THE STRENGTH OF THE EARTH'S CRUST 545 



At the distance of 47 km. the anomaly would be from 0.148 to 

 0.157 dyne, five times the observed value of 0.031. Clearly then 

 the initial interpretation as a sphere, although it satisfies the deflec- 

 tion residuals of the line of traverse, is far from the truth. The 

 mass must have horizontal dimensions much greater than the 

 vertical. Assume for trial that the mass has the form of a vertical 

 cylinder with the same mass and depth to center as the sphere, 

 but of a proportion of height to breadth which shall satisfy approxi- 

 mately the gravity anomaly. The result is shown in the third line 

 of Table XXIX. The gravity anomaly of 0.035 ^-t the epicenter 

 would correspond in a cylinder of these proportions to a value only 

 slightly less at 47 km. But the radius of the cylinder, 200 km., is 

 now far too great. Other cylinders of similar form will, however, 

 give the same anomaly at the epicenter if the depth and dimensions 

 are all divided by any number, n, and the density multiplied by the 

 same number. This gives a series of similar cylinders in which the 

 density varies inversely with the dimensions. Of such a series 

 that shown in the fourth hne, obtained by giving n a value of 2, 

 comes fairly close to satisfying all the requirements. The exact 

 degree of adjustment which would be needed to satisfy both the 

 gravity anomaly at 47 km. and the deflections on the line of traverse 

 has not been calculated. If this were done and the dimensions 

 adjusted accordingly, it would complete a second approximation to 

 the real form and mass of No. 2. Such an extended treatment of 

 the subject would, however, be beyond the immediate purpo.ses 

 of this article and beyond the limits of space which it should occupy. 

 The data also are at present hardly of a sort which would justify 

 further computations. It should be emphasized, however, that 

 such a complete investigation is not difficult and would require 

 but little further data, properly chosen, to check the conclusions. 



In the first approximation, the mass was assumed to have a uni- 

 form distribution about a center, giving a sphere. In the second 

 approximation, the vertical axis is assumed to be different from the 

 horizontal axes, but the latter being kept aHke, the horizontal 

 section would still be a circle. A single observation of the gravity 

 anomaly near the epicenter suffices to give this second approxima- 

 tion. The third approximation would be to consider the three 



