IB OBJECTS, ADVANTAGES, AND 



is only one particular case, relates to the motions of all bodies, which 

 are attracted (or influenced, or drawn) by any power towards a certain 

 point, while they are, at the same time, driven forward by some push 

 given to them at first, and continuing to act on them while they are 

 drawn towards the point. The line in which a body moves while so 

 drawn and so driven, depends upon the force it is pushed with, the 

 direction it is pushed in, and the kind of power that draws it towards 

 the point; but, at present, we are chiefly to regard the latter circum- 

 stance, the attraction towards the piont. If this attraction be uniform, 

 that is, the same at all distances form the point, the body will move 

 in a circle, and the point to which it is constantly drawn will be the 

 centre of the circle. Thus, a stone in a sling;, when whirled round the 

 hand, moves for this reason in a circle, while it remains in the sling ; 

 the force that draws it towards the hand being- always the same, and 

 the hand either stopping after setting the stone a-whirling, in which 

 case it is the centre of the circle, or going round in a smaller circle, in 

 which case the point is the centre of the two circles, the one the stone 

 whirls round in, and the one the hand moves round in. (Of course 

 we speak not now of the line the stone moves in after leaving the 

 sling ; that is a parabola, as before stated.) If the force that draws 

 the moving body changes at different distances, so as to make the body 

 move quicker, by drawing it more strongly towards the point, the 

 nearer it is to that point, then the body will move, not in a circle, but 

 in other curve lines of various kinds, according as the proportion of the 

 force to the distance varies, and according also to the direction of the 

 forward push, and the force with which it was originally given. If the 

 force drawing towards the point is such, that, at two feet from the 

 point, it is four times less than at one foot ; at three feet, nine times 

 less; at four feet, sixteen times less; and so on, always lessening in the 

 same proportion, that is, as the squares of the distances increase; and 

 if the body is pushed forward with a particular degree of force ; the 

 line in which it moves will go round the point, but it will not be 

 a circle ; it will be an oval or ellipse ; the curve described by means of 

 a cord fixed at both ends, in the way we have already explained ; the 

 point of attraction will be nearer one end of the ellipse than the other, 

 and the time the body will take to go round, compared with the time 

 any other body would take, moving at a different distance from the 

 same point of attraction, but drawn towards that point with a force 

 which bears the same proportion to the distance, will bear a certain 

 proportion, discovered by mathematicians, to the average distances of 

 the two bodies from the point of common attraction. If you multiply 

 the numbers expressing the times of going round each by itself, the 

 products will be to one another in the proportion of the average dis- 

 tances multiplied each by itself, and that product again by the distance. 

 Thus, if one body take two hours, and is five yards distant, the other, 

 being ten yards off, will take something less than five hours and forty 

 minutes. 



Now, this is one of the most important truths in the whole compass 

 of science ; for it does so happen, that the force with which bodies fall 

 towards the earth, or what is called their gravity, the power that draws 

 Or attracts them towards the earth, varies with the distance exactly in 



