in the polarized Tints of certain Crystals with one Axis. 337 
n = _. sin 6 x tan 0 , the laminae being supposed all of one 
(/ 
class, (?. e. all positive, or all negative,) or t being regarded as 
negative for those of a contrary class. The periods performed 
by the same ray in traversing the second lamina will be 
t 
n' — - X sin 6 x tan 0, and so on, and, according to what the same 
l' 
eminent philosopher has proved, the ray will assume at its emer- 
gence from the system the same plane of polarization as if it has 
executed n 4 n' 4 n" 4 , &c. periods in one lamina. If, then, we 
take n 4 n' 4 n" 4 , &c. — N ; t 4 t 4 t" 4 ? &c. — J\ we have 
( i t f' \ T 
- + — 4 — 4, &c. I X sin $ x tan 0 = — x sin 6 x tan 
l V If' / L 
T t t' 1 " 
provided we take Z, so that -=- = — 4 — -4? &c. 
1 j L L L 
Let p , p\ p " , & c. represent the polarizing power of each la- 
mina on the given ray, and P, that of a lamina equivalent to 
II 1 
the compound system, and we have p = — _ ? &c. - , so 
l l L 
and P 
that T. P — t,. p 4 t'.p' 4 t".p" 4 , &c. 
t.p 4 f y 4 r.p" 4 , be. , . 
4 - — . I r, then, 7 be so assn- 
14 14 14, &c. 
med, an imaginary plate, whose polarising power is P, and thick- 
ness that of the compound plate ( t 4 t' 4 , &c.) will exercise pre- 
cisely the same action on the ray as the system so constructed, 
and it appears from the nature of this formula, that it is indif- 
ferent in what order the elementary laminae are distributed ; so 
that all those of the same species may be conceived grouped to- 
gether and united into one. 
Now, suppose the colour of the ray to vary, and let c be any 
quantity whose magnitude determines its place in the spectrum 
(as, for instance, the reciprocal length of one of its fits of easy 
transmission and reflexion in vacuo). Then, if we represent, as 
we have done before, the quantity c by the abscissa of a certain 
curve, p) (a function of c), may be represented by its ordinate ; 
p f (another function of c), by the ordinate of another curve, and 
so on ; and P, the ordinate of a similar curve, for the compound 
plate may be computed by the above formula. 
