MECHANICS. 123 



And, again, if the machine is loaded very lightly, 

 it will give great velocity to the load, though, 

 from the smallness of its quantity, the effect will 

 still be inconsiderable. Between these two loads 

 there must be some intermediate one, that will 

 make the effect the greatest possible. 



If the moving power observe the same law that 

 has been already ascribed to animal force, viz. 



v\* 



P (1 1 , (which will be afterwards 



W 



shewn to be the law that regulates the force 

 of fluids in motion), the effect will be expressed 



by W v 9 or by P v (1 -- ) , which is a maxi- 



4P c 



mum when W = -g- , and when v = g . The re- 



a 



sistance should be ~ of that which the power, 

 y 



when fully exerted, is just able to balance, or of 

 the resistance that is sufficient to reduce the ma- 

 chine to rest ; and the velocity of the part of the 

 machine to which the power is applied, should be 

 one-third of thje greatest velocity of the power. 



193. If, therefore, the moving power in any 

 machine follow the law expressed by the equation 



yj-v 2 



W n P (1 - ) ; and if the load or resistance 

 c/ 



which is just able to keep the machine at rest, or to 



prevent 



