406 BELL SYSTEM TECHNICAL JOURNAL 



ciency of the transmission of the higii freciuoncies involved in carrier 

 and radio circuits, such a unit is parlicuhirly desirable. 



3. Based on Power Ratio. This is desirable because the power 

 ratio is the real measure of transmission efficiency. As pointed out 

 above, the current ratio can be used only when it is equal to the square 

 root of the power ratio. Having the unit based on a power ratio 

 does not, of course, require that measurements or computations l)e 

 made on a power basis. 



In considering the conversions between sound and electrical energy, it 

 is obviously advantageous to ha\'e a unit based directly on a power ratio. 



4. Based on Some Simple Relation. This is desirable in connection 

 with the matter of getting a unit which may be widely used and may 

 find applications in several fields. 



5. Approximately Equal in Effect on Volume to a "Mile of Standard 

 Cable." One reason for this is the practical one of avoiding material 

 changes in the conceptions which have been built up regarding the 

 magnitude of such things as transmission service standards. Also, the 

 sound power changes which can be detected by an ear are of the 

 order of that corresponding to a mile of standard cable. In measuring 

 telephone lines and apparatus with single-frequency currents, it has 

 been found that an accuracy of about one-tenth of a mile can be 

 obtained readily and is sufficient practically. 



6. Convenient for Computations. This refers to the matter of chang- 

 ing from computed or measured current or power ratios to trans- 

 mission units or \ice versa. 



Properties of the Transmission Unit 



A consideration of the above qualifications and of the various 

 units suggested, led to the adoption of the power ratio of lO"'^ as the 

 most suitable ratio on which to base the unit of transmission effi- 

 ciency. The transmission unit is logarithmic, distortionless, is based 

 on a power ratio and its relation to that ratio is a simple one. Its 

 effect on the transmission of telephonic power corresponding to speech 

 sounds is about 6 per cent less than that of one mile of standard cable. 

 Regarding its use in computations, it has the advantage that the 

 number of units corresponding to any power ratio, or current ratio, 

 can be determined from a table of common logarithms. 



For a power ratio of 2, the logarithm is 0.301 and the corresjionding 

 number of units is, therefore, this logarithm multiplied by 10, which 

 is 3.01 T U. F"or a power ratio of 0.5, the logarithm is 9.099 — 10 = 

 — 0.301 and the number of units is —3.01 T U. A power ratio of 2 



