172 Mr. J. C. M c Connel on Di 'fraction- Colours. 



yellow, orange-yellow, coppery red, purple-red, and dull violet, 

 which is analogous to the succession of the colours of the first 

 ring of diffraction-coronas presented by thin clouds " *. This 

 evidence will probably be considered conclusive. 



Some observers thought the red ring had some connexion 

 with an ice halo, as it happened to have about the same 

 radius : and it may be remarked that, wheu the ice prisms are 

 small, diffraction must greatly modify the appearance of a 

 halo. The narrow beam of light, which passes through the 

 two faces of a hexagonal prism in the position of minimum 

 deviation, must behave as if it had passed through a narrow 

 slit in an opaque screen. Thus I find that a beam of red 

 light which traversed a prism of 0*03 millim. greatest diameter 

 would be spread out by diffraction to an angular breadth of 

 5 C , and other colours less in proportion to their wave-lengths. 

 This spreading out would probably be fatal to such an in- 

 distinct phenomenon as an ordinary halo. Still, if the mass 

 of prisms were of great depth, the halo might survive with an 

 aspect very different to its usual one. One thing that enables us 

 to say with certainty that Bishop's ring was a corona and not 

 a halo, is that, however a halo be moditied, the brightness 

 outside the red ring will be greater than that inside, while in 

 a corona the reverse holds good, and Bishop's ring was the 

 outer border of a bright space. 



Mr. Douglas Archibald, from a consideration of all the 

 observations, selects the following radii : for the inner border 

 of the red ring 10° 30', for the middle 15° 10', for the outer 

 border 22° 4cb f . Taking 15° 10' and applying the figure 

 given in the table above for the first red with spheres, we find 

 the average diameter of the particles to be O0023 millim. 

 The ring was evidently broadened out by the irregular dia- 

 meters of the particles. Assigning the outer border of the riug 

 to the first purple and using the radius 22° 45', we find for 

 the diameter of the particles O00167 millim., and we can 

 assert that there were a considerable number as small as this. 

 It does not follow that smaller sizes were not well represented. 

 The brightness of the diffracted fight is proportional to the 

 fourth power of the diameter of the particle, so the smaller 

 sizes are severely handicapped. With regard to the upper 

 limit of size, we may perhaps take the first yellow as the inner 

 border of the brownish or reddish ring, which gives 0*0027 

 millim. By using the value for the red, we find that there 

 were certainly not many particles broader than 0'0033 millim. 



Mr. Douglas Archibald f used the formula sin (radius) = 

 y\/d. where d is the diameter of the particle and N a constant. 

 * L. c. p. 252. t L. c. p. 257. 



