540 BELL SYSTEM TECHNICAL JOURNAL 



We may, however, use it as the basis for a derived measure which 

 does meet the practical requirements. To do this we arbitrarily put 

 the amount of information proportional to the number of selections 

 and so choose the factor of proportionality as to make equal amounts 

 of information correspond to equal numbers of possible sequences. 

 For a particular system let the amount of information associated with 

 n selections be 



H = Kn, (4) 



where X is a constant which depends on the number 5 of symbols 

 available at each selection. Take any two systems for which s has 

 the values Si and 52 and let the corresponding constants be Ki and K^. 

 We then define these constants by the condition that whenever the 

 numbers of selections Wi and n^ for the two systems are such that the 

 number of possible sequences is the same for both systems, then the 

 amount of information is also the same for both ; that is to say, when 



5i"i = 52"% (5) 



H = Kifii = K2fh, (6) 



from which 



(7) 



K\ K2 



log 5i log 52 



This relation will hold for all values of 5 only if K is connected with 5 

 by the relation 



K= K, log 5, (8) 



where Kq is the same for all systems. Since Kq is arbitrary, we may 

 omit it if we make the logarithmic base arbitrary. The particular 

 base selected fixes the size of the unit of information. Putting this 

 value of K in (4), 



H = « log 5 (9) 



= log5». (10) 



What we have done then is to take as our practical measure of infor- 

 mation the logarithm of the number of possible symbol sequences. 



The situation is similar to that involved in measuring the trans- 

 mission loss due to the insertion of a piece of apparatus in a telephone 

 system. The effect of the insertion is to alter in a certain ratio the 

 power delivered to the receiver. This ratio might be taken as a meas- 

 ure of the loss. It is found more convenient, however, to take the 

 logarithm of the power ratio as a measure of the transmission loss. 



