William Allen Whitworth

Quick Info

1 February 1840
Runcorn, Cheshire, England
12 March 1905
London, England

Allen Whitworth became an editor of the newly founded journal Messenger of Mathematics while still an undergraduate at St John's College, Cambridge. He was later elected a fellow of the College and wrote several popular teaching books. He later had a career in the Church and, because of his proposal and encouragement, St John's College set up a Mission for the disadvantaged in London.


W Allen Whitworth was the son of William Whitworth (1797-1869) and Susanna Coyne (1805-1867). William Whitworth was ordained and was a schoolmaster at Runcorn, later becoming a Perpetual Curate at Little Leigh, Cheshire. Susanna Coyne was the daughter of George Coyne of Kilbeggan, County Westmeath, Ireland.

William and Susanna Whitworth were married on 11 April 1839 in Runcorn, Cheshire. They had five children, all born in Cheshire: William Allen Whitworth (born Runcorn in 1840), the subject of this biography; Frederic Joseph Whitworth (born Runcorn in 1843); Alfred Edward Whitworth (born Daresbury in 1845); George Clifford Whitworth (born Great Budworth in 1846); and Clara Susannah Whitworth (born Little Leigh in 1849).

At the time of the 1851 Census, William Allen Whitworth was eleven years old and is described as a scholar studying at home. Later in 1851 he entered Sandicroft School, Northwich, a town about 5 km south east of Little Leigh. On 7 July 1858 he was admitted to St John's College, Cambridge as a sizar. He matriculated in the Michaelmas term of 1858 and began his study of the Mathematical tripos. We learn from The Eagle (the St John's College Magazine) that he was Secretary of the Lady Somerset Boat Club in 1860-61 (see [7], [8]), was First Class in Third Year Mathematical Tripos, Christmas Examinations [8] and First Class in Third Year Mathematical Tripos, June Examinations [9]. In 1861, his Third Year, he was elected a scholar [9]. Remarkably at this stage in his undergraduate career, he was an editor for the new publication The Oxford, Cambridge, and Dublin Messenger of Mathematics. A Journal supported by Junior Mathematical Students and conducted by a Board of Editors. In fact the first part of Volume 1 of the new journal appeared in November 1861 and the first paper in this part was The equiangular spiral, its chief properties proved geometrically by Whitworth. The paper begins:-
Of the following propositions, those only which give geometrical constructions for the centres of gravity of a spiral arc and area present results which will probably be new to the reader. But the other propositions are added as it is thought convenient to have geometrical demonstrations of the principal properties of this beautiful curve collected into a continuous paper, and it is hoped it will be found at once profitable and interesting to view the curve under the somewhat novel aspect under which it is here presented.
In total there are five papers by Whitworth in the first volume of The Messenger of Mathematics. The other four are: On a certain form of Equations representing a Straight Line in Trilinear Coordinates; Additional Note on the Equiangular Spiral; The Sphere, referred to Quadriplanar Coordinates; and Quadrilinear Coordinates.

Whitworth was awarded a B.A. in January 1862, and was 16th Wrangler in the Mathematical Tripos. His remarkable abilities seem to merit a much higher ranking than 16th. The author of [32] writes:-
Probably, as often, his impetuous and creative mind had refused to submit entirely to the conventional training for the Tripos. Possibly also he had devoted time, energy, and thought to objects less beneficial to himself. The writer thinks he remembers a report that Whitworth did much for the infant years of this 'Eagle': and certainly he was, if not a founder, at a very early date leading editor of a new mathematical periodical, 'The Messenger of Mathematics' - a revolt against the somewhat high-dry investigations favoured by the aristocratic journal of the time.
For a version of the obituary [32], see THIS LINK.

Whitworth was appointed Mathematics Master at Portarlington School in Portarlington, County Laois, Ireland but, in 1862 became First Mathematical Master of Rossall School, near Fleetwood, Lancashire. He left Rossall School in 1864, was ordained deacon in Chester in 1865 and priest, also in Chester, in 1866. He was curate at St Anne's, Birkenhead in 1865, then a curate at St Luke's, Liverpool from 1866. He was appointed to Queen's College, Liverpool in 1866 and gave lectures on arithmetic there in the Michaelmas Term, 1866. These lectures were published as Choice and Chance. Two Chapters of Arithmetic (1867). Whitworth writes in the Preface:-
Many of the students to whom the lectures were addressed were just entering upon the study of algebra, and it seemed well, while the greater part of their time was devoted to the somewhat mechanical solution of examples necessary to give them a practical facility in algebraical work, that their logical faculties should be meanwhile exercised in the thoughtful applications of the arithmetical art with which they were already familiar.
For the complete Preface to this book and information about other mathematical texts written by Whitworth, see THIS LINK.

