Rothamsted in the Making of Sir Ronald Fisher Sc.D., F.R.S

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Rothamsted in the Making of

Sir Ronald Fisher Sc.D., F.R.S.

John Aldrich

Economics Department

University of Southampton

Southampton

SO17 1BJ

e-mail: [email protected]

Abstract

In 1919 the agricultural station at Rothamsted hired Ronald Fisher (1890-1962) to analyse historic data on crop yields. For him it was the beginning of a spectacular career and for Rothamsted the beginning of a Statistics Department which became a force in world statistics. Fisher arrived with publications in mathematical statistics and genetics. These were established subjects but at Rothamsted between 1919 and -33 he created the new career of agricultural research statistician. The paper considers how

Rothamsted, in the person of its Director Sir John Russell, nurtured this development while supporting

Fisher’s continuing work in mathematical statistics and genetics. It considers too how people associated with Fisher at Rothamsted, including assistants Wishart, Irwin and Yates and voluntary workers Tippett, Hoblyn and Hotelling contributed to establishing Fisherian statistics.

September 2019

Introduction

In 1919 a 29 year-old Cambridge mathematics graduate with no established profession started at Rothamsted Experimental Station; he died in 1962 “the most famous statistician and mathematical biologist in the world”—thus Irwin et al. (1963:

159). Sir Ronald Fisher Sc.D., F.R.S. was Balfour Professor at Cambridge when he was knighted and had been Galton Professor at University College but the higher doctorate and Fellowship of the Royal Society came when he was at Rothamsted.

Ronald Aylmer Fisher would be another Galton and Balfour Professor but at

Rothamsted he was the first Chief Statistician or even statistician. Between 1919 and

1933 he made a career for himself by creating the career of agricultural research statistician. What he did is sketched by Irwin et al. and detailed in Box’s Life (1978) and in numerous technical studies—see Aldrich (2003/19)—but here I look behind the what to consider how Fisher managed—and was helped—to do it. Rothamsted stimulated him to do the work in agriculture and, more surprisingly, encouraged the work in mathematical statistics and genetics that brought him fame; it also helped create a following to bestow that fame.

Fisher at Rothamsted sits in larger histories—of mathematical statistics, of mathematicians in British statistics, of statistics in agriculture and of agricultural science in Britain—and I have drawn on these literatures.1 I also glance at parallel lives and institutions and at Fisher’s experience after Rothamsted, developing Box’s

(1978: 96) observation that he “was never happier professionally than during the years he spent there.” But I start with the ideas, people and institutions that together provided a launch-pad for the career of agricultural research statistician.

1 Thus Parolini (2015a) tells much of the present story from another angle.

1 A platform for the agricultural research statistician

In 1948, when Frank Yates Fisher’s successor at Rothamsted was made FRS, he told

Sir John Russell that the award “must be personally gratifying to you also in that you are as it were the god-father of agricultural research statistics.”2 That god-paternity went back to the time when, as Director, Edward John Russell (1872-1965; FRS

1917), contemplated the “mass of valuable data” from the Rothamsted experiments and looked forward to a time when “conditions become more normal.”3 Russell

(1917: v) mused, “I cannot help thinking that the application to them of modern statistical methods would yield information of high value both to the man of science and to the practical agriculturist.” Men of science were already using statistical methods and I recall their work as it prepared the way for the office of agricultural research statistician and treated problems—especially in field experiments and agricultural meteorology—later taken up by Fisher. I start with the research setting and the sources of statistical expertise before proceeding to the scene at the close of the Great War.

The pre-war agricultural research community was small and, though dispersed across experimental stations, agricultural colleges, universities and even businesses, strongly inter-connected with findings disseminated through academic, trade and official publications. The leading professional forces were Rothamsted Experimental

Station, the Cambridge University School of Agriculture and the Journal of

Agricultural Science—of this last Russell (1966: 286) wrote, “for some forty years it published almost all the chief papers in agricultural science in Great Britain.”

Rothamsted, the life work of John Lawes and Henry Gilbert, started in 1843 while the

2 Yates was replying to Russell’s letter of congratulation.

3 For Russell see his Autobiography (1956) and Thornton’s (1966) memoir.

School and journal dated from 1899 and 1905 respectively. Public support for agriculture and agricultural research—much increased after 1910—was through the

Board of Agriculture and Fisheries, renamed Ministry in 1919.4

The Board had a branch responsible for agricultural statistics, i.e., the statistics of the agricultural sector—the numbers for agricultural economics.5 The numbers also interested the statisticians of the Royal Statistical Society and the close link between

Board and Society is illustrated by the award of the Society’s highest honour, the Guy

Medal in gold, to the Board’s P. G. Craigie (1843-1930) for “extraordinary services to statistical science in connection with the development of agricultural statistics.” 6 The

Society’s domain was economic, demographic and social statistics with interest in statistical theory confined to a few, notably Edgeworth, Bowley and Yule.7 In 1869 the Journal had published a “statistical description” of some Rothamsted experiments—by Frederick Purdy, a compiler of Poor Law statistics—but this was an isolated venture and agricultural experiments only became the Society’s statistics in the 1930s; see §7 below.

The Society’s statistics did not stretch to matters like ascertaining “the conditions under which the plant grows and the soil supplies it with nutriment”—the purpose of

4 Russell (1966: ch. VII-VIII) and Vernon (1997) survey the entire scene. For Rothamsted, see Russell (1917), for the School, Wood (1922), and for the JAS, Bell (1980).

5 “On the Home Produce, Imports, Consumption, and Price of Wheat etc.” (1880a) the one paper written by Lawes and Gilbert for statisticians illustrates the point; Gower (1988: 181-2) comments on them as statisticians.

6 Craigie headed the Board’s Statistical, Intelligence, and Educational Branch; see Anon

(1930).

7 Aldrich (2010a) examines the place of theory in the Society.

4 the Rothamsted experiments, as stated by Hall (1906: vi). However, in 1907 the

Journal published a piece on agricultural meteorology which was agricultural science—cf. Lawes and Gilbert (1880b). The author of “Correlation of the weather and crops” was R. H. Hooker (1867-1944), a younger Society/Board figure abreast of modern biometric techniques like correlation.8 Hooker was developing a theme from

“Seasons in the British Isles” by Napier Shaw of the Meteorological Office—the

Society maintained a watching brief for all official statistics. Hooker’s paper did not realise Craigie’s expectation that it would be “the beginning of a series of papers in which the practical knowledge of agriculturalists and the theoretical methods of arithmetical expression might be brought together” and Hooker’s research into crops and weather proved of more interest to meteorologists.9

Agricultural researchers looking for statistical methods turned to the theory of errors or to biometrics.10 Error theory/least squares theory had been developed by mathematicians in the early nineteenth century for measurement problems in astronomy and geodesy and was widely taught and disseminated in textbooks of different levels while biometrics was newer and less accessible. The leader of the biometricians, Karl Pearson (1857-1936) of University College, was a great proselytiser but he was not directly involved with agriculture and his “journal for the statistical study of biological problems”—Biometrika—published its first specifically

8 See Aldrich (1995: 370ff.) for the time series correlation analysis developed by Hooker and his friend Yule. Hooker’s life is recalled by Yule (1944). For Yule see below.

9 The first reference to Hooker in the JAS was Fisher (1921). More immediately Gosset responded to a point raised in the discussion with his “Probable error of a correlation coefficient” (1908b). Hooker eventually became President of the Meteorological Society.

