SIR G. GREENHTI.L ON ELECTROMAGNETIC INTEGRALS. 
4r. 
In Mixchin’s dissection of the circle on AB by lines radiating from M, ‘Phil. 
Mag..’ Fehiaiaiy, 1894, the solid angle cut out hy a complete revolution of PQ about 
/ PM\ 
PM at a constant angle is 1 — ) 'Itt, so that for an elementaiy angle 
‘■C 
( 7 ) 
dQ = ( 1 — dt], and |-MQ^ r/>; = ^MY . a dO, 
X 
if MY = A cos 0 + a is the perpendicular from YI on the tangent at Q ; so that 
( 8 ) 
dQ = d ,,-= d,,-dQ (MQ). 
MQ^ 
PQ 
In a complete circuit of the circle on AB, grows from 0 to 27r, if M is inside the 
circle on AB (a > A, f <. I-), 
(9) 
Replacing Aa cos B by (MQ^— 
Q = 27r-i}(MQ). 
( 10 ) 
( 11 ) 
1 r-"rt"-A" hde 1 [hde 
Jo MQ^ ■ PQ J PQ 
= 2B + 
r 
.1 
Q — 27r 
— + 2Ct zn '2 f CP + 2Gry^ sn 2 J'G', 
(1 —J ) — 20- zn 2— 2G'y^ sn 2 J Gr^. 
This agrees in making fi = '2ir when P is at E and AB is viewed close up, and 
= 0 when J — I and P is at D, where the circle AB is seen edgeways ; and then, 
with this value of B in (12), § 4, 
(P3) L = TrJ^ah + mh-TT (fd-A^) {27r-Q). 
In making the circuit of the circle EPD, and starting from E, where f = 0, Q = 27 r, 
then / grows from 0 to 1, and ii diminishes from 2 i 7 to 0 at D. After passing D, f 
grows from 1 to 2, and 12 is taken negative for the reverse aspect of the circle AB, 
and on arrival at E again with f = 2, Q = —2-7r. 
1 bus Itt must be added in crossing AB if P circulates counter-clockwise. But 
with the clock, the other way round, Itt must be subtracted in crossing AB, just as 
twelve hours is deducted on the clock in passing through XII o’clock. 
