178 Proceedings of the Royal Society of Edinburgh. [Sess. 
a refracted ray of light is concave above. The characteristic optical accom- 
paniments are : 
1. A depression of the plane of the apparent horizon of the lake * below 
its normal position ; the apparent horizon is lower than the true 
horizon. 
2. The apparent exaggeration of the rotundity of the earth, which be- 
comes evident to the eye, although normally it is unrecognisable. 
3. The approach of the circle of the horizon, much less distant than it 
ought to be according to the height of the observer’s eye above the 
surface of the water. 
4. The apparent exaggeration of the crests of waves, which show like 
crenations along the line of the horizon. 
5. The phenomenon of “ mirage ” : “ the mirage of the desert.” Objects 
lying low over the surface of the water and situated beyond the 
circle of the horizon are seen as inverted images below Bravais’ 
“ ligne de partage.” f These images lie in the zone which separates 
the “ ligne de partage ” from the apparent horizon of the lake. 
These details become more marked as the difference of temperature 
between the cold air and the warm water is increased. 
The phenomena associated with refraction over cold water are rarer 
than the preceding. They appear only during the afternoon hours of warm 
days in spring and summer, and occasionally in the morning hours of very 
hot days in the height of summer. In this case the air is warmer than the 
water, and the lower layers of air cooled by contact with the water are 
characterised by a thermal gradient of the direct type. The curve of a 
refracted ray of light is concave below. The characteristic optical 
accompaniments are : 
1. An apparent elevation of the plane of the horizon above the normal 
position ; the apparent horizon is higher than the true horizon. 
2. The apparent concavity of the surface of the lake, resembling a broad 
valley rising with gentle slopes towards the margin. 
3. The apparent extension of the circle of the horizon ; distant boats, 
which to the observer’s eye should have been on the circle of the 
* The true horizon is the tangent cone to the surface of the lake, the vertex of the cone 
being at the eye of the observer, and the calculation being made on the assumption of no 
refraction ; the circle of the true horizon is the curve of contact of the cone with the surface 
of the lake. The cone and circle of the apparent horizon are similarly defined in terms of the 
rays of light as they enter the eye after having been displaced by atmospheric refraction. 
These cones are so flat that they may be spoken of as planes. 
+ This is the line which separates the erect and inverted images in the usual mirage. 
