has recently found in the Marienbad water^ formic, acetic, succinic, and even oleic and stearic acids. M. Belhommef has ascertained the presence of a colouring matter in Monarda didyma, which from all its properties is evidently carmine. It resides principally in the corolla ; and as it is contained in tolerable quantity, it may be advantageously extracted and had at a cheap rate. Samples of silks dyed with it have given satisfactory results. ♦ Liebig's Annaleuy gep'^"fT ^'A^ssuming the Russian observations to be the best, as they probably are, it will be seen that a troy pound deduced according to the method prescribed by the Act, would be 2-829 grains too heavy ; while, if the Austrian observations had been accepted as the best, the troy pound would have been 4-707 grains too heavy. On the other hand, it was possible to recover the weight of the lost standard in air to within a fraction of 0*001 grain, by means of the troy pounds which j>< i., .. >.^ ...300 Sp :ii:U-0-00857 29-722 65-62 ehofiuq yflbpening the balance-case, except in the middle of the series, for the purpose of changing the pans. A sufficient number of preliminary comparisons of Sp, RS, Sb, K, ' lEx, L, Ed having been made in 1844, the results were reduced, ;^«when the material of one weight was platinum and that of the other ^•brass, to what they would have been in air (^=65"66, 6=29'73), 3or, of the mean density of the air during the comparisons of Sp and RS with U in 1829. Using U, Sp, RS, &c. to denote the apparent weights of U, RS, &c. in air (^=65*66, 6 = 2975), it was foimd that— jjj 1829. In 1844..^ RS=Sp +0-()051 RS=Sp +0-0057 Sp =Sb +0-0022 Sp =Sb +0-0030 RS=Sb +0-0073 RS=Sb +0-0032 K =Sp +00420 K =Sp +0-0362 I. yd K =RS + 0-0369 K =RS + 0-0304 K =Sb +0-0442 K =Sb +0-0317 In the interval between 1829 and 1844, the difference between the two platinum troy pounds Sp and RS had undergone no very sen- sible relative change. If, as appears probable, Sp and RS have 'tindergone no sensible absolute change, Sb has gained 0*0046 grain, and K has lost 0-0061 grain. Qn the same supposition it appears *^^*lnl824. '''''"'fnr^m. Ex -U= +0^010 Ex -U = +(H)099 L -U= +0-0005 L -U = +00151 Ed - U = - 0-0015 Ed - U = +0-0206 D -U = +0-0022 D -.U= +0-0248 KM-U=« +0-0021 (1829) RM-U- +0-0089 Increase of Interval gr. in years. Ex 0-0089 20 L 0-0146 20 Ed 0-0221 20 D 00226 20 RM 0-0068 5 Prof. Miller on the Imperial Standard Pound, 545 ^ With the single exception of K, all the brass weights have become n heavier since they were compared with U, in consequence probably 3iof the oxidation of their surfaces, while U, which was made in 1758, - was protected from further change by the coat of oxide already h formed. One of these weights, Sb, appeared to have been protected ^ by gilding, though imperfectly, since parts of its surface were slightly K'rtarnished. Ex and L were brighter than Ed and D. K, though it t^had become lighter, was much tarnished. The discordances pre- . fflented by the different weighings of K appear to have greatly per- .■)plexed both Professor Schumacher and Captain Kater, and were Siiprobably the cause of the numerous and accurate comparisons of the - ^several troy pounds placed at the disposal of the Committee with the -blost standard, on which alone depends the possibiHty of restoring it '; with sufficient accuracy. Previous to the comparison of K in 1844, ; a small fragment of wood, like a grain of coarse sawdust, was found .adhering so firmly to its under surface, that it was detached with ■ some difficulty. It appears probable that the changes of the weight iiof K were caused by this bit of wood being weighed with it after 4 the first comparison of K by Captain Kater, and by the gradual -r oxidation of the surface of K. The discrepancies presented by the /♦weighings of the brass troy pounds at different times, due to the is effect of oxidation or other causes, are so large, that I resolved, with ;,ithe consent of the Astronomer Royal, to rest for the evidence of the weight of the lost standard entirely on the 300 comparisons of Sp ^ and the 140 comparisons of RS with U. If we consider the discordances presented by the weighings of the i brass troy pounds simply as errors of observation, without paying ,( any regard to their probable causes, the resulting value of U will not I be very different from that given by the platinum troy pounds alone. t! By the observations of 1824 and 1829, hmojl £i:-.v ,0u ou:- gr. jJ^ ,^ji ^.iveaghfc^ilgisy? U=Sp 4-0-0081 „ov r ctI 30^ij5iij U=RS +0-0030,^" 14 ,rU=Sb :^.^m +0-0103. 04. Cf8=8a6 rU=K -0-0339=0+ d8=:qf^ 9 < U=KEx + L + Ed + D)-0-0022.o+ d8=:aa.6 By the observations of 1844, u^-iO'0+ q8~ JA. tiso-#d«=. ii =sp +0-0057, :a u , A »%-f. A =SP +0-0030^ . . _ oil? n'iaw:>9d soirj^tiD ^Ai _g^ +0-0363^*^^ ^" ^^ .imrr^wori ^frog^_^Ed + D=:2(Sb + K) + 0-02G0^"^^^"^'f^ ^^* "Whence, supposing the errors of weighing in 1844 to be insensible, !,' co?^pared with the discordances of the brass troy pounds,,^| -^ |,^, '"'^ gr. weight. ^A (1) U=Sp + 0-0081 30 , . '^^" "^h ''"^m U=Sp + 0-0087 14 ■ ^^ m C'Booo (|a U=Sp+0-0i33 i»hM«6^ r^--ir~ xa OS bmrOQk) u=Sp+o-oo24 ^'^<>«$+=-5^- ^j; - ' (5) U=Sp + 0-0261 '■ " (i ~ ^ -yl ^ The mean of all the equations gives U=Sp-|-0'0096 graim^Mg 546 Royal Society : — Excluding the last, which depends upon the weighings in 1824, U=Sp + 0-0079 grain. Excluding all except the results of the comparisons of U with the two platinum troy pounds, U=Sp + 0*0083 grain. The temperatures were determined by means of three thermo- meters by Bunten, having centesimal scales etched upon the tube, and two thermometers having arbitrary scales traced upon the tubes with a diamond point. The zero-pouits of these were determined at distant intervals. They were often compared with each other, and, lastly, with an excellent standard thermometer constructed at Kew under the directions of Mr. Welsh, in order to form tables of the errors at any point of their scales, and to determine the position of their zeros at any given time. The barometer employed was a portable cistern barometer by Ernst of Paris, the scale of which was divided into milHmetres. It was compared first with the standard barometer