40 Art. 7.— K. Terazawa : 



D = - -V--^ // 



The values of (zz)o and Du might give the condition of rupture of 

 the surface. 



§32. Now we shall apply this solution to the geophysical 

 phenomena mentioned in the introduction. Dr. C. Chree"^ 

 followed by Prof. Nagaoka^* finds a formula. l;>y using the solution 

 obtained by Boussinesq, to calculate the deviation of the direction 

 of gravity due to the attraction of a material loading on tlie 

 surface of the earth. The same result will be attained of course 

 from our solution. The expression of the vertical displacement 

 at a point on the surface 



ivX = ./^^ fliJcrjdJ^ l'piy)J,hr')r'dr' 



where pO'') is the pressure produced by the material load, can be 

 transformed into 



(y\ = —- . ' / — — r Circle 



I ^ ' i - 



bv making use of Nei'maxn's addition theorem for the Bessel 

 function, where R' stands fur 



B' = ^y--2yy' CO:, ç+r'-) 



On the other hand, if we denote the attraction constant by r, and 

 gravity, prior to the application of the load, l)y (/, then the 

 gravitation-potential at a point on the surface due to the load can 

 be expsessed by 



a .' J R' 



q •' •' R 



provided the height of the material load is negligibly small 

 compared with the distance of the point under consideration from 



1) Phil. Majj. (V) vol. iS (1897) p. 177. 



2) Tokyo, Sug. But. Kizi (VI) (1912) p. 20S. 



