MECHANICS. 



The process by which a machine is thus brought to 

 its permanent state of working, is most rapid in the 

 beginning, and becomes slower as it advances. In- 

 deed, if the laws of physical action admitted of 

 mathematical exactness, or rather, if our senses 

 enabled us to trace their progress with perfect ac- 

 curacy, it would be found that a state of uni- 

 form motion is never fully acquired by any ma- 

 chine, and that it cannot be acquired in less than 

 an infinite time. The curve of which the abscis- 

 sae represent the time, and the ordinates the velo- 

 city of the machine, can never pass into a straight 

 line ; but it may have, for an assymptote, a 

 straight line parallel to its axis, to which it may 

 soon approach so near that they can no longer be 

 olistinuished. 





On the motion of machines, see EULEE, de Machinis in 

 genere, Nov. Com. Petrop. torn. in. (1750, 1751), 

 p. 254., &c. Also Principia Theoria Machinarum, 

 by the same author, Nov. Com. Petrop. torn. vnr. 

 (1760, 1761), p. 230, &c. 



190. When a machine attains its state of uni- 

 form motion, the momentum of the power is equal 

 to that of the resistance, and is the same that 

 would be in equilibria with the resistance, if there 

 were no motion at all. 



If it is by a stream of water that the machine is dri- 



ven, the stream is, by the supposition, at first 



much more than able to overcome the resistance, 



and the machine accelerates till the relative veloci- 



3 ty 



