9,2© Dr. Brewster on the laws of polarisation, &c. 
point where A,B, crosses the middle ring will be black, 
as the action of the calcareous spar is there exactly counter- 
balanced by the action of the rock crystal. The rings within 
CD, EF will be positive, in consequence of the action of 
the rock crystal predominating, and those without them 
will be negative, in consequence of the action of the cal- 
careous spar predominating. If the plate of rock crystal or 
sulphate of lime produces the rings at a, b, instead of A,B, then 
in the other two quadrants, c, d, the tints will be those which 
are produced by the sum of the actions of the crystals, and 
the tints at c and d will be double of that which is produced 
at these points by the calcareous spar alone.* 
One of the most interesting features of the system of 
coloured rings, is the black cross MN, PR, where the two 
arms are exactly at right angles to each other. If the plate 
which produces this system of rings is turned round its axis 
O, the rings and the black cross will preserve an invariable 
® The developement of colours by the opposite action of two crystallized plates, 
which are not capable of producing them separately, was first effected by M. Biot, 
before the discovery of the coloured rings, and by the aid of his divided apparatus ; 
but the preceding method of developing the rings by these opposite actions, is more 
general, and is so extremely simple, that it can be easily done by any person, merely 
by holding the crystals in his hands. The difficulties experienced by M. Biot are 
thus stated by himself : “ Mais telle est l’exactitude qu’il faut mettrea ces recherches 
que mes premieres tentatives n’eurent aucun succes, parce que je m’etais borne a 
operer le croisement a la main au lieu d’ employer les appareils divises qui m’avaient 
servi jusqu’alors. Car la grande energie du spath d’Islande fait que si l’on s’ecarte le 
moins du monde des positions indiquees par la theorie, on passe ala polarisation totale 
et les couleurs ne peuvent plus se developper. Cette cause faisait aussi qu’il etaitplus 
difficile de tomber precisement sur la proportion des epaisseurs de chaux sulfatee 
qui pouvait servir a compenser les lames de cristal d’Islande soumises a l’experience.” 
Mem. de VInstitut. Lu 27 Dec. 1813. 
