144 PHILOSOPHICAL TRANSACTIONS. [aNNO ISq/, 



crooked line by the supervening tendency towards the earth's centre; and the 

 planets being supposed to be projected with a given force, and attracted towards 

 the sun, after the aforesaid manner, are here proved to describe such figures as 

 answer exactly to all that the industry of this and the last age has observed in 

 the planetary motions. So that it appears, that there is no need of solid orbs 

 and intelligences, as the ancients imagined ; nor yet of vortices or whirlpools 

 of the celestial matter, as Descartes supposes; but the whole affair is simply and 

 mechanically performed, on the sole supposition of a gravitation towards the 

 sun, which cannot be denied. 



The motion of comets is here shown to be compounded of the same elements, 

 and not to differ from planets, but in their greater swiftness, by which over- 

 powering the gravity that should hold them to the sun, as it does the planets, 

 they fly off again to such a distance from the sun and earth, that they are soon 

 out of our sight. And the imperfect accounts and observations antiquity has 

 left us, are not sufficient to determine whether the same comet ever return 

 again. But this author has shown how geometrically to determine the orbit of 

 a comet from observations, and to find his distance from the earth and sun, 

 which was never done before. The third thing here accomplished, is the theory 

 of the moon, all the inequalities of whose motion are proved to arise from the 

 same principles, only here the effect of two centres operating on, or attracting 

 a projected body, comes to be considered ; for the moon, though principally 

 attracted by the earth, and moving round it, does, together with the eartli, 

 move round the sun once a year, and is, according as she is nearer (ir farther 

 from the sun, drawn by him more or less than the centre of the earth, about 

 which she moves; whence arise several irregularities in her motion, of all wliich, 

 the author in this book has given a full account. And though by reason of the 

 great complication of the problem, he has not yet been able to make it purely 

 geometrical, it is to be hoped, that in some further essay he may surmount that 

 difficulty; and having perfected the theory of the moon, the long desired dis- 

 covery of the ^longitude, which at sea is only practicable this way, may at length 

 be brought to light. 



All the surprising phaenomena of the flux and reflux of the sea are, in like 

 manner, shown to proceed from the same principle. If the earth were alone, 

 that is to say, not affected by the actions of the sun and moon, it is not to be 

 doubted but the ocean, being equally pressed by the force of gravity towards 

 the centre, would continue in a perfect stagnation, always at the same height, 

 without ever ebbing or flowing ; but it being here demonstrated, that the sun 

 and moon have a like principle of gravitation towards their centres, and that 

 the earth is within the activity of their attractions, it will plainly follow, that 



