118 MR JAMES CLERK MAXWELL ON THE 



Fig. 2. Fig. 4. Fig. 3. 
curves for every fifteenth degree of inclination. They correspond to the lines of 
equal variation of the needle in a magnetic chart. 
From these curves others may be found which shall indicate, by their own 
direction, the direction of the principal axes at any point. These curves of direc- 
tion of compression and dilatation are represented in fig. 4; the curves whose 
direction corresponds to that of compression are concave toward the centre of the 
triangle, and intersect at right angles the curves of dilatation. 
Let the isochromatic lines in fig. 2 be determined by the equation 
1 1 
P: @y¥)=15=0@-P) > 
where I is the difference of retardation of the oppositely polarized rays, and g and 
p the pressure in the principal axes at any point, z being the thickness of the 
plate. 
Let the lines of equal inclination be determined by the equation 
2 (%, y) = tan 0 
6 being the angle of inclination of the principal axes; then the differential equa- 
tion of the curves of direction of compression and dilatation (fig. 4) is 
d 
$s (% )=57% 
By considering any particle of the plate as a portion of a cylinder whose axis 
passes through the centre of curvature of the curve of compression, we find 
d 
q—p=r ek) 
Let R denote the radius of curvature of the curve of compression at any 
point, and let S denote the length of the curve of dilatation at the same point, 
p;(% y)=R (41 Y=S 
dp 
7—p—E 
