168 Mr. A. Campbell on the Use of 
In fig. 12 let the two circles be H and G, of radii a and A 
respectively, b being the distance between their planes, and 
Fig. 12. 
T 
H c 
I 
I 
3 ..L 
«-A- 
q the distance between their axes. Let the circle H' be the 
projection o£ H on the plane of G, and let BCD be an 
elementary strip concentric with H/ of radial width Br, where 
0'B = r-. Let CO'B = 0. Then the M between circle H and 
strip BCD 
= -. (M of circle H and annulus TBD) 
7T 
= ^.||_^ in2v/ -{(,_^ Fl+ | El j 10 -,] d ,, 
or 
where . , . (18) 
k = 2 sjwj \ r (a-fr) 2 + ^ 2 = sin 7, 
h' = cos 7, 
and F T and E 2 are complete elliptic integrals to modulus k. 
Also ,. _ A 
6= cos * i . 
Irq 
Thus when a, A, b, and q are given, by calculating dM 
by (18) for a series of equally spaced successive values of r, 
from r=#~ A to q + A, and adding in the usual way, the 
value of M can be approximately found. By this process 
