Page:Popular Science Monthly Volume 63.djvu/542

538 by the same author. Now of the 41,500 periods of the 'History,' there are forty-five hundreds whose average is less than twenty words per sentence. These we may take to represent the dialogue portions of the work. The exact average of these 4,500 periods is 18.62 words per sentence, that is, 4.81 words per sentence less than the average for the entire 'History.' If we replace these sentences by others of normal length, we augment the total aggregate by 4,500 times 4.81 or 21,645 words. That is, if the portions of the 'History' which contain an excessive amount of dialogue were replaced by an equal number of sentences of normal length, the five volumes would contain $$41,500 \times 23.43 + 21,645$$ or 993,990 words. Dividing this number by 41,500 we obtain 23.95 words per sentence, a result not essentially different from the actual average, 24.43.

But whether the presumption is for or against limitations of the Sherman principles is of little consequence in a matter so easily tested by experiment. I have prepared a table giving the approximate sentence-lengths for widely divergent forms of composition by the same author. The averages by hundreds, as well as the final average, have been given in order to show the variation in the averages of consecutive hundreds in each work.

It is needless to continue this table, for a mere inspection of the figures already given must once and for all settle the 'single set of constants' theory. In fact the question suggests itself, whether the number of different sets of constants which an author may employ is not limited merely by his versatility as a writer. So far as sentence length is concerned, this conjecture is fully corroborated by a partial examination of Goethe's works. The results are exhibited in the following table: