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Percival Frost

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Born
1 September 1817
Sculcoates, Kingston upon Hull, England
Died
5 June 1898
Cambridge, England
Summary
Percival Frost became a private coach for the Mathematical Tripos at Cambridge. His most famous pupil was William Kingdon Clifford. He wrote three excellent mathematical texts each of which ran to several editions.
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Biography

Percival Frost was the son of Charles Frost (1782-1862) and Jane Hollingworth (1795-1887). Charles Frost had a sister Elizabeth Frost, one year younger than he was, who wrote novels and historical romances. She married John Byron and began publishing under the name Elizabeth Byron, but he died aged 25, and eight years later she married the artist Jacob George Strutt. She is probably best known today for her novels and travel guides published under the name Elizabeth Strutt.

Charles, an [11]:-
... antiquary, born at Kingston upon Hull, Yorkshire, and baptised there on 3 January 1782, was the son of Thomas Frost, a solicitor in that town, and his wife, Elizabeth. He followed his father's profession, and succeeded him as solicitor to the Hull Dock Company, an appointment that he held for over thirty-three years. From his father he acquired a taste for genealogical and historical research, and while still articled he gained a reputation as an expert black-letter lawyer.
Charles married Jane Hollingworth in Holy Trinity Church, Hull, on 22 August 1814. Jane, the daughter of the merchant and mayor Andrew Hollingworth and his wife Isabella Bromby, was born in Kingston upon Hull on 19 January 1795. Charles and Jane Frost had four children: Thomas Frost (1815-1848), Isabella Frost (1816-1884), Percival Frost (1817-1898), the subject of this biography, and Andrew Hollingworth Frost (1819-1907). Charles Frost was at one time Vice-President of the British Association and several times President of the Hull Literary and Philosophical Society. Percival Frost, born 1 September 1817, was baptised on 22 September 1817 at All Saints Church, Sculcoates, Hull.

Percival Frost attended Beverley School in Beverley, a town about 12 km north west of the centre of Hull. Beverley School is probably the oldest State School in England. He attended this school until 1833 when he moved to Oakham School in Oakham School in Rutland. This famous school, founded in 1584, had John Doncaster as headmaster at this time. Doncaster had been a pupil at Oakham School before [17]:-
... he went up to Trinity College, Cambridge, as sizar, but migrated to Christ's College with a scholarship in 1791, taking his degree three years later as 13th Wrangler in the mathematical tripos and first Chancellor's Medallist, becoming a Fellow of his college in 1796 and a Doctor of Divinity in 1816.
Let us note at this time that Frost's younger brother, Andrew Hollingworth Frost (born in Hull on 26 April 1819) was also educated at Oakham School. He studied the Mathematical Tripos at Cambridge and was 11th Wrangler in 1842. Andrew Frost was appointed Mathematical Master in the Manchester Free Grammar School. He joined the Church and, after serving as a curate at Burton on Trent and at Meltham Mills, Huddersfield, he became Church Missionary Society's missionary at Nasik, Bombay 1853-69. Let us note here that he contributed papers to the Quarterly Journal of Mathematics on "Nasik Cubes", a type of magic cube, and other subjects. In 1866 he constructed and published the first known perfect cube (it is 7 × 7 × 7).

Percival Frost thrived at Oakham School under John Doncaster and began his studies of the Mathematical Tripos at Gonville and Caius College, Cambridge on 4 April 1835. He transferred to St John's College, Cambridge on 14 October 1835 where he held a scholarship. At this time Charles Babbage was Lucasian Professor of Mathematics and George Peacock was appointed Lowndean professor of astronomy and geometry at Cambridge in 1836. His tutor at St John's College was John Hymers who was, like many at Cambridge at that time, combining a career in mathematics with ordination to the Church. Hymers had been appointed a fellow of St John's College in 1827 and, in 1832, became a tutor at the College. He was Moderator of the mathematical tripos in the years 1833 and 1834, but was also studying divinity. He was ordained priest in 1834, was awarded a B.D. in 1836, became a senior fellow of St John's College in 1838 and in the same year was elected a fellow of the Royal Society of London.

