The chief cause of all this trouble is that the mechanisms are not seen, or not recognised, because their proper nature, the kinematic linkwork with its laws, has not been present in the thoughts of the mechanician. The acquaintance with this would, in nine cases out of ten, have shown him any near-lying result immediately, and would have greatly shortened the way to results further off. For the scientific theory of mechanisms, if it give a complete mastery over analysis, sweeps entirely away a great portion of the difficulties, and entirely alters the nature of those which remain. While the empirical method is only a groping in the dark in the hope that by good luck we may lay hold of the solution, we come here to the application of an inductive method, based upon a well-understood analysis. The difficulties now consist only in the increased demands upon the capacity for induction. In this itself, however, Kinematics follows its own strict laws, like all other sciences. There will be further frequent opportunity for showing how great the difference is between this method and the old one, at this point I can only place it before the reader in general propositions.
We see now the Machine-problem theoretically solved, or in other words, we have the general features of the method of solution sketched in an abstract form before us; these point out the direction in which we must work. The general propositions laid down as to pairs of elements, chains and mechanisms, are, as it were, only the titles of volumes as yet unopened, the contents of which we must now commence to study page by page; for it is necessary, in order that our solution of the problem may be brought down from general first principles to their detailed applications, that the latter should be carefully examined. This study we shall begin in the following section.
It can be readily understood that such an investigation is neither simple nor easy, to me at least it does not appear possible to pass quickly over such wide-reaching questions. Whoever attentively examines the nature of the machine, discovers in it so many phenomena having mutual relations difficult to understand that he cannot penetrate to the deep under-lying laws which connect them, and he comprehends how it has often taken the whole power of single men to carry forward even one step some of the problems which present themselves. When we
