THE THEORY OF TERRESTRIAL MAGNETISM. 425 



In all other cases 



A v v i v v ,1 m(n-m)\ 



and 



16. From the differential equation for H n (taking H n for H} we have 



and (!-) * - 2, " + , (, + 1) - f , 5., = 0. 



Multiply by (1 /u, 2 ) H Ui and (1 p) H n respectively and add, then 



n-w- , 7T ., 9 /I *\ TT n > TT n 



-^-H ni -- + H n ~ d ^^-^( -X)^-^. H-^f' 



+ [> (w + 1) + n, K + 1)] (1 -M 2 ) fi.^., - %?H n H ni = 0. 



/l ** TT dH " , Tf dH . 



But ^ -^ ) "' " " ^ 



cm 



therefore 



/I _ 2^ d I TJ M n>p[ "'-"B. I _ ^ /^ _ 2 \ I ff ^* n + Jf ^_^n 



Or again 



d - TT d ^ n . TT d ffn\~ . d 



A. II. 



54 