of the Paris Observatory, and afterwards with a standard barometer, having a tube of very large bore, belonging to the Taylor Library of Sidney Sussex College, Cambridge. According to Ritter (Memoires de la Societe de Physique de Ge- neve, t. iii. p. 361), the observations of Regnault show that in Paris, lat. 48° 50' 14", GO metres above the mean level of the sea, a litre of dry atmospheric air, containing the average amount, 0*0004 of its volume, of carbonic acid, the density of which is 1*529 of that of atmospheric air at 0° Cent., under the pressure of 760 mm. of mer- cury at 0° Cent., weighs 1*2934963 gramme. If G be taken to denote the force of gravity at the mean level of the sea in lat. 46°, the force of gravity in lat. X, at the mean level of the sea, = G(1 -0*0025659 cos 2\) (Baily, Mem. Ast. Soc. vol. vii. p. 94). The force of gravity in a given latitude at a place on the surface of the earth at the height g above the mean level of the sea = 'j 1— f2— - -j-r X force of gravity at the level of the sea in the same latitude, where r is the radius of the earth, p its mean density, and p' the density of that part of the earth which is above the mean level of the sea (Poisson, Traite de Mecanique, t. ii. p. 629). According to Regnault, the expansion of air und* constant pressure from 0° to 100 Cent., is 036706 of its volume at 0° Cent.; also at 50° Cent., the mercurial thermometer is about 0°*2 in advance of the air thermometer (Memoires de I'lnstitut, t. xxi. p. 91. p. 238, Annales de Chimie, 3 serie, t. v. p. 99). HencCi density air at 0° : density air at t= 1 +0*003656^. The density of the vapour of water is 0*622 of that of air. Hence, if t be the temperature of the air in centesimal degrees, 6 its barometric pressure, v the pressure of vapour, both in millimetres of mercury at 0° Cent., the weight in grammes of a litre of air at a place on the surface of the earth at a height z above the mean level of the sea in lat. X, will be 1*2930693 6-0*378t;/, , oo-^Vi a nno^^^^n o^^ , 1 + 0*003656^ _^^^^^l-.1.32-j(l-0*0025659cos2X). Regnault finds that in rooms dot heated artificially^ the pressure of vapour is two-thirds of the maximum pressure corresponding to the Prof. Miller on the Imperial Standard Pound. 547 temperature (Memorie della Societa Italiana della Scienze in Modena, t. XXV. p. 1). The weight of air used in reducing the weighings was calculated from the above expression. The mean rate of expansion of brass, for 1° Cent., from 0° Cent, to 100° Cent., usually assumed 0-0000187 of its length at 0° Cent., is considerably larger than the rate of expansion at ordinary atmo- spheric temperatures, according to the observations of Mr. Sheep- shanks, who found that at about 17° Cent, the coefficient of the linear expansion of brass =0*00001722 for 1° Cent. This value of the expansion has been accordingly adopted. The Hnear expansion of platinum is assumed to be 0*00000900 for 1° Cent., as given by Schumacher in his first table (Phil. Trans. 1836). The expansion of water is calculated from a mean of the experiments of Despretz, I. Pierre and Kopp, corrected for the error of the assumed expansion of mercury by Eegnault's observations, and assuming the temperature of maximum density to be 3°' 945 Cent., in accordance with the result obtained by Messrs. Playfair and Joule. The logarithms of the expansion to 7 places considered as integers, are given with sufficient accuracy, between 4° Cent, and 25° Cent., by 32'72(^-3-945)2-0-215(^-3-945)l Though it appears that only two of the nine weights with which U was compared in 1826 and 1829 are in a state of unexceptionable preservation, and that the number of trustworthy comparisons is reduced from 669 to 440, these are amply sufficient for the purpose of ascertaining the weight of U in air ()^=65°-66 Fahr., 5 = 2975 inches). But in order to find the absolute weight of U, or indeed its apparent weight in air of a density different from that which it has when f=65°-66 Fahr., 5 = 2975 inches, a knowledge of the volume of the lost standard is requisite. An indirect way of arriving at it was suggested by Professor Schumacher, by an examination of certain Parliamientary Reports, presented May 26, 1758, April 11, 1759, March 2, 1824. It appears from the first of these, that Mr. Harris, then Assay Master of the Mint, presented to the Com- mittee three troy pounds made under his direction, one of which was the lost Imperial standard ; and from the third, that one of the two remaining pounds came into the possession of Mr. VandomC, and the second into the possession of Mr. Bingley of the Mint. Pro- fessor Schumacher then observes that we can still either determine, with the highest degree of probability, the density of the lost Im- perial standard, or know with certainty that all hope to arrive at this knowledge is lost. It will be only requisite to ascertain with the greatest care the densities of both pounds, the one in the possession of Mr. Bingley, the other in the possession of Mr. Vandome. If the density of both is found the same, we might from that circumstance draw the highly probable conclusion, that the three single pounds of Mr. Harris, according to my hypothesis, were really made of the same identical metal ; and the density of the two remaining pounds might with safety be considered as that of the lost standard. If, on the contrary, the two remaining pounds prove to be of BfciditV— t>M= 1 7*38. These dififerences show that the volume of the lost standard cannot be inferred with any high degree of probability from a comparison of the remaining pounds. The only resource now remaining was indicated by Professor Schumacher's remarks on the figure of the lost standard : — " As soon as the Imperial standard troy pound was brought to Somerset House, Captain Nehus's first care was to make an accurate drawing of its shape and marks, measuring all its dimensions with the greatest care. The annexed drawing represents this pound in its actual dimensions ; and is now, since the original has been destroyed by the calamitous fire that con- sumed the two Houses of Parliament in 1834, the only thing remain- ing which can preserve an idea of it." By a comparison of the figure of U