MAGNETIC SURVEY OF JAPAN FOR THE EPOCH 1895.0. 145 



the source approaches the surface from the center, and back 

 again from to -^ as it recedes from there to infinite distance. 

 The reciprocal relation of inside and outside positions of the 

 source might well be expected, considering it as a kind of an 

 unbalanced electric image. 



When the depth is small we may neglect the curvature of 

 the surface near the point. Putting D = R — r for the depth, (1) 

 becomes ry,_ m 3^ ^ 



TT, m^ . ., I 



xl = -TyT sm Ç cos-c I 



The former is maximum at the epicenter and the latter at 

 c = tg-'— ^ which is the result given in Thomson and Tait's Natural 

 Philosophy § 786. 



The north and west components are to be obtained by ex- 

 pressing d in terms of the longitnde and latitude, and multiply- 

 ing the result by cosine and sine of the azimuth, thus 



X' = 



Y' = 



—mr< cos (p sin ^0 — sin ip cos ç?,, cos (-^ — ^0) [ 

 ]R"+r-— 2yR[sin^sin^o + cos^cos^,jCos(i^ — i^o)][^ 



wircos^osin(/^>— ^) 

 j R- + T" — 2rR[sin ip sin ^„ 4- cos ^ cos (p^^ cos(>i — 4)] ( ^ 



K9) 



where /« and ^0 are the longitude and latitude of the epi- or sub- 

 center, or pericenter which we substitute for the two words. 

 The North Component X' vanishes along the nodal line 

 cos(>^-^)tg^ = tg^o 

 It is the locus of points where the circles of equal horizontal 

 force touch the meridian arcs, and consists of a pair of spherical 

 ellipses, one through the pericenter and its nearest geodetic 