10 For the theory of errors and biometry see Stigler (1986).

5 agricultural article in 1923. However, Gosset and Yule—who may be thought of as

Fisher’s forerunners—had been Pearson’s students and two of his American followers, the zoologist Raymond Pearl and botanist J. Arthur Harris, worked in experimental stations and took an interest in agricultural experiments.11 Pearson’s core interest was in biology, including eugenics, and he advocated the use of statistics in medicine though his influence there was chiefly through his disciple Major

Greenwood who was at the Lister Institute from 1910. 12

A harbinger of the post-war development of agricultural statistics as the statistics of agricultural experiments was a session on “error in agriculture experiment” jointly organised by the Agricultural and the Statistical Sections for the 1910 British

Association conference.13 The papers reflected thinking on how the theory of errors could be used in agricultural research and, in particular, the inferential possibilities of the probable error—how it could make precise statements like this from Hall (1909b:

362), “Plot 12 is probably better than Plot 3 by more than 8.1, and less than 11.9 per cent.” The prime movers were not marginal or junior figures but A. Daniel Hall

(1864-1942; FRS 1909), Russell’s predecessor as director of Rothamsted and reviver of its fortunes after the deaths of the founders, and Thomas Wood (1869-1929; FRS

1919), professor of agriculture at Cambridge, both founding editors of the JAS.

Russell (1966: 470) judged them “the greatest figures in the remarkable outburst of agricultural science during the early years of the present century.”

11 See Pearl and Surface (1916) and Harris (1912). Bellhouse (2009) describes Pearson’s following in America.

12 See Matthews (1995: passim).

13 No statistician contributed to the joint session.

Hall and Wood were concerned with experimental error as it affected the confidence to be attached to the results of field experiments: Hall (1909a: 370) contended, “it is only by recognising and measuring the extent of the inevitable error that we can reach a due measure of accuracy in the conclusions we reach” and Wood (1911: 37),

“the experimentalist who submits his figures to the simple statistical tests suggested

[here] will be saved from delaying the progress of agricultural science by making unfounded recommendations.” Hall’s investigations appeared as Hall (1909a) and

Mercer and Hall (1911); a chapter of his textbook Fertilisers and Manures (1909b) was devoted to the subject. Russell (1943: 238) remarked of Hall’s efforts, “although no mathematician he acquired sufficient grasp of the methods to make some pioneering investigations.” Russell, who worked for Hall before succeeding him, had been a fellow-traveller—see Hall and Russell (1911).

A catalyst for this activity was William Sealy Gosset (1876-1937) head of the experimental brewery of Guinness, the brewers: Gosset and Hall were acquainted for

Hall was Guinness’s authority on growing hops. Gosset had faced the same statistical challenge as Hall a few years earlier.14 A chemist—like Hall, Wood and Russell—

Gosset had learnt the theory of errors from textbooks, including one by a chemist,

Lupton (1898), but the books only went so far and in a 1904 report on “The

Application of the ‘Law of Error’ to the work of the Brewery” Gosset expressed his frustration:

We have been met with the difficulty that none of our books mention the

odds, which are conveniently accepted as being sufficient to establish any

conclusion, and it might be of assistance to us to consult some mathematical

physicist on the matter.

14 For Gosset see E. S. Pearson (1939, -90); the 1904 report is discussed in (1939: 213ff.).

University connections led to Karl Pearson but he was not retained as a consultant, instead Gosset went to learn from him—not, however, the theory of errors but the new biometric statistics Pearson was developing to supersede it.15

Gosset went on to develop a side-line as a consulting and research statistician publishing in Biometrika as ‘Student.’ E. S. Pearson (1939: 230-4) describes his pre- war work in agriculture, emphasising his association with the maltster Edwin Beaven

(1857-1941), a supplier to Guinness and self-taught scientist.16 Beaven began consulting Gosset around 1905 and Gosset is mentioned in Beaven (1909: 130) but this pre-war work with Beaven was not otherwise published. Gosset’s only writing for an agricultural audience was on design: he contributed a “Note on a method of arranging plots so as to utilise a given area of land to the best advantage in testing two varieties” to Mercer and Hall’s JAS paper. His Biometrika paper on “The probable error of a mean” was aimed at statisticians though after twenty-odd pages of theory it

(1908a: 21) has some examples on the theme, “cases where the tables will be useful are not uncommon in agricultural work.” The cases chosen were from the reports of field trials J. A. Voelcker published in the Journal of the Royal Agricultural Society.17

Those reports presented results and, using no statistical machinery, inferences like, “It may now fairly be concluded that …” (1906: 306). When ‘Student’ (1908a: 22-3) applied his tables to the same data he found odds of 32 to 1. Although Gosset was known in the research community, there is no sign that either agriculturalists or statisticians shared Fisher’s (1927: 145) view that this “anonymous genius” was the

15 For the new statistics of Pearson (and Yule) see Stigler (1986: ch. 10). Aldrich (2010a) describes how it penetrated the Statistical Society

16 For Beaven see Russell (1966: 260-3) and Palladino (1994: 419ff).

17 For Voelcker and his work at Woburn see Russell (1966: 172-5).

“spiritual father” of all the worthwhile developments in pre-war agricultural experimentation.18

Hall and Gosset had identified a skill they needed and taught themselves—though

Gosset went further and, after instruction, became an expert. Wood took a different and collaborated with an expert. A year before Mercer and Hall (1911) the JAS had published a paper on a similar theme: “The Interpretation of Experimental Results” by

Wood and Stratton (1910). Frederick Stratton (1881-1960; FRS 1947) was an astronomer and fellow of Wood’s college.19 He taught the theory of errors and found new applications without advancing the theory or proselytising on a Pearson scale: his teaching formed the basis for Brunt’s Combination of Observations (1917) which includes material from Wood and Stratton. Wood’s collaboration with Stratton was only temporary, perhaps because Cambridge agriculture was set to internalise its statistical consulting.

At the time the School of Agriculture was expanding, as recalled by Wood (1922:

298), “Lecturers were also appointed in agricultural zoology, agricultural law, veterinary science, accountancy, and statistics, the last jointly with the Department of

Economics.” The lecturer, G. Udny Yule (1871-1951; FRS 1922), had been a student of Pearson before joining the statisticians: in 1912 he must have looked a better fit for economics as he had published nothing on agriculture.20 However, he was author of a

18 ‘Student’ mentioned his mean results in his JAS note but nobody used them: a lonely exception was the medical statistician Janet Lane-Claypon—see Winkelstein (2004).

19 For Wood and Stratton see HGH (1931) and Chadwick (1961) respectively.

20 For Yule see Kendall (1952), Yates (1952) and Mills (2017) with Yates commenting most on his agricultural work. Aldrich (2010a, -b) discusses Yule’s links to the RSS and the economists.

9 pioneering textbook, Introduction to the Theory of Statistics and papers on statistical theory, population and economic statistics and genetics.

The Yule’s teaching? Yule was a natural collaborator—having worked with Hooker amongst others—and soon joined the new Plant Breeding Institute directed by

Rowland Biffen (1874-1949; FRS 1914) the Professor of Plant Botany. No publications came from that association but Yule published with Wood and with the wheat researcher Frank Engledow (1890-1985; FRS 1946): Engledow and Yule

(1914) applied Pearson’s χ² to the estimation of genetic linkage while Wood and

Yule’s (1914) statistical examination of the results of feeding trials was concerned with the amount of fat, work, or milk produced by a diet supplying a known amount of starch equivalent above that required for maintenance.21 Statistics in agriculture involved more than trials or agricultural meteorology.

