50 



NA TURE 



\_Nov. 19, 1874 



" I should also have observed that when I was upon 

 the eastern hill, the cape of land called Dungcness, which 

 extends nearly two miles into the sea, and is about sixteen 

 miles distant from Hastings, in a right line, appeared as 

 if quite close to it, as did the fishing-boats and other 

 vessels which were sailing between the two places. They 

 were hkevvise magnified to a great degree." 



I have stated that the phenomena which constitute 

 mirage are due to the bending of rays of light in the 

 atmosphere, and I now proceed to point out the princ''p'.;s 

 by which this bending is governed. 



Plate I. 



My esteemed colleague, Dr. James Thomson, has 

 greatly contiibuted to the clearness of our knowledge, as 

 .regards the d sturbing effect of the atmosphere upon the 

 direction of a ray of light. He has recently published an 

 investigation,* which, to say the least, is simpler and 

 more satisfactory than any before given, of the precise 

 law which determines the curved path of a ray through 

 the air. 



Referring you for the details to the last chapter but 

 one of my own recently published edition of Deschanel's 

 " Natural Philosopliy," I will merely say that when a ray 

 is passing through a portion of air which is not equally 



* liri'ish Association Report, 1872, p. 41. 



dense all round it, it is deilected towards the side on 

 whicli the density is greatest ; and that the shar[)ness of 

 the curv.aturc, as measured by the change of direction for 

 a given length of the ray, is directly proportional to the 

 rate at which the density varies along the normal. Strictly 

 speaking, I ought, instead of " density," to have said 

 "absolute index of refraction, diminished by unity ;" but 

 experiment has shown that the difference between these 

 two statements, when there is no substance in question 

 except air and aqueous vapour, is quite insignificant. 

 Supposing the stratification of the air to be strictly 

 horizontal, it follows that a ray tra- 

 velling vertically will not be bent at 

 all, since there is no variation of density 

 in the direction of its normal; and of 

 all rays which traverse the same point, 

 those which are horizontal will be bent 

 the most, because the whole change of 

 density is normal to them, and has a 

 direct tendency to bend them down- 

 wards. For rays which are nearly 

 horizontal, the curvature will be very 

 nearly the same ; and, as it is by such 

 rays that we see the images which con- 

 stitute miiMge, the maximum bending 

 of atmospheric rays is available for 

 the explanation of the phenomena. In 

 the average state of the atmosphere, 

 the curvature of rays which are hori- 

 zontal, or nearly so, is about one-fifth 

 or one-sixth of the curvature of the 

 earth's surface ; though it is to be re- 

 marked, by way of caution, that the 

 connection between these two curva- 

 tures is merely accidental ; the curva- 

 ture of the earth is not the cause, nor 

 even a partial cause, of the curvature 

 of rays. 



Oiher things being equal, the curva- 

 ture of rays should be greater in cold 

 than in warm air, and greater with high 

 than with low barometer ; but these 

 are not the principal modifying ele- 

 ments. The circumstance which it is 

 most important to know, at any time, 

 in order to predict the degree of curva- 

 ture, is the rate at which the teinpera- 

 turo changes with the height. The 

 average change is a fall of about ;rjjj of 

 a degree Fahr. per foot of ascent. A 

 fall of one fifty-third of a degree per 

 foot of ascent would make the air 

 equally dense at all heights, and 

 would cause rays to travel in abso- 

 lutely straight lines. A more rapid 

 fall than this would render the air 

 aloft denser than that below, and would 

 cause rays to bend up instead of down. 

 The existence of denser, and therefore 

 heavier air aloft, is obviously incom- 

 patible with stability of equilibrium ; 

 but unstable equilibrium may endure for a time, even 

 under statical conditions ; and when there is a powerful 

 cause at work, tending to raise the temperature of the 

 lower strata, it is quite conceivable that the lower air may 

 be heated faster than it can get away (if I may be allowed 

 a somewhat loose expression) ; so that, although there is 

 a perpetual diffusion going on, the heated air ascending, 

 and cooler air from above tak ng its place, there is, never- 

 theless, a difference of temperature perpetually main- 

 tained, exceeding one-fiftieth of a degree per foot. The 

 circumstances under which the Egyptian form of mirage 

 is observed are precisely such as are fitted to produce this 

 state of things. A fierce sun scorching the parched 



