accordingly, in his computation of a formula for that purpose, :1 Ursse
Majoris, at 70° 10’ zenith distance, was the lowest star included in
his estimate. By applying that formula to stars below 80° zenith
distance, Mr. Groombridge has since found some correction to be
necessary; for the refraction at the low altitudes is not really so
great as might be presumed from that of stars less distant from the
zenith. He has consequently been induced to make a course of ob-
servations on other circumpolar stars, beyond the former limits, and
as near to his north horizon as the situation of his observatory would
permit. Since the formula of Dr. Bradley appears most conveniently
applicable to the purposes of the practical astronomer, but not quite
correct in the numbers assumed for refraction at 45°, and for the co-
eflicient of .r, the author has endeavoured to find out such numbers
as would correspond more accurately with observation, and has found
that the same formula may be made to serve as low down as to 87°
of zenith distance, by increasing the amount of the numbers before
r'nentioned still a little more than he had formerly done.
But for stars of less altitude than this, or within three degrees of the horizon, he found that the same formula could not be made to serve throughout, but that it became necessary to vary the amount of the coefficient 3/ nearly in proportion to the excess above 87° zenith distance.
The table of observations on which these estimates are founded is divided into two parts; the former of which is the result of more than 240 observations made upon sixteen stars between 80° and 87° zenith distance; and the latter is founded upon six other stars be- tween 87° and 88° 42' zenith distance.
The difference of the obliquities of the ecliptic, as deduced from the summer and winter solstices, or disagreement between the eleva- tion of the equator, thence deduced, and the zenith distance of the pole, as inferred from the zenith distance of circumpolar stars, is ascribed by the author to error in the quantities of refraction, which was assumed too small by Dr. Bradley. And he remarks, that, on the contrary, his observations of the solstices, when reduced accord- ing to his own improved formula for refraction, agree in giving re- sults that correspond with his observations of circumpolar stars.
With respect to thermometrical corrections, Mr. Groombridge observes, that his results appear to be most correct when reduced by the state of the thermometer without-doors instead of that which is within; and that the difference is very considerable where the zenith distances are so great as those included in the present remarks.
