30. 



NOTE ON DELAUNAY'S EXPRESSION FOR THE MOON'S PARALLAX. 



[From the Monthly Notices of the Royal Astronomical Society. Vol. XLIII. (1883).] 



THE process employed in Uelaunay's Theory of the Moon consists hi 

 making a great number of successive changes from one system of elements 

 to another, these changes being so conducted that the equations which give 

 the variations of the elements always retain their canonical form, until at 

 length all the sensible periodic terms in the disturbing function are got 

 rid of, and the elements are thus reduced to three constants and three 

 angles which vary in proportion to the time. 



After each such change of elements, the expressions for the three co- 

 ordinates of the Moon, which are supposed to be known in terms of the 

 old system of elements, must be transformed so as to be expressed in terms 

 of the new. 



These transformations being made independently, we may, if we choose, 

 find some of the coordinates with a greater degree of precision than others. 



Delaunay has, as is well known, followed the example of Plana in 

 developing his coefficients in series of ascending powers of the small quantities 

 m, e, e' and y. 



Now, two of the Moon's coordinates, viz. the longitude and latitude, 

 can be directly compared with observation, whereas the third coordinate, viz. 



