148 A. TANAKADATE. 



at the critical value of t the two circles coincide with that of 

 the maximum variation at 



<^=-|--sin-y-^- =35° 15:9 from the epicenter. (16) 



When the depth of the source is small, neglecting the curva- 

 ture of the surface as before, the first of (3) takes the form 



^^' ''*-(3cos\'-cos\:) (17) 



9s ~ D^ 



D being the depth of the source and c the same as before; this 

 holds either for the source above or below, D and cosç chang- 

 ing sign at the same time. The variation is now maximum at 

 c=tg-^2, and vanishes at c=tg-V2~= 54° 44:i and ~, 



The effect can be described in words as follows (see Fig. 7 

 below) : — Suppose at first the source to be placed at the center of 

 the sphere, the vertical variation of the vertical component arising 

 from it will be uniform all over the surface being ""-tjt- Now 

 displace it along any particular line through the center, the up- 

 ward decrease will be greatest at the epicenter and least at the 

 antipode : as it recedes further from the center, the maximum 

 and minimum will become more and more pronounced, and 

 when the source reaches the critical depth of about 0.21 K, a 

 new set of maximum and minimum will begin to appear at the 

 angular distance of 60°. 9 from the epicenter. After this value 

 is passed there will be two circles on the sphere, on one of 

 which the decrease is less and on the other greater than any 

 values in their neighbourhoods. As the dejith becomes still 

 less, the place of least decrease will be shifted toward the 

 epicenter becoming more and more prominent, and the minimum 

 toward the antipode becoming more and more smooth ; and 



