1870.] 



Mr. I. Todhuntcr on Jacobi's Theorem, fyc. 



171 



may be termed the equator of the solar motion ; that is, the great cirele 

 having the apex of the sun's motion as a pole. This circumstance points 

 to that remarkable cluster, rather than to the Pleiades, as the centre of 

 the sidereal system, if, indeed, that system have a centre cognizable by us. 

 When we remember that for every fixed star in the Pleiades there are 

 hundreds in the great cluster in Perseus, the latter will seem the worthier 

 region to be the centre of motion. I should be disposed, however, to 

 regard the cluster in Perseus as the centre of a portion of the sidereal 

 system, rather than as the common centre of the Galaxy. 



The peculiarities of the apparent proper motions of the stars seem to 

 me to lend a new interest to the researches which Mr. Huggins is pre- 

 paring to make into the stellar proper motions of recess or approach. 



III. " On Jacobi's Theorem respecting the relative Equilibrium of a 

 Revolving- Ellipsoid of Fluid ; and on Ivory's Discussion of the 

 Theorem." By I. Todhunter, M.A., F.R.S., late Fellow of 

 St. John's College, Cambridge. Received November 23, 1869. 



(Abstract.) 



Jacobi discovered the theorem that a fluid ellipsoid revolving with uni- 

 form angular velocity round its least axis might be in equilibrium. Ivory 

 discussed the theorem, and made several statements regarding the limita- 

 tions of the proportions of the axis. Ivory's statements contain various 

 errors and truths based on erroneous reasoning. The object, of the pre- 

 sent memoir is to correct Ivory's errors, to supply his imperfections, and 

 to add something to what is already known respecting the theorem. 



January 27, 1870. 



ARCHIBALD SMITH, M.A., Vice-President, in the Chair. 

 Professor Wyville Thomson was admitted into the Society. 



The Presents received were laid on the Table, and thanks ordered for 

 them, as follows : — 



Transactions : — 



Cambridge, Mass. : — Museum of Comparative Zoology. Bulletin. Xos. 



8-13. 8vo. Cambridge 18G9. The Museum. 



Copenhagen : — Kongelige Danske Yidenskabernes Selskab. Skrifter, Xat. 



og Math. Afd. Bd. VIII. 1, 3, 4, 5. 4to. Kjobenhavn 1868-G9. 



Oversigt, 1868, No. 5 ; 1 869, No. 2. Svo. Kjobenhavn 1868-69. 



The Society. 



