PROFESSOR TAIT ON MIRAGE. 571 
23. In order to calculate roughly the number, position, and dimensions of the 
images visible to an eye looking through the media nearly horizontally at a 
distant object, all that is necessary is to draw the caustic, as in fig. 8. It 
consists, so far as the transition stratum is concerned, of the two (practically) 
equal and similar curves AB, A’B’ ; which touch the stratum above and below, 
and have as common asymptote the path of the most deflected ray. So long as 
the eye is not within the region BAC, only one image is seen. But from any 
point within this region two tangents can be drawn to the caustic, and a line 
can be drawn to the object so as to pass altogether below the stratum. Thus 
there are three images. In order that the middle one may be distinctly visible, 
the eye must be 10 inches or so beyond the point of contact of the corre- 
sponding ray with the lower caustic. Then the image is an inverted one. The 
others are always direct. [It may be remarked, in passing, that the intersection 
of the ray AC with the screen is always definite and measurable. | 
Here the upper image is always seen by diverging rays, the middle one by 
diverging or converging rays according to the position of the eye. Contrast this 
with the results givenin § 20. This middle image changes its direction far more 
rapidly than the others when the eye is moved vertically. It coincides with the 
upper image when the eye, gradually moved downwards, reaches the line DB. 
When they meet, both become blue and then disappear by moving the eye 
farther down. On moving the eye upwards, the middle image approaches the 
lower one, and they unite and disappear when the eye reaches the line DC. 
These results are easily verified by trial, and I have mentioned them only with 
the view of bearing out my statement, that this form of experiment, unless the 
tank be long enough, does not give results the same as those of Mirage. 
4 (Read 19th June 1882.) 
A few days ago, while finally preparing the above pages for press, I had 
occasion once more to consult WoLLAsTon’s paper, and inadvertently took down 
the wrong volume of the Phil. Trans. Init (the vol. for 1803) I found another 
paper on Mirage by Wo.taston, in which he speaks of certain articles by 
WOLTMANN and GRUBER, and regrets his inability to read German. ‘This led 
me to consult the Register-band of Gilbert's Annalen; and I thus learned the 
existence of a very elaborate memoir by Biot* which I had never seen referred 
to, and in which the subject of mirage is exhaustively treated both by calcula- 
* Mém. de l'Institut, 1809; Récherches sur les Réfractions extraordinaires qui ont lieu prés de 
Vhorizon. I presume that my having been altogether ignorant of the existence of this memoir is con- 
nected with the fact that itis unintelligible without the plates, and that these were not issued along with 
it. For in each of the three first libraries which I consulted, that of the Society being one, this volume 
of the Mém. de l'Institut is devoid of plates. Bror’s memoir, however, was issued also as a separate 
volume, and a copy of this, containing the plates, I procured at last from the Cambridge University 
Library. 
