180 Proceedings of the Royal Society of Edinburgh. [Sess. 
extreme positions of nearly 8 minutes of arc above and fully 4 minutes 
of arc below. 
Let us now study the sequence of phenomena on a fine day towards the 
end of spring or the beginning of summer, when, as hour follows hour, the 
air being at first colder than the water surface becomes warmer, while the 
temperature of the water remains comparatively constant. The temperature 
of the air, lower than that of the water in the morning, becomes equal to it 
towards midday, and exceeds it in the afternoon. Consequently the two 
normal types of refraction succeed each other in time. Let us suppose, for 
example, that the temperature of the morning air is 15° C., that of the water 
18° C. The phenomena that are associated with refraction in air over warm 
water are in all their perfection ; the apparent horizon of the lake is depressed 
below the true horizon. As the day progresses, the air heats rapidly under 
the powerful action of the solar radiation ; the water also grows warmer, but 
at a slower rate because of its great thermal capacity. The temperature of 
the air soon equals that of the water, and is not long in passing it. In the 
afternoon the water may have risen in temperature to 20° 0., and the air to 
26° or 28° C. The phenomena associated with refraction in air over cold 
water are developed, the apparent horizon is elevated, the surface of the lake 
appears concave. 
But the transformation from the one type to the other does not 
take place slowly or progressively. The depression of the horizon 
due to refraction over warm water does not diminish little by little 
until its value is zero ; and the elevation of the horizon does not grow 
little by little, starting from zero when the temperatures of the two 
media are equal, and attaining a maximum when the difference of tempera- 
ture is the greatest. The transformation does not occur simultaneously 
over the whole lake. The change takes place suddenly at each region, and 
successively from point to point. At a particular instant there may 
appear at different parts of the lake the two types of phenomena clearly 
recognisable. 
It is at such an instant that the Fata Morgana appears, represented, as 
I have already said, by a striated zone of rectangles in juxtaposition. Its 
features are at first quite disconcerting. When first recognised, it may appear 
in any azimuth. It movesjslowly, in one or other direction, along the shores 
of the lake. It was from a study of the manner of the shifting in position 
that I gained the key to the explanation of the phenomenon, which may be 
summarised under four heads : — 
I. The Fata Morgana has its origin in the region between the two regions 
where the opposite types of ^refraction rule ; in the one region the morning 
