< Apology for the Postscript on the Refractions,’’ &c. 19 
will be acquired ; and we may so determine the arbitrary quan- 
tities as greatly to diminish, and even almost to annihilate, the 
differences between the formula and observation, or between the 
formula and a given table of refractions. And this, I conceive, 
is a just and sufficient account of the coincidence between the 
tables of mean refraction in the Nautical Almanack and the 
Connaissance des Tems. 
Suppose Dr. Young’s formula with literal coefficients was given 
to each of two computers, one in London and one in Paris; and 
they were directed to determine the numerical values so as to 
represent the French table: it is by no means clear that both 
would hit upon the same numbers for the coefficients. It will 
not appear improbable to any one who has attended to the va- 
riety of numerical formule for calculating the refractions *, that 
the result of such an experiment might be, two different for- 
mule equally representing the prescribed table. 
Tt will not, 1 hope, be inferred from any thing that has been 
said, that an empirical table of refractions is supposed to be of 
little value. It can indeed have no value at all unless it have a 
proper foundation of its own, which can only be the case when 
it is constructed from an extensive series of observations made 
in every diversity of circumstances. A table, however con- 
structed, that is a mere copy of another, can have no authority 
which the original does not possess. 
Upon the method of allowing for the variations of the baro- 
meter and thermometer, I made no observatious. It would be 
very difficult to prove in a strict manner either its correctness or 
incorrectness. Besides, it is independent of the new method for 
the mean refractions, which alone I undertook to examine, This 
independence of the two methods arises from the empiricism, of 
the formula. For had the formula been theoretical, the coeffi- 
cieuts, instead of being numbers, would have contained the 
quantities that vary with the state of the atmosphere ; and one 
expression would have served, as ought to be the case, both for 
the mean refractions, and the mutations they undergo by the 
barometrical and thermometrical changes. The safest way to 
deal with this part of the table, is to compare it with some other 
table of at least equal authority. That of Dr. Brinkley will 
answer best, because the two tables agree in having the same 
mean horizontal refraction. Thus, for bar. 30 and ther, 50°, the 
horizontal refraction is, 
Dr. Brinkley) .. «= oe 33” 50" 
N, A. er ae ee 
Now, suppose a change of temperature of 18°, and compute 
* De Lambre’s Astronomy, vol. i. chap. 13, 
C2 the 
