John McCowan's parents were William McCowan, a tailor and clothier, and Mary McKay. His birth was registered at Causewayhead, just north of Stirling, on 19 February 1863. William and Mary had been married in Glasgow on 21 March 1862, and John was their first child. William McCowan's father, also named John McCowan like his grandson, had also been a tailor in Bridge of Allan. He had earned extra income by running a lodging house for visitors who came to Bridge of Allan to take the waters. In a letter written to his sister on 29 April 1869, when his grandson was six years old, John McCowan Senior paints a picture of what Bridge of Allan was like. We quote the letter at length since it gives a feel for the times in the town when the subject of this biography was growing up :-
We are all well at present. This is a time when a great many strangers are here at the wells. Our houses here are mostly let to Lodgers. I intend to buy a Bridge of Allan paper on Saturday to send to you, in which you will see that there are a great deal of people here at present. This is our busiest time in the year to make up our rents. My wife is very much toiled in cooking for them. You have here the picture of the house where the mineral water is drunk, also of the baths for invalids, a much frequented place. They have always a great many lodgers. They are making a great addition to the bath house this season, and when completed it will be a great building and will contain a great many Lodgers itself, which may be against other peoples houses letting but the place is always increasing. We have new houses getting up every year. It vexes me often to think that I might have had a house of my own when I have it not, but have to pay a heavy rent, but I must not repine. My days here cannot be long now, but I may be thankful that at present I am so well, for a short time ago I was confined to my bed. The rest of my family are just about the same way as when I wrote last.
John McCowan attended the University of Glasgow, taking classes in Latin and Greek in Session 1879-80. In Session 1880-81 he took the B.Sc. Chemistry class and the Junior Class of Civil Engineering and Mechanics in which he was placed fifth. In 1881 he was awarded the Malcolm Kerr Bursary in Natural Philosophy by examination, then in the next session, 1881-82, he was extremely successful being awarded the Certificate in Engineering Sciences. He also passed B.Sc. Natural Philosophy, Civil Engineering and Mechanics, Office and Field Work in Engineering, and M.A. Mathematics and Natural Philosophy in April 1882. He received many awards in Session 1881-82 such as the First Prize in Engineering, the First Walker Prize for the Written Examination, and the First George Harvey Prize. He was also First Equal in the Senior Class of Office and Field Work in Engineering, and Second Equal in Laboratory Studies. He graduated with a B.Sc. in 1883, taking courses in mathematics, natural philosophy and geology, but given his outstanding engineering work from the previous session it is a little surprising that he was only awarded a B.Sc. with Second Class Honours in Mathematics and Natural Philosophy. It is worth noting that taking a B.Sc. as a first degree, although the norm today, was unusual in the 19th century since most Scottish students at this time took an M.A. as a first degree, then those who were so inclined took a B.Sc. as a second degree. In fact references to McCowan in the Minutes of the Edinburgh Mathematical Society in 1885 wrongly put M.A. after his name instead of B.Sc. He had already taken some M.A. courses and in 1883 he was taking further M.A. courses, being the best student in Second Year Mathematics.
After graduating with a B.Sc., McCowan was awarded the Thomson Experimental Scholarship for Session 1883-84. McCowan was recommended for this Scholarship, founded by Sir William Thomson(later Lord Kelvin) in 1869, for showing :-
... zeal and ability in experimental investigations in the Physical Laboratory.
By the terms of the scholarship, he had to engage in continuous investigation for at least nine months and, from October 1883 to June 1884, McCowan reported to Thomson on the progress of his work. We give an indication of the content of McCowan's reports to show the experimental research he was undertaking while holding the Scholarship (see ): 15 October 1883 - comments on his work testing a variation to the accepted method of testing bar magnets. Also mentions his use of a ballistic galvanometer in an experiment carried out with the aid of William Henry Watkinson; 27 October 1883 - gives the results of tests carried out with Geoffrey A Jackson to ascertain the strength of magnetism in each part of some selected magnets; 2 November 1883 - concerns experiments with Geoffrey A Jackson on the strength of magnetism; 29 November 1883 - reports on experiments involving the weighing of electricity; 27 February 1884 - gives tables of results of tests involving the use of a galvanometer and Clark's Cells; 8 May 1884 - discusses adjustments to apparatus mentioning current standardizers; 14 May 1884 - discusses the deficiencies of the current-standardizer; 15 May 1884 - more on the defects of the current-standardizer; 22 May 1884 - explains his delay in providing results of tests; 23 May 1884 - gives further details on the current-standardizer; 23 May 1884 - second report that day giving a table of results of tests on a second current-standardizer; 26 May 1884 - gives further details on the current-standardizer with a table of results; 29 May 1884 - reports on the arrival of a new design of current-standardizer; 29 May 1884 - second report on this day describing further tests involving the current-standardizer, ammeters, Clark cells and magnetism. The report also mentions Lord Rayleigh and ends with a table of results; 30 May 1884 - gives results of an experiment involving the use of galvanometers. Report includes tables of results; 2 June 1884 - reports on tests on an amperemeter.
