266 Dynamics. 



It is not, therefore, by the mass only which the man supports, 

 that we are to estimate his strength ; but we must consider, also, 

 the number of times that he is able to exert an action equal to 

 that which gravity communicates every instant to the body. 

 Now if g represents the velocity which gravity is capable of 

 giving to a free body in a second of time ; and d t represents an 



267 - infinitely small portion of any time J, g d t will be the velocity 

 which gravity gives during the instant d , t being supposed to 

 be reckoned in seconds. Therefore, if m be the mass which it is 

 proposed to sustain, mgdt will be its weight, or the quantity of 



2 ' 2 ' motion which gravity gives it each instant d t ; it is accordingly 

 the effort also which must be exerted each instant by the force 

 which is to support m, either directly or by the aid of a pulley. 

 Therefore, during any time /, this force must expend a quan- 

 tity of motion equal to 



Pmgdt or mgt. 



Therefore, if t denotes the time at the end of which the agent is 

 no longer able to support the mass ra, m g t may be regarded as 

 the measure of his strength. We do not mean by this that he is 

 no longer capable of exerting any effort ; but his force having 

 become unequal to the effect to be produced, it is considered as 

 nothing with respect to this effect. Let us, for example, suppose 

 that in order to support a weight of 50 lb for an hour, it is pro- 

 posed to employ a force, which acting by equal and infinitely 

 small degrees, is known to produce in a mass of 20 lb , a velocity 

 of 50 feet in a second, at the instant when this force is exhausted. 

 It is manifest that this mass of 20 lb will have a quantity of motion 

 equal to 



20 lb X 50 or 1000. 



Let us see, then, if this quantity of motion be equal to what 

 the quantity m g t becomes, by putting 50 lb for m, an hour or 3600" 

 273. for J, and 32,2 feet for g. It appears to fall far short of it ; such a 

 force, therefore, would not support a weight of 50 lb during an 

 hour. If we wished to know during what time, or what number 

 of seconds, it would support it, we have only to suppose 



mgt = 1000; 



