(2 Mr Sang on some prevailing' misconceptions 



rous, are summed up in one law, called the principle of virtual 

 'velocities. My first object will be to exhibit this principle in 

 a clear light ; not, indeed, as I would do in a scientific treatise 

 on the subject, but in such a manner as appears to me to be 

 best fitted for removing those prejudices, the existence of which 

 has occasioned this paper. 



When two weights balance each other by means of the wheel 

 and axle, it is well known that they are to each other inversely as 

 the diameters ; but if the machine be turned a little round, the dis- 

 tances through which the weights move are directly as the same 

 diameters, — so that, if each weight be combined with the distance 

 through which it moves, the two results are exactly equal to each 

 other. The descent of one pound through ten inches would, for 

 example, be accompanied by an ascent of ten pounds through one 

 inch, and thus whatever is gained or lost in intensity of pres- 

 sure, as much is lost or gained in distance. It will be readily 

 seen that the same thing is true of the straight lever, and of 

 those combinations of pulleys which have their strings pa- 

 rallel : but in the case of the inclined plane, of the bent-lever, 

 and, in general, of all machines in which the relations of the 

 pressures are altered by a change in the position of the instru- 

 ment, the application of the same rule is not so easy ; and the 

 slight difficulty that attends it has elicited the assertion, that 

 the principle of virtual velocities is there at fault. 



The relative motions of the different parts of a machine can 

 easily be deduced from its geometric properties. The princi- 

 ple of virtual velocities enables us, from these motions, to com- 

 pute the forces, and thus connects the geometric with the me- 

 chanical properties of machinery. This principle, one of the 

 most beautiful and most pervading in nature, may be thus ex- 

 pressed : — 



If the position of any machine be slightly disturbed, and if 

 each pressure which has yielded be combined with the distance 

 through which it has yielded, and each pressure which has ad- 

 vanced with the distance through which it has advanced, the 

 sum of the one set of results will be exactly equal to the sum 

 of the other set. 



Now, in the case of the inclined plane, says the objector to 

 the reality of this law, the weight raised and the weight which 



