Raouit's Law of the Lowering of Vapour-Pressure. 411 



rotates. The plane-polarized rays into which the vibration 

 may be resolved are represented as before by cos <ot . cos nt. 

 There is of course one case in which these complications fail 

 to occur, i. e. when the axis of rotation coincides with the 

 axis of vibration ; but with axes distributed at random we 

 must expect vibrations (w + ft>) to be almost as important as 

 the vibration n. The law of distribution of brightness in the 

 spectral line would probably be exponential, as when the 

 widening is due to motion of molecules as wholes in the line 

 of sight. 



It will be of interest to compare the magnitudes of the two 

 effects. If v be the linear velocity of a molecule and V that 

 of light, the comparison is between &> and nv/V, or between 

 et) and v/X. If r be the radius of a molecule, the circum- 

 ferential velocity of rotation is tor, and we may compare <or 

 with vr/X. Now, according to Boltzmann's theorem, rco would 

 be of the same order of magnitude as v, so that the import- 

 ance of the rotatory and linear effects would be somewhat 

 as X : r. There is every reason to suppose that X is much 

 greater than r, and thus (if Boltzmann's relation held good) 

 to expect that the disturbance of homogeneity due to rotation 

 would largely outweigh that due to translation. 



Your results seem already to interpose serious obstacles in 

 the way of accepting such a conclusion ; and the fact that 

 light may thus be thrown upon a much controverted question 

 in molecular physics is only another proof of the importance 

 of the research upon which you are engaged. 



I am, 



Yours very truly, 



Rayleigh. 



September 23, 1892. 



XLVIII. An Attempt to give a Simple Theoretical Expla- 

 nation of Raouit's Law of the Lowering of Vapour- Pressure. 

 By F. G. Donnan * 



EAOULT'S Law, as is well known, applies to the lowering 

 of the vapour-pressure of a liquid, due to the solution 

 in it of a non-volatile substance. It asserts that the relative 

 lowering of vapour-pressure is proportional to the ratio of 

 the number of molecules of the dissolved substance to the 

 total number of molecules in the liquid. Expressed in sym- 

 bolical language this is 



/-/' , n 

 f N + n' 



* Communicated bv the Author. 



