colours which accompany them in calcareous spar. 281 
This, however, is true only when the pencil is incident at an 
angle of between 12 0 and 14 0 , as described in Sect. I.,* and we 
have already seen that in this case the images are reduced to 
two. In every other position of the incident ray, the pencils 
are subdivided by the second prism. 
The division of the pencil into two parts after it has pene- 
trated the first surface, or before it has emerged from the 
second surface of calcareous spar, enables us to explain the 
curious fact observed by Malus, relative to the light reflected 
from the interior surface of doubly refracting crystals. He 
discovered that the ray refracted ordinarily at the second 
surface was reflected at this surface in two pencils, one ordi- 
nary, and the other extraordinary ; and that the ray refracted 
extraordinarily at the second surface, was also reflected in 
two pencils ; so that there were four reflected rays, and only 
two emergent ones. These four rays returning to the first 
surface of the crystal, emerge in four parallel pencils, which 
form with this surface the same angle as the incident ray. 
The cause of this singular fact will be understood from 
Fig. 5, where ABCD is a piece of calcareous spar, and mn , (tv, 
the lines within the crystal at which the extraordinary refrac- 
tion takes place. A ray of light RS will be divided into two 
pencils Sa, Sb, which will emerge in lines a a, b( 3 , parallel to 
RS. The reflected portions bd, ac will be subdivided at c and 
d, just as if they had been incident in the directions Su.xa, 
and will form four pencils ce, cf, dh , dg, which is the pheno- 
menon observed by Malus. In order to show experimen- 
tally that the rays a a., b (3 are subdivided at c and d, when 
received upon the rhomboid in the directions $b, xa, cement 
* I shall have occasion to consider this law in a subsequent Paper. I have stated 
the angle at between 1 2° and 1 4 0 as the pencil dh Fig. 4. vanishes at a less angle than ce. 
MDCCCXV. O O 
