130 Prof. R. J. Anderson on an Apparatus 



kept there by means of a small weight. The ratio of the 

 vertical to the horizontal axes may be easily altered by means 

 of the weights. The approximation of the lateral pulley gives 

 rise to the octahedron. The number of the sides may be 

 increased by increasing the cords and pulleys. 



In order to show other figures two hoops are fitted to the 

 framework, above and below. The cords of the pyramids 

 are hooked out, and the cords connected with the hooks 

 pass over pulleys and are attached to weights. A cord is 

 made to go through the rings (hook-rings) above and below. 

 By running down the rings and unhooking the weights above 

 and below, the hexagonal prism is produced. 



Prisms with more sides can be produced by increasing the 

 number of the cords, which correspond to the edges. The 

 pyramids surmounting the prism are produced by drawing 

 out the cords at the extremities of the prism. Figures with 

 fewer sides are produced by causing the pulleys to approach. 

 Forms the result of bevelling and truncation are produced by 

 pulling out the cords of the terminal pyramids and running 

 other cords through the rings. The original double six-sided 

 prisms are produced by causing the hoops to approach one 

 another. 



The ikosahedron is produced by forming the five-faced 

 equilateral pyramid above and below, and approaching the 

 hoops towards one another^ so that the distance between the 

 hoops is equal to the perpendicular of one of the triangles. 

 Then it is only necessary to rotate the lower hoop though 36°, 

 and to connect the obtuse angles of the rhombus. In this 

 way the figure can be produced. 



The relations of the hexagonal to the rhombohedral division 

 of the sixth system may be shown in this way. Take the 

 double pyramid, hook up each alternate horizontal angle, and 

 hook down the others. Adjust suitably the superior and in- 

 ferior angles, and the rhombohedron is produced. The cords 

 in reality follow the course of the lines in the glass models. 



This method is very interesting in this way, that by a little 

 dodging the rhombohedron can be converted into the cube, 

 so that the relations between the sixth and other systems are 

 rendered more distinctly apparent. 



The rhombohedron may be easily changed into the hexa- 

 hedron by unhooking the weights and pulling in the cord. 

 The hoops are shown in the lower part of fig. 3, PI. II., with 

 the rhombohedron attached. The hexagonal prism is figured 

 separately for the sake of distinctness. 



The ikosahedron may be produced by hooking up and 

 down the horizontal cords of the decahedral pyramids. If 



