MOTION, MECHANICS, ETC. 167 



confirms that famous proposition of Kepler, viz. That the 

 squares of the periodical times of the planets round the sun, 

 are in proportion to the cubes of their distances from him; 

 and that the sun's attraction is inversely as the square of 

 the distance from his centre ; that is, at twice the distance, 

 his attraction is four times less ; and thrice the distance, 

 nine times less ; at four times the distance, sixteen times 

 less ; and so on to the remotest part of the system. 



8. Take off the catgut string, E, from the great wheel, D, 

 and the small wheel, H, and let the string, F, remain upon 

 the wheels D and G. Take away also the bearer, M X, from 

 the whirling-board, and instead thereof put the machine, 

 A B (Fig. 170) upon it, fixing this machine to the centre of 

 the board by its screw. In this 



machine are two glass tubes, a 

 and b, close stopped at both 

 ends, and inclined to an angle f 

 of 30 or 40 degrees; and each 

 tube is about three quarters full 

 of water. In the tube, a, is a 

 little quicksilver, which naturally 

 falls down to the end a, in the water, because it is heavier 

 than its bulk of water ; and on the tube, b, is a small cork, 

 which floats on the top of the water at e, because it is lighter ; 

 and it is small enough to have liberty to rise or fall in the 

 tube. While the wheel, with this machine upon it, continues 

 at rest, the quicksilver lies at the bottom of the tube a, 

 and the cork floats on the water near the top of the tube b. 

 But, upon turning the winch, and putting the machine in 

 motion, the contents of each tube will fly off towards 

 the uppermost ends, which are furthest from the centre of 

 motion, the heaviest with the greatest force. Therefore the 

 quicksilver in the tube, a, will fly off quite to the end /, and 

 occupy its bulk of space, there excluding the water from that 

 place, because it is lighter than quicksilver ; but the water 

 in the tube, b, flying off to its higher end, e, will exclude the 

 cork from that place, and cause the cork to descend towards 

 the lowermost end of the tube, where it will remain upon 

 the lowest end of the water, near 6 ; for the heavier body, 

 having the greater centrifugal force, will therefore possess 

 the uppermost part of the tube ; and the lighter body will 

 keep between the heavier and the lowermost part. 



9. If one body move round another, both of them must move 



