and that the
glasses had lost their parallelism from the contraction of the brass. In
measuring the error he perceived that the diameter of the sun's image was
considerably short of twice the semi-diameter, a proof of the uncertainty
of celestial observations made during these intense frosts. The results
of this and another similar observation are given in the footnote.*

(*Footnote. The observed meridian altitude of sun upper limb was 2
degrees 52 minutes 51 seconds. Temperature of the air minus 45.5 degrees.
By comparing this altitude, corrected by the mean refraction and parallax
with that deduced from the latitude which was observed in autumn, the
increase of refraction is found to be 6 minutes 50 seconds, the whole
refraction therefore for the altitude 2 degrees 52 minutes 51 seconds is
21 minutes 49 seconds. Admitting that the refraction increases in the
same ratio as that of the atmosphere at a mean state of temperature the
horizontal refraction will be 47 degrees 22 seconds. But the diameter of
the sun, measured immediately after the observation, was only 27 minutes
7 seconds, which shows an increase of refraction at the lower limb of 3
minutes 29 seconds. The horizontal refraction calculated with this
difference and the above-mentioned ratio is 56 minutes 3 seconds at the
temperature minus 45.5 degrees. So that in the parallel 68 degrees 42
minutes where, if there is no refraction, the sun would be invisible for
thirty-four days, his upper limb with the refraction 56 minutes 3 seconds
is in fact above the horizon at every noon.

The wind was from the westward a moderate breeze and the air perfectly
clear. January 1st, 1821. Observed meridian altitude of sun lower limb 2
degrees 35 minutes 20 seconds, sun apparent diameter 29 degrees 20
minutes. For apparent altitude 2 degrees 35 minutes 20 seconds the mean
refraction is 16 minutes 5 seconds (Mackay's Tables) and the true, found
as detailed above, is 20 minutes 8 seconds which, increasing in the same
ratio as that of the atmosphere at a mean state of temperature, is 41
minutes 19 seconds at the horizon. But the difference of refraction at
the upper and lower limbs increasing also in that ratio gives 55 minutes
16 seconds for the horizontal refraction. Temperature of the air minus 41
degrees. Wind north, a light breeze, a large halo visible about the sun.
January 15th, 1821. Observed an apparent meridian altitude sun lower limb
4 degrees 24 minutes 57 seconds. S