Ok Oy ee 
XXXVII. On the new Method proposed by Dr. Youne for cal- 
culating the Atmospherical Refraction. By JamEs Ivory, 
M.A. F.R.S. i! 
Ix the last Number of the Quarterly Journal of Science (No. 22), 
' Dr. Young has reprinted what he calls 4 Postscript on Atmo- 
spherical Refraction, which was first published in the Philoso- 
phical Transactions for 1819. The problem is a very difficult one, 
and has been treated of by geometers of the first rank; and, in 
the new point of view in which it is here presented, it is supposed 
that the principal difficulties have been evaded or overcome. 
No apology will therefore be necessary, if we endeavour to ap- 
preciate the improvement thus achieved in mathematical science, 
Hy candidly inquiring how far the preténsions held out are ful- 
lled. 
The leading idea of Dr. Young’s method is to develop the 
density of the air in & series of terms containing tne powers of 
the refraction sought. By this means the problem is brought to 
the solution of an equation, or to the reversion of a series. 
All the methods for computing the refractions that have gained 
celebrity among astronomers, if we except that of Laplace, are 
equivalent to the solution of an equation of the second degree. 
This is true of the rules of Bradley, of Mayer, of Simpson; 
which are sufficiently accurate for all altitudes within a few de- 
grees of the horizon. It is therefore certain that the two first 
terms only of Dr. Young’s series, namely, those containing the 
first and second powers of the unknown quantity, will be suffi- 
cient for the greater part of a ‘Table of Refractions. The im- 
provement effected by the new method must therefore consist in 
enabling the calculator to complete the Table, by carrying. the 
refractions quite down to the horizon; for which purpose all the 
_ former methods, except that of the French astronomers, are found 
to be insufficient. The principal point we have to inquire into 
will therefore relate to the convergency of the new series for low 
altitudes, and more particularly in the extreme case of the hori- 
zontal refraction. 
Two different ways may be supposed to have occurred to the 
author for examining the convergency of his series. . The most 
scientific way was to ascertain the rate of the decrease of the 
terms, by determining the general law of the coefficients. It 
may be doubted whether this is practicable in the present case, 
more particularly in the mode of calculation followed by the au- 
thor, Another way was to take some example about the accu- 
racy of which no doubt existed; and to compare the known re- 
sult with that obtained from the same data by the new method. 
» Vol. 58, No, 281, Sept. 1821, Xx For 
