MAGNETIC SURVEY OF JAPAN FOR THE EPOCH 1895.0. 151 

 P 



/9=co.s-'— , tlie nodal circle of the vertical force. 

 r 



R< r <co 



always changing sign at those points. The maximum and 

 minimum are given by roots of the cubic equation 



co.^^ + (2i,--|_)cos^^-(4.f(Ry)co.s^ + (4A_^)=0. (18) 



■ When 0<r<R 



there is only one possible value of 6 which gives maximum value 

 of the variation, the angle lying between and ~^. 



When R<r<a) 



there are two possible values of 6 ; the smaller angle gives the 

 maximum and the larger minimum ; the value are and -n: when 

 r = J{, and tends to ^ and ' for large values of r. 



Wlien the depth is small, neglecting the curvature and put- 

 ting D for the depth as before, the second of (3) becomes 



= TTTT— sin c cosV (19) 



which is maximum at c = tg'''-^ or at a distance of half the 

 depth from the epicenter measured on the surface. 



In words, suppose the source is placed at the center of the 

 sphere, there is no horizontal force and no variation all over the 

 surface; displace it slightly, the horizontal force decreases upward 

 at every point of the sphere except at the epicenter and antipode 

 where it vanishes, and greatest in the vicinity of the great circle 

 midway between these points. As the source recedes fui'ther 

 from there, the circle of the greatest upward decrease shifts in 



