SIMPLE PENDUI.UM. 4^5 



=jiri. We have therefore 



K/viii-u").{i+k,in^' 



an expression which integrated between the hmits «'=i and 

 «'= — 1 as before, gives 



a series exactly similar to that above found, and derivable 

 from it by introducing the factor K,, and changing k to k^. 



It is evident that a third series may be derived from this 

 by introducing a new factor Jr=v'^l+3v'(l— A"i)|,and chang- 



j • i f ^+\/(t — k,') , , ... 



mg ki into kj = — — -^- r— - ; and that a simuar process may 



l+3v^(l A"' 'J 



be continued ad intiniium. We shall therefore have 



or rejecting the second, third, ^c. terms of the series in the 

 brackets as indefinitely small, 



^'^-^'< K,.K,.K. . . . k} - ("" 



This 13 an elegant expression for the determination of (t). 



