AN ELONGATED PROJECTILE. 
587 
where k 1} are the equatoreal and polar radii of gyration of the shell, 
and putting — = 1, c 66 = c u = MJc-f, c u - e 33 = M (a — y). 
c n 
Now, 
and similarly, 
Therefore 
therefore 
7T a'c 
• g (« 2 + C 2 ) (l — p) 
4 2 
— TVQrC 
o 
211 1 
171 X 5 
(>-S) 
+ c 2 ) 
211 
= Yyj X 2« 2 5 if c = 3a ; 
^s 2 — 
25 
3 5 2 o 
T3 X 5 ffl2 
3 s 
211 
_ 171 X 
^2 —— 
2 /211\ 2 4 
77 x (l7j) X 25 
„ 211 O ? f 
4X __ X2x£(a- 
2117T 2 
50 X 171 X £ (a-y) 
(J 
log 211 = 
2-3242825, 
log 7r 2 = 
09943018; 
log 21177-2 = 
3-3185843, 
log 50 = 
1-6989700, 
log 171 = 
2-2329961, 
log ~ = 
cr 
4-3831655, 
log (a — y) = 
1-8336825 
= 
0-1488141; 
log ft 2 — 
3-1697702, 
log n — 
1-5848851, 
therefore 
log 
n = 38*449. 
In the service guns n is generally made equal to 35. 
Secondly, consider the case of double shell, unfilled, which must, for 
purposes of theoretical calculation, be considered as prolate spheroids 
