Francis Bashforth

Quick Info

8 January 1819
Thurnscoe, near Doncaster, Yorkshire, England
13 February 1912
Brunnen, Woodhall Spa, Lincolnshire, England

Francis Bashforth was an applied mathematician who invented the Bashforth Chronograph and conducted experiments to determine air resistance. He became the leading British authority on ballistics in the late 19th and early 20th centuries.


Francis Bashforth was the son of John Bashforth (1792-1862) and Ann Haigh (1795-1868). John Bashforth, born on 24 May 1792 in Bolton Upon Dearne, Yorkshire, was a farmer who farmed land owned by the church in Thurnscoe. He married Ann Haigh, also from Bolton Upon Dearne, on 9 April 1818 with witnesses Jane Caroline Bashforth, William Bashforth, Sarah Haigh and Francis Haigh. Francis, the subject of this biography, was John and Ann Bashforth's eldest child, having younger siblings Elizabeth Bashforth (born about 1822), Charles Bashforth (born about 1825), John Bashforth (born about 1826), Thomas Bashforth (born about 1827), Timothy Bashforth (born about 1829), William Bashforth (born about 1831), Henry Bashforth (born about 1833), Ann Bashforth (born about 1836), and Catharine Bashforth (born about 1839).

Let us point our here that the obituary for Bashforth that appeared in The Times [6] gave incorrect information about Bashforth's parents and his early life. This was carried forward to other obituaries such as [7]. Bashforth's son, Charles Piggott Bashforth, pointed out these errors and gave a correct version in a letter sent to The Times which was published as [3]. There are still minor inconsistencies, however, in some of the available information about Bashforth's family which may be due to incorrect transcription from census forms or errors in filling in these forms.

Francis attended school in Brampton Bierlow, about 7 km south west of Thurnscoe, before entering Doncaster Grammar School. He was admitted as a sizar to St John's College, University of Cambridge on 3 July 1839. Being a sizar meant that he was given financial assistance but had to earn this by acting as a servant to other students. Bashforth matriculated and began his studies of the mathematical tripos at the start of the Michaelmas term in October 1839. John Couch Adams was a fellow student, also at St John's College, and with similar mathematical interests. The two competed during their undergraduate years but later became firm friends; forty years after graduating they collaborated in the publication of a book. Bashforth's excellent undergraduate performance led to him becoming a scholar and he was Second Wrangler in the tripos examinations of 1843 when he was awarded a B.A. The Senior Wrangler that year was John Couch Adams whose performance was said to have been one of the best ever. Not surprisingly Adams was the 1st Smith's Prizeman but both Bashforth and Adams were elected fellows of St John's College, Bashforth being elected on 26 March 1844.

After graduating, Bashforth followed two distinct paths. He was a Tutorial Fellow at St John's College working towards being ordained, a necessary career path for fellows until the mid 19th century, and he also worked as a civil engineer. New railway companies were springing up at this time and he worked for them surveying potential routes for new lines. This work meant that he developed his practical skills which later he would combine with his theoretical mathematical skills to make major advances in ballistics. Let us give some examples of his work as a civil engineer. In [13] Bashforth has two articles: Remarks on the mathematical principles of Mr Dredge's patent suspension bridge, and On the proper depths below water mark of cills used for drainage. He is also involved in discussions in articles (in fact his name appears 26 times in this volume). In [14] Bashforth has the article: On atmospheric traction, and he is involved in discussions in articles such as On atmospheric railways, On change of motion, and On the Aust passage bridge. A short piece by Francis Giles in this volume, illustrates the work on which Bashforth was involved:-
The proposition to build a bridge across the old passage of the Bristol Channel, at Chepstow, has arisen from the intended improved connection of South Wales with England by means of railways, and whatever may be the objects of the crossing of the Bristol Channel elsewhere, the old passage is unquestionably the point where the nearest junction of South Wales with Bristol, the West of England, and London, can be effected.

