460 I. P. Kocx. 
only comes to a few minutes. In other words, mirages in Nature 
are almost always seen in a direction, which does not deviate very 
much from the horizontal one; only in those rare cases where the 
surfaces between the strata of air are not very nearly horizontal, 
can one see mirages in directions deviating considerably from the 
horizontal direction. 
The downward mirage is in particular connected with the 
first thin ice cover of the autumn, but is by the way also to be seen 
in the summer and spring. When the temperature in September— 
October falls to + 10° to + 20° in calm weather, immediately above 
the thin ice heated by the water, a stratum of warm air forms, 
which for a time may stand rather sharply against the cold air 
higher up. In the transition between the two strata of the air, the 
rays of light are broken or deflected and produce the downward 
mirage in the case of an observer, who finds himself just above the 
boundary between the strata of air and thus in the denser medium. 
Fig. 143. 
In Fig. 143 FF indicates the surface of the sea, whereas the line 
5550515394 indicates the bounding surface between the two air strata. 
The angular limit for the total reflection be &. The observer finds 
himself in О; his horizon lies in the direction OS,. 
The ray of light S,s, is totally reflected to O; in the direction 
Os, is thus visible a reflected image of a point of the celestial vault. 
Similar conditions hold good as regards the ray of light S,s,. 
The reflected image and the directly seen image come into contact 
in the direction OS,. As these two images are entirely alike and 
lacking details, the boundary line between them is wiped out i.e. 
the real horizon which lies in the direction OS, is not visible, but 
instead of that a false horizon has appeared in the direction Os,; 
in other words, the horizon is apparently lowered the angle 5, Os. 
