EQUILIBRIUM OF ELASTIC SOLIDS. 117 
and if the retardation at o be taken for unity, the isochromatic curves 2, 4, sur- 
round A, and A,; that in which the retardation is unity has two loops, and 
passes through O; the curves x tare continuous, and have points of contrary 
flexure; the curve 2 has multiple points at C, and C,, where A, C,=A, A», and 
two loops surrounding B, and B,; the other curves, for which = = &c., con- 
sists each of two ovals surrounding B, and B,, and an exterior portion surround- 
ing all the former curves. 
I have produced these curves in the jelly of isinglass described in Case I. 
They are best seen by using circularly polarized light, as the curves are then 
seen without interruption, and their resemblance to the calculated curves is more 
apparent. To avoid crowding the curves toward the centre of the figure, I have 
taken the values of I for the different curves, not in an arithmetical, but in a geo- 
metrical progression, ascending by powers of 2. 
Case XIV. 
On the determination of the pressures which act in the interior of transpa- 
rent solids, from observations of the action of the solid on polarized light. 
Sir Davin Brewster has pointed out the method by which polarized light 
might be made to indicate the strains in elastic solids; and his experiments on 
bent glass confirm the theories of the bending of beams. 
The phenomena of heated and unannealed glass are of a much more complex 
nature, and they cannot be predicted and explained without a knowledge of the 
laws of cooling and solidification, combined with those of elastic equilibrium. 
Tn Case X. I have given an example of the inverse problem, in the case of a 
cylinder in which the action on light followed a simple law; and I now go on to 
describe the method of determining the pressures in a general case, applying it to 
the case of a triangle of unannealed plate-glass. 
The lines of equal intensity of the action on light are seen without interrup- 
tion, by using circularly polarized light. They are represented in fig. 2, where 
A, BBB, DDD are the neutral points, or points of no action on light, and CCC, EEE 
are the points where that action is greatest; and the intensity of the action at 
any other point is determined by its position with respect to the isochromatic 
curves. 
The direction of the principal axes of pressure at any point is found by trans- 
mitting plane polarized light, and analysing it in the plane perpendicular to that 
of polarization. The light is then restored in every part of the triangle, except 
in those points at which one of the principal axes is parallel to the plane of 
polarization. A dark band formed of all these points is seen, which shifts its 
position as the triangle is turned round in its own plane. Fig. 3 represents these 
