Precession on the Hypothesis of the Eartlis Solidity. 329 



where i is the inclination of the Moon's orbit to the ecliptic, y 

 the ratio of the Earth's mass to that of the Moon. 



In all these formulae, or in any others by which the pre- 

 cession can be calculated, the Moon's mass enters directly or 

 indirectly. When Mr. Hopkins made his calculation, more 

 than forty years ago, he appears to have taken the value of 

 the Moon's mass and all his other numerical data from the 

 early editions of Airv's ' Tracts.' He uses 366*26 for the 

 Earth's period, 27*32 "for the Moon's. He makes 1 = 23° 28', 



i=5° 8' 50", and the Moon's mass = ^ of the Earth's mass. 



All of these values require revision ; and it may be remarked 

 that Sir George Airy has more recently expressed the opinion 



that £7) may be taken as the value of the Moon's mass. 



(Monthly Notices of the Eoyal Astronomical Society, Decem- 

 ber 1878, p. 140). On this question, I may be permitted to 

 remark 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 theMoon ; 2, the Tides ; and 3, the Nutation of the 



Earth's axis. The largest mass, or =~ nearly, has been ob- 

 tained from the first, and the smallest from Nutation. But 

 the values obtained from Nutation are not very accordant, and, 

 moreover, the close connection between Nutation and Preces- 

 sion makes it a doubtful matter to calculate the amount of 

 one from a quantity depending on the other. The Moon's 

 mass obtained from the Tides is that which has been employed 

 by Laplace, Poisson, and other mathematicians 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, give us reason to place much 

 confidence in the result. If we call ~P 1 the precession for a 

 homogeneous spheroid whose ellipticity is E, then from (1) 



P 1= |— E (l+ 7 ) cos I. 



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 7 employed by Poisson 

 Pontecoulant, and Resal: if we also employ for E the value 

 which Colonel Clarke shows good grounds for deeming the 

 Phil Mag. S. 5. Vol. 22. No. 137. Oct. 1886. Z 



