COEFFICIENTS OF SOLENOIDS. 



ductance for two coaxal circles Mq at the distance c from each 



other can be written from (2) in the form 



M 2 



= ^:zq^ (1 + e) 



where e = '^q'-^q'+'dq^-l2q''+-' (4) 



and 



where ^i = S2q,^ - 40.// + 4Sq,' - (4') 



In tliese expressions, q and qi are to be calculated by the well- 

 known expressions 



.4..(^)Vi<^j 



+ 



l^l=Vl , ,, = i^1^ ; (5) 



l + i/7c' 1 + l/i 



and /c-=— — 1-=— -— — ., =sm-y , 



7/.. Ci— Co (yl— rt)- + c- 

 Cl — e.. (^ + a)- + c^ 



When k or /;' is very small, we may calculate I or /i by the 

 formulae 



^" 8 "^IG"^ 512 "^ 1024 "^ ^'^^ 



'~ 8 "^16 512 1024"^ 



It is to be remarked that for most practical purposes, it is 



generally sufficient to put q= ,-> or qi= -^' For k=sin 4:5°,— = 



0.0432139, and Ty] = 0.00000015, so that the sixth decimal is 

 not affected by neglecting the second term. 



