

Field of Circular Currents. 387 



whence we notice that 



»+ + ?- = H{ i -AS + (- 3i ^ +280 ^ 2 



- i52 " 4 )«i + -}' 



2P r 8 rf 1 

 n + « , -" ! ifc{ 1 +155* + ■.-•> 



2f J , 36, ! 1 



n + ?-=l^t 1+ 25a3 + --j' 



?£± 



v/ y++ v ? -_ = 2 A /|{i-i^+c-3ir + 2oofv 



It will not be out of place to illustrate the advantages of 

 g-series (II.) in the calculation of X and Y in the case 

 of double coils. If we use the formulae (II.) for the 

 calculation of X + , X_, and Y + , Y_, the second term in X 

 contains q 9/2 , and the third term in Y q 11/2 . Take for 

 example the case f =0'2, rj = 0*2 ; then 



q+ = 0-031 and q_ = 0*041 nearly : 



so that 



qf = 0-000 00016 and q 9 ] 2 = O'OOO 000057, 



and q^ 2 = 0*0000 00005 and q i y 2 = 0*0000 00024. 



Thus three terms are generally sufficient to attain the limit 

 of practical accuracy, q must, however, be calculated to 

 six or seven significant fio-ures. 



Substituting the values of q + , q_ in the expression 

 for X + , X_, and Y + , Y_, as given for a single coil in 

 (A) and (B), we easily find that 



X = JSShf7(V-3p)+ (0) 



b25 >f Da° 



an. 



showing that at the middle point of the coils 



(D 



OJiTT 



X = ; and Y = "f" (23) 



5 v 5 a 



