REFRACTION. 
a prieri, but also from precise astronomical 
observations : for there are numberless ob- 
servations, by which it appears that the 
sun, moon, and stars rise much sooner, 
and appear higher, than they should do ac- 
cording to astronomical calculations. Hence 
it is argued, that as light is propagated in 
right lines, no rays could reach the eye 
from a luminary below the horizon, unless 
they were deflected out of their course, 
at their entrance into the atmosphere ; and 
therefore it appears that the rays are re- 
fracted in passing through the atmosphere. 
Since the stars appear higher by refraction 
than they really are ; to bring the observed 
or apparent altitudes to the true ones, the 
quantity of refraction must be subtracted. 
Accordingly the ancients, as they were not 
acquainted with this refraction, reckoned 
their altitudes too great. Refraction length- 
ens the day, and shortens the night, by 
making the sun appear above the horizon 
a little before his rising, and a little after 
his setting. Refraction also makes the 
moon and stars appear to rise sooner, and 
set later, tlian they really do. The appa- 
rent diameter of the sun or moon is about 
32' ; the horizontal refraction is about 33' ; 
whence the sun and moon appear wholly 
above the horizon when they are entirely 
below it. Also, from observations it ap- 
pears that the refractions are greater nearer 
the pole than at lesser latitudes, causing 
the sun to appear some days above the ho- 
rizon, when he is really below it ; doubtless 
from the greater density of the atmosphere, 
and the greater obliquity of tlie incidence. 
Stars in the zenith are not subject to any 
refraction : those in the horizon have the 
greatest of all : from the horizon the refrac- 
tion continually, decreases to the zenith. 
All which follows from hence, that in the 
first case, the rays are perpendicular to the 
medium; in the second, their obliquity is 
the greatest, and they pass through the 
largest space of the lower and denser part 
of the air, and through the thickest vapours; 
and in the third, the obliquity is conti- 
nually decreasing. The air is condensed, 
and consequently refraction is increased, by 
cold ; for which reason it is greater in cold 
countries than in hot ones. It is also 
greater in cold weather than in hot, in the 
same country ; and the. morning refraction 
is greater than that of the evening, because 
the aii; is rarified by the heat of the sun in 
the day, and condensed by the coldness of 
the night. Refraction is also subject to 
some small variation at the same time of 
the day in the finest weather. 
The horizontal refraction, being the great- 
est, is the cause that the sun and moon ap- 
pear of an oval form at their rising and 
setting ; for the lower edge of each being 
more refracted than the upper edge, the 
perpendicular diameter is shortened, and 
the under edge appears more flatted also. 
Again, if we take with an instrument the 
distance of two stars when they are in the 
same vertical and near the horizon, we shall 
find it considerably less than if we measure 
it when they are both at such a height as to 
suffer little or no refraction ; because the 
lower star is more elevated than the higher. 
There is also another alteration made 
by refraction in the apparent distance of 
stars : when two stars are in the same pa- 
rallel of declination, their apparent distance 
is less than the true ; for since refraction 
makes each of them lighter in the azimuth 
or vertical in which they appear, it must 
bring them into parts of the vertical where 
they come nearer to each other ; because all 
vertical circles converge and meet in the 
zenith. This contraction of distance, ac- 
cording to Dr. Halley, (Philos. Trans, 
numb. 368) is at the rate of at least one 
second in a degree ; so that, if the distance 
between two stars in a position parallel to 
the horizon, measure 30", it is at most to be 
reckoned only 29", 59', 30''. 
The quantity of the refraction at every 
altitude, from the horizon, where it is great- 
est, to the zenith where it is nothing, has 
been determined by observation, by many 
astronomers ; those of Dr. Bradley and Mr. 
Mayer are esteemed the most correct of 
any, being nearly alike, and are now chiefly 
used by astronomers. Dr. Bradley, from 
his observations, deduced this general rule 
for the refraction, r, at any altitude , a, what- 
ever ; viz, as rad . 1 ; cotang. a-\-Sr 57" -.r" 
the refraction in seconds. This rule is 
adapted to these states of the barometer 
and thermometer, viz. either 29.6 inch ba- 
rometer and 50" thermometer, or 30 inch 
barometer and 55" thermometer, for both 
which states it answers equally the same. 
But for any other states of the barometer 
and thermometer, the refraction above 
found is to be corrected in this manner ; 
viz. if h denote any other height of the ba- 
rometer in inches, and t the degrees of the 
thermometer, r being the refraction incor- 
rected, as found in the manner above. Then 
as 29.6 : 5 : : r : R the refraction corrected 
