people that those who cannot read often make more money than those who are great scholars. This is very true; and if money-making were all that there is to be thought about in this life, perhaps schoolboys and schoolmasters might save themselves a world of trouble. But those unlettered money-makers prove my case; for it is clearly to the use of their natural faculties, and not to flourishing ciphering-books and the 'Tutor's Assistant,' nor to technical rules of any kind, except those which they may have made for themselves, that they owe the marvellous power of mental arithmetic which some of these expert dealers possess, without being able to give an account of how the ready-reckoner in their brain is constructed.
It is just this free, instinctive mental power which it is the aim of all sound arithmetical and mathematical training to evoke. It cannot be put into a boy,—it must be called out of him. The first point is a thorough mastery of the four first rules of arithmetic, and a power of applying them to facts; next, the practice and theory of fractions; after which a boy will be more capable of understanding the principles contained in the earlier rules and the Rule of Three.
I should be inclined to name next, with a view to art and trade, the practical construction (without the mathematical proofs) of geometrical forms, such as may be gained from the introductory works used at Marlborough House. This would lay a foundation for mechanical and architectural drawing, and give a boy neatness in the use of his fingers,—in short, the command of the rule and compasses. But, as I have said above, I would set before all boys in the middle classes, without exception, a portion of Euclid as the great work to be mastered. Algebra, so essential as the foundation of higher mathematics, appears to me, for boys of the class referred to, less important. Algebra is certainly not equal to geometry as a means of mental discipline; and though, if carried far enough, it throws much light on arithmetic, and gives great command over scientific calculation, the introduction of algebra into the education of the farmer is something like erecting a steam-engine on a farm which has hardly work for a team of horses.
Natural Philosophy.
With a sound preparation in the use of ordinary language, in arithmetic, and geometry, the pupil (still keeping in view only what is to be useful in business) will be ready for the study of the laws of the natural world, especially of those having relation to mechanism. A knowledge of the first principles of mechanical philosophy is most valuable to men of business for two reasons: first, because their life is spent in moving material substances,