Choice and Chance ran to five editions, the last being in 1901. Irwin writes in [5]:-
The book is essentially a work on combinatorial chance. It uses only elementary algebraical methods. The author's genius consists in the fact that, with an exposition which is always of extreme clarity, he uses these methods.

(i) To discuss combinatorial analysis systematically in a remarkably extended field, to obtain results some of which are still considered recondite because later writers have used more sophisticated methods to obtain them;

(ii) To obtain a number of important probability distributions which are of the utmost importance in statistical theory and practice today.
On probability, Whitworth wrote in Choice and Chance:-
The measurement of chance may be approached 'ab initio' from the consideration of the price that may reasonably be paid for 'a gain contingent on some doubtful occurrence'. And to many minds this method appears easier than any other. ... Now there is only one meaning which we can give to the word 'fair'. The fair price at which the transaction can be made between the parties must be such that if the transaction were repeated indefinitely, say for millions of times, there would be no presumption beforehand that either party would be the winner. ... The fair price can sometimes be calculated mathematically from 'a priori' considerations; sometimes it can be deduced from statistics, that is the recorded results of observation and experiment. Sometimes it can only be estimated generally, the estimate being founded on a limited knowledge or experience. If your expectation depends on the drawing of a ticket in a raffle, the fair price can be calculated from abstract considerations: if it depends upon your outliving another person, the fair price can be inferred from recorded statistics: if it depends upon a benefactor not revoking his will, the fair price depends upon the character of your benefactor, his habit of changing his mind, and other circumstances upon the knowledge of which you base your estimate. But if in any case you determine that £300 is the sum which you ought fairly to accept for your prospect (£1000) this is equivalent to saying that your chance, whether calculated or estimated is 3/10.
On Monday, 4 November 1867, Whitworth was elected a fellow of St John's College, Cambridge. It is certainly unusual for someone ranked as 16th Wrangler to be elected to a Fellowship, so it is clear that the authorities of the College were well aware that his tripos performance did not represent his true abilities. He continued to teach at Liverpool and in 1869 he is listed as Vice-Principal of Queen's College, Liverpool. He remained a curate at St Luke's, Liverpool until 1870 when he became perpetual curate of Christ Church, Liverpool. We note that addresses on the Prefaces to his books give his address as Liverpool on 15 September 1866 and on 1 February 1867, but St John's College on 1 January 1870.

Whitworth was invited to preach in the St John's College Chapel several times, the first being on 7 and 14 July 1872. In 1875, because of his success with parochial missions in Liverpool he was appointed to London [12]:-
Rev W A Whitworth has been appointed to the Vicarage of St John the Evangelist, Hammersmith. He does not vacate his Fellowship by the preferment.
Whitworth preached a sermon in St John's Chapel on Sunday 28 January 1883. This sermon was to lead to a major project on behalf of St John's, College namely the London Mission [20]:-
The sermon appealed to [members of the College] as the 'Trustees of Knowledge,' in relation to many who are 'Victims of Ignorance.' Mr Whitworth asks whether or not the College, or rather Members of the College aggregately though not corporately, could not undertake the support and stimulation of a Mission among the uneducated in London ...
The College responded very positively to Whitworth's proposal [21]:-
The proposal was warmly received, and carefully discussed by senior and by junior members of the College. It was felt that a Mission might be beneficial in many different ways. The work would be in the spirit of the foundress, Lady Margaret; it would serve as a bond of union between rich and poor, educated and ignorant, and generally between class and class. If efficiently conducted, it would have a double value - to the district chosen for the Mission, and to the many members of the College, who it is hoped would, in various ways, take a practical interest in it.
This Mission was highly successful and further details of how it operated in Walworth, London are given at THIS LINK.

