**Charles Weatherburn**'s parents were Henry Weatherburn, a railway engineer, and Amelia Olding Cummins. Both Henry and Amelia had been born in England. Henry Weatherburn, the only son

*of Martin Weatherburn, a railway engine driver born 1805, and Ann Kilby King, was born in Leicester on 31 May 1849. Henry became an apprentice at the Midland Railway Workshops in Leicester in 1864 but was orphaned four years later when his mother died in May 1868 and his father in July 1868. At that time he decided to emigrate to Australia but continued to work at the Midland Railway Workshops until he emigrated on Brunel's "SS Great Britain" on 17 December 1871. He arrived in Melbourne, Australia, on 21 February 1872 and became one of the founders of the railways in Australia. Amelia Cummins, the fifth child of Richard Cummins, a tailor, and his wife Eliza was born in Bristol on 1 August 1849. The family, having seven children by this time, sailed on the "Morning Light" to Melbourne, Australia, in August 1859. Henry Weatherburn married Amelia on 1 May 1876; they had six children, Edith (born 1877), Martin Henry (born 1879), Margaret Eliza (born 1880), Percy (born 1882), Charles Ernest, the subject of this biography, (born 1884), and Lilly (born 1889).*

Charles was educated at Blackfriars School, Chippendale, Sydney and the Sydney Boys' High School which he entered in 1897. This school had been opened on 8 October 1883 and had moved to new premises in Mary Ann Street, Ultimo, in 1892. This was the first building designed as a High School in any of the Colonies and it was in this building that Weatherburn studied. He graduated from the High School in 1900, having been school captain, and later that year entered the University of Sydney. He studied under Horatio Scott Carslaw at the University of Sydney graduating with a B.A. in 1904, a B.Sc. in 1905 and an M.A. in 1906. His performance was outstanding, he was awarded the university medal in mathematics and earned the following praise from his teacher Carslaw [26]:-

Following the award of his M.A., Weatherburn went to England in 1906, after the award of a scholarship, and studied at Trinity College Cambridge where he attended lectures by Alfred North Whitehead, Edmund Whittaker and G H Hardy. He sat the Mathematical Tripos examinations in 1908, the same year as Selig Brodetsky, and was awarded a First Class degree. Returning to Australia, Weatherburn married Lucy May Dartnell (1883-1972) (described as "his childhood sweetheart" in [26]), the daughter of Thomas Dartnell and Harriet Evans, at St Andrew's Anglican Church, Summer Hill, Sydney on 6 March 1909. Charles and Lucy May Weatherburn had three sons, one of whom was Alan Keith Weatherburn (1911-2006). Weatherburn was appointed as a teacher of mathematics and physics at Sydney Boys' High School in 1909.He is without doubt the most distinguished of the mathematical graduates of Sydney in the thirty-one years during which I have been head of our Department.

In addition to teaching at the High School, Weatherburn also taught mathematics and physics at St Paul's College, an all male College affiliated to the University of Sydney. He left Sydney in 1911 when he was appointed to Ormond College of the University of Melbourne. The professor of mathematics at Melbourne was John Henry Michell and he encouraged Weatherburn to write a book on vector analysis. The result was *Elementary vector analysis, with application to geometry and physics* (1921).** **Certainly vector analysis was not universally accepted at this time and Weatherburn fought the battle for its acceptance against opposition from people such as Harold Jeffreys. Early exponents of the vector calculus had been J Willard Gibbs and Oliver Heaviside while its chief opponent had been Peter Guthrie Tait. When Weatherburn published the first of his two volumes on vector analysis in 1921 he wrote in the introduction:-

James Byrnie Shaw writes in a review [18]:-The work of Gibbs and Heaviside drew forth denunciations from Professor Tait, who considered any departure from quaternionic usage in the treatment of vectors to be an enormity.

For further reviews of this book, reprinted 14 times, and of other books by Weatherburn, see THIS LINK.The author's object in this book is to present the simpler portions of vector analysis and to apply them to portions of mechanics. He adheres to the notation of Gibbs. He gets as far as differentials and integrals, but does not bring in the notions of curl, convergence, and other ideas that belong to the general study of fields. The definitions are geometric for the scalar and the vector products, the vectors being always thought of as lines, or geometric vectors.

Pitman, writing in [16], describes how Weatherburn taught him as a student at the University of Melbourne (1916, 1917, 1920):-

In [26], Weatherburn's son, Alan Keith Weatherburn, writes of his father's time in Melbourne working under John Henry Michell:-There were very few honours students, and I was the only Ormond student doing honours mathematics in my year. I went to his room once a week, and sat near his desk while he talked and wrote notes for me. Always he wrote on the back of foolscap paper, the front of which was filled with an early draft of a section of one of his books. He took me through the topics in his two books on vector analysis, and perhaps also some differential geometry. ... He was neat and clear and interesting, and for me it was a very easy and efficient way of mastering vector analysis.

During his time in Melbourne, the general theory of relativity had been published by Albert Einstein. In 1920 Weatherburn wrote (see [5]):-Like Michell, he was a man of refinement, reserved and highly principled.

Frank Gamblen writes in [5]:-I have received from Einstein himself a copy of his recent papers, and I shall always consider it an honour to have done so. But still I am at liberty to say that the theory does not impress me as holding the secret of the laws of nature. I feel much more disposed to trust the classical theory, modified perhaps so as to recognise the principle of equivalence. Einstein's theory is wonderful - wonderful in its complexity and in the mathematical difficulties overcome. Newton's is even more wonderful - wonderful in its simplicity and in its agreement with nearly all the experimental evidence of two and a half centuries. I cannot agree with those who would make nature more akin to the complex than to the simple.

