130 Mr. Whewell on calculating the angles of crystals. 
The inverse problem, knowing two dihedral angles of the 
secondary figure to determine the symbols of the planes, is 
resolved by the same formulae. In the case where the angles 
made with the primary planes are given, we have a direct 
solution. In the other cases we find the indices of the symbol 
of trial ; and if the limits of the present paper allowed it, it 
might be shown how we might, after some trials, proceed 
directly to find the law. 
P. S. The greater part of the formulae in the preceding 
pages were calculated before my notice was directed to a 
paper by Mr. Levy, in the Edinburgh Philosophical Journal 
for April 1822. Mr. Levy there employs the principle which 
is the basis of the investigations now given, viz. the mode of 
expressing a secondary plane by means of its equation to 
three axes coinciding with the edges of the primitive form. 
From this principle he deduces, with great simplicity, the 
law of a secondary plane in a particular case; viz. when the 
intersections of that plane with two known planes, are parallel 
to their intersections with two others.* In order however to 
deduce the general' formula, a new and different series of 
theorems is necessary, as appears in the course of this paper. 
W. W. 
• It may be observed, that the result in this case is easily obtained from the for- 
mula in Art. 14. 
' 1 • 
