6 
MR. RUMKER’S OBSERVATIONS 
With these latitudes should be classed the 
c. Latitude by Solstices*. 
Southern Solstices. 
December 1821. 
December 1822. 
December 1823. 
December 1826. 
December 1827. 
Tropic Zenith Distance 
Mean obliquity 
o / // 
10 21 2.23 
23 27 45.70 
10 20 58.2 
23 27 45.3 
O / // 
10 21 4.02 
23 27 44.90 
1°0 20 57-9 
23 27 43.7 
O / // 
10 21 4.2 
23 27 43.3 
Latitude 
33 48 47-9 
33 48 43.5 
33 48 48.92 
33 48 41.6 
33 48 47.5 
Northern Solstices. 
June 1822. 
June 1823. 
June 1826. 
June 1827. 
June 1828. 
Zenith Dist. of Tropic. 
Mean obliquity 
57 16 25.9 
23 27 45.5 
57 16 27.0 
23 27 45.1 
57 16 30.9 
23 27 43.9 
57 16 23.0 
23 27 43.5 
57 16 22.8 
23 27 43.1 
Latitude 
33 48 40.4 
33 48 41.9 
33 48 47.0 
33 48 39.5 
33 48 39.7 
Latitude by a mean of the Southern Solstices 33 48 45.9 
by a mean of the Northern Solstices 33 48 41.7 
by Northern Stars as before 33 48 45.3 
by repetitions North of Zenith 33 48 44.3 
ditto South as above „ „ 59.3 
by a mean 33 48 51.8 
Difference between observation N. and S „ „ 15.0 
This shows that the zenith distances have been observed too small ; and the 
solstice moreover seems to indicate that the error increases with the zenith 
distance. Without investigating the cause of this error, we may suppose 
equal zenith distances on either side of the zenith equally influenced by it. 
Calling therefore <$ and 2 the declination and observed zenith distance of the 
northern, and S' and z' those of the southern star in his superior culmination, 
and x the correction of the zenith distance, we have, if both stars have south 
declination (in general if latitude and declination are of the same name) 
z + x -f 8 = latitude 
and 8' — z 1 — x = latitude 
v z — z' 8-4-8' 
whence ___ + — L_ _ latitude. 
And thus the error x of the instrument is eliminated. 
* The solstices of 1821 and 1822 were observed by Sir Thomas Brisbane and myself conjointly ; 
those in 1823, by Sir Thomas Brisbane ; and the remainder by myself alone. 
