Paradigm, No. 27 (February, 1999)

My subject is a collection of letters written for a very specific purpose and to a very specific person. The letters amount to a correspondence course in calculus, trigonometry and electromagnetism, aimed at first-year science for London University Intermediate exams: they were never used by anyone other than by the recipient, nor indeed read by anybody else until I started on them. They were certainly teaching material, giving detailed instruction and explanation in these subjects: whether they constitute a text-book is another question.

The author was born in 1887. He was Barnes Wallis, an engineer, designer and inventor of some note. Regrettably in some ways, the reason why most people remember him is for the bomb which breached the dams of the Ruhr valley in the second world war. I say regrettably, because his achievements ranged very widely: airships, heavier-than-air craft, most notably the Wellington [bomber, ed.], variable-geometry aircraft, submarines, bridge design, telescope construction, medical callipers, racing skiffs, school furniture and buildings, household gadgets, and a technique for accurate wood-carving.

You might expect from all this, and from the fact that he ended up an F.R.S. [Fellow of the Royal Society, ed.], knight, fellow of many learned societies and holder of honorary doctorates from innumerable universities, that he had had what might be called a full education. He was well grounded at Christ's Hospital, a school to which he gave unreserved affection, loyalty and service throughout his life thereafter, and which he regarded as his alma mater. He had the good fortune to be taught science by C. E. Browne, who had been a pupil and was a devotee of Professor Armstrong and his heuristic methods of teaching: the benefit of this was, as Barnes claimed, that he was taught to 'think'. But he left school at 16, failing London matriculation, which he had attempted on his own. He made the decision to leave, much against everybody's will, partly for reasons of family finance, but more because he wanted very strongly to be an engineer. In 1904, the year in which he left school, engineering was not accepted as a profession for gentlemen; public schools did not expect, and therefore did not facilitate in any way, entry into it. For this reason, no teaching relevant to the matriculation syllabus, which would enable entry to a less prestigious university, was given; entry into these universities was not expected. Young Barnes wanted to learn on the job, indeed he had no other genuine opening, and so he left and took up an apprenticeship. He learnt the hard way, on his own, by reading, and from his experience on the shop floor and drawing office. Using the Cambridge Correspondence Course, he passed his Matric, became an associate of the Institution of Civil Engineers, then a Member, and thus professionally acceptable. Finally in 1920, because of financial difficulties in the airship industry which he had joined in 1913, he was laid off as chief designer in the airship division of Vickers Engineering; but he turned misfortune into an opportunity, and got his B.Sc. in 5 months, without any outside assistance.

The recipient presents a very different picture. Born in 1904, she was brought up in a large and very close family, an odd mixture of Victorian rigour and personal eccentricity. She had a full education of the kind that was normal for a young lady of the time, passed her matriculation, and entered University College London determined to read medicine. This involved the routine science subjects in the first year, but her education had left her with a very inadequate knowledge of physics, and little facility in or understanding of mathematics.

The two of them, Barnes and Molly, met for the first time in early 1922; he at 35, was experienced and highly respected in his profession, and had knocked about a bit, though he had never had any close female contact since his mother, to whom he was devoted, died in 1911. She at 17, was without any experience of the world of work or of men, or of anything outside the family fence, and was even more naïve than a well brought-up girl ought to be. They were cousins, through second marriage, and hence contact was not at first something that was questionable. Both were attracted, love at first sight they both affirmed ever afterwards. Doubtless her freshness, innocence and straightforwardness appealed to him. Certainly the attention of someone so mature, experienced and clever intrigued her.

The course began in 1922, in Molly's first term at University, and continued until the spring of 1924, ending as she took her mock intermediate exams, but it is not obvious why it took the form of a correspondence course. Barnes and Molly were cousins, both lived in London, and therefore might have met for lessons safely chaperoned by her aunt or in her family home. He was not of an undesirable character, young, flighty or irresponsible so why did he have to embark on this arduous, and less advantageous method of distance teaching?

In the first place, being out of his proper employment, he took a job teaching mathematics at an English college in Switzerland -- yet he had absolutely no teaching experience and his own experience of schooling had ended 18 years earlier and was curtailed at that. Molly, starry-eyed, wrote about her difficulties with the course. Barnes, eager to help, to teach, inspired by affection and totally enthusiastic about mathematics, wrote back at length, and thus it started.

