recognized and directly aimed at. As we have before stated, it is by the science of Kinematics that the laws governing the means for attaining this object are determined.
We have recognized and examined in certain pairs of kinematic elements the property of force-closure, by which a certain amount of kosmic freedom is left in the machinal system, and seen that it has been for thousands of years the aim of invention to limit or destroy this freedom, and that many new tasks have been made possible only by its complete restriction. We can now see in this force-closure also the borderland between the kosmic and the ideal machinal systems. In force-closure we have that distinct although not sharply-defined boundary-line,—discussed already in speaking of the limits of the machine-problem (§ 1),—which divides the two systems. In this line of contest between pair-closure and force-closure I believe that the future historian of machine development will find the thread to guide him through the complex but not altogether planless course of his subject. It will, besides, be of the greatest value in the further designing of machinery if the problem be entered upon from the beginning with the distinct knowledge that in the substitution of kinematic- for force-closure there lies the very central idea of progress, and that the more rigidly this idea is carried out the sooner will the desired end be reached. To impart a clear and distinct understanding of this process should be, in my opinion, the function of polytechnic school instruction. We have here undoubtedly an idea before us, put in a separate and distinct form, which is of the greatest and most urgent importance to the inventor, although often not understood by him. It is therefore in every way right and necessary that the study of it should be closely entered into.
By this means another important end may also be gained. It will partly strengthen and partly create a sense of the fundamental connection between the special work of the machine-designer and the whole region of practical mechanics, and hence with the whole domain of human activity. Hitherto the tendency has been to weaken this sense, until now in some places it has almost disappeared. The popular cry of "division of labour" has, entirely in opposition to its own principles, contributed to this.
This principle has been applied,—wrongly,—beyond the limits
