The Law of Error.

Cambridge: Cambridge University Press,, 1904. Rare original offprint Original offprint of Edgeworth's major work, "the most important of the papers relating to this subject" (Bowley). "The 1905 article 'The Law of Error' crowns Edgeworth's two-decade-long efforts concerning sums of elementary errors and simultaneously summarizes his previously achieved results on this and related topics. This voluminous paper is quite difficult to read, though by no means long-winded, and full of interesting details. 'Edgeworth expansions' are introduced and derived by three different methods. There is also a discussion of - in Edgeworth's own words - 'reproductive' distributions (stable distributions in modern terminology), and their significance as limit laws for sums of identically distributed random variables is demonstrated. Edgeworth illustrated his series expansions by discussing particular cases, such as sums of two-valued or rectangularly distributed random variables. He also tried to generalize his results toward multidimensional errors, certain functions (not only sums) of elementary errors, or weakly dependent elementary errors. Edgeworth explicitly stated and discussed his assumptions on the properties of the elementary errors, even if in a verbose and not always entirely precise form. In his analytic methods, he followed Laplace and Poisson regarding the use of Fourier analysis, he was influenced by Crofton's idea of partial differential equations, and he applied Karl Pearson's method of moments. Apparently, Edgeworth neither knew modern contributions to the [central limit theorem] or the analytic theory of moments, nor was he familiar with the analytic style of post-Weierstrassian era. His 1905 article... nevertheless is impressive because of the analytic and stochastic intuition of its author, as well as due to its quest for far-reaching generalizations" (Fischer, pp. 122-132). Rare - WorldCat and Library Hub record only a handful of institutional holdings, and there are no copies in auction records. Quarto. Original green wrappers, front cover lettered in black. Housed in a black cloth flat-back box by the Chelsea Bindery. Spine frayed and repaired in places, leaf edges a little dogeared with the odd small chip and short tear; occasional pencil marginal calculations; a very good copy. F. Y. Bowley, Edgeworth's Contributions to Mathematical Statistics, 1928; Hans Fischer, A History of the Central Limit Theorem, 2011.