120 BELL SYSTEM TECHNICAL JOURNAL 



formula, is given in the Appendix. ^ In order to express the radio 

 transmission loss in some general manner which will be comparable 

 to the expression of wire transmission loss, these conditions have been 

 taken for the radio case: 



(1) That we will use as the measure of the transmission loss the 

 ratio of the square root of the power radiated from the sending 

 antenna to the square root of the power delivered in the re- 

 ceiving antenna. This is, of course, the same criterion as is 

 used for wire transmission. 



(2) The radiation resistance of the two antennas, sending and 

 receiving, are made equal, analogous to the equality of line 

 impedance at the two ends of the wire system. 



(3) Also the internal antenna resistance, which corresponds to 

 the terminating impedance in the wire case, is made equal to 

 the radiation resistance for both ends. This is the condition 

 of maximum power transfer between the " line " and the 

 terminal. 



These assumptions set up the two cases, radio and wire, on a com- 

 parable basis and facilitate a comparison of them. They are favor- 

 able to radio in that they do not take account of practical limitations 

 which obtain in antennas. The radio curves should be read, there- 

 fore, as giving the minimum possible losses for daylight transmission 

 over water. 



These curves show the manner in which the transmission loss 

 varies with distance, for various frequencies, for both radio and wire. 

 The ordinates are plotted in terms of the logarithm of the ratio of the 

 sent to the received currents, or voltages, in circuits of equal im- 

 pedances. In so doing we are plotting the losses on the straight 

 attenuation basis upon which they are usually plotted in the wire 

 art; that is, the ordinates represent the exponent («/) of the wire 

 attenuation law, and may be directly interpreted in terms of miles 

 of standard cable^ by multiplying by 21. approximately. The ad- 

 vantage of dealing with the exponent rather than the current ratio 



* Measurements on ship-shore transmission made since the above was written, 

 indicate that the Austin-Cohen law holds quite well for frequencies as high as about 

 1,000,000 cycles. 



'For the mile of standard cable the attenuation a (at 800 cycles) equals 0.109. 

 Therefore the equation for current ratio, in terms of miles of standard cable, becomes 



7, oU 0.109/ 



- ■'* 

 from which 



I = 



1 , ^1 Olio, A 



0.109 



log -^ = 21.13 log.o Y- 



