ASTRONOMY of the BRAHMINS. ijg 



54. Of this, the method employed to calculate the place of 

 any of the five planets from thefe tables, affords a confirma- 

 tion. But, in reafoning about that method, it is neceflary to 

 put out of the queftion the ufe that is made of the parallax of 

 the annual orbit, or of the fchigram, in order to have the ar- 

 gument for finding the equation of the centre, which is evi- 

 dently faulty, as it makes that equation to be affected by a 

 quantity, (the parallax of the annual orbit), on which it has 

 in reality no dependence. To have the rule free from error, it 

 is to be taken, therefore, in the cafe when there is no parallax 

 of the annual orbit, that is, when the planets are in opposition 

 or conjunction with the fun. In that cafe, the mean anomaly 

 is fir ft corrected by the fubtraction or addition of half the 

 equation that belongs to it in the table. It then becomes the 

 true argument for finding, from that fame table, the equation 

 of the centre, which is next applied to the mean anomaly, to 

 have the true. Now, this agrees perfectly with the conclufion 

 above ', for the mean anomaly, by the fubtraction or addition 

 of half the equation belonging to it in the table, is converted, 

 almoft precifely, into the anomaly of the eccentric, and be- 

 comes therefore the proper argument for finding out the equa- 

 tion, which is to change the mean anomaly into the true *.• 

 There can be no doubt, of confequence, that the conclufion 

 we have come to is ftrictly applicable to the planets, and that 

 the orbit of each of them, in this aftronomy, is fuppofed to 

 be a circle, the earth not being in its centre, but the angular 



z 2 velocity 



* This method of calculation is fo nearly exac~r, that even in the orbit of Mars, the 

 equation calculated from the mean anomaly, rigoroufly on the principle of his angular' 

 motion being uniform, about a point diftant from the centre, as defcribed above, will 

 rarely differ a minute from that which is taken out from the Indian tables by this rule. 

 It was remarked, (§ 37.) that it is not eafy to explain the rules for finding the argument 

 of the equation of the centre, for the planets. What is faid here explains fully one part 

 of that rule, viz. the correction made by half the equation manda ; the principle on 

 which the other part proceeds, viz. the correftion by half the equation fchigram, is ftill 

 uncertain. 



