334 G. H. KNIBBS. 
For altitudes greater than 15° it will always be sufficient to 
use the following sctiaias for the radius vector, viz. 
S, = 8 — $c¢(1 + cos 26) (35) 
2 
the derivation of whcol from (32) is obvious. This formula 
neglects the secondary term in the expansion for the ellipse, and 
assumes that the difference between the refracted and elliptical 
forms is negligible. 
14. ZLliptical image of the sun tangent to two diaphragm wires 
inclined at any angle.—As the sun is often observed at the 
moment it is tangential to two diaphragm wires, it is necessary to 
so correct the instrumental record as to obtain the altitude and 
azimuth of the image of the sun’s centre,! for it is to that point 
only that the tabulated places in an ephemeris refer. The dia- 
phragm wires cannot be assumed to be in perfect adjustment, 
consequently we shall suppose them to be slightly out of position, 
in order to make the treatment of the case quite general. 
In Fig. 3 let MC denote a vertical line drawn through the 
centre C of the sun’s elliptical image N Q M P, tangent at the 
points P and Q to the diaphragm wires I P, 1 Q. Since C M and 
Fig. 3. 
1 Not of the centre of its image. ee 
