479 
Mr. Ivory on the astronomical refractions. 
The French tables are also liable to some inaccuracy at 
low altitudes, from the manner in which they are constructed. 
The calculations are originally made for the temperature 
zero of the centigrade scale, and the barometric pressure 
29.92 English inches ; and from the numbers so computed, 
the refractions are in every case deduced, on the supposition 
that they vary in the same proportion as the density of the 
air. But, besides this alteration of their quantity, the refrac- 
tions undergo other variations, as the elementary quantities 
of the formula change with the state of the air; namely, 
those contained in the second and third terms of the fore- 
going rule for calculating by the new table. Now, the varia- 
tions here alluded to are neglected in the French table, al- 
though they are of considerable amount near the horizon. 
They are neglected, however, not because the eminent 
mathematicians who constructed the table were not aware of 
their existence, but because they deemed them of little mo- 
ment in a case of so great uncertainty as the refractions at 
low altitudes. Properly speaking, the table in the Connais- 
sance des Terns is not one of mean refractions; that is, the 
numbers in it are not the same that would be found by sub- 
stituting, in the fundamental formula, the elementary quan- 
tities reduced to the proposed standards of temperature 
and pressure. The true mean refractions computed in this 
manner would all be less than the quantities actually con- 
tained in the table. In practice, therefore, there is a kind of 
compensation that takes place between the excess of the 
numbers in the table above the exact values of the mean re- 
fractions, and the manner of correcting for the barometer and 
thermometer ; a compensation which is very happy in many 
