CONSTITUTED OF BTHOKULLT SYMMETRICAL MOLECULES. 1 7.1 



of 1/6, and that later terms become important in the case of vapours, though for 

 ordinal -y gases these, the first two, terms appear to be enough. 



As we have seen, the above laws of variation with temperature given by our theory 

 have txjen announced before. The difference between our formula? and the earlier 

 ones chiefly consists (as regards viscosity) in the numerical constants. We have 

 already seen, in the case of the coefficient of conduction, to what grave errors 

 (f 1'60 instead of 2'50) the older elastic-sphere theory may lead. The expression 

 given by MEYER for the viscosity differs considerably from the present one; JEANS* 

 made an undoubted improvement in the older theory by allowing for the persistence 

 of velocities after molecular collisions. The fact that this important consideration had 

 been previously overlooked illustrates the imperfections of that theory. As it is, the 

 correction for persistence of velocities is itself of uncertain amountt ; however, by its 

 means the discordance between the formula of the older theory, and that given by 

 the present theory for the case of elastic spherical molecules, is reduced almost to 

 10 per cent.J 



From equations (54) and (55) we proceed to determine what evidence the various 

 hypotheses lead to, as regards the size of molecules. Those formulae are strictly true 

 only for monatomic gases, but can be applied to polyatomic gases with much more 

 safety than could the formulae for the conductivity of gases, where the internal 

 energy (which here plays little or no part) was very important. The formula (56) 

 could also be used to determine the relative force constants of the molecules when 

 assumed to be point-centres of force, but as this is of less interest we shall not trouble 

 to do so. 



The said equations contain R/m, which can be determined from data as to the 

 density of a gas at a given temperature and pressure. A table of values of R/m for 

 several gases is given by JEANS (p. 113, loc. cit.). To determine <r, the radius of the 

 molecule, we also require to know m, or, since p = vm, we require to know v, which is 

 AVOGADRO'S constant. JEANS used the value 4x10'*, the best one then available ; 

 but recent researches agree in indicating 277 x 10 1B as the correct values, which we 

 shall therefore use here. In the following table are given the values of /u u , an( l 

 o-xlO 8 for some gases, the latter being calculated according to the two hypotheses 

 considered. It will be noticed that the radii of the molecules on the hypothesis that 

 they attract one another is less than that when no such forces exist ; of course, in the 



* " Dynamical Theory of Gases," p. 238, p. 250. 



t Ibid., p. 250, lino 13, where it is assumed for the sake of simplicity that the excess of momentum 

 above that appropriate to the point of collision goes in equal proportions to each molecule. 

 J In our notation, JEANS' formula (581) may be written 



S * /l 



Jw \** \m 

 which is '896 times our own expression. 



S SrniKUi.AM) ( 1'liil. Mag.,' 1909, February, p. 320) quotes RUTHERFORD as the authority for this 

 figure, and mentions that it is in good agreement with PLANCK'S value 2 80 x 10'". 



3 P 2 



