500 Lord Rayleigh on the Pressure of 



form, in which a factor T is introduced in the denominator. 

 The most natural extension of the formula would be by sub- 

 stituting a quadratic for a linear form of F in (21). We 

 should then write 



iSp*M = ^7-AT+B/*'a + C-^j£) l • (23) 



A, B, C being arbitrary constants ; and the pressure equation, 

 when written after Van der Waals' manner with neglect of 

 v~ 2 , becomes 



{p+$(BSa + C ^)} U- <^} =ET. . (24) 



As has already been said, Van der Waals' form corresponds 

 to C = 0. On the other hand, the Rankine and Clausius form 

 requires that B = 0, while C remains finite. It will be 

 evident that the two alternatives differ fundamentally. 

 According to the latter the cohesional terms tend to vanish 

 when T is sufficiently increased. 



If the cohesional terms are to vanish when T is infinite, 

 the forces concerned must be of an entirely different character 

 from that contemplated in Laplace's and Van der Waals' theory. 

 It has been suggested by Sutherland * that the forces may 

 be of electric origin and in themselves (except during actual 

 collision) as much repulsive as attractive. This is not 

 inconsistent with the preponderance of attraction in the final 

 result. " There is this fundamental distinction in the effects 

 of attractive and repulsive forces whose strength decreases 

 with increasing distance, that the attractive forces by their 

 own operation tend to increase themselves, while the repulsive 

 forces tend to decrease themselves.'" The forces contem- 

 plated by Sutherland are such as are due to electric or 

 magnetic doublets, but a rather simpler illustration may be 

 arrived at by retaining the single character of the centres of 

 force, and supposing them to be as much positive as negative, 

 under the usual electrical law that similars repel while 

 opposites attract one another. When T is infinite, so that 

 the paths are not influenced by the forces, the cohesional 

 virial will disappear, but it may become finite as the tempera- 

 ture falls and room is given for the attractive forces to 

 assert their advantage. There is nothing in the argument 

 upon which (21) was founded which is interfered with by 

 the occurrence of the two kinds of particles, and it would 



* Phil. Mag. vol. iv. p. 625 (1902). 



