system, so that his classification does not carry conviction with it. He wishes to adhere consistently to his fundamental principle of relative motions, and so finds it necessary to treat together very various kinds of mechanisms; and as a single mechanism frequently contains in itself several kinds of relative motions, he is compelled repeatedly to enter upon repetitions of an extended kind. Other objections might be raised against the modified classifications of Laboulaye, Girault, Belanger, Haton and the others, generally as well as individually, for no true science can be moulded at will in six or eight different ways.
The real cause of the insufficiency of the system is not, however, the classification itself; it must be looked for deeper. It lies, as I have already pointed out, in the circumstance that the investigations have never been carried back far enough,—back to the rise of the ideas; that classification has been attempted without any real comprehension being obtained of the objects to be classified. The formation of a science cannot be entered upon in medias res; it requires that we should start, as in mathematics, from the very simplest elements, the axiomatic beginnings. Without the determination of these the goal can never be reached. A single trial of the method commonly employed shows this very clearly.
In the old classification a commencement was made very commonly with the changing of one rectilinear motion into another; but no one asked whence the first rectilinear motion came, why it existed, how it had been created. To take a special case, Hâchette and Lanz choose for their first mechanism the so-called "fixed pulley." In this case it is the rectilinear motion of the cord as it runs off the pulley which is changed into another such motion in the part of the cord running on in the opposite direction. Why, however, the first motion is rectilinear we do not understand. Indeed it is not necessarily rectilinear, for the cord running off may be pulled to one or the other side, if it only be kept stretched, without in any way altering the mechanism. Then also the motion of the cord originates in the circular motion of the points of the pulley or drum; only after this motion do we have that of the cord itself. Thus the very first problem takes us beyond the limits of the class. The same indeterminateness which has been pointed out in the motion of the one cord belongs also to the other. We see therefore that, even in the very first example,