It is interesting to look at the position Whitworth takes on gambling for here we have a topic where both his mathematical skills and his religious views play a role. Irwin writes in [5]:-
... for his attitude to gambling we have three sources of information, the chapter in Choice and Chance on "The Disadvantage of Gambling", his Gresham lecture of 1893 on 'Applications of the Laws of Chance' and his sermon of 1895 on 'The Law of the Wager'. The former two can be regarded as purely scientific treatments of the subject, but inevitably coloured by his moral attitude, which however was extremely broad-minded. The chapter on the disadvantage of gambling starts with the definition of a fair bet as one in which each person's stake is proportional to his mathematical chance of winning. An "even" bet is defined to be one in which each person stakes the same sum. An even bet may or may not be fair. Whitworth points out that a fair bet implies that neither party stands to gain or lose in the long run; but, in successive repetitions, if one party is obliged ta stop at some particular moment he may be at a disadvantage. This will be the case if one is poorer, for he must stop when he has lost all he has. In this chapter he considers formally the cases of absolute and of relative repetitio.
In his Gresham lecture, Whitworth said:-
Of late years gambling has been denounced in unmeasured terms from platform and from pulpit by speakers who have never taken the trouble to define the thing which they denounce or to discover wherein the evil consists. ... But if the assertions thus hastily made be followed out to their legitimate conclusions, we find not only that it is wrong to play whist for penny points, or to join in a raffle, or to bet a pair of gloves with a lady on an event in which she is interested, but that it is equally wrong to buy a piece of land on the expectation that its value will improve, it is equally wrong for a trader to purchase a commodity largely because he thinks there will be a demand for it. In a word if the principles of these moralists are to be rigorously applied, money must never be risked in the expectation of receiving a contingent advantage: trade and commerce must come to an end.
In his sermon The Law of the Wager (1895) he said [33]:-
Within the limits of moderation it is

(i) Immoral to back one's private knowledge.

(ii) Justifiable to back one's skill.

(iii) Foolish to back one's luck.
Commenting on Whitworth's approach to gambling, the statistician Cedric Austen Bardell Smith (1917-2002) said [5]:-
Whitworth is to be particularly commended on judging the morality or desirability of gambling through its consequences, both financial and psychological; for example, the possibility of addiction. He adopted mostly a deductive approach. But many social problems could be approached similarly from an investigation of the actual consequences of various actions, both deductively and empirically, rather than by laying down the law on the basis of preconceived ideas.
Returning to Whitworth's career in the Church, we noted above that he was made vicar of St John the Evangelist in Hammersmith, London in 1875. In 1885 St John's College made him the rector of Aberdaron in Wales. This was one of the sinecures that the Cambridge Colleges were able to give to favoured people. It had no church, no congregation yet gave the appointed rector a small income. Whitworth accepted the position but was not one to use such for personal profit, and he gave half the income to a neighbouring parish and the other half he used to help the work of the Church. His son, George Elwes Allen Whitworth (see below) said [5]:-
Aberdaron was a sinecure for my Father; it was in the gift of St John's College, Cambridge, and the gift was no doubt in further recognition of his mathematical work, the award involved no residential or parochial responsibility and I do not know what increase was involved, but I read once in the St John's College Magazine that my father would not use it for his personal needs. Certainly he visited Aberdaron from time to time; and it may be his link with Wales led my Father to establish at All Saints (Marylebone) a Welsh chaplaincy with a Sunday Service in the Welsh language. All Saints was then in a residential district including Margaret Street (now a centre for wholesale trade in women's clothes) and a large number of Welsh women and girls were employed in domestic service in the neighbourhood and it was hoped to meet their needs.
On 10 June 1885 Whitworth married Sarah Louisa Elwes (1854-1952)at St John the Evangelist, Hammersmith. Sarah, born in Ipswich, was the only daughter of the fund-holder Timms Hervey Elwes (1819-1865) and Louisa Weston (1814-1891) who had married in June 1840. Allen and Sarah Whitworth had four sons all of whom graduated from Trinity College, Cambridge: William Hervey Allen Whitworth (1887-1960), became a schoolmaster; George Elwes Allen Whitworth (18 February 1888 - September 1969), became a priest serving many churches including being vicar at St Mary the Great, Cambridge and rural dean of Cambridge; Eric Edward Allen (1889-1971), became a headmaster; and Cyril Clinton Allen Whitworth (12 December 1890 - 8 October 1955) who became an Anglo-Catholic priest, a member of the Society of St John Evangelist and was vicar of St Peter, Mazagon, in the diocese of Bombay, India, and principal of St Peter's school in Mazagon. Many more details are given in [4].

