548 BELL SYSTEM TECHNICAL JOURNAL 



Study of such cables led him to the conclusion that the extent to which 

 the cable limited the dotting speed was given by KR, that is, the 

 product of the total capacity and total resistance. Had he stated 

 his results in terms of permissible speed he would have had the re- 

 ciprocal of this quantity, which corresponds very closely to the 

 damping constant which we arrived at as a measure of the rate of 

 communication. It should be noted, however, that his consideration 

 was limited to a fixed number of symbols, and did not involve the 

 relation here developed between this number and the dotting speed. 



The more complicated systems are similar to the simple case just 

 treated in that the contribution of any one symbol, a, to the inter- 

 ference with any other symbol, b, is determined by the free vibration 

 of the system which results from the change applied to it in the 

 production of symbol a. This free vibration, instead of being expres- 

 sible by a single exponential function as in the case just considered, 

 may be the resultant of a large number of more or less damped oscil- 

 latory components corresponding to the various natural modes of 

 the system. The total interference with any one symbol is the 

 resultant of a series of these complex vibrations, one for each inter- 

 fering symbol. The instantaneous values of the various components 

 of the interference are so dependent upon their phases at the particular 

 instant of observation that it is difficult to draw any general conclusions 

 as to the magnitude of the total interference. It is equally difficult 

 therefore to draw any general conclusions as to the relation between 

 the rate of transmission over a particular circuit and the number of 

 available symbols. 



Relation to Storage of Energy 



Even though for any one system there exists a number of available 

 symbols for which the rate of communication is greater than for any 

 other number, it is still possible to make a generalization with respect 

 to the storage of energy in the system and its effect on the rate of 

 transmission which is of considerable practical importance. 



Each of the natural modes of vibration of a linear system has the 

 general form 



i = Ae~^' cos {wt - e), (21) 



where the natural frequency c<j and damping constant a are character- 

 istic of the system and the amplitude A and phase 6 depend on the 

 conditions of excitation. Wherever the time appears in this expression 

 it is multiplied by either the damping constant a or the frequency oj. 

 Consequently if both a and co be changed, say in the ratio k, the 

 instantaneous value of this mode of vibration in the new system will 



