1. William Thomson's method of images in electrostatics
1.1. William Thomson to George Boole - 2 September 1845
I have been getting a great many new ideas on problems relative to the distribution of electricity on spheres and planes. One result I have arrived at is that if three spheres cut one another at angles which are submultiples of π, the distribution of electricity upon the broken bounding surface, subject to any external influence can be expressed algebraically. It is a case which exactly corresponds to the kaleidoscope. The leading principle is that of what may be called images. Thus the image in a circle of a point Q (or sphere) may be defined to be another point Q', in CQ, such that CQ' is a third proportional to CQ and the radius. Following out this definition we find that the image of a circle is a third circle. The image of two circles cutting at a (real or imaginary) angle is two circles (or planes if the centre of the circle in which the image is taken be a point of intersection of given circles) cutting at the same angle. Also if two points, Q, Q' be reciprocal with reference to a circle A and if the system be reflected in another circle, and q, q', a be the images, then q and q' will be reciprocal with reference to a. Thus any case of the distribution on a number of spheres which pass through one point may be reduced to a problem relative to planes, forming a solid angle. Also, the distribution on a spherical cap, or hemisphere, subject to the influence of any electrical masses, or merely insulated and charged, may be reduced to a corresponding problem relative to a circular disc. Thus from Green's solution of the problem when a circular disc is subjected to the influence of a point on its axis, the distribution on an insulated and charged segment of a sphere, subject to no external influence, may be determined algebraically, by reflecting the disc, and influencing point, in a sphere so taken that the image of the influencing point shall be the centre of the sphere which is the image of the plane or circular disc. The principal of images also leads to some remarkable transformations of double integrals.
I have been here [Knock near Largs] for a few days, and shall remain where I am for a fortnight, after which I shall be moving about till the first of October. I then return to Cambridge. Any letter posted before the 25th of the month and addressed to me here would be sent after me, but after that time, they would be sent to Cambridge, and if you write to me any time after the 25th it would therefore be better to address to Cambridge.
1.2. George Boole to William Thomson - 19 September 1845
... the method of images which you mention appears to be very remarkable ... but I do not profess as yet being fully to understand the principles of the method.
2.1. George Boole to William Thomson - 30 June 1846
In answer to your request that I would express my opinion on your qualifications as a candidate for the professorship of Natural Philosophy, now vacant in the University of Glasgow, I have great pleasure in stating that judging from your mathematical investigations on various departments of physical science, I conceive that you are qualified in an eminent degree for the discharge of all the higher duties of such an appointment. Your researches on the subject of the equilibrium of fluids generally, and their applications to statical electricity and to magnetism in particular, appear to be to be likely to lead to considerable advances in our knowledge of these subjects. I should rejoice to hear of your election, because I should confidently anticipate that it would open to you a career of honourable exertion, not less conducive to the interests of Science, than advantageous to the University with which you would stand connected
2.2. George Boole to William Thomson - 30 June 1846
My impression of such things is that they should be written with modesty and sincerity and that they should contain nothing which the writer cannot certify of his own knowledge . I have endeavoured to keep these principles in view in writing to you. Indeed I might with truth have said more than I have done but that the very appearance of flattery should be avoided even when the thing itself is wanting.
2.3. William Thomson to George Boole - 7 July 1846
I thank you most heartily for your testimonial, and for your letter which accompanied it. It must have great influence with the electors, especially on account of its explicitness.
The final decision will not be made by the electors till the 9th of September but they are to hold a meeting for "deliberation" on the 5th of August after which I hope to know something more definite than I can at present of my prospects of success. ...
I was sorry to hear that your health has not been vigorous, and that your work in teaching has been too much. I hope that, sooner or later you will be able to spend some time at your own work in mathematics, without the necessity of over-exertion on this account.
2.4. William Thomson to George Boole - 11 September 1846
I have come up from Knock this morning (intending to return again in the afternoon) so that I may know at the earliest the result of the election, which will take place in a few hours . I shall communicate it to you before closing this letter, which I commence now, while I have some time free.
I was glad to hear of the progress you have been making in getting testimonials. It will be of great importance for you to bring forward evidence, in as many ways as possible, of your success as a teacher. I have not sent you a testimonial yet, and I still delay as I have good reason to do so, but pray let me know if you would find it convenient to have it immediately; if I do not hear from you I should not be later in writing it than a fortnight from this time. ...
Today I cannot go out, as I am sitting in a state of suspense, and the way I have been spending my time has been better for myself than it will be amusing to you .
The good news has just arrived I have been unanimously elected professor of natural philosophy.
2.5. George Boole to William Thomson - 15 September 1846
Let me congratulate you on your happy and honourable success. In every respect it must, I should think, be gratifying to you. Association with your earliest friends, a reputation already high and rapidly increasing, together with a consciousness of occupying a position which may enable you to devote high talents to great objects and through them to the promotion of the common good must render your lot, so far as in the uncertainty of all human things we may dare to speak of the future, a very happy one . May I venture before quitting the subject to offer my respectful congratulations to your Father, whom I had the happiness of meeting in Cambridge, on an event so honourable to you both.
