Propagation of Electric Currents in Telephone Telegraph Conductors
Propagation of Electric Currents in Telephone Telegraph Conductors
John Ambrose Fleming
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= A Cos (2w-2w+l) |^Cos (k. T-4). The current at the with coil is also (V). =^. Cos (2^-2^+1) ~ Cos (k t t-4>)' If these coils are one wave length apart, then (i m ) 8 = (*, ni ) s, and mi ??i is the number of coils covered by one wave. But then we must have Hence mi n = = /> and this last expression is there- o fore the number of coils covered by one wave length of the sth harmonic. In the second case it can be shown in a similar manner that A 4- V . S7r 1 2S + 1 7T 1 2?T Accordingly instead o...f and ~~ we can wn ^ e * If we consider 27r to represent the wave length and y the angle which is the same fraction of 2?? that the distance d between two consecutive coils is of a wave length, then 2-Tr : y = \ : d, and therefore ZTT/V S = y. 1 TT Sir - _.. 1 . STT Hence 3 7 == - = ^ and Sin g y = Sin ^. Now on comparing equation (40) for the frequency of free oscillations in a uniform cable with equation (56), which gives the same quantity for the non-uniform loaded cable, it is clear that if the coils are so close that o 7 is practically the same as Sin -& y, then the loaded line has free vibrations like the equivalent equally loaded cable.
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