On Machines in General. So.'^ 



for it is in general this quantity which we must oeconomize 

 as much as possible-, in order to draw all the effect we can 

 from one agent. 



If it be required to raise a weight, water for example, to 

 a given heisht ; yoa will be able to raise more in a given 

 time, not from having exiiaiisted a greater quantity of power, 

 but in proportion as you have exercised a greater momentum 

 of activity (XLIV). 



If it be required to turn a mill, either by water, or wind, 

 or animals, it is not necessary that the shock of the water, 

 the wind, or the effort of the animal be greater ; but these 

 agents should be made to consume the greatest momentum 

 of activity possible. 



If we wish to make a vacuum in the air in any way what- 

 ever, we must, in order to succeed, consume a momentum of 

 activity as great as that which would be necessary for raising 

 to the height of 30 feet a volume of water equal to the 

 vacuum which we wish to produce. 



If it be a vacuum in an indefinite mass of water like the 

 sea, we must consume the same momentum of activity as if 

 the sea were a vacuum ; as if the vacuum which we wish to 

 make were a volume of sea water, arid as if we must raise 

 this volume to the height of the level of the sea. 



If it be required to produce a vacuum in a vessel of a 

 given figure, it is evident that we cannot succeed without 

 causing to ascend the centre of gravity of the total mass of 

 the fluid in a quantity determined by the figure of the vessel ; 

 we must therefore consqme a momentum of activity equal to 

 that which would be necessary to raise all the water in the 

 vessel in a quantity equal to that from which the centre of 

 gravity of the fluid must ascend. 



In a machine at rest, where there is no other f)rce to 

 overcome except the vis inerlice of the bodies, if wg. wish to 

 produce any movement by insensible degrees, ihs momentum 

 of activity which wc have to coasurae will be equal to half 

 the amount of the active forces we wish to produce ; and if 

 it be merely required to change the movement it has already, 

 the momentum of activity to be produced will only be the 



quantity 