There were a number of excellent undergraduate mathematicians at St John's College in the same year as Frost. In 1839 he graduated with a B.A. being ranked Second Wrangler (Wrangler equals First Class degree). In fact the top four Wranglers in the Mathematical Tripos were all students of St John's College: Senior Wrangler, Benjamin Morgan Cowie; Second Wrangler, Percival Frost; Third Wrangler, Charles Colson; and Fourth Wrangler, George Fearns Reyner. Before continuing to describe Frost's career, let us say a little about the careers of the other three Wranglers just mentioned.

Benjamin Morgan Cowie (1816-1900) became a fellow of St John's College, 1839-43, and was ordained a priest in 1842. He was Professor of Geometry in Gresham College, then one of H.M. Inspectors of Schools, 1857-72, and Dean of Manchester, 1872-83. He was much involved in educational causes when in Manchester, serving as a governor of Manchester grammar school, a member of council of Owens College, and a supporter of the founding of Manchester High School for Girls. Charles Colson (1818-1901) entered the Church being ordained in 1841 and was vicar of Great Hormead, Hertfordshire from 1842 to 1874. George Fearns Reyner (1817-1892) became a fellow and Senior Bursar of St John's College and then Rector of Staplehurst for sixteen years.

Although Cowie was Senior Wrangler, it was Frost who was chosen as First Smith's Prizeman in 1839. He was elected a fellow of the St John's College on 19 March 1839. His tutor John Hymers advised him to study law and indeed he took this advice and began his studies being admitted to the Inner Temple on 12 November 1839. During the 1840 summer vacation, he returned to Cambridge and coached private pupils for the Mathematical Tripos and, enjoying teaching mathematics far more than studying law, he took up full time tutoring.

On 2 June 1841 Frost married Jennett Louisa Dixon, the daughter of Richard Routh Dixon and Jennett Baillie of Oak Lodge, Finchley. The wedding was in St Mary Church, Finchley, and the witnesses included Percival Frost's father Charles Frost, his brother Andrew Hollingworth Frost, his sister Isabella Frost, and the bride's father Richard Dixon. Percival and Jennett Frost had one son, Charles Frost (1842-1906) who, from 1876, called himself Charles Frost Foster. At the time of Percival Frost's marriage, the rules did not allow college fellows to be married, so Frost had to resign his fellowship at St John's College. He joined the Church, being ordained deacon at Ely in 1841 and ordained a priest in the following year.

He was a Mathematical Lecturer, first at Jesus College, Cambridge, from 1847 to 1849 and afterwards at King's College, Cambridge, from 1860 to 1890. He was elected a Fellow of the Royal Society on 7 June 1883 having been proposed by J C Adams; A Cayley; N M Ferrers; W H Besant; Rayleigh; I Todhunter; E J Routh; J W L Glaisher; Charles C Badington; and R B Clifton. The citation for his election is as follows [10]:-
Citation for the Revd Percival Frost. Author of the following separate Works, viz Newton's Principia, Sections I, II, III. with Notes & Illustrations. 3rd Edn; Solid Geometry. 2nd Edn. 1875; An elementary Treatise on Curve Tracing. 1872; and of numerous original papers on subjects in Pure and Applied Mathematics, published in the Cambridge and in the Cambridge & Dublin Mathematical Journal, and in the Quarterly Journal of Mathematics, including papers in Algebra, Theory of Curves, Solid Geometry, Lunar & Planetary Theories, Potentials & Attraction of Ellipsoids, Electro-Dynamics &c, &c. He is distinguished for his knowledge of Mathematical Science.
He was elected a Fellow of King's College, Cambridge, also in 1883. In 1882 Cambridge had introduced the degree of Sc.D., Doctor of Science, and Frost was awarded the degree in 1883. Throughout his career, he privately tutored students for the Mathematical Tripos and in this he was very successful. His most famous pupil was William Kingdon Clifford who, like Frost himself, was a Second Wrangler [27]:-
Early in [Clifford's] career at the University he read such portions of the Tripos subjects as possessed any interest for him, and soon turned his attention to the study of the original writings of Sylvester, Cayley, Salmon, and some of the great Continental masters. In vain did his private tutor, the Rev Percival Frost, who always had the highest admiration for him, and was anxious that he should attain his proper place in the Mathematical Tripos, urge him to devote a little more attention to examination subjects; his mind could tolerate no such restraint; nothing but the fresh and original thoughts of the greatest mathematical writers could satisfy his wants. His neglect of the examination subjects was such that it is said he only once wrote out a paper of bookwork questions, and that under the impression that he was solving problems; many also, well qualified to judge, were agreeably surprised when he obtained the position of second Wrangler in the Mathematical Tripos of 1867, while his success in obtaining the second Smith's prize was doubtless anticipated from the wider scope for his talents by that examination.
Among the many other students Frost tutored let us mention John Rigby (1834-1903) who studied the Mathematical Tripos at Trinity College, Cambridge, graduating as Second Wrangler in 1856 and also placed Second Smith's Prizeman in that year. Rigby was called to the Bar at Lincoln's Inn in 1860 and became a Queen's Counsel in 1881. He was elected as a Liberal Member of Parliament, sitting in the House of Commons 1885-86 and 1892-94. He resigned in 1894 when he was appointed a Lord Justice of Appeal. Frost was also the tutor of Joseph Wolstenholme who has a biography in the MacTutor Archive. Wolstenholme studied the Mathematical Tripos at Corpus Christi College and was Third Wrangler in 1850. The First Wrangler in that year was William Henry Besant (1828-1917), who became a lecturer at Cambridge teaching William Burnside and George Ballard Mathews, and the Second Wrangler was Henry William Watson. Frost was also tutor to the Senior Wrangler Augustus Vaughton Hadley of 1856. Hadley became a clergyman and H.M. Inspector of Schools but died aged 33 in 1867.

