COEFFICIENTS OF SOLENOIDS. 11 



Adding these four expressions, we obtain the formula (6) as given 

 by Maxwell. Proceeding to the second approximation 



This extension of Maxwell's formula was first given by Rosa 

 and Cohen.(^) 



ir. Mutual Inductance of Coaxal Solenoids. 



§ 7. Returning to formula (3) for the mutual inductance of 

 two coaxal solenoids with the number of turns per unit length 

 71 and n, we have 



I 1% th d?:. (3) 



d-V -I 



Substituting for J/q from (2), the integral can be easily 

 transformed into 



:!.i, ^i ,r V^^' + rt' + (2 - y^'f + 2.-^1« cos (/' 





J J {A^ + ar + {z-zJ-2Aacos0 

 Integrating with respect to z and z, 



M = 47r nn' Aa {I, -L-J. + J^) (7) 



1 T i C sm^é i/A'+a^+c'—2Aacos é ,, .o\ 



where ^ = Aa I ^^ - — ^ — — ^ r dip, (8) 



J {A^-\-a^—2Aacosip) ^ ^ ^ 







and I=Ii for c=d + l+l' , 



= I, „ c = d+l-l' , (80 



= h V c = d-l + l' , 



= I4 „ c = d—-l — l' 



(1) liosa and Cuhen, Bulletin Bur. Standard-;, 2, P- 2GG, 1900. 



