TRANSMISSION OF INFORMATION . 541 



If we put n equal to unity, we see that the information associated 

 with a single selection is the logarithm of the number of symbols 

 available; for example, in the Baudot System referred to above, the 

 number 5 of primary symbols or current values is 2 and the informa- 

 tion content of one selection is log 2 ; that of a character which involves 

 5 selections is 5 log 2. The same result is obtained if we regard a 

 character as a secondary symbol and take the logarithm of the number 

 of these symbols, that is, log 2^, or 5 log 2. The information associated 

 with 100 characters will be 500 log 2. The numerical value of the 

 information will depend upon the system of logarithms used. In- 

 creasing the number of current values from 2 to say 10, that is, in 

 the ratio 5, would increase the information content of a given number 



of selections in the ratio -; ~ , or 3.3. Its effect on the rate of 



log 2 



transmission will depend upon how the rate of making selections is 



affected. This will be discussed later. 



When, as in the case just considered, the secondary symbols all 

 involve the same number of primary selections, the relations are 

 quite simple. When a telegraph system is used which employs a 

 non-uniform code they are rather more complicated. A difficulty, 

 more apparent than real, arises from the fact that a given number 

 of secondary or character selections may necessitate widely different 

 numbers of primary selections, depending on the particular characters 

 chosen. This would seem to indicate that the values of information 

 deduced from the primary and secondary symbols would be different. 

 It may easily be shown, however, that this does not necessarily follow. 



If the sender is at all times free to choose any secondary symbol, 

 he may make all of his selections from among those containing the 

 greatest number of primary symbols. The secondary symbols will 

 then all be of equal length, and, just as for the uniform code, the 

 number of primary symbols will be the product of the number of 

 characters by the maximum number of primary selections per char- 

 acter. If the number of primary selections for a given number of 

 characters is to be kept to some smaller value than this, some restric- 

 tion must be placed on the freedom of selection of the secondary 

 symbols. Such a restriction is imposed when, in computing the 

 average number of dots per character for a non-uniform code, we take 

 account of the average frequency of occurrence of the various char- 

 acters in telegraph messages. If this allotted number of dots per 

 character is not to be exceeded in sending a message, the operator 

 must, on the average, refrain from selecting the longer characters 

 more often than their average rate of occurrence. In the language 



