166 BENJ. PIKE'S, JR., DESCRIPTIVE CATALOGUE. 



circumference is only one -half of the circumference of the 

 wheel, H or G, and over the pulley, s, to keep it tight ; and 

 let four times as much weight be put into the tower, P, as 

 into the tower, O. Then turn the winch, B, and the ball, V, 

 will revolve twice as fast as the ball IT, in a circle of the same 

 diameter, because they are equidistant from the centres of 

 the circles in which they revolve ; and the weights in the 

 towers will both rise at the same instant ; which shows, that 

 a double velocity in the same circle will exactly balance a 

 quadruple power of attraction in the centre of the circle. 

 For the weights in the towers may be considered as the at- 

 tractive forces in the centres, acting upon the revolving 

 balls ; which, moving in equal circles, is the same thing as 

 if they moved in one and the same circle. 



7. If bodies of unequal weights revolve in unequal circles, 

 in such a manner that the squares of the times of their 

 going round are as the cubes of their distances from the 

 centres of the circles they describe ; their centrifugal forces 

 are inversely as the squares of their distances from those 

 centres. For, the catgut string remaining as in the last ex- 

 periment, let the distance of the ball, V, from the centre, x, 

 be made equal to two of the cross divisions on its bearer ; 

 and the distance of the ball, U, from the centre, 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 re- 

 volve in two seconds, the squares of which are one and four, 

 for the square of 1 is only 1, and the square of 2 is 4 ; 

 therefore the square of the period, or revolution 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 U is 3, the cube of which is 32, very 

 nearly, in which 8 is contained four times ; and, therefore, 

 the squares of the periods of Y and U are to one another 

 as the cubes of their distances, from x and w, which are the 

 centres of their respective circles. And if the weight in the 

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

 tance of V from the centre, x j and the weight in the tower, 

 P, be ten ounces, nearly equal to the square of 3|, the dis- 

 tance 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 



