beneath continents and oceans compared. 113 



uniform thickness and density. This would lead us to think 

 that the stable condition must at some time have been forcibly 

 disturbed, as it would have been according to my hypothesis that 

 the oceanic areas were produced by the disruption of a portion of 

 the earth's crust, which flew off to make the moon*. But this is 

 a digression. 



Let us now suppose that the crust of the earth on the land 

 side consists of two layers of thicknesses c x and c 2 , and densities 

 0! and <p 2 , and that beneath them there is a substratum of 

 unknown depth and of density a. 



On the side of the ocean let 8 be the depth of the water at any 

 place, /x its density, and suppose the solid crust at that place to 

 consist of two layers of thicknesses ki and k 2 , and densities p x and 

 p 2 , and suppose the density of the substratum there to be a , and 

 let us take into consideration the state of affairs down to a depth d 

 measured from the surface. 



fcaPa i c 2#! 



5 n 















< 





a' 





a 



This is a generalization ; for when considered throughout its 

 whole thickness at any place, the crust must be either of uniform 

 mean density, or else it must be on the average more dense in 

 the upper than in the lower portion, or vice versa, and the upper 

 or lower portion may be the thicker or thinner of the two. It 

 will appear that our formulae enable us to discover what the 

 relations as to density and thickness are. 



Then if % m (r$) refers to the ocean side, and 1 p (r't') to the land 

 side, and if this arrangement of thicknesses and densities approxi- 

 mately represents the case of nature, they must satisfy the equations 

 on p. 110, viz. 



'S tm (rt) = l p (T't'), 



&c. = &c. 



Taking account of the overlapping of the t's, it will be seen 

 that on the side of the ocean 



O"' = T l I Pi = Ti + To, pi = T 1 + To + T 3 , }X = Ti + To + T 3 + T 4 . 



Also ti = d, t a = B + k 1 + k s , t 3 = 8 + ki, t 4 = 8. 



Hence r i = fi—p u T 3 = p l — p. 2 , T i = p 2 —<r', Ti = <t', 

 and similarly on the side of the land. 



* Nature, Vol. xxv. p. 243. 1882. 