Wood and Yule made no use of Yule’s distinctive statistical methods but a model application—its use of regression and correlation reminiscent of Yule’s pauperism studies—appeared in the JAS in 1913. “On the accuracy of estimating a cow’s milking capability by her first lactation yield” was by William Gavin (1886-1968), scientific dairy farmer and a model product of the School’s Diploma programme.22

When war came in 1914 it virtually shut down agricultural science and its statistical branch: two-thirds of the Rothamsted staff left, Engledow joined the army—taking

Bateson’s Heredity and Yule’s Introduction with him—Gavin joined the navy, Yule became a civil servant and Gosset concentrated on brewing Guinness. Peace returned

Gosset to life as ‘Student’ and Yule and Engledow to Cambridge but agricultural

21 For Yule and Biffen see Charnley (2011: 63), for Yule and Engledow, Edwards (1996).

22 Gavin’s career was not in agricultural research but in business and public administration: see “Sir W. Gavin” The Times 5/6/1968 p. 10.

10 statistics there did not regain the momentum and promise of 1912: Yule would be much occupied with time series analysis and find a new biologist collaborator, the evolutionist J. C. Willis. At Rothamsted, however, there was expansion—the scientific staff went from 9 in 1912 to 29 in 1920—and the possibility of change.23

Russell revived his 1917 project. There is no contemporary evidence bearing on the skills he thought required and when he reminisced decades later he (1966: 325; 1956:

131) emphasised experience with masses of data: “I knew that the Census authorities had methods for extracting information from great masses of data.” He seems to have thought that a new skill coming from a different direction was needed: what he got in

Fisher was a composite of Gosset, Stratton and Yule with light actuarial shading and a powerful mathematical imagination whose methods in agricultural meteorology and the analysis of experimental results involved extensions of least squares theory.24

2 The “wilderness”

Fisher would later recall—cf. Box (1978: 237)—that in 1919 he had failed in two occupations yet, while an actuary and schoolmaster, he had written important papers on the distribution of the correlation coefficient (1915) and on reconciling biometric findings and Mendelian theory (1918). Box (35) characterises Fisher’s years between leaving Cambridge and getting a job where he “could employ his abilities” as “in the wilderness” but school teaching did not preclude a research career, as the life of the mathematician Francis Macaulay (1862-1937; FRS 1928) shows, and actuarial science was largely created by employees of insurance companies. Also, statisticians were used to the wilderness: those who did statistical research without having a career

23 See the Report for 1915-17 (1918: 7) and Report for 1918-20 (1921: 7).

24 For Fisher’s statistical education see Aldrich (1997: 162-5).

11 in research included Gosset a brewer, Hooker a civil servant, Yule an educational administrator (for ten years) and Pearson a professor of applied mathematics (for 25 years). Things, however, were changing for the developments in agriculture were paralleled in medical research and industrial research through bodies like the British

Cotton Industry Research Association (Shirley Institute).25

When the war ended Fisher resigned his teaching post and looked for employment:

Box (1978: 60-1) describes the search and how Fisher was helped by his friend and benefactor, Leonard Darwin (1850-1943). Fisher looked to his old university—to his college Caius and to the School of Agriculture—but without success though Caius later awarded him a nonresident fellowship. Out of the blue came an offer from

Pearson offering him the position of Senior Assistant. This had its attractions: no- one’s interests were closer and the position might be a step towards succeeding

Pearson when he retired: Darwin, as President of the Eugenics Education Society, reflected to Fisher, “I should much like to be sure that the place is filled by a eugenist and not a mere mathematician.” However, Pearson was clear that he wanted “a man who will throw himself wholeheartedly into the work of the Laboratory as it is at present organised, not a research worker who would follow his own individual lines regardless of the general scheme of work.” This was not an unreasonable requirement but it was probably why Fisher rejected the offer.26

The other offer came from Russell, to realise the thought of 1917. Fisher had not studied agricultural science but he was attracted to farming and had been in touch with two of the contributors to pre-war developments: Stratton was his director of

25 For statistical activity before and during the War see Aldrich (2019).

26 See Pearson to Fisher on August 2nd 1919 and Darwin to Fisher on the 9th. See Bennett

(1983: 117) and Box (61).

12 studies at Cambridge and had encouraged his first publishing effort in the theory of errors (1912), while Gosset was an occasional correspondent on matters of statistical theory. Gosset tipped Fisher off about the prospect at Rothamsted but it came about through a connection of Darwin’s. Gosset’s reaction on learning of the appointment was that, “there should be a lot of interesting work to be done there and they might easily have got someone there who would have been worse than useless.” 27

Fisher’s appointment was initially for 6 months and a first report on the project of

1917, Fisher (1921), duly appeared in the list of publications in the Report for 1918-

20. But the Report presented much more—a statistical department and a commitment: the Introduction (8) declared, “There are four great divisions in the laboratory—the biological, chemical, physical and statistical—which may be regarded as the pillars on which the whole structure rests.” Russell wrote to similar effect in the Preface to the new edition of his Soil Conditions and Plant Growth (1921: v-viii) and subsequently missed no opportunity to promote his new department—only Rothamsted had such a unit. For Fisher’s part, it is not clear how long he intended to stay or indeed whether

Rothamsted was itself a wilderness to endure: Box (239) reports that from 1923 he was arguing that Cambridge create a Chair of Mathematical Statistics.28

As a friend, Darwin welcomed Fisher’s appointment but with a reservation, “I am only a little sad that you may not have much time for Eugenics.”29 Fisher found time for eugenics and more besides and before picking up what he did in agriculture in

Section 4, I consider what he did elsewhere. Doing elsewhere was part of Fisher’s

27 Letter of September 19th 1919. For Gosset and Fisher see Aldrich (2008).

28 Manchester created such a chair in 1946 and Cambridge in 1962; see Aldrich (2019).

29 Letter of August 23rd 1919.

Rothamsted life from the beginning unlike Pearson who only took up biometrics after a decade of successful work in applied mathematics.

3 Rules of engagement and doing elsewhere

In an assistant Pearson wanted someone whose work would serve the interest of the laboratory as a whole and, once he had a laboratory, Fisher expected the same; see §7 below. At Rothamsted that interest was Fisher’s to define but only within limits and statistical theory, genetics, evolutionary theory and eugenics seemed beyond them.

Yet his research in those fields flourished: of around 200 items in his bibliography for

1919-33, about half fall in the category Genetics, Evolution and Eugenics and half in

Statistical and Mathematical Theory and Applications with applications to agriculture accounting for only 20 or so, or 10% of the total.30 I have found no contemporary documents bearing on his understanding with Russell but one may speculate that

Fisher was able to safeguard his old interests because his output was immense, his performance at the job surpassed all expectations and Russell gave him a lot of freedom.

The freedom Russell accorded Fisher reflected a general approach to management with special allowances for the person. According to Thornton (1966: 464), “Russell believed that close personal control of the researches by the Director was no longer desirable or indeed feasible when the station had reached a certain size. He therefore gave the heads of departments a wide responsibility for their specialized programmes.” The Fisher factor was Russell’s (1966: 326) belief that “more than a

30 See Bibliography of the Publications of R. A. Fisher. The figures should be taken cum grano but the impression they convey of someone doing much outside his day job is true enough.

14 man of great ability, he was in fact a genius” developing a new science. As Russell

(1956: 132) recalled, his attitude to Fisher was not unopposed,

I was not going to limit his investigations, because I was certain that,

whether they were concerned with our data or not, the science he was

building up would be of the greatest help to us later on. But High Authority

did not take this view, and I got a personal letter urging me to change the

programme. This I was not prepared to do: fortunately the matter dropped

before it reached the official stage.

I have not been able to identify the High Authority or date the intervention.

