In its complete form the machine consists of one or more mecha- nisms, which can, in the way we have already pointed out, be separated into kinematic chains, and these again into pairs of elements. This separation is the analysis of the machine, the investigation of its kinematic contents, arranged in mechanisms, kinematic chains, and pairs of elements. The reverse of this operation is synthesis, the placing together of the kinematic elements, chains and mechanisms, from which a machine can be built up so as to fulfil its required function.
There is a large region among the exact sciences in which analysis and synthesis can exist without each other, where at least important results can be obtained by the use merely of de- duction from fixed general laws. In our case, however, the two intellectual operations cannot go on separately, because the machine never, or scarcely ever, comes to us as a ready-made pro- duction of nature, but as something which we ourselves have made, because, that is, it has been created by us essentially by a synthetic method. The induction by which we have arrived at it has often been very indistinct, and hence deduction and analysis are or must become means enabling us to reach it by an induc- tion or synthesis which is conscious and definite.
The synthesis is here, as in most cases, by far the more difficult of the two processes. On this account it has scarcely ever been un- dertaken other than empirically. Its province is simply that which is assigned, in common language, to invention, and about which we spoke at length in the Introduction. Essentially, invention is nothing other than induction, a continual setting down and there- after analysing of the possible solutions which present themselves by analogy. The process continues until some more or less distinct goal is reached, a goal which generally seems itself to be indefinite on account of the haziness which envelopes the whole procedure. In this way a result lying close to the starting point is too often reached only after traversing a whole labyrinth of solutions each one depending upon the one before it, and each thrown away as soon as it has been found. I do not doubt that many of my readers, who have spent hours and days poring over mechanical problems, have found, after many laborious trials, that they have been travelling through a circle of experiment only to reach some well known, but unfortunately not so well recognised, problem.
