PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 57 



in part to the use of the red glass, since, as has been already remarked, the planes of polarization 

 of the blue were more crowded towards the plane of diffraction than those of the red. On this 

 account the dot ought to be slightly raised to make this experiment comparable with its neigh- 

 bours. On the other hand it will be seen by referring to Table II, that No. 23 was a much better 

 experiment than No. 15, which is represented by the 6th dot, and apparently also better than 

 No. 17, which is represented by the 4th dot. No. 21, represented by the 2nd dot, seems to 

 have been decidedly better than No. 13, which is represented by the 3rd. Nos. 14 and 22, repre- 

 sented by the 1st and 3rd crosses respectively, were probably much better, especially the latter of 

 them, than No. 2, which is represented by the 2nd cross. Now, bearing in mind the character of 

 the experiments, conceive two curves drawn with a free hand, both starting from the origin, where 

 they touch the axis, and passing, the one among the dots, and the other among the crosses. 

 The former of these would apparently lie a little below the curve marked I. E, and the latter 

 a very little below the curve II. E. 



Hence the observations are very nearly represented by adopting Fresnel's hypothesis 

 respecting the direction of vibration, and, whether the grooved face be turned towards or from 

 the incident light, suposing the wave broken up before it reaches the grooves. 



I think a physical reason may be assigned why the supposition of the wave's being broken 

 up before it reaches the grooves should be a better representation of the actual state of 

 things than the supposition of its being broken up after it has passed between them. Till 

 it reaches the grooves, the wave is regularly propagated, and, according to what has been 

 already remarked in the introduction, we have a perfect right to conceive 

 it broken up at any distance we please in front of the grooves. Let the I 



figure represent a section of the grooves, &c, by the plane of diffrac- ff.JP v.h.... 



tion. Let a A, Bb be sections of two consecutive grooves, AB being ( y NL-^ . |/_ 



the polished interval. Let eh be the plane at which a wave incident in 

 the direction represented by the arrow is conceived to be broken up. Let 

 O be any point in eh, and from O draw ORS in the direction of a ray 

 proceeding regularly from O and entering the eye ; so that OR, RS are inclined to the normal at 

 angles 9, 9\ or 9', 9, according as the light is passing from air into glass or from glass into air. 

 The latter case is represented in the figure. Of a secondary wave diverging spherically from O, 

 which is only partly represented in the figure, those rays which are situated between the limits 

 OA, OB, and are not inclined at a small angle to either of these limiting directions, may 

 be regarded as regularly refracted across AB. In a direction inclined at a small angle only to 

 OA or OB, it would be necessary to take account of the diffraction at the edge A or B. Let 

 <y be a small angle such that if OR be inclined to OA and OB at angles greater than y the 

 ray OR may be regarded as regularly refracted, and draw Ae, Bg inclined at angles -y to OR, 

 and Af, Bh inclined at angles — y. Then, in finding the illumination in the direction RS, 

 all the secondary waves except those which come from points situated in portions such as ef, gh 

 of the plane eh may be regarded as regularly refracted, or else completely stopped, those which 

 come from points in fg and similar portions being regularly refracted, and those which come 

 from points to the left of e, between e and the point which bears to a the same relation that h 

 bears to b, as well as those which come from similar portions of the plane eh, being completely 

 Vol. IX. Pakt I. 8 