It is, perhaps, as an author of textbooks that Frost is best remembered today. He published three mathematics books, all of which have run to several editions. These were mentioned in the citation for his election to the Royal Society of London (see above). The first editions of these are: Newton's Principia, Sections I, II, III with Notes and Illustrations also A collection of problems principally intended as examples of Newton's methods (1854); (with Joseph Wolstenholme) A Treatise of Solid Geometry (1863); and An Elementary Treatise on Curve Tracing (1872). The first of these, Newton's Principia, ran to three editions, the second being in 1863 and the third in 1880. Changes in these editions are minimal. He writes in the Preface to the Third Edition of 1880:-
In this edition I have introduced some notes on the geometrical solution of some problems relating to maxima and minima, and I have placed the investigations of the properties of the curves, which, after the conic sections, are the best examples for illustrating geometrical methods, in a more prominent position, at the end of the first section.
It was republished by Forgotten Books in 2018 and, remarkably, the Amazon website still (in 2024) claims to sell new copies of the 1863 edition. You can read the Preface to the first two editions at THIS LINK.

Frost co-authored A Treatise of Solid Geometry with Joseph Wolstenholme and the joint work was published in 1863. The Second Edition of 1875 is, however, a single authored work by Frost. He explains the reason in the Preface:-
It was with a feeling of great discouragement that I began the preparation of another Edition of this work, deprived, as I was, of the valuable assistance of my friend Mr Wolstenholme, in working with whom I had had so much pleasure while writing the First Edition. Mr Wolstenholme, who is now Professor of Mathematics in the Royal Indian Engineering College at Cooper's Hill, thought that there would be great difficulty in carrying on this work satisfactorily by correspondence, even if the important duties in which he is engaged did not fully occupy his time; I was, therefore, reluctantly obliged to undertake the whole labour of remodelling our original work.
This edition was republished by BiblioBazaar in 2009 and new copies, both hardback and paperback, are still available today (2024) at Amazon. For the Preface of the 1863, the 1875 and the 1886 editions, see THIS LINK.

We should note that Frost published Hints for the Solution of Problems in the Third Edition of Solid Geometry in 1887. He writes in the Preface:-
The fulfilment of my promise to give an appendix, containing solutions or hints for the solution of all the problems given in my Third Edition of Solid Geometry, has entailed much labour; but this labour will not have been thrown away if it should in any degree have added to the usefulness of the book; at all events it has enabled me to detect many errors and omissions in the statement of the problems which might have given trouble to the student.
The third book by Frost which we mentioned above is An Elementary Treatise on Curve Tracing. A second edition was published by Frost in 1892. In 1918 a Fourth Edition was published, revised by the Scottish mathematician Robert John Tainsh Bell. Harold Hilton writes in the review [13]:-
Doubtless many will welcome this new edition of an old friend of 1872, to which has been added an index and classified list of curves. But perhaps the reviewer may be forgiven for a wish that Dr Bell had undertaken the bolder task of entirely reconstructing Dr Frost's material and bringing the whole up to date. It seems that the book was originally intended to provide interest and exercise for the student before he enters on the study of the calculus, mechanics, and the field of the Physical Sciences. Such a suggestion now appears to emanate from another world, and the dodges employed by Dr Frost to avoid the use of the calculus are fortunately quite obsolete.
A fifth edition of this book was published by the Chelsea Publishing Company in 1960, almost a hundred years after it was written. In 2012 RareBooksClub reprinted the 1892 edition. You can read the Preface to the 1872 edition at THIS LINK.

