371 
Steam Engine, 
space of a minute. So that 50 x 32-J- x 112=216160, is 
the proper representative of the power expended, as well 
as of the work done. Were the rope to be cut and the 
weight suffered to fall for a minute, the same number would 
likewise denote the labour of the horse in restoring it to 
its original place, provided that could be accomplished in 
an equal space of time, without the horse changing his 
situationo 
It may not, perhaps, be entirely useless to state this 
matter rather more universally. To this end, let Mre» 
present any mass or body, feet, the velocity com- 
municated to a body falling freely in the first second of 
time, and t an indefinitely small portion of any time what- 
ever t. Then will g t be the velocity generated in thq^ 
instant t\ and M ^ the corresponding quantity of mo- 
tion ; this, therefore, measures the effort which must be 
exerted at each instant to sustain the weight, whether that 
effort be applied immediately, or through the intervention 
of a single fixed pulley. Hence it follows, that daring the 
whole time tj the force will have consumed a quantity of 
motion equal t 0 5 M^^*=M^^: that is to say, if t de- 
note the time at the end of which the agent is no longer 
able to sustain the mass M, we may regard M ^ ^ as 
being an adequate measure of the force Q of that agent. 
If the agent not only prevent the mass from falling, but 
actually raise it with a given uniform velocity V during 
the whole time then we must add the quantity of mo- 
tion MV to the former, which gives Q=MV x M ^ M 
{V x^/.) And lastly, if the agent possess inertia, its 
mass must also be considered. Thus, in the case of a 
horse whose mass is H, moving along with the veiocit} 
V during the time and raising the mass M, we shall 
have Q=(M x H) V x M ^ And from similar princi- 
ples formulas may be investigated to represent the pov/cr 
of a first mover in more complicated cases 
