D2 REPORT—1862. 
Rudberg used the formula for the ray-axes instead of that for the wave-axes, 
which made the theoretical inclination in air appear about 2° greater than 
the observed*. A very exact measure of the angle between the optic axes of 
Arragonite for homogeneous light corresponding to the principal fixed lines 
of the spectrum has recently been executed by Professor Kirchhoff +, by a 
method which has the advantage of not making any supposition as to the 
direction in which the crystal is cut. The angle observed in air was reduced 
by calculation to the angle within the crystal, by means of Rudberg’s indices 
for the principal axis of mean elasticity ; and the result was compared with 
the angle calculated from the formula of Fresnel, on substituting for the con- 
stants therein contained the numerical values determined by Rudberg for all 
the three principal axes. The angle reduced from that observed in air proved 
to be from 13! to 20! greater than that calculated from Fresnel’s formula. 
This small ditference seems to be fairly attributable to errors in the indices, 
arising from errors in the direction of cutting of the prisms employed by 
Rudberg. The angle measured by Kirchhoff would seem to have been trust- 
worthy to within a minute or less, 
It is doubtful, however, how far we may trust to the identity of the 
principal refractive indices in different specimens of the mineral. Chemical 
analysis shows that Arragonite is not pure carbonate of lime, but contains a 
variable though small proportion of other ingredients. To these variations 
doubtless correspond variations in the refractive indices; and De Senarmont 
has shown how the inclination of the optic axes of minerals is lable to be 
changed by the substitution one for another of isomorphous elements. More- 
over, M. Des Cloizeaux has recently shown that in felspar and some other 
minerals, which bear a high temperature without apparent change, the 
inclination of the optic axes is changed in a permanent manner by heats$ ; 
so that even perfect identity of chemical composition is not an absolute 
guarantee of optical identity in two specimens of a mineral of a given kind. 
The exactness of the spheroidal form assigned by Huygens to the sheet of 
the wave-surface within Iceland spar corresponding to the extraordinary ray, 
does not seem to have been tested to the same degree of rigour as the ordinary 
refraction of the ordinary ray; for the methods employed by Wollaston || and 
Malus 4 for observing the extraordinary refraction can hardly bear comparison 
for exactness with the method of prismatic refraction which has been applied 
to the ordinary ray ; and observations on the absolute velocities of propagation 
in different directions within biaxal crystals are still almost wholly wanting. 
This has long been recognized as a desideratum, and it has been suggested 
to employ for the purpose the displacement of fringes of interference. It 
seems to me that a slight modification of the ordinary method of prismatic 
refraction would be more convenient and exact. 
Let the crystal to be examined be cut, unless natural faces or cleavage 
planes answer the purpose, so as to have two planes inclined at an angle 
suitable for the measure of refractions; there being at least two natural 
faces or cleavage-planes left undestroyed, so as to permit of an exact measure 
of the directions of any artificial faces. The prism thus formed having been 
mounted as usual, and placed in any azimuth, let the angle of incidence or 
* Annales de Chimie, tome xlviii. p. 258 (1831). 
+ Poggendorff’s Annalen, vol. cviii. p. 567 (1859). 
{ Annales de Chimie, tome xxxiii. p. 391 (1851). 
§ Annales des Mines, tome ii. p. 327 (1862). 
|| On the Oblique Refraction of Iceland Spar, Phil. Trans. for 1802, p. 381. 
‘| Mémoires de l'Institut; Say, Etrangers, tome ii, p, 308 (1811), 
