NEW ADDENDUM. 49 



a solid mass, wink- its pressure imparts to the shell the requisite couple to preserve 

 the precision unchanged. 



2d. The same practical rigidity is, with entire reason, attributed to the heteroge- 

 neous fluid by which (fearing out of view minute relative oscillations which do not 

 affect the mean resultant in other natural phenomena and should not in this) the 

 shell and fluid take a common precession. 



3d. The two inu>s< -s retaining their configurations, mutual relations, and rotary 

 velocities, essentially unaltered by the hypothesis of internal fluidity, it would be 

 a violation of fundamental mechanical principles were the resulting precession not 

 identical with that due to the entire mass considered as solid. 



4 tli. The common and identical precession of fluid and shell resulting from the 

 analysis, is indispensable to any conception of precession for the earth as composed 

 of thin shell and fluid; for otherwise internal equilibrium would be destroyed and 

 the " figure of the earth" cease to have any assignable expression. The entire 

 miss, fluid and solid must (without invoking the aid of "viscosity"), be "carried 

 along in the precessional motion of the earth." The analysis I have examined de- 

 monstrates the possibility and exhibits the rationale of such a community of pre- 

 cession, but fails in the attempt to exhibit a test of the existence or absence of 

 internal fluidity. 



5th. The powerful pressures that would be exerted upon a thin and rigid shell 

 would probably produce in it noticeable uutational movements; 1 while if the shell 

 be not of a rigidity far surpassing that of the constituents of the cognizable crust, 

 the " precessional motion of the earth" would, owing to the neutralizing effect of 

 tidal protuberances, scarcely be observable. 



% 



1 Vide p. 44, and note 2: without reference to conventional "Nutation" which is but a form of 

 ;i;vivsxi'oM. In connection with these relative motions of shell and fluid, it is in place to allude to 

 tlu % " Vindication of Mr. Hopkins' method against the strictures of M. Delaunay," by the late 

 Archdeacon Pratt (" Figure of the Earth," 4th ed., p. 132). He reasons, that, if at any moment, 

 the crust and fluid be arranged as to density, "exactly as if they hod been hitherto one solid mass 

 and be moving alike, this state cannot possibly continue." For the shell will be acted upon not 

 only by the foreign attraction but by the fluid pressure, and will "begin to move quicker," with a 

 precession due to both the thence arising couples. That this should not occnr requires, he esti- 

 mates, the counteracting centrifugal force of a tidal protuberance, in a crust supposed 100 miles 

 tliii-k, of seventy-four feet. 



The writer does not seem to be aware that the author whom he vindicates finds no such relative 

 acceleration of the shell (vide p. 44, 2, of this Addendum) as resulting from the pressure; and, 

 strangely, for an authority on the " Figure of the Earth," fails to recognize that "an elevation of 

 the outer surface of the crust" that is a tidal distortion of a single, foot, would relieve the shell 

 from all pressure. This is, perhaps, a natural result of the use of an expression (Prof. Hopkins') 

 for the pressure which disregards the influence of " Figure." 



March, 1873. 