in the Philosophical Transactions for 1836, with a profile of V traced mechanically, the axis and the extreme diameter of the knob and cylindrical portion of U, appeared to be a very little greater than the corresponding dimensions of V. On comparing the profiles of JJ and V, it did not seem possible to suppose that the volume of U iras less than that of V. But the volume of O, as well as tliat of M, being less than that of V, it appeared that of the three weights V, O, M, V approximated most nearly to U in volume. As the exist- ing data were utterly insufficient to determine how much, if at all, U exceeded V in volume, it appeared safest to assume the volumes of U and V to have been equal. This eourse vf^ also recommended by Professor Schumacher. It was afterwards found that O was 0-144 grain lighter than U, AO=8-4004; and that M was 0*047 grain lighter than U, AM=8*34^1. ,„.J^i,^ l^^^^;,fi;^ :Wil)wn.AWler*.Epqw,,pf fte P^.^of JEfi^di Prof. Miller on the Imperial Standard Pound. 549 dated August 22, 1855, I was apprised of the existence of a fourth troy pound of 1 758. This weight was 0*249 graiu heavier than U ; its density =8'3175. •iiirui^ro'vi mn ■.d^'io ■,■n\^i'i ; If U, the lost standard, be supposed to have the same density dH V, tfce comparisons of Sp and RS with U by Captain v. Nehus in 1829, giyfirj-^rrafoi ^iv/f '^ > w ^' y>>'^>' r.x-, TJ nmh mlff:2i( (liirp^ RS=U-0*52444. '>\dt him ,\-mt,\-^=.^ L The Commissioners for the Restoration of the Standards of Wefght and Measure, in their Report, dated December 21, 1841, recom- mended that the avoirdupois pound of 7000 grains be adopted instead of the troy pound of 5760 grains, as the New Parliamentary Standard of Weight, and that the new standard and four copies of it be constructed of platinum. ■ In accordance with this recommendation, five weights were made by Mr. Barrow, a little in excess of 7000 grains, of platinum pre- pared by Messrs. Johnson and Cock. The form of these pounds is that of a cylinder, nearly 1*32 inch in height and 1*15 inch in dia- meter, with a groove round it, the middle of which is about 0*34 inch below the top of the cylinder, for insertion of the prongs of a forked lifter of ivory. They are marked PS 1844 1 lb. ; PC No. 1 1844 1 lb. ; PC No. 2 1844 1 lb.; PC No; 3 184411b;; PC No. 4 1844 1 lb., respectively. i;Khm(ma:}>l niH \o mniw The weights of 7000 grains might havfe be^ii^derited frdn^'^that if 5760 grains, by the use of either a decimal or a binary system of weights. In either case, however, the number of weights to be com- pared with one another and with the weights of 7000 and 5760 grains would have been large, and the errors of their compansons among themselves might, by their accumulation, sensibly aifect the resulting weight of 7000 grains. Also, the repeated comparison of weights made up of the sum of several others, was a very troublesome pro- cess, previous to the use of the detached pans, already described, which had not been thought of when the weights were ordered. These two evils were in a great measure avoided by the use of a platinum weight T of about 5760 grains, or more correctly very nearly equal to Sp or RS, and of the following auxiliary weights, also of platinum, and all constructed by Mr. Barrow : A, B, C, D each of 1240 grains ; F of 800 grains ; G of 440 grains ; H of 360 grains ; K, L, M, N each of 80 grains ; R, S each of 40 grains, nearly. The numbers of the weights of each denomination, and their values, are given by the quotients and divisors obtained in the conversion of Ifl^ into a continued fraction. The errors of these weights are found by the following comparisons : — Sp and RS with T ; T with A + B + C + D + F; each of the weights A, B, C, D withF + O; F with G + H ; G with each of the weights H + K, H + L, H + M, H + N; HwithK + L4-M + N + RandK+L + M + N + S;eachof the weights K, L, M, N with R + S. Sp and RS, instead of being true troy pounds, and, consequently, equal to U in a vacuum, had been adjusted so as to appear nearly as heavy as U when weighed in air of ordinary density, and are there- fore lighter than U by about 0'53 grain, the weight of the air con- tained in the space equal to the difference between the volume of 650 Royal Society ; — U and that of Sp or RS. A space equal to the diiference between the volume of 7000 grains of metal of the assumed density of U, and 7000 grains of platinum, contains about 0*645 grain of air. Calling this Q, PS may be compared with each of the weights T+A-fQ, T -f B + Q, T -I- C -f- Q, T + D + Q. In order to determine Q with the greatest precision, Mr. Barrow supplied ten weights Qof about 0*645 grain each, so accurately adjusted that no appreciable difference could be detected between them ; a weight V of 6 -4 5 1 grains, and a weight W of 12*901 grains, all of platinum. Then Y and Z being two platinum weights of 20 grains each, the following comparisons became pos- sible : — each of the weights R and S with Y + Z ; each of the weights Y and Z with W + V+ each of the weights Q in turn ; W with V + sum of ten weights Q ; V with the sum of the ten weights Q. lu comparing PS with each of the weights T + A + Q, T + B + Q, X-i-C-f-Q, T + D + Q, the weight Q was changed at the end of every four comparisons, and thus each of the ten weights Q used in turn in a series of forty comparisons. By numerous weighings in air and in water the densities of the several weights were found to be as follows : — T 21-1661 PS 21*1572 PC No. 1 .. 2M671 PC No. 2 .. 21*1640 PC No. 3 .. 21*1615 PC No. 4 .. 