COEFFICIENTS OF SOLENOIDS. 17 



2w-e\ = ^.^{v) , where /^ = 1,2,3. 



§ 10. The numerical evaluation of the term jj'vh/^^v-Wy^^ (y)j 

 requires little explanation. By means of the formula 



p'v = --/4{pv-ei){2)V-€o){pv — e^) , 



p'v can be calculated from the values of the three quantities 

 under the radical ; but it is more accurate to calculate it by 

 the relation (10) 



Since ,o,-^-(^0-:y.^-=^^|-:3F- + ZT=5^-ZT:=?^4 



il. n 



nv . 



where ~2^^ '^«•' , 



it is necessary to calculate z from the know^n values of pv. Practi- 

 cally the quantity within the parenthesis is nearly equal to 1, so 

 that only for very accurate determinations is it necessary to take 

 the first term of 2's into account. 



In the present case eoKpv^e^; then 



J^ X/e^—e-s, -y/ pv — e^— %/ e^— e^ -y/^w — e^ qcos2mo — q^cosß7iw 



= s 



^ ^e^ - 63 Vjjv - e, + ^e-i — e.iVpv — e^ 1 + ^q^cosATZw + . . . 



With great approximation 



CObl-KW = , 



since q is generally small ; sometimes (^cos^tzw may enter as a 

 small correction. Knowing s, we can accurately find cos27iio= ~h. 



Thus a2+2--=-2i , 



whence z ■\-z-'^=iy2{h—\) , 



