*THE POPULAR SCIENCE MONTHLY*

one another, or stand farther distant asunder." He says perpendicular means level, or a plumb line. Webster, in his 1828 dictionary, says an angle is the space comprised between two straight lines that meet in a point; but he adds also that an angle is the quantity by which two lines diverge from each other.

Though the term *per cent,* in arithmetic is a simple one, the definition of it in practically all the arithmetics and dictionaries wraps it in a fog. A very considerable part of the trouble pupils in school have with percentage is due to obscurity in this definition. This seems like a bold statement to make, but the reader can judge for himself whether it is probably true when he hears the case stated. In simple English the word per cent, means *hundredths.* Thus, six per cent, means six hundredths. Instead of giving this definition the books say per cent, means "by the hundred" or "in the hundred." If this is so then 6 per cent, means six by the hundred, which means nothing. Dr. Johnson, who was no mathematician, said that per cent, meant "in the hundred," and all the lexicographers seem to have followed his lead, merely varying his preposition. Webster (1828) says: "In commerce per cent, denotes a certain rate by the hundred. Ten per cent, means ten in the hundred." Webster's International states that per cent, means "by the hundred," "in the hundred." Of course there is a way of giving concrete meaning to these words. Thus 2 per cent, in commission can mean that the agent gets $2 *in* every $100 worth of goods he sells, or he gets $2 *by* every $100 worth of goods he buys. One sees the obscurity in these phrases, however, very clearly, by using another denominator. Thus, what does 2 by the 8 mean?

In the preface to his dictionary Dr. Johnson says: "Every other author may aspire to praise; the lexicographer can only hope to escape reproach, and even this negative recompense has been yet granted to a very few." Evidently from this lexicographers had a harder time in those early days than they have now; for nowadays it would seem as though the dictionaries were to be regarded as sacred writings, to criticize which would be sacrilege. Had the dictionary makers been criticized more, most likely they would have improved the quality of their work. The writer has heard it said that the dictionaries are as weak in defining other similar technical terms as in their definitions of mathematical terms, and that they are far behind the progressive cyclopedia makers in the quality of the matter they print. It would seem judging from the preceding mathematical definitions as though the greatest opening for a progressive publisher would lie along the way of bringing out a new unabridged dictionary adapted for the use of the mass of twentieth century Americans.