334 Proceedings of the Boyal Physical Society. 



28. It is necessary at this point to explain more fully 

 what is meant by the index in Crystallography. Taking 

 111, already referred to as an illustration, that index informs 

 us that the plane represented by that is one which touches all 

 three axes, a, h, c, at their full length. 101, means that the 

 plane it represents touches the first axis at its full length, 

 does not touch the second, that is to say, the plane is parallel 

 to it, and touches the third at full length. It is customary 

 to take the front-and-back axis a first, the right-and-left axis 

 h second, and the up-and-down axis c as the third figure. 

 (035) means that the plane referred to is parallel to a, cuts 

 h at ONE-THIRD of its length measured from o, and cuts c at 

 ONE-FIFTH from the same point. (749) means that the plane 

 is one which cuts (or intercepts) a at one-seventh from o, 

 and the other two at one-fourth and one-ninth respectively. 

 These fractions might, of course, be written as h i^ il ^^^ 

 if the fractions are always so arranged that the nnmerator is 1, 

 it is obvious that it can be understood, and we may write the 

 denominator simply in place of the fraction. This mode of 

 expressing the relationships of the faces of a crystal by its 

 INTERCEPTS, which in no case exceed unity, was invented by 

 Whewell and brought into use by Miller, and is now almost 

 universally used in place of each of the many cumbrous 

 notations which have been from time to time invented and 

 used. 



29. In all cases in which the index consists of more than 

 one fractional length, we may simplify the work by the 

 method based upon the following : — Suppose the index is 

 305. This signifies that the plane whose inclination is so 

 expressed cuts a at one-third from o, is parallel to h, and cuts 

 c at one-fifth from o. Draw a right angle on a separate piece 

 of paper, and mark the angle o. Measure off one-fifth from 

 o along one axis and one-third from o along the other, and 

 join the two points by a straight line. If the lines were 

 short to begin with, we may find the fractional lengths 

 inconveniently small for practical work. Now, as we are 

 concerned with directions and not with magnitudes in this 

 case, it matters not how far the plane in question is from o 

 provided its direction remains the same. So we may multiply 



