For, leaving out only some very small classes, what are all men employed in?  They are employed in the production, preparation, and distribution of commodities.  And on what does efficiency in the production, preparation, and distribution of commodities depend?  It depends on the use of methods fitted to the respective natures of these commodities; it depends on an adequate acquaintance with their physical, chemical, or vital properties, as the case may be; that is, it depends on Science.  This order of knowledge which is in great part ignored in our school-courses, is the order of knowledge underlying the right performance of those processes by which civilised life is made possible.  Undeniable as is this truth, there seems to be no living consciousness of it:  its very familiarity makes it unregarded.  To give due weight to our argument, we must, 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.