Dr. Brewster on the laws of polarisation , &c. 249 
equal rectangular positive axes of the same intensity as the 
negative axis, and lying in a plane perpendicular to that axis. 
This fundamental principle being established, we may pro- 
ceed still farther in the resolution of the axes into axes of 
equal intensity, but differing in their character and position. 
Thus in PI. xvi. fig, 9, the negative axis A being equivalent 
to the positive axes B,C, we may again resolve B into a ne- 
gative axis at C and another at A. Hence the original axis 
at A is equivalent to a negative axis at A, a positive axis 
at C, and a negative axis at C. But these two last axes 
destroy each other; and therefore the negative axis A is the 
only one that is left. If we also resolve the other positive 
axes C into two negative axes at A and B, we have the 
original negative axis A, equivalent to four negative axes, 
two at A, one at C, and one at B. We therefore conclude, 
2d. That the effect of a single negative axis may be re- 
presented by three rectangular negative axes, provided two of 
them are equal, and the third has a greater intensity than 
the other two ; and vice versa a single positive axis may be 
represented by three rectangular positive axes, provided 
two of them are equal, and the third has a less intensity than 
the other two. 
Hence it follows that by leaving one axis at A, the effect of 
the other three negative axes must be to destroy each other, 
a result which will afterwards be established in a different 
way, and will lead us to some important consequences. The 
same is true of positive axes, mutatis mutandis. 
Hitherto we have resolved the axes of crystals into other 
axes differing in position and character, but having the same 
intensity. If we consider, however, that any one axis at A 
mdcccxviit. K k 
