GEOMETRY AND CRYSTALLOGRAPHY. 
417 
FURTHER CHANGES IN THE SCIENCE CODE. 
Since the preceding article went to press, the following changes have 
been made in the Science code. 
1. In addition to the teachers’ examinations, held annually at South 
Kensington, London, there will be a simultaneous one in Edinburgh 
and Dublin, “if five candidates register themselves in Ireland or 
Scotland.” 
We have great pleasure in 'publishing this alteration in the code, as being 
an important step towards facilitating the admission of ladies amongst science 
teacher si) 
2. In 1864, books will no longer be given to second and third class 
prizemen, but “ cards of merit, recording the result of the examina- 
tion,” will be substituted. 
3. Only one (instead of two) silver medals, and two (instead of three) 
bronze medals, will be granted to successful students in each 
subject. 
( This change will inflict serious injury upon the whole movement, the boohs 
being one of the chief inducements to young persons to become students : and 
the chance of gaining a medal is already sufficiently small in subjects in which 
there are many competitors.') 
4. The travelling expenses of candidates for teachers’ certificates will in 
future only be paid to those who are bond fide engaged in tuition or 
preparing for it. 
GEOMETRY AND CRYSTALLOGRAPHY. 
On the Divisions of the Cube , by Mr. Charles M. Willicli. — Mr. Charles 
M. Willich, Secretary to the University Life Assurance Society, has, for a 
considerable period, been engaged in researches in pure and applied 
geometry, on the divisions of the cube, and the solids which result from 
these subdivisions. As early as October, 1860, he had brought before the 
notice of the French Academy of Science a memoir in which he had 
arrived at extremely curious results, which we propose to recapitulate. 
The solid triedral angle of the cell of the bee is formed of three plane 
angles, having each an angle of 109° 28' 16". The ordinary dodecahedron 
with rhombic faces may be deduced from the cube in many different ways. 
If, from the centre of a cube, planes of divisions be made passing through 
the edges of the six squares which form its surface, there will result six 
pyramids with square bases. If these six pyramids have their square 
bases placed on the six faces of another cube of similar dimensions, the 
ordinary rhombic dodecahedron is formed, which has, consequently, the 
volume of two cubes. Two of the pyramids deidved from the cube being 
joined base to base, form an octahedron, the volume of which is one-third 
of that of the cube, and, consequently, one-sixth of the volume of the 
above described dodecahedron. If one of these pyramids be cut into 
two equal parts, and the two halves be brought together by turning them 
