1902.] The Dissipation of Energy by Electric Currents. 373 



c{m-cy\o s ^ c cie (G), 



COS— 1 ))! 



where the limits in D' when m>l are and 7r/2. Taking this case 

 first and integrating by parts, 



V = - [~(sm 4 - 2 (cs + 0) m 3 + 2 (ch + 2s) m 2 - J (2ch + 3cs + 3(9) m 

 2 L 



777 _1_ z* - 1 7r/2 



+ J-,(3 C % + 4^ + 8 S ))log^J o (H), 



7r/2 



+ "2^J ^2— 2 [(^ + ^ 2 + A) s - w ( 2 ^ 2 + f) cs 

 + (2m 2 + T 4 j ) c 2 s - mcH + \cH 



-m(2m 2 + %)0-]de (K). 



The integrated part vanishes at the limits, and the remainder on 

 integration becomes 



777/7 5 r~ _ 



Tl + 4m 2 + T \) (m - v'K - 1) ) 



- + (l - ^(m^ 1) tan-i J_ ) 



+ (2m 2 + T 4 ,) j (m - ^(m 2 - 1) ) 2 



-»(-* +nlS ( 1 -^- 1 ) ta ^^I))) 

 + tk (I™ ~ Sty - l)] 4 + 2[m- ^/(m 2 - 1)] 2 ) 



-2(8«» + #)(*-^+|-,...)] (L) 



where k = m- J(m 2 - 1). 



In the particular case when m == 1, the value is — 



8 _ 7tt 83tt _ 7 17tt _ 2 3tt 

 3 16 + ~30 2 + 30 3 + 80 



167r/ 2 E 2 10- 16 ^ 



«V2 4 [_3 16' r ~30 2' 7 "30' 



+ •••)]• 



The value of the series 1 - L + L _ * + _ C an be found to be 



32 52 72 



0-9160. Hence we obtain for the number of watts — 



4-095 / W10 " 6 . 



P 



