ALTAZIMUTH SOLAR OBSERVATIONS, 331 
temperature and pressure of no correction in the Besselian 
refraction table. For the sun’s’ semidiameter the difference 
between plane and spherical codrdinates can never reach 0-005, 
hence we may use the former without sensible error. By taking 
points on the sun’s edge at 224°, 45°, 674°, and 90° from the 
intersection of the vertical through its centre, with the upper and 
lower limbs, computing very rigorously the refractions thereat, 
_Temembering that these refractions are displacements, not in lines 
parallel to the central vertical, but on the verticals through the 
several points; we obtain the codrdinates of their positions in 
the sun’s refracted image. Then by describing two semiéllipses 
with the contracted horizontal semidiameter as major axis, and 
the upper and lower vertical contracted semidiameters as minor 
axes; and computing the ordinates for points thereon whose 
absciss, measured on a great circle at right angles to the vertical 
through the image of the sun’s centre, are the same as in the 
refraction computation, we are able to compare the two results, 
and thus determine the error of the elliptical assumption. Taking 
the image of the sun’s centre as the origin of the coérdinates we 
obtain the following results in which + denotes increase of zenith 
distance, and the angles from the vertex are for the real sun, not 
its image, 
: Upper Limb. 
Angle from vertex 0° 924° Ge OS. 
Abscissee 0 367-29 678-66 886-71 959-77 
Ord. by Refract. — 937-08 — 865-69 — 66243 — 358-40 -0-01 
Ord. by Ellipse same —865-75 — 662-61 - 358-60 -000 
Difference nil 40:06 +018 +020 —0-01 
_ Lower Limb. 
Angle from vertex 90° l 124° 135° 1574° 180° 
Abscissee 959-77 816-71 678-66  367°29 0 
Ord. by Refract. — 0-01 4358-11 +661°50 +864:11 +935-23 
Ord. by Ellipse  — 0-00 + 357-89 +661°31 +864-04 same 
Difference O01 -0-22 .<019. +O0% «ail 
