248 KINEMATICS OF MACHINERY.
appears likely to become still greater in the future with the increase in the variety of chain-forms employed. It has become, too, equally necessary to be able to survey the inner relationships of mechanisms as well as their differences. We are here led involuntarily to look for some means of facilitating the expression of both.
In similar circumstances Mathematics, and afterwards Chemistry, have taken to their aid special symbolic notations, which have now become so essential to both sciences that neither could proceed without them. Both adopted them so soon as the real nature of their fundamental operations had been determined. The ideas connected with our subject are now so distinctly and individually before us, their mutual relations can be so definitely determined, that their concise expression by means of simple signs becomes not only justifiable but practicable. We shall therefore use these important aids to the furthest extent possible in our work.
It is very easy to see what an immense advantage there is in the possibility of so expressing a complex idea that when it is employed along with another of the same kind they may both be expressed by a single sign. The continual returning upon already defined conditions becomes unnecessary, while the conciseness of the expression allows conclusions to be arrived at as to the mutual relations of the parts combined, which with the common method of expression can only be formed with great difficulty, and can scarcely be communicated at all. The reader need not fear that any continual alteration of his accustomed ideas will be demanded from him in making himself familiar with the system of contractions which we are about to describe. For a scientific symbolic notation is in essence nothing else than a systematised method of contraction, it is not a hieroglyphic system, mysterious to the uninitiated. Our examination of it here will not be simply parenthetical, but will give us opportunity for examining more closely the real nature of several important kinematic chains.
53. Former Attempts.
Attempts have not been wanting to express machine combinations in some concise form. Clockmakers, among others, and
