Mr. Ivory on the astronomical refractions. 483 
the same difference ; and how far this is actually the case, 
will appear by the inspection of the following table. 
Distance 
from 
zenith. 
Log. y. 
Difference. 
N. Table. 
Bessel. 
O 
45 
I.76612 
1.75961 
0.00651 
55 
1.92039 
I.91385 
0.00654 
6 5 
2.09568 
2.08910 
0.00658 
75 
2.33184 
2.32510 
0.00674 
80 
2.50541 
2.49849 
0.00692 
81 
2.54874 
2 - 54 I 75 
0.00699 
82 
2.59624 
2.58923 
0.00701 
83 
2.64875 
2.64174 
0.00701 
84 
2.70740 
2.70042 
0.00698 
85 
2.77367 
2.76683 
O.OC684 
86 
2.84951 
2.84321 
0.00630 
87 
2.93754 
2.93246 
0.00508 
88 
3.04122 
3 - 039 0 3 
O.OO219 
As far therefore as 86° from the zenith, it appears that, in 
a practical point of view at least, the law of the refractions is 
the same in both tables ; and the real difference between 
them is no more than a small variation in the constant of re- 
fraction. But, from 86° or 87° to the horizon, the two tables 
diverge so much from one another, that no comparison can 
be instituted between them. 
The first instance of a rule for correcting the mean refrac- 
tions different from the common one, which supposes that 
the variations are proportional to the changes in the density 
of the air, occurs in a formula of the eminent astronomer, 
T. Mayer, of Gottingen. The rule is given in the author's 
lunar tables without the demonstration ; and it has been very 
generally misunderstood and decried ;* so very uncertain is 
* See the Article Refraction in the Tables Astronomiques. 
