634 PHILOSOPHICAL TRANSACTIONS. [aNNO 1723. 



twice as far from c, as the weight at a. And in general, let the make of the 

 engine be what it will, let the mechanical powers be combined in any manner, 

 when two heavy bodies, by means of the machine, act on each other in dif- 

 ferent directions, if their velocities be reciprocally as their masses, they will 

 destroy each other's force, and come to rest. 



As this is true in respect of mechanical pK)wers, so is it also in respect to the 

 shock or blow given by falling bodies. A heavy body, falling with an accele- 

 rated motion, goes through a space of 1 foot in a quarter of a second, and 

 acquires a velocity, which would carry it 2 feet in the same time with a uniform 

 motion; the same body falls through a space of 4 feet in half a second, and 

 acquires a velocity that would, with a uniform motion, carry it 8 feet in half a 

 second. Therefore, as the time of the fall through a space of 4 feet is twice 

 the time of a fall through I foot, the velocity in the latter case is double 

 that of the first, and consequently the blow, that the body will give, will 

 be double. 



Exper. 2. Let the weight p of lib. fig. 10, be placed in the scale suspended 

 at the end a, of the balance ab, which bears on the gnomon, or iron supporter, 

 khi. Then if the weight c be let fall from d, or 1 foot, it will by its stroke 

 on the end of the beam b, raise up the opposite end a with the weight p, so 

 high, that the spring gh will fly from the button i, which kept it straight and 

 upright before the shock. If the weight p be of 2 lb. it cannot be raised by 

 the fall of c from any height less than p or 4 feet; whereas, if the force of the 

 shock was proportionable to the space, without any regard to the time, as 

 Leibnitz and his followers have affirmed, p ought to be raised, when c falls 

 only from e, or 2 feet; which never happens ; or, if the stroke was proportion- 

 able to the mass multiplied into the square of the velocity, when c falls from 

 p, then p might weigh 4 lb. whereas the experiment will never succeed under 

 those circumstances. 



Exper. 3. If, in order to avoid friction, instead of a blow struck on the 

 end B, by the falling body, the body c be fastened to a pretty long string tied 

 to the button m, as at c, and first lifted up 1 foot, and then let fall; so that in 

 falling 1 foot, it may pull down b, and lift up a with the weight p of lib. 

 whenever p is 2 lb. c must fall from a height greater than for 4 feet, otherwise 

 it will not raise the brachium a, especially if it be let fall between e and f. 



Exper. 4. I took the weight c of 17 ounces Troy, which was a round ball 

 of lead, with a hole through the middle; and having passed the string nx 

 through it, before it was fastened to the hook x, I placed the whole n)achine 

 in such a manner, that the string being stretched by the weight n, went through 

 the hole of the weight c, and also through the hole of the brachium b, upon 



