Measure of Forces applied to Machines. 265 



u La 



and hence we see that the distance of the centre of percussion 

 of a free body depends on the ratio of the velocity of rotation to 

 the velocity of the centre of gravity ; and particularly that it is 

 nothing when the velocity of rotation is nothing, as in fact it ought 

 to be. 



We may hence determine at what point to place an obstacle 

 in order to stop a free body which has a progressive and rotato- 

 ry motion at the same time ; namely, at the centre of percussion 

 of this body, or the point where it would give the strongest blow 

 or exert the greatest force. 



Method of estimating the Forces applied to Machines. 



385. Any force has for its measure, as we have already said, 

 the product of a determinate mass, into the velocity which the 

 force in question is capable of giving to this mass. It seems 

 proper, in this place, to add something by way of illustrating the 

 application of this principle to machines. 



When two weights act against each other by means of a sim- 

 ple fixed pulley, it is necessary in order to an equilibrium that 

 their masses should be equal ; and this equilibrium once estab- 

 lished, will always remain. 



But if instead of opposing a weight to a weight, we oppose 

 the force of an animal, as that of a man, for example, although 

 it be true that, in order to an equilibrium, this man has only to 

 exert an effort equal to the weight to be sustained, that is, equal 

 to the quantity of motion represented by the mass of this body 

 multiplied into the velocity which gravity communicates in an 

 instant ; it is, nevertheless, evident that if the man were capable 

 of but one such effort, the equilibrium would continue only for 

 an instant, because gravity renews each successive instant the 

 action which was destroyed in the preceding. 

 Mech. 34 



