274 TERRESTRIAL REFRACTION AND MIRAGE. 
the real horizon is found by drawing a tangent to the surface, which 
would be in fact to the point P, but by reason of the curvature of the 
ray with the concavity presented downwards the point Q appears 
upon the horizon and very often the horizon in this way recedes 10, 15 
or 20 miles and even more. 
I now come to other cases that may present themsclves in the density 
of the air. The case that we have considered already is that in which 
there is a diminution of temperature upwards at the rate of 345 degree 
Fahr. for every foot of ascent. In Great Britain the diminution is very 
seldom more than about 45 degree or less than 4, degree Fahr., 
but in other climates it is different. If the temperature were to fall at 
a more rapid rate, the air would be very much more nearly of uniform 
density, and that would result in a smaller curvature of the ray. If 
the fall were at the rate of about 345 degree Fahr. for every foot of 
ascent, it would result in the density of the air being uniform, and there 
would be no terrestrial refraction at all. This state of the atmosphere 
we might represent by lines drawn at equal distances apart. A more 
rapid fall of temperature still would cause arise of air density upwards, 
and that would cause a curved ray with the concavity presented upwards 
as shewn in Fig.5. In sucha case, where the density increases upwards 
Fre. 5. . 
and the concavity is presented upwards, the refraction is said to be 
negative, whereas in the case that we had formerly the refraction is 
said to be positive. On the other hand a rise of temperature upwards 
causes a rapid diminution in air density in ascending, and this causes 
the ray with the concavity presented downwards to be more curved 
and, in the extreme case in which the rise of temperature upwards is at 
the rate of z'5 degree Wahr. for every foot the curvature of the ray would 
be the same as that of the earth, and in that case (which of course would 
never actually present itself) we would be able to see completely round 
the globe simply because the ray would encircle it. 
Again climatic conditions may lead to another distribution of the 
density. We might get a gradual rise in density upwards to a certain 
stratum of maximum density and then a diminution of density upwards; 
in which case you might represent the state of the atmosphere as in 
Fig. 6, then the ray of light would pass in a curious sinuous path with 
Fria. 6. 
