46 



NEW ADDENDUM. 



tities (j/,) and (7,) in (y). The brief account given, p. 43, will show how, as re- 

 sulting from tlie analysis, a rotating homogeneous fluid enveloped and confined by 

 a shell reacts, with a pruclical rigidity conferred by rotation, against the shell, 

 (when the respective axes of rotation are slightly separated) and thereby receives 

 an angular motion "precisely as if it were solid," (Phil. Trans., 1839, p. 394). It 

 is clear that, through this interaction, the shell, likewise, must receive an angular 

 motion, and that these several angular motions must be in inverse ratio to the 

 respective movements of inertia of shell and nucleus ; and so, for homogeneous- 

 ncss, the analysis makes them. AVhen we come to heterogeneousness, the same 

 modus operandi is (and rightly) attributed to the fluid ; and again, most clearly, 

 the relative angular motions of shell and fluid should be in above-mentioned in- 

 verse ratio; whereas their ratio is quite differently computed to be — of which 



the value has just been given. The error (for there is clearly one) is in the com- 

 putation of the pressure-couple developed in the fluid and exerted upon the shell 

 by centrifugal force, wlien their axes of rotation are slightly separated. 



The same error of computation (exhibiting itself by the identical symbol, -^ \ 



enters into the expression for the pressure-couple developed by solar attraction, and 

 introduces ofj dn the above symbol as the third term of the second factor of (?/). 



Without going into lengthy discussion, it is sufficient to remark that both tlie 

 centrifugal foice and the foreign attraction produce in the strata of equal density 

 of a heterogeneous fluid, sp)ecial covfiguratlons, and expend themselves in so doing; 

 and, moreover, that tlie prior establishment of these forms of equilibrium is 

 assumed, and necessarily assumed, in the analysis. It is, therefore, unwarrantable 

 to integrate (as is done) througli the fluid mass these forces, as free forces, to get 

 its pressure upon the shell. ^ 



I have shown, I think, that in the expression (?/) the first factor should be corrected 



to be, as it is in (x^, -. . 



The correction consists in substituting for ^^i^ in the fhst factor of (>/), — 



(/o) ' o (aj— ff (rt) 



instead of ~ — - [or its value, p. 45]. The same correction for - -A_ , introduced 

 9 — i ?* — 1 



into the second factor, would require e I" p''," da to be substituted for the second 



o da 



term of numerator of (r). But that (r) sliould belong to entire solidity we require 



"a rfaV , '-' 



oP-j ' '^«'- ^"ow these quantities difl"er inappreciably, for taking the entire 



/; 



' It is obvious that the taking account of the internal motions by wliich the configurations pro- 

 duced by foreign attraction adapt thoniselvcs to the diurnal rotation, does not meet the point made. 



' Altliough the errors in the two cases liave tlic same expression, it does not follow that the cor- 

 rections should be ulenlical. The configurations of strata of like density due to foreign attraction 

 are superinduced on the previously established configurations due to the centrifugal force, which 

 have the varying ellipticity /. The correction should involve this ellipticity, and it is probable that 

 the above symbol is, if we disregard the slight i„lenwl 7nolions, the true one. Indeed, I think I may 

 venture to affirm, that, given a heterogeneous fluid wholly enveloped by a rigid bounding surface, 



