Theory of Surface Forces. 293 



K is also infinite. It seems therefore that nothing satisfac- 

 tory can be arrived at under this head. 



As a third example we will take the law proposed by Young, 

 viz. 



cf) (c) = 1 from s=0 to z=a, \ ,,-, 



cf){z)=0 from z=a to c=x :J 

 and corresponding therewith, 



U(z) = a—z from z = to z — a. 1 ,.._ 



II(s)=0 from z = a to c=x . J 



t(e)=ia(aW)-J(a 3 -, 3 ) 1 



from 0=0 to s=a, >■ . . (19) 

 ^(»)=0 from s=a to c= x . J 



Equations (12) now give 



K.= ^p&=^ .... (20) 



-fj> = 



7ra 

 40 



(21) 



The numerical results differ from those of Young*, who finds 



© 7 



that "£fc contractile force is one-third of the whole cohesive 

 force of a stratum of particles, equal in thickness to the interval 

 to which the primitive equable cohesion extends" viz. T = JtfK : 

 whereas according to the above calculation T = ^QrtK. The 

 discrepancy seems to depend upon Young having treated the 

 attractive force as operative in one direction only. 



In his Elementary Illustrations of the Celestial Mechanics 

 of Laplacef, Young expresses views not in all respects con- 

 sistent with those of his earlier papers. In order to balance 

 the attractive force he introduces a repulsive force, following 

 the same law as the attractive except as to the magnitude of 

 the range. The attraction is supposed to be of constant inten- 

 sity C over a range c, while the repulsion is of intensity R. 

 and is operative over a range r. The calculation above given 

 is still applicable, and we find that 



6 .... (22) 



* Enc. Brit. ; Collected Works, vol. i. p. 461. 

 + 1821. Collected Works, vol. i. p. 485. 



