Illustrating Crystal Forms. 12# 



cords may with their transverse cords be lowered to the level 



of the bar again, and the octahedron again produced. 



The cube and the corresponding forms of the pyramidal 



and prismatic systems may be easily constructed by running 



the cords as follows : — 



Take the cube as , ,, , ,, 

 a o c a 



e' f g' h' 

 where the first row represents the upper face, and the second 

 the lower, as in fig. 2. 



The cords will have the following course : — 



V g' hf f V a! V g' If a' 



e f d f c' f e' V c' h! e V 



f a' df g' f c< d f e' f c f 



d hf e' V V If, d> V f h f 



g' c' a! d g' 

 The faces of the cube corresponding to the angle of the octa- 

 hedron. 



Now by drawing out the cords opposite the middle of the 

 faces (that is, the diagonals of the faces) a 24-sided figure is 

 produced which can be reduced in the limit to a 12-sided 

 figure, namely the rhombic dodecahedron. 



If the sides be connected by cords with pulleys and drawn 

 out, and at the same time cords connecting the centres of 

 the sides with the centres of the faces be drawn out, then the 

 trapezohedron is produced. 



Cause the two lateral pulleys of the cube to approach 

 above and the longitudinal pair to approach below, and the 

 tetrahedron is produced. A prism surmounted by pyramids is 

 produced by drawing out the diagonals of the terminal faces ; 

 from this the corresponding octahedron may be obtained by a 

 simple method. 



The other part of the framework is shown in the drawing 

 (fig. 1, left-hand) as containing the double hexagonal pyramid. 

 Sliding-pulleys, as in the part already described, are fitted 

 above and below. Rider-pulleys are attached to the bars at 

 the sides. Two are shown on each side. 



The cords are attached in this way : — A bundle of six are 

 fastened together above to a cord, and drawn by this cord 

 through a ring. The cord passes over two pulleys and reaches 

 a weight outside the framework. The six cords pass through 

 the rings marked £, 7, 8, f, 0, and e in the figure, then down 

 to be attached to a cord below, which goes through a pulley- 

 sheaf. The rings marked by the Greek letters are seen at- 

 tached by cords to weights, through each of these a cord 

 passes. This cord is carried through one of the rings and 



