626 BELL SYSTEM TECHNICAL JOURNAL 



Other words if Six) is the classical Fourier Series representing f{x) 

 in the interval < x < a then S{x) = fix — no) where n takes on 

 the values w = 0, ± 1, ± 2, • • • corresponding to the various intervals 

 na < X < in -\- \)a. 



The author has shown how a generalized Fourier Series Siix) may 

 be obtained representing a function in the intervals wa < :x; < (w + l)a 



as follows: 



Sxix) = b"f{x - na), 



where n takes on the values w = 0, ± 1, ± 2, • • •, and b is any real 

 constant. 



In this paper is described a still more general Fourier Series Snix) 

 representing a function in the intervals wo < x < (w + l)tt as fol- 

 lows : 



Snix) = [6"/(x — na)~\n^, 



where corresponding to the above intervals w takes on the values 

 w = 0, ± 1, ± 2, • • •, & is any real constant, and the subponent 

 notation n-^ denotes the rotation of the plane of the curve about the 

 X axis through an angle n-^ with the XY plane. 



Current Propagation in Electric Railway Propulsion Systems. John 

 RiORDAN.8 This paper presents a systematic method of attack, 

 based on the superposition theorem on the problems of electric railway 

 propulsion systems arising from the presence of tracks and other leaky 

 conductors. The treatment is limited to systems in which the tracks 

 and other leaky conductors may be represented with sufficient accuracy 

 by a single conductor, but includes series and shunt discontinuities in 

 this equivalent conductor. The general equations of current propa- 

 gation in a single conductor in the presence of a conductor carrying 

 a fixed current are taken in a form similar to the transmission equations 

 ordinarily employed for power transmission and telephone lines, appar- 

 ently due to H. Pleijel, Report to Swedish Royal Railway Adminis- 

 tration, 1919. Though these equations are not rigorous they have 

 been found to agree with experimental observations within engineering 

 accuracy. 



The starting point of the treatment is the development of the 

 properties of a basic circuit consisting of a straight conductor of finite 

 length connected at its terminals to a parallel leaky conductor or track 

 which is continuous and infinite. The circuit involves the greatest 

 degree of continuity in the track, subject to the connection of other 



8 Presented at the A.I.E.E. Summer Convention, Cleveland, Ohio, June 20-24, 

 1932. To be published in AJ.E.E. Transactions. 



