READING RATES 515 



maxima for vocabularies of optimal sizes. Table Yl compares the various 

 rates computed. 



As it is much easier to make up lists from the 2,500 monosyllables 

 among the first 8,000 words with equal probabilities than it is to make 

 up lists from among all words with a different probability for each class, 

 and as the information rates computed were close together, the former 

 alternative was chosen. 



The use of scrambled prose provided an easy way to make up good 

 lists. 



Appendix II 



TRACKING EXPERIMENT 



A well-known formula for channel capacity R in bits/sec is* 



R = B logo. (^1 + (2.1) 



This gives the limiting rate at which information can be transmitted 

 over a channel with a bandwidth 5 by a signal of power P^ , in the pres- 

 ence of a gaussian noise of power P„ , with an error rate smaller than any 

 assignable number. 



In most cases, the actual rate is much smaller than this limiting rate. 

 In general, the rate is the entrop}- of the received signal minus the 

 entrop}" of the noise. In the particular case of a gaussian signal source as 

 well as a gaussian noise, each represented by 2B samples a second, the 

 calculation based on entropies gives exactly (2.1). Let us then apply 

 (2.1) to the tracking experiment. 



Suppose that a large number A" of samples do have a gaussian dis- 

 tribution of mean square amplitude x^. Suppose that we make an error 

 dn in reproducing the nth sample, that these errors are gaussian, and 

 that the mean square error is d'^ 



^ = ^r S ^ 



We see from (2.1) that ideall}" we can use these reproduced samples 

 to transmit M bits of information where 



M =tl log, (^1 + ^ j (2.2) 



In the reading and tracking experiments, randomized words from the 

 2,500 commonest monosj'llables were arranged with equal vertical 



