ELASTICITY AND CRYSTALLINE FORMS. 
285 
lar to those of the coefficients A. In the iimhral notation, umbrae are usually distin- 
guished from symbols denoting actual quantities by being enclosed in brackets thus: 
(a), (/3), &c 
and each coefficient A is represented by enclosing in brackets that product of umbrae 
with which it \s covariant thus: 
= ). 
The Umbral Notation is applied to abbreviate the expression of determinants in a 
manner of which the following are examples : — 
^5 7 . 
a? 7? 
&c. 
&c. 
denotes 
(«^) 
(a/3) 
(«7) 
&c. 
(a/3) 
m 
(M 
&c. 
(a7) 
(M 
(f) 
&c. 
&c. 
&c. 
&c. 
&c. 
a, 7, 
7, 
K 
&c. 
&c. 
denotes 
(a/3) 
(M 
(W 
&c. 
M 
(f) 
(7§) 
&c. 
(a§) 
(7^) 
&c. 
&c. 
&c. 
See. 
&c. 
February 24, 1856. 
2 p 
iuucccLvr. 
