View of the Undulatory Theory of Light. 23 



In this case also the moving force will have for its projec- 

 tions, expressions analogous to those before given (l.), which 

 will be 



AS 



r cosa + - - , ^, "1 



m 



f cos 13 + -- ^ 1 



mSU ____JLf(r(l+s))J 



r cosy + ~- 1 



^S|.. --^?;^f(r(l+e))j 



(8. 



For abbreviation, let us assume a function /(r) such that we 

 have 



l(!_(i±!)) = a/(r)+fW (9.) 



Also, by supposition, Af, &c., and s are very small quan- 

 tities, so that terms of these quantities of two dimensions may 

 be neglected. Combining this consideration with that of the 

 equations (5.), we shall see that two terms will disappear from 

 the coefficients of m in (8.) when expanded by introducing 

 the value (9.)? or those coemcients will take the form 



S |m ^Afj+ S{m/(r)ecosa} 

 S4m-^A>)|H-S {mf{r) e cos /3} (10.) 



S ^m ~ A^\+ S {mf{r) s cos y}. 



Again, from equation (6.)? on the same supposition of neg- 

 lecting the powers above the 1st, we shall have a value of e 

 which will be, 



6 = — (cosaAf + cos/3A>j + cosyA? (11.) 



But the coefficients of m represent the accelerative force 

 which solicits the molecule m due to the action of the molecules 

 ?», m', ?w", &c. On the other hand, by the principles of dy- 

 namics, these accelerative forces parallel to the three axes 

 will be expressed by the second differential coefficients of 

 ^, >j, ^, related to the variable t. If, then, we take the simpli- 

 fied expressions (10.), and introduce the value of s (ll.)> we 

 shall finally obtain the expressions 



