﻿264 ON THE ASTRONOMICAL COMPUTATIONS 



circumference of a circle consisting of 4331500, and 

 described round die earth as a centre with a radius 

 equal to his mean distance, which is properly all that 

 is meant by the "olshcambha , and which, therefore, is 

 increased or diminished according to his equated mo- 

 tion. This in three signs of anomaly is equivalent to 

 32' 24"; for, as 4331500 to 360% so 6500 to 32' 24". 

 The Europeans determine the same to be 32' 22". In 

 the same manner, the sun's vishcambha in the mean 

 cacsha of the moon, or the portion of her orbit in Yo- 

 juris, included in this angle, is found, as 4331 500 

 is to 324000, so is 6500 to 486 Yojan or n, 0, of use 

 in solar eclipses ; but this I am endeavouring to ex- 

 plain is a lunar one. It is evident that the diameter 

 of the earth's shadow at the moon will be c, d y — c y 

 a 4- />, d 9 or a b when her distance is A e ; and that 

 c a and ^^ will be found by the following proportion : 

 as Ak is tofi—g h=f g + hi, so is Ae to c a -\-b d. 

 But it has been observed that Ak and/ / are propor- 

 tioned by the Hindus according to the moon's distance 

 A e, the apparent motion of the sun and moon, and 

 the angles subtended by their diameters. The Hindu 

 rule therefore states, As the sun's inshcambha or dia- 

 meter is to the moon's, so is the difference of the dia- 

 meters of the sun and earth, in Ycjans, to a fourth 

 number, equal to ca 4- b d to be subtracted from the 

 suchk or hn=cd to find a b ; also, that the number of 

 Yojans, thus determined as the diameters of the moon 

 and shadow, may be reduced to minutes of a great cir- 

 cle by a divisor of fifteen. For, as the minutes con- 

 tained in 36o°=2i6oo, are to the moon's orbit in Yo- 

 :2400c, so is one minute to fifteen Yojan, 



The diameter of the moon's disk, of the earth's 

 shadow, and the place of the node being found, for 

 the instant of opposition or full moon, the remaining 



