326 Proceedings of the Royal Physical Society. 



rigtit-and-left axis is to be marked at both ends (&), and the 

 up-and-down axis is to be signed at both ends (c). 



9. If the diameter of the ball is about four inches, that is 

 a useful size for experimental work. We shall now need 

 some means for drawing zones on the ball from point to 

 point with some approach to accuracy. To do this I use 

 two strips of clock-spring about eight inches in length, and 

 connected side by side by two small strips of brass soldered 

 across the ends, a sufficient space being left between the 

 steel strips to admit a fine needle. If this is bent around 

 any part of the sphere over which zones have to be drawn, 

 it is easy to mark by a needle point a position anywhere 

 intermediate between two other points and in the same line 

 with them. Furthermore, it will not be found difficult to 

 mark on this little instrument the degrees of a quadrant of a 

 circle, so that when it is folded over the sphere in any direc- 

 tion, the angular distance of any one point from another may 

 be laid down with ease, and quite near enough for the work 

 at this stage. And if these points so determined are marked 

 with small pins pushed into the ball, the morphology of the 

 crystal will gradually come more and more clearly into view. 



10. It is well at this stage to refer to the several poles by 

 the letters or symbols used in the work which happens to be 

 chosen. The indices which those symbols denote will be 

 dealt with further on. 



11. By this concrete method a large amount of real know- 

 ledge can be readily and easily acquired, and can be stored 

 up in a form which (when only a small number of species is 

 under observation) is extremely useful in many ways, some 

 of which have not yet been referred to. I find, in practice, 

 that hollow india-rubber balls answer, after some proficiency 

 has been obtained, almost as well as the wooden balls. It 

 may be mentioned here, as an illustration of the use to which 

 these wooden balls, pinned out into zones, may be put, that 

 they serve to indicate the direction of the intersection edge 

 between any two faces. Ml that is needed is to describe on 

 the ball, around each of the poles as centres, two circles. 

 Their intersections on opposite sides give two points through 

 which the required line is to be drawn. In arranging the 



