74 W. G. WOOLNOUOH. 



rod is held so as not to touch any of the mirror faces, but 

 to project between them from the trihedral angle, the forty- 

 eight centronormals of a hexoctahedron appear, and so on. 

 Obviously the edges H-^-S, S^-V, V-^H correspond respec- 

 tively with the positions of the quaternary, ternary and 

 binary axes of symmetry of the group. 



A different procedure is adopted in the case of the 

 monoclinic model. Here we have a plane of symmetry at 

 right angles to it (and therefore also a centre of symmetry) 

 with a dyad axis of symmetry. One of the large rectangles 

 has a hole bored in its centre. Through this is passed an 

 axis, working freely in the hole, and kept normal to the 

 mirror by means of a cork on each side of the glass. These 

 corks, by their friction with the glass, keep the axis in 

 any position it may be placed. Two exactly similar pieces 

 of card of convenient size and shape are cut to represent 

 faces. One of these is fixed by one of its vertices to the 

 outer end of the axis, its opposite side supported just clear 

 of the mirror by means of two long pins fixed in the cork 

 to the card. With this card in any convenient position 

 the other card is fixed to the mirror by means of a paper 

 hinge in such a way that it exactly coincides with the 

 first one. A narrow " bridle " of paper is then fixed to the 

 free surface of this second card and to the mirror to keep 

 t in position when the other card is removed. With the 

 cards in coincidence the reflection in the mirror shows how 

 the plane of symmetry necessitates the development of 

 another face (fig. 1). Now lift the hinged card a little, 

 rotate the axis through 180 degrees and allow the hinged 

 card to drop into its former position (supported by the 

 bridle), and the four faces of the most general form of 

 the normal group of the monoclinic system at once appears 

 in a way which appeals very forcibly to the imagination 

 of the pupil (fig. 6). 



