MR. S. S. HOUGH OH THE ROTATION OF AN ELASTIC SPHEROID. 
333 
Since in the small terms which already contain S 2 as a factor we may treat the 
spheroid as a sphere of radius a, we have 
Y « = y , z 1 
4i = u, —f- V-, - -f w, = - 
1 a 1 co 1 a a 
2B — y 
A a 2 
n 
S s .(26). 
and therefore 
whence 
v 
' _ 4 
1 — 5 
rrpal i = j np 
2B - 4 ^ ‘ - 
74 
So, 
< - </£i = (t npa — f TV pa) = - yV np 
2B — | 
A« 2 ‘ 
S 3 . . (27). 
Consider now the different terms of the left-hand members of the boundary 
equations (20). By means of the formula 
we obtain at the boundary 
Also we have 
q r 2 0S 2 r 7 3 / S 2 
X 3 5 3.x 5 0x \ ?’ 5 
. J a 2 0S 2 3 / S 2 
x\fj = A 
5 3x 
1 A 2 
_ /VW __ 
0 X \ 7’° 
A 
^0/- V Ml “ * 74 ^ d:C X « 5 74 V ‘ dx{~^) ’ 
and from (25) 
i 1 i 28 * -tf& + 2B & 
7 74 [ 5 0X 5 0X \ 7' 5 / J 7 74 0X 
0S 2 
0L ; 
therefore, at the surface, 
0 , , ! Ac. 2 0S 2 oR 0S 2 2 A 
& = - * * & + 2B & + * » “ 
_0 /S. 
3x 
Lastly, from (27), 
a « - gh) - 
tT 
2B - i — 
2 0S 2 7 0 / S, 
a~ o-« a — 5 / 
dx dx \ 7“° /_ 
and therefore the first boundary equation becomes 
^ { A | - *A«» - 5-Art 3 + 2»B + (2B - 4 A ,f 
3x 
+ ct 5 . 
yas, 
5 3x 
0 /S a ' 
-Ay- y^5Aa 3 + #5Aa 3 - T&rpa 2 ( 2B 
3x \ r 
a) 3 /So 
x Ax 2X - 
5 3x 
