130 EXPERIMENTS AND INVESTIGATIONS 



and not first by one and then by others in succession ; and 

 this clearly proves that after a first flexion takes place, no 

 other flexion is made by the body on the same side of the rays. 

 This is easily shown. 



For a plane surface is a series or succession of edges in- 

 finitely near each other ; and a curve surface in like manner 

 is a succession of infinitely small and near plane surfaces or 

 edges. Let a b (fig. 9) be the section of such a curve surface. 

 The particle P coming first near enough the 

 ^' * ray RR' to bend it, then the next particle 



/* is only further distant from R R', the unbent 



e_____^ ray, than the particle P by the versed sine of 

 IZ-----"'"^ the infinitely small arch P. But is not 

 at all further distant than P from the ray 



IV at ail lurtner distant man r ironi tne ray 



bent by P into 17?% and yet we see that O 

 produces no effect whatever on the ray after 

 P has once bent it. Xo more do any of the other particles 

 within whose spheres of flexion the ray bent by P passes. 

 The deflected ray.^ r' no doubt is somewhat 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 

 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 ori- 

 ginal path, and the particles after the first are in consequence 

 of that first particle's flexion nearer the bent ray, at least in 

 the case of inflexion. But it is to be observed, moreover, that 

 in the experiment with two opposite edges, inflexion enters 

 as well as deflection, 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 ob- 

 served 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 be- 

 hind the other, and the second producing no effect if placed on 



