consider the spinning-machine, for example, which has been gradually developing for three generations into its present form, (one still capable of further improvement), notwithstanding that the best mechanics have worked at it; or look at the changes through which the sewing-machine has passed, and examine each step by step, we can form some conception of the difficulties which the theory has to overcome. In addition to this, the propositions to be developed are completely new. They therefore require that numerous details should be carefully entered into, of which some may appear to the engineer to be already well understood, although in reality the laws upon which they depend have not yet been investigated, and in the light of these they may be seen in many new aspects. It will therefore be some time before we arrive at such propositions as are adapted for direct application.
When, however, we have gone so far as to have demonstrated these existing laws and their mutual relations, we shall have reached the limits up to which theory can be our guide.
For the right application of these laws demands certain special qualities in the designer of a machine besides a mere knowledge of its theory, if his work is to be what is called " practical," by which is meant that the required object is to be fully and permanently attained, without too great an expen- diture of means. This art of making practical work can be but very partially communicated by teaching, it can only be made quite clear by example. The scientific abstraction only serves to show the possibility of the machine, it affords no means what- ever of judging between "practical" and "unpractical." This is often cited as an essential imperfection of theory, a notion which only arises from an obstinate ignoring of its real province. We have separated the department of practice from that of ab- stract theory in order to see more clearly the complicated course of our subject. Every time, however, that we have to choose between the useful and the useless, we are compelled to return from the abstract to the concrete. In the school, therefore, kine- matic science must frequently be connected with its practical applications it has not only to show what theoretical solution applies to problems already solved empirically, but in. most cases to construct the theory as well as to find it. It is remarkable that there is scarcely any kinematic problem, scarcely any turning,
