352 : G. H. KNIBBS. 
change between the observations, to be applied to the means of 
the observed zenith distances, will be respectively — 4(c, - ¢,) cos &” 
and —1(c,-¢,) cos é’, see (45); that is to say these quantities 
must be added' to the mean of the observed zenith distances in 
order to obtain the mean of the zenith distances of the sun’s centre 
for the same instants. In order therefore to make the afternoon 
corrected mean zenith distance the same as the morning one, we 
must subtract d{' say, derived from (45), and determined by the 
equation 
d('= —} (c'-c’) cos &” (8,0, — B,9,)...... (52) 
the values of ¢ being the tabular contractions, Table VII, § 11. 
Thus we may regard (52) as the error of the afternoon observation. 
The cosine term may be omitted since it is sensibly unity. The 
afternoon mean azimuthal reading will of course require to be 
corrected for the above error d¢’, see (48), which, since the after- 
is generally considerably greater than the forenoon temperature, 
is usually positive. 
The above contractional-variation-correction must not be con- 
founded with the correction of the refraction, required when the 
mean of the observed zenith distances is employed, see Table II. 
§6. Taking e from the table, the error of zenith distance in the 
afternoon will be 
d¢(” =e (8,0, —B,9,) (53) 
which is usually negative, and . zero if h’'=h’. 
The last error has the same sign as the absolute refraction cor- 
rection, see (47), hence for observations of the wpper and lower 
limbs of the sun, we may write for the total error d¢ of the zenith 
distance—other than instrumental—for which a correction must 
be ~~ to the mean of the second azimuthal readings, see (48). 
dé=[r-4 (c - 0") +6] (8505 — B191).... eee (54 
_It may be remarked that ¢ must necessarily be very small if the 
observations are made in the manner indicated in the preceding 
programme.” 
"ins ee See 
1 That is with the sign attached : numerically they must be subtracted. 
2 A practised observer will not require the time taken by a = to 
secon rvation. It is well however, not to hur e secon morning 
nae for the same rapidity in observing may 2 not be Sey in 
ernoon 
