EQUILIBRIUM OF ROTATING MASSES OF FLUID. 
407 
C 
a 
15w 2 
^ lt)7r 
Difference. 
1 
r 
•1 
•9949 
•9949 
*0000 
Large 
•2 
*9798 
•9799 
•0001 
9799 
•3 
•9539 
•9544 
•0005 
1909 
•4 
*9165 
•9182 
•0017 
540 
•5 
•8660 
•8705 
•0045 
193 
•6 
•8000 
•8111 
•0111 
73 
•7 
•7141 
•7399 
•0258 
29 
•8 
•6000 
■6595 
•0595 
111 
■9 
•4359 
•5869 
T510 
3-9 
The measures of inaccuracy corresponding to the values of e in the first column, or 
the values of c/a in the second, are the reciprocals of the numbers in the last column. 
We thus see that there is still a considerable degree of approximation when c = '8, 
or when the ratio of the axes is 3 to 5, for the measure of inaccuracy is -jy ; but for 
e = '9 the approximation is bad. 
Now the shapes of certain egg-like bodies have been computed by the spherical 
harmonic method, and it seems safe to assume that the approximation has given 
about the same degree of accuracy as would hold in the case of an ellipsoid of 
revolution whose minor axis bears to its major axis the same ratio as the shorter axis 
of the egg to the longer. 
Turning now to our computation, and considering only the more elongated or 
meridional sections, we see that, when /3 = y, the longer axis is 1*355 + T230 = 2*585, 
and the shorter 2(1 — '227) = 1*546 ; and the ratio 1*546 : 2*585 is *6, which corre¬ 
sponds to the measure of inaccuracy 1/11*1. It might, however, be more legitimate 
to adopt two different measures, and at the pointed end of the egg to take the ratio 
*773 : 1*355 = *57, which will correspond to a measure of inaccuracy about yy; and at 
the blunt end to take the ratio *773 : 1*230 = *63, which would correspond to a 
measure of inaccuracy yy or yy 
In the case of /3 = \ the two masses cross one another, and the result has been 
used to give an approximate picture of the dumb-bell figure of equilibrium. We now 
see that even in this case there is a sufficient degree of approximation to give a very 
good idea of the accurate result. 
In the case of the meridional section, where /3 = y, we have for the ratio of axes at 
the pointed end of the egg 
1 - *1717 
1*2712 
*8283 
1-2712 
= *65, and measure of inaccuracy about 
_*1717 -8983 
-y 5 -; and at the blunt end — -- 4 c ^ = ‘71, and measure of inaccuracy - 2 y 
1-1746 
In the case of (3 = \ the similar figures are, for the pointed end, 
and measure of inaccuracy about -gy; and for the blunt end 
measure of inaccuracy perhaps about d 0 . 
1 — *137 
208 
*863 
1-208 
*72, 
1 - -137 *863 _ . 
1-139 IT39 76, aTK 
