^2 NEW ADDENDUM. 



NEW ADDENDUM.^ 



A TKW words arc in placo lierc concerning the results of the late Prof. Hop- 

 kins' investigation (against which M. Delaunay's objections, (note, page 38,) are 

 especially directed), briefly stated, pages 34, 35. They are as follows: First for 

 IIOMOGENEOUSNESS. "Supposing the earth to consist of a homogeneous spheroidal 

 sliell (the ellipticities of tlie outer and inner surfaces being the same) filled with a 

 fluid mass of the same uniform density as the shell;" then, "the precession will 

 be the same, whatever be the thickness of the shell, as if the whole earth were 

 lioinogcneous and solid." 



Second, for heterogeneousness, his result may be thus expressed: 



(a) P,_P'=.pJl- 



" where P^ denotes tlic precession of a solid homogeneous spheroid of which the 

 ellipticity =(?,, that of the earth's exterior surface, and P' the precession of the 

 earth, supposing it to consist of an interior heterogeneous fluid contained in a 

 heterogeneous spheroidal shell, of which the interior and exterior ellipticities are 

 respectively e and f„ the transition being immediate from th,e entire solidity of the 

 slicU to tlie perfect fluidity of the interior mass." 



In the multiplier of -, second member of (a), q is the ratio of external to internal 



polar radius of the shell ; s depends on the varying ellipticity and density of the 

 strata of equal density of the shell ; Ji depends on the density of the fluid interior. 

 For a thin crust the coeffi^;ent in question is unity nearly; for a thick one it will 

 be somewhat greater if e be less than fj. 



It cannot fail to be observed that, ixnder the conditions just before expressed for 

 homogeneousness—i. c, equality of external and internal ellipticities — we get from 

 tlie formula (s becoming zero) the same result, i. e , P' = P„ as for that case. 



In accordance with rational hypothesis as to the internal condition of the earth, 

 equalities of ellipticities for the surfaces of a thin crust (and corresponding equality 

 of densities), or closely approximate equalities would be expected. The necessity 

 for a thick crust arises, therefore, from the alleged discrepancy between the observed 

 and calculated annual precessions (50 seconds and 57 seconds), which, according 



to Frof Hopkins, makes '~ = |, nearly, assuming the moon's mass j\, and 



the earth's ellipticity ^J^. (The real discrepancy is probably very much less. See 

 page 34, et sequentia.) 



. ' y'"" "'■'5'""' Addendum, hurriedly written while the work was in the printer's bands, has been, 

 in what follows, somewhat modified and amplified. 



