MODIFICATIONS. 277 



Intermediary decrements on the superior angles. 

 (B'p B q B"r : B P B'p B"r) represents class d. 



The inferior plane angle at O, and the lateral plane 

 angle at E, both belong to the lateral solid angles, all 

 of which are similar, according to the definitions 

 already given. 



The planes modifying the angles at E are therefore 

 similar to those modifying the angle at O, but are 

 reversed in their position on the crystal. The laws 

 of decrement producing both are consequently simi- 

 lar. But if we refer the decrements producing the 

 planes belonging to any of the classes e, J\ g, h, i, k, 

 /, to the solid angle at E, the symbols representing 

 them will differ from those which would represent 

 the same planes, if we refer the decrement to the solid 

 angle at O. 



A single example will sufficiently illustrate this 

 observation. Let us imagine the lateral solid angles of 

 a rhomboid to be modified by two planes, which inter- 

 sect the primary planes parallel to their oblique diago- 

 nals. If the decrement producing these planes were 

 referred to the angle at E, it would appear as a sim- 

 ple or mixed decrement, and its symbol would be 

 E /p P E. But if it be referred to the angle at O, it 

 might be regarded either as a simple or mixed, or as 

 an intermediary decrement, of which latter the symbol 

 would be (D' P D q b /; P : Dp D' q b /; P ). If we regard 

 these symbols with a little attention, we shall per- 

 ceive that the variation in their form, does not alter 

 the identity of their character, which is derived from 

 the parallelism of one edge of each of the secondary 

 planes to an oblique diagonal of the primary. But 

 this character is implied in the supposition of a sim- 

 ple or mixed decrement, which the first symbol 



