^ Sulpliato4ri-Carhonate of Lead. 289 
dng angles, like A and B, Fig. 1., in the supposed regular six- 
sided prism. The remainder, ABA', of the terminal face of one 
of the individuals, is inclined to the similarly situated face of the 
other at an angle of 1 79° 10', to which, on the opposite side, 
corresponds a re-entering angle of 180° 50'. Both these facts I 
had observed separately in numerous specimens, but the small- 
ness of well-pronounced crystals, and the impossibility of dis- 
tinguishing by the eye an angle of 119° 50', from one of 120° 
20', rendered it very difficult to combine these observations 
into one representation of its forms. The observation, that 
the plane of the resultant optical axes passes through a line 
parallel to A'A, Fig. 1., led me to inquire whether the face 5, 
which I had before supposed to be one of the faces of an ob- 
Jique-angular four-sided prism, might not be parallel to the short 
diagonal of the prism produced by the enlargement of the faces 
c, c, &c. The examination of a small, but beautiful, and very 
regularly formed twin-crystal, in the collection of Mr Allan, 
carried on upon this supposition, gave at last the results which 
form the substance of this paper. One of the individuals of that 
regular composition is represented in Fig. 2. ; and Fig. 3. is its 
projection, on a plane parallel to the face the whole of the 
crystal having been duly completed. 
If enlarged to their mutual intersection, P and P' produce 
the fundamental form of the species, a scalene four-sided pyra- 
mid, in which the axis of the form, is inclined to a line perpendi- 
cular to the base, at an angle of 0° 29'. In the method of Pro- 
fessor Mohs this angle is called the Inclination of the Aoci§.^ and 
the variable quantities considered are, the line perpendicular to 
the base of the pyramid, which line is called a, the diagonal 5, 
in the plane of inclination, the other diagonal c, and a fourth 
line d, which corresponds to, or subtends, the angle of inclina- 
tion. 
The ratio of these lines a:b:c: d, which gives a result agree- 
ing nearest with observation, is that of 120 : 95 : 54.5 : 1. Up- 
on this supposition the angles of the fundamental form are the 
following : Inclination of P upon P over the face 72° 36'; 
of P' upon P', on the opposite side, = 72° 10' ; of P upon P/ 
contiguous to the same apex, = 124° 50'; of P upon P', conti- 
guous to the opposite apex, = 137° O'. 
