PROFESSOR TAIT ON MIRAGE. 569 
Now if we take the value of ¢ as in § 18, we have 0:004 for the greatest 
value of 6+, which is consistent with the rays not passing through the transi- 
tion stratum. This corresponds to 
6=0:0033=45,=12/ nearly. 
Hence, with this value of ¢, other assumptions remaining the same, even the 
upper erect image could not (on account of the earth’s curvature) be elevated 
more than about 12’ above the horizon, and the nearest object of which mul- 
tiple images could be formed would be at a distance of about 13 miles. 
Greater values of ¢ might remove this difficulty, but they would introduce 
greater changes of temperature. This shows, therefore, that the assumption 
of a lower stratum of uniform density is untenable. If there is to be a s¢mple 
arrangement in that stratum, it must therefore be such that the refractive 
index diminishes with elevation, but, of course, less rapidly than in the lower 
half of the transition stratum. The effect of this would be to slightly raise the 
images, and to reduce the critical distance. 
Instead of the upper image, consider the lower one. ‘This would be, at its 
Jarthest, within the distance of the visible horizon as seen from an elevation of 
50 feet. Hence no inverted image of the hull of a vessel could be seen if it 
were more than 18 miles’ distant ; and even then it would be seen horizontally. 
The only ways of reconciling this with ScorEssy’s observations are (1) to 
assume that the lower uniform stratum is much more than 50 feet thick ; (2) 
to assume that it is not uniform, but gives rays a concavity downwards. The 
former alternative is inadmissible on several of the grounds already mentioned ; 
so we are again forced to assume the latter, which certainly holds if the tem- 
perature throughout the lower stratum be constant. 
22. In order that the above calculations may be applicable to the phenomena 
.shown by inter-diffusing solutions, it is necessary that the length of the vessel 
in which the solutions are contained be great enough to allow all rays (by 
which the images are seen) to enter and escape from the transition-stratum by 
one of its horizontal surfaces, and not by its ends. By using a vessel nearly 4 
feet long, containing a layer of weak brine diffusing into pure water above, I 
have verified the general accuracy of the results just given. For those rays 
which enter or escape by an end, the calculation is by no means so simple, and 
trial shows that the law determining the relative magnitudes of the images is 
considerably modified. On the other hand, when the vessel is so short and 
the rays so nearly horizontal, that each ray, while passing through the vessel, may 
be supposed practically to move in a stratum of uniform rate of change of 
refractive index, a very simple calculation suffices to give the general nature of 
the phenomena produced. For the curvature of a ray, in the vessel, may now 
