The following practical suggestions are offered as an answer to the question of ever-increasing interest, “How, when, where, shall the child begin arithmetic?”

The importance of the science of number, as a great teacher has shown, is enormous, not only in its relation to the study of abstract mathematics and in its dominance over the prosperity of nations, but in the fact that it is the “conclusive science which we have to apply all our days to all our affairs.”

When Algebra, fair Daughter of King Arithmetic, is nearing her age of adolescence her eyes fall on Prince Limit, and there cometh a change upon her. Her tender heart goes forth to him, and in her lithe and nimble frame she feels a torture from end to end as it would fall to pieces. She is in love, and the Prince reciprocates her love.

Happily they are wedded. The King gave away his Daughter, the Angels witnessed it, and all was joy. The marriage was performed with the Hymn of the Transcendent Number and Ratio, preceded by the Song of Limits, and followed by the Chorus of Continuity and Convergence.

Messrs. Godfrey and Siddons in the preface to their Geometry express both a hope and an expectation that a recognized sequence of propositions will ultimately be adopted not widely differing from that of Euclid. In the Athenœum of January 9th, 1904, the writer of a review on Messrs. Godfrey and Siddons’ book scouts the idea.