TRANSMISSION OF INFORMATION 



543 



tion. Obviously over any given time interval the magnitude may 

 vary in accordance with an infinite number of such functions. This 

 would mean an infinite number of possible secondary symbols, and 

 hence an infinite amount of information. In practice, however, the 

 information contained is finite for the reason that the sender is unable 

 to control the form of the function with complete accuracy, and any 

 distortion of its form tends to cause it to be confused with some 

 other function. 



TIME 



Fig. 3 



A continuous curve may be thought of as the limit approached by 

 a curve made up of successive steps, as shown in Fig. 3, when the 

 interval between the steps is made infinitesimal. An imperfectly 

 defined curve may then be thought of as one in which the interval 

 between the steps is finite. The steps then represent primary selec- 

 tions. The number of selections in a finite time is finite. Also the 

 change made at each step is to be thought of as limited to one of a 

 finite number of values. This means that the number of available 

 symbols is kept finite. If this were not the case, the curve would be 

 defined with complete exactness at each of the steps, which would 

 mean that an observation made at any one step would offer the 

 possibility of distinguishing among an infinite number of possible 

 values. The following illustration may serve to bring out the relation 

 between the discrete selections and the corresponding continuous 

 curve. We may think of a bicycle equipped with a peculiar type of 

 steering device which permits the rider to set the front wheel in only 

 a limited number of fixed positions. On such a machine he attempts 

 to ride in such a manner that the front wheel shall follow an irregularly 



