514 THE BELL SYSTEM TECHXICAL JOURNAL, MARCH 1957 



becomes 



Vs = 2-^'' (1.5) 



since there is only one B. 



Shannon's determinantal equation 



1 E IF^'--^'' - S,, I = 



s 



becomes 



S2~'''^ = 1 (1.6) 



In (1.5) and (1.6) we have a means of evaluating -ps in order to attain 

 the maximum inlormation rate R. 



The data we actually have concerning words is that for some class s 

 of words, say, the monosyllables in the 8,000-9,000 words in order of 

 familiarity, the reading time has some value ts , presumed to be the 

 same for all words in the class, and that there are Ns words in this class. 

 In this case we must assign to each word in the sth class the same prob- 

 ability Ps given b}^ 



Ps = 2-^'^ (1.7) 



and we must have 



J^NsPs = i:-V^2-^'' = 1 (1.8) 



s s 



Using the same amount of data given in Fig. 3, for the 20,000 most 

 common words, but for a different reader, estimates were made of Ns 

 and ts for all the classes consisting of words of each number of syllables 

 in each range of occurrence of 1 ,000 words. Then the optimum values of 

 Ps for word.s in each class and the maximum rate R were computed. 



Using (1.4), rates were also computed for choosing words with equal 

 probability from among the first w thousand words and from among 

 the first ?n thousand monosyllables, as functions of m. These rates had 



Table VI 



Nature 



Maximum Rate 



Maximum for equi-probability monosyllables (from first 8,000 



words) 



Maximum for equi-probabilitj- among words of all lengths 



(first 5,000 words) 



Computed Rate, 

 bits/sec 



33.5 



32.4 

 30.2 



