COLOURS OF THICK PLATES. 



[175] 



which becomes, when a s and c 3 are expressed in terms of a and c, 



a== _U + - + £.. . , 



\p c hi c h 



(36) 



If a', /3' be the projections of the angle of diffraction LPE 3 , (where E 3 denotes the image of 

 the eye,) we may find a', /3' from a, /3 by interchanging a, b, c, and /, g, h, and changing the 

 sign. If now we change the signs of the resulting expressions, in order to allow for re- 

 flexion at the back, and so compare the circumstances of the two diffractions, we shall obtain 

 the very same expressions as at first, since (36) and the corresponding expression which gives /8 

 remain unchanged when a, b, c, and /, g, h are interchanged. Hence in the general case, as 

 well as in the particular case first considered, the two diffractions take place under the same 

 circumstances, and therefore the interference rings are not affected by any irregularities which 

 may attend the mode of diffraction. Furthermore, should the diffraction take place with 

 a certain degree of regularity, as in the case of lycopodium seed, so as to exhibit rings 

 or fringes in the aggregate effect of all the particles which send light into the eye in such a 

 direction as to be brought to a given point on the retina, the diffraction rings and the 

 interference rings are seen independent of each other*. 



37. If 3 be the small angle of diffraction, & = a 2 + /3 2 , whence from (36) and the other 

 equation which may be written down from symmetry, 



Hence the loci of the points for which the angle of diffraction has given values form 

 a system of concentric circles. Referring to (29), we see that the co-ordinates of the centre of 

 the system are £ M »?,, so that the centre is situated in the point in which the mirror is cut by 

 the line joining the eye and the image of the luminous point. This result might have been 

 foreseen, since 8 vanishes only for the regularly refracted light, and this enters the eye only in 

 the direction of the line joining the eye and the image. By introducing the co-ordinates ?,, i;,, 

 the equation (37) may be put under the form 



*- 6+ i-SV--*/ +&-*«■ 



(38) 



Since the diffraction becomes very sparing when the angle of diffraction becomes at all 

 considerable, it follows that the interference rings are but weak at a considerable angular dis- 

 tance from the image of the luminous point. This agrees with observation. In the experi- 

 ment in which a flame is placed in the centre of curvature of a concave mirror, and is then 

 moved to one side, although the rings are symmetrical with respect to the flame and its image, 

 so far as regards their forms and colours, they are not symmetrical so far as regards their 



* From some rough experiments which I have myself made 

 with gauze stretched in front of a concave glass mirror, of which 

 the surface was clean, I am inclined to think that the squarish 

 rings observed by the Duke de Chaulnes in the experiment with 

 muslin, already mentioned, were due to a combination of the 

 coloured rings of thick plates, and of the appearance produced 



by a cross-bar grating. If so, the independence of the two 

 systems would have been rendered evident by slightly inclining 

 the mirror, when the latter system would have had the image 

 for its centre, whereas the former would have had for its centre 

 a point situated midway between the luminous point and the 

 image. 



