48 NEW ADDENDUM. 



was practically solved under Prof. Hopkins' treatment of it when it was shown 

 that, for homogeneousness, the precession for internal fluidity was the same as for 

 solidity, and when it appeared that the analysis applied would exhibit the action 

 of the heterogeneous fluid as if disposed in strata of like ellipticity with that of the 

 inner shell surface. The erroneous computation of pressures has merely the 65*001 

 of exaggerating in a like ratio the densities of all the fluid strata. Hence, and 

 hence only, a resulting precession differing materially from that which would result 

 from solidity. 



In conclusion, I remark, 1st. The analysis of Prof. Hopkins, in its application 

 to a homogeneous fluid and shell, seems to establish (and the result is confirmed 

 by its harmony with tidal phenomena as developed in p. 43) that the rotation im- 

 parts to the fluid a practical rigidity 1 by which it reacts upon the shell as if it were 



with decreasing internal ellipticitics, for fluidity of nucleus less precession than would belong to soli- 



1 -rtr 



dity. This is obvious since his is greater than the ratio r (nearly) which should take its place 



on the latter hypothesis! " ~ 



1 I do not concur with Sir William Thomson in the opinions quoted in note, p. 38, from Thomson 

 and Tail, and expressed in his letter to Mr. G. Poulett Scrope ("Nature," February 1st, 1872), so 

 far as regards fluidity, or imperfect rigidity, within an infinitely rigid envelope. I do not think the 

 rate of precession would be affected. 



That no increase arises from fluidity I have endeavored to show ; and it is unquestionably a 

 corollary of Prof. Hopkins' investigations. As regards imperfect rigidity, Sir William Thomson 

 bases his argument upon the assumption that "the whole would not rotate as a rigid body round 

 one ' instantaneous axis' at each instant, but the rotation would take place internally, round axes 

 deviating from the axes of external figure, by angles to be measured in the plane through it and the 

 line perpendicular to the ecliptic in the direction towards the latter line. These angular deviations 

 would be greater and greater the more near we come to the earth's centre. ***** Hence the 

 moment of momentum round the solsticial line would be sensibly less than if the whole mass rotated 

 round the axis of figure." 



If I do not misunderstand his language, Sir William Thomson assumes that the same bending 

 distortion which would ensue from the application of a couple to the external portions of a non- 

 rotating spheroid, would, equally and identically, take place in a rotating one : thus causing the 

 angle made by the planes of the external rings of matter and the solsticial line to be increased ; 

 with a corresponding diminution of the component of Cn about this line. 



In the case specified by him (an extreme one) while sensible and important nutational movements 

 would ensue, the mean precession would be insensibly affected ; but I do not think precisely such 

 elastic yielding would take place. 



As an extreme case of an infinitely rigid and infinitely thin shell containing matter completely 

 destitute of rigidity, take the fluid spheroid of p. 36, and conceive it enveloped by such a shell. It 

 is still, as shown, p. 43, susceptible (and susceptible only) of the extremely minute deflections of 

 its planes of rotation by which precession is completely annihilated. Confer now upon the con- 

 tents of the shell rigidity, uniform, or varying from surface to centre, continuously or discontinu- 

 ously, in any arbitrary manner, and you have every possible case of imperfectly rigid matter con- 

 tained within a perfectly rigid crust. I can attribute no other effect to the conferred rigidity than 

 a restoration of the lost precession in whole or in part ; nor can I suppose the shell enveloping 

 imperfectly rigid matter to change its obliquity more than that which contains the fluid ; regard 

 being had to conditions of equilibrium without reference to living forces generated. 



I must remark that this hypothetical case, though as admissible for argument as any other form 

 of " preternaturally rigid" crust, is exceptional. With a shell of finite moment of inertia, having 

 some comparable relation to that of the fluid contents, the precession, instead of being annihilated, 

 would be that due to the entire mass 



