**John Brinkley**'s mother was Sarah Brinkley, a daughter of the butcher John Brinkley, and his father was John Toler, a wine merchant. Sarah Brinkley and John Toler never married and, on 18 October 1770, Sarah married Jacob Boulter of Boot Inn, Great Bealings, Suffolk, who was an innkeeper. Great Bealings is about 4 km from Woodbridge, both towns lying north-east of Ipswich. Although John Brinkley was illegitimate, he was brought up by his mother and step-father who supported him financially.

There is some confusion concerning John Brinkley's date of birth. He was baptised in Woodbridge, Suffolk, on 31 January 1767 but some biographies give this incorrectly as 1763. Brinkley's date of birth of July 1766, which we give above, is a guess based on the following data. His memorial at Trinity College Dublin gives his age at death as 70 in September 1835 while his matriculation record at Gonville and Caius College, Cambridge gives his age as 17 on 29 August 1783, the date when he was admitted to the College. No date of birth can be consistent with both of these but July 1766 would agree with the matriculation record and he would be in his 70^{th} year when he died. His memorial tablet in Cloyne Cathedral gives his age at death as 69 years, consistent with our guess. Other biographies give dates of birth from 1763 to 1767.

Brinkley's schooling was for a year with the Rev Mr Dimsdale in his school in Benhall, Suffolk, and for three years he received private tuition by the Rev Mr Black, of Woodbridge, at the Rev Black's home. He showed an excellent ability for mathematics when he was being schooled and that he had an exceptional talent for this topic became clear after he began his university education. He entered Gonville and Caius College, Cambridge as a sizar on 29 August 1783. As a sizar, Brinkley would have been charged reduced fees and living costs in exchange for working as a waiter for the other students at meal times and performing other duties. His abilities soon allowed him to be relieved of these duties and he matriculated in the Michaelmas Term (the first term) of 1784 as a scholar, meaning that he had won a scholarship. During his time as an undergraduate, Brinkley spent two periods at the Royal Greenwich Observatory as an Assistant to the Astronomer Royal, Nevil Maskelyne. The first was for seven weeks from 23 June 1787 to 9 November 1787 and the second was for two months from 27 January 1788 to 25 March 1788. Brinkley had two reasons to undertake this work; he gained some observing experience and he earned some money to allow him to return to Cambridge to complete his studies. He graduated in 1788 as Senior Wrangler, meaning that he was ranked at the top student. We note that Brinkley wrote the answers to the examination questions although the questions themselves were dictated. It was only two years after Brinkley graduated that written questions were produced and 1790 is considered the year that the Mathematical Tripos examinations began in Cambridge. Having graduated, Brinkley was one of a small number of students who took a further examination in higher mathematics for the Smith's prize which he was awarded. For four years, from 1788 to 1792, Brinkley was a fellow of Caius College, Cambridge. During this time he was awarded an M.A. in 1791 and he also entered the Church. He was ordained deacon in Ely Cathedral in 1790 and became a priest at Lincoln Cathedral in the following year.

Henry Ussher (1741-1790) was the first Andrews Professor of Astronomy at Trinity College, Dublin. Following his death in 1790, the Board of Trinity College wrote to the Astronomer Royal, Nevil Maskelyne, asking if he knew of a suitable candidate to fill the position. Maskelyne had no hesitation in recommending Brinkley although he was only 24 years old. However, it was far from a foregone conclusion that he would be acceptable to the Board since there was another local candidate. John Stack (1760-1813), had entered Trinity College Dublin in 1777, and was made a fellow in 1784. He served as secretary of the Royal Irish Academy from 1789 to 1791 and had written the book *A short system of optics* (1787). The Board of Trinity voted on which of the two candidates should be appointed and Stack was the winner by a very clear majority. However, the Provost of Trinity College, Hely Hutchinson (1724-1794) had the power of veto over the Board's decisions and he vetoed their decision to appoint Stack. The reason the Board voted for Stack appears to be mainly because he was Irish and a fellow at Trinity College. The reason that Hely Hutchinson was strongly opposed to Stack was that he had corresponded with Maskelyne who had replied that Stack's knowledge of astronomy was not (see for example [9]):-

Unable to appoint Stack after the veto, the Board had little option but to appoint Brinkley at a meeting on the 11... sufficient to qualify him for the office of Professor.

^{th}December 1790. However, there was strong opposition following the announcement [1]:-

In 1791 Brinkley took up his appointment as the second Andrews Professor of Astronomy at Trinity College, Dublin. He also became Royal Astronomer of Ireland from 1792. F E Dixon writes [9]:-The national press of the day commented on the preference shown to the young Englishman, Brinkley, over his Irish rival. An animated controversy ensued. The Provost himself condescended to enter the lists and to vindicate his policy by a long letter in the "Public Register" or "Freeman's Journal," of21December,1790. This letter was anonymous, but its authorship is obvious. It gives the correspondence with Maskelyne and other eminent astronomers, whose advice and guidance had been sought by the Provost. It also contends that "the transactions of the Board ought not to be canvassed in the newspapers."

