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A Geometrical Problem connected with the above. 
— A very simple, but at the same time a very interesting 
geometrical problem is submitted in connection with the 
faults, viz., If there be a horizontal separation between two 
beds, what amount of elevation has caused this separation ? 
See Plate, fig. 3. 
This question is solved as follows : — Suppose B A C a 
portion of the earth, C the centre of the earth, A B a 
portion of the surface, which has been raised from the 
position X Y by the action of expanding deposits at F ? The 
question is, to find the distance X A, that the strata has 
been raised. 
Suppose the distance A B to be 10 miles, and that in this 
distance the various beds have been separated in horizontal 
distance a total amount of 50 yards. Then taking C A, the 
present radius of the earth to be 4,000 miles, A B to be 10 
miles, X Y to be 10 miles, less 50 yards, we should have the 
following proportion : 
C A is to A B, as C X is to X Y, and thus C A, A B and 
X Y being known, we can find C X, which in the present 
example would enable us to find that A B must have been 
raised 11 miles at least to produce a horizontal separation of 
50 yards in 10 miles. This amount, although apparently 
large to us, is still not one six -hundredth part of the 
thickness of this globe, and would be comparatively as 
insignificant as one-tenth part of the thickness of the peel 
of an orange, to the orange itself. 
From the above problem we could, if given the horizontal 
distance between two sides of a fault, immediately find the 
amount of elevation which had caused it. 
It is to be hoped that those geologists who devote their 
time to collecting details and facts, will give some more 
information than at present exists, connected with the 
horizontal distance separating the various beds. Whilst a 
