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\noindent{\bf Arthur Lyon BOWLEY}\\
b. 6 November 1869 - d. 21 January 1957
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\noindent{\bf Summary.} Inspired by an early acquaintance with 
socialists and slums, Bowley, a pioneer in the development of 
statistical tools for the analysis of matters of economic and 
social concern, is remembered for his development of sampling 
techniques as applied in the social sciences.
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Questions of foreign trade, wages, poverty, industry, the national
income and the general welfare of the citizens of a country 
have long been of concern to governments. It was only
with the development of appropriate statistical tools in the late
nineteenth and early twentieth centuries, however, that the
analysis of such matters was placed on a
more scientific footing. Bowley was one of the pioneers in the
development and use of such tools.

The son of James William Lyon Bowley and his second wife Maria
Johnson, Arthur Lyon Bowley was born in
Bristol, England, where his father was vicar of SS Philip and Jacob. James
died in 1870, and Maria was left as mother (or step-mother) to
seven children. From 1879 to 1888 the young Arthur (so named
because of his mother's fondness for the works of Tennyson) was
educated at Christ's Hospital, London, where he won various prizes
for classics and mathematics. In later life Bowley pleasurably
renewed his ties with the school as a representative of the
University of London on the Council of Almoners from 1936 to 1947,
being {\it ipso facto} a governor during that period.

A major scholarship in mathematics took him to Trinity College,
Cambridge, where, despite poor health (so poor, in fact, that a
trip to Egypt, financed by several dons, had to be taken, and this
was followed by a lengthy stay in the more bracing atmosphere of
Bournemouth), he was bracketed tenth Wrangler in 1891. His previous
ill health necessitated his spending a further term in residence
before the degree could be awarded, and so from October 1891 to
March 1892 Bowley studied physics, chemistry and economics,
following a reading course in the latter under the supervision of
Alfred Marshall.

In 1892 Bowley's early interest in economics and statistics was
publicly recognized in the award of the Cobden Prize for his essay
{\it A Short Account of England's Foreign Trade in the Nineteenth
Century}, and two years later he was awarded the Adam Smith Prize
for a paper on changes in average wages.

A bequest of {\pounds}9,000 from Henry Hunt Hutchison to the Fabian Society
in 1895 enabelled Sidney and Beatrice Webb, together with
like-minded individuals, to found the London School of Economics.
Among the part-time lecturers at the start of the first session in
October of that year was Bowley (appointed on Marshall's
recommendation), who was charged with the giving of lectures in
statistics. Bowley fulfilled his obligations by cycling some
eighteen miles from St John's School, Leatherhead, where he was a
teacher of mathematics, on the afternoons of his Wednesday
half-holidays. 

On taking up his lectureship, Bowley consulted F.Y. Edgeworth (q.v.)
for information on the nature and literature of statistics, starting
a friendship which lasted until Edgeworth's death.
The lectureship became a Readership in 1908, and in
1915 Bowley was given the title ``Professor", becoming, in 1919, the
first incumbent of the University of London's newly-created Chair
in Statistics, tenable at the London School of Economics. It was on
receiving this full-time post that he left his position at
University College, Reading, where he had been lecturer in
mathematics (1900-1907), in economics (1913-1919) and professor in
both (1907-1913). Bowley remained at the London School of Economics
until 1936, when he became emeritus professor. But his energy and
enthusiasm continued after retirement: he carried on with a number
of his activities at the London School of Economics, and from 1940
to 1944 he was acting (and an active) director of the Oxford
University Institute of Statistics.

While Bowley may have started his working life as a teacher of
mathematics, his two prize essays and the start of a long series of
papers (many co-authored with G.H. Wood) in 1898 clearly showed the
way of his future career. As a boy Bowley had been acquainted with
socialists and slum conditions in Bristol, and at Trinity College
he tried, though with indifferent success, to further social
equality by entertaining the dining-hall waiters to light
refreshments and conversation. Indeed, the contrast between Bristol
slums and Trinity wealth did much to sharpen his interest in
socialism, and although Bowley never become a socialist in the
sense in which the Webbs did, he channelled his liberal concept of
progress into his research.

Bowley's Cobden Prize essay was published as a book in 1893.
Intending this as an introductory text to provide the reader with
easy access to the ``fundamental facts of this century's commerce",
Bowley set out the more important events and causes affecting the
growth of trade with their due prominence, and indicated the more
obvious of the social effects of this growth. (One notes, with
approval, Bowley's especial use of the comparative degree.) Here
tables of figures were largely eschewed, being replace by
diagrams.

The Adam Smith Prize essay, in a revised form, was presented to the
Royal Statistical Society in 1895, and resulted in the award of the
Guy Medal in Silver (the Guy Medal in Gold followed in 1935). Here
Bowley found the actual changes in the total sum paid in wages and
the average money wage, the changes in the gross receipts of
profits and interest, and the income of the nation as a whole.
Special features were (a) statements of wages were never compared
unless they were given by the same authority and (b) ratios,
rather than amounts, of wages were considered. The paper is an
excellent example of what such a study should be, and it can still
be read with profit and enjoyment. Indeed, if some of Bowley's work
today seems hackneyed or trite, it is only because it has become
commonplace.

Bowley's statistical lectures at the London School of Economics
resulted in two text-books. The first of these, {\it Elements of
Statistics} (1901), was intended primarily for those wishing to
understand, appraise and criticize official and similar
statistics, this word being understood as ``the science of the
measurement of the social organism, regarded as a whole, in all its
manifestations". The contents range from the collection and
tabulation of data through moments, graphical methods, correlation
and index numbers (in Part 1), to the application of mathematics to
statistics (in Part 11), the examples in this part being chosen
principally with reference to sociological and economic
investigations.

