Dr. Brewster on the laws of polarisation, &c, 257 
of an axis of an opposite name to that of the three axes 
and coinciding with the resultant of the other two; but if 
one of the axes is stronger than the other two, the result will 
be an axis of the same name with the three axes, and coin- 
ciding with the strongest axis. 
Let us now consider what will be the effect if the three 
negative axes C,A,0, PL xv. fig. 4 , are all different ; C 
being the strongest and O the weakest. The two axes 
C and A will, by their joint action, produce resultant axes 
P,P' lying in the plane COD. Let the third axis O be re- 
solved into two positive axes at C and A, then we have a 
negative axis A, and a positive axis equal to O acting at A, 
and the negative axis C, and a positive axis equal to O 
acting at C ; but O is less than A or C, therefore we have 
a negative axis equal to A — O acting at A, and a negative 
axis C — - O acting at C ; and as the last of these is the 
strongest, the general effect will be the production of two 
resultant axes in the plane COD. But as C — O has to 
A — O a greater ratio than C has to A, the poles of no 
polarisation P,P' will be removed farther from O than they 
were by the action of C and A alone. 
The equilibrium of the three axes may also be disturbed by 
another cause, namely, by a deviation from perfect rectan» 
gularity. In order to understand the effect of this irregu- 
larity, let ABC, PL xvi. fig. 10 , be the three rectangular 
axes, and Ba, C/3 the deviation of the axes « and j3. Then 
the effect of the equal and inclined axes u, /3 is to produce 
poles of no polarisation, one of which is seen at G in the 
plane EGA, bisecting the angle formed by the planes passing 
MDCCCXVIII. L 1 
