See also: Henry Glanville Barnacle – astronomer
Septimus Tebay, born in 1820, the son of a publican in Ellel, near Lancaster, moved with his family to Preston as a teenager where he became recognised as a mathematical prodigy. So remarkable were his abilities that a group of local gentlemen in the town funded his studies at Cambridge where he gained a first-class degree and was a serious contender to become senior wrangler, the title given to the graduate gaining the highest marks in the final exams.
After graduation, he took holy orders and shortly afterwards was appointed headmaster of Rivington Grammar School where he served for nearly 20 years, leaving to run private schools in Bolton and Farnworth. He does not appear to have prospered, for by the last decades of his life he was living in terraced houses in the back streets of Farnworth. He died in the Farnworth workhouse, where he had been admitted by reason of ‘old age and destitution’. None of his family seems to have matched him in middle-class respectability, with the exception of one of his daughters who married an architect. All the other family connections I have been able to trace are firmly working class, many of them illiterate, including, at the time of his marriage, his wife.
Anne Kidson, a descendant of one of Septimus’s brothers, has been researching the family for years. Her discoveries about Septimus which she has very generously shared can be found here.
Septimus was born 14 April 1820 to Jonathan Tebay, a publican of Ellel, near Lancaster, and his wife Grace. He was baptised 4 May 1820 at St Michael’s, Cockerham.  His name suggests aspirations to gentility on the part of his parents, but, in fact, the name was a favoured first name for the Tebays, a decidedly plebeian family living on the borders of Westmorland and Yorkshire. The use of the name can be traced back to the 17th century when a Septimus Teeba was baptised at Sedbergh on 10 July 1684.  Another, more contemporary Septimus was born 5 July 1802, the son of Septimus Tebay, at Newton and baptised at Michael the Archangel, Whittington. And another Septimus Tebay was baptised on 1 May 1837 at All Saints, Wigan, the third son of Thomas and Margaret Tebay, of Winstanley. 
The Tebays were still at the Ellel public house in 1821, when Septimus’s sister, Nancy, was born. In the baptism records Jonathan is described as an innkeeper at Ellel. By 1824, when another daughter, Agnes, was born, they had probably moved; she was baptised at Lancaster, and in the 1861 census she is listed as born in Dolphing. The birth place is probably a mishearing of the place name Dolphinlee, for by 1826, when Septimus’s brother Jonathan was born, the father was described as a farmer of Bulk, a district on the north-east outskirts of Lancaster, of which Dolphinlee was a part. The same baptism records have Jonathan farming at Bulk in 1832, but at nearby Skerton in 1834, when a daughter, Elizabeth, was baptised. 
While the family were living in the Lancaster area it is possible that Septimus attended Lancaster and Heversham grammar schools. The listing for Septimus in Frederic Boase’s Modern English Biography records him as being educated at Lancaster and Heversham.  Boase cites his source as Sparke’s Bibliographia Boltoniensis which states that Septimus ‘was educated at Lancaster School, and winning a scholarship, proceeded to Heversham School’. This conflicts with a report that he had at best a rudimentary early education (see below). 
By 1836 the family had moved to Preston and were then living in Walker Street, for in that year young Elizabeth was buried there.  At the 1841 census the family, husband, wife and six children, were living in Tank Row in the town. Father Jonathan was working as a coffee roaster, Septimus, now aged 20, was described as a french polisher, and the next three eldest children were all working in cotton factories. 
An account that appeared in the Preston Chronicle when he graduated from Cambridge provides more detail about Septimus’s early years in Preston:
Mr. Tebay was originally a labourer in a mechanic’s shop in Preston, and had received scarcely more than the ordinary education of that class. After he had been thus employed for some years, he was upon one occasion attracted by a work on one of the lower departments of mathematics at an old book stall, and, purchasing it, it formed for some time the amusement and occupation of his evenings. He speedily made himself master of its contents, and he then pursued the study into the higher branches. His fondness for the pursuit became with him a passion, and he soon became known by his contributions to the Ladies’ Diary, and other mathematical publications, as a master of the exact sciences. 
By 1843 he was writing to learned journals, as shown here. 
