Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 233 
why an extensive cavity within the earth should be nearly 
horizontal. Adhering then to this case, it is manifest that the 
extension of each component lamina of the mass will depend 
on the form assumed by it when the mass is elevated, since its 
boundaries, by hypothesis, remain immoveable. Consequently 
the direction of the tension in the tangent plane before men- 
tioned must also depend upon the form of the lamina. This 
direction is not generally horizontal, but since it will usually 
be nearly so, and will always determine the horizontal direc- 
tion, or azimuth, of a vertical plane drawn through it, we shall 
be understood when it may be convenient to speak of the ho- 
rizontal tensions. 
It is manifest then that the determinations of the directions 
of the tangential tensions in the elevated mass, must in cases 
such as the above be a purely geometrical problem, as may be 
easily elucidated by a few instances. In the elevation already 
described (of which the segment of a cylinder, by a plane 
parallei to its axis, may be regarded as the approximate type, 
and which may therefore be termed cylindrical) it has been 
shown that this tension lies entirely in a vertical plane perpen- 
dicular to the axis. If the elevation approximate to the form 
of a cone (which may be conceived to be formed by the super- 
position of similar conical shells), it may be shown*, that if 
each lamina remain unbroken, the direction of the only ten- 
sion will be parallel to the slant side of the cone, and will pass 
through its axis; but that if a dislocation exist along the ver- 
tical axis, the principal tension at any proposed point (parti- 
cularly near the vertex) will be perpendicular to the vertical 
plane passing through that point and the axis, there being 
also another tension in that plane. If again the form of the 
elevation should approximate to the segment of a sphere, there 
will be two tensions at each point of the mass, one of which 
will lie in the plane through the proposed point and the verti- 
a axis of the elevation, the other being perpendicular to that 
ane. 
The above are some of the most simple forms which the 
elevated masscan be conceived to assume; they may, how- 
ever, be taken as the approximate types of many of the general 
elevations which present themselves to our observation, con- 
sidered independently of their local irregularities. When the 
superficial boundary of the elevated mass is very irregular, 
(particularly if the superficial extent be not very great,) the 
directions of greatest extension, or of greatest tension, will be 
very different in different points; and it may become very dif- 
* See Memoir, p. 47. 
