30 ON MAGNETISM. 



In expanding these brackets, it will quickly be found 

 that, in order to secure the same accuracy as in the de- 

 velopment of Article 14, it is necessary to use the 

 binomial theorem one step further : 



therefore ( 1 --- 1 -- 5 1 



\ c c J 



ra + 1/ 2a a 2 +& 2 \ ra+l.m+3/ 2a 2 +&V 

 = 1- x --- h 2 M --- cr~A - --- 1" 2" 

 2 \ c c J 2.4 \ c c 2 J 



m + l.m43.m + o/ 2q q 2 + & 2 \ 3 

 2.4.6 ~\~ c ?~~ J 



TO + 1 . m + 3 

 . __ .. 



Multiply this by ( 1 -- ) , and we obtain 

 \ o/ 



a m.ra+1 a 2 m + 1 b* m.m 

 U ~* 



2.3 V 



m . r?i + 1 cib* 

 ~~2 ? 



Similarly the second bracket is 



a m.ra + 1 a 2 m+1 6 2 m.m+l.m + 2 a 3 



c 2 * 2V 23 V 



m . m + 1 



and the whole large bracket is 

 a m . m + 1 . m + 2 a 3 

 2w c + - 3 -- ^ 



