Among the attempted improvements in arithmetic, what is generally denominated 'mental arithmetic,' stands conspicuous. That arithmetics in former times were too abstract, too little applied to the business of life, is undoubtedly true. To obviate this, mental arithmetic has been introduced. This exercise the scholar generally commences at the beginning of his course. A little of it might not be unprofitable; but it is believed that the tendency, at present, is to give it too great a prominence. It would seem as if, in the view of some writers on this subject, the first efforts of the child in numbers should be to invent to himself rules of arithmetic, a work to which he is utterly unequal. In some recent arithmetics, vulgar fractions will be found mingled, with simple addition, and the child will be required to solve difficult questions in the former, before he is well acquainted with the latter. This is altogether preposterous. Mental arithmetic has much less application to the business of life, than is often supposed. Few men of business rely very extensively on mental calculations, in preference to their pen or their slate, for two reasons. The one is, that in written calculations there is more certainty of correctness, and the other is, that they are incapable of inventing shorter and better rules for arriving at their results, than the rules of a good arithmetic. As an exercise of the mind, mental arithmetic may serve to sharpen the ingenuity, and give vigor to the faculties. But there is another exercise, which has been strangely overlooked by the writers of arithmetics for schools, which would be superior to it as a mental discipline, and that is, a demonstration of the rules of arithmetic, in which the reasons for every operation, in every rule, should be scientifically unfolded. The scholar would thus be led, in the true analytical method, to unravel the mental process by which the inventor of the rule arrived at it as a conclusion. Not more than two or three arithmetics, intended for common schools, have attempted this, in a general and scientific manner. Among the improvements in regard to text-books for schools, many familiar treatises on general science stand conspicuous. School-literature is taking a wider range than formerly. Even in common schools, by the introduction of such a work as the 'Scientific Class-Book' as a reading-book, two important objects would be secured at the same time; while youth are learning to read with propriety, their minds will also be stored with many of the principles of natural philosophy, astronomy, chemistry, botany, and political economy, with other important subjects. Reading-books for schools have extensively been of that character usually denominated 'light reading.' But too much light reading, it should never be forgotten, is exceedingly well calculated to make light heads. Works for the youth of our schools, should be filled with substantial and systematic knowledge.