Illustrating Crystal Forms. 131 



we begin with the double octahedral pyramids, the rhombic 

 dodecahedron can be easily produced by hooking up the cor- 

 responding alternate edges above and below, and running cords 

 through the hooks looped up and those rings still stationary. 



In order to show the effects of uniting and separating forces 

 the form shown at fig. 2 is useful. The instrument consists of 

 a frame in which hoops revolve, some on vertical and others 

 on horizontal axes. The hoops carry sliding-pulleys as shown 

 on the plate. The cube is easily constructed by running cords 

 over eight pulleys fixed on two rings revolving on a vertical 

 axis. Cords are carried through small rings above and 

 below (fig, 2, of h' d d! <1 f g' li). 



Without going into details, it will be easily seen that one 

 orthogonal hexahedron can be easily changed into another, 

 and into the corresponding octahedron. The octahedron of 

 the first system, a bed ef, if constructed by running cord 

 over the pulley B, and the pulley attached to the same ring 

 below, may be changed into the octahedron of the dimetric 

 or trimetric system, or of either of the oblique. The latter is 

 accomplished by causing the hoop to revolve, and for the 

 triclinic the vertical hoops come into action. Adjustment 

 of the weights leads to an alteration in the axes, and the 

 relations of the weights for a special form may be studied. 



It is evident that the dodecahedron and trapezohedron may 

 be produced in this instrument as in the first, and that the 

 forms due to truncating or bevelling of the sides are obtained 

 very readily. 



The following are the advantages of the apparatus : — First, 

 it shows clearly the effect of changes of force in producing 

 changes of form. The weights can be approximated or sepa- 

 rated, and thus the relations of allied forms may be studied. 

 The number of weights may be increased, and the change of 

 form by grouping may in this way be well shown. 



If we take an india-rubber tissue ball inflated with air as 

 an example of an infinite number of forces acting from a 

 centre, and a piece of stretched cord with a weight attached 

 as the other extreme limit, many of the intermediate conditions 

 where strings are made to form the edges of figures may be 

 easily understood from the arrangements I have described. 



It is true that such methods as are here suggested are open 

 to the objection that mathematical principles of a very im- 

 portant kind are involved. I think the same objection may 

 be made to any mechanical contrivance; but so far from 

 getting rid of a difficulty without explaining it, I hold that 

 the apparatus, whilst it will produce a better conception of 

 crystal forms, and the actual work in the crystals themselves, 



