140 ON THE INTERACTION OF NATURAL FORCES. 



much about them. Bewildered intellects, however, proclaimed 

 often enough that they had discovered the grand secret; and as 

 the incorrectness of their proceedings was always speedily mani- 

 fest, the matter fell into bad repute, and the opinion strength- 

 ened itself more and more that the problem was not capable of 

 solution; one difficulty after another was brought under the 

 dominion of mathematical mechanics, and finally a point was 

 reached where it could be proved that at least by the use of 

 pure mechanical forces no perpetual motion could be generated. 



We have here arrived at the idea of the driving force or 

 power of a machine, and shall have much to do with it in future. 

 I must therefore give an explanation of it. The idea of work 

 is evidently transferred to machines by comparing their per- 

 formances with those of men and animals, to replace which 

 they were applied. We still reckon the work of steam-engines 

 according to horse-power. The value of manual labour is de- 

 termined partly by the force which is expended in it (a strong 

 labourer is valued more highly than a weak one), partly, 

 however, by the skill which is brought into action. Skilled 

 workmen are not to be had in any quantity at a moment's 

 notice ; they must have both talent and instruction, their edu- 

 cation requires both time and trouble. A machine, on the 

 contrary, which executes work skilfully, can always be multi- 

 plied to any extent ; hence its skill has not the high value of 

 human skill in domains where the latter cannot be supplied by 

 machines. Thus the idea of the quantity of work in the case 

 of machines has been limited to the consideration of the expen- 

 diture of force ; this was the more important, as indeed most 

 machines are constructed for the express purpose of exceeding, 

 by the magnitude of their effects, the powers of men and animals. 

 Hence, in a mechanical sense, the idea of work has become 

 identical with that of the expenditure of force, and in this way 

 I will apply it in the following pages. 



How, then, can we measure this expenditure, and compare 

 it in the case of different machines 1 



I must here conduct you a portion of the way as short a 

 portion as possible over the uninviting field of mathematico- 



