[2] A diagram illustrative of this number of results was given in Nature (Sept. 1, 1887). In calculating, as above, the different means, I may remark that the original results were given to three decimal places; but, in classing them, only one place was noted. That is, 29.9 includes all values between 29.900 and 29.999. Thus the value most frequently entered in my tables was 30.0, but on the usual principles of interpolation this is reckoned as 30.05.
[3] There is some ambiguity in the phraseology in use here. Thus Airy commonly uses the expression ‘Error of Mean Square’ to represent, as
here, √ ∑e2/n. Galloway commonly speaks of the ‘Mean Square of the Errors’ to represent ∑e2/n. I shall adhere to the former usage and represent it briefly by E.M.S. Still more unfortunate (to my thinking) is the employment, by Mr Merriman and others, of the expression ‘Mean Error,’ (widely in use in its more natural signification,) as the equivalent of this E.M.S.
The technical term ‘Fluctuation’ is applied by Mr F. Y. Edgeworth to the expression 2∑e2/n.
[4] Practically, of course, we should allow for the expansion or contraction. But for purposes of logical explanation we may conveniently take this variation as a specimen of one of those disturbances which may be neutralised by resort to an average.
[5] More strictly multinomial: the relative frequency of the different numbers being indicated by the coefficients of the powers of x in the development of
(1 + x + x2 + … + x9)10.
[6] By Mr Merriman, in his work on Least Squares.