3.1. George Boole to William Thomson - 17 August 1846
A letter which I yesterday received from Mr Cayley contains, after a due measure of linear transformations and elliptic functions, an extract from a letter of yours in which you are so good as to suggest that l might possibly succeed in obtaining one of the new Irish professorships. I was very much gratified to think that you were interested for one and venture on this assurance of your good will and friendly feeling to explain to you my present views and situation.
I should certainly prefer an appointment of the kind you name to the mastership of a private school; - partly because it might, I think, be made a position of greater usefulness; - partly because it would be more congenial to my tastes; and partly because, while not without its due responsibilities, it would be free from that uncertainty and dependence which are inseparable from the profession of a schoolmaster, at least in the present state of society . I suppose that as respects the prosecution of mathematical studies I might look for advantages also which I do not at present enjoy. Indeed it has often been with me a matter of grave and serious reflection whether I ought not in my present situation to relinquish those studies and I regard it as a weakness that I have not been able to carry out my convictions in this respect. These are reasons why I should aim at some more congenial occupation. On the other hand my position, could I but quietly confine myself to the duties of it, is one of sufficient comfort and respectability to satisfy moderate wishes. My parents both aged and infirm are both living with me and it behoves one to consider how far a change might affect them. Still I think that on balancing the probabilities should there be a fair chance of obtaining a mathematical professorship by honourable competition in an open field it would be my duty to make the attempt.
In estimating the chances of success it ought to be remembered that I have not taken a university degree. Perhaps you did not duly consider this. At a time when I had an offer of being supported at the University and was, so far as inclination went, most anxious to avail myself of it, it became through family circumstances an imperative duty that I should forgo the advantage and open a school. This I only mention that you may see that it is through external causes alone and not through reluctance or disapproval that I have not availed myself of the benefits of college discipline. Still it may not the less be a disqualification. I may however mention that I have been in the habit of lecturing to classes and of setting papers in the way of the Cambridge examinations. I have also a student of St John's reading with me for the second time so that I am not quite unaquainted with college business.
Perhaps you will be able to give me some information on the nature of the appointments, the periods and the proper mode of application andc. Have they been advertised? Any assistance that you can give I shall be very grateful for. I should also be much interested to hear the present state of your own prospects in the university of Glasgow.
3.2. George Boole to William Thomson - 26 August 1846
I have decided to become an applicant for one of the professorships and have followed your directions in writing to the Secretary at Dublin Castle but of course have not yet received an answer. I shall be very grateful for any assistance you can render me and venture to ask you for a testimonial if you think that from what you have seen of my papers you can give me one. I suppose that the number which I shall be able to procure will be very small. Cayley who is here will give me one and Ellis will I think be disposed to assist me also. Perhaps too I may get something from Graves, Kelland, and De Morgan with whom I have had some little interchange of letters. I rather regret that I did not accept an offer of Graves's to introduce me to Sir W R Hamilton but I did not at the time feel that I had any claim to his notice.
3.3. William Thomson to George Boole - 11 September 1846
I was glad to hear of the progress you have been making in getting testimonials. It will be of great importance for you to bring forward evidence, in as many ways as possible, of you success as a teacher.
3.4. George Boole to William Thomson - 15 September 1846
I shall get such evidence of my success as a teacher, agreeably to your suggestion, as I am able to do but from the fact of my school having been chiefly a commercial one, and from my own teaching having been much more given to classics than to mathematics it will be impossible for me to bring that species of evidence which is most wanted and the open and the manly course seems to be to meet the difficulty at once by a plain acknowledgment of its truth. I have a pupil with me now who is doing exceedingly well at St John's and he could speak were it any use, to my skill in explaining difficulties and ability as a teacher so far as his experience goes. He had six months training with me, dividing his time between classics and mathematics, and at the end of his freshman year was 19th in the first class of about 40. Re knew nothing of mathematics when he first came to me. I have thought that it might be desirable for me to spend a month in one of the Universities if it could be arranged.
3.5. William Thomson to George Boole - 26 September 1846
I am most anxious that you should succeed, more so than I could say in the testimonial, and shall be glad to hear of your progress, also, especially whether you have any idea of visiting Dublin.
3.6. George Boole to William Thomson - 30 September 1846
I yesterday received your very kind testimonial and lose no time in writing to thank you for it and to assure you not only that it is in every way satisfactory but that it expresses far more than I could have flattered myself that I had any right to expect. I shall continue to set a high value upon it whether my present application is successful or not.
3.7. George Boole to William Thomson - 22 December 1846
I hear nothing from Ireland. The wretched state of the country physically and morally is I suppose quite enough to tax the energies of any government. What is to be the end of it all God knows.