About a year after he arrived in Dublin, Brinkley married Esther Weld, a daughter of Matthew Weld, the Sheriff of Dublin, of Molesworth Street, Dublin and Elizabeth Kane. John and Esther Brinkley had three children, John Brinkley (1793-1847), Matthew Brinkley (1797-1855) and Sarah Jane Brinkley (1801-1827).Brinkley must have felt embarrassed, and also very anxious to justify his appointment. The lack of instruments did not deter him. As well as lecturing in astronomy he wrote a text book on the subject which went through at least six editions, with three more incorporating other authors' revisions, the most recent being as late as1886. He also found time for important mathematical research, and revolutionised astronomical calculations by introducing what is known as the "method of least squares," by which it is possible to estimate accurate results and also the degree of accuracy achieved.

When Brinkley took up his roles as professor and Royal Astronomer at Dunsink Observatory, the Observatory was lacking in good equipment for observing. In particular Henry Ussher had negotiated with Jesse Ramsden (1735-1800) for a 10-foot circle and this had been approved by the Board of Trinity. However, Ramsden discovered that he had been too ambitious and he had great difficulty in making this very large instrument. When Brinkley was appointed to Dunsink Observatory, the instrument had still not been delivered and, as years went by, it still failed to be delivered. Ramsden reduced the size, first to a 9-foot circle and then, when even this was proving beyond his capabilities, an 8-foot circle. When Ramsden died in 1800 the 8-foot circle was still not complete but construction continued. The problems with lack of quality instruments at Dunsink Observatory must have been a great frustration to Brinkley but, on the other hand, it led to a number of positive outcomes. It allowed Brinkley the opportunity to engage in mathematical research and to influence the reform of the teaching of mathematics at Trinity College, Dublin. At the time that Brinkley was appointed as Andrews professor of astronomy, Richard Murray was Professor of Mathematics, a post he held until 1795 when he became Provost. He was influential as a teacher but over the following years the teaching of mathematics at Trinity College did not introduce the latest developments and was very out of date. Brinkley was keen on the latest Continental developments in the calculus and played an important role in setting the scene for the reforms in mathematics teaching introduced by Bartholomew Lloyd after he became professor of mathematics in 1813 [12]:-

[As examples of Brinkley's mathematical papers we list the following seven papers (many of which have long descriptive titles):Brinkley]was isolated from University life because of his position at Dunsink and it was perhaps because of this that he was able to take the lead in introducing a knowledge of continental mathematics and physics into Dublin without raising a hornet's nest of opposition in the University. He was the first Dublin professor to use the analytic notation early in the new century and this is of great significance in understanding the roots of the advanced analysis in Dublin.

*A General Demonstration of the Property of the Circle Discovered by Mr Cotes, Deduced from the Circle Only*(1800);

*A Method of Expressing, When Possible, the Value of One Variable Quantity in Integral Powers of Another and Constant Quantities, Having Given Equations Expressing the Relation of These Variable Quantities. In Which Is Contained the General Doctrine of Reversion of Series, of Approximating to the Roots of Equations, and of the Solution of Fluxional Equations by Series*(1800);

*General Demonstrations of the Theorems for the Sines and Cosines of Multiple Circular Arcs, and Also of the Theorems for Expressing the Powers of Sines and Cosines by the Sines and Cosines of Multiple Arcs; to Which Is Added a Theorem by Help Whereof the Same Method May Be Applied to Demonstrate the Properties of Multiple Hyperbolic Areas*(1800);

*On Determining Innumerable Portions of a Sphere, the Solidities and Spherical Superficies of Which Portions Are at the Same Time Algebraically Assignable*(1802);

*A Theorem for Finding the Surface of an Oblique Cylinder, with Its Geometrical Demonstration. Also, an Appendix, Containing Some Observations on the Methods of Finding the Circumference of a very Excentric Ellipse; including a Geometrical Demonstration of the Remarkable Property of Elliptic Arcs Discovered by Count Fagnani*(1803);

*An Investigation of the General Term of an Important Series in the Inverse Method of Finite Differences*(1807); and

*Observations Relative to the Form of the Arbitrary Constant Quantities, That Occur in the Integration of Certain Differential Equations; and, Also, in the Integration of a Certain Equation of Finite Differences*(1818).

In 1813 Brinkley published his textbook *The Elements of Astronomy*. A second edition was published in 1819. In 1871 John William Stubbs and Francis Brünnow published *Brinkley's Astronomy* which was a revised and partly rewritten version of Brinkley's original work.

