336 Proceedings of the Royal Physical Society. 



zone; so from 520 gives 025, from 230 gives 032, from 150 

 gives 051, and so on, the indices on Ic being simply those on 

 ah in reverse order. It will be also evident, as the vi^ork 

 becomes more familiar, that the intervening indices follow 

 each other along such zones in a definite order of change : 

 thus in the zone 110-011 they run in this order: — 121, 132, 

 143, 154, 165, 176, 187, 198, there being, as is seen, an 

 addition to the initial index of the final term of the series. 



32. In like manner, drawing lines from E through any 

 given point on ah — say from m 110, the line cuts ac at the 

 corresponding position, in this case at 101 — the second and 

 third figures of the index changing places, and the inter- 

 mediate indices changing by the continued addition of the 

 final term of the series, as in the case just described. Thus 

 from 110 to 101 we have first 211, 312, 413, 514, 615, and 

 so on. Or, if the line cuts onh at, say, 120, the terminal 

 index on ac is, by the rule, 102. The continual addition of 

 this latter gives us 1 20 + 102 = 222 ( = 111), 324, 426 ( = 123), 

 528, 6.2.10 (which is the same as 315), 417, 519, and so on. 

 It is useful also to know that along the zone ao lines radiat- 

 ing from E give indices whose second and third figures are 

 alike, and are the sum of the indices on ah-hc. Thus the 

 line from E through 210 to 201 cuts ao at 411, that from e 

 through 520 to 502 gives on oa 10.2.2 ( = 511), so from 230 

 to 203 gives 433. 



33. Again, lines from d cutting oh give indices whose first 

 and third figures are alike, and are the sum of those on ab 

 added to those on ch. Thus: — d through 110 to Oil gives 

 on oh 121, through 230 to 032 gives 262 (-131), 130 to 031 

 gives on oh 161, and so on. The same is true of all the in- 

 dices along each zone ; so that if we have before us any three 

 in the same zone, the fourth and succeeding indices can at 

 once be stated. This property forms the basis of an im- 

 portant law in Crystallography. 



34. The poles on mc, which are usually of much import- 

 ance in Crystallography, have the first and second figures 

 alike, and are less than the third on oc, while those on om 

 are greater than the third. They are always the sum of 010 

 Q)) with the indices on ac\ or the sum of 100 {a) with the 



