SPATIAL PROBLEMS IN GEOMETRICAL SEISMICS 47 



lies on the equator EMS at the point S. The equator EMS and the meridian 

 ZEZ' are represented by two mutually perpendicular diameters MTV and ZZ' 

 of the projection circle, the projection of the meridian coinciding with the 

 polar axis of the sphere ZZ'. The remaining meridians are represented 

 by circles passing through the poles Z and Z' and intersecting the equator. 



Let us consider for example the meridian ZM^Z' for which the angle 

 EOMi is oc°. The projection (wj) of the point at which the equator intersects 

 the meridian (M^) will be distant from an amount 



Uin^ = K tan — , 



where R is the radius of the sphere. 



The parallel* with the co-ordinate q = 15° = ZK lies at this number 

 of degrees from the pole along all the meridians ; we can therefore plot Zat 15° 

 from the pole round the circle of the projections on both sides, and we can 

 also plot the segment ZK =15° along the straight line OZ on the stereo- 

 graphic scale from the point Z. We thus obtain three points belonging 

 to the parallel. These points are sufficient to enable us to construct the 

 whole parallel. 



The meridianal stereograpliic net constructed through 2° for a sphere 

 R = 10 cm, was first introduced into crystallography by Vul'f (2) and 

 bears his name (normally as Wulff in English) (See Fig. 2). 



Operations with a Wulff Net 



The Wulff net is a transparent sheet by which any construction can be 

 transferred to transparent paper (wax paper or ordinary tracing paper) 

 without the use of compasses or a ruler. The tracing paper is centred and 

 a mark is made on it to indicate the end of a meridian which is the point 

 of origin for counting off the azimuths. This fixes the initial position for 

 the tracing paper, and by means of this index the paper can be subsequently 

 brought back into the initial position. 



We shall now consider problems in geometrical seismics which can be 

 solved by means of a Wulff net. 



PROBLEMS ENCOUNTERED IN GEOMETRICvy;. SEISMICS 



Every direction in space can be unambiguously determined by two angles. 

 Let these angles be the azimuth (a), that is the angle counted from the 

 northward direction in the clockwise sense which varies from to 360°, 



* Throughout the paper the term "parallel" is used as parallel of latitude or small, 

 circle [^Editor's note]. 



