George Gabriel Stokes spent most of his life at the University of Cambridge, where he undertook his undergraduate degree and later became Lucasian Professor of Mathematics and Master of Pembroke College. However, he spent the first 13 years of his life in Skreen, County Sligo, Ireland, a rural area right by the coastline, overlooking the Atlantic Ocean. As this paper will discuss, the time he spent there was short but its influence on him and his research was long reaching, with his childhood activities of walking by and bathing in the sea being credited for first piquing Stokes' interest in ocean waves, which he would go on to write papers about. More generally, it marked the beginning of an interest in fluid dynamics and a curious nature regarding natural phenomena in his surroundings. Stokes held a special affinity for the ocean for the rest of his life, constantly drawing inspiration for it in his mathematical and physical studies and referencing it in his correspondences. This commentary was written to celebrate Stokes' 200th birthday as part of the theme issue of Philosophical Transactions A.

This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

1. Introduction

George Gabriel Stokes was born on 13 August 1819 in Skreen, Co. Sligo, to Gabriel Stokes, the Protestant minister to the parish of Skreen, and Elizabeth Haughton. Despite only spending 13 years [1] there, Stokes' early life in Skreen had a massive impact on him, and on his research areas in particular. Stokes' childhood home is a mere 3.7 km from Dunmoran Strand, a sweeping stretch of a beach overlooking the Atlantic Ocean (figure 1). It is untamed and unspoilt still, so it is easy to look out on the water, as Stokes would have done, and see the expanse of blue-grey sea before you, waves churning, rising and then crashing as they break onto the shore (figure 2). Stokes spent much of his childhood walking upon these shores, and on other Irish coasts in Antrim and Malahide later in his life. The scope and breadth of his research was impressive and varied, but as the French physicist Marie Alfred Cornu said in his 1899 Rede Lecture, the overarching theme of his work was concerned with waves [2]. Although this is a varied term when used in physics, the physical phenomena of sea waves fascinated Stokes as he used his mathematical prowess to explain. Following a recommendation from his coach [3], William Hopkins, Stokes undertook research in hydrodynamics following his completion of his undergraduate degree. His first published papers were in the field of fluid dynamics, namely his 1842 paper ‘On the steady motion of incompressible fluids’ [4] and his 1843 paper ‘On some cases of fluid motion’ [5]. In William Thomson's (better known as Lord Kelvin) address in Stokes' Copley Medal presentation, he referred to the ‘exceeding difficulty of the mathematical work’ that Stokes undertook in hydrodynamics which added a ‘previously unknown province’ to the field [1]. Following his appointment to the newly established Meteorological Council in 1866, Stokes turned his attention to practical problems involving ocean waves. And, of course, Stokes' derivation of what are now known as the Navier–Stokes equations, the mathematical basis for the solving of problems in fluid dynamics [6]. These equations, which have the capability to describe fluid flows over a large range of scales, now have a range of applications in our modern world such as in climate modelling, vehicle design and blood flow study. The open question of the regularity of solutions to the Navier–Stokes equations is also one of the seven Millennium Prize Problems set out by the Clay Mathematics Institute [7]. In this very brief summary, it is indisputable that Stokes' contribution to the study of fluids made him a giant of the field. But he may never have pursued this field at all, and made the contributions that he did, were it not for his childhood growing up beside the Atlantic in Skreen.

Figure 1. Dunmoran Strand in County Sligo on a spring day. (Online version in colour.)

Figure 2. Waves crashing onto the shore at Dunmoran Strand. (Online version in colour.)

2. Childhood and growing up by the sea

Stokes himself described his early life as an ‘uneventful one’, saying he had ‘not much to record’ regarding it. He was the youngest of eight children. His father provided religious teaching but also a broader introduction to education: an alumnus of Trinity College Dublin, Gabriel Stokes was able to teach his children Latin grammar. Elizabeth Stokes, George Gabriel's sister, said that her brother was ‘very well-grounded in Latin by my father before he went to school’. George Coulter, the parish clerk of Skreen, also taught Stokes before he left for Dublin to study at the Revd R. H. Wall's school on Hume Street, Dublin. Stokes' talent for mathematics was evident from a young age, with Coulter remarking that Stokes worked out ‘new ways of doing sums, far better than those given by Voster's Arithmetic; and clever people were surprised by the questions which he used to solve by the arithmetical rule of False Position’. Skreen was an isolated location, described as an ‘out-of-the-way quiet place’ where ‘no coach or vessel came near’. Both of Stokes' parents had much influence over Stokes and his siblings, despite being very different in character: their mother was ‘a beautiful and somewhat stern’ woman, whereas their father was of a more ‘taciturn nature’. The children had a large Newfoundland dog named Bronte: in a letter not long before her death, Stokes' sister Elizabeth asserted that ‘he and George were great friends’. This letter also provides insight into how Stokes had a curious and questioning mind, even at a very young age, with Elizabeth stating that he ‘asked many questions, as, for instance ‘But, William, is the hawk a bird, and does he really eat mice?’. Despite his early curiosity, Stokes' mother grew worried about him as he was very slow in learning to read. However, Elizabeth's letter claims that the material in question was simply ‘too childish for his mind’, and that upon 1 day requesting from his mother that he might read the psalms, there was ‘no further difficulty’ with his reading ability.

