/ ON PHYSICAL OPTICS. ' 445 



Other ; for each point of the sun may be considered as affording a distinct 

 arch of each colour, and the whole disc as producing an arch about half a 

 degree in breadth for each kind of light; so that the arrangement nearly re- 

 sembles that of the common mixed spectrum. There is, however, another ' 

 cause of a further mixture of the colours: the arch of any single colour, which 

 belongs to any point of the sun, is accurately'defined on one side only, while 

 on the other it becomes gradually fainter, the breadth of the first minute con- 

 taining about five times as much light as a minute at the distance of a quarter 

 of a degree: the abrupt termination is on thesideof the red, that is, without 

 the inner bow, and within the outer, so that, for this reason, the order of colours 

 partakes, in some degree, of the nature of the red termination of a broad beam 

 of light seen through a prism ; but it is more or less affected by this cause, on 

 account of some circumstances, which will be explained when we examine 

 the supernumerary rainbows, which sometimes accompany the bows more com- 

 monly observed. A lunar rainbow is much more rarely seen than a solar one, 

 but its colours differ little, except in intensity, from those of the common 

 rainbow. (Plate XXIX. Fig. 430.) 



In the highest northern latitudes, where the air is commonly loaded with 

 frozen particles, the sun and moon usually appear surrounded by halos or 

 coloured circles, at the distances of about 22 and 46 degrees from their 

 centres; this appearance is also frequently observed in other climates, espe^ 

 cially in the colder months, and in the light clouds which float in the highest 

 regions of the air. The halos are usually attended by a horizontal white 

 circle, with brighter spots, or parhelia, near their intersections with this circle, 

 and with portions of inverted arches of various curvatures: the horizontal 

 circle has also sometimes anthelia, or bright spots nearly opposite to the sun. 

 These phenomena have usually been attributed to the effect of spherical 

 particles of hail, each having a central opaque portion of a certain magnitude, 

 mixed with oblong particles, of a determinate form, and floating with a 

 certain constant obliquity to the horizon. But all these arbitrary supposi- 

 tions, which were imagined by Huyg^ris, are in themselves extremely com- 

 plicated and improbable, and are wholly unauthorised by observation. A 

 much simpler, and more natural, as well as more accurate explanation, which 

 was suggested at an earlier period by Mariotte, had long been wholly for- 

 gotten, until the same idea occurred to me, without any previous knowledge 

 of what Mariotte had done. The natural tendency of water to crystallize, in 