In the session of 1845 I recommended, in my evidence upon the South Wales Railway, that this bridge should be constructed with a span of 1,000 feet from pier to pier, and height of 120 feet above high water mark of spring tides. Since then, I have had a correct plan and sections made of the Channel, from which I find it practicable to place the piers on rock foundations, accessible at low water, but at distances of 1,100 feet apart. The bridge will therefore require four spans of this length, and one at each end of nearly 550 feet. In addition to which, another bridge should be built across the Wye, with one span of about 500 feet in length, and one at each end of about 250 feet each. I expressed my opinion in the session of 1845, that the suspension principle adopted at Menai Bridge and elsewhere, would not be sufficiently steady for the Aust Bridge without material improvements in it. I have accordingly, in conjunction with Mr Francis Bashforth, Fellow of St John's, Cambridge, designed a bridge for the Aust Passage, which the accompanying engraving represents; the calculations for which are subjoined, for the scrutiny of scientific men, and I have great pleasure in associating my name with Mr Bashforth's in this work.
In [15] Bashforth has two articles: Description of a universal time table, and General table for facilitating the calculation of earthworks. The first of these begins as follows:-
The calculation of Railway Time Tables is attended with considerable difficulty and liability to error, owing to the various velocities of different classes of trains and the variation of gradients and stations stopped at. The importance of the correctness of these tables, coupled with the difficulty of obtaining that result, have led me to contrive a little instrument which, when the stoppages and the time of starling and arrival are determined, will give the times of arrival at each station exactly as they appear in the bill, regard being had to varying gradients, and consequently varying velocities. There could be no doubt of the perfect success of a mere geometrical contrivance, but to remove any doubt that might he felt, and to explain my notions to my friends, I have constructed a universal time table for the main line of the Manchester and Leeds Railway, which is about 61 miles long, and has 21 stations.
The second of the 1847 articles led to his 32-page booklet [2] published in 1855, General Table for facilitating the Calculation of Earthworks, for Railways, Canals, etc with a Table of Proportionate Parts. The Preface to this highly mathematical work begins as follows:-
It appeared to the Author that a Table for facilitating the calculation of Earthwork might be so formed as to unite the great requirements of accuracy, generality, and facility of use. The accompanying Table is applicable to all combinations of "slopes" and widths of "formation level," (even when the slopes on the two sides are different,) and requires the extraction of only one number for each prismoid. It can be used with expedition for parliamentary estimates and rough comparisons, and is also capable of showing the contents of prismoids with great accuracy, by the simple addition of a few numbers when the heights are given to the 110\large\frac{1}{10}\normalsizeth or 1100\large\frac{1}{100}\normalsizeth of a foot. This is effected by a method of proportional parts similar to that employed in Tables of Logarithms.
As a Tutorial Fellow at St John's College, Bashforth was concerned about the welfare of the undergraduates he was teaching and, in 1849-50, he led a call by twenty-two of the teaching staff of the College for an increase in the number of staff involved in teaching. He took orders in the church, being ordained Deacon in 1850 and Priest in the following year by the Bishop of Ely, Dr Thomas Turton. Turton was, like Bashforth, a mathematician who had various clerical appointments. He had studied mathematics at Cambridge, had been Senior Wrangler in the mathematical tripos of 1805, and equal 1st Smith's Prizeman. He was Lucasian Professor of Mathematics at Cambridge from 1822 to 1826, Regius Professor of Divinity 1827-1842 and the Bishop of Ely from 1845. The College had various livings, consisting of land, property and churches, from which they had an income and fellows, after being ordained, were provided with a career path enabling them to marry by accepting a living. Bashforth accepted the living of Minting, near Horncastle, Lincolnshire in 1857 [12]:-
Minting was originally a Vicarage, but Dr John Newcome, Master of the College, acquired the Rectorial property and the Advowson of the Vicarage. He attached the impropriate Rectory to the Vicarage and bequeathed the Advowson to the College. When Mr Bashforth arrived at Minting he found the Church in a dilapidated condition. It was rebuilt at a cost of £816, some of which was raised locally, and help also came from College friends.
In the 1861 Census, Bashforth is recorded as rector and vicar of Minting, living in the parsonage there. He is unmarried and has three servants, a house keeper, a house maid, and a groom and gardener. He was looking to further his career in mathematics, however, and the chance came in 1864 [9]:-
Bashforth was anxious to obtain a post as professor of mathematics in the provinces, but such appointments were rare in those days. In 1864, however, he was appointed professor of applied mathematics to the advanced class of artillery officers at Woolwich, which afterwards developed into the Artillery College.
Of course, he could not both carry out his duties as vicar in Minting and as professor of applied mathematics in Woolwich [8]:-
But when the Government decided to create the Advanced Class of Artillery Officers, no candidate could be found more suitable than Bashforth; and so pressure was brought to bear on the Archbishop for leave to appoint a locum tenens of the living, while Bashforth was engaged on his official work at Woolwich, on which he entered in February, 1864.
On taking up this new position, he decided that he would undertake research, conducting experiments to determine air resistance. A knowledge of air resistance was, of course, vital information for the science of ballistics having major military applications. Moreover, it had become apparent in the Crimean War (1853-1856) that the British suffered from having obsolete equipment. He wrote:-
Feeling that the satisfactory solution of any question in gunnery depends upon the construction of a trustworthy chronograph, it therefore became my duty to recommend that a proper instrument should be procured, and that a systematic course of experiments should be undertaken to determine, in the first instance, the resistance of the air to the motion of projectiles.
He invented the Bashforth Chronograph, beginning experiments with it in April 1864. He reported on these experiments in a series of works: Description of a Chronograph adapted for measuring the varying velocity of a body in motion through the air and for other purposes (1866), A mathematical treatise on the motion of Projectiles founded chiefly on the results of experiments made with the author's chronograph (1873), and Revised account of the experiments made with the Bashforth Chronograph, to find the resistance of the air to the motion of projectiles, with the application of the results to the calculation of trajectories according to J Bernoulli's method (1890).

