440 PROCEEDINGS OF THE AMERICAN ACADEMY. 



— 1J (414). Observed three times on two crystals, but variations in 

 position too great to permit of its acceptance (Figure 7). 



p 

 Crystal 6 -77° 36' 52° 00' bad. 



6 —78 00 54 00 " 



" 12 —76 55 51 01 " 



Calculated -77 35 52 18 



Computation of the Elements. — Since the monoclinic character of 

 leadhillite has been generally accepted, the elements commonly u^ed 

 have been those of Laspeyres 2 and of Artini, 3 determined on crystals 

 from Sardinia. 



Laspeyres, a : b : c = 1.7476 : 1 : 2.2154. /? = 89° 47' 38" 

 Artini, a : b : c = 1.7515 : 1 : 2.2261. /3 = 8 ( J° 31' 55" 



The result of our computation of elements, based on the measure- 

 ments of 112 best faces of 15 crystals of the Utah leadhillite is inter- 

 mediate between these values: 



a : b : c = 1.7485 : 1 : 2.2244. (3 = 89° 30' 28" 



We have followed Goldschmidt, however, in halving the values of a 

 and c, these elements giving on the whole simpler symbols for the form 

 series, and the elements used by us, therefore, read as follows: 



a : b : c = 0. 8742 : 1 : 1.1122. (3 = 90° 29' 32," 



which are derived from the polar elements, whose computation follows, 

 by the relations, 



/?=180°-/,, a = — ^°— , c = -^-. 



p sin fx sin fx. 



Believing that this axial ratio is. more thoroughly established than 

 those earlier deduced, we have calculated a new table of angles based 

 upon it to replace that found in Goldschmidt, Winkeltabellen, p. 217 

 (Table V. p. 460). 



In order to test the angles yielded by the new axial ratio as compared 

 with those calculated from Laspeyres' elements as given in Goldschmidt, 

 Winkeltabellen, the following measurements are recorded, made on a 

 very perfect untwinned crystal of leadhillite from Sardinia, under con- 

 ditions similar to those used in the study of the Utah crystals. Al- 

 though the differences are of course slight, the agreement is in almost 

 every case better with the new angles. 



2 Zeit. fur Kryst., 1, 193 (1877). 



3 Giorn. Min., 1 1, (1890). 



