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Proceedings of the Boyal Society 
of Sir David Brewster on crystalline reflexion appear to counten- 
ance such a supposition ; but the problem of crystalline reflexion 
is involved in obscurity. 
28. Since all the properties of crystals, as the values of the prin- 
cipal refractive indices, the wave velocities, the form of the wave 
surface, &c., depend on the values of a', h', c', it follows that the 
complete solution of the problem of the connection between the 
form and optical properties of crystals consists in determining 
a', 5, c' as functions of a, 5, c. 
^ _ c'2 
JfFc~fabc~ffd^ 
wdiere a' h' c' are in descending order of magnitude, 
then f.ahc -fahc = (a — If (a -hfSy 
fahc —fabc = (b- cf (b — c V3)^ 
^ 
■ ' (a - bf (a - b\^3y c^ + (b- c)^ (b ~ c\/3)'^ -1 - fabc 
b_f 
~(b- c)'\b - cfSy^a^ + fabc 
~fabc 
Hence only one function remains to be determined. Sym- 
metry would suggest the value (c-af (c - aV3)'^ b^ for fabc. We 
have not as yet, however, attempted to determine the value of fabc 
by the comparison of this formula with observation. 
29. The investigation of the optical properties of crystals belong- 
ing to the oblique system is still in progress. The following is the 
method employed in this investigation. Each crystal is referred to 
three rectangular axes, one axis being perpendicular to the plane of 
the optic axes, the other two being the internal and external 
bisectors of the angle between the optic axes. The new parameters 
are calculated by means of formulae investigated in a paper on the 
‘‘ Ehombohedral System ; ” and thence the angle between the optic 
axes is found, as if the crystal belonged to the prismatic system, 
by means of the formulas given in this note. The augle between 
the optic axes of one mineral belonging to the oblique system has 
been calculated by this process ; and the calculated has been found 
