JOUENAL OF THE COLLEGE OF SCIENCE, IMPEKIAL UNIVERSITY, TOKYO. 



VOL. XXXVII., ARTICLE 6. 



Numerical Calculation of the Jacobian Ellipsoids. 



By 



Ryosuke KAIBARA, Hi<jaktishi. 



Professor of Physics, Imperial Peers' College, Tohtjo. 



1. The Jacobian ellipsoid, or the ellipsoidal figure of equili- 

 brium of a rotating mass of homogeneous fluid, was first calculated 

 numerically by Darwin" for the whole range of the ratios of axes 

 and angular velocity. In a previous paper, -^ I solved the same 

 problem by a different method of treatment, and then interpolated 

 values which I intended to compare with those given in Darwin's 

 table. In his Scientific Fajier^^^ Darwin has recomputed a part of 

 his table, and pointed out the discrepancy between his results and 

 mine; he has also given an evidence for the incorrectness of some 

 of the interpolated values. The discrepancy is, in general, very 

 small, but in a few of the results, it amounts to several units of the 

 third decimal place. These considerable discrepancies occur in those 

 values, for which, by the nature of the method I adopted, the 

 calculation was the most tedious, and an inaccuracy in the inter- 

 polations of the order mentioned was therefore unavoidable. It 

 may be remarked, however, that a majority of my results agree 

 better with Darwin's corrected values than with his original ones. 



More accurate results on this subject being desirable, I have 

 greatly modified the method so as to remove its imperfection in 

 the previous paper as far as possible, and have repeated the whole 

 calculation.^^ In the following paragraphs, this improved method 

 will be explained and tables of numerical results added. 



1) O. H. Darwin, Proc. Roy. Soc. London, 41 (1887), p. 319. 



2) R. Kaibara, Proc. Tokyo Math.-Phys. Soc, 4 (1907), p. 98. 



3) G. H. Darwin, Scientific Papers, 3 (1910), p. 130. 



4) Some of my notations in the former paper are also altered to conform to those usually 

 adopted. 



