226 Dr. Brewster on the laws of polarisation , &c. 
i . On the form of the rings or isochromatic curves , and on the 
nature of the tints in crystals with more than one axis. 
We have already seen that when a crystal has only one ap- 
parent axis of double refraction, the isochromatic curves, or 
lines of equal tint are perfect circles having the axis of extra- 
ordinary refraction passing through their centres ; but when 
these curves are the result of two separate axes they assume 
the more complicated form represented in PI. XV. fig. 4, 
If we transmit polarised light in every possible direction 
through a crystal, COD 0, PL XV. fig. 5, ( which is a section of 
the sphere in Fig. 4, through the great circle CODo,) we shall 
find that there are -two diameters P p, P ' p' in which there is 
neither polarisation nor double refraction. To these lines I 
have given the name of resultant axes or diameters of 710 polari- 
sation, P,P p,p' PL XV. figs. 4 and 5, being the poles of no 
polarisation. Each of these poles is surrounded with similar 
sets of rings, the tints of which commence at P, P ' p, p' increase 
towards O, C, D,A, and B, and reach their maximum at 
A and B. When the distance PP' or the inclination of the 
diameters of no polarisation is considerable, the rings near 
P,P are almost circular, but the circularity soon ceases as 
they recede from the pole. If PP' is less than 90, the tints 
at C,D, which are always equal, are higher than those at O, 
and when P,P is exactly 90°, the tints at C, 0 , 0, D are equal, 
and the rings are symmetrical round P,P'. 
As PP' is always less than 90°, the great circle ACBD 
may be called the Equator of maximum double infraction or 
polarisation , since the double refraction and the polarisation 
are always greatest in this line. The great circle AOBO, 
