706 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



'^l. .9 .b .7 .9 .4 



Amplitude. 



Figure 2. - 

 tlie lirst t)-J kil 

 tion-constant o 



.3 .1 



r,2 



60 



68 



56 



64 



62 



50 



48 



46 



44 



42 



40 



38 



36 



34 



32 



28 



26 



24 



22 



20 



18 



16 



14 



12 



10 



.3 .1 .6 .6 .7 .U .» 1. 



2 a 



o 



A a 



ity by (26) may be re- 

 duced, with low frequen- 

 cies, to 10,000 kilometers 

 per second, or less. 



As the electromagnetic 

 wave starting from A at 

 time ^ = runs over the 

 circuit, containing within 

 it both a voltage wave, or 

 electrostatic-flux wave, and 

 a current wave, or magnetic- 

 flux wave, it dwindles or 

 attenuates at the rate of 

 c~" per kilometer ; so that 

 after running Li miles, both 

 the voltage and the current • 

 will have become weakened 

 by the attenuation-coefii- 

 cient £"■^1" ; or 



e^E^-^'" volts (28) 



and 

 i = /(, f-^'"^ amperes (29) 



where a is the attenuation- 

 constant of formula (16). 

 This logarithmic attenua- 

 tion is represented for a 

 particular circuit and fre- 

 quency in Figure 2, but 

 the same curve, A B C D, 

 may be used to represent 

 any circuit and frequency, 

 by suitably changing the 

 scales of co-ordinates. The 

 length of the horizontal axis 

 is determined byai, the real 

 part of the attenuation- 

 constant a in (18), and the 

 wave-length is determined 

 by Oj, the imaginary part. 

 The greater a^, the shorter 

 the length of circuit that 

 will fit the curve AB CD. 



Piirvo of Wiivo attenuation for 



oinctcrs of a circuit of attcuua- 



0.07675 -HiO.7854 per kilometer. 



