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\noindent{\bf Francis Ysidro EDGEWORTH}\\
b. 8 February 1845 - d. 13 February 1926
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\noindent{\bf Summary.} His writings reflecting the advantages 
of a classical education, Edgeworth made contributions to the moral 
sciences, economics, probability and statistics. His early and 
important work on index numbers and utility was followed by later 
statistical work now perhaps seen as `Bayesian'.
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What is one to make of an author whose disparate writings cover
topics from Matthew Arnold's interpretation of Butler to the
generalized law of error, via index numbers, the theory of banking,
correlation, least squares, the labours of Hymenoptera, hedonism
and examination statistics? And how much more difficult is any
comprehension, let alone assessment, when classical tags abound,
when neologisms are rife, and when an English style awkward to the
modern eye prevails! This is the kind of problem besetting one
commenting on Edgeworth.

Francis Ysidro Edgeworth (for this is the way the world knows him,
despite his Christian names being registered in the reverse order)
was born in Edgeworthstown, County Longford, Ireland, on the 8th
February 1845. His grandfather, Richard Lovell Edgeworth
(1744-1817), keenly interested in the applications of science to
industry, perfected a number of inventions which won him gold and
silver medals from the Society for the Encouragement of Arts and,
in 1761, a Fellowship of the Royal Society. Richard worshipped at
the altar of Hymen to the extent of four marriages, with twenty-two
offspring issuing in forty-eight years. His second child and eldest
daughter, Maria, became a well-known novelist, and their circle of
friends included people such as Jeremy Bentham, Sir William Rowan
Hamilton, Sir John Herschel, Thomas Malthus (q.v.), David Ricardo and Sir
Walter Scott. Francis Ysidro's father, Francis Beaufort
(1809-1846), was the son of Richard and his last wife, Frances Anne
Beaufort, a woman of Huguenot extraction and the sister of the
inventor of the Beaufort Wind Scale. At the age of twenty-two
Francis Beaufort married Rosa Florentina Eroles, a sixteen-year-old
Catalan refugee. After a few years in Florence and the failure of a
private tutoring establishment in Eltham near London, Francis
Beaufort returned to Ireland to manage the family estates, where
Francis Ysidro was born some eighteen months before his father's
death during the Irish Famine.

As might be expected, fecundity such as that described above
resulted in complex family ties, and Francis Ysidro was distantly
related to Sir George Gabriel Stokes and Sir Francis Galton (q.v.).
However emigration to the New World and mortality took their toll
of the bearers of the Edgeworth name, and despite his being only
the fifth son of a sixth son, Francis Ysidro inherited the family
estates (by then almost impoverished) in 1911. He never married,
and his death on the 13th February 1926 saw the end of the male
line in Europe.

At seventeen, after having been privately tutored from childhood,
Francis Ysidro entered Trinity College Dublin to read modern
languages. He seems to have taken no degree there, and in 1867 he
moved to Oxford. After short spells at Exeter and Magdalen Halls,
he was admitted to Balliol in 1868. A first in Greats (Literae
Humaniores) was awarded in 1869, though the degree was not
conferred until 1873, the formal M.A. following in 1877.

It appears that Edgeworth moved to London on leaving Oxford, where
some private study must have followed; for in 1877 he was admitted
to the Bar by the Inner Temple, though he is not known to have
practised.

Edgeworth held various minor lecturing posts in London until he
became Professor of Political Economy at King's College in 1888,
succeeding Thorold Rogers in 1890 as Tooke Professor of Economic
Science and Statistics. In 1891 he again followed Rogers, this time
as Drummond Professor of Political Economy at Oxford, where he
became a Fellow of All Souls College and remained until his
retirement with emeritus status in 1922.

The stimulus for Edgeworth's interest in literature, science and
mathematics is evident in his family background, and his training
at Trinity and Oxford may account for his penchant for classical
quotation. He himself wrote ``After leaving Oxford, I studied
mathematics for some years" (Newman [1987, p. 85]), and his
emphasis on the calculus of variations and his aesthetic views on
mathematics may both be ascribable to Hamilton's influence
(mathematical {\it reasoning} or {\it rhetoric} was always
important to Edgeworth). Bowley noted, however, that Edgeworth's
mathematical work shows a lack of systematic training, with ``a want
of facility and neatness in his handling of problems", though
exhibiting ``great insight into the principles of mathematics"
[1934, p. 114].

Edgeworth's early interest in ethics resulted in his first major
work, {\it New and Old Methods of Ethics} in 1877. Here a hedonic
calculus (divided into economics and utilitarianism) is
established, and the importance of optimization stressed.

From the measurement of pleasure Edgeworth was led naturally to the
measurement of utility (and consequently to an interest in
economics), then to the measurement of belief, and thence to
probability and statistics.

