280 RELATION OF DECREMENTS TO 



forms, comprise planes which are produced by very 

 different laws of decrement. And it may possibly 

 appear to some of my readers, that different classes 

 ought to have been established for the planes pro* 

 duced by the several varieties of laws. But this would 

 have rendered the tables of modifications less gene- 

 rally applicable to the description of secondary forms, 

 independently of the theory of decrements, than they 

 are at present. This will become very obvious if we 

 refer to the classes a, &, c, or J, of the modifications of 

 the doubly oblique prism. All that can be known 

 of any individual plane belonging to either of these 

 classes, independently of calculation, is that it be- 

 longs to such a class, and inclines on two of the 

 adjacent primary planes at particular angles ; and this 

 enables us to record the particular plane. 



If we refer to p. 274, we may perceive that the 

 planes belonging to either of those classes might be 

 produced by four different kinds of decrement. 



Let us suppose that we have observed a plane upon 

 a doubly oblique prism produced by one of those 

 decrements. As it replaces the solid angle O, we 

 refer it without hesitation to our present class, a. 



But if class a had been divided into four classes, 

 we could not, without previous calculation, know to 

 which of those the observed plane ought to be re- 

 ferred ; and the measurement of the crystal would 

 not in such case, enable us to describe the secondary 

 form, by the assistance of the tables only. 



The symbols used in this volume to represent 

 planes produced by intermediary decrements, contain 

 indices which are always whole numbers ; whereas the 

 symbols used by the Abbe Haiiy to represent similar 

 planes, frequently contain fractional indices. 



