Sivipler Methods in Crystallography. 337 



indices on he — in both cases along lines from h or a, as the 

 case may be. 



35. A few examples worked out on a very large scale 

 gnomonogram will teach other principles of the same kind, 

 which, although of considerable importance in practical 

 work, as well as in their purely mathematical aspect, need 

 not be considered in further detail here. I may, however, 

 remark that I have constructed a large scale gnomonogram 

 on a sphere of projection of 50 centimetres radius, upon 

 which a large number of poles have been laid down by an 

 extension of the methods described. Such a map is of great 

 practical use, as showing at a glance what three poles lie in 

 the same zone, and in giving at once the position of the zone 

 axis belonging to those poles. 



36. Eeturning now to a simpler case, such as that pre- 

 sented by Barytes. We have already seen how the seven 

 primary poles are determined ; and we have next to consider 

 how those of secondary position may be determined without 

 going through what would often prove to be a somewhat 

 tedious process if we were restricted to the mode just 

 described. For this purpose more construction lines have to 

 be added to the working map. We wish, for example, to 

 mark the exact positions of 301, 103, 607, 908. The middle 

 index being zero, they will all lie upon ac. Therefore in 

 quadrant IV. produce od to any convenient length, sign it D, 

 and erect a perpendicular upon oz to meet the line from od, 

 and figure it 7. Do the like from ox, and figure the line 8. 

 All the indices in which the first is the greatest figure will be 

 upon da, and those in which it is least upon dc. To deter- 

 mine 301, therefore, measure one- third of 8 from its termina- 

 tion at ox, and draw a line from that point to o. The 

 distance of this point from a along ac is the length required, 

 which is transferred to the gnomonogram. For 103, in like 

 manner, measure one-third of 7 from oc, and proceed as 

 before. It is also the case that 607 is at a distance of one- 

 seventh of 7 measured from D, and 706 may be measured 

 one-sixth from D on 8 ; all lines being transferred to ae by 

 radii from o as before. 



37. In like manner, if we have to determine the position 



