Mr. 0. Heaviside on a Test for TelegrapJi Lines. 437 

 whence 



1 Y • • C 1 ) 



J 



where a and 6 are undetermined constants. 



If now the potential and current at A are v 1 and y 1? and the 



same at B are v 2 and y 2 , then it may easily be shown from 



equations (I) that 



v 2 — ?j 2 

 ki=. ' 2 (2) 



Since the length of the line does not appear in (2), the rela- 

 tion therein expressed applies to any two points of the line. 

 The reason is that the product of the conduction and insulation 

 resistances is the same for any length, the one varying directly 

 and the other inversely as the length. Now the insulation of 

 land-lines is in this country very variable, while the real con- 

 duction resistance (i. e. its resistance if it w T ere perfectly insu- 

 lated) is nearly constant. It follows that (2) may be used for 

 determining i, considering k as constant. In (2), 



Bj. and R 2 being interposed resistances are, of course, known; 

 so that three quantities have to be observed, viz. E, y 1? and 

 y 2 ; or equivalent information must be obtained. To make 

 the test in its simplest form, let the resistances R : and E 2 be 

 small compared with the line resistance. . Also, let equally 

 sensitive tangent-galvanometers be used, and let n t and n 2 be 

 the deflections corresponding to y 1 and y 2 , and n 3 the deflec- 

 tion E gives through 1000 ohms. Then (2) becomes 



H=-Jl_ 2 xl0 6 3 (4) 



n\ — n\ 



where k and i are both in ohms ; or if k is in ohms and i in 

 megohms, the 10 6 must be cancelled. 



If Ri and R 2 are taken into account, then instead of (4) we 

 have 



^ (lO^-R^) 2 -^) 2 



"^ — 2 2 J 



n \ — n 2 



and if the galvanometers are not equally sensitive, the deflec- 

 tion n 2 must be multiplied by the ratio of the sensitiveness of 

 the galvanometer at B to that at A. 



Using formula (4), the test can be easily made, though it is 



