VOL. XXXII.] PHILOSOPHICAL TRANSACTIONS. 635 



which c lay, without touching the sides of the hole, either in the weight or 

 balance ; then having put such a weight p in the opposite scale, as c falling 

 from the height of one inch, was able to raise high enough, to let loose the 

 spring gh from the button i; I added to p another weight equal to it, and then 

 letting fall c along the string that guided it, from a height of 2 inches, then 

 of 3, and then exactly of 4, it would not raise the double weight p to the 

 former height, but falling from 5 inches, or a little higher, it raised it up. 



Exper. 5. Leaving every thing else as before, I changed the weight c, for 

 another leaden ball of twice the weight, which falling from one inch, raised 

 the double weight p to the usual height ; then changing the weight p in any 

 proportion, whatever height was required for the heaviest ball c, or c2, to fall 

 from, in order to raise the weight at p ; more than 4 times the height was re 

 quired for the first ball c, to raise the same weight so high as to let loose the 

 spring. 



Exper. 6. I tried the experiment with the weight c hanging at the string 

 mc, as in exper. 3, and a fall from a height of 5, or near 5 inches, was required 

 to raise double the weight in the opposite scale, that a fall from 1 inch would 

 raise; only here the height above 4 inches was not so great as in the former 

 experiment, the friction being something less. Then I suspended the great 

 ball c, or c 2, by the string mc, and when by falling 1 inch it raised the weight 

 p, the little weight c could not produce the same effect, without falling from a 

 greater height than 4 inches. 



It is here to be observed, that which way soever these experiments are tried, 

 the objections rising from the friction do no way serve to confirm the new opi- 

 nion, because they show that, on account of the friction, the heights must be 

 something more than in a duplicate proportion of the velocities, but never less, 

 to give a blow with the same body in proportion to the velocity. 



That the momentum of bodies is in proportion to the mass multiplied into 

 the velocity, is almost evidently shown from the congress of elastic bodies, as 

 has been demonstrated by Newton in his Principia, in the Corollaries to his 

 Laws of Motion. I had often tried the experiments there mentioned with balls 

 of ivory and balls of glass, and some of them with two balls of steel, of 2 

 ounces each, and found every thing answer, allowing for the want of perfect 

 elasticity in the bodies. But now on this occasion, as the objections to the 

 received opinion were renewed, I was willing to repeat the experiments with 

 the utmost accuracy ; and therefore, as ivory balls are not equally dense in all 

 their parts, and glass balls break after two or three strokes ; I caused balls to be 

 nicely turned of steel, and made as hard, that is, as elastic, as possible, and 

 their weights were precisely as follows: two balls of 12 ounces Troy each, one 



4 M 2 



