378 Notices respecting .Neiv Books. 



K 2 4 



of the globe, — =#= -f.nQh' ; and if O denotes the angular 



V ° 2 K 2 4 



velocity of the satellite, £2 = — T = ^7tGd, which is independent of 



the radius r n : and then the fraction 



b) 2 li) 2 _ to 2 2/ /(jJ \ 2 



2° 



to which a definite physical meaning can be attached. 



If the globe could retain its spherical shape when the angular 

 velocity was raised to £2, bodies at the equator would be lively on 

 the surface, like the mud particles on the top of the wheel of the 

 old hansom cab seen through the side- window, and everywhere 

 else the plumb-line would be parallel to the polar axis. 



For the Earth this must be 170- fold, £2=17w. 



Maxwell suggested as the universal unit of time, for the Solar 

 System, and ail space beyond, the period of the grazing satellite 

 of a sphere of water, instead of such a parochial unit as our 

 terrestrial mean solar day ; this new unit proves to be about 

 2u0 minutes. 



It would be impossible to go into details here of the extra- 

 ordinary audacity of the mathematical attack • a mere summary 

 of the results must suffice, considered under the heads of 



I. The Tidal Problem. II. The Eotational Problem. III. The 

 Double Star Problem. 



Starting with the gravitating globe at rest, in the Tidal Problem 

 the motion is through a series of prolate spheroids : in the Eota- 

 tional Problem the motion is first through a series of oblate 

 spheroids (Maclaurin's spheroids) and then through a series of 

 ellipsoids (Jacobi's ellipsoids) : in the Double-Star Problem the 

 motion is through a series of ellipsoids. 



The second half of the essay undertakes an additional difficulty 

 in developing a general theory of the configurations of equilibrium 

 of a compressible mass, in its departure from the state predicted 

 in an incompressible model. 



Here the difficulty is great enough when rotation is absent, and 

 the gas is stratified spherically, and various plausible physical 

 assumptions must be made to allow the equations to be integrable. 

 Dr. Schuster's results from the limiting case of y = l'2 are of very 

 great importance, but a closer examination seems required to show 

 that the agglomeration would be unstable at the core, if a rotation 

 was imparted. 



The object of this investigation of a compressible mass is to 

 frame some theory of the internal state of density in the Spiral 

 Nebulae visible in the telescope, conjectural Solar Systems in the 

 making; a feeler into Space, like Eelativity, but without abandoning 

 Newtonian Dynamics. 



The whole essay is a direct frontal attack on impregnable pro- 

 blems, and will require to be reinforced by outflanking equations 

 of related problems that will yield to solution. 



