4B4 Mr. Ivory on the astronomical refractions. 
even an improvement in the abstruser parts of science. 
Doubts are entertained whether the rule was found by theory, 
or constructed in conformity to actual observation. The 
latter supposition cannot but seem very improbable when we 
attend to the formula; which is, besides, deduced very readily 
from the method of investigation pursued in this paper. M. 
Bessel is the first astronomer who has accurately computed 
all the variations of the refractions produced by the changes 
of temperature and pressure ; and we shall next compare 
the new table in this respect with the result of his theory. 
Now, in his table, at the zenith distances 83°, 85°, 88°, the 
total corrections for the temperature t are respectively, 
— o".9821(t— 50), — l".3678 (r — 50), 2". 9944 (r — 50): 
but each of these quantities involves the usual correction 
proportional to the change of the air's density, equal to 
— '480' x ( T 5°) ; and, when this part is separated, they 
will stand as under ; 
at 83, — o . 9131 (r — 50) — o . 0690 (r — 50), 
85, — 1 . 2178 (r — 50) — o . 1500 (t — 50), 
88, — 2 . 2792 (t — 5 o) — o. 7150 (t — 50), 
A 
the latter parts being equal to -j~ x (t — 50) in the notation 
of this paper. In the new Table the values of -j— x ( r — 50 ) 
are respectively, — o . 074 (r — 50), — o . 159 (r— 50), 
— o . 722 (r — 50) ; differing insensibly from the calcula- 
tions of M. Bessel. 
To complete this examination of the new Table, we shall 
add some particular instances. We begin with the two 
examples at p. 159 of the Connaissance des Terns. 
