ARISING FROM THE LOAD OF NEIGHBOURING OCEANIC TIDES. 
37 
produced by that load. Dr. C. Chree,* and afterwards more completely Prof. H. 
Nagaoka,! find a formula, by using the formula obtained by Boussinesq, to calculate 
the deviation of the direction of gravity due to the attraction of a material load on 
the surface of the earth. 
The same result can be attained, of course, from our solution. The expression for 
the vertical displacement at a point on the surface can be transformed into 
a+ 2 /x r 2n 
2 (AT /x) /u J o 
/(s) 
B/ 
x dx d</> 
by making use of Neumann’s addition theorem for Bessel’s functions, where B/ 
stands for 
B' = x /(r 2 —2rx cos <j> + x 2 ). 
On the other hand, if we denote the attraction constant by y, and gravity, prior to 
the application of the load, by g, then the gravitation-potential at a point on the 
unloaded surface due to the loading can be expressed by 
Vo 
/ j’" I 
J ii . ii g 
/(ft) 
B' 
x dx d<p, 
provided the height of the loading material is negligibly small compared with the 
distance of the point under consideration from any point in the loaded area. 
Comparing the above two expressions, we have 
V„ = ^( M y. 
g AT 2 fx 
Thus the direction of gravity becomes in consequence of the attraction of the 
loading material inclined to the vertical at the angle i/r which will be determined by 
tan ^ = 2 U X + L (|T) 
g AT2 /j. \dr Jo 
(5) 
while its tilting effect is expressed by 
tan , = ( -■ 
3 u. \ 
( 6 ) 
The total effect of the loading will thus be 
c 5 
(p + \fs 
in a close approximation. 
( l I 2?r v (ATm) \ /3 u\ 
\ / AT2 p ) \dr /o’ 
* ‘Phil. Mag.,’ V., 43, p. 177 (1897). 
t Toky6, ‘ Sug. Buts. Kizi,’ VI., p. 208 (1912). 
Gr 
9 
