crystallized bodies on homogeneous light. 63 
A more scrupulous examination however will show, that 
its origin must not be sought in any cause of this nature, 
for (not to mention the impossibility of explaining the phe- 
nomena of the virtual poles by this hypothesis) if we place the 
principal section of the crystal in the azimuth zero, the extra- 
ordinary image will be found to vanish completely for every 
angle of incidence, and whatever be the thickness of the plate. 
I may add too, that I have in my possession a crystal of quartz, 
which exhibits with tolerable distinctness in some parts the 
phenomena of two axes, and the appearances produced by 
the interference of the secondary tints in this specimen, while 
they agree completely with M. Biot’s explanation, differ 
entirely from those which form the subject of this Paper. 
Neither are the phenomena above described explicable on 
any supposition of a peculiar action of the crystal on the diffe- 
rently coloured rays, analogous to its ordinary or extraordi- 
nary dispersive power, by which the periods of alternate polar- 
isation of the molecules of some colours, should be length- 
ened, and of others contracted, so as to disturb that exact 
proportionality to their periods of easy reflection and trans- 
mission, which M. Biot has proved to be a necessary condition 
for the production of the tints of Newton's scale. It is true, 
such laws of action may be imagined, and I shall presently 
show must really exist ; in all crystals probably to a small 
extent, but in two instances at least, to a surprising degree. 
But this alone will avail us nothing. To show this, and at the 
same time obtain a general analytical expression for the tint 
developed at any inclination, and for every hypothesis of the 
action of the crystal on the differently coloured molecules, 
let us denote by c, the length of a complete period of easy 
