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 but in whatever manner those persons conduct themselves, who associate with children, whether rationally or irrationally, such will the children be.

8. The elements of arithmetic can scarcely be propounded to children in the third year; but soon they can count up to five or ten, or at least pronounce the numbers correctly; they may not at first understand what those numbers really are, but they will of themselves observe the use to which this enumeration is applied. In the fourth, fifth, and sixth years it will be sufficient if they count up to twenty in succession, and be able clearly to distinguish that seven is more than five, and fifteen more than thirteen; what is an even and what an odd number, which they may easily learn from the play which we call odds and evens. To proceed farther than this in arithmetic would be unprofitable, nay, hurtful; for nothing is so difficult to fix in our minds as numbers.

9. About the second year the principles of geometry may be perceived, when we say of anything it is large or small; they will afterwards know easily what is short or long, wide or narrow. In the fourth year they may learn the different forms; for example, what is a circle, what are lines, what a square. At length they may learn the names of the common measures, such as a finger’s breadth, a span, a foot, a pint, a quart, a gallon. Whatever comes spontaneously to their own knowledge, they themselves should be shown how to measure, to weigh, thus comparing the one with another standard of measurement.