56 o 
Mr. Airy on the 
their solution is possible, and the equilibrium with the assumed 
figure is therefore possible. 
( 15. ) At the surface these equations become 
(e— f + A)^-(f-Ve).igl-^^(x+ 4 e)-|. 
° = -(t+A) e4 ^ + ^»ea’+|--^- 
(16). The force on any point in the direction of r is found 
by differentiating the expression at the end of (13) with re- 
spect to r. For since, by (13), the force in the direction of 
X—-7-, if we conceive oc to coincide with r, the force in the 
ax 
direction of r—~. In this expression a is a function of r ; 
but it will be found ( as may also be proved by independent 
reasoning) that the terms produced by differentiation with 
respect to a destroy each other. The force then in the 
direction of r (with its sign changed, as we have to esti- 
mate not a repulsive but an attractive force) is 
- (- ^ ■ + f • 3 boo - '(«)} Hi-f ^ + 
At the external surface this is -ML ~ . 1—3 f**— 
3 l r 8 5 r 4 
7 + ^ (-£ - f (*'+ ~ } • ob- 
JJL 
zT 
.2 r. 1 
serving that ~ | 1 -~2e. 1 - — f * 2 •+ 3 e 2 1 — f * 2 -f* 
sA.|*’— k*) ; (1— 4 e. 1 — |* s ) :r=a(i + e. 
_!_= JL ; the force on a point of the surface in the direction of 
T 6 2. 
49 T ( 
r = -rl 
<? (al 
a" 
2 e . <p (a) 
. 1 t "- 3 + 
+ (a) 
1 — 3 K 
3 ^ 
2T 5 
2a. 1 — p . 2 -f- 
3 e a .f(a) 
f * 2 + 
A 2 . p (a) 
12 e.^(a) 2 2 3 ^ n r n "i T^l 2 1 ^ ■ — ( 
45 , 2 I *\l 
yi^T 2 Hi • 
b — f* 
(a) ( 9 
14 
»(a) 
a 5 . 
