294 Mr. Henderson on the difference of meridians 
These various results differ so little from each other, that 
their arithmetical mean, y m 2i 8, 45, may be assumed to be near 
the truth. But it may not be improper to ascertain the 
most probable value, and its probable error, by the calculus 
of probabilities as practised by Gauss, Bessel, &c. to serve 
as a rule for other investigations of a similar nature, in which 
it may be more requisite. Each night's result is liable to an 
error occasioned by the errors in the observed times of the 
signals, and of the transits of stars, whereby the clocks were 
compared with the heavens. The probable error of a single 
observation of a signal and a transit, appears from a consi- 
derable number of observations, to be one tenth of a second ; 
and this divided by the square root of the number of these 
phenomena observed at any station, gives the probable error 
of the mean of the observed times at that station. But the 
results are exposed to other causes of error, such as the 
small deviations of the transit instruments from their meri- 
dians, the peculiar state of the eyes of the different observers, 
atmospheric circumstances, and various others which fluc- 
tuate from night to night, but may be supposed constant 
during the same night. Each night’s result is equally liable 
to these errors, which have no tendency to be diminished by 
an increased number of observations upon that night. The 
probable error of each result arising from this cause is 
assumed to be two tenths of a second, and it is not likely to 
be more. Errors in the comparison of the chronometers 
employed for the observations of signals at Greenwich and 
Paris with the transit clocks, are also to be apprehended, 
which errors at each observatory may be supposed to be one 
tenth of a second. A probable error of one tenth of a second 
