482 Mr. Ivory on the astronomical refractions . 
in the hypothesis of Cassini. Bessel determines e = 
nearly ; which is quite inconsistent with the value of — 
at the surface of the earth, and with the elevation necessary 
for depressing the thermometer one degree, as found by ex- 
periment. Accordingly, although the refractions in his 
table represent Dr. Bradley’s observations with great exact- 
ness as far as 86° from the zenith ; yet, at lower altitudes, 
they diverge greatly from the truth ; and the horizontal re- 
fraction comes out very nearly the same as in an atmosphere 
of uniform temperature. In this last hypothesis the refrac- 
tions agree with nature as far as between 70° and 8o° from 
the zenith ; and, by means of the arbitrary quantity e, they 
are bent to a conformity with observation a few degrees 
farther. 
The preceding remarks have been made with the view of 
showing how it happens that the refractions in M. Bessel’s 
table agree with observation to a certain extent, and after- 
wards differ so widely from the true quantities. In comparing 
the two tables, we must attend to the points in which they 
are different from one another. In the table of M. Bessel 
the constant of refraction is a little less than in the new table : 
the mean temperature is 48^° of Fahrenheit in the former, 
and 50° in the latter ; and the standard barometers are 2 9.6 
inches and 30 inches. Now, supposing the two tables to re- 
present the true mean refractions equally well, the differences 
we have mentioned will hardly have any other effect than to 
introduce a constant factor, by means of which the one 
table would be reduced to the other. The logarithms of the 
numbers in the two tables ought, therefore, to have constantly 
