10 
MR. RUMKER’S OBSERVATIONS 
Remarks. — These results are somewhat contradictory to the last, the southern 
stars giving rather less for latitude than the northern, which would prove that 
the zenith distances had been observed too great. 
When a method leaves us in uncertainty, we must resort to another that is 
independent of those errors that vitiated the former. One of the effects of 
gravity is, that it causes eccentricity in the repeating circle when used in the 
manner last described, by depressing the small circle, which carries the tube, 
below the centre of the great circle’s division ; so that the optical axes, or radii 
of the double zenith distances, are removed downwards parallel to themselves, 
and thus subtending a greater arc of the limb, make the observed zenith 
distance too great. The observations alternately direct and by reflection, 
are free of these errors, for the displaced vertex of the observed arc remains 
in the diameter that is parallax to its chord. 
In the preceding observations, the refraction corresponding to the mean 
height of the barometer and thermometer has been applied to the mean of the 
zenith distances. There is no error in this, the change of the refraction being 
in all tables assumed proportional to that of the barometer and thermometer 
in so small limits. But I have also employed the true south polar distance 
corresponding to the mean date, instead of correcting it for each particular 
day. The error thence resulting is within the probable limits of the steadiness 
of the level, from its being differently influenced by temperature on different 
days. 
IV. Latitude by Observations alternately direct, and by Reflection from 
Mercury. 
1 . Observations of the Sun with the Mural Circle near the Southern 
Solstice, December 1827. 
1= 
1827. 
Barom. 
Therm. 
Observation. 
Microscopes. 
Refr. 
Parall. 
I. 
II. 
III. 
IV. 
L 
Dec. 25 
inches. 
29-71 
102 
direct 
67 4 31.6 
1 " ~ 
4 48.6 
/ // 
4 46.5 
/ // 
4 45.8 
// 
9-53 
// 
1.6 
L 
28 
30.03 
83.3 
direct 
67 10 22.2 
10 25.6 
10 18.3 
10 28.0 
10.19 
1.6 
L 
Jan. 130.05 
85 
by reflection. 
225 26 50.0 
26 58.0 
27 7.5 
26 50.3 
10.4 
1.65 
U 
2,30.044 
89 
by reflection. 
225 54 47.0 
54 58.0 
55 1.0 
54 53.3 
9-83 
1.6 
L 
4,30.114 
86 
by reflection. 
225 11 13.7 
11 24.7 
11 30.3 
11 20.5 
10.70 
1.7 
L 
10 29.758 
80. 
direct 
68 22 38.9 
22 54.5 
22 49.8 
22 52.3 
11.40 
1.8 
