D02 ADDITIONS. 



Mr. Airy undertook the task; employing for that purpose, the Obser 

 vations of the Moon made at Greenwich from 1750 to 1830. Above 

 8000 observed places of the Moon were compared with theory by the 

 computation of the same number of places, each separately and inde- 

 pendently calculated from Plana's Formula}. A body of calculators 

 (sometimes sixteen), at the expense of the British Government, was 

 employed for about eight years in this work. When we take this in 

 conjunction with the labor which the observations themselves imply, 

 it may serve to show on what a scale the verification of the Newtonian 

 theory has been conducted. The first results of this labor were pub- 

 lished in two quarto volumes ; the final deductions as to correction of 

 elements, <fec., were given in the Memoirs of the Astronomical Society 

 in 1848.' 



Even while the calculations were going on, it became apparent that 

 there were some differences between the observed places of the Moon, 

 and the theory so far as it had then been developed. M. Hansen, an 

 eminent German mathematician who had devised new and powerful 

 methods for the mathematical determination of the results of the law 

 of gravitation, was thus led to explore still further the motions of the 

 Moon in pursuance of this law. The result was that he found there 

 must exist two lunar inequalities, hitherto not known ; the one of 273, 

 and the qther of 239 years, the coefficients of which are respectively 

 27 and 23 seconds. Both these originate in the attraction of Venus ; 

 one of them being connected with the long inequality in the Solar Ta- 

 bles, of which Mr. Airy had already proved the existence, as stated in 

 Chap. vi. Sect. 6 of this Book. 



These inequalities fell in with the discrepancies between the actual 

 observations and the previously calculated Tables, which Mr. Airy had 

 discovered. And again, shortly afterwards, M. Hansen found that 

 there resulted from the theory two other new equations of the Moon ; 

 one in latitude and one in longitude, agreeing with two which were 

 found by Mr. Airy in deducing from the observations the correction of 

 the elements of the Lunar Tables. And again, a little later, there was 

 detected by these mathematicians a theoretical correction for the mo- 



1 The total expense of computers, to the end of reading the proof-sheets, was 

 48002. 



Mr. Airy's estimate of days' works [made before beginning], for the heavy part 

 of calculations only, was thirty-six years of one computer. This was somewhat ex 

 needed, but not very greatly, in that part. 



