276 CLASSICS OF MODERN SCIENCE 

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

 incorrectness of their proceedings was always speedily manifest, the 

 matter fell into bad repute, and the opinion strengthened itself more 

 and more that the problem was not capable of solution ; one difficulty 

 after another was brought under the dominion of mathematical me- 

 chanics, 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, there- 

 fore, give an explanation of it. The idea of work is evidently trans- 

 ferred to machines by comparing their arrangements 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 labor is determined partly by the force which is expended in it 

 (a strong laborer is valued more highly than a weak one) , partly, how- 

 ever, by the skill which is brought into action. A machine, on the con- 

 trary, which executes work skilfully, can always be multiplied 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 expenditure of force; this was the more impor- 

 tant, 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 is become 

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

 apply it. 



How, then, can we measure this expenditure, and compare it in the 

 case of different machines ? 



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

 possible — over the uninviting field of mathematico-mechanical ideas, in 

 order to bring you to a point of view from which a more rewarding 

 prospect will open. And though the example which I shall here 

 choose, namely, that of a water-mill with iron hammer, appears to be 

 tolerably romantic, still, alas, I must leave the dark forest valley, the 

 spark-emitting anvil, and the black Cyclops wholly out of sight, and 

 beg a moment's attention to the less poetic side of the question, namely, 

 the machinery. This is driven by a water-wheel, which in its turn is 



