ALTAZIMUTH SOLAR OBSERVATIONS. 353 
The values of c’ and c” may be obtained from the table here 
under with sufficient exactness by adding half the semidiameter, 
or say 8', to the observed apparent zenith distance when the upper 
limb is read, or by subtracting 8’ when the lower limb is read, for 
the argument with which to enter table. The quantities in the 
table, similarly to those in Table VII., require to be multiplied 
by the factor (29) § 11, that is by 86, but not when used in the 
formule immediately preceding. 
TasLe 1X.— Vertical Contraction of the Sun’s Semidiameter. 
S, =16, Bar. 29-6, Therm. 48°75° Fahr. 
Observed Zenith Distance, not corrected for refraction. 
° ° ° ° ° ° ° ° 
Zen.Distance 0 15 30 40 50 55 60 65 70 
Contraction 0-23 0:24 0:32 0-46 9-63 0-79 1-04 1:46 2:23 
Zen. Distance 75 78 80 81 82 83 84 844 85 
Contraction 3-81 5-75 7:98 9-60 11°79 14-74 18-84 21:59 24:99 
In applying the corrections of (45) to the results of observations 
according to the preceding programme we have not yet taken 
account of the Y—or horizontal—correction. Rejecting the 
negligible quantities, the mean of the recorded azimuthal angles 
for the morning observations, measured from the elevated pole, 
requires the correction 
~}% Ssin €” (sec h”—sec h’) +} (c’ —c”) sin &” sec h....... (a) 
h denoting altitudes ; and the mean of the afternoon observations 
require the same correction with the signs + and —. Hence we 
may correct only the afternoon azimuthal angle by adding thereto 
dA’ = § sin &” (sec h” — sec I’) - (c’ —c”) sin &” sec h...(55) 
h being the mean of the observed altitudes, and h’ and h” the 
‘approximate altitudes of the centre of the sun. The correction 
must necessarily be very small, hence 2 @ factors may be ignored. 
: The more usual method of making equal altitude observations 
18 to record the direction and altitudes for the positions marked 
2 in Fig. 4. “When the lines A Bor a b, the latter bisecting the 
angle EJ F, are not vertical, the observation is not on a point 
defined by a vertical circle tangent to the side of the sun. In 
W—Dee. 2, 1896, 
