22 R. E. Moritz 



Py^S=Q (2) 



where €=^13.57 the mean of the slightly varying values 13.-I- 



How nearly this equation fits our data may best be seen from 

 the graphical representation in fig. 2. The curve 



13-57 



S \ S 



4'. 



as well as the P's and ^''s from our table have been plotted, by 

 using the values of 6" as abscissas and ten times the correspond- 

 ing values of P as ordinates. The resulting points have been 

 numbered i, 2, 3, etc., to correspond with the index numbers in 

 the table. 



The relation symbolized by equation (2) may be easily stated 

 in words. For, if P^, S-^^, and Po, S. are any two pairs of corre- 

 sponding values of P's and S's, we have by virtue of (2) 



/il/5i=i 3 • 57— -P-2yJ Si nearly, 

 hence 



Pi : P^^y/S^ : 1/6*1, 



that is to say: 



The predication-averages of various zvorks are inversely pro- 

 portional to the square roots of their simple-sentence-percent- 

 ages. ^ 



^This law, owing to the meagerness and uncertainty of the data upon 

 which it is based, must be considered no more than a rough approximation 

 to the truth. There is no reason to suppose that it will give with equal 

 accuracy the true relations between the values /'and 5" for every other work. 

 Of the other common sources of error in inductive reasoning, biased data, 

 and reasoning from accidental common marks of a limited number of 

 samples to a property of the class, the first I think has been eliminated by 

 my mode of selecting the data. As to the other I can only say that the 

 mathematical probability is practically zero that each of eleven pairs of 

 numbers chosen at random should manifest a definite relation like the one 

 in question. I have computed the limits between which each value of S 

 could vary and yet satisfy the relation P\/ S=^\Z-\- for the given values of P. 

 The numbers in bold face are the .S's from our table; immediately above 



250 



