July 4. 1895] 



NA TURE 



221 



LETTERS TO THE EDITOR. 



( The Editor does not hold himself 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 NATURE. 

 No notice is tahen of anonymous communications. ] 



The Size of the Pages of Scientific Publications. 



It was with much surprise that we received the circular of the 

 Royal Society stating that it had been decided to abandon the 

 present size of its Proceedings in favour of royal octavo, 

 accompanied liy a voting card on the question of a similar change 

 in the size of the Transactions. At the Oxford meeting of the 

 British Association, a Committee was appointed, by Section A, to 

 endeavour to secure greater uniformity in the sizes of the pages 

 of the Transactions and Proceedings of all societies which publish 

 mathematical and physical papers. In view of the report which 

 that Committee will present shortly at Ipswich, it is much to be 

 hoped that the Council of the Koyal Society will take no 

 immediate steps toward carrying their recommendations into 

 effect. 



A considerable degree of uniformity already exists. The 

 present octavo size of the Proceedings of the Poyal Society is very 

 nearly the same size as the l^hilosophical Magazine, the Report 

 of the British .Association, the Proceedings of the London Mathe- 

 matical Society, and of the Cambridge Philosophical Society, and 

 many other publications. The Annalen der Physik iind Chcmie 

 is so very little smaller, that reprints from it can be bound up 

 with others from the afore-mentioned sources, without paring 

 down their margins excessively. For papers involving long 

 mathematics or large diagrams, the quarto size of the present 

 Philosophical Transactions approximates to uniformity w ilh the 

 American fournal of Mathematics, the Comples rcndus of the 

 -Vcademie des Sciences of I'aris, the Cambridge Transactions, 

 the Edinburgh Transactions, and numerous other quarto 

 Transactions, such as those of the Institution of Naval Architects. 



It is very important that specialists in any branch of science 

 should be able to collect, and bind together, reprints of papers on 

 their own particular subjects, and such volumes are of permanent 

 value as works of reference. So long as there are only two 

 sizes to deal with — the above-mentioned quarto and octavo — there 

 is little difficulty about this, but occasionally one comes across a 

 pajjer of intermediate size, which cannot be bound up with 

 either, and the collection is thus necessarily incomplete. It is 

 hoped that the report, .so shortly to be presented, will be a guide 

 to authors of papers in indicating which publications to select, 

 and which lo avoid, if ihcy desire to conform to the average 

 standard sizes. .-Vlthough the work of the Committee is at 

 jiresent confined to mathematical and physical |)apers, it might 

 jierhaps be of advantage that the matter should he discussed in, 

 and re]ircsentatives on the Committee appointed from the other 

 .Sections of the British A.ssociation as well. The question of 

 changing the size of the Proceedings was recently discussed by 

 the London Mathematical Society, but it was decided to retain 

 the existing form, at any rate for the present, mainly on account 

 of its uniformity with other jjublications. It will be most 

 unfortunate if the Royal Society takes any retrograde step w hich 

 may prevent the sizes of its Proceedings and Transactions from 

 being adopted as the standards. 



C. H. Bryan. 

 Svi,v.\Ms P. Thompson. 



On the Minimum Theorem in the Theory of Gases. 



Vor woulil oblige me by inserting the following lines in 

 Nati'RK. The last remark made by Mr. Burbury points out, 

 indeed, the weakest point of the demonstration of the H-thcorem. 

 If condition (.\) is fnlfdle<l at / = o, it is not a mechanical 

 necessity that it should be fulfdled at all subsequent limes. But let 

 the mean path of a molecule be very long in comparison with 

 the avcriige distance of two neighbouring molecules ; then the 

 absolute position in space of the place where one impact of a 

 given molecule occurs, will be far reinoved from the jilace 

 where the next impact of the same molecule occurs. For this 

 reason, the distribution of the molecules surrounding the place of 

 the second inqiact will be inde[ieiideiit of the conditions in the 

 neighbourhood of the place where the first impact occurred, and 

 therefore independent of the motion of the molecule itself. 

