Mr. Ivory on the astronomical refractions. 429 
and, if the observed object be just 9 o° from the zenith, then 
Now s = j ; and neglecting the effect of temperature, 
s = -l. Let v be the angle at the earth's centre contained 
by lines drawn to the observer and the object ; then, x being 
the height between the surface of the earth and the tangent 
to that surface drawn from the place of the observer, we have 
a. v* = 2x; and hence 2 j = j= j/=L: consequently, 
and, in numbers, 
t __ » 
2 — " 10.36 ' 
Now r is the sum of the angles which the tangents, drawn 
from the extremities of the arc intercepted between the ob- 
server and the object, make with the chord of the arc ; and, 
as the curvature will vary but little in a small extent, the 
two angles may be considered as equal, and ~ will be the 
refraction at the eye of the observer. When the terrestrial 
refraction, as found by actual observation, is compared 
with the angle at the earth's centre, it is very irregular, 
varying from — to In a case, where such excessive 
irregularities occur, no great confidence can be placed in 
a mean, even of a great number of observations ; more 
especially as local peculiarities have so much effect, that the 
mean at one place does not agree with the mean at another. 
In the English Survey, ~ is allowed for the terrestrial 
