68 BULLETIN OF TllE 



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 (/, 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, A, is on the side of the dip, d, then the hard bed will be 

 indefinitely repeated in a second ridge, b, parallel to the first. The 

 distance between the two ridge lines may be called the offset, t ; then 

 t =^h cotan. d. The fault may lie anywhere between the two ridges. 

 Such a fault economizes a formation in allowinpf a triven 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 h overlaps the south end 

 of a, and the overlap p equals t cotan. e, or h cotan. d cotan. e. 



D. If the fault run square with the ridge, Fig. 6, there will be an 

 ofiset 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 of an 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 elsew^here 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 

 ci'ossed 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 



