JSTRONOMT of the BRAHMINS. 173 



47. The Brahmins having thus obtained the variations of 

 the length of the day, at any place, or what we call the afcen- 

 fional differences, apply them likewife to another purpofe. As 

 they find it neceffary to know the point of the ecliptic, which 

 is on the horizon, at the time when an eclipfe happens, they 

 have calculated a table of the right afcenfions of the points of 

 the ecliptic in time, to which they apply the afcenfional dif- 

 ferences for the place in queftion, in order to have the time 

 which each of the figns takes to defcend below the horizon of 

 that place *. This is exadlly the method, as is well known, 

 which the moft fkilful aftronomer, in like clrcumflances, would 

 purfue. Their table of the differences of right afcenlion is 

 but for a few points in the ecliptic, viz. the beginning of each 

 fign, and is only carried to minutes of time, or tenths of a 

 degree. It is calculated, however, fo far as it goes, with per- 

 fedl accuracy, and it fuppofes the obliquity of the ecliptic, as 

 before, to be twenty-four degrees- 



Such calculations could not be made without fpherical tri- 

 gonometry, or fome method equivalent to it. If, indeed, we 

 would allow the leafl fkill pofhble to the authors of thefe tables, 

 we may fuppofe, that the arches were meafured on the circles 

 of a large globe, or armillary fphere, fuch as we know to have 

 been one of the firft inftruments of the Egyptian and Greek 

 aftronomers. But there are fome of the tables where the arches 

 are put down true to feconds, a degree of accuracy which a 

 mechanical method can fcarcely have afforded. 



48. In another part of the calculation of eclipfes, a diredt 

 application is made of one of the mofl remarkable propo- 

 fitions in geometry. In order to have the femiduration of 

 a folar eclipfe, they fubtradl from the fquare of the fum of 

 the femidiameters of the fun artd moon, the fquare of a certain . 

 line, which is a perpendicular from the centre of the fun on 

 the path of the moon ; and from the remainder, they extradl 



tha 



* Acad, des Scien. 17 J 2, IL P. 205. 



