GEOLOGICAL SOCIETY OF DUBLIN. 
165 
If this engineering problem, be inverted, and a geological one sub¬ 
stituted for it, viz., to find the horizontal force necessary to produce 
fracture in a mass of rock or gravel, it is not difficult to infer the follow¬ 
ing results :— 
I. If a horizontal thrust be applied to a bank of rock (Plate XX., 
Pig. 1), there is a certain plane oa, along which the fracture of the rock 
mass is easiest, which I shall call the il Natural Plane of Fracture” de¬ 
termined by the equation— 
« = 45° + |. (3) 
II. There is a certain other plane oh, which I shall call the “ Plane 
of impossible Fracture,” up which it would require an infinite force to 
push the rock mass. This plane is determined by the condition— 
u = (/). (4) 
III. If, from any cause, the fracture of the rock mass take place 
along some other plane ox, the force requisite to push the mass up the 
plane is determined by the condition— 
P = L/ix 2 tan% cot ( u - 0). (5) 
The second case is illustrated in Plate XX., Pig. 2, which represents 
the reaction of the plane of impossible fracture as horizontal, because 
<p = u, and therefore it would require an infinite force to push the weight 
up the plane. 
In Pig. 3 I have illustrated a remarkable case of oblique anticlinal 
axis, occurring at Loughshinny, county of Dublin, with fracture along 
the inclined line of overturned beds xy, and a slight reversed fault along 
the plane of fracture. The figure is accurately drawn with respect to 
the inclination of the beds and of the fault. 
The bed a'h ' is a bed of crystalline crinoid limestone, and is the 
first which has undergone fracture. Its inclinations are 25° and 55° at 
each side of the axis, and the underlay of the fracture xy is 50°. 
The planes oa and oh are the “ planes of natural fracture and of 
impossible fracture,” and their underlay, as found from equations (3) 
and (4) are— 
oa = 62° 30', 
oh = 35°; 
assuming 0 to be 35°, which cannot be far from the truth. 
The actual plane of fracture xy is intermediate between these two 
planes, and is occasioned by the plane of weakness caused by the bending 
over of the contorted strata. 
Equations (2) and (5) give the forces requisite to keep from slipping 
down and to push up a mass of rock along any given plane ox; and since 
the weight of the mass kept from slipping down or pushed up is— 
W = \yx % tanw; 
VOL. V.-PROC. SOC. 
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