If Stokes' curiosity was one trait that was going to stick with him throughout his years, then so too was his strong sense of morality. Elizabeth spoke of his ‘strict sense of honour and truthfulness’, even at a young age, stating: ‘I do not think he ever told a lie’. His principles were developed at a very young age and stayed with him for life, often manifesting themselves as stubbornness: Elizabeth also recounted an anecdote about when Stokes pretended to be a bird, only to be told by his brother William that that meant he must eat a worm. Although initially objecting, following encouragement from William that it was the right thing to do, ‘he opened his mouth’. Much future paradox of his character could be seen during childhood: he was very exact. When being asked the time as a young boy he said ‘I can't tell you what o'clock it is now, but when I was at the clock it was such an hour’. However, he was equally absent-minded, one day returning from running errands without any tasks completed, stating ‘I forget who sent me and what it was about’. It's clear that Stokes’ childhood presents many of his traits that would be recounted in anecdotes and correspondences in later years. His need to ask questions and examine things, his steadfast beliefs in his religion and his principles, his absentminded yet exact nature: these are all traits we see as we examine Stokes' life in later years. And with this in mind, it is fair to claim that his childhood of growing up by the sea influenced Stokes’ research interests in his later mathematical life. His interest in scientific questioning and experimentation evidently began at a young age, and so it's viable and probable that the sea piqued his interest and never really left [1].

In a much quoted passage written by Stokes' daughter, Isabella Humphry, she writes that her father was ‘one of a large family living in a country village near the sea. The home-life in the Rectory at Skreen was very happy, and the children grew up in the fresh sea-air with wellknit frames and active minds’ [1]. The sea is mentioned twice in these introductory sentences about Stokes' life, indicating at the importance this held for the man and his work (figure 3).

Figure 3. Dunmoran Strand at sunset. (Online version in colour.)

3. The sea in later life

It seems that the ocean never really left Stokes, even when he was living away from it. Following his graduation, Stokes was once observed at a party hosted by the Cambridge Observatory entirely engrossed in ‘making waves with the spoon in his tea-cup, watching their formation in abstracted silence’ [1]. Creating and observing these waves was a ‘habit which he never lost’, according to his daughter [1]. It was also an observation that he tried to make others consider: in a collection of notes for students prepared by Stokes and William Thomson, Stokes references this habit in an attempt to illustrate the viscosity of fluids: ‘The subsidence of the motion of the motion in a cup of tea which has been stirred may be mentioned as a familiar instance of friction’ [8].¹

Humphry also recounted the many excursions she and her father took in her youth, which almost entirely involved a coastline of some sort. During one vacation in Antrim, Humphry recalled a walk from Port Ballintrae to Portrush to attend a picnic. Stokes, however, was eager to carry out some experiments ‘on waves in a cave near Portrush’. After wading out, he ‘worked away at his waves, so that we waited rather long, and the tide was quite high when we set off back’, an anecdote Humphry recounts fondly despite the fact that it led to them missing the picnic’. It is through Humphry's recounting of her childhood memories with her father that we see how the sea continued to play an important role in Stokes' life: he was ‘fond of walking on the Velvet Strand’ when they would stay with his sister Elizabeth in Malahide. Many long vacations were spent at the Observatory at Armagh, Elizabeth Haughton's homeplace, and Humphrey recalls visiting ‘some seaside place, oftenest the magnificent neighbourhood of the Giant's Causeway’. These times were productive ones for Stokes. He spent the afternoon undertaking ‘long walking expeditions’ and climbing cliff paths. The family visited the Land Cave following storms on the Atlantic, described as ‘a sort of window opening into it from the land, so that we could see the great waves come in, making the cave dark; it was striking to see such great masses of water fall without sound upon a bed of foam’. Humphrey said that her father made many observations about waves while they were in the Land Cave, saying he was ‘trying to find out the relation of the waves to one another and why the ninth wave was so much larger than the others’. These observations probably resulted in Stokes' 1883 paper ‘On the highest wave of uniform propagation’ [9].

Humphry says that it was one of the ‘great disappointments’ of her young life that she never got to visit Skreen with her father [1]. She had been too young to go with him when he returned once alone, and it seemed odd that they never visited ‘as for many years a good part of every Long Vacation was spent in Ireland’. Stokes spoke fondly of his homeplace, telling his daughter of his ‘happy childhood’ and wishing to ‘visit the dear place again’. Humphry begged to visit with him, and he agreed, but although the trip was organized, Stokes’ feeling of duty to his work always took precedence, and a ‘pile of papers to look over from the Royal Society’ disrupted the plan’. Humphry was disappointed that she didn't get to visit ‘those old places always so dear to him’, indicating the fondness with which he spoke about Skreen. She said he spoke very often about his early years, and that to her they seemed far more interesting to him than his time as an undergraduate. Humphry felt that if she had visited Skreen, she ‘should perhaps have better understood how he came to be all he was’, showing that even his own daughter felt that his homeplace of Skreen had a major influence on the man Stokes was to become.

