High Vacuum,- Spectra of Gases. 253 



in size and mass compared with those of the other kind. In 

 this case it is easy to calculate first approximations to k t for 

 molecules which behave like centres of forces proportional 

 to the inverse nth. power of the mutual distance. The results 

 for a few typical values of n are : — 



n =5, 7, 9, 13, 17, 33, ». 



kt = 0, 0-156, 0-227, 0-291. 0*326, 0*372, 0*417. 



The last case also corresponds to rigid elastic spherical 

 molecules. Now the values of n which give the best repre- 

 sentation of actual gas molecules are found, from the invest- 

 gation of the variation of viscosity with temperature, to 

 range from 5 to 12 (cf. Jeans's * Dynamical Theory of Gases,' 

 p. 302, 2nd edit.) . In the case of such a gas mixture as we 

 are now considering, therefore, the value of k t is likely to be 

 less than one half the value calculated on the hypothesis of 

 rigid elastic spherical molecules : and although, in the case 

 of the gases to which our experiments relate, the mass- 

 ratio and size-ratio are not such that the above calculations 

 apply strictly to them, the general character of the result 

 is likely to be the same. The calculated values of k t (0*138 

 and so on) are slightly too small for rigid spherical molecules 

 (since further approximations would increase them by a few 

 per cent.), but they are probably twice or thrice too large for 

 actual gas molecules ; and when this is allowed for, the expe- 

 rimental confirmation of the theory, within the limits of the 

 experiments, appears to be as satisfactory as could be- 

 desired. 



Cambridge, December 1916. 



XXIII. High Vacuum- Spectra of Gases. By Prof. D. N. 

 Mallik, JD.Sc, F.R.S.E., and Prof. A. B. Das, M.Sc* 



[Plate IV.] 



1. "TTTHEN an electric discharge is passed through a 

 m vacuum-tube it seems to be reasonable to argue,. 

 a priori, that there would be a change in the character of the 

 spectrum at very high vacua. For in a discharge-tube, when 

 the contained gas is at moderately high pressure, there are 

 mutual collisions of corpuscles, positive particles, atoms, and 

 molecules, so that the modes of motion of a luminous gas- 

 particle in such a tube must be many — though limited by the 



* Communicated by the Authors. Paper read before the Third All- 

 India Science Congress, 1916. 



