434 On the Cause of Iridescence in Clouds. 



ference is no doubt considerably more than compensated by 

 the tendency of water-drops to coalesce and lose their uni- 

 formity of size. 



Coronae, too, are sometimes seen in water-mists, surround- 

 ing the point opposite the sun. In this case the expression 

 no longer contains the variable l/^ 2 , and for the first spectrum 

 has the value '000002a. Theory renders it highly improbable 

 that such coronse should ever be seen in ice-clouds. For we 

 have for the first spectrum the very small value • 0000000 la/yjr. 

 It is curious that the brightness increases with the size of the 

 ring. But even with such a large ring as ^fr = 20°, the bright- 

 ness is only one tenth of that for a water-cloud. The reason 

 is that comparatively few filaments are in a position to send 

 light in the required direction. 



Since the above was set up in type I have come across, in 

 a paper by Lord Eayleigh, a reference to a very important 

 proposition proved by Ve relet*. This is to the effect that, 

 owing to the finite angular magnitude of the sun, we can 

 only consider an uniform plane wave of direct sunlight to 

 extend over a circle about 100 X in diameter. At points sepa- 

 rated by a greater distance than this there is no permanent 

 relation of phase between the vibrations. 



Now the ice-filaments are no doubt often much longer than 

 100 X. So we must divide them into sections, each somewhat 

 shorter than 100 X, and treat each section as a separate fila- 

 ment. This will make no difference to the result ; for, on 

 referring to the argument above, it will be seen that the 

 length h disappears in the course of the proof. It is true that 

 the light from each filament is diminished, the diffracted light 

 being proportional to the square of the area ; but, on the other 

 hand, a greater latitude of orientation is permissible. 



In the case of the coronse cited above, the thickness of the 

 filaments must have nearly reached the theoretical limit. And 

 it is at least probable that coronae of that size would be seen 

 in clouds in which the filaments were of very irregular thick- 

 ness. Those of smaller diameter would be ineffective owing 

 to their weaker diffracting-power, while those of greater dia- 

 meter would be incapacitated by being outside the theoretical 

 limit. 



* Tome i. § 28; and Strutt, " On Coronas," London Math. Soc. vol. iii. 

 No. 36. 



