t, therefore, realise this truth to the reader by a
rapid review of the facts.

Passing over the most abstract science, Logic, on the due guidance by
which, however, the large producer or distributor depends, knowingly or
unknowingly, for success in his business-forecasts, we come first to
Mathematics. Of this, the most general division, dealing with number,
guides all industrial activities; be they those by which processes are
adjusted, or estimates framed, or commodities bought and sold, or
accounts kept. No one needs to have the value of this division of
abstract science insisted upon.

For the higher arts of construction, some acquaintance with the more
special division of Mathematics is indispensable. The village carpenter,
who lays out his work by empirical rules, equally with the builder of a
Britannia Bridge, makes hourly reference to the laws of space-relations.
The surveyor who measures the land purchased; the architect in designing
a mansion to be built on it; the builder when laying out the
foundations; the masons in cutting the stones; and the various artizans
who put up the fittings; are all guided by geometrical truths.
Railway-making is regulated from beginning to end by geometry: alike in
the preparation of plans and sections; in staking out the line; in the
mensuration of cuttings and embankments; in the designing and building
of bridges, culverts, viaducts, tunnels, stations. Similarly with the
harbours, docks, piers, and various engineering and architectural works
that fringe the coasts and overspread the country, as well as the mines
that run underneath it. And now-a-days, even the farmer, for the correct
laying-out of his drains, has recourse to the level--that is, to
geometrical principles.

Turn next to the Abstract-Concrete sciences. On the application of the
simplest of these, Mechanics, depends the success of modern
manufactures. The properties of the lever, the wheel-and-axle, etc., are
recognised in every machine, and to machinery in these times we owe all
production. Trace the history of the breakfast-roll. The soil out of
which it came was drained with machine-made tiles; the surface was
turned over by a machine; the wheat was reaped, thrashed, and winnowed
by machines; by machinery it was ground and bolted; and had the flour
been sent to Gosport, it might have been made into biscuits by a
machine. Look round the room in which you sit. If modern, probably the
bricks in its walls were ma