AN ELONGATED PROJECTILE. 
585 
Numerical Applications. 
As numerical examples, consider firstly common unfilled shell, which 
may, for the purposes of theoretical calculation, be considered as 
prolate spheroids of which the length is three diameters, the cavity 
being formed by a similar surface of two-thirds the linear dimensions 
of the external surface. 
Here c = 3 a, and therefore 
^= ig -^' /3l0g£(3 + ' /8) } 
0 =^ V2l0g£(3 + ' / 8 ) ~ A }- 
Now, 
log V8 = 0-4515450, 
therefore 
s/S — 2-82843, 
3 + V8 = 5-82843, 
log 10 (3 + s/ 8) = 0-7655493. 
But 
log € (3 + *</ 8) = (x log 10 (3 + */ 8), 
where 
[a = 2-30258509, 
and 
log l0 fx — 0*3622185, 
logio lo gio (3 + s/ 8) = 1*8839736 ; 
therefore 
log 10 lQg e (3 + x/8) = 0*2461921, 
and 
log € (3 + ^8) = 1-76276. 
Also, 
log V2 = 0-1505150, 
therefore 
log l0 log* (3 + V8) = 0-3967071, 
and 
x/2 log € (3 + V8) = 2-49291, 
and 
~ n/ 2 log £ (3 + ^8)== 0-15581. 
Therefore 
a? A = | — -0779 
O 
= *3750 
- -0779 
= -2971 ; 
a>C- 15581 — A 
= *15581 
— -08333 
== -0725. 
75 
