Variation of Sentence-Constants in Literature 



23 



It will be interesting to test this law on some particular work 

 not included in our table of averages. Macaulay's History of 

 England is the only work available for this purpose, for it is the 

 only work whose constants P and S have been determined with 

 sufficient accuracy, without tampering with the composition or 

 punctuation of the author. Using S=--^4.2,'^ that one of the 

 two constants P and vS" which is most readily determined by 

 count, our formula gives 



P^ 



1184 _ I184 _ 



2.32, 



and below are the limits within which they could vary and still satisfy our 

 law. 



Now not only are the limits comparative!}' narrow, but in most cases S 

 occupies a mean position between them. 



I am aware, however, that strange numerical relations may occur where 

 there is no law. In evidence of this I take liberty to quote an example from 

 C. S. Peirce's essay, ^4 Theory of Probable Inference, published in the 

 Johns Hopkins Universitj' Studies of Logic, an essay which every one who 

 ventures upon the field of .scientific induction would do well to peruse. 

 The first five names of poets and their ages at death, taken from a certain 

 biographical dictionary are, 



Aagard 



Abeille 



Abulola.. . 

 Abunowas. 

 Accords . . . 



Now, although no sane person would expect a law connecting the digits of 

 the numbers representing the ages at deaths of poets, it is nevertheless true 

 that for the given five numbers, 



1. The difference of the two digits, divided by three, leaves a remainder 

 of one. 



12. The first digit powered by the second, the result divide I by three, 

 leaves a remainder one. 



3. The sum of the prime factors (including one) of each number is divis- 

 ible by three. 



^Gerwig gives 34. But Gerwig gives only the integral parts of the values 

 for .S", while the values for /-"are given to two decimal places. To be con- 

 sistent, he should have either retained the first decimal places in 5", or have 

 dropped also the second decimal places in P. 



251 



