80 ' PHILOSOPHICAL TRANSACTIONS. [aNNO 1776. 



half the time taken up in making 20 revolutions in the 1st experiment. It also 

 appears, that the velocity acquired is simply as the impelling power compounded 

 with the time of its action ; for a quadruple impulsion acting for 7% instead of 

 14% generates a double velocity, while the mechanic power employed to gene- 

 rate it is quadruple, for 3'2 X 25-i- =; 808. And here the mechanic power em- 

 ployed being 4 times greater than the first, it holds here also, that the mechanic 

 power, to be necessarily employed, is as the square of the velocity to be gene- 

 rated ; that is, in the same proportion as turned out in the 3d experiment, 

 where the mechanic power employed was only a 4th part ol the first. — 5thly. 

 The 5th and 6th experiments were made with a mechanic power 4 times greater 

 than those employed in numbers 2 and 3 respectively ; and since the same de- 

 ductions result from these as from numbers 2 and 3, they are additional con- 

 firmations of the conclusions drawn from them and from the last article. — 6thly. 

 In the 7th experiment, the disposition of the apparatus is tiie same as number 

 1, only here the bodies are placed on the arms at the half length ; whence it ap- 

 pears, that the same mechanic power still produces the same velocity in the 

 same bodies; for though 20 revolutions were performed in 14f^ (see column 7,) 

 which is nearly half the time that 20 revolutions were performed in the first ex- 

 periment ; yet, since the circles in which the bodies revolved in the 7th are only 

 of half the circumference as those of number 1 , it is obvious, that the absolute 

 velocity acquired by the moving bodies in the two cases is equal. But, by column 

 6th, the time in which it was generated is only half; yet this will coincide with 

 the former conclusions, if the intensity of the impelling power is compounded 

 with it ; for though the barrel was the same with the same number of turns as 

 in number ], and therefore the lever the same, by which the impelling power 

 acted, yet as the bodies, on which this lever was to act, were placed on a lever 

 of only half the length from the centre, the impelling power, acting by the 1st 

 lever, would act on the 2d with double the intensity, according to the known 

 laws of mechanics ; that is, it would require a double weight opposing the 

 bodies, to prevent their moving, in order to balance it. An impulsive power 

 therefore of double the intensity, acting for half the time, produces the same 

 effect in generating motion, as an impulsive power of half the intensity, acting 

 for the whole time. — 7thly. The 8th and gth experiments afford the same de- 

 ductions and confirmations relative to the 7th experiment, that the 5th and dth 

 do respecting the 4th, and that the 2d and 3d do respecting the 1st; and from 

 the near agreement of the whole, when the necessary allowances before- 

 mentioned are made, together with some small inequality arising from the mecha- 

 nical power lost by the difference of the motion given by gravity to the weight 

 in the scale : I say, from these agreements, under the very different mechanical 

 powers applied, which were varied in the proportion of 1 to l6, we may safely 



