of the Sulphato-tri-Carbonate of Lead. 221 



tion of its forms. The observation, that the plane of the result- 

 ant optical axes passes through a line parallel to A' A, Fig. 1., 

 led me to inquire whether the face b, which I had before sup- 

 posed to be one of the faces of an oblique-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 exami- 

 nation of a small, but beautiful, and very regularly formed twin- 

 crystal, in the coUection 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. 3. ; and Fig. 4. is its projection, on a 

 plane parallel to the face a, the whole of the crystal having been 

 duly completed. 



The number of faces which constitute this crystalline form is 

 so great, and the form itself is, on that account, so complicated 

 at first sight, that it will be more convenient to begin with con- 

 sidering some simple varieties of the substance, in order tq afford 

 a more distinct idea of its Series of Crystallisation. 



One of these varieties is represented in Fig. 5. Beside the 

 faces of Fig. 1., all those edges which are not parallel to the axis 

 are replaced by the inclined faces e, e', P, and P'. If enlarged to 

 their mutual intersection, P and P' produce the fundamental 

 form of the species, Fig. 6., a scalene four-sided pyramid, in which 

 AX, the real axis of the form, is inclined to AP, a line perpendi- 

 cular to the base BCB'C', at an angle of 29'. In the method 

 of Professor MOHS the angle MAP is called the Inclination of the 

 Axis. This method of considering hemiprismatic forms, is best 

 calculated to render more striking those analogies which exist be- 

 tween the series of crystallisation of the species in which the axis 

 is perpendicular, and of those in which it is inclined to the base 

 of the fundamental form. The development of the formulae ex- 

 pressing the angles of this kind of pyramids, depends upon the 

 comparison between the lines AP, MB, MC, and MP. 