Added to the problem of distance was Molly's father's Victorian unwillingness to countenance any idea of close contact with a man for his favourite daughter. When Barnes came home for the Christmas vacation, he was foolish enough to tell Molly of his love. Molly in her turn was so excited, and so naïve, that she rushed home and told the glad news to her family. Her father told Barnes exactly what he could do with himself, and forbade letters or visits. However, there was the problem of the maths, and the help that Barnes was undoubtedly able and willing to give. Thus in the end, letters were allowed, once a fortnight, and no personal nonsense. But the letters accompanying the lessons, although readable by anybody, were not exactly chilly.

Now we come to the first hints of Molly's problems. It was her cri de coeur written soon after her course at University started which precipitated the matter:

Physics is positively hopeless, the old boy dashes along at such a rate that I can't possibly keep up with him, and the terms he uses are all so much Greek to me. I've never done any before.

Not an auspicious beginning, you may think. Barnes wrote in answer:

You cannot get really far in physics without a good ground work of maths to help you. I suppose it's silly of me to think I might be of any help by writing to explain things to you? Would you let me try? You see I've had so much difficulty with these things myself, as I have had to learn all I know without any tutor, or sometimes by correspondence, that I can often see the hard parts better than other people.

Two weeks into his career as a schoolmaster, Barnes reported on his teaching of physics to the boys. He had them:

up to units, fundamental and derived, and so to the idea of dimensional equations . . . . . . . I find dimensional equations a terrific help myself [Here he inserts an example, which was probably unintelligible to Molly]. Then when you come to deal with forces and accelerations you can set them down like that, and see just what you are doing. If you do think I could help, just send a postcard and I will write by return. Please let me try.

A postcard crossed the Channel at once:

thank you, Barnes, for offering to help me. I'm afraid the matter is that I am so terribly stupid. Our lecturer goes so fast that I simply can't follow him. He started by telling us what displacements all the velocities and acceleration, etc. are. He uses so many letters and there are so many equations that I get hopelessly muddled. I've never heard of fundamental and derived units, or of dimensional equations. If there is anything which is hopelessly muddling, I will let you know.

Barnes answered:

if only you knew the elements of Calculus, all these things become so simple. Take as an example. [See Figure 1.]

These pages are somewhat confusing, but I have used them because they illustrate certain aspects of the course, not because of their detail. They are taken from the early letters, personal ones, before the embargo, which resulted from Barnes's declaration of love, was laid down; so they are not strictly part of the course, they simply set it going. They show how, from the beginning, Barnes was out of touch with Molly's requirements -- he presents his formulae without being sure of her grounding here. It is clear that he was at a disadvantage in not knowing in what terms she was being taught, and what formulae were being used. He was probably also disadvantaged on this point particularly by having himself used notations that were now not current. In this example he changes his use of 'v' to 'u', and 'f' to 'a'.

Characteristics that run through the lessons proper show here at the beginning. Here is Barnes's irrepressible enthusiasm, his absorption in his own line of thought, to the almost complete exclusion of any attention to syllabus requirements, and therefore what his pupil actually needed; and the eccentric mixture of the complex and high-flown, the simple detail, and the warm care and concern for his pupil which we see in the last sentence. He must have realised on reflection that the example he had given might not be familiar or intelligible to Molly. He comes down to earth and apologises:

only I am so keen on maths and on helping you if I can [a significant conjunction]. All I can do is to lay my experience at your feet, for you to take or leave as you please.

But on the next line he is off again, irresistibly drawn by a second fundamental formula for dealing with kinetic energy.

Molly seems to have taken all this in her stride; but confessed that she did not understand about differentiation -- an expression she had never heard before. This was a challenge and Barnes took it up.

What a task you have set me, to explain the calculus by post, but how very gladly I will do it now here begins lecture one, from me Barnes to you Molly on the very delightful subject of the calculus.

Here is the first part of the discourse copied out in Molly's neat schoolgirl writing. It originally appeared in a personal letter, which she preferred not to include when she collected the letters into a 'book', as she called it (although there is nothing in the letter that needed to be hidden).

