SIR Ct. (ireeneiill on electromagnetic integrals. 
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 ) 
AO(^ = 9, 
V t.-t:, 
ABO = 
EB DB 
= y 
sm w 
EA DA 
sn eG, w = am eG, 
ABg = AQP] = am (l — e) G, AQg' = am (l + e) G, 
EQ = EA dn eG, Eg = EA dn (1 -e) G. 
On fig. 2, where the circle AB is seen edgeways, 
PA EA 
OBP = X’ sin X = = aV ~~ = sii 2/G', X = am 2/G', 
()AP = x^ = BPF, sin x^ = y' sin x, cos x^ = ^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 be 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 
dil 
(1) 
^^M 
dA 
11 
cZM 
dh 
= — 
.27rA' 
( 
(2) 
d (Aff) 
d / , 
dil 
= 0, 
dA \ dA/ 
db ' 
db } 
(3) 
d /I r?M\ 
d /I 
r/M 
)-0, 
dA (a cZA j 
db (a 
db / 
c/A’ 
and a line of force along M a constant is at right angles to a surface of constant t}. 
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, to) or {z, p) of some writers, or Maxwell’s {b, A). 
Then these equations (2) and (3) will appear in the familiar form , 
( 4 ) 
d I \ 
dx \ dxj 
(ff\ 
dy) 
= 0, 
(5) 
VOL. CCXX-A. 
d /1 dM \ d /1 c/M \ 
dx \y dx / dy \y dy / 
H 