21-1556 By 286 comparisons of T with Sp and 122 comparisons of T with RS, assuming the density of U to have been the same as that of V, T=5759*47141 grains, of which U contained 5760. By numerous comparisons of the auxiliary weights with each other and with T, A= 1239*88621, B= 1239*88604, C=1239*88596,D= 1239-88579, Q=0*64509. By 80 comparisons of PS with each of the woights T + Q+A, T4-Q+B, T + Q+C, and 100 of PS with T + Q+D, gr. t. b. PS52: T + Q + A--0002936 19*47 758-38 PSii T + Q+B-0*001731 19*19 759*31 PS£: T4-Q+C-0*001621 18*83 754-38 PS£: T4-Q+D-OOOO774 19*63 764-43 Mean gr. PS:fi: T + Q+i(A + B-hC-f-D)-0*00177 19*28 759-12 whence, supposing U to have the same density as V, PS = 7000-00090 grains, of which U contained 5760. Results of comparisons of PC No. 1, PC No. 2, PC No. 3, PC No. 4 with PS : — gr. No. of Comparisons. PC No. 1=PS-|-0*00051 200 PC No. 2=PS-0*00089 216 PC No. 3=PS-0*00178 204 PC No. 4 = PS-0-00316 204 ' The weights Sp, Sb, K were returned to Professor Schumacher accompanied by a weight V such that, by a mean of 200 compari- sons, Sp-f VilP8-0-00071 gram in air (^=13-1, 6=759*09). Prof, Miller on the Imperial Standard Pound, 551 By the good offices of M. Arago, permission was obtained from the French Government to compare the new English weights with the standard kilogramme of platinum, known as the kilogramme des Archives, and which will be denoted by the letter %. The compa- rison was made by two perfectly independent methods. In one of these ^ was compared sixty times with PC No. 1 + PC No. 2 + auxiliary weight B+ a platinum weight V of nearly 192-436 grains. In the other, ^ was first compared 200 times with the platinum kilogramme ^, purchased for the British Government. (2B was after- wards compared with PS + each of the four platinum copies of the pound in succession, together with a platinum weight of about 1432'324 grains, the weight of which was found with great precision by a process to be described presently. ^ ^ had never been weighed in water. By observations made with 'i^he stereometer, it was found that at 0" C. the volume of % exceeded that of ^ by a quantity equal to the volume of 21-119 grains of water at its maximum density. By weighing (2B in air and in water, it was found that A^= 20-548/7. Some time after these observa- tions were made, the Committee received from Professor Schumacher some observations of his own in manuscript, and a copy of Professor Steinheil's paper, entiled *Das Bergkrystall-kilogramm,' from the fourth volume of the Transactions of the Bavarian Academy of Sci- ences, containing the determination of the volume of % by comparing its linear dimensions with those of a platinum kilogramme of his o^w ^, the density of which had been found by weighing it in air and in water. The two weights being cylinders, and the linear dimensions measured with an extremely delicate instrument con- structed by Gambey, this kind of observation admitted of being made with great accuracy. The resulting difference between the volume of ^ and that of (!B, was found to be equal to the volume of 20*933 grains of water at its maximum density. On account of the large number of observations, and the extreme care with which they were made, this value of the volume ^— volume (JB is to be preferred to that which was obtained by the stereometer, and has accordingly teen used in reducing the observations for comparing the weights of % and (t. ,. ^ was compared with PS by the method which had proved so , satisfactory in deducing the avoirdupois pound from the troy pound, let I, K, L, M, N denote PS and its four platinum copies, A, B, T, A, platinum weights of about 1432*322 grains each, Z a weight of about 1270- 708 grains, 6 a weight of 161*629 grains, made up of weights the values of which had been carefully determined. ^ was compared with each of the weights I-f K + A, I + L + B, 1 + M + r, I-f N-|-A, each of the lbs. K, L, M, N having been previously compared with I ; I with A + B + r-FA + Z; each of the weights A, B, T, A with Z + 0, in this manner it was found that the kilogramme des Archives weighed 15432-34874 grains, of which the new Imperial Standard pound contains 7000, or kilogramme =2-20462125 lbs. This is pro- bably the best determination of the weight of % in terms of the English standard of weight. The value of %, as deduced from the direct comparison of ^ with 552 Intelligence and Miscellaneous Articles » K+L+B-fV, is subject to some uncertainty, arising from the cir- cumstance that the platinum, of which A, B, C, F were made, had been very badly prepared and contained cavities filled with some hygroscopic substance which rendered the weight of B slightly variable, according to the greater or less amount of moisture present in the atmosphere. According to these observations, the kilogramme des Archives =15432'3481G grains. By the observations of Schumacher and Steinheil on the ratio of the weight of ^ to that of Sp, subject to tai uncertainty of 0*00139 grain, on account of an error of the press, and the comparison of Sp with PS, the weight of ^ is either 15432-34873 or 15432-35012 grains, of which PS contains 7000. The French standard of commercial weight is a brass kilogramme H, known as the kilogramme type laiton. It is deposited at the Ministere de I'lnterieure. According to a comparison of H with ^, the result of which is published in the 25th volume of the Modena Transactions, the apparent weight of H, when weighed in air at Somerset House, the mercury in the barometer, reduced to the free- zing-point, standing at 29' 75 inches, and the thermometer at 65-66 F, (i=755-64mm., ^=18-7 C), is 15432-344 grains, of which the English commercial standard contains 7000. LXXI. Intelligence and Miscellaneous Articles. NOTE ON THE NEW ZEOLITE FROM SKYE, ANALYSED BY MALLET. BY DR. HEDDLE. n^HE mineral analysed by Mallet (Silliman's American Journal, ■*- Sept. 1856, p. 179) is Laumonite, somewhat effloresced from having been " several years " in his possession. An analysis of a similar specimen was published by Scott (Jameson's Journal, October 1852, vol. liii. p. 284), which specimen also bore the name hypo- stilbite, and I have seen many other specimens in cabinets in this country with the same name attached. As it bears but very slight resemblance to the substance called hypostilbite by Beudant, the christening may be explained by the ignorance of some unprincipled dealer resorting to a rare title in order to rid himself of a superabun- dance of an insignificant-looking substance. It occurs in a vein at the Storr in Skye, in immense quantity ; the vein has an average thickness of about \\ inch, and the appearance is exactly as de- scribed,— " a mass of minute crystals resembling loaf-sugar, breaking easily, and crumbling under the fingers into a coarsish crystalline powder." The external characters of hardness, gravity, transparency, &c.,as