TransactionsPublished under the care of the General Secretary and the Treasurer . on Eesistance In the Steady State. HarvardEngineering Journal, May, 1903, pp. 135-168. (12) Edwin J. Houston and A. E. Kennelly: Eesonance In Alternating-Current Lines. Trans. El. Engrs., Vol. 12, pp. 133-169, April, 1895. (13) Albert G. Crehore, , and George 0. Squier, : A Practical Transmitter Using The Sine Wave For CableTelegraphy; And Measurements With Alternating CurrentsUpon An Atlantic Cable. Trans. Am. Inst. El. Engrs.,Vol. 17, May 18, 1900, pp. 385-443. A Practical Telegraphic Transmi
TransactionsPublished under the care of the General Secretary and the Treasurer . on Eesistance In the Steady State. HarvardEngineering Journal, May, 1903, pp. 135-168. (12) Edwin J. Houston and A. E. Kennelly: Eesonance In Alternating-Current Lines. Trans. El. Engrs., Vol. 12, pp. 133-169, April, 1895. (13) Albert G. Crehore, , and George 0. Squier, : A Practical Transmitter Using The Sine Wave For CableTelegraphy; And Measurements With Alternating CurrentsUpon An Atlantic Cable. Trans. Am. Inst. El. Engrs.,Vol. 17, May 18, 1900, pp. 385-443. A Practical Telegraphic Transmitter Using Int. El. Congress at Paris, 1900, Vol. 2, pp. 276-285. (14) M. I. Pupin, : Wave Transmission Over Non-Uniform Cables And LongDistance Air-Lines. Trans. Am. Inst. El. Engrs., Vol. 17,May 19, 1900, pp. 445-513. 9i EENNELLY: SPEED OVER CABLES. APPEXDIX. Table of Hyperbolic Fuxctioxs of Semi-Imagixaryquaxtities. Tables are readily obtainable which supply the hyperbolic func-tions of a real variable x; namely, sinh x; cosh x; tanh xj cosech xj \195. Fig. 13.— Loci of sinh, cosii, taxh, coth and cosech x /45° between THE limits of 0 AXD 10 OF THE RESULT. sech X and coth x. If x be an imaginary qi;antity such as jy;tlien the preceding quantities become respectively J sin x; cos x ; j tan x ; -j cosec x\ sec x and - j cot x. KEXXELLY: SPEED OVER CABLES. 93 The theory of alternating-current transmission on eircnits prac-tically devoid of leakance and indvictance brings into prominencehyperbolic functions of quantities of the type {x-\-jx) ; or havinga real component numericall} equal to the imaginary quantities may be described as semi-imaginary written vectorially, semi-imaginary quantities are of thetype z/45° or z \45°. For convenience in the application of the theory, the author hascomputed the following table of sinh {z /45°) cosh, (s /45°) tanh(3 /4o°), cosech (2 °), pech (s /45°), and coth (z °),
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