218 ON THE PHYSICAL STRUCTURE OP THE EARTH. 



tbat there are three diflerent phenomena from which the Moon's mass 

 has been determined: (1) Tlie pertnrbations of the Earth's motion iu 

 its orbit around tlie Sun by tiie action of the moon; (2) the tides; and 

 (3) the natation of the Earth's axis. The hirgest mass, or .j\, nearly, has 

 been obtained from the first, and the smallest from nutation. But 

 the values obtained from nutatiou are not very accordant, and more- 

 over the close connection between nutation and precession makes it a 

 doubtful matter to calculate the amount of one from a quantity depend- 

 ing on the other. The moon's mass obtained from the tides is that 

 which has been employed by Laplace, Poisson, and other mathemati- 

 cians as the most probable. It appears that a recent discussion of the 

 tides in the United States, made by Mr. Ferrel, has given the same 

 value as that found by Laplace. This circumstance, as well as the fact 

 that the value so obtained lies between the values found by the other 

 methods, gives us reason to place much confidence iu the result. If we 

 call Pi the precession for a homogeneous spheroid whose ellipticity is 

 E, then from (1) 



If we take the value of the Moon's mass given by the tides, or rather 

 the ratio of the Moon's action to that of the Sun thus given, we shall 

 use the value of y employed by Poisson, Pontecoulant, and Resal ; 

 if we also employ for E the value which Colonel Clarke shows good 

 ground for deeming the most probable,* that is ^vsTJi instead of .,-^,7 or 

 even smaller fractions hitherto accepted, I find that Pi becomes 56"0.j. 

 By Pratt's formula and the numerical values he employs. excei)t for 

 E, I find 



Pi=54"-879. 



If we take -^ for the Moon's mass iu Poissou's formula, y becomes 

 2-2UG2, and 



P,=53"-574. 



If we change y to 80 in Pratt's formula with 



^=-.-«^T-e, i'.=52"-95. 



The value for the observed precession now generally admitted is 

 50"-37. Jt is therefore manifest that the difference between this and 

 the precession of a homogeneous equi-elliptic spheroid can not be 

 admitted to be as great as Mr. Hopkins has declared it to be. From 

 the values of 1\ which 1 have calculated we should have 



Pi— P=5"-68 and 4"-507, with the Moon's mass=iji5j 



* Seo Colonel Clarke's pjipor in the J'hilo^opldial ilnnazine. for August, 1878, wliero 

 he ni.iiiitaiiis that recent geodetical results tend to iucreawi the value of i\w Earth's 

 ellipticity and to niako the lueaHured value approach to that ohtained from pen- 

 dulum observations. 



