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XXIIL.—On Mirage. By Professor Tair. (Plate XX XIII.) 
(Read 5th December 1881.) 
I was led to the following investigations while seeking an elementary, and 
at the same time instructive, application of HAmILton’s General Method in 
Optics.* They were completed in all but a few of their numerical details 
before I met with the remarkable paper by WoLLAsTon,t in which the subject 
of multiple atmospheric images seems first to have been treated by a sound 
physical method. Wot.asTon’s experiment with a long bar of iron raised to 
a high temperature suggests undoubtedly the true explanation of at least many 
of the curious phenomena seen by VincE,{ Scorespy,§ and others. But he 
seems to have thought that sufficient temperature-differences for the natural 
production of the phenomena could not exist in the atmosphere; and thus the 
latter part of his paper, in which he tries to explain them by the agency of 
aqueous vapour, presents a singular contrast to the strength and correctness of 
the earlier part. A good deal of what follows is implied, if not directly 
stated, in WOLLASTON’S paper; but I think there is sufficient novelty in what 
remains to justify my bringing it before the Society. 
The subject is one which offers immense facilities for the construction of 
elegant “Problems,” but I have confined myself to the simplest hypotheses 
which (while enabling me to obtain exact results) promised to throw light 
upon it :—feeling that anything else would be out of place in endeavouring to 
explain a class of phenomena which have probably never occurred twice in 
exactly the same way. I have, however, shown at least the general nature of 
the alterations to which my results would be subject in consequence of modi- 
fication of the assumptions. 
1. Most of the images seen by ScorEsBY were inverted, and elevated above 
the apparent position of the object seen directly, and each series of them (when 
there were more series than one) can be explained at once by the existence of a 
horizontal stratum of air in which the rate of diminution of refractive index in 
ascending is greater than that in the air immediately below. [This is merely 
the sort of arrangement which, as is perfectly well known, produces the mirage 
of the desert ; but turned upside down.| But the chief phenomenon figured by 
* Trans. R.I. A., 1833. + Phil. Trans., 1800. 
t Phil. Trans., 1799. § Greenland, and Trans. Roy. Soc. Edin., ix. and xi. 
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