TRANSMISSION OF INFORMATION 561 



horizontal dimension is increased and the vertical dimension left 

 unchanged. Let the scanning strips run in a horizontal direction. 

 If we consider the magnitude-distance function representing the 

 variation along any horizontal strip, the effect of the enlargement is 

 to increase the wave-length of each steady state component in the 

 ratio of the increase in linear dimension. The wave number of each 

 component is therefore decreased in this ratio, and so the wave- 

 number-range is also decreased in the same ratio. The product of 

 the wave-number-range by the length of the strip remains constant, 

 as does also the sum of the products for all of the strips, that is, for 

 the entire picture. The second step consists in increasing the vertical 

 dimensions with the horizontal dimensions fixed. By considering the 

 scanning strips as running vertically in this case it follows at once 

 that the product of wave-number-range by distance remains constant 

 during this operation also. 



Since the information transmitted is measured by the product of 

 frequency-range by time when it is in electrical form and by the 

 product of wave-number-range by distance when it is in graphic form, 

 we should expect that when a record such as a picture or phonographic 

 record is converted into an electric current, or vice versa, the corre- 

 sponding products for the two should be equal regardless of the velocity 

 of reproduction. That this is true may be easily shown. Let v be 

 the velocity with which the recorder or reproducer is moved relative 

 to the record. Let the wave-number-range of the record extend 

 between the limits Wi and W2. If we consider any one component of 

 the distance function which has a wave-length X, the time required 

 for the reproducer to traverse a complete cycle is X/v, or 1/vw. This 

 is the period of the resulting component of the time wave, so the 

 frequency / of the latter is the reciprocal of this, or vw. The fre- 

 quency-range is therefore given by 



J2 — h = ^'(^2 - wi). (24) 



If D is the length of the record, then the time required to reproduce 

 it is 



r = - , (25) 



from which 



(/2 -Ii)T = (W2 -w,)D. (26) 



This shows that the two products are numerically equal regardless 

 of the velocity. 