The ‘Ladies’ Diary’ mentioned in the above Chronicle article was a serious magazine devoted mainly to mathematics. Septimus’s contribution to the 1844 issue is discussed in a recent book, Combinatorics: Ancient and Modern. The magazine editor had set the following problem:
‘Determine the number of combinations that can be made out of n symbols, p symbols in each; with this limitation, that no combination of q symbols, which may appear in any one of them shall be repeated in any other. Only two solutions were sent in, one of which ‘misunderstood the problem altogether’ and a correct one from Septimus, who was described as ‘of the Gas Works in Preston’.’ 
He was soon setting and answering mathematical questions in the Chronicle, as in the example from September 1844, which is the earliest I have found. 
In the next example, from the following year year, the problem he has set was probably too hard for readers, so he answers it himself and the next, which he did not set. 
In 1845, at the age of 24, he gave a lecture on algebra at the town’s Institution for the Diffusion of Useful Knowledge, which was then in Cannon Street. The lecture was covered in detail in the Chronicle, in which Septimus was described as ‘an intelligent operative of the town and a first-rate mathematician’.
Its dryness of tone perhaps indicates that he would not have been a particularly inspirational teacher, although the fact that he was cheered by the audience on several occasions possibly indicates there was more to the lecture than the Chronicle reporter captured. And the racy dialect poems he was writing later in life show another side of his character (see below). I have transcribed the report and broken it into paragraphs for ease of reading. I think it is well worth quoting in full, for it shows the level of literacy which Septimus had attained:
On Tuesday evening last, Mr. Septimus Tebay, an intelligent operative of the town, and a first-rate mathematician, delivered, at the Lecture Room of this Institution, a very able lecture on Algebra.
He observed—“Algebra is a branch of the mathematics which has for its object whatever can be expressed by number, either exactly or by approximation. In this respect, and also in its employing arbitrary signs to denote the quantities of which it treats, it agrees with arithmetic. The analogy between the two sciences induced Sir lsaac Newton to denominate it ‘Universal Arithmetic’; but by the application of algebra to geometry, the science has acquired a new character, and new powers, which render this appellation too limited, and not sufficiently descriptive of its nature.
In its present state, it is nearly alike related to arithmetic and geometry; and in its application to both sciences the reasoning is carried on by general symbols. Its true character, however, consists in this—that the results of its operations do not exhibit the individual values of the quantities which are the subject of investigation; such as we obtain in arithmetical calculations or geometrical constructions. They only indicate the operations, whether arithmetical or geometrical, which ought to be performed on the given quantities, to obtain the values of the quantities sought. In arithmetic there are ten characters, which being variously combined, according to certain rules, serve to denote all magnitudes whatever.
But this method of expressing quantities, although of the greatest importance in every branch of the mathematics, (for we must always have recourse to it in the different applications of that science to practical purposes,) is yet found to be inadequate, taken by itself, to the more difficult cases of mathematical investigation; and it is therefore necessary, in many inquiries concerning the relations of magnitude, to have recourse to that more general mode of notation, and more extensive system of operations, which constitute the science of algebra.”
He then gave, in a most familiar manner, several examples of the earlier rules of this interesting branch of mathematics; which were attentively observed by a numerous audience who several times expressed their approbation by cheering. At the close, the Rev. E. D. Rendell tendered the thanks of the Institution to Mr. Tebay for his instructive discourse, and congratulated the members on having among them an operative so conversant with the higher branches of mathematics, and willing to instruct his brother members. Mr. M. Holden also expressed his high gratification at the lecture, and the excellent way in which Mr. Tebay had delivered it. 
The Chronicle report of his Cambridge success mentioned above suggests that his studies took their toll:
Application to his studies brought upon him serious illness, which incapacitated him for some time from attending to either work or books. On his recovery, he was for a few years employed in a subordinate capacity by the Preston Gas Company, during which time he continued to make further progress in his favourite pursuit. 
Such academic interests among the working classes of Preston and the surrounding towns were far from unusual, as demonstrated by a short autobiography of Thomas Turner Wilkinson of Burnley published in the journal of the Historic Society of Lancashire and Cheshire by his friend the historian Willian Abram. 
