24. 



272 Dynamics. 



successively to the moveable body, according to the directions 

 of the plane, in the time / ; thus the power will be required to 

 have a quantity of motion equal to 



m v + m g t sin i ; 



and if the friction be the -- part of the weight, it will be neces- 

 sary to employ beside a quantity of motion equal to 



a 

 mv -f- m g t sin i -f m g t. 



Having, therefore, determined by experiment one value of 



a 



mv -{- mg t sin i -\ m g , 



it will be necessary when we wish to determine whether the 

 same power be capable of moving a given mass m, with a known 

 velocity t?, during a known time /, upon a plane whose inclina- 

 tion is i, and upon which the friction is a known part of the 

 weight ; it will be necessary, I say, to determine whether the 

 value which 



a 

 m v + m g t sjn ^ -j mg , 



will then have, is less than that in the experiment, or at most 

 only equal to it; in either case the thing will be possible. 



If the time /, during which the machine is to be in motion, be 

 not given ; still if we know the space which the power or the 

 weight must x describe with the velocity v ; then, as we suppose 

 that the motion is uniform, if we call s the space which the weight 



is to pass through, we should put instead of t its value -. 



Such is in substance, the method which is to be pursued in 

 estimating forces applied to machines. Each machine requires 

 particular considerations as to the nature of the power and the 

 manner in which it is applied to this machine. But by going 

 back to the quantity of motion to be expended by the agent, we 

 may always determine whether he be capable of a proposed 



