. 
328 G. H. KNIBBS. 
that no confidence can be placed in any theory of its apparent 
contraction, or in the value of the refraction ; and it may further 
be observed that the imperfect definition of the limbs at low 
altitudes renders accurate observation impossible, so that the 
order of the difference between the upper and lower semidiameters, 
even at 85° zenith distance, is practically almost negligible. The 
reduced vertical semidiameter will hereafter be denoted by S:. 
12. Elliptical figure of the Sun’s image.—Since the variation 
of the refraction for small variations of zenith distance is nearly 
linear, it follows that the form of the sun is nearly elliptical. The 
departure from the outline of a perfect ellipse is perhaps always 
negligible, as will be seen from the following comparison of an 
extreme case between the outline approximately computed on the 
elliptical assumption and that obtained from the refraction theory 
by supposing the air temperature and pressure to be that of no 
correction in Bessel’s table, and the érwe altitude of the sun’s 
centre to be 5°. The upper limb is taken for comparison. In 
Fig. 2 let the line C N be trisected, and parallels be drawn to the 
verticals through the centre, from the points u, v, so found. Then 
neglecting horizontal contraction, and assuming the refraction to 
act in the direction of these parallels, which is nearly true, we 
have since M M’ is 22-92 
By refraction U U’ = 21:67” V V'=17:25" 
By ellipse 21°61 16-09 
Difference 0-06 0:16 
This order of difference, viz. one or two tenths of a second of are, 
is really negligible because of the imperfection of definition at so 
low an altitude. The difference however may easily be taken 
into account as a small correction on the hypothetic elliptical 
form, as shewn in the more exact treatment of the next section. 
What the illustration establishes is that, at least to a first approxi- 
mation, the hypothesis of an elliptical outline for the sun’s image 
is justified. : 
13. Contraction of inclined semidiameters and departure from 
elliptical form.—We have seen that while the contraction of the 
