178 REMARKS on the 



the relation of the equation of the centre to the anomaly of a 

 planet, are fo far the fame, that they are proportional to the fine 

 of that anomaly ; and it becomes therefore neceflary to fearch 

 among thefe hypothefes, for that by which the feries of 

 fmall differences, defcribed above, may be beft reprefented. 

 It is needlefs to enter here into any detail of the reafonings 

 by which this has been done, and by which I have found, 

 that the argument in the table bears very nearly the fame 

 relation to the correfponding numbers, that the anomaly 

 of the eccentric does to the equation of the centre. By the 

 anomaly of the eccentric, however, I do not mean the angle 

 which is known by that name in the folution of Kepler's 

 problem, but that which ferves the fame purpofe with it, 

 on the fuppofition of a circular orbit, and an uniform an- 

 gular motion about a point which is not the centre of that 

 orbit, but which is as diftant from it, on the one fide, as 

 the earth (or the place of the obferver) is on the other. It is 

 the angle, which, in fuch an orbit, the line drawn from the 

 planet to the centre, makes with the line drawn from thence to 

 the apogee ; and the argument in the Indian tables coincides 

 with this angle. 



This hypothefis of a double eccentricity, is certainly not the 

 fimpleft that may be formed with refpect to the motion of the 

 iheavenly bodies, and is not what one would expect to meet with 

 here ; but it agrees fo well with the tables, and gives the equa- 

 tions from the arguments fo nearly, efpecially for the moon and 

 the planets, that little doubt remains of its being the real hy- 

 pothefis on which thefe tables were conftrucled *. 



54. Of 



* The formula deduced from this hypothefis, for calculating the equation of the cen- 

 tre from the anomaly of the eccentric, is the following : Let x be the equation of the 

 centre, <p the anomaly of the eccentric, e the eccentricity of the orbit, or the tangent of 



. 2e*Jin.iq> 2e s /in.cp 

 half .the greatelt equation j then * =: 2ejin.q>-i -\ - H &c. 



