MUTUAL INDUCTION OF TWO COILS. 125 



coefficient of mutual induction of the two coils. For the flow of 

 force Q issuing from the coil, and which traverses the circle, is 



If y is the mean radius a' of a coil with a rectangular channel, the 

 dimensions of which are 2 &/ and 2 C ', the total flow of force from the 

 first coil, and which traverses the different windings of the second 

 that is to say, the coefficient of mutual induction of the two coils will 

 be obtained if we multiply the value of Q by n\dy x n[dx, and then 

 integrating between the values y c and y + c', x U and x + b'. 



dy 



rx+v 



Qdx. 



Jx-V 



Suppose, for instance, that the dimensions of the coils are such 



that we can neglect the fourth powers of the ratios - , - , and 

 r a a a 



- , retaining the letters , b and c to denote the dimensions of the 

 a 



larger of the two coils. Equation (39) of (740), which gives the 

 value of x, will also give the expression for the mean action F^ by 

 the ordinary rule (753) and it is sufficient to make the integrations, 

 which present no difficulty. 



We thus find if / and /' are the lengths of the wires, n and n the 

 numbers of windings for the two coils, and putting 



rc 2 /' 2 

 (16) M = -' 



M 



__ 



I 



2.2 2 2 _ 2.3V* 2 a" 2 2.3 a 2 J 



2.3 a 



32527 ?-* I i+^l -4- ) 



4(2 



2 5 2 7 a' 6 [ ,7^A 2 ^ 2 \_^9 ^+^"1 

 . 4 .6) 2 6 L 2.3\ 2 'V 2.3* a 2 



+ 



The series is always converging, for the ratio is less than unity. 



a 



