THE STRENGTH OF THE EARTH'S CRUST 



543 



a formula as follows: Let there be two masses M and M„ with 

 centers at depths D and D„ ; below a horizontal plane. For points on 

 the plane similarly situated with respect to their respective centers 

 let the components of the deflection force be Fy and Fx for the one, 

 Fyn and Fxn for the other. Then 



Fx„Dn^ 



"" FyD' ' 



also M„-- 



FxD' 



-M 



The results of the application of this formula are shown in the 

 last column of Table XXVIII. They have been carried out to two 

 significant figures, but the second is not to be regarded as accurate. 



TABLE XXVIII 



Interpretation or Residuals in Terms of Equivalent Spheres 



even if the original data are accurate to the second place. This is 

 because the error of the square of a quantity is approximately twice 

 as great as the original error, and for values EE' above i . oD the 

 error in even the first power of D is appreciably greater than the 

 error in the measured quantities. This of course is a consideration 

 of the error in the determination of the depth and mass of the 

 hypothetical spheres, not a consideration of the errors in the deflec- 

 tions themselves, nor related to the fact that the masses are in 

 reality not spheres. 



It has been shown previously that the interpretation of the 

 outstanding masses in terms of spheres will give depths too great 

 unless the real masses have their greatest dimension vertical. For 

 the same reasons the hypothetical spheres will be of greater mass 



