Technical Points.—It is more than fortunate that in nearly every figure, the original outline of the hair is safe. Geometry's has scarcely been retouched at all, except at the ends, once in single knots, now in confused double ones. The hands, girdle, most of her dress, and her black carpenter's square are original. Face and breast repainted.

VII. ARITHMETIC. Having built your house, young people, and understanding the light of heaven, and the measures of earth, you may marry—and can't do better. And here is now your conclusive science, which you will have to apply, all your days, to all your affairs.

The Science of Number. Infinite in solemnity of use in Italy at this time; including, of course, whatever was known of the higher abstract mathematics and mysteries of numbers, but reverenced especially in its vital necessity to the prosperity of families and kingdoms, and first fully so understood here in commercial Florence.

Her hand lifted, with two fingers bent, two straight, solemnly enforcing on your attention her primal law—Two and two are—four, you observe,—not five, as those accursed usurers think.

Under her, Pythagoras.

Above, medallion of king, with sceptre and globe, counting money. Have you ever chanced to read carefully Carlyle's account of the foundation of the existing Prussian empire, in economy?

You can, at all events, consider with yourself a little, what empire this queen of the terrestrial sciences must hold over the rest, if they are to be put to good use; or what depth and breadth of application there is in the brief parables of the counted cost of Power, and number of Armies.

To give a very minor, but characteristic, instance. I have always felt that with my intense love of the Alps, I ought to have been able to make a drawing of Chamouni, or the vale of Cluse, which should give people more pleasure than a photograph; but I always wanted to do it as I saw it, and engrave pine for pine, and crag for crag, like Albert Dürer. I broke my strength down for many a year, always tiring of my work, or finding the leaves drop off, or the snow come on, before I had well begun what I meant to do. If I had only counted my pines first, and calculated the number of hours necessary to do them in the manner of Dürer, I should have saved the available drawing time of some five years, spent in vain effort.

But Turner counted his pines, and did all that could be done for them, and rested content with that.

So in all the affairs of life, the arithmetical part of the business is the dominant one. How many and how much have we? How many and how much do we want? How constantly does noble Arithmetic of the finite lose itself in base Avarice of the Infinite, and in blind imagination of it! In counting of minutes, is our arithmetic ever solicitous enough? In counting our days, is she ever severe enough? How we shrink from putting, in their decades, the diminished store of them! And if we ever pray the solemn prayer that we may be taught to number them, do we even try to do it after praying?