Wilkinson, an acquaintance and admirer of Septimus, was another self-taught student of mathematics. He, too, was a regular correspondent of the Ladies’ Diary and a solver and setter of mathematical problems in the Preston Chronicle, as in Question 28 in the illustration above. His autobiography provides the following example, from Mellor, near Blackburn, where he grew up, of the meetings of groups of similar autodidacts:
About the year 1830 there were resident in Mellor a number of youths who were anxious for intellectual advancement, and we formed a Mutual Improvement Society, which met once a week at the homes of the members in rotation. On these occasions I had one of the spare rooms at Abbot House fitted up with a table and seats; and we used to study certain subjects, and discuss the knotty points which presented themselves, when we met. I derived much benefit from these meetings. We also clubbed our pence together, and formed a small library of books for general reference. 
I could not see how Septimus could have attained the levels of literacy and numeracy he had achieved by early adulthood without the benefit of a formal education. But clearly it was possible, to judge by Wilkinson’s mention of ‘William Harwood [who] was a weaver at Mellor, and taught himself to read after he was 22 years of age. He was a fair mathematician.’ 
Wilkinson continued a member and promoter of such organisations in East Lancashire for the rest of his life. In recording these activities he includes the following comment on Septimus:
Septimus Tebay, B.A., then of Preston, but latterly head master of Rivington School, occasionally joined us at Blackburn, when we met at Mr. Garstang’s; he is one of the ablest of our Lancashire mathematicians, and has gained many prizes in the Diary. He is also the author of an excellent treatise on Mensuration. 
Relations between the two men must have deteriorated later in the century when Septimus accused Wilkinson of plagiarism. The person who reported their dispute supported Septimus, writing, ‘There is an article on porisms in one of the numbers of the Educational Times by Mr Wilkinson, almost entirely the work of another man, who in turn borrowed most of his work from the papers of Mr Butterworth.’ 
Three years after he delivered his lecture at the Institution, at the age of 28 on 5 December 1848 Septimus married Mary Singleton, a 21-year-old weaver, of North Street, Preston, at St John’s parish church. In the church records Septimus is described as an overlooker at the town’s New Gas Works. Mary was probably illiterate since she signed the register with her mark. At that time, Jonathan Tebay’s occupation was given as labourer, Septimus’s father-in-law’s as moulder. 
Six months later, on 24 June 1849, the couple’s first child, also named Septimus, was born. They were then living in North Street and Septimus’s occupation was given as bookkeeper. A second child, Ann, followed a year later and was baptised on 16 February 1851. By then the young couple were living in Upper Lawson Street and Septimus was again described as bookkeeper. 
His remarkable abilities won him considerable local renown, and support:
Many gentlemen, to whom his acquirements had become known, considered it desirable to place him in a position where his powers would have a better scope. The late and the present Mr. Lowndes, Mr. C. R. Jacson, Mr. Grenfell, the Rev. J. Clay, and others, interested themselves in Mr. Tebay’s favour, and ultimately be was sent to St. John’s College, Cambridge … 
There must have been a momentous change in his circumstances later in 1851 for in that year he is writing a four-page article ‘On the Motion of a Pendulum affected by the Earth’s Rotation’ for the London, Edinburgh and Dublin Philosophical Magazine of July-December 1851, signing himself ‘Septimus Tebay, Mathematical Master, Bruce’s Academy, Newcastle-upon-Tyne’.  In a notice he placed in the Chronicle a few years later, discussed below, he describes himself as ‘formerly mathematical master in King Edward the Sixth’s Grammar School, Norwich; and Bruce’s Academy, Newcastle-upon-Tyne’.
I have been unable to trace any further information on his time in Norwich, but it does seem a remarkable transformation to go from gas works bookkeeper to grammar school mathematical master. These various employments would have him a bookkeeper at the time of his daughter’s baptism on 16 February 1851, followed by teaching at two schools for the next 18 months before he began his studies at St John’s College, Cambridge, at Michaelmas, where he graduated BA in 1856. In his entry in the Venn biographies of Cambridge alumni he is described as a ‘labourer in Preston gas-works, who had taught himself mathematics and been sent to Cambridge by “some gentlemen in Preston” ’ and, by then in ‘holy orders’, had gone on to serve as headmaster at Rivington Grammar School, with no mention of any earlier educational employment.  Nor is there any mention of his earlier teaching roles in the Chronicle article about his success at Cambridge.
