Arthur Milne was born in Hull where his father, Sidney Milne, was the headmaster of a Church of England school. His mother, Edith Cockcroft, was also a teacher. Arthur was the oldest of his parents' three children, all boys, all of whom became scientists. The family moved to Hessle, near Hull, when Arthur was nine years old. Before this he had been attending his father's school.
Milne attended Hymers College (an endowed school) in Hull for his secondary schooling and from there he won an open scholarship in mathematics and natural science to study at Trinity College, Cambridge. It was a remarkable achievement for not only did he win this scholarship in 1914, he gained the largest number of marks which had ever been awarded in the examination. At Cambridge, in the eighteen months during which he studied there, he was inspired by Chapman and Hardy.
Milne's defective eyesight prevented him from active service in World War I. However, in 1916 he joined a team working on ballistics at the Anti-Aircraft Section. Meg Weston Smith writes in :-
In 1916 he abandoned his studies to join an innovative research team examining the behaviour of shells, fuses etc. Beyond producing the relevant mathematics, he flew in early aircraft, hanging over the wing to take readings of temperature and pressure, and he supervised the eminent statistician Karl Pearson in drawing up new firing tables, based on the team's findings, which were issued throughout the armed services. Milne also increased the understanding of wind and sound, in the course of refining the huge binaural listening trumpets which detected aircraft at night. Under the team's leader A V Hill, and R H Fowler (with whom Milne later collaborated) Milne received a marvellous training in how to do research. Thus his three years with the team probably ranked equally in importance in his education with his one and half year's at Cambridge.
In 1919 Milne returned to Cambridge but not with the intention of either completing his undergraduate degree or of studying for a doctorate. Elected a Fellow of Trinity College shortly after he came back to Cambridge, Milne was appointed assistant director of the Solar Physics Observatory in Cambridge in 1920. He worked there under its director H F Newell who suggested that he turn his attention to work on stellar atmospheres.
Milne's work on the atmospheres of stars extended work done earlier by Schuster in 1905 and by Schwarzschild in 1906. Schuster had studied the transfer of radiation where it was assumed that no absorption was taking place in the atmosphere, while Schwarzschild studied equilibrium states for radiation in an absorbing atmosphere. Milne combined the two approaches and came up with an integral equation of great mathematical interest which is now known as Milne's integral equation.
In 1922 Milne won a Smith's Prize at Cambridge for an essay on the darkening of the limb of a stellar disk. He calculated the amount of darkening of the limb resulting from a given energy distribution in the star's spectrum, and compared his theoretical results with the known values for the sun. He then studied the inverse problem of deducing the energy distribution in a star's spectrum from the limb darkening. We mentioned above that Milne collaborated with R H Fowler; they cooperated in 1923 in studying absorption lines in stellar spectra.
Sydney Chapman resigned as Beyer professor of applied mathematics at Manchester in 1924 in order to take up the chair of mathematics at Imperial College London. Milne was appointed to succeed Chapman as Beyer professor of applied mathematics at Manchester, taking up the post in 1925. While at Manchester he continued his research into radiative equilibrium and the structure of stellar atmospheres, and his work on these topics led to his election to a Fellowship of the Royal Society. In 1928 he accepted the Rouse Ball Chair at Oxford, becoming the first holder when he took up the appointment in January 1929. His Royal Society Bakerian lecture in 1929 on The Structure and Opacity of a Stellar Atmosphere marks the end of his research into this topic.
In 1928 Milne married Margaret Campbell. They had two daughters and one son, but tragically his wife died during the birth of the son. He married again in 1940, this time to Beatrice Brevoort Renwick from New York. This second marriage produced one daughter but sadly his wife died five years after the marriage.
From around the time that Milne took up the Rouse Ball Chair at Oxford, he moved on to another research topic, this time studying the structure of stars. The main thrust of his work on this topic was to give different ideas to those of Eddington. Whitrow writes in :-
Although much of Milne's criticism of Eddington's work has not been generally accepted, his methods led to important developments ...
After about three years concentrating on a mathematical theory of stellar structure, Milne turned his attention to cosmology. He developed a new form of relativity called kinematic relativity, an alternative to Einstein's general theory of relativity, which also met with considerable opposition. However, his work made people rethink old ideas and led to new approaches to the fundamental concepts of space and time.
Milne's books include Thermodynamics of the Stars (1930) which contains material relating to his Smith's Prize essay discussed above, Relativity, Gravitation and World-Structure (1935), and Kinematic Relativity (1948). These were all scholarly texts written for his fellow academics and, unlike most of the other famous astronomers of his time, he wrote no texts intended for the general public.
Milne received many honours during his career. He was elected to the Royal Society in 1926 and invited to give its Bakerian lecture in 1929. In 1941 Milne was awarded the Royal Medal of the Royal Society:-
... for his researches on the atmosphere of the Earth and the sun, on the internal constitution of the stars, and on the theory of relativity.
He was President of the Royal Astronomical Society from 1943 to 1945 having been awarded the Society's gold medal in 1935.
Milne's abilities and style as a lecturer and author are described in :-
He was notably gifted with the power of lucid expression in speech and writing, and it was highly interesting to see and hear him threading his way with surety through the steps of a complex argument. But complementary to his breadth of view was an intense interest in detail, which sometimes for his hearers obscured the main lines of his exposition.
As to Milne's character Whitrow writes in :-
Small in stature, Milne had outstanding qualities of mind and was a continual fount of inspiration to others as well as himself. ... Milne had the humility and simplicity of character that often goes with scientific genius, and he bore personal misfortunes with courage, dignity, and religious conviction.
In  he is described as:-
... very human, sharing in the delights of home and family, of meals, and of social ceremony. His happiness depended greatly on the good will and approval of his scientific colleagues; in spite of his unmistakable brilliance and achievement, in moments of depression he was sorely tried by a sense of inadequacy.
As a young man Milne had suffered from encephalitis lethargica. This was a type of inflammation which swept across Europe in an epidemic after World War I. Milne contracted the disease in 1924, and had made a good recovery by 1925. Usually associated with the disease there are Parkinson type symptoms which appear later in life, and this was so with Milne, in whom the after effects appeared around 1945. He suffered another tragedy in this same year when his second wife Beatrice died. Milne died from a heart attack in Dublin while attending a conference of the Royal Astronomical Society.
Article by: J J O'Connor and E F Robertson