The {\it Elementary Manual of Statistics} of 1910 is less demanding
of the reader: it is concerned more with official than mathematical
statistics, the Index leading from ``Abatements, income-tax" via the
``Panama Canal" to ``Zinc production".

In 1913 Bowley published {\it A General Course of Pure
Mathematics}. Designed for those who used ``pure mathematics as an
instrument in mechanics, engineering, physics, chemistry and
economics", this work met with a mixed reception, being received
with enthusiasm by E.T. Whittaker but somewhat more coldly by G.H.
Hardy.

Bowley's {\it Mathematical Groundwork of Economics} of 1924 was a
laudable attempt to present, in a unified form, the mathematical
methods used by some of his economic predecessors. Unlike his
mathematical and statistical texts, however, it was intended for
the practising (professional) economist rather than the tiro.

Bowley's pioneering activities in economics were two: the first
consisted of a number of studies on the definition and measurement
of the national income. while the second was his work with the
London and Cambridge Economic Society, which continued until 1953.
But his major contribution, as much to statistics as to economics,
was his work on the development of sampling techniques as applied
in the social sciences.

Until around the turn of the century it was widely held that
complete enumeration was the only way to obtain precise results in
demographic studies, an attitude criticized by Bowley in his
presidential address to the British Association for the
Advancement of Science in 1906. Bowley, however, was not one to
preach without practising: in 1912 he conducted a sample survey of
Reading, one whose design, implementation and analysis still serve
as models for such surveys. Similar surveys of Northampton,
Warrington and Stanley were conducted by A.R. Burnett-Hurst under
Bowley's supervision, and published, together with the Reading
survey, in {\it Livelihood and Poverty} in 1915. A separatum was
issued in 1920, giving the results of a similar survey carried out
in Bolton. The results obtained about poverty were both surprising
and shocking. The accuracy of the results was subjected to careful
criticism, and possible sources of error (and the steps taken to
avoid them) were discussed. A follow-up study in 1924 resulted in
{\it Has Poverty Diminished?}, a question that was answerable in
the affirmative.

Bowley's insistence on the importance of sampling (or the
representative method, as it was then called) led to his membership
of a committee set up by the International Statistical Institute in
1924, and resulted in his report ``Measurement of the precision
attained in sampling" in which he set out the first clear statement
of the foundation of the modern theory of sample surveys.
Here Bowley (a) explained the
nature and role of a sampling frame, (b) developed a theory for
proportionate stratified sampling, and (c) developed a theory for
purposive sampling. There is no doubt that the cause of official
statistics would have been advanced had bureaurocracy not been
obdurate in the acceptance of the wisdom and institution of
sampling.

A prominent aspect of this report was the demonstration of the
superiority of stratified over simple random sampling, though
Bowley was not always careful to distinguish between the latter and
cluster, or systematic, sampling. Bowley's continuation with this
research culminated in what he himself regarded as his most
important work: the {\it New Survey of London Life and Labour}
undertaken from 1930 to 1935. Bowley in a sense moved out of ``pure"
economics into econometrics in the path-breaking {\it Family
Expenditure}, co-authored with R.D.G. Allen in 1935 (when Bowley
was sixty-six). Here the expenditures of individual families were
compared with those of individuals within families, the
goodness-of-fit of an empirically derived linear law being
examined by a $\chi^2$ test.

In 1913 Bowley
received an Sc.D. from Cambridge, while an honorary D.Litt.
(Oxon.) and a D.Sc. (Manchester) followed later. He occupied, at
various times, high positions in the Royal Statistical Society, the
Royal Economic Society (elected Fellow in 1893), the International
Statistical Institute, the Econometric Society and the British
Association for the Advancement of Science (Section F: economic
science and statistics). In 1897-1898 and again in 1927-1928 he was
Newmarch Lecturer at University College London. In 1922 he was made
a Fellow of the British Academy, in 1937 he was appointed a
Commander of the British Empire, and he was knighted in 1950.

In 1904 Bowley married Julia Hilliam, instructress in wood-carving
at Reading College, an arithmetic progression of daughters (Ruth,
Agatha and Marian) following.

Bowley is painted by those who knew him as ``dour" in committees
(whether {\it obstinate, sullen or grim} I cannot say), a man of
discretion, shy and retiring, respected by colleagues and friends
but intimate with few. After a life marked by a sincere and
sympathetic concern for the human condition, Bowley died on the
21st January 1957 at Haslemere, Surrey. 
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\noindent{\bf References}

\noindent Allen, R.G.D. (1968). Bowley, Arthur Lyon, pp. 134-137 in D.L.
Sills (Ed.), \emph{International Encyclopedia of the Social
Sciences}, Vol. 2, The Macmillan Company \&amp; The Free Press.

\noindent Allen, R.G.D. \&amp; George, R.F. (1957). Obituary. Professor Sir Arthur
Lyon Bowley, \emph{Journal of the Royal Statistical Society A},
{\bf 120}, 236-241. [Contains a comprehensive list of Bowley's writings.]

\noindent Darnell, A. (1981). A.L. Bowley, 1869-1957, pp. 140-174 in D.P.
O'Brien \&amp; J.R. Presley (Eds), \emph{Pioneers of Modern Economics
in Britain}, Macmillan.

\noindent Maunder, WY. (1977). Sir Arthur Lyon Bowley, pp. 459-480 in M.G.
Kendall \&amp; R.L. Plackett (Eds), \emph{Studies in the History of
Statistics and Probability}, 11, Charles Griffin.
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\hfill{A.I. Dale}


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