The table on the following page will then express the series of movements and their results.

If now only those divisions struck or pointed at by the clock A be attended to and written down, it will be found that they produce the series of the squares of the natural numbers.  Such a series could, of course, be carried by this mechanism only so far as the numbers which can be expressed by three figures; but this may be sufficient to give some idea of the construction—­and was, in fact, the point to which the first model of the calculating engine, now in progress, extended.

250.  We have seen, then, that the effect of the division of labour, both in mechanical and in mental operations, is, that it enables us to purchase and apply to each process precisely that quantity of skill and knowledge which is required for it:  we avoid employing any part of the time of a man who can get eight or ten shillings a day by his skill in tempering needles, in turning a wheel, which can be done for sixpence a day; and we equally avoid the loss arising from the employment of an accomplished mathematician in performing the lowest processes of arithmetic.

251.  The division of labour cannot be successfully practised unless there exists a great demand for its produce; and it requires a large capital to be employed in those arts in which it is used.  In watchmaking it has been carried, perhaps, to the greatest extent.  It was stated in evidence before a committee of the House of Commons, that there are a hundred and two distinct branches of this art, to each of which a boy may be put apprentice:  and that he only learns his master’s department, and is unable, after his apprenticeship has expired, without subsequent instruction, to work at any other branch.  The watch-finisher, whose business is to put together the scattered parts, is the only one, out of the hundred and two persons, who can work in any other department than his own.

252.  In one of the most difficult arts, that of mining, great improvements have resulted from the judicious distribution of the duties; and under the arrangments which have gradually been introduced, the whole system of the mine and its government is now placed under the control of the following officers.

1.  A manager, who has the general knowledge of all that is to be done, and who may be assisted by one or more skilful persons.

2.  Underground captains direct the proper mining operations, and govern the working miners.

3.  The purser and book-keeper manage the accounts.

4.  The engineer erects the engines, and superintends the men who work them.

5.  A chief pitman has charge of the pumps and the apparatus of the shafts.

6.  A surface-captain, with assistants, receives the ores raised, and directs the dressing department, the object of which is to render them marketable.

7.  The head carpenter superintends many constructions.