— 
441 
We have here, he said, the results of three distinct series 
of experiments, conducted upon different principles, and by 
different processes ; and, as we observe, the mean values of the 
coefficient thus deduced present the most complete agree- 
ment, the greatest difference amounting only to ‘00011. It is 
almost indifferent under these circumstances, which of these 
results be adopted; but in order to do complete justice to 
the subject, we shall here investigate the most probable value 
of the final mean, as given by the calculus of probabilities. 
In order to do this, it is necessary to deduce, in the first 
instance, the probable error of each mean, as derived from 
the results of its own series. This error, it is well known, 
is expressed by the formula 
utes 455 = (a — a)? 
TP aig says? 
in which = (x —a)? denotes the sum of the squares of the 
differences of each partial result and the mean, and n the 
number of observations. The results of this calculation are 
given in the last column of the annexed Table. 
Series. n m E 
l ll ‘01151 ‘00031 
2 19 01150 “00005 
3 24 ‘01140 “00006 
The most probable value of the final mean, will now be 
given by the formula 
from which we find m = *01145. 
In the preceding deduction we have supposed that the 
only errors to which the separate values of m are liable are 
the errors of observation, in which case the positive and - 
