on Atmospherical Refraction , &c. 195 
and this subtense of the arc agrees very nearly with that of 
y Draconis, by Dr. Maskelyne, which he has communicated 
to me, being 35, "3 1. Several of those made by Lieut. Col. 
Mudge were single observations, with the zenith sector in 
one position only, and therefore were reduced by the mean 
coilimation, found from the other stars ; but the result shews 
the accuracy of his observations. The latitude of Greenwich, 
when corrected from the mean of circular instruments, as 
proposed by Mr. Pond, and by the refraction for the excess 
of 57", will not differ more than half a second, from the above 
determination. 
Having found by this hypothesis, the mean astronomical 
refraction at 45 0 , I shall proceed to compare the same, with 
the observations of other astronomers. M. Piazzi has very 
ingeniously, and with great labour, made his deduction of the 
mean refraction, from the observations of Procyon, a Lyrse 
and Aldebaran at equal altitudes, from 38° to 89° 30' zenith 
distance, in addition to several circumpolar stars, for his latitude : 
this advantage having been obtained from his instrument 
moving in azimuth. The result thereof gives the mean re- 
fraction at 45 0 — 57/3 into the formula of Dr. Bradley, tang. 
z—gr; which I have found, as above, 58, "107. M. Piazzi, 
therefore, shews in his table of mean refractions, that at 
45° = 5 7 >"3 x tang. 45°- 3 r = 57, "2 ; which will be = 58", 01 
in my table. On a comparison with the present French tables, 
the latter give 58/' 2, at 45 0 , which is in excess of my own. 
The formula of M. de la Place, as given in his Mecanique 
Celeste, which is very elaborate and ingenious, being applied 
to a constant quantity, 60, "616, as determined from obser- 
