OF CENTRAL FORCES. 39 



as in the last experiment, let the distance of the ball V LECT. 

 from the center x be made equal to two of the cross di- ^^-^ 

 visions on its bearer ; and the distance of the ball U 

 from the center w be three and a sixth part ; the balls 

 themselves being of equal weights, and V making two 

 revolutions by turning the winch, in the time that U 

 makes one : so that if we suppose the ball V to revolve 

 in one second, the ball U will revolve in two seconds, 

 the squares of which are one and four ; for the 

 square of one is only one, and the square of two is 

 four ; therefore the square of the period or revolu- 

 tion of the ball V, is contained four times in the 

 square of the period of the ball U. But the distance of 

 V is 2, the cube of which is 8, and the distance of 

 V is 3j, the cube of which is 32 very nearly, in which 8 

 is contained four times ; and therefore, the squares of 

 the periods of V and U are to one another as the cubes 

 of their distances from x and w, which are the centers 

 of their respective circles. And if the weight in the 

 tower O be four ounces, equal to the square of 2, the 

 distance of V from the center x ; and the weight in the 

 tower P be 10 ounces, nearly equal to the square of 3 

 the distance of U from w; it will be found upon turning 

 the machine by the winch, that the balls U and V will 

 raise their respective weights at the same instant of 

 time. Which confirms that famous proposition of KEP- 

 LER, 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 attrac- 

 tion is inversely as the square of the distance from 

 his center : 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. 



