70 E. I. Gal'perin et al. 



tion of +4° on reflection. In this way we determine the directions of the 

 remaining rays after reflection. 



Having determined the direction of the rays after they have been reflected 

 from the dome and having constructed the projections of these directions 

 on the plane, we can now find the projection of the traces of the intersection of 

 the ray surface under consideration with the inclined refracting boundary. 

 For this purpose we use the methods which have been described to find 

 the projections of the points of intersection of the reflected rays with the 

 refracting interface, and then we join these points on the i3lan by a smooth 

 line. The ray which we are considering, after emerging from the source 

 with an azimuth of 300° and striking the reflecting boundary at a point the 

 projection of which on the plan is point 6, intersects the refracting boundary 

 at a depth of 443 m; the projection of this jDoint on the plan is denoted by 

 the letter c (see Fig. 10). In Fig. 10 the projection of the trace of intersec- 

 tion with the inclined refracting boundary of the ray surface after reflec- 

 tion is shown by the line 5. After being refracted at points on the line of 

 intersection of the ray surface with the refracting boundary, the rays 

 strike the first medium. The directions of the rays in the first medium after 

 refraction are determined from the Wulff net. This is shown in Fig. 11 for 

 the ray under consideration. 



As we have shown above the ray we are considering has undergone azi- 

 muthal deviation on the reflecting boundary and after reflection has an 

 azimuth of 309° and an angle with the vertical of 59°. It must be remem- 

 bered that the incident ray is plotted with inverse azimuth (309° — 180° = 

 = 129°) and that in determining the direction of the refracted ray we take 

 the inverse azimuth. We mark the direction of the incident ray on the 

 tracing paper by means of the Wulfif net (point E) and also the direction of 

 the normal to the interface N^-^ (180 and 10°), and then make both direc- 

 tions coincide with one of the meridians of the net. In the plane of the rays 

 which we have thus obtained, we measure the angle between the normal 

 and the point E — angle of incidence — and after calculating the angle of 

 refraction according to the formula given above we plot it from the normal 

 in the direction of the incident ray. The point F is marked by a cross since 

 the ray lies under the plane. We now rotate the tracing paper to its origi- 

 nal position and take the co-ordinates of the point F from the net— the 

 azimuth and the angle with the vertical. 



We thus find that the direction of the ray after refraction is 312° and 50°. 

 Consequently, on refraction the ray undergoes an azimuthal deviation equal 

 to 3°. The Fig. 15 shows how the direction of the refracted rays of the 30° 

 ray surface is determined. The points where the ray emerges are determined 