Henry Arthur Morgan recalls in [15] and [16] other aspects of Frost's interests and abilities:-
But it was not only in Mathematics that Dr Frost's talents lay. On the contrary he was a many sided man. He found pleasure in music and painting, and had read widely. I remember when at Heidelberg he said he was ready to challenge any German there to a match in playing Bach's music at sight. His pretty water colour sketching was also an unceasing source of delight in his vacations spent on the Continent and elsewhere. He was also a very skilful billiard player with a thorough knowledge of the science of the game, an accomplished chess player, and before he was troubled by lameness brought on by sciatica, the result probably of sitting on damp ground, he took much active exercise and was proficient as a tennis player, in cricket, in running and swimming.
The following account is given in [21] about Frost and cricket:-
"While at Cambridge," says Mr McCormick, "I was one day playing on Parker's Piece, and Percival Frost, the celebrated mathematician, was in with me. I hit a very fast bowler hard to leg and ran 9 for it. It took three men to throw the ball up. Visiting Cambridge only a few months before Frost's death, he said at a dinner-party, "I remember one of your hits, when you nearly killed me with running! That was the hit for 9."
John Robert Lunn (1831-1899) was Fourth Wrangler in the Mathematical Tripos in 1853. He was ordained a deacon in 1855 and a priest in the following year. He was elected a fellow of St John's College and was Sadleirian Lecturer of Pure Mathematics 1857-1864. Lunn was a remarkably talented musician and, during the years that he was at St John's College, Frost would often visit his rooms and the two would enjoy sharing music and conversation. Lunn's obituary [24] contains the following:-
It is acknowledged that he and the late Mr Percival Frost were the first amateur Bach performers in England ...
In 1891 Frost and his wife celebrated their golden wedding. The Hull Daily Mail contained a report which begins as follows [1]:-
The Fellows' Gardens of King's College were the scene of no less an auspicious and almost unique event than the celebrating of the golden wedding of Dr Frost (the Senior Fellow of King's) and Mrs Frost, whose popularity has won for them a large circle of friends, in both town and University. Some 350 ladies and gentlemen, including several of the masters of the College, as well as gentry of the neighbourhood, attended the festivities, and were well received by the happy and favoured couple in a marquee, handsomely furnished in drawing room style. Many were the token of congratulation tendered to Dr and Mrs Frost, and the more valuable presents consisted of a pair of gold candlesticks, gold cup, a gold chain and truss, and a gold workbox. The pleasant proceedings were brought to an ultimate termination by a heavy rain shortly after 5.30, which necessitated a hasty retreat to some substantial shelter.
For the whole of this report and four obituaries of Frost, see THIS LINK.

Frost died at Cambridge on 5 June 1898, in his house at 15 Fitzwilliam Street, and was buried on 10 June in the Mill Road cemetery. His grave lies in the parish area of St Mary the Less and is located on the north side of the path leading from the centre circle to the east path. The inscription on his grave reads [14]:-
To the dear memory of the Rev Dr Percival Frost F.R.S. Fellow of King's College Cambridge born Sept 1 1817 died Trinity Sunday June 5 1898. "The souls of the righteous are in the hand of God and there shall no torment touch them. Wisdom [3.1]"
His wife Jennett Louise Frost died on Epiphany Sunday, 6 January 1901, aged 82. She is buried in the same grave as her husband.

Let us end by clearing up some confusion. The Online Books Page gives publications by Percival Frost but the list gives books by two different authors with the same name. The confusion is totally understandable since both wrote under the name "Rev Percival Frost, M.A., Late Fellow of St John's College." The mathematics texts are, of course, by the subject of this biography, but those involving translation from Greek and Latin are by a different Percival Frost. This Percival Frost (1825-1877) was born in Hull on 15 October 1825, the son of the master mariner Samuel Frost. He studied classics at St John's College, was awarded a B.A. in 1848, and was ordained a priest in 1849. The confusion is increased by the fact that, in 1850, he married Fanny Dixon, the younger sister of Jennett, the wife of the mathematician Percival Frost.

