On Machines in GtveraL 297 



have supported the globe, it would have been his fixed 

 point: all his art would have consisted not in redonbling 

 his efforts to contend against the mass of the globe, but to 

 put in opposition two great forces, the 04ie active, and the 

 other passive, which he would have had at his disposal : if, 

 on the contrary, it had been requisite to produce an eflcctive 

 movement, in this case Archimedes woidd have been obliged 

 to draw it entirely from his own proj)cr person ; and yet it 

 would have been very small, even after several years : let us 

 not attribute therefore to active forces, what is owino- to the 

 resistance of obstacles only, and the effect will not appear 

 more disi.Toportioned to the cause in machines at rest thaa 

 in machines in motion. 



LVI. What is the true object therefore of machines in 

 motion ? We have already said, that it is to procure the 

 faculty of varying at pleasure the terms of the quantity O, 

 or the momentum of activity which sliould be exercised bv 

 the moving forces. li time be precious, if the effect must 

 be produced in a very short time, and if we have only a 

 power capable of very little velocity, but of a great effort, we 

 may find a machine capable of supplying the velocity neces- 

 sary for the force : if, on the contrary, we must raise a very 

 considerable weight, and we have but a weak power, al- 

 though capable of great velocity, wc may contrive a ma- 

 chine with which the agent will be in a condition to com- 

 pensate l?y its velocity the force of which it is deficient. 

 Lastly, if the power is neither capable of a oreat effort nor 

 of a great velocity, we may still, with a proper machine, 

 make it produce the effect desired, but then it will require 

 much time; and herein consists the well-known principle, 

 that in machines in movement, ue alicai/s lose in time or in 

 velocity uhut we gain in force. 



Machines are therefore very useful, not by augmentina; 

 the effect of which powers are naturally capable, but by 

 modifying this effect : it is true we shall never succeed by 

 means of them in diniinishing the expense or momentum oi 

 activity necessary for producing an effect proposed ; but they 

 will assist us in n}aking a proper division of this quantity 

 ior attaining the design in view ; it is by their assistance 



that 

 4 



