ALTAZIMUTH SOLAR OBSERVATIONS. 311 
the right, looking through the telescope, inasmuch as the circles 
are graduated ‘“‘clockwise”—the collimation correction to the 
horizontal circle is, for the altitude A, 
p and ¢ being in the same units, seconds say. If, looking through 
the telescope, the left hand side of its pivots be raised so that the 
rotation axis is inclined 7 with the horizontal, the similar correction 
X for the same-altitude is,— 
A and 7 being in the same units. 
Since these corrections are always very small, they may be 
applied independently, without introducing sensible error except- 
ing near the zenith, a case with which we are not here concerned, 
since such points are unsuitable for azimuth determinations. The 
effect of applying the corrections is obviously to reduce the 
recorded direction to that which would be given by a perfectly 
adjusted instrument. In regard to the recorded altitude, it need 
only be remarked that if the alidade level alter from the position 
of adjustment, the reading must be corrected by the whole amount 
of the level movement. In order to eliminate the corrections (1) 
and (2) from the results of observations, it is usual where possible 
to reverse the instrument for each pair, so that the constants, 
having then opposite signs, will involve the disappearance of the 
nearly equal corrections from the mean of the observations. It 
will be sufficient to observe that since ¢ and é are always very 
small, slight changes of altitude do not vitiate this proceeding, by 
importing into the result errors of sensible magnitude, in conse- 
quence of regarding the corrections as exactly equal. ‘This will be 
Seen by differentiating (1) and (2) for we shall then have for the 
differential corrections at any altitude, for a small change thereof 
dp = csechtanh dh......... (3) 
dX = isec? h dh (4) 
in which dh will of course be expressed in radians or ‘circular 
Measure,’ the other units being as before. These differential — 
Sorrections and their differentials again, both increase when the 
