88 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
that of oblique illumination can then be used and the refractive index deter- 
mined with an accuracy of 0.001. 
The following method for producing an intense monochromatic flame 
has been found convenient and satisfactory in practice.* A 25 cc. platinum 
crucible, filled with a mixture of equal parts of sodium chloride and sodium 
carbonate and held in a special mounting of thick 
platinum wire, is heated over a Bunsen burner, as in- 
dicated in Fig. 55. A wick of fine platinum wires car- 
ries the molten salts from the base of the crucible out 
into a strong and constant blast-lamp flame, the high 
temperature of which produces an intense sodium 
flame which lasts for days until the salts in the cruci- 
ble are exhausted. The fumes from the salts are 
carried off under a hood. An oxyhydrogen blast may 
be used in place of the blast lamp. It gives a much 
more intense flame, but requires careful regulation ; otherwise it may melt 
down the platinum wick. 
In case only one side of a mineral grain or plate be observed, the phe- 
nomena observed vary slightly with the character of the boundary surface, 
as indicated by the following figures and calculations : 
In Fig. s6f let n\ be a mineral plate in the thin section and w 2 a second 
plate adjoining n\, the refractive indices of the two plates being n\ and j 
with ni < H 2 ; let the junction plane be vertical. A ray of light B\C\ entering 
HI will be deflected to D, where again it is deflected to F 2 and finally to H* 
in air. The relation of the direction H^Fz to BiCi or the angle t? 2 to ai is 
readily found by use of the sine relations 
sin ai = i sin ft (i) 
But </ 1 DCi = 0- 
. ' . rtj sin (90 y t ) = n\ sin (90 ft) = n\ cos ft (2) 
Squaring both sides of (i) and (2) and adding, we find 
sin 2 ai+ n\ sin 2 (90 - ? 2 ) = n\ (3) 
We have also : 
sin i? 2 = n 2 sin y t (4) 
sin 2 t? 2 = sin 2 oi-f n 2 2 2 i (5) 
I COS2?i I COS 2di 
- = -- ha w 2 i ' cos2t? 2 = cos2ai 2( 2 j n 2 i) (6) 
2 2 
In like manner it can be shown that 
cos 2?i = cos 2a 2 +2( 2 j n 2 i) (7) 
For the limiting angle a 2 at which total reflection just occurs at the junc- 
tion between n\ and 2, (heavy line, Fig. 57) t?i = o 
accordingly 
cos 2i?i = i and cos 2a 2 = i 2 (n j j n\) or sin 1 a 2 = n 2 2 n\ 
Amer. Jour. Set. (4). 27, 19}. 1909; 31. 185. 1911. 
1 1n Pigs. 56 and 57 the rays from the condenser lens are represented as coming to focus at the point D. 
This has been done purposely in order to render the figures as simple as possible. In actual work, this con- 
dition, however, is only approximately attained, the foci for the rays in the higher refracting substance MI 
being farther away from the incident surface c\ci than the foci of those in m. In both figures the directions 
are angle true for the refractive indices given. 
