18 MINERALOGY 



of the plane a'bV on the axis b. In the same manner parameters 

 are derived for the axes a and c. In general the parameters of any 



plane xyz would be 



oy ox , oz 



_a V . c ' 



a ^ Kf \* 



oa ob oc 



in this case 12 a : 3 b : 6 c are the parameters. They definitely fix 

 the inclination to the axes. The actual length of the intercepts 

 varies with the size of the crystal and is unimportant. It is the 

 relative length, one to the other, or their ratio, which determines 

 the inclination of the faces, and fixes the interfacial angles. The 

 plane abc, intersecting all three axes at unit lengths from the 

 origin, is designated by a : b : c, and is crystallographically identical 

 with the plane a'bV (8 a : 8 b : 8 c) ; multiplying all the coefficients 

 by 8 simply moves the plane out from the origin parallel to its 

 former position. It still stands with the same inclination to the 

 axes and will intersect all three planes with the same angle as before ; 

 the crystal is only increased in size. It is the custom to simplify 

 the parameters by moving any plane back or forward on the axes 

 until the intercept on one axis is unity. If the parameters 12 a : 

 3 b : 6 c of the plane xyz are divided by 3, they become 4 a : b : 2 c ; 

 the coefficient of b is reduced to unity. This is the same as moving 

 it to the position x'yV> cutting the axis b at unity, parallel to the 

 original position. It represents the same crystal in either posi- 

 tion. When a plane is parallel to an axis, it intercepts that axis at 

 infinity, and is expressed oo a ; when a set of parameters contain 

 two infinities, the plane is moved until the remaining intercept is 

 unity and the parameters are written oo a : oo b : c. This system of 

 denoting crystal faces was one of the earliest methods devised, and 

 is known as the parameter system of Weiss ; it has the advantage of 

 simplicity and directness in expressing the relation of intercepts 

 which enables one to see at once the relation of the plane to the 

 axes. In the drawing of crystals it is practically necessary to reduce 

 all other symbols to their equivalents in Weiss's system, in order to 

 lay out the axial intercepts ; for this reason it is well to become 

 thoroughly accustomed to the notation of Weiss in the very begin- 

 ning. 



'Indices of Miller. There are a number of other notations which 

 are in use, the most important of which is Miller's system of in- 

 dices, now generally used in all works on crystallography. The 

 most general form, or the indices of any plane, are written hkl; 

 the three axes always maintain their usual order. The indices 



