VOL. XLVI.] 



PHILOSOPHICAL TRANSACTION-S. 



673 



given the side Ea, and the angle esu, = BEa (the sum or difference of the angles 

 BEi and lEas) : therefore the sides ei and ai may be found. But e» is the dis- 

 tance of the moon from the sun in the ecliptic, and ai + afi the moon's latitude 

 at the time when the centre of the shade is at 9 ; which may be compared with 

 the computation from the tables for that time. 



By this means Mr. D. compared the aforesaid solar eclipses with the tables, 

 and found the difference in longitude and latitude as follows : 



A.D. 



304 

 977 



97sU 



Apparent Time at 

 Greenwich. 



Dist. Da© 

 from El. 



June 16, 2" 4 

 Dec. 12, 19 12 30 

 une8, 1 16 10 



20=39 41 in conseq. 

 43' 39 in antec. 

 29' 3 in conseq. 



Lai. 3) 

 from ti 



34' 37" N. 



30 23 N. 



8 24 s. 



Da© 

 by Tab. 



Lat. J 

 by Tab. 



35' 25' 



36 

 37 



3 

 48 



37' 26" N, 



31 50 N 



3 21 s. 



DifF. from Obser. 



in Long.j in Lat. 



— 4' l6"l + 2'49' 

 + 7 36 +1 27 

 + 8 45 1 — 5 3 



— 2' 

 + 3 



36" 



38 



The agreement between the last 2 of these differences in longitude, shows 

 that the tables represent the mean motion of the moon's apogee very well for 

 above 700 years, the moon being very near her perigee at the time of one of 

 those eclipses, and near her apogee at the time of the other. 



By the same method he also compared the sun's eclipse, July 29, 1478, 

 (which appears, from what is related of it, to have been carefully observed by 

 Walther at Nuremberg,) with the tables, and found the difference in longitude 

 to be + 10' 29", and in latitude + 9' 12". This wide diff'erence in latitude, 

 from the tables, that agree so well with the former ancient observations, con- 

 firmed the opinion, that the Nuremberg observations are too inaccurate to de- 

 termine any thing from them in this affair. 



The eclipses recorded by Ptolemy in his Almagest, are most of them so loosely 

 described, that if they show us the moon's mean motion has been accelerated in 

 the long interval of time since they happened, they are wholly incapable of 

 showing us how much that acceleration has been. There are indeed 2 or 3 of 

 them attended with such lucky circumstances, as not only plainly prove that 

 there has been such an acceleration, but also help us to guess at its quantity. 

 One of these is the eclipse said by Hipparchus to have been observed at Babylon, 

 in the 366th year of Nabonassar, the night between the 26th and 27th days of 

 Thoth, when a small part of the moon's disk was eclipsed on the north (east, 

 half an hour before the end of the night, and the moon set eclipsed. This was 

 in the year before Christ 313, Decemb. 22. The middle of this eclipse at Baby- 

 lon (supposing with Ptolemy) the meridian of that place to be 50"^ in time east 

 of tlie meridian of Alexandria,) by Mr. D.'s tables, was Dec. 22^* 4*' 4"" appa- 

 rent time ; the duration was l'' 87"", Ptolemy makes it 1 '' 30"' nearly ; hence 

 the beginning should have been about 8'' 1 5"" after midnight : according to 



VOL. IX. 4 R 



