machines has very distinctly revealed itself. Even those, however, which are worthless practically have proved useful to kinematic science, and thus indirectly to practice also. For it is just the great number of the cases existing which has on the one hand so emphatically called for an examination of their general laws, and on the other hand furnished sufficient examples to render such an examination possible.
I believe that it is not too much to hope that, as the recognition of the principles here laid down, becomes more and more general, the aimless search for new solutions of an old problem may gradually cease, and at length disappear; and that our investigations may have materially assisted the scientific comprehension of the rotary steam-engine and pump. In the two preceding chapters, too, we have been able already to gain some insight into the direct application of a synthetic method to the production of new machines. The progress of the analysis furnished us several times with means for applying the converse process. The possibility of replacing "invention," in the old sense of the word, by a scientific method of development—alluded to in the Introduction—has therefore already proved itself to exist. We shall have to return to this part of our subject further on (Chap. XIII.).
