592 
ROTATION FOR STABILITY Of 
and 
a — y — 
A + C 2 A 
2 A 2 — AC — C 2 
2^ {A + (7) 
2 A + C A — C 
— X 
2 A 
A + C 
W^V)^ X + 
x 2 + 2 
X ( X 2 — 1) ( X 2 — l)f 
x 2 -2 1 
a? H — 1) + — l)t 
1 
a? 
log (x -f \/x 2 —■ 1) 
log (x + y x 2 — i) 
- (x 2 — 1)£ 
x 
x yx 2 —i — log (a? + yx 2 — i) 
(x x} S ^ X<2 ‘ — ^ ^ l 0 g ^~~ ^ 
x ~ ~ <A 2 — 1 + log {x + \/^ 2 1) 
If tlie cavity be a similar spheroid of 4 th the linear dimensions of the 
external surface,, 
t ra 2 c i (a 2 -f c 2 ) (\ — 1 ^ 
^2— 5 \ *» 6 / 
7 ra 2 c ( 
i-L) 
V 
m 3 / 
and 
m 5 — 1 l,o. ov 
v = _^-i; 3 
w 5 — m 2 5 
p weight of shell 
__ 1 \ density of iron 
m s / density of air 
tr weight of displaced air 
( ’ 
Therefore, generally, we must have 
a /m 5 — 1\ 2 4 
\m 5 — vi 2 ) 25 
8 -1 
,2 — 
density of iron 
® F - 1 1 (a si+I*)7« - r) " deilsityofair 
density of iron 
tv? — o 
4 a 2 
= 5 ^ ( X " m*) ?+l X a - X 
y density of air ? 