The next step was to get Molly on to harder stuff -- Barnes's method is an amusing example of imaginative teaching. As the spring term began, Molly complained of further unintelligible formulae including the abbreviation 'Lt', and an arrow sign between two symbols, to neither of which she could assign any meaning. 'What does Lt mean?' she asked. 'The first time I saw it was in this formula:
 

To explain these -- the 'limiting value' indication Lt and the linking arrow showing 'symbol 1 tends towards symbol 2', Barnes launched into an updated version of Jack and the Beanstalk.

Jack, heaved the beans out of the window in disgust at 12 noon, noticed the phenomenal growth, and having had a London County Council education and being a very bright lad indeed, he measured the growth at 1/2 hourly intervals with his mother's tape measure and plotted these.

After delightful details and explanation Barnes lays out the graph.

 Jack was re-invented to help Molly understand the two apparently unrelated ideas of small quantities and instantaneous values. Barnes had introduced the topics of small quantities and orders of magnitude in another fascinating and detailed discussion.

Now I don't know how they define the orders of magnitude in astronomy, but, in mathematics it is done like this: to take an example, in the time I think of Elizabeth, people began to find that the subdivision of the hour into quarters of an hour, was not quite minute enough for their purposes. People began to get busier, and the time of appointments for merchants had to be made with more exactitude. Clocks in those days had, I believe, only the one hand -- the hour hand, and each of the 12 divisions marking the hours was divided into 4 parts, not 5 as we have them now. Then the hour hand, as it moved from one hour to the next, moved over these 4 subdivisions, thus telling the quarter and half hours, and this was as near as people could get. So they went to their mathematicians and said they wanted something better, and the mathematicians said 'very good, we will divide the hour very minutely. We will divide it into sixty minute (with the accent on the -ute) parts; and further we will give you another hand, geared so that it rotates once every hour, and we will call it the minute hand. Then you only have to divide the hour spaces into 5 instead of 4 parts, and the whole thing will be complete.' So they did, and it was so; and because the English always have a tendency to throw the accent in a polysyllable word as far forward as possible, it was not long before the new divisions came to be called 'minutes'.

This contented them for, quite a long time, until -- again I am uncertain, but I think Newton, found that in his scientific experiments even the minute was not minute enough; so he established a subdivision of the 'second order of magnitude' and, following the usual mathematical procedure in such cases, since the minute was one sixtieth of an hour, he made the new division one sixtieth of a minute. And since it was of the second order, it very soon became generally known as the 'second' for short. So you see a 'second' is a 1/60th of 1/60, while a '3rd' would be 1/60 of 1/60 of 1/60; and so on. The fraction need not be 1/60 -- it could be 1/100 or 1/1000 or anything -- the point is that the second order becomes 1/100 of 1/100, and the 3rd order becomes 1/100 of 1/100 of 1/100 etc. etc., so that you see that the orders of magnitude in mathematics diminish very quickly.

An entirely original character was invented to illustrate the outcome when a small quantity of the first order of magnitude is reduced to second and subsequent order: Count von In-The-Limit.

I've made him a Count because he's a wandering cosmopolitan sort of fellow that is always turning up in unexpected places. And so we say that if we continue our process of choosing our first quantity smaller and smaller, then in the limit (Hullo Count, you here!) when our first quantity is indefinitely small the 2nd and subsequent orders are in fact zero.

Barnes's imagination is vivid, but it does not obliterate his purpose. To avoid misunderstanding he is careful to define 'indefinitely small' not, as normally, as 'more or less small', but as 'reduced beyond any finite or conceivable limit'. This is an example of the care with which he prepared his material -- as far as possible nothing should be left unclear. There are little explanatory footnotes all over the text -- even to how to pronounce algebraic formulae.

The next character, the Duke of Delta Eks, is conjured up to demonstrate the validity of a series of calculations. Here he comes, to illustrate instantaneous values.

These vivid presentations allow Barnes to demonstrate finally that dy/dx = 2x.

He is careful not to allow misconceptions and adds one of his footnotes, to the effect that what he has given is not a proof of this statement, which is 'absurdly difficult' as he put it, but only a demonstration.

These characters have a surreal flavour that harks back to a late 19th century and early 20th century approach to children's literature and information. In this period, magic carpets fly about teaching geography, fairies turn up in flowers and insects; children make amazing journeys inside the human body. Alice is confronted by logic and linguistics. Even x and y seem to be half invested with personalities -- 'poor old y, whose value depends on x', says Barnes sympathetically.

