442 LECTURE XXXVII. 



they may be very completely imitated, as Dr. Wollaston has shown, by 

 looking at a distant object along a red hot poker, or through a saline or 

 saccharine solution with water and spirit of wine floating on it. The effect 

 of refraction on the apparent places of terrestrial objects must be frequently 

 disturbed by circumstances of this kind; but its magnitude is usually about 

 one tenth of the angular distance of the object, considered as a part of the 

 earth's circumference. (Plate XXIX. Fig. 428, 429.) 



The atmospherical phenomena of rainbows and halos present us with ex- 

 amples of the spontaneous separation of colours by refraction. The rainbow- 

 is universally attributed to the refraction and reflection of the sun's rays in 

 the minute drops of falling rain or dew, and the halos, usually appearing in 

 frosty atmospheres, are in all probability produced by the refraction of small 

 triangular or hexagonal crystals of snow. It is only necessary, for the for- 

 mation of a rainbow, that the sun should shine on a dense cloud, or a shower of 

 rain, in a proper situation, or even on a number of minute drops of water, scat- 

 tered by a brush or by a syringe, so that the light may reach the eye after 

 having undergone a certain angular deviation, by means of various refraction^ 

 and reflections; and the drops so situated must necessarily be found some- 

 Avhere in a conical surface, of which the eye is the vertex, and must present 

 the appearance of an arch. The light, which is reflected by the external sur- 

 face of a sphere, is scattered almost equally in all directions, setting aside the dif- 

 ference arising from the greater efficacy of oblique reflection ; but when it first 

 enters the drop, and is there reflected by its posterior surface, its deviation never 

 exceeds a certain angle, which depends on the degree of refrangibility, and is, 

 therefore, different for light of different colours: and the density of the light 

 being the greatest at the angle of greatest deviation, the appearance of a lumi- 

 nous arch is produced by the rays of each colour at its appropriate distance. 

 The rays which never enter the drops produce soother effect, than to cause a 

 bright ness, 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 op- 

 posite 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 Mould appear at the distance of ab<mt 42 degrees 

 trom the sun. The colours of both rainbows encroach considerably on each 