This opposition within would have added to Russell’s inclination to publicise

Rothamsted statistics and Fisher’s personal achievement. Russell plugged them in his own writing as well as in the Reports: he noted the meteorological results in his

(1923: 468) and detailed them in Plant Nutrition and Crop Production (1926: 33-6) while he expounded the new thinking on experiments in his (1926). Russell communicated Fisher’s papers to the Royal Society—on rainfall at Rothamsted

(1924) but also the science-building mathematical foundations (1922)—and promoted

Fisher’s candidacy for a fellowship. Fisher did his bit for the publicity campaign— thus when he summarised his science papers for the Report he would stress the applicability of the science: the summary of his mathematical foundations paper in the

Report for 1921-2 (p. 34) ends, “Many such tests are applied to current statistical methods, and in particular to the estimation of the numbers of soil protozoa by the dilution method.”

Rothamsted seems not to have accorded equal recognition to the different streams of Fisher’s outside research. The Reports listed and summarised every statistical theory and genetical publication, suggesting that Russell considered these streams as

15 contributory to the science being built up. Yet Box (1978: 167 & 186) relates that

Fisher did his genetical work at home and the genetical stream is not represented in his retrospective “Contributions of Rothamsted to the development of the science of statistics” (1933). His (admittedly, more ephemeral) publications in the Eugenics

Review were not recorded in the Reports.

Rothamsted affected Fisher’s outside pursuits in different ways. There was no hard border between devising new statistical theory and devising new applications: theory and applications are run together in the “Contributions” while Statistical Methods for

Research Workers (1925: vii) declares, “Daily contact with the statistical problems which present themselves to the laboratory worker has stimulated the purely mathematical researches upon which are based the methods here presented.” Yet some sub-streams of theory were seemingly unaffected by Rothamsted: they include an estimation stream, a χ² stream and a correlation stream culminating in the 1928 paper on multiple correlation. The first two streams were largely an expression of dissatisfaction with Pearsonian statistics and “Karl Pearson’s theoretical errors and the advances they inspired”—Stigler’s phrase—could serve as leitmotiv for Fisher’s work until well into his Rothamsted period. Once Fisher had made these advances his work was self-propelled and apparently uninfluenced by his Rothamsted surroundings. 31

There appears to have been no Rothamsted effect on Fisher’s work in genetics— surprising perhaps when elsewhere genetics and plant breeding were closely associated: indeed Charnley (2011: 256) remarks of Rothamsted and John Innes

(where Cyril Darlington worked) that “these were exactly the sorts of places that important developments in the history of genetics occurred.” Rothamsted, however,

31 Accounts of Fisher’s contributions to the mathematical theory of statistics, such as Aldrich

(1997, 2005) and Stigler (2006, -7, -8), find no Rothamsted discontinuity.

16 had no Engledow or Biffen and Fisher was the only geneticist and his special concern was in improving people, not plants—around a third of the Genetical Theory of

Natural Selection (1930) is devoted to the human race. Neither the book nor any of the papers leading up to it had Rothamsted input.32 Nor was there any Fisher input into the introductory Evolution, Heredity, and Variation (1925) by Ward Cutler,

Rothamsted’s Head of Microbiology.

There was no Rothamsted discontinuity in the allied field of eugenics. Fisher continued in his role as an Honorary Secretary of the Society and the great flow of contributions to the Eugenics Review slowed only temporarily on his appointment.

There was some interest in eugenics among the Rothamsted colleagues and Fisher tried to generate more but none worked so tirelessly for the cause: Cutler was on the

Society’s Council in 1926 but otherwise contributed little. 33

4 Research and publishing in agricultural statistics

Yule brought statistical expertise to the projects of subject-matter specialists and they acknowledged his help in their writings or enrolled him as a co-author. There is the same pattern in Fisher’s collaboration (1922-34) with the bacteriologist Gerald

Thornton (1892-1977: FRS 1941).34 Thornton and Cutler developed an experimental technique for counting bacteria in soil and Fisher’s help was acknowledged in their papers, Cutler et al (1923) and Thornton (1922). The latter generated a full paper for

Fisher (with Thornton and Mackenzie) (1922) which appeared in the Annals of

32 See Bennett (1983) for the genesis of this work.

33 See Mazumdar (1992: ch. 3) and Edwards (2005: 860) Box (195-6).

34 For Thornton’s association with Fisher, see Nutman (1977: ).

Applied Biology of which Cutler was co-editor; for Fisher the work involved an application of χ².

A different, and dominant, pattern was laid down with Fisher’s work on the historical data relating to agricultural meteorology, a field in which Rothamsted had no specialist. Russell (1966: 327) recalled how Fisher “reported weekly at tea at my house and always favourably” and the research produced under this light direction was Fisher’s and appeared under his name only; the first report was published in the

Journal of Agricultural Science as “Studies in Crop Variation. I.” A series was an expression of the creator’s ambition and authority and Fisher’s joined Pearson’s

“Contributions to the Mathematical Theory of Evolution” and the “Experimental

Researches on Vegetable Assimilation and Respiration” of F. F. Blackman, who taught the Rothamsted plant physiologists Maskell and Clapham. Fisher’s series run to eight parts and included work by followers.

The statistician writing solo—or as head of a team—in an agricultural journal was a novelty and so was the mathematical level: the orthogonal polynomial time trends of

Fisher’s ‘Studies I’ and the analysis of variance of ‘Studies II’ were worlds away from the averages and time plots of Rothamsted Experiments or the pre-war explorations of the probable error. Those early explorers were wary of pushing statistical methods too far: thus Wood (1911: 37) judged the “higher walks of statistical theory” best avoided when “the sources of inaccuracy in field and feeding experiments are so numerous.”

Stratton had applied textbook methods and done something to explain them but Fisher introduced novel and highly technical procedures as he applied them without giving any explanation. The Studies invested application with theory unlike Gosset’s papers in Biometrika in which the theory is first set out and followed by illustrative applications. Fisher’s papers were a challenge and it must have helped his cause that

18 he wrote from a leading establishment, had a patron, Russell, on the journal’s editorial board and enjoyed the confidence of the resident statistical expert, Yule.35

The Journal of Agricultural Science published seven Fisher papers and his 1933 retrospective mentions 22 contributions from associates. The JAS was not only critical for the success of Rothamsted statistics, it was for Fisher’s own: it was the single main journal outlet for his research in the 20s. Presented as theory, Fisher’s submissions faced opposition and scepticism but, as applications to agriculture, they were trusted.36 Fisher’s relations with journals were so fragile that it is worth noting that there are no signs of any break-down in his relationship with the JAS.37

Studies I was an “examination of the yield of dressed grain from Broadbalk” a field at Rothamsted that had been under uniform cultivation since 1852. The paper has three sections, the variation in wheat yield, theory of polynomial fitting and possible causes of slow changes. 38 There are none to provide background or perspective, to register Fisher’s contribution; The paper has three references, to Hooker (1907)

Pearson’s Tables for Statisticians and Biometricians (1914) and Mitscherlich (1909).

Fisher completed his original assignment with “The influence of rainfall on the yield of wheat at Rothamsted” (1925). Agricultural meteorology remained a Rothamsted

35 For Yule’s support of Fisher see Aldrich (2018).

36 For opposition from Biometrika and the JRSS and scepticism from the PCPS, see Aldrich

(2018) and Aldrich (2009) respectively.

37 For Fisher’s struggles with Biometrika, JRSS, PCPS and Biometrics over his statistical theory work; see Aldrich (2019).

38 Box (1978: 100-5) summarises the paper, Hald (1998: 558ff.) places its technique in the history of orthogonal polynomials and Aldrich (2005/19) reflects on Fisher’s attitude to priority.

