160 A. TANAKADATE. 



confirmed by the large variations of tlie west component which 

 has its maximum value on that curve : two points of this curve, 

 if accurately known, are sufficient to assign the line through the 

 image and the earth center by (10). 



Again -^ changes sign in the North Japan between I 

 and II, so that one of the circles of no vertical variation of the 

 vertical force passes also through the country. This assigns at 

 once the maximum limit to the depth of the image, 0.1835 

 times earth radius by (lö). 



The vertical variations of the rectangular components of the 

 horizontal force being resolved in the same ratio as the forces 

 themselves, the plane of the great circle whose azimuth is deter- 

 mined by considering these variations as vectors, will pass through 

 the image provided there is such in existence ; and since their 

 signs are contrary to those of the forces when the image is be- 

 low, and the same within the nodal circle of no vertical force 

 when it is above ; we can determine the sense of the force and 

 hence the sign of m when the position of the image is known. 

 From the first and second rows of differences in Table XXI 

 those azimuths are 



I. II. III. IV. V. 



9G.°3 96.°3 96.°3 8.5.°3 83.°4 



measured in the direction north-west-south-east. 



Great circles drawn in those azimuths through each of the 

 points, give twenty ])oints of intersections, ten of which lie in 

 Asia and the other ten about South America. In order to save 

 arithmetical labour for the rough work, those circles were 

 layed on a large terrestrial globe of 30 inches diameter which 

 was carefully covered all over with flexible Japanese tracing 