I do not know why Septimus did not use his clerical title. He is listed in the 1868 edition of Crockford’s Clerical Directory , but in all other references I have found he styles himself, or is styled, Mr Tebay. One exception is the carte de visite (above), probably from around 1860, which uses both titles, bearing the caption ‘Revd. Mr Tebay’. 
While Septimus was at Cambridge his brother Jonathan was married on 4 December 1853 at St John’s church in Preston. His occupation was given as piecer and he was living in Patten Street. Both bride and groom signed the register with a cross, suggesting both were illiterate. Jonathan senior was still working as a coffee roaster. 
The serious illness referred to above recurred while he was coming to the end of his time at Cambridge and may have cost him even greater distinction in the final examinations:
In the college examinations of St. John’s, in mathematics, he was generally next to the gentleman (Hadley) who is the Senior Wrangler. Last week, as we have stated, he was placed in the list of wranglers. His position would have been considerably higher, but a few weeks ago intense application induced an attack of his old complaint, and he was compelled to leave the university for some time for change and relaxation, and he was far from recovered when he entered the arena of the Senate House to compete with some of the most distinguished sons of Alma Mater for her honours. 
The Wikipedia entry gives some idea of what Septimus had attained, and what, because of his illness, he narrowly missed:
The Senior Wrangler is the top mathematics undergraduate at Cambridge University in England, a position which has been described as ‘the greatest intellectual achievement attainable in Britain.’
Specifically, it is the person who achieves the highest overall mark among the Wranglers – the students at Cambridge who gain first-class degrees in mathematics. The Cambridge undergraduate mathematics course, or Mathematical Tripos, is famously difficult.
[…] The difficulty of the examinations is illustrated by the identities of some of those who have performed well, but less well than the Senior Wrangler.
Those who have achieved second place, known as Second Wranglers, include Alfred Marshall, James Clerk Maxwell, J. J. Thomson, Lord Kelvin, William Clifford, and William Whewell.
Those who have finished between third and 12th include Karl Pearson and William Henry Bragg (third), George Green and G. H. Hardy (fourth), Adam Sedgwick (fifth), John Venn (sixth), Bertrand Russell and Nevil Maskelyne (seventh), Thomas Malthus (ninth), and John Maynard Keynes (12th). 
The Hadley that the Chronicle article names as senior wrangler was Augustus Vaughton Hadley. He, by an odd coincidence, served as H. M. Inspector of Schools at Preston from 1865-67, and died in the town in March of that last year. 
Septimus became a father for a third time while he was at Cambridge. Daughter Agnes was baptised on 18 June 1854 at St John’s church, Preston. Septimus was listed as student. A fourth child, Herbert Slee, was baptised in Preston on 18 July 1856. The family were then living in North Street and Septimus was describing himself as gentleman. 
Number seven North Street was the address that Septimus gave when he advertised his services as a teacher of mathematics on 1 March 1856. Surprisingly, he makes no reference to previous teaching experience: 
A year later Septimus was appointed headmaster of Rivington Grammar School.  While Septimus was at the school he had four more children, one of whom died in infancy. The first of the Rivington Tebays, Percival Mee, was born 2 July 1859. 
Shortly after arriving at Rivington he was completing work on an extended journal article: ‘On the Law of Bode, with a remarkable coincidence in reference to the Satellite System of Jupiter; and on the Rotation of a Heavenly Body. By Mr. Septimus Tebay, B.A., Head master of Queen Elizabeth’s Grammar School, Rivington, Lancashire,’ which he signed from Rivington, 8 February 1858.  At the time his correspondents included the Astronomer Royal Sir George Biddell Airy. 
A short article in the Guardian provided a succinct explanation of the rather abstruse subject
It was back on the first day of the 19th century that [the dwarf planet] Ceres became the first object to be discovered in what we now know as the asteroid belt between Mars and Jupiter.
That something was orbiting in that gap was suspected because of a numerical curiosity noticed a few years before. Known as the Titius-Bode Law, it begins with the sequence 0, 3, 6, 12 etc, where each number after the 3 is double its predecessor Add 4 to each and divide by 10 to arrive at 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, etc. To within 5% or so, these correspond with the distances of the known planets at the time when expressed in astronomical units (AU), the unit of the Earth’s average distance from the Sun. Mars sits at almost 1.6AU and Jupiter at 5.2AU, but nothing was known at 2.8AU. Belief in the law was boosted, though, when Uranus was discovered in 1781 very close to the next-predicted distance of 19.6AU.
