of Attractive and Repulsive Forces. 185 



Suppressing also the periodic term in this value of T 2 , we 

 finally obtain 



a- a* = 7-0 siir cos 4 0. 



4/r 



The whole pressure on the hemispherical surface estimated in 



the direction from towards C is 2tto- \ era' sin 9 cos 0cW, 



taken from = to 6= ^-. The result is, 



7r 3 P>z 2 6 6 m 2 

 .Pressure = — 



48k 2 



18. Combining with this pressure that which was found in 

 art. 16 to be due to condensation, apart from the effect of con- 

 strained motion along the surface of the sphere, the whole 

 pressure, or moving force, in the direction of the propagation 

 of the waves is 



iPkntfm 2 77 s Irh' 2 b & m 2 i^hnl/nr /. irhnlrirX 



> 0T Q-I— I 1 



8* 4 48k 2 ' 8* 4 \ 6/ 



It is important to remark here that all the literal quantities in 



the second term within the brackets have fixed values, if the 



radius of the sphere be given, excepting the arbitrary factor k. 



If the sphere be supposed to be a physical atom, and the unit of 



space be not larger than the ten-millionth of a square inch, the 



area irlr referred to that unit would still be an exceedingly small 



fraction. It follows therefore that kn may be an exceedingly 



i i i -l jj; it. irknlrir , , 



large number, and at tne same time the term r be less 



° b 



than unity. In that case the pressure on the sphere would be 

 in the direction from towards C, which is that of the propa- 

 gation of the waves, and would correspond to repulsion. But 

 as k is a quantity entirely arbitrary, it may be supposed to 

 receive a value which would make that term greater than unity; 

 in which case the resulting pressure would be in the opposite 

 direction, and would correspond to attraction. 



19. These conclusions completely justify the theoretical 

 views respecting atomic repulsion and molecular attraction 

 which I communicated in an article on " A Mathematical 

 Theory of Heat," contained in the Philosophical Magazine for 

 March 1859. Similar views are advocated in the theories of 

 heat and of molecular attraction proposed in the l Principles 

 of Physics,' pp. 459-465 ; but the reasoning is there vitiated 

 by the admission of the hypothesis (subsequently rejected) 

 that the condensation emanating from a centre varies inversely 

 as the square of the distance from the centre instead of in- 

 verselv as the distance. In the article above mentioned I 



