In my former paper on atmospherical refraction, communicated to the Royal Society by my late friend, Dr. Maskelyne, I considered the few observations made below 80° of zenith distance, as not sufficiently to be depended on, for the computation of a general formula of refraction: and I therefore used
ŋ
Ursæ Majoris (78° 10' zen. dis.) as the lowest star for that purpose. Having since applied the computed refraction from the formula thence obtained, to observations of stars below 80°, I have noticed, that such stars so corrected, appeared to be further from the zenith below the Pole, than they ought to have been, from the observations above the Pole: and therefore that the refraction was less at those distances from the zenith, than I had assumed. This has induced me, in the years 1811 and 1812, to make a course of observations of stars below the Pole, above 80° zenith distance; and as near to the horizon, as the trees in Greenwich Park would permit; these being higher than the level of my Observatory. It may also be remarked, that those stars in my former table below 80°, produce the co-latitude in excess; as a confirmation, that the same formula will not apply to those larger arcs, where, from the rapid increase of the tangents, a small error in the assumed quantity becomes more sensible. Although various hypotheses may be formed, from the known density and temperature of the atmosphere; and from these causes may be computed the effect they should have on a ray of light passing through the same: yet we must resort to observation, for the verification of the theory; and reduce the quantity so found, to the most simple and convenient formula. I shall proceed to deduce, from this course of observations, such formulae as will appear to result, for the computation of the refraction; from the zenith, to the lowest star which I have observed: these may be considered as sufficient for the observation of the sun at the winter solstice, in high latitudes since those of the moon, from its great parallax, and the planets from their general invisibility, would probably not be attempted. Nevertheless, it is to be wished, as a matter of curiosity, or from which some useful deductions might be made, that in those Observatories, wherein from their elevated situations it might be practicable, the true quantity of refraction should be ascertained to the horizon. Of all the formulae for computing the mean refraction, that proposed and used by Dr. BRADLEY, is the most convenient and applicable for the practical astronomer. But as it is now acknowledged, that the numbers he had assumed for the coefficient of
r
(the refraction ; ) and of
x
(the quantity at 45°) were too small: their real values will appear to be the mean of several arcs, and such as I now propose to be adopted. I have found, that the same formula will serve to 87° of zenith distance; possibly this might not happen in low situations, where the height of the vapours would form a greater angle with the horizon: yet in more elevated places, we may reasonably suppose, that a general formula might be carried nearly to the horizon.
IV. Lunar influence on temperature
