458 Proceedings of Philosophical Societies. [Dec. 
sulphate of lime, begins to give colours anew when the thickness of 
the second plate of that substance comes within the limits/e + 42. 
of a millimetre. It preserves, then, in this case, durable’ traces of 
the physical impressions which it had undergone in passing through 
the first crystallized plate, and these impressions are proportional to 
the thickness e of that plate; while the ray polarized by simple 
reflection is modified completely, as if it had passed a crystallized: 
late of infinite thickness. The difference between the two rays: ° 
shows itself likewise in several other phenomena indicated by the’ 
theory, and which it would have been difficult, if not impossible, 
to divine otherwise. 
In his preceding researches on doubly refracting erystals, the 
author has shown that we may obtain extraordinary and ordinary 
coloured pencils with thick plates as well as with thin plates, by 
opposing the polarizing actions successively exercised by the two 
plates on the same luminous ray. When these plates are of the 
same nature, the opposition always takes place when their axes of. 
double refraction cross at right angles. But when they are of a 
different nature, we must in certain cases cross their axes, and in 
others place them parallel to each other. This last case takes place 
when we combine plates of beryl with those of quartz. When the 
axes of these two substances are placed in the same manner rela- 
tively to a polarized ray, the impressions which they communicate 
to it are such, that if they are successive they destroy each other. 
On the contrary, they continue and increase the effect if their axes 
are crossed at right angles, which is precisely the opposite of what 
we find when we combine two plates taken from the same crystal. 
Thus in this sort of effect which the crystals produce on luminous 
particles traversing them, we must distinguish two modes of im- 
pression different and opposite to each other, as is the case with 
vitreous and resinous electricity, or the north and south poles of a 
magnet. We may call them guartzy and berylly polarization. 
The following is a list of some substances which arraage themselves 
under the one or the other of these denominations. 
Quartzy Polarizxation.—Rock crystal, sulphate of lime, sulphate 
of barytes, topaz. 
_ Berylly Polarixation.—Calcareous spar, arragonite, phosphate of 
lime, beryl, tourmaline. 
When we combine together two crystals the polarization of 
which is of the same nature, we must cross their axes to obtain the 
differences of their actions; and on the contrary, we must place 
them parallel if their polarizations be different. We see that the 
primitive form of a erystal has no evident relation with the kind of 
polarization which it exercises, no more than it has with the elec- 
trical properties of minerals. 
In studying the action of the tourmaline on light, M. Biot ob- 
served in it the singular property of having double refraction when 
thin and single refraction when thick. To show these phenomena, * 
he polished the inclined faces of a large tourmaline, so as to forma ° 
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