John Hellins

Born: 1749 in North Tawton, Devon, England
Died: 5 April 1827 in Potterspury, Northamptonshire, England

John Hellins was born into a poor family. His father worked as a labourer at Ashreigney, a small village about 5 km west of Chulmleigh, in Devon. Both these places are around 20 km south of Barnstaple. His date of birth is unknown but his age at death, namely 78, is recorded in the Potterspury Burial records. R Polwhele describes Hellins' education (or perhaps, more accurately, we should say lack of education) in [6]:-
... he learned to write by himself; but, be that as it may, his education at best did not extend beyond the first four rules of arithmetic. By occasionally looking on, he literally stole the art of a cooper, and worked at that business as a livelihood till about twenty years old.
In fact he worked as a cooper, making and repairing wooded casks and barrels, at Chumleigh. However, during these years he taught himself elementary mathematics and this led to his finding work as a school teacher [6]:-
Having in the meantime purchased Emerson, and some other mathematical books, without the help of a master, he made himself well acquainted with algebra, etc. Showing his books one day to a schoolmaster of the vicinity, the latter, on conversation with him, perceived more learning than generally falls the lot of a maker of pails, and being asked, soon after, whether he knew of any young man fit to teach writing etc in a small neighbouring school then vacant, he recommended our cooper.
In fact the small school where Hellins had become a master was at Bishop's Tawton, a village close to the south side of Barnstaple. While he was teaching at this school, he became friendly with Malachy Hitchins (1741-1809), who had done computations for Nevil Maskelyne working in his own home and later had worked at Greenwich for a while as his assistant. At the time when he became friendly with Hellins, Hitchins had taken holy orders and left Greenwich to become vicar of Hennock, Exeter. He was later vicar of both St Hilary, Cornwall, and of Gwinear. He recommended Hellins to Maskelyne, suggesting that he would make an excellent assistant. In 1773 Hitchins became Maskelyne's assistant at the Royal Observatory at Greenwich. He was given board and lodgings at the Royal Observatory and, in addition, an annual salary of £86. He continued to study, however, making up for the schooling he had missed [6]:-
While his nights were engaged at [the Royal Observatory at Greenwich] in stargazing for Dr Maskelyne, he was employed by day in studying Latin and Greek, which at length enabled him to get into holy orders.
Note that Hitchins had also taken holy orders while he was Maskelyne's assistant. From 1779 Hellins served as a Curate at the village of Constantine, Cornwall, 8 km south west of Falmouth and less than 40 km from Land's End. In 1780 his paper Theorems for computing logarithms was published in the Philosophical Transactions of the Royal Society, having been communicated by Nevil Maskelyne. We learn something of Hellins' character from this paper so we quote the introduction and the conclusion [4]:-
The utility of logarithms is so well known, that much need not be said upon it. In our days he must be a slender mathematician who does not know that they are useful, not only in trigonometry, navigation, astronomy, the calculation of compound interest and annuities, but also in the finding of fluents, and the summation of infinite series. Some of the greatest mathematicians that this kingdom ever produced, as Sir Isaac Newton, Dr Halley, Mr Cotes, and Mr Simpson, have thought it not beneath them to improve the construction of logarithms, which strongly argues the utility of those artificial numbers, and may suggest to us that the construction of them cannot be much further improved. Now, although we should be very diffident in our expectations of improvement in any part of the mathematics after it has been handled by such great men, yet, if the method of computing be in general long and tedious, or if there still remain any particular difficulty, I believe, no good reason can be given why every attempt to abridge the one, or remove the other, should be discouraged.
After giving his theorems, Hellins then writes:
The observations and reasonings which led me to the discovery of the above theorems, I imagine, need not here be mentioned. Such as they are, I beg leave to lay them before the candid an skilful in these matters, in hopes that the invention will appear to them, as it does to me, to be a useful one. It has, indeed, been objected, by a gentlemen of my acquaintance, that improvements in the construction of logarithms cannot now be useful, because logarithms are already constructed. I answer, that argument, if it has any weight, operates equally against Sir Isaac Newton, Dr Halley, Mr Cotes, and Mr Simpson, and several other ingenious mathematicians; for logarithms were invented, and tables of them constructed, before their time; so that if I should be thought to have misemployed my time in improving the computation of these artificial numbers, I have some consolation in thinking that I have therein followed the example of the very respectable company just mentioned. I trust, however, that, with mathematicians, every improvement in calculation will be acceptable.
In 1783 Hellins left Constantine to take up a position at Easton Neston, near Towcester, Northamptonshire, as a teacher of mathematics to Lord Pomfret's children, George and Thomas Fermor (who were fifteen and thirteen). In 1789 he returned to a position in the Church, being appointed as a Curate in Green's Norton, south of Northampton, and just to the north of Towcester. This was close to where he had taught Lord Pomfret's children for the Easton Neston estate and Green's Norton are on opposite sides of Towcester. On 4 July 1789 he was admitted to Trinity College, Cambridge as a 'Ten-year man' to undertake work in divinity for a B.D. which he was awarded in 1800. A 'Ten-year man' was a mature student who could proceed to the divinity degree without first obtaining a B.A. Hellins only held the curacy at Green's Norton for a year before he was presented as vicar at Potterspury, Northamptonshire, by Henry Bathurst, the Second Earl Bathurst. On 10 November 1794 Hellins married Anne Brock of North Tawton; they had one son.

