OF EQUILIBRIUM OF A ROTATING MASS OF LIQUID. 
On substitution we find 
= I (A - 1 + m (- - i)‘(- - 
303 
• (3) 
•s = 2 ; type DEC, {v) = ^(IqP^{v) + {v), with q.^ = I. 
The equation for ,8(r is 
i/3M3, 1} {3, 2} ^ 
4 -/So- 1 - jySo- 
/Scr = 
We have already defined as I + 15^^, and find the proper solution of the 
quadratic equation to he 
I3a= - 2 (^ 1 - 1 ). 
Also 
_ - 13, 1} {3, 2} _ -4(i?,-1) 
A 
4 - /So- 
yS- 
, with = 1, 
With the known values of Pg and of P^, we find 
= + .(4). 
A comparison with (1) for 6" = 0 shows that the last factors in each only differ in 
the sign of Pp 
V o 1 +j3 
Since Pg^ [v) = 1 bv{v- — 1), we have at once 
P/M= 15 .(^ - 
• ( 5 )- 
/ o I+/3 
. = 3 ; type 000, Pg^ (.) (-)], with q.^ 
The equation for /8cr is 
= I. 
/So- 
_ - i^M3, 2) {3, 3} _ - 15/S^ 
8 — /So- — 6/S 8 — /3o- — 6/S 
We have already defined 
{Ihf - 1 - f/3 (1 - /3), 
and find for the proper solution 
Ba- =4(1 — 1/3 - Pa). 
