Mr. G. Darwin on Maps of the World. 433 



worth while to give a figure. The meridians on the equatorial 

 faces converge so little that it is more convenient to set them 

 out by finding two points through which they pass. The broken 

 lines in the figures are merely constructional. 



In order that the meridians and lines of latitude may fall 

 symmetrically on each face, it is better to set them every 9° or 

 6°, instead of every 10 as is usually done. For the whole globe, 

 there are required 10 equatorial hexagons, 10 equatorial penta- 

 gons (5 in N. and 5 in S.), and 2 polar pentagons. 



This 32-faced figure is a very close approximation to the 

 globe. 



The Murchison Fund of the Geographical Society (£W) has 

 been granted for carrying this scheme out practically ; and a 

 Committee has been appointed, of which General Strachey and 

 Mr. Francis Galton are members. The scale is large, the poly- 

 hedron being designed to circumscribe a sphere of 10 feet 

 diameter. The various sheets of the map are stretched on light 

 wooden frames ; and they can be hasped on to a kind of umbrella, 

 of which the handle is held horizontal. It is expected that it 

 will be finished shortly ; and it will, I believe, be placed in the 

 rooms of the Society. 



Another somewhat similar plan has occurred to me, and 

 seems to me preferable, at any rate for somewhat smaller globes 

 than the one above referred to. 



Suppose A B C to be one face of a regular icosahedron 

 inscribed in a sphere (see fig. 5), and that we bisect the arcs of 

 great circles subtended by the sides A B, B C, C A respectively 

 in D, E, F. Then pass a plane through D E F, and three others 

 through AEF, BDF, CDE respectively. The face ABC 

 may be replaced by the equilateral triangle D E F and the three 

 isosceles triangles A E F, B D F, C D E. If this be done with 

 every face of the icosahedron, we have a solid figure of 80 faces — 

 20 equilateral triangles, and 60 isosceles (but nearly equilateral) 

 triangles — inscribed in the sphere. If we project the globe on 

 to this surface, with the vertex of projection at the centre, we 

 obtain an excellent approximation to the true globe. 



Now this plan would be very complicated if it were necessary 

 to have 80 different map-sheets. Fortunately, however, the. 

 form of the triangles makes it advantageous to have four sheets 

 united together, viz. the equilateral triangle and the three 

 isosceles ones which have replaced the face of the original 

 icosahedron. 



Fig. 6 represents one of these sets of four sheets when spread 

 out Hat. These four sheets may be printed from a single plate, 

 and may be pasted on to quasi-triangles, such as A B C (fig. 6), 

 which are hinged or creased along the lines D E, E F, FD. 



Phil. May. S. 4. Vol. 50. No. 333. Dec. 1875. 2 F 