19 interest but subsequent publications came from members of Fisher’s team, Mackenzie

(“Studies III” 1924), Tippett (1926), Irwin (1929) and Wishart & Mackenzie

(“Studies IV” 1930), and even continued after Fisher’s departure with Cochran

(1935). Russell (1926: 33-6) broadcast some of the results and a visitor F. E. Allen

(1930) worked on the mathematical theory for orthogonal polynomials.

“Studies I” started a local tradition and its methods had the potential to transform time series analysis generally but they did not carry. “Studies II” (1923) started a new line for the variation was in “the manurial response of different potato varieties” found in recent experiments at Rothamsted. In July 1924 the Imperial Botanical

Conference was held in London

5 “Scrutiny in the Statistical Department”

The Report for 1923-4 has a tellingly titled section, Statistical Control of the Field and Laboratory Observations, which (1925; 38) describes a new dispensation

It is one of the distinguishing characteristics of the recent Rothamsted work

that the field and laboratory observations are, wherever possible, subjected

to close scrutiny in the Statistical Department, with the view of estimating

the degree of probability attaching to the results, and of indicating

modifications in the plan of the experiments that may increase their

accuracy.

Where did this dispensation come from? The publications giving the intellectual grounding for this development have scant information on the genesis of the ideas or how they built on pre-war work: the only old piece to become part of the literature of the new was Mercer and Hall (1911) on uniformity trials though Fisher used it for his own purposes in Statistical Methods (1925: 225ff).

Wood and Hall had moved away from experiments with Hall (1932: 9) confined to taking “a sort of paternal interest in the subject.” The other pre-war figures remained in the field. In 1920 Gosset became responsible for the statistical aspects of the barley experiments conducted by the Irish Department of Agriculture and he resumed work with Beaven.39 Yule and Engledow were back too, collaborating on teaching and then publishing “The principles and practice of yield trials” (1926).40 In September 1922

Gosset and Fisher met for the first time.41 thSection 1 described how the matters of assessing results and planning experiments had been broached before the war—indeed However, there was a seeming discontinuity for the only old work that became part of the literature of the new was

Wood and Stratton (1910) and Mercer and Hall (1911) on uniformity trials, the latter

Fisher used for his own purposes in Statistical Methods (1925: 225ff). However, apart from Fisher, the planners of the 20s had all been there in 1914.

39 See E. S. Pearson (1939: 234).

40 For Yule’s collaboration with Engledow see Bell (1986: 195). Yule’s wide-ranging research included a venture into evolution with the botanist J. C. Willis.

41 See Box (1978: 113ff) and Box (1980).

—“Studies in crop variation. II” (1923), Statistical Methods for Research Workers

(1925) and “The arrangement of field experiments” (1926)— “Studies in Crop

Variation. II” (1923) concerned the variation in “the manurial response of different potato varieties” found in experiments at Rothamsted conducted by Thomas Eden (b.

1897) a Manchester graduate in chemistry. Eden appears in the Report for 1921-2 as a chemical assistant and in 1923-4 as an ecologist in the department of Field

Experiments; he left in 1928-9 for the Tea Research Institute of Ceylon. 42 Eden

(1926:) reports that

The relevant section of his book opens with a wonderfully assured reference to “the principles underlying modern methods of arranging field experiments.”

New were the authority of the Statistical Department and the methods it was using— the analysis of variance and a design theory organised around the principles of replication, randomisation, and blocking. 43

The Report for 1925-6 (1926; 26-9) has a section, Methods of Field Experimentation which supplies some background “The new methods are the outcome of long previous investigations in which several workers, including the agriculturist, the ecologist, the plant physiologist and the statistician took part.” Also Russell (1926: 1000). The workers were Russell (presumably), Thomas Eden (1897-), Ernest John Maskell

(1895-1958) and Fisher certainly. The experiments on the manurial response of different potato varieties had been conducted by Thomas Eden (1897-. In the

Rothamsted Report for 1921-2 Eden appears as a chemical assistant and in 1923-4 as an ecologist in Field Experiments in and then leaves for Tea Research Institute in 28-

42 See Parolini (2015a: 318).

43 From the writings of statisticians and historians of science see, inter alia, Cochran (1976, -

80), Preece (1990) and Atkinson & Bailey (2001) and Hall (2007) and Parolini (2015).

9. a crop ecologist Box (162) Eden (1926) describes the experiments. Ernest John

Maskell (1895-1958) appears as in 1923-4 as plant physiologist in Field Experiments

44 Maskell’s PhD (published as (1928) supervisor was Frederick Frost Blackman

‘Experimental researches in vegetable assimilation and respiration’ wich

It was recognised that in the past more useful information had often been obtained from field observations during the growth of the crops than from the final weighings at the end. A field laboratory was therefore built on the experimental fields and equipped *'ith appliances for making measurements on the growing plant, and an ecologist (T. Eden) and a plant physiologist (E. J. Maskell) devoted their whole time to measuring and observing such things as rate of growth. […] These observations promise to be of great value in explaining the effect of soil and season on plant growth and on fertiliser action. The figures for final yield, however, must always be the chief, and have often been the only, test of any agricultural treatment.

The paper contained the first published analysis of variance table—quite incidentally for the point of the paper was to answer the following concern (311).45 :

if important differences exist in the manurial response of varieties a great

complication is introduced into both variety and manurial tests; and the

practical application of the results of past tests becomes attended with

considerable hazard.

Among the conclusions (320) were:

44 See Briggs et al. (1961). After a short stay at Rothamsted he joined T. G. Mason in 1926 at the Cotton Research Station newly established in Trinidad. Fisher (1935: 195) mentions

Maskell Aldrich (2000: 158)

45 For the analysis see Box (1978: 109-112) and Cochran (1980: 17-21).

(1) The data show clearly significant variation in yield due to variety and to

manurial treatment.

(2) There is no significant variation in the response of different varieties to

manure. received March 20th 1923 —eight in the series, “Studies in Crop Variation.” T

This had not been Fisher’s original mission and he had gone a long way since 25 July

1923 when Gosset remarked to him of the experiment analysed in “Studies in Crop

Variation. II.” “[it] seems to me quite badly planned, you should give them a hand in that; you probably do now.” What Fisher went on to do far exceeded Gosset’s expectations: tAccording to Box (1978: 156), Fisher designed his first experiment in

1924—a randomised Latin square design—not for Rothamsted but for the Forestry

Commission which had sought advice from Rothamsted. H

Fisher must have asked for an explanation for the next week first sign that Fisher was interested in design comes in correspondence with Gosset. Gosset had told Fisher

(Letters 25/7/23) that the Gosset (30/7/23) was listing the principles he would use.

There is no indication of how Fisher developed his ideas. Russell’s (1932: 6) recollection was that “The next step was to develop a correspondingly rigorous field technique, and this was done by Dr. Fisher in co-operation with T. Eden and E. J.

Maskell.” The chief difficulty was to overcome the effects of the irregularities in the soil which had long been a serious stumbling-block to field experimenters, In SMRW he introduces the technique of plot experimentation (§48 VIII) saying, "The statistical procedure of the analysis of variance is essential to the understanding of the principles underlying modern methods of arranging field experiments." "Modern methods" is typically tendentious---they had never been described before! Statistical Methods

24 presents the basic principles of randomisation, replication and blocking. The arguments are developed in The Arrangement of Field Experiments (1926) the first of a series of articles culminating in the book The Design of Experiments

6 Statistical Methods for Research Workers

Statistical Methods for Research Workers (1925) was a Rothamsted book: it appeared in a series of Biological Monographs and Manuals edited by Cutler and the Edinburgh animal geneticist F. A. E. Crew.46 Years later Fisher recalled, “It was Cutler who approached me, probably after consulting Crew, and certainly he came at the right moment, for I did not have to do any mathematical research ad hoc, but only had to select and work out in expository detail the examples of the different methods proposed.”47 His turned out to be the only Rothamsted contribution to the series for

Cutler’s projected monograph on the physiology of protozoa did not appear. It was also the only manual though a Mathematics for Biological Research Workers by the

Edinburgh physiologist Eric Ponder was projected.

