(J36 PHILOSOPHICAL TRANSACTIONS. [aNNO J 723. 



of 6 ounces, one of 3, one of 2, and one of 8 dwt. Then making pendulums 

 of these balls, and hanging them on the machine contrived by Mariotte for 

 the congress of bodies, and lately improved by Dr. Gravesande, I measured 

 574- inches between the centre of suspension and the centre of gravity of the 

 balls, and then every degree of the circle they described in their oscillation was 

 1 inch, and the degrees being marked on a line of chords on a brass ruler above 

 the balls, by their strings successively covering the cross lines of division, the 

 degrees that the balls fell from, and those to which they rose, were very dis- 

 cernable to an eye placed at a convenient distance. 



Exper. 7 . I took the two balls 12, and removing each from the lowest point 

 of their equal and respective circles, up to 4 inches, or 4 degrees, I let them 

 fall so that they met at bottom, and were both reflected again to 4, the place 

 from whence they fell. 



Exper, 8. Every thing else being as before, instead of one of the balls 12, 

 I took the ball 6, then letting 6 go from 8°, and 1 2 from 4, after reflection 

 12 was driven up again to 4, as before. 



Exper, g. The ball 3 falling from l6°, met the ball 12 that fell still from 

 4, and after reflection 12 went up again to 4. 



Exper. 1 0. The ball 2 falling from 6°, and 1 2 from I °, 12 was reflected to 

 1 ; and when 2 fell from 12°, and the ball 12 from 2, the 12 was reflected 



to 2. 



Exper. 1 1 . The ball of 8 dwt. which weighed only -^ of the ball 1 2, fall- 

 ing from 15 inches or degrees, raised up 12, that fell from half a degree, to 

 the same place again. 



In all these experiments, the error, or want of perfect reflection, was greater 

 in the little balls than in the large ones, on account of their going through a 

 greater arc of a circle, by which they deviated more from a cycloid than the 

 great ones ; as also on account of the resistance of the air, which must be 

 greater because of the little balls going through a greater arc, moving with 

 more velocity, being suspended by a string as thick as that of the great ones, 

 and having more surface in proportion to their weight. But all the errors do 

 not bring the phaenomena any thing near what they ought to be, if the force 

 of the bodies was as the square of their velocities multiplied into their masses, 

 for then the ball 12 would have been driven to heights very different from 

 what it rose up to. 



In the 8th experiment, the ball 12 should have risen to near 5^ inches, 

 for the ball 6 falling with the velocity 8, must have had its force = 8 X 8 x 

 6 = 384; and then, that the ball 12 might have the same force or quantity of 

 motion, it must rise near to 5,7 because 5,7 X 5,7 X 12 = 389,88. 



