372 Mr. William Phillips on the Oxyd of Tin, 



of the edge ef on the edge fa over the apex of the crystal, is 

 112°, 10', and that oi fa on ah 123°, 55\ it will follow that the 

 triangular planes ai h and e i c are not equilateral^ but isosceles^ 

 triangles, of which the outer sides a h and e c are the longest, 

 the two others being equal. Now, six isosceles triangles, similar 

 to those of a i h and etc, fig. 198, are not equal to the comple- 

 ment of a regular six-sided plane, fig. 197, as will be seen by fig. 

 199. The made delineated by fig. 188, therefore cannot be a 

 regular dodecahedron with triangular faces. By an attentive ex- 

 amination it will be generally found to exhibit only three or four 

 sections of the prism similar to fig. 196 : and although this circum- 

 stance is commonly attributed to interrupted crystallisation, that is 

 not in fact the cause of its assuming that appearance. 



In my collection there is a made obligingly presented to me by 

 Mrs. Lowry, of about half an inch in diameter, and almost per- 

 fect, which as it demonstrates that six sections of the prism, fig. 

 196, are not equal to the complement of the dodecahedron, is highly 

 interesting. It is represented by fig. 189, which shews, that in- 

 stead of exhibiting, as in the preceding figure, equal and similar 

 planes 1, 1, of equal portions of fig. 196, it has only 3, each of 

 them, alternating with facets of another form, having between them 

 a re-entering angle. 



Let fig. 201 represent a close combination of three isosceles 

 triangles, a b c, acd and ade^ similar to those produced by the 

 lines of section on fig. 198. Then let ^y^: ^^ represent one of 

 those triangles, and one-half of each of the other two. By com- 

 paring the plane afc d g with afc d g of fig. 200, which is the 

 plane that would be the base of each pyramid of the made des- 

 cribed by fig. 189, by a section between them, it will be seen that 

 there is a perfect agreement between each j and it will also be seen 



