OF WHICH IS MOVING- ROTATIONALLY AND PART IRROTATIONALLY. 399 
First suppose 
Then 
d> 2 
'CO < — < — 
/ Ob 
\/ a 3 +e= 
d> 2 
—a—+ - 
f a 
V l f) aW 
so that 
y/b 2 -\-e= 
/ i 
a/(-; 
a/ (a 2 -he)(6 s +e): 
4 
f) aPb 2 
<& 2\l 7 a> 2 
-a- + - ( —6— t— 
f aA / & 
o >\ 3 4 
// a 2 5 2 
and the equation in e is satisfied. 
Next suppose 
Now 
2 cb a 2 + b~ 
ab^~ a?b 2 
\/« 2 +e= 
w 2 
a - 
/ * 
4 
f] aW 
^b 2 +e = - 
, &) 2 
/ & 
a/(! 
2 _ 4 _ 
\/y 
These values, however, do not satisfy the equation in e. 
Hence it appears that if 
the elliptic cylinder for which 
w 2 
a 2 + & 2 d> 
aW f 
~ / ft >\® 4 
f) a 2 b 2 
