Dr. Brewster on the laws of polarisation, &c. 265 
elliptical plates heated in oil, and in the act of sudden cooling, 
the combined spheroids will constitute the class of crystals 
like mica, nitre , &c. in which the negative force predo- 
minates. 
The variation of density which these solids necessarily 
require, in order to develope a force varying as the fourth 
power, or an influence upon the tints varying as the square of 
the sine of the angle which the ray forms with the axes of the 
crystals, will be understood from PI. xvi. fig. 14,. Let MaNfe 
represent the section of the sphere through one of its great 
circles, then if we suppose that the density is a maximum in 
every point of the line MN, and that it diminishes from M to 
ah, and from L to dc, at first very slowly, and then very 
rapidly, like the cosines of the angles reckoned from MP, so 
that the lines of equal density in every section of the sphere 
passing through MN are diameters, the sphere will represent 
one of the integrant particles of the positive crystals, like 
ice, zircon, quartz , &c. having MN for its axis of double 
refraction and polarisation. In like manner, if the density is 
a minimum in the line MN, and increases in a similar man- 
ner, towards ab and cd, the sphere will represent an integrant 
particle of the negative crystals, such as beryl, calcareous spar, 
&c . When the polarised ray is transmitted along the axis 
MN, the polarising force will be nothing ; when it passes 
along RS, the variation of density is greater, and conse- 
quently the polarising force will be increased ; and when it 
is transmitted along ah, the polarising force will be a maxi- 
mum, as the variation of the density is a maximum in that 
line. As the same is true of every other section of the 
sphere passing through MN, it follows that there will be a 
mdcccxviii. M m 
