Crofton, Morgan William

(1826-1915), mathematician

by Eugene Seneta and Irene N. Johnson

© Oxford University Press 2004 All rights reserved

Crofton, Morgan William (1826-1915), mathematician, was born on 26 June 1826 in Dublin, the eldest of twelve children of the Revd William Crofton (1795-1851), rector of Skreen, co. Sligo, and his first wife, Melesina (1799?-1881), daughter of the Revd Henry Woodward. He was educated at Edgeworthstown School, Mostrim, co. Longford, and entered Trinity College, Dublin, in October 1843, graduating with honours in spring 1848 as senior moderator and gold medallist in mathematics and physics.

From 1849 to 1852 Crofton was professor of natural philosophy (physics) at the newly founded Queen's College, Galway. On 15 July 1851 he was received into the Roman Catholic church by John Henry Newman, for whom he retained a lasting reverence, whereas his brother, the Revd Henry Woodward Crofton (1827-1894), made his career in the established church. Crofton moved in 1852 to the Catholic University College, Dublin, where Newman was then rector, as professor of mathematics. In August 1857 he married Julia Agnes Cecilia (1826-1892), third daughter of J. B. Kernan of Cabra, co. Monaghan. Newman resigned the rectorship in 1858 and Crofton also departed, taking employment at Jesuit colleges in France before being appointed mathematics master at the Royal Military Academy, Woolwich, in February 1864.

James Joseph Sylvester FRS (1814-1897), a mathematician of international renown and professor of mathematics at the academy from 1855 to 1870 'stimulated into activity the exceptional mathematical prowess of his colleague, and communicated some of his original work to the Royal Society ... with the result that at his first nomination, in 1868, [Crofton] was elected a Fellow' (Larmor, xxix). Crofton sent only one paper to the society, its lengthy title explaining what is now known as geometric probability: 'On the theory of local probability, applied to straight lines drawn at random on a plane, the methods used being also extended to the proof of certain new theorems in the integral calculus' (PTRS, 158, 1868, 181-99).

The subject of geometric probability had originated in France about 1777 as the Buffon needle problem and was attracting growing interest in Britain due to numerous notes in the Educational Times and important questions posed by Sylvester and published in the British Association Report for 1865. Characteristically, one seeks the probability of a convex disc intersecting a line when tossed at random onto a plane ruled by parallel lines. French scholars took up Crofton's ideas; eventually two theorems bore his name and the subject became of applied importance. In their day his contributions were viewed as a new methodology of integral calculus. Crofton recapitulated his own contributions in 'On local probability', the last section of his major article, 'Probability', published in the ninth edition of the Encyclopaedia Britannica (1885), 19.768-88.

On Sylvester's departure from the academy Crofton, although a junior member of the mathematical staff, was appointed professor in February 1870. His subsequent research focused more on statics and mechanics, in line with his teaching responsibilities. He was on the council of the London Mathematical Society in 1871-3, serving as its vice-president in 1872 and published in its Proceedings from the inception of the journal in 1866. He published at least twenty articles after 1862, in addition to his contributions to the Educational Times. When the Royal University of Ireland was created in 1882 he served as one of the Catholic fellows for about a decade.

Crofton retired from the academy in March 1884. He appears to have been estranged from his wife, for shortly after her death in Dublin on 27 March 1892 he married Catherine (Kate) Charlotte (1853?-1945), daughter of Holland Taylor. Crofton was an exceedingly private individual. According to Larmor he 'had a large acquaintance with the classical and general literature. This, in addition to a most amiable and kind-hearted disposition, endeared him greatly to those who had the privilege of his acquaintance' (Larmor, xxx). Of Crofton's five children William John Camille Crofton (1858-1940), born at Orléans, France, became a teacher and astronomer within the Jesuit order; his daughters, Marie Robertine Crofton (b. 1860) and Josephine Adrienne Crofton (1862-1890), were at the time of the 1881 census nun and scholar respectively at the Convent of the Sacred Heart, Putney, London. Little is known of John Louis Crofton (b. 1863, d. after 1910), who was specifically excluded from his father's will; Henry Joseph Crofton (1865-1887) joined the Royal Engineers and died of a fever in Bangalore, India. The Croftons were living in Worthing, Sussex, in 1899, in Ryde, Isle of Wight, in 1906, and were at 23 Montpelier Place, Brighton, Sussex, when Morgan Crofton died at his home on 13 May 1915. According to his obituarist in The Tablet, Crofton 'remained to the end a staunch and uncompromising Catholic, singularly pious and devout in his bearing and in his habits'.

EUGENE SENETA and IRENE N. JOHNSON

Sources  
H. T. Crofton, W. B. Wright, and H. A. Crofton, Crofton memoirs (1911)
J. Larmor, 'Morgan William Crofton', Proceedings of the London Mathematical Society, 2nd ser., 14 (1915), xxix-xxx
R. Deltheil, Probabilités géometriques (Paris, 1926)
H. Salomon, Geometrical probability (Philadelphia, 1978)
R. E. Miles and J. Serra, eds., Geometrical probability and biological structures [Paris 1977] (1978)
The war office list and directory for the civil departments of the British Army, 1863-1937 (1986) [list for 1905]
J. S. Crone, A concise dictionary of Irish biography (1928)
F. C. Burnand, ed., Catholic who's who and yearbook (1915)
'Father William Crofton', Our dead: memoirs of the English Jesuits who died between June 1939 and December 1945, 1 (1947-8), 108-12
The Tablet (22 May 1915), 662
CGPLA Eng. & Wales (1915)
Burtchaell & Sadleir, Alum. Dubl.
The letters and diaries of John Henry Newman, ed. C. S. Dessain and others, [31 vols.] (1961-), vol. 4, pp. 308-10
census returns, 1881
British Civil Registration Index, June quarter 1892
CGPLA Eng. & Wales (1945) [Catherine Charlotte Crofton]
V. G. Plarr, rev., Men and women of the time (1899)
d. cert.

Wealth at death  
£6553 13s. 1d.: probate, 7 July 1915, CGPLA Eng. & Wales


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