254 Penfield — Solittioii of Problems in Crystallography 



Engineering Department of the Sheffield Scientific School. 

 The beam is constructed from a round stick of hard wood, 

 finch diameter, sawed lengthwise. The needle-point jt? is pre- 

 pared by gluing the surfaces of two pieces of hard wood, 

 placing a needle between them and pressing in a vise. After 

 hardening of the glue, the piece is trimmed down to con- 

 venient size, and is held firmly in place between the half- 

 rounds by means of two screws. Two rings r and r (obtained 

 from a harness shop) serve to grip the pencil firmly between 

 the two sticks. The block h is not essential, serving simply 

 to hold the pencil (fastened by an elastic at e) when its posi- 

 tion is shifted. A fine adjustment is had by moving the upper 

 end of the pencil, which gives a much slower motion to the 

 point. In order to adjust the ]3encil quickly with reference to 

 scales 1 and 2 of the drawing paper, it is convenient to have 

 these scales pasted on the beam. The writer has found com- 

 passes of this description most convenient, and rather prefers 

 them to the beam-compasses listed by dealers in drawing in- 

 struments at a rather high price. 



A curved ruler is indispensable for drawing some very flat 

 circular arcs. The form first suggested by Wulfi"^ and modi- 

 fied, by the present writerf is recommended. The ordinary 

 drawing instruments need no especial comment. Two tri- 

 angles of transparent celluloid (45° and 60°), measuring 

 about 12 inches along the hypothenuse, are recommended. 

 Their edges serve as rulers, and when held one against the 

 other, the edge of the farther triangle being set at any desired 

 angle, the direction may be transferred to any point by sliding 

 the farther triangle along the edge of the near one, held firmly 

 against the drawing paper. 



As the scale upon which the plotting is done is rather small, 

 a lens is recommended, and it is especially convenient to have 

 one mounted on a stand. The kind suggested by the writer, 

 and shown in figure 33 of his earlier |)aper, though expensive, 

 has proved most useful. 



Having described the necessary outfit, attention may next 

 be directed to consideration of the principles upon which the 

 methods of plotting are based. 



The Spherical Projection. — The stereographic is often called 

 the spherical projection^ but it is believed that it would be best 

 to restrict the use of the latter term, in so far as it concerns 

 crystallography, to the projection of the faces of a crystal upon 

 a sphere. This latter conception is a very simple one : A 

 crystal is supposed to be located at the center of a sphere, 



* Zeitschr. ftir Kiyst., xxi, p. 253, 1892. 



f The Stereographic Projection and its Possibilities, loc. cit., p. 138. 



