510 



Sir W. Thomson on the Division of Space 



this diagram suffices to allow a perspective drawing from any 

 point of view to be made by " descriptive geometry." 



14. No shading could show satisfactorily the delicate cur- 

 vature of the hexagonal faces, though it may be fairly well 

 seen on the solid model made as described in § 12. But it is 

 shown beautifully, and illustrated in great perfection, by 

 making a skeleton model of 36 wire arcs for the 36 edges 

 of the complete figure, and dipping it in soap solution to 

 fill the faces with film, which is easily done for all the faces 

 but one. The curvature of the hexagonal film on the two 

 sides of the plane of its six long diagonals is beautifully shown 

 by reflected light. I have made these 36 arcs by cutting 

 two circles, 6 inches diameter, of stiff wire, each into 18 parts 

 of 20° (near enough to 19° 28'). It is easy to put them 

 together in proper positions and solder the corners, by aid of 

 simple devices for holding the ends of the three arcs together 

 in proper positions during the soldering. The circular cur- 

 vature of the arcs is not mathematically correct, but the error 

 due to it is, no doubt, hardly perceptible to the eye. 



15. But the true form of the curved edges of the quadri- 

 lateral plane films, and of the non-plane sufaces of the hexa- 

 gonal films, may be shown with mathematical exactness by 

 taking, instead of Plateau^ skeleton cube, a skeleton square 

 cage with four parallel edges each 4 centimetres long: and 

 the other eight, constituting the edges of two squares each 



Fig. 5. 



Fig. 6. 



s/2 times as long, or 5 '66 centim. Dipped in soap-solution 

 and taken out it always unambiguously gives the central 



