202 M E M O I R S of the 
decreafes as t>\e fquare of the diftance encreales, that is, the 
weight of bodies and the force of their M is lels, in parts more 
removed from the centre, in proportion to the Iquares of the 
diftances • lb as, for inftance, a ton weight on the lurface of the 
earth, if it were railed to the height of 4000 miles, which 
Mr. Halley fuppoles the femidiameter of the earth, would weigh 
but - of a ton, or five hundred weighty if to 12000 miles or 
three lemidiameters from the lurface, that is four from the centre, 
it would weigh but i# part of the weight on the lurface, or a 
hundred and a quarter^ fo that it would be as eaiy for the 
ftren^th of a man at that he ight^to carry a ton weight, as here on 
the lurface 100 i 5 and in the fame proportion the velocities of 
the foil of bodies decreafe 5 for whereas on the furface of the 
earth all bodies fall 16 foot in a iecond, at one femidiameter 
above this lurface, this M is but four foot, and at three femi- 
diameters, or at four from the centre, it is but |^ of the fall at 
the furface, or but one foot in a fecond^ and at greater di (lances 
both weight and fall become very fmall 5 yet at all given diftances, 
it is dill Vomething, tho' the effeft become infenlible • at the dif- 
tance of the moon, which we will luppole 60 lerai-diameters of 
the earth, 5600 pounds weigh but one pound, and the fall of bo- 
dies is but -V^oD of a foot in a fecond, or 16 foot in a minute 5 
that is, a body lb f^ir off delcends in a minute no more than the 
fame at the lurface of the earth would do in a fecond of time j as 
was laid above, the fame force, decrcafing after the fame manner, 
is evidently found in the fun, moon, and all the planets, but 
more efpeqially in the fun, whole force is prodigious, becoming 
fenfible even at the immenfe diftance of latum; this gives room 
to fuipefl, that the force of gravity is in the celeftial bodies pro- 
portional to the quantity of matter in each of them 5 and the fun 
bein'7 at leaft ten thoufand times as big as the earth, its gravita- 
tion,' or attra£live force, is found to be at leaft ten thoufand times 
as much as that of the earth, a61:ing on bodies at the lame 
diftance. 
This law of the decreafe of gravity being now made out be- 
yond contradiction, Mr. Ne-zi'tofi dues, with great^ lagacity, en- 
quire into the necelfary conlequences of this fuppoiition^ where- 
by he finds the genuine caule of the fevcral appearances in the 
theory of the moon and planets, and difcovers the hitherto un^ 
known laws of the motion of comets, and of the ebbing and flow- 
ing of the fea ^ and this latter Mr. Halley explains from Mr. 2Se\.v* 
Ton's principles, in the following manner. 
If 
