132 POPULAR SCIENCE MONTHLY. 



ON THE SIGNIFICANCE OF CHARACTERISTIC CURVES 



OF COMPOSITION. 



By ROBERT E. MORITZ, 



UNIVERSITY OF NEBRASKA. 



A FEW months ago, while studying the variation and interrelation 

 of certain sentence constants, as average sentence-lengths, predi- 

 cation averages and simple-sentence frequencies in prose composition, 

 my attention was called to an allied investigation, directed by Dr. 

 T. C. Mendenhall, which takes for its basis the words used by an author 

 rather than the sentences. The investigation in which I was then 

 employed made it clear that the theory which asserts that an author 

 uses invariable average sentence proportions is not true except when 

 modified in essential respects, and I recognized at once that similar 

 modifications would become necessary if the word instead of the 

 sentence were taken as the element of composition. 



The allied investigation to which I refer is set forth in two papers 

 by Dr. T. C. Mendenhall, one in Science, March 11, 1887, entitled 

 'The Characteristic Curves of Composition,' the other, 'A Mechanical 

 Solution of a Literary Problem' in The Popular Science Monthly, 

 December, 1901. 



These papers deal with the relative frequency of words of different 

 lengths employed by an author. It was found that different groups 

 of a thousand words each, taken from the same author, manifested a 

 rather remarkable uniformity in the frequency of words containing a 

 given number of letters. Larger groups showed still greater uni- 

 formity, and hence it was inferred that if sufficiently large groups of 

 words from the same writer were examined, they would yield prac- 

 tically the same relative frequencies of words with a given number of 

 letters. 



The results were exhibited graphically. The number of letters 

 per word were used as abscissas, the number of words per thousand 

 containing a definite number of letters were taken for ordinates, and 

 the resulting points connected by straight lines. Thus a graph or 

 diagram was obtained which presents to the eye in a simple manner 

 the relative frequencies of words of different lengths. Two such 

 diagrams from the same author will agree more or less closely, de- 

 pending upon the number of words in the groups upon which the aver- 

 ages are based. In the writer's own words: "When the number of 



