218 ON THE PHYSICAL STRUCTURE OF THE EARTH. 



that there are three different phenomena from which the Moon's mass 

 has been determined: (1) The perturbations of the Earth's motion in 

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

 (3) the nutation of the Earth's axis. The largest mass, or -f^ nearly, has 

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

 the values obtained from nutation 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 in the result. If we 

 call Pi the precession for a homogeneous spheroid whose ellipticity is 

 U, then from (1) 



Pl=^^^(l + ;.)COS/. 



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 tiie Sun thus given, we shall 

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

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

 ground for deeming the most probable,* that is g-g-^n? instead of 3^^ or 

 even smaller fractions hitherto accepted, I find that Pi becomes 5G"-05. 

 By Pratt's formula and the numerical values he employs, except for 

 JE, I find 



Pi=54"-879. 



If we take g^ for the Moon's mass in Poisson's formula, y becomes 

 2-2002, and 



Pi=53"'574. 



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



-^^=^^^413, ^i=52"-95. 



The value for the observed precession now generally admitted is 

 50"*37. It 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. Sopkins has declared it to be. From 

 the values of Pi which I have calculated we should have 



Pi— P=5"-68 and 4"-507, with the Moon's mass=7L. 



* See Colonel Clarke's jiaper in the Philosophical Magazine for August, 1878, where 

 he maintains that recent geodetical results tend to iacreabe the value of the Earth's 

 ellipticity and to make the measured value approach to that obtained from pen- 

 dulum observations. 