McCowan sat the University of Glasgow M.A. examinations in Mathematics and Natural Philosophy in November 1884 before leaving to take up an appointment at the Royal College of Science in Dublin. At this College the Professor of Applied Mathematics was Sir Robert Ball and the Professor of Physics was Sir William Barrett, both being very eminent scientists. In January 1885 McCowan was proposed for membership of the Edinburgh Mathematical Society by Thomas Muir, the proposal being seconded by Andrew Barclay. He was duly elected to the Society at the meeting of 13 February 1885. Having passed examinations in earlier years, he was awarded an M.A. with First Class Honours in Mathematics and Natural Philosophy by the University of Glasgow in 1886. After four years in Dublin, McCowan returned to Scotland by 1888, being appointed as a demonstrator of physics and assistant in mathematics to Professor John Steggall at University College, Dundee. He held this position until his death. In his report on Session 1888-89 Steggall explains new developments in the Department as well as noting McCowan's appointment :-
... the Mechanical Laboratory in the Technical Institute has been opened, and the students in my department have derived great advantage thereby: the additional space was much needed, and the propriety of the development of our laboratory work on the mechanical side of natural philosophy seems proved by the great interest taken by my students in this special branch of the work. The practical examinations in natural philosophy for the degree of B.Sc. at St Andrews largely consists of mechanics, and this gives us additional reason for appreciating the extension. The new lecture room has also proved of the greatest service. ... After five years' loyal service my friend Mr Capstick left us for Cambridge. He was succeeded by Mr John McCowan, whose attainments as a mathematical physicist have been of great value to my department.
In his report for Session 1890-91 Steggall writes :-
I have much pleasure in reporting that my assistant Mr John McCowan has read and published three original papers during the past session; two of them dealing with Applied Mathematics are concerned with important problems on the conduction of heat in electrically heated conductors, and on the form of the solitary wave in water of finite depth.
McCowan read papers at meetings of the Edinburgh Mathematical Society frequently during a very active period between 1891 and 1895. The first paper he read was On the heating of conductors by electric currents, and the electric distribution in conductors so heated at the meeting on 9 January 1891. The next paper, read on 8 May 1891, was On the solitary wave. This paper, perhaps the most important work by McCowan, was published in Philosophical Magazine. Here is a brief explanation of the context and main result of the paper:-
Boussinesq (1877) was responsible for the most frequently quoted profile of a wave. Interestingly, this followed from a first approximation to the effects of surface curvature on the hydraulic pressure assumption for long waves. McCowan applied Stokes' notion for breaking to obtain the maximum relative height to breadth of 0.78.
This brilliant work on waves led to him being awarded a D.Sc. in April 1892. In his report on Session 1891-92 Steggall wrote about McCowan's lecturing duties and his D.Sc. :-
In the evening an earnest class of four students took Senior Mathematics under Mr McCowan; while the Laboratory Class absorbed both his energies and mine on Wednesday evenings as usual. ... I have pleasure in reporting that Mr J McCowan, Assistant Lecturer and Demonstrator in my Department, has received the degree of D.Sc. under the new regulations, from the University of Glasgow, on presenting as credentials his original papers on wave motion and on heat conduction, to which I directed your attention last year.
A regular attendee at meetings of the Edinburgh Mathematical Society, he presented the papers: On a representation of elliptic integrals by curvilinear arcs (12 June 1891); On the solution of non-linear partial differential equations of the second order (13 May 1892); and Note on the solution of partial differential equations by the method of reciprocation (11 November 1892). At this meeting McCowan was elected to the Committee of the Society, then at the November meeting in the following year of 1893 he was elected Vice-Chairman. He continued to present papers: On ridge lines and lines connected with them (8 December 1893); On the highest wave of permanent type (8 June 1894); and On the solitary permanent wave: a continuation (9 November 1894). At this meeting he was elected as President of the Society. The paper On the highest wave of permanent type was published in the Philosophical Magazine in 1894. In it he proved that the breaking angle of a wave in shallow water is still 120, though it is tipped out of vertical symmetry. McCowan presented one further paper to the Society, namely On the operation of division on 10 April 1895.
Florian Cajori, in his A History of Mathematics (1893), briefly discusses McCowan's contributions:-
J McCowan of University College at Dundee discussed this topic [waves] more fully and arrived at exact and complete solutions for certain cases. ... methods of approximation were given by Lord Rayleigh and John McCowan.
In his report on Session 1897-98 Steggall writes :-
I need hardly add that I have been loyally supported by Dr McCowan, whose cooperation and advice I am always glad to receive.
Sadly McCowan' health deteriorated, forcing him to reduce his research activities. The cause of his illness appeared to be heart problems. In Session 1898-99 Steggall writes :-
Dr McCowan was prevented by illness from discharging his duties which were in consequence taken up by Mr Hugh Mitchell, B.Sc. of Edinburgh.
Further deterioration led to him being given six months leave from University College, Dundee, and he lived in Henderson Street, Bridge of Allan. Henderson Street is the main road through the centre of the small town and he now lived with his father William McCowan, who had by this time retired from his occupation as a tailor and clothier. His mother had died some years earlier. John McCowan died at 6 a.m. on the morning of 24 November 1900. The death certificate was signed by Dr James Hosack Fraser, an eminent Bridge of Allan doctor, and gives the cause of death as 'Heart Disease'.
At the meeting of the Edinburgh Mathematical Society on 14 December 1900, the chairman, John Watt Butters, made a sympathetic reference to the death of Dr John McCowan who was president of the society during Session 1894-95. At the meeting of the Society on 11 January 1901 John Steggall explained that the mathematical papers of the late Dr McCowan had been handed over to him "for examination with a view to their ultimate publication". It was agreed that Steggall should consult with George Alexander Gibson. The society hoped that some of Dr McCowan's papers could first of all be published in the Proceedings. In his report on Session 1900-01 Steggall writes :-
The early part of the session was marked by the sudden death of Dr McCowan, who had obtained leave of absence on account of ill-health. The College has lost one who was not only an admirable teacher, but also singularly gifted as a scholar, both as regards his erudition and his originality. his place has been taken by a former student in the Department, Mr R Norrie. It will be remembered that during the previous session the unexpected failure of Dr McCowan's health caused considerable inconvenience to the Departments of Mathematics and Physics. At the beginning of the present session we were still more unfortunate in the former department, for until the middle of November it was impossible to find a substitute.
Article by: J J O'Connor and E F Robertson