Fisher (1925: vii) relates how he had “been working in somewhat intimate co- operation with a number of biological research departments; the present book is in every sense the product of this circumstance.” Rothamsted data figures in several examples and work by Rothamsted colleagues is referred to.

46 For general accounts of the book see Edwards (2005) and Yates (1951)—the latter one of a number published by JASA to mark the book’s 25th anniversary.

47 Quoted by Edwards (2005: 861). Edwards (860-1) also quotes Crew’s reaction, “he spoke of its quality, the formative work it contained, and urged publication if only on the grounds that statistics in future must form part of research work in every science.” The editors of the

JAS probably felt the same when they accepted his articles

The “prime object” (16) of the manual was

to put into the hands of research workers, and especially of biologists, the

means of applying statistical tests accurately to the numerical data

accumulated in their own laboratories or available in the literature.

The means involved five tables—for the normal, χ², t, correlation coefficient and z distributions—with more than thirty examples showing their use plus some general expository matter and a few examples serving other purposes. The result was a cross between a textbook, like Yule’s Introduction, and a book of tables, like Pearson’s, and indeed there was some overlap of material with these works.

The book—like Yule’s—drew heavily on the author’s own research: ten examples involve agricultural meteorology or field experiments and, representing Fisher’s outside interests, seven examples from biometry, four from genetics with five of methodological interest. The only ‘alien’ examples are from social statistics and physiology—Ex 28 from Yule’s pauperism studies illustrating partial correlation and

Ex. 19 & 20 reworking Student’s (1908a) analysis of Cushny and Peebles’ data.

Fisher (vii) told the reader, “Daily contact with the statistical problems which present themselves to the laboratory worker has stimulated the purely mathematical researches upon which are based the methods here presented.” Hotelling (1927: 411) appreciated the effort:

Most books on statistics consist of pedagogic rehashes of identical material.

This comfortably orthodox subject matter is absent from the volume under

review, which summarizes for the non-mathematical reader the author’s

independent codification of statistical theory and some of his brilliant

contributions to the subject, not all of which have previously been published.

However, Fisher gave no easy path to those researches: the “Sources for Data and

Methods” (233-6) include 10 of his works but the index has only one entry to his name; for Pearson and “Student” the corresponding figures are (both) 1 and 3.

Most reviewers were cooler than Hotelling for established opinion held with Harris

(1914: 830) that “serious harm has been done by telling the beginner that he need not understand the formulae to use them.” Fisher had not heeded the warning when he wrote for the JAS and he did not with Statistical Methods. There is no knowing what the target audience of biologists/non-mathematical readers made of the book for it was reviewed by statisticians and these, apart from Gosset, worked in other areas of applied statistics.48 Opinion divided on the significance of Fisher’s “brilliant contributions” for statistics generally and on his attitude to statistical authority but it was agreed that the book was a difficult read for its intended audience: the generally positive “Student” (1926: 150) warned, “it should not be expected that full, perhaps even in extreme cases any, use can be made of such a book without contact either personal or by correspondence with someone familiar with its subject matter.” The

Nature reviewer thought it probable “that the book will be read as much by statisticians who wish to study Mr. Fisher’s methods and views as by those research workers who merely want to apply the methods he describes.”

Despite the warnings, the book found an audience and four editions appeared while

Fisher was at Rothamsted. Sales grew and so did the size of the book: the 1st edition

(1925) of 239 pages sold 1050 copies, the 2nd (1928) of 269 pages sold 1250, the 3rd

(1930) of 283 sold 1500 and the 4th (1932) of 307 sold 1500. As expected, it was first cited by statisticians—like Neyman (1926)—or scientists in contact with Fisher—like

48 Gosset’s review did not appear in an agricultural or biological journal but in the Eugenics

Review—arranged, presumably, by Fisher. See Aldrich (2003/19) for other reviews.

27 the Rothamsted algologist Bristol Roach (1926). Eventually guides materialised and the book acquired the status indicated by a recollection of Henry Daniels (1982: 261),

“When I was learning statistics from John Wishart in the mid-thirties there were two recommended textbooks: Fisher’s Statistical Methods, which one read with respect, and Tippett’s Methods of Statistics, which provided understanding.”

Wishart, the Cambridge teacher, and Tippett, the textbook writer, had both been at

Rothamsted, as assistant and as a voluntary worker. The first with those roles were

“Mr. E. Somerfield, and Miss W. A. Mackenzie” whose help was acknowledged in the preface of Statistical Methods (1925: vii). These roles were part of the Rothamsted economy and it is time to consider them and how those filling them contributed to

Fisher’s productivity and success.

7 Working for Fisher—at Rothamsted and beyond

Like Pearson, Fisher found others to propagate his kind of statistics with Wishart and

Yates and Tippett and Hotelling in the roles of Yule and Gosset: “Contributions of

Rothamsted” mentions over 20 contributors responsible for over 50 pieces. Most of the contributors were from the Statistics Department—assistants, voluntary workers or students—though Eden and A. R. Clapham of the Department of Field Experiments figured too: Eden published with Fisher but Clapham did not, though Fisher contributed to his work on sampling.49

49 Clapham (1929: 231) thanked Fisher for “valuable criticism and advice.” Willis (1994: 75-

6) describes Clapham at Rothamsted and his relations with Fisher. Fisher (1934b: 615-6) recounts Clapham’s contribution to sampling.

The Statistics Department started with one Assistant Statistician and later there might be two—even three at one time. Voluntary workers stayed for different periods and there might be up to four in the course of a year.50 The groups were tiny compared to those Yates led at Rothamsted in the 1960s with over 20 scientific staff but in Fisher’s time all the Rothamsted departments were small and, for groups of statisticians, tiny was normal. At Cambridge Yule remained alone in a post shared with Economics, at the LSE Bowley was joined by a second statistician in 1924 and even Pearson’s Eugenics and Applied Statistics empire had—in 1930—a Reader in

Medical Statistics, a Senior Lecturer, a Lecturer and two Research Fellows.51

The five assistants came from different parts of the statistical world, four with mathematics degrees, like Fisher, but none with his interest in biology or in the foundations of statistical inference. The three men came with more research experience but all five came without knowledge of Fisher’s approach and needed training. The men all went on to big careers and became important propagators of

Fisherian statistics—two came from Pearson and their ‘turning’ helped shift the balance between the two rivals.

The first assistant was Winifred Alice Mackenzie (1896-1954) a statistics graduate of the LSE where she had contributed to Bowley’s history of incomes project–see

Mackenzie (1921).52 Fisher developed his approach to agricultural meteorology and

50 Parolini (2015a: 328-331) lists the voluntary workers. The Department also employed computers but these did not figure as authors or co-authors: see Parolini (2015c).

51 For Pearson’s empires see Magnello (1999).

52 For this she received the first Frances Wood Memorial Prize, offered “for the best investigation of any problem dealing with the economic or social conditions of the wage-earning classes.”

