266 REMARKS ON SIR GEORGE AIRY'S NUMERICAL LUNAR THEORY. [32 



Argt. My Coefficient. Delaunay's. 



2D-2f+l 140,25 146,4 



2D-1-2S 146,1 132,6 



4Z 119,8 121,0 



2D + 1 + S 137,3 117,2 



W-l-S 184,1 86,8 



3D-1 105,2 58,1 



4D + 1 93,5 54,05 



2D + 31 51,2 51, 



4D-21-S 87,7 46,5 



3D 14,6 46,2 



2D + 2/-21 42,6 43, 



D + Z + S 38,9 38,9 



1-2S 38,3 38,3 



2D-1 + 2S 37,4 37,4 



2D-21-S 37,1 37,1 



This table shews at a glance how great the errors of Delaunay's co- 

 efficients of parallax, when reduced to the form in which they are employed 

 by Sir George Airy, in many cases really are. Hence the discordances 

 which he met with in the results of the substitutions should occasion no 

 surprise. In the Introduction to the Numerical Lunar Theory, p. 4, line 

 20, it is stated through inadvertence that the factor which Sir George Airy 

 calls M is a quantity "depending on the proportion of the masses of the 

 Earth and Moon." This is not the case however, since M is simply the 

 ratio of the sum of the actual masses of the Earth and Moon to the sum 

 of the masses which would be required to make the Moon describe an 

 undisturbed orbit about the Earth in which the periodic time and the 

 mean parallax were the same as in the actual orbit. 



The theoretical value of M is simply expressed as the cube of the 

 constant term in Delaunay's value of - . This value is given analytically 



in p. 802 or p. 914 of the second volume of Delaunay's Theory, but only 

 to the fifth order of small quantities, which is not accurate enough. The 



development of the constant term of - has been carried by me to a much 



greater extent at p. 472 of Vol. xxxvin. of the Monthly Notices (see p. 203 

 above). Turning this expression into numbers, and cubing it, we find the 



