92 



ON NEW TABLES OF THE MOON'S PARALLAX. [17 



The agreement thus found between the several theories is most satis- 

 factory, the difference of the separate values of each coefficient and the 

 general mean rarely amounting to a hundredth of a second. There are 

 only two instances in which this amount is much exceeded. One of these 

 relates to the constant of Parallax, the value of which, given by M. Hansen's 

 method, is 0"'06 less than the corresponding value found from the same 

 fundamental data by the other methods, and the second relates to the term 

 whose argument in Damoiseau's notation is t + z, the coefficient being 0"'146 

 according to Damoiseau and Plana, 0"'140 according to Pontdcoulant, and 

 0"'181 according to Hansen. 



The values of the constant of Parallax which I have deduced from 

 the theories of Damoiseau, Plana, and Pontecoulant agree perfectly with 

 one another, and from the particular examination which I have given to 

 this subject, I am induced to place considerable reliance on the result. It 

 is possible that M. Hansen's definitive value of the constant may differ 

 slightly from that which he has given in the paper above referred to. 



From the value of the constant of Nutation found by M. Peters, it 

 follows that the ratio of the Moon's mass to that of the Earth is as 1 

 to 81 '5 nearly. Employing this ratio, together with the dimensions of the 

 Earth according to Bessel, and the length of the seconds' pendulum in 

 latitude 35J, deduced from Mr Baily's Report on Foster's Pendulum experi- 

 ments, I find the value of the constant of Parallax to be 3422"'325. 



Now Henderson, in the paper cited above, has found the value of the 

 constant, by comparison with Damoiseau's Tables, to be 3422 //- 46. 



It should, however, be remarked that what the Table calls the Parallax 

 is more strictly the sine of the Parallax converted into seconds of arc. In 

 Henderson's calculations he has taken the tabular quantity to denote the 

 Parallax itself, so that the value found must be diminished by 0"'15 in 

 order to obtain the constant of the sine of the Parallax. Thus the value 

 deduced in this manner is 3422"'31, a result admirably agreeing with that 

 just derived from theory. 



I have carefully transformed the expression for the Parallax given by 

 theory, so as to make it depend on Burckhardt's Arguments of Longitude, 

 and from the resulting formula Mr Farley has calculated the Tables which 

 are appended to this paper. Constants are added to the several equations 

 so as to render them always positive. 



