TRANSMISSION OF INFORMATION ■ 547 



i,= (5 - l)|.-<'- (15) 



If we sum this expression for all values of q from one to infinity, we 

 get the combined effect of all the preceding symbols, that is, the 

 intersymbol interference. Calling this i„ 



ii= (s- l)f E%-""^ (16) 



R 



a=i 



This obviously increases as the interval t between selections is de- 

 creased. If this interval is made small enough, the intersymbol 

 interference may cause confusion between symbols. Since the inter- 

 ference is here always of one sign it can cause confusion only when it 

 becomes as large as the minimum difference, is, between symbols. 

 Placing these two quantities equal, we get from (12) and (17) as the 

 minimum permissible value of r, 



ri = (18) 



a 



The maximum number, n, of selections that may be made in t seconds 

 is given by 



n = -- (19) 



From (18) and (19) 



n log 5 . 



— J — = a- (20) 



Here the numerator is, in accordance with our measure of information, 

 the amount of information contained in n selections, so the left-hand 

 member is the information per unit time or the rate of communication. 

 This is equal to the damping constant of the circuit. We therefore 

 conclude that for this particular case the possible rate of communica- 

 tion is fixed solely by the damping constant of the circuit and is 

 independent of the number of symbols available at each selection. 

 It is, of course, true that the larger this number the more susceptible 

 will the system be to the effects of external interference. 



Probably the practical system which most nearly approaches this 

 idealized one is the non-loaded submarine telegraph cable when 

 operated at such low speeds that its inductance may be neglected. 

 It is of considerable historical interest to note that Lord Kelvin's 



