He next compares the refraction aboverdeduced, with the results
of other astronomers. Piazzi, having an instrument which turns in
azimuth, has deduced the actual refractions at all distances from
the zenith, by means of numerous observations on Proeyon, n Lyrae,
and Aldebarau, at various altitudes, from 38° to 89° zenith distance,
in addition to several circumpolar stars. Piazzi's result is, that the
mean refraction at 45° is 57"‘3, which is less by eight tenths of a
second than that of the author; but by the present French tables it
is stated to be 58"“2, which, on the contrary, is rather greater. But
beside the difi'erence in the quantity of mean refraction at 45°, Piazzi
observes that the law assigned by Bradley does not obtain ; for though
the actual refractions, so far as 80° from the zenith, are, in fact, greater
than was supposed by Bradley, the refractions within the remaining
10° of the horizon are less than he supposed them to be.
In the series of observations given by the author, a similar want of conformity to Bradley's law is observable; and he observes, that the change of difi'erence, from greater to less, takes place at 80° zenith distance, which is the same point of the heavens assigned by Piazzi.
Mathematicians, who have endeavoured to reconcile the known laws of refraction through difi'erent media, with the actual quantity deduced from observation, have proved that the refractions vary nearly as the tangents of zenith distance; but in order to reconcile this rule with the fact at low altitudes. they have found it necessary to intro- duce a correction of the zenith distance, and have invented a formula, consisting of a tangent of the zenith distance, diminished by some multiple of the refraction. The magnitude of this multiple has been estimated difi'erently by different authors. By Simpson it is rated at 2‘75; by Dr. Bradley 3: by Bong-oer 3'23 ; by Cassini 3226. Mr. Groombridge computes that this multiple should be as much as 3'3625.
In addition to the above endeavours to determine the mean re- fraction, and its variations at difi'erent altitudes, the author also con- siders the corrections which should be made for the states of the ba- rometer and thermometer, and explains the means by which he de- duced those that he has adopted, in order that any error therein may he more easily detected.
The principal object of Dr. Maskelyne in making this communication, is to inform the Society of a discovery, made by Dr. Brinkley, of the parallax of the annual orbit, which he has ascertained by oh. serrations on a Lyrae.
