Nov. 26, 1874] 



NATURE 



69 



mella is a product of the periotic capsule, such as the stapes 

 has been assumed to be ? 



Here, I think, there is considerable ground for hesita- 

 tion. It appears to me that the stapes is not so much 

 " cut out " of the cartilaginous periotic capsule as the 

 result of the chondrification of a portion of that capsule 

 which remains unchondrified longer than the rest. More- 

 over, the Urodcla all possess a band of ligamentous 

 fibres which extends from the stapes to that part of the 

 suspensorium with which the hyoid is connected, and to 

 the hyoid itself. It is conceivable, and certainly not im- 

 probable, that this stapcdio-suspensorial ligament repre- 

 sents the dorsal extremity of the hyoidean arch. But the 

 columella aitris, in its early condition in the frog, so 

 nearly resembles the stapedio-suspensorial ligament par- 

 tially chondrilied, that it is hard to suppose that one is 

 not the homologue of the other ; in which case the colu- 

 mella, and even the stapes itself, may, after all, represent 

 the metamorphosed dorsal end of the hyoidean arch or 

 the hyomandibular of a fish. And it must be admitted 

 that the relations of the portio dura nerve to the hyoman- 

 dibular in such a fish as the Ray, speak strongly in favour 

 of this view. 



ON MIRAGE* 

 II. 



WE will now modify our imaginary distribution of 

 density in such a way as to adapt it to a convex 

 earth. To do this we have merely to bend our diagram 

 to the earth's curvature. 



The result is shown in Fig. 3 (Plate I.), where the dotted 

 line represents a level line coincident with a stratum of 

 equal density in the earth's atmosphere, and, like any other 

 level line, partaking of the general curvature of the earth. 

 It is o£ the same length as the dotted line in our first 

 diagram, and ordinates (offsets), equal to those in Fig. I, 

 are laid off from it, in normal directions, at the same 

 number of equidistant points. The curves thus obtained 

 possess all the properties, as regards foci and images, 

 which we have pointed out as belonging to those of Figs. 

 I and 2 ; and we can now aft'ord to dispense with the 

 difficult physical postulate of a diminution of density 

 downwards from the plane of reference. One of the rays 

 in Fig. 3 is everywhere concave downwards, and there- 

 fore the air which it traverses increases in density down- 

 wards. 



If we suppose the law which gave Figs, i and 2 (Plate I.) 

 to hold only on one side of the plane of reference, while on 

 the other side of this plane the density is uniform, we shall 

 have conjugate foci for points in the plane of reference, but 

 for no otlier points. The conjugate foci wiU themselves be 

 in the plane of reference, and the distance from any 

 point to its conjugate will be constant. Rays coming to 

 the plane of reference from the side on which the density 

 is uniform will be bent round so as to meet the plane of 

 reference again at a constant distance in advance of the 

 points at which they entered, and the angle of emergence 

 will be equal to the angle of incidence. More generally, 

 whenever there is a layer of air in which the density 

 diminishes very rapidly from one side to the other, while 

 the density elsewhere is comparatively constant, rays 

 entering this variable stratum from the denser side will 

 (if their inclinations to the stratum are not too great) 

 bend round in it and emerge from it again on the same 

 side, as in Figs. 4 and 5. In Fig. 4 the dotted line may 

 be supposed to represent a plane, beneath which the 

 density diminishes more rapidly down to the ground 

 (which is represented by the shading). In Fig. 5 the 

 shading represents a stratum in which the density dimi- 

 nishes rapidly in ascending, the diminution being most 

 rapid at the middle of the stratum. In both cases, the 



•* A Paper read by Prof. J. D. Everett, M.A., D.C.L., before the Belfast 

 Natural History and Philosophical Society. (Continued from p. 52. ) 



appearance presented to ;ai eye at E will be nearly the 

 satrie as if the rays had been reflected from a plane 

 mirror behind and parallel to the stratum ; 1 say tiearly 

 the same, because the position of the equiv.ilent plane 

 mirror will not be precisely the same for rays at different 

 inchnations to the stratum. Objects will thus be seen 

 inverted, without being necessarily either magnified or 

 diminished. Fig. 4 is intended to illustrate tlie mirage 

 of the desert, and Fig. 5 to illustrate the formation of 

 inverted images in looming. In Fig. 4, tracing the three 

 rays backwards from the observer's eye at E, the lowest 

 of the three at the eye end is bent up just sufficiently to 

 prevent it striking the ground, and then goes away to the 

 sky, so that he will see the sky as if reflected from the 

 ground. The second ray does not pass quite so near the 

 ground, and it goes away to a lower part of the sky. The 

 third ray follows a similar course, not descending quite so 

 near the ground, and going off in a direction more nearly 

 horizontal. We may suppose it to be terminated by a 

 tree, hill, or other tall object, which will accordingly be 

 seen reflected beyond the image of the sky. 



Rays a little higher than this will escape the upward 

 bending which has produced these effects, and which is 

 due to the action of a comparatively thin stratum of air 

 near the ground. The same objects which have been 

 seen apparently reflected by the ground will thus be also 

 seen erect in their true positions. The relation between 

 tlie appearances of the true and the reflected objects is 

 almost precisely the same as if there were a sheet of 

 water occupying the place of the ground ; and the flicker- 

 ing of the air as the hotter and colder currents ascend 

 and descend will bear a close resemblance to waves 

 ruffling the surface of the imaginary lake. 



The earliest explanation of mirage, I believe, on re- 

 cord is that of Monge {Ann. dc Chiin. ,\xix. 207), one of 

 the savans who accompanied Bonaparte in his expe- 

 dition to Egypt. The following is the passage in the 

 Aiuialcs, which purports to be an abstract of a memoir 

 read at a meeting of the Institute, held at Cairo : — ■ 



•' At sea it often happens that a ship seen from afar 

 appears to be floating in the sky and not to be supported 

 by the water. An analogous effect was witnessed by all 

 the French during the march of the army across the 

 desert. The villages seen in the distance appeai-ed to be 

 built upon an island in the midst of a lake. As the 

 observer approached them, the boundary of the apparent 

 water retreated, and on nearing the village it disappeared, 

 to recommence for the next village. Citizen Monge 

 attributes this effect to the diminution of density of the 

 inferior layer of the atmosphere. This diminution in the 

 desert is produced by the augmentation of temperature, 

 which is the result of the he.at communicated by the sun 

 to the sands with which this layer is in immediate con- 

 tact. ... In this state of things the rays of light which 

 come from the lower parts of the sky, having arrived at 

 the surface which separates the less dense laj'er from 

 those which are above, do not penetrate this layer ; they 

 are reflected, and thus form in the eye of the observer an 

 image of the sky. He thus sees what looks like a por- 

 tion of the sky beneath the horizon, and it is this which 

 he takes for water." 



The only objection which I think can be taken to this 

 explanation of Monge, is that it seems to imply not a 

 curvature, but an angle, in the course of the rays, just as 

 in the case of what is called total internal reflection at the 

 bounding surface of a piece of glass when the angle of 

 incidence exceeds the critical angle. 



Now, the formation of an angle (even a very obtuse 

 angle) in a ray would require a perfectly sharp transition 

 from one degree of density to another, instead of the 

 gradual transitions which are more in accordance with 

 our knowledge of the properties of air. We have shown 

 that no such harsh supposition is necessary. 



As to the propriety of applying the name reflection to 