Hellins published many papers; the following were all in the Philosophical Transactions of the Royal Society: A new method of finding the equal roots of an equation by division (1782); Dr Halley's method of computing the quadrature of the circle improved; being a transformation of his series for that purpose, to others which converge by the powers of 60 (1794); Mr Jones' computation of the hyperbolic logarithm of 10 compared (1796); A method of computing the value of a slowly converging series, of which all the terms are affirmative (1798); An improved solution of a problem in physical astronomy, by which swiftly converging series are obtained, which are useful in computing the perturbations of the motions of the Earth, Mars, and Venus, by their mutual attraction (1798); A second appendix to the improved solution of a problem in physical astronomy (1800); and On the rectification of the conic sections (1802). He was elected a fellow of the Royal Society in 1796 and, mainly for his 1798 paper mentioned above, he received the Copley Medal from the Royal Society in 1798. Again to illustrate Hellins' contributions, we quote from his 1802 paper whose title we gave above:-

The utility of hyperbolic and elliptic arches, in the solution of various problems, and particularly in the business of computing fluents, has been shown by those eminent mathematicians, Maclaurin, Simpson and Landen; the last of whom has written a very ingenious paper on hyperbolic and elliptic arches, which was published in the first volume of his 'Mathematical Memoirs', in the year 1780. I have indeed heard that some improvement in the rectification of the ellipse and hyperbola had been produced, and some of the same theorems discovered by a learned Italian many years before Mr Landen's 'Mathematical Memoirs' were published; but, as Mr Landen has declared that he had never seen or heard any thing of that work, and as various instances are found of different men discovering the same truth, without knowledge of each other's works, I see no reason for disbelieving him. But I have seen no writings on this subject which contain anything more than what is very common, besides those of the three gentlemen above mentioned, and Dr Waring's 'Meditationes Analyticae'; and, while I have no inclination to detract from their merits, I may be allowed to say that I have borrowed nothing from their works.
Hellins also published articles in other journals, for example in the British Critic, a quarterly church review journal established in 1793. In this journal he published On Mr Wales method of finding the longitude in 1795. This was a commentary on William Wales (1734-1798) work The Method of Finding the Longitude by Timekeepers (1794). He published On Bishop Horsley's mathematical treatises in 1803. This discussed treatises by Samuel Horsley (1733-1806) who was a mathematician and bishop of Rochester from 1792. Hellins published three articles in the British Critic entitled On Donna Agnesi's 'Analytical Institutions' in 1804 and 1805. In fact Hellins had edited the translation by Colson of Maria Gaetana Agnesi's Instituzioni analitiche ad uso della gioventù italiana. This English translation of the 1748 Italian work had been published in 1801. Next he published, On Keith's 'Trigonometry', in the British Critic in 1808, discussing An introduction to the theory and practice of plane and spherical trigonometry by the English mathematician Thomas Keith (1759-1824). Finally let us mention Hellins' 1811 article On F Baily's work on the 'Doctrine of Interest and Annuities' which discussed The Doctrine of Interest and Annuities (1808) written by the astronomer Francis Baily (1774 -1844) who is famed for 'Baily's beads' observed during an eclipse of the Sun.

Davis Gilbert, President of the Royal Society, explained another aspect of Hellins' contributions in a tribute some months after he died (see [5] and [2]):-

Mr Hellins at one time computed for the National Almanac. He afterwards assisted at Greenwich. And, what is now perhaps almost unknown, he furnished the late Mr Windham with all the calculations and tables on which that gentleman brought forward his new military system, as Minister of War, in 1806.
Jack Clamp writes in [3] about Hellins' founding of a school in Potterspury during his time as the vicar there:-
John Hellins carried out his work as a country vicar, and perhaps mindful of his own early years, in 1817 he persuaded the local landowner, the 4th Duke of Grafton to donate land and money to construct a school for the village. The school opened in March 1817 and was attended by about 50 boys - girls were not actually excluded, but none applied as they were apparently all too busy lace-making. The school was initially housed in a single room, but by October a new school building was under construction and in March 1818 Hellins reported that the building was nearly ready to have glass installed in the windows. This building is still at the heart of John Hellins School today.
Today the John Hellins School is a small primary school for children aged 4 to 11, with around 120 pupils, in Potterspury. It was named the John Hellins School in 1990.

Hellins continued to serve as vicar of Potterspury until his death in 1827. The parish church of St Nicholas, in Potterspury, contains a small white marble plaque in its North Aisle which reads:

In Memory of The Revd. John Hellins, B.D. & F.R.S.
upwards of 36 years Vicar of this parish,
who died April 5th 1827
aged 78 years.
of Anne Hellins his widow,
who died June 3rd 1827. Aged 72.

Davis Gilbert, President of the Royal Society, spoke to the Royal Society about Hellins a few months after his death (see [5] and [2]):-

John Hellins was one of those extraordinary men who, deprived of early advantages, have elevated themselves, by the force of genius and industry, to a level above most persons blessed with regular education. ... I have known Mr Hellins for above forty years, and I can testify to his virtues, It once happened that, through the late Dr Maskelyne, I had nearly obtained for him the Observatory at Dublin. The failure cannot, however, be lamented, since Brinkley was appointed in his stead.

Article by: J J O'Connor and E F Robertson

January 2013
MacTutor History of Mathematics