346 LECTURE XXXVII. 



solution of the problem in all its extent. But for practical uses, the refrac- 

 tion may be determined with sufficient accuracy by an approximation 

 which is easily remembered ; the deviation being at all altitudes one sixth 

 part as great as the refracted ray would undergo at the horizontal surface 

 of a medium six times as dense as the air. When a celestial object appears 

 exactly in the horizon, it is actually more than half a degree below it, 

 since the refraction amounts to 33 minutes, when the barometer stands at 

 29-^V inches, and Fahrenheit's thermometer at 50. 



The accidental variations of the temperature of the air at different parts, 

 produce, however, great irregularities in its refraction, especially near the 

 horizon. The most remarkable of these is occasioned by the rarefaction of 

 the air in the neighbourhood of the surface of water, of a budding, or of 

 the earth itself, in consequence of which a distant object appears to be 

 depressed instead of being elevated, and is sometimes seen at once both 

 depressed and elevated, so as to appear double, one of the images being 

 generally in an inverted position, as if the surface possessed a reflective 

 power; and there seems indeed to be a considerable analogy between this 

 kind of refraction and the total reflection which happens within a denser 

 medium. These effects are known by the appellations looming, mirage, 

 and Fata Morgana ; they may be very completely imitated, as Dr. Wollas- 

 ton as 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 

 examples 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 formation 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, scattered 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 refractions and reflections ; and the drops so situated 

 must necessarily be found somewhere 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 surface of a sphere, is scattered almost 

 equally in all directions, setting aside the difference 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, there- 

 fore, 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- 

 * Ph. Tr. 1800, p. 239. See also ibid. 1803, p. 1. 



