crystallized bodies on homogeneous light. 85 
Resuming our general equations (b) and (d) if we sub- 
stitute the value now determined for 4/, and write — for we 
have 
l'. cos <p'. sin 9 . sin 9 ' = l . cos <p . sin (9 — fa -j- f <p). 
sin Sa + $<p) ; (g) 
whence it is easy to derive (independent of any approximation) 
cos 2 (tf + ^ ) = cos 2 <P f + 2 T '^7^ - si 11 9 • sin O'; (h) 
while our approximate equation ( d) furnishes the following 
very convenient formula for incidences nearly perpendicular 
sin 8 a — 
sin 0 . sin 0' 
sin 2 a 
(>) 
The simplest supposition we can frame relative to the va- 
lues of the constant elements l, V is their proportionality to 
those of c, c' , or the lengths of the fits of easy reflection and 
transmission This cannot certainly be far from the truth in 
crystals with one axis, in which the coincidence of the tints, 
with those of Newton’s scale, is for the most part exact. In 
sulphate of lime too, and mica, the only crystals with two axes 
which have been examined with sufficient exactness, and under 
the proper circumstances for ascertaining this important point, 
the law of proportionality seems to be sustained with great 
precision. This may seem to authorize the general conclu- 
sion, that in all cases, -L = — • Let us see how this agrees 
with the measures given in the former part of this paper. 
In sulphate of baryta, if we take Dr. Brewster’s measure 
of the dispersive power,* we have ^R = 0-019, and conse- 
quently, calculating on the data determined in page 71, we 
must have, at the virtual pole, 
(p = 21°5 / 30 // <£>'== 20° 50' go" 8 <p= — 15' 
Now, if we suppose /= 6-3463 /' = 3-9982, the values of c 
* = 0-019. Treatise on new Philosophical Instruments. 