given, agree with those of Laumonite ; — the latter has a pearly lustre on cleavage planes, and is raonoclinic ; gelatinizes, which stil- bitic minerals do not do ; and the fact that minute crystals of stilbite do occur in small cavities of the substance, may explain the -87 of potash with some soda. Being Laumonite, the several years have told upon the proportion of water, but in other respects the analysis agrees with those of Laumonite, especially with that of Scott ; and it may be observed that those by Connell and Babo, of Skye speci- Intelligence and Miscellaneoits Articles, 553 mens, diflFer from the per-centage proportions required by the for- mula in precisely the same particulars. I heartily agree with Mr. Mallet in the opinion he expresses in his concluding sentence, that it is far from " desirable to add to the already numerous names of stilbite-like minerals ; " and the sincerity of his expressed opinion is most strikingly evinced by his refraining from naming the substance till time should have tested its specifijc individuality. P.S. For the sake of comparison with Mr. Mallet's description, I quote from a paper (which I have just laid my hands upon) on the Geology and Mineralogy of Skye, read some years ago at the Edin- burgh Geological Society. Speaking of the minerals to be found at the Storr, " Laumonite is here found in veins of about 1 inch in thickness, which consist of a congeries of minute crystals, so con- fused as to have a granular appearance ; this mineral, strange to say, used to pass under the name of hypostilbite, and under that name came into Dr. Scott's hands, who analysed it." To the Editors of the Philosophical Magazine and Journal. Gentlemen, I believe the great question at issue between M. Riess and my- self is the exactitude of a law of " electrical heat " which M. Riess thinks he has discovered. Now, without seeking to prolong a painful controversy, or further canvas the accuracy of the several statements relative to myself found in M. Riess's last communica- tion, I trust you will be so good as to grant me the privilege of a few lines immediately bearing upon the law of electrical heat just referred to. The course of experimental research pursued by M. Riess amounts to this : — He accumulates and discharges through a wire a given quantity of electricity. First the given quantity is collected on a certain number of coated jars, then on a larger number. He says, that in the latter case the tension or intensity (or whatever he may please to call it) of the accumulated charge has suffered a change, and that in consequence of this change the heating power is dimi- nished ; that the heat is in fact inversely proportional to the surface over which the electricity has been expanded, all other things being the same. I take occasion, in opposition to all this, to remind M. Riess of some well-known phsenomena of electrometer indications, and cer- tain generally admitted laws of electrical force and measurement by- such instruments. I show, and I believe very clearly, that these instruments signalize nothing whatever of any change in quality of the accumulated charge ; that they are altogether influenced by conditions quite foreign to all such views ; that what we learn from Phil Mag. S. 4. No. 82. Buppl VoL 12. 2 0 654 Intelligence and Miscellaneous Articles, such instruments is merely the relative state of activity of the whole or of a portion of the charge, in a given direction, taken in terms of a given statical force, either attractive or repulsive, and by the instru- mentality of which we may occasionally infer the quantity oi electricity in operation at the instant of discharge. I further show, by reference to investigations prior to those of Dr. Riess, that the diminished effect of the electrical discharge observed in accumulating and dis- charging a given quantity of electricity from an increased surface, taken in parts, as in the case of extending a battery by the addition of other jars, arises solely from the resistance we thereby introduce into the circuit of discharge, and not from any change of tension in the accumulated electricity itself; and in confirmation of this, I call Dr. Riess's attention to the fact, as a crucial experiment, that when the given quantity of electricity is accumulated on an undivided sur- face, that is to say, when it is collected on the extended surface of a single large jar, for example, instead of an extension of surface by means of several lesser jars, the surfaces being in each case alike extended, — or when collected on two separate jars of such unequal surfaces and magnitudes as to give electrometer indications of ex- tremely different intensities, — then no change takes place in the heating effect of the discharge ; consequently the mere extension of the surface of the battery, taken alone, has really no influence on the result ; and Dr. Riess's law of electrical heat falls to the ground. Now to this experiment Dr. Riess makes no reply. It would be easy for me to animadvert effectively upon all Dr. Riess has advanced in his last communication. I am not certainly open to the censure of having taken Haldane's method of measuring quantity as my own ; and in confirmation of this I beg to refer to my paper in the Transactions of the Plymouth Institution, also to page 358, Phil. Mag. vol. xi., referred to by Dr. Riess himself, I cer- tainly resorted to the method at first, without being aware that the same method had been already employed by Haldane ; but I was very cautious in claiming any precedence, or stating, as Dr. Riess has done (Pogg. Ann. vol. xl. p. 324), that I was the " first to apply this method" practically, although I certainly employed it many years previously to the appearance of Dr. Riess's paper in Poggen- dorff, and precisely in the way described by him, that is to say with a Lane's bottle in communication with the external coating, instead of a Cuthbertson's balance as used by Haldane. . I have the honour to remain, Gentlemen, Your very obliged and obedient Servant, 6 Windsor Villas, Plymouth, W. Snow Harris. Dec. 20, 1856. 