of the Sulphato-tri-Carbonate of Lead. 223 



According to the method of crystallographic designation of 



MOHS, the faces P, P, next the observer, and contiguous to 



P 

 the upper apex of the fundamental form, are denoted by g, 



and the other faces P' P', contiguous to the same apex, are 



T> 



denoted by . If we suppose the axis of a series of 



such pyramids of equal bases, to increase and decrease according 

 to the powers of the number 2, the limits at which this series will 

 arrive are, on one side, a plane figure parallel to the base, on the 

 other a four-sided prism parallel to the axis of the fundamental 

 form. The face a, in the combination Fig. 5, corresponds to the 

 first, and the faces cc to the second of these limits ; while their 

 crystallographic signs will be P co and P + GO . The inclina- 

 tion of the axis being so slight, the difference between the angles 

 of the base of P and those of the transverse section of P + oo 

 does not amount to 1' ; P + oo is therefore = 59 40'. 



Supposing the faces a and b to disappear from the combina- 



tions, the faces e will assume the figure of a rhomb NOQP, 



P 

 Fig. 7, at the solid angle of combination between ^ and P -f oo . 



As the diagonals of any rhomb bisect each other ; NR will be 

 - RQ. Draw NT parallel to BQ, and QT parallel to BM. Since 

 the angle NRS is = BRQ, and RSN RBQ, and the line 

 NR RQ, the triangles NRS and QRB will be equal and similar; 

 therefore NS = BQ, and also = ST, which will make NT 2.NS. 

 If a tangent plane, laid on the terminal edge AB of the fundamen- 

 tal pyramid produces the horizontal prism P r , that plane, the 

 corresponding axis of which is double the axis of the former, will 

 produce a prism belonging to P -f- 1> and e, therefore, receives 



the crystallographic sign - T ^ . The inclination of e to a is 



= 112 0'. As the situation of e' is analogous to that of e, its crys- 

 tallographic sign is r <^ , and the inclination of e' to a 

 ll'. Since the edges of combination between e and b are 