Ceres fitted the 2.8AU slot almost exactly and when other bodies began to be found at similar distances the idea grew that these are the debris from a single shattered planet. We now realise that Jupiter’s powerful gravity has never allowed the material there to coalesce into a single object. Whether the Titius-Bode Law is anything more than a coincidence is still debated, but its prediction of 38.8AU fails for the outermost planet, Neptune, which orbits at close to 30AU. 
More recently, interest has been growing in the Titius-Bode Law and its application to predicting the positions of exoplanets, to judge by the following article abstract:
We report the application of Titius-Bode’s law on 43 exoplanetary systems containing four or more planets. Due to the fact that most of these systems have their planets located within compact regions extending for less than the semi-major axis of Mercury we found the necessity to scale down the Titius-Bode law in each case. In this short article we present sample calculations for three systems out of the whole set. Results show that all systems studied are verifying the applicability of the law with high accuracy. Consequently our investigation verifies practically the scale invariance of Titius-Bode law. The results of this study build up the confidence in predicting positions of the exoplanets according to Titius-Bode’s law besides enabling diagnosing possible reasons of deviations. 
So possibly Septimus was on to something after all.
Two years after becoming headmaster of Rivington School Septimus was enlisting the help of another St John’s graduate, Frederic Wace (3rd wrangler 1858), to test his pupils, which he did over the course of two days in June 1860. Mr Wace’s report on the school was printed in the Chronicle in its report on the school’s end of year prize day.
In general, it reflected well on Septimus’s endeavours to raise the standards at the school, although Wace expressed some slight reservations on the pupils’ performance in algebra, writing that he regretted ‘that the subject had not been able to receive in the school the attention it deserves’. He said the same comment applied to the teaching of Euclid at the school.
It perhaps gives some insight into Septimus’s character that, to judge by the Chronicle report, it was the minor criticisms in Wace’s report that he chose to dwell on:
With regard to those subjects mentioned by the examiner as not having received the attention they deserve, Mr. Tebay said he could not at present suggest any remedy without neglecting other subjects of equal importance in a school like this. That one hour is insufficient to do justice to two classes of Euclid, and two classes of algebra, no one will deny. It was his wish to raise the character of the school, and not to lower it; and to suspend the Euclid classes altogether would not be satisfactory. 
At the 1861 census Septimus was recorded as the headmaster of the grammar school, living at Turner’s Farm, Rivington, with his wife, five children and a servant. The same census recorded his father as still working as a coffee roaster.  A sixth child, Mary Grace, was born at Rivington and baptised at Rivington church on 18 July. She died the following year. 
At the end of the 1861 school year Septimus was looking to leave Rivington and establish his own school in Preston, placing the following advertisement in the Chronicle :
The project was abandoned because of the ‘present state of the times (the cotton famine)’, according to the historian of Rivington School, and he stayed on at Rivington. Bispham Street was a strange choice of site for a school designed to educate the middle classes. 
In 1862 Septimus’s brother William was married at St John’s, Preston, on 11 January. He was described as a spinner of Saul Street, Preston. His wife was listed as a weaver, she and one of the witnesses signed the register with a cross.
A link to Septimus’s days at the Preston Gas Works came on 26 June 1870 when, at Holy Trinity Church, Preston, William Cowell, an inspector of gas meters, named a son Septimus Tebay Cowell. 
Septimus and Mary had two more children, although I have not been able to trace their baptismal records. The 1871 census records them as Eliza G., then aged six, and Walter L., the couple’s last child, aged four. That census shows the family living at the School House, Rivington. Septimus junior is described as a painter and sisters Ann and Agnes as dressmakers. There were also four boarders, three boys and a girl aged between seven and 13; they were probably pupils at the school. No servant. 
Septimus junior was still working as a painter when he married on 18 May 1872 at St John the Evangelist in Blackpool, which town he gave as his address. In 1874 when his daughter was baptised on 8 August at Rivington Church he was back in the village, working as a painter.