For Bashforth's Prefaces to some of these works, in which he gives fascinating information about his approach and difficulties he encountered, see THIS LINK.

On 14 September 1869 Bashforth married Elizabeth Jane Piggott (1841-1916), daughter of the Revd Samuel Rotton Piggott, vicar of Bredgar, Kent, and his wife Catherine Elizabeth Debaufer. They had one son, Charles Piggott Bashforth, born at Minting on 14 July 1872, who like his father became a priest in the Church of England.

In the 1871 Census, Bashforth is recorded as vicar of Minting, Lincolnshire, but he is living at 15 Campbell Terrace, Plumstead, Kent. The only other person living with him is his wife Elizabeth Bashforth. He had in fact planned to return to the parsonage in Minting in the spring of 1868. He had written in a letter [12]:-
Sometime ago I intimated to the Council of Military Education that I should feel it to be my duty to avail myself of the first convenient opportunity to make a definite choice between my Living and Professorship; for my Living being distant, I am seldom able to visit it, and I have a decided objection to become the permanent non-resident incumbent of a Living. In many respects I regret that circumstances compel me to give up Woolwich, and I suggest that the spring of 1868 (when the members of the Advanced Class disperse) will be a convenient time for my retirement. By that time I hope that the experiments at present authorised will have been completed.
In fact he did not return to his role as vicar until 1872. Although after that he did no more experimenting, he did mathematical calculation on results of experiments which were sent to him and he wrote a number of books. One of these books was co-authored with John Couch Adams, namely An attempt to test the theories of capillary action by comparing the theoretical and measured forms of drops of fluid, with an explanation of the method of integration employed in constructing the tables which give the theoretical forms of such drops (1883).

In 1904 he was elected an Honorary Fellow of St John's College and received the following notification [12]:-
At last I am able to congratulate the College on your election, by the unanimous vote of the Council, to an honorary fellowship. Again and again, for many years past, I have tried to bring this about, but for want of professional backing up, I could not carry my point. Now Greenhill has borne testimony and all were heartily glad to do you justice. Thus Adams, Gifford and you, three B.A.'s of 1843, have received the highest honour which the College can confer. I hope you enjoy and may long enjoy good health. I am sure Mrs Adams will rejoice when she hears the news, ever yours John E B Mayor.
As to Bashforth's interests outside applied mathematics, his family and his duties as vicar of Minting, we note [12]:-
In his younger days he spent his vacations in walking tours, visiting Germany, Switzerland, the Tyrol, and other places. In 1866 he visited Scotland with the late Professor J C Adams.
Bashforth died in Woodhall Spa, aged 93, after three weeks' illness.

References (show)

  1. Bashforth, Francis, in Encyclopaedia Britannica 30 (1922).
  2. F Bashforth, General Table for facilitating the Calculation of Earthworks, for Railways, Canals, etc with a Table of Proportionate Parts (E & F N Spon, London, 1855).
  3. C P Bashforth, Correction, The Times (23 February 1912).
  4. Fabio, Gli Inizi, Introduzione alla balistica esterna (3 November 2010).
  5. Francis Bashforth 1819-1912, Science Museum Group.
  6. Francis Bashfort, The Times (14 February 1912).
  7. Francis Bashfort, Yorkshire Weekly Post (17 February 1912).
  8. G Greenhill, The Reverend Francis Bashforth, B.D., The Eagle 34 (1912-13), 109-111.
  9. G Greenhill (rev. A McConnell), Bashforth, Francis (1819-1912), Oxford Dictionary of National Biography (2004).
  10. J H Hardcastle, Bashforth, 1819-1912Arms and Explosives 20 (1912), 108-111.
  11. Obituary. Rev Francis Bashforth, B.D., The Eagle 33 (1911-12), 215-216.
  12. Obituary. Rev Francis Bashforth (1843), The Eagle 34 (1912-13), 257-260.
  13. The Civil Engineers and Architects Journal VIII (1845).
  14. The Civil Engineers and Architects Journal IX (1846).
  15. The Civil Engineers and Architects Journal X (1847).
  16. J Venn and J A Venn (eds.), Bashforth, Francis, in Alumni Cantabrigienses: A Biographical List of All Known Students, Graduates and Holders of Office at the University of Cambridge, from the Earliest Times to 1900 Volume 2: From 1752 to 1900. Part 1: Abbey-Challis (Cambridge University Press, 2011).

Additional Resources (show)

Other websites about Francis Bashforth:

  1. Dictionary of National Biography

Cross-references (show)

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