There is much more in calculus which, in a brief article must be omitted. In April 1923 Barnes returned from teaching in Switzerland, called back by Vickers. But Molly's father's embargo still remained in place. Molly wrote in April:

I wonder if you would mind telling me a little about Trigonometry next time. After much thought and mentally drawing a triangle, I can remember what the sine, cosine and tangent are. But our Physics man says something about equating the sines to their angles if the angles are small; or have I got hold of the wrong end of the stick? And can you have a sine of an angle when it (the angle) isn't in a triangle?

Barnes' life was a great deal more complicated now; he had rejoined the airship design team, but plans and finance were very uncertain. However, he found time somehow to respond to Molly's request and sent lessons. These began, as with calculus, from the foundations:

To start right from the beginning, I must run thro' the convention adopted for representing positive and negative quantities by plotting (or drawing) on paper. If you know this, so much the better.

Barnes rather grandiosely claimed here that this 'is the basis of the modem method of teaching trigonometry', but immediately qualified the claim by adding 'at least the way I taught it -- it seems the simplest'. His principle of starting from the beginning arose from his own hard experiences.

Just a word first to draw your attention to what I mean by a convention*. When I was learning -- generally on my own, there was never anyone to tell me what things were merely conventions, and what things were unalterable (for want of a better word), facts. Consequently I used to spend much time and trouble worrying over the 'reason why' of things that had no 'reason why' beyond their great convenience. For instance, its no good trying to work out why [square root sign/a] Öa means the 'square root of a'; it only means that, because we choose to give that funny sign that particular signification; so you just have to accept the fact without mental argument. In other words, it is a convention. And conventions, in mathematics are almost invariably adopted or, created, because they enable us to express in convenient and concentrated form, what is often a very complex idea. Who would bother to write 'Ratio of length of the circumference of a circle to the length of the diameter of a circle', when he can express the whole idea for everyone, including himself by writing p? Why p? I don't know, nor do I very much care! It is merely a convention and may therefore be accepted by you without further argument or question as being the acknowledged practice of mathematics throughout the world. The author of the particular convention that I am going to explain was a Frenchman called Descartes. He did it I think in the 18th century. Hence it is called: the Cartesian system of rectangular co-ordinates. We are only going to bother about this system for lines or points that all lie in the same plane, e.g., the plane represented by this sheet of paper.

The lessons continued through axes, locations and plotting of points, quadrants, the measuring in degrees of a rotating line, and the concepts of zero and infinity. The fact, which Barnes demonstrated graphically, that when a function, y, passes through infinity it changes its sign from negative to positive produced a flash of the humour that had enlivened calculus. When zero appears as a denominator for x,

poor old y has got to shoot out to infinity and back the other side whether he likes it or not. I always imagine him getting more and more annoyed as x approaches the critical value, muttering to himself 'I don't want to go, I was just settling down so comfortably -- why I haven't even packed my bag and the things aren't back from last week's wash'. And then you give him a kick, and off he goes reappearing punctual to the second, a little breathless perhaps, to crawl over the top edge of your paper, and flinging his bag on the floor exclaims angrily 'I won't be a discontinuous function any longer'. It looks discontinuous to us, but poor old y knows better, for he has to tear along like anything to get round again the back way.

But try as he might, trigonometry did not fire Barnes as calculus did. He wrote:

Somehow one cannot make any fun out of trig. It's all so matter of fact -- it's difficult to say just what I mean -- calculus is an art -- it endows you with wonderful powers; you can let your imagination go to all sorts of lengths and not pass out of the realm of reality -- calculus is like chocolate meringues -- elementary trig is like very thick stale bread and margarine.

A very significant comment!

Added to his personal feeling about trig, Barnes was heavily involved in the demands of his renewed job in Vickers. It is remarkable how he found time to write the lessons at all. There are points where he corrects something that he felt was not clear, or was in error in a previous lesson. They are very small details, but he did not let them pass. This indicates either remarkable recall for what he had written, or a very detailed plan, or a copy kept -- though there is no evidence of either of these latter two. He must have despatched as he wrote, or he would have corrected any errors in the chunks written but not sent. It seems therefore that he did have a detailed memory for what he had sent off. He certainly did not plan out the course ahead in any finalised structure, as one would normally do when laying out a series of lessons; particularly in distance teaching where the next lesson cannot be based on an immediate response to the previous one. In fact he scarcely ever asked for feedback from Molly, apart from asking her to say if something was not clear. Only once did he set her some test questions, at the end of the calculus lessons; though there are several points in the course where he poses a question and then answers it himself, not asking her to do so.