555 INDEX TO VOL. XII, ACRYLE and its compounds, on the constitution of, 310. Airy (G, B.) on Scheutz's calculating machine, 225 ; on the mean density of the earth, 228 ; on some pendu- lum experiments undertaken in the Harton Colliery, 467. Alcohol, on the action of nitric acid on, 3f)l ; on the synthesis of, 631. Alcohols, on new classes of, 309, 532. Aldehyde-ammonia, on the action of chloride of benzoyle on, 303. Aldehydes, on the formation of, 57. Algebraic equations of the fifth degree, on the resolution of, 124. Alison (Dr. S. S.) on a new sphygmo- scope, 387. Alkaline metals, on the electric con- ducting power of the, 199. Aluminium, on the specific heat and atomic weight of, 494. Amidobenzoic acid, 302. Ammonia, on the oxidation of the con- stituents of, by porous media, 457- Anisic alcohol, on the production and properties of, 188. Anisoinic acid, on the formation and constitution of, 56. Arsenic, on the use of, in steeping grain, 53. Atkinson (Dr. E.), chemical noticesby, 51, 188, 297, 531. Babbage (C.) on the action of ocean- currents in the formation of the strata of the earth, 69. Baily (W.) on the fossils of the chalk- flints and greensand of Aberdeen- shire, 152. Bechamp (M.) on the conversion of albumen into urea, 537. Belhomme (M.) on the presence of carmine in Monarda didyma, 538. Belli (Prof. G.) on the simultaneous existence of opposite electrical cur- rents in the same conducting wire, 485. Bentley (C. A.) on an improved con- struction of Ruhmkorff' s induction coil, 519. Benzoic acid, on some derivatives of, 301. Benzoic aldehyde, on a new method for the formation of, 192. Bertagnini (M.) on anisic alcohol, 188. Berthelot (M.)on the relation between formic acid and carbonic oxide, 51 ; on the decomposition of hydro- bromic acid, 52; on the synthesis of organic compovmds, 531 ; on the neutral compounds of the saccharine matters with acids, 535 ; on the ac- tion of chloride and bromide of phosphorus on glycerine, 536. Biformene, 534. Binamidobenzoic acid, 302. Bineau (M.) on ozone, 324. Bismuth, on the form of an alloy of, 48._ Bleiniere, chemical examination of, 126. Blood, on the condition of the oxygen absorbed into the, 478. Books, new : — Delesse's Materiaux de Construction, 464. Boracic acid fumaroles of Tuscany, on the, 1.93. Boracic aether, on the formation and analysis of, 300. Boussingault(M.)on the use of arsenic in steeping grain, 53. Bowen (H. G.) on the geology of Trinidad, 151. Brodie (Rev. P. B.) on the Keuper of Warwickshire, 71. Brooke (H. J.) on a substance named Bleiniere, 126. Cahours (A.) on a new class of alco- hols, 309. Cambridge Philosophical Society, pro- ceedings of the, 316, 397. Cannizaro (M.) on anisic alcohol, 188. Carbonic oxide and formic acid, on the relation between, 5L Carius (M.) on a compound of sesqui- oxide of manganese with sulphuric acid, 58. Carmine, on the existence of, in Monarda didyma, 538. 2o2 556 INDEX. Cassehnaun (M.) ou the oxychlorides, 188. Cay ley (A.) on the cones which pass through a given curve of the tnird order m space, 20 ; on the theory of logarithms, 354 ; on quantics, 477' Cements, on the composition of cer- tain, 464. Challis (Prof.) on the composition of colours on the hypothesis of undu- lations, 329, 421 ; on the transmu- tation of rays of light, 521. Charcoal, on a peculiar power pos- sessed by, of removing matter from solution in water, 23. Chemical Notices from Foreign Jour- nals, 51, 188, 297, 531. Chiozza (M.) on the artificial produc- tion of oil of cinnamon, 55. Chlorides, on a new method of esti- mating, 57. Chloroform, on some experiments with, 297. Chlororubian, on the preparation and properties of, 270 j action of acids npon, 272; action of alkalies on, 278. CiraiaoMHi, on the artificial production of the oil of, 55, Clausius (Prof. R.) on the mechanical theory of heat, 81 ; on the applica- tion of the mechanical theory of heat to the steam-engine, 241, 338, 385, 426, 463. Cloez(S.) on the employment of iodide of potassium as a reagent for ozone, 237. Cobalt, on the specific heat of, 496. Cockle (J.) on the resolution of alge- braic equations of the 5th degree, 124. Colours, on a theory of the composi- tion of, on the hypothesis of undu- lations, 329, 421, 521. Cones, observations on, 20. Crystals, on the cleavage of, 35. Cysticercus cellulosa, on the structure and development of the, 141. Datiscetine, 01. Datiscine, on the preparation and pro- perties of, 59. Davidsonite, on the composition of, 386. Davy (Dr. J.) on the vitality of the ova of the Salmonidic, 305. Debus (Dr. H.) on the action of nitric acid on alcohol at common tempe- ratures, 361. De la Rue (W.) on the cleavage of compressed white lead, 157. De Luca (M.) on the action of chlo- ride and bromide of phosphorus on glycerine, 536. De Morgan (Prof.) on the question, what is the solution of a differential equation? 320. Diamagnetic force, on the polarity of, 161. Dick (A.) on an alloy of bismuth, 48. Diploceras, on the structure of the new genus, 7'^. Drach (S. M.) on Col. Sabine's pe- riodic and non-periodic temperature variations at Toronto, 406. Duppa (F. B.) on the bromide of ti- tanium, 232. Earth, on the mean density of the, 50, 228, 314; on the action of ocean- currents in the formation of the strata of the, 69 ; on the influence of the internal structure of the, on the length of the day, 99. Earthwork, on the mathematical theory of the stabiUty of, 468. Elasticity, on a mathematical theory of, 539. Electric conducting power of the al- kaline metals, on the, 199. Electrical currents, on the simulta- neous existence of opposite, in the same conducting wire, 485. discharge, on certain phaenomena of, 136. Electrolytical investigations, 157. Electro-magnetism, on the measure- ment of the speed of a railway train by means of, 487- Equations, differential, on the solution of, 320. Eye, on the structure of the, 148. Faraday's lines of force, observations on, 316. Fluids in motion, on the thermal effects of, 466. Fluorides, researches on the, 53. Formic acid, on the relation between, and carbonic oxide, 51. Fossils, of the Keuper sandstone of Leicester, on the, 71 j on the dis- tortion of, 409. INDEX. 