Weatherburn did indeed apply his own vector methods to the theory of general relativity and published the paperAt this time Einstein's Theory of General Relativity was only4or5years old. Very few had taken the trouble to make a thorough study of it, most were willing to accept it on the strength of Einstein's reputation. The young Weatherburn, however, read practically all the accessible literature and applied his own vector methods in an endeavour to arrive at a decision on the theory. The above quotation gives us a good insight into the character of Weatherburn - a man who would not take a decision lightly, who would not be swayed by others simply because of their standing and reputation, and a man who firmly believed in the simplicity and goodness of life.

*Vector algebra in general relativity*in 1921. He gives the following introduction to that paper:-

This paper was one of twenty that Weatherburn published while at Melbourne. Among these twenty, we also mention:The theory of general relativity was developed by Einstein with the aid of the absolute differential calculus of Ricci and Levi-Civita. All subsequent writers on the subject have followed his example in the use of this calculus, though the average reader admittedly finds great difficulty in the analysis, and really understands it even less than he thinks he does. It is the purpose of the present paper to give a presentation of the algebra of Einstein's covariant and contravariant vectors along the lines of matrices and ordinary vector analysis, in the hope that this will provide a more attractive approach to the theory of general relativity than the calculus of Ricci and Levi-Civita.

*Singular parameter values in the boundary problems of the potential theory*(1914);

*Vector integral equations and Gibbs' dyadics*(1916);

*On the hydrodynamics of relativity*(1917);

*Some theorems in four-dimensional analysis*(1917); and

*Green's dyadics in the theory of elasticity*(1923). For a list of all Weatherburn's papers, see THIS LINK.

Weatherburn left Sydney in 1923 to take up the chair of mathematics and natural philosophy in Canterbury College, University of New Zealand. At about this time his research interests changed from vector analysis to differential geometry. He wrote two major volumes *Differential geometry of three dimensions* (1927, 1930) as well as nearly 30 papers on this topic. Willian Hodge, reviewing the second volume, wrote [11]:-

For extracts from reviews of these two volumes, see THIS LINK.Much of the volume is devoted to subjects to which the author has himself contributed in the last few years, particularly in the theory of families of curves and surfaces, and of small deformations. Other topics are however included, with the result that the two volumes together give an account of most of the principal branches of classical differential geometry. An elementary account of Levi-Civita's theory of parallel displacements is given.

In 1929 Weatherburn returned to Australia taking up the chair of mathematics at the University of Western Australia (founded 1911), becoming the first holder of this chair. He held this post until he retired in 1950 but his excellent sequence of research papers stopped in 1939. He published *An Introduction to Riemannian Geometry and the Tensor Calculus* in 1938 and it was reissued in 1966. His work on this book had been funded by a grant from the Carnegie Corporation of New York which he held in 1935-36. This grant also enabled him to travel to the United States where he met Luther P Eisenhart and Oswald Veblen at Princeton.

After 1939 his only publication was a textbook on statistics, *First Course in Mathematical Statistics,* which he published in 1946. He begins the Preface as follows:-

Perhaps, surprisingly, we have found more reviews of this book on statistics than on his other books. Extracts from some of these reviews are given at THIS LINK.The object of this work is to provide a mathematical text on the Theory of Statistics, adapted to the needs of the student with an average mathematical equipment, including an ordinary knowledge of the Integral Calculus. The subject treated in the following pages is best described not as Statistical Methods but as Statistical Mathematics, or 'the mathematical foundations of the interpretation of statistical data'. The writer's aim is to explain the underlying principles, and to prove the formulae and the validity of the methods which are the common tools of statisticians. Numerous examples are given to illustrate the use of these formulae; but, in nearly all cases, heavy arithmetic is purposely avoided in the desire to focus the attention on the principles and proofs, rather than on the details of numerical calculation. The treatment is based on a course of about sixty lectures on Statistical Mathematics, which the author has given annually in the University of Western Australia for several years. This course was undertaken at the request of the heads of some of the science departments, who desired for their students a more mathematical treatment of the subject than those usually provided by courses on Statistical Methods. The class has included graduates and undergraduates whose researches and studies were in Agriculture, Biology, Economics, Psychology, Physics and Chemistry. On account of such a diversity of interest the lectures were designed to provide a mathematical basis, suitable for work in any of the above subjects. No technical knowledge of any particular subject was assumed.

From the time of his appointment in 1929 until 1938 he had been assisted in teaching mathematics at the University of Western Australia by members of the physics department. However, after 1938 he had to undertake all the mathematics teaching with the assistance of only one lecturer. However this [26]:-

He received several honours for his mathematical contributions, including the award of the Hector Memorial Medal and Prize by the Royal Society of New Zealand in 1934 and an honorary degree from the University of Glasgow, Scotland, in 1951. In 1971, a mathematics lecture theatre at the University of Western Australia was named in his honour.... drew from him 'businesslike qualities of a very high order'. He was unstinting in his assistance to students. His peers acknowledged his gift of lucid exposition, his love of teaching and his power of easy control in his classes.

Gamblen writes in [5]:-

His body was cremated after his death and his ashes were buried in Karrakatta Cemetery, Nedlands, Western Australia.After retirement[in1950]he and Mrs Weatherburn continued to live in their home at Nedlands and he became a keen and active member of the local Bowling Club. From the time of the death of his wife in1972until a few days before his own death on18October1974he lived alone in the family home - always pleased to welcome for a cup of tea and a chat old students and friends who cared to drop in, and whether the call was early or late he was always as immaculately dressed as in his lecturing days.

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