226 NOTE ON THE CONSTANT OF LUNAR PARALLAX. [28 



This relation will still be approximately though not exactly satisfied 

 when the Moon's perturbations are taken into account. 



Hansen himself, in a paper in the 17th volume of the Astronomische 

 Nachrichten, p. 299, in which he gives the results which he had obtained 

 in a preliminary investigation of the lunar perturbations, finds that the 

 number corresponding to the constant term in the logarithm of the sine 

 of the parallax requires to be augmented by 2"' 71 in order to reduce it 

 to the constant term in the sine of the parallax itself. 



Calling the parallax p, Hansen finds that the value of the constant 



. , / Sill JO \ . 



term in log f n is 

 = \sm 1 / 



log(3419"'35; 

 and hence he concludes that the constant term in ( , ,,, ) is 3422 //- 06. 



By repeating Hansen's calculation and taking into account some small 

 terms omitted by him, I find the amount of the reduction to be slightly 



less than the above, viz. 2"'G7, so that the constant term in ^ n according 



sin 1 



to Hansen's preliminary theory would be 3422"'02. 



This value, however, is not immediately comparable with my own, being 

 founded on different elements. 



Both values are purely theoretical, depending on the ratio of the Moon's 

 mass to that of the Earth, the ratio of the Earth's equatorial and polar 

 axes, and the ratio of the Earth's radius to the length of the seconds' 

 pendulum in a given latitude. 



If M denote the mass of the Earth, 

 m that of the Moon, 

 A the Earth's equatorial radius, 

 R the Earth's radius at a point of which the sine of the latitude is 



J^ 



73' 



P the length of the seconds' pendulum at the same point ; 



