206 TKEATISE ON ALTEKNATING CURRENTS. 



Also 



di . dt = - Cdx . d V 

 therefore 



dx~ '~M 

 Differentiating (1) we get 



d*V _ di 

 dx z ~ 

 by (2)- 



In the case of an infinitely long cable with an applied P.D. e 

 whose periodic time is T, the solution is 



IT -V-* - 27T 



V = e* . sm - 



where c is the base of Naperian logarithms and x is the distance of 

 P from the point of application of e. 



Thus at every point of the cable the current leads one-eighth 

 of a period before the corresponding P.D. 



For further information on this point we refer the reader to 

 " Alternating Current Phenomena," by Mr. C. P. Steinmetz, and 

 to " Alternating Currents of Electricity," by Mr. T. H. Blakesley. 



APPENDIX F. 



CURRENT IN THE ARMATURE OF AN TI-PHASE EOTARY CONVERTER. 



The current in the armature is, for unit power factor ( 122, 

 Chap. XV.), the difference between the currents on the alternating 

 and continuous current sides respectively. 



The alternating current in a section whose axis makes an 

 angle 9 with that of the mean section is given by 



i'i = /i sin (pt - 0) (1) 



