ACTION OF A COIL AT A SMALL DISTANCE. 



97 



x . 



converge more or less rapidly, so long as the ratio - is less than 

 unity. We thus obtain 



271- 







r 



i. 3 * 2 j I.3-5* 4 1-3-5-7 



2 r 2 2.4 r 4 2.4.6 



1^-T 2 I -3 2 5^ 2 *-3-5 2 7* 4 i.3-5-7 2 9* 6 

 2 2 r 2 L 2 r 2 2.4 r 4 2.4.6 r 6 



2 7 2 9^, i-3-5 2 7 2 9 2 "^ 4 



r= + 2.4 ^ "J 



In order to obtain the component X in respect of a coil with 

 a rectangular channel, the dimensions of which are zb, and 2C, it 

 is sufficient to multiply the preceding value of X x by n 1 ifx l and 

 n^dr^ and then to integrate between the limits x - b and x + b 

 on the one hand, and r - c and r + c on the other that is to say, 

 to calculate the integral 



(38) 



Tr+c fx+b 



= n\\dr X/*, 



Jr-c Jx-b 



in which r would be replaced by the mean radius a of the coil. 



If the conditions are such that the fourth powers of the ratios 



- , - and may be disregarded, we thus find when all the 

 a a a 



reductions are made 



2HTT 



(39) 



VOL. II. 



+ ' 



3 2 S 



3 2 5 2 7 



2.3 a 



i + 



2.3*2 2.3 a 2 



- 2 7-9^-3 

 ? 2 2.3 a 2 



