May 12, 1892] 



NATURE 



29 



the author not only knows his subject thoroughly, but 

 understands how to deal with it in a way that shall be 

 readily intelligible. His main object has been to direct 

 attention only to important facts and principles, and to 

 bring out the various links by which they are logically 

 connected with one another. There are eleven chapters, 

 in which he treats of thermometry, dilation of bodies, 

 calorimetry, production and condensation of vapour, 

 change of state, hygrometry, conduction, radiation, 

 thermo-dynamics, terrestrial temperatures, aerial meteors, 

 and aqueous meteors. Few changes have been made in 

 the present edition, but the author has introduced a col- 

 lection of elementary problems, which, as he says, may 

 be " advantageously solved in connection with the subject- 

 matter to which they appertain." 



LETTERS TO THE EDITOR 



{The Editor does not hold him ielf responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of UxTXlKt.. 

 No notice is taken of anonymous communications.] 



Aurora. 



There was a fine aurora visible in this locality on 

 Saturday night, April 23. It was seen at intervals, when- 

 over the clouds broke away, until after midnight. This display 

 is specially interesting, because it forms the continuation of a 

 series of recurrences, at the precise interval of twenty-seven 

 days, which began in December, the dates being as follows : 

 December 9, January 5, February 2, February 29, March 27, 

 and April 23. Some of these displays have been brilliant, and 

 all of them have been well defined. In the table of auroras 

 which I have constructed, based upon a periodicity correspond- 

 ing to the time of a synodic revolution of the sun — namely, 

 t^\enty-seven days, six hours, and forty minutes — there was, for 

 several years preceding the sun spot minimum in 1889 and 1890, 

 a return each spring of series of recurrences associated with the 

 same part of the sun as that above described. A corresponding 

 systematic tabulation of the records of solar conditions shows 

 that this association bears a direct relation to reappearances at 

 the eastern limb of an area which has been much frequented by 

 spots and faculse, and which has been located persistently south 

 of the sun's equator. In like manner there are other areas 

 located in the sun's northern hemisphere which have been 

 much disturbed, and whose reappearances at the eastern limb 

 have been attended year after year by series of recurrences of 

 the aurora, in the autumn months chiefly, if not exclusively. 

 From this it would appear that, in order that a solar disturbance 

 may have its full magnetic effect upon the earth, it is necessary 

 that it should be at the sun's eastern limb, and as nearly as 

 possible in the plane of the earth's orbit. It appears, also, that 

 the disturbances which recur upon certain parts of the sun so 

 persistently year after year have greater magnetic effect than 

 those of comparatively sporadic character located elsewhere. 



Lyons, N.Y., April 25. M. A. Veeder. 



The White Rhinoceros. 



In my '• Naturalist in the Transvaal" (p. 5), I recently 

 deplored the supposed fact that a perfect skin or skeleton of 

 Rhinoceros simus was unknown in any Museum ; and I relied for 

 my information on the interesting communication in your 

 columns made by Dr. Sclater (vol. xlii. p. 520). 



I have just received a very welcome letter from Dr. Jentink, 

 the Director of the Leyden Museum, stating that there are two 

 skins to be found in that collection, " one in a rather bad state, 

 but the other a beautiful stuffed specimen, measuring more than 

 3^ metres." 



Dr. Jentink had published this information in Notes from 

 the Leyden Museum (October 1890), a communication I had 

 not seen when I returned from the Transvaal and wrote on the 

 matter. 



This is a most gratifying fact for all zoologists, and the Leyden 

 Museum appears to have a unique treasure. 



Purley, Surrey, May 3. W. L. Distant. 



NO. II 76, VOL. 46] 



The Line Spectra of, the Elements. 



In Prof Runge's article on the spectra of the elements in last 

 week's issue of Nature (p. 607) he refers to my explanation of 

 double lines in the spectra of gases (" Cause of Double Lines in 

 Spectra,"Trans.ofthe Roy. Dublin Soc, vol. iv. 1891, p.563); and 

 says :— " I do not understand the decomposition of the arbitrary 

 curve " [rather, of the actual motion of the electric charge 

 within the molecules of the gas] "in a series of superposed 

 ellipses " [rather, into a series of pendulous motions in ellipses]. 

 " For the movement is supposed not to be periodical " [rather, 

 is not known to be periodical], "and Fourier's theorem then 

 would not apply, at least the periods of the superposed ellipses 

 would not be definite, as long as there are no data except the 

 arbitrary curve itself " [rather, no data except those furnished 

 by the positions and intensities of the spectral lines]. 



Prof Runge will pardon me if I say that this objection seems 

 to me to be of the same kind as a doubt with respect to the 

 value of tables of logarithms on the ground that many logarithms 

 are incommensurable with integer numbers, and therefore 

 cannot equal decimal fractions. 



Take, for example, a simple vibratory movement of an 

 electron within the molecules, represented by 



. . (I) 



= a sinl 2ir -.- J + i" sm I 2w . 1, 



which would give rise to two lines in the spectrum with oscilla- 

 tion-frequencies m and irm in each jot of time. This, Prof. 

 Runge objects, cannot be analyzed by Fourier's theorem, 

 because it is not periodic. But 



, . / 3'I4I59 int\ 



U-«^-^'^:'""\ . . .(2) 



V J I 



sin (2,-) 



sin(2.'^') + *sin(2.3-Hi5^3'«£^,. 



sin(2.^')-f<^sin(2.3-'4i5927-/>), 



.(3) 



(4) 



&c., 



&c.. 



&c 



being periodic, can be so analyzed. The motion represented by 

 the first of these (Equation 2) approximates for a certain time to 

 the actual motion which is represented by Equation I . The 

 motion represented by the next (Equation 3) approximates more 

 closely and for a longer time ; and so on. So that Fourier's 

 theorem can be applied to motions which approximate to the 

 non-periodic motion represented by Equation i, in any assigned 

 degree and for any assigned time ; just as a decimal can ap- 

 proximate in any assigned degree to the value of log 8, although 

 no decimal can equal that logarithm. 



G. Johnstone Stoney. 

 9 Palmerston Park, Dublin, May i. 



On a Proposition in the Kinetic Theory of Gases. 



In last month's Philosophical Magazine there is a paper by 

 Lord Rayleigh criticizing a demonstration by Maxwell of the 

 equalhy of the products dpy. . . dpn, dq^. . . dijn, and d?^ . . . dPn, 

 rf'Qi . . . dQ„, where the /s and P's are the momenta, and the 

 </'s and Q's the co-ordinates, of a system at the beginning and 

 end of any interval of time. 



Lord Rayleigh correctly points out that the assumption of E, 

 the total Energy, as an independent variable, vitiates the proof, 

 and he suggests the substitution of Hamilton's principal function 

 S for the characteristic function A, with /, the time, as an inde- 

 pendent variable. 



Prof Boltzmann took a similar objection to Maxwell's de- 

 monstration in a paper to the Philosophical Magazine in the year 

 1882, in the course of some comments on my use of the proof 

 in a small treatise on the kinetic theory of gases, and I then 

 privately suggested to him the substitution of S for A, with / 

 independent, as proposed by Lord Rayleigh. But unfortunately, 

 as I now see, the proposition dpy . . . di/„ - </P, . . . dQ,i, with 

 t independent, although doubtless true, has no application to 

 the particular problem in the kinetic theory of gases to which I 

 was applying it. 



My object was to abbreviate and simplify the proof of a funda- 

 mental theorem in the subject originally given by Bolizmann, 

 and which may be fairly well illustrated by the following simple 

 case :— . 



Suppose that in the plane of a projectile there are two mhnite 



