SYSTEM OF PROJECTION 177 



Two lines may or may not intersect. They will intersect if the point 

 of intersection of their projections represents points of equal altitudes on 

 the two lines; otherwise they will not. Lines in the same plane always 

 intersect unless they are parallel; and if lines intersect, the point of in- 

 tersection of their projections will be the projection of their actual point 

 of intersection. If we wish to determine the distance between two points, 

 or the angle between two lines, we revolve the plane, containing the 

 points or lines, around its trace until it is horizontal. All points and 

 lines in it will then appear in their true relations to each other. We have 

 virtually used this method in indicating the dip by the dip-triangle in 

 the reference plane ; other examples will be found farther on. 



Classification of Faults 



The displacement of a mass as a whole from one position to any other 

 can always be represented by a parallel displacement, or translation, and 

 a rotation. When the first and last positions are given the direction of 

 the axis and the amount of rotation is fixed, but we are at liberty to 

 choose the location of the axis at will, and we can then determine the 

 translation necessary, with the rotation, to represent the total displace- 

 ment of the mass. There are an indefinite number of ways of doing 

 this, according to the location we choose for the axis of rotation. If there 

 is no rotation, the displacement becomes simply a translation. If there 

 is no translation, the displacement becomes a simple rotation. 



We may therefore classify faults as follows : 



f f Strike-faults. 



I Plane strata < 



[ Diagonal and dip-faults. 

 Parallel displacements i 



(Strike-faults. 

 Diagonal and dip-faults. 

 {Simple rotation without translation. 

 Rotation with translation. 



In parallel displacements all parts of the rock mass remain practically 

 parallel with their original positions; whereas, when rotatory displace- 

 ments occur, the rock, at least on one side of the fault-plane, rotates 

 about an axis. For geometrical reasons we treat plane strata, faults, 

 where parallel displacements take place, and other nearly plane surfaces 

 as though they were true mathematical planes. If we deal with large 

 areas, this assumption is far from true ; but over small areas, even though 



