48 ADDENDUM 



Mr. Airy (Tides and Waves, Art. 127) bases his demonstration of the theorem exclusively upon 

 the principle of the conservation of areas, remarking at the outset, " if the earth and sea were so 

 entirely disconnected that one of them could revolve for any length of time with any velocity, in- 

 creasing or diminishing in any manner, while the other could revolve with any other velocity changing 

 in any other manner, we could pronounce nothing as to the effect of the fluctuation" (tidal) " upon 

 precession." 



A spheroidal nucleus wholly covered by an ocean of regular depth, suffering no resistance, does 

 not seem to me to lack mnch for fulfilling the above conditions ; especially if the " regular depth" be 

 constant. 



If velocities are generated in the waters of the ocean by solar (or lunar) attraction, the centrifugal 

 forces due to them might be looked to (though not alluded to by Laplace) as agents for transferring, 

 from the fluid to the nucleus, the precession-producing couples due to the fluid mass, especially in 

 the above hypothetical case. It will be found, however, by reference to the expressions [2260], 

 that they give rise to no couple, and are, moreover, very minute. 



The motion which the displacements [2260] [2261] indicate is a slight oscillation of the axis of 

 the fluid envelope, moving as a solid, about the axis of the nucleus, the angular distance between 

 these axes being slightly less than 2 seconds: it is, I presume, that which a non-rotating shell would 

 have were the attracting body, with constant distance and declination, to move, with angular velocity 

 n, in right ascension. In the case in hand it is the fluid shell which revolves and, suffering no sensible 

 change of form, would be itself affected by its proper precessional couple. 



