176 Mb KELLAND, ON THE DISPERSION OF LIGHT, 



be less than - ; if the arc be greater than this = - + i suppose, since 



the expansion instead of proceeding in terms of the arc itself must 

 proceed in terms of its supplement, and an analogous rule applies to 

 larger arcs : 



as long then as ^ is less than -, 



op irop 1 w^op 



sm ir-^ = -— * g ■ ' + 



\ X 6 X' 



when — lies between i and 1, we have 



sm-^ = sm.-^ = .(l-fj- g (1-f) +&c. 



and so on for other values. 



The expansion, then, with this restriction, which is perhaps not re- 

 quisite, as at any rate the principal terms are those which arise from 



particles near P, proceeds with powers of r^; and we obtain 



Suppose the function which expresses the mutual action of two par- 

 ticles on each other, some power of the distance, or let r<p(r) = -; 



r" 



Fir) = - '^.. 