Ramsden's 8-foot circle was completed by Matthew Berge after Ramsden's death and was eventually delivered to the Dunsink Observatory in 1808, twenty-three years after it had been ordered. Once the instrument was installed, Brinkley began the major research of his career, namely his attempts to measure the parallax of stars. He chose fifteen bright stars on the assumption that bright stars would be closer to the sun. He then attempted to measure their apparent movement against the faint distant stars using as a base line the diameter of the Earth's orbit round the sun. [The Earth moves through the diameter of its orbit every six months.] Out of his fifteen original choices, Brinkley then chose four on which to concentrate his efforts. For three of these he found a parallax of 1 arc-second while for the fourth he found a parallax of 2.7 arc-seconds. He published several papers on this topic, for example: *On the Parallax of Certain Fixed Stars *(1818); and *An Account of Observations Made with the Eight Feet Astronomical Circle, at the Observatory of Trinity College, Dublin, since the Beginning of the Year 1818, for Investigating the Effects of Parallax and Aberration on the Places of Certain Fixed Stars; Also the Comparison of These with Former Observations for Determining the Effects of Lunar Nutation* (1821). In the Preface to the second edition to his book *Elements of Astronomy* (1819) Brinkley writes:-

Other astronomers could not reproduce the results claimed by Brinkley on parallax and a controversy arose which went on for a considerable time. It was John Pond (1767-1836), the Astronomer Royal, who argued with Brinkley from 1810 to 1824 about his results. In fact Brinkley was wrong and his false results can be attributed to his 8-foot circle. In fact the parallax of the stars investigated by Brinkley is too small to be discovered with his equipment. However, his work and methods on this topic made an important contribution and led eventually to the measurement of the parallax of 61 Cygni by Wilhelm Bessel in 1838.It was expected that an opportunity might occur of again mentioning the subject of the parallax of the fixed stars. The observations lately made at our Observatory, part of an intended extensive course for re-examining this interesting question, confirm in the strongest manner those heretofore made. No doubt seems to remain that the changes observed are not occasioned by variations of refraction, or by any change in the instrument. They are explained by attributing a visible parallax to certain stars; and observations that have been made elsewhere seem by no means sufficient to overturn this conclusion.

Walter Scott, the famous author, visited Dunsink Observatory on 17 August 1825 and one of his party recorded the incident writing:-

As a professor, Brinkley was not well paid so he sought additional funds from the Church. From 1806 to 1826, he was collated to the prebend of Kilgoghlin, Elphin and, from 1806 to 1810, to the rectory of Derrybrusk, Clogher. He was appointed vicar at Laracor, Meath, on 23 February 1808, but resigned this position in December of 1808. From 1808 to 1826 he was Archdeacon of Clogher. Throughout this period he continued to hold his Professorship of Astronomy at Trinity College and his position as Royal Astronomer for Ireland. However, in 1826 he resigned his astronomy positions when he was appointed Bishop of Cloyne. When he was appointed as Bishop, it was said in Ireland that "he might thank his stars" for his promotion! It was fitting that after Brinkley resigned his chair and position as Royal Astronomer of Ireland, both positions were filled by William Rowan Hamilton. It had been Brinkley who had taught Hamilton mathematics and encouraged him when he was a young boy. At that time, there was nobody else except Brinkley at Trinity College who had knowledge of the latest mathematical developments.We drove then four or five miles to the Observatory, where Dr Brinkley had a capital haunch of venison and everything suitable, except the company, which was rather insipid.

The first meeting of the Astronomical Society took place in London on 10 March 1820. This Society later became the Royal Astronomical Society. Brinkley attended the meeting held on 12 May 1820 when he explained that he had not come to the founding meeting due to "accidental delay in receiving the original circular." The Astronomical Society became the Royal Astronomical Society in 1831 when the King signed its new Charter. Brinkley, by this time Bishop of Cloyne, was elected as the first President of the Royal Astronomical Society under its new Charter at its meeting on 11 February 1831. This appointment was made under the new Charter but the King did not sign the Charter until 7 March 1831 so Brinkley's appointment was not seen as valid. To ensure that his position was official, he was elected as President for a second time at the meeting of the Society on 6 April 1831. He served as President until 1833, which was the maximum term allowed under the Charter, when Francis Baily took over the presidency.

By 1833 Brinkley's health was causing him concern. We see a little of this from a letter Brinkley sent to Stephen Peter Rigand (1774-1839), a mathematical historian and Savilian Professor of Astronomy at Oxford. The letter, sent on 13 May 1833 from Bangor, begins:-

Brinkley received many honours both for his mathematical work and for his contributions to astronomy. In 1803 he was elected to the Royal Society of London:-I shall have much pleasure in reading the sheets of your work if you have an opportunity of sending them to me at Cloyne. Before I left Bath I committed to the care of Mr Duncan your interesting manuscript on Sterling. It was directed to you and Mr Duncan promised to have it conveyed safely. I am returning to Ireland much improved, thank God, in my health and trust I shall be well able to meet all the unpleasant things that are likely to occur there. Happy England if its happiness were properly appreciated. I expect to be in Dublin in two or three days and in Cloyne in about ten days. ...

He was awarded the Society's Copley medal in 1824 for his work on stellar parallax. At the time of the award, it was not realised that his results were incorrect. Nevertheless, despite the error, it was important work deserving recognition.... as the author both of a practical method of determining longitude and as a mathematician who had contributed a new method of solving equations.

He was elected, in 1822, President of the Royal Irish Academy and continued in this position until his death in 1835.

P A Waymen writes [16]:-

Brinkley died at his home on Leeson Street, Dublin, and was buried in Trinity College Dublin chapel.Brinkley had a gentle and peaceable character and his reluctant dispute with Pond was carried through without rancour. His humble origin was, for its time, unusual for a man of his eminence.

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