0*74 Prof. J. Perry on 



to proceed by any kind of experimental adjustment. He 

 spoke o£ various kinds of contrivance involving combinations 

 of condensers and inductance coils and transformers and even 

 rotary motors and generators ; some in series with the line 

 and others as shunts to earth. 



Exact investigation of what occurs in telephonic and 

 telegraphic signalling in general is quite impossible. Trans- 

 mitting and receiving instruments are various in their 

 complexity ; signals give rise to all sorts of functions of time 

 and space ; cables are not uniform in character, and when 

 they are loaded with inductances, capacities, &c, the ex- 

 pressions employed in exact mathematical analysis are too 

 complex for even the greatest mathematicians to deal with. 



Ordinary people like myself ought to keep on the lower 

 levels and not talk about " waves " in such problems. The 

 fundamental equation for v or c in an ordinary cable is 

 exactly the same as that for the conduction of heat through 

 a solid bounded by parallel plane faces ; in the heat problem 

 nobody dreams of talking about waves. It is easy to convert 

 the differential equations into wave equations, and in the 

 hands of exceptionally clever men the physical ideas involved 

 become important. Even when Mr. Brown's problem is 

 taken up in a mere mathematical way it is troublesome, and 

 I can offer no exact solutions. I have, however, found a 

 simple method of making the kind of calculation required, 

 correct enough for all practical purposes and the method 

 can be applied by non-mathematical persons. I mean that 

 the necessary calculations may be made by any person wdio 

 understands formulae sufficiently well to be able to apply 

 arithmetic to them. The idea came to me at St. Louis when 

 I was listening to a paper by Prof. Kennelly, but I then had 

 no interest in pursuing the subject. Prof. Kennelly has pub- 

 lished many illustrations of the great value of the use of cosh 

 and sink functions ; he gets no more credit now than 

 Columbus did after he showed how- to make the egg stand 

 upright. 



Let me say that much of the arithmetic consists in con- 

 verting such an expression as <x + j3i, where i means V — 1, 

 to the shape r (cos 6 + i sin 0) , which is conveniently written 

 r(#). I need hardly say that if this is raised to the >ith 

 power the result is r n (?i6) where n may be negative or 

 fractional. Also when r{6) operates upon such a function 

 of the time as asmqt it converts it into ar sin (qt + &). 

 Coshr(6) and sinhr(0) will be found tabulated (for (9 = 45°) 

 by Prof. Kennelly. Unfortunately for onr purposes we use 

 only small values of r for which Prof. Kennelly 's tables 



