Xumerical Calculation of the Jacobian Ellipsoids. 3 



obtained for the angular velocit}^, of which the following two will 

 be utilised hereafter: ^^ 



1 + f'i + (h- + Pii'i - 4/>i' ' ^'^^ 



Let li, e, i be the quantities which measure the moment of 

 momentum il/, the kinetic energy E, and the intrinsic 

 energy / respectively of the ellipsoid, and which are defined 

 according to Darwin thus: — 



Writing m for the whole mass of the ellipsoid, we have 



this we put equal to 



5 



3. 1 



m"- (abc) ^. (X, 



SO that /^ = ^(^>.ft) '^(l+piWii. (7) 



Again, E = —^^oM = m-(ahc) . e, 



where e = ^L^^^^^ij^ (8) 



Lastly, if V be the potential of the ellipsoid at an internal 

 point, and d/\ an element of its volume, then 



2. 



2./ 



= --^-o' Ysßv-Flx-dv-QJy-dv-BjzHv\, 



or, evaluating the integrals and introducing (4), we find 



5 



2 _i 



1= ——^7:amS = m\ahc) "*. (i — 1), 



1) In the previous imper, SL was calculated from an equation deduced from 



-C = 1 —{ 1 + p;- + 9r)li. 



But I have found that the two forms in the text, though less simple, are more suitable for 

 obtaininof accurate numerical results. 



