34 PRECESSION OF TUE EQUINOXES AND NUTATION 



the oartli iiulicat. an ollipticity greater rather than less than J^-^; *^id the latest 

 determination makes it ^,J.,t by giving which valne to e wc obtain — ^=299" 



Therefore tlie obs(>rv(>d precession is to that which wonld result in a homogeneous 

 spheroid, from the fornudas, with tlie latest determined value of e introduced, as 



299 : oil. 7, provided tlie relative mass of the moon lx< but -^^X 



The value of Ti' "^vould be the same for a homogtmeous shell of which the inte- 



rior surface had the same eH!pticUy, c, as the exterior ; or it would be the same for 

 a shell of which all the elementary strata had the same cllipticity, in which the 

 density constant through each stratum, should vary according to any law, from 



24 



stratum to stratum. The ratio of 299 : 312.7, so nearly unity (= 0.96 ^^, nearly), 



wliilc tlie ratio of mean to surface density of the earth is so high, indicates nearly 

 uniform cllipticity of stratification, and hence fluidity of origin; while, on the other 

 liand, the considerable inequalities in tlie equatorial axes indicated in the note 

 below are iucompatible with the hypothesis of actual fluidity beneath a thin crust, 

 and are, to the measure of their probability, a disproof of it. 



The effect upon the axial movements of such a shell Avhich would result from the 

 pressures of an internal fluid has been made the subject of an elegant mathematical 

 investigation by W. Hopkins, F.R.S., in the Philosophical Transactions of 1^39- 

 40-42. On the supposition of a uniform density of shell and fluid, and the same 

 cllipticity for inner and outer surfixces of the shell, the precession will be the same 



* Airy, "Figure of the Earth," Eucyc. Metroj). ; Guillcmiu: Madler, Am. Journ, of Science, Vol. 

 30, I8G0, makes the iiolar compression of greatest meridian 



292.109 



of smallest meridian 



302.004 



(Article translated by C. A. Schott, U.S. Coast Survey, from Prof. Hcis' "Astronomie, Mctcorologie 



tt Geographic," Nos. 51, 52. 1859.) 



t Appendix "Figure of the Earth" to the "Comparisons of Standards of Length," published 



18G6 by the British Ordnance Survey, gives for a "spheroid of revolution," " '^= ; for a spheroid 



of three axes, —-=-_-_, —^'^ sisss ' ~<r^ 32(i.<Jb ' The probabilities of the latter sup- 

 position to the former being 154 : 138. 



J There is yet great uncertainty as to the relative mass of the moon, and as long as that point is 

 unsettled, so is also the ratio of observed to calculated precession. Laplace, from observations of 



the tides at Brest, fixed it at ^_ , which number is adopted by Pontecoulant. Former determinations 

 from the observed nutations make it g^y^S ' ^^^ sf ^^^ ^^'^ determination from the coefficient of 

 nutation of Lindenau. Guillemin gives gg-, and these two last numbers coincide nearly with that 

 used by Poinsot. A discussion by Mr. Wm. Ferrell, member of National Academy of Sciences, of tidal 

 observations made for a series of years at the port of Boston, as well as those at Brest, gives results 

 coulirmatory of the larger ratio of Laplace. Serret (Annates de I'Observatoire Imp. 1859) assumes 



83 ""'^ ^'^"'" %'^- = -3U6 = ^•^'^•^-^- Tlicse ratios are adopted by Thomson and Tait, §§ 803, 

 823. Archdeacon Pratt (" Figure of the Earth," 4lh ed. 1871) adheres to Laplace's determination. 



