Page:Popular Science Monthly Volume 65.djvu/138

134 remark that 'the reader is at liberty to draw any conclusion he pleases from this diagram' only strengthens the impression that the conclusion intended is considered unavoidable, though we are told at the outset that 'the investigation is not to be looked upon as a final solution of the principal problem.'

Considering that it is now over fifteen years since the theory of characteristic curves was first outlined and that no denial of it has appeared, it must be taken for granted that the theory has found general acceptance. It is for this reason that I undertook an investigation, which proved laborious and unattractive in the main, in order to combat with facts an error which to me seemed obvious from the outset. The data which I have now at hand, though necessarily meager, are amply sufficient to establish a duality, if not a multiplicity, of characteristic curves for many authors. But this amounts to a denial of Dr. Mendenhall's major premise, and consequently invalidates his conclusion. Fig. 20, instead of furnishing a convincing proof, or even contributary evidence, leaves the problem of disputed authorship wholly untouched. In fact, my results throw considerable doubt upon the very existence of characteristic curves in the sense that the word has been employed by Dr. Mendenhall. I shall, therefore, use the term word-curve when referring to curves representing the relative frequencies of different length words used in composition.

Dr. Mendenhall states that the validity of his method as a test of authorship implies two assumptions: first, that the author makes use of a vocabulary which is peculiar to himself, and the character of which does not change from year to year during his productive period; and second, that in the use of that vocabulary in composition, personal peculiarities in the construction of sentences will, in the long run, recur with such regularity that short words, long words and words of medium length will occur with definite relative frequencies.

These two assumptions are of course independent. Suppose it be granted that authors use vocabularies peculiarly their own. It does not at all follow that these peculiarities will manifest themselves in varying word-lengths. Obviously an indefinite number of different vocabularies is conceivable, each yielding the same average word-length or even fitting to the same word-curve. Now, it is true that if authors are endowed with a word-sense or word-instinct by means of which personal traits are reflected through their vocabularies (first assumption), and if, moreover, this word-sense manifests itself in measurable differences in the relative frequencies of words of a given length (second assumption), then these personal traits or peculiarities of an author will in general modify the contour of the word-curve. But the converse of this by no means follows, that the differences in the