3.8. William Thomson to George Boole - 5 February 1847
I am afraid for the present all matters are standing still in Ireland except the great fight with hunger. The prospect is dreary enough, for many months, but it is to be hoped that summer and autumn will be the beginning of a better time.
3.9. George Boole to William Thomson - 8 December 1848
I am about to resume my application for a professorship of mathematics at one of the Queen's colleges . I believe that I should not have decided on doing this but for Graves who has shown himself the most generous of friends. Of course the future is very uncertain but I am not ambitious and can bear greater disappointments than would be the losing of an election. If I do succeed I should like to spend sometime at one of the Scotch Universities as well as at one of the English ones. If I come to Glasgow for a week or two could I attend your lectures and your father's? I should give you no trouble in any other way ... Thank you and your father for all your good wishes and offers of assistance. I think in case of success or failure the pleasantest thing to look back upon is that having taken no part beyond sending in of one's legitimate testimonials.
3.10. William Thomson to George Boole - 12 December 1848
As you have now resolved to become a candidate for one of the Irish Professorships I must cordially wish you success.
I hope you will give our University the visit you propose. My father and I would have great pleasure in seeing you daily in our Classes , and in giving you any information you might desire regarding the general working of the system we follow. In the course of a week or a fortnight you would be able to see a good deal of our practice (and of that of other professors also, should you desire it) and to make yourself acquainted with the principle features of the University system here; which as you are aware differs most materially from that of Cambridge and Oxford.
Thank you for the specimen of "ante-baconian physics" you have sent me, which is quite new to me. The earliest physics I have myself looked into at all is Gilbert's Treatise "de Magnete" which I suppose may be called "ante-baconian."
4.1. George Boole to William Thomson - 17 January 1849
I cannot bear from writing to offer to you the tribute of my sympathy in that domestic calamity which you have just caused to be announced to me - and I do this with the most sincerity because a similar loss has lately befallen my own home. On the 12th of December, exactly one month before the day of your father's decease, I lost mine. Death was in this case, however, an event long looked for and even ardently desired, and I suppose that when it came it was with as few circumstances of awe and terror as can ever accompany a change so great and so solemn.
From all that I know of your father (although indeed my personal acquaintance with him was very slight) I should think that you will feel it an increasing source of consolation to know that he did not live in vain, and that you will reflect with filial pride and reverence upon the long career of his useful and honourable labours. For my own part I shall not forget that the little intercourse which passed between us was on his part one of kindness manifested, and of benefits conferred.
Let me just add that if at this period I can render you any service in looking over papers for the Journal, or in any other way, I shall gladly avail myself of the opportunity of thus showing you how truly I am, My dear Thomson, Your sincere friend.
4.2. George Boole to William Thomson - 28 March 1850
You will I am sure be gratified to learn that our college is progressing in numbers and, as I have good reason to believe, in real usefulness and public favour. For my own part I can say with perfect truth that I feel a daily increasing delight in my new duties.
5.1. George Boole to William Thomson - 30 November 1854
I think it worth while to write to you and explain how it was that I did not meet you on the Sunday in Edinburgh according to my promise.
When you told me that you would call upon me at my hotel I quite forgot that I had an engagement with my old colleague Prof. Nicol of Aberdeen to dine out with him on the Sunday evening in company with my sister. At the time when I left the hotel you had not called. I therefore left a note with the waiter to be given to you in case you should call, inviting you to join us at Mr Nicol's in the evening. When I returned to the hotel I found that the note had not been delivered to you. I accordingly took a coach the next morning to your lodgings to ask you to breakfast with me, it having been arranged that my sister and I were to leave Edinburgh at noon. I carried a note with me which I should have sent up to you but the servant who came to the door told me that you were up - that he had seen you in your sitting room. I therefore went up expecting to see you. It might have been better, as I afterwards thought, to send the note.
6.1. George Boole to William Thomson - 7 February 1855
I think, upon again reading the testimonial, that it speaks too highly of my acquirements in Natural Philosophy. Such testimony from you now implies more than it did when you wrote the testimonial. On this account I feel doubtful whether I shall use it. I am certainly not ignorant of mathematical physics but I feel that there are scores of men who know far more of the subject than I do. It is, as I have said, my intention to learn more of the subject, but until then I certainly feel that I am not "highly qualified for a professorship of Mathematics or Natural Philosophy". I feel sure at the same time that you thought when giving me the testimonial that you were doing only what was just. What I do profess to understand, speaking of course relatively, is Mathematics and the philosophy of mathematics. That is all to which I have established anything like a right, still, of course only relatively to the general state of knowledge on these things and not to that which is to be known. I make this explanation to you that you may clearly understand why if I do not use your testimonial I refrain from doing so. I have acted in a similar way toward a friend with whom I felt that I could take the same liberty and who has given me a testimonial which I thought above my merits