Lunar observations, ,] 
APPENDIX. 
257 
The refraction of the heavenly bodies given in the tables, being 
calculated for a mean height of 50 0 of Fahrenheit's thermometer, and 
29.6 inches of the barometer, it has been corrected for the difference 
between these means and what was the state of the atmosphere at 
the time of observation. 
3rd. In reducing the apparent to the true distance, Mr. Crosley 
has used the method of Joseph Mendoza de Rios, Esq., F. R. S., 
given with his Nautical Tables, second edition, 1809 ; and the tables 
from which the corrections were taken and the computations made, 
are those of the same valuable work. 
4th. The reduced distance, found as above, has been corrected 
to the spheroidal figure of the earth, according to the theory ex- 
plained in the Philosophical Transactions of the Royal Society of 1797 ; 
and for doing which, rules are given by Mr. Mendoza with his 
Nautical Tables of 1801. This calculation is tedious, and the correc- 
tion, more especially in low latitudes, too small to be necessary in 
common cases. 
5th. In the nautical almanack the distances are given to every 
three hours, but the irregularities of the moon's motion being such 
as to cause some inequality in the different parts of this interval, the 
distance at the hour preceding, and at the hour following the time 
of observation, was found by interpolation from the two nearest 
given on each side ; and having the distances at Greenwich for each 
hour, the observed distance can never fall more than half an hour 
from one of them ; and the moon's inequalities do not then produce 
any sensible error in the corresponding time, as obtained from com- 
mon proportion. The correction arising from this process is seldom 
so important as to be necessary in sea observations. 
6th. The longitude deduced from a comparison of the true 
distance at observation with the hourly distances at Greenwich, is 
contained in the following tables under the head of Longitude from 
Nautical Almanack. But as it frequently happened, that the observa- 
tion was not taken exactly in the place which it is intended to fix, 
\ 
