340 Mr. Groou'qki'dg'e* s further Ohsewations 
in a decreasing ratio. To discover the law of variation for each, 
would have been complex ; therefore retaining the value of jc 
as general, I found y to vary as the minutes of each degree 
above 87° x ,00462 ; the co-efficient (y) of r when so reduced 
is given ; the mean refraction resulting, is contained in the 
following column ; and being corrected for the new factors of 
the thermometer, there remains the final error. 
With a view to assist me in ascertaining whether the re- 
fractions were affected by local vapours, Dr. Brinkley has 
kindly communicated to me some observations of low stars ; 
which when reduced by the same formula do not materially 
differ from my own. 12 Can. Ven. at 87° 2' and « Lyrie at 
87® 42' of which there are the greater number of observations, 
the former gives the same result within half a second, and the 
latter 1^". 
Several of the fixed Observatories in Europe being situated 
in sufficiently high latitudes to obtain the elevation of the pole 
with mucli correctness; we are thence enabled, by the cir- 
cumpolar stars, to find the true quantity of refraction, for all 
zenith distances : and this having been so ascertained, we may 
appl}^ the same to the observed zenith distance of the sun, at 
the winter solstice, as a test of its accuracy. With the smaller 
quantities of refraction, which were used by Dr. Bradley 
and others, fifty years since, it was not possible, that the 
latitude deduced from the elevation of the pole, and the mean 
of the solstices, could agree; the distance of the pole from the 
equator, so computed, would be less than yo*. Hence also, the 
two solstices would shew an error of double that difference in 
the obliquity of the ecliptic, wdien obtained from the greatest 
and least zenith distances of the sun. The small number of 
