on whose survey the land is purchased; the architect in designing a mansion to be built on it; the builder in preparing his estimates; his foreman in laying out the foundations; the masons in cutting the stones; and the various artisans who put up the fittings; are all guided by geometrical truths. Railway-making is regulated from beginning to end by mathematics: alike in the preparation of plans and sections; in staking out the line; in the mensuration of cuttings and embankments; in the designing, estimating, and building of bridges, culverts, viaducts, tunnels, stations. And similarly with the harbors, docks, piers, and various engineering and architectural works that fringe the coasts and overspread the face of the country; as well as the mines that run underneath it. Out of geometry, too, as applied to astronomy, the art of navigation has grown; and so, by this science, has been made possible that enormous foreign commerce which supports a large part of our population, and supplies us with many necessaries and most of our luxuries. 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. When from those divisions of mathematics which deal with space, and number, some small smattering of which is given in schools, we turn to that other division which deals with force, of which even a smattering is scarcely ever given, we meet with another large class of activities which

this science presides over. On the application of rational mechanics depends the success of nearly all modern manufacture. The properties of the lever, the wheel and axle, etc., are involved in every machine-every machine is a solidified mechanical theorem; and to machinery in these times we Owe nearly 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 seed was put in 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 machine-made; by machinery the flooring was sawn and planed, the mantelshelf sawn and polished, the paper-hangings made and printed; the veneer on the table, the turned legs of the chairs, the carpet, the curtains, are all products of machinery. And your clothing-plain, figured, or printed-is it not wholly woven, nay, perhaps even sewed by machinery? And the volume you are reading-are not its leaves fabricated by one machine and covered with these words by another? Add to which that for the means of distribution over both land and sea, we are similarly indebted. And then let it be remembered that according as the principles of mechanics are well or ill used to these ends,

comes success or failure-individual and national. The engineer who misapplies his formulæ for the strength of materials, builds a bridge that breaks down. The manufacturer whose apparatus is badly devised, cannot compete with another whose apparatus wastes less in friction and inertia. The ship-builder adhering to the old model, is outsailed by one who builds on the mechanically-justined waveline principle. And as the ability of a nation to hold its own against other nations depends on the skilled activity of its units, we see that on such knowledge may turn the national fate. Judge then the worth of mathematics.

Pass next to Physics. Joined with mathe matics, it has given us the steam-engine, which does the work of millions of laborers That section of physics which deals with the laws of heat, has taught us how to economize fuel in our various industries; how to increase the produce of our smelting furnaces by substituting the hot for the cold blast; how to ventilate our mines; how to prevent explosions by using the safety-lamp; and, through the thermometer, how to regulate in numerable processes. That division which has the phenomena of light for its subject, gives eyes to the old and the myopic; aids through the microscope in detecting diseases and adulterations; and by improved light houses prevents shipwrecks. Researches in electricity and magnetism have saved incalculable life and property by the compass; have subserved sundry arts by the electro

type; and now, in the telegraph, have sup- plied us with the agency by which for the future all mercantile transactions will be regu=lated, political intercourse carried on, and perhaps national quarrels often avoided. While in the details of indoor life, from the improved kitchen-range up to the stereoscope on the drawing-room table, the applications of advanced physics underlie our comforts and gratifications.

Still more numerous are the bearings of Chemistry on those activities by which men obtain the means of living. The bleacher, the dyer, the calico-printer, are severally occupied in processes that are well or ill done according as they do or do not conform to chemical laws. The economical reduction from their ores of copper, tin, zinc, lead, silver, iron, are in a great measure questions of chemistry. Sugar-refining, gas-making, soapboiling, gunpowder manufacture, are operations all partly chemical; as are also those by which are produced glass and porcelain. Whether the distiller's wort stops at the alcoholic fermentation or passes into the acetous, is a chemical question on which hangs his profit or loss and the brewer, if his business is sufficiently large, finds it pay to keep a chemist on his premises. Glance through a work on technology, and it becomes at once apparent that there is now scarcely any process in the arts or manufactures over some part of which chemistry does not preside. And then, lastly, we come to the fact that in

these times, agriculture, to be profitably carried on, must have like guidance. The analysis of manures and soils; their adaptations to each other; the use of gypsum or other substance for fixing ammonia; the utilization of coprolites; the production of artificial manures--all these are boons of chemistry which it behoves the farmer to acquaint himself with. Be it in the lucifer match, or in disinfected sewage, or in photographs-in bread made without fermentation, or perfumes extracted from refuse, we may perceive that chemistry affects all our industries; and that, by consequence, knowledge of it concerns every one who is directly or indirectly connected with our industries.

And then the science of life-Biology: does not this, too, bear fundamentally upon these processes of indirect self-preservation? With what we ordinarily call manufactures, it has, indeed, little connection; but with the all-essential manufacture that of food-it is inseparably connected. As agriculture must conform its methods to the phenomena of vegetable and animal life, it follows necessarily that the science of these phenomena is the rational basis of agriculture. Various biological truths have indeed been empirically established and acted upon by farmers while yet there has been no conception of them as science: such as that particular manures are suited to particular plants; that crops of certain kinds unfit the soil for other crops; that horses cannot do good work on poor food;