260 Rev. O. Fisher—Thickness of Marine Deposits. 
To find the thickness of deposit which, irrespective of expansion, 
would raise the sea-bottom by a given amount. 
(Fie. 1.) 
Let d be the height to which the sea-bottom is raised, k the 
original thickness of the crust, r its density, s the density of the 
liquid substratum, m the density of the sea. Let y be the thickness 
of the deposit, n its density ; 4’=k—=sx the thickness to which the 
original crust is reduced by melting off at the bottom. 
Then we have by the conditions of hydrostatical equilibrium, 
md-+-rk-+s (y+k—x—d—k)=ny+r (k—x) 
whence— 
s—m s—r 
It may be noticed that the original thickness of the crust k does 
not appear in this expression. 
When d is equal to the original depth of the sea, the sea will 
have been filled up, and the deposition must come to an end at that 
place. Let us then find the thickness of deposit which would fill 
up the sea under two conditions. 
First suppose there is no melting off. Then ~=0, and the possible 
thickness of deposit will be, 
s—m 
y d. (1) 
where d is the original depth of the sea. 
Secondly, suppose that there is melting off. Then when d and x 
have both of them attained their greatest values, y will cease to 
increase. It is evident that the greatest value of d will be the 
original depth of the sea. We may conclude that, when the deposit 
and what remains unmelted of the original crust have been reduced 
by melting to the thickness of the original crust, no further melting 
will take place ; and this will correspond to the greatest value of a. 
Then we must have, 
~ s—n 
ytk—av=k. 
or vy. 
Substituting y for a, 
s—m s—r 
Y= sn t smal 
s—m 
or y= pont (2) 
which gives the final depth of the deposit, d being here also the 
_ original depth of the sea. 
We can now make some probable numerical estimates. 
Let us take, as explained already, s=2:96, r=2:68, m=1. For 
the density of the deposit we may fairly assume n=2°5. With these 
——"=426, the 
greatest thickness of deposit will be 4:26 times the depth of the sea. 
values, if none of the crust is melted off, since 
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