284: C. Falache — Crystal Measurement, etc, 



give directly tlie axial values <2: J :<?(=!), which are readily 

 transformed to the usual form, a :!) {=!)'. chj interchange of 

 axes. 



In the monoclinic system the additional elemental value, 

 angle yS, is found directly by the angular distance from the 

 pole S to the projection of the basal plane. 



In like manner in the triclinic system the angles a, /3, 7 are 

 found in the projection if the pinacoidal planes are present, or 

 by calculation if sufficient values are given by the measure- 

 ment. 



The unit form being chosen in the projection, the symbols 

 of the other forms may be read off directly by measurement 

 of their coordinates in terms of the axial units, and the sym- 

 bols so obtained are the same as the Miller index symbols 

 except that the third index is always made unity. 



[ I ' r /^--^M 



The zonal relations of the faces are also well exhibited in 

 the gnomonic projection, tautozonal planes being projected in 

 a' straight line. A disadvantage of this projection consists in 

 the fact that the prism faces, being normal to the plane of pro- 

 jection, are projected to infinity (/? = 90, d= tg p = co). But 

 their relative positions are given adequately by their angles cf). 



When the projection is carried out with care the results 

 obtained for axial elements by measurements taken from it are 

 very accurate, often agreeing with calculated results to the 

 second or third decimal place. 



The calculations are simple and may be carried on simul- 

 taneously with the projection, the two serving as mutual checks 

 against errors. The form of the measurements enables all 

 good faces of the crystal to be employed in the final determi- 

 nation of the crystal elements, a notable advantage over the 

 older method which is dependent for these values on the per- 

 fection of one or two zones. 



For an example of the form in which the discussion and 

 computation of measurements taken on the goniometer with 

 two circles may be best carried out, the reader is referred to a 

 paper by Prof. Goldschmidt, Phosgenit von Monteponi, Zeit. 

 fiir Kryst., xxi, 1893, p. 321. The compactness and simplicity 

 of the whole is there made manifest. The use of spherical 

 trigonometry is dispensed with and the whole computation is 

 constantly before the eye, so that the detection of errors, if such 

 occur, is comparatively easy. 



The gnomonic projection serves further as a basis for the 

 construction of other projections. By a simple construction* 



* G-old Schmidt, Ueber Projection und graphigche Krystallberechcung, BerliD, 

 1887, p. 38. 



