Excerpt from The Application of Hyperbolic Functions to Electrical Engineering Problems
Hyperbolic functions have numerous, well recognized uses in applied science, particularly in the theory of charts (Mercator's projection), and in mechanics (strains). But it is only within recent years that their applications to electrical engineering have become evident. Wherever a line, or series of lines, of uniform linear constants is met with, an immediate field of usefulness for hyperbolic functions presents itself, particularly in high-frequency alternating-current lines.
The following pages are intended to cover the scope and purport of five lectures given for the University of London, at The Institution of Electrical Engineers, Victoria Embankment, by kind permission of the Council. May 29 to June 2, 1911, bearing the same title as this book.
The central ideas around which those lectures, and this presentation, have been framed are -
(1) That the engineering quantitative theories of continuous-currents and of alternating-currents are essentially one and the same; all continuous-current formulas for voltage, current, resistance, power and energy being applicable to alternating-current circuits, when complex numbers are substituted for real numbers. Thus there appears to be only one continuous-current formula in this book (277) which is uninterpretable vectorially in alternating-current terms; namely, as shown in Appendix J, that which deals with the mechanical forces developed in a telegraph receiving instrument, such forces being essentially "real" and not complex quantities.
(2) That there is a proper analogy between circular and hyperbolic trigonometry, which permits of the extension of the notion of an "angle" from the circular to the hyperbolic sector.
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