TRANSMISSION OF INFORMATION ' 557 



Modulation may, of course, be necessary to bring the message-range 

 to the proper part of the frequency scale. The time required for the 

 reproduction of a message involving a given number of selections 

 varies inversely as the velocity of the tape in reproduction, and 

 therefore also inversely as the frequency-range required by the repro- 

 duced sequence. Thus the product of frequency-range by time for 

 the reproduced message, which is also the required product for the 

 line, is independent of the rate of reproduction, and depends only on 

 the information content of the message in its original form. 



In case the available line range calls for reproduction at a consider- 

 ably increased speed a single operator cannot conveniently keep the 

 sending apparatus supplied with tape. Multiplex operation may 

 then be employed in which the line is used by the various operators 

 in rotation. It is interesting to note that this distributor type of 

 multiplex utilizes the frequency-range of the line as efficiently as would 

 a single printing telegraph channel using the same dotting speed, 

 and more efficiently than does the carrier multiplex method. By the 

 distributor method each operator utilizes the full frequency-range of 

 the line during the time allotted to him and there is no time wasted 

 in separating the channels from each other. In the carrier multiplex, 

 on the other hand, while each operator uses the line for the full time 

 it is available, a part of the frequency-range is wasted in separating 

 the channels because of the departure of physical filters from the ideal. 

 Also both side-bands are generally transmitted in telegraphy, in 

 which case a still greater line- frequency-range is required for the 

 carrier method. 



If the message is produced originally as a continuous time function, 

 as in speech, the same method may be used by substituting for the 

 tape a phonographic record. That here also the required line-fre- 

 quency-range varies directly as the speed of reproduction and inversely 

 as the time of reproduction is obvious when we consider an imperfectly 

 defined wave as equivalent to a succession of finite steps or a perfectly 

 defined wave as a succession of infinitesimal steps. From the steady 

 state viewpoint, all of the component frequencies are altered in the 

 ratio of the reproducing and recording velocities, and hence the range 

 which they occupy is altered in the same ratio. 



Thus we see that for all forms of communication which are carried 

 on by means of magnitude-time functions an upper limit to the amount 

 of information which may be transmitted is set by the sum for the 

 various available lines of the product of the line-frequency-range of 

 each by the time during which it is available for use. 



