BULLETIN OF THE GEOLOGICAL SOCIETY OF AMERICA 

 Vol. 2, pp. 365-382, PL. 14 MAY 4, 1891 



ON THE RECOGNITION OF THE ANGLES OF CRYSTALS IN 



THIN SECTIONS.^ 



BY ALFRED C. LANE. 



{Read before the Society Aiignst 19, 1890.) 



CONTENTS. 



Page. 



Introduction 365 



I 1 — Applications of the Problem 365 



^ 1 — The Stereographic Projection 366 



Location of a random Section ^ 368 



^ 3 — Solution of the Problem with aid of an axial Image 368 



^ 4 — Solution for three traced Paces 368 



§ 5 — Probable Difference between solid Angles and their Traces 372 



§ 6 —Solution for Faces of one Zone 373 



g 7 — Application to Augite, etc. 374 



I 8 — Determination of optical Axes from a random Section 377 



I 9 — Solution in the Case in which the Section must be in a given Zone : 



Application to Tourmaline 379 



Introduction. 



Applications of the Problem. 



§ 1. The morphologic properties of cr3^stals, that is to say, their outer forms 

 and their structural plaues, whether the latter are of cleavage, of twiuuing, 

 of enclosures, or of alteration, are among their most important properties. 

 They are, in fact, the only ones by which we can recognize complete pseudo- 

 morphs. They are also of great help to the petrographer in determining 

 minerals, for the habits of minerals are so constant and the important planes 

 so few that we may often pretty surely recognize them, either from external 

 forms, or from cleavage, etc. Yet our assurance is often not so great but 

 that we should welcome tests of the correctness of our assumptions, which 

 would give them objective as well as subjective validity. 



I wish to show how such tests may be applied ; and I shall illustrate the 

 more general cases by applications to one or two simple cases typical of those 



* Work for the Michigan Geological Survey, published by permission of M. E. Wadsworth, State 

 Geologist. 



LIV— Bull. Geol. Soc. Am., Vol. 2, 1890. (365) 



