134 Proceedings of the Royal Society 
for each foot of rise. But that caused by the lessening of the at- 
nnospheric pressure is only *00114, or less than the fourth part of 
what is needed; and therefore we conclude that no light can ho 
retroflected in the usual condition of the atmosphere. 
Inverted images, then, can only be seen when the air is in an un- 
usual condition ; there must he unusually light air above. Now, in 
these, as in all investigations on the subject, the air is assumed to 
be disposed in horizontal layers, each of uniform density ; without 
such an arrangement no definite refraction can take place, no dis- 
tinct image, whether distorted or not, can be formed. 
The absolute need for smoothness of arrangement may easily be 
illustrated : — The sun’s light is certainly reflected from the surface 
of the sea ; yet we do not see an image of the sun in the water : 
we see only a confused brightness. When the air is quite still, the 
sea becomes smooth enough to give an image, which, however, the 
slightest breath of wind destroys. We cannot use a dish of water 
as an artificial horizon, we must cover even our trough of mercury 
with a glass screen to prevent the ripple caused by the wind. 
Here gravitation tends to produce and to preserve the evenness of 
the surface. Water is some seven hundred, mercury is ten thou- 
sand times heavier than air, and yet the friction of the air produces 
such disturbance. 
Suppose then that we had a liquid as light as, or only a little 
heavier than air, and that we had poured this liquid into a flat dish. 
Paying no attention to the density of the wind which may blow 
upon it, let us think how calm the air would need to be that there 
may be no ripple on the surface. But let us add to this the con- 
sideration of the fact that the almost equality of the two densities 
deprives gravitation of its power to stratify, and we must admit 
that the slightest horizontal motion would be destructive of all 
smoothness. 
Imagine a stratum of air of the requisite depth and in its usual 
state quite level on its upper surface, and let us place upon that a 
layer of light air of the requisite refractive power, we shall then 
have inverted images. But our strata are not liquids ; they must 
be pressed upon to keep them from expanding, there must be air 
above them. If the superior air have its density conformable to the 
lower stratum so as to be in equilibrium with the general atmo- 
sphere beyond, it must be denser than the inserted layer, and the 
