J40 POPULAR LECTURES A XI* ADDRESSES. 



(2) That with an ellipticity of interior surface 

 equal to ...,',, if the precessional motion were 

 26,000 times as great as it is, the motion of the 

 liquid would be very different from that of a rigid 

 mass rigidly connected with the shell. 



(3) That with the actual forces and the sup- 

 posed interior ellipticity of r,^, the lunar nineteen- 

 yearly nutation might be affected to about five 

 per cent, of its amount by interior liquidity. 



(4) Lastly, that the lunar semiannual nutation 

 must be largely, and the lunar fortnightly nutation 

 enormously affected by interior liquidity. 



lint although so much could be foreseen readily 

 enough, I found it impossible to discover without 

 thorough mathematical investigation what might 

 bi: the characters and amounts of the deviations 

 from a rigid body's motion which the several cases 

 of precession and nutation contemplated would 

 present. The investigation, limited to the case of 

 a homogeneous liquid inclosed in an ellipsoidal 

 shell, has brought out results which I confess 

 have greatly surprised me. When the interior 

 ellipticity of the shell is just too small, or the 



