VOL. XXIII.J* PHILOSOPHICAL TRANSACTIONS. 13 



particularly to show the methods of determining the orbits of the earth and 

 planets, their excentricities, position of their apsides and nodes, and describes 

 all the tables that are necessary to calculate their motions, together with the 

 manner of making them ; and he also shows the way of finding out the magni- 

 tudes, densities and figures of the sun and planets, and the distances of the 

 fixed stars, where he takes notice, that the annual difl^erent distances of a fixed 

 star from the pole (which Mr. Flamsteed in his letter to Dr. Wallis, printed in 

 the third tome of the Doctor's works, says, he has observed in the polar star) 

 does not necessarily arise from their parallax ; but may proceed from other causes; 

 so that from this observation, we cannot conclude the parallax of the fixed stars, 

 nor does it directly prove the motion of the earth, which Mr. Flamsteed thinks 

 he has done by it. And it is the more likely that this variation of the star's 

 distance from the pole, observed by Mr. Flamsteed, proceeds from some nuta- 

 tion, since the young Mr. Cassini has demonstrated, that in the polar star it 

 cannot arise from the parallax of the magnus orbis; and our author has given 

 good arguments to prove the fixed stars to be at so great a distance, that the 

 diameter of the magnus orbis is insensible in respect of it. 



Having thus established the theory of the primary planets ; in the 4th book 

 he gives that of the secondary, whose motions are much more composed and 

 intricate than any of the first, theirs being only compounded of a uniform pro- 

 gressive motion forward, and that of gravity, by which, as it were, they are 

 drawn towards the sun ; whereas the secondaries are not only attracted towards 

 their respective primaries, but also towards the sun, and that with the same 

 accelerating force of gravity as the primaries, when at the same distance, with a 

 greater force when nearer, and a less when farther from the sun, than the 

 primaries are. Which variety of the force of attraction, according to the vari- 

 ous positions of the secondaries orbit, its inclination to the orbit of its primary, 

 and the place of the secondary in this orbit, must necessarily produce various 

 inequalities and irregularities in the motions of the secondaries; all which he 

 considers at large, and from thence he explains the motions of the apsides for- 

 wards, that of their nodes backwards, the changeable inclination of the orbits 

 to the planes of their primaries orbits, the difl^erent velocities of the secondaries, 

 according as their position, in respect of the sun and their primaries, varies; and 

 he applied the whole to the motions of the moon. All this, before the happy 

 discoveries of that celebrated philosopher Mr. Newton, was not to be attempted 

 by any physical explication, the greatest advancement that was made, being 

 only to solve them by an astronomical hypothesis. He also gives an account of 

 the tables necessary to calculate the moon's place seen out of the earth, and 

 the manner of using them; and to this he joins Mr. Newton's own theory of 



