Simpler Methods in Crystallography. 429 



the sum of all three, e.g., (211), 2/4 = 1/2; (322), 3/7; (433), 

 4/10 = 2/5, etc. The Dyad Axes are cut at a fractional 

 length whose numerator is the first figure of the index, 

 and whose denominator is the sum of the first and second, 

 e.g., (211), 2/3 ; (322), 3/5 ; (433), 4/7; and so on. Lines joining 

 these points with the others complete the figure required. 

 To draw the Four-faced Cube, otherwise known as the 

 Fluoroid, the Tetrahexahedron,etc.,the principle here adopted 

 is much the same. The Tetrad Axes remain at their normal 

 length ; the Triad (and also the Dyad) Axes are cut at a 

 fractional length whose numerator is the first figure of the 

 index, and whose denominator is the sum of the first and 

 second. The Dyad Axes are not used. Dana gives a list of 

 thirty-five of these. As examples may be given (210), one of 

 the commonest; 320, 430, 540, etc. In all of these the first 

 index is greater than the second, and the third is o. Lastly, 

 amongst the holohedral forms of the Cubic System is the 

 Six-faced Octahedron, otherwise known as the Hexocta- 

 hedron, the Adamantoid, etc. In this all the indices are 

 different, and are -greater than o. In drawing this form the 

 Tetrad Axes are taken at their normal length. The Triad 

 Axes are cut at a fraction of their length from o, whose 

 numerator is the first figure of the index, and whose de- 

 nominator is the sum of all three, e.^. (731), 7/11 ; (432), 

 4/9; (1L5.3), 11/19; (15.11.7), 15/33; (543), 5/12; (821), 

 8/11, etc. The Dyad Axes are cut at a fraction of their 

 length from o, whose numerator is the first figure of the 

 index, and whose denominator is the sum of the first and 

 second, 6.^., (731), 7/10; (432), 4/7; (11.5.3), 11/16 ; (15.1L7), 

 15/26; (543), 5/9 ; (821), 8/10 = 4/5, etc. 



Lines for the common intersections of any two of these 

 forms can usually be made out by reference to a good 

 gnomonogram of the Cubic System. Mine is a quadrant 

 drawn to touch a sphere of five inches radius at (111). 

 This is large enough to ajfford space for a considerable 

 number — practically all — of the commoner forms; and it 

 is supplemented by a smaller stereogram to five inches' 

 radius, which serves to show the zonal relationships over 

 a larger area of the sphere of projection. In the few cases 



