240 
LORD brougham’s EXPERIMENTS AND OBSERVATIONS 
and a curve surface in like manner is a succession of infinitely small and near plane 
surfaces or edges. Let ab (fig. 9) be the section of such a curve surface. The 
particle. P coming first near enough the ray R R' to bend it, then the next particle O 
is only further distant from R R', the unbent ray, than the particle P by the versed 
sine of the infinitely small arch O P. But O is not at all further distant than P from 
the ray bent by P into q r, and yet we see that O produces no effect whatever on the 
ray after P has once bent it. No more do any of the other particles within whose 
spheres of flexion the ray bent by P passes. The deflected ray qr^ no doubt is some- 
what more distant from O than the incident ray was from P, but not so far as to be 
beyond O’s sphere of deflexion ; for O acts so as to make the other fringes at greater 
distances than the first. Consequently O could act on the first fringe made by P as 
much as P can in making the second, third, and other fringes ; and if this be true of 
a curve surface, it is still more so of a plane surface ; all whose particles are clearly 
equidistant from the ray’s original path, and the particles after the first are in con- 
sequence of that first particle’s flexion nearer the bent ray, at least in the case of in- 
flexion. But it is to be observed, moreover, that in the experiment with two oppo- 
site edges, inflexion enters as well as deflexion, and consequently this demonstration, 
founded on the exact equality of the fringes made by compound double edges, appears 
to be conclusive. For it must be observed that this experiment of the different edges 
and surfaces, plane and curve, having precisely the same action, is identical with the 
former experiment of two edges being placed one behind the other, and the second 
producing no effect if placed on the same side of the ray with the first edge. These 
two edges are exactly like two successive particles of the same surface near to which 
the rays pass. Consequently the two experiments are not similar but identical ; and 
thus the known fact of the edge and the back of a razor making the same fringes, 
proves the polarization of the rays on one side. Thus the proposition is proved as to 
polarization. 
Exp. 3. The proposition is further demonstrated, as regards disposition, in the 
clearest manner by observing the effect of two bodies, as edges, whether placed di- 
rectly opposite to each other while the rays pass between them so near as to be bent, 
or placed one behind the other but on opposite sides of the rays. Suppose the edges 
directly opposite one to the other, and suppose there is no disposition of the rays to 
be more easily bent by the one edge in consequence of the other edge’s action. Then 
the breadth and distension and removal of the fringes caused by the two edges acting 
jointly, would be in proportion to the sum of the two separate actions. Suppose that 
one edge deflects and the other inflects, and suppose that inflexion and deflexion are 
equal at equal distances, following the same law ; then the force exerted by each 
edge being equal to d, that exerted by both must be equal to 2d. But instead of 
this we find it equal to 5c?, or 6c?, which must be owing to the action of the two in- 
troducing a new power, or inducing a new disposition on the rays beyond what the 
action of one did. 
