TRANSMISSION OF INFORMATION . 545 



which precedes it. However, it is always possible for the sending 

 operator so to make his selections that any one selection is preceded 

 by that sequence which causes the maximum possible interference. 

 Hence every selection must be separated from those preceding it by at 

 least a certain interval which is determined by the worst condition of 

 interference. If longer intervals than this are used, the transmission 

 is unnecessarily retarded. Hence to secure the maximum rate of 

 transmission the selection should be made at a constant rate. It might 

 appear at first sight that the selections could be made at shorter inter- 

 vals near the beginning of the message where there are fewer preceding 

 symbols to cause interference. This assumes, however, that the system 

 has previously been idle. Actually the previous user may have finished 

 his message with that sequence which causes maximum intersymbol 

 interference. 



Relation to Damping Constant 



How the intersymbol interference limits the rate of communication 

 over the system depends upon the properties of the particular system. 

 The relations involved are very complex, and no attempt will be made 

 to obtain a complete or rigorous solution of the problem. We may, 

 however, by treating a very simple case, arrive at an interesting 

 relation. Consider a resistance in series with a capacity. Let one 

 terminal be connected to one terminal of a battery made up of a very 

 large number of cells of negligible internal resistance. Let the other 

 terminal be connected to the battery through a switch. This switch 

 is so arranged that by pressing any one of s keys the circuit terminal 

 may be moved up along the battery by any number of cells from zero 

 to 5 — L Let the sending operator make selections among the 5 keys 

 at regular intervals, and let the receiving operator observe the current 

 through the resistance. The most advantageous time for this observa- 

 tion is at the instant ^ at which the key is pressed, since the current has 

 then its maximum value. The finest distinction to be made by the 

 receiving operator is that between two currents which result from 

 battery changes that differ from each other by one cell. The difference 

 between two such currents is equal to the initial current which flows 

 when one cell is introduced into the circuit. This is 



is-^, (12) 



where E is the electromotive force of one cell and R the resistance of 

 the circuit. 



^ Results identical with those which follow may be obtained if he observes the 

 average current over a period beginning when the key is pressed and lasting not 

 longer than the interval between selections. 