After the course had ended, Barnes, made a rough estimate of the time that it had cost him:

I wonder if you ever stop to think of how much time I spend in writing to you. I suppose ever since I started the maths In Switzerland, it has rarely been less than 10 or 12 hours a week. Those articles used to take me ages to do.

The grudge he was expressing was not against Molly herself, but against her father, who had kept them apart for so long.

In spite of all, Barnes plodded on through angles, degrees, radians, arcs and chords, pi, scalars and vectors, ordinates and abscissae, trigonometrical ratios and similar figures, sines, cosines and tangents, until the beginning of 1924, when the subject changed in answer to questions from Molly. For the first time Barnes asked her about the content of her university course. Previously, his only comments had been rhetorical questions of the 'I don't know whether you know this' kind. The course as a whole is a curious mixture of the didactic and pedantic, and the apologetic and gentle. He was, after all, teaching: he was extremely anxious that his pupil should be properly informed and successful; and he was very involved in his subject on both the broad and the detailed scale. These underlie the pedagogy. But he was equally concerned to be as far as possible hand in hand with his pupil: to retain her interest and affection, not to bore her or overwhelm her. And so every now and then, when dealing with basic details, he apologises, asking her to overlook such and such a comment if she knows it already. And conversely, he protects her from worry by telling her not to concern herself over understanding complex foundations or outcomes, which he includes for completeness. As he says frequently, he is very disadvantaged by not knowing what course she has already been through, and what was now demanded of her. Given the ad hoc nature of the course and the pressures of time and work, this is perhaps understandable. But equally important is the individualistic, idealistic and perfectionist nature of Barnes himself. It is difficult to imagine him teaching to a syllabus. It would be fascinating to know what the boys at Chillon College experienced.

The queries Molly put forward concerned pendulums and sound waves, and so the subject matter shifted to physics. This section is far briefer than the other two and contains only two chapters, on electrostatics. The first chapter, headed 'a note on potential, charge and capacity', begins with hydrostatics which, Barnes says, will give insight into the concepts to be discussed. Thus he took Molly through the terms 'unit charge', with beakers of varying sizes containing equal measures of water; and 'unit capacity' -- this being the charge which will fill the beaker to a defined height.

You will notice that defined in this way 'capacity' does not mean the total quantity the beaker will hold. But was it not the Caterpillar in Alice who paid his words double and made them mean what he liked.

Humour, mixed with careful detail as before. He then moved on to the pressure of the water in the beaker and its dependence on the height of the water. He went on 'All these properties are exactly analogous to their electrical equivalents', thus tying the hydrostatic examples to the purpose of the chapter and continuing with examples from electricity. Molly pursued this:

Supposing you have a can and you are trying to build up a charge on it, you can do it by giving a very small charge -- say a +ve one -- to another can, and putting a sphere inside it and earthing the sphere while it is in contact with the can; then the sphere has a -ve charge which you can give to the other can. And when the sphere is touching the other can you earth the sphere, when it gets a +ve charge which you can give to the first can, and so on.

Barnes could not immediately make sense from this muddled exposition:

You poor child. I'm jolly glad you are puzzled. It shows you do understand, because what you describe couldn't possibly happen. I suppose you took it down from quick lecture notes? . . . . It took me the spare time of 2 days to make it out myself.

Molly's queries and comments throughout seem to indicate either a rather poor quality of teaching, or a signal lack of tutorial and pastoral input from the staff involved. It is difficult not to come to this conclusion. If no particular expertise was expected before joining the course, and none seems to have been, it would have been appropriate to check the knowledge and capability of students before starting courses. However, it may be that most others were better equipped by their schooling than Molly: males were probably more in evidence and this could well have applied to them. Furthermore, there is no evidence at all that lecturers would not have responded if she had asked questions; but equally, she was young and uncertain and may simply not have known what questions to ask, since it was foundation information which, seemingly, she lacked. Barnes's method of teaching, with its humour and sometimes childlike quality, and its emphasis on building up from what could well be thought time-wasting detail, is in striking contrast: but then of course, he had no experience at all of what was normal at university level.

