VOL. XIX.] PHILOSOPHICAL TRANSACTIONS. ]43 



distance. Thus a ton weight on the surface of the earth, if it were raised to 

 the height of 4000 miles, which I suppose the semidiameter of the earth, would 

 weigh but -| of a ton, or 500 weight ; if to 12000 miles, or 3 semidiameters 

 from the surface, that is 4 from the centre, it would weigh but -^ part of the 

 weight on the surface, or 100 and 4; so that it would be as easy for the 

 strength of a man at that height to carry a ton weight as here on the surface a 

 1-1- cwt. And in the same proportion does the velocities of the fall of bodies 

 decrease ; for whereas on the surface of the earth all things fall 1 6 feet in a 

 second, at t semidiameter above the surface this fall is but 4 feet, and at 3 

 semidiameters, or 4 from the centre, it is but -fV of the fall at the surface, or 

 but one foot in a second ; and at greater distances, both the weight and fall 

 become very small ; yet at all given distances they are still something, though 

 the effect become insensible. At the distance of the moon, which I will suppose 

 60 semidiameters of the earth, 3600 pounds weigh only 1 pound, and the fall 

 of bodies is but -j-i-l-b- of a foot in a second, or l6 feet in a minute; that is, a 

 body so far off would descend in a minute no more than the same at the surface 

 of the earth descends in a second of time.* 



As was said above, the same force decreasing after the same manner is evi- 

 dently found in the sun, moon, and all the planets, but more especially in the 

 sun, whose force is prodigious, becoming sensible even at the immense distance 

 of Saturn ; this gives room to suspect, that the force of gravity is in the celes- 

 tial globes, proportional to the quantity of matter in each of them; and the sun 

 being at least 10000 times larger than the earth, its gravitation, or attracting 

 force, is found to be at least 10000 times as much as that of the earth, acting 

 on bodies at the same distance. 



This law of the decrease of gravity being demonstratively proved, the author 

 inquires into the necessary consequences of this supposition ; by which he finds 

 the genuine cause of the several appearances in the theory of the moon and 

 planets, and discovers the hitherto unknown laws of the motion of comets, and 

 of the ebbing and flowing of the sea. ,i, 



Now, the theory of the motion of the primary planets is here shown to be 

 nothing but the contemplation of the curve lines, which bodies projected with 

 a given velocity, in a given direction, and at the same time drawn towards the 

 sun by its gravitating power, would describe. Or, which is the same, that the 

 orbits of the planets are such curve lines as a shot from a gun describes in the 

 air, being thrown according to the direction of the piece, but bent into a 



* That is, 3000 times the space fallen in a second, because the spaces descended are in proportion 

 as the square of the times. 



