32. 



REMARKS ON SIR GEORGE AIRY'S NUMERICAL LUNAR THEORY. 



[From the Monthly Notices of the Royal Astronomical Society, Vol. XLVIII. (1888).] 



IN the Report of the Council on the subject of Sir George Airy's 

 Numerical Lunar Theory, it has been explained that the large discordances 

 which have been found by the author to result from the substitution of 

 the values of the Moon's coordinates, as found by Delaunay, in the differ- 

 ential equations of motion, are caused by the large errors of Delaunay 's 

 coefficients of parallax, which Sir George has employed. It may be useful 

 and not uninteresting to give on this subject some additional details. In 

 the first place it will be well to prevent a possible misapprehension. In 

 speaking of the errors of Delaunay's coefficients it is not intended to imply 

 that there is any mistake in Delaunay's theory. The terms of the analytical 

 expression for the Moon's parallax which Delaunay gives are all correct, 

 but they only extend to the fifth order of small quantities, and are therefore 

 not nearly precise enough to be used for the purpose to which the ex- 

 pression for the parallax is applied by Sir George Airy. Delaunay intended 

 this value of the parallax to be employed merely in reducing the apparent 

 place of the Moon to its place as seen from the Earth's centre, and for 

 this purpose the value is perhaps sufficiently accurate. 



If the several transformations of the elements given by Delaunay in 

 his great work had been applied to the analytical expression for the reciprocal 

 of the radius vector, and if Delaunay had carried the developments to the 

 same extent as he had done in the case of the Moon's longitude and 



