674 PHILOSOPHICAL TRANSACTIONS. [aNNO 1 740. 



Ptolemy, the night at Babylon was at that time 14'^ 24"" long, and therefore sun 

 rise at 7*" 1 '2™ after midnight ; and as the moon had then south latitude, and was 

 not quite come to the sun's opposition, her apparent setting must have been 

 something sooner, i. e. more than an hour before the beginning of the eclipse, 

 according to the tables ; whereas the moon was seen eclipsed some time before 

 her setting ; which demonstrates, that the moon's place must have been for- 

 warder, and consequently her motion since that time less than the tables make 

 it by about 40' or 50 . But the computed place of the moon, in each of the be- 

 fore-mentioned solar eclipses, observed at Cairo, being about 8' before her place 

 from observation, shows us that the mean motion of this luminary has been some- 

 thing greater in the last 700 years than the tables suppose it, and therefore must 

 have been accelerated. 



This acceleration is further confirmed by the eclipse which Hipparchus savs 

 was observed at Alexandria, in the 54th year of the second Calippic period, the 

 l6th day of Messori, when (he says) the moon began to be eclipsed half an hour 

 before her rising, and was wholly clear again in the middle of the third hour of 

 the night. This was in the year before Christ 201 , Sept. 22. The middle of 

 this eclipse at Alexandria by the tables, was Sept. 22, 7^ 44"^ apparent time ; and 

 the duration 3'^ 4™, which makes the beginning at 6^ 12"" apparent time, 

 that is about 10"" after the rising of the moon at Alexandria, or 40"" later than 

 the beginning from observation. This difference in time makes a difference of 

 near 20' in the moon's place. 



The most ancient eclipse of which we have any account remaining, namely 

 that related by Ptolemy, as observed at Babylon the first year of Mardokempad, 

 in the night between the 2!}th and 30th days of Thoth. in which the moon be- 

 gan to be eclipsed when one hour after her rising was fully past ; if by reason of 

 the latitude of the expression, it be not a direct proof of the acceleration, it may 

 nevertheless help to limit its quantity. This eclipse was in the year before Christ 

 721, March IQ. The middle at Babylon, by the tables, was March ig'' lo"" 

 26"" apparent time ; and the beginning at S*" 32"", the apparent rising of the 

 moon at that place was about 5'' 46"" afternoon ; so that the observed beginning 

 of the eclipse was at least 6^ 46"^ afternoon, i. e. not above l^*" before the be- 

 ginning, by the tables : therefore the moon's true place could precede her place 

 by computation, but little more than 50' at that time. 



If we take this acceleration to be uniform, as the observations on which it is 

 grounded are not sufficient to prove the contrary, the aggregate of it will be as 

 the square of the time: and if we suppose it to be lO" in 100 years, and that 

 the tables truly represent the moon's place about a.d. 700, it will best agree with 

 the before-mentioned observations ; and the difference between the moon's place 

 by the tables, and. her place in the heavens, will be as follows. 



