C. Palache — Crystal Measurement^ etc. 279 



Art. XLI. — On Crystal Measurement by means of Angular 

 Coordinates and on the Use of the Goniometer with two 

 Circles ;^ by Charles Palache. 



The methods of crystal measurement in general use at the 

 present time are based on the determination of the interfacial 

 angles from which are deduced the system and elements of the 

 crystal and the symbols of the forms. 



There is, however, another system of measurement which 

 leads to these results more simply and more directly. We 

 may term it the measurement of crystals by determination of 

 angidar coordinates. 



In the familiar spherical projection the crystal faces are rep- 

 resented by the points of intersection of the face-normals with 

 the surface of a sphere described about the crystal center. 

 The relations of these points upon the sphere are known, if we 

 determine the angular distances between them (measurement 

 of interfacial angles) or if we determine the position of each 

 one with reference to a set of coordinates (measurement by 

 angular coordinates). These operations are strictly analogous 

 to well known geographical operations ; the first is comparable 

 to triangulation, or the measurement of angular distances 

 between points on the earth's surface ; the second is like the 

 determination of localities by latitude and longitude — that is, 

 by reference to an equator and a meridian as fixed coordinates. 

 The latter operations are so nearly alike that it is found con- 

 venient to retain the geographical terms for the crystallographic 

 coordinates, and we accordingly speak of the equator and 

 meridian of the crystal. 



Any great circle of the sphere of projection may be taken 

 as equator and the pole will lie at a distance of 90° therefrom. 

 Any great circle at right angles to the equator may be taken 

 as first meridian. In practice the choice of coordinates is lim- 

 ited to a few cases. 



The means of applying this principle to crystal measurement 

 is found in the goniometer with two circlesj; of which fig. 1 is 



* A better name for this instrument tlian the literal translation of its German 

 title (zweikreisiges goniometer), given above, is highly desirable but has not 

 occurred to the writer. Neither of the names employed by Fedorof " Universal- 

 (Theodolith-) goniometer " seems fully or correctly descriptive. Some such term 

 as dicircle or biaxial goniometer may be found to be as simply descriptive as 

 any, 



f The instrument here shown is the original one constructed for Prof. Y. 

 Goldschmidt. Minor changes have since been introduced into its construction, 

 which, however, do not affect its principle. It, as well as the other instruments 

 to be described, is made by the mechanic P. Stoe, Jubilaumsplatz 10, Heidelberg, 

 and the writer can testify to the careful and thorough construction. The same 



Am. Jour. Sci. — Fourth Series, Yol. II, No. 10. — October, 1896. 

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