liLliCTRIC Clh'Cl'ir 'rilliOKY 



63 



I'\)r small \aliK's of r and co' ihcsf iiite.urals can Ix.' nnnicrically 

 e\-aluate(l wilhout great labor. Mechanical devices, such as the 

 Coradi Harmonic Analyzer, are here of great assistance. In fact 

 the Coradi AnaKzer gives these progressixe integrals automatically. 

 It may be said, therefore, that a complete mathematical investiga- 

 tion of the building-up of alternating current and voltage waves 

 on the non-inductixe cable presents no serious difficulties, although 

 the labor of computation is necessarily considerable. One fact makes 

 the complete inxcstigations much less laborious than might be sup- 



iO t-4t/x2RC 



Fig. 7 — Non-inductive cable (G = 0), building-up of alternating current. 



4 

 Applied e.m.f. cos co/; a) = 27r ^-^5^ 

 x-K L 



posed. This is, if the foregoing integrals are calculated for a gi\en 

 value of co', the results apply to all lengths of cable and all actual 

 frequencies w/2ir, such that aco is a constant. Then if we double the 

 length of the cable and quarter the frequency, the integrals are un- 

 affected. 



The solid curve of Fig. 7 shows the building-up of the cable voltage 

 in response to an e.m.f. cos w/, impressed at time / = 0. The fre- 

 quency a)/27r is so chosen that co' = q:w/4 = 27r, and the cur\e is cal- 

 culated from equations (194-b) and (194-e). The dotted curve shows 

 the corresponding steady-state voltage on the cable; that is, the voltage 

 which would exist if the e.m.f. cos wt had been applied at a long time 

 preceding /= \ We observe that, for this frequency, the building-up 

 is effectually accomplished in about one cycle, and that the transient 

 distortion is only appreciable during the first half-cycle. 



