80 E. K Dana — Chondrodite from the Tilly-Foster Iron Mine. 



supposition. It is to be noticed that when ratios of this character are 

 allowed, a slight change in the measured angle will alter entirely the 

 calculated index ; the liberty in this respect is not, however, quite so 

 great as it would stem at first sight to be. For example, the ratios 

 t(M) ^"<^ f(f f ) approach pretty closely to each other, and it might be a 

 question which was to be accepted as the true ratio of the two axes 

 for a certain plane ; and yet if the ratio of one of these axes with 

 the third be unqiiestionably expressed in sevenths, e. g., f , then there 

 seems little doubt but that the ratio f is to be accepted, for that would 

 give 8*4'7 or f-2, while the other supposition would give .35-72'63 or|--^f. 

 This principle has been accepted in obtaining all the indices given in 

 the following tables. 



A remarkable fact connected with these planes, — in fact, implied in 

 what has already been said, — is that there is so little tendency among 

 them to lie in zo^es. For example, cc^, a-^, y~ and y^ lie very nearly 

 in a zone with each other and Z^, and yet the reflections in the gonio- 

 meter deny that this is exactly true, while no satisfactory indices 

 can be obtained on this supposition, (.e^, i^ and y^ are, however, 

 in a zone.) 



In regard to these planes two points are to be noticed. In the first 

 place, the question suggests itself whether, if referred to a common 

 fundamental form (see above), or to that of either of the other types, 

 the relations of the planes would be at all more simple. This is an- 

 swered in the negative, as will be seen to be necessary if the trial is 

 made, and also evidently because planes whose normals make angles 

 of a few degrees only with one another can never bear simple rela- 

 tions to each other, no matter wliat axes be assumed. 



In the second place, it might be urged that such ratios as those 

 above given being accepted, there is no reason why we should at- 

 tempt to express the relations of the prominent planes — those of 

 humite, type II, for example, with simple numbers (see above, page 

 7). But, as has just been stated, the attempt to refer these planes 

 themselves to other axes leads to disastrous results, while further, as 

 has been shown, these planes are truly secondary and subordinate 

 and bear no relations to other types of the species. 



This case has l)een dwelt ujjon at considerable length, because it 

 was believed that theoretically the existence of such planes w^as a 

 matter of some interest and importance, and because this single crys- 

 tal offered opportunities for exact determination which did not exist 

 to the same degree in any other case. Almost all of tlie twenty and 

 more smaller crystals examined showed some of these secondary 

 planes. In some cases, however, there was a tendency to rounded edges 



