1814.] Crystals from Spherical Particles of Matter. 65 



a sphere on each of two opposite faces. The next in order is the 

 cube, which is two tetrahedrons, whose solid angles mutually pro- 

 trude through each other's faces, having an octohedron in their 

 centres common to both; or it may be considered as an octohedron 

 or rhombeid with a sphere on each face : the rhomboidal dodecahe- 

 dron partakes of a degree of simplicity with the above figures, in 

 having its surface marked out by a point at each solid angle, and 

 having none but them to designate its edges : the last figure I have 

 discovered deviates from the above simplicity, in having some 

 intermediate spheres between its solid angles to mark its edges — it 

 may be remarked that every sphere that is completely enveloped in 

 this structure is surrounded by twelve in the form of a canted cube. 

 The formulas for ascertaining the number of spheres necessary 

 to make anv of the above figures may be serviceable : let the 

 number of spheres on the edge of the required fig ure =g n ; then 



the tetrahedron = ^ , the octohedron = 



— 72% the rhomboid = n\ the cube = «' + re — * x 3 re. 

 Let n represent the number of spheres on the edge of the cube in 

 what follows ; then the number of spheres on the edge of the 

 largest tetrahedron contained in the cube = 2 7J — 1 j the number 

 on the edge of the contained octohedron or rhomboid = n, being 

 always the same as the cube. Hence the contained rhomboid is = 

 «' ; and the remaining spheres necessary to make the rhomboid a 

 cube will be = n — iV^ x 3 re, which may be considered a square 

 prism. 



The relation between tha rhomboid and the cube shows that the 

 Equiaxe of Haiiy might be easily constructed from a rhomboid 

 formed of oblate spheroids, similar to that described by Dr. Wol- 

 laston in the Bakerian Lecture, 1813. 



In hopes that the above remarks may eventually prove useful to 

 crystallography, your insertion of them in the Annals of Philosophy 

 will greatly oblige. 



Sir, your most obedient servant, 



Somen' Totcn, London, Bee, 14, 1813. N. L LaRKINS. 



Article VII. 



Astronomical and Magnctical Observations at Hackney Wick. 



By Col. Beaufoy. 



Lalididr, 51° 32' 40" Norili. Longilude West iaTirae 6"y%\. 



Immersion of J W ^g ^^ 20 Apparent Time. 



5'' 50' 57" Mean Time. 

 6 02 20 Apparent Til 



The unilluminated part of the moon's disk was well defined, the 



