[174] PROFESSOR STOKES, ON THE 



vibrations /, J may be supposed equal to each other, and likewise those of the vibrations T, J'. 

 It is true that the diffractions take place at different distances from the source of light, on 

 account of the finite thickness of the glass, but the difference of distance compared with either 

 of the absolute distances is a small quantity of the order t, which may be neglected. 

 Hence the two resultants / + /', J+ J' belong to a diffraction ring of the same kind, and 

 in fact differ in nothing but in phase ; the phase of the former exceeding that of the latter 

 by v. Hence the two kinds of interference go on independently of each other. It is true 

 that in the preceding reasoning we have considered only two interfering streams /, /', and that 

 in calculations of diffraction we have to consider the resultant of an infinite number of streams. 

 But the same reasoning would evidently hold good whatever were the number of streams 

 J, /', I"... with their correspondents J, J', J"... 



35. When an irregular powder, or anything of the kind, is used to scatter the light, no 

 diffraction rings are visible, because a given point M in the plane of the rings would belong to 

 a diffraction ring of one kind so far as one particle of dust was concerned, and to a diffraction 

 ring of another kind so far as another such particle was concerned ; and therefore nothing is 

 seen but the interference rings belonging to thick plates. But when lycopodium seed is used 

 the lycopodium rings and the interference rings are seen together. The former are always 

 arranged symmetrically around the image, as ought to be the case, since they depend only on 

 the angle of diffraction, which is the same for all points of a circle described round L 3 as a 

 centre. By this circumstance they are at once distinguished from the latter, the centre of 

 which falls half way between the luminous point and its image. On scattering some lycopodium 

 seed on a concave mirror, and placing a small flame near the centre of curvature, at such a 

 distance laterally that the two systems of rings intersected each other, I found in fact that 

 whatever colour appeared in that part of a lycopodium ring which lay outside the interference 

 system was predominant in the latter system throughout the remaining part of a circle described 

 round the image. When the flame was placed in the axis, an abnormal inequality in the 

 brilliancy of the rings of the interference system became very apparent. This inequality was 

 easily seen to correspond to the alternations of intensity in the lycopodium system. 



36. Let us now turn to the general case, in which the luminous point and the eye are 

 supposed to have any positions, either in the axis or not far out of it. 



The equations of the lines PL S , PE are 



£ - « 3 v - h £ - c 3 



" 5 



C 3 



o 3 - * h — y 



f-as g-y h 

 Let the small angle L^PE be projected on the planes of ssw and ssy, and let a, /3 be the 

 projections, measured positively towards oe, y, and from PL 3 towards PE. The preceding 

 equations give 



x-a z w-f 



a= - — , 



c 3 n 



