Maximum Effect of Machines. 28 1 



Resolving this after the manner of an equation of the second de- 

 gree, we obtain 



= D 



P ( + *) 

 When r = 0, we have 



j> (n + i) 



This case takes place when the resistance to be overcome exerts 

 a contrary strain on the machine, while it consists merely in the 

 inertia of the impelled body ; as in driving a millstone, a fly, or 

 in pushing a body along a horizontal plane. 



When/ = 0, 



. _ __ mr 



This case takes place when the friction is so small that it may 

 be disregarded, which often happens in good wheel work, where 

 the surfaces that touch one another are very small. 



When r = 0, and/ = 0, we have 



~^(n + ) ._ D I m 

 (n+i}* \ n + i ' 



_ D - D 



This case takes place when the circumstances of the two preced- 

 ing cases are combined. 



When n = 0, we have 



+P 2 i m (r + / ) 



pi 



This case takes place in the grinding of corn, the sawing of 

 wood, the boring of wooden or iron cylinders, &c., where the 

 quantity of motion communicated to the flour, the saw dust, or 

 the iron filings, is too trifling to be taken into the account. 

 Meek. 36 



