CHARACTERISTICS OF TOLL TELEPHONE CABLES 325 



direct division of the measured attenuations by the lengths. This is, of 

 course, not strictly accurate, but the errors are very small at these fre- 

 quencies. This is nonloaded cable and frequencies measured were from 10 

 kc. to 200 kc. The values check closely the values shown in the previous 

 figures for frequencies below 100 kc. The 13-gauge figures are the first of 

 such data given herein but the first laboratory measurements on reel-lengths 

 (begun in 1921) included reels of 13-gauge cable, and curves of 13-gauge 

 attenuation and impedance were given in a paper by E. H. Colpitts and 

 O. B. Blackwell. 



Corresponding data on impedance show the values given on Fig. 26. 

 The wavy characteristic of these curves, as mentioned in the section on 

 Impedance above, is caused by small irregularities in the pairs, particularly 

 differences between pairs in successive reel-lengths giving rise to reflection 

 currents at certain frequencies^*. In new construction smoother impedance 

 characteristics can be obtained when it is important to do so, by close con- 

 trol of the product during manufacture, followed by suitable splicing 

 methods. 



ACKNO WLEDGM ENT 



It is practically impossible to name all my associates in the Bell Telephone 

 Laboratories whose work has been drawn upon in assembling these data, 

 but I am especially indebted to Mr. Pierre Mertz and Mr. E. I. Green for 

 their helpful suggestions and continued encouragement. 



APPENDIX 



Wave Propagation over Two Parallel Wires: The Proximxty 

 Effect — Inductance* 



In his paper* on the Proximity Effect, J. R. Carson carried out the detailed 

 computations for the ratio C of the a-c. resistance of two parallel wires to 

 the a-c. resistance of a wire when the return conductor is concentric. He 

 gave a formal expression for the impedance (equation 64 of his paper), viz., 



R + iX = 2Z -h ipL (la) 



This simple equation is complicated by the fact that Z and L are given by 

 two complex expressions involving Bessel functions and the set of harmonic 

 coefficients of the Fourier-Bessel expansion for the axial electric force in 



"E. H. Colpitts and O. B. Blackwell, "Carrier Current Telephony and Telegraphy," 

 Jour. A. I. E. E. XL, Feb. 1921, pp. 205-300. 



* This work, done under the direction of Mr. J. R. Carson, was completed in April, 

 1922. For the general theory of wave propagation on parallel conductors see a paper by 

 Chester Snow, "Alternating Current Distribution in Cylindrical Conductors," Proc. Int. 

 Math. Congress, Toronto (1924) Vol. II, pp. 157-218. 



