in certain elementary demonstrations that geometrical figures could be removed from the paper, turned over and laid down again,—­the so-called “method of superposition,” now generally regarded as quite allowable.  Of course, a figure can be treated in this way only in imagination and for this season, probably, the method was not employed by Euclid.  Its use, however, leads always to true results, as anyone may see; and it was quite characteristic of Professor Newcomb that he should have taken it up, not having the fear of the Greek geometers before him.

Such was Newcomb; it will be long before American science sees his equal.  Mathematical genius is like an automobile,—­it is looked upon in two opposing fashions as one has it or has it not.  A noted educator not long ago announced his belief that the possession of a taste for mathematics is an exact index of the general intellectual powers.  Not much later, another eminent teacher asserted that mathematical ability is an exotic,—­that one may, and often does, possess it who is in other respects practically an imbecile.  This is scarcely a subject in which a single illustration decides, but surely Newcomb’s career justifies the former opinion rather than the latter; the amount and kind of his mental abilities along all lines seemed to run parallel to his mathematical genius, to resemble it in quantity and in kind.

The great volumes of astronomical tables without which no astronomer may now venture upon a computation are his best monument; yet the general reader will longer remember, perhaps, the lucid expositor, the genial essayist, the writer of one of the most readable autobiographies of our day.

THE COMPANIONSHIP OF BOOKS[5]

    [5] Read before the Pacific Northwest Library Association,
        June, 1910.

Are books fitted to be our companions?  That depends.  You and I read them with pleasure; others do not care for them; to some the reading of any book at all is as impossible as the perusal of a volume in Old Slavonic would be to most of us.  These people simply do not read at all.  To a suggestion that he supplement his usual vacation sports by reading a novel, a New York police captain—­a man with a common school education—­replied, “Well, I’ve never read a book yet, and I don’t think I’ll begin now.”  Here was a man who had never read a book, who had no use for books, and who could get along perfectly well without them.  He is not a unique type.  Hundreds of thousands of our fellow citizens might as well be quite illiterate, so far as the use that they make of their ability to read is concerned.  These persons are not all uneducated; they possess and are still acquiring much knowledge, but since leaving school they have acquired it chiefly by personal experience and by word of mouth.  Is it possible that they are right?  May it be that to read books is unnecessary and superfluous?