ALTAZIMUTH SOLAR OBSERVATIONS. 325 
the cosine of the zenith distance, consequently the semidiameter 
S, at any zenith distance is 
ig 
2 
1 - sinz, cos ¢ 
Hence, rejecting the powers of the small quantity in the denom- 
inator higher than the first, and using mean values of the parallax 
and semidiameters the actual value of the semidiameter will be 
S, = 8S + 0°0412” cos ¢ .........(26) 
The successive hundredths of seconds are the corrections for the 
following altitudes, viz., 14°, 29°, 46° and 73°. It is evident 
that generally the correction may be ignored without vitiating 
the results of observations. If computations were carried out to 
0°01 and finally expressed to 0°”1 it might affect the last unit. 
It is preferable, however, when tabulating the effects of refraction 
on the sun’s diameter, to take cognizance at the same time of the 
augmentation, and combine these in the tabular value, and this 
will be done in the subsequent sections. 
ce 
10. Contraction of the Sun’s horizontal by refract 
—Since the effect of the refraction is to diminish the zenith 
distance of any point, the extremities of the sun’s horizontal 
diameter will apparently approach one another through refraction 
by an amount which is equal to the product of the convergency 
of the vertical circles passing through the extemities, into the 
displacement by the refraction. The convergency increases as the 
tangent of the altitudes, and it has already been mentioned that 
the refraction may be put in the form 7 = & tan ¢ in which 4, 
though not absolutely constant, is nearly so, and may be taken 
from tables of refraction.! Consequently we have for s’ the con- 
traction of the horizontal semidiameter 
s =r Scot ( = ktan (cot (S =k SG... (27) 
If we take & from a refraction table it must be multiplied by are 
1 for the value of s in seconds. It is convenient to combine the 
Contraction with the augmentation treated of in the preceding 
section. Denoting the augmentation term—0~"0412 cos (—by 9, 
Perr treuane ie Pisa Ramer a eS 
1 See (m) § 6. 
