The textbook in question is

*An Introduction to the Calculus: Based on Graphical Methods*, G A Gibson, MacMillan & Co Ltd, London 1901-65 (23^{rd}printing)

I acquired this excellent little treatise in my usual way, at a second-hand bookshop, and in due course realised that its treatment of the catenary was by far the clearest and most rigorous of any texts I had available (including the internet).

But only now has it also occurred to me that there are levels of coincidence involved that would have had Arthur Koestler sitting up on the edge of his chair.

In 1901, the year of first publication of this textbook, George Alexander Gibson was Professor of Mathematics at the Glasgow and West of Scotland Technical College – where Robert Waddell was taking mathematics lectures during the first year of his course in Naval Architecture, in which a study of advanced calculus would have been essential. It is therefore highly probable that this very textbook would have been recommended to the students as an up-to-date resource to invest in. It is also conceivable that Gibson himself would have been closely involved in the delivery of the course, and may even have taken the podium himself.

The following information has been extracted from the University of Glasgow website www.universitystory.gla.ac.uk/biography/?id=WH0269&type=P.

George Alexander Gibson (1858-1930) was Professor of Mathematics at the University from 1909 to 1927. He was awarded an LLD in 1927. The Gibson Lectureship in the History of Mathematics was founded in 1927 from funds raised by his friends, and provides for periodic lectures.

Born in Glasgow, Gibson graduated with an Ordinary MA from the University in 1881 and gained a Euing Fellowship in Mathematics and Natural Philosophy. He became Assistant to the Professor of Mathematics in 1883 and then a lecturer. He was Professor of Mathematics at the Glasgow and West of Scotland Technical College from 1895 until he was appointed to the University Chair in 1909.

Gibson was a respected mathematician who wrote several text books and was recognised as a leading historian of the development of his discipline.

See also the interesting biographical link www.glasgowwestaddress.co.uk/1909_Glasgow_Men/Gibson_George_Alexander.htm

But what really makes the hairs stand up on the back of ones neck is the next link, www.theglasgowstory.com/image.php?inum=TGSD00063, in which Professor Gibson is depicted in a high-wire performance on, of all things, a catenary!!!

Cartoon in *Glasgow University Magazine* 31 October 1923 by "Psi" (Ian Phillips), depicting Professor George Alexander Gibson.

Gibson (1858-1930) entered the University of Glasgow in 1874 and after graduating he became assistant to William Jack, Professor of Mathematics. In 1895 he became Professor of Mathematics at the Glasgow and West of Scotland Royal Technical College. He left in 1909 to become Professor of Mathematics at the University of Glasgow, where he reorganised and raised the level of teaching, providing tutorials for all students and dividing the classes into smaller groups.

Gibson wrote a number of widely used textbooks, mainly on calculus, and became an authority on the history of mathematics. He was also one of the early members of the Edinburgh Mathematical Society. A series of lectures was instituted in his name after his retirement and in 1930 the first lecturer in the series was Albert Einstein.

Reference: Glasgow University Archive Services, DC198/32a

And now sit back and enjoy his incisive account of the catenary equation.

Title page

p 164 (a vital preliminary)

p 184

p 185

p 186