326 G. H. KNIBBS. 
and putting s for the contraction diminished by the augmentation, 
we then sah 
— g’ g ( 28) 
by means of er the stollowiig table is prepared. The geocentric 
semidiameter S, is supposed to sg 16’, bar. 29-6 in. and therm. 
48°75° Fahr. The horizontal ter corrected for refraction 
and augmentation will hereafter be denoted by S, so that S,=S+8s. 
Taste VI.—Horizontal Contraction of the Sun’s Geocentric 
Semidiameter. 
S,= 16’ Bar. 29°6in. Therm. 48-75° Fahr. 
True Zenith Dist.0° 20° 47° 70° 75° 85° 87}° 90° 
Contraction 0°23” 0:23” 0:24” 0-25” 0:25” 0:23” 0-20” 0°"07 
These results are affected by the augumentation and must not 
therefore be further corrected by (26). For different values of 
the semidiameter, pressure and temperature, the tabular values 
require the same factor as c’ in (29) hereafter; obviously however, 
- the correction may be ignored because of the smallness of the 
tabular value. 
11. Contraction of the Sun’s vertical diameter by refraction.— 
If a great circle be supposed drawn through the true centre of the 
sun’s disc, at right angles to the vertical through the same point, 
it will divide the apparent disc unequally, because the refractions 
are greater for the lower limb and centre, than for the centre and 
the upper limb. If therefore, in Fig. 2, § 13, the vertical through 
the centre C of the sun, be followed downwards, M © from the 
upper edge to the centre, will always be greater than C M, from 
the centre to the lower edge, and both will be less than the 
geocentric semidiameter. This contraction of the vertical diameter 
is sensible to the order of 0-1 right up to the zenith, within 30° 
of which the refraction is about 1-"1 per degree. The difference 
between the upper and lower semidiameters however, only becomes 
sensible as we closely approach the horizon—as is apparent in 
Table VII. hereunder. As in the preceding section, it is also 
convenient to include the effect of augmentation, which slightly 
reduces the contraction, because in this way the apparent form is 
