CERT.tlX f-.ICIOkS .Ill-ECTIXG TELF.GHAl'U Sl'liliP 3-JJ 



elements (ler character, then the tdtal iniinher of characters wliicli 



can l>e construed equals ni". In order that two such systems should 



be e(iuivalent, the total nunil)er of characters tli.it cm lie disiin- 

 guisluxl should be the same. In other words, 



»i"=const. (1) 

 This i-<iii,iti(>ii m.i\' also be written 



n log in = const. (2) 



The speed with which intelligence can Ix; transmitted over a circuit 

 is ilirectly proportional to the line speed and inversely profwrtional 

 to the numlwr of signal elements per character provided that the 

 relations above are satisfied. Hence, we may write 



ir = .'; ./ (3) 



where s is the line speed. Substituting the value of it deri\ed from 

 the etiuation alxjve, this equation becomes 



const, 

 which may also he written 



ir = A' log in (5) 



In applying this formula to practical cases it will be found im- 

 f)ossible to comply strictly with the condition expressed by equation 

 (1). As an example, consider the comparison between a three- 

 current-value code where each character is made up of three signal 

 elements, and a two-current-value code where each element is matle 

 up of five signal elements. It is obvious that the speed with which 

 characters can be transmitted in the former case is five-thirds the 

 speed in the latter ca.se for a given line speed. In other words the 

 ratio is 1.67:1 whereas the formula gives the ratio 1.58:1. It should 

 Ix! noted, however, that the former code pos.sesses only 27 characters 

 whereas the latter possesses 32. In other words one character of the 

 latter code represents the transmission of more intelligence than one 

 character of the former. Thus the figure 1.67 for the relative speeds 

 of transmission of characters and the figure l.-iS for the relative speeds 

 of transmission of intelligence are not incompatible. 



It will Ix; noted that the formula has been deduced for codes ha\ing 

 characters of uniform duration and that it should not be expected 

 to be anything but an approximation for codes whose characters are 

 of non-uniform duration. To establish the formula for the latter 

 case it would be necessary- to make an assumption as to the relati\'e 

 Irequencies of the various characters. It seems reasonable to sup- 



