VOL. LXVI.] PHILOSOPHICAL TRANSACTIONS. 79 



ounces in the scale, deliberately descending, by 5 turns of the larger barrel, 

 through a perpendicular space 25^ inches, will represent the quantity of me- 

 chanic power which causes the two heavy bodies, from a state of rest, to acquire 

 a velocity, such as to carry them equably through 20 circumferences of their 

 circle of revolution in the space of '2g^ ; and that the time in which the mechanic 

 power produced this effect was 14i% as appears by the 6th column. And this 

 mechanic power we shall express by the number 202, the product of the number 

 of ounces in the scale multiplied by the inches in its perpendicular descent, for 

 8 X 25i= 202. 



2d. By the 2d experiment, as 1 turns of the smaller barrel are equal to the 

 same perpendicular height as 5 turns of the larger, it follows that the same me- 

 chanic power, viz. 202, acting on the same heavy bodies to accelerate them, pro- 

 duces the very same effect in generating motion in the bodies as it did before, 

 viz. 20 revolutions in 294-% the small difference of 4 of a second being no more 

 than may reasonably be attributed to the unavoidable errors arising from friction 

 of the machine, want of perfect accuracy in its measures, resistance of the air, 

 and imperfections in the observations themselves, which must not only be 

 allowed for in this, but the rest ; but as the impelling power is acting here on a 

 lever of but half the length, and consequently but half the intensity, when re- 

 ferred to the bodies to be moved, it takes just double the time to generate the 

 same velocity. 



.Deduction. — Hence it appears, that the same mechanic power is capable of 

 producing the same velocity in a given body, whether it is applied so as to pro- 

 duce it in a greater or a less time ; but that the time taken to produce a given 

 velocity, by a uniformly continued action, is in a simple inverse proportion of 

 the intensity of the impulsive power. 



3dly. The 3d experiment being made with 2-i- turns of the less barrel, the 

 same weight in the scale of 8 ounces descending only one quarter part of the 

 former perpendicular, the mechanic power employed will be only one quarter 

 part of the former, viz. 50-l ; but as only one quarter part of the mechanic 

 power produces half of the former velocity in the heavy bodies ; that is, they 

 make 20 revolutions in 58"i ; that is, nearly 10 revolutions in ig" ; we may 

 conclude, in this instance, that the mechanic power, employed in producing 

 motion, is as the square of the velocity produced in the same body ;- and that the 

 velocity produced is as the time that an impelling power, of the same intensity, 

 continues to act on it, as appears by the near agreement of numbers 2 and 3, 

 column dth. — 4thly. In the 4th experiment, the apparatus is the same as the 

 first, only here tlie weight in the scale is 32 ounces ; that is, the impelling 

 power is the quadruple of the 1st, and here a double velocity is given to the 

 bodies; for they make 20 revolutions in 14% which is a small matter less than 



