46 



E. I. Gal'perin et al. 



lines (in general the latter can be considered as circles of infinitely great 

 radius). 



Stereographic projection is equiangular projection, that is, the angle be- 

 tween the projections of lines on the sphere is equal to the angle between the 

 lines on the sphere themselves. This property of stereographic projectionsy 

 which is also possessed by certain other projections, is a necessary and 

 sufficient condition for a given projection to be conformal, meaning that 

 figures on the sphere which have infinitely small dimensions in all direc- 

 tions are projected as infinitely similar small figures. A further characteristic 

 of stereographic projections is that the projection of a circle is a circle. 



The Stereographic Net 



A projection onto the diametral plane of a sphere divided into degrees is 

 called a stereographic net. Depending on the position of the projection plane 

 a stereographic net can be polar (when the projection plane coincides with 

 the equator, and the observation point with the nadir— the lower pole) or 

 meridianal, when the observation point lies on the equator and the projec- 

 tion plane is a meridian lying at 90° from the point of observation. 



Fig. 1. Construction of a meridianal stereographic net (after M. K. Razumovskii). 



For purposes of geometrical seismics the meridional net is the most inte- 

 resting. Let us now look at this in detail. Fig. 1, wh^'ch we have taken from 

 Reference C^^, shows a construction of a meridianal stereographic net. 

 Here the plane of drawing coincides with the meridian ZEZ', and the plane 

 of projection {n) coincides mth the meridian ZMZ' . The point of observation 