29 experimental trials with her assistance—as in Fisher and Mackenzie (1922; -23)—and she then worked alone along lines they had laid down—as in Mackenzie (1924; -26); the independent work led to the award of a higher degree in 1924: see Box (1978:

137-8). In 1927 Mackenzie left Rothamsted—and statistics—to marry and do missionary work in the Belgian Congo. The other female assistant, (Alice) Margaret

Webster came in 1929 straight from a London mathematics degree. By then Fisher had an established repertoire and Cochran (1935: 510) reports that Webster started to investigate the effects of rainfall on the wheat and barley yields from Woburn. Her statistical career ended when she married the Director’s son, E. Walter Russell.

Mackenzie’s successor, John Wishart (1898-1956), like all the men, arrived older and more established.53 He had assisted Pearson on a project on computing tables of the Beta function and had four publications in Biometrika. In his time with Fisher he published on the Rothamsted staples of weather and experiments and also on the

Fisher specialities of mathematical tables and distribution theory.

In 1931 Wishart left to replace Yule at Cambridge. The appointment was really a new beginning for Wishart taught mathematics students as well as agricultural and he had a longer spell of peace ahead of him. Wishart did not have a big place in

Cambridge mathematics but Cambridge so dominated British mathematics that for mathematical statistics his was the most important teaching position in Britain: besides Daniels, Wishart taught F. J. Anscombe, M. S. Bartlett, W. G. Cochran, D.

Finney, H. O. Hartley, O. Kempthorne, D. N. Lawley and W. M. Stevens. (Several later worked at Rothamsted and Stevens worked for Fisher in London). Wishart was more effective at promoting statistics in Cambridge than Yule but he also did more for agriculture at the RSS: Yule had been a great figure in the Society but none of his

53 See the obituaries by Bartlett (1956) and E. S. Pearson (1957).

30 agricultural work appeared in its journal while Wishart helped form the Industrial and

Agricultural Research Section and published on agriculture. 54

J. Oscar Irwin (1898-1982) arrived in 1928 and left for the Medical Research

Council Unit at the London School of Hygiene in 1931.55 Like Wishart, he learnt statistics from Pearson for whom he worked from 1921-8; published four papers in

Biometrika. He contributed on Rothamsted themes but not as prodigiously as Wishart and after his departure went his own way.

Frank Yates (1902-94), like Irwin a Cambridge mathematics graduate, came from the geodetic branch of error theory.56 Having appointed him, Fisher contemplated a training regime: on the 2nd May 1931, it was by “reading up what one might call the biometrical side of statistics, and in particular the work on tests of significance and the analysis of variance as this is the method which everyone who comes here wants to know, and on which the sooner you are an authority the better” and on the 9th

Fisher was advising on “mathematical reading on the subjects I want you to feel comfortably acquainted with, not by next October, but, say, by the October following.” Yates (1979: 505) recalled that he worked “under Fisher—perhaps worked alongside him would be a better description, for Fisher was never one to command, or indeed to supervise closely.” Yates was soon publishing in the JAS— without benefit of Fisher’s co-authorship though he (1933: ) acknowledged “his helpful advice and criticism.” Yates succeeded Fisher as Head of Department and, as

Finney (559) notes, they “became fast friends in a collaboration that lasted 30 years.”

54 See Aldrich (2010: §6).

55 See the obituary by Armitage (1982).

56 For Yates see Finney (1995) and (558-9) for his Rothamsted induction. Finney reports that

Yates came on the understanding that he could use half his time for his own research.

Their relationship was poles apart from that between Yates and his successors: Finney

(572) recalls his reaction to the idea of a group photograph, “he dismissed the idea with a characteristic snort of disapproval ‘I don’t agree with any of them!’” Yates, however, agreed with Fisher and Rothamsted stayed Fisherian in his long tenure.

From the many voluntary workers four may illustrate the variety of experience—

Somerfield, Tippett, Hoblyn and Hotelling.57 Edward Somerfield, the first, worked for

Guinness and was sent by Gosset but, having published on a Rothamsted theme as

“Mathetes” (1924), disappeared from public view. Leonard Henry Caleb Tippett

(1902–1985) stayed in view and eventually became President of the RSS. As a fresh physics graduate, Tippett was sent by the Shirley Institute to learn statistics from

Pearson and then from Fisher: the ensuing publications reflected both his interests and his masters’—Pearson and Tippett (1924) and Tippett (1925) and Tippett (1926) and

Fisher and Tippett (1928). When Tippett published his Methods of Statistics Irwin

(1932: 325) endorsed it in the JRSS, “This is a book which may be unhesitatingly recommended to biologists and, indeed, to all working in statistics.” From a world perspective, Harold Hotelling (1895-1973) was the most important of the voluntary workers for he carried Fisher’s ideas and name to America: “It is no exaggeration to state that during the 1930s and early 1940s, Hotelling nearly single-handedly brought

American statistics into the modern age and laid the foundation for the extraordinary development of the subject after the Second World War” wrote Arrow & Lehmann

(2005: 11). Hotelling pressed Fisher on the American statistical public and was unique among assistants and visitors in wanting to work with Fisher on statistical

57 Box (1978: passim) has information on all four. See also Pearce (1974) for Hoblyn, and for Hotelling, Arrow & Lehmann (2005)

32 inference.58 Thomas Noel Hoblyn (1898-73) spent his career at East Malling horticultural research station. Pearce (261) describes, how a need for statistics being realised, “It so happened that [the director] Hatton was cousin to Karl Pearson, who was consulted; as a result Hoblyn was sent to study under the great R. A. Fisher, whom he always revered.”

8 FRS and moving on

In 1929 Fisher was elected Fellow of the Royal Society. The election certificate records him as M.A., Sc.D. and “sometime fellow of Caius College” with profession,

“Head of Statistical Department.”59 Russell (1966: 290) records that by 1962 sixteen

Rothamsted figures had got into the Society but in 1929 Russell was the only Fellow on the staff though the same year saw the election of A. D. Imms (1880-1949) Head of Entomology. Fisher’s election was a personal triumph: younger than average, he had only been a full-time scientist for ten years and was elected at the first attempt.

The award recognised a “long series of original contributions to the mathematical theory of statistics, in particular the theory of sampling, and applications to agriculture, biology and meteorology.”60

The existing statistical fellows were Pearson (born 1857; FRS 1896), Yule (born

1871; FRS 1922) and Greenwood (born 1880; FRS 1928). Fisher was a geneticist too and Crew (1969: 12) states that the entry of geneticists and cytologists was opposed by Pearson and the Lamarckian Ernest MacBride who “stood at the entrance of the

Royal Society like the leogryphs which guard the portals of a Burmese Buddhist

58 For Fisher and Hotelling generally, see Stigler (2007) and Aldrich (2010; 2007/19).

59 Fisher clung to his past affiliation with Caius.

60 Royal Society Certificate of election.

33 temple.” Fisher was proposed by Yule and seconded by Eddington with support from

Russell and Hall, the geneticist Reginald Punnett, the meteorologist Gilbert Walker, the mathematical physicist Ralph Fowler and the Imperial College botanists Sir John

Farmer (1865-1944) and Vernon Blackman (1872-1967).61 Farmer was the

Rothamsted Treasurer and Rothamsted connections provided roughly half of Fisher’s backing.

As soon as he became F.R.S. Fisher was asking Russell about a pay rise and threatening a move. In May he wrote “since I must face the possibility of being disappointed in this matter, I had better put my name in for a Chair of Mathematics, and I should be glad if you would write me a testimonial as to my ten years’ work here.” Fisher had a respectable list of mathematical publications but there is no sign that he actually considered such a move and his letters to Darwin show him contemplating something different—in February he wrote,

I wonder if you have any words of wisdom on a contingency which I

suppose is not too improbable to be considered. If I were offered Pearson’s

Chair what in your opinion should I aim at making of that place? It would be

easy to continue mathematical researches, and possibly in time to build up a

reasonable biological outlook. Is that the whole programme?

