264 PHILOSOPHICAL TRANSACTIONS. [aNNO 1 685-6, 



Other cause, than the great height of my place of observation above the surface 

 of the sea, by which the gravity being diminished, the length of the pendulum 

 vibrating seconds is proportionably shortened.* 4. That gravity equally afFects 

 all bodies, without regard either to their matter, bulk, or figure ; so that, the 

 resistance of the medium being removed, the most compact and the loosest 

 the greatest and smallest bodies, would descend the same spaces in equal times ; 

 the truth of which appears from the experiment before cited. In these last 

 two particulars, is shown the great difference between gravity and magnetism, 

 the one affecting iron only, and that towards its poles, the other all bodies alike 

 in every part. From hence it will follow, as a corollary, that there is no such 

 thing as positive levity; those things that appear light, being only comparatively 

 so ; and whereas several things rise and float in fluids, it is because, bulk for 

 bulk, they are not so heavy as those fluids ; nor is there any reason why cork, 

 for instance, should be said to be light because it swims on water, any more 

 than iron because it swims on mercury. 5. That this power increases as you 

 descend to, and decreases as we ascend from, the centre, and that in the pro- 

 portion of the squares of the distances from it reciprocally, so as at a double 

 distance to have but a quarter of the force ; a principle on which Mr. Newton 

 has made out all the phaenomena of the celestial motions, in so easy and na- 

 tural a manner, that its truth is past dispute. Besides, it is highly rational, that 

 the attractive or gravitating power should exert itself more vigorously in a small 

 sphere, and weaker in a greater, in proportion as it is contracted or expanded ; 

 and if so, seeing that the surfaces of spheres are as the squares of their radii, 

 this power at several distances will be as the squares of those distances reci- 

 procally ; and then its whole action on each spherical surface, be it great or 

 small, will be always equal. And this is evidently the rule of gravitation to- 

 wards the centres of the Sun, Jupiter, Saturn, and the Earth ; and thence is 

 reasonably inferred, to be the general principle observed by nature in all the 

 other celestial bodies. 



These are the principal affections of gravity, from which the rules for the 

 fall of bodies, and the motion of projects are mathematically deducible. Mr. 

 Isaac Newton has shown how to define the spaces of the descent of a body, let 

 fall from any given height, down to the centre, supposing the gravitation to 

 increase, as in the fifth property ; but considering the smallness of height, to 

 which any projectile can be made to ascend, and over how small an arch of 

 the globe it can be thrown by any of our engines, we may well enough suppose 



* Hence it would appear, that Dr. Halley was not then aware that the slowness of the vibrations, 

 which required the shortening of the pendulum, was owing to the decrease of gravitation, consequent 

 on the oblate figure of the earth, and the centrifugal force from the rotation. 