Although Stokes was far from a sporting man, he was a ‘venturesome swimmer’ [1]. As a young man he was ‘somewhat rash’ both on foot and in the water, having had ‘narrow escapes among the mountains of Westmorland and Cumberland’. ‘Stokes was one of the first members of a new bathing group in the Grantchester meadows and was recognized as ‘a bold and strong swimmer’. Prof. George Downing Liveing, a Professor of Chemistry at Cambridge swam with Stokes, and in his appreciation piece on Stokes he said that Stokes spoke ‘with warmth of the keen enjoyment of a battle with the waves when there was a good sea on and he was just as fond of a sharp walk in the face of a biting nor-easter’.

4. Influence on his work in hydrodynamics

Stokes’ contributions to maths and science were wide and varied, but here I will focus on those of the initial field he chose to study: hydrodynamics. When Stokes was awarded the Copley Medal in 1893, his friend and successor to the presidency of the Royal Society, William Thomson, presented the medal. In his speech, Thomson provided a recollection of ‘great work’ Stokes had completed throughout his career, but began with mentioning that ‘fifty-two years ago he took up the subject of fluid motion’ before outlining his ‘wholly original genius for discovery in properties of real matter, which enhanced the superlative beauty of the mathematical problems by fresh views deep into the constitution of matter’. Reading the rest of Thomson's speech and the encounters Stokes had with the sea and the elements during his childhood in Skreen cannot but be noted as Thomson outlines Stokes' affinity for waves: ‘from the “infinitely small” waves of Cauchy and Poisson to deep-sea waves of such considerable steepnesses and lengths and heights as are seen in nature—on water 500 fathoms deep, or more—after a severe gale far away from land’. As well as the mathematical studies of the waves, there were also the more practical applications where Stokes showed how his solution could be carried ‘right up to breaking waves at sea and tidal bores in shallow water’. Thomson also highlighted the importance of Stokes' work on the motion of viscous fluids, which had applications in many natural phenomena such as the distance of audibility of sound, the suspension of clouds in the air, ripples on a pond and waves on the ocean after wind stops [1].

In Stokes' letters and papers, he often references the Atlantic Ocean. In a letter about the theory of ear trumpet, Stokes was insistent that the best way to visualize the problem at hand was to imagine an Atlantic swell: ‘Perhaps the state of things would be better pictured to the mind by thinking of a long Atlantic swell coming into a creek 20 or 30 feet long. Suppose the water deep; then the rise of the water at the end would depend on the tapering form of the creek’. In a later letter, Stokes mentions a phenomenon of miniature thunderstorms by the Atlantic in southwest Ireland when discussing electricity, and more specifically electricity in the condensed vapours emitted by volcanoes. ‘There is a place somewhere on the southwest coast of Ireland where miniature thunder storms are of frequent occurrence. Air laden with vapour comes from over the Atlantic up a valley between two mountains, and gets condensed, and the result is that there are frequent little thunder storms. The vapour is here caught in the act of condensation, and the condensed vapour of giving out electricity’ [1].

Stokes also asserted that the best place to study the mathematics of surface waves was at the ocean itself: ‘It is only I imagine on an oceanic coast, and even there on somewhat rare occasions, that the form of the waves of this kind, of nearly the maximum height, can be studied to full advantage’.

5. Conclusion

Stokes is known and admired for much more than just his work in fluid dynamics. However, his major contributions to the field mean that this was an important area of his contributions to mathematical and physical sciences as he sought to sate his curiosity and explain phenomena seen in everyday life. His time as a child in Skreen may have been brief, but it was influential in forming many aspects of his character. There is currently a plaque in Skreen at Stokes' birthplace to commemorate him (figure 4), reading:

George Gabriel Stokes

Born in the Old Rectory

Skreen 13 August 1819

Died Cambridge 1 February 1903

Mathematical Physicist

Lucasian Professor of

Mathematics at Cambridge

President of Royal Society.

Figure 4. Commemorative plaque at Sir George Gabriel Stokes' birthplace in Skreen, County Sligo. (Online version in colour.)

But perhaps that commemorative plaque should stand at Dunmoran Strand, on the beach he walked on as a child which gave way to the great expanse of the Atlantic. For it was there that Stokes first had a glimpse of the subject that was to be such a huge part of his life, and he a huge part of the subject. As his daughter recorded: ‘He told me that he was nearly carried away by one of these great waves when bathing as a boy off the coast of Sligo, and this first attracted his attention to waves’ [1]. If Stokes' father had been posted to a different parish rather than Skreen, it seems that the field of fluid dynamics would have suffered for it.

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Competing interests

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Footnotes

1 The observation about the spin-down of the fluid in a tea-cup misses the key process of Ekman pumping. Spin down ignoring these layers can be simply demonstrated to take much longer than observed (and also would not lead to the commonly observed pre-teabag phenomenon of tea leaves accumulating at the centre of the base). I thank one of the anonymous referees for drawing my attention to this point.

One contribution of 14 to a theme issue ‘Stokes at 200 (Part 1)’.