158 REMARKS on the 



make the moon's motion lefs than Mayer's, for the above 

 mentioned interval, by 5°, 44', 14", which therefore is, ac- 

 cording:: to them, the quantity of the acceleration. 



27. Now, it is worthy of remark, that if the fame be com- 

 puted on Mayer's principles, that is, if we calculate how 

 much the angular motion of the moon for 4383 years, 94 days, 

 dated from the beginning of the Calyougham, muft have been 

 lefs than if her velocity had been all that time uniform, and 

 the fame as in the prefent century, we fhall find it to be 

 5°, 43', 7", an arch which is only i', 7", lefs than the former. 

 The tables of Chrifnabouram, therefore, agree with thofe of 

 Mayer, when corrected by the acceleration within i', 7", and 

 that for a period of more than four thoufand years. From this 

 remarkable coincidence, we may conclude, with the highefl pro- 

 bability, that at leaft one fet of the obfervations, on which 

 thofe tables are founded, is not lefs ancient than the Calyoug- 

 ham ; and though the poffibility of their being fome ages later 

 than that epoch, is not abfolutely excluded, yet it may, by 

 ftridl mathematical reafoning, be inferred, that they cannot 

 have been later than 2000 years before the Chriftian era *. 



28. This 



* The reafoning here referred to is the following : As the mean motions, in all 

 aftronomical tables, are determined by the comparifon of obfervations made at a great 

 difiance of time from one another; if x be the number of centuries between the begin- 

 ning of the prefent, and the date of the more ancient obfervations, from which the 

 moon's mean motion in the tables of Chrifnabouram is deduced ; and if y denote the 

 fame for the more modern obfervations : then the quantity by which the moon's mo- 

 tion, during the interval *• — v, falls fliort of Mayer's, for the fame interval, is 



If, therefore, m be the motion of the moon for a century in the laft mentioned tables, 

 ra(a; — y) — 9 (x* — -j') will be the mean motion for the intervals; — y in the tables of 

 Chrilnabouram. If, then, a be any other interval, as that of 43.83 centuries, the mean 

 motion afligned to it, in thefe laft tables, by the rule of proportion, will be 



— i — :- =: ma — ^a{N+/), Let this motion, aftually taken from the ta- 



N~y 



bles 



