widely upwards and less widely downwards, but in other directions more
or less as they approximate to these two extremes. This being so, it
necessarily follows that every line intersecting one of these waves at
right angles will pass above the point A, always excepting the one
line which is perpendicular to the horizon.

[Illustration]

Let BC be the wave which brings the light to the spectator who is at
B, and let BD be the straight line which intersects this wave at right
angles. Now because the ray or straight line by which we judge the
spot where the object appears to us is nothing else than the
perpendicular to the wave that reaches our eye, as will be understood
by what was said above, it is manifest that the point A will be
perceived as being in the line BD, and therefore higher than in fact it
is.

Similarly if the Earth be AB, and the top of the Atmosphere CD, which
probably is not a well defined spherical surface (since we know that
the air becomes rare in proportion as one ascends, for above there is
so much less of it to press down upon it), the waves of light from the
sun coming, for instance, in such a way that so long as they have not
reached the Atmosphere CD the straight line AE intersects them
perpendicularly, they ought, when they enter the Atmosphere, to
advance more quickly in elevated regions than in regions nearer to the
Earth. So that if CA is the wave which brings the light to the
spectator at A, its region C will be the furthest advanced; and the
straight line AF, which intersects this wave at right angles, and
which determines the apparent place of the Sun, will pass above the
real Sun, which will be seen along the line AE. And so it may occur