ALTAZIMUTH SOLAR OBSERVATIONS. 337 
is marked, its neglect therefore will not sensibly prejudice the 
evaluation of the lengths of the radii vectores CP, CQ. With 
regard to the former it is evident from (32), § 12, and from an 
inspection of Table VIII., that we can take C P = O M without 
sensible error if I P be not more than 1° or 2° from the perpen- 
dicular to the vertical through I. For the error of such an 
assumption will obviously be 
esin? 0 = 4c vers 20, 
hence if the vertical contraction amount even to 25”, the corrections 
would amount in the cases supposed, only to 0-"008 and 0-030 
respectively, the former even, being an extreme case. Again 
with respect to C Q, it may for the same reason be taken equal to 
the contracted horizontal semidiameter, if IQ be nearly vertical, 
as A B, Fig. 4, hereinafter. If however the wire be inclined about 
20° to the vertical as in Fig. 3, an error of 1° in the estimation 
of that angle will cause an error of only 0°”22, for a vertical con- 
traction of 20”; and as the convergency can amount only to about 
1’, it is clear that its neglect will cause an error of not more than 
0-"004 in the length of the line CQ. We may therefore rotate 
the axes of the ellipse through the are equal to the convergency 
without sensible error. In regard to this it ought perhaps to be 
remarked that as the form of the sun’s image approaches a circle 
the effect of rotation becomes more and more negligible, and is of 
course absolutely indifferent for a circular image. We have seen 
in Table VIT., § 11 that the ellipticity is only about 7+; at an 
altitude even so low as 10°: hence it is necessary to consider the 
Consequences of rotating the axes, only for the altitude correspond- 
ing to the conditions of most marked ellipticity, or say practically 
at an altitude of 5°, 
Rejecting very small quantities, the rotation equal to the con- 
vergency v, to make C M-parallel to the vertical through J, is 
given by the equation 
v = (S cosec y — 8, cot y+j) cot ¢ approx....(v) 
Y denoting the angle F I P, and j the rectangular distance between 
the verticals through J andI. Taking S=16', 8S, =153', y = 70°, 
V—Dee. 2, 1896, 
