78 Dr. Young’s remarks on the reduction 
We might obtain a conclusion nearly similar by considering 
the sum of the squares of the errors, amounting always to n 2” : 
but besides the greater labour of computing the sum of the 
squares of the errors of any series of observations, the method, 
strictly speaking, is somewhat less accurate, since the amount 
of this sum is affected in a slight degree by any error which 
may remain in the mean, while the simple sum of the errors 
is wholly exempted from this uncertainty. In other respects 
the results here obtained do not materially differ from those 
of Legendre, Bessel, Gauss, and Laplace : but the mode of 
investigation appears to be more simple and intelligible. 
It maj therefore be inferred from these calculations, first, 
that the original conditions of the probability of different 
errors, though they materially affect the observations them- 
selves, do not very greatly modify the nature of the conclu- 
sions respecting the accuracy of the mean result, because their 
effect is comprehended in the magnitude of the mean error 
from which those conclusions are deduced : and secondly, 
that the error of the mean, on account of this limitation, is 
never likely to be greater than six sevenths of the mean of 
all the errors, divided by the square root of the number of 
observations. But though it is perfectly true, that the pro- 
bable error of the mean is always somewhat less than the 
mean error divided by the square root of the number of 
observations, provided that no constant causes of error have 
existed ; it is still very seldom safe to rely on the total absence 
of such causes ; especially as our means of detecting them 
must be limited by the accuracy of our observations, not 
assisted, in all instances, by the tendency to equal errors on 
either side of the truth : and when we are comparing a series 
