394 APPENDIX ON THE 



duced by a simple or mixed decrement on a lateral 

 edge of the prism ;* and the parallelism of the diago- 

 nal of the terminal plane, to the edge at which the 

 secondary plane d intersects that plane, indicates a 

 decrement by 1 row on the lateral edge of the prism ; 

 for it is obvious that the edges of the defect are here 

 proportional to the primary edges. 



Cases however of a much more complicated nature 

 may be determined by means of the parallelism of 

 the edges of crystals. 



We are indebted to the Abbe Haiiy for the earliest 

 observations which occur on this subject. He re- 

 marked, among other instances, that whenever the 

 terminal edges, and the solid angles, of the hex- 

 agonal prism, were replaced at the same time, if 

 the decrement in breadth on the edge happened to 

 be double that on the angle, the opposite edges of 

 the plane replacing the solid angle would be paral- 

 lel, and the figure of that plane would be a rhomb. 



A memoir by Mr. Monteiro, on the determination 

 of the law of decrement producing a new variety of 

 carbonate of lime, was inserted in No. 201 of the 

 Journal des Mines for September 1813, and an out- 

 line of it is given here as an example of the method 

 used to determine that law. This memoir illustrates 

 the utility of this method of determining the laws of 

 decrement, by its application to a case where the 

 angle could not be measured at which the secondary 

 plane whose law of decrement was required, inclined 

 on the primary, or on any other plane} whose rela- 

 tion to the primary was known. 



* It is apparent that the plane d is parallel to the edge it replaces ; 

 and it may be observed generally, that whenever the edges of a 

 secondary plane are parallel, the plane itself is parallel to the edge it 

 replaces. 



