SIR G. GRKEXHILL ON ELECTROMAGNETIC INTKURA.LS. 43 



5. The various quantities required are shown geometrically on the diagram of 

 fig. 1 and 2. The front aspect is shown in fig. 1 of the circle on AB, and 



(1) . 



sin <o = A/ ~ - = sn eG, w = am eG, 



t'2 t- A 



ABg = AQE = am (l-e)G, AQ?' = am ( 1 + e) G, 

 EQ = E A dn eG, Er/ = EA dn.( l-e) G. 



On fig. 2, where the circle AB is seen edgeways, 



PB EB 

 = = 



OBP = x , sin x = - = A/T^ = sn 2 / G/ ' X = am 2/G', 



OAP = x ' = BPF, sin x ' = y' sin X) cos x ' = A x = dn 2/G', 

 Pp = ED cos x ' = ED dn 2/G'. 



The circle on ED is orthogonal to the circle on AB when turned round into the 

 same plane as in fig. 1, and in fig. 2 the two circles on AB and ED may he taken to 

 represent the typical electric and magnetic circuit linked together. 



6. MAXWELL goes on to show that M is the stream function (S.F.) of a (P.F.) 

 potential function Q, such that 



. <hl dM 



= * TA jT > ~jT ' 

 do do 



db \ 



, } _ ( \ + l \ 



+ db\A db) 



and a line of force along M a constant is at right angles to a surface of constant Q. 



If a return should be made to the usual co-ordinates, it is preferable to employ the 

 ordinary (x, y) of plane geometry, and not the cylindrical or columnar co-ordinates 

 (z, ra) or (z, p) of some writers, or MAXWELL'S (b, A). 



Then these equations (2) and (3) will appear in the familiar form 



(4) + 



dx\ dxj dy\ dy 



(5) d ( l d^} | d ( -- 0, 



dx \y dx / dy \y dy I 



VOL. ccxx A. 



