ideal method is not that it employs the inductive instead of the deductive method; that would indeed be no advantage, but it might still be defensible. No, it has been entirely unmethodical. It has chosen no fixed method of investigation, or rather, it has not found any in spite of zealous search; indeed it has so often cried Eureka that it now rests quietly in the impression that some such fixed standpoint has really been found.
In the development of every exact science, its substance having grown sufficiently to make generalisation possible, there is a time when a series of changes brings it into clearness. This time has most certainly arrived for the science of Kinematics. The number of mechanisms has grown almost out of measure, and the number of ways in which they are applied no less. It has become absolutely impossible still to hold the thread which can lead in any way through this labyrinth by the existing methods.
It cannot be denied that the difficulties in the way of remodelling the science are great. We often do not know ourselves how closely wedged-in our ideas are by the boundaries which education and study have drawn around us. If new ideas therefore are to be substituted for the common ones, it can only be by a wrench sufficiently powerful to overcome the cohesion of established notions and prejudices. There are the traditional courses of instruction in the schools,—the widely extended and important technical literature,—the force of habit, acquired with difficulty, and on that very account firmly rooted; there is also the real difficulty that the new study requires to be grasped as a whole, and not taken up partially and occasionally,—all these pile up mighty hindrances. I cannot therefore shorten the way, although the truths to which it leads are of great simplicity. The careful removal of preconceived ideas, the slow seeking of the right path among those inviting us, prevents rapid motion. The following chapters are therefore intended not so much to add to the positive knowledge of the mechanician as to increase his understanding of what he already knows, so that it may become more thoroughly his own property. For, to conclude in the words of Göthe, "What is not understood is not possessed."
Note.—Had Prof. Reuleaux been acquainted with Prof. Rankine's "Machinery and Millwork," the first edition of which was published in 1869, he would no doubt have mentioned it here. Some 300 pages
