in the Analysis of Crystalline Forms. 3 



ced from the fundamental form. As my object here is to ex- 

 emplify the mode of deduction only, and not to give an expo- 

 sition of the method, I shall merely put down the steps by 

 which each of the faces of a certain complicated figure may be 

 analyzed, giving in the margin the enunciations only of the 

 theorems which it is necessary to assume. 



The notation which I shall employ is different from that of 

 Mohs, but seems to me to be that to which Mr Mohs's natu- 

 rally bends when we remove a few anomalies and arbitrary 

 designations, and replace them by such modes of representa- 

 tion as the symmetry of the method, and the principle of 

 avoiding any superfluous assumption plainly suggest. 



The example which I shall take belongs to what has been 

 called the rhombohedral system ; which includes such figures 

 as can be derived from a rhombohedron. These may be de- 

 scribed generally as forming at each extremity of the figure 

 3-and 6-sided pyramids. 



Let the equilateral 3-sided pyramid, which is formed by 

 the faces of the fundamental rhombohedron, be called R. 



Let any equilateral 3-sided pyramid, on the same base, and 

 with an axis equal to p times the former be called pR. 



Let any 6-sided pyramid be deduced from /?R by three 

 symmetrical faces of planes, each plane being drawn through 

 an angle of the base, parallel to the next slant side ; such, 

 that if we k draw from the angle corresponding to this slant 

 side a perpendicular on the opposite side of the base, the por. 

 tion of this perpendicular produced, which is intercepted by 

 the plane, shall be m times the perpendicular. And let the 

 form bounded by such planes be pRm. 



When any of these figures is turned round its axis, through 

 180°, it is represented by pW on pB/m; and the forms are 

 said to be transverse to the former ones. 



Any 3-sided pyramid, or rhombohedron which can be de- 

 duced from R, may be represented by pK or pR ; , and any 

 6-sided pyramid which can be deduced, may be represented 

 by^Rm, or^R'ra. 



Let now Fig. 1. of Plate I. represent a crystalline form, (for 

 instance a crystal of carbonate of lime,) belonging to the rhom- 



