258 
APPENDIX. 
[■South Coast. 
this longitude is reduced to that place by the application of the dif- 
ference shown by the time keepers to have existed between the two 
situations. In ascertaining this difference, the rates of going allowed 
to the time keepers are generally those found at the place which is 
to be fixed ; whether applied to observations taken before arriving, 
or after quitting that place. This, however, could be done only at 
those stations where rates had been observed ; at the intermediate 
points, where the result of lunar distances is given principally as an 
object of comparison with the time keepers, the rates allowed in the 
reduction are those found at the station previously quitted ; but then 
the difference of longitude is corrected by the quantity consequent 
on the following supposition : that the time keepers altered their 
rates from those at the previous, to those at the following station, in 
a ratio augmenting in arithmetic progression. The difference of longi- 
tude, thus corrected when necessary, is given under the head of 
Reduction by time keepers; and the longitudes reduced by it to the 
place intended to be fixed, are taken to be of equal authority with 
those resulting from observations made in the place itself. 
7th. But these longitudes, whether reduced to, or observed in, 
the place to be fixed, still require a correction which is of more im- 
portance than any of those before mentioned. The theories of the 
solar and lunar motions not having reached such a degree of perfec- 
tion as to accord perfectly with actual observation at Greenwich, the 
distances calculated from those theories and given in the almanack 
become subject to some error; and consequently so do the longitudes 
deduced from them. The quantities of error in the computed places 
of the sun and moon, have been ascertained at Greenwich as often as 
those luminaries could be observed ; and Mr. Pond, the astronomer 
royal, having permitted access for this purpose to the table of 
errors kept in the Observatory, Mr. Crosley has calculated the cor- 
responding effects on the longitude, and proportioned them to the 
time when our observations were taken. The combined effect of 
the two errors forms a correction to the longitudes obtained from the 