In 1875 Rivington School was merged with Blackrod Grammar School and Septimus’s job disappeared. At the time he was being paid £125 a year and he was given £400 severance pay. According to the Rivington School historian ‘His somewhat tall, scholarly figure in frock-coat and silk hat is still remembered by old inhabitants.’ His successor ran the school into the ground in five years, and it closed for a while before opening on a new site. 
Septimus seems to have used the severance pay to help fund the opening of a private school in Bolton. In the 1876 Post Office directory for the town he is listed among the proprietors of boarding and private schools in the town at 9 Back-o’th-Bank. 
By 1878 the family appear to have made the short move to Farnworth, for two of the Tebay girls were recorded as living there when they married that year. Agnes, then 24, married her architect husband at St John the Evangelist on 12 November and Annie, then 26 and recorded as a dressmaker, when she married the son of a publican on December 25. For both marriages Septimus was listed as a schoolmaster. Agnes’s marriage to an architect is the only connection found in any of the Tebay family records that is not working class. 
The family were established in Farnworth at the 1881 census, living at 119 Peel Street, with a tailor and his family on one side and the Rawson Arms on the other. The three youngest children were still at home, working as joiner, bootmaker and errand boy. Septimus, now aged 60, was described as ‘schoolmaster (private school)’.  By then Septimus junior, aged 31, had recently moved to London where he was living with his wife and five children and working as a plumber. He had named his eldest son Septimus.  When his son William, a clerk living at Bootle, married on 28 September that year Septimus elected to style himself ‘gentleman’ in the register at St Aidan’s, Billinge.
In 1891 the family were still living in Farnworth but had moved a short distance to 94 Presto Street. In the census return of that year Septimus, now aged 70, was listed as an unemployed schoolmaster. Two of his children were still at home: Eliza Grace was employed as a boot top fitter and Walter Lowndes as a shoemaker. The family had taken a boarder.  Later that year his wife died and her death was recorded on their gravestone.
By Septimus’s final decade three more of his children had married and church records show one son working as a police constable, another as a joiner and a daughter working as a fitter married to a cooper.  Septimus’s decline was proceeding apace: from as early as 1893 he is found in the Farnworth workhouse, his stays there becoming more frequent until he finally died there, having been admitted because of ‘old age and destitution’ in 1897 at the age of 76.
He was buried in the graveyard at Rivington Church. His gravestone mistakenly records his birth year as 1828 and gives him an MA rather than BA. (See Anne Kidson’s account for more information on this period of his life.)
A short anonymous obituary appeared written from the Athenaeum Club by an acquaintance from his early years:
I knew Septimus Tebay about fifty years ago. He was then connected with the Gas Works at Preston, occupying a subordinate position, and living with his wife in a very humble way. I think he had no children, but he was certainly very poor. Mr. John Garstang had a private school at Blackburn, and I was his assistant, living with him. We were both contributors to the mathematical portion of the Lady’s and Gentleman’s Diary, and Tebay used to walk over, a distance of eight or nine miles, to discuss with us the questions proposed in the Diary. His knowledge of mathematics was wider than ours, and I rather think we learnt more from him than he did from us. We often walked with him half way back to Preston.
Early in the fifties some gentlemen in Preston raised a fund to enable Tebay to go to Cambridge, providing meanwhile for the maintenance of his wife. Tebay had great difficulty in getting through the Previous Examination, his knowledge of Latin, Greek, Paley’s Evidences, and in short everything (save mathematics) being very weak; but somehow he passed. He entered St. John’s College. His position in the Tripos disappointed his friends. In his year (1856) there were thirty-five Wranglers, and he came out twenty-seventh. Soon after he was appointed Headmaster of Rivington School, but I heard that he fell into habits of dissipation and drunkenness, and lost his situation. He afterwards kept a public-house at Farnworth, Bolton. 
The fact that the writer was unaware that Septimus had fathered eight children does not inspire confidence in the accuracy of some of this obituary. It is possible he knew Septimus well early in life and trusted to gossip for the account of his latter years. No trace so far has been found of Septimus keeping a public house.
A final unresolved question is whether Septimus was, in fact, educated at Lancaster and Heversham grammar schools as one source insists: research continues.