96 Mr. J. Brill on "Densities in the Earth's Crust." 



and 



Similarly we can obtain expressions for the remaining terms. 

 Now 



f27rf+l f+l 



if n be a positive integer. Hence that portion contributed 

 to the value of gravity by the crust, which does not depend 

 on the position of the point P, will be 47raC r Besides this 

 there will be a minute residual effect, the most important 

 term in whose expression will be 



where 



("277 p+1 



a i I uv djui d<p y 



i 



and 



We cannot evaluate this term until we know the manner 

 in which u depends upon /j, and cj>. As //- and (/> vary the 

 quantity u will experience discontinuities in its variation, but 

 it is doubtful if anything of the nature of an abrupt discon- 

 tinuity would arise. If such discontinuities arise they must 

 be rare. Of course at the seaboard there is an abrupt variation 

 in the density of the topmost layer, but the depth of the sea 

 is at first quite small as regards our problem, and afterwards 

 increases with a fair approximation to continuity. 



We have supposed m layers to exist, but this is to be taken 

 as the maximum number. There may be less than m in 

 certain portions of the crust, and this may be provided for by- 

 considering certain pairs of consecutive &'s to be equal 

 throughout the said portions. 



The equations introduced above as assumptions are prac- 

 tically the same as those discussed by Mr. Fisher. It is 

 evident that we cannot introduce more than a certain number 

 of these assumptions without making the crust to consist of 

 uniform concentric shells. But, working on the assumption 

 that this is not the case, we find that we have to stay our 

 approximation at a still earlier point than this consideration 



