25 2 Dr. Brewster on the laws of polarisation, &c. 
and the resultant axis must intersect each other at an angle 
of 90*, and their intensities will be as the squares of the 
sines of their respective distances from the resultant axis. 
The ratio of the intensities, however, can never exceed that 
of 1 to Sin. 2 <p, <p being the distance of the resultant axis from 
the plane passing through u, ( 3 . 
It would be needless to pursue this subject any farther. 1 
have briefly illustrated the general principles of the resolu- 
tion of the axes of crystals, and the reader will have no dif- 
ficulty in deducing other combinations by which the pheno- 
mena may be represented. A very important question is 
naturally suggested by the results to which we have arrived. 
Are there any physical circumstances either of a general or 
a particular nature which may lead us to ascertain the real 
position of the axes of crystals, and to determine the character 
of the forces by which the phenomena of polarisation are pro- 
duced ? When we consider the case of Iceland spar, we per- 
ceive no peculiarities which can induce us to refer its polarising 
force to two or more positive axes in preference to a negative 
axis ; but in rock crystal , the secondary tints discovered by 
M. Biot along the axes of the prism, seem to indicate 
that its apparent positive axis is merely the resultant of two 
or more equal and rectangular negative axes. M. Biot in- 
deed ascribes these secondary effects to new forces inde- 
pendent of the principal polarising force; but I have dis- 
covered them also in crystals with two axes, and have 
observed some phenomena which seem to prove that they 
have their origin in the unbalanced action of the two prin- 
cipal axes. 
With regard to the nature of the forces we are not left 