Other Mathematicians born in England
A Poster of Percival Frost

References (show)

  1. A Golden Wedding, Hull Daily Mail (25 June 1891).
  2. E I Carlyle, Frost, Percival (1817-1898), Dictionary of National Biography 1901 Supplement 2 (The MacMillan Company, New York, 1901).
  3. P Frost, Newton's Principia Sections I, II, III with Notes and Illustrations also A collection of problems principally intended as examples of Newton's methods (MacMillan and Co, Cambridge, 1854).
  4. P Frost, Newton's Principia Sections I, II, III with Notes and Illustrations also A collection of problems principally intended as examples of Newton's methods (Second Edition) (MacMillan and Co, Cambridge, 1863).
  5. P Frost and J Wolstenholme, A Treatise on Solid Geometry (MacMillan and Co, Cambridge, 1863).
  6. P Frost, A Treatise on Solid Geometry (Second Edition) (MacMillan and Co, Cambridge, 1875).
  7. P Frost, A Treatise on Solid Geometry (Third Edition) (MacMillan and Co, Cambridge, 1886).
  8. P Frost, An Elementary Treatise on Curve Tracing (MacMillan and Co, Cambridge, 1872).
  9. P Frost, An Elementary Treatise on Curve Tracing (Second Edition) (MacMillan and Co, Cambridge, 1892).
  10. Frost; Percival (1817 - 1898), Record, The Royal Society.
    https://catalogues.royalsociety.org/CalmView/Record.aspx?src=CalmView.Persons&id=NA6657
  11. G Goodwin, Frost Charles, Dictionary of National Biography 1885-1900, Vol 20 (MacMillan and Co, 1889), 285.
  12. G B Halsted, Percival Frost, The American Mathematical Monthly 6 (8/9) (1899), 189-191.
  13. H Hilton, Review: An Elementary Treatise on Curve Tracing by Percival Frost, The Mathematical Gazette 9 (139) (1919), 327.
  14. Jennett Louise Frost; Percival Frost, Mill Road Cemetery.
    https://millroadcemetery.org.uk/frost-jennett-louise/
  15. H A Morgan, Obituary: Percival Frost Sc.D., F.R.S., The Eagle 20 (1899), 445-448.
  16. H A Morgan, In Memoriam. Rev Dr Frost F.R.S., The Cambridge Review (16 June 1898), 405.
  17. B Needham, Oakham School's Masters and Ushers 1584-1875, Rutland Record 32 (2012), 66-78.
    http://www.rutlandhistory.org/rutlandrecord/rr32.pdf
  18. Percival Frost, Cambridge Alumni Database, University of Cambridge.
    https://venn.lib.cam.ac.uk/cgi-bin/search-2018.pl?sur=&suro=w&fir=&firo=c&cit=&cito=c&c=all&z=all&tex=FRST835P&sye=&eye=&col=all&maxcount=50
  19. Percival Frost, The Online Books Page.
    http://onlinebooks.library.upenn.edu/webbin/book/lookupname?key=Frost%2C%20Percival%2C%201817%2D1898
  20. Percival Frost, Mill Road Cemetery.
    https://millroadcemetery.org.uk/frost-percival/
  21. A W Pullin, Talks with Old English Cricketers (William Blackwood and Sons, 1900).
  22. Rev Andrew Hollingworth Frost: Obituary, The Eagle 29 (1908), 222.
  23. H M Taylor, Frost, Percival, Proceeding of the Royal Society 64 (1898-99), vii-viii.
  24. K H S, Obituary: The Rev John Robert Lunn, The Eagle 20 (1899), 730-731.
  25. Success of a Hull Lady, Hull Daily Mail (16 June 1886), 2.
  26. J Tompson, Frost, Percival, Oxford Dictionary of National Biography (Oxford University Press, 2004).
  27. William Kingdon Clifford, Nature (13 March 1879), 443-444.

Additional Resources (show)

Honours (show)

Honours awarded to Percival Frost

  1. Fellow of the Royal Society of London 1883

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update June 2024