K. S. Dana — ChondrocUte from the Tilltj- Foster Iron Mine. 79 



The calculated symbols are also striven with the aii^jles which be- 

 long to theui. It will be noticed tliat /- (27 = 021) is itself one ot 

 the minute planes of the same character as those suironndino- 

 it, and its presence gives a reality to them whiclj they would not 

 otherwise have, and .shows what degree of reliance is to be placed on 

 the angles. Cases of a similar character will be noted hereafter. 



The symbols * calculated for this series of ])lanes are certainly not 

 simple; and yet a moment's consideration will sliow that this was 

 exactly what Avas to be expected. Crowded togetlicr so closely, 

 they would be abnormal if occurring on crystals of any species, while 

 this becomes still more true for a mineral like chondrodite. The 

 constantly recurring, common planes have ratios which in anv 

 other species Avould be considered next to impossible : thus, in tyj)e 

 II, 1 : -^ : -i-: I ; and in type III, 1, ^, ^, 4, ^, ^^. It is to be noticed 

 that these are the true ratios of the r series of pyramids, which exist 

 no matter what change be n\ade in the assumed axes. It is not sur- 

 prising, then, that these secondary planes should themselves have sym- 

 bols totally at variance with the accepted law of simplicity of the 

 indices. Many cases of planes with what may be called abnormal 

 indices have been described, but frequently they are to be explained 

 as has been done by Brezina in the case of the f|--7 (25-0'24), which he 

 proved to exist in wiserine, as a tendency to a plane Avith a simjjle 

 index (1-7=101), which has resulted in a plane Avith approximately 

 the given index. The case in hand, hoAvever, is quite different. 



It will be noticed, hoAvever, that, laAvless as they appear at first, 

 there is an attempt at system in the symbols given. Thus in the 

 ratio of the brachydiagonal to the vertical axis, we have : 



and so on. The ratios for the other axes might be draAs^n out in the 

 same Avay, but they are already contained in the symbols given in 

 the table. A little surprise is felt at first that the uniformity in ratio 

 is not greater, that, for instance, x'^ is not 2-13*7, instead of 2-12"V; 

 but the measurements are too good and reliable to allow of such a 



* In the symbols given in the tables (i. e., those according to Naumann) the dash 

 over the second figure, or fraction, has been omitted (in order to simpHfy the work of 

 the printer). This has also been done in all the following tables, being made 

 possible by the fact that all these planes, with one or two exceptions, belong to the 

 macrodiagonal series. 



