# Andrew Searle Hart

### Born: 14 March 1811 in Limerick, Ireland

Died: 13 April 1890 in Kilderry, County Donegal, Ireland

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**Andrew Hart**'s parents were George Vaughan Ledwich Hart and Maria Murray Hume. The Rev George Hart (1754-1839), from Glenalla, County Donegal, was a son of John Hart and Catharine Barnard. The Rev George Hart was a curate to the Dean of Derry and then the rector of Castlebar, County Mayo. In 1791 he married Maria Hume (born 1771), a daughter of the Very Rev John Hume, the Dean of Derry, and his wife Jane Murray. Maria inherited Glenalla, County Donegal, from her mother's relatives, the Murray family, in 1801. It was at Glenalla that Andrew spent much time as a child. He was the youngest of his parent's children and outlived all his elder siblings except for one. The children were John Hart (born 1792, died as a baby), John Hume Hart (1794-1821), William Henry Hart (1796- lost at sea), Jane Alicia Hart (1797-1808), George Vaughan Hart (1799-1836), Catharine Elizabeth Hart (1801-1883), Thomas Barnard Hart (1803-1866), Edward Hume Hart (1806-1872), Jane Maria Hart (1809-1895), and Andrew Searle Hart, the subject of this biography.

Andrew Hart was a pupil at Foyle College in Londonderry. This school dates back to 1617 but only took the name Foyle College in 1814 when it moved to a new site outside the city walls. In addition to this schooling, Andrew also had lessons from a private tutor. In November 1828 he entered Trinity College Dublin. There he was in the same class as Isaac Butt who became a barrister, politician and a strong supporter of home rule. Hart and Butt became close friends although they never agreed in their political views. At Trinity College, Hart was one year ahead of Charles Graves who entered in 1829. At the time when Hart began his studies William Rowan Hamilton was Andrews' Professor of Astronomy in Trinity College Dublin while Franc Sadleir (1775-1851) was Erasmus Smith professor of mathematics. James MacCullagh was appointed junior assistant to the mathematics professor in 1832. Bartholomew Lloyd was Erasmus Smith professor of Natural and Experimental Philosophy when Hart entered but he became Provost of Trinity College Dublin in 1831 and was succeeded as professor of Natural and Experimental Philosophy by his son Humphrey Lloyd. Hart graduated with a B.A. in 1833 and he was awarded the Science medal for his excellent performance. He decided to take the Trinity College Fellowship examinations:-

Hart was elected a fellow of Trinity College, on 15 June 1835. We note that James Booth, who was four years older than Hart, took the fellowship examinations for the first time in the same year but failed to gain a fellowship. In the autumn of 1835 Hart began legal training when he entered King's Inns, Dublin and in 1836 he enrolled in Gray's Inn, London. On 13 February 1837 he was elected to the Royal Irish Academy, and in the following year he was called to the Irish bar. Back at Trinity College, Dublin, he was awarded an M.A. in 1839, and he received an LLB and an LLD in 1840.The examination for fellowship was formidable, being held on twelve days preceding Trinity Sunday from nine to twelve in the forenoon and two to five in the afternoon of each day. The subjects of the examination were pure and applied mathematics, experimental physics, mental and moral philosophy, Greek language and literature, Latin language and literature, and Hebrew and cognate languages.

On 6 August 1840, at Clontarf, Hart married Frances MacDougall, the second daughter of Henry MacDougall QC, of Dublin. The marriage was conducted by the Rev Charles Stanford. Andrew and Frances Hart had ten children: George Vaughan Hart (1841-1912); Andrew Hart (1842-1869); Fanny Allman Hart (1843-1857); Mary Hart (1844-1858); child born in 1844 died as infant; Henry Chichester Hart (1847-1908); child born in 1848 died as infant; Henrietta Catherine Hart (1850-1881); William Hume Hart (1852-1884); and Louisa Elizabeth Hart (1853- died as an infant). We see from this list that, of Hart's ten children, only two survived him, namely George Vaughan Hart, who was professor of Feudal and English Law at Trinity College from 1890 to 1909, and Henry Chichester Hart, who became a botanist and explorer. Henry Chichester Hart's most important work was the book

*Flora of the County Donegal*.

In the 1840s Hart published two mathematics books,

*An elementary treatise on mechanics*(First edition 1844, Second edition 1847) and

*An elementary treatise on hydrostatics and hydrodynamics*(First edition 1846, Second edition 1850). You can read Hart's Prefaces to these books at THIS LINK.

In addition to his position as a fellow of Trinity College, where he was connected to the School of Engineering, Hart also served as Professor of Real and Personal Property in King's Inns, Dublin. He also played a major role on the Synod of the Church of Ireland.

Hart published a number of papers on geometry. For example

*On the Form of Geodesic Lines through the Umbilic of an Ellipsoid*(1849),

*Geometrical demonstration of some properties of geodesic lines*(1849),

*On geodesic lines traced on a surface of the second degree*(1849), and

*An account of some transformations of curves*(1853). For the full references to these papers, and a list of several more of Hart's papers, see THIS LINK.

His most important result was contained in his paper

*Extension of Terquem's theorem respecting the circle which bisects three sides of a triangle*(1861). This paper was written after an investigation which had been suggested by William Rowan Hamilton in a letter he wrote to Hart. In addition Hart corresponded with George Salmon on the same topic. This paper contains the result which became known as Hart's theorem. This theorem is a generalisation of Feuerbach's Theorem. Hart's Theorem states:

In his masterpieceTaking any three of the eight circles which touch three others, a circle can be described to touch these three, and to touch a fourth circle of the eight touching circles.

