*THE MYSTIC PROPERTIES OF NUMBERS.*

interested in securing due recognition of altruistic rights by his fellows. The evils resulting from business frauds affect the welfare of the community. To quote the illustrative cases cited by Mr. Spencer, "The larger the number of a shopkeeper's bills left unpaid by some customers, the higher must be the prices which other customers pay; the more manufacturers lose by defective raw materials or by carelessness of workmen, the more must they charge for their fabrics to buyers. The less trustworthy people are, the higher rises the rate of interest, the larger becomes the amount of capital hoarded, the greater are the impediments to industry; the further traders and people in general go beyond their means, and hypothecate the property of others in speculation, the more serious are those commercial panics which bring disasters on multitudes and injuriously affect all."—*Knowledge.*

THE MYSTIC PROPERTIES OF NUMBERS. |

ONE of the earliest French mathematical books is the arithmetic of Étienne de la Roche, in which, the title-page states, are given tables of different accounts, with their canons, calculated by Gilles Huguetan, native of Lyons: "in which may easily be found the accounts all made, as well of purchases as of sales, of all kinds of merchandise. And, principally, of goods which are sold or bought by measure, as by the ell, by the cane, by the toise, by the palm, by the foot, and the like. By weight, as by the pound, by the quintal, by the thousand-weight, by the load, by the half-pound and the ounce, by the piece, by the number, by the dozen, by the gross, by the hundred, and by the thousand. With two tables of use to booksellers, in selling and buying paper, together with a table of expense, showing, at so much a day, how much one spends by the year and the month, and at so much a month how much it comes to by the year and the day, and at so much a year how much one spends in a month and how much it comes to for each day.

"Further, tables of the fineness of gold and silver, showing, according as the coin contains of alloy or fine metal, how much it is worth in the weight of fine gold or of fine silver.

"Sold at Lyons, at the sign of the Sphere, by Gilles and Jaques Huguetan Brothers, 1538."

We give the first chapter of this curious work, which treats of the first twelve numbers, their properties and perfections. Our modern works, while they are less unsophisticated, are certainly far less amusing in expounding the beginnings of arithmetic:

"Number, according to Euclid, at the beginning of the seventh