concerning the Actions of Machines. 75 



phoronomic properties of machines is this ; that the change in 

 the entire quantity of motion is proportional to the difference 

 between the separate amounts of the accelerating and of the re- 

 tarding forces ; the quantity of motion being estimated by com- 

 bining each moving mass with the second power of the number 

 which represents its velocity. Now, I have already said, that, 

 whatever be the nature of a machine for communicating force, 

 the amount of force delivered during a minute instant of time 

 at the one end, is exactly equal (throwing out of view the fric- 

 tion and the weights of its parts) to that communicated during 

 the same instant to the other end ; so that the same change is 

 produced in the entire quantity of motion, whether the force be 

 applied directly to the moving mass, or whether it act upon it 

 through the intervention of machinery. This most important 

 principle I shall endeavour to illustrate by example. 



Borrowing my illustration from the steam-engine, I shall 

 suppose one in which the piston acts directly upon the fly- 

 wheel, by means, say, of a double rack working alternately on 

 each side of a toothed wheel. Here it will not be denied that 

 the accession to the quantity of motion in the machine during 

 a half-stroke will be exactly what is due to the agency of the 

 pressure of the steam upon the piston through the whole length 

 of the cylinder, less, of course, by all the amount of all the re- 

 tarding forces during the same period. Contrast this with 

 what happens in the common steam-engine. Let the connect- 

 ing rod be so nearly in a line with the crank, that a pressure of 

 one hundred pounds on the piston exerts only a pressure of 

 one pound in the direction df rotation ; then does it follow, from 

 the principle of virtual velocities, that if the piston advance 

 minutely in the cylinder, the extremity of the crank will ad- 

 vance one hundred times as far along its path. The quantity 

 of motion generated in the machine then will be what is due to 

 a pressure of one pound acting through one hundred times the 

 advance of the piston, or, what is the same thing, to the pres- 

 sure of one hundred pounds acting through that advance itself. 

 The same thing is true for every other minute motion of the 

 piston, and, therefore, the whole amount of motion communica- 

 ted to the machine through the crank is exactly equal to that 

 communicated to it by means of the double rack and toothed 

 wheel, or by means of any other contrivance whatever. 