557 Foucault (M.) on the employment of induction apparatus, 403. Fremy (M.) on the fluorides, 53. Gardenia lucida, on the gum of, 64. Gases, on the endosmose of, 325. Geological Society, proceedings of the, 68, 149, 482. Geometry, remarks on a system of, 45.9. Geuther (M.) on the products of di- stillation of theTorhane Hill mine- ral, 65. Glass, on a new method of silvering, 58. Glycerine, on the action of chloride and bromide of phosphorus on, 536. Glycol, on the formation and consti- tution of, 532. Glyoxylic acid and salts, on the pre- paration and composition of, 362. Gold, on the possible origin of veins of, in quartz and other rocks, 73. Gravatt (W.) on rotatory motion, 477. Griffin (Dr. F. W.) on the explosive action of sodium on water, 78. Grimm (Dr.) on a new platinum salt, 301. Hamilton (Sir W. R.) on a new sy- stem of roots of unity, 446. Hansteen (Prof.) on the secular changes of the magnetical system of the earth, 466. Harley (Dr. G.) on the condition of the oxygen absorbed into the blood during respiration, 478. Harris (Sir W. S.) on certain phseno- mena of electrical discharge, 136; oil Riess's law of electrical heat, 553. Harrison (A. A.) on the theory of heat, 399. Haughton (Rev. S.) on the density of the earth, 50 ', on slaty cleavage, and the distortion of fossils, 409. Hautefeuille (M.) on the presence of mercury in the native argentiferous copper of Lake Superior, 238. Hay ward (Mr.) on a direct method of estimating velocities, 397. Hearder (J. N.) on a powerful form of the induction coil, with some new statical and thermal effects of the induced current, 377^ 443. Heat, on the mechanical theory of, 75, 81, 103; on the application of the mechanical theory of, to the steam-engine, 241, 338, 399, 426> 463 ; of chemical combinations, on the, 65, 74, 155, 233, 321. Heat, electrical, on a law of, 322, 553. , specific, of simple bodies, on the, 489. Heddle (Dr.) on the Davidsonite of Thomson, 386 ; on the new zeolite from Skye, 552. Heintz (M.) on chloroform, 297; on the action of chloride of sulphur on formiate of baryta, 299. Hennessy (J. P.) on the theory of par- allels, 283, 371, 452. Hennessy (Prof. H.) on the influence of the earth's internal structure on the length of the day, 99. Herschel (Sir J. F. W.) on slaty cleavage and the contortions of rocks, 197. Hofmann (Dr. A. W.) on insolinic acid, 146; on some of the meta- morphoses of naphthalamine, 226 ; on a new class of alcohols, 309. Hoppe (M.) on heat as the equivalent of work, Tb. Hunt (R.) on a peculiar power pos- sessed by porous media of removing matter from solution in water, 123. Hydrobromic acid, on the decompo- sition of, 52. Ibbetson (L. L. B.) on the possible origin of veins of gold in quartz and other rocks, 73. Induction apparatus, on the employ- ment of, 403. Induction coil, on new arrangements ofthe, 337, 443,519. Insolinic acid, on the preparation and constitution of, 146. Iodide of silver, on the behaviour of, towards ammonia, 157. Iridium, on the specific heat and atomic weight of, 494. James (Lieut.-Col.) on the mean spe- cific gravity ofthe earth, 314. Jamin (M.) on the endosmose of gases, 325. Joule (J. P.) on the heat absorbed in chemical decompositions, 155, 321; on Clausius's application of the mechanical theory of heat to the steam-engine, 385 ; on the thermal effects of fluids in motion, 466. Kolbe, on a new method for the for- mation of benzoic aldehyde, 192. 558 INDEX. Kopp (Prof.) on the boiling-points of corresponding chlorine and bro- mine compounds, VJi). Kraut (M.) on the changes which toluylic acid undergoes in the sy- stem, 193. Lallemand (M.) on some new deriva- tives from thy mole, 534. Laumonitc, analysis of, 552. Leucine, on the occurrence of, in the thymoid gland, 67. Liebig (Prof.) on a new method of silvering glass, 58. Light, on the demonstration of Fres- nel*s formulae for reflected and re- fracted, 1, 104, 266 ; on the trans- mutation of rays of, 521 . Limpricht (Dr.) on thioformic and anisoinic acids, 56; onanewmethod for the formation of aldehydes, 57 ; on some compounds of salicyhc acid, 1 92; on the actionof chloride of ben- zoyle on aldehyde-ammonia, 303. Liquid, on the constitution of jets of, issuing from circular orifices, 286. Lithia, on the phosphate of, 190. Lithium, on the specific heat and atomic weight of, 502. Logarithms, on the theory of, 354. Lophine and salts, on the constitution of, 55. M'Rea (W. C.) on the measurement of the speed of a railway train, 486. Magnetic disturbances, on periodical laws discoverable in the meanefi'ects of the larger, 231. Magnetism, on the optical properties of transparent bodies submitted to the action of, 483. Magnus (Prof.) on electrolysis, 157 ; on the allotropic conditions of sul- phur, 526. Mallet (Dr. J. W.) on a zeolitic mine- ral from the isle of Skye, 406, 552. Manganese, on a compound of sesqui- oxide of, with sulphuric acid, 58. Mannite, on some new compounds of, 535. Marett (C.) on the causes of the in- tervals between high-water and slack-water, 184. Martin (P. J.) on the anticlinal line of the London and Hampshire basins, 447. Masonry, on the mathematical theory of the stability of, 468. Matthiessen (Dr. A.) on the electric conducting power of the alkaline metals, 199. Maxwell (Mr.) on Faraday's lines of force, 316 ; on the elementary theory of optical instruments, 402. Mayer (M.) on the phosphate of lithia, 190, Mercurial interniptor, description of the, 403. Mercury, on the presence of, in the native argentiferous copper of Lake Superior, 238. Metals, on the electro-dynamic pro- perties of, 393. Meteorological observations, 79, 159, 239, 327, 407, 487. Miller (Prof. W. II.) on the form of an alloy of bismuth, 48; on the construction of the Imperial stand- ard pound, 540. Mineral waters, detection of organic acids in, 538. Mohr (M.) on a new method of esti- mating chlorides, 57. Moon, on the mountains of the, 475. Moore (J. C.) on the Silurian rocks of Wigtonshire, 68. Naphthalamine, on some of the meta- morphoses of, 226. Natanson (M.) on the artificial pro- duction of urea, 194; on acetyl- amine, 195. Nickel, on the specific heat of, 496. Nitrification, remarks on, 457- Optical instruments, on the element- ary theoiy of, 402. Orthoceras, description of a new, 72. Osmium, on the specific heat and atomic weight of, 493. Owen (Prof.) on the Stereognathus ooliticus, 482. Oxy chlorides, on the, 188. Ozone, on the employment of iodide of potassium as a reagent for, 237; observations on, 324. Parallel lines, on the doctrine of, 220, 283, 371, 375, 452. Pendulum experiments, account of some, 467. Perkin (Mr.) on the metamorphoses of naphthalamine, 226, Phaseomannite, on the preparation and constitution of, 304. Phillips (Prof. J.) on a drawing of the lunar spot Copernicus, 474. INDEX. 