If z is a function of y having a differential coefficient at a certain point, and y is a function of x having a differential coefficient at the corresponding point, then z is a function of x having a differential coefficient at that point, and this differential coefficient is given by the formula

This theorem, thought not always stated so carefully, will be found in all texts on the calculus; but, so far as I am aware, no English writer, not even the most exact, offers a valid proof.

Very few teachers ever have the chance of noting the advantage or disadvantage of a change, introduced into their methods of teaching, and of profiting by the same. I desire now to put on record the results of such a change and the method by which they were attained.

The number of systems of teaching dynamics is great, and still the results are deplorable as judged by the knowledge possessed by the average engineer some years after he leaves college. Teachers are either biassed in favour of the Gaussian system or the Perry system, or some other system of their own, and are loath to change because they can train their students to solve the necessary problems, and if a mistake is made by omitting g or some other quantity it is merely a mistake and costs nothing. It is not so with the poor student, however, when he is launched on the world without his teacher to help him.