THE STRENGTH OF THE EARTH'S CRUST 451 



factor gives the force at the second point acting in the direction of 

 the radius of the attracting sphere. This value is laid off as Fr 

 and then resolved into two components Fv and Fh, vertical and 

 parallel respectively to the surface of the earth. The ratio of Fv 

 to Fh is tan d. With increasing distance from the epicenter 6 

 becomes increasingly greater than it would be if the earth's surface 

 were regarded as a plane. Therefore for distances of 5 to 10 

 degrees and more from the epicenter Fv begins to hold an appre- 

 ciably higher ratio over Fh than it would if curvature were neglected. 

 It is seen that Fv = Fh for = 45°. Nearer the epicenter Fv is in 

 excess; at greater distances Fh is the greater. Fv is a maximum 

 for ^ = 90°. Fh is a maximum for = 55° if curvature be neglected. 

 For the earth's curvature and a depth of 319 km. to the center of 

 mass, is a maximum for 53°=^. The point giving this is at a 

 distance from the epicenter of o. 75 the depth. The ratio of maxi- 

 mum Fv divided by maximum Fh is approximately 2.7. In Fig. 

 8C are shown the effects of two spheres of opposite sign but of 

 equal mass. If these two spheres were superposed they would 

 of course completely neutralize each other. Upon moving them 

 horizontally apart to i . 5 times the depth, the maximum value of 

 Fh becomes twice the value for a single sphere. This occurs half- 

 way between them, and the value of Fv for this point is zero. The 

 ratio of maximum Fv over maximum Fh becomes i . i . Two 

 equal masses of like sign would, on the contrary, give a maximum 

 value of Fv and a zero value of Fh at a point halfway between them. 

 These represent the extreme departures from the case of a single 

 spherical disturbing mass. More distant masses show less over- 

 lapping of their fields of force and tend to have their individual 

 effect upon a point between them neutralized by the larger number 

 of masses acting from various directions. The values of Fv are 

 much more under the control of the individual masses than are the 

 values of Fh. 



Returning to the single dominating mass of spherical form as 

 shown in Fig. 8A, let the values of Fv and Fh be represented by 

 ordinates as shown in the figure; then the surface representing 

 the gravity anomaHes, Fv, would be a dome of double curvature, 

 like a craterless volcano; the surface representing the deflection 



