inO A. TANAKADATE. 



current flowino- in tlio atniospliero to 1)0 negligibly small. It 

 is free from any special assumption as to the distribution of 

 magnetism either inside or outside the earth ; local disturbances 

 being eliminated by taking sufficient number of well distril)uted 

 stations. 



Taking the rectangular co-ordinates x y z reckoned positive 

 towards noi-th, west and zenith as l)efore, we have the well known 

 equations 



, OX ÖZ 



4- v=- 



4r m ■■ 



'dx ()y 



1 , ÖX , 9Y OZ 



and 4-0= — + — + -a^ 



()x ny oz 



where X, Y, Z, are components of magnetic force, and 11 v w 

 those of electric current, and /' the density of free magnetism. 



We have no precise means of ascertaining the horizontal 

 components of current ft. and v ; but from the distributions of 

 X and Y, the vertical component w has ah-eady been computed, 

 the extreme value found being 0.43 Ampere per square kilometer. 

 Hence supposing tc and v to l)e of the same order of magnitude, 

 the error committed by neglecting those will be of the order 

 4- X 0.043 X 10-"' X 10"' = 0.4 X 10-''" hy per kilometer which is only 

 a little greater than what the probable errors of those coefficients 

 will produce. The value of 4.-'> arising from the heterogeneity of 

 the atmospheric air is utterly insignificant being only 6.4 x lO^V 

 per kilometer in middle part of Japan, taking the susceptibility 

 of the air to be 3.2x10-' g-z/is.4 kno,,,.^ Hence putting u=v = o 

 and ,0=0 we have 



