268 Dynamics. 



m = 25 lb , g = 32,2 ft , and t = 8 h == 28800". 

 The substitutions being made, we have 



roz> -h mg*= 2 J 5 -I- 23184000 = 23184092. 



By means of this number, we can judge whether the strength of 

 a man be sufficient to produce a proposed effect. For instance, 

 if it be asked whether it be possible for a man, with the machine 

 above referred to, to raise a weight of 60 lb with a velocity of 10 

 feet in a second, during 6 hours, we shall perceive that it is not. 

 For we should have in this case 



ro = 60 lb ; v= 10; g = 32,2; f = 21600"; 

 which gives 



mv + mgt = 600 + 41731200 = 41731800; 



as this greatly exceeds 23184092, it follows that a single man is 

 unequal to such an effect. 



It may be remarked that in these two examples, the velocity 

 v with which the man is supposed to move the weight, is of very 

 little" consequence in estimating the force required; for in the 

 first example, the quantity of motion which answers to this veloc- 

 ity, is 3 J 5 ; and in the second, 600; quantities which are very 

 small compared with 23184092 and 41731800. Therefore, in 

 the second example, if we are unable to produce the desired 

 effect, it is not because-the velocity is greater than in the first 

 case, but chiefly because the mass and the time during which it is 

 to be moved, require of the agent too great a quantity of motion. 



While therefore the velocity required in the agent is small com- 

 pared withg /, that is, with the velocity which a heavy body falling 

 freely would acquire in the time during which the agent is sup- 

 posed to be employed, we may take simply for the measure of 

 the force in question, the quantity mgt] and we shall have 



mgt = 23184000. 



Thus, if the mass (the velocity with which it is to be moved be- 

 ing moderate) multiplied by the velocity which a heavy body 

 falling freely would acquire in the time during which the power 



