ALTAZIMUTH SOLAR OBSERVATIONS. 329 
horizontal diameter is sensibly constant at all altitudes, that of 
the vertical diameter greatly varies with the altitude, so that 
regarding the sun’s apparent figure, as an ellipse, the eccentricity 
of the figure will continually diminish as the zenith is approached, 
the circular form being attained only when the centre is at the 
zenith. We shall have occasion to find the length of an inclined 
semidiameter. This may most readily be done by finding a 
quantity such that if subtracted, not from the geocentric semi- 
diameter, but from the contracted horizontal semidiameter it will 
give the value of the inclined semidiameter as affected by refraction 
and augmentation. Denoting the values in Tables VI. and VIL., 
§ 10 and § 11, by s and ¢’ as before, we have for the reduced hori- 
aii ae reduced vertical semidiameters respectively, 
S= 8§ re ig hfe a fae 
consequently, if we use RK to express the difference of the semi- 
diameters, the value of ¢ is given by 
Ce 8. — By tee 28 icectc venus 30) 
that is to say, c is the difference of the reduced horizontal and 
vertical refractions. 
Ignoring primarily the defect of the elliptical hypothesis, let 
CP the inclined semidiameter as affected by refraction and 
augmentation, see Fig. 2, be denoted by S,; the inclined contrac- 