Darwin’s reply came in two letters: the first gave his assessment of Fisher’s chances and why, should he get the job, it would be “far from a bed of roses”; the second suggested that his “broad aim” should be to help eugenics by basing hereditary theory

61 Blackman’s obituarist, Porter (1968: 55), recalls his early enthusiasm for statistics: he “had seized on the work of T. B. Wood, who was his contemporary at Cambridge, as providing a long-wanted precision tool for the biologist. Students and staff alike were given Wood’s account of ‘probable error’ and enjoined to make use of the concept.”

34 on “more sure” foundations. The Pearson chair was not then on offer but in

November a new chair in social biology at L.S.E. appeared: Fisher was attracted and thought about what he might do and the specialists he might employ—Darwin responded, “would it not be wise to catch your goose before trying to fatten it?” For some reason Fisher never applied for the job.62

Rothamsted made an event of Fisher’s departure—heads of department usually left without fanfare, as Imms did in 1931. The Report for 1933 contained two valedictories—a sketch (1934: 42-3) of the past, present and future of the Statistical

Department by Russell (presumably) and the detailed “Contributions” by Fisher. In the first, tribute (42) was paid to Fisher on his leaving to take up “new duties” in

London: his work “has revolutionised the science of statistics and the technique of biological experimentation, and agriculture must consider itself indeed fortunate to have had his especial attention for so long.”

Fisher’s at, and out of, Rothamsted turned out to be the theme of the inaugural meeting of the RSS’s Industrial and Agricultural Section in January 1934. Wishart spoke on “Statistics in agricultural research” and the occasion turned into a celebration of Fisher’s achievement at Rothamsted and lament at his leaving agriculture: Wishart (1934: 51) closed with “I trust that somehow we shall be able to carry on”. Fisher (1934a: 52) responded, “[Wishart] speaks of me as having severed my connection with the subject which he is now carrying on. My post-bag tells a different story. I am afraid I am engaged in as much discussion on agricultural and other experimental topics as I ever was.” The public expression of this engagement was the book Design of Experiments (1935) and papers on the combinatorics of design. The long partnership with Yates which produced Statistical Tables (1938)

62 Tabery and Sarkar (2015) give details.

35 flourished after he had left. Fisher did not move home when he went to University

College and continued to be involved with Rothamsted as an honorary consultant.

When UC was evacuated to Wales in 1939 Fisher took what was left of his department to Rothamsted.

9 “Never happier professionally”

Fisher succeeded Pearson as Galton professor of eugenics at University College in

1933 and Punnett as Balfour professor of genetics at Cambridge in 1943.63 The appointments may have seemed more like destiny than jobs with “interesting work”: there was a sweetness associated with the idea of them and a thought to be relished,

“My 1918 paper was refereed [adversely] by Pearson and Punnett, both of whom I later succeeded.”64 Yet the anticipated sweetness was not realised and Box (1978: 96) reports that he “was never happier professionally” than during his Rothamsted years.

He had lost his freedom of manoeuvre and sense of being centrally important.

The Galton appointment both contradicted and fulfilled Darwin’s expectations of

1919: Fisher did get the job but only part of it with the rest going to a “mere mathematician,” an insider favoured by Pearson, his son Egon. In 1929 Darwin had tried to restrain Fisher’s dreams for his own department by pointing out that members of staff who hold regular university appointments “cannot be got rid of.” Just before starting Fisher told Wishart, “The Department at University College looks like being the Hell of a job to pull together, but one can but try.” The department’s difficult external relations involved demarcation with Egon’s Department of Applied Statistics

63 Box (257ff & 398ff) and Edwards (1990: 901-3) describe his London and Cambridge experience.

64 Quoted by Edwards (2012: 10).

36 and its internal relations involved dealing with staff inherited from Karl. One clear advantage over Rothamsted was that Fisher could make appointments in genetics:

Kenneth Mather (1911-90) joined in 1934 and the Blood-Group Serum Unit was established in 1935. Although there was regular teaching and his Rothamsted book

The Design of Experiments was written at University College, the statistics side was not so well-served: an assistant W. L. (Tony) Stevens (1912-58) was recruited in 1935 but he did not have the same impact on British statistics as his Rothamsted predecessors and the UC students did not become the disciples like the earlier voluntary workers.65

When Fisher arrived in Cambridge the war was on and the Department was “so let down as to be almost non-existent.” As in London, he built up a department but it was a genetics department and, though he went on publishing statistics and served as

President of the Society, he had no responsibility for the subject: Edwards (1990) recalls him saying at the end of his Cambridge career, “I have never been consulted on any appointment to a University post in statistics or genetics outside my own

Department.”

10 What Rothamsted did for Fisher

In his Fisher Memorial Lecture George Box (1979: 792) presents Fisher in 1919 as choosing between working in “the most distinguished statistical laboratory in Britain” and being “the sole statistician is a small agricultural research station in the country.”

I have tried to develop the point that the small station in the country was the country’s leading agricultural research institution in a phase of rapid expansion with a director,

65 For Stevens see Yates (1959), for Mather see Lewis (1992). Box (261-2)

John Russell, prepared to take a chance on creating the office of agricultural research statistician that would reflect well on Rothamsted. The Rothamsted opportunity came at the right time: the ground was ready but the only institutional development was a gesture from the Cambridge School of Agriculture. Biometry and medical statistics had been established for twenty years or ten while industrial statistics was not yet ready to go. Fisher played his part brilliantly and Russell backed him with noisy PR becoming—after Leonard Darwin—Fisher’s greatest champion.66

Besides the positive things that Rothamsted did for Fisher, there were the ‘non- negatives’—what Rothamsted might have done but did not. Most importantly Russell protected Fisher’s space to do other things with spectacular results in mathematical statistics and genetics. Being the sole statistician (and geneticist) was to Fisher’s advantage: no colleagues quarrelled with the content of his work and he chose his closest colleagues.

References

Aldrich, J. (1995) Correlations Genuine and Spurious in Pearson and Yule, Statistical

Science, 10, (4), 364-376.

______(1997) R. A. Fisher and the Making of Maximum Likelihood 1912-1922,

Statistical Science, 12, (3), 162-176.

______(2003/18) A Guide to R. A. Fisher

http://www.economics.soton.ac.uk/staff/aldrich/fisherguide/rafreader.htm

66 See Bennett (1983) for an overall account of the Fisher-Darwin relationship and

Aldrich (2019) for an example of Darwin’s wisdom in mediating between Fisher and the RSS.

______(2005/19) Leon Isserlis and the JRSS review of the 1st edition of R. A.

Fisher’s Statistical Methods for Research Workers at

http://www.economics.soton.ac.uk/staff/aldrich/fisherguide/Isserlis.htm

______(2006/10) The Mathematics PhD in the UK, website,

http://www.economics.soton.ac.uk/staff/aldrich/PhD.htm

______(2007) Information and Economics in Fisher’s Design of Experiments,

International Statistical Review, 75, (2), 131-149.

______(2007/19) Harold Hoteling’s review of the 1st edition of R. A. Fisher’s

Statistical Methods for Research Workers http://www.economics.soton.ac.uk/staff/aldrich/fisherguide/Hotelling.htm

______(2008) [Student and Fisher] Comment on S. L. Zabell’s paper: On Student's

1908 paper “The probable error of a mean”, Journal of the American Statistical

Association, 103, 8-11.

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