# Page:Popular Science Monthly Volume 16.djvu/224

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THE POPULAR SCIENCE MONTHLY.

"Whether the multiplication of fractions is an increasing process?" In order to prove that to multiply means to increase, he bases his argument on Scripture, and clinches the whole by quoting the promise to Abraham, "I will multiply thy seed like the stars of the firmament." To this devout logician there would be no joke in the common conundrum that proves Abraham to have been a mathematician because he increased and multiplied on the "face of the earth." But how is this to be reconciled with the numerical result in the cases under consideration? He supposes the units of the product to be of greater virtue and significancy than those of the factors: thus, if 12 and 12 represent the sides of a square, their product will represent the area of the square.

The first actual mention of real decimal fractions is in a Flemish work published in 1590. There the mixed number 27·847 is written

 (0) (1) (2) (3) 2 7 8 4 7.

To the present advocates of the metric system it may afford encouragement to know that Stevinus, in this work, enumerates the advantages which would result from the decimal subdivision of the units of length, area, capacity, value, etc.

In 1619 the contents of the Flemish book were embodied in an English work — "The Art of Tens, or Decimal Arithmetike, exercised by Henry Lyte, Gent., and by him set forth for his Countries Good." After enlarging upon the value of his system to all classes, he adds: "If God spare me life, I will spend some time in most cities of this land for my countries good to teach this art. I hold the lively voice of a meane speculator somewhat practised, furthereth ten fold more in my judgement than the finest writer that is," Rather severe on those "meane speculators," his contemporaries, Francis Bacon and William Shakespeare.

 SPENCER'S DATA OF ETHICS.
By ALEXANDER BAIN, LL. D.,
PROFESSOR OF LOGIC IN THE UNIVERSITY OF ABERDEEN.

IN the immense abundance of literary production a great deal of criticism is avowedly calculated to supersede the perusal of the works themselves. Such a book as the present, however, is among the rarest; and being on the most interesting of all themes, and withal lucid and short, the critic would be much mistaken in assuming that it will not be read by his own readers and many besides.

The field of ethics has been crossed and recrossed in many directions; and we are now called to follow a new and unbeaten track. Our interest and expectation are awakened, not simply on account of the general philosophic ability of the writer, which disposes us to