with special reference to Coronce and Iridescent Clouds. 285 



example of the application, suppose that the red, green, and 

 violet components of two colours are *536, *338, '042 ; '265, 

 •114, *084 respectively. The components of white are 2*01, 

 3*27, 3*22. Reducing the first two triplets in proportion to 

 the components of white, we have *267, '104, *013 ; '132, *035, 

 *026. These may be considered as mixtures of two standard 

 colours with some white light. Subtracting the white light, 

 and taking the greater of the remaining components of each, 

 we find the brilliancies are in the ratio *254 : *106. Treated 

 in this manner the brilliancies of the ten points in the spectrum 

 I have chosen come out proportional to 20, 47, 39, 30, 18, 26, 

 31, 19, 10, 5. The maxima fall in the orange and the blue- 

 violet. The intermediate minimum is in the green-blue, a 

 part of the spectrum where the colour is generally considered 

 poor. It seems probable that, when nearly swamped with 

 white light, the colours would assert themselves nearly in pro- 

 portion to their brilliancy. At the worst the brilliancy curves 

 will be useful for comparing colours of similar hues. 



In Plate X. is given a curve representing the brilliancy of 

 iridescent ice-clouds in accordance with the expression (6). 

 Owing to the occurrence of £ in the denominator the bril- 

 liancy is infinite when £ is zero, and decreases rapidly as £ 

 increases. The ordinates of the latter portion of the curve 

 are drawn on a scale five times as great as those of the former. 

 The points where the nearest approach is made to the pure 

 colours of the spectrum are marked by the letter p. Under 

 the most favourable circumstances in the clouds, when all the 

 filaments are of the same size, there are two important causes 

 of blurring. The first is the finite diameter of the sun, which, 

 of course, prevents the brilliancy from being infinite. When 

 the first purple is at 5° from the sun — about an average dis- 

 tance — the colours over a range of 40 of retardation will be 

 all mixed together. This effect will be less marked when the 

 particles are finer and the colours further out. Another 

 cause, more serious than the other, especially for large re- 

 tardations, is the effective diameter of the filaments varying 

 from 1 to 1*155. 



Let us now deduce the successive colours from a study of 

 the two diagrams, assuming the particles are of such a size as 

 to give 100 of retardation to a degree of arc. Up to 1° or 

 1^° from the centre of the sun the light is very bright and of 

 a perceptibly bluish hue. If the cloud be dense even the face 

 of the sun will be tinted blue. From 1 J° to 2^° the light is 

 practically white. Then a yellowish tinge asserts itself, which 

 attains its greatest brilliancy at 3-§° and its greatest purity at 

 4^°. Between this and 5^° intervenes a narrow ring of 



Phil. Mag. S. 5. Vol. 28. No. 173. Oct. 1889. Y 



