NATURAL PHILOSOPHY. 143 



has come to the conclusion that the diurnal variation, observable in magnetic 

 phenomena, is produced by a feeble perturbative force which turns round the 

 horizon from cast to west in twenty-four hours. " When this force proceeds 

 to the south, the horizontal intensity diminishes, the inclination augments, 

 and the declination has its mean value (about ten hours before midday); 

 when it proceeds to the north, the horizontal intensity increases, the inclina- 

 tion diminishes, and the declination assumes its mean value, which takes 

 place about an hour before sunset ; when it proceeds towards the west or the 

 east, the respective declination augments or diminishes (one hour after mid- 

 day, eight hours before midday or midnight"). The inclination or dip, 

 which is now decreasing, will reach its minimum, Hansteen thinks, in Western 

 Europe, in 1878, and has already reached it in Siberia. Its maximum was in 

 1678, indicating a period of two hundred years. 



OX A NEW METHOD OF RENDERING VISIBLE TO THE EYE SOME OF 

 THE MORE ABSTPtUSE PROBLEMS OF CRYSTALLOGRAPHY, HITH- 

 ERTO CONSIDERED ONLY AS MATHEMATICAL ABSTRACTIONS. 



There are some propositions of crystallography which require some me- 

 chanical means beyond that of the use of solid models, to make them appeal 

 to the eye for clearer perception. The most perfectly symmetrical solid forms 

 of the crystallographer belong to the cubical or tessular system. There are 

 seven different kinds or orders of forms belonging to this system, perfectly 

 symmetrical, four of which admit of an infinite variety of species. These 

 forms are associated in nature, as well as in their mathematical relations to 

 each other. They are found in crystals of the same substance, either in 

 their simple forms, or else associated in combination with each other, in the 

 different faces of a compound crystal; thus the cube, the octahedron, and 

 the rhombic dodecahedron, are found as simple crystals of the diamond; or 

 faces parallel to all three or two of them, may be discovered on a more com- 

 plex natural crystal. The three forms we have just enumerated, the cube, 

 the regular octahedron, and the rhombic dodecahedron, may be considered 

 as the permanent or limiting forms of the cubical system; they admit of no 

 varieties; their angles, whether those of the inclination, of adjacent faces, or 

 of the planes constituting their faces, are invariable ; they are also limiting 

 forms. Between the octahedron and the rhombic dodecahedron, we may 

 conceive an infinite number of varieties of the three-faced octahedron, pass- 

 ing from the form of the octahedron to that of the rhombic dodecahedron; 

 similarly, the octahedron and the cube are limiting forms of an infinite series 

 of twenty-four-faced trapczohedrons, and the cube and rhombic dodeca- 

 hedron of a series of four-faced cubes. The forty-eight-faced scalcnohedron, 

 or the six-faced octahedron, is a form varying within the limits of all the 

 others. To represent to the eye the passage of all the varieties of these 

 forms between their respective limits, is the object of the mechanical con- 

 trivance which is the subject of this paper. A skeleton or armillary sphere 

 is constructed of iron wire, so as to mark out the principal zones of the 

 sphere of projection of the forms of the cubical system; three circles are 

 united at right angles to each other, so as to represent eight equilateral spher- 

 ical triangles, each of whose sides are arcs of 90. The six points where the 

 arcs cross each other are the poles of the six faces of the cube; the lines 

 joining each pair of opposite poles represent the cubical axes, each axis 

 being perpendicular to two faces of the cube which can be inscribed in the 



