21 
The marks ** in the dates signify, that the error of collimation 
was changed at that time. 
The amount of the correction for the mean of the three micros- 
copes was not changed between the 17th and 19th October 1818 ; 
but the relative position of the right and left microscopes was 
changed, in consequence of an adjustment of the horizontal 
axis of the circle. 
From September 20, 1819, with the exception of a few observa- 
tions, the observations were made off the meridian. One observa- 
tion was made a few minutes before the time of coming to the 
meridian, and the other after the passage over the meridian, the 
instrument having been reversed. ‘The position of the face of the 
instrument, whether east or west, is marked with the reading of the 
bottom microscope. 
This method of observing off the meridian is considered to have 
rendered the observations more exact. 
The zenith distance is obtained by the mean, without any cor- 
rection for collimation, and without danger of a change in collima- 
tion, from an interval of some days having occurred. | 
This method adds considerably to the trouble of computation, but 
that is of no consequence compared with the other advantages. 
I prefer making the computation of the corrections by Logarithms 
to taking the numbers out of a table.—If P be the distance in time 
from the meridian reduced to seconds, then in Lat. 53°.23'13",5. 
log. Ist. corr. =6,51230 + log. sin. N. P. D. + cosec. Z. D.+2log P 
log. 2d. corr. =7,1564 + log. sin. N. P.D.+cosec. Z. D.+4log P 
log. 3d. corr. =2 log. Ist. corr.+ 4,58454+cotan. Z. D. 
(AbovePole) Mer. Z. D.=observation—( Ist corr—2d corr—3d corr. ) 
(Below Pole) Mer. Z.D.= observation + (Ist corr—2d corr + 3d corr.) 
The 2d and 3d corrections are very small, and may easily be con- 