In the can-ridden letter, there is an interruption to the pedagogic material of the course, which shows that by this time they were having some lessons a deux. Molly says;

You know I find it most awfully difficult to take a thing in when you are explaining it to me yourself -- because all the time I'm listening to your voice and hearing something fresh in it which I have to think about, so that every now and then I miss two or three words. And when you are drawing or pointing to something at the same time, it makes it even more difficult because then there are your hands to be reckoned with.

Barnes answers with feeling.

It's all very well to say you find it hard to take things in when I am saying them. Do you stop to think how fearfully difficult it is for me, in your dear presence, to collect my thoughts and plunge into scientific explanations of things more than half forgotten.

However, plunge he did, on paper, dealing finally with what he called:

A perfectly awful subject. It always puzzles me, and having read up all my text book has to say I don't feel any better qualified to attempt to explain it to you. Anyhow, all these explanations are sort of conventions to help one to understand what happens, although they may leave you rather in the dark as to how and why happens.

You know of course, that in order to explain all these phenomena, it is usual to assume that there are two kinds of electricity (whatever that may be) called for want of better terms positive and negative. I don't think it is necessary for your purpose that you should attempt to understand the latest real theory, even if I could explain it which I can't, but briefly its something like this: An atom of matter consists of a core or centre which is positively charged, and around which rotate at enormous speed a number of negatively charged 'corpuscles' I believe they call them or 'electrons'. Never mind the name. Lets say 'electrons' it sounds nicer. Now apparently there are generally a dozen or two negative electrons too many, or at least not so firmly attracted to the centre core as are the others, and the structure of the atom does not break down if these surplus negative electrons are removed or driven off by any means.

Now the condition usually referred to as 'positively' charged is held really to be that a lot of the surplus -ve electrons have been removed from a substance, while a I negative' charge is when a substance has more than its usual allowance of surplus -ve electrons.

This means that when you rub a plate of ebonite with fur you are rubbing or otherwise transferring surplus -ve electrons from the fur to the ebonite. The fur would then have a deficiency, although its atoms still remained as it were 'fur' atoms, while the ebonite would have a surplus of -ve electrons although its atoms too would remain 'ebonite' atoms.

As there is a pretty average crush of atoms inside the ebonite, all of whom are already 'full up' with surplus -ve lodgers as it were, the poor old surplus have to remain on the surface, and are jolly well pushed off to find 'a better "ole"' at the first opportunity. Similarly the fur has now a number of rooms to let.

Dear Mother Earth has vast reserves of both -ve lodgers and rooms, and if you connect the ebonite to her she promptly accommodates all the poor unwanted surplus. On the fur applying to earth to find lodgers, she again obliges, and all is happy and contented as before.

Instead therefore of thinking of a 'positively' charged body as discharging to earth when the connection is made, it is more correct (as I understand it), to think of a flow of negative electrons coming up from the earth and occupying the vacant lodgings on the so-called positively charged body. Whereas a 'negatively' charged body when connected to earth does in fact get rid of the unwanted surplus.

Whether totally accurate or not, Barnes considers he has explained 'induction' more adequately than the 'old theory of two kinds', a comment which possibly did not greatly reassure Molly. Perhaps feeling this might be so, he illustrates the argument with a humorous and cheerful metaphor using landladies, lodgers and rooms to let (see Figure 5).

This continues for some time, getting more and more complicated. Finally, he comes back to Molly's cans, demonstrating the real sequence as he finally sorted it out, with more delightful illustrations headed 'the Celebrated Film entitled The Charge, by Molly Bloxam and Barnes Wallis, featuring two cans and one sphere' -- which was what Molly had asked about in the first place in her muddled way.

'Reel IV to Infinity next week' he finished up; and there the course ended. But the story does not. Molly sat her 1st-year exams, and got through, though it cannot be said with flying colours. She had already decided on her life's course, and it was not medicine. Her father, under much pressure from all sides, had reluctantly agreed to an engagement when Molly was 20 -- three months after her exam. But she had made up her mind not to go back to college. A profession and marriage did not mix at that time for her sort of family; and in any case she longed for motherhood. Barnes had already quite clearly assumed that the career-option was closed if she should decide to have him, which theoretically he did not know until her birthday. The personal letters make fascinating reading here. However, she did decide to have him, and settled into the life of wife and mother for the next fifty years. The teaching papers were put in a box on a shelf, and were never read again, though the story was often told.

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