MECHANICS. 117 



If, however, the moving power be one that acts 

 always with the' same force, and if the resistance 

 is also uniform, the machine will be continually 

 accelerated. But as a motion continually accelera- 

 ted is incompatible with many of the purposes of 

 machinery, it is either contrived, that, by an increa- 

 sed resistance, the motion shall become uniform, or 

 that the moving power shall at intervals cease alto- 

 gether, or become a retarding force, so that the 

 velocity of the machine, though continually chan- 

 ging, may be confined within certain limits. 



M. D'ALEMBERT'S principle ( 120.) is very useful for 

 determining the action of machines working with a 

 variable velocity. One of the simplest examples of 

 this is contained in the investigation of the follow- 

 ing theorem. 



186. Let A and B be two given weights, appli- 

 ed to the ends of the arms of a lever, of which the 

 lengths are a and b, and let A x a be greater than 

 B x b, so that A may preponderate ; the space over 

 which B will be raised in one second, (g being the 

 velocity which a heavy body acquires in the first 



,1 fi i . (Aa ~Bb)b , 



second of its descent), is ^a 2 4-B6 2 Xf g. 



Call x the velocity of B, then -L. will be the velocity 



of A. If the bodies were free to fall by their own 

 gravity, the velocity of each would be g ; therefore 



the 



