436 Mr. 0. Beaviside on a Test for Telegraph Lines. 



one has been able to discover the true and most active cause 

 of those currents, as well as of the electrical phenomena of 

 the atmosphere in general. In fact there are good grounds 

 for asserting that none of the explanations given, up to the 

 present, of these phenomena will bear the examination of scien- 

 tific criticism. If, till now, no one has seen in these pheno- 

 mena the results of the unipolar induction of the earth, it is, 

 without any doubt, because an idea has been formed of the 

 nature of that induction which did not permit its application 

 to this object. 



There still remain many things that are obscure in the phe- 

 nomena of the aurora borealis and atmospheric electricity. 

 Of these it will be sufficient to indicate the secular periods in 

 the frequency of aurorse boreales. The relation of these pe- 

 riods with the solar spots gives positive evidence of the coope- 

 ration of extratellurian forces. The preceding statement has 

 no claim to be presented as a complete theory of atmospheric 

 electricity and aurorae boreales. My intention has been simply 

 to show that the unipolar induction of the earth plays a most 

 important and significant part in the explanation of those phe- 

 nomena, and that it ought not to be neglected by those physi- 

 cists who hereafter apply themselves to this matter. 



LV. On a Test j or Telegraph Lines. 

 By Oliver Heaviside*. 



THE true conduction and insulation resistances of a uni- 

 form line may be found from the potential and current 

 at the ends, when a constant electromotive force acts at one 

 end. Suppose at one end A of the line there is a battery of 

 electromotive force E, and a galvanometer, the two together 

 of resistance B^ ; also at the other end B of the line a galva- 

 nometer of resistance R 2 > the circuit being completed through 

 the earth. If the potential at distance x from A, where # = 0, 

 is v, the current at the same point <y, the conduction and insu- 

 lation resistance k and i respectively per unit of length, then 



drv 



where 



I 

 and 



_ \ dv 

 7 ~ kdx' 9 



* Communicated bv the Author. 



