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



responding observations at Greenwich and Cambridge. In this paper Mr 

 Henderson compares the Parallaxes deduced from observation with those 

 calculated by means of the Tables both of Burckhardt and Damoiseau. It 

 is remarkable that he finds a difference of 1"'3 in the value of the mean 

 Parallax, according as one set of Tables or the other is employed in the 

 comparison, and not knowing which value to prefer, he adopts the mean 

 of the two for his final result. 



If we consider, however, that the only part of this process which 

 depends on the Tables consists in the reduction of the actual Parallaxes 

 at the times of observation to the mean value, it is plain that so large 

 a difference in the mean of thirty-four observations can only arise from 

 intolerable errors in the periodic terms of Parallax given by one of the two 

 sets of Tables. 



The Parallax in Damoiseau's Tables is given at once in the form in 

 which it is furnished by theory, but that in Burckhardt's Tables is adapted 

 to his peculiar form of the arguments, and requires transformation in order 

 to be compared with the former. When this was done, I found that 

 several of the minor equations of Parallax deduced from Burckhardt differed 

 completely from their theoretical values given by Damoiseau. 



On further inquiry, I discovered that the difference between Burckhardt's 

 equations of Parallax and those of Burg and Damoiseau had been long since 

 remarked by Clausen in a comparative analysis of the three sets of Lunar 

 Tables given in the seventeenth volume of the Astronomische Nachrichten, 

 but no notice appears to have been taken of this remark. 



With regard to the Parallax, Burckhardt professes to have followed 

 the theory of Laplace, but this agrees very closely with that of Damoiseau, 

 so that errors have evidently been committed by him in the transformation 

 of Laplace's formula. 



These appear to have originated in the following manner : 



In the formation of Burckhardt's Arguments of Evection and Variation, 

 the mean longitude of the Sun is employed. Now four of the errors in 

 the coefficients of the minor equations may be accounted for, by supposing 

 him to have erroneously employed the true instead of the mean longitude 

 of the Sun in forming the above-mentioned arguments. In another of these 

 equations, the coefficient is taken with a wrong sign, and in another a 

 wrong argument is employed. 



