Maximum Effect of Machines. 



287 



which corresponds in the table to 1,3928, the value of r when 

 />=!.-, But, in the present case, p = 8, consequently 



1:8:: 1.3928 : 11.1424, 



the value of r when p = 8. 

 t 



399. The subject of the maximum effect of machines may 

 be considered in a very simple point of view, if we suppose, what 

 is by no means improbable, that the moving power in machinery 

 observes the same law that has been found to exist with regard 

 to animal force, and also with regard to the force of fluids in 



motion. Upon this hypothesis, we shall have r = p fl -- ) , 



and the effect of the machine will be r -o' = p v' fl -- j , 



r d 4 



which will be a maximum when = - , and when v' = \ v. 



D 9 r 



In these formulas, p is the load that is just sufficient to bring the 

 machine to rest, or prevent it from moving, v is the greatest ve- 

 locity of the power when no work is done, and t/ the velocity of 

 the impelled point of the machine. The above equation, both 

 members being multiplied by 9, is equivalent to the proportion, 

 D is to #, or the velocity of the impelled point is to the velocity 

 of the working point, when the effect is a maximum, as 9 r to 4 p. 



394. 



Table of the Strength of Men, according to different Authors. 





