APPENDIX CALCULATION OF THE 



Hence, when through the operation of a decrement 

 on an edge of any parallelepiped, a single row of 

 molecules is abstracted, the parts which are removed 

 from the two edges adjacent to that on which the 

 decrement has taken place, will be proportional to 

 those edges respectively ; and the ratio of those edges 

 may therefore constitute the unit of comparison for 

 decrements on the edges of parallelepipeds. 



If a decrement take place by one row on an angle 

 of a parallelepiped, a single molecule is first abstracted 

 from its solid angle; and the parts thus abstracted 

 from the three edges which meet at the solid angle, 

 are respectively proportional to those edges. 



The ratios of the three adjacent edges of any paral- 

 lelopiped, therefore, may be taken as the units of 

 comparison for determining the various laws of de- 

 crement on the angles of that class of primary forms. 



And, by analogy, we may take the ratios of the three 

 or four edges adjacent to the solid angles of any class of 

 primary forms, to express the ratios of the edges of 

 the defect occasioned by a decrement by one row of 

 molecules. 



But other lines may be traced on some of the 

 classes of primary forms, proportional parts of which 

 will also be intercepted by decrements by one row of 

 molecules. 



The ratios of these may therefore be taken as the 

 units of comparison, if we find them more convenient 

 for our calculations than those of the primary edges. 



When the edges, or other lines, from which the unit 

 of comparison is to be derived, are equal, their ratio 

 will be = I, and in this case the lowest whole numbers 

 which will express the ratios of the edges of the defect of 

 the primary form, will also express the law of decrement. 



And whenever an edge of any primary form is re- 

 placed by two similar secondary planes, as in 



