Note 3 — Chapter VIII · ToC

"The observed meridian altitude of ☉ upper limb was 2° 52' 51". Temperature of the air -45° 5'. 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' 50", the whole refraction, therefore, for the altitude 2° 52' 51" is 21' 49". 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' 22". But the diameter of the sun measured immediately after the observation, was only 27' 7", which shews an increase of refraction at the lower limb of 3' 29". The horizontal refraction calculated with this difference, and the above-mentioned ratio, is 56' 3", at the temperature -45° 5'. So that in the parallel 68° 42', where if there was no refraction, the sun would be invisible for thirty-four days, his upper limb, with the refraction 56' 3", 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 ☉ lower limb 2° 35' 20". ☉ apparent diameter 29° 20'. For apparent altitude 2° 35' 20", the mean refraction is 16' 5" (Mackay's Tables), and the true, found as detailed above, is 20' 8": which increasing in the same ratio as that of the atmosphere, at a mean state of temperature, is 41' 19" at the horizon. But the difference of refraction at the upper and lower limbs, increasing also in that ratio, gives 55' 16" for the horizontal refraction. Temperature of the air -41°. Wind north, a light breeze, a large halo visible about the sun. January 15th, 1821.—Observed an apparent meridian altitude ☉ lower limb 4° 24' 57". ☉ apparent diameter 31' 5". For apparent altitude 4° 24' 57", the mean refraction is 10' 58" (Mackay's Tables), and the true, found as detailed above, is 14' 39", which, increasing in the same ratio as that of the atmosphere at a mean state of temperature, is 43' 57" at the horizon. But the difference of refraction between the upper and lower limbs increasing also in that ratio, gives 48' 30" for the horizontal refraction.

Temperature of the air -35°, a light air from the westward, very clear.

The extreme coldness of the weather rendered these operations difficult and dangerous; yet I think the observations may be depended upon within 30", as will appear by their approximate results in calculating the horizontal refraction; for it must be considered that an error of 30", in the refraction in altitude, would make a difference of several minutes in the horizontal refraction."—Mr. Hood's Journal.