THE STRENGTH OF THE EARTH'S CRUST 305 



Then tR^H= the volume, a constant. To find the ratios of H 

 to R which give maximum attraction for unit mass 



Let R^H= I and solve for various values of R the equation 



P=^^.r p'+')/^'+- ] 



Several solutions are as follows: 



For ^" = 0. 75, i? = i.i5 

 H=i.oo, R — i .00 

 H = i.5o, R = o.8i 

 H=2.oo, R = o.'ji 

 H = 4.oo, R = o.^o 



F={2irpy) 0.523 

 F=(2Trpy) 0.586 

 F—{2irpy) 0.609 

 F=(2Trpy) 0.586 

 F=(2Trpy) o. 200 



This shows that the gravitative force is a maximum for a cylinder 

 of constant volume and mass in which the depth varies from one- 

 half the diameter to four-thirds the diameter. The force varies 

 but slightly between those limits. The cylinders of columns 3, 5, 

 and 6, of Table XXI, lie within these limits. Thus all the assump- 

 tions thus far made favor the minimization of the negative load 

 which produces the Seattle anomaly. 



Taking the mean density of the outer part of the lithosphere 

 as 2.80 it is seen that the cylinder of column 2, Table XXI, has a 

 density below that of the lightest rock-making minerals and would 

 require the existence of a molten magma or of abnormal pore space 

 to great depth. It may therefore be eliminated as not probable. 

 Cylinders 3, 4, and 5 show densities within the hmits of granite, 

 the lightest of the abyssal igneous rocks. It may be concluded, 

 therefore, that the deficiency of mass, if of approximately cyHndrical 

 form, is equivalent to a negative load of between 5,000 and 10,000 

 feet of rock, extending over a distance of from 50 to 100 km., or 

 a somewhat less local load superposed upon a broad but small 

 regional load of the same sign. The nature of the assumptions 

 has been such that we may conclude with confidence that the Seattle 

 anomaly corresponds to at least 5,000 feet of rock and may reach 

 a considerably higher figure, perhaps 10,000 feet. Furthermore, 

 Hayford's unit mass, extending to the areal limits, 100 feet thick 

 and density 2 . 67, would here produce an anomaly as low as between 

 o.ooio and 0.0020 dyne. 



