68 BULLETIN OF THE 
Variations from these simple conditions can be easily introduced after- 
wards. Several cases may be distinguished, depending on the relative 
directions of the fault and the strike of the beds. 
A. If the fault (7, Fig. 4) run parallel to the strike of the mono- 
cline, and its outcrop lie behind a ridge, a, made by the hard bed, and 
the heave, h, is on the side of the dip, d, then the hard bed will be 
indefinitely repeated in a second ridge, 6, parallel to the first. The 
distance between the two ridge lines may be called the offset, ¢; then 
¢=h cotan. d. The fault may lie anywhere between the two ridges. 
Such a fault economizes a formation in allowing a given thickness to 
cover a great width of country. 
B. If the heave is on the side of the ascent of the monocline, some of 
the beds will fail to appear at the surface. This is, in contrast to the 
preceding, a wasteful arrangement. 
C. If the fault, with heave of the same value and on the same side of 
the fracture as in A, run oblique to the strike with an angle e between 
the two lines, Fig. 5, the offset remains as before, but the two ridges 
are not indefinitely repeated ; the north end of } overlaps the south end 
of a, and the overlap p equals ¢ cotan. e, or 2 cotan. d cotan. e. 
D. If the fault run square with the ridge, Fig. 6, there will be an 
offset as before, but no overlap. 
E. If the heave be on the other side of the fault, e being less than 90°, 
Fig. 7, there will still be an offset as before but in the opposite direction, 
and instead ofan overlap there will be a space in which there is no ridge. 
All these are special cases, easily generalized. If the values of dip, 
heave, and angle between strike of beds and fault-line are represented as 
in C, the formula there given will apply to all cases; a negative heave 
meaning a change in the side of the uplift, and a negative offset mean- 
ing a loss of visible outcrop, as in case B. 
To the student, at least, there is here seen good reason for the ety- 
mological connection of geometry and geology. In the geometrical 
conceptions, the angles are to be seen all sharp and precise; in the 
geological occurrence they are rounded off and obscured. 
Thus prepared by a deductive review of principles that have been 
learned elsewhere and that may find application here, further explora- 
tion can be most profitably undertaken. 
A little north of the point where the anterior ridge of High Rock was 
crossed in the morning, it falls off and ends in low ground at the south- 
ern point of the reservoir (4); but a little way to the west another and 
very similar trap ridge (5) begins, with offset of a little more than a 