In November 1886 Whitworth was made vicar of All Saints, Margaret Street, Marylebone, London. This was, and still is, a high Anglo-Catholic church. He remained in this position for the rest of his life. In 1900 Mandell Creighton, the bishop of London, appointed Whitworth prebendary of St Paul's Cathedral, London. He was honoured by being appointed Hulsean lecturer at Cambridge for the session 1903-04. These lectures, established with an endowment by John Hulse to the University of Cambridge in 1790, consisted of a series of four to eight lectures on Christian theology. Whitworth gave the series Christian thought on present-day questions. The lectures were published in 1906 as a 214-page book.

After becoming ill, he was taken into Home Hospital, 16 Fitzroy Square, and underwent a major operation on 28 February 1905. He died less than two weeks later, and was buried on 16 March at St Alban the Martyr, Holborn. All Saints Church, Margaret Street, has a slab in the floor to Whitworth's memory.

References (show)

  1. Anon, Review: Churchman's Almanac, by W A Whitworth, Bibliographer 3 (4) (1883), 112.
  2. Anon, Review: Churchman's Almanac, by W A Whitworth, The Eagle, Lent 1883, Vol XII (1883), 307.
  3. Anon, R Whitworth, William Allen (1840-1905), Current Science 9 (2) (1940), 88.
  4. M Bain and C Hickton, An Anglo-Catholic Congress Clergy Directory of 300 associated with the 1920 Anglo-Catholic Congress, Anglo-Catholic Congresses, England, Project Canturbury (December 2015).
  5. J O Irwin, William Allen Whitworth and a Hundred Years of Probability, Journal of the Royal Statistical Society. Series A (General) 130 (2) (1967), 147-176.
  6. D J Owen, Rev Alan Yoshioka, Whitworth, William Allen (1840-1905), mathematician and Church of England clergyman, Oxford Dictionary of National Biography (2004).
  7. The Eagle, Michaelmas 1860, Vol II (1861), 206.
  8. The Eagle, Lent 1861, Vol II (1861), 258-259.
  9. The Eagle, Michaelmas 1862, Vol III (1861), 66-67.
  10. The Eagle, Michaelmas 1867, Vol VI, no XXX (1868), 72.
  11. The Eagle, Lent 1873, Vol VIII, no XLV (1873), 253.
  12. The Eagle, Lent 1875, Vol IX, no LI (1875), 250.
  13. The Eagle, Michaelmas 1879, Vol XI, no LX (1880), 54.
  14. The Eagle, Michaelmas 1881, Vol XII, no LXVI (1882), 55.
  15. The Eagle, Easter 1885, Vol XIII, no LXXVII (1885), 370.
  16. The Eagle, Michaelmas 1886, Vol XIV, no LXXXI (1887), 246.
  17. The Eagle, Michaelmas 1900, Vol XXII, no CXXIII (1901), 112.
  18. The Eagle, Lent 1903, Vol XXIV, no CXXX (1903), 258.
  19. The Eagle, Michaelmas 1903, Vol XXV, no CXXXII (1904), 89.
  20. W A Whitworth's London Mission, The Eagle, Lent 1883, Vol XII, no LXX (1883), 304; 307.
  21. W A Whitworth's London Mission, The Eagle, Easter 1883, Vol XII, no LXXI (1883), 380.
  22. W A Whitworth's London Mission, The Eagle, Michaelmas 1883, Vol XIII, no LXXII (1884), 62-63.
  23. W A Whitworth's London Mission, The Eagle, Lent 1884, Vol XIII, no LXXIII (1884), 82-86.
  24. W A Whitworth's London Mission, The Eagle, Lent 1885, Vol XIII, no LXXVI (1885), 313-314.
  25. W A Whitworth's London Mission, The Eagle, Easter 1887, Vol XIV, no LXXXIII (1887), 415-417.
  26. W A Whitworth's London Mission, The Eagle, Michaelmas 1888, Vol XV, no LXXXVII (1889), 297-300.
  27. William Allen Whitworth (1840-1905), The Times (13 March 1905).
  28. William Allen Whitworth (1840-1905), The Guardian (15 March 1905).
  29. William Allen Whitworth (1840-1905), The Guardian (22 March 1905).
  30. William Allen Whitworth (1840-1905), Church Times (17 March 1905).
  31. William Allen Whitworth (1840-1905), St John's College Archives.
  32. William Allen Whitworth M.A., The Eagle, Easter 1905, Vol XXVI, no CXXXVII (1905), 396-399.
  33. W A Whitworth, The Law of the Wager, in W Carter (ed.), Christian Thought on Present-day Questions: Sermons on Special Occasions (Macmillan, London, 1906).

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Written by J J O'Connor and E F Robertson
Last Update September 2021