ON PHYSICAL OPTICS. 347 



nous arch is produced by the rays of each colour at its appropriate dis- 

 tance. The rays which never enter the drops produce no other effect, 

 than to cause a brightness, or haziness round the sun, where the reflection is 

 the most oblique ; those which are once reflected within the drop exhibit 

 the common internal or primary rainbow, at the distance of about 41 

 degrees from the point opposite to the sun ; those which are twice reflected, 

 the external or secondary rainbow, of 52 ; and if the effect of the light, 

 three times reflected, were sufficiently powerful, it would appear at the 

 distance of about 42 degrees from the sun. The colours of both rainbows 

 encroach considerably on each other ; for each point of the sun may be 

 considered as affording a distinct arch of each colour, and the whole disc 

 as produciflg^an arch about half a degree in breadth for each kind of light ; 

 so that the arrangement nearly resembles that of the common mixed spec- 

 trum. 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 containing about five times 

 as much light as a minute at the distance of a quarter of a degree ; the 

 abrupt termination is on the side of 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 

 commonly 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, 

 especially 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 suppositions, which were imagined by Huygens,* are in 

 themselves extremely complicated and improbable, and are wholly unau- 

 thorised by observation. A much simpler, and more natural, as well as more 

 accurate explanation, which was suggested at an earlier period by Mariotte,t 

 had long been wholly forgotten, until the same idea occurred to me,^ 



* Ph. Tr. 1670, v. 1065. Op. Rel. vol.ii. 

 f Trait6 des Couleurs, Paris, 1686. OEuv. i. 272. 

 x J Jour, of the Roy. Inst. ii. 4. 