559 Phosphoric acid, on a new method of estimating, 192. Picard (M.) on the presence of urea in the blood, 537. Plant (J.) on the Keuper sandstone and its fossils, 71- Plateau (M. T.) on the recent theories of the constitution of jets of liquid issuing from circular orifices, 286". Platinum, on a new compound of, 301. Potassium, on the specific heat and atomic weight of, 500. Powell (Rev. B.) on the demonstra- tion of Fresnel's formulae for re- flected and refracted light, and their applications, 1, 104, 266. Prestwich (J.) on the correlation of the middle eocene tertiaries of Eng- land, France, and Belgium, 153. Projectiles, on a construction for the range of, 112. Ptychotis Ajowan, on the oil of, 63. Quantics, memoir on, 477- Quaternions, on extensions of the,446. Railway train, on the measurement of the speed of a, 486. Rainey (G.) on the structure and de- velopment of the Cysticercus cellu- loscc, 141. Rankine (W. J. M.) on heat as the equivalent of work, 103 ; on the mathematical theory of the sta- bility of earthwork and masonry, 468. •Regnault (M.V.) on the specific heat of some simple bodies, and on the isomeric modifications of selenium, 489. Reissig (M.) on a new method of esti- mating phosphoric acid, 192. Rhodium, on the specific heat and atomic weight of, 493. Riess (Dr. P.) on a law of electrical hea 322, 553. Ritter (M.) on thioformic and aniso'inic acids, 56 ; on the aldehydes, 57. Rose (Prof. H.) on boracic aether, 300. Rotatory motion, observations on,477. Royal Society, proceedings of the, 59, 141, 226, 305, 387, 466, 539. Rubian, action of alkalies and oxygen on, 200 -, action of chlorine on, 270. Sabine (General) on the larger mag- netic disturbances, 231. Salicylic acid, on new compounds of, 192. SalmonidcB, on the vitality of the ova of the, 305. Salter (J. W.) on a new genus of Cephalopoda, 72 ; on the fossils of the chalk-flints and greensand of Aberdeenshire, 152. Sand, on a peculiar power possessed by, of removing matter from solu- tion in water, 23. Sawkins (J. G.) on the movement of land in the South Sea Islands, 73. Scheerer (Prof.) on the detection of several organic acids in mineral waters, 538. Scheutz's calculating machine, ob- servations on, 225. Schmidt (Prof.) on the boracic acid fumaroles of Tuscany, 193. Schonbein (Prof.) on the oxidation of the constituents of ammonia by porous media, and on nitrification, 457. Schunck (Dr. E.) on rubian and its products of decomposition, 200, 270. Secchi (P. A.) on a drawing of the lunar spot Copernicus, 474. Selenium, on the isomeric modifica- tions of, 489. Silicium and titanium compounds, on the formulae of, 190. Silicon,on an allotropic condition of,54 . Silurian rocks of Wigtonshire, on the, 68. Slaty cleavage, on the theory of the origin of, 35, 127, 197, 409. Sodium, on the explosive action of, on water, 78 ; on the specific heat and atomic weight of, 497. Sorby (H. C.) on the theory of the origin of slaty cleavage, 127. Sphygmoscope, description of a new, 387. Spratt (Capt.) on the geology of Varna, 150. Steam-engine, on the application of the mechanical theory of heat to the, 241, 338, 385, 426, 463. Stenhouse (Dr. J.) on certain vege- table products from India, 59. Stereognathus ooliticus, observations on the, 482. Stevelly (Dr. J.) on the doctrine of parallel lines, 220, 375. Stokes (Prof. G. G.) on a theory of the composition of colours, 421. 560 INDEX. Sulphur, on the allotropic conditions of, 526. Sylvester (Prof. J. J.) on a construc- tion for the range of projectiles, 112. Symonds (Rev. W. S.) on trap dykes, 73. Teeth, on the structure of the, 470. Tellurium, on the specific heat and atomic weight of, 504. Thames water, on the composition of, 23,114. Thioformic acid, on the formation and constitution of, 56. Thomson (Prof. W.) on the electro- dynamic properties of metals, 393 ; on the thermal efilects of fluids in motion, 466; on a mathematical theory of elasticity', 539. Thymole, onnewdenvativesfrom, 534. Tides, observations on the, 184. Titanium and silicium compounds, on the formulae of the, 190, 232. Toluric acid, on the preparation and properties of, 193. Tomes (J.) on the presence of fibrils of soft tissue in the dentinal tubes, 470. Tyndall (Prof.) on the cleavage of crystals and slate rocks, 35, 129; on the polarity of the diamagnetic force, 161. Ultramarine, artificial, on the consti- tution of, 300. Unity, on a new system of roots of, 446. Urea, on the artificial production of, 194; on the production of, from albumen, 537 ; on the presence of, in the blood, 538. Velocities, on a direct method of esti- mating, 397. Verdet (M.) on the optical properties of transparent bodies submitted to the action of magnetism, 483. Vogel (Dr. A.) on the behaviour of iodide of silver towards ammonia, 157. Vohl (Dr.) on a triple sulphate of magnesia, manganese and zinc, 304; on a new saccharine matter from Phaseolus vulgaris, ib. Voit (M.) on some benzoyle com- pounds, 301. Waller (Dr. A.) on the organ of vision, 148 ; on the vagus and spinal accessory nerves, 472. Water, on the purification of, 23. Weald-denudation, observations on the, 447. Wedgwood (H.) on a system of geo- metry derived from an analysis of our ideas of direction and position, 459. White lead, on the cleavage of com- pressed, 157. Wilkens (M.) on artificial ultra- marine, 300. Witt (H. M.) on a peculiar power possessed by porous media of re- moving matter from solution in water, 23 ; on the variations in the chemical composition of the Thames water, 114. Wohler (Prof.) on an allotropic con- dition of silicon, 54. Woods (Dr.) on the heat of chemi- cal combinations, 65, 74, 233. Woodward (S. P.) on an Orthoceras from China, 72. Wurtz (Dr.) on a new series of al- cohols, 532. END OF THE TWELFTH VOLUME. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.