I.=\ + 



Thcori/ of Ixefraction in Gases. 491 



Hence 

 _j0001478P I ^7P 1 |._^-095^.,/i j,p\^ 



(i + -6o3()507t; 1 (i + -oo3(i07T;7 \ '^" e \ o^v] 



Hence 



'00 0295(i P I -0007 P ] r , ;095(9o ] 



"^ (1 + -003650 7'^ I u + -ooai^oTG J I e~ J * 



Hence at 7(3 cms. and 1(3° C. we get 



Iv = l + -000304. 



Boltzmann gives K = l + •000250 at 16° C. ; but this is 

 the mean of two series o£ experiments which gave resjjectively 



K = l + -000272, 



K = l + -000228. 



Thus Boltzmann's experiments do not admit of great ac- 

 curacy; and this is not surprising in view of the tremendous 

 difficulty of measuring the value of K— 1 for hydrogen. 



(9) Conclusions. 



I think it must be admitted that the numerical test has 

 been very severe, and the agreement most satisfactory when 

 we remember the uncertainty of the experimental values of 

 the dispersion and temperature deviations. The agreement 

 is particularly oood in the two cases where we have most 

 data^ SO2 and NH3 ; and in these cases the value of K — 1 is 

 very much greater than the values of fj? — 1 in the visible 

 spectrum. 



The theory gives a substantial explanation of all the essential 

 facts connected \\ith refraction and the dielectric constant 

 which I summarized at the beginning of the paper. It shows 

 that dispersion is controlled by the temperature and not by 

 free periods of vibration ; but notwithstanding this the dis- 

 persion does not vary much with temperature except near 

 the point A. In the case of hydrogen we should expect that 

 by raising the temperature a few hundred degrees the dis- 

 persion ought to be completely reversed. 



If the theory is correct, it throws great doubt on estimates 

 of molecular quantities based on theories which do not explain 

 the temperature effects, and shows that until we have experi- 

 ments over a much greater range than the visible spectrum 

 it is unwise to trust much to an approximate formula which 

 represents only some of the facts in a comparatively limited 

 region. 



