240 Mr KELLAND, ON THE MOTION OF 



Fr w + 1 



for — = - ^^^ ; 



Fr ^ ,^ . JSx S.r + Sf + 5s- - (« + 1).5«= . . kSx 

 ■•• i<pr + -^^^) ^^^'-^ " ?^' "2~ 



5»/ + Sx' — w^a;- . , kSx 



and aliffr = al%^fr; 



Fr ^ , . Ji^x ^hr-n^x- . , k^x 

 hence, a ((^r + —^^0 snr -j- = <^ ^,,-,3 sin- — . 



No%v on expanding the sine, it is clear that when — becomes 



greater than unity, or which is the same thing, when Sx becomes greater 



than - , we must put the supplement instead of the arc in the expansion ; 



but we saw reason in the case of light to suppose that the expression 

 for the whole force has the same sign, as the expression for the force 

 exerted by those particles only which lie within the range of the first 

 half wave. 



In fact, if the different half waves give different signs, it is evident 

 that they must give them aUernatehj; and thus the above hypothesis 

 would be confirmed ; we shall therefore retain only the first term in the 



7 5. 



expansion of sin' — - , and reduce our investigation to the consideration 



of the sign of o- — ~^^ ^ ^x\ taken within the range of the first 

 half wave. 



For every value of ly within this range there is a corresponding 

 equal value of Ix, and vice versa: so that we may write the above 

 expression as follows ; 



n\h /^-lx')-i^ltf l^ 



