96 



Professor J. A. Fleming 



[March 27, 



Bending end. This last fraction is the recii^rocal of the base of the 

 Napierian logarithms. Hence, if the attenuation constant is O'l, 

 then in lo miles run along the cable the wave amplitude will be 

 reduced to about one-third of that at the sending end. The wave 

 length constant is a number the reciprocal of which multipKed bj 

 6 • 28 gives the wave length or distance from crest to crest of the 

 waves." The wave velocity is the product of the wave length and 

 frequency. These numbers can all be calculated from the four 

 primary constants of the cable. 



If we take any cal)le, such as the cable used in telephony, as a 

 standard of comparison, which has a resistance of 88 ohms, an 

 inductance of 1 millihenry, and a capacity of 0*05 of a microfarad, 

 all per loop mile (that is, a mile nm of lead and return), and if we 

 calculate the above quantities for it for various frequencies, we can 

 set them out as in Table I. You will see that as the frequency 

 increases, the attenuation and the wave velocity both increase, whilst 

 the wave length diminishes. 



This shows that there is no particular velocity of electricity 

 along a wire. It depends upon the wire and upon the speed of the 

 oscillations. 



The average frequency which we have to consider in telephony 

 is about 800, although some oscillations, such as those of the higher 

 harmonics, ai'e quicker, and some fundamental tones are lower. This 

 frequency has, however, been selected as the mean or standard 

 frequency for telephonic speech. It corresponds nearly to a note on 

 the musical scale represented by the upper G in the treble clef. 



Table I. — Attenuation Constants, Wave Length, and Wave Velocities 

 FOR Various Frequencies along a Standard Telephone Cable 

 HAVING Resistance of 88 Ohms, Inductance 1 Millihenry, and 

 Capacity op 0-05 Microfarad, all per Loop Mile. 



For this frequency (800) and for the standard cable, the attenua- 

 tion constant is about 0"1, which means that in 10 miles the wave 

 amplitude has decreased to 0-3G7 of its value at the sending end. 

 The wave length is 58*1 miles and wave velocity 46,480 miles per 



