42 HISTORY OF MECHANICS. 



the weight raised moves as much slower than the 

 power, as it is larger than the power. This was 

 explained with great clearness by Galileo, in the 

 preface to his Treatise on Mechanical Science, pub- 

 lished in 1592. 



The motions, however, which we here suppose 

 the parts of the machine to have, are not motions 

 which the forces produce; for at present we are 

 dealing with the case in which the forces balance 

 each other, and therefore produce no motion. But 

 we ascribe to the Weights and Powers hypothetical 

 motions, arising from some other cause ; and then, 

 by the construction of the machine, the velocities of 

 the Weights and Powers must have certain definite 

 ratios. These velocities, being thus hypothetically 

 supposed and not actually produced, are called 

 Virtual Velocities. And the general law of equi- 

 librium is, that in any machine, the Weights which 

 balance each other, are reciprocally to each other 

 as their Virtual Velocities. This is called the Prin- 

 ciple of Virtual Velocities. 



This Principle (which was afterwards still fur- 

 ther generalized) is, by some of the admirers of 

 Galileo, dwelt upon as one of his great services to 

 mechanics. But if we examine it more nearly, we 

 shall see that it has not much importance in our 

 history. It is a generalization, but a generalization 

 established rather by enumeration of cases, than by 

 any induction proceeding upon one distinct Idea, 

 like those generalizations of Facts by which Laws 



