496 Lord Rayleigh on the Pressure of 



operate, but it remains undisturbed even when we introduce 

 such forces, provided that they be of the character considered 

 in the theory of capillarity, that is extending to a range 

 which is a large multiple of molecular distances and not 

 increasing so fast with diminishing distance as to make the 

 total effect sensibly dependent upon the positions occupied 

 by neighbours. Under these restrictions symmetry ensures 

 that the resultant force upon a sphere, situated in the interior 

 and not undergoing collision, is zero ; and the whole effect 

 of such forces is represented (Young, Laplace, Van der Waals) 

 by an addition to the pressure of a quantity independent of 

 the temperature and inversely proportional to the square of 

 the volume. In Van der Waals' well-known form 



(p+^)("- J )= RT > ( 5 ) 



the relation between p and T is still linear. Even if the 

 particles depart from the spherical form, the virial of col- 

 lisional and cohesive forces remains a linear function of the 

 temperature*. 



The forces above considered are partly repulsive and partly 

 attractive. Repulsion at a certain degree of proximity seems 

 to be demanded in order to preserve the individualitv of 

 molecules and to prevent infinite condensation. It will be 

 remembered that Maxwell proposed a repulsion inversely as 

 the fifth power of the distance, partly as the consequence of 

 some faulty experiments upon the relation of viscosity to 

 temperature and partly no doubt on account of a special 

 facility of calculation upon the basis of this law. So far as 

 viscosity (rj) is concerned, its relation to temperature (T) 

 when the force of repulsion varies as p~ n is readily obtained 

 by the method of dimensions f- It appears that 



3 



2n— 2 



V or T^" 2 (6) 



The case of sudden collisions may be represented by taking 

 ?i = go , so that 



i] cc T* : (7) 



while if n = 5 



V a T . { 8) 



According to experiments on the more permanent gases n 



* "On the Virial of a System of Hard Colliding Bodies," 'Nature,' 

 xlv. pp. 80-82 (1891) ; Scientific Papers, iii. p. 469. 



t Proceedings Royal Society, lxvi. p. 68 (1900) ; Scientific Papers, iv. 



