324 G. H. KNIBBS. 
and as the sine of the parallax for any geocentric zenith distance’ 
¢ is equal to the sine of horizontal parallax multiplied by the sine 
of that distance, we have, putting S, for the sun’s mean semi- 
diameter, and substituting the arcs of the very small angles for 
their sines, 
- 
fee. 3: SA sin ¢ (25) 
\ af 
as the general equation for cee The negative sign denotes 
that it is always to be subtracted from the zenith distance. With 
this factor, the extreme values are 8°900 and 8°’694, correspond- 
ing to the semidiameter values 16-'2922 and 15-7555 while that 
for the earth’s mean distance is 16-0197.2_ In the following table 
the corrections are given ‘with the argument apparent zenith 
distance® corrected for refraction, 
TaBLE V.—Swun’s Parallax in Zenith Distance. 
un’s True Zenith Distance 
Semidiameter 90° 76° 55’ 72° 4’ 68° 15. 64° 58’ 58° 9’ 52° 27’ 
16’ 0” 8:83” 8-60" 8-40" 8-20” 8-00". 7:50” 700° 
Corr. for 10” -092 090 -087 085 083 ‘078 ‘073 
Sun’s True Zenith Distanc 
Semidiameter 52°27’ 42° 49’ 34° 30’ 26° 56 19° 52’ 13° 6’ 6° 30’ 
16’ 0” 7-00” 6:00” 5-00” 4:00” 3-00” 200% 1:00" 
Corr. for 10” 073 -062 052 042 031 021 010 
9. Augmentation of the Sun’s semidiameter.—As the sun’s 
altitude increases, the distance from the observer diminishes, 8° 
that when it is in the zenith that distance is less, very approxi- 
mately by the whole value of the earth’s radius. Theoretically 
therefore, there should be an increase of the geocentric value given 
in an ephemeris, depending upon the zenith distance. If the 
distance to the sun be regarded as unity, the earth’s radius is 
sin z., that is the sine of the equatorial horizontal parallax, and 
the diminution of distance is sensibly this quantity multiplied by 
1 Corrected for refraction but not reduced to its geocentric value. 
2 According to Auwers 
3 It is really immaterial what zenith distance be used. 
