MODIFICATIONS. 279 



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2. Intermediary decrements on the lateral solid angles. 



The general symbols to represent the modifications 



produced by these, are, 



(D' P b"r D q : D' q b"r Dp). | (Dp D" q Br : D q D% Br). 

 Ifri=j9, the symbol represents the planes be- 

 longing to class h, as described above, 

 r ^> p, the planes of class i are represented. 

 r <^ p, the planes of class I, and class f, are 



represented. 



Although these two classes are represented by a 

 common symbol, there is this distinction between 

 them ; that the edge produced by the intersection 

 of the planes belonging to class/, is always paral- 

 lel to the vertical axis of the rhomboid ; and that 

 their indices p, q^ and r, are in a constant ratio to 

 each other, as will be shewn in the appendix; while 

 the planes belonging to class k do not intersect 

 each other parallel to the axis of the rhomboid, nor 

 is there any constant ratio between their indices. 



Decrements on the superior edges. 

 General symbol P B P . 



If p =z 1, the symbol represents mod. m. 

 p ^> 1, class n\ 



Decrements on the inferior edges. 

 General symbol P D P . 



If p 1, the symbol represents mod. a. 

 p ^> 1, class p. 



It may be remarked, that several of the classes of 

 modifications on the angles of some of the primary 