Edgeworth's work in the moral sciences was perhaps first impelled
by his contact at Balliol with Benjamin Jowett, though the interest
in economics is probably more directly attributable to the
association with his close neighbour in Hampstead, William Stanley
Jevons (q.v.) (contact with Alfred Marshall followed at a later date). In
1881 Edgeworth published what was perhaps his most important
contribution to economics: {\it Mathematical Psychics: an essay on
the application of mathematics to the moral sciences}, a work
essential to the understanding of Edgeworth's later writings and
described by Keynes (q.v.) as an ``amalgam of poetry and pedantry, science
and art, wit and learning" [1972, p. 258]. Intended as an essay,
from a utilitarian point of view, on ``the calculus of {\it
Feeling}, of Pleasure and Pain", the book was divided into two
parts, concerned respectively with the applicability and the
application of mathematics to sociology. Here Edgeworth disclosed
indifference curves and their relation to the contract curve, his
own contributions to utility theory being relegated to the
appendices.

While Edgeworth's activities were directed in the main to
probability and statistics after 1881, three notable contributions
to economic theory were made in the 1890s: ``The pure theory of
international values" (1894), ``The pure theory of monopoly" and
``The pure theory of taxation", both in 1897. A major contribution
to the subject of index numbers was made by Edgeworth as secretary
to the British Association for the Advancement of Science.

His third book, {\it Metretike: or The Method of Measuring
Probability and Utility} (1887), dealt with probability as the basis
of inductive reasoning, with both weighted means and the most
advantageous mean, and although Keynes states [1972, p. 261] that
Edgeworth himself was disappointed with this tract, it perhaps
gained importance with the later works of F.P. Ramsey and L.J.
Savage.

After this Edgeworth turned his attention more and more to
probability and statistics. His most important writings on
probability {\it per se} are perhaps ``The philosophy of chance"
(1884) and the article on probability in the eleventh edition of
the {\it Encyclopedia Britannica}. Edgeworth's first paper on
statistics was published in 1883. It was devoted to the law of
error (our Normal distribution), a topic that was to concern him to
the last, and the whole plan of his statistical work can be seen in
his important ``Methods of Statistics" of 1885.

In 1891 Edgeworth became the first editor of the {\it Economic
Journal}, and he continued in one or another editorial capacity
until his death. As editor he penned a number of reviews of books
and articles, frequently with commentary on contemporary work, his
own thoughts often being relegated to footnotes.

Edgeworth did not establish a school of followers: his only
disciple seems to have been Sir Arthur Lyon Bowley (q.v.), who, on his
appointment to the London School of Economics in 1895, consulted
Edgeworth for information on the nature and literature of
statistics, starting a friendship which lasted until Edgeworth's
death. It was in fact Bowley's 1928 tract on Edgeworth's work in
mathematical statistics that probably saved this work from
oblivion.

Most of Edgeworth's biographers (even Bowley) got to know him only
in his middle age, and so opinions of him as a young man are
lacking. In 1889 Beatrice Webb (then Potter) described him as ``a
gentle-natured and intellectual man with queer cramped nature,
excessively polite and diffident in manner" (she also said that he
was pathetic and that he bored her). Keynes notes Edgeworth's
all-embracing tolerance and says ``He was kind, affectionate,
modest, self-depreciatory, humorous, with a sharp and candid eye
for human nature; he was also reserved, angular, complicated,
proud, and touchy, elaborately polite, courteous to the point of
artificiality, absolutely unbending and unyielding in himself to
the pressure of the outside world" [1972, p. 265]. As a lecturer
Edgeworth was apparently not a great success: Bowley notes that
``the few courses of lectures he gave were not well attended, for
indeed he had no faculty for that method of teaching" [1934, p.
1231, while Schumpeter writes that Edgeworth was ``the worst speaker
and lecturer imaginable" [1954, p. 831].

Edgeworth was perhaps more a philosopher than a practitioner of
statistics. Yet in his statistical work (much of which one would
today term ``Bayesian") one finds essentially the $t$-distribution
(his ``subexponential" distribution, derived as the posterior for a
Normal mean with uniform priors for $\mu$ and ${\sigma}^{-1}$), 
the Edgeworth
expansion and the Edgeworth series, the method of translation (now
called variate transformation) and its extension to bivariate
surfaces, the asymptotic theory of maximum likelihood estimates,
the rejection of outhers, stochastic models, tests of
goodness-of-fit and an anticipation of a two-way analysis of
variance. He also introduced a number of statistical terms, some of
which, like ``modulus" and ``fluctuation" (our $\surd{2}\sigma$. 
and $2{\sigma}^2$
respectively) have to a large extent disappeared, while others,
such as the ``coefficient of correlation", remain. We are also
indebted to him for the `$k$' in {\it Biometrika}. It is fashionable, if
not obligatory, when writing on Edgeworth to comment on the
obscurity of his style. However in preparing this note I found that
I had to agree with Bowley that ``if one studies carefully a
treatise as a whole, with some knowledge of Edgeworth's general
lines of thought, and then reads it a second time, one finds that
the whole is coherent, the arguments valid and consecutive, the
theme is made clearer and more vivid by the variations" [1934, pp.
123-124].

Honoured for his work in economics and statistics, Edgeworth
received a D.C.L. from Durham University. He was twice president of
the Economic Section of the British Association, President of the
Royal Statistical Society (receiving the Guy Medal in Gold in
1907), Vice-president of the Royal Economic Society and an original
Fellow of the British Academy (1903).

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\begin{thebibliography}{3}
  Francis Ysidro EDGEWORTH
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