232 Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 
unextended dimensions of each to have been the same. 
Again, suppose a third lamina superimposed in the same 
manner, and then a fourth, and so on, till a mass of any as- 
signed thickness shall have been thus composed. It will then 
follow, from what has been shown, that the tension at any 
point c of the mass in this state must lie in the plane of the 
section, and in the direction to the tangent of the curve-line 
acb, formed by the intersection of the vertical plane of the 
section with the lamina in which the point ¢ may be situated. 
The only difference between this hypothetical mass and 
any proposed actual mass of the same form and dimensions, 
will consist in this—that in the former there is no cohesion 
whatever between the successive ]aminz of which we have 
supposed it to be formed. If, however, our lamine should 
be superposed on each other in their unextended state, and 
made to cohere firmly together, (in which case the mass would 
differ in no wise from any actual mass,) and then elevated to 
the position represented in the diagram, it is easily seen that 
the position of each point of the mass would be exactly the 
same as in the hypothetical case above stated. Consequently, 
the extension of any portion of the mass (and therefore the 
tension) must be the same in the two cases. Hence then it 
follows that if A BB! A! represent any actual elevated mass, 
the direction of the tension at any point ¢ will be that of the 
tangent line at that point as above described. 
There is no difficulty in extending reasoning precisely si- 
milar to the above to any more complicated form of the ele- 
vated mass, of which the upper and lower surfaces were ori- 
ginally parallel, and horizontal, and we shall arrive at this 
conclusion.—J/ we conceive the mass, previous to its elevation, 
to be composed of horizontal lamine (or thin strata) the direc- 
tions of the tensions at any proposed point of the mass when ele- 
vated but still unbroken, will lie in the tangent plane to the 
curved surface formed by that originally horizontal lamina in 
which the proposed point may be situated ; and the intensity of 
the tensions will be the same*, in different lamine at points 
similarly situated in each. 
If the mass in its undisturbed position be not of uniform 
depth, (2. ¢. if the upper and lower surfaces be not parallel,) the 
above reasoning would not be accurately applicable. ‘The 
case, however, we have considered may be taken as the stand- 
ard one to which others will approximate with more or less 
accuracy, particularly as physical reasons might be assigned 
* There are causes why this should be only very approximately true, 
(See Memoir, p, 42.) 
