46 PRECESSION OF THE EQUINOXES AND NUTATION. 



Of course, the practical application (briefly sketched at p. 42) of Prof. Hopkins' 

 result to the case of the earth should anount only to this that, so great a differ- 

 ence as j| between calculated and observed precession is not in accordance with 

 prolable laws of density. On the other hand, Thomson and Tait show, 828, 

 that for entire solidity, the observed precession is quite consistent with the actual 

 mean density and probable (Laplace's) law of density. 



In conclusion, it has been shown, that according to the celebrated investigation 

 which I have examined, the entire mass of the spheroid, fluid and solid, is " carried 

 along in the precessional motion of the earth ;" and under that point of view only, 

 (regarding the crust as rigid) I incline to the opinion of Mr. Delaunay that " the 

 consideration of the phenomena of precession and nutation can furnish no datum 

 for estimating the greater or less thickness of the solid crust of the globe." 



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 On about this line. 



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

 would ensue, the mean precession would be very slightly 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, 



PUBLISHED BY THE SMITHSONIAN INSTITUTION, 

 MAT, 1872. 



