entirely "practical," and although they may be able for a while longer to get on without them. The theoretical questions, however, which are here to be treated, are of so deep-reaching a nature that I entertain the hope that those who are practically, as well as those who are theoretically concerned with the subject, may obtain help from the new method of treating them. I am thus obliged to lay before both equally the grounds upon which I have given up the customary ideas upon the subject and put others in their place.
In attempting to place the theory of the constitution of the machine upon a new basis I do so with the conviction that my trouble will be repaid only if it prove of some actual advantage in the right understanding of the machine. I venture to promise such a result with confidence. He who best understands the machine, who is best acquainted with its essential nature, will be able to accomplish the most by its means. It is not a matter of merely setting forth in a new form and order what is already well known, or of substituting a new classification and nomenclature for the old. Possibly with such improvements the subject might be more conveniently and elegantly taught, but for practical purposes the old forms might be used for a long time to come. On the contrary, if the new theory is to lay claim to general interest, it must be capable of producing something new; it must make problems solvable which before could not be solved in any systematic way. This may certainly be said to be the case if it succeeds in making Machine-Kinematics, down to its simplest problems, truly scientific.
This subject has indeed, in a certain sense, been scientifically treated hitherto, in so far, namely, as particular portions of it admit of mathematical treatment. But this concerns a part only of the subject, and not that part which is peculiarly its own; so far as the treatment has been scientific, too, it has been mathematical or mechanical, and not kinematic. This last in its essence, in the ideas belonging specially to it, has been left indistinct, or made clear accidentally at a few single points only. It is like a tree which has grown up in a dark tower, and thrown out its branches wherever it could find an outlet; these, being able to enjoy the air and light, are green and blooming, but the parent stem can only show a few stunted twigs and isolated leaf-buds.