*Principles of geometry*(1925), Henry Baker devotes a whole chapter to Hart's Theorem, namely Chapter 2 which is titled "Hart's Theorem, for Circles in a Plane, or for Sections of a Quadric." Here are the opening paragraphs of this chapter [1]:-

As a final comment on Hart's Theorem, we quote the opening sentence of Gabbatt's paper [3]:-Given three lines in a plane, there are four circles touching them; these circles, we know, are all touched by another circle, the nine-points circle(Feuerbach's theorem; see Vol. II). In other words, given three lines, we can add to them a circle such that the four, these lines and the circle, are all touched by four other circles. In the present chapter we show how, given any three circles in a plane, we can add to them another circle, which we call the Hart circle, such that the four circles are all touched by four other circles(Hart, 'Quart. J. of Math.', IV(1861), p.260). The three original circles are in fact touched by eight other circles, as we shall prove. There are fourteen ways of choosing, from these eight, four circles which touch another circle. In six of these ways, the four circles chosen have a common orthogonal circle; and the four circles consisting of the original circles, and their Hart circle, have also a common orthogonal circle. We have shown that circles in a plane may be regarded as projections of plane sections of a quadric. We prove the results enunciated as theorems for such plane sections. This appears greatly to increase the interest and clearness of the matter.

Returning to look at Hart's career, he was made a Senior Fellow of Trinity College, Dublin on 10 July 1858 and was also the College bursar. In 1873 he was appointed as registrar. To put other events of 1873 into context we need to briefly explain the position of Irish universities at this time. Trinity College, Dublin, was originally restricted to members of the Anglican Church of Ireland but from 1791 Roman Catholics were admitted. However, fellows and professors were still required to be Anglicans. The secular Queen's University of Ireland, founded in the second half of the 1840s had three colleges, Belfast, Cork and Galway. The Catholic University of Ireland had been founded in Dublin in 1851 but was not recognised by the government. In 1873 William Gladstone, British Prime Minister, introduced the Irish University Bill. This Bill proposed abolishing Queen's College, Galway, and making all the others colleges of the University of Dublin. Under the Bill, this university would be secular and its Faculty of Theology would be taken over by the Church of Ireland. The Bill was opposed by the Roman Catholic Church in Ireland and also by the faculty of Trinity College, Dublin. In February 1873, three members of staff of Trinity College were sent to London to lobby MPs in an attempt to defeat the bill. Hart was one of the three and they achieved their aim since the bill was narrowly defeated by just three votes. Gladstone's failure to get his bill passed was a major factor in ending his first spell as Prime Minister.It is well known that in non-euclidean geometry a plane triangle has four circumcircles, and that each of these circles touches each of four other circles. The latter theorem, which is an extension of that of Feuerbach, is essentially due to Hart.

In 1876 Hart was elected as vice-provost of Trinity College. At this time the provost was Humphrey Lloyd who was 76 years old and in failing health. This meant that over the following few years Hart undertook many of the duties of the provost. We note that in the same year as he was elected as vice-provost, Hart's wife died. Hart never gave up his mathematical studies and published

*On Nine-Point Contact of Cubic Curves*(1875),

*On the Intersections of Plane Curves of the Third Order*(1879),

*On Twisted Quartics*(1884) and

*On the Linear Relations between the Nine Points of Intersection of a System of Plane Cubic Curves*(1887). Here is the first part of Hart's Introduction to his paper

*On Twisted Quartics*:-

On 25 January 1886, Hart was knighted at Dublin Castle by Queen Victoria's representative Lord Carnarvon:-A twisted algebraic curve is the complete or partial intersection of two algebraic surfaces, and its degree is defined to be the number of points in which it meets any arbitrary plane. It is easy to see that such curves of any degree higher than the second can be traced on a quadric surface, and it is also obvious that there are many such curves which do not lie on any quadric; and further, that both those which lie on quadrics, and those which are the complete intersections other surface in a number of points equal in each case to the product of the degrees of the curve and surface. It is generally assumed that this property is true of all algebraic curves, but I am not aware that it has been proved except in special cases, such as those above mentioned. The object of the present investigation is to show that the classification of twisted quartics, which is founded on this property, includes all possible twisted quartics; and thus indirectly to show that the property is true of all these curves; or, in other words, that if a twisted curve meets every plane in four points, it will meet every surface of the nth degree in4n points.

The Headmaster of Foyle College in 1886 was Maurice Hine and he wrote to Hart to congratulate him on his knighthood. Hart replied to the Headmaster of the College he had attended as a boy:-... in recognition of his academic rank and attainments.

Hart's sister, Jane Maria Hart, had married a cousin who, rather confusingly, was also named George Vaughan Hart. They lived at Kilderry House, Kilderry, County Donegal, and it was in their house that Hart suddenly died aged 79 years.Many thanks for your congratulations on a honour which is liable to be misunderstood. It was intended by His Excellency as a parting compliment to Trinity College, and my claim to a share in the honour rests solely on the fact that no other living man has been so long connected with the College as I. This is a claim which I can safely undertake to maintain against all the world, which gives me an advantage over many men who have been similarly honoured.

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

**List of References** (8 books/articles)

**Mathematicians born in the same country**

**Additional Material in MacTutor**

**Other Web sites**

- Dictionary of National Biography
- MathWorld The Hart Circle
- ERAM Jahrbuch entry