326 
PEorp:ssoii g. h. darwin ox the pear-shaped figure 
Ill the paper on tlie Jacobian ellipsoid referred to above the moment of momentum 
is tabulated by means of /x, where the moment of momentum is (f77p)ia^p,. The 
formula for /x is given in (25) of that paper, and, moditied to suit the j^i'esent 
notation, is 
IX = ~ {A cos y) “ (1 + A~) 
or 
\47rp 
For the critical ellipsoid I find /x = '389570. 
The following table gives the numerical values for a number of Jacobian ellipsoids, 
lieginning with the initial one and terminating just beyond instability. The last line 
gives the corresponding values for the critical ellipsoid. 
Jacobi’s Ellipsoids. 
7- 
,sin 'k. 
cos ^A. 
fl/a. 
4/a. 
rjix. 
p.. 
0 t tt 
0 / 
0 / 
54 21 27 . . 
0 0 
0 0 
•6977 
1-1972 
1-1972 
•18712 
30375 
55. 
17f 
•697 
1-179 
U216 
•18706 
•304 
57. 
34f 
284 
•696 
1-123 
1-279 
-186 
•306 
60. 
49 7 
40 54 
•6916 
1-0454 
1-.3831 
•1812 
•3134 
65. 
64 19 
54 46 
•6765 
•9235 
1-6007 
•1659 
•3407 
70. 
74 12 
64 43 
•6494 
•Sill 
1-899 
•1409 
•3920 
69 49 
73 54 
64 24 
65066 
•81498 
1 -88583 
•14200 
•38957 
* I have been criticised with respect to paper on JacobTs ellipsoid, from which these results arc 
extracted, Iry M. S. Kruger (Xienw Archief voor AViskunde, Tweede Reeks, Derde Deel and 
‘ Ellipsoidale Evenwichtsvoi'inen,’ Ac., Thesis for Degree of Doctor, Leiden, J. AV. van Leeuwen, 
Hoogewoerd 89, 1896), l)ecause I wrote it in ignorance of certain previous work, especially of a paper 
by Plana (‘Ast. Xachr.,’ 36, n. 851, c. 169). Rut I cannot but congratulate myself on mj^ ignorance, 
since it appears that Plana gave a number of numerical residts which were wholly wrong. xV knowledge 
of that paper would no doubt ha^■e caused me much further trouble. 
Aly pa 2 )er gives a number of solutions of the irroblem which I believe to be correct. Ujifortunately 
the methods of the pajrer are clumsy, and thei'c are several mistakes. The formula for w- used in this 
present paper, is much better than that given there. 
The complicated formula on p. 325 is susceptible of reduction to a simple form, for on substituting for 
7 its approximate form (i) we have simjjly 
7 - 6 = Ik- sin 8 cos S, 
where 6 = 51° 21 ' 27". 
The final numerical result was, howc\er, nearly right, for I now find 
sin -a = sin (7 - 6 ), 
whereas I had '9266528. The sin x is ihc same as the k used here. 
The formula at the top of p. 326 which is reproduced as ( 22 ) on j). 828 is, 1 think, illusory, for if in the 
