428 Mr. T. H. Blakesley on the Differential 



i. e.j it consists of a constant factor, a logarithmical factor, 

 and a rhythmical or harmonic factor. 



Substituting for 6 its value — . t, 



-it, - 27r t . 2ir 



ih = a.e t tanp sm — . t, 



9 



~Ei = ae tan /3 sin 6, 



<£E e_ a e_ 



-—.=ae tan /s cos — . ^e tan p sin 



dd tan ft 



L. . E 



= ae tan^ C 0SC7 



tan ft 



■«£ tan j3 sin0— : ~ « tan P COS fl 



</<9 2 tanftdfl tan ft 



i_^_ L/^5 4 E 



therefore 

 Now 



tan ft d# tan ft I dd tan ft 



2 cm f i i . 



tanftdt? I "*" tan 2 ft/' 



} 



2 tan ft dE tan 2 ft d 2 E _ 



+ 1+ tan 2 ft rf0 + 1+ tan 2 ft d6> 2 ~ ' 



15 ~ ~di ' dd ~ It ' 2ir 

 therefore 



dm _ <m m dt_ t^ _ dm /t*\ 2 



d6 2 dt 2 dd 2tt dt 2 V2tt 

 therefore 



F 2tanft t 2 dE 

 + 1+ tan 2 ft27r* dt + 



tan 2 ft /^ 2 \ 2 ^ 2 E_ 

 l+tan 2 ftV27rJ dt 2 ' 



which, since tan ft = — ~, becomes 

 t 2 



F , ih dB , tf dm _ n 

 + (1+ tan 2 /3) rf« + (1+ tan 2 ,3) d« a 



and if U is written for 



(1+ tan 2 /3) 



An equation which is at once comparable with those obtained 

 in the Electrical problem. 



