(yi-7 2 ); .... (3) 



254 Dr. C. V. Burton on the Possible Dependence of 



ierms (2) have to be taken into account ; and in this case, ii> 

 addition to the strictly Newtonian forces of attraction, the 

 sun's gravitational field gives rise to forces on the earth and 

 moon which are nearly equal and opposite, the corresponding 

 acceleration-terms, both measured from the sun, being for 

 the earth 



MG m 2 

 R x 2 ??i 1 + ?w s 



and for the moon 



, MG n h 



+ R7^^ 2 (7l_72) (4> 



Now 71 — 72, if not actually zero, is so small that the effects 

 to be looked for have not yet been definitely disentangled from 

 the available observations ; hence in the expressions (3) and 

 (4) it will suffice to identify R x and R 2 in direction and 

 magnitude with the radius R drawn from the sun to the 

 mass-centre of the earth-moon system, and the acceleration 

 of the moon relatively to the earth has thus a component 



MG(7 1 -7 2 )R- 2 = A 6R- 2 , .... (5) 



say, measured in the direction of R. Again, we may dis- 

 regard the inclination (5° 9') of the moon's orbit to the 

 ecliptic without affecting, to a first order, our estimate of 

 the lunar longitude-terms arising from the acceleration (5). 

 A great simplification may also be effected by treating the 

 orbit of the earth-moon mass-centre as circular and uniformly 

 described, the moon's orbital motion around the earth being 

 similarly assumed as circular and uniform, except for the* 

 small fluctuations to be investigated. This substitution of 

 mean for actual radial distances, &c, still leaves the calculations- 

 abundantly accurate for comparison with the observations. 

 6. It is the motion of the moon relatively to the earth which 



we have to consider. Through G, the mass-centre of the 

 earth-moon system, draw the arbitrary initial line GL in. 



