StltFHURET OF LEAD, COPPER, AND ANTIMONY, <SE# 



divide*? at the points V W into equal parts, which shall be Mode in whufc 

 to those of the side A C, fig. 28, of the terminal faces, in the P' imiti ^ 

 the ratio of 33-94 to 24: these divisions representing the SSJii" *" 

 diagonals of the crystalline molecules placed on the whole 

 diagonal Q S. From the point S, the extremity of the line 

 Q S, draw the lines g- S r, e $ a, q S </, and m S/, so as to 

 make "with (his line angles of 125°, 134°30', 150° 30', and 

 172°, and produced indefinitely above the point S. The 

 lines S^r, . S e, S q, and S m, will represent the direction of 

 the planes produced by the four different retrogradal ions, 

 that take place at the angles of the terminal faces of the 

 primitive prism. As every retrogradation, that takes place 

 at the angles of crystals by diagonals, is equivalent in the 

 effect it produces to a retrogradation that takes place sim- 

 ply by semidiagonals; to find the height, which. that of tin- 

 four that takes place only by a single row would give, in 

 order to see whether it would accord better with nature than 

 that of 3 to 5 given by the observations that have been 

 made on the retio^radatiou along the edges of the terminal 

 laces; from the point R, half of the diagonal W S, erect 

 the perpendicular Rg, cutting the four lines S g ; , Se, S q, 

 and S m, representing the directions of the substituted 

 planes. Inquiring now whether any of these planes may be 

 produced by the simple retrogradation of a single row, £ 

 perceive immediately, that for the same reason as was given 

 respecting the retrogradation along the edges of the termi- 

 nal faces, those planes must be excluded, the direction of 

 which is represented by the lines eS and g S. There re- 

 main then those denoted by the lines q S and m S. For the 

 same reason likewise as was given before, that which an- 

 swers to the direction m S cannot be adopted ; consequently 

 our choice is confined to that in the direction q S. The re- 

 solution of the rectangular triangle q R S would give Q-6 

 for the height of the molecule, the side of the terminal 

 faces being still supposed 24 : so that this height would be 

 to the side in the ratio of y-6 to 24, or of 2 to 5. Observ- 

 ing then, that the result of the calculation made with tlve 

 ratio of 3 to 5 agrees better with what the inclination of the 

 secondary faces of the endellion exhibits in nature, than 

 that made with the latter ratio: remarking too, that the 



same 



