1 6 R.E. M or its 



I shall now endeavor to show that the principle just stated 

 applies also to the other sentence-constants, predication-averages. 

 and simple-sentence-percentages. 



It will not be necessary to produce a chain of different predi- 

 cation-averages or simple-sentence-percentages corresponding to 

 the chain of sentence-lengths which we found in Goethe. We 

 need only show that there exists a functional relation between 

 the various sets of constants, such that a variation in one set 

 produces a variation in each of the other sets. Mathematically 

 expressed, we need only show that 



P=f{L) S=<i>{P) 



where L^sentence-length, 



Pi^predication-average, 

 5=simple'sentence-per cent, 



from which it immediately follows that 5 itself is a function 

 of L. 



A priori we should expect no less than that the shorter sen- 

 tence contains fewer predications, and that as the sentence grows 

 shorter the percentage of simple sentences increases, the limits 

 being respectively single predications in the one case and none 

 but simple sentences in the other. However, inasmuch as no 

 attempt appears to have been made to verify this prediction, the 

 only statement that I can find bearing on it being exactly op- 



History of England, particularly the second volume, contains much dia- 

 logue, which might cause us to expect a lower average than is actually the 

 case. The explanation is, that taking the History as a whole Macaulay's 

 normal style predominates to such an extent as to practically obliterate the 

 "bearish" tendency of the dialogue passages. This can be easily demon- 

 strated. There are in all 45 hundreds of periods whose average is less than 

 20 words per sentence. These we may take to represent approximately the 

 dialogue portions of the History. The exact average of these 4,5'JO periods 

 is 18 62, that is, 4.81 words less per sentence than the average for the entire 

 History. If we replace these sentences by others of the normal length, we 

 swell the total aggregate of words by 4,510X4.81 or 21,645 words. That is, 

 if the portions of the History which contain an excessive amount of dia- 

 logue were replaced by an equal number of sentences of normal length, the 

 five volumes of Macaulay's History would contain 41, 500X23. 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. For the 

 data employed see Univ. Studies, vol. I, no. 2, p. 130; Ibid., vol. I, no. 4, 

 pp. 351, 352. 



244 