 Then the probability that a second molecule moving with 

 given velocity should fall within the sjiace traversed liy the first 



NO. 1340, VOL. 52] 



molecule, can be found by multiplying the volume of this space 

 by the function/. This is condition (.K). 



Only under the condition, that all the molecules were arranged 

 intentionally in a |rarticular manner, would it be possible that 

 the frequency (number in unit volume) of molecules with a given 

 velocity, should depend on whether these molecules were about 

 to encounter other molecules or not. Condition {\) is simply 

 this, that the laws of probability are applicable for finding the 

 number of collisions. 



Therefore, I think that the assumption of external dis- 

 turbances is not necessary, provided that the given system is a 

 very large one, and that the mean path is great in comparison 

 with the mean distance of two neighbouring molecules. 



LlDWIG Bol.TZ.\IANN. 



9 Tuerkenstrasse, Vienna, June 20. 



Argon and the Kinetic Theory. 



The spectrum exhibited by argon undoubtedly shows that, 

 under the conditions of the experiment, the molecules composing 

 the gas are set into an intense state of vibration, while the ratio 

 of the specific heats (5/3, about) shows, according to the equation 



J3 = | , that (8=1, and therefore the gas is, as pointed out by 



7- I 

 Lord Rayleigh, monatomic, and cannot therefore be capable of 

 vibrating. But there is, I think, a very simple explanation of 

 this apparent contradiction, and that is, that the above equation 

 is not tnie, and that it should be, as will be proved hereafter, 

 ^ ~ 3^'(> ~ t)> where k is very nearly i for argon and other so- 

 called permanent gases. This latter equation gives 2 for the 

 value of 3 in argon, a value easily understood. 



The virial equation for smooth elastic spheres of finite magni- 

 tude is fPV = 2.Joti''- - J2R/-; and since the resilience is unity 

 and r finite, the term - A2R/' cannot vanish. Now the term 

 SPV represents work or its equivalent of energy ; hence the 

 right-hand member of the equation must represent the same, 

 and since the term 2Jwt'- is obviously kinetic energy, or its equiva- 

 lent of work, the term - i2R'' must also represent work or 

 energy. Now we can find the value of |PV in terms of 'S.hmi^, 

 as follows. Imagine a cube box so constructed that one side of 

 each pair can be used as a spring to discharge any mass in con- 

 tact with a velocity r. And suppose three smooth elastic 



spheres each of mass — to be discharged by the three spring 



3 

 sides with the above velocity into the interior of the box. Then 



M 

 the work done on each mass will be 4 . — w-. Put this equal to 



PV and take V equal to the volume of the box. The total work 

 done is evidently 3PV = AMf-'. If, instead of three elastic 

 spheres, we imagine a very great number of very minute ones of 

 the same total mass to be discharged by the spring sides with the 

 same velocity, the energy will be the same as before, and the 

 above equation will still be applicable ; and the state of affairs 

 now represented would be that of an ideal gas. But owing to 

 collisions after first starting the velocities of the particles will 

 vary, and therefore we must write the equation 



3PV = PU^=; (I) 



where v' is the mean square velocity of the particles. By hypo- 

 thesis V has the same value in the above equation as in the virial 

 equation ; and P can be proved, if necessary, to have the same 

 value in the two equations as follows. 



Ify = the mean acceleration or retardation, as the case may be, 

 of the cr. of gr. of an elastic sphere impinging directly against a 



plane; then ft = v. Also /= —,.'. t = — Mere / is half 



2s V 



the time of impact, and v the velocity normal to the plane 



before and after impact. Now if it can be shown that the time 



taken by the spring side of our im.aginary Ixix to give the same 



velocity is the Siimc as the above, then it is obvious that the 



mean pressures in the two cases must be identical. 



Assume i' to be the volume of the cul>e box, then s" is the 



area of each side. Now let the spring side be drawn back so as 



to act through a distance s on the mass — with a constant pres- 

 sure P per unit of surface ; then Pr* x j = PV represents the 

 work done. The velocity given to the mass is v, and the ac- 

 celeration constant. Hence the mean velocity of the spring 



