ALTAZIMUTH SOLAR OBSERVATIONS. 351 
positions marked 2; the criterion for determining this point being 
discussed in the preceding section, viz.,§ 18. In case 1, the line 
CD is supposed to be ‘horizontal,’ 7.e. perpendicular to a vertical 
through I or J. Let the angle between the line C D and this 
perpendicular to the vertical, be é” as in (45) § 16, and be regarded 
as positive when the D end droops. Itis obvious that the tangent 
point observed will not be vertically above the sun’s centre except 
when £” is zero: therefore the values of X and Y in equation (45) 
must be taken into account as corrections to the results given 
immediately by observation. This may practically be avoided, at 
least in part, by observing in the manner indicated hereunder. 
In the suggested programme of observations, RO denotes the 
‘referring object,’ that is an object on the line, the direction of 
which is to be ascertained ; and N and R denote respectively the 
‘normal’ and ‘reversed’ positions of the instrument, that is 
the position when the face of the vertical circle is to the right 
and when to the left, or vice versa. 
Type l. 
Morning Observations. 
Instrument N : read direction R O: put on dark glass: 
N Alt. h’: upper limb, read direction and time: reverse instr. 
R ,, kh’: lower ,», remove dark glass: 
instr. being R Deread diréstion R O: aks means. 
Afternoon Observations. 
Instrument R: read direction R O: put on dark glass: 
R Alt. 2”: lower limb, read direction and time: reverse instr. 
My Ae: mppor 5: yo y,_-«Femmove dark glass: 
instr. being N re-read direction R O: take means. 
Tf the temperature and pressure be nearly identical in the after- 
noon there will be no sensible correction for the error of altitude. 
Tf not let ¢’ and ¢” denote the contractions of the vertical diameter 
in the successive observations ; and B and @ as before the refrac- 
tion correction factors for barometer and thermometer, the suffixes 
land 2 denoting morning and afternoon, respectively. Then, 
neglecting very small quantities, the correction for contractional 
