122 A. TAXAKADATE. 



§ 11. Vertical Current. 



It is usual in magnetic surveys to calculate the amount of 

 the vertical current of electricity by taking the line integral of 

 the magnetic force round the periphery of the country. The 

 same was tried here in the circuit indicated in Fig. 4 by taking 

 the integral along the co-oi'dinate lines thus : — 



IÜ 



which may be put for numerical calculation 



«y = ^^^(Y„ cos w,-Y, cos ^,)j;.-^(X„-X,)J^ 



where the suffixes n, 5, u\ e, denote the values of those quanti- 

 ties on the north, south, west and east side of the circuit, and 

 R the mean radius of the earth ; the positive sense of the co- 

 ordinates X, y, z are north, west and up respectively.* Per- 

 forming the operations above indicated we have 



R 



4 



^^(Y,, cos (p,-Y, cos f ,)J/= 0.03973 x length of 1° 



4^J(X.-X,)J^ 



= 0.04146 X 



whence w= -0.00173 x -^- "''' ^ ^^' x .0174.") 



4;r 



= — l.i31 c.g.s. el. mag. units. 



The area of the circuit is '3.701x10' sq. kilom. hence the mean 

 current density is 



-1.331x10 



~~, .-7^ =-0.027 Ampere per s<j. 



o./OlxlO' 



kilom. 



minus sign indicating the downward direction. 



* This is the same as tliat adopted by Prof. Schuster; the sense of y and z are con- 

 trary to that used bv Gauss and other continental writers. 



