70 



NA TURE 



\Nov. 26, 1874 



an action such as that represented in Figs. 4 and 5, it is 

 perhaps just as proper as the application of the name 

 refrai-tion to the bending of rays which tal<es place in the 

 atmosphere ; the term refraction being primarily employed 

 to denote bending not into a curve but into an angle, at 

 places where a ray passes by a sharp transition from one 

 mediu m into another. 



The shaded region in Fig. 5 represents a portion of the 

 atmosphere in which there is a rapid diminution of 

 density upwards. We may regard it as the region of inter- 

 mixture, between two portions of air, which differ greatly 

 from each other in density, the denser portion extending 

 downwards to the earth without any very rapid changes, 

 and the rarer portion extending in a similar gradual 

 manner upwards to the clouds. If these two dissiniilar 

 portions of air have been only recently brought into 

 proximity, as by the commencement in the upper regions 

 of a wind from some warm quarter, we should expect to 

 find a border tract, where the transition would be un- 

 usually rapid, the border tract itself being indefinite in its 



boundaries above and below, and the transition being 

 most rapid in its central parts. The figure has been 

 drawn to suit these suppositions, and it shows, besides 

 two rays which have been reflected, a third ray which has 

 barely been able to get through. 



Anyone who is fresh from the study of optics will be at 

 once struck with the analogy between the behaviour of 

 these rays and of rays passing or endeavouring to pass 

 from water into air ; and the analogy is quantitative, as 

 well as qualitative. For — 



I. As regards those rays which get through, it can be 

 shown that the total change of direction for a ray of a 

 given incidence depends only on the densities above and 

 below the region of intermixture, and is altogether inde- 

 pendent of the thickness of this intermediate region. 

 This is on the assumption that the surfaces of equal 

 density are parallel planes. If, as in the case of air, the 

 extreme relative index of refraction differs but little from 

 unity, the change of direction is proportional to the 

 tangent of the angle of incidence, and is equal to the 



fs i ii Si S i ^ 



I g II e IIP'' 



i i.i. g a iii 

 i i B la § Big 



product of this tangent by fx — i, jx denoting the relative 

 index. This is the law which governs the refraction 

 of rays from the heavenly bodies, in traversing the earth's 

 atmosphere ; except when these bodies are so near the 

 horizon that the curvature of the earth and its atmosphere 

 produces a sensible effect. 



2. As a consequence of the preceding point of agree- 

 ment, the critical angle which separates those rays which 

 get through from those which are turned back, is also 

 dependent solely on the comparison of the two extreme 

 densities ; that is, on the value of the relative index of re- 

 fraction. 



In the comparatively rare instances in which several 

 inverted images of the same object have been seen in the 

 sky, as in the third figure of Plate II., which represen's a 

 elescopic appearance observed by .Scoiesby. a possible 

 explanation tray be found in irregularities of form in the 

 strttum of intern ixture, which, ijsteHd nf b> ing nuly 

 horizontal, may be tilted to slightly unequal degrees in 

 different parts, so that it acts, not like 07ie plane mirror, 



but like several plane mirrors slightly inclined to each 

 other. Another, and I think more probable explanation, 

 is the existence of more than one layer of rapid transition. 



Whenever an image is inverted, the rays by which it is 

 seen must have crossed ; that is to say, the two rays 

 which come to one and the same point of the eye from 

 two neighbouring points of the object must have crossed 

 each other once on the road. If they have crossed twice, 

 the image will be erect ; if three times, inverted ; and so 

 on. 



When all the rays are circular arcs, and their curvatures 

 are all equal, it will be impossible for them to cross, and 

 hence no inverted image can be formed ; neither can 

 there in this case be any increase or diminution of 

 apparent size. This is evident from the consideration 

 that a diagram indicating the paths of such rays to the 

 eye only needs to be bent with a curvature equal and 

 opposite to that of the given rays, in order to render all 

 these rays straight ; and such bending will not affect the 

 sizes of the images. 



