34 PRECESSION OF THE EQUINOXES AND NUTATION 



the earth indicate an ellipticity greater rather than less than _--;* and the latest 



1 J CA 1 



determination makes it gg^f by giving which value to e we ohtam ^ = 2 99' 



Therefore the observed precession is to that which would result in a homogeneous 

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



299 : 311.7, provided the relative mass of the moon be but J 



CA 



The value of f=f would be the same for a homogeneous shell of which the inte- 

 G 



rior surface had the same ellipticity, e, as the exterior ; or it would be the same for 

 a shell of which all the elementary strata had the same ellipticity, 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), 



2o 



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

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

 hand, the considerable inequalities in the equatorial axes indicated in the note 

 below are incompatible 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 which 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 1839- 

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

 ellipticity for inner and outer surfaces of the shell, the precession will be the same 



* Airy, "Figure of the Earth," Encyc. Metrop. ; Guillemin: Miidler, Am. Journ. of Science, Vol. 

 30, 1860, makes the polar compression of greatest meridian 



of smallest meridian 



292.109 

 1 



302.004 



(Article translated by C. A. Schott, U.S. Coast Survey, from Prof. Heis' "Astronomic, Mete'orologie 

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



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



18C6 by the British Ordnance Survey, gives for a " spheroid of revolution, "?I = ; for a spheroid 



a c 1 b c 1 ab 1 295 



;eS '~ = 285.W ~ = 3!^3T = 32G9T- 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 Ponte'coulant. Former determinations 



1 i 



from the observed nutations make it -^-^ but gy was the 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 

 confirmatory of the larger ratio of Laplace. Serret (Annales de 1'Observatoire Imp. 1859) assumes 



"83 and deduces $- = "3og- = - oo:i2 ^ These ratios are adopted by Thomson and Tait, 803, 

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



